AISC Seismic Design Manual 2nd Edition (7civil.com)

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AMERt'CAN 'INSTITUTE

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STEEL CONSTRUCTION

SECOND EDITION

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1 General Design Considerations

2 Analysis

3 Systems Not Specifically Detailed for Seismic Resistance

4 Moment Frames

5 Braced Frames

6 Composite Moment Frames

Composite Braced Frames and Shear Walls

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8 Diaphragms, Collectors and Chords

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9 Provisions and Standards

10 Engineered Damping Systems

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Index

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, AISC Q 2012

DEDICATION

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American Institute of Steel Consuuction "'-:"" . .,,,. -~ '..· ~ ~.-'\ "' ' "'}./ ISBN J-56424:()61-4 ;:, ~>:. ~

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All rig~ This part rhereo} miist nothe reproduced in any fom1 without the written pennission of the publisher. The AISC.~gl' f;e~si?jd tr
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•.• .. .. . .. . Th~ information presented in this publication has been prepared in accordance with recognized engineering principles and is for .$~A-Yf.ll information only. While it is believed to be accurate, this information should nott~. ~s'&I"'oc relied upon for any specific application without competent professional exa~~Jj
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. Caution must be exercised when relying upon ocher specifications and codes developed by other bodies and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the printing of this edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial publication of chis edition. Printed in the United States of America First Prin{ipg: September 2012 . ~

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Clarkson ("Piiiky") W. Pinkham

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This-edition of the AISC SeiSmic Design Manual is dedicated to the· memory of Clarkson W. Pinkham, a long-time member of the AISC Committee on Specifications and 'Taskr Committee 9-Seismic Design. Mr. Pinkham, or Pinky as he was- aJ!'ectionately known to' . his professional collea'gues, was pCC$ident ana member of the Los Angeles consulting structuial-engineering firm,. S.B. Barnes and Associates, for 62 years. He sei;ved on the AISC ( Committee on Specifications from the mid-1970s until the yeatioo:i: and Thsk Comin.ittee · .· 9-Seismic Design from-the mid-1990s. until 2010. As a member of :rask·Comn1ittee'9 and technical secretary for-the 1997 AISC Seismic Provisions for Structural Steel Buildings, he was a major contributor -aiid instrumental ii1 the early development of that standard. Pinky rwas one of the fuit proponents of including composite systems. in "the AISC Seismicl Provisioru and, for the first time; this·Seismic Design Manual includes two chapters on' such ·.: systems. Pinky received the AISC Lif~time Achievement Award in 1999. Through a career that spanned more than six decades, he\.$pent a lifetime sharing his expertise with others in j · the field. He was passionate about learning up until his death in 2012 at the age of 92. Pinky -.. was generous in sharing his abundance of structural engineering experience and knowledge through committee involvement and with those who requested it o~ the subjects o~ ~tructural ~': steel, concrete and masonry design, cold-formed structures, and timber. By prov1dmg solu-l: lions and recommendations in this way, Pinky improved the integrity of numerous ~=., structures; in particular, their capacity to resist seismic-generated forces. He was elected president of the Structural Engineers Association of Southern California (SEAOSC) in .· 1971, and later served as president of the Structural Engineers Association of California I (SEAOC) in 1975. He was twice given the S.B. Barnes Award for Research, and in 1994 ~ was inducted into the SEAOC College of Fellows, the highest honor awarded by SEAOC. In 2009, the Structural Engineering Institute of the American Society of Civil Engineers~ awarded Pinky the Walter P. Moore. Jr., Award in recognition of his dedication to and tecb-l ·. oical expertise in the development of structural codes and standards. AISC will always remember his dedication to the development of standards related to the design and con- ~ stnJction of structural steel and it is especially fitting that the 2nd Edition of the AISC L Seismic Design Manual be dedicated to the memory of Clarkson W Pinkham.

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PREFACE

FOREWORD

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The design

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demonstiate' an ai>Pr0ach~to design, and

~nc?~ intended to suggest that' the approach presented is the oiiry approach.' The commicteifr~nsible for !he development of these desjgn examples ·reeognizes that Ciisigoers have altel"ll!lt~ approaches that worlc'best for them and their'ptojects. Design approache~ that difter-~iii._iliose ~ei:ited ~ these examples iire .son'sidered viable as long as the AISC Sped/icarii>n and AISC Sez'smic Proviswns, sound ~ngiii~ring~ and project srecific require· ' · mentS are satisfied. The.following major changes and improvements have been made in this revision:

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• More thorough and comprehensive design examples, updated for the 2010 AISC

Seis111ic Provisions • Side-by-side LRFD and ASD design methodologies for design examples Addition of Part 2: Analysis • Addition of column base plate design exampl~· • Extended discussion in Part 8 on collector elements • · Addition of Part 10: Engineered Damping Systems • Addition of buckling-restrained bf
By the AISC Committee on Manuals and Textbooks,

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• 2010 Seismic Provisions for Structural Steel Buildings (ANSIIAISC 341-10) ~ 2010 Prequaliji~d· Connections for Special and /111ennediau Steel Moment Frames for Seismic Applicafi9hs including' Supplement No. 1 (ANSI/AiSC 358~ 1Oand ANSl/ AlSC 358sl~l) 1 ' . :

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The Institute's objeetive is to make ;~aurai .steel the material of choice, by being the leader in structural-steel-related technical and market-building activities, including: specificatism.and code development, research,-educa!ion, tecl!Jlical.assistance, quality e
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This is the secood edition Q{ the AISC Seismic Design Manual, in~eoded to assist ·d~signers in properly applying AISC standards and provisions in the design of steel frames to resist high-seismic loadings. This Ma,nual is intended for use in conjunction with the AISC SruJ 111 Consm.u:tion Manual, 14th Edition. The following consensus standards are printed in Part 9 of this Manual:

The American Institute of Steel Construction , founded in 1921, is the nonprofit technical specifying and trade organization for the fabi:icated structural steel industry in the United States. Executive and engineering head~ of AISC are maintained in Chicago. The Institute is supported by four classes of membernhlp: Active Membecs engaged in the fair rication, production and sale of structurefst~l~ ~ociate Members, who include Erectors, Detailers, Service Consultants, Software bevel.~pers, and Steel Product Manufacturers; Prof~sional Members, who are individu~l{~iJmµ~ engaged in the practice of architecture or engineering, including arcbitecturarand~eilgfu.~iltig educators; and Affiliate Members, who include General Contractors, Building inspCHo~ and.Code Officials. The continuing financial support and active parti<'.ipatioti of M~~~ .in µi~ engineering, research and development activities of the Institute make PQssible,·th~ publishing of this Seismic Design

Manual

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Mark V. Holland, Chairman Gary C. Violette, Vice-Chairman Abbas Amirunansour Charles J. Carter Harry A. Cole Brad Davis Bo Dowswell Lanny J. Flynn Patrick I . Fortney W. Scott Goodrich Christopher M. Hewitt W. Steven Hofmeister William P. Jacobs Bill R. Liodley, lI

Ronald L. Meng Larry Muir Thomas M. Murray Rafael Sabelli Cliffor~ W. Schwinger William N. Scott William T. Segui Victor Shneur Marc L. Sorenson William A. Thornton Michael A. West Ronald G. Yeager Cynthia J. Dun~, Secretary

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and the AISC Subcommittee on Seismic Design, Heath E. Mitchell Kevin s. Moore · · Larry Muir ' · Clinton 0. Rex John A. Rolfes

' · Wtlliam A. Andrews

Richard M Drake Michael D. Engelhardt Patrick J. FortneY. Timothy P. F~~; · °John L. Harri_s,."in.,: James 0. M~ley '

SCOPE Bren R. Manning

Rafael Sabelli, Chairman Thomas A. Sabol, Vicc--Chairman ··· Allen-Adams ; "· ·, :;-:Scott M. Adak ··~·

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William N. Scott Victor Shneur ,Hru-old 0. Sp~gu,e ,,. .. .. ~t H. Yart11<1 . . ;•

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Leigh Arber, Sec~tary

The committee giq.tefully acknowledges the contributioqs made to ,this Manual by the following individ1,1ils.:. Eric B~lin. Areti Maria·E. Chumbiu, J~et Cummins, Thomas Dehlin, Richard." Dfcike, Tu.<;.a ~ischer, Louis Geschwindner, .Arp,ir .Gilani, Keith Gr.u~b, Jeroqie Hajjili-, · ~an.v:inde,. ~cha,rd Kaehler, · Ryan Kersting,_ Zhichao Lai, D awn Lehman, Bre~t Leu, Kit Miyai:O()tci; Palmer, Davis Parsons. Il, Paul Richards, Kimberly l,lobinson, ·Chai:tes Ro~~~f· B.randt Saxe~, Thomas Scblafly•. Bahra~ Shafu.~z, Chia-Ming Uang, and Jie Zuo. ·

Carter;

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Keith

The specification requirements and other dCsign recommendations and considerations summarized in this Manual apply in general to the design and construction of seismic fore(:: resisting systems in steel buildings and other structures. The AISC Seismic Design Manua f is intended to be applied in conjunction with the AlSC Steel Construction Manual, which provides guidance on the use of the AISC Speeijic.ation for Structural Steel Buildings. In addition to the requirements of the AISC Specification, the design of seismic for~: resisting sy~tems must meet the requirements in the AISC Seismic Provisions for Structurak_ Steel Buildings, except in the following cases for which use of the AISC Seismic Provisions is not required:

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• Buildings and ~er structures in Seismic Design Category (SDC) A 'f.::. • Buildings and other structures in SOC B or C with R 3 systems (steel systems not specifically detailed for seismic resistance per ASCEJSEI 7 Table 12.2-1) • Nonbuilding structures similar to buildings with R = 1~ braced-frame systems or R 1 moment-frame systems; see ASCFJSEI 7 Table 15.4-1 '-• Nonbuilding structures not similar to buildings (see ASCFJSEI 7 Table 15.4-2), which are designed to meet the requirements in other standards entirely ..

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Conversely, use of the AISC Seismic Provisions is required in the following cases:

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• Buildings and other structures in SOC B or C when one of the exemptions for steel. , seismic force resisting systems above does not apply • Buildings and other structures in SDC B or C that use composite seismic force resistl ing systems (those containing composite steel-and-concrete members and those composed of steel members in combination with reinforced concrete members) Buildi~gs. in SOC D, E ~r F . Nonbuildiog structures m SOC D. E or F when the exempuon above does not apply ·

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The Seismic Design Manual consist.S, of ten parts addressing various topics related to the; design and construction of seismic force resisting systems of structural steel and structura( · steel acting compositely with reinforced concrete. Part I stipulates the specific editions of-"· the specifications, codes and standards referenced in this Manual, and provides a discussion of general design considerations related to seismic design. Part 2 provides some guidancef.:· on structural analysis procedures employed. For the design of systems not detailed for seis~- mic resistance, see Part 3. Parts 4 through 7 apply to the various types of seismic fore~·. resisting systems, including design examples. Part 8 discusses other systems, such as . diaphragm chords and collectors, which are important in seismic design. Part 10 addresses'. engineering damping systems. For applicableAISC seismic standards, s~ Part 9. ·

tr AM£1UCAN fNS1TTUl'E Of STEEL C ONSTRUCTION

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GENERAL DESIGN CONSIDERATIONS

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APPLICABLE SPECIFICATIONS, CODES •

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Specifications, Codes and Scandards for Structural Steel Buildings . ·.· ......... 1-4 . . . . .. . . ~;,'. :it . ... :1 .. Other AISC Reference Documents ........ . ............................. 1-5

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~3 !SEISMIC DESIGN OVERVIEW AND _I>ESIGN CON~IDSRATIONS ........ 1- 5

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!Applicable Building Code .............................. ·.... ·.......... 1-6

Risk Category and Seismic Design Category ........... : .., ....' . . . . . . . . . . . . 1-7 Earthquake Ground Motion and Response·Spectrum .... ~ :;.·.·. ..... ..... : ... 1-7

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Systems DefinedinASCFJSEI 7 ...... . ............................... 1-10 .

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Maximum Considered Earthquake and DeSign ~asis Eanhqu~e .. ............ 1-10

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Maximum Force De~ered by the,s;st~m ... ......... ..... ... .~ •......... 1-16 I . Building Joints ...... . ._.,, .. ...... .,. . .· _. . •.. •.· ....... ........... , ........ 1-16 Expansion Joints .. . . ......... .................. : . ......... :·.: :.. : .. : . .'l- 16 Seismic Joints .·.... .".~:-'.. ! ••

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Building Drift ............... : . .·.'.': ... : .. .... .=... ·. '..... :

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Lowest Anticipated Service Temperature . ......... , . . .. ,, . . ..... r.· .•.... 1- 18

Quality Control and Quality Assurance;., .• .,................... " •.... . , .. l- 19 Design Drawing Requirements ....... . ............................... 1-21

Structural Design Drawio~ Requirements ............................ 1-2 1 SPRS Member and Connection Material Specifications .............. . ... 1-21 ! !.

Demand Critical Welds ......... ..... ........... . .... . ............ l-21 AM1!JUCAN (Ns-rmrrE OF Sn::a CoNSTRUCTION

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TABLE OF CONTENTS

Locations and Dimens ions of PrOlCfJ:.ed ZoQcs ................. ... ..... 1- 22

Table 1-9a Design Coefficients and Factors for Steel and Steel and ~ Concrete Composite Seismic Force Resisting Systems ..................... 1- 5

Adclitional Structural Design De~ Requirements in the P«}vis\ons$ r.- . ••• : ~-,,·.-i · -'· ·' ...•.· ..•...· ...... ~ . .-:~ .- , .. : ........ . 1-22

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AWS 01.8 Structural Welding Code-Seismic Supplement ............ ... 1-23

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Composite Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23

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1.4 DESIGN TABLE DISCUSSION ........ ............. ... . .. : . ......... 1-25

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Seismic Weld Access Hole 'Confi&uratlon ..... .' .. .' .......... .' ........... 1-25 "~· : · ~ : •).-' •I J' '• t···. ..i 4;i ·..,.,:"~ 't 1•. ,. : ' I • • • • • ~··•• Mein~r D'~c'tiuty· Req~f~meniS '::::: ~ ..... ~: ........... : .... :: . ." ..... 1-25 'lo•

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Table 1-C. Limiting Width-to-Thickness Ratios for Rectangular ,._ · HSS W~ls in Compression,.,,,._, :, ·,~>: · ~ - ; ,i,- ·: . . . . • • • . • . . . . . • . .. ....

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Table 1-D. Lirrpting Width-to-Th.i_c)gless Ratiq~ f~r ~oun_d. HSS . , and Pipe Walls in·Compression . : '. : .'..... .......... ... : ........ : . . . . 1-29 . :. ... ._,;, ~ "-: Strength of Steel Headed Stud Anchors ................................. 1-30 -

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Table 1-4. Sections That Satisfy Seismic Width-to-Thickness · · ., L Requirements, Angles .... . ..... ...... ...... . ........... : ... : ... ~ .... 1-52

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Table l-5a. Sections That Satisfy Seismic Width-to-Thickness · ·, .~ ~ Requirements, Rectangular HSS .... ... ...................... 1 ••, ., •• ••• l-53

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Table 1-8. Shear Stud Anchor Nominal Horizontal Shear Strength •. and 25% Reduced Nominal Horizonw Shear Strength for Steel Headed Stud Anchors . ........... . ... . ......................... l- 58

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Table 1-7. Sections That Satisfy Seismic Widlh·tO·Thfok:ness Require ments, Pi~ ... . ...... . . .. .. .. . ..... . ...•....... ~ · .. : ... : .... 1-57

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· Table 1-3 .. Sections That Satisfy Seismic Width-to-Thickness . - Requirements, W-Shapes ......... : . : ..... : ...... . .... .... ....:.. .. . : . 1-36

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DESIGN TABLES ............... ... . .' ................ -.. : ~ ... ·.......... l-33 Table 1-1.- Workable Seismic Weld Access Hole Configurations·.............. 1-33

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PART 1 REFERENCES ............. ...... .......... ...............-..... 1-31 -

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, The design consderations fU~z.ed in lh:i-S Part apply .~ ~~ to the design and ~nstruction of steel buildmgs for seismic applications. The specific editions of s~j.fications, cod~s and oilier references listed below are referenced thrOughout tills Manual. · · '

1.2 APPLICABLE SPECIFICATIONS, CODES AND OTHER REFERENCES 1

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Specifications, Codes and Standards for Structural Steel

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I Buildings a I Subject to the requirements in the applicable building code and the contract documents, the

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design, fabrication and erection of structural steel buildings is governed as indicated in the AISC Specification Sections Al and B2, and AISC Seismic Provisions Sections A2 and B2

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1. ASCE/SEI 7: Minimum Design Loads for Buildings and Other Stru~tures, ASCEI SEI 7-LO (ASCE, 2010). Available from the _American Society of Civil Engineers, ASCE/SEI 7 provides the general requirements for loads, load factors and load combinations. 2. AISC Specification: Specification for Srructural Steel Buildings, ANSI/AISC 360-10 (AISC, 20 lOa). This standard provides the general requirements for design and construction of structural steel buildings, and is included in Part 16 of the AISC Steel Construction Manual and is also available at www.aisc.org. 3. AISC Seismic Provisions: Seismic Provisions for Structural Steel Buildings, ANSI! AISC 341-10 (AISC, 20l0b). Th.is standard provides the design and construction requirements for seismic force resisting systems in structural steel buildings, and is included in Part 9 of this Manual and is also available at www.aisc.org. 4. ANSUAISC.358: AISC Prequalified Connections for Special and Intermediate Steel MoTMnt Frames for Seismic Applications, ANSI/AISC 358-10 (AISC, 2010c): This standard specifies design, detailing, fabrication ~d quality criteria for connections that 'are prequalified in accordance with the AISC Seismic Provisions for use with special and intermediate moment frames. It is .included in Part 9 of this Manual and is also available at www.aisc.org. 5. AISC Code of StandLJrd Prac1ice: AISC Code of Standard Practice for Steel Buildings and Bridges (AISC, 2010d). This document provides the standard of custom and usage for the fabrication and erection of structural steel , and is included in Part 16 of the AISC S1eel Construction Manual and is also available at www.aisc.org. Other referenced standards include:

I. RCSC Specification: Specification for Struc1ural Joints Using High-Strength Bolts (RCSC, 2009), reprinted in Part 16 of the AISC Steel _Construction Manual with the 'i>ermission of the Research Council on Structural Connections and available at www.boltcounciLorg, provides the additional requirements specjfic to bolted joints with high-strength bolts.

1-5

1.3 SEISMIC DESIGN OVERVIEW AND DESIGN CONSIDERATIONS

2. AWS 01.1: Sirucfl!!Ul.Welding Co~teel, AWS Dl.11Dl.1M:2010 (AWS, 2010). AviµJ.able froQ,lJ~:J\meri~a.n Welding Spciety,._AWS Dl.l·prQvi
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other AISC Reference Documents "IPe !JSC Steel Cons~cti.on Manual (J}ISC,:20 ~ l ), referred to as the AISC Manual is availaple· f~m AJSC at .~.aisc.Qr:g. 'I)lis puP.lication provi4~ . design fe(;ommeoda.tions and speci.fic;atio~~ui.refll~I)ts for vljri~us topips related to ste,el b1,1ilding design and copstruction. ..... ~

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; .3 .SEISMIC"DESIGN OVERVIEW AND DESIGN ... CONSIDERATIONS.· .... . . ,. " . . : .- . . '

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Seismic design is the practice of proportioning and detailing a structure so that it can withstand shaking from an earthquake even:t with acceptable perfonnance. The AISC Seismic Provisions Joi Structural Steel Buildings are intended to provide a of designing structures constiucted to respond to maxiroll.m considered earthquake ground shaking, as defined in ASCFJSEI 7, with low probabili~ of collapse, while potentially sustaining significant · inelastic behavior and structural damage. Fundamental to seismic design is the practice of proportioning and detailing the structure so that it can wit11stand Iafge..de_fop:na.~9n d~m~d$. accommodated through inelastic behavior in structural elements ihat have been specifically deSigned to withstand this behavior acceptably. This requires carefui proportioning ofthe sthlCtu.ral system so that inelastic behavior oecw-S in pre-selected cleinents that have apprOpnate1section properties to sustain large inelastic deformation demands without loss of strength, and a5suring that connections of srru.Ctural elements aie adequate to develop the strength of the connected members. · · ·· Performance apj:>ropnate to the· fun~tion of the structure is· a fuiidaniental consideration for seismic design.' Potentlill conside'rations are post-earthquake reparability and serviceability for earthquakes of different · severity,· Most structures are designed only with an expectation of protecting life safety, rather tlian assUring either the feasibility of repair or post-earthquake utility. Buildings assigned .to Risk Categories ID ·and IV, as defined in ASCEISEI 7, are expe.cted to withstand severe earthquakes with limited levels of damage, and in some cases, allow·post-earthquake occupancy. 'l)le criteria of the AISC Seismic Provisions, when ~sed together with the· requirements of ASCEJSEI 7, are intended to

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. . · .. GENERAL DESIGN CONSIDERATIONS

t.J·SEISMIC DESIGN OVERVIEW AND DESIGN CONSIDERATIONS

provide performance appropriate to the structure's risk category 1• For some buildings, peifOnnance that exceeds-these expectations may be appropriate. fuitbose.cases, designers must develop supplemCJitaiy-criteria to those ·contained in the AISC .SeiSmic Provisions and :ASCFJSEI ·?. :-·:, · '· ;~-- · . ,:,.·• .:;: ,.. . Building performance is not a function of the suuctural system 'alone. ·Man)> bi:iilding structures have exluoited ill effects from diinage to nonstructural components;' including breaks in fire protection systems and impaired egress, which have pre.clucted building functions-and thus impaired performance. Proper conSidei-ation of the behavior of nonstructural eomponents is essential to enhanced building performance. Industrial and nonbuilding structures· 6ften oontairi 'elements that require :s·o me measure of pfotection from large deformitions. · ". , '~ " " \, Generally,' seismic :force resisting systems (SFRS) are classified into three levels of inelastic response capability, designated as ordinary, intermediate or special, depending on the level of ductility that the system is expected to provide. A system designated as ordinary is designed and detailed to provide limited abµity ~- e~bit in~lastiQrespoDS;C witb~fa~" ure or collapse. The design requirements for such systems, including limits on proportioning aD
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~ational model building «~es are published. so that state and loccµ authorities may adppt

the code's prescriptive provisions to standardize design and constru~tioq practices in_their jurisdiction. The currently used model code in the U.S. for the structural des\gp of bl!ildi?_gs and nonbuilding s_trucrures is the International Building Code (IBC), published by the International Code Council (ICC) (ICC, 2012). Oftentimes the-84opted provisions are amended pase4 on jurjsdictional requirements to, develop . l<><;al bl,tllding _<;odes (e.g., California l3uildjng Code and,IJ\e Building COOe of, ~~w York City). LOcal codes are then enforced by law and any devia~on m.ust be apprQved by the lqcal buildil).g~thority. M the IQC8] code provisions may chapge betweenjurjajicti9hs, the AISC Specijicaticn and AI~C Seismic Provisions refer t6 this code as the appli~ble building <:09e. . 1

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Codes have hiStOrically used occupancy category. This classification was changed

10 risk category·in ASCE/SEJ 7-10 and me 2012. Where class.ification by occupancy category is still employed. the more stringent of the two is used.

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The primary perfonnanc;:e objective of these model codes is that of "life safety" for building occupants for all the va4ous demands to \'(mch.lhe building will:be subjected. To satisfy this-Objective,fof-. stiuctures required to resiststrong ground motions· from earthquakes;1hese codes reference ASCEISEI-'.7•for.-&eismic analysis and design provisions:-Se.ismic design criteria iii this standard.prescribe- minimum reql!llementS for both rhe>strength and stiffness of SFRS and the strot:tnr:il elements they include: Tue seismic design criteria in ASCFJSEI 7 for the most part are based.on the NEHRP Recommended Provisicns for Seismic Regulaticn.s for New Buildings and Other Structures (FEMA, 2009). The seismic design of nonbuilding structures is addressed separately in ASCFJSEI 7 in Chapter 15. Nonbuilding structures are defined as all self-supportiiig structures that carry gravify loads and that may be required to resist the effects of s~isftuc loads, with certain exclusions. ASCEJSEI 7 develops an appropriate interface with builf!i,ng structures for those types of nonbuilding structures that have dynamic behayiors similar to buildings. There are other nonbuilding structures that ha_ye JJttl~. simifurily to buildings in terms of dynamic response, which are not specifically covered by AISC documents.

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In ASCEJSEI 7, the expected perfonnance of a structure is detennined by assigning it to a risk category. There· ~ four rislC ca'tegories (I. II, ' iliand IV), base(on the risk posed to society .a s a conseq~of suiictural failure or loss of function. In seismic design, the risk category is used in dinjunctioh with parameters ~t define' the ilite~ity of design ground shaking in determining the importance-factor and.the seismic design category (SDC) for which a structure muSt be dC$igned'. The're are six SOC, designa~ by-the letters A through L F. Structures assig~~·-to ;Seismic; Design Catego;y.·A are not' ailtiC"ip~ted to experience ground shaking of sufficientJnte·ngity tO cause unacceptable performance, even if they are not specifically designed for se!smic resistance.,Structu{Cs in Seismic Design Categories B If or C can experience motion capable of producing unacceptable damage when the structures L have not been designed for seismic resistance. Structures in Seismic Design Category D are expected to expentooe iii~"ground\shaking, capable of produang unacceptable performance in strucni~. ~t)~_ave qnfavorable structural,. ~yste~~s ll!l~ ~which have not been r • detailed to provide b~ levels inelastic deformation response withcn1t failure. Structures assigned to Seismic ~i.11!! C*gooes E and F are Jocated _wi~: a few miles of major .. $. . · - "c"otei~ ->-'°~ active faults capable of producmg large magnitude earthquakes and ground motions with i-~' peak ground accel~.~~ceeding 0.6g. Even well-designe
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Earthquake Ground Motiqn and Response Spectrum An earthquake causes ~d mo~ons that may proJ~gate from .the} h_yp0center in any direction. These motions ~nee horizontal and vertibal ground accelerations at the earth's surface, which in it is to use earthquake ::1: ground motions ~ in past earthquakes to simulate the ~havior of structures, the required analysis prOcedwes are complex, and the ~~:tlysis resulls are sensitive to the characteristics of the individual groi.Jnd motions selecOOcJ; ~hich may not actually be similar to those a structure will ~rie~ ~. the future. To sit~plify the uncertainty and complexity ' - · • I • .t•, i • • ' ·.'

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associated with using recorded motions' 10 predict a scructure's response, response earthquake

spectra are used. A response,specti\mr.for a given earthquake ground motion indicates the maximum (l\hsolute value), expressed either-as acceleration, velocity or displaoe.tneot, that an elastic single--Oegrce-of-frccdom (SDOF) oscillator will experience as a function of the structure•s period and equivalent damping factor. Figure 1-la shows an example of an acceleration response spectrum. On average, low-rise buildings (Figure 1-lb) tend to have short periods. J

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t.3 SEISMIC DESIGN OVERVIEW AND DESIGN CONSIDERATIONS

Maximum Considered Earthquake and Design Basis Earthquake · ' · · ··· ·, '

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Systems Dpfi_fl~~-J r:a ASCE/_S~I ? A steel SFRS is generally classifl~ i~t~-"iliree feveis of expected inelastic response capability, designated aS ordinary, intermediate or special, depending on the level of ductility that the system is expected to provide. Systems designated as ordinary are designed and detailed to provide limited ductility, but the requirements are not as stringent as those systems classified as intermediate or speciaJ. In some cases, an SFRS cap be classified as a "structure not specifically detailed for seismic resistance" in accordance with the applicable building code. Each classification is characterized by the following seismic performance factors: !

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composite systems designated as ordinary where the counterpart reinforced concrete syscems have designated values of R and design requirements for SOC B and C. I Applications where R is greater than 3 mtended for buildings that are designed to t:.: meet the ~~irements of both, the AI~Ef ~eifmic Provisi.ons and the AISC SpecificaJiofl. The use of R greater than 3 in the calcufanon of the seismic base shear requires the use of r a ~isniically designed and detailed system that is able to provide the level of ductility ~m mensurate ~ith the v~lue of R selected in the design. This level of ductility is achieved . through a ~mbination of proper material and section selection, the use of low width-tothic~~s..roembers for the energy dissipating elements of the SFRS, decailing member eonn~tioos to resist the local demands at the capacity of the system, and providing for ~:.. system lateral stability at the large deformations exi>ected in a major eanbqil.ike. Consider f the following three examples:

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Ground motion hazards in ASCFJSEf 7 are defined as maximum consjdered earthquake ground motioos.-They are-based on the proximity of the site to active faults, the activity of these faults, magnitude of the-event these faults can produce, and the regional and local geology at 1l site. The design intent of ASCFJSEI 7 is- to assure that ordinary occupancy structures (sttuctures assigned to Risk Categories I and have not greater than a 10% chance of collapse should they experience maXimum considered earthquake shaking. Except for regions located withln a few miles of·major active faults, such as some sites in coastal CalifOmia. the maximum considered earthquake is selected with an annuaJ frequeQcy that will provide a unifonn collapse·risk of 1% probability in 50 years (denoted MCER). In regions close to major active faults prob~bilistic estimates of ground shaking at these annuaJ frequencies are very. intense and impractical for use in design. Tbetefore, on such sites, the MCER is capped by a conser.v.ative detenninistic estimate of the ground motion resulting from a maximum magnitude earthquake.on;the nearby fault, resulting in a higher collapse risk. This·is a change from prior editions of AS.CEJS,EI 7. SeeASCE (2010)' commentary and FEMA (W09)' for further infonnation.-Tue MCER is. represented by a generalized elastic acceleration response spectrum (see previous). TIUs response spectrum is subsequently reduced by two-thirds to represent the elastic response for the design basis earthquake for which a structure is designed. Detailed information about this reduction can be found in FEMA (2009).

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Sped~ concentrically bqiced fame (SCBF) systems-SCBF ~ystems are generaJly (,_ configured so that energy' dissipation will occur by tension yiel~ing and/or compression buckling in the braces. The connections of the braces 10 the. columns and beams r and between the columns and beams themselves must then be pr~portioncd to remain : 1 • essentially elastic as they undergo these defonnjltions.- See Figure 1-3. 2. Eccentrically braced frame (EBF) systems-EBF systems are generally configured so

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Wheq, used in combination, factors quantitatively outline the expected performance ' of an SFRS. Other factors that io,fluence the performance are the importance factor, I,, and redundancy factor, p. These factQCS are discussed in the following. Desigrung to meet the seismic requifements of the AISC Seismic Provisions is mandatory for structures where they have been specifically referenced in Table 12.2- 1 of ASCFJSEl 7. For steel structures, typically this occurs in SOC D and higher where R is greater than 3. However, lhere are insiAoces where an R less than 3 is- assigned to a system and the Provisions are still required. These limited cases occur in ASCE/SEI 7 Table 12.2-1 for cantilevered column systems and Table 15.4-1 for nonbuilding structures simHar to buildings. For composite steel-concrete structures, there are .cases where the Provisions are required in SOC B and C, as specified in Table 12~1 of ASCFJSEl 7. This typically occurs for

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Seismic Perfo"!l'ance Factors Response MQdification CoefficietJt.

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a structure. SlJ'UctuJCS designed with a large value of R mµst have extensive capability tu wilhstand large inelastic defom11ltioo demands during design shaking. Structures designed with an R approx,imating 1 are anticipated: to. experience design shaking while rcma.in,ing esscnri.aUy elastic. F'lgure J-6 shows the relatiOO:'lhiP between R and the design-level fo'rces, along with the corresponding lateral deformation of the suuctural system (FEMA, 2009). Factors that·detennine the magnitude of the response modification factor are the vulnerability of the gravity load resisting system to a failure of elements in the.SFRS, the level and reliability of the ioelasticity the system can attain, and potential b_ackup frame resistance such. as that which is provided by dual-frame systems. As illustrated in Figure H>. in order for a system t<(utilize .a higher value of R, other elements of the system must have adequate strength and deformation Capacity to remain stable at the maximum lateral deflection .levels. If the system redundancy and system overstrength cannot be achie-:ed. a lower value of R should be incorporated in the design and detailing of the structpre. Values of R for all st.Qlc~ tural systems are defined in Table 12.2-1 of ASCEJSEI 7. Tables l-9a and l-9b in this Manual summarize the R-Factors and other factors specified in ASCPJSEI 7 for steel c-0mposite systems. More detailed discussion on the system design parameters can be found in FEMA (2009).

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low the requirementS of the 'AISC Seismic Provisions. The resulting systems have ductility

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detailed. for seismic resistance possess some inherent amount of seismic resistance, which may be adequate to resist a limiled amount of seismic demand. · It is rerogniz.ed that when the designer bas' the option to design a building to meet the AISC SpecijicQtion with R 3, such a design will generally be more cost effective than·the same sti:ucture designed in accordance with the AISC Seismic Prrwiswns using a higher value·of R. The extra fabrication, erection and inspection costs nee.ded to achieve the high ductility commensura~ with the higher R. more than offset the additional st.eel toonage required•by theR l::::3 system.. The R 3 option is not generally available for composite steel--0oncrete systems. For composite systems, the designer must follow the requirements outlined in Table-12.2-1 of ASCEiSEI7.

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·Most seisicic fQ~ resisting systems ~ly on dissipation of earthquake energy through vary.ing levels of inelastic behavior. Steel seismic system definitions in the AlSC Seismic

f.rovtsion.r,:d~j.&!late ~e elements µttendeil to dissipate the majority of this eneriY through

ductile response: and those that are intended to remain essentially elastic. The application of an overstrengi.h factor, is applied to some seismic load combinations in ASCFJSEI 7 and in certain c~es in the AISC Seismic Provisions to provide a design foree that will result in essentially elastic re8ponse for sp~cific components. These load combinations are invoked for members or connections whose inelastic behavior may cause poor system performance. They generally meet the following criteria: They are critical elements on the load path, and they are not likely to perform well in the itielastic range. Members ~d connections requiring the special seismic load combinations incoiporating the overstrength factor, in ASCEJSEI 7, include the following (the apptic3ble sect.ion of ASCEJSEI 7 is provided in parentheses):

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Elements supi)orting discontinuous "".alls or frames (Section 12.3.3.3) Collectors f0r structures in SOC C through F (Section 12. 10.2.l) Batter piles (Section 12.13.6.4) Pile anchorage (Section 12.13.6.5) 5. Pile splices (Section 12.13.6.6)

In the AISC Seismic Pr,ovisions, this concept is addressed using the term, amplified seismic load. In some cases, the amplified seismic load defers to the use of the ASCfJSEl 7 load combinations that include 0... while for other situations, the amplified seismic load is a term defined in the AISC Seismic Provisions to meet a capacity design requirement Sections of the AISC Seisf!liC Provisions where the amplified seismic load is invoked for the design of certain elements or connections include:

1- 15

1.3 SEISMlC DESIGN OVERVIEW AND DESIGN CONSIDERATIONS

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. Section D 1.4a- Required compressive and iensile strength of columns Section D2.5b-Required stren·gth of column splices .. 1 Section D2.6a-Rcquired axial strength of column bases • ' . b Section D2.6b-Required shear strength of column bases •.. · •: . • ·• · ;. Section D2.6c-Requircd flexural strtogth of~lumn bases '• 1 J Section El .6b--Required shear strength of beam-to-column connections for ordinary I -t~

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Sections E2.6d and G2.6d-Required shear str~ngth of ~~to-column. connections for ,. 1 . • . " intermediate moment frames and-composite intermediate moment frames Sections E3.4a and G3.4a-Moment ratio check for special momenc frames and composite · special moment frames (also referred to as the strong-column-weak-beam calculation) _ Sections E3.4c and G3.4c-Required column strength at unbraced beam-to-column con- ;,.. nections for special moment frames and composite special moment frames ·--~ Section E3.6d and G3.6d-Required shear slrength of beam-to-column conn~tions for special moment fran1es and e-0mposite special moment frames Section E4.31>-Required strength of noospecial segment members and.connections for i s~ial truss moment frames · Sbetion E5.4a- Requi£Cci' streilgtb of columns in ordinafY cantilevelcolumn systems Section E6Aa-Requi.red strength ofbolLitnns in si)ecial cantilever column ·systems Section Fl.2-Detenhlnation of eccentric 'inoments in members for ordinary concentri. : cally. braced frames, if an ~centricity is present " ., .. . t. . . . S~tion Fl.4a-Detennination pf required strength of beams.'ui.V-br~ced an~ invertedV-braW:i ordinary roocentrically braced frames ~. Section Ft.6-Diagonal br~ce connections in ordinary concentrically braced fr~es Section F2.3-Required strength of_ c9lumns, beams and connections in s~ial concen- [ tricaJly braced frames . · .... : . . . , · · ,, . . Sec.tio~ F2.4a-Provides an excepti~~ to the lateral forcedistnbution i:equir~;m~nt in spe- 0 ,, . cial concentrically qraced fi-!lJlle~, I' , . . · · Sections F3.3 and F3.6c-Required strength of diagonal braces and their ~onqections, f beams outside links, and columns for eccentrically braced frames Sections F4.3 and F4.6c-Required strength of beams, columns and connections in buck- · ling-restrained braced frames • , . Sections FS.3 and F5.6b-Required strength ofhonzontal and vertical boundary elements :~ , • •• u· I and connections in special plate shear walls , · .. . . ~-

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Redundancy is an important prope.r ty Ioi strucrures designed with the expectation that d~- . age will occur. Redundant structures have alternative load paths so that if some elements are .. severely damaged and lose load carrying capacity, other elements will be able to continue to [. provide a safe load path. Adequate redundancy is ensured when a large number of plastic hinges must fonn tl1roughout the structure in a progressive manner before formation of a · mechanism and when no one element is required to provide the full seismic resistance of '. the struc1urc. To encourage provision of a minimum level of redtindancy in the structure, ASCVSEl 7 Section l 2.3.4 stipulates a redundancy factor, p, based on the structure's AME~ICAN L'ISTrl'\fm OP STI!a CONSTRllCnON

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configuration and the number 9f independent seismic force resisting elements present. When structures do not satisfy minimum criteria. this factor·amplifies lhe required strength of the Iateral system. The elastic analysis !lf ~$FR£ is pt.tfonned usi.n& V. the total design lateral force, based on !he tabul~ value ofR, and pis applied to.~e resultin&Qs·member force effects, where QE is the. effect of horizontal seismic forces. , , , · ·,

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Maximum Force Delivered by the Syster:n

Where steel framing changes direction -· Separating wings of L, U and T shaped buildings • At additions to existing buildings • At locations where interior beating conditions change, such as where heated offices abut an unhcar.ed warehouse • To break very long structures into shorter structures

Seismic joint.S are similar in fonn to expansion joints but are the result of very different structural considerations. They must accommodate movement in both orthogonal directions simultaneously and their spacing is not typically affected by building length or size. Seismic joints 'a.re used to separate an irregular structure into multiple regular structures in an effort to proyide better seismic performance of tile overall building. The design of seismic joints is complex and includes efforts by all members of the design team to assure that lhe joint is properly sized, adequately sealed from weather, and safe to wallc on, as well as to provide for adequate movement of other systems crossing the joint and means to mainta.i.\l the .fire ratings of the floor, roof and wall systems. Seismic joints are costly and architecturally undesirable, so they should be incorporated with discretion. When seismic joints are determined to be necessary or desira~le for a panicular building, the locations of the joints are often obvio~ and inherenL Many of the locations appropriate for expansion joints are also appropriate for seismic joints..Requirements for determining the seismic separation between buildings are prescribed in ASCFJSEI 7. The width of seismic joints).n IllQdem,puil9ings can vary from juSt a few inches to several feet, depending on building height and siiffness. Joints in more reoent buildings· tend to be .much widel' than !heir predecessors. ,This is due to several major factors, the most important of which.is chrulges in the cod~. Other contributing factors are the lower lateral stiffness of many modem build,ings and the.greater recognition by engineers of the magnitude of reaJ. la~ia,\-defonnations induced by an ~quake. Seismic jo.i,nts o{ten result in somewhat complicated structural framing conditions. In 1be simplest of joints, ~te columns are placed at either side of the joint to p,rovide lhe n~ essary structural support. This is comroon in parlcing struetures. When double columns are not acceptable. lhe slrUCtUte must either be cantilevered from more widely spaced columns or seated connec.ljom must be used. In' lhe case of seat¢ conn~tjons, there is the temptation to limit the .travel of the sliding Clement, because longer•sliding surfaces using Teflon sliders or s.imilar devices are costly and lbe seat element may in~ere with other elements of the building. It js SJrongly ~mmeoded \hat seated coonections be designed to allow for movements that exceed those ~cu.lated for .the design basis earthquake to allow for th~ effects of greater earthquakes and because the consequences of the sttucture falµng off of the seat may be disastrous. Wi,ete thi.s is not possible, restraint cables such as those often used on bridges. should be considered.

11\e vyidth of an expansion joint is determined from the basic them1al expansion

Bui/ding Separations

The maximum force delivered by lhe system is a concept used in several applications in the practice of seismic design. The ma:x.imum force deliyercd by lhe system is oftell one of the limits for requited strength of a seismic resisting element For example, a thorough.diSC'Ussion of how this force may be detennined for SCBP brace connections is contained in the AISC Seismic Provisicns Commentary Section F2.6c.

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Expansion join~ .i,n a stru~fµre a,re vr.ovided t(),?YOid impairing.the function of the fac~lity or c.ausini c~.amage to the structural ~. ~hitec~al components. 'the ~umber and l~tion of building e)(pansion joints is a design iS.sue not fully trealed in tecfun~ai literature. · •

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• The Al.SC Spec_ificaJion considers expansion joints a servie&.bility issue, and. Section • L7 states that 'The effects of tbe.nnal expansion and contraction of a building shall be

considered. Damage to building cladding fu cause water penetration and may lead to corrosion." · ' • ASCE/SEI 7 also considers expansion joints a serviceability issue indicating in Se<:tion 1.3.2 that "Structural systems, and members thereof, shall be designed to have adequate stiffness to limit deflections, lateral drift, vibration, or any other deformations that adversely affect the intended use and P.Ctfonnance of buildings and other struct11res."

'fypjcal locations of expansion joints include: ,

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Separations between adjacent buildings that a.re coosuuct.ed at different times, have different ownership, or are otherwise not compatib)e with each other may be necessary and unavoidable if bolh buildings are located at or near the common property line. ASCFJSEI 7 prescribes setbacks for property lines. An e:itception can be made where justified by ra.tion:i1 analysis based on inelastic irsponsc to design ground motions. •''"·


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Building Drift

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L3 SEISMIC DESIGN OVERVIEW AND DESIGN CONSIDERATIONS

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Deflection Compatibility ASCEISEI 7 prescribes requirements for deformation compatibilicy for Seismic Design Categories D through F to ensure that the SFRS provides adequate defom1ation control to protect elements of the structure that are not part of the seismic·force resisting sys~em. Thi~ is intended to c'nsure that componentS'designed as gravity supporting only can''alscnesist P-L'J. moments, based on total story drifts: . .

. Lowest Anticipated Service Temperature

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· Most structural steels ·can fracture eitlfer in a ductile or in a brittle mariner. The mode of frac· ··~,ure is governed by the temperature at fracture, the rate at whidi the loads ate applied, llnd tlle magnitude of the constraints' that would prevent plastic deformation. Fracture toughness is a measure of the energy required to cause'an element to fiacrure;· the 'm'ore energy that is iequir~( the tougher the·material, i.e., it takes more energy tO fracture a ductile material than a brittle material. Additionally, lower temperatures have an adverse impact on material ductility. Fracture toughness for materials give an S-curve as·shown in Figure·1~7. Usually, three specimens. are-tested at a given temperature and' the results averaged. .1. • ' Carbon and low alloy steels exhibit a change in fracture beliavior as the temperarure falls with the failure mode changing from ductile to brittle. At high teinperatures, the fraclUI'e is characterized by pure ductile·tearing. At low temperatures, the fracture surface is characterized by cleavage fractures. The decrease in fracture toughness at low temperatures decreaseS the fracture capacity of the member, resulting in poorer cyclic bel)avior. (Austenitic stainless steels do not show thjs change in fracture behavior, with the fracture remaining ductile even to very low temperatures. This is one reason ~hy these types of alloys arc ustdin cryogenic applications.) · The AlSC Seismic Provisions Commentary Section A3A acknowledges that in structures with exposed structural steel, demand critical weids may be subject to ser\iice temperatures

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less than 50 °P on a reglliaf basis. In these cases, the AISC Seismic Provision:s Commentary !r suggests that the minimum qualification temperature provided in AWS Dl.B·Annex A be ~~ adjusted such that the test tem)'.lerarure for the CVN toughness qualifica~on tests be no more .,., than 20 "F above the lowest anticipated serVice temperature (LAST). It is recognized that the LAST is defined diff~ntly in diffeicnt industries:For example, ITT: the current AASJITO CVN't~ghness requirements are specified to avoid bri!tlc 'fracture in [H: steel bridges abOve the LAST, which is defined.in terms of three tem~rattlre zc:>n'es. In arc- ·· tic offshore applications the LAs:r can be either tile minimum deiign temperature or a .w selected value below the design tempetature, de~nding upon the consequences.of failure. j;~~ The AISC Seismic Provisions are intenoed to ensure' ductile performance for a low prob- ;;h, ability earthquake event. The LAST is O?,WlallY .defin,ed to ensure ductile, perfOtJAance for a low probability temperature extreme. The direct combination of two low probability events i~ would be statistically very unlikely. As a. result, the definition of LAST need'not be execs- :;~ sively restrictive for seismic applications. For purposes of the AISC Seismic Piovi.siOns, the :;.. LAST may be considered to be the lowest one-day mean temperature compiled .from ~ National Oceanic and Atmospheric Administration data. For more information, go to !!; www.noaa.gov and www.climate.gov. ' ': \!~.

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,, ,.. . Story drift is the maximum lateral displacement within a story (i.e., the displacement of one tloor relative to the floor below caefsed by the effects of seismic loads). B\'liJdingfsubjected to earthquakes need drift control to limit damage to fragile nonstnictural elements, and to minimize differential movement demands 0n the structure. It is expected that the desigh of moment resisting frames, and the design of tall, narrow shear-wall or braced-frame buil~gs will be governed at least in part by drift considerations. · The allowable story drift limits arc defined in ASCE/SEI 7 Table ·1.2.12-1 and are a flJ!l~ tion of the seismic lateral force resisting system and the building risk category. The p~~cribed story drift limits are. applicable to ea9,h story. They mus! n.ot,bi ex~ed i1;1 any story even though the drift in other stories may be ~ell below the liril.it.

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statement in Section Jl of the AISC Seismic Provisions gives the f~llowing explanation for ~ . . quality control and quality assurance: E~ ~ ~

Quiµity control (QC) as specified in this chapt_e r shall be provided by the fabrlcaior, erector, or other responsible contractor as applicabl~. Quality assuranee (QA) as specified in this chapter shall be provided by others wh~b rcq\iired oy the authority hiiving jurisdiction, applicable building code, purchaser, owrier, or ef!gi~~r of ~ord (EOR).

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When ductile seismic response should be assured and the AlSC Seismic Provisions govem the design, fabrication and erection, steel framing needs to rnecc speciaJ quality requirements as appropriate for the various components of the structure. These requiremenis, applicable only to members of the SFRS, are provided in: • ANSI/AISC 341-10, Seismic Provisions/or Structural Steel Buildings (AISC, 2010b) • AWS Dl.8/Dl.8.M:2009, Smtcrural 'Welding Code-Seismic Supplement (AWS, 2009) • . ANSI/AISC 358-10, Prequalified Connections for Special and lnremrediare Steel Moment Frames for Seismic Applications (AISC, 2010c) • 2012 International Building Co
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The requirements of AlSC Seismic-Pfovisions Chapter J specify QC and QA special requirem~nts for all responsiple parties related to the following: .. . . ,·: ·. .

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quality requfrements are sjieCified in: .

• ANSI/AISC 360-10, Specification for Structural Steel Buildings (AISC, 2010a) • ATSC 303-10, Code of Standard Practice for Steel Buildmgs and Bridges (AISC, 2010d) . • AWS Dl.l/D1.IM:2010, Structural Welding Code-Steel (AWS, 2010) • 2009 RCSC Specification for Structural Joints Using High-Srrtngth Bolts (RCSC, 2009)

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GENERAL DESIGN CONSJOERA'DONS

• • .• • • •

Fabricator and erector documents Quality assurance asency documents Inspection and nondestructive testing personnel Inspection tasks . Welding inspectj.on and nondeStructi'.ye te~ting Inspection of high-strength bolt.4lg . · Other steel structure _inspections · • Inspection of composite stnicrures • Inspection of piling

To meet the requirements of the International Building Cns, resources and records to be used to provide assurance that the structure complies with the engineer's quality requirements, specifications and contract documents. Chapter J of the AISC Seismic Provisions provides the minimum acceptable requirements for a QAP fo~ .the SFRS, including requJrements for the contract documents, quality assurance agency documen~. inspection points, and frequendes, along with spec1aJ requirements for weld and bolt inspections. AJSC Sei.rmic Provisibn.r Chapter J bas specific requirements for nondestructive testing of welds. in addition to those in AISC Specification Section N4.5, which must be shown on the contract documents. Quality assurance requirements for bolting include verifying that faying surfaces meet the specifiCAtion requirements and that the bolts are properly tensioned per the R.CSC Specification.

1.3 SEISMIC DESIGN OVERVIEW AND DESIGN CONSIDeRATIONS

Design Drawing Requirements

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Structural Design Drawing Requirements For systems not requiring seismic detailing, structural design drawings are to meet the requifements in the AISC Code of S(4ndard Practice as stip~ated in AlSC Specification Section A4. Shop and erection drawing~ should follow design documencs to convey specified information for fabrication :md erection. for systems desi~ed to meet Lhe AISC Seismic Provisions, additional requirements are provided in A1SC Seismic Provisions Section A4 with supplementary discuss.ion in the Provisions Commentary Section A4. Tt is important to define all structu1?11 elements in the building that resist seismic loads, including struts, collectors, chords, diaI?fl:agms and trusses. Also, the SFRS members should be indicated in both plan and elevation drawings. If the SFRS includes other materials, these elements should be defined as such where the steel connects to them. '

SFRS Member and Connection Material Specifications SFRS material requirements are discussed in ATSC Seismic Provisions Section A3.l and in the material sections of the various prequaJified connections in ANSI/AISC 558. Wide flange shapes will generally be ASTM A992 material. ASTM A992 has spedfied maximum yield stress and milximum yield-to-tensile ratio to ensure ductility along with a'!imit on the carbon equivaJent to ensure weldabillty. Material requirements for the connection elements must be consistent with the prequalified details in ANSI/AISC 358. Bolt materi:ll grade, sjze, location and tensioning must be shown on the design drawings. Bolts typically are designed as bearing-type connections with standard holes and all Q
Demand Critical Welds Welds ate designated demand critical' in the AISC Seismic Provisions oased on considerati~n' of tlie inelastic strain dema,td and the consequence of failure. The·l~ation of these deriland critical welds is given in lhe AlSC Seismic Provisio.ns and in ANSIIAISC 358 in the section applicable to Lbe designated SFRS. As specified ul AISC Se~ic Pro~isions Section A3.4b, demand critical welds shall be. made with fil,Jer metals m~ting 'ilie requirements of AWS D(8 clause·6.3. Clause 6.3 requires a arinimum Charpy V-notch toughness of 40 ft..lb at 70 °F for a LAST of 50 °f C?r greater. See AWS Dl.8 for detail~ testing requirements and for a LAST less than 50 °F. There are a num9er of other quality c?nlr91 3:0d quality assurance items associated with dCJ'.!land critical welds that are covered in the AISC Seismic Provisions and AWS D 1.8. Items sucii as use of backing bars and run-off tabs, including requirements for trimming and fin· ishing of run-off tabs, are specifically addressed.

1-22

1.3 SEISMIC DESJGN OVERVIEW AND DESJGN CONSIDERATIONS


SFRS, some consideration should be gi-qen to·developing a limited ·amount of base · shear either by embedment or by bearing on the anchor rods. AISe Seismic Provisions } Section D2.6b stipulate.S the required shear strength for column bases, including those w not designated as part of the SFRS. ' 4. Width-to-thickness ratios of SFRS members must be less than those that are resistant to local buckling in order to achi~ve the required inelastic deformations required. While the width-to-thickness ratios given in the AISC Specificarion ·Table 84.l for compact sections are adequate to prevent buckling before the onset of strain hardening, tests have shown that they are not adequate for the requi:J:ed ·inelastic perfonnance in several SFRS. AISC Seismic Provisfons Table D 1.1 gives the limi~ng ~idth-to-thiekness ratios for moderately ductilea:na highly ductile members.:ClassificatiQn of members as moderately or highly ductile may govern member size for the various systems. 5. Requirements for stability bracing of beams are provided for each system. The braeing required is stipufated in AISC Seismic Provisions Section Dl.2 and-depends on ,, whether the beam is moderately or highly ductile. Special. bracing is :required adjacent to plastic !tinge locations. If the bracing_ requirement can~ot be m~t by the floor slab \· and the elements of the-moment connection, then the requrred bracmg merober(s) 'and connection(s) should be-,shown. For example, .special moment frame beams require _ bracing that satisfy the.provisions for highly ductile members as given inAISC S~~smic Provisions D l.2b. While the floor slab typically will:brace the top flange, addmonal ·. braces should be shown where required with the neeessary·connections. · ·· ~

Locations and Dimensions of Protected Zones, 0

Protected zones are designated by the AJSC Seismic Provisions for different systems-and generally are areas encompassing the plastic hinging region. The FEMNSAC testing bas demonstrated· the seiisitivity of these areaS to fracture caused by discontinuities resulting from welding, penetrations, changes in section. or construction-caused notches (Riel es et al., 2003). Fabrication and erection work, the subsequent work by other trades, have the potential _to cause discontinuities in the SFRS'. AlSC Seismic Provisi.ons Sections DI .3 and 12.1 provide detailed requirements for the protected zone. The"loclltidns and dimensions of these protected zones for rrioment'ccinnections ~spec ified in the AISC .Seismic Prdvisions and in ANSI/AfsC 358 for each SFRS. For e,·~ample, accbrdin'g to AISC Seismic Provisions Section F2.5c, the prbfected zone for special concentrically ·braced ~rames includes "the center one-quarter of the brace length and a zone adjacent to each conneetion equal ici the brace depth l.n the plane of buckling" as well as "elements that connect braces to beams and columns." For eccentrically braced frames, AISC Seismic Provisioris Section F3.5c defines protected.zone as the Jjnk. In any case, . the reql!ireme~ts ~n AISC SeiS1J1ic ProvisioTJS Sections D1.3 and 12.1 must be satisfied. - When· !oca~ed in the protected rone th~ ~&c.ontinuities are req~ _to be repaired by !he .resI?onsible contractor..tQ _the satisfaction of the engi!ieer of record: The AISC Seismic P_"rovisions r~qufre th;it tµ.e prot~9ted zones.,be sh9wn on the design drawings. The .s:ontractor n~s to \ise tltis information to ~ontrol ~nstru'ction activities in this area.

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AWS DL8,. sutx;lause 1;2.1 lists the information that the engineer o~ record_ 1s r~mred to C. protjde o~ the c0n~c~ dqcurn~nts SP,CCi.6<;ally related.to welding of t11e .SF.RS. Additipn~lly, gouges l!Jld.notcbes.!l!e not peDUitt~,and w_lJ!le gpndipg to a flus~.cQndi.·tion is not requin:d, the contour should provide a s~oo~, tranSttio,Q.. AVf.S D1.8 p~ovtde~ xe,i::?.nynended details ~ for these areas, _ .. . . . , ·· · · · •i . · · · AWS D.1 ;8..con~~ a numrn;r Qf otper special r~irements tha~ sho~4 pe specifisallY referenced j.n th~. C ~e~g ~tical w~ds h~ve the following requ.trepients:, ., .. • . ,•:. . .

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l'.ollowing ,~t'. some of the.additional ~eci~ifements from _the AISC peismic Provisions .that may_ .~~t c~tructural design dr~wing d,etails: ...

L SFRS ·column splice -requirements are given in' AISC Seismic.. Provisions Section D25a. The splices need to be loca~ away from beam-to-column connections, with the proviSions stipulating 4 ft otmore away from the connection; ·iiowever, in general, splices should be in the middle thtrd of the column (see Exceptions in Section D2.5a). Because of the splice strength requirements in Section D2.5, it is important that the splice be fully detailed on the design drawings. Where bolted splices are used there must be plates or channels on both sides of the web. 2. C~lUJllll: spl~c~ requirements for columns that are not part of the SFRS are given in the min.imuni shear foice8 required to be . . ;. ~IS.C $eiSmic ProVisions Section D25c. .·· , .d~el~f.'?fin .th7.5e.splices .".'ill require a special column splice and this detail should . also De snown .on the desjgn drawings. . 3. SFRS coi~mn bases must.meet the requh;ements of AJSC Seismic Provisions Section ·· D2.6 and anc~or rOd embedment and re.irdorcing steel should be designed according to ACI 318 Appendix.D. Anchor rod sizes ~d locations, along with washer require-; .merits, hole sizes an~ base plate welds must meJt lhese design requirementS and must be shown. Special embedment used for base fixity must also be shown on the Struc. tura1 dt:sigi;i. ilraw_ings. The Comment:Uy JO Section D2.6 gives a good discussion a!C?ng . ' with examples of b.ow to develop these fo~ces. For column b8Ses that are not part of . . ··.. . ' " . . ~.

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ManiiractureC'~ eertificates bf c'onfonnance for fiite{met?Is . .-··' .' . · S~ial restrictions on care and exposure of elec4odes · ., .. '· :· ·-· ;·."' · · · -• Suppl~~Snlar. wClaer qu~fi.cation fiir restrlct~(i''accds ~elding' for tJ?ttorl?'"!J_~g~

·-·· ·weliliilg· throu~ a~s liole$ ·· · · ·. · ·1• " · • · . • •· ' · i sPe<;i:iI weid sequence ror'bottom fiange·welding ihiough aceess holes . . •'' Suppiementary'teqmremenis for qrialification of ultrasonk,test\.ilg. tecluiicians

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For buildings with composite inenibe/s and/or com~site SFRS_. aa importan! ch~g~ in." th· 2010 AISC Seismic Provisions is tile' integration ofwhat were formerly presented separately in Pa.rtS I (steel) and II (composite) into a combined sel of provisions. This edition of th. ~ Seismic Design Manual follows that approach by adding examples for composite systems.

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The 2010 AISC Seismic Provisions for the seismic design of composite structural steel and reinforced concrete buildings are based upon the 1994 NEHRP Provisions (FEMA. 1994) and subsequent modifications made in the 1997, 2000, 2003 and 2009 NEHRP Provisions (FEMA, 2009) and in ASCE/SEI 7. Because composite systems are comprised of integrated steel sod concrete components, both the AISC Specification and ACI 31 g form an important basis for provisions related to compos.ite construction. There is, at present, limited experience in the U.S. with composite building systems sub· jected to extreme seismic loads. Extensive design and performance experience with this type of construction in Japan clearly indicates that composite systems, due to their inher· ent rigidity and toughness, can equal or exceed the perfonnance of buildings comprised of reinforced concrete systems or structural steel systems (Deierlein and Noguchi, 2004; Yamanouchi et al.. 1998). Composite systems have been extensively used in tall buildings throughout the world. Careful attention to all aspects of the design is necessary in the design of composite systems, particularly with respect to the general building layout and detailing of members and connections. Composite connection details are illustrated throughout this Manual to convey the basic character of the force transfer in composite systems. However, these decails should not necessarily be treated as design standards. The· cited references provide more specific information on the 'design of composite connections. F-0r a general discussion of these issues and some specific design examples, refer to Viest et al. {1997). The design and construction of composite elements and systems continues to evolve in practice. Except where explicitly stated, the AlSC Seismic Provisions are not intended to limit the application of new. systems for which testing and analysis demonstrates .that the structure has adequate strength, ductility and toughness. It is generally anticipated that the dverall behavior of the composite systems herein will be similar to that for counterpan structural steel systems or reinforced concrete systems and that inelastic deformations will occur in conventional ways; such as flexural yielding of beams in fully restrained moment frames or axial yielding and/or buckling of braces in' braced frames. When systems have both ductile and nonductile elements, the relative stiffness of each sh<'uld be properly modeled; the ductile elements can defoon inelastically while the nonductiJe elements remain noniinally elastic. When using elastic analysis, member stiffness should be reduced to account f6r the degree of cracking the onset of significant yielding in the structure. Additionally, it is necessary to account for material overstrength that may alter relative strength and stiffness. Parts 6 an~ 7 of t,his.Manual provide discussion and example problems for the design of members and connections for composite moment frame and braced frame systems, respectively, as well as guidelines for traversing through lhe AISC Seismic Provisions alld AISC Specification relative to specific building system. Where possible, the e.umple problems presented were developed to be companions to the example problems presented in other parts of this Manual. For instance, the example problem for the composite speci:ll moment fraine system illustrates the application of the composite requirements when a concr«;te-filled tube column replaces the steel column of the special moment frame strucru.re illustrated in the example problems in Part 4 of this Manual.

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1.4 DESIGN TABLE D JSCUSSlON

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1.4 DESIGN TABLE DISCUSSION Seismic Weld Access Hole Configurations Table 1-1. Workable Seismic Weld Access HoJe Configurations Fourteen configurations arc given based upon the minimum scisffiic weld access bole profile. This table is intended to be used in conjunction with Table 1-3 for quick selection of weld access hole geometry for wide-flange beams when the special seismic weld access hole is used. A workable seismic access hole configuration from Table 1-1 is given .in Table 1-3 for each shape listed. Where a dash is shown, no configuration shown in Table 1-1 meets all criteria. · AJSC Specification Section Jl.6 provides general requirements for weld access holes. It should be noted that the geometries shown in Table 1-1 represent only one set of configurations that satisfy the dimensions and tolerances in AWS Dl.8 Figure 6.2. Other configurations that comply with AWS Dl.8 Figure 6.2 may also be used. The special seismic weld access hole is required for beams in ordinary moment frames per AISC Seismic Provisions Section El.6b(c), and for beams in welded unreinforced flange-welded web (WUF-W) moment connections per ANSI/AISC 358. ,. ··

Member Ductility Requirements Table 1-2. Summary of Member Ductility Requirements Ductility requirements are summarized for SFRS members per Chapters E, F, G and H of the AlSC Seismic Provisions.

Local Buckling Requirements I Table 1-3. Sections That ~atisfy Seismic Width-to-Thickness Requirements, W-Shapes "

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W-shapes with F1 50 ksi (ASTM A992) that satisfy the moderately or highly ductile width· to-thickness requirements per th~ AISC Seismic Provisions Table D 1.l are indicated with a "•" in the column correspond.i.tig to the member requirements for specific SFRS. This includes W-sbapes th:ll incorporate reduced beam section moment connections. See Table 1-2 for a summary of the member ductility requirements for the SFRS in the AISC Seismic Provisions. A wide-flange section satisfies these requirements if its flange and weh width-to-thickness ratios are less than or equal to the corresponding limits listed in Table l ·A, which is summarized from the requirements in Table D 1.1 of the AISC Seismi· Provisions. For cases where the limiting web width-to-thickness ratio is a function of th member's required axial strength, P,, or P,,, the member will satisfy the width-to-lhickne •· requirements if P., or P~ is less than or equal to the value tabulated for P,. maJC or Pa ,,, respectively. The nominal axial yield strength of a member, P,, is calculated as F1 A1 . N<'"·· that in these cases it is 3SSUmed that Ca= Pul9cP1 > 0.125 or D..;P0 1P1 > 0.125. Exceptic

l - 26

GENERAL DESIGN CONSlDERATfONS

for intermediate moment frame and special moment frame beams with Ca< 0.125 are i.ndicated in the footnotes of Table 1-A. Where a dash is shown, there is no limitation on the values of Pu or P0 . Aloo provided is the maxirol!m spacin$ ?f beam bracing for moderately ducti,le and highJy ductile beams, L1nnu. wnere for moderately ductile beams, Lb'max= 0.l1r1 E!Fy, and highly ductile beams, Lb mo.x =0.086ry EIF,. Note that W-shapes that do not Satisfy "either moderhighly.d1,1ctite w.idth-to-thickness ratios not included in Table 1-3 • ately or •• .. • ,I//

are

....

..

l i .

Table 1-A

limiting Width-to-Thickness Ratios for W-Shape Flanges and. Webs in. Compression Limiting Width-to-Thickness

Limiting Width-to-Thickness

Ratio

Ratio

Range, b/.t.

Web, hit.,

Member

01agona1 Brace

0.38P,

1.4 DESION TABLE DISCUSSION

Table 1-4. Sections That Satisfy Seismic ·Width-to-Thickness Recfuirements, Angres·

c

..

>.

.•

:s m

a 0

::!:

..

Pu '= -~Py

Diagonal' • '

...

:; .§ Q

b

JZ

~ -

:i:

C,

=OcP

1

C>

Ratio

-::0 :::> oC

' (l.RFD)

·~

.·

~,,

.,

-

..

~

.

··"".....

lit '

.

;

0.38JE!F1 '

Diagonal » .,

Br~,

en<>

Chords In

:c;; -:.: Q:::>

(ASO) •

..

Olagonal Brace

::;:

Py

o.3op,·

Brace

C>

where

-;

.ii!:'

e= .. 0

c, >0.125 C

l·

·:Limiting Widih-to·Thickness Ratio ...

· Wlath-to-l!lici
Member ·

1.12J E I F1 (2.33- C1 )"?.1..49JEIT,"

o.33,[fff;

Column,EBF Unk•

"C

For

~-

l

Limiting Width-tQ-T.l)ickn~s~ · Ratios for Angle Legs in Compression

3.76,.fEI F1 (1 - 2.75C,)

Beam,'

L

Table 1-B

1.49J[ff;

.•

..

,, ~'

Angles with F1 =36 ksi (A36); inctudiDg_botb single and double angle configurations, that satisfy AJSC Seismic Prpvisiory, locaJ byckJ.i9g requirements fQr, use: fiS, diagonal b~aces 1 SCBF, OCBF, EBP, and the special segment of STMF chords are indicated wilh a "•" in I} corresponding column. An angle satisfies these requirements if the greatest leg width-tolhickness ratio is Jess than or equal to tbe·corresponding limits listed in Table 1-B, which i~ summarized from the requirements in Table DI. l of the AISC Seismic Provisions. Note th. angles that do not satisfy either moderately or highly ductile width-to-thickness ratios a1 nor included in Table 1-4.

For c, s 0.125

"' ~ :::>

I:

1 -.

bit

0.30JE1Fy

STMFSpeclal Segment

I

!

, ..

I

\

1.49JE!F1 ffi( C, S0.125

Column, ChOfds in STMf SP,ecfal Segment,EBF Un~SPSW VBE&HBE

..

2.45JE I F1

-

Beam,'

(1 - 0.93C,)

ffi(C, :>0.125

o.nJE IF, {2.93-C,)~1.49,.JE IF,

o;JOP,

Where

c. "' ..!!... (l.RFD) ~Py

'

.

I

I

,

C,,.. OcP1 ~D)

Pr • FcrW~ beanslnSMF systemS YIMre

c.1s les:s 111an or~ 1o0.125, lhe.fmrtlno raliO 11/ 1,,shal not exceed 3.76./fff;.

• Applle$ IO eBf links meeting the exctl)tlcn In SdofJ F3.5b(1).

.

• Fcr W~ beams In SMF S)'SlemS where C. ls Im 111ar1 or~ 1o 0.125. the lmillnO Wldlll-~ ralio 11/t. .rial not

~ 2.45.fElF,.

::

.-.

-'

J . ·' .... ..... :.

} • ..l

l

w

~l

1-28

I ..

GENERAL DESIGN CO:"!SJOERATIONS

Table 1-5a. Sections That Satisfy Seismic Width-to-Thickness Requirements, Rectangular HSS

Table 1-6. Sections That Satisfy Seismic Width-to-Thickness Requirements, Round HSS

Table 1-Sb. Sections That Satisfy Seismic . Width-to-Thickness Requirements; Square HSS

Round HSS sections with F1 =42 ksi (ASTM A500 Grade B) that satisfy the AISC Seismic Provisions local buckling requirements for use as braces or columns in SCBF and braces in OCBF and EBF are indicated with a ...~ in the corresponding column. A round HSS satisfies these requirements if its width-ro-thick:ness ratio is less than or equal to the corresponding limit listed in Table 1-D. Note that round HSS sections tlut do not satisfy cuber moderately or highly ductile width-IO-thi.ckncss ratios are not included in Table 1-6.

Rectangular aod square HSS with F1 =46 ksi (ASlM A500 Grade B) that satisfy the AJSC Seismic Provisions local buc.kJing ~uirements for use as diagonal braces or columns in SCBF, and bT'aCC$ in OCBF and EBF are indicated wilh a "•" in the corresponding column. A rectangular or square HSS s.atisfies these. requirements if its flange and web width-tolhickness ratios are less than or equal 10 the corresponding limits listed in Table 1-C. which is summariz.ed from !he requ.irernents of Table D 1.1 of the AlSC Seismic Prr:n·isioru. Note that HSS sections tha1 do not satisfy either moderately or highly ductile width-to-lhick:ness ratios arc not included in Tables l-5a or l-5b.

r:•

.• i

::.-,

:

Member 2::-

Bo

{

e=s ... <.> '& c5

·'''·

::e

..~:9 ,. "

Wltttfl. to-Thidaless Ratio

limiting Wfdth.to-Tlllcl
RaUo

.

Diagonal

Brace, Beam,

bit

0.64JE IF1

'

Column

limiting Width-to-Thickness Ratios for Round HSS and Pipe Walls in Compression Member

s~ "8 g

Diagonal Brace, Beam, Column

>- 0 ~5

Diagonal Brace, Beam,

ii., ~

<.> -"' :::> :c Cl

Width-to-Thickness Ratio

Limiting Width-to-Thickness Ratio

Olt

D.044 (EIF1 )1

.

. Oft

Column .

-

>- ..

~~

!:I ::&:: Cl

bit

o.ssJE IF1

Column

•The lm#ing wlddHI>·~ r1lio ot walb (JI rec:tingllal !!Id sq.11r1 HSS memlleta used as beams OI coblr.s shell not eoaed 1.12../fF,.

0.038(EIF1 )

.

• The li!ni1Jng dlameler-to-11lic1QvlsS ratiO of wall1 of round tlSS members used as beams OI CXllumns sllll1 not exteed 0.07 EIF,_.

Diagonal

Brace, Beam,

.

Table 1-D

Table 1-C

limiting;Width-to-Thickness Ratios for Rectangular and Square HSS Walls in Compression

....·.~=~ ·.

·:....\·

1.4 DESlGN TABLE DISCUSSION

... I

"

I


1- 30

Table 1·7. Sections That Satisfy Seismic Width-to-Thickness Requirements, Pipe

=

Pipes with F, 3S ·ksi.(ASTM A53 Grade B) that satisfy AISC Seismic Provisions local buckling requii'Cinents for use as braces columns in SCBF and braces in OCBF and EBF are indicated with a "•" in the corresponding column. A pipe satisfies these requirements if its width•to-thickness ratio, Dlt, is less than oi equal to the corresponding limit listed in Table 1-D. Note that pipe that do not satisfy either moderately or highly ductile width-tothickness ratios are not included in Table 1-7.

Strength

or

o! Steel Headed Stud Anchors

Table 1-8. Nominal Horizontal Shear Strength and 25% Reduced N_ ominal Horizontal Shear Strength for One Steel Headed S~~ ~pchor The nominal shear strength of steel headed stud anchors is given in Table 1-8, jn accordance with AISC Specification Chapter I. This table provides the nominal shear strength for one steel headedst)ld anchor embedded in a solid concrete slab or in a composite slab with decklng, ~given in AISC Specification Section J8.2a.The nominal shear strength wich the 25% reduction as specified in AISC Seismic Provisions S~tion D2.8 for intermediate or special SFRS of Sections G2, G3, G4, H2, H3, HS and H6 is also given in Table 1-8. . According to the. User Note in AISC Seismic Provisions Section D 2.8, lhe 25% reduction is not necessary for gravity or collector components in structures with intennediate or special seismic force resisting systems designed for the amplified seismic load. Nominal horizontal shear strenglh values are presented based upon the position o f lhe steel anchor, profile of the deck, and oriental.ion of the deck relative to the steei anchor. See AISC Specification Commentary Figure C-18. l.

~ I I I

t -31

PART I REFERENCES

PART 1 REFERENCES

..

ACI (2008). Building Code Requirements for Structural Concrete, ACJ 318-08, American · :.Concrete Institute, Fannington Hi)Js, Ml'. ' AISC (2010a), Specification fo r Str~~,i;ral Steel Buildings, ANSTJAISC 360-10, American Institute of Steel Construction, Chicago, CL.

ATSC (2010b), Seismic Provi.rion.r for Structural Steel Buildings, ANSIIAISC 341-10, American Institute of Steel Construction, Chicago, U.. AISC (2010c), Prequalified Connections for SpecW.I and lntennediate Steel Momeni Frames for Seismic Applicatibns, ANSI/AISC 358-10, American Institute of Steel Construction, Chicago, IL. AISC (2010d). Code of SuwJard Practice for Steel Buildings and Bridges, American Institute of Steel ConstJUction, Chicago, IL. AISC (2011), Steel Con.rtrucrion Manual, 14th&!., American Institute of Steel Construction, Chicago, n...

ASCB (2010). Minimwn Design Loads for Buildings and Other Structures, ASCE/SEI 7-10,

AS:e~:;?::::::d~::: ~:~~::;~:;;~::;;~r

l

AWS (2007), Standard Symbols for Welding, Brazjng, and Nondesrrucrive Examination,

l:

Impact Testing of Metallic Maternus, ASTM E23-07ael, ASTM International, West Conshohocken, PA.

I

AWS A2.4, American Welding Society, Miami, FL.

l

AWS (2009), Structural Welding Code-Seismic Supplement, AWS Dl.8/Dl.8M:2009, American Welding Society, Miami, FL.

.

.

AWS (2010). Structural Welding Code-Steel, AWS Dl.1/Dl.1M:2010, Amencan Welding Society, Miami, FL. \

ASCE/SE' 7 [)esign CoefficiEmts and Factors for SFRS Tab.l e ·1-9a. Design Coefficients and Factors for Steel and Steel and Concrete Composite Seismic Force Resisting Systems This table is based on ASCE/SEI 7 Table 12.2-I and provides design coefficients and factors for steel and composite seismic force resisting systems (ASCE, 2010).

Table 1-9b. Design Coefficients and Factors for Nonbuilding Structures Similar to Buildings This table is based on ASCFJSE17Table15.4-1 and provides design coefficients and factors for steel and composite seismic force resisting systems in nonbuilding sLruclures similar to buildings (ASCE. 2010).

Chopra, A.K. (2007), Dynamics of Sb-uctures: Theory and Applications to Earthquakt Engineering, 3rd Ed., Prentice Hall, Upper Saddle River, NJ. Deierlein, G.G. and Noguchi, H. (2004), "Overview of US-Japan Research on the Seismic Design of Composite Reinforced Concrete and Steel Moment Frame Structures:· Jouma ~ of Structural Engineering,ASCE, Vol. J30, No. 2, pp. 361-367, Reston, VA. ·

FEMA (1994), NEHRP Recommended Pro1risions for Seismic Regulations for New Buildings and Other Strucrures, Washington, DC. [ ::

FEMA (2009), NEHRP Recommended Provisions fo r Seismic Regulations for

New·.;~

Buildings and Other Structures, FEMA P-750, Washington, DC. lCC (2012), lnlemational Building Code, International Code Council , Falls Cl)urch, VA. RCSC (2009), Specification for Structural Joinls Using High-Smmgth Bolts, Research· Council on Sllllctural Connections, American Institute of Steel Construction, Chicago, U..

t~

I

Ricles, J.M., Mao, C., Lu, L.W. and Fisber, J.W. (2003), "Ductile Details For Welde. Unreinforced Moment Connections Subject To Inelastic Cyclic Loading," Journal OJ'· l Engineering Strucrures, Elsevier, Vol. 25, pp. 667-{)80.

.J:

1- 32


DESIGN TABl.ES

Vicsi. T.M., Colaco, J.P., Furlong, R.W., Griffis, L.G., Leon, R.T. and Wyllie, L.A., Jr. (1997), Composite Construction: Design for Bu~ldin!s, McGraw-HilVASCE, Reslon, VA.

Table 1-1

Yamanouchi, H., Nishiyama, I. and Kobayashi, J. (1998), "Development and Usage of Composite and Hybrid Building Structure in Japan," ACI SP-174, American Concrete Institute, pp. 151- 174.

Workable Seismic Weld Access Hole Configurations .

, •

@

~ri

,1•.

tbl

@ ·'·

fY©

®

..

I

t.

I

®

·•

i I

IA'©

(1)Ct

11

_/

@

t%"min.

t/J(

.,

~

·l

i ~·

Dimension for weld access hole geometry In accordance with AWS 01.8/01.SM subdause 6.10.1

Access Hole Type

CD degrees

A

G H I

J

.

l M N

2 12

3 3'/t 4

:.

4

,,,,

'

.

,I

1 r,, 1 112 .... ·21h . 31n-

'I•

3 3 1/• 3 3/•

1

K

1/2

.1 1 114 1 1/z Pl• 2 2 11, 2 1/z 23/4

1 11• 1 'lz Pl• 2 2 114

F

tn.

'I•

'h

'I• 1

0 E

in.

in.· .

In. 'h

c

®·

@

30

8

@

®

;

4 1'2

51/z 6 1/z l!h 8 1iz 9 112

•It

11 12 1'2 14

15

! I

-

J- 34


.

DESIGN TABLES

1- 35 }:.

Table 1-2

Summary.of Member Ductility Requirements •· System

.

"

Highly Ouctile

Moderately

Aw

A.""

Dui:tile

.

... ..

Special Cantilever Column Systems (SCCS) • Columns

E2.5a E2.Sa

.

. .

..

Buckling-Restrained Braced Frames (BRBF) • Beams • Columns

.

F2.5a F2.5a F2.5a

..

.

'

F1.5a

~

Eccen~lly Braced

Frames (EBF) • Diagonal Braces • Columns • link Beams • Beams outside of the Link

•

F3.5a F3.Sa F3.5b(1) F3.5a

•• • • •

.•

ES.Sa ES.Sa

. '·. .

E4.5c E4.5c

IQgllly Ductile

System

Moderately Ductile ~

'AM

F4.5a F4.5a F5.5a F5.5a F5.5a

.

•

.

.

Composite lntennediate Moment Frames (C-IMF) • Steel and Composite Beams • Steel and Composite Columns

seismic PflJVislons Section Reference

l:

G2.5a G2.Sa .

• I

• •

G3.?a G3.5a G3.Sa

.

ob

• • .•

• •

.

.

I• \

\

\

. •

••

• Steel Coiipllng Beams

• Encase
semems

.

I~

;

'

.

G4.5a G4.5b

•

H2.5a H2.5a H2.5a

.. .

H3.5 & F3.5a HJ.5& F3.5a H3.5 & F3.5b(l) H3.5 & FJ.Sa

• •

. H4.5b(l) H4:5b(1)&(2)

.. •• ••

:.1

Ht.Sa

Compbsiie:O«fmary Shear Walls ~C..QSW)

• Steel and COmpoSite Vertical Boundary

li

t

'

Composite Special Concentrically Braced Frames (C-SCBF) ~ CompoSite Columns • steel Braces or Composite Braces I • Steel or Composite Beams

Composite Plate Shear Walla (C-PSW) • Steel and Composite Horizontal Boundary

~;

-

•

Coniposite Partialiy Re~ained Moment Frames (C:.fif\MF) • • Steel ·Colµrims • cOmpos~e Beams

Comj>osite EQ:entrically Braced Frames (C-EBF) • Oi3gonaJ Braoes -•• Columns UokBeams • Beams olitside of the Link

..

..

eorTiposite Specia!. Moment Frames (C·SMF) •Steel and Composite Beams ~ Steel and Composite Columns · • Reinforced Concrete,Encased Beams

Bements 61.S

No Ductility Requirements per Seismic Provisions

I

.

eomposite Ordinary Braced Frames (C-OBF)

..

Ordinary Concentrically Braced Frames (OCBF) • Diagonal Braces

I See exteptlon$ in Section F3.5b(1). • See extej)don In Section C>3.5a.

El.Sa

Seismic

E3.5a E3.5a

Ordinary Cantilever Column Systems (OCCS)

Composite Ordinary Moment FramH (c--OMF)

.

• •

Special Truss Moment Frames (STMF) • Chords in Special Segment • Special Segment Diagonal Webs

Speclal Plate Shear Walls (SPSW) • Homontal Boundary Element • Vertical B6undary Element • Intermediate Boundary 8ements

Provisions Section Reference

.

Speclal Moment Frames (SMF) • Beams • Columns

Speclal Concentrlcally Braced Frames (SCBF) • Diagonal Braces • Beams • Cotumns

Sutnmary 'of Member:DuCtility . Requirements·' -, ~

No Ductility Requirements per Seismic Provisions

~

Ordinary Moment Frame (OMF) Intermediate Moment Frame (IMF) • Beams • Columns

I l; I"

Table 1-2 (continued}

HS.Sb HS.Sb H.S.5c, F3.5b(1) H5.5c,d, F3.5b(1)

'

.

HS.Sa

•

H6.5a

I

l

~=~

l~

•See exceptions fn Section F3.5b(1). • See~ in Section G3.5a.

AMEluCAN INSTTI\ITE OF STSEL Cor.rST!UJCnO.~

I

~~

uJ:.N£RAL DESIGN CONSlDER.ATJONS

..

Width"':to~Thickn~ss

i~

ll

W40x392 x331 x327 , x294 x278 c· x264

x235 x211 x183 x167 X149

SMF

STMf

... .. .. •

• •

•

• • •

•

SCCS

W-Shapes

OCBF

SCBF

• •

. •

;

'

:

~

'

1

.. ... .•

.. ..• • •

'··-

... ..• . • .. . .• ... ... .. •• . .• .•• .. . .. .. .. .. .. .. .. .. ..• .,. ... .;.

I'

.. ..

.. ..• .

..

.. "

~

.

. ..~1J

Shape °Amd

14.5 14.5 14.4 14.3.

28.7 28.7 28.5 28.2

W44x335 x290 x262 x230

31.2 30.6 " 30.0 1~.2 15.1 29.9 15.0 29.6 15.0 29.6 14.9 29.4' 14.7., 29.1 14.9. 29.4 14.8 29.2 14.7 29.1 14.3 28.3

W40x593

11.0 10.7 10.7 10.6 10.5 10.5 10.~ 10. 10.4 9.98 9.52

W40x392 x331 x327 x294 x278

15.8 15.5

•;.r l •'l

·~

,,

'• ~

"

-

Diagonal Braces Columns

'A,hd

~

-

EBF

Lo- f t

:

. .

..

I'

Widtli~to-;;..Thickness

Fy = 50 ksi

W-Shapes

.. .. .. .. .• •• .. ..• ...• .• .. . . • •. .• • • • • . . • • . • • . ..• .. .• .. .. .. .. .. .. ... • . • .• .. .. .• ..• ... ..• ... i

:>

Requirements

Beams Beams· and Diagonal Diagonal and Chord Columns Columns Segment Columns Brace$ Braces Columns "Beams

W44x335 x290 x262 x230 W40x593 x503 x431 x397 x372 x362 , x324 x297 x2n ,_x_2.49 x2.15 x199

,_

.. IMF

r1

Fy = 50 ksi

. Requirements

I

I

Sections .That Satisfy Seismic

Sections JThat .Sati$fy Seismic

I Shape

Table 1~ (continued)

:.:• Table 1-3

"

21.7 2.1.1 21.2 21.0 20.7 20.7 20.9 20.6 20.5 19.7 18.8

x183 x167 x149

SPSW

Beams

HBE

and

and

Columns

VBE' .

.it....,, kips LRFD

i..m11 4080 2540 1710 910

•

• •

.. ··-.

•

•.

.. •

•

•

•

.. •

\

'\

• • •

• •

I

3790 2940 . 2110 1090 1010

•

0

G G G F E

E E 0 i)

H

~

•

G G

.. •

E E

I H

..

•

F

J

•

•

•

Web I

Auessi Ho!es I

•

x503 x431 x397 x372 x362 . x324 x297 ')(ln x249 x215 x199

x264 x235 x21 t

Unl
8R8F

169

2500 1790 911 043· 625

F F F E

e

0 D

c

I

1-38


.. Shape

Width-to~Thickness

IMF

SMF

Beams and

Beams and

•

~30

x302

x282 x262 x247 x231

W36x256 x232 x210 x194 x182 x170 x160 x150 x135

x201 W33x169 x152 x141 Xl30 x118

so k~i

W-Shapes

I

I

OCBF

SCCS

SCBF

-

Chord Diagonal Diagonal Segment Columns Braces . Braces Columns Beams '

I

...

.. .. ' ... .. . ... ..• . '

.•• .•• ... ...

I

;

• • • •

..•

• . .• . .• .• ... .••. ... . .• ii . I

.•• .. .. •

• •

iI I;

'

~- ,

I

..•

I•

'

•..

.... ..

.. . .. .

;

'

• •

• •

.• .. • .• • I•

.. .. •

1

.. ... .. .. ..• • • •

..• ... .. .. .• .• ..

.. . • .• .. .. •• • ..• . .• .• .•• I

Beams and

Dlagornil Brace$ Columns

P.,MX> kips LRFO

BRBF

EBF •

Li.maxi ft

Shape

•'

x318

><221

.. ..• .. . . . . ... .. .. ..• .. .. . . .. .• • .• • • • • . • .• . .•• ..• .• .• . . • • . •• .• ... ..• ...

STMF

'

xS61

x241

Fr=

Satisfy Seismic Width-to-Thickness Requirements

W-Shapes

~

x291 x263,

Fy=50 ksi

Requirements

W36X652 x529 x487 x441 ·

W33x387 x354

Sections ~That

Sections Jhat S~tisfy Seismic

Columns Columns

I

TabJe 1-3 (continued)

.

Table 1-3 (continued)

I

J )<"

DESIGN TABI,BS

Unks·

Columns

HBE

HoIll$

and

VB'E·,

Ahd

Amd

'Au

A.,,,.,

17.0 16.6 16.5 16.3 16.1 16.0 15.9 15.9 15.8 15.6 15.5 15.4

33.7 32-9 32.5 32-2 31.9 31 .6 31.5 31.4 31 2 30.9 30.7 30.5

W36x652 x529 x487

K

X441 X395

H

11.0 21.8 10.9 21 .5 10.7 21.2 10.6 21.0 10.6 21.0 10.5 W.8 10.4 20.5 10.3 20<.3 9.89 19.6

\Y36x256

15.7 15.5 15.4 15.3 15.2 15.0 14.9 14.8 .

31.0 30.7 30.5 30.2 30.1 29.7 29.5 29.3

W33x387

IOA 20.5 10.3 20.3 10.1 20.0 9.93 19.6 9.64 19. 1

W33x169

G G F F

x361 x330 x302 x282 x262 >

x247

x231 x232 x210 x194 x182 x170· x160 x150 X135

X354

x3t8 x29l

x263 x241

x221 x20f x152 x141 x130 x118'

3650 3020 2500 2010

3690

E

3170 2750 2350

E

2810

2900 2450 1940 1610 1260 1020 .

2290

• • •

1240

805 506 I

I

..

..

•

'

262

809

160

582

•

..

• •

•

• • • •

•

• 3180 2510 1810

-

II I

f

E

E E D D D 0

c

c

G G F F E E

2650

0

2090

D

m

1sa;l 1170

D

4TT. 245 128

917 712 483

1160

1

D F

1650

I

Web Acc~

D

t.

l

'

t ~ f

f.i

c c I:; c

;.'

t t·: ,.1

U.E::SlGN TABLES

l -41


I Shape


Sections That Satisfy Seismic Fy = 50 ksi Width-to-Thickness Requirements W-Shapes STMF

IMF

SMF

Beams

Beams and

SCCS

OCBF

W-Shapes SCSF

x326

:<

:.<292 x261 ><235 x211 x191 x173

:~ l

---- ··=

W30x148 x132 x124 x116 x108 x99 )(9t)

W27>:-5391 ~

x336

x307 x281 x258 x235 x2t7 xl94 x178 X161 Xl-16

I

I I·

W27x1~

x11 4 x102 x94 X84

..• ..• .. . • • •

.. •

..

.• •

• •

.•• .•• .•• . ..• ..·-- ..• .. .• .. .. . . . .• '

• •

•

.. ••• .• .. . • • • • •

• • •..

4....,tt

EBF Shape

Diagonal Diagonal and Chord Columns Columns Segment Cotumns Braces Braces Columns Beams W30x391 xS57

Sections:That Satisfy:Seismic Fy = 50- ksi Width-to-Thickness Requirements

.

..• ..• .. ..• .

.• .. .. . .

.•• .. .. . ·~

I•

... . .

..• .. ... ..• .• .. ~

.• •• .. .• .•• ••• ... .•• .. .• .. .• .. .. .. .. .. .. . .. . . .• •• .. .• .. •• .. .. .. .• .• .. ..• ..• .•• .•• • • ..•. .•• .. •• • ..• •


BRBF

SPSVf

Beams

llBE

and

and

cor11mns

VBE

~

Atr.4

15.3 15.1 15.0 14.9 14.7 14.6 14.5 14.4 14.2.

30.2 29.9 29.6 29.4 29.0 28.8 28.7 28.4 28.1

W30x391

9.48 9.35 9.27 9.10 8.94 8.73 8.69

18.7 18.5 18.3 18.0 17.7 17.3 17.2

W30x148 xl32 x124

•

x116

•

30.0 28.6 28.3 28.0 'l.7.9 'l.7.6 27.4 27.3

W27x539 x368 x336 . x307 x281 x2S8

15.2 14.5 14.3 14.2 14.1 14.0 13.8 13.8 13.7 13.5 13.4 13.3

v.o 26.7 26.5 26.3

18.2 17.9 17.7 17.4 8.60 17.0

9J9 9.06 8.94 8.81

•

Unks

•

x357 x326 ~ x292 x261 x235 x211 x191 x173

x146

•

x84

'Ah11

H G G F E E

•

2260 1670

2350 1670

1350 982 720 542

1550 1230 1010 859 701 530 235

364 171 32.4

.'•

•

~ I

• •

•

•

• •

•

0 0

Coro

c c c c 8 K H

•

G G

•

F F

E E E 0

• 2110 1570

•

D D

•

•

•

Web Access Holes

'Ji.mt1

•

W27x129 x114 xl02 x94

kips LRFO

P11.QJJ.I)

•

x108 x99 x90

x235 x2l7 x194 · x178 x161

I

2120 1690

0

c

1340

1460

965 527

1140 788

324 128

615

c c c

418

8

0

1-42

.

I W24x370 x335

x306 x279 x250 x229 x207 x192 x176 x162 x146 x131 x117 x104 W24x103 x94 x84 x76

~ W24x62 x55 W21x201 x182 x166 x147 x132 x122 x111 x101 W21 x93 x83 x73 x68

x62 x55

Table 1·3 (continued)

Table 1·3 (continued)

Sections That Satisfy Seismic Width-to~Thickne.ss

Fy ·= 50 ksi

sees

STMF

.• • •

'

•

•

..• .. ,.

.. ' •

'

• •

·-·

• •

• . ..

..• ..• . ..• .. .

• •

.. .• • • . • • • • • .• .. .. • • • .. • .. • • • .• • • .• • . • • .• •••

.. .. .. .. .• - •• .- . • " .• .. ••• ..•• .• .. •• '

'

.

I•

SCBF

.•• .• ... ..•

•

.• •

• •

..

.. ..

•

'

Lb ltl#h ft

.• • •

.• ..• ..• • • • • •

.. •

• •

• • • • •

•

~1 I

• •

'

.• •

-

• • • •

..• •

•

• •

• • I

• •

.. • • •

..• .• .. .• . .. ..• .• .• • • •

.• .• . .•

Ahd

Amd 26.9 26.5 26.3 26.0 25.8 25.6 25.3 25.2 25.0 25.1 24.7 24.4 24.2 23.9

8.27 .8.23 8.11 7.98 7.77

16.4 16.3 16.0 15.8 15.4

5.74 11.3 5.57 11.0

7.65 7.61 7.52 7.48 7.36 7.19

II I

13.6 13.4 13.3 13.2 13.1 12.9 12.8 12.8 12.0 12.7 12.5 12.3 12.2 12.1

12.6 12.5 12.4 12.3 12.2 12.1 12.1 12.0

I I ! I

1

'

I I

I

W·Shapes EBF · Shape Diagonal Braces Columns

I ''

~J

Links

BRBF

Sf'SV/

Beams

HBE

· anti

and

Columns · YBE

x279 x250 >;<229 x207 x192 x176 x162 x146 x131 x117 x104

•

.

W24x103 x94 x84 x76

•

..•

15.1 15.0 14.9 14.8 14.5 14.2

W21x93 · x83 x73

•

·~

•

x68 x62 x55

Holes °Ahd

•

E

• •

• •

• •

..•

•

•

• •

•

•

•

•

• •

•

• • •

• •

• • •

•

\•

E E D 0

1260 837

1360 1010

1110 836 506 290 114

1200 968 . 698 517 364

187 58.5

387 223

•

• • • • • ~

•

•

•

II ll!.

I I

l

c c c c 1· c c c

l

r I A!~ j B.

~l( ~ }

• •

• •

• • •

• •

F F

1220

1260

1060

1080 776 642 487 347

685 521 330

170

Nola 1: Unks in EBF Illa! meet ll'le exception ln the AISC Seismic ltrwlsions Section F3.5b(l) need ooly me6I the limil$ for mod«ately dooite memllefS.

l

'>..ma

•

•

I

W21 x201 x182 x166 x147 x132 x122 x111 x1Q)::

Web Access

G

• •

x68

W24x62 x55

UIFD

•

• •

• •

PuRtUi kips

•

x335

x306

l

I H G

\Y24x370

24.8 24.7 24.6 24.2 24.1 24.0 23.8 23.7

..

I

S.e.ctions That'-Satisfy Seismic Width-to:Thickness Fy =50 k;;i Requirements

I

OCBF

Beams Beams and and Chord Diagonal Diagonal Columns Columns Seg.n:ient Cotumlls · Braces Braces Columns Beams

.. .. ..• .. • .•• ..• .. •

4

:i

W,Shapes SMF

~

t

Requirements IMF

Shape

1-43

DESIGN TABLES

GENER.AL DESION CONSIDERATIONS

~

1·

c c c c c

lI'

c

l!

B .

AorB

I

.,..;:f:

,....

l

1-44

GENERAL DESIGN' CONSIDERATIONS

DESIGN TABL6S



I W18x311 x283 x258 x234 x211 x192 x175 x158 x143 x130 x119 x106 x.97 x86

x76 Wl8x71 x65 x60

x55 x50

Wl8x46 x40

. I\~ I i'

:1

; I

><35

W18x100 x89

xn

x67

W16x57 x50 x45 ><40 ><36

Requirements W-Shapes

ae.rn'

SMF

STMF

SCCS

OC8F

4,.,X> ft

SC8F

.• .. •

.. • ..• .•• .• .• .. ... .. .•• .. .. .• .• .

EBF

llelms

Shape

Diagonal Diagonal end and Chord Columns Columns Segment Columns Braces Braces Columns Beams

Yl21x57 x50 x44

Widtli~to'-'Thickness

=50 ksi

Fy

W-Shapes IMF

Shape

Sections That Satisfy Seismic

Sections That Satisfy Seismic Fy =50 ksi Width-to-Thickness Requirements

• •

.. .. .. ..• .. .• ..• • . • .• .. . .• .•

..

.•

.. .. • ..• ..• ... ... .. .. . ..... .. • •

..

. .. .•

..·. ... . ..•

.. ..• .• .•

..

..• ... .. .. .• ..

• •

... .. .. ... ..

.. . ... ... .. ..•

...

..• .• .. . . . ..• ... ..•. ... .• . . .• .. .. . .

.. . ... • . •

• •

•

... .• •

. • •

. .. • •

•

..• .•• . • •

')..,,.,


!..""'

5.61 1t.1 5.40 10.7 5.24 10.4 12.3 12.1 12.0 11.8 11.7 116 11.5 11.4 11.3 11 2 11.2 11.1 11.0 10.9 10.8 7.07 7.02 8.98 8.94 6.86

24.2 23.9 23.7 23.4 23.2 22.9 22.7 22.5 22.3 22. 2 22.1 21.9 21.8 21.6 21.4 14.0 13.9 13.8 13.7 13.6

5.36 10.6 5.28 10A 5.07 10.0

10.•

20.6

t0.4 t03

20.5 20.3 20.2

10.2

6.65 13.t 6.61 131 6.53 12.9 6.53 12.9 6.32 12. 5

UnkS

BRBF

SPSW

Beams and COiumns

t!BE

W21x57 x50 x44

P.,.....,klps LRFD

Holes

hfl4

1.,...,

326 176 57.6

461 330 201

I

·1

I

Wl8x71 ,.65 x60 x55 x50 \Vl8x46 x40 x35

W16xt00

•

•

xn

E D D D

• • •

I

895

932

668 520 326

709 588

•

• • • •

319 98.3 46.5

433

411 235 161

x50 )(45

x40

c c c c c c

I

A!BI B AorB AorB

c

~

•

l<67 W16'c.57

Aor B

F E

)(89

I

B

Aor B I H G G F

x283 x258 x234 x21l x192 x175 x158 x143 x130 x1 19 x106 x97 x86 x76

Web

Access

and

VBE

• •

W\8x311

I.

•

an

881

604 427

62-4 483 322 261

224 160

~

I

Sor C1

c I B

Aor A01 A0t " ;

1-46

GENERAL D~IGN CONSlDERAnONS



..

Fy = 50 ksi

Width-fO:.::ThicKness R·e quirements

F

1

Widttt~tO:-Thickriess

=so ksi

Requirements W-Shapes

W-Shapes SMf:'

JMF Shape

Sections .ThattSatisfy~Seismic

Sections~;'That ·Satis~ Seismic

I

1-47

DESIGN TABLES

Beams Beams ,and and Columns C~lu[ll®

.• .

W16x31 .xZ6

" _STMF

··::1

SCCS

Chord

Sestnent

.·.•. '

• -

. .. .

... .. • .. .·-• .. ... .. .. • .. .• ..• . .. • • ··• - .• • • • • • • '

•

.

.

Diagona1 Diagonal Colunins : Braces Braces Columns Beams 4~

•

-

... .

. .•

.• .•

• •

• •

• • •

.. • .• • • . • . . .!. • • ... •• •• .. .• • • • . . .. •• .•.. .. • .. .• •• ••• . . . . •• ..•· •• •• .• . •• ••• .• • • . .. . . .• .. ..• .. .• .• .• .• .• . • .. . . . . • . .. . . . .

x2S7 xZ33 >;<211x193 >;<176 x159

.•• ..•• .•..• . • •

-·

:

-

~:

1.

..

I•

:;<14r .

-

-

;

..

W14x132 x120. x109 ·, W14x82 '" · x74 x68 x61

~

;.

-

-

'

W14x53" x48 x43 W14x38

x34 x30

'

Diagonal lmr1

4.86 4.66

9.61 9.20

W16x31 x26

15.6 15.5 15.5

30.9 30.7 30.6 ; ; ·..,

W14x132 · x120 x109

•

10.3, 10.3 102 10.2·

20.4 20.4 20.2 20.1

W14x82 x74

• •

7.98 15.8 7.94 15.7 7.&6 15:5

W14x53 · x48 x43

6.44 12.7 6.36 12.6 6.19 12.2

W14x38 x34

17.5 17.3 17.2 17.0 16.9 16.8 16.7 16.6 16.5

' Beams · and · Unks Columns

SPS\'l

Po maxi kips

I.RFD

Web

Access

HBE Abd

'J..m<1 Aor B 171 77.5 AorB

N M

•

•

t. (

•

....

:i:c:370·

x342 .

...

. • .

- ..

x311·

xZ83 • x257 x233

•

X211

X193 x176 x159 x14s

xsS

•

•

• • • • •

•

•

-

• •

•

x61 .

•'·

• 518

535

400

434 329

273 192

x30

258

Nate 1: Uni\$ in EBF ttl31 the ~xceptlon In the.AISC Seismic ProviSionsSectlon F3.5b(1) neOO only meet tne limits for mod8f3tl!ly ductile mernllm-

me«

-

t

Holes

and

VBE

60.6 13.9

..

W14x730 - x665 x605, ·x550 x500 x455: . «426 X398-

...

AMERICAN INSTITUI1l 01' STEEL CONSTJtlJCTION

!!ra<:eS Columns

38.S 38.0 37.4 36.9 36.4 36.0 35.7 35.4 35-1 34.8 345 34.3 33.9 33.7 33.4 33.3 33.0 32.9 32.7

19.5 19.2 18.9 18.7' 18.4 18.2 . 18.0 17.9 17.7_

.. ..• .. .. .• •• .• .• . h.& .• .• .·-• .• .• .• ..• .•• .·-•

• • .. • . • . •

.•

• •

Shape

'J..hd

BRBF

EBf.;

£.,,,_,ft

SCBF

.

.•

• • •

W14x730 · x665 ><&05 x550 x500 x455 x426 x398 x370· x342 x311 xZ83

OCBF

I

l


1-48

...

DESIGN TABLES

-~S

I

r

I

Sections-,J hat .Satisfy Seismic Fy = 50 ksi Width-to·-Thickness Requirements

~~

I

~l

~lw :1

,, fll

· W14x26 x22 W12x336 x305 x279 x252 x230

x210 x190 x170 x152 x136 x120· x106 x96 . x87 x79 x72 Wl2X58 x53 W12x50 x45 x40 W12x35

x30 x26

'( ~:

W12x22 x19 x16 X1 4

~

- -·~Ml ~,.

SMF .

STM°F

Requirem~nts W.-Shapes

OCBF

SCCS

SCBF

Bµms Beams 2nd Diagonal Olagooal and Chord Columns Columns Segment Columns Braces Braces .Columns Beams

.

,

. . •

.•

.• .. .• •• .. • • .. •• •• .• •• .• •• •• .• •• .•• ••• ... ... ••• .• •• .. .. •• .. ••• .• .• •••

I•

•

.

'

• •

.. .. .. •

• •

• •

....•

•

•

•

. • •

•

•

I•

'

I 0

.• ... . • 11

•

• •

•

• • • •

•

• •

:

• •

. .• •• .•• . .• .• •..• •

'

•

•

•

EBf

Lb,,,., ft

.,

..• • .• ·• • • ..• ••• .. .•· .• •• ..• .•• .• .•

I

Sections That Satisfy' Seismic Width-to-Thickness Fy = 50 ksi

W-Shapes IMF

, Shape


':: t


"~T

I

~t~:I

,I

AM

Amd

4.49 4.32

8.87 8.55

Shape


28.5 28.1 27.8 27.4 27.2 27.0 26.7 26.5 26.2 26.0 25.7 25.6 25.4 25.2 25.1 25.0

W12X336 x30S x279 x252 x230 x210 x190 .. x170 x152. x136 x120 x106

10.4 10.3

20.6 20.4

W12X58 x53

8.15 16.1 8.11 16.0 8.06 15.9

W12X50 x45 x40

6.40 12.7 6.32 12.5 6.28 12.4

W12X35 x30 x26•.

6.97 6.75 6.35 6.19

SPSW

Beams and Columns

HBE

W14x26 x22

14.4 14.2 14.0 13.9 13.8 13.6 13.5. 13.4 13.3' 13.1 . 13.0 12.9 . 12.8 12.8 12.7 12.6

3.52 3.42 3.2J 3.13

Links

BllBF

LRFD

Wei> ACCI!$$ Holes

and

VBE

Aha

7'ma

•

116 30.4

189 103

AorS AorB

•

•

I H

G

•

G

• • • •

• • •

.•

x96 x87 x79"· x72

Puma,r, kips

-

~

•

•

B I

•

•

•

W12x22 x19 x16 x14

•

•

Acr . Aor S;

267

458 309

132

200

197 110 56.4 16.0

228

453

• •

•

:';

• •

• •

155 106 59.3

. .

~ 1: Unks In EBF that meet t!lv excepUon In the AISC Seismic Prov/skins sectbt f3.5b(1) need only meet lhe llmllli for mcderately cludlle meml>efs..

AMlllUCAN

lNS'ITJVlll OF STEEL CoNsnUJC'TlON

c c c c c

Acr !!'

\

.

. .

F F E E 0 0

A or Bl Aor ~ 1 Acr 2 i Aor lJ; A0< Bj A

1-51

l-50

GENI:RAL DESIGN CONS£DERA110NS

pESlGN TABLES



I Shape

W10X112

xtOO i<88

xn

x68 x60 l<54 x49

W10X45 Y39 x33 WI0-..<30

x26 x22 W10x19 x17 x15 x12 w~

x58

x48 x40

x35 x31

Sections That Satisfy Seismic Fy =50 ksi Width-to-Thickness Requirements

x24 Wllx2l xl8

W-Shapes

W-Shap es IMF

SMF

8eatn$

Beams

and

and

Columns

corum"'

... ..

..• .. ... .. . .. ..• . ..• .•

. .. .. -

..• . . • • . .• . I

Yl8x28

Sections That Satisfy Seismic Fy = 50 ksi Width-to-Thickness Requirements

STMF

SCCS

OCSF

1

SCBF

Diagonal Dia genti Chord Segment Columns Braces Braces Columns Beams

... .•

. .. ..

... .• .

.. ..

.. ... ..• .• . .. .

... ..

I• I•

. .. .

'

... ..• ..• ..• . . .• • . • .• . .• . • • '

-

... .•• .. .•• .• . .. . .• ... .. .• • .. ... .. .•• . .• . .• I•

'Ahd

/.1114

11.1 11.0 10.9 10.8 10.8 10.7 10.6 106

220 21.8 21.6 21.4 21.3 21.1 21.0 20.9

BRBF

EBF

LtllWO ft

11.3

W10x30 x26 x22

•

W10x19

•

x17

x15 x12

Web

\V8x67 i<58 ...48 x40 x35 >C31

13.3 13.2

Y.'Sx28

5.24 10.4 5.11 10.1

W8x21 xl8

275

281

21 1 169

216 179 96.0

66.4 I

I

8.81 17.4 8.73 17.3 865 17.1 8.48 16.8 8.44 16.7 840 166 6.73 ssg

LRFD

x54 x49

5.69 5.65 5.53

6.45

Pu,.,,., kips

•

x77 x68 x60

W10X45 x39 >C33

718 6.94 6.66

1

;cl()()

xes

16.5 16.3 15.9

3.63 3.51 3.37 3.26

.I

WtOX112

8.35 8.23 8.06

11.2 10.9

SPSW

I

•

•

><2.4

•

•

A Of A A

,l

1-52 GENERAL DESIGN CONSIDERATIONS

("••

:l i I ,.~ ,

;

Sections That Satisfy"SeismicWidth-to·.:.Thickness Fy = 36 ksi Requirements

L

STMF

Shape

Chords

.•

L8x8x1 1/a xl x 7/a x3/4

OCBF and EBF Diagonal Braces

..

• •

L8x4x1 x1/s x3/,

•

• •

9

x /ts

I

-.:·

£

I

'· 1 ~

l6x4x 7/s x3/4 x5/a xiitie L5x5x7/a x'I• x5/s x 1h L5x3112x31. x 5/a x 1h LSX3x1h L4x4x'/• x5ta. x 1/2 x7/ts x3/a

.

L4x3x5/a x1h XS/a

•

•

• •

• •

• .. • • • .. . . ..• .. • • • .. •• •

• •

• •

L31/zx3 1/2X 1'2 x 7/1s

x3/a l31/zx3x1'2 x 7'16 x3/s

.. .•• •

.. •

•

•

.•• .•

Sectioris That Satisfy4: Seismic Fy =46 ks i Width-to-Thickness Requirements

OCBF

Shape

L4x3 1hx 1/2 x%

•

Table .1 -5a

D

Rectangular HSS

.•

•

.

L7x4x3/, L6x6x1 x7/s x3/4 x.5/a

SCBF Diagonal Braces

• • •

.

L8x6x1 ·x7/a xl/4

1:9.r

1-53

Table 1-4

Angles

II

DESIGN TABLES

STMF

andEBF

Chords

Diagonal Braces

. .. .. . .• .• ..• .. .• •

L31/2X2 1/
•

l3x3x'f2

• • •

x7'1s x3/s · x51ts

L3x21'2x1/2 x7/t6 'X:°l/a x.5/la LJxzx112 x3/a x.5/ta

• •

• • •

• •

.• .. .••

• • • •

SCBF Diagonal Braces

• • •

.• .. •

.•. •

• •

..

OCBF SCCS and EBF SCBF andSCBP Diagonal Diagonal Braces Braces Columns

Shape

HSS10x4x.5/a

. .•

HSS9x7x5/s

•

HSS9x5x5/s

•

HSS8x6x5/s

•

HSS1 Ox8x5/s HSStOx6x5/a

HSS8x6x11z HSS8x4x.5/a HSS8x4x1'2 HSS8x3x1'2 ~7x5x1'2 ~7x4x 1fl

HSS7x3x1'2 HSS6x5X1/2 x 3/a HSS6x4x1'2 x3/e

HSS6x3x1'2 x3/a HSS6x.2x3/a HSS5x4x1'2 x3/a x5/ts

.•

HSS5x3x1'2 x3/s x.5/ts

•

.

HSS5x2x5/a x!/te


Shape

• •

HSS4x3x3/a x 5/ts x11•

.

• • • • •

.

. . .

• •

. .

. - .. • •

•

• • •

• •

HSS4x2 /:zx3/e

•

• •

.

.

1

HSS4x21/ixSfi5 x1/4

•

HSS4x.2x3/s x5'16 xl/4 HSS3112X21/2x'S/a x.5/1s x 114 HSS31/2x2x1/, HSS31/2X1 /zx1/4

• •

HSS3x21"1x5/t6

.

•

x3'16

•

•

x'I•

HSS3x2x5'1s x 1/4 fiSS3x11/'tX1/4

. .. •

· x3fie HSS3xlx3/ts

• •

.•

•

• •

.•

•

. .• . •

.

HSS2112X2x11, x3/t&

HSS21/2X1X~/t8

HSS21/«2x3/1s

.

HSS2x1 1hx3/10 x 1/a

' Sections also satisfy STMF truss chords.

J\..ll(EJt!CAN .INsnrors OJ' St'EEL CONSTRUCllON

•

•

..

...

.••

..•

•

•

. ..

• •

HSS21/zx1 1hx1/4 x3/ta

.

.. .

• •

... ... . .• ..• .. . .•

1

SCCS SCBF andSCBP Diagonal Braces Columns

.• ..

• • •

.

.•

..

•

•

• • •

• • •

.

.. •

•

.• •

Shape

HSS10><10X5fa HSS~/a

HSS8xexS/a

x'h HSS7x7x5/a xlf2 HSS6x6x5/a xl/2 x3/a

HSS51hx5 1/:zx3/a x5'16 HSS5><5x1'2 x3/s x 5hs HSS41/zx4 1lrx112 x3/a x5f1s

~·

Sections That Satisfy Seismic Fy =46 ks i Width-to-Thickness Requirements

Sections·.:Yhat Satisfy Seismic WidtH-fo-Thickness Fy ::::42 ksi Requirements

• •

.. .• •

. •

.• .• . .. .

SCCS SCBF andSCBP Olagonal Braces Column$

.

.

•

•

.• .• .

.• .•

.

OCBF

• • • • •

.. .• .

and ESF

Shape

Olagonal Braces

HSS4x4x1h x3/a x5'1& x1/ 4 HSS31/2X3 1hx3/a x5ho X1/4

HSS3x3x3/a x0/15 x1J4

I

•

x3h& HSS21/»<21/~'1s

x'I• x3h& HSS2 /~ /«11• 1

1

x3h&

HSS2x2x1/•

x3'16

l

.. .• .• • •

• • •

.•• • • • •

SCBF Dlagonal Braces

SCCS SCBP

~nd

Columns

.. . . .• - ..• . • .•• ... • •

..• .• .•

Shape

.•• .• ..

-

SCCS OCBF and SCBP and EBF SCBF Diagonal oragonal Columns Braces Braces

HSS16x0625 HSS14x0.625 x0.500 HSS12.750><0.500 HSS10.750x0.500 HSStOx0.625 x0.500 x0.375 HSS9.625x0.500 x0.375 HSS8.625x0.625 x0.500 x0.375 ><0.322 HSS7.625x0.375 x0.328 HSS7.500x0.500 x0.375 x0.312 HSS7x0.500 x0.375 x0.312 x0.250 HSS6.875x0.500 x0.375 x0.312 x0.250

. 'Soctloos also satlsty SlMF trvss c1lord requlremenn;.

Qi

Round HSS

Square HSS OCBF and EBF Diagonal Braces

I

Table 1-6

Table 1-5b

DJ

l-55

oESJGN TABLES


1-54

HSS6.625x0.500 x0.432 x0.375 x0.312 x0.280 x0.250

. ..

. . .. . .. .. .. .• .. .•• .• .•• . .. .. ..

Shape

HSSE))<().500 x0.375 x0.312 x0.280 x0.250

.

.

. .•

. •

HSS5.563x0.500 x0.375 x0.258

•

•

.. . .• .. • ..•

.•

HSS5.500x0.500 x0.375 x0.258

•

HSSSx0.500 x0.375 x0.312 x0.258 ><0.250 x0.188

•

• • I

HSS4.500x0.375 x0.337 x0.237 x0.188

•

\ .

.. •

• •

.. •

• ~also sa1isty STMF 11\lSS cbofd requirements.


•

.••

.•

-

. ..• ..

HSS4x0.313 x0.250 ><0.231 x0.226 x0.220 x0.188 HSS3.500x0.313 x0.300 x0.250 x0.216 x0.203 x0.188 x0.125

.

..• .. .. . .• . .. • • • • • •

.. •

•

• •

.• • •

.• ..•

secs SCBF and SCBP Dlagonal Braces Columns

.. .. . • •

. .. . .. • • •

.• • • •

•

• • • • • •

.. • •

I I

..• • I .•• • I •

• •

.. I • .• I .•• I •

• • • • •

l

. I • •

• • •

.

I

)

OENERAL DE.SIGN CONS!DERATTONS

1-."

DESIGN TABLES


Sections.That-.Satisfyr Seismic Width-to-Thickness Fy =42 ksi Requirements

0 Shape ~.250

x0.216 Xfl.203 x0.188 x0.152 x0.134 x0.125 HSS2.875x0.250 x0.203 x0.188 x0.125 HSS2.500x0.250 x0.188 x0.12.5

11

.. .. ... ..• . •

. •

SCBf Dtagonal Braces

.. .• .. . .. .. ..•

SCCS andSCBP

Pipe OCSF and EBF Diagonal

Shape

Columns

.. ... .• ...

01

Sections That Satisfy Sei~mic Fy= 35 ksi Width-to-Thickness Requirements

Round HSS OCBF and EBF Diagonal Braces

I

Table. 1-7

Braces

HSS2.375x0.250 x0.218 x0.188 x0.154 x0.125 .. HSS1.900x0.188 x0.145 x0.120 HSS1.660x0.140

SCCS SCBF and SC8F' Diagonal Braces Colllmns

.. ..•

•

.. •

. .••

.• .. ..•

• •

.

.

. .

.

• •


Shape

Standard Weight (Std.)

. . .• .• . .. . .

Pipe 10 Std. Pipe 8 Std.

Pipe 6 Sid.

'

Pipe 5 Std. Pipe~ Std.

Pipe 31'2 Std.

Pipe 3 Std.

..

Pipe

.

I

t~

2112 Std.

Pipe 2 Std.

•

I

Pipe 11'2 Std.

. .

Pipe 11/4 Std.

.

Pipe 1 Std.

. .

Pipe 3/4 Std•

.

•,

SCCS SCBF ;n~SCBP Diagonal Braces COiumns

Pipe

112 Std.

Braces

. . . .•

Pipe 12 x...strong

•

Pipe 1ox-Strong

•

Pipe 8 x-strong

. .

Pipe 31/u·Strong

Pipe 3 X·~trong

.• .• . .

•

Pipe 2112 x-Strong

•

. • . . . . '. • '\ . •

secs SCBF andSCBP Diagonal I Braces Golumr.s

Extra Strong (x-Strong)

r

.• . . . . . .

OCBF and EBF Diagonal

Shape

Pipe 6 X·Strong Pipe 5 x-Strong Pipe 4 X·Strong

Pipe 2 x·Strong

Pipe l1f2X·Strong

PipeW• x...strong Pipe 1 x·Strong

Plpe ,,, x-Strong Pipe 1/2 x..str(lng

. .

. . • •

. . .•

. . . .

.• . . . . . . . .

. . • . . . . . . . . .• . . .

. . . .

Double-Extra-strong (xx·Strong) 'f'

.

~'

Pipe 8 xx-Strong

.

Pipe 6 xx-Strong Pipe 5 xx-Strong

-

Plpe 4 xx-Strong Pipe 9 xx-Strong

.

Pipe 2112 xx-Strong

Pipe 2 xx-Strong

~

.

• •

. . . . .

• • • •

. .

i

•

I

:

. ! I

I

Sections abo sat!s1y STMf truss cllold l'lqUliemenll;.

' Sectioos also utbty SllM' tl\ISS c:tiord requiremeots.

I

I AMERJCAN IiosTmm! OP STEEL CONSTRUCTION

.AMERICAN l'NsTirora OF S"IE:a. CoNsi:RucnoN

J- 58

Fu= 65 ksi

Table 1-8

Table 1-9a

Shear Stud Anchor

Design Coefficients and Factors for Steel and Steel and Concrete Composite Seismic Force Resisting Systemsj

Qn

Nominal Horizontal Shear Strength and 25% Reduced Nominal Horizontal

'

Shear Strength for Steel Headed Stud Anchors, kips Normal Weight Concrete

Ugtrtwelglrt Concrete

Wc=1Gpcf

We= 110 pcf

Stud

Diameter

Deck Condition

f~

=3 ksl

f~=

25%

Jn.

Nominal

'le

5.26 9.35 14.6 21.0 5.26 9.35 14.6 21.0 4.58 8.14 12.7 18.3 4.31 7.66 12.0 17.2 3.66 6.51 10.2 14.6 3.02 5.36 I 8.3$ 12.1 5.26 9.35 14.6 21.0 4.58 8.14 12.7 18.3 3.77 . 6.70 10.5 15.1

1/2

No De<:k

5/a 3/4

~

~~1.5 h,

3/4

~ ~<: 1.5

Q

h,

1

..

.Q

'C

0.

.a

'

l

~

.. co

2

.¥

~

~ ..,

I§

3/a '12 5/a

3

1

""...

·i::

8.

f"" ~

3/a 'h S/a 3/4 3/a

'12 S/a 3/4 3/• 'h 5/a 3/4 3/a lft 5/• 3/4 3/a l/2

5/a 3/4 3/•

2

117

s,, . 3/• 3/a . 1f1 $/a

Red~ed

4 ksl

f~ = 3

ksl

'o=41
25%

25%

25%

Haminal Reduced Nominal Reduced Nominal

3.95 .5.38 7.01 9.57 11.0 " 15.0 15.8 . 21.5 . 3.95 5.38 7.01 9.57 15.0. 11~0 . 15.8 21.5 3.44 4.58 6.11 8.14 9.53 12.7 13.7· 18.3' 4.31 3.23 5.75 7.66 9.00 12.0 12.9 . 17.2 2.75 3.66 4.88 6.51 7.65 10.2 11.0 14.6 2.27 . '3.02 4.02 5.36 6.29 8.38 9.08 12.1 3.95 5.38 7.01 9.57 11.0 15.0 15.8 21.5 3.44 4.58 8.14 6.11 9.53 12.7 13.7 18.3 2.83 3.n 5.03 6.70 7.88 10.5 11..3 15.1

4.04 7.18 11.3 16.1 4.04 7.18 11.3 16.1 3.44 6.11 9.53 13.7 3.23 5.75 9.00 12.9 2.75

4.88 7.65 11.0 U.1

4.02 6.29

9.08 4.04 7.18 11.3 16.1

3.44 6.11 S.53 13.7 2.83

4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.l 4.28 7.60 11.9 17.l 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 3.n 6.70 10.5 15.1

3.21 5.70 8.93 12.8 3.21 5.70 8.93 12.8 3.21 5.70 8.93 12.8 3.21 5.70 8..93 12.8 2.75 4.88 7.65 11.0 2.2.7 4.02 6.29 9.08 J.ZI

5.70 8.93 12.8 3.21 5.70 8.93 lUJ 2.83

5.31 9.43 14.7 21.2 5.31 9.43 14.7 21.2 4.58 8.14 12.7 18.3 4.31 7.66 12.0 17.2 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 5.31 9.43 14.7 21.2 4.58 8.14 12.7 18.3 3.77 6.70 10.5 15.1

Redu~

3.98 7.(Ji7

11.0 15.9 3.9.8 7.07 11.0 15.9 3.44 6.1 1 9.53 13.7 3.23

5.75 9.00 12.9 2.75 4.08 7.65 11.0 U.7 4.02 6.29 9.08 3.93 7.07 11 .0 15.9 3.44 6.11 9.53

13.7 2.83

5.03 5.03 5.03. 3 7.88 7.88 7.88 11..3 11.3 tt ..3 N
''•

I

I

l-5·1

DESIGN TABLES


SeiSmlc Force Resisting System

Resp. Mod. Coeff., R'

strength

Deflection Amp.

Factor,

Factor,

Over·

n,

cl

I

Seismic Oesign Category 4

o•

E

P

5

NL NL

NL NL

160 160

160 160

100 100

5

: : :: ::: ::11

2 2

31/•

2

8 7 8 7

(STMF) Steel intermediate moment frames (IMF) Steel ordinary moment frames (OMF) steel special cantilever column systems (SCCS) Steel ordinaJ'y cantile\w column systems (OCCS} Steel systems not specifically detailed for seismic resistanee

4

6

2 3 3 3 3 Jl/4

3

3

511z

NL NL NL

4

I~

·NL

160 NL 160

160 NL 100

100 NL NP

NL

NL

3S1'

NP"

tlP"

35

35

NP.

NP'

Nf'

3

NL

NL

NP

NP

NP

I

4

NL

NL

160

160

100

1

NL

NL

160

160

10i

Ii

NL

Nl

NI'

NP

NP \:

6 51/2

3 21h

NL

It

NL:

~; ~; ~~ ~~ ~ I

f·

I l.

COMPOSITE SYSTEMS Steel and concrete composite eccentrically braced frames (C·EBF) Steel and coocrete composite special concentrically braced frames (C-SCBF) Steel and coocrete composite ordinary braced frames (C-OBF}

I

c

STEB. SYSTEMS

8

I

a

'i

Steel eccentrically braced frames lEBF) Steel special concentrically braced frames tSCBF) Steel ordinaiy concentrically braced frames (OCBF) Steel buckling-restrained bfaced frames (BRSF) Steel special plate shear walls (SPSW) Steel siiecial moment frames (SMF) steel special truss moment frames

J

Structutal System Limitations Including Structural Height, h,,, Limits In tt• 1

8 5

2

3

2

3

I

• Response modification coefficient, R, used lhrougllout ASCfJSEI 7 (ASCE, 201O). · · • .. • DetleclJOn amplflcallon ractor, tor use In ASCEISEI 7 SeciSooS 12.8.6, 12.8.7 and 12.9.2
c,,.

hoof 100moment nor lessframe is permitted lo be used In lieu d irQrmedlate moment frame tor SeiSmic Ot$lgn categories B or C. ·1·" • OrOinalY • s:eei ordill3IY conc;enlrically tnceCI frames are pennilled In ~-!tor}' buildings up to a structural heigltl, h,. of 60 fl (18.3 n . wtiere 111e dead IOad of tile roof dOes not exceed 2.0 psi. •See ASCEISEI 7 Secbon 12.2.S.7 tor tlm4tltlons kl S1n1t11RS ;migried to Seismic Design Categones 0, E oi F. See ASCEJS8 7 See1ion 12.2.5.6 lo< ffmlt:ltfons In "1UCUes ~ried to Seismic Design Categories 0, E or F. 1 This table Is baSed en ASCfJS8 71'1lle 12.2·1 and Is~ with permission from ASCE. I

:

l

1

Cf.NE'RAJ.. DESIGN CONSIDERATIONS

Table 1-9a (continued)

Table 1-9a (continued)

r·· \

1-()!

DESIGN TABLES

Design Coefficients and Factors for Steel and Steel and Concrete Composite Seismic Force Resisting Systemsj

Design Coefficients and Factors for Steel and Steel and Concrete.Composite Seismic Force Resisting Systemsj Structural Sy$1lln Limitations

Seismic Force ResiWng System

Resp. Mod. Coeff.,

R•

Overstrength Factor, llo

tndudlng Structural Height, h111 limits In fl•

Deflection Amp.

Factor,

Sebmlc Force Resl$ting System

Seismic ~n Category

cd-

8

c

D'

E'

__

;: j

_, ·::f.·,.

ii

6h 6

21'2

5

S'h

NL

NL

160

160

100

5

NL

NL

160

160

100

4112

NL

NL

NP

NP

NP

8

3

5112

NL

NL

NL

NL

NL

5

3

4112

NL

NL

NP

NP

NP

6

3

51h

160

160

100

NP

NP

3

3

2112

NL

NP

t.'P

NP

NP

.

OUALSYSnMs Dual Systems with SMF c;cpabi. of res1sting at tent 25% of prescribed Ul$lll!C forces Steel eccentrically braced frames Steel special concentrically braced

rrmes

t:

!:

Steel buci<.llng-restralned braced frames Steel special plate shear w-.,J;s Oual Systems with IMF capable of l'ISlsting at least 25% ot p
•'

:1

slren:llh ~.

R'

n.

Cl

6

21!1

8

Structural System Umitatioos tncludlng Structural Height, h,,, Umlts In ft'

Se1'111ic Design Category

a

c

o•

Ei

p

5

IJt.

NL

35

NP

NP

21!2

4

NL

NL

NL

Ill

NL

6

2112

5

NL

NL

Nl

UL

NL

Steel aoo cooaeto comf,'W.e plate shear waHs

71/l

21{2

8

ti'l

Nl

NI.

t.'L

NL

Steel and concrete composite special shear walls Steel and concteto composite ordln:vy she3twalls Dual Composite Systems with IMF capable of resisting at least 25% of prescribed seismic forces Steel and concrete composite sped3I concenUically braced frames Steel and concrete composite ortllnary braced frames Steel and concrete composite ordinary &hear walls

7

21h

6

NL

NL

NL

NL

NL

6

Z'h

5

NL

NL

NP

NP

NP

8 7

NL Nl

Nl

Ill

NL

NL

NL NL

NL NL

5112

21/t

4112

~L

NL

160

100

NP

8

5

NL

NL

NL

NL

tJL

3112

21/t

3

NL

Hl

NP

NP

NP

8

61/2

NL

NL

NL

NL

NL

5

3

411z

NL

NL

NP

NP

NP

Steel tpeCial C(lllQ!Otrica!ly braced frames' DUAL COMPOSITE SYSTEMS Dual Composite Systems with SMF capable of resisting at least 25% ol pmcrlbed seismic lotus Steel and eooctete composite eccentncany braced frames Steil! end concrete composite Sl)edal coocentrlcaJty ~ frames

•Response modlflc\ltlon coelfident.11, used lll«>OOhout ASOOSEJ 7 "5CE, 2010). • Oeftection ampfficatlon fac10t, ~for use In ASCEJSEI 7SdlllS12.8.6, 12 8.7 Wld 12.9.2 • II. .. not dmlled and NP .. llOI permotted. • See ASCE/S8 7 Secilon 12.2.5.-4 rar ao.nptlon of seismic bte resiillnQ systems ltnl:ed 111 buildJnO$ W!lh a stnJci11111 lleigl11. 11,. a1 240 ncir i.ss • See ASCEJSB 7 Secilon 12.2.SA IClr a ~lptlcn of ~ bte resi$llnQ l'fSlems lml'.ed 111 llullc!ings wl1ll • ~ height, II. ol 160 nor less ' Orctnwy mom.Ill frame Is penni1lzd IO be ~ In lieu at ~ moment lrame fClr Selsmc Design Categcriel 8 or C. 'S1ee1 ordinary coruutrlc3l!y braced llamlf twe per1Tlllllcl In~~ up ID a m.ic:unl l'leOll. i,. crl 60 It (18.3 m) ~ dellj loml al Ille rocrl doa llOl ~ 20 ~ •s.. ASGfJS8 1 ~ 122.S.7IDr1ma11ons 111 sb'udlret SS!9l8d Ill Selamlc Design Cnlgortla o. e or F. ' see ASCEIS0 7 Stcl..on 1u.s.s 1ar llnbtlOI\$ 1n struct1nS adpd 10 s.lsmiC DellQrl Cat9QOl1es o, e or F. 1 This table Is based on ASCt:/S8 Hable 12.2·1 and Is ~-.1!11 poonis;IOll from ASCE.

°"

;•

Mod. Coeff.,

Oeflection Amp. Factor,

DUAL SYSTEMS 1

restrained moment lme$ (C.PRMF) Steel and concrete composite 01dlnary moment frames (C·OMF)

!Mr·

p

COMPOSITE SYSTB~S Steel and concrete·composi!e plate shear walls C·PS\'•1 Steel and concrete composile spec;tsl shear walls (C·SSW) Steel and concrete composite orornary Shear walls (C·OSW) Steel and concrete comlJOSi:V special moment frames (C·SMF) Steel and concrete composite 11\tennedlate momem frames (C· IMF) Steel and coocrete comjl()Sile partially

Resp.

I

'

l-62

GENERAL DESIGN CONSrDERATIONS

PART2

Table 1-9b

.

l~

.,

ANALYSIS

. ,~ Design Coefficients and Factors for Nonbuilding .Structures· Similar to Buildingse

I 2.1 SCOPE ........................................................... 2-2

Structural System Limitations lncludlng Structural Response Over· Deflection Mod. . strength Amp. .. Height Umlts, h,.. in ft• Coeff., . · Factor, Factor, Selsmfc Design Category no R C4 B c 0 E F

Nonbuildlng Structure Type

Steel Storage racks

4

Building frame syS'lems: Steel special concentrically braced frames (SCBF)

3112

2

NL

NL

NL

Nl

NL

Ductile Design Mechanism ............................................ 2-.. I:: Capacity DC$ign ......... '. ...•..... ·....... · · .. ·. · · · · · · · · · · · · · · · · · · · • 2-3 I.

I

2.3 ANALYSIS PROCEDURES .......................................... 2Elastic, Inel~tic and Plastic Analysis ........ ...... .......... ........... 2-4

Stabi~ty Desi.go ~1ethods in the AISC Specification ........................ 2- ~ \, 2

6

5

Steel ordinary concentrically braced ft3mes (OCBF) ·

31/4

With permitted heiljht increase

2 2

31/4

21/2

With unlimited helgllt

1''2

1

1''2

2112

NL

NL NL NL

NL

160

160

100

Direct Analysis Method ........... .... ... · · ... · . · · · · · · · · · · · · · · · · · · · 2-

I;

Effective Length Method ....... . ... ...... ......................... . 2-5 Method ..... · · · · '. · · · · · · · · · : .. · · · · · · · · · · · · · · ··· · · · 2-

I

NL

35b

35b

NPb

NL NL

160

160

100

NL

NL

NL

Firs~-Order An~ysis

Analysis ~etho
Moment-resl$1ing frame systems:

1

L

2.2 ROLE OF STRUCTURAL ANALYSIS lN DESIGN .... ........... ....... . 2-

Steel special moment frames {SMF)

8

3

fNz

3 2

4

NL

NL NL NL 35c.• NP'-d NPc.•

With permitted Mfght increase

4112 21/2

NL NL

Nl

Steel Intermediate moment frames OMF)

2112 .

NL

NL

160

With unlimited height

111z

1

i 1h

Steel ordinary m0ment frames (OMF)

3 12

3

3

NL NL

NL

1

Wrth permitted height increase

211z

2

2''2

NL

NI.

100


1

1

1

NL

NL

Ill

..

160

100 NL• NL

NL NL NPc.• NP"' NP"'

Modal Response Spectrum Analysis and the Direct Analysis Method ....... . 22.4 STRUCI1JRAL MODELING .. ......... , ............... .. ..... .... ... · 2-". 2 Strength of Structural Elements ... · . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Stiffness of Structural Elements ....... ... ......... . . ..... .............. 2-

"t·

Steel Elements ................................................... 22 Compos'.te B _ements ...... \ · · · · · · · · · · · · · · · • · · · · · · · · · · · · · · · · · · · · · · · Connecuons and Panel Zones . . , . . . : ... ............. . .......... ..... 2·

100 NP'-' NL NL

I

Column Bases and Foundations . .................. ........... . ...... 2-11

.

Diaphragms for Tbree-Dimension:h Analysis ................... : ..... . 2- \Gravity Loads ................ ·.................... : ............. · · · 2-1

2=~ ~i~~~~~ ~.~~ ~~~-~~i~ ~'.~t~-~~~-~~-:::::::::: ~ l 1

PART

. • r.. • not llmited illld NP .. not pennlned. • Sleel «dNry tnced frames are permitted kl pipe racks up to 65 fl

·~~~

'

.

• Steel Ofdinely momen! lranle$ and lnltrmediale moment trames we pennil1ed In pipe raclls up 10 a ~I cl 65 It where Ille moment Joint; ol llelcl COMeCtloot are constructed ol bolted end plates. • S1eol ordln&ry moment framet and lrrlennedi3te moment rrames 8te pennhted In llilJe racils up to a height ol 35 fl • This table Is based oo ASC£IS8 7 Tuble 15.4·1 and is t11printed wl1ll permission fllJm ASCE

J

'.,

J-62

GENER.Al. DESIGN CONSIDEAAnONS

PART2

Table 1-9b

ANALYSIS

.:. Design Coefficients and Factors ·for Nonbuilding ,Structures Similar . to Buildings0

.:: .. ·

2.1 SCOPE ........................................................... 2-2

Response Mod. Coeff.,

Nonbuilding Strueture Type

R

Steel Storage racks

4

Structural System Limitations Over· Odlectlon lnduding Structural stnngth Amp. Height Limits, h,,. In ft' . Factor, F2ctor, Seismic Design Category

n.

Cd

2

3''2

8

c

0

E

f

NL

Nl

NL

Nl

Nl

2.2

ROL~ OP S~RU~ ANALYSIS IN DESIGN

t

.... · .. · · · · · · · · · · · · · · · · 2-

Ductile Design Mecharusm ........................................... 2-.. ... Capacity Design .................................................... 2-3

I li

2.3 ANALYSIS PROCEDURES .......................................... 2Elastic Inelastic and Plastic Analysis ................ ........... ........ 2-1

.

'

SWlding frame sr.;tems: Steel special concentrically braced frames (SCBF)

6

2

5

NL

NL

160

160

100

Steel ordinary cof\Centrically braced frilmes (OCBF) ·

31/4

2 2

31/4

NL NL NL

NL

J5b

35b

NP•

NL NL

160

160

100

Firs~-Order An~ysis Method ....... ··'.···· .. ····:·. · ·················· 2-

Nl

Analysis Methods m ASCE/SEI 7 and the Direct Analysis Method ............ 2-, .

..

Stability Design Methods in the AlSC Specification · ·: · · · · · · · · · · · · · · · · · · · · · 2-r Direct Analysis Method ........................ . . : .... . ...... .... .. 2-

;

Effective Length Method .................. . ..... .. ·.. ......... . ..... 2-5 21/2 l1/2

Wrth permitted height Increase


1

2''2

1'12

m.

NL

I

Equivalent Lateral Force Analysis and the Direct Analysis Method : ........ 2-6

Moment-resisting frame sr.;tems:

Steel special moment frames (SMF) Sieel intermediate moment frames ~MF} Wrth permitted height Increase With unlimited height Steel ordinary moment frames (OMF) With permitted height Increase With unlimited height

8 4'12 2112 1112 3''2 2112

3

5'12

tll

3

4

NL

2

2112

1

2

Ph 3 2112

1

1

1

3

NL

NL

tll

35c.•

NP"' r-:pc.•

NL

NL NL NL

160

160

NL

NL

NL

NL NL NL

NL NL NL

l'if'C.d

NL NL NP<.' NP'·'

100

100

100 NP<.'

NL

NL

NL

f·

Modal Response Spectrum Analysis and the Direct Analysis Method ........ 22.4 STRUCTURAL MODELING .................. , ...................... 2-'.

Strength of Structural Elements .............. .. ...... : ....... : ......... 2-" ,. Stiffness of Structural Elements ................... . ................... . 2Steel Elements ................. . ........ : . ~: .. . . . ... . ·............ . 2~ Composite

Elemen~·

......

.

I

~. · .. · · · · · · · · · · · ·.- · · · · · · · · · · · · · · · · · · · · '.; 2· I

Connections and l'anel Zones ....................................... 2·

..

Column Bases and Foundations ..................................... 2-11 Diaphragms for Three-Dimensional Analysis ..... .. ·......... ··· : .······ 2-

l

Gravity Loads ...... .. ·....... . ·................... . : ............ · . · . 2-l PART 2: : ; :

...

~i.a~~~ ~~~~ ~~~.~~i~ ~'.~t~.~~~.~~-s.::::::::::: I

1.

' tL = not limited and NP • not penritted. ' Slee! onlin8ty blaud trll1* art pelmlt1ed In pipe rac1cs up tD 65 IL • S1eel ordina(y moment frames and lnlennedlale lllOll*lt frames we pMlll:lld In lli&ll racll$ up lo a height of 6S II where Ille moment joints (II field connet1lons art ~ of bolted encl plateL • Steel «dlnaly moment fral1* IN! lntermedlale moment ftam8s are pem.:ted in lliP8 racllS up IO a height of 35 ft. • This tallle is ~on ASCflS8 7 lllllle 15.4·1 and is repmted Wflll pem'i$$lon lrom ASa..

•

' •

tl :~~

2-2

ANALYSIS

2.1 SCOPE This Part provides an overview of the analysis provisions in ASCEJSEl 7, the AISC Specification, and theAISC Seismic Provisions, and how they are applied to ~ismic design.

2.2 ROLE OF STRUCTURAL ANALYSIS IN DESIGN

,. - --,

~:j ;.~·

-;:

f

The basic role of analysis in seismic design is to provide the engineer with an understanding of the structure's behavior under design earthquakes. In itS most simple fonn, analysis will consist of simple static linear methods and will provide information on the required design strength and system deformation under specified loading. For some structures, analysis may include static or dynamic nonlinear methods that provide infoml3tion on tbe nonlinear deformation of individual elements, patterns of mechanism formation, and tbe peak demands that can be delivered to individual structural elements and their connections. The method of ·analysis selected must as a minimum conform to the requirements of the applicable buildfog code. Since the results of seismic analysis inherently depend on the assumed properties of the structural elements, seismic analysis must often be perfonned in . an iterative manner, initiating with assumed member sizes and configurations, and refined as member selection is confinned. Chapter C of the AJSC Seismic Provisions requires that analysis of a structure for strength design of seismic force resisting components conforms to Lbe applicable building code and the AISC Specificarion, as well as additional system-level requirements prescribed in the respective system sections.

Ductile Design Mechanism 1

~·

"· ·;

''!

design mechanisms. Thus, the design and detailing requirements of the AISC Seismi< Provisions and ANSUAISC 358 are intended to desensitize the structu(e to earthquake characteristics so that multiple mechanisms do not lead to undesirable modes of failure.

Capacity Design

:~

ANALYSIS PROCED\JRF.S

Sttuctures required to resist the effects of earthquake ground motions should be designed · to allow controlled inelastic, ductile deformations of the system. Accepted design practice is to limit these inelastic actions to certain components of the seismic force resisting system (SFRS) in order to develop a reliable ductile design mechanism that dissipates energy. Components of the ductile design mechanism are then designed and detailed to maintain the structural integrity of the system at.large inelastic deformations. How this energy dissipa:ion occurs depends on the structural system type used as the SFRS. Each SFRS in the AISC Seismic Provisions includes a "Basis of .D esign" se<:tion that defines the locations where inelastic actions are intended to occur. Accordingly, the provisions in ASCEISEl 7, the AISC Specification, the AISC Seismic Provisions, and ANSI/AISC 358 are intended to work·together to ensure that the resulting frames can undergo controlled deformations in a ductile manner and !hat those defonnations are distributed throughout the frame. Clearly identifying the intended ductile design mechanism will provide insight oo which aspects of lhe stn1ctural model may need detailed consideration. Many of the ductile design mechanisms shown in Part I were identified from structural behavior at large deformations from nonlinear static analyses using lateral forces that approitimate the fundamental elastic mode shape. Real structures in eanhquakes exhibit variability in the formation of ductile 1

The tenn, duclile design mechanism, is hnellded to c;aptW'C all possible system-specific mechanisms !hat

are di9CUSS<:d in the AJSC S
Capacity design is a design philosophy wherein inelastic actions under strong ground motion are presumed to be concentrated in predetermined critical zones of the SFRS. The AISC Seismic Provisions employs this methodology by stipulating that the required strength of certain elements of 1l1e SFRS be defined by forces corresponding to the expected capacity (based on available strength) of certain designated yielding members. The adjacent nonyielding members and connections are then protected be.cause they are designed to remain nominally elastic regardless of the magnitude of ground shaking; in essence. these protected componenL
where '\ EmJi =DcQ.e =horizontal seismic load effect including overstrength factor Oq = overstrength factor as defined in Tables 12.2-1 , 15.4-l and 15.4-2 of ASCE/SE! 'J Q£ =effect of horizontal seismic (eanhquake-induced) force~

E,

=vertical seismic load effect

The load effect, Em11, is based on code-specified loads and the code·specified overstrengtl; factor. However, the AISC Seismic Provisions sometimes redefines E,,,h as the forces resul· · ing from the e;i;pected strengths of the designated yielding members of the SFRS.

2.3 ANALYSIS PROCEDURES To determine the required strength of structural steel systems, members snd connectio· AISC Specification Section B3.l pennits design forces to be determined by elastic, inci· tic or plastic analysis. Note that AISC Specifi.carion Appendix 1, Inelastic Design, is intended for sejsm.ic design. For a discussion of the application of the AISC Specificath ; AISC Seismic Provisions, and ASCEJSEI 7 in seismic analysis. see Nair et al. (201 l ). AM.llkJCAN INs-ITTIJTll Of' STCEL CONSTl
ANALYSIS

While non-SFRS' members and connections may be analytically assun1ed not to re:sist horizontal ground motion (i.e., ±pQE from ASCE/SEI 7), they must be reliable in resisting the vertical inertial forces induced by vertical ground motion (i.e., ±0.2SDsD from ASCFJ SEI 7). Non-SFRS members must also be designed to ensure defonnation compatibility at large lateral displacements to maintain structural integrity of the structure. Equally, the destabilizing effect that non-SFRS framing Cl\11 have on a stn1crure (e.g., leaning column effects) must be addressed in the analysis and design of the stabilizing SFRS. The SFRS also consists of diaphragms, chords and collectors.

Elastic, In.elastic and Plastic_Analysis • .•> :.· j

•

-

•

Elastic seismic analysis procedures in ASCFJSEI 7 reduce the seismic response by a factor of l/R, where R is the response modification coefficient. The intent of this reduction is to target the· elastic response at the onset of the first significant yield (e.g., plastic hinge in a beam or compression buekling of a brace). Consequently, inelastic or plastic analysis as outlined in Append.ix I of the AISC Specification is not permitted for detennining the component design forces . from seismic effects-see the AISC Specificatio11 Commentary to Appendix 1' for further discussion. · Therefore, analytical consistency with the AlSC Specification and the AISC Seismic Provisions is primarily maintained using an elastic analysis procedure. Although a .nonlinear response history analysis is permitted; it is not commonly used. to determine =member design forces, but as an assessment tool to judge acceptance of a design: In spedfic cases, a nonlinear static analysis may be used to capture the nonlinear ela..-tic'response of a component or coru1ection, such as when rotational springs are tlsed to represent partially restrained connections. AISC Specification OU.pter C requires that a rigorous second-order analysis be used to detennine .the required strengths of components using the appropriate load combinatiollS. The analysis must include consideration of certain effects that can influence the stability of th~ ~tiucture and its elements, inciucling second order effects (both P-6 and P-o). AdditjoiJal discussion can be found in Wilson and HabibuUah (1987), White and Hajjar (1991), and Geschwindner (2002). There are different methods by which to address second-order effects, in~luding iterative or pqniterative solutions with either stationary or incremental loading. For example, som~ computer programs use a vertical load combination in conjunction with the approximate geoJ?etric stiffness matrix to reduce the structural stiffness to account for geometric nonlinearities. The resul~g structural stiffness from this initial analysis is used for all subsequent load analyses (e.g., dead, live, lateral). This method~ advantageous as it allows superposition-of individual Joad effects because the stiffness is held constant. This approach typically captures only the P-A effect, and P-o is either neglected or approximated by segmenting membe!'S into two or more sections. Some programs can iterate by ramping the gravity loads in conjunction with the geometric stiffness matrix to more ac_curately capture the change in system stiffness d~ring eacp load step. Lateral loads can then be iterated by ramping them so rhat the analysis captures the additional changes to the system stiffness during each step. In this melhod, superposition of individual load effects is not appropriate and the vertical loads would therefore need to be in~luded in lhe anaJysis. ·· · With reference to seismic analysis, the structural stiffoess is constant (reduced based on an initial analysis) when using the ASCEJSEI 7 modal response spectrum analysis (MRSA)

ANALYSlS PROCEDURES

to determine the total lateral seismic forces and linear response bist0ry analysis. The results of these analyses are I.hen combined wiih other load effecLs based on the same reduced stifJ ness. Th.is procedure is not applicable to a nonlinear response ti.me history analysis as tl"· structural stiffness would need to be updated at each time step based on all Joad effects included ju·the analysis. · · . Gravity loads should be ~eluded in the seismic analysis i'n order to accurately addre! second-order effects, including the destabilizing effect generated by oon-SFRS framing, anu the effect of these loads on the periods of a structure. A three-dimensional mathematical model can be developed that captures all loading conditions or, in the case of a two-dime[ sional analysis, an ancillary P-Delta column, as a minir~um, can be .modeled as a substiru1 for the gravity (non-SFRS) framing system. The P-Delta column is commonly modeled to provide no lateral stiffness to the SFRS, but could be calibrated to provide the same stiffne~~ as that provided by che gravity system. As an alternative to a rigorous second-order analysis, second order effects can be approx imated by amplifying the axial forces and moments in members and connections from a first-order analysis through an approximate second-order analysis outlined in AIS• Specification Appendix 8. The provisions for performing th.is amplified first-order analys; were developed on the basis of elastic theory and are not appropriate for inelastic analysis.

t: ..; ·"

! !i'. ::

I I. · 1

l· :; ·

Stability Design Methods in the AISC Specification The AISC Specification outlines three stabiliiy design methods and corresponding elastic analysis requirements (see Table 2-2 in the AISC.Manu.al) as follows:

.

• Direct analysis method (AlSCSpeci.ficacion Sections C2 'a!id C3) Effective fength method (AISC Specification Append.ix 7, Section 7.2) ·· • First-order.analysis method (AISC Specification Appendix 7, Section 7.3)

ea~h ~ese meth~s sei~mic

~iscu:.·

L f{

l'

· The use of of in desigri is explained in the following .,i sions. Additional information on each·of.the·methods can be found in the Commentary to"·

It

the applicable sections in the AISC sp.rification.

Direct Analysis Method

l

Provisions for the direct analysis method (DM) are outlined in AlSC Specification Sectior C2 and C3. This analysis procedure is permitted for all steel· structures and is require t;: when t.he ratio of ma.'timum second-order drift to maximum first-order drift, whlch can be'' taken as B2 inf\ppendix 8 using nominal stiffness properties, exceeds ·i.s. The PM requir•·" !;'~Delta effects to be considere~ eitbe_.r thro9gb a second~order elastic analysis 1 through an amplified fust-ord,er analysis: . : : :~

l ii.

dueetly

Effecthfe Length Method

·

1~

f

- . . for the euecuve " ., l ength me thod· (ELM) are ou t1ined in . AlSC 'Speciiji·callOd~ . Prov1s10ns Appendi.:< 7, Section 7 .2. When permitted by Section 7 .2.1, the.re are no deviations from the elastic analysis provisions in ASCFJSEI 7. The ELM addresses P-Delta effects ejtti, directly through a second-order elastic anaiysis or through an amplified first-order analysi .... J

t

~·.·

AM.EJUCAN l!
....t" ~'

1

26

ANALYSTS

ln the ELM procedure, interaction between frame behavior an
=

First-Order Analysis Method

..

.,;

l~• 111

ti :·

:·:

:""" 1 ,, I.

~:

"f: 1.

:.·

Provisions for the first-order analysis method (FO~i) are outHned in AISC SpecificaJion Appendix 7, Section 7.3. With this approach, second-order effects are captured through the application of an additional lateral load equal to at least 0.42% of the story gravity load applied in eac~ load case. No further second-order analysis is necessary. 1nc required strengths arc taken as lhe forces and moments obtained from the analysis and the effective length factor is K = 1.0.

Analysis Methods in ASCE/SEI 7 and the Direct Analysis Method ASCE/SEl 7 Section 12.6 outlines three seismic a11alytical procedures as follows: Equivalent lateral force analysis (ELF) (ASCEJSEI 7 Section 12.8)

• Modru response speccrurn annlysis (MRSA) (ASCFJSEI 7 Section 12.8) • Seismic response hiStory procedures, linear and nonlinear (ASCE/SEI 7 Chapter 16) Detailed information can be fouod in tbe conuncntary to Section 12.6 of ASCE/SEI 7 and in the NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (FE.\lA, 2009a). The foJiowing discussion summarizes the ELF and MRSA analysis methods and how they relate to the direct analysis method of the AlSC Specification.

Equivalent Lateral Force Analysis and the Direct Analysis Method The provisions for the OM are consistent with the elastic analysis provisions given in ASCE/ SEJ 7 Section 12.8 for the ELF, provided th& the following conditions are maintained throughout lhe analysis: • The mathemsticaJ model for analysis considers :ill fonns of deformation of the structural component$, including stiffness reductions and geometric imperfections in accordance with AJSC Specijicaticn Chapter C. The stability coefficient, 9, will generally limit Bz to less than 1.7, permitting geometric imperfections to be neglected in the analys.is for seismic load combinations. Consequently, notional loads should be applied in 1he tnllthematical model for gravity-only load combinations (if 1he same model is used) in lieu of mOdeling the out-of-plumbness by shi(ting work points. • The fundameo~l period of the structure. T. is limited lo T0 or C,,T,, if T 1s computed by :maJyticru methods. lf the computed value for Tis Jess than C,,T0 then T is used as

AJllEJUCAI( f~ OJ' Srm. CONSTIUJCTION

STRUCTURAL MODELING

, .."

~

the fundament.11 period fhis is because T., has been statistically derived from actual build mg ~pon.ses the1efore capturing all influential factocs. See ASCE/SEI 7 Section 12.9.4. . • Forces and deformations resulting from analysis with seismic forces reduced by factor of 1/R, where R is the response modification coefficient. include second-order effects either through a second -order analysis, an amplified first-order analysis, or . hybrid combiO;lltOO of the two methods, independent of the Stabilily C<.'Cflicient, 0, in ASCEISEJ 7 The A lSC SpecijicaJicm and the AlSC Seismic Provisions deal directly with strength &!sign of members and connections Verification of seismic drift limits and potential postearthquake iostabiUty are nddressed 10 the spplicable building code. As such. some of the. provisions for lbe DM arc not direcily applicable for a drift ana.lysis. However, they can Iii.: conservatively appUed for dnft anal)~is. Other methodologies for applying the OM have been proposed by Nair et al. (2011).

Modal Response Spectrum Analysis and the Direct Analysis Method The provisions for lhe OM are consistent wilh elastic analysis provisions in ASCE/SEJ 7 for .MRSA, provided that tbe following conditions are maintained throughout tJ1e analysis: • All lhe requirements fated previously for the ELF are maintained. • Forces and drifts are ~caled as required by ASCE/SEI 7 Section 12.9.4. Note that used in this ~caliog is limited as discussed previously for the ELF. The same procedure is followed in regards to a drift analysis. Though the scaling of drifts is not required unless assigned to n certain seismic design category, allowable drift limits and stability provisions of ASCE/SEl 7 are applicable.

2.4 STRUCTURAL MODELING A mathematical model used for structural analysis is simply an interpretation of wbat co~ figuration of components, mechanical characteristics, and mass distn"bution is signific11r1 to the distribution of force:; and deformations in the syslCm. Models can be simple (such ::.'I a tw
Strength of Structural Elements The strength of structural elements is typically nol a modeling consideration for elasr;. analysis. Jnfonnntion on modeling component strengths for nonlinear dynamic analysis c· be found in NCJV (2010), Oeterleio ct al. (2010), PEER (2010), PEER/ATC (2010), FE:. (2009b), nod ASCE (2006).

Z.-8

ANALYSIS

STRUCTURAL MODELING

Stiffness of Structural Elements AlSC Seismic Provisions Chapter C states that stiffness properties of components for an elastic analysis should be based on lhe elastic sections and lhat the effects of cracked sections shall be considered for composite components. AJSC Specification Chapter C and the commentary to AISC Seismic Provisions Chapter C give recommendations for effective stiffness vaJues to be used in analysis.

(2- 1)

..

I.

where E, = modulus of efastkity of steel, ksi

ho As

= l,+A,(YENA-d3'f '+(f,Q,,IF1 )(2d3+d1 -Ym-.)2 , in.4 =area of st~! cross section, in.2

(Spec. Eq. C-13- 1)

'EQ,. =sum of the nominal shear strength of steel anchors between the point of maximum

Steel Elements The stiffness properties of steel beams, columns and braces used in lhe mathematical model will depend upon the stability design method selecfed and, potentially, the magnitude of slmining the member undergoes. Reduced stiffness for all members contributing to the lateral stabifay of the structure is required when using the DM to determine design forces. It is important to note that the stiffness reduction tenns in the DM include a component representing material nonlinearity (e.g., accounting for residual srresses) and a component reprcsencing member out-of-straightness and other uncertainties. Conseque.nLly, stiffness reduction is separated inro a load-dependent factor and load-independent factor, complicating ii$ direct application to dynamic analysis. Research has d·einonstr:ued that residual strbsses have a lesser effect on shear stiffness than flexural siiffness. For sunplibty; the shear modulus. ·a, can be reduced in proportion to the reduction in the modulus of elasticjty, E, with no further reduction to account for axial load effects. It is common to model steel &earns that are part of the SFRS without composite action because the reliability of the composite ~tiffness at large inelastic deformations is questionable due to the potential for failure of steel ·headed stud anchors. If composite action is taken into account. the following applicable effects should be considered.

Composite Elements The stiffness properties of steel members acting compositely with concrete should include the following applicable effects: concrete cracking of the section, steel reinforcement ratio, section configuration, material properties. of the concrete, and variations of these factors along the member length. The flexural stiffness, Eleff, and a.-tial stiffness, E.Aeff• based on a transfonned cracked section analysis (that also accounts for variations along the member length) should be "1Sed in lieu of EI and EA in all analysis methods. Recommendations are provided in AISC Seismic Provisions Chapter C Commentary based on ACI 318 prov is.ions. For steel beams with a composite slab, composite action can be included where the slab and shear connection to the beam have been designed and detailed to provide acceptable behavior (see Commentary to Chapter G in the AISC $eismic Provisions). For concrete.encased steel beams and beams acting compositely with a concrete slab, a plastic stress distribution corresponding to tbe ultimate nominal strengths of each component can be used to compute a lower-bound elastic moment of inertia, Tu. For a steel beam with a composite slab in a moment frame with double curvature bending, the effective flexural stiffness. Eltff• can be taken as lbe average of the stiffness in the positive and negative bending regions, as follows:

positive moment and the point of zero moment to either side, ldp$ =moment of inertia of steel cross section, in.4 YE.~ =distance from bottom of the steel section to the elastic neutral axis, in. ,;, [A,d3 + (T.Q,,IF1)(2d3 + d 1)]/(A, + (I:Q,./F1)J, in. (Spec. Eq. C-13-2) di =distance from the compression force in the concrete to the top of the steel section, in. =distance from the resultant steel tension force for fulJ section tension yield (P1 =

1,

b~A:: ::st:::~:: :~::~:~on,

lu, t: is recommended in lieu of 75% of AISC Specification Chapter I commentary), wher~

1,~uiv

(see

(Spec. Eq. C-B-4)

t\

li

where c1 =compression force in concrete slab for fully composite beam; smaller of A1F1 and I· 0.85fc'Ac. kips ~ 4 lrr =moment of inertia for the fuiJy composite uncracked cransfonned section, in. AISC Seismic Provisions Commentary Chapter G discusses limitations on using partially composire beams in certain composite systems. The flexural stiffness of composite columns and braces (encased or filled) can be taken as E/,_qprescribed in AISC Specificati~n Chapter I. The axiafstiffness can be taken as

EAJ =E A$+CJEcA.: 1

(2-2)

l!

.l

where Ac= area of concrete slab within the effective width. in.2 Ee= modulus of e_lasticity ?f concrete, ksi c3 = 0.4 for filled sections and 0.2 for encased sections

fquation 2-2 is taken from the LRFD ~pecificationfor Structuraf Steel !311-ildings (AISC 1-.: 2000). :.,.;

Connections and Panel Zones .

I

l.

Connections and panel zones can contribute significantly to the overall l::iteral flexibility o a system and the resulting deformations are required to be addresse
..

I

~,, ~

2.-10

•,

1:f. ·:,· "·'

ANALYSJS

Research (FEMA, 2000a) has demonstrated that panel zone deformations in steel moment frames can have significant impact on earthquake-induced lateral drift. However, modeling framing using center line-to-center line dimensions for the framing clements can approximate the effects of panel zone flexibility reasonably well for elastic analysis (see Figure 2-1 ). Zero-stiffness end offsets may be modeled to analytically provide forces at the panel zone faces but not influence the periods of vibration. AJtematively, panel zone models that include web doubler plates and continuity plates CAil be explicitly modeled or implicitly included by modeling partially rigid end offsets. fully rigid offsets alone should not be assumed to be the only source of panel zone stiffness (fsai and Popov, 1990). Several panel zones models are illustrated in FEMA 355C (FEMA, 2000a). .Explicit connection modeling by rotational springs is penuitted when based on analytical and experimenml test data. Such an approach may be warranted when accounting for I.he effects of panially restrained connections or other mechanical characteristics of a connection such as bolt slip. Alternatively, beams can be modeled with an equivalent flexural stiffness, Eltff Beams with reduced beam se.ctions (RBS) can be addressed by physically modeling a prismatic or parabolic tapered section at the RBS location. If a prismatic section is used, one possibility is to take the moment of inertia at the outer edge of the center two-thirds of the RBS (ANSJ/AISC 358 Chapter 5). The flange width, ht.RBS• is:

,..

f:" .;~ ,~.

~~:

~~:;

b1.~s =2(R- c)+b1 -2JR -(~J 2

L~

(2-3)

=center-to-center length

dJ2 c E

~'. .llll

------. ~: 1

~

End offset Zero rigidity; Flexible length Full rigidity: Flexible length

= L,,

= 4- d~ 1

:,.

,. .,

~ ·~··

Anal ·ca1 beam

~:.

!,

> ",

Actual beam

1·,~'<

Actual panel zone

!1 ~;

·~

·:: ;.

·: ; >: ~:

'

J 1

Assumes same column depth at both ends of beam

Fig. 2-1. Modeling end offse1s aJ panel Z.Orn!S.

2.- l !

STRUCTURAL MODEJ...JNG

where

R

4c 2 +b 2

8c "" radius of cut from ANS VAISC 358 Figure 5.1

This approach may be counteracted by neglecting composite action with the concrete slab between protected zones. It is also common not to explicitly model the RBS and to use either an Eleff for the berun or simply to amplify the elastic story drifts to account for thl! reduced stiffness, as shown in .Example 4.3.1 of this Manual. Additional infom1a1ion on steel moment frames can be found in ANSUAJSC 358, FEMA 350 (FEMA, 2000b), and NEHRP Seismic Design Technical Brief No. 2 (Hamburger et al., 2009). For composite frames, the effects of cracking on the beam-to-column joint stiffness should be included. A common question regarding connection deformations in braced frames is whether the ends of a brace should be considered as a moment resisting or pinned connection. The answer will depend on lhe gusset connection detailing. Fundamentally, a brace-end _connec· rion at a beam-to-column joint or at a beam interior segment can be assumed pin ri~-1 out-of-plane and fixed in-plane, because the out-of-plane stiffness of the gusset plate is si5 nificantly smaller than the in-plane stiffness. . Similar to beam-to-column joints in moment frames, partially restrained end zones c· ancillarv stub members can be modeled at the ends of braces to represent the increased inplane.fl~xural stiffness provided by the gusset"conne.ctions. The flexural stiffness at these sectio~s typically ranges from 2 to 4 times that of the~ brace. The beam-to-column connection where a brace member intersects can be modeled as a fully restrained connection: oilierwise the connection can be modeled as a simple connection depending on project specific requirements. Additional infonnation concerning steel braced frames c~ be found in NCJV (2010) and Carter (2009). AISC Design Guide 20, Steel Plate Shear Walls (Sabelli and Bruneau, 2006) provides information regarding modeling practices for special plate shear walls. For composite constniction, the effects of cracking on the beam·te>-columrrjoint stiffness should be included. • I

Column Bases and Foundations ASCE/SEI 7 Section 12.7 states that for the purpose of detemUning seismic loads, t~i: structure can be considered fixed at the base. That is, the base where seismic motions ar~ introduced into the structure is globally restrained horizontally, vertically and rotationally about the horizontal axes. Altema1ively, flexibility of the supporting soil (inclucling defor mations of the foundation components) or soil-structure interaction may be included. The theoretical derivation of soil-structure interaction effects was developed on the basis of a rigid foundation. Therefore, support flexibility and soil-structure interaction cannot ~ applied concurrently. · of the supporting soil is co,mmonly modeled using soil springs assum.in~ -~ '' flexibility foundation component is rigid. Alternatively, foundation components may be exp1Jc1t1 modeled to address their flexibility. For nonlinear resp'.onse history analysis, soil sprir. should directly model the nonlinear behavior of the supporting soil. Column base modeling is a function of frame mechanics, detailing and rigidity of 1', foundation components, and is 001 related to the global restraint of the seismic base. Parti;~. restrained base models may be used to more accurately capture rotational characterL~. ;, ·

2-12

STRUCTURAL MODELING

ANALYSIS

r

Diaphragms for Three-Dimensional Analysis Diaphragms, chords, collectors and associated elements distribute seismic forces to the

diaphragm as rigid, semi-rigid or flexible depending on its in-p130e stiffness. A diaphragm made up of a composite slab can be modeled as rigid when the diaphragm's span-to-depth ratio is 3 or less in structures with no horizontal irregularities. This assumption simplifies calculations because the diaphragm moves as a rig.id body about the center of rigidity of a given story and the total mass can be assumed to be lumped at the' cemer of mass. Alternatively, a semi-rigid diaphragm explicitly models the diaphragm's in-plane stiffness. In either model, lateral forces are distributed to the various SFRS in proportion to their relative elastic lateral stiffness and distance from the center of rigidity: For flexible diaphragms, an SFRS is assumed to resist forces proportional to lbe mass that is tributary to the SFRS. Diaphragm slabs can be modeled using either membrane or shell elements. In-plane stiffness reduction factors should be applied t.o account for cracking of the concrete and other factor~,that decrease 1be stiffness of the diaphragm. Membranes differ .from shells in that mem?ranes do not provide out-of-plane or rotational stiffness which ·c an increase the computational demand and the flexural stiffness at joints. Howe,·er, membrane.edges have to be supponed by framing. The_axial forces developed in horizontal members on a given floor ai=e dependent on lhe in-plane stiffness of the diaphragm model assigned to that floor. Caution should be exercised in as~igning diaphragm models where horizontal members are designed to transmit or redistribut~ seismic forces to and between SFRS. In many ~es, these members are requir~d to be designed !or amplified seismic loads including the overstrenglh factor: and thereby, are intended to remain essentially elastic. . . A rigid diaphragm model prevents relative fo-plane movemenc between nodes on a given floor. Thus, axial forces will not develop in horizontal members connected to the diaphragm, inhibiting the design of members that tiansmit forces to or between SFRS or chords of a vertical truss spanning between levels (e.g., outriggers). The effect of this node lock will increase forces carried by diagonal members between diaphragms. Alternatively, a semirigid diaphragm can be modeled. A disadvantage of this model is that the magnitude of lhe axial force 1n a horizontal member wjll depend on the in-plane stiffness at the node and how the diaphragm is modeled along the length of that member. . Another alternative is to release nodes from the diaphragm constrrunt. This may also include restructuring the extents of the rigid diaphragm so rhat a core area is a rigi
no,

1.

transferred to the SFRS and/or modeling errors. It is recommended that lhe analys1 perfo~ a parametric study wilb various diaphragm assignments and assemblies 10 determine ti most efficient model 10 adequately capture a re3Sonable esrimate of the diaphragm behavi . and required axial force.

of base plate connections based on e)(perimental results. Alternatively, pinned bases may be modeled to account for connection, foundation and sou flexibility, although lhe column base may be detailed to be fixed to the foundation component.

SFRS. The diaphragm model used in analysis should rea listically model the diaphragm's inplane stiffness and the distribution of lateral forces. ASCE/SEI 7 Section 12.3.l classifies a

2-

. '

' I

~I

i

Gravity Loads

't·. ::

"

l

All gravity loads should be modeled in the analysis in order to accurately address sccondorder effecis and to capture the distribution of gravity load effects on vertical force-resisti. members. A mathematical model is commonly analyzed as a fully constructed, cohes1 structure for each load effect or load combination. This practice is not, however, consistenl · with how a structure is built, where some load effects are distributed based on constructi"" sequence. This is particularly true for the distribution of self-weight in braced frames a strucrures with outriggers or hat trusses where installation of diagonal members may ~ completed after the surrounding framing and floor system is constructed and at differem story elevations. ~n _the latter case, dead load eff~cts created during construction in _exten j:: vertical force-rcs1strng members can be underesumated because these members can JO eff, ::· hang from the stiffer outrigger/truss system in the analysis, increasing the forces in the i.nte rior vertic~I suppo~ syste~. Si~ilarl~, _gravi.ty effects can be distributed to diagonal braces\". in proportion to lhe11 contnbuuon to JOtOt stiffness. , For cases when the distribution of dead load effects is a concern, a staged constrocti analysis can be performed. In its fundamental form, the mathematical model of a complete system is broken down in10 assemblies, commonly story levels. and the. analysis wi!l inc- 1· mentally add each group and superimpose the results onto the previous analysis. C: ;'. should be exercised when gravity effects produce sway and when geometric imperfection . are included in the analysis (by either method discussed previously) as a staged analysis cannot handle sway of different assemblies and superposit~on must b~ applica~le. Alternative some analysis programs allow the analyst to automatically not mclude diagon~ memb· during the gravity lond analysis. Though this is more related to analysis than modeling, a, altemative modeling technique wou~d be to provide axial force releases in the diagor ~t members for 1be gravity load analysis~In these cases, the method used to address geome1 nonlinearities within the analysis program is of critical importance, and this will dictm which technique can be used. Another consideration is clifferentjal settlement of vertic force-resisting systems under dead load effects.

l: r

Gravity Loads in Diagonal Braces and Special Plate Shear Walls

l I

,,;

The AISC Seismic Provisions stipulate that the gravity forces be neglected in braces :;: buckling-restrained braced frames and web plates in special plate shear walls. These provisions are intended 10 restrict the use of SFRS components that are required to uissip significant amounts of energy by i~elastic actions to simultan~ously . provide s~clt . ; integrity of lhe structure under gravny loads. Many of the capacity design analysis pro' . sions have been developed based on this concept. This approach can be a concern for complex structures that ~ontain pu~_seJy slope<. stepped non-SFRS columns or where diagonal braces are required to stabilize a struct .,. that undergoes sidesway from gravity loads (e.g., sloping siructural system) or are require-·

·f.

l

" ANAJ..Y))lS

r

to directJy participate in carrying gravity loads (e.g., diagrid system). A lhtee-
PART 2

R.EFH~<.:I~

PART 2 REFERENCES AJSC (2000), Load and Rt!sistanu Factor Design Specification for Structural Stu/ Buildings, Amencan Jnsutu1c of Steel Construction, Chicago, IL.

ASCE (2006), St!isrnic Rt!IUJbilrtarion of Existing Buildings, ASCE41-06. American Society of Civil Enginee~. Restoo, VA.

Carter. C.J. (2009). ''Origins of R =3," Proceedings of1hc 2009 Structures Congress. ASCE, Austin. TX. April 30 May 2, 2009, pp. 1-10. Deierlein, G.G .• Rcinhom, A.M. and Willford, M.R. (2010), ''Nonlinear Strucrural Analysu for Seismic Design," NIST GCR 10-917-5, .NEHR.P Seismic Design Technical Brief No. 4, N'EHRP Consultants Joint Venture_ pannership of the Applied Technology Council and the Consortium of Uoiversillcs for Research in .Earthquake Engineering, National Institute of Standards and Technology. Gaithersburg, MD. FEMA (2000a), Stott! of thl! Art Report 011 Sysums Performance of S1eel Moment Framu Subject to Eanhquak.e GroWJd Shaking, fEMA 355c, prepared by the SAC Joint Venture for the Federal Emergency Management Agency, Washington, DC. FEMA (2000b), Recommended Seismic Design Criteria for New Steel Moment-Frame

Buildings, Fa.IA 350, Federnl Emergency Management Agency, Washington, DC. FEMA (2009a). NEHRP Rt!commended Seismic Pro\'ision.s for New Buildings and Othtr Structures, FEMA P-750, Federal Emergency Management Agency, Washington, DC.

FE.MA (2009b), Quantification of Building Seismic Perfomwnce Factors, FEMA P-695. Federal Emc:rgency Management Agency. Washington, DC. Geschwindncr, LF. (2002), "A Practical Approach to Frame Analysis, Stability and Leaning Columns," Enginuring lounUJI, AISC, Vol. 39, No. 4, 4th Quaner, pp. 167-181. Hamburger, R.O , Kra1,1,inlcJcr, H., Malley. J.O. and Adan, S.M. (2009), "Seismic Design of Steel Special Moment Frames: a Guide for Practicing Engineers," NIST GCR 09-917-3, NEHRP Seismic Design Technical Brief No. 2, NEHR.P Consultants Joint Venture, part· nership of che Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering, National Institute of Standards and Technology, Gaithersburg, MD.

..

...

..

Nair, S., Malley, J.O. and Hooper, J.D. (2011), "Design of Steel Buildings for Earthquake and Stability by Application of ASCE 7 and AISC 360," Engineering loumal, AlSC, Vol. 48, No. 3, 3rd Quarter, pp. 199-204. NCJV (2010), faa/11ation of the FEMA P-695 Merltodclogy for Quantification of Buildin.~ Seismic Perfonnance Facton, NIST GCR 10-917-8, NEHRP Consultants Joint Venture, partnership of the Applie4,I Technology Council and l.he Consortium of Universities for Research in Eariliquakc Engineering, National Institute of Standards and Technology Gaithersburg, MD.

PEER (2010), Seismic Design GuuJelinesforTall Buildings, Pncific Earthquake Enginci;.;;ng Research Center, Unjversity of California at Berkeley, Berkeley, CA.

AMEIUCAN .l Nsrm.m! OP Srw. O:lNSTRVCTION

2.-16

ANALYSIS

PEER/ATC (2010). Modeling and Acceptance Criteria for Seismic De.sign and Analy.sit of Tait Buildings, PEER/ATC 72-1 Report, Applied Technology Council, Redwood Ci1y. CA, October.

Sabelli, R. and Bnineau, M. (2006), Srtel Plate Shear Walls. Design Guide 20, AlSC. Chicago, IL.

PART3

SYSTEMS NOT SPECIFICALLY DETAILED FOR SEISMIC RESISTANCE

Tsai, K.C. and Popov. E.P. (1990}, "Seismic Panel Zone Design Effect on Elastic Story Drift lJl S1ecl Frames," Journal of Structural Engineering, ASCE, Vol. 116, No. 12, pp. 3235-3301.

3.J SCOPE ...................... . · . · · · · · · · · · · · · · · · · - - · · · · · · · · · · · · - - · · 3

White, D. and H~ijar, J. (1991), "Application of Second-Order Elaslic Analysi~ in LRFD: Research to Practice," Engineering Journal, AISC, Vol. 28, No. 4, 4th Quarter, pp. l33- 148.

3.2 GENERAL DISCUSSION ............. · .. · . · · . · · · · · . · · · · · · · · · · · · · · · · · 3 3.3 DESIGN EXAMPLE PLAN AND ELEVATIONS ..... .·:. .. · . · · . · · · · · · ..... · · 3-3.4 MOMENT FR.AMES ...... .. ................ . ......... . ......... ... 3

Wilson. E.L. and Habibullah, A. (1987), "Static and Dynamic Analysis of Multi-Story

Example 3.4.1. Moment Frame Story Drift Check .... -.•....... -.... · - · - . :

Buildings Including P-Della Effects," Earthquake Spectra, Earthquake Engineering Research Institute, Vol. 3, Issue 3.

I J -1

Exnmple 3.4.2. Moment Frame Column ~ign . - · · · · · · · · · · · · · · · · · · · · · · · · · 3 Exnmple 3.4.3. Momenl Frame Beam Design ............. · · . · · . · . · · · · · · · 3-

Examplc J.4.4. Moment Frame Beam-to-Column Connection Design .. · · · · · · · 3-l.3

l

3.5 BRACED FRAMES ... · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · .•. . . 3 faumple 3.5.l. Brace
. · · · · · · 3-2 •

r

Example 3.5.3. Braced Frame Brace-10-Bcam/Colurnn Connection Design ... - . 3PART 3 REFERENCES .... . ........ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-.

I \

.

. I

:<

A MOUC>.N {NSmVl'll OP Srnm. Co.N$TRVCTION

~

16

ANAl..YSJS

PEER/ATC (2010), Modeling and Acceptance Criteria for Seismic Design and Analy.fis of Tall Buildings, PEER/ATC 72-1 Report. Applied Tcclmology Council, Redwood City,

CA, October.

Sabelli, R. and Bnineau, M. (2006), Steel Plate SMar Walls, Design Guide 20, AISC, Chicago, IL. '

Tsai, KC. and Popov, E.P. (1990), "Seismic Panel Zone Design Effcd on Ela.sue Story Drift in Steel Frames." Journal of Structural Engineering, ASCE. Vol. I 16, No. 12, pp. 3235-3301. White, D. and Hiljjar, J. (J991), "Application of Second-Order Elastic Analysis in LRFD: Rese:irch to Practice," Engineering Joumal, AISC, Vol. 28, No. 4, 4th Quarter, pp.

133- 148. Wilson. E.L. and Habibullah. A. (1987), "Static and Dynamic Analysis of Multi-Story Buildings Including p. Delta EffectS," Earthquake S~ctra, Earthquake Engineering Research Institute, Vol. 3, Issue 3.

PART3 SYSTEMS NOT SPECI FICALLY DETAILED FOR SEISMIC RESISTANCE

3.J SCOPE .... . . - . . . .

. ... - . - .. - . - · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3

3.2 GENERAL DISCUSSION . . . . . . . . . . . . . . ... · . · · · · . · · · · · · · · · · · · · · · · · · 3

3.3 DESlGN EXAMPLE PLAN AND ELEVATIONS ..... :.'. .... · · .. · · · · · : . · · 3-.... 3.4 MOMENT FRAMES .. · · .... · · · .. · · · · · · · · .......... · · · · · · · · · · · · · · · .' 3

l

Example 3.4. l. J\fomem Frame Story Drift Check . ................ · · · · · · · : 3u:imple 3.4.2. Moment Frame Column Design · · · · · · · · · · · · · · · · · · · · · · · · · · ·

3-1

Example 3.4.3. Moment Frame Beam Design ................ · · · · · · · · · · · · 3-

Example 3.4.4. Moment Frame Beam-to-Column Connection Design ..... ·. ·. 3-1: 3.S BRACED FRAMES · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · .......... 3- · 1 Example 3.5. l. Brace.d Frame Brnc:.e Design ............. · . · · · · . · · . · · · · · · 3fuample 3.5.2. Braced Frame Column Design ............... · · .... · · · · · · 3-2

faample 3.5.3. Braced Frame Brace-10-.Beam/Column Connection Design .... . 3-

I

PART 3 REFERENCES . . . ............ · · · · · . · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-. ·•

1

I \

'

SVS'J'l:.MS NUT Sl'bUl-lLAL.L.X Ul:. IAlU:.U FOR SEISMIC RESISTAN<.'.il

3.3 DESIGN IDCAMt'l..t. t'l..A.N "

' .. u ~ Vi\J 1ur.:.

3.1 SCOPE This Pan shows member and connection designs for braced and moment frame systems that are not specifically detajJed for seismic resistance. Seismic design of the seismic force resisting system in accordance with the AISC Seismic Provisi<>ns is referred to as "seismic detailing" by the applicable building code. The systems in this Part are designed according 10 the requirements of the AISC Specification. The SC-Ope s1atement al the front of this Manual discusses the differentiation between seismic force resisting systems that require special detailing for seismic resistance and those that do not.

~ •, :·

"·:

3.2 GENERAL DISCUSSION '· !·

t:

___..., rl::::i

Systems requiring structural Steel design in accordance with the AISC Specification only are addressed in this Part. It is a common misconception that when seismic detailing of lhe seismic force resisting system is not required, there are no other seismic design requirements. Regardless of the seismic detailing requirements, structures assigned to Seismic Design Categories B through F are subjec1 ro many other seismic design considerations prescribed in the applicable building code. For example, ASCE/SEI 7 contains numerous requirements, such as:

:i:-m l-'-----1----

,- -,

:r:---.-,.:r:

~

!

- - - - · · - - - - -....

. :J;..:.'----:r:---

•

_fj i

~ l ---. - -- J_ _ _ _ _ _J.\ _ _ _ _ __J~-·-'· --.

- -------...---- - - ----. -. ..-. -----. --Braced frame investigated in design examples. For elevation see Figure 3-3.

• • • • •

Table 12.3-1, Horizontal Structural Irregularities Table 12.3-2, Vertical Strucrural Irreguiarities Section 12.4. Seismic Load Effects and Combinations Section 12.5. Direction of Loading Section 12.8.4.3. Amplification of Accident:i.1 Torsional Moment • Section 12.10.2, Collector Elements • Section 12.13, Foundation Design

\ _ Moment frame investigated in design examples. For elevation see Figure 3-2.

Fig. J.J. Floor plan/or Pan 3 design examples.

4

3

2 30'-0"

30'-0·

30'--0"

W18x50

W18x50

W18x50

3.3 DESIGN EXAMPLE PLAN AND ELEVATIONS The following sections consist of design examples for 3 typical building not requiring seismic detailing. See Figure 3-1 for a typical floor plan for this building with composite flooring. D~ign Examples 3.4. l through 3.4.4 demonstrate the cf.esign of a typical moment frame for the building. See Figure 3-2 for an elevation of the moment frame. Design Examples 3.5.l through 3.5.3 demonst:rate the design of 3 typical braced frame for the build· mg. See Figure 3-3 for an elevation of the braced bay. The code spccilied lo~ng is as follows: Dftoor D100f

= 85 psf =68 psf

~r

=80psf S 20 psf Curtain wall 175 lb/fl

= =

:· t

.' '

I

Wtnd loads nre determined according to Chapter 28, Part 2 of ASCE/SEI 7. The assumed are: 83.Sfo Wmd Speed is 115 miles per hour (3 socood gust), Wind Exposure Category is B, topographic factor 1(1 is 1.0, 3Jld the bwlding is in Risk Category Il. Required parametCIS

0Roof
0Foorth Level

ll

W18x50

W18x50

W18x55

W18x55

..,"'

...~ N

W1Sx50

~

Third

0Level

0 0

second Level

N .....

...

~ ~

W18x55

~

W18x55

~...

~

ease Column splk:e 4a- above finished floof (1YP.)

Fig. 3-2. M~nt frame tW.'Olion for E.xam.ptu 3.4.1, 3.4.2, JA.3 and 3.4A. For floor plan. stt Figure J-1 .

=

SYSTEMS NOT SPECIFlCALLY DETAILED FOR SEJSMTC RES1STA:.'1CE

strengths from load combinations that include wind loods were shown not to govern over load combinations that include seismic loads for both the braced frame and the moment frame. Therefore, wind loads are not included in the design examples in Part 3,. T he necessary parameters for determining seismic loading are given with each design

example.

-

~ 1

3.4 MOMENT FRAMES

Because the momeol frame in the following examples does not require seismic detailing. it is designed in accordance with the provisions of the AlSC Specification. . \.:

Example 3.4.1. Moment Frame Story Drift Check Given: Determine if the moment frame satisfies the ASCE/SEI 7 seismic story drift requirements.

3.4 MOMENT FRAMES

!·: 1

Moment frames resist lateral forces and displacements through flexure and shear in the beams and coliunos. The necessary restraint must be provided by the moment connections between the beam and the columns. Moment frames tend to have larger and heavier beam and column sizes than braced frames. The increase in member sizes and related co.sts is often accepted lo gain lhe increased flexibility provided in the architectural and mechanical layout in the structure. The absence of diagonal bracing members can provide greater freedom in the confilmration of walls and in the routing mechanical ductwork and piping. Moment frames are ~ften positioned at the perimeter of the structure, allowing maxi.mum flexibility of the interior spaces. Drift control is required by the applicable building code to help limit da1itage to both the structural and nonstructural systems.

of

Refer to the moment frame elevation shown in Figure 3-2. The applicable bui]ding cod .: 1 specifies the use of ASCFJSEI 7 for seismic story drift requirements. In ac~rdance wit. •.. ·: ASCFJSEl 7: Risk Category: Il Seismic Design Category: C Deflection Amplification Factor, Ca. 3 Seismic Importance Factor,/~: 1.0 Allowable Story Drift, !:>a: 0.020hsx

I

Solutio n: From a second-order elastic analysis of the structure, the elastic displacement comput' under strength-level design earthquake forces at each level are:

,

r f

o~

~

= t.87 in.

04, = 1.54 in.

8:3, = 1.03 in. Si, =0.477 in.

2s·--0·

Roof

I·:

I:

OM=O in.

N

The deflection at level xis:

Fourth

I I

Level

(ASCFJSEl 7 Eq. 12.8-1

Column splices

~

48" above finished

N ....

tloOr (typ.)

Third

Tue allowable story drift al level x, from ASCEJSEI 7 Table li.12-·1, is:

11 0

Level

~ N

t·: .,.,,·;.

=0.020h.u

...~~ ~·

where h~ = story height below level

Second

x, ft ·~.

level

Between the roof level and level 4:

~ ...,.

...

Cd (0,., -o.i,) 1.

Base

Fig. J-3. Braced frome elevation for Examples 3.5. I, 3.5.2 and 3.5.3.

..

\.,·~"

3(1.87 in.-1.54 in.) 1.0 =0.990 in.

For floor plan, see Figure 3-J.

t·:

fI

SYSTEMS NOT SPECIFICALLY DETAILED FOR SEISMIC RE.SlSTANCE

6a

•

I

3.4 MOMENT FRAMES

=0.020(12.5 ft)(l2.0 in./fl) =3.00 in.> 0.990 in. o.k.

LRFD

Between level 4 and level 3:

. ... ~

04 =Cd (84• -03,)

.,

~: :-:·

=0.020(12.5 ft)(I2.0 in.lit) =3.00 in.> 1.53 in. o.k.

Between level 3 and level 2:

(including the 0.5 load factor on l permitted in ASCEISEI 7 Section 12.4.2.3) from ASCE/SEI 7, this structure is assigned to Seismic Design Category C (p = 1.0) and SDs = 0.352. The required strengths of Column CL-1 determined by a second-order analysis including the effects of P-o and P-a with reduced stiffness as required by the direct analysis method are:

03 =Cd (fo., -fue)

LR.FD

J,

=3(1.03 in.-0.477 in.) ~: :~-

=

Aa =0.020(12.5 ft)(l2.0 in./ft)

=3.00 in.> I.66 io.

P.,

v.,

1.0 1.66 in. · -

,,.;-:~ -

(1.0+0.14SDs )D+ H +F+O.?pQE

(1.2+0.2SDs)D+p!2£+0.5l+0.2S

3(1.54 in.-1.03 in.) 1.0 = 1.53 in.

} '

ASD Load Combination 5 from ASCE/SEI 7 Section 12.4.2.3

· LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.2.3

le .

6a

ASD

ASD

=233 kips 35.0 kips

Pa Va

=

=165 kips = 23.4 kips

Muwp =201 kip-ft

Ma top= 131 kip-ft

Mubot=-320 kip-ft

Ma bot =-'210 kip-ft

o.k.

Between level 2 and the base level: 02 =Cd (02, -obe) I,

= 3(0.477 in.-0 in.)

LO

=1.43 in. Aa =0.020(14.0 ft)(l2.0 in./ft) =3.36 in.> 1.43 in. o.k.

There are no transverse loadings between the floors in the plane of bending, and the bean::; framing into the column weak &Jtis are pin-connected and produce negligible moments. Solution: From AISC ManlUll Tabie 2-4, the material properties are as follows:

ASTMA992 F1 =50 ksi F,. =65 ksi

I

\

•

From AISC Manual Thble 1-1, the geometric properties are as follows:

Comment: In this case, the member sizes resulted from strength requiremencs. The seismic story drift requirements do oot always govern the design of moment frames.

Example 3.4.2. Mome nt Frame Column Design Given: Refer to Column CL-1 in Figure 3-2. Verify that a W12x87 ASTM A992 W-shape is sufficient to resist the following required strengths between the base and second levels. The applicable building code specifies the use of ASCE/SEI 7 for calculation of loads. The load combinations that include seismic effects ru:e: :·

:~

":·

W12x87 rx= 5.38 in.

r1 =3.07 in.

Available Compressive Strength of Column CL-1

Because the member is being designed using the direct analysis method, K is taken as 1.0.

KLx

l.0(14.0 ft)(12.0 in./ft) rx 5.38 ill. =31.2 KLy J .0(14.0 ft)(12.0 inlft) -;:; = 3.07 i.n.

=54.7

governs

SYSTEMS Nor SPECIFICALLY DETAJLED .FOR SEISMIC RESISTANCE

3.4 MOMENT FRAM.ES

From AISC Manual Table 4-J, the available compressive strength is: .

1-------L_RFD _ _ _ _ _ _- l -_ _ _ _ __A_s_o______ LRFD

ASD

4>cPn =925 kips

Cb=

Cb=

12.5.M......, 2.5MfNJJI +3M,.. +4Ms+3Mc

Pn =616 kips

Available Flexural Strength of Column CL-1 Check the unbraced length for ffex_ure

I: ·1

+3(70.8kip-ft)

+3(45.6kip-ft)

+ 4(59.4 kip-ft)+ 3(190 kip-ft)J

+ 4(39.8 kip-ft)+ 3(125 ltip-ft)]

t.

=2.19

i•

From AIS.C Manual Table 3-10, with Lb= 14.0 ft, the availabie flexural strength of W12x87 is:

Lr=43.lft

Lp
Oi, .

= 1,050 kip-ft

LRFD

/

=13 l kip-ft

M,, t>ct =-210 kip-ft

M(x) ·= M1op-(M"'P ~Mbi>, )x

.,,(

rn .t) = M10p

=201 kip-ft-(201 Jcip-ft + 320 kip-ft}:c . 14.0 ft 201 kip-ft-(37 .2 kips):c

-

=

-

-

jM(x = 3.50 ft) I= MA

jM(x= 3.50 ft) I= M..,

-(31.2 kips)(J.so tt) 1

jM(x =7.00 ft) I= Ms

=I 131 kip-ft

-(31.2 kips)(1.oo tt) 1 =59.4 kip-ft

= 39.8 lcip-ft

=10.5 ft) I= Mc =1201 kip-ft -(37.2 kips)(I0.5 ft) I

=190 kip-ft =320 kip-ft

- (24.4 kips )<1.00 ft)

I

=I Bl kip-ft -(24.4 ki.ps)(10.s fl) I = 125 lcip-ft = 210 kip-ft

= ~cPn , as detetm.ined previously

=925kips Pr

jM(x = J0.5 ft) I= Mc

-

Pc

233 kips Pc 925 kips =0.252

•

fle~ure

~SD

LRFD

jM(x= 7.00 ft) I= Me

= 1201 kip-ft

t~

Using AISC Specification Section HI( c~eck the inte~ction of compression and Column CL-1, as follows: \. _ ·

-(24.4 kips}(3.5ott)1 =45.6 kip-ft

= 70.8 kip-ft

I'·

nb

Therefore, the.yieiding limit state governs.

=I 131 kip-ft

= 1201 kip-ft

M; =3~9 ~;~·~696 kip-ft

Interaction of Flexure and Compression in Column CL-1

=13 1 kip-ft-(24.4kips)x Quarter point momenlS are:

!

j:'.:

'------- ----------''---------- - -- - - ·.·

= 131 ki ft-(131 kip-ft+210 kip-ft) p14.0 ft . x

Quarter point moments are:

l_·..

Check yielding (plastic moment) limit state; -~sing AfSC Manual Table 3-2,

QbM1 ;;: 495 kip-ft< l, 050 kip-ft

[Mt"P -l M"°') x

1

=696 kjp-ft,

. .: Check yielding (plastic moment) limit state; using AlSC Manual Table 3-2,

ASD Ma rop

f.f

l--Qb_A-._1n.:....=_2-.2-0-(4_7_7-ki_p-_ft_)-------l-M-,.-::::-2-.1-9(_3_18- ki-.p-.....:_ft)-----=--

Calculate Cb using AISC Specification Equation Fl -1.

Mu 1op =201 kip-ft Mwbot =-320 hp-ft

'•

I

ASD

LRFD

Therefore, I.be member js subject to lmral-torsional buckling.

M max

I

I

Lp = 10.8 ft

jM(x

i,.

=112.5(210 kip-ftw12.5(210 kip-ft)

=:2.20

From AISC Manual Table 3-2:

12.5M__, 2.5M,._ +3M.., +4Mp +3Mc

=112.5(320 kip-ft)J/12.5(320 kip-ft)

Q,.

I

3-

I

;

Pr= 165 kips Pc 616 kips =0.268

Because P,fPc~ 0.2, use AlSC

Because P,!Pc ~ 0.2, use AlSC

Specification Equation Hl- Ia,

Specification Equation Hl-la,

t

("

Pc "" ~: , as determined previ9usly =616 kips

in

'

I

t

ii

~

.t

··t ·

3-10

SYSTEMS N
LRFD

Mry)

320 .i!( kip-ft + 0) = 0.827 9 495 kip-ft

0.827 < 1.0

=0 kips v., =33.9 kips M., l
P.,

Pr + 8(Mrx Mry) -+ - ::;;1.0

9 Mo:

Pc

Mey

210 o.26s+!( kip-ft +o)=o 835 9 329 kip·ft . 0.835< 1.0

o.k.

o.k.

~

.i !

Pa

=0 kips

Va

= 23. l kips

' !

Mat~JI =-212kip-ft

Mel

McL = 58.6 kip-ft M., nghI = 167 kip-ft

=40.6 kip-ft

Ma ,,,111=106 kip-ft

Solution:

Available Shear Strength of Column CL-7

.

ASD

LRFD

ASD

P, 8(Mrx+ - :s;J.O -+Pc 9 Mex Mcy

0.252 +

3.4 MOMENT~

From A1SC Manual Table 2-4, the material properties are as follows:

From AISC. Manual Table 3-2, the available shear strength of a W12x87 is: ASTMA992

~

I

LRFD .

qi.v,. =193 kips> 35.o kips

Vn 1.0.,, =129 kips> 23.4 kips

-0.k.

F1 =50 ksi

ASD

-

'

Fu= 65 ksi

o.k.

.

From AISC .Manual Table 1-1, the geometric properties are as foUows: The W12x87 is adequate to resist the required strengths gi,·en for Column CL- I.

W18x55 d= 18.l in. r11 = 2.00 in.

Note: Load combinations that do ~~t include seismic effects must also be investigated.

r...,=0.390 in. J = 1.66 in.4

r1

3

Sx = 98.3 in.

Assume that the beam flanges are braced at the columns.

Given: Refer to Beam BM-I in Figure 3-2. Verify that a W18x55 ASTM A992 W-shape is sufficient to resist the following required strengths. The applicable building code specifies the use of ASCFJSEI 7 for calculation of loads. See the Design Example Plan and Elevation section for code specified loading. · .:·

Available Flexural Strength of Beam BM- 1

-

• •

From AISC Manual Table 3-2:

L,, = 5.90 ft L,. = 17.6 ft

The load combinations that include seismic effects are: LRFD

LRFD Load Combination 5 from ASCEJSEI 7 Section 124.2.3 (1.2+0.2SDs)D+pQe+0.5L+0.2S

Zx= 112 in.3

h 0 =17.5 in.

Example 3.4.3. Moment Frame Beam Design 4

\

The limit states of yielding and lateral-torsional buckling are applicable, as given in AISC Specificaticn Section F2.

ASD


.'

(1.0+0. 14Sns )D+ H + F +0.1pQs

(including the 0.5 load factor on l permitted in ASCE/SEI 7 Section 12.4.2.3)

Calculate Cb using AISC Specification Commentary Equation C-Fl-5, which applies !.;. gravity loaded beams with the top flange late.rally restrained; the top flange is restrained by the composite slab. ASD

LR.FD

~--------+--------- ·-·

M0 =Muufi=-3161<.ip-ft From ASCE/SEl 7, !his structure is assigned to Seismic Design Catego.ry C (p = J.0) and Sos=0.352. The reqwred strengths determined by a second-order analysis including Lhe effects of P-0 and P·A with reduced stiffness as required by the direct analysis method are:

II I

=1.67 in.

Mo =Ma ltfi =-212 ltip-ft M1 =Ma rilht

Mei.

=58.6 kip-ft

=106 kip-ft

Mel =40.6 ltip-.ft

AMl!JUCAN

lNsrmJTE OP STE!!L CONSTllOCTION

3-12

SYSTEMS NOT SPECfFJCALLY DETAll..ED FOR SEISMIC RESJSTANCE

LR.FD

=-316 kip-ft'

=-212 kip-ft

=63.1 ksi(98.3in.3) =6. 200 kip-in.

because Mi is positive

because M1 is positive

=517 kip-ftSMp

(Mo+M1)° =Mo

Cb= 3.o-~(Mi)-~/ Mel J 3 Mo . 3 (Mo+Mif

}--!(

M,,

Cb=30-2(MiJ -8, Ma . 3 M0 3 (M,,+M1f

Mp

l

= 3.0- ~( 167 kip-ft 58.6 kip-ft J 3 -316 lc.ip-ft . 3 -3 16 kip-ft

= 3 .o-~( 106 lcip-ft )-~( 40.6 kip-ft)

=3.85

=3.84

3 -212 kip-ft.

I

3--1 :

1------------L~RFD-----------i----------A-s_n__________~· I ~

ASD

(Mo+M1)• =Mo

3.4 MOMENT FRAMES

3 -212 kip-ft

M,.

=62.9 ksi(98.3 in.3 ) = 6, 180 kip-in.

.. 1

f

=515 kip-ftSMp

=F1 Z.r

Mp= F:yZx

=50ksi(112 in. 3)(1 ft/12 in.)

==50ksi(112in.3

)(l ft/12in.)

=467 kip-ft

=467 kip-ft

controls

controls

Mn

9bM,. =0.90(467 kip-ft) o.k.

::; 420 kip-ft> 316 kip-ft

II I

467 kip-ft 1.61

n,, =

= 280 kip-ft> 212 kip-ft

o.k.

I:

Per the User Note in AJSC Specification Section F2, the W18x55 is compact for F). = 50 ksi. Because AISC Manual Table 3-10 does not provide a strength for a Wl 8x55 with an unbraced length of 30 ft, calculate the strength from the AISC Specificarion. From AISC Specifica1i01l Section F2, with compact flanges and web and lb > Lr, the applicable lirnit states are yielding and lateral-torsional buckling.

Available Shear Strength of Beam BM-1 Prom ATSC Manual Table 3-2, the available shear strength of the W18x55 is:

LRFD (Spec. Eq. F2-3)

~

..v,. =212 kips> 33.9 kips

L--(Spec. Eq. F2-4)

ASD

-

-

-

-

l. V,, I ilv. =141kips>23.l kips o.k. I - " - - -- - - - - - ~ <·

o.k.

-

The W18x55 is adequate 10 resist the loads given for Beam BM-1. Note: Load combinations that do not include seismic effects must also be investig::ited.

Example 3.4.4. Moment Frame Beam-to-Column Connect~on Design

Jc

s.1io =o.ooo96s LRFD

r

Fer= 3.8Snl(29,000 ksi)

,

r30.0 .1\(12 inJft) 2.00 in.

CT

~I+ 0.078(0.000965)130.0 ft(l~ inlft)r 2.00 ltl.

=63.1 ksi

F, _

3.84n2 (29,000 Jcsi) [30.0 ft(l2 inJft) 2.00 in.

r

x 1+0.078(0.000965)130.0 ft(l~ inJft) 2.00 ltl. =62.9 ksi

l

Given: " ·' Refer to Joint JT-1inFigure3-2. Design a bolted Oange-plated fully. restrained moment connection between Beam BM-1 and Column CL-1. The beam and column are ASTM A9~ l W-sbapes and ASTM A36 is used for the connecting material. Use ASTM A325-N bolts ai . 70-ksi electrodes. ·:,

ASD

l

r

p_le--3._4_.3_._th_e_re_q_u~_·_ed__str_en __gths __~are,._:____________________~l

-F-ro_m_Ex_am __

LRFD V., = 33.9 kips Mu= 316 kip-ft

ASD Va

=23.1 kips

Ma = 212 kip-ft

Solution: From AISC Manual Table 2-4, the material properties are as follows:

.,,,

3-14

SYSTEMS NG'I' SPECIFICALLY DETAll..ED FOR SEJSMJC RESJSTANCE

ASTMA36 Fy 36 ksi Fu= 58 ksi

3.4 MOMENT FRAMES

.,

J--15

The available nexuraJ strength of the W18x55 is:

=

ASD

LRFD

ASTMA992 Fy = 50 ksi

¢Mn = 0.90(391 kip-ft)

= 352 kip-ft> 316 kip-ft

Fu= 65 ksi

o.k.

Mn= 391 kip-ft n l.67 =234 kip-ft> 212 kip-ft

o.k.

From AlSC Manual Table 1-1, the geometric properties are as follows:

W18x55

d = 18.l in.

Single-Plate Web Connection

=0.390 in.

t,..

9"= 0.630 in.

S.r = 98.3 in.3

br= 7.53 in.

Available Flexural Strength 9f Beam BM-1

AISC Specification Secrion Fl 3 requires chat tensile rupture of the tension flange be investigated if FuAJn < _fiFyAJg Since Fy!F,,

=50 kSV65 ksi =0.77 < 0.8:

¢R,, = 48.9 kips> 33.9 kips

For cwo rows . oO~-in.-diamerer ASTM A325-N bolts in standard boles in I.he beam tens·ion flange, usrng AISC Specification Section B4.3b: =b1ti

Ajn

I

ASD

LRFD

y; =1.0

Ajg

The single pl:lte connection in an FR moment connection need not be designed for eccentricity on the bolts; however, AlSC Manual Table 10-lOa is appHed here for simplicity. Conservatively, using AlSC Manual Table 10-lOa, select a 'l16·in.·thick ASTM A36 plate wi!h (3) Ye-in.·dfameter ASTM A325-N bolts (Group A) in standard holes connected to the besm web, and a Y"'in. fillet weld to the column flange. The available strength of the singleplate connection is:

Rn

o.k.

n

=32.6 kips> 23. l kips

o.k.

Be<::ause the bolt bearing limit state is included in Table 10- lOa, the beam web is acceptable by inspection, as the beam web thickness of 0.390 in. is greater than the plate thickness of

=7.53 in.(0.630 in.)

5/i6

=4.74 in.2

Use a s1i6-in.-thick, single-plate connection with (3) 31-in.·diameter ASThf A325-N bolts in standard holes to the beam web and \.4-in. fillet weld lo the column flange.

=.-<\r,-2(dll+ 1A6in.)r1

in.

2

=4.74 in. -2(1.00 in.)(0.630 in.)

Range Plate Connection

=3.48 in. Y,FyAJg =1.0(50 ksi)(4.74 in.) 2

.

Determine the required number of bolts in the flange plate

The flange force is:

= 237 kips F.,Afa

=(65 ksi)(3.48 in.2 )

LRFD

=226kips

P.

Since FuAfa < Y1FyAfg, the limit state of tensile rupture of the flange applies.

Mn = Fu~f,n S.r A/1 = 226

kip~ (98.3 in.3)

4.74 in.

=4,690 kip-in. = 391 kip-ft

(Spec. Eq. Fl3-J)

M ..

u1=7 = 316 ldp-ft (12.0 in./ft} 18.l in. :::210 kips

ASD

! I ·Il

Ptt1 =Ma d = 212 klp-ft(12.o in.tft} 18.1 in. = 14lkips

I I

3-16

9r,.

- .24.3 kips/bolt

r,, /O 14lkips =16.2 kips/bolt

= 8.64 t>olts

=8.70 bolts

210 kips

R,.

.

n,

x[7.00 in. -2( 1 ~'16 in.+ 1...16 in.)]Cl.0) =218 kips >210 kips

-

F.,A,.U

=--

=0.75(58 k<:i)(l.00 in.)

n,,.;,. = Pat

Timflo=_!![_

Fu~ -=-n n,

9R11 =~,F.,A.t =91F.,A,.U

ASD

P.

ASD

LRFD

From AISC Manual Tlblc 7-1 for bolt shear, the required number ofYi·in.-diameter ASTM A325-N bolts is. •

LRFD

J.IJ

3.4 MOMENT FRAMES

SYSTEMS NOT SPECIFICALLY DtrrAlLf:.D FOR SElSMlC 'RESISTANCE

J

= (l/2.00)(58 ksi)(l.00 in.)

o.k.

x[7.00 in.-2(15/1& in.+ 1116 in.)] x{l.0)

=145kips > 141 kips

Try ten bolts on 3 4-m. gage. Using AJSC Manual Tables 7-4 and 7-5 for bearing strength with le = 2 in. and s =3 in.• the available bearing streoglh of the beam flange is:

o.k.

~

Using AJSC Man110I T:ibles 7-4 and 7-5 with L.. =2 in. ands= 3 in., the be
LRFD ~R,,

ASD

~

=1t(~r,. )tI =8(102 kip/in.)(0.630 in.)

o.k.

ASD

) I

•

lf

= 8(68.3 kiplin.)(0.630 in.)

+2(89.6 kip/in.)(0.630 in.) =6Tl kips>2JO kips

(

LRFD

I

n-=n nr,, ) Rn

=8(91.4 kip/in.)(l.00 in.)

+2(59.7 kip/in.)(0.630 in.) = 419 kips> J41 ldps o.k.

+2(79.9 kip/in.)(1.00 in.) =891 kips> '.HO kips

..

Size the flange plate for the tension force The minimum lhickncss of a 7-in.-wide plate for tension yielding is:

R,, (rn) fl=JI f2 I p =8(60.9 kiplin.)(1.00 in.)

9Rn =n(~rn) tp

o.k.

+2(53.3 lcip/in.)(l.00 in.) - 594 kips> 141 kips o.k.

Check the flange plate and beam flange for block shear rupture

t·;

The two cases for which block shear must be considered in the flange pl3te are shown i

LRFD t,,.;,,

=

P"t

9F1 bp

ASD

.

210 kips 0.90(36 ksi)(7.00 in.) = 0.926 in.

=

t . mm -

Figure 3-4.

Case l involves the tearout of the tw~ blocks outside of 1he two rows of bolt holes in Ll 1· flange plate. For this case, the tension area has a width of 2(1 'I.I in.). Case 2 involves Ll tearout of the block between the two rows of boles in the flange plate. For this case, the teo sioo area has a width of 4 in. Because lhe shear areas are the same in both cases, Case l governs for the flange plate. The beam flange must also be cbed-ed for Case l , but need n 1~ be checked.for Case 2 due to the presence of the web.' ~:

P
Fybp/ O. 141 kips

=(36 ksi)(7.00 in.)/ 1.67 =0.934 in.

Try a l in. x 7 in. plate. The avrulable tensile rupture s~ngth of the plate according to AISC Specification Section D2 as follows:

is

determined

~nominal strength for the limit state of block shear rupture is given by AISC Specification

j.!

f.quation 14-5: I

R,,

= 0.60F.,A..v+UbsFu~ .S:0.60F1 A,..+Vb1F A,., 11

•

:i

3-18

,......, ! \ f

,Check the flange plate toiCa'se 1 From AISC Specification Equation 14-5:

LRFD :

LR.FD R,. UosFu.Aru -=

$Rn = q>UbsF.A,., +min (cp0.60FyAgv, cp0.60F.;Anv)

'!1

-~;

\

...,., '~ ~

ubs = 1.0 fc,r uniform t~nsion. ~~ess

i11

It

Shear ruplure component from AISC Manual Table 9-3c:

cp0.6FuA;,v =2(248 kipfm.)(1 in.)

0. 6 FuA,,v = 2(165 kip/io.)(1 in.)

n

n

Tension rupture component from . ~ISC Man,ua( Tab.le 9-3a:

+min(0.60FyAgv, 0.60Fu.Alfl') 0. .Q

= 541kips>210 kips

o..k.

-~.

2 (15 I kip/in.) (I in.)

ASD

LRFD $UbsFuA;,1=2(1.0)(60.9 kip/in.)(0.630 in.)

s;

Ubf-'A111

=76.7 kips

·

.

Q.6FyAgv ='2(210 kip/iu.)(0.630 in.) . .Q

=397 hlps

.

=265 kips

$0.6FuA,,v = 2(278 kip/in.)(0.630 in.)

=3.So kips 1

,

= 2(1.0)(40.6 kip/in.)(0.630 in.)

-51.2)cips

=302 kips

::.-.-.

1

o.k.

=360kips>141 kips

Ubs = 1.0 for unifonn tension stress

~6.6F1Agv =2_(315 kip/in.)(0.630 in.)

~'

n

Check the beam flange for Case 1

=?.8.0 lops

.Q

Rn = S8.0 kips+ 302 kips

From AISC Manual Tables 9-3a, 9-3b and 9"3c for Leh= 13A in. and Lev= 2 in.:

Ubs;;Ani =2(1.0)(29.0 kip/in.)(! in.)

0.6FyAgv

=330 kips

Rn= 87.0 kips+454 kips

Shear yielding component from AISC Manual Table 9-3b: · .

$0.6FyAgv =2(227. kip'(in.)(l in.) . ' .. -' . =45.4 kips .

n

=496 kips

Tension rupture component from AISC Manual '.fable 9-3a:.

Shear yielding component from AISC Manual Table 9-3b: .

ASD

Shear rupture component from AISC Manual Table 9-3c:

U1;, = 1.0 for uniform tension stress

1;1

.

ASD

. ;r

3.-l MOMENT FRAMES

SYSTEMS NOT SPECIFICALLY DETAILED FOR.SElSMlC RESISTANCE

0. 6FuAnv = 2(185 kip/in.)(0.630 fo.) .

n

'\

•\

,

.

=233 kips

\

~Rn

= 76.7 kips+ 350 kips

= 427 kips> 2io kips

Flange

=284 kips> 141 kips

o.k.

Use (5) rows oO~-in.-diameter ASTM A325-N bolts in standard holes at a 4-in. gage to con nect each flange plate to i.be·beam flange. Use 2-ID.: edge distance and 3-in .•spacing for the bolts.

PL

Check the

•N

1~· 11 Case 1

o.k.

Rn·= 51.2 kips+ 233 kips _n _

4·

I/n~·

Case2

Fig. 3-4. Block shear failure paths for the flange plate in Example 3.4.4. AMERICAN L'ISTTTlTIB OP STEa CONSTR\lCTlON

flar:qe plate for the compression. rc:rce

t r==-·

.Jf2

LOO in.

=712 = 0.289 in.

3-20

SYS'feMS NOT SPECIFICAlLY DETAILED FOR SEISMIC RESISTANCE

From ~ISC Specification Co1nmcntary Table C-A-7.1, use K edge distance plus !-7-in. beam setback):

=0.65, and l =2!i7 in. (2-in.

3.5 BRACED FRAMES

Tue final connection design and geometry is shown in Figure 3-5.

3.5 BRACED FRAMES

Kl = 0.65(2.50 in.) r 0.289 in. = 5.62

1

~ccording to AlSC SpecificaJion Section J4.4, because Kllr $ 25, Fer =Fy and the compressive sirength of the flange plate is:

Pn

•

=FyAg

(Spec. Eq. 14-6)

= (36 ksj)(7 .00 in.)(1.00 in.)

=252 kips LRFD

ASD

.

·;

Pn

9Pn = 0.90(252 kips) = 227 kips > 210 kips

o.k.

n

=252 kips

Braced frames gain their srrength and their resistance to lateral forces and displacements pJ marily from the axial strength and stiffness of the bracing members. Braced frames are arrange such that the centerlines of the framing members (braces, columns nnd be:irns) coincide o. ·· nearly coincide, thus eliminating the majority of flexure that might occur due to lateral forces. Braced-frame systems !end to be more economical than moment-resisting frames wh• material, fabrication and erection costs are considered. These efficiencies are often offset t. reduced flexibility in floor pl:m layout, space planning, and eleclrical and mechanical rout-· ing encountered as a result of the space requirements of the brace members. J. Braced frames typically are located jn walls that stack vertically between floor levels. [ !he typical offi~e building, these walls generally occur in the "core" area around stair and ek vator shaflS, central restrooms, and mechanical and electrical rooms. 'I11is generally allowe for greater architectural flexibility in placement and configuration of exterior windows a

l

l ,.

·-'

1.67

=151kips>141 kips

W12x87

o.k.

column

Use 1 in. x 7 in. ASTM ~6 flange plates. Design the weld betWeen the flange plates and column flange

PL 1•x1• (A36)

The directional ~trenglh increase is used in determining the required weld size. The length of the weld, l...,, 1s taken to bet.h e width of the 7-in. plate less twice-the weld size.

@ 4" gage (top and bot.)

(10) ~· dla. A325-N bolts in std. holes

DetermitJe the weld size ~olving for Dmin from AISC Manual Equation 8-2 and applying the directional strength rncrease of AISC Specification Equation 12-5:

LRFD D,,,;,, =

ASD

P1if 2(1.5)(1.392 kipfm.)lw

Dmm = Paf 2(1.5)(0.928 lcipflll.)l,,. 141 kips

210 kips

2(1.5)(1.392 kiplin.)(5.88 in.)

=8.55 sixteenths

PL ¥ie"x4" (~6)

2(1.5)(0.928 kipfm.}(5.88 in.)

W18x55beam

=8.61 sixteenths

L. -

Use o/i6-in. fillet welds on both sides to connect the.flange places to the column flange. Comment: The column must be checked for panel zone and stiffeitlng requirements. f-or further information, see AISC Design Guide No. 13, Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applicaiions (Carter, 1999). AM£RJCAN lNsrnvrs OP STESL CONSTRUCTION

~is.

(3) 3i• A325-N bolts In std. holes

Note: Allow fQ( finger shims as needed

Fig, 3-5. Connection as designed in Examp~ 3.4.4.

\.

l

...

SY~"fEMS

,...., '

·:

N
c~adding. ~ependiog on the plan location and the sue of lhe core area of IJ1e building, tbe torsional resistance offered by the br3Ced frames may become a controlling design p:lnUlleler Differential drift betv•cen stories at the building perio,leter rnus~ be considered with this type of layout, as rotational displacements of the floor diaphragms may impose deformation demand~ on the cladliing system and other nonslJUcturaJ elements of tbe building. Because the braced f111me in the following ex.am pies docs not re
Assume that the cods of the brace arc pinned and braced against translation.

Example 3.5.1 . Braced Frame Brace Design

The eff~tive length of the brace is:

Ul

The governing load combinations include seismic effects :tS follows:

LRPD

ASD

Max.imum brace compression from LRFD Load Combination 5 from ASCEISEI 1 Section 12.4.2.3

Maximum brace compression from ASD Load Combination 5 from ASCFJSEI 7 Section 12.4.2.3

(l.O + 0.14SDs)D + H + F+0.7pQ£

(1.2 + 0.2SD.S)D + pQe + 0.5l + 0.2S (including the 0.5 factor on L permitted by ASCE/SEI 7 Section 12.4.2.3) Ma.'timum brace tension from LRFD Load Combina1ion 6 from ASCFJSEI 7 Section 12.4.2.3

From ASCE/SEI 7. tbis structure is assigned Sos=0.352.

(0.6-0.14SDs)D + 0.7pQ£+H 10

Seismic Design Category C (p = 1.0) and

The required strengths of Brace B R-1 determined by a second-order analysis including the effects of P-o and P-A with reductd stiffness as required by the direc1 analysis method are:

LRFD Maximum Compression

t(: ,. ,

= 127 lcips

M:u.i.mum Tensfoo Pu:::

89.6 kips

ASD Maximum Compression

P. =83.~ kips Maximum Tension Pa= 60.2 kips

2

=17.7 ft This unbraced length has been conservatively dctennined by calculating the distance between the work points based on the interse.ction of the centedines of the brace, columr and beams, and using K 1.0. Shorter unbraced lengths may be used if justified by the eng

=

oeer of record. Brace Selection Select a trial brace si.z.c based on the effeeti.ve length and the compressive strength of llw brace. Based on the discussion in AJSC Specificarion Commentary Scc1ion J 1.7, it 1 assumed that the effect of the load eccentticity with rel>pect 10 the center of gravity of the brace 1s neglig.ible and can be ignored. Use AISC Manual Table 4-9 to select Iris! brace sections. Possible double angle brnces include 2L5x5x~. 2L6x6x%, or 2L6x4x~ LLBB. Use a 2L6x4x~ LLBB for the trial design due lo architecrural ne.eds. From AISC Manuai Table 4.9, the available strength of che 2L6x4x~ LLBB brace ('h-in. s~paration) in com pression with KL= 17.7 ft is controlled by the y-y a.'tis. By interpolation:

Maximum br:lce tension from ASD Load Combination 8 from ASCFJSEI 7 Section 12.4.2.3

(0.9 - 0.2SDs)D + pC2E + l.6H

P.,

F1 =36 ksi F.=58 ksi

KL =( l.O)J(l2.5 ft) +(12.5 ft)

Select an ASTM A36 double-angle section to act as Brace BR-1 in Figure 3-3 :!lld resist the following axial forces. The applicable building code specifies the use of ASCEISEl 7 for calculation of required strength. Sec the Design Example Plan and Elevation section for code specified loacling.

- ----- ~~--.

ASTMA36

1

Given:

~

Solution: From AISC Manual Table 2-4, the material properties sre as follows:

I

LRFD $cPn ::: 143 kips> 127 kips

o.k.

I

ASD

\

Pn

nc

=94.6 ltips > 83.4 kips

o.k.

The 2L6x4x;i LLBB is adequate.

Element Slenderness Tuble 4-9 considers che AISC Specification Section E6.2 requirement that the effective sle· demess ratio, Kalrb of each of the component shapes between fasteners may not excev three-fourths -times lhc governing slenderness ratio of the built-up member. Per AlSt' Manual Thble 4-9, at least twO welded or pretensioned bolled intCJ1lledinte connectors x:n• be provided.

3-24

-·

SYSTEMS NOT SPECrPTCALLY Db"fAJt.ED FOR SEISMIC RE-.SISTANC'b

Available Tensile Strength of Brace Prom AlSC Manual Table 5-8, the available strength of 1he 2L6x4x'A brace for tensile yield· ing on the gross section is

LRFD

From ASCEJSEI 7, this structure is nssigned to Seismic Design Dtegory C (p - I .0) and Sos=0.352. Tue required sll'Cngths of Column CL-2 detennined by a ~nd-order aruslysis ancluding the effects of P-o and P-6 with reduced stiffness as required by the direct analysis method are:

ASD

91Pn =379 kips> 89.6 kips

o.k.

n, =252 kips> 60.2 kips Pn

LRFD

ASD

Maximum Compression

Mn..'timum Compression

o.k.

P0

Pu= 35 1 !Ops

The 2L6x4~ is adequate for 1ensile yielding on 1he gross area. See Example 3.5.3 for calculations c-0nfmniog that the ten!'ile rupture sttength on the effective net section of the brace is adequate with a single row of (5) ~-in. bolts spaced at 3 in. coOllecting the double-angle brace to a gusset plate.

Use 2L6x4x~ LI.BB \\-jth a

3..5 BRACEO FRAMES

~-in.

11

=253 kips

I

Maximum Tension

Maximum Tension

PIC

If

=42.1 kips

Pa= 28.7 kips

Consider that the ends of the column are pinned and braced against translation for both ~

separation, assuming a Va-in. gusset plate, and 1wo mtermediate conne.:tors for Brace BR- l.

x-.r and y-y a.'es.

Note that the intennedinte connectors can be fastened by welding or wi1h pretensioned bolts.

Solution:

1f bolted intennediate connectors are used, a net section tensile rupture check at the con-

From AISC Man11al Table Z-4. the rnatcrial properties 3re as follows:

f~

nectors is aJso required. ASTMA992

Example 3.5.2. Braced Frame Column Design Given:

Fy =50 ksi FIA= 65 k$i Using AJSC Manual Table 4-1 with KL= 14 ft, select a W 12x50.

Refer to Column CL-2 in Figure 3-3. Select an ASTM A992 W-sbape with a nominal depth of 12 in. to resis1 the following required strengths. The applicable building code specifies the use of ASCFJSEI 7 for the calculation of the required strength. See the Design Example Plan and Elevation section for code specified loadfog.

tl>cPn =384 kips> 351 kips

Maximum column compression from LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.2.3

(1.2 + 02.sos)D + pQE + 0.5L + 0.2S (incl uding the 0.5 load factor on L permitted by ASCEJSEl 7 Section 12.4.2.3) Ma;wnum column tC1nsion from LRFD Load Combination 6 from ASCFJSEJ 7 Section l2.4.2.3

(0.9. - 0.2Sos)D + pQe + t.6H

o.k. I

I

T he load combinations that include seismic effects are:

LRFD

ASD

LR.FD

ASD Maximum column compression from ASD Load Combination 6 from ASCEJSEI 7 Section l2.4.2.3

.!'.!!.. =255 kips> 253 kips

nc

. o.k.

The W12x50 is adequ:tte. There is net tension (uplift) on the column. Using AISC Manlltll Table 5-1. the availab (:. strength of the W12x50 in axial tension is adequate.

..

Use a W12x50 for braced-frame Column CI.....2.

(1.0 + 0.lOSos)D + H + F + 0.525pQE

+'0.15L + 0.75S

Maximum column tension from ASD Load Combination 8 from ASCEJSEI 7 Section 12.4.2.3

(0.6 - 0.14Sos)D + 0.1pQE + H

Example 3.5.3. Braced Frame Brace-to-Beam/Column Connection Design Given:

}:;

l

Refer 10 Join1 JT-2 in figure 3-3. Design the connection between the brace, beam ar. • column. Use a gusset plate concentric to the broce and welded to the benm with 70elecrrodcs. Connect the gusset and the beam to the column using 3 bolted single-pl ~ connection. Use ASTht A36 for all plate material, u~ lhe brace and column as designed

3-26

SYSTEMS NOT SPECD"ICALLY DE'l'NLED fOR SEISMIC RESISTANCE

Examples 3.5.1and3.5.2, res~tively, and use an ASTM A992 W18x35 for the beam, ns required for slreng1h and connection geometry. The applicable buiJding code specifies the use of ASCE/SEI 7 for calculation of the required strengths. See the Design Example PJan and Elevation section for code spedfied loading.

,.....

The required strengths are:

: I

LRFD

ASD

Beam Shear

Beam Shear

Vu :::: 4.00 kips

Va =2.63 kips

Brace Compression

Brace Compression

Pu= 127 kips

Pa= 83.4 kips

Brace Tension

·'.f"': •. ~

Pa= 60.2 lcips

Using AISC Manual Table 7-3 for 'A·in.-diameter ASTM A325 (Group A) sliJK:ritical bolt~ in double shear, Class B faying surfaces, oversized holes in the gusset, and standard boles

in the brace, the available shear strength and the required number of bolls is:

LRFD

;~

Try (5)

ASTMA992 F1 =50 ksi F.,=65 ksi

$Rn 127 kips

=4.63 bolts

at 3-in. spacing.

An= Ag - 2(dh + Vi6 io.)r = 11.7 in.1 - 2 (7h in.)(% in.)

= 10.6 in.2

W18x35

=17.7 in.

t..,

=0.300 in.

~= 0.425 in,

kw= 0.827 in.

From AISC Specification Table 03.1:

x

Column

U= l- 1

W12x?O

=12.2 in.

t,., = 0.370 in.

t.J= 0.640 in.

Brace

= 1.03 in. for single angle

Jc.u, = 1.14 in.

=l-

1.03 io. 4(3.00 ill.)

=0.914

LLBB

A1 = 11.7 in.2

x

Rn / Cl. 83.4 kips 18.0 kips/bolt

Check brace net section for tens}te rupture strength

Beam

2L6x4x~

~-in.·diameter bolts

= --

The net area of the brace is:

17°m AISC Manual Tables 1-1, 1-7 and 1-15, the geometric properties are as follows:

d

pd .

llr~q'd

=4.72 bolts

F1 =36 ksi F,.=58 ksi

=l.67(10.8 kip~) = 18.o kips/bolt

26.9 kips/bolt

ASTMA36

d

n

Pu =--

From AISC Manual Table 2·4, the material properties are as follows:

.. t ,.

Rn

:::: 26.9 kips/bolt

nuq' d

I

ASD

$Rn =I.67(16.1 kips)

Fr
Solution:

y = 2.03 in.

I

Brace-to-Gusset Connection Design Choose to use oversized holes in the gusset plnte and standard holes in lhe brace. In th e."tample-, decisions related to hole sizes should be carefully considered. Oversized holes could be used in all plies if required for extra tolerance. Providing different sized boles ii various plies csn make squaring and plumbing the strucrure difficult and is therefore generally avoided. Providing consistent bole sizes in all plies allows drift pins to be used i squaring and plumbing the structure. Providing oversized hole sizes allows for more fit-uitolerance but requires connections to be designed as slip critical. Providing standard hole~ limits the available fit-up tolerance but generally will result in fewer bolts designed based on the bearing values.

Brace Tension

P,, =89.6 lcips

3•.

3.5 BRACED FRAMES

Ae=A11U = (10.6 in.2)(0.914) =9.69 in.1

(Spec. Eq.

0

4

3-28

SYSTEMS NOT SPECIFICALLY DETAlLEP POR SEISMlC RESISTANCE

Pn =F11Ae

(Spec. Eq. D2-2)

=(58 ksi)(9.69 in..2) =562 lcips

~.t.

, The available tensile strength of the brace due to the limit state of tensile rupture is determfacd from AISC Specificarior1 Section D2, as follows:

3.5 'BRACED FRAMES

~~~~~~~~~~~.,.-~~~~-A~s=o~-.-~-:---~1

LRFD •·- lh gles edge 11 earoUt Su ...og OO 3J1 • (assuming I.SO in. edge distance):

4>Rn

ASD

LRFD

-=-n,

q,,Pn =0.15Pn -

o.k.

562 kips 2.00 =281 kips> 60.2 kips

between bolts:

o.k.

Check bolt bearing on the brace and shear strength of the bolts According to lbe User Note ih AJSC Specification Section J3.6, the strength of the bolt group is ta.ken as the sum of the effective strengths of the individual fasteners. 1n the following calculations, the available. bearing strength and tearout strength limit states from AISC Specification Equation J3-6a are separated for clarity. Assume that bolt hole defor-

mation is a design consideration. · LRFD.

-

ASD

Design shear strength per bolt from AISC Manual Table 7-1 is:

'

q,R,. =35.8 kips/bolt

lj>R,.

= 0.75(2.4)('A

Allowable bearing strength on angles R,.

2.4drF,.

Q

n

in.)(58 ksi)

in.)(2)(-* in.)(58 ksi) 2.00 =65.3 kips

Design bearing strength on gusset lj>R,. =$2.4dlFu 0.75(2.4)(3A in.)(3h in.)(58 ksi) =29.4 kips

Allowable bearing strength on gusset Rn

Tearout strength on angles, spacing between bolts:

=143 kips

¢Rn =$1.214.F..

11

n =(1/2.00)(1.2)(2)(% in.) x(3.00 in.-H/i6 in.)(58 ksi)

in.)

Tear--0ut strength on gusset, edge......... assume 2-in. edge distance: Rn l.2tLcFu -=--n n =(1/2.00)(1.2)(~ in.)

x(2.00 in.-%i in.)(58 ksi)

x(2.00 in.-1¥12 in.)(58 ksi)

=30.0 kips

Tear-out strength on gusset. spacing, between bolts:

=lj>l.2t4F., =0.75(1.2)(-* in.) x(3.00 in.-1-'/i6 in.)(58 ksi) =40.4 kips

1·

, = 95.2 kips

Tear-out strength on gusset, edgeassume 2-in. edge distance:

=0.75(1.2)(~

I

I:

l.2tLcFu

n

x(3.00 in.- 13/16 in.)(58 ksi)

$Rn

(2.4)(~

=97.9 kjps

=

= 0.75(1.2)(2)(* in.)

Allowable shear strength per bolt from AISC Manual Table 7-1 is:

- = - -in.)(2)(3h

x[l.50 in.-'h(1 ~6 in.)](58 ksi)

1· 1· .

-=---

n

=92.4d1Fu

= (J/2.00)(1.2)(2)(-* in.)

Rn

=91.21L.:Fu

R,, = 23.9 ldpslbolt

Design bearing strength on angles

Rn l.2t4Fu -:::--n n

=47.6 kips

Tearour strength on angles. spacing

$Rn

""-6

u.uu.u

=71.4 kips

2.00

=0.75(562 .kips) =422 .kips> 89.6 kips

=4>1.2U-tFu =0.75(1.2)(2)(* in.)

Tearout strength on angles, edge (assum:~g 1.50 J.ll •• aA"'e distance);

x[l50 in.- 1h(1¥i6 in.)](58 ksi)

Pn

Pn

l

l-2'

=20.0 kips

Tear-out strength on gusset, spacing between bolts: R,.

n

1.211.;F.,.

n = (1/2.00)(1.2)(% in.)

x(3.00 in.-.,/i6 in.)(58 ksi) =26.9 kips Since all bearing limit state strengths

exceed the slip-criticaJ ~trenglh of 18.0 ki,Pslbolt, bearing, does not govern.

2.4dtFu

-=--n n

=(2.4)(~ in.)(}i in.)(58 ksi) 2.00

=19.6 kips

J.:

3-30

SYSTEMS NOT SPECTF!CALLY l)l!fAU.ED FOR SEISMIC RESISTANCE

Check block shear strength of brace r" '

j

,..,..., '

II

:::::

Check the gusset compression buckling strength Using the Whitmor_e section as discussed in the AJSC Manual Part 9, the available width is

5

4,= 11hm.

gre.1ter than the Whitmore width determined as follows:

411= 21hfo. I,., From AJSC Sptcificarion Equation J4-5:

I

~Rn

=21 tan 30° =2(4)(3.00 in.)tan 30°

=13.9 in.

LRFD

'. '

3.5 BRACED rRAMES

ASD

The radius of gyration of the gusset plate buckling in the weak dfrection is:

=$UbsF,,.A,,,

r

r=-:fii

+min(¢>0.60FyAgv, t0.60FuA11v)

+ . (0.60FyArv 0.60FuAnvJ mm n · n

*in.

=J'if =0.108 in.

Tension n1pture component from AlSC Manual Table 9-3a:

$UbsFuAn1=2(1.0)(89.7 kjp/in.)(Y's in.)

Tension rupture component from AISC Manual Table 9-3a:

Ub,FuAnt -2(1.0)(59.8 kip/in.)(~ in.)

n

=112 laps

11

·;\ "..

Shear yielding component from AISC ManUtJI Table 9-3b: ~0.60F1 A1v =2(219 kip/in.)(* in.) =274 kips

~0.60F,,,A,,, =2(250 kip/in.)(* in.)

n

= 313 lcips

..-...:"

¢>R,, = 112 kips+274 kips = 386 lcips > 89.6 kips

=2(166 kip/in.)(~ in.)

o.k.

!•

n

..

'·'

Fa:::

n.:

o.k.

19.9 ksi

I

I

The design compressive strength is: \

The ~-in.

gus~et

The allowable compressive strength is: R,.

~Rn =~/?rAg

= (29.9 ksi)(13.9 io.)(t\ in.) o.k. = 156 kips> 127 !tips

Use (5) ~-in. ASTh1 A325-SC bolts to connect the bmce angle m the gusset plate. Use Class B faying surfaces, Sl.aJld.9.rd holes fn the brace, and oversized boles in the gusscl Try a ~-in. trial gusset plate thickness.

ASD

29.9 ksi

=74.8kips+183 kips

=258 kips > 60.2 kips

=36 ksi. the available critical stress js:

LRPD ~c:Fcr =

=208 kips R,,

From AISC M011ual Table 4-22 for Fy

2(146 kip/in.)(* in.)

Shear rupture component from AJSC .~fanual Table 9-3c:

0.60FNAnv

0.65(6.50 in.) 0.108 in.

=39.l

=183 kips

Shear rupture component from AISC .\.Jarmai Table 9-3c:

KL r

Shear yielding component Crom AISC Manual Table 9-3b:

n

=

-=---'---~

=74.8 kips

0.60FzA1v

The a\'erage length of the gusset plate beyond the connection on the Whitmore wjdth is approximately 6.5 in. For a fixed-fixed buckling condition, K 0.65 [see Dowswcll (2006)), and

n

= fc,A1 n

=(19.9 ksi)(l3.9 in.)(~ in.) =104 kips> 83.4 kips

o.k.

plate is o.k. Additionnl checks arc required as follows.

Connection Interface Forces

The forces ~ulting from the applied brace force at !he gusset-to-beam, gusset-to-column, and beam-to-<:olumn interfaces are determined using the Uoifonn Force Method (~•. The planes of uniform forces will be set as the vertical bolt line and the gusset/beam int.face. The assumption of a plane of uniform force at the verucru bolt line allows the bolts ·.• the column connection to be designed for shear only (no eccentricity}. However, this ccYcoienc assumption for connection design requires that a corresponding moment be resolw ,

3- 32

SYSTEMS NOT SPECIFJCALLY DETAILED FOR SEISMIC RESISTANCE

in the design of !he members: In lhis case, the moment will be assigned to the beam. It should be noted that this assumption is different than that made for the typical cases of lhe UFM shown in the AISC Manual and is nor a requirement for this type of connection. Appropriate work points and uniform force planes can often be selected conveniently to balance engineering, fabrication and erection economy. As is demonstrated in the following, the application of the UF.M in tenns of equations used will remain unchanged despite lhe change in interface location to the column bolt line. Using the connection geometry given in Figure 3-6 and using the UFM described in AISC Manual Part l 3, de1ermioe the connection interface forces as follows. The beam eccentricit:y to the plane of uniform force is:

3.5 BRACED FRAMES

3-3

1.

where db is the depth of lhe beam. The column eccentricity to lhe plane of uniform force is:

ec = 0.5dc + 2.5 in. =0.5(12.2 in.)+ 2.5 in. =8.60 in.

I;

where de is the depth of the column. The horizontal eccentricity from the plane of uniform force to the cencroid of the beam-to gusset connection is:

a= 0.5(20.75 in.)- 2.50 in.+ 0.500 in.

eb= 0.Sdb

=8.38 in.

= 0.5(17.7 in.)

=8.85 in. ~·

l

Assuming four bolts arc used in the gusset-to-single plate connections spaced at 3 in. start ing 3~ in. from the top of rhe beam, the vertical eccentricity from the plane of uniform fore i: to the centroid of the gusset-to-column connection is:

1'-8%~

iL 3 50 in.+~--~ . 3(3.00 in.) I'- . 2 =8.00 in.

12)-2"

0=45°

Sinc.e the gusset-to-beam connectioo is more rigid than the g~sset-to'.-c~lumri connection, tli beam can be assumed to resist the moment generated by eccentricity between the actual gu~

.I.

set centroids and the ideal centroids calculaled using the UFM. Thirefore:

~ = ~= 8.00 in.

I

l

a=K+~tan0

'

(Manual Eq. 13-15)

where

I

\I

' .. •

. (Manual Eq. 13-16)

Therefore:

Cf.

beam

t

-

a= (eb +~)tan 0-ec: =(8.85 in.+ 8.00 in.) tan (45°) - 8.60 in. =8.25 in. The distance from work point to centroid of gusset is:

Plane of uniform

W12x50 column

column

I

I .

W18x35 beam

force

Cf.

I;

r=

Jco.+ec) +(~+eb) 2

2

(Manual Eq. 13-1

l

=Jcs.25 in.+8.60 in.}2+(8.00 in.+8.85 in.)2 ::23.8 in.

Fig. 3-6. Initial connectwn geometry for Example 3.S.3.

t

SYSTEMS NOT SPEC.lFlCALLY DETAD..EO FOR SEISMIC RESISTANCE

The IJ1-.in. difference between the ideal centroid, a, and the actual centr0id. Ci, determined previously, could be neglected but is included here to illustrate the UFM procedure. From

The free body diagram forces are determined as follows. From AISC Manual Equation 13-2: 1

Vue

AISC Manual Equation 13-17:

LRFD

=~P., r

ASD Voe

8 00 = · ~· (127 kips) 23.8in. · =42.7 kips

LRFD

=~Pa r

M.JJ::::

8 00 = · ~n. (83.4 kips) 23.8 m. .· =28.0 kips

,,•..

From AISC Manual Equation 13-3:

:~

ASD

-

v..bla-Cij

Mo11

I

= Vabla-01

:::: 47.2 kipsl8.25 in.-8.38 in~

= 31.0 kipsl8.25 in.-8.38 in~

= 6.14 kip-in.

= 4.03 kip-in.

Tue moments at !he column-gusset plate interface and the column-beam interface due to the plane of unifonn force set at the ve.rtical bolt line are as follows:

1~ ·

~:

3.5 BRACED FRAMES

'

:~ ·' ~--- ~:--,

Mucg = Vuce

H uc=-Pu ec

Hac=ec P,,

r

=

!·

60

LRFD

.·

ASD

LRFD

~n. (127 kips)

- 3.8 ill. =45.9 kips

r 60 8 = · in. (83.4 23.8in. =30.1 kips

ki~)

= 28.0 kips(2.50 in.)

= 107 ldp-in.

= 70.0 kip-in.

V,.be ::::: 47.2 Jdps (2.50 in.)

;:: 118 kip-in.

111

~ Vl
·.-.,:,.

= =

.i;

ASD

=8.85 in. (83.4 kips) 23.8 io. =31.0 kips


~~

ASD

LRFD

~.:

a

Hub =- P.,

';::

,. ,,

I

r

= 8.25 in. (l 2 7'k:ips) 23.8 in. =44.0 kips

I

I

I I I

a

Hab=-Pa r

=8.25 in. (83.4 kips)

23.8 in. =28.9 lcips

Mocb

=Vabe = 31.0 kips (2.50 in.) = 77.5 kip-in.

I 1

II

!

. ;

i

The LRFD and ASD geometry and required strengths are shown in Figures 3-7 a and 3-7b. respectively.

..

eb

Vab =-Pa r

Mo.
= 42.7 kips(2.50 in.) Mucb::::

From AlSC Manual M_uation. P-4:

ASD

.

.3-36

SYSTEMS NOT SPEClFJCALLY DETA.Il..ED FOR SEISMIC RESISTANCE

Gusset-to-Beam Interface

p.,. .. 89.8 kips

i

89.8 kips

127 kips

.-------.IL kl~ 89.8

107 kip-in. 42.7 kips~ '-2.7 kips 1 45.9klps\ ( v..,·'- 2· 1tC>s

_J

J

I

~5.9 kips

fkips 427

L

45.9 kips

107 kip.in.

I

2

11"825 •

6.14kip-ln.~

r

J

47.2 klps

Pue

=t89.8 kips

c

~5.9klps

118 klp-ln.

.tT.2 ldps

·-.-~

lup$

4

=108 in.3 /in. The forces along the gusset-to-beam 'interface are:

44.0 kips

__J

89 ~

45.9 kips

59.0 kips

28.9 kips 20.75 in. =1.39 kip/in.

=

vub f..o=-

J.00 -_ vab

lw

lw

47.2 lcips

31.0 kips

= 20.75 in.

,.:::r t·i~r:·~r. . . J ~0.1

zs.otklps

kips

30.1 kips

70.0 kip.In.

·

~"

8.00 in.

H.i." 28.9 kip\-.-s_,--'-- - - ' •• v.... 31 .01c1ps 1 4.03 kip-ln. ~ 4.03 kip-In.~

77.5 kip-In.

30.1

31.0

kips~

kips\ ( _J

J

31.0 kips

~0.11\lps

77 •5 kip-in.

31.0 kips

r

30.1 kips

The resultant fo.rce is:

fu.pet:A

28.9 kips

30.1 kips

31 .0 kips

t

59.0ldps

Fig. 3-7b. ASD free body forces and nwmems.

-

59.0 kips

I •

=4.03 kip-in.

I

108 in.3 /in.

I \

= 0.0373 kip/in.

.

The resultant force is:

1

(1.39 kipfm.)2

='+(2.27 kiplin.+0.0569 kip(m.)2 = 3.15 kip{m.

'

fo.,xok = JJ~+(faa + fab)

=~J~:Uuo + /111>)1 (2.12 kipfm.)2

31.0~s

_J

AMEIUCAN .1Ns'muni OF STE£L CoN$'TltVCI10N

=6.14 kip-in. =0.0569~~

=a.2s in.

.

z...

Zw

.

=

\ +(1.49 kipfm.+0.0373 kip/in.)

=2.07 kip/in.

I

I

Mab fob=-

fwb = M ub

108 in.3 fm.

.u 111.

,.

= 1.49 kip/in.

83.4 kips

.------.. . !L59.0 ~

t

fw

=

= 20.75 in. =2.27 kip/in.

I

P,.. •

I..,

44.0 kips 20.75 in. = 2.12 kip/in.

Pee = 59.0 kips

r

av -

47.2 klps

.

1

f, _ Hob .

f. - H ..,, UV -

.

ASD

LRFD

47.2 kips

t __eb,. 8.85 in.

Fig. 3-7a. LRPD free body forces and moments.

'

neating the welds as a line:

(20.75 in.) z... =.!.....---=--

=8.38 In.

ii " 8.00 in.

1 6.14 kip-in. '-....!._/

kips~ _J 45.9

-

Design the gusset-t~beam weld

/,.. =20.75 in.

H.o,. 44 Okips\. - _ ,. -: . . - - - - ' · •• v..,. .. 47.2kips

118 kl!Hn. 47.2 45.9 kips'\ (

I:

3-37

3.5 BRACED FRAMES

.

t

I

n

3-38

SYSTEMS NOT SPECIFlCALLY DETAILED FOR SEJSMJC RESISTANCE

LR.FD

/..•.., =o.5(!•. J"'<'k +~1:..+(f.,,-f.b)2 ) 3.15 kip/in. = 0.5 (2.12 kiplin.)2 + +(2.27 kiplin.-0.0569 kipfm.)2

--= f,,, a11g

J•. ,,., =0.5(!•. "".x +J11.+U"" -

foh)

2

3.15 kip/in. 3.11 kip/in.

Use a 20.75-in. ·long, double-sided Yi6·in. fillet weld to connect the gusset plate lo the beam.

)

2JJ7 kip/in.

= 0.5 . /<1.39 kip/'lD.)2 [ +V+(I .49 kip/'lD. - 0.0373 kipJin.}1

A conserv:itive method to detem1ine the minimum gusset plate thickness is to set lhe shear ruprure strength of tbe base metal of lhe gusset plate equal to the required shear rupture strength of the weld. From AISC Manual Equation 9-3:

6.19D

6.l9D

Tm;n=~

!min=--

F,,

Fu

=1.01

Since/p
Sincefp~a>.lfa-.>g < l.25, the weld ductility factor of 1.25 will be appUed. For a discussion of the weld ductility fact0r, see AISC Manual Part 13.

Load angle:

Load angle:

=6.19(1.06 sixteenths)

_ 6.19(1.07 sixteenths) 58 ksi =0.114 in.S:* in.

58 ksi =0.113 in.s;% in.

o.k.

o.k.

Therefore, the gusser plate thickness of ¥s in. is acceptable.

Check the beam web at the beam-to-gusset interface

e= tan-!( /aa~/ab)

fub)

ASD

LRFD

fa.pea>. _ 2.07 kip/in. fa, avg - 2.04 kip/in.

= 1.01

S= tan-1(/ua ~

The weld size is controlled by the mirumum size of fillet weld given in AISC Specificatior. T:lble J2.4.

=2.04 kipfm.

: 3.11 kip/in. fu.~ak

l

.

ASD

3-2)

3.5 BRACED FRAMES

The nonnal and flexural forces at the gusset-to-beam interface can be converted into an effective nonnal force in order to facilitate the web local yielding and web local crippling

=tan-1 (2.27 kipfm. + 0.0569 _kip/in.) 2.12 kip/in.

=47.7°

Required weld leg. D, including the weld ductility factor and directional weld strength increase:

fu,avg

I

2$Rn [1+0.5sin 1 ·~ (0)]

=1.25 x

vatively calculated as:

1.39 kip/in.

=47.7°

D~ 1.25[

checks. The effective normal force for use with the full length of che gusset can be constr·

=tan- t(l.49 kiplin.+0.0373 kip/in.)

3.'11 kip/in. 2(1.392 kipfm,)li+0.5sin 1.s (47.7°))

= 1.06 sixteenths For a derivation of the weld shear strength, $Rn = 1.392 kip/in., see AISC

Manual Part 8.

4Mui, L

N4=Vu1J+-\

=47.2 kips+ 4(6.14 kip-jn.) D :2: l.25

20.75 in.

fa,""'

2(Rn/U)(t + 0.5sin 1·s (0)]

=l.25

2.04 kip/in. 1

=48.4 kips

I

x 2(0.928 kipfm.)[1+0.5sin .s (47.7")J

=1.04 sixteenths For a derivation of lhe weld shear R strength. ~ 0.928 kip/in., see AISC

=

Manual Part 8.

ASD

LRFD

Required weld leg, D, including lhe weld ductility factor and dir«:tional weld suengtb increase:

'

I

4Mab Neff =Vab+-L

_ ki 4(4.03kip-in.) - 310 . ps+ 20.75 in. =31.8 kips

Check beam web loC8/ yielding The beam force is applied at a= 8.25 in. from lhe beam end. Because a< d

R.,

=Fywtw(2.5k+lb) =(50 ksi)(0.300 io.)[2.5(0.827 in.)+20.75 in.] =342 kips

= 17.7 in.,

(Spec. Eq. JI0-3)

SYSTEMS NOT SPECIFICALLY DETAILED FOR SEISMIC RESISTANCE

'

LRFD 342 kips .Rn -=

oJc.

.Q

3

LRFD

ASD

Rn= 1.00(342 kips) = 342 kips> 48.4 kips

3.5 BRACED FRAMES

ASD

Tension yielding on gross section, from AfSC Specification ~uation 14-1:

1.50

= 228 kips> 31.8 kips

o.k.

Rn

$Rn= $f).A8

=0.90(36 ksi)(l4.0 in.)(% in.)

Check beam web local crippling

::::: 170 kips> 45.9 l
Since the framed beam-to-column co11Dection will provide significant restraint to the web relative to· crippling, AJSC Specification Equation Jl0-4 is used despite the fact that the force is applied less than d/2 from the end of the beam. ' Using AISC Manual.Table 9-4 and Equations 9-49a and 9-49b:

LRFD

FyA

r.

(36 ksi)(14.0 in.)(% in.)

j

8 -=-.Q Q

o.k.

f<:~

:~

1·;

1.67

=113 kips > 30.1 kips

o.k.

Check block shear relative to shear load, n =4, Lev::::: l~ in., Leh= 2.in.

Check block shear relative to shear load, n=4,Lev= 11hin.,41i=2in.

From ATSC Specification Equation J4-5:

From AISC Specification Equation J4-5 :

I f:·

ASD
$R3 = 38.7 kips ~

Tension yielding on gross section, from AISC Specification Equation J4-1:

l.

=3.89 kip/in.

R3/Q=25.8 kips R1 / .Q =2.59 kip/in.

'

~ :z2[R3/il+lb (~/Q)]

$Rn =2(R3+lb(~)) = 2[38.7 kips+ 20.75 in.(3.89 kip/in.))

=239 kie_s > 48.1 kips

o.k.

-

=2(25.8 kips+20.75 in.(2.59 kip/in.)] =159 kips>31.8 kips ·· o.k.

+ min($0.60FyAgv, $0.60FuAnv)

U1;s= 1:0 (

Tension rupture component from AISC Manual Table 9-3a: $V1>sFuAn1 = (1.0)(68.0 kip/in.)(Vs in.)

Gusset-to-Column Interface

Tension rupture component from AISC

Manual Table 9-3a:

Ubs~~nt =(LO)(45.3 kip/in.)(% in.)

=25.S kips

=17.0 kips

Check the gusset at the gusset-to-column interface Try a length above the top of beam of 14 in. to allow for shaping of the gusset if desired.

Shear yielding component from Al~C Manual Table 9-3b: ·. I

Shear yielding component from AISC

Manual Table 9-3b:

I

LRPD

ASD

Forces at interface

Vac

=

=28.'0 kips

Hae= 30.1 kips

Shear yielding on gross section, from AISC Specification Equation J4-3:

=1.00(0.6)(36 ksi)(14.0 in.)('h io.) o.k.

.-

Shear yielding on gross section from AISC Specification Equation J4-3:

Rn

Rn =.$0.6FyAgv.

-= Q

0.6FyAgv

n

= (0.6)(36 ksi)(l4.0 in.)(% in.) 1.50 75.6 kips> 28.0 kips o.k.

=

0. 60FyAgv

n

=63.8 kips

Forces at interface

Vue= 42.7 kips Hue 45.9 kips

= 113 kips> 42.7 kips

cp<).60FyAgv =(170 kip/in.)(% in.)

Shear rupture component from AISC Manual Thble 9--3c: · ¥>.60FuA,,,,

=(194 kip/in.)(% in.)

=(l 13 kip/in.)(% in.) =42.4 kips

She~ nipture compon~nt from AISC Manual Table 9-3c: 0.60F,,Anv :::: (J2g kip/in.)(% in.)

n

=72.8 kips · tRn = 25.5 kip/in.+ 63.8 kip/in. = 89.3 kips> 42.7 kips o.k.

r'

.

=48.4 kips

Rn =17.0 kip/in.+42.4 kip/in.

n

=59.4 ldps > 28.0 kips

o.k.

(

SYSTEMS NOf SPECLFJCALLY DETAILED FOR SEISMIC RESISTANCE

LRFD

)

.

CaJcufa1e tension rupture component: ~Ub,F,,An1

f~ .

Block shear relative to nonnal load Calculate tension rupture component·

=0.75(1.0X58 kips~ in.)

(l / 2.00)(1.0)(58 Jcips)(}i in.)

x (10.5 in. - 3.5(0.875 in.)]

x[l0.5 in.-3.5(0.875 in.)]

= 121 kips

Calcu~te shear

n

Calculate shear rupture component: {l / 2.00)(0.60) (58 ksi)(}i in.)

:l
=10.2 kips

q,R. = 12 t kips+ 12.2 kips

= 89.0 kips> 30.1 kips

2

45.9 kips) +(42.7 kips) ( 133 kips 89 3 kips

LRFD

ASD

~ =(~)'

tRn =$r11 t = (78.3 kip/in.)(1' in.)

= 29.4kips>l7.9kips

= (52.2 kip/in.)(::i in.)

o.k.

= 19.6 kips> 11.9 kips

·o.k.

=0.337 < 1.0

o.k.

:·

The resultant forces that will be resisted by I.he bolts in the gusset plate are:

LRFD

LRFD o.k.

Shear yielding on gross section, from AISC Specification Equation J4-3:

2

R,, =J(Vuc) +(H-<)

R,, =J(Voc) +(Hoc) 2

.

.

$Rn= $0.60F1 Arv =1.00(0.60)(36 ksi)(12.0 in.X}\ in.) = 97.2 kips> 42.7 kips o.k.

ASD

1

+(45.9 kips)

Check single plate-assume }'o-in.-thick plate

kips)

Gusset-to-single-plate connection desif)n

=6'2.7 kips

o.k.

Using ArSC Manual Tables 7-4 and 7-5 to check bolt bearing on the gusset plate withs= 3 in. and l. =2 in.. the ava.il:ible bearing strength based on one bolt is:

2

{

=J(42.7 kips)

=47.6lops>411 kips

Use (4) ~-in.-diamcter ASThl A325·N bolts to connect the gusset plate to I.he column.

30.1 kips) +(28.0 ( 89.0 kips 59.4 kips

=0.348 < LO

i:f!

o.k..

Single plate design

o.k.

Combined shear and nonnal block shear:

2

2

= 71.6 kips > 62. 7 kips

:; ={4)(1t.9kips)

Therefore, bolt shear governs over bolt bearing.

Q

o.k.

Combined &bear and normal block shear:

!;

=(4)(17.9 k1p:1)

R,. =80.9 kips+S.10 kips

=133 lc.ips > 45.9 kips

2

From AlSC Manual Table 7-1, (4) A325-N bolts are required

3A-in.-diameter ASTM

x[2.00 in.-0.5(0.875 in.))

= 15.3 kips

.

~Rn

x(* in.)(2.00 in.)

c)0.60F,,An• =0.75(0.60)(58 ksi)(* in.)

...

FromAlSCManua/Thblc 7 I, (4) A325-N bolts are required.

~-in.-diameter ASTM

=8.10 kips

I,

Calculate shear n1pture component:

yielding component:

0.60~,Atv = (J / 2.00)(0.60)(36 ki.i)

ci»0.60.f)Ar =0.75(0.60)(36 ksiX~ in.) .x (2.00 in.) = 12.2 lcips

2

ASD

=80.9 kips

Calculate shear yielding component;

I·

LRFD

ASD

Block shear relative 10 normal load

r

3.5 BRACED FRAMES

ASD Shear yielding on -gross section, from AISC Specification Equation 14-3:

Rn = 0.60FyAgv

n

n

=(0.60)(36 ksi)(l2.0 in.)(~ in.) 1.50 = 64.8 kips > 28.0 kips

2

=J(28.0 kips) 2 +(30. 1 kips) 2 =41.l kips

;:

o.k.

SYSTEMS NOT SPEClFICALLY DET.'\Il..ED FOR SEISMIC RESISTANCE

LRFD

ASD

Shear rupture on net section, from AISC Specification Equation 14-4:

Shear rupture on net section. from AISC Specification Equation 14-4:

n

=0.75(0.60)(58 ksi) x[l2.0 io. - 4(0.875 in.)}(% in.)

=83.2 kips > 42.7 kips

Tensile yielding on gross section, from AlSC Specification Equation 14--1:

$Rn=4>F1Ag. = 0.90(36 ksi)(l2.0 in.)(}i io.)

=146 kips> 45.9 kips

F1 Ag

=(36 ksi)(12.0 in.)(% in.) 1.67

o.k.

Tensile rupture on net section, from AISC Specificaiion Equation J4-2:

Rn:::: FuAe

$Rn=9FuAe

n

=0.75(58 ksi) x[l2.0 in. - 4(0.875 in.)](% in.) o.k.

n

=(1/2.00)(58 ksi) x [I2.0 in.-4(0.875 in.)](% in.)

=92._4 kips> 30.1 kips

Block shear on single plate relative to shear load, with n =4, 4., = 11h in., Le11=2'12 in.

From AISC Specification Equation 14-5:

From AISC Specification Equation J4-5:

$R'I =4>UbsFuA>ll ,, +min (cj>0.60F,,A8 ,., ~.60F,.Anv)

0·6°FuAm• 48.4 kips, from gusset-

9Q.60FuA 111• =72.8 kips, from gussetto-column interface check

n

$Rn:::: 33.6 kips + 63.8 kips =97.4 kips > 42. 7 kip$

Rn = 22.4 kips+42.4 kips

n

o.k.

= 64.8 lcips > 28.0 kips

Tension rupture component from AISC • Manual Table 9-3a:

UbsF,,A,u -(1.0)(59.8 kip/in.)(% in.)

n

=22.4 kips

o.k.

Block sbe:.tr on single plate relative to normal load

.Block shear on single plate relative to normal load

Calculate tension rupture component:

Calculate tension rupture component:

$UbsFuAn1 =121 kips, from gussetto-column interface check

UbsFuAnt = 80.9 kips, from gussel-

n

to-column interface check Calculate shear yielding compqnent

1

:

Calculate shear yielding component:

\

I

90.60FyA8 v =0.75(0.60)(36 ksi)('h in.) x(2.50 in.) = 15.2 kips Calculate shear rupture component:

ubs =t.o

$UbsF..An1 = (1.0)(89.7 ki¢n.)(% in.) = 33.6 kips


o.k.

.Block shear on single plate relative to shear load, with n =4, Lev,= 11h in., L~h= 21h in.

Tension rupture component from AlSC Manual Table 9-3a:

Shear rupture component from AJSC Manual Table 9-3c:

to-column interface check

=97.0 kips > 30. l kips

=139 kips > 45.9 kips

o.k.

-=-n n

o.k.

Tensile rupture-on net section, from ATSC Specification Equation J4.2: ·

0.60f).A8 ., . fro ---''--"'n =42.4 kips, m gusset-

=63.8 kips, from gusset-

to-column interface check

Tensile yielding on gross section, from AISC Specifjcation Equation 14-1:

Rn

She;µ- yielding component from AISC Manual Table 9-3b:

to--column interface check

=(l/2.00)(0.60)(58 ksi) =55.5 kips> 28.0 kips

Shear yielding component from AlSC Manual Table 9·3b: ~.601).Agv

n

x[12.0 io. - 4(0.875 in.)]{% in.)

o.k.

ASD

LRFD

Rn 0.60F,.Anv --=

$Rn= ~.60F,,Atw

3.S BRACED FRAMES

0.60FyAgv _ 0.60(36 ksi)(% in.)(2.50 in.) n 2.00 =10.1 kips Calculate shear rupture component:

· ~A..v = (1/2-.00)(0.60)(5~ ksi)(~ in.)

9<}.60FuAnv =0.75(0.60)(58 ksi)('h in.) x[2.50 in. - 0.5(0.875 in:)) =20.2 kips

06

$Rn= 121 kips + 15.2 kips =136 kips> 45.9 kips

R,. = 80.9 kips+ IO. I kips o.k.

x[2.50 in.-0.5(0.875 in.)]

' = 13.5 !Ops

}:

I".

i

t 1·

J:

.::i

1

l

n

=91.0 kips> 30.1 kips

I

o.k.

r

J I:

SYSTEMS NOT SP~CU"ICAU,Y DETAlU.!O FOR SFJSMIC RESlSTANC6

LRFD

.L'.> URALEIJ l'l

LRFD

ASD

!

ASD -~

r r

Combined shear and nonnal block ~he3n-

( 42.7 kips 97-4 kips

+ ( 45.9 kips J36 kips

=0.306 < 1.0

Combined shear and normal block ~hear:

( 28.0 kips 64.8 kips

r

o.k.

+( 30.1 kips 9 J.0 kips

r

=0.296< 1.0

lI

R" -('" n} p

= (78.3 kjplin.)(* in.) o.k.

= 29.4kips >17.9 kips

I

=(52.2 kip/in.)( ~ in.) = 19 6 kips> 11.9 kips

o.k.

o.k.

Therefore, bolt shear governs over bearing.

I'

Use a *-in.-thick single plate.

i·

'

Beam single-plate-to-column connection weld Beam-to-Column Single Plate Connection

,,i,

Treating the welds as a line:

The forces on the connection are:

;:'•

-

I

n-

¢R,. = ¢r11tp

l,.

LRFD

l

,. ~·

~ .-.,:,_.,,

ASD

Vu = Ru+ Vub = 4.00 kips+ 47.2 ldps =51.2 kips

Va = Ra+ Vob

H., = Huc

Ha = !lac

=36.0 in. ~/in . The forces nlong the beam-to-column in1erfacc arc: LRFD

The resohan1 force that will be resisted by

The resultant force that will be resisted

the bolts is:

by lhc bolts is:

R., =J(51.2kips) +(45 9 kips)

..

4

=30.1 kips 2

~.

Zw =(12.0 in.}1

=2.63 kips+ 31.0 kips =33.6 kips

= 45.9 kips

'• ,,

2

2

Ra= J(33.6 kips) +(30. l kips)

f,.

From AISC Manual Tuble 7-1, (4)

~-in.

diameler ASTM A325-N bolts are

From AISC ManualThble 7-1, (4) diameter ASTM A325·N bolts are

required.

required.

=7 1.6 kips > 68.8 k,;ps

~- in.

~ = (4)(11.9.ldps)

kips)

o.k.

ASD

= 51.2 kips

/ .,

12.0 in. ::::: 4.27 rJ p/in.

2

= 45. 1 kips

=68.8 kips

~Rn= (4)(17.9

=12.0 in.

fa

=45.9 kips

fo

12.0in. = 3.83 kip/in.

\

118 kip-in.

= 47 .6 kips> 45. l kips

/b

= 3.28 kip(in.

Use (4) ASTM A325-N bolts to connect the beam to the column.

=

Using AJSC Manual Tables 7-4 and 7-5 for boll bearing on the single plate, with s 3 in. and~= 2 in. (note that~ = 2 in. is used conservatively 10 employ Table 7-5). The avail· able bearing strength of the plate b
/peak.= J1i+(J. + fb)

12.0in. ::::: 2.SO kip/ in.

=30.J kips 12.0in.

= 2.51 kip/in.

'

= 36.0 in.j lin.

_ 33.6.kips

77.5 kip-in.

=36.0 in.3 Fm. =2.15 kip/in.

J

2

f P"k = f.,2 +(fa+ fb ) 2

= J4.27 2 +(3.83+ 3.28)

2

=8.29 kip/in.

=Jz.so2 +(2.51+2.15)2 =5.44 kipfin.

.i. I

AMDJcNI [NS'TTT\)'T1! OF STt.EL CONSTR\JCl"l(»I

AMl.:IUCAN

lNmnml OP Srm. eoi-·s·nuJCTIOH

'

i

I. I

SYSTEMS NOT SPECIRCALLY DETAILED FOR SEJSMJC RESISTANCE

LRFD

....

3.5 BRACED fRAMBS

~-4

LRFO

ASD

ASD

n.

Losd Angle

Load Angle

0 ::: tan-I ( 3.83 kip/ in.+ 3.28 kip/ in.) · 4.27 kip/in.

9 = tan

=59.0°

Tensile rup1ure on net so.:tion from AISC Specificatior1 Equation H -2:

1(2.51

kip/ in.+2.15 kip/ in.) 2.80 kip/ in.

$Rn-$F.,A, in.))(~

x[ 12.0 in. - 4(0.875 D?.

8.29 kip/ in. 2(1.392 IJp/ in.)j 1+0.5sinl.5 (59.0°))

D~

S.44 kip/in.

= 139 kips> 45.9 kips

2 2 47.2 k1ps) +(45.9 kips.} ( 97..1 kips 136 kips =0.349 < 1.0

Determine the single plate thickness

Try a Vs-in.-thick plate.

LR.FD

ASD She:ll' yielding on gross section, from AJSC Specification Equation J4-3:

=1.00(0.60)(36 kSi)( 12.0 in.)(* in.) =97.2 kips> 512 kips o.k.

Shear rupture on nel section, from AISC Specificario11 Equation J4-4:

n

= 0.75(0.60)(58 ksi) x[l2.0 in. - 4(0.875 in.)](* in.) = 83.2 kips> 47.2 kips

(0.60)(36 ksi)(12.0 in.)(~ in.)

1.50 =64.8 kips> 33.6 kips

Specificarion

n

3.83 Jdplin. + 3.28 kip/in. 0.90(36 ksi)(~ in.)

in.)](* in.)

=0.585 < 1.0

o.k.

o.k.

Tensile yielding on gross section, from AISC Specification Equ:ition J4 I

(use stresses calculated for weld):

/"1>

2.51 kip/in.+2.15 kiplin. F)tp / O - (36 ksi)(~ in.)/1.67 = 0.576 < l .O o.k.

/ 04

x[l2.0 in.-4(0.875 in.)](}~ in.) -" 92.4 kips> 30. l kips o.k. Combined shear and nonnsl block shear sttcogtlls from gusset-to-column checkusing values from gusset-to-column single plate: 2

2

31 .0 kips) +(30.l kips) ( 64.8 kips 9 l.O kips

=0.338<1.0

o.k.

o.k.

With beam 11:mge intnct, only axial force will caure block shear.

Block ~hear relative to normal load:

ASD Block shear relative to normal load:

$Rn =$Ub,FuA,., +min($0.60F1 A1v. ¢0.60P.iA,.,)

. (0.60FyAgv

+mm

n

'

0.60~uA11v)

J-

(1/2.00)(1.0)(65 ksi) x[9.00 io.-3(0.875 in.))

x(0.300 in.)

x(0.300 in.)

= 93.2 kips

cP().60F1 A1 v =2(0.75)(0.60)(50 ksi) x(0.300 in.)(2.00 in.) = 27.0 kips

,:.:

I t;

I

If,~

I

web

¢UbsFuA"' = 0.75( l.OX65 k.si) x(9.00 in. -3(0.815 in.)]

=(J/2.00)(0.60)(58 ksi) = 55.5 kips> 31.0 kips

_

I

""c112.00)(58 ksi)

=0.60F,.A,,,. x[l2.0 in.-4(0.875

o.k.

Tensile yielding on gross sectioo,-from AISC Specification Equation J4- l (use stresses cnJculatcd for weld):

o.k.

Shear rupture on net section, from AISC Equation 14-4:

n

Check block shear at beam

I} l

n

LRFD

n ""

R,.

¢Rn= ~.60F,.Anv

fua + f ub ¢F1 t,

-

R,, ..,, 0.60FyA1.,

4>Rn =~.60FyA 1.,

o.k.

Combined ~hc:ir and nonnal block ~hear strengths from gusset-to-column checkusing values from gusset-to-column single pla1e·

A ~6-in. fille1 weld on both sides of the single plate is :idc~uate.

Shear yielding on gross section, from AlSC Specification Equ3tion 14-3:

in.)

2(0.928 kip/in.)[ I+ 0.5sinl.5 (59 0°)]

:: 2.10 sixteenths

= 2.13 sixteenths

Sp::fi:a_~_·:_: Equation 14- 2: n

=0.75(58 ks1)

=59.0°

Ten~ile rupture on net sec1ioo from AISC

l I l

= 62.2 kips 0.60FyA,, - 2(1/2.00) (0.60)(50 k.si)

n

x(0.300 in.)(2.00 in.)

=18.0 kips

SYSTE'MS Ncrr SPECIFICALLY DBTAll.EO FOR S.EJSMJC RESISTANCE

>-SO

LRFD 0.60F.,Anv Q

x[2.00 in. - 0.5(0.875 in.)) x(0.300 in.)

(

=2(1/2.00) (0.60)(65 ksi) x (2.00 in.-0.5(0.875 in.)) x (0.300 in.)

=27.4 kips ::=

cl>R,, =93.2 kips+ 27.0 kips

= 120 kips> 45.9 kips

o.k.

,. ·,

{

~

I

3.5 BRACED

3-51

FRAMES

LRFD

....

f u.b

Muct =--

ASD

f db

z,..

= J07 kip-in.

.~

Moc8 =--

Zw

= 70.0 kip-in. 36.0 in. 3 /in. l.94 kip/in .

36.0 in.3 /in. = 2.97 kip/in.

~

18.3 kips

R,. =62.2 kips+l8.0 kips Q = 80.2 ldps > 30.l kips

' ~

ASD

¢0.60F.,A,,.. = 2(0.75)(0.60)(65 ksi)

~.

=

-:~

f,,,p
o.k.

Since the gussel-to-column and the beam-to-c.olumn single plates are created as identical plates, several ch&ks related to these can be combined.

=JJ:fv+(J,,,, + f,,b )"

J

fa. peak = [1.,+ (Joo+ f db )2

= J3 .562 + (3.83 + 2.97f

=J2.332 + (2.5 l + l.94)2

=7.68 kip/in.

= 5.02 kip/in.

e=tan-1(fua+fu1>)

Single plate to column weld design

The beam-to-column and gusset-co-column single plates will be treated as separate connections. Conservatively, each single plate will be assumed to be 12 in. long to maintain symmetry relative to the actual loads. Consider only the portion of the single plate attached to the gusset, design the single plate to column weld. Treating lhe welds as a line:

(12.0 in/ 4 36.0 in?/in.

LRFD

=42.7 kips 12.0 in,

=3.56 kip/in.

I

r r>:

Hw

J

.. I ~:

!""=-· I..,

=45.9 kips 12.0 in. = 3.83 !tip/in.

=62.4°

D>

= tan

- 1

2.33 kip/in.

= 62.4°

7.68 lcip/in.

- 2(1.392 kipfm.)[l+0.5sinl.5 (62.4°)]

D~

5.02 kip/in.

2(0.928 kip/in.)[ I+ 0.5sinl.5 (62.4°)j

=l.91 sixteenths

Note: Since the bolts in the single plate will add ductility to the connection and also make this interface less rigid lhan the gusset-to-beam interface, the weld ductility factor applied to the gusset-to-beam interfuce need not be applied here.

The forces along the gusseHo-single plare interface are:

I..,

3.83 kipfm. + 2.97 kip/in.) 3.56 kipfm.

A :Y1<1-in. fillet weld on bol..h sides of lhe single plate is adequate.

=

JIN= Vue.

_ 1(

=1.95 sixteenths

l,,, = 12.0 in.

Z,,,.

=tan

laa;:lan ) (2.51 k:ip/in.+1.94 kip/in.)

a ::= Uln- 1(

fuv

ASD

J.av --

V,,,, 1..., 28.0 kips = 12.0in.

=2..33 kip/in.

J.aa-_Hoc lw

= 30. 1 kips 12.0 in. =2.511.cipfm.

Regarding the design of the weld to the single plate, from AISC Specijicacion Table J2.4, the m.ininrnm size fillet weld allowed for I.be pans being connected is o/16 in. The AJSC Manual Pan 10 recommends developing the strength of the plt1ce to ensure plastic yielding of the plate., instead of .fracture in the fillet weld. A mini.mum fillet weld of~ times 1be plate thickness for both sides of I.be plaie is needed 10 develop the plate streng1h. Since this rcquiremeni is intended to ensure that the simple berun end rotation can be accommodated in a ductile manner, it need not be applied 10 R = 3 bracing connections. Use a Vt6-io. fillet weld. The final connection design and geometry is shown in Figure 3-8.

SYSTEMS NOT SPCCJFICALLY DETAil. ED FOR SElSMlC RESISTANCE

3-52

-

column

Y.i"

1·-a~·

W12x50

<(5) 3A• dia. A325-SC

2>'.l"

bolts with ovs. holes In gusset, std. holes in brace and Class 8 faying surfaces \

l

PART 3 REFERENCES

PART 3 REFERENCES Carter. C.J. (1999), Srifftning of Wide-Flange Column at Moment Co11nec1io1u: Wind and Seismic 1\pplicatio1u, Design Gujde I3, AISC, Chicago, IL.

l

Dowswell, B. (2006), "Effective Length Faciors for Gusset Plate Budding;• Engineering Jo11mal, AISC, Vol. 43, No. 2, 2nd Quarter, pp. 91- 101.

(2) L6x4x%

%" A36PL

If.

.....u...-~11---"'- ~{8) ~· dia. A325-N

beam

W18x35 beam

bolts in std. holes

Fig. 3-8. Connection as designed in Example 3.5.3. ·

I

I \

.

t •'

.l

·..

.J.

.·.\

J

.1 AMWC>Ji lNsrmm! OF STEEL COl'ISTRUC'l10N

...t

3-54

SYSTEMS NOT SPECIFlCALLY DETAILED FOR SEISMIC RESISTANCE

4-1

PART4 MOMENT FRAMES

4. l SCOPE ..............................•............................ 4-2

4.2 ORDINARY MOMENT FRA.i\tfES (OMF) ............................... 4-2 OMF Design Example Plan and Elev:ition .... , .. ......................... 4-3 Example 4.2. l. OMF Story Drift and Stability Check .........•............. 4-5 Example 4.2.2. OMF Column S1rength Oteck ............................ 4-1 Example 4.2.3. O.MF Beam Strength Check ............................. 4-12 Example 4.2.4. OMF Beam-Column Connection Design ................... 4-16

4.3 SPECIAL MOMENT FRAMES (SMF) AND INTERMEDIATE M0?\.1ENT FRAMES (IMF) ................. ......... ................ 4-33 SMF Design Example Plan and Elevation ...... . ........................ 4-36 faample 4.3.1. SMF Story Drift and Stability Check ....... ......... ..... 4-36 Example 4.3.2. SMF Column Strength Check ......... . ... . .............. 4-42 E\ample 4.3.3. S~fF Beam Strength Check. . . . . .

. ... ........... ...... ~

Example 4.3.4. SMF Beam-Column Connec1ion Design .. ............ . .... 4-57 4.4 COLUMN SPLICE AND COLUMN BASE DESIGN E..'
DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .. ... ..... 4-122

Tuble 4-1. Comparison of Requirements for SMP, IMF and OMP ... ..... ... 4-122 Table 4-2. S:MF Design Values ....................................... 4-124 PART 4 REFERENCES ................................................ 4-138

MOMENT FRAMES

4.1 SCOPE The following types of moment frames are addressed in this Part: ordinary moment frame (OMF) systems, intenncdiate moment frame (IMF) systems, and special moment frame (SMF) systems. The AISC Seismic Pro"•isions requ.iremenlS and other design considerations summarized in this Part apply 10 the design of the members and connections in moment frames that require seismic detailing according to the AISC Seismic Provisions. Moment frame systems resist lateral forces through the flexural aud shear strengths of the beams and columns. Lateral displacement is resisted primarily through the flexural stiffness of the fr:iming members and the restraint of relative rotarion between the beams and columns at the connections, or "frame action."' Moment frame systems tend to have larger and heavier beam and column sizes than in braced frame systems, because the beams and columns are often sized for drift control rather than strength. The increase in member siLeS and related costs, however, may be acceptable because of the increased flexibility in the architectural and mechanical layout in the structure. The absence of diagonal bracing members can provide greater freedom in the configuration of walls and in the routing of mechanical ductwork and piping. On the other hand. the flexible nature of the frames does warrant some additional consideration of the interaction between the steel frame and more rigid architectural cladding systems. AISC Design Guide 3, Serviceability Design Considerations for Steel Buildings (West and Fisher; 2003), discusses recomniended drift limits for various cladding systems.

4.2 ORDINARY M OMENT FRAMES (OMF)

4-3

(a) FR moment connections are designed for s required flexural strength equal to the expected flexural strength of the beam multiplied by l. J, as follows:

Jhe required shear strength of the connection is determined using a shear force duo to earthquake loads associated with the development of these expected flexural moments simultaneously 3t each end of the beam. (b) FR moment connections are designed for a required flexural screngtb and shear strength equal to the max.imum moment and corresponding shear that can be transferred to the connection by the system, including the effects of material overstrength and slrain hardening. As discussed in AISC Seismic Provisions Commentary Section E l.6b, specific examples of potentially limiting aspects of the system include:

• Flexural yielding of the column when the flexural strength of the column is less than that of the beam • The panel zone shear strength of the column, in recognition of lhe fact that testing has shown that panel zone shear yielding provides a fairly ductile response in this joint • The foundation uplift • The earthquake force detemtined using an R value of 1 ·cc) FR moment conne.ctions between wide fl:."lnge beams and the flange of wide flange columns are designed according to the connection design requiremenis of the IMF (AISC Seismic Provisions Section E2.6) or SMP (AISC Seismic Provisions Section E3.6). or a connection is used that resembles the tested WUF-W or WUF-B connections that are included in ANSI/AISC 358. See ATSC Seismic Provisions Section El .6b(c) for detailed requirements.

(4-la)

(4-lb)

where Ry =ratio of the expected yield stress to the specified minimum yield stress, P7 Mp= nominal plastic flexural strength of the beam AMERICAN .INSTmrra Ol' STEEi.. Cof'l.$1"!\UCTION

}:

t

required to develop available strengths similar to those of FR moment connections. In addition, PR moment connections must have a nominal flexural strength no less than 0.50Mp of the connected beam (or O.SOMp of the column for one-story structures). The strength and fle:tibility of the connection must be considered in the design, including the effect on over· · all frame stability. OMF systems are not required to have, any special detailing of the panel zones, and have no special requirements for the relationship between beam and column strength. This is indicative of the overall OMF system; where the detailing requirements are reduced and the seismic forces are larger than moment frame systems intended to provide higher ductility. This basic design philosophy for OMF systems alJows for their use as an economical moment frame system when OMF systems are permitted by the applicable building code. According to ASCE/SEI 7 Section 12.2.5.6, OMF frames are permitted to be used in Seismic Design Categories D, E and F for one-story structures under certain height and loading limitations.

OMF Design Example Plan and Elevation

or

Ma =(1.1/1.5)RyMp (ASD)

\:I

As described in AJSC Seismic Provisions Section El.6c, PR momem connections are

The only system-specific requirements for an OMF penain to the beam-to-column moment connections. The general intent of the OMF design provisions provided in AISC Seismic Provision$ Section El is that connection failure should not be the first significant inelastic event in the response of the frame to earthquake loading, recognizjng that a connection failure is typically one of the least ductile failure modes of a steel frame. Thus the basic design requ"irement is to provide a frame with strong moment connections. In accordance with AJSC Seismic Provisions Section El.6, two connection types are permitted when designing OMF systems-fully restrained (FR) and partially restrained (PR), as defined in AISC Specification Section B3.6b. AU FR connections in OMP systems must satisfy at least one of the following three options given in AISC Seismic Provisions Section El.6b.

Mu =LIR,,Mp (LRFD)

4.2 ORDU-SARY MOMENT FRAMES

Tue following section consists of four design examples for an OMF system. See Figure 4- I for lhe roof plan :md Figure 4-2 for lbe elevation of the building moment frames. The code-specified gravity loading is as follows: D

= 15 psf

S

=20 psf

.,

..

;l ·~:l

'

MOMEm FR.AMl:S

From ASCEISEl 7, lbe following parameters apply: Risk Category IT, Seismic Design Category D, R = 3~. !1,, = 3, Cd= 3. !< = 1.00, Sos= 0.528, and p = 1.0. According to ASCE/SEI 7"S'ection 12.3.4.2, p = 1.0 if each story resists more 1ban 35% of 1he base shear in the direction of interest and loss of moment resistance at the beanHo-column connections at both ends of a beam will not result in more than a 33% reduction in story strength, nor does the resulting system have an extreme torsional irregularity. p is taken·as I.0 for this r~son.

4-5

4.2 ORDINARY MOMENT FRAMES

Example 4.2.1. OMF Story Drift and Stability Check Given: Refer to t.he root: plan s.hown in Figure 4-1 and the OM.P elevation shown in Figure 4-2. Determine if the frame satisfies lhe drift and stability requirements. The applicable building code speciJies the use of ASCFJSEI 7 for c.a.lculation of loads. The loading and applicable ASCE para.meters are as given previously.

The seismic design story shear, V_., is 11.5 kips.

From an elastic analysis of the structure that _includes second-order effects and accounts for panel-tone deformations, the elastic drift at the top of the story is: 01e =0.980 in. At the base of the structure:

Obe = 0 in.

® ];--:--:--:--:- ,..--,---;-_,... . .,. . . ., ,.....,..--,--...,.--~ ,..-----'----'-:!

l!~'8> --

Solution: Drift Check

CR.- - - -

2-0~~ ::e~:a~~ ~ :e~i:nexamples. For elevation, see Figure 4-2.

"CRi--------!

--

Section 12.8.6 of ASCEJSEI 7 defines che design story drift, .1. as the largest difference of the deflections of \'ertically aligned points at the top and bortom of the story under consideration along any of the edges of the structure. This calculated deflection includes the effects of elastic and inelastic drift, which in this example includes second-order effects. From ASCE/SEI 7 Equation 12.8-15:

::::: CJ(Ore-Obe)

J

6

'~

3(0.980 in. - 0 in.) LOO = 2.94 ill.

:::

Fig. 4-1. O/.fF roofplan.

'•

~!

·'

:·

~-i-----;:;.3~f .~·-0·

[ I•

~: ~-

W18x40 BM-1

30·.o·

W18x40

FromASCEISEI 7 Table 12.12-l, the allowable story drift at level x, 6.a. is 0.020hu. where ltn is the story height below level x. Tl is assumed in this example that t.., can be increased to 0.025h~ because interior walls. partitions, ceilings, and exterior wan sys1ems are designed to accommodate these increased story drifts. ASCEISEI 7 Section 12.12.l.J requires, for seismic force resisting systems comprised solely of moment frames in structures assigned to Seismic Design Category D, E or F. chat the design story drift not e.JCceed AalP for any story. Determine the allow:\ble story drift as follows:

t:.,, p

= 0.025hsr

l.O 0.025(17.0 ft)(12 ioJft) 1.0 = 5. l 0 in. > 2.94 in, o.k.

Fig. 4-2. OMF tlevat-um.

'\

MOMENT FRAMES

I


~

e

Frame Stability Check

Check the maximum permitted

ASCE/SEl 7 Section 12.8.7 investigates potential for instability by use of a stability coefficient. e, calculated as:

The stability coefficient may not exceed 011kn· The ratio of shear demand to shear capacity for the story between levels x and x-1 is ~. Couser'(
P,,D.1,'

(1::::

· VJthnCa where

P.t A

0

(ASCFJSEI 7 Eq. 12.8-16)

1HAt -

o.s

~Cd

<025

t:


- .

.,

0.5 =-1.0(3)

=total vertical design load at and above level x =design story drift occurring simultaneously with V)C

I; I

':.

=0.167 ~ 0.25

ft ::: s~ismic importance factor Vx ::: seismic design story shear acting between levels .t and x-1 hu ::::: story height below level :c Cd deflection amplification factor

The adjusted stability coefficient satisfies the maximum:

0.0666 < 0.167

=

o.k.

Tue moment frame meets the allowable story drift and stability requirements for seismic loading.

ASCE/SEl 7 does not explicilly specify load factors to be used on the gravity loads for determining P.,. except Section 12.8.7 does specify that no individual load factor need exceed LO. For this example, the load combination use
Example 4.2.2. OMF .Column Strength Check Given:

to

Refer Column CL-1 in Figure 4-2. Determine the adequacy of the ASTM A992 W12x35 column for the.following loading. The required strength of columns should be determined in accordance with AISC Seismic Provisions Section Dl.4a. The applicable building code ~i specifies the use of ASCEISEI 7 for calculation of loads. ~, 1

The total vertical design load is:

Px = 120 ft(75 .0 ft)[l.0(15 pst)+ 0.2(20 psf)] / 1,000 lb/kip

Tue governing load combinations that include seismic effects are:

=171 kips

1

;

LRFD ., ASD I :;i 1--L-RFD--L-oa_d_C_o_m_bi-n-au-·o_n_5_fr_o_m_ __ -+-_A_S_D_Lo-ad_C_o_m_b_in_a_ti_o_n_6_f_ro_m _ __ --1I

The stability coefficient, e. from ASCE/SEI 7 Equation 12.8-16 is:

l :·.

= 9

171 kips(2.94 in.)(1.00) 11.5 kips(l7 .0 ft)(12 in./ft)(3)

ASCE/SEI 7 Section 12.4.2.3 (1.2+0.2Sos)D+pQE +0.5L+0.2S

=0.0714 Because a second-order analysis was used to compute the story drift, e is adjusted as fellows according to ASCE/SEI 7 Section 12.8.7 before checking 0,,_.

J.

ASCE/SEI 7 Section 12.4.2.3 (l.0+0.10Svs)D-t:0.525pQE

I"':;

+H+F+0.75L +0.75S

(including the permitted 0.5 factor l in Section 12.4.2.3)

\.

i~ 1 ...;::

L---------------L-------------~

e 0.0114 = 1+ e 1+ 0.0114

t;

From a second-order analysis including the effects of P-6 and P-o effects as well as th: reduced stiffness require
=0.0666

ASD

LRFD

Per ASCE/SEI 7, if 0 from a first-order analysis or 0/(1+9) from a second-order analysis i:s less than or equal to 0.10, second-order effecis need not be considered for computing story drift. Note that whether or not second-order effects on member forces must be considered per ASCE/SEI 7 has to be verified, as it was in this example; however, Chapter C of tbe AlSC Specificarian requires second-order effects be considered in all cases.

v..

= 15.2 kips 3.78 kips

Pa V0

M .. U)p

:= 64.3

Ma top = 43.7 kip-ft Ma wt= 0 kip-ft

P,..

=

kip-ft

M,, /xJI:;:; 0 kip-ft

r

~.:,.

=l7.5k.ips

=2.57 kips

MOMENT FRAMf,S

!""" The higher ASD required axial strength compared to LRFD could be explained by the higher • load factor on snow load. S. of 0.75 for ASD versus 0.2 for LRFD.

I[

According to ASCE/SEJ 7, the load combinations including amplified seismic loads (incJml· ing overstrength factor. flo) are:

.,.•...

i ~

From AlSC \fanual Tab!~ 3-2: Lp=5A4 ft L, = L6.6 ft

Lb> Lp~ therefore, the limit state of lateral-torsional buckling applies.

LRFD

ASD

LRFD Load Combinations 5 and 7 from ASCEJSEI 7 Section 12.4.3.2

ASD Load Combinations 5, 6 and 8 from ASCE/SEJ 7 Section 12.4.3.2

( 1.2 + 0.2Sos) D + OoQe + 0.5L + 0.2S

(l.O+O.J4SDs)D+ H +F+0.70 0 Qi::

Mu wp = 64.3 kip-ft

(0.9-0.2Sos)D+ 0 0 Qt + l.6H

(l.0+0.105SDs)D + H + F+ 0.5250.,Q.e +0.75L+0.75S

Mw bet =0 k.ip-ft

=43.7 kip-ft Ma b<>I =0 kip-ft

Quarter point moment-: are:

Quarter point momentS arc:

(including the 0.5 factor on L penniueJ by Section 12.4.3.2)

.;· I

Calculate Cb using AJSC Specification Equation F 1- 1.

(0.6-0.14Sos)D+ 0.7Q.,(k- + H

'. I

P.

=2LO "'"'

I

LRFD

P.

=20.6 ljpo

ASO

M(.t = 12.75 fi) =Mc

=0.75(43.7 kip-ft) =32.8 kip-ft

::: 48.2 kip-ft

From AISC Manual Table 2-4. the material properties are as follows:

C

=64.3 kip-ft

12.5M,,_ -(2.5Mmax+3MA ) +4.\ls +3Mc

b-

1From AISC Manual Thblc I - 1. the geometric properties arc as follows: W12x35 ry

=1.54 in.

ISection El .5a of lhc AlSC Seismic Pro\•isions states that there are no tirnit:ltions on width!O· thickness ratios of members of an OMF, beyond those in the AlSC Specification.

I.

Available Flexural Strength Per the User Note in AlSC Spuificatk>n Section F2. the colwnn has compact flanges and web. The available flexural strength is the lower value obtained according to lhe limit states of lateral-torsional buckling and yielding.

With no interior brace poinL'I, the unbl'3Ced column length is Lt, = 17.0 ft.

C b=

•I

= 12.5(64.3 kip-ft)+3{16.1 k:ip-fi)

l

+ 4 (32.2 kip-ft)+3(48.2 kip-ft) = 1.67

= 43.7 kip-ft

M,IUU

12.5(64.3 kip-ft)

Fu= 65 ksi

.; •'

= 21.9 kip-ft

=0.75(64.3 kip-ft)

Mmax

=5.25 in.

=0.50(43.7 kip-ft)

=12.75 ft)= Mc

Solution:

r,

M(x = S.50 ft) =Ms

= 0.50(64.3 kip-ft) =32.2 kip-ft M (x

ASTMA992 F1 =50 ksi

'

= l 0.9 kip-ft

= 16.1 kip-ft

There are no transverse loadings between lhe column supports in the plane of bending and the columns are considered to be pinned at the base.

,.!~

= 0.25(43.7 kip-ft)

0.25(64.3 kip-ft}

I

tlI

~

M(x = 4.25ft) =M;.

M(.x =8.50 ft) = MB

l~

I ~:

Ma '"P

M(x= 4.25 ft) = MA

erning load combination that includes the amplified sei~mic load is:

,~

ASD

I .Rm

----~ 3 (::J' From the frame analysis, the maximum required ;Uial strength in this column from the gov·

~

4 9

4.2 ORDINARY MOt-ff.NT I RAMES

12.5Mmar

(2.5Mma:1: +3MA

) +4Ms +3Mc

12.5{43.7 kip-ft)

'

=12.5(43.7 kip-ft)+3(10.9 lcip-ft)ll +4(21.9 kip-ft)+3(32.8 lcip ft)

=1.67

Check lateral-torsional buckling using AJSC Manual Table 6-1 with Lb = 17.0 ft and the modification to bx for when Cb> 1.0 (AJSC Manual Equation 6-5).

4-10

MOMENT PRAlv!ES

LR.FD b,,

=0.00766 (kip-ft)-J

$bMn =cb(~)[:J

Because the W12x35 is not included in AISC Manual Table 4-l, use AISC Manual Tab!."' 6-1 co determine the available compressive strength. with KLy = 17.0 fl:

ASD b..

=0.0115 (kip-nr

4.Z ORDINARY MOl\ltENT FRAMES

1

LRFD

Mn =Cb(!)(.!.) Qb 9 bx

61(!)( l 9 o.011s(kip-rtr

=167(!)( I ) · 9 o.00166(k.ip-ftr1

-1

= 194 kip-ft

=129 kip-ft

- ·

1)

Use bM,.

=192 kip-ft

- 0.0113 kips-I

0.00754 kips-•

Mp

-=-

= 192 kip-ft< 194 kip-ft

nb

nb

n1>

=128 kip-ft

Available Axial Compressive Strength

P,

15.2 kips

Pc

133 kips

P, = 17.5 kips Pc 88.5 kips

=0.198

=0.114 Because P,IPc < 0.2, use AJSC Specificarion Equation HI -Ib:

Tue direct analysis method de.scribed in Section C of the AJSC Specification states that the effective length factor, K, of all members-shall be taken as unity unless a smaller value can be justified by ratiooal analysis.

~ +(Mnc + .'rf,,) s l.O

Therefore:

0.114 2

Kx = 1.0 Ky= 1.0

KxLx

=l.0(17.0 ft)(l2.0 in.Ill) 5.25 in.

rx

2Pc

Mex

Because PrlPc < 0.2., use AISC Specification Equ~on ill-lb:

Mey

+(&u kip-tl +o)= 0_392 192 kip-fl

0.392 < 1.0

The slenderness ratios about the strong and wealc axis are:

t·

ASD

LRFD

The unbraced length of the column fur buckling about boch the strong and weak axis is .0 ft. The column has slender elements according to AISC ;\la1111al Table 1-1.

17

I

I

=88.5 kips

Combined Loading Using AlSC Specificarion Section Hl, determine whether the applicable interaction equ tion is satisfied, as follows:

= 128 kip-ft< 129 kip-fl

Use Mn

l

l

ASD

M11

=o.oi 13 kips- •

P,. -= !le p

Check yielding using AlSC Manual Table 3-2.

$bM,. =; $bMp

p

= 133 kips

LRFD

I

ASD

=0.00754 kips- •

p

\ '

!l_ +(Ml'%+ M"):o:t.O 2Pc Mex M" 0.198 +(43.7 kip-ft+ 2 128 !tip-ft 0.440 < 1.0

o.k.

o) =0_440

o.k.

chc~ l:

Alternatively, Section Hl.3 of the AJSC Specification ma; be used for th,e interaction for this column since the column is only S\Jbject to bending about a singie ax.is. The interaction equations in Section Hl.3 would result in a rugher column strength than demonstrat I

t~·

by this procedure.

:~;

=38.9 K1 l 1 =1.0(17.0 ft)(l2.0 in./ft) ry 1.54; in.

=132

governs

1

Required Axial Strength of Column Including Amplified Seismic Loads Determine the required axial compressive strength using load combinations includi amplified seismic loads per Section D l.4a(2) of the AISC Seismic Provisions.

Per Section D.1.4a(2) of the AJSC Seismic Provisions, it is permitted to neglect moments ·

t "

t

the column for detemunation of required strength because the column moments do : t result from loads applied between points of lateral support. ~: A1.t£JUCAN

!J.ISTTIUT1? OP ST£D.. COl'ISTRUCJlON

MOMENT FR.AMES

4--12

Solution: From AJSC M<1nual Table 2-4, the maicrial propenics :ire as follows:

ASD

~c =88.5 kips > Pa = 20.6 !Ops

$cP" =133 kips> P11 = 21.0 kips

ASTh1A992

Fy

Fu Available Shear Strength

LRFD

... ··~

Beam W18x40

ASD

o.k.

Vn,x

n.

=75.0 kips> V., =2 57 kips

rx =7.21 in. o.k.

The W 12x35 IS adequate to resist lhe required strengths given for Column CL-1.

Example 4.2.3. OMF Beam Strength Check Refer to Beam BM- I in Figure 4-2. Determine the :1dequ:1cy of the ASTM A992 Wl 8x40 for the folloY.ing loading. The applicable building code specifies the use of ASCEISEI 1 for c:ilculation of loads. The govemins lo:1d combinations which include ~eismic effects are: LRFD LRFD Load Combination 5 from ASCE/SEI 7 Section 12.4.2.3

.1 .... I·

1:

(1.2+ 0.2Sos )D+pQE +0.5L+0.2S (including the 0.5 factor on L permitte
!·" ~=

r·

~;

ASD

ASD Lo:id Combination 6 from ASCEISEI 7 Section 12.4.2.3 (1.0 + 0. !OSos )D + H + F + 0.525pQe +0.15l+0.15S

From a second-order analysis considering P-a and P-o effects as well :is the reduced stiffness required by the direct :inalysis method. the beam required strengths arc:

..

ry= l.27 in.

AISC Seismic Proi;ision.r Section El.5:1 states that there are no limjtations on widLh-tolhickness ratios of members of ao OMF, beyond those in the AISC Specificarimi. AJSC Seismic Prol-irions Sccuon El.5a also stat.es that there are no requirements for stability bracing of beams or jointS in 01\.fF, beyond those in the AlSC Specificatio11. Available Flexural Strength

Given:

:-

=50 ksi =65 ksi


Using AJSC Manual Table 3-2, the available shear strength for a W12x35 is:

¢YViu = 113 kips> Vu =3.78 kips

4-! l


Per the User Note in AJSC Spccificotion Section F2. the beam has compact flange.~ and web. The available flexural strength is the lower V31ue obtained :iccorcling to lhc limit Slates of lateral-torsional buckling :ind yielding.

Note: The infill befilns or joists are not described m th.is eumple. ll is presumed !hat the combination of these memben. (with suitable connections) and a roof deck diaphragm will provide an au equate lateral br3Ce for the top flange Of this beam. With appropriate detailing, I.he bottom Oange of the beam could also be braced by 1he infill beams or joistS. This i~ assumed to be the case in this example. The unbraced beam length is:

Lo (top flange in compression)= 6.00 ft (spacing of infill beams) Lo (bottom flange in compression) =6.00 ft From Manunl Table 3-2 for a W18x40:

.l.p=4.49ft

L,.=13.lft

Lo> Lp; lheTCforc, the limit :.tale of lateral-torsional buckling applies. ASD

LRFD P., =2.54 kips

M,. = 82.9 kip-ft

v.. =10.9 kips

Pa =0.784 kips Ma = 78.0 kip-ft Va =I 1.8 kips

The top 3Jld bottom beam flanges nre braced every 6 fl by infiJl beams.

Calculate Cb using AISC Specification Equation FJ-1. ASD

LRFD

=78.0 kip-fl

MlfllU = 82.9 lc.ip-ft

M...u

= 67 .0 kip-ft = 52.2 tip-ft Mc 38.3 kip-ft

M,..

""61.0kip-ft

MB

=45.3 kip-ft

Mc

=30.9 k.ip-ft

M,.. MB

=

4-14

MOMENT FRAMES

LRFD

l

-l-15


l

Usjng the AISC Manual Table 6-1 with an unbraced length of 6.00 ft in the weak ox.is, the available axial strength is:

ASD

l2.5Mm
=(2.5Mmax+3.MA

12.5(82.9 kip-ft) -12.5(82.9 kip-ft)+ 3(67.0 kip-ft)l

12.5(78.0 kip-ft) = [2.5(78.0 kip-ft)+ 3(61.0 k.ip-fl)l

+4(52.2 kip-ft)+3(38.3 ldp--ft)

+ 4( 45.3 kip-ft)+ 3{30.9 ldp-ft)

J2.5M-.t +4Ms +3Mc

= 1.42

ASD

LRFD

)

p = 0.00379 kips-I Pn I

= 0.00252 kips- •

p

I

-=-

4'cPn =-

nc

p

p

I

=

=0.00252 l
= 1.50

f 0.00379 kips-I

=264 kips

""397 kips Compute the lateral-torsional buckling strength using AISC Manual Table 3-10 with Lb= 6.00 ft: Combined Loeding

LRFD

ASD

cJ>bMn =Cb (274 kip-ft) = J.42(274 kip-ft) .>:.= 389 kip-ft

M,. =Cb (183 kip-ft) nb

Pc

397 kips

Pr 0.784 l
=0.00297

M,.

Mpx

nb

Qb

P,. + ( Mrx + Mry ) 2Pc Mc., Mey

-=-= 196 kip-ft< 275 kip-ft Use

~

Because Pr !Pc < 0.2, use AISC Specification Equation Hl-lb:

Because P,lf>c < 0.2. use AISC Specijicatio11 Equation HI-lb:

ASD

Use bMn =294 kip-ft

2.54 kips =0.00640

Check yielding using AISC Manual Table 3-2:

bMn =¢bMpx =294 kip-ft< 389 kip-ft

P,

.!!..+(Mrx + Mry)~I.O 2f>c Mex Mcy

~ LO

0.00640 +(s2.9 kip-ft + o) =0_285 2 294 kip-ft

=196 kip-ft

0.28.5 < 1.0

I

ASD

LRFD

= l.50(183 kip-ft) =275 kip-ft

LRFD

\

.0.00297 + (78.0 kip-ft+ 2 196 kip-ft 0.399 < 1.0

o.k.

o) = 0 _399

o.k.

Available Axial Compressive Strength

Available Shear Strength of Beam

The infill beams provide br:icing in the bewl's weak axis and the unbraced length, Ly, is 6.00 ft The beam is not braced in the strong ax.is.

From AISC Manual Table 3-2, the available shear strength for a W18x40 is:

KxLx

1.0(30.0 ft)(l2.0 in./ft) --= rx 7.21 in.

=49.9 K1 L, = 1.0(6.00 ft)(l2 .0 in.lft) r1 1.27 in. =56.7

L

'•

~

_ _ _ _ _LRFD _ _ __ __ _1-_ _ _ _ _ A_so _____ <1>~V,.

=169 kips> V., =10.9 kips

o.k.

V"

n,,

=113 kips > Va =11 .8 kips

o.k.

t

1··

~~

Tue W18x40 is adequate to resist the required strengths given for Beam BM-1. Note that load combinations that do not include seismic effects must also be investigated.

governs

AMIAA:AN lNSTm.ml 01' STEEi.. CONSTRUCT10N

t·

Using AISC Specification Hl, determine whether the applicable interaction equation is satisfied, as follows:

AMERICAN .INST11VTS OF STEF;J. COl"ISTlllJCTlON

Ji

t

The process could be iterated until the shear and moment values converge, but the difference is negligible between the initial calculation and the convergence. For simplicity, us~ this value as the required flexural strength.

3bcJt1t) Rne =0.60(1.l}R Fydcl,. (1+-1

dbdctw

'i

=0.60(1.1)(1.1)(50 ksi)(l2.5 in.)(0.300 in.) x !1 + 3(6.56 in.)(0.520 in.)2

'··

17.9 in.(12.5 in.)(0.300 in.)

!

l

'Therefore. the column panel tone shear strength controls the maximum force lhat can be delivered by the system co the connection, in accordance with AISC Seismic Provisions Section El.6b{b) and Commentary Section EJ.6b(b).

=147 kips LRFD

,•

=147 kips

•;

ASD

Va.,= Rn~/1.5 = 147 kips/1.5 = 98.0 kips

Vue= Rne

:, I

4-19

4.2 OROlNARY MOMENT FRAMES

4-JS

Calculate the corresponding shear for the beam-to-column connection design using AISC Seismic Provisions Section EJ .6b(b}. The required shear strength of the connection is based on the load combinations in the applicable building code that include the amplified seismic load. m detennining the amplified seismic load, tbe effect of horizontal forces including overstrength, Em11, is dctennined from: (Provisions Eq. El -l)

where The required flexural strength is:

ii---1

Lq =clear length of the beam

LRFb M.,.

ASD

=Vue(d11- t1)

=Vae (db -lf)

M,ie

".' 147 kips(ly_.9 in-_-0.525 in.)

=98.0 kips(l7.9 in. -0.525 in.)

=2,550 kip-in.

= l, 700 kip-in.

=30.0 ft(l2 inJft)-12.5 in.

=348 in. Because AISC Seismic Provisions Section El.6b(b) is used, the term 1.IRy1Hp is sub~tituted with M11.e (LRFD} or Mru (ASD) based on the panel Z\'ne strength as calculated. The shear in the column is:

There is also shear in the column due to story shear.

ASD

LRFD .LRFD

ASD Mae Voe=-H l, 700 kip-in. (17 .0 ft)(l2 inJft)

Vu .= M,., • H

2,550 kip-in.

- (17.0 fi)(12 in./ft) = 12.5 lcips

V

?M.,,, V due to Em1r =---

Let

\

- 2(2,770 !tip-in.) 348 in. = 15.9 kips

due to Em>i

2Ma.e =-

lcJ'

I I

2(1,850 kip-in.) 348 fu. ""10.6 kips

-

=8.33 kips

This shear should be added to the panel zone strength to recalculate the required flexural strength, as follows:

ASO

LRFD Miu =(V,,,;+ V.,c)(db -11)

Moe= (Ya•+ Vac)(db-fJ)

=(147 kips+ 12.5 fjps)

= (98.0 kips+ 8.33 kips)

x(l7.9 in.-0.525 in.)

x(l7.9'in.-0.525 in.}

=2, 770 kip-in.

=1,850 kip-in. AMERICAN lNSlTIVT'B OP STm. Co~UCOON

AMERIC»I ~OP SJ'Ea CONSTRUCOON

"{'

4-20

LRFD

ASD

Use ~-in.-diameter ASTM A325-N bolts in standard holes. Cslcuhlle M,.p based on the ~-.in.-diamc1cr A325-N bolt suenglh with Ab = 0.442 in. from I,: AlSC Manual Table 7-1. as follows: 2

Load Combination 6 from Section 12.4.3.2 with f!oQE =E1r.Ji

permitted for certain occupancies and 0.oQs= !:.',,.,;,

V,,-:: (l.2+0.2Sos)D+ Em1t +0.5L+0.2S

=[1.2+ 0.2(0.528}](4.86 kips) + 15.9 kips+ 0 kips+ 0.2(6.49 kips)

P,

=F,.,A.,, = 90 ksi (0.442 in.2) = 39.8 kips

Vo =(1.0+0.105Svs)D+H +F + 0.525EmJi + 0.75L+ 0.75S "' [LO+ 0.105(0.528)](4.86 kips)

+O kips+0.75(6.49 kips)

Mnp

QM,,p= ¢[2P, (U.,)J

= 15.6 kips

End Plate Design .

The design methodology used for 1he moment end-plate connections is taken from AlSC Desigri cfuide 4, Extended End-Plate Moment Connections-Sei~mic and WindApplication.s (Murray and Sumner, 2003). ANSl/AISC 358 outlines requirements and design methodology for prequalified moment end-plate connections for speciaJ and intermediale momeot frames. However, for an ordinary moment frame, the basic design equations and methodol9gy described inAISC Design Guide 4 can be used. Note that Design Guide 4 includes only the LRFD. method and the equations are modified here for ASD.

= 2P,(L.f,,) 2(39.8 kips}

I

x(22.6i~.+19.6 ~- ) +15.1 m.+12.l m.

=

=4,140 kip-in.

I

Q

.0.

2(39.8 kips)

= 0.75

II

ASD

LRFD

+ 0 kips+ 0.525(10.6 kjps)

I

(22.6 in.+ J 9 .6 in. ) x +15.1 in.+12.I in.

I

2.00

= 2,760 kip-in.

4,140 ldp-in. > 2,770 kip-in.

o.k.

o.k.

2, 760 kip-in.> 1,850 kip-in.

l:

Bolts

Figure 4-3 illustrates the configuration ll?d key dimensions associated with thjs type of connection. Continuity plates I

·:;\

(when required)

• •

·1

d/J, rtqd

=

2Miu .1t$F,.,(rdn)

=

'

2(2, 770 kip-in.) rt(0.75)(90' ksi) (22.6in.+19.6 in. ) x +15.1 in.+12.1 in.

=0.614 in.

db, rtgd

=

=. ~

20Mae nF,,, (U,,)

2(2.00)(1,850 kip-in.) 7t{90 ksi) (22.6 in.+ 19.6 in. } x +15.I in.+12.l in.

=0.614 in.

t

tpl

Detemri.ne the required bole diameter, db,,...¢• from AISC Design Guide 4 Equation 3.6 using the bolt spacing provided in Figure 4-4 and ASTM A325-N bolts, as follows: ASD

I ,'·

Based upon preliminary calculations, it was determined that an eight-bolt stiffeoed end-plate connection would be required to make the column flange work in bending.

LRFD

j,

From AISC Design Guide 4 Equation 3.8. the flexural design strength of the connection is:

+O kips

= 23.5 kips

l t·

The value of Fn 1, the nominal tensile strength of 1hc boll, is from AISC Specijicatio11 Thble J3.2 and U,, is I.he srun of h1 through h4·

The controlling load combinations from ASCE/SEI 7 are:

Load Combination 5 from Section 12.4.3.2, including lbe 0.5 factor on L

4-21


MOMENT FRAMl:S

I

l

I I I I .i I I I

• • -• • J.JL

Beam

• •

w I

Fig. 4-3. Conjigurarion for eiglu-bolt stiffened end-plate con11ection.

t.

;·~

l .t

.a..i:.

4-22

,.....

MOMENT 'FRAMES


Determine the required end plate thickness . 22.6 7.00 in.

The required end place lh.ickness is determined from AISC Design Guide 4 Equation 3.JO. The necessary parameters are determined as follows based on Figure 4-4. From Table 3.3 of AlSC Design Guide 4: '

=--

2

"·

in.( 2{1.25 , 1 in.) )+19.6 in.(-2.001-in.)

+15.1

I

s

=}__Jb;i

22.6 in. ( J.25 in.+

2

=!J1.oo in. (4.00in.) 2

·~

;,~

4

in.)) + 12.1 m.. (2. 65 .m.+ 3(3.00 in.)) + 4.00 .m. 4

= 232 in.

=1.25 in.

From AISC Design Guide 4 Equation 3.10, the required end plnte thickness is:

Because d. < s, Case I of AJSC Design Guide 4 applies. From Table 3.3 of AISC Design Guide4: Yp = bplhi(-)+112 (-1]+"3(-l)+ht(.!.)) 1

2

in.)) + 19.6 m.(2.00 .m.+ 3(3.00 in.))

+ {3.00 in.)2

=3.00 in. Pfo =2.00 in. Pfi =2.00 in. de

4

4

4.00111.

Pl>

_______, L~

(3 00

1

in.(-- ) 2.65 in.

2 ( (3.00 +--.+ 15. 1 in. 2.00 in.+

=2.65 in.

...

1 in.(-)+12.1 2.00 in.

2d.

PJo

P/i

ASD

LRFD Ip/, Y
=

s

~I l

=

/1.1 Iq>M,,, $

Ipl.Y<<;.I --

F, y

b yp p

/1.11(0.75)(2,770 kip-in.) 0.90(36 ksi)(232 in.)

·~

::· .

Use a

r.· stiffener

tktyp.

plate. typ. (A36)

;:;i-

:;· I

Total of (16) ~· dia. A325-N bolls (pretensioned)

:•

.·

• •

Wx3•stiffener plates N.S. & F.S. (A36)

%"thick end plate (A36)

• • W18x40 beam

. •· =.3 ~ LJ.:J I

Fig. 4-4. Derailed OMF co1111ec1io11.

nF y

y p

/l.ll(l.67)(1,850 kip-in.)

2.00(36 ksi)(232 in.)

=0.453 in.

=0.554 in.

·~

=

/l.1 lf4Ma,

~-in.-lhick ASTM

A36 end plate.

Size the end-plate stiffener Match the stiffener strength to the beam ~eb·sctength using AISC Design Guide 4 Equation

3.15. ts1. rcqd

=l,.b (-Fyb) Fys =0315 in.(so ksi) 36 ksi

=0.438 in.

Use a ?li6-inAhick ASTM A36 plate for the stiffener. The height of the stiffener is:

It,,::::: Pfa +Pb+ d., =2.00 in.+3.00 in.+l.25 in. =6.25

in.

4-24

MOMENT FRAMP.S

The length of the stiffener is detennined from AlSC Design Guide 4 Equation 2.11. ls1

LRFD

=_.!!!!._

QvV~

tan3o·

w,'4 = 2¢>{0.60)(Fm

6.25 in.

=--1an3o·

=10.8 in. Use Ls1 = 11.0 in. Check for local buckling of the stiffener. The stiffener slenderness ratio is:

4-2S

4.2 ORDINARY MOMENT FR.AMES

ASD .Q V,./0.v

)/Ji

ll'rtq

= 2(0.60)(FE.:a' )/../2 2.00(9.45 kipfm.)/1.50

1.00(9.45 kipfm.) =2(0.75)(0.60)(70 kr.i)/Ji.

=

=0.212in.

=0.212 in.

2(0.60)(70 ksi)/72

Use \4-in. fille1 welds. 1.

I!

Check end-plate bolts for beam shear transfer Per AISC Desi go Guide 4, a conservative check is to assume that only lhe bolts opposite 1he t: compression flange of the beam transfer the shear loads. In this case, this would be a total of (8) ~-in.-diameter ASTht A325-N bolls. From AISC Manual Table 7-1, the available J·. ihear strength of the bolts is: ..

6.25 in. 'Vt6 io.

=---

=14.3

~

The limiliug slenderness ratio from AISC Specificarion Table B4.1 a Case l is: ASD

LRFD

=0.56

29,000 ksi . 36 ksi

\.

~ =n(~)

$Vn =n(
:::: 8(11.9 kips)

:::: 143 kips

=95.5 kips

,i;

=15.9 143 kips> 23.5 kips

14.3 < 15.9; therefore, the stiffener is not subject to local buckling.

o.k.

95.5 kips> 15.6 kips

o.k.

Check compression bolts bearing!tearout per A/SC Specification Section J3.10

Determine type and size of stiffener welds AISC Design Guide 4 st.ates that the weld of this stiffener plate to the end plate :.hould be a complete-joint-penetration groove weld if ts1 >ti in.; therefore, weld the M6-in.-thick stiffener plate to the end plate with a complete-joint-penetration groove weld.

For all eight bolts, the bearing strength' ~vhen deformation at the bolt hole at service load i~

l·

a consideration is:

Rn =2.4dtFu AISC Design Guide 4 states that the weld of this stiffener plate to the beam flange should be capable of developing the shear yield strength of the stiffener plate. For the 'V16-in.-thick ASTM A36 plate:

Vn =0.60FyAgv

1:

(Spec. Eq. 14-3)

=0.60(36 ksi)('V16 in.)

= 9.45 kip/in. For a two-sided fillet weld, cakulate lhe requfred leg size, wr,9 • by setting the available shear yield strength of the plate equal to the available shear slfength of the weld and solving for W~q·

=2.4(3A in.)(* in.)(58 ksi) =65.3 kips/bolt for the s~x inn~r boll~, the tear~ul stren~th when d~fo~ation at the bolt hole at service !oar is a cons1derauon, with le:= 3 10. - 13/16 m. = 2.19 10., is: i 1

.l,.)

R,. = I .2lctF,,

=l..2(2.19 in.)(~ in.)(58 ksi) = 95.3 kips/boll For the two o~tside_ bolts'. the cearoot. sttength ~hen deforma~on ~l the bolt hole at servic"" load is a cons1deraaon, Wllh le = l \4 m. - ( 1¥16 m.)12 = 0.844 in., is:

k

f I ~.J..

MOMENT FR"-MES

4-26

Rn

=1.2/ctF., ><'rrt

LRFD

ASD

Rn 6(65.3 kips)+2(36.7 kips) -= 2.00 n = 233 kips 233 kips> J5 6 kips o.k.

=0.75(6(65.3 kips)+2(36.7 kips)) =349 kips

349 kips> 23.5 Jcips

o.k.

Design of Beam Range-to-£nd-Plate Weld

The beam flange-to-end-plate weld is designed based on the recommcndatjoos of AlSC Design Guide 4. Design tbe weld for the flange force, bu1 no less than ¢Rn or RrJQ given as follows: LRFD R,.

-=

= 0.90(0.6)(50 ksi)(6.02 in.)

=85.3 kips Ffa = M,,, d-t1

..

2, 770 kip-in.

=159 kips Design beam tlangc-to-end-plate welds for a required strength, FJil = 159 kips

!.

159 kips =0.75(060)(70 k"i/Jl)(!.5)(11.7 in.)

2.00(106 lcips) - (0.60}(70 k.sl/"2)(1.5)(11.7 in.)

=0.407 in.

=0.407 in.

Use t'1G-in. fillet welds (two-sided) for the beam t1ange-to-end-plate weld. Design of Beam Web-to-End-Plate Weld AISC Design Guide 4 requires that the beam web-to-end plate weld develop the availabi< tensile yield strength of the web in the vicinity of the tension bolts. 1be aYailable tensile yield strength of the bc:un web anJ required weld size arc:

<

F

¢ 1 T,. =9,F ,.t,.

fa

= 0.90(50 ksi)(0.315 in.)

(0.6)(50 ksi)(6.02 in.)(0.525 in.) l.67 56.8 kips

=l~.2 kip/in.

Wnq

d-t1

J,850 kip-in. 17.9 in.-0.525 in. = 106 kips

=

Design beam flange-to-end-plate welds for a required Slrenglh, Fta = 10§ kips

Effective length of weld available, le. on both sides of flanges: I, =b1+(b1- tw) =6.02 in.+(6.02 in.-0.315 ln.)

=11.7 in. A factor of 1.5 is applied 10 the weld strength because u)e weld is at a 90° angle 10 the load, occording to AJSC Specification Section J2.4, as follows:

T,,

n,

F..,.1.,.

=-·-

n,

=(50 ksi)(0.315 in.) 1.67

=9.43 kip/in.

The t1ange force is:

F ,\.fac ta=--

ASD

LRFD

=

=J7 .9 in. - 0.525 in.

•·. s:

n

Q

x(0525 in.)

The flange force is:

0.6F,.,,b;t1

I I

0.60( FEXX I "2) 1.51~

=¢0.60(F£XX/J2}1.54

ASD

~R,: ¢0.6FyphJIJ < Ffa

'

ASD

LRFD

'"l.2(0.844 111.)(* in.)(58 ksi) - 36.7 kips/bolt

4>Rn

1 .2 ORDINARY \IOMCNT FRAMES

= 2~(0.60FEXX / ./2)1.5

Wreq=

2(0.60Frn/J2)1.5 2.00(9.43 kip/in.} 2[0.60(10 ksi)/ Ji]u

14.2 kip/in. = 2(0.75)10.60(70 ksi)/ J2}1,5

=

= 0.213 in.

=0.212 in.

Use ~-in. fillet welds (two-sided) for !he beM1l web-to-end-plate weld. Column Flange Flexural Strength Wilh no column flsnge stiffeners, AISC Oaign Guide 4 Tuble 3.5 gives lhe following:

.

s=~Jbfc8 = !J6.56 io.(4.00 in.) 2 =2.56 in.

MOM.ENT FRAMES

Pl> =3.00

in.

Wiu1 stiffeners added, AISC ~sign Gujde 4 Table 3.5 provides the following equation:

Psa "" 2.00 in.

Pli

o!.2 ORDil'lARY MOMENT FRAMES

Y, =bi lhi(;)+~(p~)+~(p~ )+~(;)]

=2.00 in.

c ::::: p#() + P.n + tI = 2.00 in.+ 2.00 io. + 0.525 in. =4.53 in.

+

i [hi[;+~ )+~(Pz~ +:b )+h3(Psl 3

From AISC Design G~tide 4 Table 3.5: 6.56 in.

=--2

6 56 1 · in. !22.6in.(-- )+12.1 2 2.56 in. 22.6 in.(3.00 in.+

+12.l

2 + - -4·00 in. +15.I 4.00 2 = 205 in.

2 +--4.00 in.

!

· ~ in.+ 2.56in.)+19.6 in.( 3 ·~ in.+ 4·5

t

(i

in.))

3.00 in.) + I2.1 .m. (2 .56 .m.+___,_ 3(3.00 in.)) +15.lin. (2.02in.+--__ .... 4 4 +(3.00 in.)2

in.)

in.( 3 ·~ in.+ 4 · 5 ~ in.)+12.1 in.(2.56 in.)

g

in.(-

1 -) 2.56 in.

3 .. 00 in.) ., . . 3(3.00 22.6 in. ( 2.56 in. +-- - + l 9.6 m. ·0 - m. + 4 4

1 in.(-)J 2.56 in.

45

:b )+ pgl+

3

l -) + 19 .6 .w. ( - l -) + 15 .1 .m. ( - l -) 22.6 .m. (- 2j6 in. 2.02 in. 2.02 in.

+~i[hi[Pb+i+s)+h2(~ +~J+~( ~ +~)+h4(s)]+~ =

+ ~}~(s+

+ 4.00 in. =239 .in.

in.

+ - --

From AJSC Design Guide 4 Equation 3.21, the available strength of ~e stiffened column flange is:

From AlSC Desi~ Guide 4 Equation 3.21. the column flange flexural strength is:

LRFD McJ

=0.90(50 k!.i)(205 in.)(0.520 in.f

n

2,490 kip-in.< 2.no kip-in.

n.g.

=F.EY,t}c

l

= 2,910 k.ip-in.

nb

J,660 kip-in. < 1,850 k.ip·in.

Mcf

-

= 0.90(50 ks\)(239 in.)(0.520 in~)

_ (50 ksi)(205 in.)(0.520 in.)2 1.67 ;: 1, 660 kip-fa.

=2,490 kip-in.

ASD

LRFD

~Mc/= qFycY,t}c

ASD

~Mif = ~bF~Y,1}c

n.g,

2

Q

F~YctJc 0& (50 ksi)(239 in.)(0.520 in.)2

Assume the stiffener thickness is

Pso =Psi c-t, ::-2 · 4.53 in.-~ in.

=2.02 in.

t,= !h !n· Then:

t

=--

l.67 = 1,930 kip-in.

2.910 kip-in.> 2,770 kip-in.

o.k.

1,930 kip-in. > 1,850 kip-in.

o.lc.

~:=~~re, the connection will be adequate if stiffeners are added as designed in the fol-

J .....

Therefore, column stiffeners must be added

2

l·

Column Stiffener Plates and Welds The stiffener design is based on lbe minimum strength determined from flange local bending, column web local yielding. and column web local crippling. TI1e minimum available strength based on these limit states will then be subtracted from the required Oange force, Ffa or Fto• to determine the stiffener .required strength. Calculate the available flexural strength of the flange using the available flexural srrength of the unsti.ffened column determined previously.

u.

,, __, MOMENT FRAMES

LRFD

~}ft)

4 2 ORDJNARY MOMl'"iT FRAMES

ASD

LRFD

ASO

'

I~

~R,. = QJfc1

R,,

-=

2,490 kip-in. 17.9 in.-0.525 in. 143 kip$

~

!

Fcu =Flit -min(¢R~}

n n(d-rJb)

d -If!>

(

Met

=159 kips

l,660 klp-in. 17.9 in.-0.525 in. =95.5 kips

= 69.0 kips

Calculate the available column web local yielding strength opposite lhe beam flange from AISC Design Guide 4 Equation 3.24. The parameter, C,, is 1.0 because the distance from the top of the beam to the top of the column is greater lhan or equal to dl2 of the column.

R,,

ASD

LRFD P. - Fa,

P. _Foo "- 2

The available column web local yielding strength is: ~:

=46.0 kips

The required axial strength per stiffener is:

={1.0(6(0.820 in.)+ 2(~ in.)j+[0.525 in.+2f~ in.)]}(50 ks.iX0.300 in.)

= 112 kips

46.0 kips 2 =23.0 kips

= -2-= 34.5 kips

ASO

From AlSC Specification Equation J4-6, the available a.'tial strength per stiffener with ~

R,, = 112 kips Q J.50

=112klps

a-l

69.0 kips

LR.FD $R,. = 1.00(112 kips}

-min(95.S, 74.7. 60.0) kips

Use 1h in. x 3 in. ASTM AJ6 stiffener plates with 'A-in. clips along the flange on both side' of the column web and at Lhe beam top and bouom flange.

=[c, (6~c.de' +2tp )+ Njf)..,.clwc

~=~ ,,S:

=106 lc.ips

-min(143, 112. 90.0) kjps

=

=

F.,=Ffe-min(~)

,:..in. clip is:

=74.7 k.ips

ASD

LRFD Calculate the colu1nn web local crippling avrulable strength opposite lhe beam flange force. The fl3llge force applied from the lop of the beam is located more than lhe hsJf lhe column depth from I.be end of lhe column; therefore use AJSC Specificotio11 Equation JI 0-4.

r

R" :0.80'!!1+3[~][:; r::-1 ..

,.

= 0.90(36 ksi)(lh in.)(3.00 in.- 3.4 in.)

n

=F_..tpbp n _ (36 ksi)(1h in.){3.00 in. - ¥- in.) 1.67

=36.5 kips

=24.3 kips

(Spec. Eq. JI0-4)

= 0.80(0.300 in.)2!1+3(0.525.in.)(0.300 '."·)1.$1 12.5 ID. 0.520 lD.

""

P,.

¢P11 =~Fytpbp

29,000 ksi(50 ksi)(0.520 in.) 0.300 in.

36.5 klps > 34.5 kips

o.k.


o.k.

From AISC Specification Equation J4-3, the available shear strength along the column web :!

= 120 kips

ASD

LRFD ¢R,,

=0.75(120 kips) =90.0 lcips

Dctermfoe the suffener required ~1rength.

Rn _ 120 kips n 2.00 =60.0 kips

ASD

LRFD

The available column web local crippling strength is:

Vn _ 0.60F)plplp

c>V,. =~0.60Fyptplp

n

= 0.90(0.60)(36 k.si)('h in.)(10.0 in.) = 97.2 kips

97 .2 kips> 34.5 kips

o.k.

n (0.60)(36 ksi)(lh in.)(10.0 in.) l.67 =64.7 ~ps


o.k.

4-32

MOMENT FRA:-.1ES

The value of Ip= 10.0 in. is based on lhe length of concact of the stiffener places includ· ~ lh · required · ' mg a red uc t'ion ior e comer clips to avoid the k-area of lhe column.

=3.00 in._ ~in.= 2.25 in.:

According to AlSC Specification Section 12.4, with bp

LRFD

ASD

Pu .

=

:/im)

06 29( ·

"°'rrqd

OP,

=

)bp (l .5)

a

2 (0.6(Fax )) bp(I.5)

J2

34.5 kips

= 2(0.75)[

2.00(23.0 kips)

=

06

· (~ ksi) )(2.25 in.)(1.5}

2{ 0.6($ ksi)1(2.25 in.)(! .5)

=0.229 in.

=0.229 in.

Use 1-4-io. fillet welds (two sided). Weld of Stiffener to Column Web

According to AISC Specificario11 Section 12.4:

LRFD Wreqd:::

Pu 0 60 29( ·

!f{J()())(1.0)lp

=

34.5 ldps

2(0.75)[ 0.60~ ksi~J(l.0)(10.0 in.)

=0.0774 in.

ASD w

QP0

_

r.qd -

2

(

Jiexx )J(l.O) tp

0 60(F.

.

_ 2.00(23.0 kips) .- 2 10.60(70 ksi)I p.0)(10.0 in.)

Ji

= 0.0774 in.

1

Use ~·in. fillet welds (two sided). Based·on AISC Specification Table J2.4, a 3/Jrin. fillet weld is acceptable; however, 'A-in. fillet welds a.re used to be consistent with the stilJenerto-column flange welds. The fully detailed end-plate connection is shown in Figure 4-4.

4-J..I

1

'·

4.3 SPECIAL MOMENT FRAMES (SMF) AND INTERMEDIATE MOMENT f:RAMES (IMF)

-

Weld of Stiffener to Column Flange

Wr.qd

4.3 SPECIAL MOMENT FRAMEs AND INTERMEDIATE MOMENT FRAMtS

k

f Special moment frame (SMF) and intermediate moment frame (WF) systems, which are addressed in AJSC Seismic Provisions Sections E3 and E2, respectively, resist lateral forces and displacements lb.rough the flexural and shear sirenglhs of the beams and columns. Lateral djsplacement is resisted primarily through the flexural stiffness of the fr:uning members and the restraint of relative rotation between the beams and columns at the connections, or "frame action." S~1F and IMF systems must be capable of providing a story drift angle of at least 0.04 rad per AJSC Seismic Provisions Section E3.6b and 0.02 rad per AJSC Seismic Provisions Section E2.6b, respectively. An overview of SMF behavior and design issues js provjded by Hamburger et aJ. (2009). SMF and IMF systems tend to have larger and heavier beam :md column sizes Utan braced-frame systems, as the beAms and columns are often sized for drifc control rather t.han for srrength. The increase in member sizes and related costs, however, may be acceptable based on the increased fle."
t

t:

f;:

l!i

AMEIUCAN INSTITUTE OF STW.. CONSTIUJCTJON

4-34

MOMENT FRAMES

anticipated to achieve jneJasticity lhrough pl!IStic rotation in the beam, al lea.st 75% of the acrual deformation must occur in the beam·hlnge l~tions when tested. _ _ Currently, there ;ire cwo primary methods used 10 move plastic hlngjng of the beam away from the column. These two methods focus on either reducing the cross-sectional properties of the beam at a defined loc;ition away from the colunu1, or special detailing of t.he beamto-column connection in order to provide· adequate strength and toughness in the connection 10 force inelasticity into the beam just adjacent to the column flange. Reduced beam section (RBS) connections are typically fabricated by trimming the flanges of the beams at a short distance away from the face of the column in order to reduce the beam section properties at a defined location for formation of !he plastic hinge (figure 4-6). Research has included a straight reduced segment, an angularly tapered segment, and a circular reduced segment. A higher level of ductility was noted in tl1e latter, and the RBS is typically fabricated using a circular reduced segment.

i·

i11 · i

ANSI/AJSC 358 includes six prequalified SMF Md IMF connections, iocludjng the reduced beam section illustrated in the examples. Each of these prequalified connections has a design procedure similar to that employed in faample 4.3.4. Designers should evaluare the requirements of their project, the abilities of local fabricators and erectors, and rhe relative cost-effectiveness of different beam-ro-column connections to determine the most appropri· ate connection for a given project. Special connection detailing for added toughness and strength takes many fonns using both welded and bolted connections. In many of the connections, both proprietary and non~ proprietary, such factors as welding proc~es. weld-access-bole detailing, web-plate attachment and flange-plate usage have been considered. For additional infonnation on the ·specification of chese connections, see ANSI/AISC 358 in Part 9.2 of this Manual. Panel zone behavior is difficult to predict and is complicated by the presence of continuity plates and doubler plates, as well as k-area toughness. Three basic approaches are most

43 SPECIAL MOMENT FRAMES AND rNTERMEDTArE MOMENT FR.AMES

commonly used: "strong panel," "balanced panel" and "weak panel ... These three terms relate the strength and inelastic behavior of !he panel in relation to the strength and inelastic behavior oft.he framing members in I.he connection. In a "strong panel," the panel-zone strength is greater than the' surrounding framing components to the point where the vast majority of the inelastic deformation of the frame occurs in the beam. In a "weak panel," the ~trength of rhe panel-zone is low enough relative to the framing members such that the majority of the inelastic deformation of the connection and frame occurs in the panel zone. A "balanced panel" falls between the strong and weak panel, where inelastic defonnation in the framing members and panel zone are similar. The requirements in the AJSC Seismic Provisions generally provide for strong or balanced panel zone designs in S~1F. The full range of panel zone designs are permitted for IMF and OMF. Another consideration ill the design of SMF systems is rhe concept of "strong columnweak beam." The AISC Seismic Provisions provide for the proper proportioning·of the frame elements in Equation E3- l.

* EMpc

--*->l.0

(Provisions Eq. E3-1)

t.Mpb · where

:C =sum of the projections of the nominal flexural strengths of the columns (includ-

EM

ing haunches where used) above and below the joint to the beam centerline with a reduction fQr the axial force in the column

CO

I

h

I'"

L I

.::

Plastic hinge wnes. Hinge locations vary depending on connection type .

'

~:

v

.

Reduced beam secticin

..... K

,,~:

+

r 1.

·'· 1.

~.

~:

fig. 4-5. Areas where inelasric deformation may be expected.

Fig. 4-6. Reduced beam sectwn (RBS) connectiorL

MUM!:.Nl M
4.3

S~F.CIA1- MtJMI

JI.I I t'KA.\\t:. ANU lN I tKMl:.L'll\I c ...v ..........., ... .......

I '£M;i, =sum of the projcc1io11s of the e."'pected Oexurnl strengths of the beam at the plastic hinge locations to the column centerline

7_30·.o·

This provisfon is Mt intended 10 elimmate all yielding m the columns. Rather, as described in AISC Seismic Provisio11.s Co~ntary $et;tiOn E3.4a. it is intended to result in framing systems that h11\'e distributed inelasticily in large seimuc events, and discourages story mechanisms. The prim11ry difference between SMF systems and IMP systems is the interstory drift angle capadties. While this requirement differs for SMF and JMP systems. there nre many requirements that are similar between the two frame types. This comparison is summarized in Table 4-1 of th.is Manual located at end of this Part.

3

2

30•-0• --+-_=....::;..--+..r.i ..

l:i.....- - - -.....c8>

30·~~r '41-:i

l<

!:!

t

the

SMF Design Example Plan and Elevation The following examples illustrate the d~ign of special moment frames (SMF) based on AlSC Seismic Pro1 is ions Section E3 Design of intennediate moment frames (IMF) reflects requirements outlined in AlSC Seismic Pro'l:isions Section E2 that are. in most instances, similar to those in Section E3 or that do not vary from frame design requirements in the AISC Speciftcatio11. For this reason, Part 4 does not present examples that focus exclusively on IMF, although these examples should prove useful when designing IMP frames as well. Table 4-1 in this Manual compares the significant design requirements for OMF, IMF and SMF systems, and clarifies which portions of the SMF examples apply to l.MF design. The plan and elevation are shown in Figure 4-7 and Figure 4-8, respectively. The code>:pecified gravity loading 1s as follows:

= 85 psf = 68 p~f Drocf = 80 psf LoJIO<>r =50 psf (reduced) lftoo, s = 20psf Curtain wall = 175 lb/ft along building perimeter at every level

I·...

\; Fig. 4-7. SMF floor plan.

l·

I

DJ!t>«

2

30·-0·

0

30·-0·

30'-0"

W21x44

W21x44

I:

I \

For the S}.IF examples, it has been detenruned from ASCE/SEI 7 that the followmg factors are appJjcable: Risk Category I, Seismic Design Category D. R = 8, 0 0 3.Cd 5'12, le= LOO, Sos= JO, and p l.O(per ASCE/SEJ 7 Section 12.3.4.2, p = 1.0 if the story resists more lb.an 35% of the base ~hear in the direction of interest, loss of one bay of SMF wilJ not result in more than a 33% reduction in story strength, nor does the resulting system have an extreme torsional im:gularicy).

=

W21x44

Roor

4

3

=

=

Fourth 0 Level

-

v

~

W24x76

Third

0Level

..,... W24x76 ..,. -----------i )(

..·

W24x76

,.._

'° •l----'"'----------r--

N

Second 0Level

Example 4.3.1. SMF Story Drift and Stability Check Given: Refer to the floor plan shown in Figure 4-7 and the SMJ: elevation shown in Figure 4-8. Determine if the frame satisfies the ASCE/SEI 7 drift and stability requirements based oo the given loading.

~ )(

W24x76 >< -'<\I-+-_.:.=..;=..::"-BM-1 ~ JT-1

~. Column splice 48• aboVe rinlshed lloor (typ.) Fig. 4-8. SMF elevation.

The applicable building code specifies the use of ASCFJSEI 7 for ca.lculatioo of loads.

. ..

n

4-38

MOMENT FRAMES

TI1e seismic design story shear at the third levels, Vx. is 140 kips as defined in ASCE/SEI 7 Section 12.8.4. From an elastic analysis of the structure that includes second-order effects and accounts for panel-z~ne defom~tions, the maximum interstory drift occurs between the third and fourth levels: Ox• 04• - 03, 0.482 in.

=

=

In this example, the stability check will be perfonned for the third level. This checks the stability of the columns supporting the rhird level. The story drift between the second and third levels is OJe - Oi. "= 0.365 in.. Solution:

From AlSC Man.ual Table 1-1, the geometric properties are as follows: W24x76

b1=8.99 in. Reduced beam section (RBS) connection~ are used at the frame beam-to-column connections and the t1ange cut will reduce the stiffness of the beam: Example 4.3.3 illustrates the design of the RBS geometry and the flange cut on one side of the web is c = 2 in. Section 5.8, Step I, of ANSl/AISC 358 states that the calculated elastic drifr, based on gross beam section properties, may be multiplied by 1.1 for flange reductions up to 50% of the beam flange width in lieu of specific calculations of effective stiffness. Amplification of drift values for cuts less than the maximum may be. linearly interpolated.

~11

For bt= 8.~9 in., the maximum cut is:

0.5(8.99 in.)= 4.50 in.

.\ 3 SPECIAL MOMENT FRAMES AND INTERMEDIATE MOiii.ENT FRAMES

4-39

mass at the top and bo11om of 1hc story under consideration, which in this case is the third level. 0

=Cdou

(ASCE/SEI 7 Eq. 12.8-15)

le

5'h(0.525 in.) LOO =2.89 in.

From ASCFJSEl 7 Table 12.12-1, the allowable story drift at level x, f:..a, is 0.020/ts_r. where hu is the story height below level x. Although not assumed io this ex.ample, 6.a can be increased to 0.025hsx if interior walls. partitions, ceilings and exterior wall systems are designed 10 accommodate these increased sLory drifts. ASCFJSEI 7 Section l 2. l 2.1.1 requires for seismic force resisting systems comprise
t. 0.020/ru -0= - -"p p 0.020(12.5 ft){12 in./ft) = 1.0 =3.00 in. D. 2.$9 in.< .\a o.I<.

=

The frame satisfies the dlifl requirements.

Thus, the total 4-in. cut is: 4.00

in.) =88.9%· of the maximum. cut m.

. l 00 (~O 4 ...1

The calculated elastic drift needs to be amplified by 8.89% (say 9%).

Frame Stability Check

ASCE/SEI Section 12.8.7 provides a method for the evaluation of the P-6 effects on moment frames based on a stability coefficient, 0, which should be checked for each floor. For the purposes of illustration, this dt=tmple checks the stability coefficient only for the third Jevcl. The St:ibility coefficient, 9, i~ determined as follows:

Drift. Check

(ASCE/SEI 7 Eq. 12.8-16)

From ·an elastic analysis of the strucrure that includes second:.Order effects, the maximum interstory drift occurs between the lhird and fourth levels. The effective elastic drift is:

Ou

AJk><>r =A,.qq1 a75ft(J20 ft)=9,000 ft

=04e -03,

Dfio<>r

=0.482 in.

2

=9,000 ft2 (85 psf) /l,000 lb/kip =765 kips

Ou IUJS =l.090xe

=1.09(0.482 in.)

DIWf =9,000 ft2 (68 psf)/(1,000 lb/kip) =612 kips

::::0.525 io. Per the AlSC Seismic Provisio11s Section Bl , lhe design story drift and the story drift limirs are those stipulated by the applicable building code. ASCE/SEI 7 Section 12.8.6 defines the design story drift, t:., computed from o_., as tbe difference in the deflections at the center of

D....011

=175 lb/ft (2(75 ft+I20 ft))/ (l,000 lb/kip) = 68.3 lcips per level

Lftoor =9,000 ft2 (50 psf)/(1,000 lb/kip)

=450 lcips AMERJCN'I lNSlnvre OF STEEL CONSTRucnON

MOMENT FRAMES

43 SPECTAL MOMF.NT FRAMES AND INTERMEDIAT6 MOMENT FRAMES

4-41

l I

f' I

4=1 = 9,000 ft 2 (20psf)1 (i.ooo lb/kip)

Therefore, the stabiUty coefficient is:

=180 kips A~~E/SEI 7 does not explicitly specify load faciors 10 be used on the gravity loads for determmmg Px, except that Section 12.8.7 does specify that no individual load factor need exceed 1.0. This means that if the combinations of ASCE/SEl 7 Section 2.3 are used, a factor of J .O can be used for dead load raLher than the usual 1.2 factor used in the LR.FD load combination •. for example. This also means that the vertical component 0.2SosD need not be con~1dered here. T~erefore, for this example, the load combination used to compute the toL'll ve~cal load on a given story, P;., acting simultaneously wilh the seismic design story shear, Vx. is l .OD.+ 0.5l based on. ASCE/SEI 7 Section 2.3 includfog the 0.5 factor on L permitted by Sect10n 2.3. where l 1s the reduced live load. Note that consistent with this the same

co~bination was used in the second order analysis for this example for the purpo;e of computmg the fundamental period, base shear, and design story drift. The total dead load in the columns supp-0rting the third level, assuming rlm 1be columns supp-0rt cwo floors of curtain wall in addition to other dead loads, is: l.OPv

=l.0(612 ldps + 2(765 kips)+ 2(68.3 kips)] =2,280 kips

140 kips(12.5 ft)(12 inlft)(51h) =0.0535

Because a second-order analysis was used 10 compute the story drift, 0 is adjusted as follows to verify compliance with 0ma.r. per ASCE/SEI 7 Section 12.8.7.

0 1+0

I.,

0.0535 l+0.0535 =0.0508

According to ASCE/SEI 7, if

e is less than or equal to 0.10, second-order effects need not

be considered for computing story drift. Note that whether or not second-order effects on member forces must be considered per ASCE/SEI 7 has to be verified, as it was in this

example; however, Chapter C of the AlSC Specification requires second-order effects be considered in all cases in the analysis used for member design.

Check the maximum permitted e

The total live load in the columns supporting the third level is:

?-512 =

r

1,820 kips(2.I9 in.)(1.0)

0

~.5[(2)(450kips)+180 kips]

The stability coefficient may not exceed 0mo.x. In detennining 0 111 ax. Pis the ratio of shear demand 10 shear capacity for the level being an::ilyzed, and may be conservatively t:iken as LO.

= 540 kips

(ASCE/SEI 7 Eq. 12.$-17)

TI1erefore, the total vertical design load carried by these columns is:

=---

Px = 2,280 kips+540 kips = 2,820 kips

1.0(5~)

.Ii··'

= 0.0909 ~ 0.25 I

The seismic design story between the second and third level, including the 9% amplification on the drift, is: . ·

The adjusted stability coefficient satisfies the maximum: 0.0508 < 0.0909

~= Cdou I,, = 5'h(L09X0.365 in.) LOO =2.19 in.

(from ASCFJSEI 7 Eq. 12.8-15)

o.k.

The moment frame meets the allowable story drift and stability reqUirements for seismic loading.

Comments:

From an elastic analysis of the structure, !he seismic design story shear at the third level under lhe s.tory drift loa~ing using the equivaleht lat.era! force procedure is Vx = 140 kips and the floor-to-floor heJght below lbe third level is hsx 12.5 ft.

=

'i

There are a total of six bays of SMF in this example. Considering the relative expense of · SMP connections and because the drift and stability limits are met, it may be more cost- ~. effective to reduce the number of bays to four, and increase member sizes to satisfy the "-' strength and stiffness requirements.

4 42

MOMENT FRAMES •

•· • ·f 0"1ENT FRAMES ANO J~:.RMEDIA'TE MOM£NT !'RAMES 4.3 srFOA... ·~ "' •

.µp

The governing load combinallOn~ for axial and Oexural sLrtngth that include seismic effects ("'

Example 4.3.2. SMF Column Strength Check Given: Refer to Column CL-1 oo the firs1 level in Figure 4-8. Determine the adequ:icy of the ASTM A992 W14x176 to resist the loads given. There is no transverse loading between the column suppol1~ in the pl:mc of bend1ng. The applicable building code specifies the use of ASCEISEI 7 for calculation of loads. The required streng1hs are determined by a second-order analysis including 1he effecLS of P-8 and P·li with reduced stiffness 3S required by the direct analysis method. The governing load combinations for shear that include seismic effeclS are:

from ASCEJSEJ 7 are:

----- LRFD

ASD

-

LRFD Lo;id Combin:\lion 5 from ASCE/SEl 7 Sc.:tion 12.4.2.3 = (l.2 + 0.2Svs )D + pQE

Pu

ASD

LRFD Load Combinalion 5 from ASCE/SEI 7 Section 12.4.2.3 V11

=(J.2+0.2Sos}D+pQ£


V.,

+ 0.SL+0.2S

=(1.0+0.J4Svs )D+ H + F +0.1pQe =22.4 kips

=32.0 lcips

P0

+0.5L+0.2S

=243 kips =(l.2+0.2Sos)D+pQE

M.,

+0.5L• 0.2S

LRFD

ASD Load Combination 6 from ASCflSEI 7 Section 12.4.2.3

Mut<•P

= 125 kip ft

Mu/KJI

=-298 k1p·fl

,'.f 0

= (1.0+0.JOSvs)D+JJ+F + 0.525pQE +0.75L+0.75S

=2 14kips = (l.0 +0.IOSDs)D+0.525pQ£

+ 0.75L + 0.75S

=

M0 '"'P 67 .0 lop-ft Mat-or= - 158 kip-ft

Solution: From A1SC Manual Table 2~. t11e material properties are as follows:

ASTh1 A992 Fy =- 50 ksi F,, = 65 ksi

(including the 0.5 factor on L permitted in ASCEISEI 7 Section 12.4.2.3)

From .A.ISC Jfamwl Table 1-1. lhe geometric properties are :is follows: AJSC Seismic Pro1;isions Section DI Aa re~uires, with limited exceptions, that che SJJlphfied seismic load (i.e., lhe seismic load multiplied by the overstrength factor, 120 ) be used to calculate required column axial strength. Moment need not be combined simultaneously w ith the amplified seismic 3.'
LR.FD :·'

!.;.

ASD

LRFD Load Combination 5 from ASCE/SEI 7 Section 12.4.3.2

P. =(l.2+0 .2Svs)D+ftQe +0.5L+0.2S

=249 kips

.

.

ASD L03d Combination 6 from ASCEISEI 7 Section 12.4.3.2 P.,

=(l.0+0.105SDS)D+ H tF + 0.525Q.Qe +0.75L•0.75S

=218 kips

Column W14x176

d - 15.2 in. A ::: 51.8 in.2 Zx= 320 in. 3 hit..,= 13.7

in. rx= 6.43 in.

lw= 0.830

oi= 15.7 in.

/_. =2,140 in.'

1, = 838 in.'

r1 =4.02 in. y= l.31 in.

kde: = 1.91 in.

s.. = 281 io.3

bJl21r 5.97

Beam W24x76 2,100 in.'

1..

=

Column Element Slenderness AISC Seismic Provisio11s Section E3.5a requires that the stiffened and uns_tiffened elements of SMF columns ~atisfy the requirements of Section DI. l for highly ducule members.

4-44

MOMENT FRAMES -.,..

From the AJSC Seismic Provisions Table D l .1. for flanges of highly ductile members:

AJuJ = 0.30

II

v

.~.

= 5.97 < ANJ, the flanges

satisfy the requirements for highly ductile

elements. The limiting width-to-thickness ratio for webs of highly ductile members is determined as follows from Table Dl. l using the goveming load case for axial load, including the amplified seismic load, as stipulated in AISC Seismic Provisions SecLion D l.4a:

LRFD

K1 L"

=0.141

Because C0 S 0.125,

1.0(14.0 ft)( 12 in./ft) 4.02 in.

f.

governs

l

1.67(218 kips)

QcP,.

Becaure Ca > 0.125,

JI (

1- 0.93C,,)

"J...,,d =

29,000 ksi SOksi [1-0.93(0.107)]

O.nJI

=0.77

F1

(2.93- Ca)
JI Fy

/29 000 k~i ;Oksi (2.93-0. 141)
50 ksi =51.7 ~ 35.9

..

= lilt..., =

ASD

LRFD

(50 ksi)(5 J.S in.2)

=53.l

elements.

1.0(14.0 ft)(l2.0 in.!ft) 6.43 in.

Using AJSC Manual Table 4-l, with K1 L1 = 14.0 ft, the available compressive strength of the W14x176 column js:

F)·Ag

= 0.107

Because A.

KxLx

--= rx

-;:;- = =41.8

= -=

=2.45

Available Compressive Strength Determine v.hat the controlling slenderness ratio of the column is:

l.67?.,

kips = 0.90(50249 ksi)(51.S in.2 )

Fy

K1 =l.O

=26.l

OcPo Ca = - Py

P., 0.90.F).Ag

~ 2.45

Kx =1.0

ASD

Pu Ca =-$cPy

'Ahd

J

The direct :malysis mefriod in AISC Specification Section C3 states that the effective length factor K of all members shaU be taken as unity unless a smaller value can be justified by rational analysis. Therefore,

= 0.30 /29,000 ksi 50ksi =7.22

=

Effective Length Factor

VF;

Because A. = b112fJ

4.3 SPECIAL MOMENT FRAMES AND INTER.MEDIATE MOMENT FRAMES

Use 'AM= 51.7.

13.7 < Ahd, the web satisfies lhe requirements for highly ductile

=2,050 kips> 249 kips

P,.

nc

=1,360 kips> 218 kips

o.k.

Available Flexural Strength 1 From AISC Manual Table 3-2, determine'. for the W14x176 whether the limit state of lat· eraJ-torsional buckling applies for flexutil strength, i.e., Lb> lp.

,. I

Lp =14.2 ft Lr= 73.2 ft 4 =14.0 ft
f

LRFD

Alternatively, Table 1-3 -in lhis Manual can be used to confirm that members satisfy the requirements for highly ductile members.

o.k.

Mex= $bMpx =1,200 kip-ft

ASD

... M

_Mpx C< -

!4

1; ....

.=798 kip-ft 0

•.\MEJuc..v.I lNSTJl'VTE OF SrEE.. COHS'flll!CTION

r,J

I',,. t

4-47

4 3 SPECIAi.. MOl'-tENT FRAMES AND lNTI'J~ME.OL\113 MOMENT FRAMLS

1f

Loadi~g

Combined · . .:) Check the mtc:racuon of comprei;sion and flexure using A!SC Spuijication Section H 1. 1, ~ and the governing load case for combined loading. l ';! }.1 3...

,. ...

ASD

LRFD

.

,,

·:

.

The applicable building code specifics the use of ASCPJSEJ 7 for calculation of loads. The rcqujred )trengl.M at the face of the column and the centerline of the. RBS ti.re dct~incd by i;ec<)nd-order analysts including the effects of P-& and P-ll wnh reduced stiffness as 3

required by the direct analysis method. Tue governing load combinations for the requiml flexural and shc:ir ~trenglh al the face of the column are:

243 kips P, -= P, 2,050 kips =0.119<0.2

P, Pc

214 kips 1,360 lcips

Therefore, use AISC Spedfic<:lio11 Equation HJ ·I b

Therefore, use AlSC Specification Equation Hl·lb

..

=0. 157 <0.2

ASD

LRFD

ASD Load Combination 5 from ASCEJSEl 7 Section 12.-t.2.3

LRFD Load Combination 5 from ASCFJSEI 7 Sc.ction 12.4.2.3

.\ f0

JJ., =(I 2+ 0.2Sos )D+pOt P,

2Pc 0.119 2

(Mrs M,.,) +-+-· +( + Mrx

M.;y

298kip-ft l, 200 kip-ft

0.308:::; 1.0

::01.0 0)- 0 308 - ·

+0.7pQE

+0.5L+0.2S

(M

P, 2Pc

+ _.!!.+-2.. M ) s 1.0 Mex Mey

0. 157 2

+( 798 158 kip-ft 0 )- 0 276 kip-ft + - ·

0.276:::; LO

o.k.

=(t.0 + 0.14Sos )D + fl + F =- 136 kip-fl

=-273 kip-n

v., =(1.2+0.2Sos ) D + pQc

\ 'o

+0.7pQ£

+0.5L + 0.2S

=22.8 kips

=33.8 kips

o.k.

=(1.0+0.l4Sos )D+ 11 + F

.

(including the 0.5 facmr on L permitted in ASCEISEl 7 Section 12A.2 3) Available Shear Strength

Using AISC Manual Table 3-2 for the W14x176 column:

.~!

Face of

ASD

LRrD

column '-..

cpv. =378 kips> 32.0 kips The W14x176 is adequ:ite

to

o.k.

~ = 252 kips> 22.4 kips

o.k.

•..">;

,,

W24x76 beam

C'y

Q:- \

resist the !oads given for Column CL- l.

Comments: The beam and column mes selected were based on a least-weight solution for drift control; thus, the column size is quite conservative for strength.

c = 2.00 in.

I.

2}.ib

= 12.0 in.

t--..-~~~~b~=---"18~·.X-!!.ln~·~~-i

Example 4.3.3. SMF Beam Strength Check

..:· j•

·~

Given: Refer to Beam BM· l in Figure 4 8. Detem1ine lhe adequ~y of I.he W24x76 ASTM A992 W-shapc to resist Lhe following Jo.1dmg. The bc:lm end connections u1ilize the reduced beam section ~S) prequal1fied .in accordance wuh ANSl/AlSC 358 and shown in Figure 4-9. Also, design the lateral bractng for the beam u~ing ASTM A36 angles. Assume that the beam fl::ingcs are braced nt the columns

a= 5)2 in.

Fig. 4-9. Initial RJJS derail for Examples 4.3.J <111d 4.3.4.

MOMENf FRAMES

The governing load combinations for the required flexural and shear strength at the cen1crline of lhe RBS are: !.

LRFD

Mu =(l.2+0.2SDs)D+pili; + 0.5L+0.2S = -246 JOp-ft

ASD

Ma= (l.0+0.14SDS)D+H +F+0.7pQE = - 168 kip-fl

4.3 SPECIAL MOMENT FRAMES Al"ll> INTERMEDIATE MOMENT FRAMES

ANSI/AISC 358 Section 5.3.1 permits calculation of 1he width-to-thickness ratio for the flanges based on a value of bt not Jess than the flange width :it the ends of the cen1er two1.hirds of the reduced section provided that gravity loads do not shift the location of the plastic hinge a significanl dist31lce from the center of 1he RBS. Assuming this is the case bere, the RBS radius of cut from ANSI/AJSC 358 Figure 5.1 and 1he dimensions given in

From ATSC MaJ1ual Table 2-4, the beam ma1erial prope11ies

3Ie

4(2.00 in/ +(18.0 in.>2 = 8(2.00 in.) =21.3 in.

as follows: bf.RBS=

ASTMA992

Fy =50ksi

=65 ksi

W24x76

b1= 8.99 in. hit..,= 49.0

rt= 0.680 in.

s.. =176 in.3

= 0.440 in. 2..: =200 in.3 lw

choose a section that satisfies the dimensional constraints listed below. For this e,,ampJe, trial values of a, band care chosen as shi;:>wn jn Figure 4-9. Example 4.3.4 demonstrates that these dimensions are acceptable. Other dimensions that satisfy the requirements of ANSI/ AISC 358 could have been selected. Dimensii:ins that satisfy the dimensional constraints listed below may still require adjustment to satisfy all of the requirements of ANSJ/AISC 358 Section 5.8.

0.1b111!> c ~ 0.25bbf

in.)2

~

bf.RBS

11.1=-2t1

6.72 in.

,,,

2(0.680 in.)

=4.94

According to the requiremenlS of ANSJ/AJSC 358 Section 5.8, Step I, lhe designer must

0.65d s b ~ 0.85d

(2-3)

=6.72 in.

=

h0 =23.2 in.

RBS Dimensions

O.Sb111s as 0.75bt-J

2(R-c)+b1-2~R2 -(~f

o 99 in.) - 2 (21.3 i·n.)2 -(18.03 = 2(21.3 in. - 2.00 in.)+ (o.

From AISC Manual Table 1-1, the beam geometric properties are as follows: .

=1.18 in. ry =l.92in.

-

At the edge of the center two-thirds of che RBS. th~ reduced flange width is, from geometry:

Solution:

kdts

tl

4c2 +b 2

R = --

The required shear strength at the RBS is not given because the shear at the face of the column is greater than at the RBS and the available shear scrength is the same at each location since the web is not modified by the RBS cut.

d= 23.9 in.

~:

~·; .

Figure 4-9 is:

8c

F..

'. I ....

(ANSI/AJSC 358 Eq. 5.8-1) (ANSUAISC 358 Eq. 5.8-2) (ANS.UAJSC 358 Eq. 5.8-3)

Check Beam Element Slendemess AISC Seismic Provi.sio11s Section E3.5a requires 1h:11 th~ stiffened and unstiffened elements of SMF beams satisfy the requirements of AfSC Seismic Provisions Section D 1.1 for h.ighly

From AISC Seismic Provisions Table DI. J, the limiting flange width-to-thickness rario for highly ductile membe(s is: \

AhJ

== 0.30 =0.30

ff, 29.000 ksi 50ksi

==7.22 Because A/< AJuJ, the flanges satisfy the requirements for highly ductile members. From AISC Seismic Provisions Table D 1.1, for webs of rolled I-shaped sections used as beams or columns, recognizing·tbat C0 = P.,1(9Pn) is assumed to be zero because no a;
ductile members.

AMERICAN lNSTmfTB OF Sn!EJ.. CoNSTRUCJ10N

I;~

•)

·.v

t

\.I;•

4-50

4.'.l SPECIAL MOMENT FRAMES AND lNTERMEDtATE MOMENT FRAMES

'Aird =2.45

[I

'{£~·

29,000 ksi

=2.451---50 ksi

= hit,., ::: 49.0 < Ahd, !he web satisfies the requirements for highly

ductile

Alternatively, using Table 4-2 of this Manual, it can be seen that a W24x76 will satisfy the width-to-thickness requiremenLs for an SMF beam.

Spacing of Lateral Bracing

AtSC 'seismic Provisions Seetion Dl.2b requires that both flanges be laterally braced at intervals not to exceed:

0.086r. >'

When designing an RBS connection, it is assumed that the flexural strength of the member at the reduced section will control the moment strengtJ1 of the beam. According to AISC Specificarion Section P2, where Lb $; Lp, beam strength is controlled by Mp· When U1e RBS section is proportioned and located according to the provisions of ANSJIAISC 358, the flexural strength of the RBS will control beam strength and this assumption does oot need to be verified. In these cases, the flexural strength of the unreduced section is limited by Mp FyZx and the Oexural strength of the reduced beam section will be MpRBS = FyZRss. where ZRas is the plastic section modulus ac the center of the reduced beam section, as defined in ANSJIAISC 358 Equation 5.8-4, and Z.x is the plastic section modlllus of the unreduced beam section. However, in cases where lb > Lp, whlch is the case in this example, Lhe assumption w111 have to be verified. Note that as a practical matter, che typical value of Cb is greater than I .O for moment frame beams and when the limits imposed by rhe AISC Seismic Provisions on unbraced length are considered, lateral-corsional buckling typically will not reduce the flexural strength of the unreduced section below Mp.

=

=59.0 Because Aw members.

4-51

29 (~J =0.086(1.92 in.1( ' OOO ksi )(- 1- ) Fy . · ' 50 ksi. 12 in./ft

For tbe unreduced section, from AISC Specification Section F2, with compact flanges and web and Lp < Lb :s; L,, the :ipplicable flexural strength limit states are yielding and later
=7.98 ft (Spec. Eq. F2-2)

Alternatively, using Table 4-2 for a W24x76, it can be seen that Lbmax is equal to 7.98 ft.

·::11.

!~: '(

:~

The composite concrete and meta.I deck diaphragm provides continuous lateral support to the top flange of the beam; however, !he only lateral supports for the bottom flange occur at the end connections. Therefore, a bottom flange brace must be provided
Lb,;, 30.0 ft 4 :::: 7.50 ft< 7.98 ft Therefore, provide lateral bracing of the bottom flange at 7 .50 ft intervals.

Cb =

12.5Mmax 2.5Mmax +3MA +4Mo +3Mc

If bracing is provided at 7.50 ft on center, there are four unbraced segments along the beam, although the two segments on each side of the beam midsp::m are symmetric assuming that the seismic load case on the beam is considered. The moment diagram from the elastic analysis has an approximately constant,slope such that the' values of M,~ax• MA. Ms and Mc can be obtained by proportioning the moment diagram shown in Figure 4-10. Thi.s approximation assumes that the impact of gravity load is such that it does not significantly influence the shape of the moment diagram resulting from lateral load.

Available Flexural Strength Check tbe available flexural strength of the beam (including tbe reduced section) as stipulated in ANSJ/AlSC 358 Section 5.8, Step l. First, check the unbra_ced· length using AISC Manual Table 3-2:

Lp:::: 6.78 ft

Lr = 19.5 ft

TI1erefore, Lp L.0 helps establish that Mp can be developed with bracing intervals further apart than 6.78 ft.

Fig. 4-JO. Moment diagram for Beam lJM-1.

>;

ii li

(Spec. Eq. Fl-1)

A.\fatJC.'\l'l l'.NSTITUTI! 01' STEEL CONSTRUCTION

4-52

'

.

MOMENT FRAMES

For the exterior segment~ of the beam, where M is the moment at the end of the beam:

Mmax = M MA =I0.87SMJ

4-53

4.3 SPECIAL MOMENT FRAMES AND INTERMEDIATE MOMENT FRAMES

Plastic Secuon Modulus at the Center of the RBS At the centerline of the reduced beam section, using ANSl/AISC 358 Section 5.8, the piss-

Ma=I0.75 Ml

]·

tic section modulus is:

Mc= 10.625.\11

(ANSJ/AISC 358 Eq. 5.8-4)

ZRBS = Zr-2ctbt(d-lbf)

Cb=

12.5M 2.SM + 3(0.875M)+4(0.75M) + 3(0.625M) =l.25

=200 in.3-2(2.00 ·in.)(0.680 in.)(23.9 in.-0.680 in.) = 137 in.3

For the interior segments of the beam:

Mmtu=O.SM MA = 10.375.MI

Ma=I0.25

Ml

Available and Required Flexural Strength at Centerline of RBS and Face of Column

Mc= 10.125MI

As determined previously, the nom.ioal llexural strength is the plastic moment of the beam, Mp. At the centerline of the RBS, the nominal and available flexural strengths are:

Cb =

12.5(0.5M) 2.S(0.5M)+ 3(0.375M)+4 (0.25M)+3(0.125M)

Mn@RBS

=1.67

=FyZRBS

t

=50 ksi(137 in.3 )

The available flexural strength of the beam end segment is detemtined in the following. The end segment is the governing case because the ratio of Cb values for the exterior and interior segments is Jess than the ratio of the maximum moments for the segments. From AISC Specification Section F2.2, for the limit state of late:ral-torsionaJ buckling, with Lp
(Spec. Eq. f2..2)

=6,850 kip-in.

=571 kip-fl LRFD

Mn@RBS 57 l kip-ft = 1.67 nb

9oMn@RRS = 0.90(571 kip-ft) =514 kip-ft

= 342 kip-ft

where

Mp =F)·Zx

(Spec.

Eq. F2-1)

=50ksi(200 in.3)(1 ft/12in.)

Mu@RBs

=246 kip-ft< 514 kip-ft

o.k.

Mo@RBS

=168 kip-ft< 342 k:ip-ft

o.k.

At the face of the column, the nominal :\f\d available flexural strengths are:

.

=833 kip-ft

LRFD

0.7 FyS" =0.7 (50 ksi)(176 in.3 ) {l ft/12 in.) =513 kip-ft

ASD

M11 Mp -=-

tj>M,. =9bMp

n

=0.90(833 kip-ft)

For the end segment:

6 tt)( 750 ft- .78 ft)] 19.5ft-6.78ft

M"

= 1,020 kip-ft Therefore, Mn = Mp = 83~ kip-ft because Mn csm1ot be greater than Mp (as indicated in AISC Specification. Equation F2-1) regardless of the value of Cb and hr.icing may be provided at 7.5 fl on center to achieve Mp-

=273 kip-ft< 750 k.ip-tl

nb

= 833 kip-ft 1.67 =499 kip-ft

=750 kip-ft

Mn= us[833 ki ft-(833 ki -ft-513 ki . pp p-

I

ASD

o.k.

M0

=136 kip-ft< 499 kip-ft

L o.k.

'.

t

...

f: AM£l!JCAl< lNsTrJvn; Of' S1UL CO~TIU.ICllO.'<

MOMf.NT FRAMES

Available Shear Strength

AhcmaLively, Table 4-2 of this Manual can be used lo determine M,. The required brace force using AlSC Specification Equauoo A-6-7 is.

Using ATSC Manual Table 3-2 for the W24x76 bcrun:

LRFD

I:·. '

I RFD

ASD

. -v"= 210 kips

.~',

Q~Vn

=3 15 kips

:1 ...•' ..·)

Vu

=33.8 kips < 3 15 kips

o.k.

v.,

= 22.8 kips< 210 kips

Lateral Bracing According to lhe AJSC Seismic Provisions Section Dl.2b. which references AISC Specification Appendix 6. the required sttengrh of nodal lateral bracing away from an expecced plastic hinge location is determined from AlSC Specification Appendix 6 as follows:

P,b = 0.02M,Cd

(Spec. Eq. A-6-7)

ho R1 - 1.l from AISC Seismic Provisions Table A3.l

..::,,

C.1=1.0 where, nccording to AJSC S~ismic Prollisions Dl.2:i(a)(2):

r

=1.1 (50 ksi)(200 in.3 ) "' I 1,000 kip-in.

=R1 F.,Z 1.5

..:;

= 1.1 (50 ksi)(200 in. ) 1.5

:;

..•.

$

I

I

= 6.32 kips

The length of the brace is a~sumed lo extend from the cenierline of lhe bottom Oange of the W24x76 SMF beam 10 the centerline of the lop tJange of the adjacent gravity beam The siu of the adjacent gravity beam 1s unknown, but assume for this calculation that lhe flange thickness is the same as 1hc W24x76. The center-to-center spacing of the beams is 12 ft 6 in., as indicated in Figure 4 7. Therefore, lhc length of lhc brace is approximately:

t =

J[i 2.5 fl(I 2 in./tt))2 + {239 in. -0.680 in.)2(I/12 in./fl)

= 12.6 ft From AISC Manuc1/ Table 4- 12 for ecceouically lo:ided single angles with the eccentricity equal to or less than 0.75 time~ the angle thickness. uy a l5x5x$fie with K = 1.0. For ASTM A36, 1he av:ul.ible axial s1rtngth of the single angle is found through in1erpolation using KL= 12.6 ft.

LRFD

ASD

~ =15.0 kips

~.,P,,

= 22.9 kips

Purl>

=9.48 kips< 22.9 kips

LRFD 3

=7,330 ldp-in.

;

23.2 in.

o.k.

Po,11 =6.32 kips < I 5.0 kips

o.k.

bracing according to Appendix 6 of the AlSC Specification. The kicker brace selected in this eumple is considered a nodal brace. Assuming a rig.id bmce support, from ATSC Specificarion Equation A-6-8, the required brnce stiffness is:

ASD

M

_ 0.02(7.330 kip-in.Xl .O)

arb -

AISC Seismic Pr
LRFD M, =R,F1 Z

P.

= 9.48 kip~

Comment;

::=. ..

ASD

o.k•

The preceding .flexural check could have been conservatively m~dc using 1he required strength at the face of the colullUl compared to the available strength al the cenlerline of the RBS. This approach might be useful if there is unc~rtsinty regarding the geometry of the RBS, particul:irly the values of a and b since these arc needed 10 Jctennine 1hc location of the RBS centerline.

flt

-

t 0) P.,,.= 0.02(11 ,000 . ,kip-in.X . 23.¥ in .

n.,

The W24x76 is adequate to resist the loads giYen for Beam BM I.

,.

4 3 SPECIAL MOMENT FRAM!:'-') -\NO L'l"TE.RME:.Dl/\11' MOMENT FRAMES

A.\iEIOCAl'f INST11V11! OP STEEL CONSTIUJCTIOH

ASD

4.3 SPEOAL MOMENT FRAMES AND INTERMEDIATE MOMENT FRA..'v!ES

4-56

LRFD where

where

= 0.75

~

n

M,::::: 11,000 kip-in.

Mr = 7 ,330 kip-in. Cd = 1.0 Lb = 7 .50 ft(J 2 in./ft) ::::: 90.0 in.

·= 90.0 in.

ho

ho =23.2in.

·~br ::::: _1_[ I 0(1 1, 000 kip-in.)( J .0)1 ,

0.75

(90.0 in.)(23.2 in.)

The SMP beam-column connection design presented in this example bas been chosen to demonstrate the application of the design pro~isions· for prequalified RBS connections in accordance with ANSI/AISC 358. This example demonstrates that the RBS geometry developed below is satisfactory. Some of the results from this example are used in Example 4.3.3. The geometry of an RBS connection is not uniqoe and alternative configurati'ons of the RBS geometry are possible.

=2.00

Cd = LO Lb =7 .50 ft(J 2 inJft) .. ...

Ex_ample 4.3.4. SMF Beam-Column Connection Design

ASD

= 23.2in.

l3t>r =

z.oo[10(7,330k.ip-in.)(1.0)1 (90.0 in.)(23.2 in.)

WD::::

e =tan

-l(

·J·

23.2in. J 2.5 ft(12 in.Jft)

=8.79"

k = 3.07 in.2 (2~,000 ksi) cos 2 ( 8 .790) 152m. = 572 kip/in.> l3or = 70.2 kip/in. k > Pbr

(

0.84 kip/ft

})IL=

0.60 kip/ft

Procedure: The procedure outlined below follows the order of the design procedure outlined in ANSI/AISC 358 Section 5.8. The term ''Step i1" indicates the actual step number in ANSI/AISC 358 Section 5 .8. The steps from ANSI/AISC 358 are augmented with some additional checks in this example. Some of the steps listed in Table 4 -A are exe.c uted in detail in Example 4.3.3, the SMF beam su;ength check. The procedure is defined for LRFD only.

=AE cos2 (9) L

l

Giv~n:

The stiffness of the L5x5x5/ 15 brace, with A= 3.07 in.2, in the horizontal plane is: k

t:

Refer to Joint JT-1 in Figure 4-8. Design the connection between Beam BM-1 and Column CL-I using the reduced beam section (RBS) shown in Figure 4-9. All beams and columns are ASTM A992 W-shapes. Plate material is ASTM A572 Grade 50. The gravity loads on the beam are:

=70.2 kip/in.

::::: 70.2 kip/in.,

~:

4-57

j..

I

In addition, panel zone and bracing requirements are checked.

o.k.

L5x5x5/1& ASTM A.36 kickers will be provided to brace the beam bottom flange at a spacing· of 7.50 ft. The brace at midspan can be designed in a similar manner with Cd 2.0, _bec;rnse it is the brace closest to the inflection point

=

Note t!Jat because this connection features a prequali.fied RBS moment connection supporting a concrete structural slab, according to ANSl/AfSC 358 Section 5.3.1(7) the slab pl~s the typical lateral stability bracing provides sufficient stability so that ·additional bracing adjacent to the plastic hinges is not required, provided that shear connectors are provided at a minimum spacing of 12 in. (but omitted in the RBS protected zone).

Solution: From AISC Manual Table 2-4, the W-shape material properties are as follows: \

\

ASTMA992

Fy= 50 ksi Fu=65 ksi From AJSC Manual Table 2-5, the plale material properties are as follows: ASTM A572 Grade 50

Fy =50 ksi F.,= 65 ksi

Comment: av~ilable flexural strength is gre.ater than the required flexural strength from code-specified load combinations at the center of the RBS, the maximum probable moment, Mpr. at the column face needs to be checked against I.be expected moment strength of the unreduced beam section. This will be done in Example 4.3.4.

In addition to chec!Ong that the beam

A.MSRJCAN 1NS1TTVTE OF $11$1.. CONSTRUCllON

From AISC Manual Table 1-1, the geometric properties are as follows: Colwnn

W14x176 A= 51.8 in.2 fJ= 1.31 in. Zx= 320 io. 3

d= 15.2 in. lfdet

=1¥16 in.

t,. =0.830 in. /ca,1= 2'h in.

b1= 15.7 in. k1=l-%in.

. t1.... ~:

4-58

MOMENT rR.AMES

The beam aJso sati~fies the ma.~imurn width-to-thickness ratios for the flange, mensurcd u1 the edge of the center two-thirds of the RBS. and the web specified by ANSl/AISC 358 Scc1ion .53.1(6). as ~howo in E.umple -i.3.3.

Table 4-A

RBS Design Procedure Per ANSI/AISC 358

Beam latcml bmcing must be provided in conformance with the AlSC Seismic Provisions This beam supports a concrete ~1ruc1ural sl.ab that is connected between the prorected zones with welded shear connectors spaced at a maximum of 12 in. Consequently, according to the faception in Set:tir.n 5 3 1(7) of ANSVAJSC 358, supplemental lateral bracing is not required at the reduced )~lion . ~11mmum ~p3cing between rhe face of the column and the first beam lateral suppon and minimum \pacing between lau~ral supports is shown 111 faample 4.3.3.

Check system limitations pe< Section 5.2. Check prequaliflcalion linllts per ~ 5 3. Step 1. Choose trial values for 1he RBS dimensions

a. band c. See also Example 4 3.3.

step 2. Compute plastic section modulus at tile center of RBS, z~ See Example 4 3.3. Step 3. Com1lu'.e the pcobable maximum moment at !he cen!Er ol RSS.

The protected zone consi~ts of the portion of the beam between the fuce of tbe column :uiJ the end of the redu..:etl beam se.;oon farthest from the face of the column. Figure 5.J of ANSl/AlSC 358 ~hows lbc locauon of the prorwed zone. This information should be clearly identified on the strucrurnl dct.ign drawings, on shop drawings. and on erection draw

Step 4 Compute lhe 6hear force at Ille center of lhe RBS at each end of beam Step 5. Compute the probable nmimum moment at Ule race ot the column. Step 6. Compute the plastic moment of Ule bfl3Jll based on e,pected yiekl Slre$S. Step 7. Check tllat moment 81 Ille tau of Ille C-Olumn. /J~ does nol exceed availaDle strength,

-~ ""·

+r#,.

v,. ol beam and beam web·to·column connection from

Step 9. Design lhe beam wet>-lc>-Clllumn connection per Section 5.6. Step 10. Check continuity plate requirements per Chapler 2.

than a W36.

Step 11 Check cdumn·beam relotionship hrn1tations accortling to Section 5.4.

The column also ~a1isfics the m:i11;imum width 10-thickness r::llios for the flanges and the web specified by Section 5.3.2(6), as shown in Eumple 4.3.2.

Beam W24x76 A= 22.4 in. 2 ft= 0.680 io.

Column lateral bracmg musr conform to lhe requirements of the AISC Seismic Provisions. Section E3.4c allows the use of a strong-column/weak·beam ratio (~SC Seismic Prorisions Equation E3-l ) greater than 2.0 to show that a column remains elastic outside of the panel zone at restrained beam-to-column connections. If ir can be demonstrated I.hat !he column remains elastic outsiJe of the panel zone, Secllon E3.4c(l) requires !he column flanges tr> be braced at the level of the beam top Oanges only. With a c-0lumn-be.am moment ratio of I.72 in this c.xample (see calculations following). t~ column cannot be assumed to rem:.a.n elastic and bracing as required at both the top and botcom flanges of the beam. Column flange bracing at these locations may be provided by coatinuily pl:ites and a full-depth shelf plate between the continuity plates al the connection of the girder framing into the weak axis of the column.

=0.440 in.

d=23.9 in.

t,.

z.. =200 in.3

r1 =1.92 in.

br· 8.99 in.

Prequalification limits per ANSllAJSC 358 Section 5.3

ANSI/AJSC 358 provides only nn LRFD design procedure for the RBS connection; there·

Check beam requirements

The W24x76 beam satisfies the requirements of ANSUATSC 358 Sec1ion 5.3.J as a rolled wide nangc member. wi1h depth less than 3 W36. weight less than j()() lb/ft, And n:mge thickness less than I.75 in. The clear span-to-depth mtio of che beam is at least 7 as required for an SMP system: Clear span /dept h :::

(360 in.-15.2 in.)

23.9 in.

::: 14.4 ? 7

t·

!

in gs. Check column requirements The W 14x176 column satisfies the requirements of Section 5.3.2 as a rolled wide Oangi> member, with the frame beam connected to lhe column Oange and witb a column depth kss

Step 8. Determine the requll'ect Shear strength, Equation 5.8-9.

System limitations per ANSI/A/SC 3?8 Section 5.2 The fr:une is a special moment frame and the RBS connection is prequalified for SMF and IMF systems.

!

4.3 SPEClAL MOMENT fRJ\MCS 1\NO fNTERMl.!OIATE MOMENT f'RAME.S

o .k.

fore , the RBS connection must be designed using lRFD, even in the case where ASD was used for Lhe remainder of 1he design. The following calculations illustrate the LRFD procedure. Trial Values for the RBS Dimensions a, b and c (Step 1 in ANSI/A/SC 358 Section 5.8) The dimensions of lhe RBS cut ~ill be determined so that the RBS has sufficient strengt1l to resist the flexural loads pre1'Cnbed by the building code as ~ell as so that I.he probable

MOMENT F'RAMF.S

maximum moment in 1he beam at the face of the column does not exceed 1he expec1ed plastjc moment capacity of the be:im. The former check is perfom1e
(ANSI/Al SC 358 Eq. 5.8· l )

= =

=

(ANSJ/AISC 358 Eq. 5.8-2)

0.65d = 0.65(23.9 in.) =15.5 in. 0.85d =0.85(23.9 in.) =20.3 in. 15.5 in. S 18.0 in. S 20.3 in.

=8.670 kip-in.

The value of Mpr is intended to represent the m:iximum moment tha1 can occur at the center of the RBS cut when the reduced section has yielded and strain hardened.

I

i:

The gravity lo3d on the beam is computed from the load combination provided in ANSJ/ AlSC 358 Section 5.8, Step 4, as follows:

I~

+ 0.2(0 kip/ft) o.k.

=1.31 kip/ft (ANSI/AISC 358, Eq. 5.8-3)

=

0.1(8.99 in.) = 0.899 in. 0.25bbf = 0.25(8.99 in.) =2.25in. 0.899 in. S 2.00 in. S: 2.25 in.

The distance from the column face to the center of the RBS cut is determined from ANSI/ AlSC 358 Figure 5.2 as follows:

sh =a+(b/2) =5.50 in.+{18.0 io./2)

=14.5 in. o.k.

l..

The distance between centers of RBS culS is:

Plastic Section Modulus at the Center' of the Reduced Beam Section (Step 2 in ANSI/A/SC 358 Section 5.8)

The value of the plastic section modulus at the center of the RBS, puted in Example 4.3.3. ·

ZRBS

=137 in.3, is com-

Probable maximum moment at the center of the reduced beam section (Step 3 in ANSI/A/SC 358 Section 5.8)

From Example 4.3.3, ZRJJs = 137 io.3 , therefore:

2F1

=1.15(1.1)(50 ksi)(I37 in. ) 3

""J.2(0.840 kip/ft)+ 0.5(0.600 kip/ft)

O.lbbf Sc S 0.15b1

~1.2

(ANSl/AlSC 358 Eq. S.8-5)

Mpr =CprR>FyZRJJs

w., = 1.2D+0.5L+0.2S

c= 2.00 in.

Fy+F.

=1.1 from AISC Seismic Provisions Table A3.1

The shear force at the center of the RBS at each end of the beam is computed from a free body diagram of the portion of the beam between the RBS centers. For this free body dfa· gram, assume the moment at the center of each RBS is equal to Mpr as compu1ed in Step 3.

o.k.

b 18.0 in. 0.65d s; b s 0.85d

Cpr =

R1

'Hll

Shear force at the center of the reduced beam sections at each end of the beam . (Step 4 in ANSI/A/SC 358 Section 5.8)

0.15b1 = 0.75(8.99 in.) =6.74 in. 4.50 in. S 5.50 in. S 6.74 in.

0.lbbf

4.3 SPECIAL MOM.ENT FRAMes i\Nl) lNTERMEDIA'l't! MUMl:.NT MtA.Mt!:S

(ANSI/AISC 358 Eq. 2.4.3-2)

50 ksi+65 ksi 2(50 ksi) =l.15s;1.2

L1t =L-2(dcoi/2)-2S1i

=360 in.- 2{15.2 inJ2)- 2(14.5 in.) =316 in. Figure 4-11 shows the key beam dimensions. Figure 4-12 shows a free body diagram of the portion of the beam between RBS cuts.

.t

As shown in Figure 4-12. V~BS and Vifusare lhe symbols used for the sbear at the center of the RBS cuts. VRss is r.he larger of che two shear forces and VR.as is the smaller of tJ1e two. By summing moments about the right end of this free body diagram, the shear forces can be computed as follows: .;.:;

l l

l!

AMERICAN li
T r· .

MOMENT FRAMES 2Mpr Wulh VRBs=--+--

Lh

If the gravity load on the beam is something olher than a uniform loau, the correct Shear forces at lhe centers of I.he RBS cuts are still obtained from equilibrium of the portion of the

2

beam between the ccnLers of the RBS cutS {i.e., by sum.ming moments about e~~h end of lhe free body di<1gram). ·

= 2(8,670 kip-in.)+ l.31 kip/ft{l ft,'12 in.)(316 in.)

316 in.

2

=72.l kips

If the gravity load on the beam s.s very large, lhere is a possibility tha1 the loca1jon of the plastic hinge may shift a significant distance outside of the RBS. lf this is the case. the design procedure in ANSI/AlSC 358 would require. some modification, sin,ce the design procedure assumes the plastic hinge forms within 1he RBS. The possibility of the plastic hinge shifting outside of the RBS can be checked by drawing the moment diagram fQr tbc portion

Summing moments about the left end:

VfuJs

=2Mpr _ Wulh l1t

.U SPECIAL MOMENT !'RAMES AND fl'fTERMEDlATE MO.MENT FRA."'IES

2

-of the beam between RBS cuts. If the point of maximum momenr is outside of the RBS and exceeds Mp of the full beam cross section, the plastic hinge loc111fon will not fon11 in lhe RBS, and the ANSUAISC 358 design procedure must be moclified. This is unlikely to occur for typical spans and gravity loads, but may be a possjbility for cases of very long beam spans and/or very large gr.Mey loads. Figure 4-13 shows the moment diagram for the portion of the beam between RBS cuts for this example. This moment diagram confinns that the maximum moments occur at the RBS cuts, :ind therefore the plastic hinges will form in the RBS cuts, as assumed in the ANSI/A.ISC 358 design procedure.

::::: 2(8,670 kip-in.) 1.31 kip/ft{I ft/12 in.)(316 in.) 316 in. 2 =37.6 kips

1 ·:J

Probable maximum moment at the face of the column (Step 5 in ANSf/AISC 358 Section 5.8)

,,

The probable maximum moment at the face of the column, Mf. is compu1ed by taking a free body diagram of the pon:ion of the beam between the center of the RBS cut and the face of the column. Summing moments for the frt;e bQdy diagram results in Equation 5.8-6 in ANSI/AlSC 358. The probable maximum moment at the face of each column is:

W24x76

~

L =~so·

~ RBS

RBS

Fig. 4-JJ. Beam dimt!nsions.

1"r1

10,000 8,000

6,000

~RBS

I

I

.~

a. :.s;: c: Cl)

E

0 ~

Mpr = 8,670 kip-in.

",,,.'

L.,,= 316" I

Fig. 4·12. Fret! body diagram ofporrio11 of /Jea11tbefll'cen RBS cuts.

4,000 2,000 0 -2,000 ·4,000 -6,000 -8,000 ·10,000 Distance along beam span, fl

Fig. 4-13. Probable AMllRICAN lNSTITUT8 Of' S11lEL CONSTRUCTION

mome111 diagram

for portio11 of beam berween centers of RBS rntt.

AM£1UCAN lNS'JTIVll! OP STEl?.l.. Co.HSTRUCTlON

MOMENT FRAJ\.1ES

Mf = Mpr + VRBSsh

(ANSVAISC 358 Eq. 5.8-6)

= 8.670 kip-in.+ 72. I k.ips(14.5 in.)

=9. 720 kip-in.

4.3 SPECIAi MOM!-;NT FRAMES AND INTERMEDIATE MOMEN'f FRAMES

Check that moment at the face of the column, Mt, does not exceed ¢c;M,,. (Step 7 in ANSI/A/SC 358 Section 5.8)

From ANSUAISC 358 Section 2.4.J

M/ = M pr + VkssS1i

=1.00

cpd

=8,670 kip-in.+37.6 kips(14.5 in.)

QdMrt = I O{l l,000 kip-in.)

=9,220 kip-in. The free body diagram corresponding to Equation 5.8-6 is shown in Figure 4-14 for rhe Jefl side of the ~-

As noted in ANSI/AISC 358, this free body diagnro and Equation 5.8-6 neglect the gravity load on lhe beam between lhe center of the RBS and the face of the column. Neglecting this gravity load introduces little error. For this e'l;ample. Jf Lhe gra\ity load of 1.31 kip/ft was included m the free body dfagram in Figure 4-14, lhe value of M1 would mcrea~e by 11.5 kip-in.

=11,000 kip-in. =9. 720 kip-in.

Mt

(ANSl/AISC 358 Eq. 5 8-8)

Mt$ ~J.\ff'< 9.720 kip-in.< 11,000 kip-in.

o.k.

Because &1uauon 5.8-8 is satisfied, the preliminary valu~ of a= 5.50 in .. b = 18.0 in .. and

c:: 2.00 in. are acctptable. lx:t~een Mt and ~dMpe• ir may be possible to rwuce the depth of lhe RBS cut. Reducing the RBS cut (the c dimension) from 2.0 in. 10 1.5 in. will ~till satisfy Equation 5.8-8, and will result in a smaller increase in story drift ratio due to the presence of the RBS cut On the other hand, increasing lhe RBS cut would reduce the shea.r demand on the panel wne, :is discussed in Step 9 of tJ1is example. For the purpose of this example. continue with the RBS dimensions of a= 5.50 in.. b 18.0 in., and c = 2.00 in.

Because there is a significant difference Plastic moment of the beam based on the expected yield stress (Step 6 in ANSllAJSC 358 Section 5.8)

(ANSI/AISC 358 Eq. 5.8-7)

Mi'< =R1 Fylx = l.1(50 hi)(200

m.3)

=

=11,000 kip-in. Alternatively. using AISC Seismic Manual Table 4-2 for Lhe ldp-fc 11,000 kip-in.

=

W24x76 beam,

R>MP::: 917

Required shear strength, Vu, of the beam and beam web-to-column connection (Step 8 in ANSl/AJSC 358 Section 5.8) The required shear strength of lhe beam and the beam-to-column connection. V,., can be calculated by taking the previously compuled value of VRss and adding the shear due to lhe gravity load on the portion of the beam between the center of the RBS nnd the face of the column:

I ·

V., =

VRBS

=72 I

+ w.SA kips+ l.31 kip/ft(l ft/12 in.)(14.5 in.)

= 73.7 kips

1)

Note that lhere is liule error in taking V" = VRBS.

Thedesi&n ~hear sucngth of the W24x76 beam, •v," is 316 kips fromAISC Afanua/Thble 3-6.

) M1 =9,720 kip-Jn. 72.1 kips

'===-_.,

L

Mpr = 8,670 kip.in.

VR8S

=72.1 kips

sh= 14.5 in. Fig. 4-14. Fru body diagram <>/portion of beam between center of RBS and face of ccl"mn.

o.k. ~

1~...

Design the beam web-to-column connection according to ANSI/A/SC 358 Section 5.6 (Step 9 In ANSI/A/SC 358 SectJon 5.8) The required shear force at the column· face is V., = 73.7 kips as detennined previously.

*

t

Select a single-plate connection with a plate al lea.st 1n. lhtclc lo suppon crecllon loads, per ANSUAJSC 358 Section 5.6(2Xa). The same secuon requires that the beam web be , welded to the column fl:inge using a complete-joint-penetration (CJP) groove weld. ..Jj

J,

4-66

MOMENT FRAMES

Wilb lhe single plate as backing. use a CJP groove weld to connect the beam web to the col·

of this e.umple. lhe column size will not be changed and '.\µ.in.-thick continuity plates are required.

From the AlSC Specification Section G2. l, the required minimum remaining web depth between weld access holes for the 73.7 kips shear force is:

Welds between lhe continuity plate and the column flanges are required to be CJP groove welds according to AlSC Seismic Pro1·isions Section E3.6f(3).

The AISC Seismic Provisions do not specify lhe width of the continuity plate. AlSC Spcciftc01ion Section J 10.8 S3ys that the minimum width of each con1inuity pl:11e plus tcwfl must be greater than bbJ/3. As shown below, however, this width does not appear to be sufficient 10 stiffen 1be column flanges due to the significant clip in the plate resulting from the column fillet.

$0.6F1 t,.,C. 73.'7 lcips 1.00(0.6)(50 ksi)(0.440 in.)(1.0) ::: 5.58 in.

By inspection, sufficient web depth remains.

From AISC Specification Section J 10.8, the minimum continuity plate width is:

o.k.

Continuity plate requirements according to ANSI/A/SC 358 Chapter 2 (Step 10 in ANSI/A/SC 358 Section 5.8)

ANSl/AlSC 358 requires conlinuity plates for the prequalified RBS connection unless the e.xceptions of AISC Seismic Provisions Section E3.6f are met and both Equations E3-8 an
= 1.31 in.

lcJ Ryb

=Ry.: =1. l from AJSC Seismic brwisions Table A3. l

111


~ 0.4 L8(8.99 in.)(0.680 in.) ( l.l )(50 ksi) .

1.31 in.
'• ~;

'ef

.

n.g.

~!!st.. 6


n.g.

Use 'A-in.-thick ASTM A572 Grade 50 continuity plates on both sides of the web.

i:

Alternatively, lhe W14x176 column could be upsizcd to a W14:x211 to avoid the need for a continuity pl:ite. The decision to upsii.c the column should also consider the need to provide a doubler plate for the panel zone, as discussed in !he following. For !be purposes

f:

1

in.I "" 0.870 .

111.

2

2

4 08 in.

15.7 in. 0.830 in. _ . --- 7.44 m.

2

2

Continuity plate

For this two-sided connection, the thickness of lhe continuity plates is required to be at least equal to th~ thicker beam flange on either side of lhe column according to AISC Seismic Pro11isions E3.6f(2). Therefore the minimum continuity plate thickness is 0.680 in..

).

I•

,.... ) o.s3o 2.58 in.- f( 1~ .rn.+ 1·am. 2

or it is as wide as the edge of the column flange:

Neither Equation E3-S nor Equation E3-9 is satisfied, S
I!

While a 2Ys-in.-wide continuity plate is lhe minimum width penn.it1ed, lhis is too narrow because the resulting conl3ct width is only 0.870 in. as shown in Figure 4-15, once the impact of the fillet is considered. AISC Sei.mtic Provisions Section 12.4, which references AWS D1.8 clause 4.1 , limits the corner clip to not rnore than 1,~ in. beyond the published kt dimension. where k 1 for a W14x176 is 1Ys in. Thus, the lenglh of contact between each continuity plate and the column flange is:

8.99 in. 0.830 in. - ---

6

1.31 < 1.50 in.

S.99 m. 0.830 in. • . - -- = 2.)8 m. 3 2

The typical practice, therefore, is to set the continuity plate so !.hat it is at least as wide as the edge of the frame beam flange:

(l .1)(50 ksi)

.,,,. 8.99 in. lefc:c---

:·..." ~

4-67

umn flange.

dmin _ 73.7 kips

:; l

4.3 SPECIAi. MOMENT FRAf..tES AND INTER.MEDlATE MOMENT FR.AMES

Fig. 4-15. Contact area between minimum-width ronti11ui1y plate and column flange. AJ,tEJUCAN lNsTm.ml OF STEEi.. Co.~~

MOMF.NT FRAMES

4.3 SPECIAL MOMENT FRAMES AND lNTE.RlvtEDIATE MOMENT FRAMES

For illustration in this example, use 6.00 in. as 1he pla1e wid1h, so that the contact \\;d1b is:

.

• ) ,, JO.+ i.< nm. 6.00 .m.- l(l~'

~Rn

0.830 in.] = 4.29 .m. 2

(Spec. Eq. J 10-11)

")( . .)l dbdcfw

= 1.00(0.60)(50 ksi 15.2 m.)(0.830 m.

According to AISC Seismic Provisions Section E3.6f(3), the strength of the sum of the welded joints of the continuity plates to the column web weld is the smallest of: (a) Sum of design strengths in tension of continuity plate contact area with the column flanges (b) Design strength in shear of continuity plate contact area with the web (c) Design s~ength in shear of the column panel zone (d) Sum of expected yield strengths of the beam flanges transmitting force to the continuity plates

3befr~} =¢0.60FrJ,tw ( l + --

X

l+

2

3(15.7 in.)(I.31 in.) · ) . ( . )(O 23.9 m. 15.2 111. •830 111.

I

= 480 kips Since this requirement applies

10

the entire panel zone, it will be divided by 2 when com·

pared wilb requirements (a) and (b). For continuity plate requirement (d):

T,. =2R1 Fybflf

=2(1.1)(50 ksi)(8.99 in.)(0.680 in.) Note that (a) and (b) can be analyzed for each continuity plate to column web on either side of the web, whereas (c) and (d) apply to the welds of both concinuity places. Assuming a ~-in.-thick plate, for contin_uicy plate requirement (a), and using AISC Specification Section J4. l (a), the design tensile strength is:

tP1Tn

=672 kips Since this requirement applies to the entire panel zone, it will be divided by 2 when com· pared with requirements (a) and (b). ·

=~',Fy(co.nt.act area)

The concinuity plate to column w·eb weld is based on the smallest of 290 kips, 156 kips, .i&O kips/2 240 kips, or 672 kips/2 :::: 336 kips. Thus. the design should be based on

= 0.90(50 ksi)(2)(4.29 in.)(* in.)

156 kips.

=290 kips

To transfer 156 kips, a lh-in. double-sided fillet weld is required over the contact length. From AISC Manual Equation 8-2a:

=

For continuity plate requirement (b): AISC Seismic Provisions Section 12.4 states that continuity plates are to be detailed in accordance with AWS Dl.8 clause 4.1. The comer clip of the continuity plate along the column web is equal to kder + 1.5 in.= 4.13 in. The contact width with the web is: Contact width= 15.2 in. - 2(4.13 in.) =6.94 in. The design shear strength of !he continuity plate based on the contact area with the web, from AISC Sp~cification Section J4.2(a), is:

D

l I .'.

f

156 kips 2(1.392 kip/in. per sixteenth)(6.94 in.) = 8.07 sixteenths

Check column-beam relationships pej ANS//A/SC 358 Section 5.4 (Step 11 in ANSf/AfSC 358 Section 5.8) AISC Seismic Provisions Section E3.4a requires that SMF c-0nnections satisfy the following strong-column-weak-beam criterion, assuming that the exceptions stated in Section E3.4a are not met.

1·

cj>..,V,. = ¢v0.60Fy(contact area)

=1.00(0.60)(50 ksi)(6.94 in.)(% in,)

=156 kips For continuiW plate reqliirement (c) and assuming that P, :S 0.75Pn the design strengch of the panel zone, $Rn, is (note that AISC Seismic Provisions Seccion E3.6e(l) revises tlie value of 4> to 1.00): ·

LM:C

(Provisions Eq. E3· 1)

- -..->LO I.Mpb

The value of M;,c in th.is example is based on projecting Mpc to the beam centerline assuming that the column shear, Ve;, is in equilibrium with the column moment, Mpc;· This is consistent with the definition of M;,c in AlSC Seismic Provisions Section E3.4a. Alternatively, the column shear could be computed to be in equilibrium with the beam moment, Mpr· The latter approach wilJ result in a smaller value of M;,c and, when applied to Equation E3-l, will produce a slightly more conservative resulL

AlllEJUCllN lNsnTvTI! OP STl?.l!L CONSTRVCTION

r

~

,. .

70

MOMENT FRMff:S

The axial load on the column must also be considered when determining the flexural strength of lhe column at lhe beam centerline. (For simplicity, the same axiol lood will be used abo\'e and below the joint although ch.is is not quite accurate.} Using P., = 249 kips as given in ~ample 4.3.2, and the height of the column to its assumed points of inflection above {h, (12.5 fl/2)(12 inJft) = 75.0 in.] and below [hb= (14 ft/2)( 12 inlft) = 84.0 in.] the beam centerline. r..u~ is detennine-0 as follows:

4.3 SPECLAL MOMENT l'RMIF.'l ANO INTERMl'OIAT6 MOMENT FRA.\.fES

L.M:.:

34, 100 kip

4- 7 1

in.

!M~ =19.800 kip-in.

=

l.72 1.72 > 1.0 o.k. Therefore, the strong-column-weak-beam check j, sati,.fied.

(Provisions Eq. E3-2a)

+ z.lb(Fy- P,,-:)[ ,\,

= 310 in 3

hb J hb -db '2

be calculated by summing the moment' at the column faces as determined by projecting the expected moments at the plasuc hinge points to the column faces; in this example, MJ and Mf.

249 (so ksi - 51.8 kips) in.

x {[ 75.0

2

in~~?2~~~ in./2)]+184.0 in~-~2~~~

in./2) ]}

~ 34, I00 kip-in.

The expected fle:(Ural demand of the beam at the column centerline is defined in ANSU AISC 358 Section 5.4 as:

''here

....

rfV"as(a+~ +; )J

L\J,,,

=

LH,.,

=summation of the probable ma."timum moment at the center of e:ich RBS

I.

Panel Zone Check AI.SC Seismic Provisions Section E3.6e spt:c1fies that the required panel zone shear Mrength

From statics, it can be seen that column panel-tone shear based on the summation of the expected moments at the column faces should be reduced by the column shear, Vr· The column shear, Ve. is not from the code-specified loads but is. instead, the column shear developed from the plastic hinging of the RBS. Assuming points of inflection at the m1dheight of the columns above and below the panel rone and as previously detcmuncd in this enmple, M1= 9,720 kip in. o n the lert side of the beam and Mf 9,220 kip-in. on the right s.idc, the value of Ve, ig1wring the small effect of gr::ivily loads between the ex peered p la.s11c hinge location and the face of the column, 1s:

=

. - .~If+ M/ \,. - h h ..!!. + ..!.

2

2

_ 9, 720 k.ip-in. + 9, 220 lop-m. -,(14.0ft+12.52ft)(l2 Ill

.!.!!2

dctemlined pre\'iously

;. l "

The term r.M 11v is the sum of the moments produced at the column centerline by the shear at the plastic !tinges. Recalling I.he values of VRas and Vfu computed in Step 4 of tbis c'l:ample and the values of the RBS cut confinned in Step 1, r.Mw is:

,·

= 119 kips where lrb

=story height above the joint, in.

h, = story heighl below tbc joint. in.

i;

The required srrenglh of the panel zone is: ~;

=(72.l kips+ 37.6 kips)(5.50 in.+ 18 ·~ in.+ 15 ·~ in.)

!:...

= 2,420 kip-in.

I ;i. .!·,

.

ITherefore, the expected flexural demand of the beam at the column centerline is: r.'tf;/>

=2 .\/pr + r.Jf =2(8,670 k.ip-in.)+ 2.420 kip-in.

R.. = rMt -Ve di.-r1

== 9,720 k.ip·in.+9,220.kip·in. _ 119 k.ips 23.9 10. - 0.680

10.

=697 kips

llV

=19,800 kip-in.

AlSC Seismic Provision.t Section E3.6c(l) requires that the design shear strength of the panel zone be determined in accordance with the li.nUt stale of shear yielding in AISC Spurftcario11 Section J 10.6 with~" :::: 1.00. Specifically, AISC Speciftcorion Section JI0.6(b) is applkable

4 72

.t.3 SP.EClAJ.. MOM.ENT FRAMES AND lNTl.!RMEDlAiE MOMENT FRAMES

because frame stability, includjng plastic panel-zone deformation, is considered in the analysis. Detennine 1he applicable equation as follows:

to the initiation and propagation of fracture at welded beam-to-column connections. In such cases, sharing of inelastic deformations between beams and panel zones is not encouraged. See Hamburger et al. (2009) for additionnl infonnation.

P,, =243 kips from Example 4.3.2

It 11as already been pointed out in this exnmple that reducing the RBS cut (i.e., dimension c) might be possible to bring Mt closer to ~tiftf~ and reduce I.he impact of the on frame stiffness. Also, increasing the RBS cut dimensions would reduce shear demand on the panel i.one and, in some cases, eliminate the need to install doubler plates.

P, <0.75Pc P,. < 0.75F1 A1

RBS

P, <0.75(50 ksi)(5J.8 in.2) 243 kips < J .940 kips

o.k.

Size Web Doubter Plate

Therefore, the shear strength of the panel zone is given by AISC Specificario11 Equation

Jl0-11:

Rn

= 0.60Fydctw l +3bctt1'j -f dbd
II+

3{15.7 in.)(1.31 inf

J

(23.9 in.)(15.2 in.)(0.830 in.)

Alternatively, using Table 4-2 of this Manual for the W14x176 column:

From Table +.2 of this Manual, for the W24x76 beam:

dt 90

Wz

90 t

0.75Py= 1,940 kips

¢Rv2


=0.250 in

From Table +.2 of this Manual, for ·the W14x176 column:

=480 kips

¢>Rv1

The minimum th.ickness of each component of the p311el zone, withour the aid of intennediatc plug welds between the column web and the doubler is:

(Spec. Eq. J 10- ll)

x

4-73

=378 kips =2,420 kip-in.

~

=0.140 in. 0.250 in.+0.140 in. =0.390 in.

The column web satisfies this requirement: t.., ""0.830 in.> 0.390 in.

4>Rv2

=Rv i + - dl>

"" 378 kips+ 2,420 kip-in.

o.k.

If the doubler plate satisfies this minimurl;l thlckness, it is penniued to be applied directly to the column web or spaced away from the web, without the use of plug welds.

23.9 in.

= 479 kips

=

Because Rw 697 kips> 9Rn. a column-web doubler plate is required. Note that if Ve had not been subtracted, the required panel zone strength would have been approximately 816 kips, which is a 17% increase in demand.

The available shear strength of the panel zone is checked using AISC Specification Equation JlQ..11 with the thickness, tw. taken as the combined thickness' of the eolumn web and doubler plate. ·

I.

(Spec. Eq. JI0-11) Comments: Tests and analyses have shown that the actual she~ strength of the panel i.one might be considerably larger than the shear force that causes global shear yielding, because of scrajn hardening and the additional resistance provided by the column flanges bounding the panel zone. Therefore, AISC Specification Section Jl0.6(b) pel1!lils utiliz.mion of this addi1ional shear resistance in design when the flexibility of the panel zone js considered in analysis. Designers should be aware, however, that significant inelastic deformntions might be associated with this increase in resistance. For connections in which beam flanges are directly welded to column flanges, large inelastic shear distortion of 1he panel zone might contribute

Where fw used in two

plac~

is replaced by t.., + fp.

II

RCsmlnging to solve for tp:

.1

MOMENT FRAMES

4-74

<:::

. ! 697 kips

··~r

0.60(50 kSi)[3(15.7 in.)(1.31 in.)2]] (23.9 in.) 1

. 0.60(50 ksi)(IS.2 in.)

Ip

C!:: 0.476

.·

l-0.830 in.

.

4.3 SPECl/\L MOMENT FRAMES AND INTERMEDIATE MOM.El\'T FRAMES

Column flnnge restraint al these locations can be provided by continuity plates and a fulldtpth shear plate between the continmty plates at the connection of the girder framing into tlle weak ax.is of the column . Specify Beam Flange-to-Column Ffange Connection Per AISC Seismic Provisions Section E3.6c, the connection configuration must comply with the requirements of the prequalified connection, or provisions of qualifying cyclic test results in accordance with Section K2. ANSI/AISC 358 Section 5.5(1) requires a cqmplete-

Use a !l.!-in.-thick doubler plate.

joint-penetration groove weld,

Because the doubler plate meets the IDlmmum thickness re.quired by AISC Stismic Provisions Equation E3-7 (0.390 in.), plug welds between the doubler and the column web arc not required. Tiie length of the clip of the continuity plate at the doubler plate is not required to meet AWS DLS clause 4.1. Use a 1 in. x 1 in. clip.

Use a complete-joint-p.-:netration groove weld to connect the beam flanges to the column flange. The weld access hole geomerry is required to comply with AlSC Spt!cificarion Section JI .6. The welds are also considered demand critical. Tue final connection design and geometry is shown in Figure 4-16.

Extend the doubler plate 6 in. above and below the beams. Attach lhe doubler plate to the column flanges using complete-joint-penetration groove welds, as stipulated in AISC Seismic Provisions Section E3.6e(3)(2). A minimum-sized fillet weld may be used across the top and bottom of the doubler plate to avoid free edges, bUt is not required.

PL '..0"x6"x12;\• wiih corner clip per AWS 01 .8 (A572 Gr. 50)

Alrematively, two doubler plates spaced away from the colunm web can be used as shown in AISC Seismic Provisions Commentary Figure C-E3.3(c). Figure 4- l6 shows the final configuration of the panel zone. Installing doubler plates can be costly, so selecting a larger column may also be considered. Upsizing the column may potentially eliminate the need for continuity plates. The amount that the column can be upsized without losing the savings associat~ wilh eliminating the doubler plate varies significantly depending on the project and geographic region, but a general rule of thumb suggests that upsizing the column between 50 to 100 lb/ft might still be more cost-effective than installing doubler plates and continuity plates. "The column would have to be upsized to a W14x257 to eliminate both continuity plates and doubler platesa weight increase of 81 lb/ft from the W14x176 used in this example. This weight increase is in the middle of the 50 to 100 lbtft range where upsizing might be costeffecti\'e and a discussion with a fabricator is rCGOmmended. Nevertheless, for the purposes of thi~ example, the W14x176 column size will be retained tO illustrate the design of the doubler plate.

:.:• doubler plate; eXten
1----i--<

AISC Seismic Provisions Section E3.4c allows the use of a strong-column/weak-beam ratio (AISC Seismic Provisions Equation E3-l) greater than 2.0 to show that a column remains elastic outside of the panel zone at restrained beam-to-column connections. If it can be demonstrated that the column remafrls elastic outside of the panel zone, AJSC Seismic Provisions Section E3.4<:(1) requires the column flanges to be braced at the level of the beam top flanges only. With a ratio of l.72 in this example, the column cannot be assumed to remain elastic and bracing is required at both the top anctbottom flanges of the beam.

CJP W24 web

%" ;Ingle-plate connection (A572 Gr. 50)

Column Bracing Requirements

"

4-15

L

W2AX/6 beam 1 " ' - Bolts as required for erectlon

W14x176 column

Note: For weld backing requirements,

see ANSIJAISC 356 Chapter 3.

Fig. 4-16. Design Example 4.3.4 co1111ection geolrn!try. AMEIUCAN

ltlsmvm OP STEE.. CoNSTRUCJlON

.l\MERJC/\tl .INS'ITTVTB OP STe:EI.. CoNSTRUCTlON

4-76

MOMB'IT FRAMES

4.4 COLUMN SPLICE AND COLUM N BASE DESIGN EXAMPLES The following design examples address the design of gravity column splices, SMF column splices, SMF column bases, and SMF embedded column bases.

Example 4.4.1. Gravity Column Splice Design in a Moment Frame Building Given: Refer to the floor plan shown in Figure 4-7 and the SMF elevation shown in Figure 4-8. Design a splice using bolted flange plates between lhe third and fourth levels for the gravity column located at the incersection of grids 2 and B. Use ASTM A572 Grade 50 for aJI splice material. The column sizes above and below the splice are AST.M A992 W12x40 and W1 2x58, respectively.

If ~

-1

4.4 COLUMN SPLICE AND COLUMN BASE DESIGN' EXAMPLES

A!isume that the gravity column splices are at the same vertical elevation as the S.MF column splices shown in Figure 4-8. This location satisfie~ AlSC Seismic Provisions Section D2.5a.

Required Shear Strength of Splice in Weak Axis of Column

From AISC Manual Table 2-4, the beam and column material properties are as follows:

1-~~--AS-D

~_=_~~-~--LR_FD

_ _ _....J...l_v"_=

L-1 ..

_ _ _1 ;

In the weak a.xis of the column. the required shear strengLh of the splice is: ASD

V: _ FyZy

V. _ FyZy ay - I.SH

uy-H 50 k.si(16.8 in.3 )

ASTMA992

r;.= 50 ksi

50 ksi ( 16.8 in.3)

=1.5(12.5 ft)(l2 in.!ft)

:z

12.5 ft(12 inJft)

Fu=65 ksi

=3.73 kips

=S.60 kips

The shear force to be resisLed by each flange splice plate is half of MpclH. Therefore, for one splice plate:

=

F,.=65 ksi

W12x58-Lower shaft

Z.. =86.4 in.3

=12 A in. Zy =32.5 io. 3

ddct

1

d

=11.9 in.

dd"

=12 in.

Z, =16.8 in.3

Vuy

=5.60 k.ips/2

I

\

=2.80 kips 1f

=0.640 in.

I

i r

Vey = 3.73 kips/2

=1.87 kips

br = lO.o in. Note that the smaller column, the W12x40, controls the required shear strength, as is stip ulated in AISC Seismic Provisions Section D2.5c.

W12x40-Upper shaft

z.. =57.0 in.3

ASD

LRFD

From AlSC Manual Table 1-1, the column geometric properties are as follows:

d= 12.2 in.

I

I

From AISC Manual Table 2-5; the splice material properties are as follows: ASTM A572 Grade 50 .Fy 50 ksi

t

AlSC Seismic Provisions Section D2.5c requires that, with respect to both orthogonal axes, the column splice be able to develop a required shear st.rengtJ1 equal to:

LRFD Solution:

~.:.

f

11= 0.515 in.

br= 8.01 in.

AISC Seismic Provisions Sections 02.1, D2.5a :lnd D2.5c have requirements for gravity column spikes. Note that these gravity column splice provisions are equaJly applicable to gravity column splices in braced-frame buildings.

Check splice location

AlSC Seismic Provisions Section D2.5a requires that the splice be located a minimum of 4 ft from the beam-to-column connections. The three exceptions to this requirement do not apply for this building. AMERICAN lNsrnvrs OP STEEL CONSTRUCTION

Conservatively ignoring frictional resisLa.nce between the upper and lower shafts due to column dead load, this force will be resisted by the splice material.

fi Required Compressive Strength of Splice

.•)

I

With the upper shaft centered on the lower shaft, the dimensions of the upper shaft are sue that it will achieve full contact bearing on the lower shaft. Therefore, the splice will not b .. required to transfer any compressive loads iflhe upper shaft is finished to bear on the lower"'~ shaft. Because a note stating, "finish to bear," is provided on the detail, Case [-A applic from AJSC Manual Part 14, Table 14-3.

4-78

MOJ\1ENT FRAMES

Splice Geometry

4.4 COLUMN SPLICE,\ND COLUMN BASE DESIGN EXAMPLES

The polar inoment of inertia of the bolt group is:

Try the column splice detail from AISC Manual Parr 14, Table 14-3, Case I-A.

Iy

W12x40

~ u} = 4(2.75 iti.2-)2 (11in.2) = 30.3 in.4 /in. 2

du=dtk1

= 12 in.

Ix"'

u-; =4(1.50 m.1)2 (ltin.2)

W12x58

=9.00 in.4 /in.2

di= d,u1

l p"" Ix+ ly

= 1214in.

4

4

=

d,, + IA in. 1214 in. du+ Vs in. = 12% in,. 121,4 in. s 121A in: :::; 12% in.

o.k.

PL3/s in. x 8 in. x 1 ft 0 1h. in.

Q

~;

gu = g1 == 51h in.

LRFD

z:

v.uySill. oo• ~

n.

=1.87 kips(l.00) 4

=0.468 kips

From AISC Manual Equation 7-4a

LRFD

$:

M14

ASD

= V.,ye =2.80 kips[1h(3in.)+1% in.]

.,

Ma= Vaye

~hat.the

eq~idistant

lrhe geometry of each bolt group is such bolts are all from the centroid of their bolt group. Therefore, the moment will be shared equally between the bolts. The x-, Y· and radial distances from the center of gravity of the bolt group to the center of each bolt fol·

~! rwing the procedure and definitions in AISC Manual Part 7, ate: Cx

I

=rpu

COS

0

_ VuyCOS90"

= J.87 kips[1h(3 in.)+ PA in.] = 6.08 kip-in.

=9.10 kip-in.

rpyu

n =

rpasin 0

= VaySin 90°

"" 2.80 kips(l.00) 4 ""0.700 kips .

"· Manual and considering the eccentricity from the center of the bolt group to the column '.:'.~ interface, this moment is: · ·

Ir

lpxa :::::

n

I Be.c ~use the centroid of each ~olt group is eccentric to the column ends, there will be a ;: I moment on each bolt group. Usmg the geometry shown in Table 14-3, Case 1-A oftheAISC

ii

from AISC Mq,nual Equation 7-3b

rpxu = rpuSin 0

~l,.

lf

ASD


Splice Bolts

....,.

2

From AISC Manual Equation 7-2a, die direct shear force on each bolt due to the concentric force, Vuy and Vay. applied at 90° with respect to the vertical is:

~d from Case 1-A of AISC Manual Table 14-3, use Type 2 flange pl_ates. i:~ ·

4

""30.3 in. /in.2 +9.00 in. /in.2 = 39.3 in. /in.

du + IA in. $ dt $ du + Vs in.

,.~~

4-79

FromAISC Manual Equation 74b

"

rpya ::::: rpa COS \

\

= VayCOS 90•

I

2.80 kips(O)

0

11 :::::

1.87 kips(O)

4 =0 kips

4

=0 kips

=2.75 in. 1

h(3-in.)

=1.50.in.

;:: Jc2.15 in.)2 + (1.50 in.)2 =3.13 in.

AMElllCAN

INS111111'E OF STF..EL CONSTRUCtfON

•:

.

'

-

The additional shear force on each of the four bolts in the bolt group due to the moment cau~cd by eccentricity is:

= 1h(5 1h in.)

Cy ;,.

-

AMERICAN INSTITUTE. OF

SlllEL CONSTRUCTION

4-80

MOMENT FRAMES


-[M,,c.,)

I· Bearing Strength of Splice Plate Using AISC .\tfanual Table 7-5 with~= I 1A in., hole type = STD, F,, = 65 ksi:

_ 9.10 kip-in.(1.50 in.)

ASD

$rn =49.4 kip/in.(% in.)

(39.3 ;'.n:'!)

-

(39.3 ::: ) ~

=0.232 kips

FromAISC Manual Equation 7-7a

From AISC Manual E.quation 7-7b

-[M.,cx)

rm)"' - - Ip

.'

_ 6.08 k:ip-in.(2.75 in.)

(39.3 ~· J m.2 4

~

I

-

'

4

(39.3 m.2 ~· )

=32.9 kip/in.(~ in.) =12.3 kips

r,,

->ro

o.k.

n

o.k. I

Bearing Strength of the Column Flanges Since lhe column flanges are lhicker and wjder lhan lhc splice plates and their tensile strength is equal to the splice material, the bearing strength of the column flanges is adequate. Block Shear Rupture of the Splice Plates A block sbear failure path is assumed as showo in Figure 4-17. The available strength for I.be limit state of block shear rupture is given in AlSC Specification Section J4.3 as follows:

J:: 1. ·~

=0.425 kips

= 0.637 kips

r,.

I

}

_ 9.10 kip-in.(2.75 in.)

rn

n

= 18.5 kips

_ 6.08 kip-in.(1.50 in.)

=0.347 kips

1~

From AlSC Manual E.quation 7-6b

rmw =(M;Pc,)

Ip

-

4-81

LRFD

riw:u- - -

-

4.A COLU~IN SPLICF. ANO COLUMN BASE DESTON E..XAMPLES

~

ASD

LRFD

f

(Spec. Eq. J4-5) ·:'

R,. = 0.60F.,Anv +UbsFuAnt ~ 0.60FyAgv + UbsFuAnt

Ubs =LO

The r~.quired strength per bolt is then:

A,,1

LRFD

r.,

=J(rP-"' + rmiu )2 + (rpyu + rmyu ) 2

=, +(O kips+ 0.637 kips) =1.23 kips

2

=

1 ( 0.468

kips+ 0.232 kips)

'+(O kips+0.425 k:ips)

o.k.

Use ~-in.-
I

2

.

:£:!

ASD

nrn =11.9 kips. rn ->r., . o.k. n

I

2

=0.819 kips

LRFD

$rn > r.,

=2.53 in.2

2 2 r., = J(rp.xa +rmxa) +(rpya +rmya)

From AISC Ma11ual Table 7-1 for a ~in.-diameter ASTM A325-N bolt (Group A):

$rn =17~9 kips

r

Agv =(5 1h in.+!~ in.)(% in.)

From AISC Manual E.quation 7-8b

2

(0.700 kips+0.347 kips)

l.5{13/J6in.+ 1/i6 in.)Ws in.)

= 1.20 in.2

ASD

FromAISC Manual Equation 7-8a

= (3 in.+l'h in.)(lh in.) -

. M

I ;~-• 1 •

8"

1~·1

SW

• 1•

8

I I I I

~-----------~-

I.:

~:

I

'·

Fig. 4-17. Bloclc shear fa.ilu~ path for splice plate. AME!ue>.N lNsTmJTE OF STE£L CONS'Tll.UCTlO/'I

...

.,

1::

I

$

Ill

~

To

T

4-82

MOMENT FRAMES

An1

4.4 COLUMN SPLJCe AND COLUMN BASE DESIGN EXAMPLES

=2 53 in. 2 -(L5)("A6 in.+ V.6 in.)(~ in.)

Shear Yielding of the Column Flanges

=2.04 in. 2

f~A"'

Because the column flanges are thicker and wider than the splice places and their yield strength is equal 10 the splice material, the shear yielding strength of the column llanges is adequate.

=65ksi(1.20in. 2 )

=78.0 kips 0.60FuAnv =0.60(65 ksi)(2.04 in. 2 )

Shear Rupture of the Splice Plates

The net area of one splice plate is:

::::: 79.6 kips

An:::: [8.00 in.- 2( 13/Jdn. + IA6 in.)](% in.)

0.60F).A8 ,, =0.60(50 ksi)(2.53 in. 2 )

=2.34 in.2

=75.9 kips R.,,

+-83

=0.60F.,Anv +Ub,F,,A,, S 0.60F).Agv +Ub,F.,A,,,

From AISC Specificaiion Equation 14-4, the av:iilable strength due to the Hmit state of shear rupture for each splice plate is:

(Spec. Eq. 14-5)

1

= 79.6 kips+l .0(78.0 kips)!:> 75.9kips+1.0(78.0 kips)

= 158 kips> 154 kips Use Rn= 1_54 kips.

Vn Q

-=

cj>Vn = ~0.60FuAnv The available strength for the limit state of block shear rupture is:

LRFD

=

$Rn::: 0.75(154

kips)

Rn 154 kips -= n 2.00 77.0 kips 77.0 k.ips ~ 1.87 kips

=116 kips

=

116 kips:?: 2.80 kips

o.k.

cj> V,.

:·

=¢0.60F1 A1 -Vn =L00(0.60)(50 ksi)(* in.)(s:oo in.) n =90.0 kips > 2.80 kips

LRFD

1

I I

ASD

.·

.

0.60F,A1

n

0.60(50 ksi)(3,i in.)(8.00 in.) 1.50

o.k.

.

ASD

Mrxx v.,,.=-H

II. _ Mpcx

""F1 Zx

FyZx =--

cu

H

50 ksi{57.0

=60.0 kips> I.87 kips

o.k.

l

o.k.

AISC Seismic Provisions Section D2.5c requires that the column splice be able to develop a required shear strength in the strong 3x.is of the column equaJ to:

From ·'.ls~ Specification Sec[ion J4.2, the available shear strength due to the limit state of shear y1eldmg of one splice place is: ,

.

0.60(65 ksi)(2.34 in. 2 )

Required Shear Strength of the Splice in the Strong Axis of the Column

o.k.

ShP.ar Yielding of the Splice Plates

LRFD

n

2.00 = 45.6 kips> 1.87 kips

ASD

.

0.60F,,Anv

=0.75(0.60)(65 ksi){2.34 in. 2 )

= 68.4 kips> 2.80 kips

.

ASD

LRFD

I.

-1.5H 1.5H

in.3)

12.5 ft(12 inJft) == 19.0 kips

..

50 ksi ( 57.0 in.3)

1.5(12.5 ft)(l2 inJft) = 12.7 kips

.B-Ollcd splice plates could be provided on the column web, but it may be possible the strong-axis shear through weak axis bending of the flange plates.

10

resis:

Since there are two flange splice plates, the applied force on each plate is one half of ll: shear calculated for the strong axis of the column.

AllU!RJCAN lNSTI'JVT6 OF STEEi.. CONSTRUCTION

ASD

LRFD

.

·-..

The required flexural ~trenglh of the plate, from AlSC Ma1111al Table 3-23 Case 23: is:

ASD

LRFD

V. _ 12.7 kips .u2 =6.35 kips

Vux = 19.0 kips 2 =9.50 kips

4-S5

4.4 COLUMN SPLICE AND COLUMN BASE DESIGN EXAMPLES

MOMENT FRAMES

Vaxl 2 6.35 kips(l.75 in.) = 2 "" 5.56 kip-in.

VIL\'.L M.=-2

Ma=--

9.SO kips(l.75 in.) 2 = 8.31 kip-in.

=

Weak-Axis Flexural Yielding of the Splice Plate

Assuming the column is rigid enough to force all defonnation into lhe splice plate, the relative movement between the columns will cause weak-axis plate bending. The bending behavior in the plate is that of a beam fixed at one end, free to deflect Yertically but not rotate at the other (Case 23 of Table 3-23 in the AJSC Manual).

· d · I ...e splice plates are PL~/a in. x 8 in. x 1 ft 0 1'2 in. Using AISC As detemune previous y, '!.' . . S eci cation Section Fl I, detemtine Lhe available flexural y1eldin_g strength of the P.1:ue. :ote~at the dimension I used in AISC Specification Section Fl 1_1s parall~l to. the axis lof · ~ bendmg, and t hereiore / -- g.00 m·. 1''or weak-axis ~bending of the splice plate m this examp e.

The limit states checked are flexural yielding of the splice plate, shear yielding of the splice plate, shear rupture of the splice plate, and prying action on the innermost bollS.

Check the limit on Lbdlt 2:

The length of bending is the distance between the bearing plane of the columns Md the innermost bolt line, which is 1.75 in. according to Figure 4-18.

Lbd - 2 r

I

1.75 in.(~ in.)

=

2

(8.00 in.)

= 0.0103 0.08(29,000 ksi) 50 ksi

0.08£ Fy

column shaft

:::46.4

Lbd O.OSE AlSC Speciification Equation Fll-1 applies. The nominal flexura' Because - -2 < -F-,

W12x40 column with std. holes

l

1

yielding strength of the plate from Equation Fl 1-1 is: ·PL %"x8"x1'-0Y2" (A572 Gr. 50) centered on column flange (typ.), with std. holes

-1

M,. = FyZ

~ I.6M1

~

=SO ksi (8.00 in.){~ in.)2 4 I

(2) ~· dia. A325-N bolts @ s~· gage (typ.)

I I I

::::: 14. l kip-in.

l.6M1 == 1.6F1Sx

_

= 1.6(50 ksi)l(8.00

in.~(~ in.)21

I

Finish to bear

::: 15.0 kip-in. 14.l kip-in.~ 15.0 k.ip-in., therefore: M,. = 14.l kip-in.

W12x58 column with std. holes

J

1 Fig. 4-18. Connection as designl!d in Example 4.4. J.

I ..

i

1

AM£lUCVI ll'ISTTIVT2 Of' ST£EI.. CoNSTR\JCTIOl'I

1·

~l ~86 -.: ~

MOl\.fF.NT FRAMES'

'l~

·~ I

l

ASD :

,..., '111>Mn

Mn

=4>bFyZ 5: l.6My =0.90(14.l kip-in.)

I

FyZ

-=-nl> .Qb

= 8.44 kip-in. > 5.56 lcip-in.

o.k.

;

'i

. "~

~

= 14. I kip·in. l.67

= 12.7 kip-in.> 8.31 kip-in.

t~

.$-87

4.4 COLUMN SPLlCE :\ND COLUMN BASE DESIGN E..'CAMPLES

;j,':!

The available flexural yielding strength is:

\

~·Jl

-'·.£:

LRFD "

~--'fl

o.k.

ASD

LRFD T

=9.50 kips

T= 6.35 kips

2 4.75 kips

=3.18 kips

2

=

Tue available tensile strength per bolt before prying action effects arc considered, B, is 19.9 kips from AISC Manual Table 7-2.

The available tensile strength per bolt before prying action effects arc considered, B, is 29.8 kips from AlSC Mamuzl Table 7·2.

The parameters required for checking prying action are defined in AISC Manual.Part 9 and . Shear Yielding of the Splice Plate

given in Figure 4-19 for this example.

Using ATSC Specification Equation J4-3:

b

LRFD $Rn

:::i

db =Y.. in.

ASD

=$0.60FyAgv =l.00(0.60)(50 ksi)O~ in.)(8.00 in.)

Rn

d · =13/i6 in.

=0.60FyAgv n

n

(Manual Eq. 9-21)

=(0.60)(50 ksi)(* in.)(8.00 in.)

=11

l.50

=90.0 k.ips > 9.50 kips

=60.0 kips > 6.35 kips

o.k.

=1.75 in.

o.k.

b' =b-db/2 =1.75 in.-¥.i in.(!..

=1.38 in. a =4.50 in. (Manual Eq. 9-27)

Shear Rupture of the Splice Plate

An•= 8.00 in.(% in.)-2(1o/l6 in.+ l/i6 in.)(% in.)

·-j 1·

5~·

=2.34 in.2

.

Using AISC Specific01io11 Equation 14-4:

LRFD '.·.•

1

0

R,. = 0.60FuAnv

$R,. =¢0.60F,.A,.,

=0.75(0.60)(65 k.si)(2.34 in.2)

n

-

Q

=0.60(65 ksi)(2.34 in.2)

114"

2.00

=68.4 kips> 9.50 kips

o.k.

"'45.6 kips> 6.35 kips

• • ---+-- . .... o2w \ • • II

ASD

o.k.

';iiII

.Q

0

\ .P =4· 1 Prying Action on the Splice Plates

recause lhe inneonost bolts wiJl dominate the resistance tO the tension fore onJ the lWO

b~lts closest to I.he interface are considered. The required strength per bolt, T. ~ tak~n as half f the shear force at each flange plate, therefore: AMERICAN WS1'1Tl!re OF STEEi.. CONS'T1UJCTION

Fig. 4-19. Prying action terminology.

4-88 MOMENT FRAMES

4.4 COLUMN SPLICE Al'-1) COLUMN BASE DESIGN l::XAMl'l...t:.:>

l

j;

where From AISC Manual Equation 9-25. ~is:

a+db/2 = 4.50 in.+~ in/2

=4.88 in.

LRFD

1J:

ASD

and

~=~[%-1)

1.25b+d~/2=1.25(1.75 in.)+* in./2

=2.56 in. 4.88 in. > 2.56 in.

I (29.8 kips 0.539 4.75 !Ops

=

Use a'= 2.56 in.

TI1is tiibutary width is limited by lhe ge-0metry of the plate. The tributary width cannot be greater than the acrual edge distance lo the end of the plate on one side and half of the bolt gage in the other direction. Therefore, use:

= /1.67(4)(19.9 kips){l.38 in.)

/4(29.S kips)(l.38 in.)

I.

(4.00 in.)(65 ksi)

0.90(4.00 in.)(65 ksi)

=0.840 in.

Because the fitting geometry is known, the available tensile strength of the bolt including the effecis of prying action can be determined as: I

T1n't'J•I= BQ

=1.25 i.n. + 2.75 in.

(Manual Eq. 9-31)

\

where Q is based on a' determined from ATSC Manual Equation 9-35.

=4.00 in.

.ASD

LRFD

The remaining variables from AlSC Manual Part 9 are as follows: 0=1-d'/p

=I .38 in./2.56 in. =0.539

pFu

Because the splice plate is thinner than tc. prying on the bolts will occur at the bOlt ultimate strength.

=10.5 in.

p =b'/a'

-r24Bb'

'c -

=0.838 in.

. =4.)1.75 in.(3.94 in.)

(Manual Eq. 9-24)

[( r I

a'---1- !.s_ -1 - o(i+p) c

= (Manual Eq. 9-26)

t.·

ASD

~ F. p"

=

p,. =4../bC

= J - 13116 in./4.00 in. =0.797

=9.75

-J4Bb'

le -

=3.94 .in.

l!

i)

The required plate thickness to develop the available strength of the bolt. B, with no prying action, is calculated from AlSC Manual Equation 9-20 as:

=2.19 in.+l.75 in.

p

I ( 19.9 kips = 0.539 3.18 lcips

LRFD

=4.50 in. s; 1.25b = 2.19 in. (Use a= 2.19 in.)

c =a+b

-1

l)

=9.78

To .calculate the tributary length, p, 1he AISC Manual refers 10 DowsweJ1 (20 11) as one method to calculate the length. According 10 this reference. the tributary length, p~. can be taken as Pe= 4./bC (Dowswell, 2011, Equation 33) where bis as defined above and where c =a+ b, and a is limited to 1.25b. For this calculation:

a

~=~(; - 1)

1 ((0.838 in. r-1] 0.797(1+0.539) 'ti in.

:=3.26

a' - - 1-

- 0(1+p)

[( r

!£. -1 /

J

_ 1 [(0.840in.r-1J - 0.797(1+0.539) 3h in. =3.28

I

f'

f .·.

t

4-90

MOMENT FRAMES

,.. . 1

LRFD

ASD

Because a.'> J, use AISCManual Equation 9-34:

Q = ( ,:

=(

r

~in.

Q=[,:

r

+0.75L+0.75S

=109 kips

The required tensile strength of the column is:

LRFD

ASD

= 10.7 kips >.4.75 kips

From ASCE/SEI 7 Section 12.4.3.2 LRfD Load Combination 7

= 19.9 kips(0.358)

. =7. 12 kips> 3.18 kips

. o.k.

From ASCEJSEI 7 Section 12.4.3.2 A.SD Load Combination 8

o.k. 1~ =(0.9-0.2Svs)D+flvQE

The final COllJ.lCCtion design and geoi:fletry for the flange connection is shown in Figure 4-18. . ' .

I

T0 =(0.6-0.14Svs)D+0.70.,QE

=8.64 kips

=15.3 kips

The required shear strength of the column is:

Example .4.4.2. SMF Column Splice Design

ASD

LRFD

Design a splice for the SMF column located on grid 4 in Figure 4-8. The column material The applicable building code specifies the use of ASCFJSEI 7 for calculation of loads. The required column strengths between the dJU:d and founh levels were determined by a secondorder analysis including the effects of P-o P-ii with reduced stiffness as required by the direct analysis me_lhod. The governing load combinations in ASCE/SEI 7, including the overstrength factor (referred to as the amplified seismic load in the AISC Sei.smic Provisions), follow. ·

and

.. ...

={i.0+0.105Sns)D+0.525q,Q£

(including the 0.5 factor on L permitted in Section 12.4.3.2)

is ASTM A992.

·:· ;;

P.,

+ 0.5L+0.2S

Given:

..t..J

From ASCE/SEl 7 Section 12.4.3.2 ASD Load Combination 6

Tamil =BQ

= 29.8 kjps(0.360)

11

From ASCE/SEI 7 Section 12.4.3.2

LRFD Load Combination 5

=140 kips

The available tensile strength of each bolt is:

=BQ

4-91

ASD

P,. =(J.2+0.2Svs)D+'l,QE

(l+o)

=0.358

The available tensile strength of each bolt is:

~

r

=(0.840 *in: r(l+0.797) m.

(1+0.797)

=0.360

Taw1il

LRFD

Because a'> I, use AISC Manual Equation 9-34:

(! +o)

0.838 in.

4.4 COLUMN SPLICE AND COLUMN 13ASE DESlON EXAMPLES

The required compressive strength of the column is:

~;

From ASCE/SEI 7 Section 12.4.3.2 ASD Load Combination 6

From ASCEJSEI 7 Section J2.4.3.2 LRFD Load Combination 5

v.. =(L2+0.2Sos)D+'l,QE + 0.5L+0.2S =47.2k:ips

\

'·

v.. =(1.0+ O.lOSSns )D+0.525q,QE =26.9 kips

from ASCFJSEI 7, use Seismic Design Category D, Oo

t I

i

=3.0, p =~.O, and Sos::::: 1.0.

Assume that there is no transverse loading between the column supportS in the plane of bending and that the connections into the column weak-axis produce negligible moments on the column .

Solution: ASTM A992 F1 =50 ksi P., = 65 ksi

lNsnnrre OF STEE.. Co.><:SJ1\ucno~

I I

+0.75L+0.75S

from AfSC Manual Tuble 2-4, the column material properties are as follows:

AMERICAN

I

MOMENT FRAMES

From AlSC Manual Table 1-1. 1hc column geometric properties are as follows: W14x68-Upper Shaft A = 20.0 in. 2 lw

d::::. 14.0 in.

= 0.415 in.

b1= JO.O in.

fJ= 0.720 in.

LRFD Vu

=47.2 lcips

ASD Va

=26.9 kips

3

Th~re. is no ~~t tensile load effect on the column; therefore, ihe requirements of AJSC Se1sm1c Prov1srons Section D2.5b(l), (2) and (3) do not apply. Splice Connection

According .to AISC Seismic Provisions Section E3.6g. welded splices in SMF columns shall be made with comple1e-joim-penetra1ion (CJ'P) groo,·e welds. The use of CJP groo,·e welds ensure~ that the required axial strength and the required flexural strength of the splice will be achieved. Use CJP groove welds 10 splice the column webs and flange.s directly :is shown in F1gure 4-20.

~ L\1pc . d . . There.ore - - govems in eternunmg

H lhe required shear strength of the splice.

~ "f..Mpc . d .. Th ere1ore - - governs m etemunmg I.SH the required shear strength of the splice.

Using AISC Specificmion Equation G2-l, I.he requfred web depth to develop this fore·' through shear yielding of the web is:

V,, .. - ¢..0.6FytwC ..

d -

_ dw-

116 kips 1.00(0.6)(50 ksi){0.415 in.)(1.0)

Per AlSC Seisr:iic.Provisions Sections D2..5b, D2.5c and E3.6g, ihe required shear strength of th~ we_b spl!cc is equ~l to lhe greater of lhe required strength determined using the load comb1~auons m the applicable building code, including the amplified seismic load and lhe followrng: '

I~-~-=_LM_H_p_c~ L-R~~~~~~L.....~_=_-~ FD ~=5H~pc- ~-AS-D~~~~~~i where LMpc ~s the sum of the nominal plastic flexural strengths of the columns above and below the .splice. Be~ause lhis requirement is for web splices. r..Mpc in the strong a.~is of the column will be collSldered.

LRFD

. . . . . . . __ _

=~------'--

=9.32 in.

Therefore, !he maximum lenglh of each weld access hole, th, permitied in the direc:tion the web is: LRFD 111

='h[d-2t1-dwJ =1h[l4.0 in.- 2(0.720 in.)-9.32,' in,] =1.62 in.

ASD 111

='h[d-2t1 -dwJ =1h[l4.0 io.-2(0.720 in.)-9.35 in.] =1.61 in.

=Fy ( Zxtop + Zxbot} H

=(50ksi)(115 in.3 + 234 in.3 ) 12.5 ft(12 in./ft)

=116 kips

I j

Therefore, specify that lhe access holes for the flange splice welds may not extend more th l 1h in. measured perpendicular to the inside flange surface as shown in Figure 4-20. Location of Splice

TMpc

H

I

ASD

!Mpc

Vu = - -

I

D.vVa 0.6FylwCv

1.50(77.6 kjps) (0.6)(50 ksi}{0.415 in.)(1.0) =9.35 in.

=~-----...:-~--~

I

I

ASD

LRFD

Required Shear Strength of the Web Splice

~:·· .

I ! I

Using the load combinations in ASCE/SEl 7 including the amplified seismic load, the required shear strength is given as: •

Z.. = 115in.3

W14x132-Lower Sh3fl

Z:r =234 in.


Vo=-l.5H

· =F1 ( Zxiop + Z.rbo,) l.5H

=(50 ksi)(11s in.3 +234 in.3) J.5(12.5 ft)(12 inJft) 77.6 kips

J

AJSC Seismic Provisions Section D2.5a requires I.bat splices be located 4 ft away from . be4lm·to-column flange connection. The clear distance between the beam-to-column cc,,.,.: nections is approximntely I0.8 ft. Because the webs and flanges nre joined by OP weklf. AISC Seismic Provisions Section D2.5a(2) perm.its the splice to be located a minimum the column depth (14.0 in.) from the beam-to-column flange connection. . . The column splice location shown in Figure 4-8 is acceptable.

=

J

---------<

4-94

Additional Weld Requirements Per AIS~ Seismic Provisions Section A3.4b, the filler metal used 10 make the splice welds must sansfy AWS Dl.8/Dl.8M clause 6.3. AdilitionaJly. AJSC Seismic Provisions Section D2.5d requires that weld tabs be removed. •.

AlSC Specification Seccion JI .6 provides additional requiremen1s for weld access hole geometry. The final connection design is shown in Figure 4-20.

r )

Ex.am,ple 4.~.3. SMF Column Base Design

The applicable building code specifies the use of ASCE/SEI 7 for calculation of loads; The required column strengths st the b,ase level were determined by a second-order, analysis including lhe effects of P-o and P-6 with reduced stiffness as required by che direct an~y sis method. The governing load combinations in ASCE/SEl 7, including the overstrength factor (referred to as the amplified seismic load in the AISC Seismic Pro\lisions), follow. In this example, two of the controlling limit states are tensile yielding in the anchor rods and bending in the base plate. For these limit states, the axial force needs .co be minimized as this will increase the overtumi11g (bending) in the base plate and increase' the tensile force in the anchor rods; therefore, the required axial compressive strength is detennined from:

I

Given:

...

1

L.,

•'•. _J

ASD

LRFD

A992

~~

4-95


MOMENT FRAMES

Refer to Column CL-1 in Figure 4-8. Design a fixed coiuffin' base plate for the ASTM W-shape. The base and other miscellaneous plate material is ASTM A572 Grade 50. The anchor rod material is A_STM Fl554 Grade' l 05: The 21.t.1~in.-diam.eter anchor rods have an em.b edment length, h,,f> of ;u least 25 in.. The columq i$ centered on a reinforced concrece foundation. The foundation concrete compressive strength, fJ, is 4 ksi with ASTM A615 Grade 60 reinforcement. The anchor rod concrete edge distances, c.,1 and c112 , are both greater than 37.5 in.

LRFD Load. Combination 7 from

ASD Load Combination 8 from

ASCE/SEI 7 Section 12.4.3.2


P,, =(0.9-0.2SDs)D+0uQE =98.8 kips

Pa =(0.6-0.14SDs)D+0.70 0 QE

I

::::64.5 kips

The required flexural stTengtb is detemuned from:

ill

column shaft ... 4 .

ASD

LRFD

· ct_ tJpper & lower



',;.

W14x68

Ma =(0.6-0.14S 0s)Mo+0.1~MQ.

M,,:::: (0.9-0.2SDs)M0 +0vMQc

=662 kip-ft

= 946 kip·ft The required shear strength is derermin~d from: \

ASD

LRFD LRFD Load Combination 5 from ASCE/S.EI 7 Section 12.4.3.2

1¥.z" max typ.

Weld access hole Specification

~---+-+-- per

Sectio~ .J1.6 (typ.)

W14x132

vu = (l.2+0.2SDs)D+nuQE

'

ASD Load Combination 5 from ASCE/SEI 7 Section 12.4.3. 2

;

'

'.

Va =(L0 +0.14Svs)D+0.70;Qe

= 67.2.kips

= 96.0 kips ..

Assume that che connection into the column weak-axis produces negligible moments on the column. From ASCE/SEI 7, use Seismic Design Category D,

no = 3.0, p = LO. and SM.= LO.

Use LRFD provisions for the concrete design. Fig. 4-20. Connection as designed in Example 4.4.2 AMl!RJCAN INS11TU11! OF S"rEEl. CONSTRUCTION

...

..

J\Mllltl<:A:N WSTITTITE OP

STEEL CONSTRUCTION

4-96

MOMENT FRAMES

4.4 COI..UMN SPLICE AND COLLIMN BASE DESIGN EXAMPLES

I

4-97

Solution: LRFD

ASD

From AlSC Manual Table 2-4, the column material properties are as follows:

T.Mpc

F1 =50 ksi, F.,= 65 ksi

I

where r.Mpc is the sum of lhe nominnl plastic flexural strengths of lhe columns above and ;: below the splice, or in this case, lhe base. Therefore:

ASTM A572 Grade 50

=50 ksi LRFD

Fu= 65 ksi From AlSC Manual Table 2-6, the anchor rod material properties are as follows: ASTM Fl554 Grade 105

From ASTM A615, the concrete reinforcement properties are as follows:

ASTM A615 Grade 60 F1 =60 ksi From AISC Ma11Ual Table I- J, the column and beam geometric propenies are as follows: W14xl76

A= 51.8 in.2 t,;. =0.830 in.

v. -

V. - IM re II J-1

4

fM,x

-

I.SH

- 2(50 ks.i)(320 in. ) - {12 in./ft)(I4.0 ft)

- 2(50 ksi)(320 in.3 )

=190 kips > 96.0 kips Use Vu =190 kips.


- 1.5(12 in/ fl)(l4.0 f1)

Use V4

=127 kips.

AISC Seismic Provisions Section D2.6c(b) requires th3t the flexural strength equal or exceed 1he lesser of lbe load combination of the applicable building code, including th ...

amplified seismic load, or lhe following: d= 15.2 in. k,us

=1.91 in.

b1= 15.7 in.

, ..!;,

t1= l.31.in.

Zx= 320 in. 3

W24x76

FromAlSC Manual Table 7-17, the 2\4-in.-diameter anchor rod has an area of A"" 3.98 in.2

Required Strengths at Column Base · AISC Seismic Provisions Section D2.6a.(a) defines the required axial strength as the ~equir~ strength ~cuJated using the load combinations of the applicable building code,

ASD

lRFD

1 - - - - - - - - l.lR + - - - - · i·.· F Z.x M.,

=23.9 in.

=1.lR1 FyZx

1 1 Ma=--<--<-1.5

l.1(1.1)(50 ksi)(320 in.3)

1

{J2in/ ft)

\

= 1.610 kip-ft> 946 kip-ft Use M.,

=946 kip-ft.

I

1.1(1.1)(50 ksi)(320 in. 3 )

=

J

l.5(12in./ft) ::::; i.oso kip-ft> 662 kip-ft Use MQ

I! ~·

=662 kip-ft.

including the amplified seismic load. By reference to AISC Seismic Provisions Section D2.5c, which references Section D2.5b AISC Seismic Provisions Section D2.6b indirectly stipulates that the required shear stren~ of the column base be the greater of the required shear strengd:t delennined from load combinations inclucling the amplified seismic load (Section D2.5b(b)) or the required column strength as stipulated in t.he system chapters (Section D2.5b(a)). Herc, the provisions of Section E3.6g apply, as follows:

AM.lllUCAN lNSTITVTE OP STl!D, CONSTJ
f.

I

ASD

3

Fu.furQ = 125 ksi

d

11!

'---~~----~-~-----'-~~~~---~----~~

From AISC Manual Tuble 2·5, lhe base plate material properties are as follows:

F1

V. _ 'flvlpc 0 1.5H

v.u - -fl-

ASTMA992

::~a~~z:1::~::::::shall

four

be large enough for the instalfation of at least anchc rods, as required by the Occupalional Safety and Health Administration (OSHA, 2008).

=

=

Try a plate with: N 32 in., B 32 in., and anchor rod edge clistance of four equ:illy space.cl rods, as shown in Figure 4-23.

=4 in. Try two row

t: \::

J

MOMENT FRAMES

Using tl1e recomm.endations from AlSC Design Guide l. Base Plate and Anchor Rod Design (Fisher and Kloiber, 2010), determine the required base place thjckness and anchor rod tension force.

N

32.0 in. =--2

For the calculation of the base plate eccentriciry, e, from AISC Design Guide 1 Equation 3.3.6:

?

LRFD

'

M,, P,,

Ma Pa

e=., :~.

l

,'

I

·: ::

r1

ASD

ecrit

Pa

=---2qwu

= (946 kip-ft)(12 in/ft) 98.8 kjps = 115 in.

2

64.5 kips =---2(94.1 kip/in.) 2

98.8 kips 2(141 kip/in.)

= 15.7 in.

\VitJ1 e > ecro. lhe eccentricity meets the AJSC Desigil Guide 1 criteria for a base plate with a large moment (Figure 4-21).

Per AlSC Design Guide I Section 3.4, the following inequality must be satisfied: 64.5 kjps

=123 in.

'N

Pr 2qT11/JX

2

(

/ +

N')

1

2

~ 2P,(e+ j)

(AISC Design Guide 1 Eq. 3.4.4)

q,n(J)C

For the calculation off

For the calculation of the critical eccentricity, ecn1:

(AISC De.sign Guide I E.q. 3.3.7)

For the calculation of the maximum plate bearing stress, qm(J)C:

f

= N - edge distance 2 32.0 in. . 4 00 m. =----. 2 12.0 in.

=

(AISC Design Guide I Eq. 3.3.4)

For the calculation, assume the concrete bearing frustum area ratio equals 2.0 from ACl 318 Se-etion 10.14.l:

e

f

~.,,

J¥=2.0

x

The available bearing strength is determined from AISC Specification .Equation JS-2. LRFD

f P<.,,_) =$(0.85J:)l£-

At 0.65(0.85)(4 ksi)(2.0)

ASD

Iip{max)--- 0.85f: l£Q

= = 4.42 ksi qtntU

'

32.0 in.

=15.6 in.

={662 kjp-ft)(l2 in/ ft)

eaiJ=----

~-~· -

.

I

e=-

i

i:::J

N

P., 2qmo.r

=---2

Base Plate Eccentricity and Critical Eccentricity

I

ASD

LRFD ecr11

I

4-9?

4.4 COLUMN SPLICE ANO COLUMN nASE OF..SJGN EXAMPLES

=f P<.max>B =4.42 ksi (32.0 in.)

=141 kip/in.

Ai

=0.85(4 ksi)(2.0)

• B

iT

qmaxY

2.31

qlNVC

= 2.94 ksi =f P<.ftllU)B =2.?4 ksi (32.0 i n.) =94.l kip/in.

N Fig. 4-21. Base plate with large momtnt (Fisher and Kloiber: 2010).

MOMENT FRA.\1ES

For the calculation of the assumed bending lines at lhe bearing interface, from AlSC Design

Therefore:

(!

2

N) ::::: +2

[12.O m.+ . 32.0 - -in.) 2 .

Guide I Section 3.1.2: 2

m=

:::::784 in.2 ASD

2P.(e+ f)

2(98.8kipsXl15in.+12.0 in.)

2P,,(e+ f)

qmox

141 kip/in.

q,,_

=178 in.

2

(1 + N)2 > 2P,(e+

N-0.95d

2 32.0 in.-0.95(15.2 in.)

=

LRFD

2

=8.78 in.

=2(64.5 kips)(l23in.+12.0 in.) 94. l kip/in. = 185 in.2

2

With

4-101


/),the inequality is satisfied and a real solution is possible.

qmill

fl=

l

B-0.8b1 2 32.0 in. -0.8(15.7 in.) 2

I. "

=9.72 in. For the calculation of the base plate cantilever bending line distance at the tension interface:

x =f _!!._+ t I

Base Plate Bearing Length

2

From AlSC Design Guide 1 Equation 3.4.3, the base plate bearing length is: · LRFD

(AlSC Design Guide 1 Eq. 3.4.6)

2

l

in. 1.31 in. =12.0 i n15.2 .---+-2 2

ASD

t

=5:06 in.

Y=(!+~)~ (!+~r

=-h84

2P.,(e+ f) Qmax

in.2 -.J784 in.2-178 in.2

= 3.38 in.

Y=(!+~)±

Nr

/+2

2Pa(e+f)

=.J7g4 in.2 -.J784 in.2 = 3.53 in.

qmilX d

185 in.2

-1

@ ,_

Required Rod Tensile Strength From AlSC Design Guide I Equation 3.4.2, the required rod rensile strength for t:he anchor group on one side of the base plate is:

LRFD Nua,,, qmnxY - P11 = 141 kip/in.(3.38 in.)-98.8 kips = 378 kips

__

I I

.....

=268 kips

I

©

- -1- - - D --I

c:: 1-

I I I I I ....

~

I I

ASD

N"=qlnlllY-P., =94.~ kipfm.(3.53 in.)-64.S kips

I

'g co

--- II - - - - - --- ©

I

I

I

I

co

c::i

©

c:

..t

0.95d Base Plate Thickness

Check the base plate for flexural yielding at both the bearing and tension interfaces. At the bearing interface, the beSnng pressures between the concrete and the plate wiU cause bending for the cantilever lengths m and n as shown in Figure 4-22. At the tension interface, the anchor rods cause bending for the cantilever length, x, as shown in Figure 4-21.

N

Fig. 4-22 Asswned bending li11es (Fisher and Kloiber; 2010).

.•r. AM.eluCAN

1Nsmvrs Of Sm61.. Coi'JSTlttJCTION

i

l

4- 102

For flcxurol yielding at the bearing interface and Y < max(m. n), from AISC Design Guide I Equation 3.3.15:

LRFD

f P<.rtt1>

=2.1

J'

f p
Fy

x(9.72 in.-

=2.11 1

r::

f p(mtUJY( max(m,n)- ~J

33

· ~ in.)

J

LR.FD

=2.11

ASD

N11aX

BFy

=2.1 I /378 kips(5.06 in.) 32.0 in.(50 ksi)

=2.31 in.

fp(req)

- JNaaX =2 .:>8 --

BF,.

=2_58 /268 kips{S.06 in.) 32.0 in.(50 ksi)

¢R,, > V. = 190 Jdps

Use a PL3 h in. x 32 in. x 2 ft 8 in. ASTM A572 Grade 50 for the base pl3te. Plate Washer Bearing Strength

According to AJSC Manual Table 14-2, use a }8 in. x S1A in. x 5\4 in. pl3te washer, welded to the top of the base plate, to transfer th·e shear to the anchor rods. Also, interpolating from Table 14-2, use a 3lh-in.-diameter bole for the 2~-in.-diameter ancbor rods. Detennine the available bearing strength assuming deformation at the bolt hole is not a design consideration.

The clear distance to the edge of lhe bearing plate, le. is Laken as:

Rn >Va= 127 kips

n

o.k.

Anchor Rod Combined Tension and Shear

Using the recommendations from AlSC Design Guide l and AISC Specification Sectior, J3.7, the available tensile stress of the anchor rod subject to combined tensile and shear load~ is checked, including the effects of bending. · Based on testing performed by Gomez et al. (2010), this approach was detennined lo provide a reasonable and conservative strength estimate for earthquake des.ign. Therefore, given the comprehensive testing and design approach, the general anchor strength requiremenr of AC1 318 Section D4.3 for resistance to combined tensile and shear loads can be satisfied. The anchor rod noro.inaJ tensile slress, from AISC Specification Table 13.2:

Fni =0.15Fu = 0.75{t25 ksi) =93.8 ksi The anchor rod nominal shear stress with threads not excluded from the shear plane from AlSC Specification Table 13.2:

F,.,,

=0.450Fu =0.450(125 ksi)

..

=56.3 ksi The anchor rod required shear slress.frv:

_ 5'A in. - 2 1..4 in. 1c- . 2

ASD

LRFD f,rv --~

Va

f,.,=-llvAg

n.Ag

=

190 kips 2

8(3.98 in. )

=5.97 ksi

.I

o.k.

2.00 =510 kips

= 2.38in.

1

= 1.50 in.

Q

=765 kips

=3.32 in.

For flexural yielding at the tension interface, from AISC Design Guide l Equation 3.4.7:

fp(rtq)

R,, 1,020 kips -=

¢R11 = 0.75(1.020 kips)

t

;~::j

ASD I

3.53 . x [9.72 m.--in. 2 =2.58, 50 ksi

50 ksi

(Spec. Eq. J3-6b)

LRFD

Fy

2.94 ksi(3.53 in.)

=3.2? in.

_ ____,

=2.581

R,, =1.51,tFultv S 3.0dtF.,nv = 1.5(1.50 in.)(* in.)(65 ksi)(8)

s 3.0(21A in.)(* in.)(65 ksi)(8) = l,020 kips< 3.070 kips

ASD

4.42 ksi{3.38 in.)

?:

4-J(i,

4.4 COLUMN SPUCE AND COLUMN BASE DESIGN l:!XAMPLES

127 kips = 8(3.98 inh = 3.99 ksi AMUtlCAN INSTlTVTE OI' S-n;a CoNSTR\iCTION

4-1()4

MOMENT FRAMPS

4-105

4.-1 COLlfMN SPLICF ..\NO COLUMN BASE Df.SJON EXAMPl.£S

Therefore. the nominal tensile stress from AISC Specification Equation 13-3 is:

ASD

LRFD

LRFD

ASD f/;J

F:U

= 1.3Fn1 -

F111 f,., < F,,,

F,:,

~Fnv

= 1.3(93.8 ksi)

93.8 ksi - 0.75(56.3 k:si) (5.97 ksi) = 109 ksi

=l.3Fn1 - QFll( /,.,, < Fn, Fnv =1.3(93.8 ksi) _ 2.00(93.8 ksi) ( ') 3 99 56.3 ksi · ksi =109 ksi > 93.8 ksi

> 93.8 ksi

Therefore use F~ = 93.8 bi

Therefore u~e F:i

F;,

¢F;, = 0.75(93.8 ksi}

n

From AISC Design Guide 1 (Fisher and Kloiber. 2010) the anchor rod be d' o • lever arm, l, is taken as: ' n m,, moment - Ip t,. aJ~r l-+--

Anchor rod bending stress

Anchor rod bending stre..~

\10 1

M lb - VIII -

M1b=flv

11,

= 190 k.ips(2.19 in.)

=

8

=52.0 kip-in. /rb

=--+-2 2

127 kips(2. I 9 in.)

8

=34.8 kip-in.

M,,,

z

./,

=34.8 kip-in.

t...

1.90 in.'

=27.4 ksi

=18.3 ksi

Combined stress

Combined sness

=51.l ksi < 70.4 ksi

I·.f

Mw

/ib = -

:::-

J,

=23.7 ksi + 27.4 kq

~in.

26$ kips 4(3.98 in. 2)

=l6.8 ksi

J, = /u+ fib

2

3 1h in.

=

= 52.0 kip-in. 1.90 in.3

+ frb

2

378 kips

93.8 ksi 2.00 =46.9 ksi

The anchor rod combined tensile and bending stresses,/,, is:

,,,A,

=4(3.98 in.2) =23.7 ksi

=93.8 ksi

l

/,,..--_ Naa

n1 A1

-=---

= 70.4 ksi

J, = f.a

N

:-!!t.

I

=fta+ fzb - 16.8ksi+18.3 ksi

o.k.

=35.l ksi < .t6.9 ksi

o.k.

I

=2.19 in. The anchor rod plastic section modulus,

...

z. 1s:

3

Z::: db 6

= (2~ in.)3

6

=1.90 in.3 Determine rod tensile s tres s, assunung · tha t only the rods on one side of the b3Se • the anchor • pJate are w tension at any time.

Concrete Anchorage Strengths The available strengths of the column base concrete clements are checked in accordanc. with ACI 318 Appendix D. Section D.3.3.3 requires the anchor design screogth associate• wilb concrete failure modes bereduce
I I

I

t

t

Design Requirements for Tensile Loading t: Although checked previously in ~ccordance with AlSC provisions, the following illustrah ~ lhe :mchor tensile loading checlcs in accordance with ACl 318 Appendix D provisiom. ., Per Section 03.3.4, to ensure anchor rod ductile behavior, the design steel tensile strength. 9N,,,. must be less than the concrete breakout, 0.15,Ncbi· pullout. 0.75¢N, •· and side-fa• blowour, 0.15,N,b, strengths. By inspection, 1hc side-foce blowout limit ~tatc is n ! applicable. "· ·

t

4-106

4.4 COLUMN SPUCG ANO COLUMN BASE DESIGN EXAMPLES

The steel tensile strength of the anchor rod group of four (on one side of the base plate): ~NS4

=¢n As~.Nf.10

for the calculauon of A,vc<>: (AO 318 Eq. D-6)

ANco =9'1!1

where

:::: 9(25.0 in.)2

=0.75 from ACl 318 Sec6on D4.4(a)(i)

~

2

A,,,N

0.9743) =41t ( do--n-, -

n,

=4.5 threads/in. from AISC Manual Table 7-17

4-10?

=5,630 in.2

•

from ACJ 318 Section RD.5. J.2

Por the calculation 1.1f N,,:

N,,

=16A.J/:1i;p

Therefore:

(ACI 318 Eq. D-8) 513

1t(2•" .

Au,N::: -

J6(1)J4,000 psi (25.0 in.)

2

0.9743 I• 1 0 . - -)

4

1,000 lb/kip

4.50 in.

= 216 kips

= 3.25-in.2

Therefore: 2

$Nsa -= 0.75(4)(3.25 in. )(125 ksi )

= 1,220 kips > N a =378 kips 11

7 430 0

~ ·:)(1.0)(1.0)(1.0)(1.0)(216 kips)

Nt:bg :( •

o.k.

5,630 m.

~285

For the design tensile concrete breakout strength of the anchor group:

kips

0.4(0.75)¢Ncbg (AO 318 Eq. D-5)

Per ACI 318 Section 0.4.2. l provide supplemental reinforcement to restrain the concrete breakouL From ACI 318 Section D.5.2.9:

where the following values are assumed. 'Yec.N

= 1.0 fromACI 318 Section D.5.2.4

'Y~t1,N

= 1.0 from ACI 318 D.5.2.5

=0.4(0.75)(0.75)(285 kips) =64. l kips< 378 kips n.g.

T,, 0.75$/y

As=---

'Yc,N = LO from ACI 3 J8 D .5.2.6 'l'cp.N

I

cp :::: 0.75

= 1.9 from ACI 318 Section D.5.2.7

.

\

378 kips

ANc :::: [(n- l)s + 2(1.5)/rq j2{1.5)1tef from ACI 318 Figure RD.5.2. l

A.-----"-0.75(0.75)(60 ksi) :::: 11.2 in.2

s

=fB-2(EdgeDisunce)]/(n-l)

=132.0 in. -

Provide at least 11.2 in. 2 of vertical reinforcing stirrups spaced within O.Shefof each anchor rod group per ACI 318 Section Rt>.5.2.9."

2( 4.00 in.)]!( 4- J)

= 8.00 in.

For tbe design pullout srrength of the anchor group, including the additional 0.75 factor stipulated in ACT 3 18 Section 0.5.2.9 nnd 0.4 factor sti pulated in D.3.3.6:

Therefore: · ANc

=[(4-1)8.00 in.+2(1.5)(25.0 in.)](2)(1.5)(25.0 in.) =7,430in. 2

•

Ii I A.t.tBUCAN

J

where

$ 'l'c,P

"'·

I ~!

0.4 (0.75)$Npn :::: 0.4 (0.75)$n'JI c,PN p

1NS'JTTUT6 OF STEEL CoNS11UJC110N

= 0.7 from ACJ 318 Section D.4.4(c)ii for Condition B

=1.0 from ACl 318 Section D.5.3.6

AMERICAN INS'TllVra 01' S1l?a CONSTROCTION

(from AO 3 18 'Eq. D-1 ..:

4-108

MOM.ENT f'RAMES

4-109

4.4 COLUMN SPLICE ANO COLUMN BASE DESIGN EXAMPLES

For 1he calculation of Np. (ACI 318 Eq. D-15) For calculation of tbe anchor head bearing area Ab try" J 1•0 x •1.< • 1.< • h · ' rz• " · ... n IO. X 4 n m. plate was er with a double heavy hex nut head on the embedded end of the anchor rod.

For rhe c:Ucul:ition of the plate washer cantilever bending moment, the plate washer cantilever distance, l, is:

l

=(B,.as/Jt; - Bn11.1 h~od ) 2

Aorg = Aplote - Au

=(4 12 in. - 3 h

Aorg ::::: ( 4 \fi in.)2 - 3.25 in. 2

=0 ..500 in.

1

1

in.)

2

::::: 17.0 ~. 2

where Bnut Juad is the heavy hex nut F dimension given in AISC Manual Table 7-l9.

Np =8(17.0 in. 2 )(4 ksi)

Therefore:

= 544 kips

ASD

LRFD

Therefore:

For the plate washer load, w0 ,

For the plate washer load, Wu,

0.4(0.75)C!>Npn

=0.4(0.75)(0.7)(4)(1.0)(544 kips) = 457 k.ips > 378 kips

N,,,,

Naa

\ V a = --

Wu=--

o.k.

,<\i,rg

.

=17.0 in.2

The plastic section modulus per unit width, Z, of the plate washer is:

=22.2 ksi

bd2 4

wa/2

Ma=--

Mu=--

2

2

4

={22.2 kip/in.)(0.500 io.)2

=0.250 in.3

~

The nomin:il tlexural strength of the plate washer is:

= (1s.8

2

::::: 2.78 kip-in.< 450 kip-in.

M,. =FyZ

'

for_a l ·in. strip of place:

. Wul 2

= 1.00 in.(1.00 in.)2

o.k. \

. l..

kipf10.)(o.so9 in.)2

2 = 1.98 kip-in.< 2.99 kip-in.

o.k.

(Spec. Eq. Fll-1)

=50 ksi(0.250

in.3 )

Therefore, from AlSC Specification Section Pl 1.l and AC! 318 Secrt"on D 3 3 6 th ·1 able flexural strengtb of the plate washer is: · · · , e av:u -

LRFD

=0.4(0.90)(12,.5 kip-in.) = 4.50 kip-in.

~-

Design Requirements for Shear Loading

= l 2.5 kip-in.

0.4$Mn

=17.0 in.2 =15.8 ksi

for a l·in. strip of plate:

Z:::::-

.: t·:

268 kips

378 kips

Anchor Rod Head Plate Washer Flexural Strength

Abrg

ASD 0.4Mn :::: 0.4(12.5 kip-in.)

n

-

J.67

= 2.99 l
Although checked previously in ae<;:ordance with Al~C; provisions, the following illustrates the shear loading checks in accordance with ACI 318 Appendix D provisions. Frictional shear resistance developed between the base plate and the concrete is neglected in consideration of earthquake loading. By inspection, the concrete breakout strength of .the anchor group in shear is not applicable. The design steel shear strength of the entire anchor group, including the grout pad factor of 0.80 (AC! 318 Section D.6.J.3) is: $Vso =cl> 0.80n0.6Au.Vfu10

t'

·-·>

(AC! 318 Eq. D-20)

where

q, =0.65 from ACI 318 Section D.4.4(a)ii

~

....., Ai.l.61UCAN INsTmTrS OF STES. CoN~Tiu.icnoN

4-110

MOMENT FRAMES

TI1creforc: cj>V,.,

Vu

9v10

=0.65(0.8)(8)(0.6)(3.25 in. )(125 ksi) 2

= l,O !Ok.ips>l90kips

190k.ips

190 kips 1,060 kips

Because V., s 0.29Vsa. the full strength in 1ension is permitted according to ACl 318 Section D.7.l. Therefore. ¢V,. is controlled by a ductile steel element Design of Column Web-to-Base Plate Weld

1,010 kips

¢V
=

= 0.179 < 0.20

o.k.

For the inter3ction of tensile and shear forces. from ACI 318 Se<:1fon D.7:

l=

4-l l t

4.4 COLUMN SPLICE Ai"ID COLUMN BASE OF..SrGN EXAMPLES

The effective Jengtl1 of weld available, I,. on both sides of web, holding welds back from the

=0. 188

"IC' region, is:

Nua 378 kips --=--¢Ns11 1,220 kips =0.310

le= d-2kdu = 15.2 in.- 2(1.91 m.) = 11.4 in.

Because Vu s 0.2
For the design pryout strength of the anchor .group, ACI 318 Sec1ion D.3.3.5 requires that the streng1h be greater than tl1e shear associated with a ductile failure of 1he attachment if the requirements of ACT 318 Section D.3.3.4 are not met Because the shear strcngrh is based on hinging in the column, the ductile failure requirement is met if the design streng1h exceeds the column shear strength. As indicated previously, the anchor rods on both. sides of the base plate are provided with supplemental reinforcement. Io the region between each anchor group, lhe supplemental reinforcement may overlap, contributing to either group. In consideration of the concrete breakout strength for prying, a conservative estimate considers only 75% of the supplemental lotal for both groups. Also, the Ncbg term is no"\¥ determined based on lhe area of supplemental reinforcement instead of ACT 318 Appendix D. Equation D-5. Therefore, lhc revised design pryout strength is:

From AlSC Manual Equation 8-2, the weld size in sixteenths of.an inch is: ASD

LRFD Dnq

D

Vu = 1.392(2/e)

_

rtq -

l90 kips 1.392kip/in.(2Xl1.4 in.)

=

Va 0.928(2/e) 127 kips 0.928 kip/in.(2)(11.4 in.)

=6.00 sixteenths

= 5.99 sixte.enths

Conservatively use Yi6-in. fillet welds (two-sided) for the column web-to-base plate weld. Design of Washer Plate to Base Plate Weld The effective length of weld available, I,~ on each of the eight plates (two sides), is: I

0.75¢ V,.p8

:::::

0.75t> kcp N,.bg

(from ACI 318 Eq. D-31)

where ~

=0.70 fromACI 318 Section D.4.4(c)jj Condition B =2.0 from AO 318 Section D.6.3. 1 Ncbg =0.75(2)(1 I .2 in.2)(60 ksi)

I,::: 2(5 1A in.) =10.S in. From AISC Manual Equation 8·2, the weld size in sixteenths of an inch is:

kcp

D

Therefore:

_

rtq -

0.15cWcpg = 0.75(0.70)(2.0)(1,010 kips)

=1,060 kips> 190 kips

o.k.

Recheck the intcrnction of tensile and shear forces, using ACI 318 Sec1ion D.7.!, wit11 $V:o 0.75 $V,.,,., as follows:

=

ASD'

LRFD

= 1,010 kips

Vu 1.392(81,)

D

190 kips 1.392 kip/in.(8)(l0.5 in.) = 1.62 sixteeolhs ::::

Vu

rtq -

=

0.928(8/e) 127 kips 0.928 kip/in.(8)(10.5 in.) 1.63 sixteenths

=

I

I

The minimum weld size based on the thinner part joined from AISC Specification Tabl<' 12.4 controls. Bnsed on the 0.830-in. web, use ¥111-in. filJet welds (two sides) for the washt f plate-to-base piste weld. ~fERJCAl'I .lNSTmtlll OF STEEL CoNSTRllCllON

4-112

4A COLUMN SPLICE AND COLUMN BASE OESfGN E.'

n,ie final connection design and geometry for the moment frame column base is shown · Figure 4-23. in

1 L

~113

'

Example 4.4.4. SMF Embedded Column Base Design

}

Given : Refer to Column CL-l in Figure 4-8. Design an embedded column base plate for the ASTM A992 W-shape. The column is centered on a 72-in.-wjde reinforced concrete foundation. The foundation concrete compressive strength,//, is 4 ksi with ASTM A6 I 5 Grade 60 rcinforcemen1. Use ASTM A572 Gr:ide 50 plate material.

N= 2'-8"

The applicable building code specifies che use of ASCEISEI 7 for calculation of loads. The required column strengths al 1he base level were decerrnined by a second-order analysis including the effects of P-o and P-t:. with reduced stiffness as required by lhe direct analysis method. The goveming load combinations in ASCFJSEI 7. including the overstrenglh factor (referred to as the amplified seismic load in the AISC Seismic Pro1•isilms), follow. PL 3~· (A572 Gr. 50) with (8) 2J4" dia. F1554

Gr. 105 bolts

In th.is example, !he concrolling limir state is yielding of the face plates. For this limit state, the axial force needs to be ma:
LRFD 4•

typ.,

_J .-----W14x176 column

ASD

LRFD Load Combination 5 from ASCEJSEI 7 Section 12.4.3.2


Po= (LO+ 0.105SDs )D + 0.52Sn.,QE

P,. =(1.2+0.2Sos)D+O.,QE

Leveling nut and washer

or shim olack 3• nonshrink grout

+0.5L+0.2S =250 kips

+ 0.75L+0.75S = 215 kips

(including the 0.5 factor on L permitted in Section 12.4.3.2)

l \

The required flexural strength is detenn.ine,d from:

LRFD

c:

.... E

(.'.,

LRFD Load Combination 7 from ASCFJSEI 7 Section 12.4.3.2 M,. =(0.9-0.2Sos)D+~Qs

=946 kip-ft

ASD ASD Load Combination 8 from ASCEJSEI 7 Section 12.4.3.2

Ma =(0.6-0.14S.os)D+0.70.,Qe = 662 kip-ft

J

·'' PL 1"x4W'X4}2" (A572 Gt. 50) washer with a double nut

Fig. 4-23. OJnnection cross section as designed in Example 4.4.3.

.. . AMF.IUCAN lNST!TVtl! 01' STEl!J.. CONSTRUCTIOl'J ',• .. ..... \

~l

MOMENT FRA.MP.S

The required shear ~tre11g1h is detcrm.iped from:

LRFD LRFD Load Combina1ion 5 from ASCEISEI 7 Section 12.4.3.2

v.,:: (l.2+ 0.2SDs )D+ OoQe =96.0 kips

Required Strengths at the Column Base

,_

ASD

....

ASD Load Combination 5 from ASCEISEI 7 Sec1ion 12.4.3.2 Vo =(l.0+0. 14Sos)D+0.70.,Qe 67.2.kips

=

Consider tha111te connection int.o the column weak-axis produces negligible moments on lhe column. With rcspecc 10 lhe fo_undation, consider that the ACI 318 reinforcemenc requirements arc adequa1e for all apphcable concrete limit states including punching shear.

AlSC Seismic Pro-.ision.~ Section 02 6a requires that rhe :Wal strength equals or exceeds lhe required strength calculated using the load combinarions of the apphcoble building code, including lhc amplified ~J\mic load.

By reference to AISC SeiJmic Pm~·isions Section D2.5c, which references Section D2.5b, AISC Seismic Pro\'isions Section 02 6b indirectly ~tipulates that the required shear strength of the column base be the greater of lhe required sheM strength determined frorn load combinations including the amplified seismic load (Section 02 5b(b)) or the required column strength as stipulated in the systC'm chapters lSecuon D2.5b(~)). Here, the pro\.is1oru. of Section E3.6g apply. as follows:

LRFD

ASD

From ASCE/SEI 7, use Seismic Design C.ategory D. n.., = 3.0. p =1.0 and Sos= 1.0.

v.,, =r.~tpc -I.SH

Use LRFD provisions for the concrete design. The final connection design and geometry for the embedded column base i~ shown in Figure 4-24. Solution:

where l.M~ is the sum d the nomin.U plastic below the splice, or in this case, the base.

From AlSC Manual Table 2-4, die column material properties 3fe as follows:

For the c."\lculation of .Hpc:

ASTMA992

= (50 ks1){ 320 in.3)(1 ft/12 in.)

From AISC Manual Table 2-5, I.be plate material properties arc as follows:

LRFD

From ASThf A615, lhe concrete reinforcement properties are as follows:

ASTM A615 Grnde 60

From AlSC Manual Table I-1, the geometric propenies arc as follows:

;·

~: ..

.i;

Column W14x176 A= 51.8 in.? TJ= l.31 in. Beam W24X76 d 23.9 in.

=

IJI tx

V11=-H

2(1,330 kip-ft)

F,. = 60 ksi

•.

ASD I

i--

::

= l,330 kip-ft Therefore:

ASTM A572 Grade 50 F1 == 50 bi Fu= 65 ksi

.·:~.

s1.rengths of L'1e columns above and

M pc =FyZx

F1 =50 k.si Fu= 65 ksi

)j

11e.~ural

= 14.0 ft =190 kips > 96.0 kips Use 11,,

d= 15.2 in.

Zx =320 in. 3

br= 15.7 in.

1..,

=0.830 in.

=190 kips.

I

v. =r..upc -I.SH 0

=

2(1,330 kip-ft) 1.5(14.0 ft)

=127 kips> 67.2 JUps Use V11

:::

127 kips.

AJSC Seismic Provisions Section D2.6c(b) requires tha.t the fle.xural s~ngr.h equals or exceeds the lesser of the load combination of the applicable building code, including I.he amplified ~ismic lood, or I.IR> F, .t.

LRFD

M,,

o:

ASD Mo= l.IR1 F1 Z.• 1.5

J.IR,F,Z.

= J.J (1.J}(50 ksi)(320 in.3)

..

190 kips 60 ksi

.

1.5(12 in, ft)

'

=1,610 kip-ft> 946 .lcip-ft

0

Required Column Embedment Depth

Co~sider the base condition similar 10 s structuraJ steel coupling beam embedded in a coms · posne speci 3 J shear w:ill, per AISC Seismic Provisions Section H5 5c Therefi

ll~.5b(l )(3) ~ill

be used co de1ennine the embedment length. For.

embedment length, ~:

=J.54,fjj ( [>,. )

Vn

th~ calcul:~~n :~t~n e

0.66

P1b1L, 0.58-0.22P1 0.88+-L

bi

(Pro~·isio11.s

=3.17 io.2 AJSC Seismic Provisions Section H4 .5b{l)(4) requires two-thirds of this reinforcement in the top layer. It is pennitled to use reinforcement placed for other purposes as pan of the required longitudinal reinforcement.

=1,080 kip-ft> 662 kip-ft UseM =662 kip-fl

Use M,, = 946 kip-ft

F,

-

= 1.1(1.1)(50 ksi)(320 in.3 )

(12 in./ft)

V.,

As=-

Eq.

H4~2)

2~

AISC Seismic Prrn:isions Section H5.5c requires that Ibis reinforcement be confined by transverse reinforcement that meets the requirements for boundary members of ACI 318 Section 21.9.6. For this ex:imple, as st:itcd above, the foundation reinforeiog requirements are considered adequate per ACI 318. Minimum Face Bearing Plate Thickness

AISC Seismic Pro\lision.t Scc1ioo H5.5c requires face bearing plates on both sides of the column at !he foce of the foundntion and near the end of the embedded reg.ion. At a minimum. the stiffener thickness should meet the detailing requiremcnis of AJSC Seismic Provisions Section F3.5b(4) "here, fmfn

where

= 0.75t.., >~ in. =0.75(0.830 in.} 0.623 in. > Ya in.

=

lh = 0.85 from ACI 318 Se.ction I0.2.7.3

J

•

g = 11

= 140ft(12 in./ft)

Yielding in the Face Bearing Plates

=168 in.

The column axial force

is distributed from the column to the face bearing plates and then to

Try an embedment length, L,, of 22 in.

the fotll'ldation io direct bearing. As outl.med in AJSC Manual P:irt 14, lhe critical face plate cantile.,.er dimension, 1, is determined 3$ the IMger of m. n or Ni' (as depicted in Figure

Therefore:

4-22). where:

V,.

~( =l.54v'l.V k.s1

0 66 72·0-.-· in ) · (0.85)(l -

15.7

IIl.

5.7 in.)( 22.0 in.) 0.58-0.22(0.85) 168 in 0.88+ . 2(22.0 in.)

m:::

·'

N-0.95d

. (Manual Eq. 14-2)

2 B-0.8b1 2

(Manuol Eq. l_W)

As indicated io AJSC Seismic Provi.sions Section H4.5b(l)(3) th L--' • . t be · · 'd • e emv=ment lS consu:lered o gm ms1 e I.he first layer of co~g reinforcement io the foundation.

. i A.f
(from ManWJl Eq. 14-4)

Longitudinal Foundation Reinforcement • S. ecti on H4.,)V\l ~~ )(4) requu:e.s · that longitudinal foundation rein· ~AISC Seismic • Provisions . 1 olrcedment w1ht l nominal u1a1 strength equal to I.he expected shear strength of the column l>e P ace over 1 e t'mbcdmcnt lenglh.

N=d

= 207 k:ips > 190 kips

o.k.

~-

n=

4

B=bt

A. = I.0 (conservative per AJSC Manual PaJt 14)

'•

l

I l

MUMhN I' H{A.Mm;

In

Therefore:

Therefore:

Ath ... 0.03(4 ksi)(22.0 in.)(15.7 in.)/60 ksi

15.2 in.-0.95(15.2 in.)

m

= 0.691 in.2

2

, b be f 11 de\ cto~• \\-here they engage the embedThe pro"icion requU'CS th.it all tran.'i•CT ars u y . r-w .l r AC! 318. ded flange. For this e."tample. consider a bar length of 36 tn. fully de\.e opcc..I pe

=0.380 in. 15.7 in.-0.8(15.7 in.)

n

'

Use (2) 1A in. x 36 in. bar~ in cilch region.

2 =I.57 in.

(2)7t(+~ in.)2

Arb=

'An'= 1.0J15.2 in (15.7 in.) 4 =3.86 in.

4

=0.884 in.·., > 0.69 I .in.·.,

o.k.

For the yielding limit state, the required minimum rh.ickness is dctermjncd from AlSC Manual Equauons 14-7a and 14-7b: LRFD fmiJt

2Pu =l · - - 09FyBN = 3.86 in. 2(250 kips) x 0.9(50 ksi)(l5.7 in.)( 15.2 in.)

=0.833 in.

ASD

t,,,;,, =I

=3.86 in.

x

Section A-A

3.33(215 kips} 50 ksi(I5'.7 in.)(15.2 in.)

=0.946 in.

Due to the different load combinations used for LRFD versus ASD, lhere is a. slight d iscrepancy between the LRFD and ASD rcsulis for the required shear strength. Typically. one .merhod should be chosen and used consistemly throughout an entire design. For the purposes of this example, the LRFD result will be used.

co<:crete foundation" '

~

.J

Because flexural yielding at the beruing interface controls the face plate design, the fillet

.,

·.:;

:·"

,, ,, .... .

~'

weld connection provisions of AISC Seismic Provisions Section F3.5b(4) are not applicable and the lh.ickness )hould be fully developed. Therefore, the face plates are welded to the

i

columns with complete-joint-penctrotion groove welds.

<>

Use }i-in.-thick ASTM A572 Grade 50 face bearing plates.

I•

...

A

Required Transfer Reinforcement AlSC Seismic Provisions Section HS.SC requires two regions of transfer reinforcement :macbcd to both lhe embedded flanges. The area of rransfer reinforcemen t is:

v

..

-

if

, .I ...

\i

(21"" d;a. x 36" deformed bar an

typ.

/

:-=~--=+-~ - L'

\ \..

~1

I I !

. c

·e >

=LJ_

.I

*

f\

reinforcement bey

"1 I'-

....

,

I..

PL Ye" face bearing ~, plate. typ. \.

b

-<;

~

{

""'

Note: The deformed

r:·\

A.b

~ 0.03//l,,bf / F7sr

P,sr =60 k.si (dcformeJ bar anchor)

(Provisions E.q. H5- l)

bar anchor-to-column nange connection should match the strength or the bar. Fig. 4-24. C(Jnnection cross sl!ction as designed in £mmple 4.4A.

\A

l''IVIVJt.J'I !

M
The weld of the defom1ed bar to the column flange should be a flux filled ni:itcrial using an electric :trc welding process, that develops the strength of lhe rebar according to AWS DJ. J clause 7.

to 0.1SPc. then the vnlues of cl>Rvi and ~Rvz or Rvilfl and R.z/fl can be used to calculate the a\-ailable panel zone shear strength. Considering st.rcngth of a column without doubler plates:

A ISC Seismic Provisions Seclion HS.Sc also requires that the not-to-exceed transfer reinforcement area is:

(Spec. Eq. JI 0-l l )

I:.A,b < 0.08~b,., - As

(Pro'l'isio11s Eq. H5-2)

< 0.08 (22.0 m.)(72.0 in.}- As < I 27 in.2 - A,,

In AJSC Seismic Pro\ isions E.quation H5-2. As is the longirudioal area of reinforccmcnl pro,ided over the embedment length. As noted in the Given statement, the foundation reinforcing requirements src considered ade
where F-, = spcclfied minimum yield ~lJ'Css of the column web, ksi bcf width of column Oangc, in. d 11 :: depr.h of beam, in. ~ depth of column. in. lcf = thickness of column nange, Ill. cw =thickness of column web, in

= =

Expanding /.JSC Specification Equnticm J10-11 yields:

The final connection de~ign and. geometry for the embedded column base is shown in figure 4-24.

Rv1 and R,'2 are defined as:

4.5 DESIGN TABLE DISCUSSION Table 4-1. Comparison of Requirements for SMF, IMF and OMF Several categories of connection and design crileria are listed in Table 4-1. The Seismic ProiiJion.r requirements for each category are given for OMP. IMF and SMF.

Rv1 =0.60Fld,t..., Rv2 = 0.60Fyd,t-. (

3::c?)

Substituting into the expth~ded version of AISC Specification E.quation Jl().. l l, the available panel zone shear streng 1s:

Table 4-2. SMF Design Tables

,

Various values useful in the design of SMF are tabulared. Values are given for W-shapes that meet the width-to-thickness requirements for SMF beams and colwnns with F. = SO ksi 1 (ASTM A992). . For cases where the limiting web ~idth-to-thickness r.itio is a function of lhe member's required a."tial streng1h, P., or Pa. according to AlSC Seismic Provisions Table Dl.J, the me~11ber will sausfy the width-to-thickness requirements for highly ductile members if P., or Pa is less than or equal to the value tabulated for Pu max or Pa max• respec1ivcly. The nominal axial yield su-ength of a member, P;. is calculated as FyA1 • Note that it is assumed that Ca"" Pul9cP, > 0.125 Ol' C,, = ~Pa1P1 > 0.125. Where a dash is shown, there is no Jimiration on the values of P,, or Pa. The value 1 JRyMp is given to aid in several calculations, including rhe derermination of the required shear strength of SMF connections and the SlvfF column-beam moment ratio. Several values are tabul:ttcd lo enable quick determination of coluroo panel zone shear strength. To determine if AISC Specification Equations Jl(). J J or JJ0-12 are :ippHcable 0.75Pc is given for comparison with the required axial sr.rength, P,. If P, is less thnn or equ~

LRFD

c

..

ASD

I

¢Rv =

~~i

¢R~1 +--

di.

I.

r

'

R.

R,1

R..2

n

n

fldb

-=-+--

To aid in the detcnnination of the minimum pruiel-wne element thicknesses, W:/90 or dl/90 arc also tabula1ed. Therefore, the rum of the corresponding wif 90 or di/90 values for the SMF beam anti column will detennfoe the minimum panel-zone element thicknesses per AISC S~ismic Provisions Equation E3-7:

Values are also tabulated to aid in the determination of lateral bl':\Cing requirements. The \ value given for l-b lllAK is the maximwn distance between lateraJ. brace--; specified in AISC ~ Seismic Provisions Section Dl.2b. The required brace strength al beam-to-column c~nnec., j tions stipulated in AISC Seismic Pro"ision.s Section E3.4c(I), equal to 0.02FybJ'J• is also given. All lateral bracing is also required 10 have a minimum stiffness based on a moment equal to RyMp = R1 F1 Z. The value of t.h.is moment is tabulated. ,

1

~ ·· AMElllCAI' l>lsmun! OP ST661. Coi;STJUJCTION

I

....

MOMENT FRAMES ~·

4-123

DESIGN TABLES

'.':

Table 4-1


Comparison of Requirements for SMF. ' · IMF and OMF

.Comparison of Req~irements for SMF, IMF and OMF

Special Moment Frame {SMF)

Intermediate Moment Ftame (IMF)

Ordinary Moment Ftame (OMF)

0.04 rad

0.02 rad

tlo specifted minimum

Story Drift Angle Connection Rexurat Strength

Connection Shear Strength

Panel Zone Shear Strength

Performance confirmed by Performance conlinned by testing per A/SC Seismic testing per AlSC Seismie Provisions Chapter K; Provisions Chapter K; connectioo achieves connectioo achieves minimum 80% of nominal minimum 80% of nominal plastic moment of the • plastic moment of the beam at story drift ~le beam at story drift angle of 0.04 rad of 0.02 rad

fR: Develop 1.1RyMp of beam, maximum moment developed by system or satisfy requirements in NSC Seismle Provisions Section El .6b, E2.6 and E3.6

Special Moment Frame (SMF)

Continuity Plates

-or -

-or-

-or-

Lesser Vpermitted if Justified by analysis. See also tile exception provided Jn AISC Seismic Provisions Section E3.6d

Lesser Vpermilted if justified by analysis. See alSo Ille exception provided in AlSC Sefsmfc ProviSfons Section E2.6d

Lesser Vpermitted if justified by analysis

For P, s 0.7SP.,, compute strength per AISC Specification Eq. :.110-11 using 9;"' 1.oo (UlFDror 1.50 (ASD)· .

No additional requirements beyond AISC~tkln

No additional

Stability Bracing of Be;;ms

requirements beyond AlSC Specification

°'

Panel Zone Thickness

f ~ (d1 + W1 )/90

.

Protected Zone ..

No additional requirements beyond AlSC Specificauon

·:

No additional requirements beyond NSC Spectncation

No additional requirements beyond A!SC Specification

Beams and columns to satisfy the AISC Seismic Provisions Section 01.1 for hlgt\ty ductile members

Beams and columns to satisfy the AISC Seismic 'Pfovisions Section 01.1 tor moderately ductile members

No additional requlrements beyond PJSC Specification

eeam bracing required tO ~atisfy AISC . Seismic ProvisfDflS Section 01 .2b for highly ductile members

Beam bracing required to satisfy AISC Seismic Provisions Section 01.2a tor moderately ductile members

No additional requirements beyona AiSC Specification

Splices shall satisfy AISC Seismic Provisions Section 02.5 and E3.6g; bolts CJP groove welds '

Splices shall satisfy AISC Seismic Prov'.sions Sections 02.5 and E2.6g; bolts or CJP groove wetds

No additional requirements beyond 14$(; Specification

P$. established by ANSVAISC 358 for each prequalified connection; generally, one-half be.am depth beyona'centertine of plastic,hinge

k> established by ANSVAISC 358Jor each prequalifled connection; generally, one-half beam depth beyond centerline of plastic hinge

'

Of \

Q,"'

Provide continuity plates as required by AlSC Seismic Provisions Section El.Sb

No additional requirements beyoncl . AISC Specification

I

Column Splice

. ,.

.,

· Ordinary Moment Frame (OMF)

l:M~>1 .0

l:Mp0

Witith-to-Thickness

Vfor load combination Vtor load combination Vtor load combination including overstrength plus including overstrenglh plus Including overstrength plus shear from application 111 shear from application of shear from appllcatJon of Emh"' 2[1.1RyMpyLh Em11= 2[T.1RyMpJ!lh Em11= 2[1.TR1 MpJ/Lcr

For P,> 0.75Pc. compute strength per A!SC Specification Eq. J10-12 . using 9•= 1.00 (!.RFD) 0,=T.50(ASO)

To match tested To match tested condition 0< ANSVAISC 358 coodition or ANSVAJSC 358 Section 2.4.4 Section 2.4.4

Seam-Column Proportion

Limi~ticms

Intermediate Moment Frame ~MF)

..

None ,

.

.,

NJUMtlN J t'K.l\M_c:)

DESlGN TN:!Lt:.::.

Table 4-2 Ry= 1.1

·SMf Design ·varues

Table 4-2

Fy =50 ksi

SMF Design Values

Fy = 50 ksi

W-Shapes

W-Shapes Panel Zone

Panef Zone

Pu mar

,.

~Rr1

kip$

W44x335 x290 x262 x230

3900 1930 887 234

kip-ft

kips

8170 7110 6400

1360 1130 1020 914 2310 1950 1660 1500 1410 1360 1210 1110 989

3710 2600 1560

S87

333 W40x392 x331 x327 · x294 x278 x264 x235 x211 x183 x167 x149

Lateral 8r.1cing

LRFO (~"' 1.00)

(I.RFD)

Shape

761 1no 1490

u

t«O 1280 1240 1150 989 887 761 753 722

2200 1320 280 259 169

9R,.z kfp-in.

4480

0.75Pc kips

369() 3200 2900 2540

15700 11200 8120 7010 6090 5820 4690 3870 3550 2870 2120

6530 5550 4760 4390 4130 3980 3570 .3270 2760 2380

7090 4980 4940 4020 3540 3210 2670 2140 1530 1130 732

4350 3660 3600 3230 3090 2900 2590 2330

3550 2870 2120

Shape

90

L•mu

ho kips

kip-ft

W44x335 x290 x262 x230

0.450 0.449 0.450 0.450

14.5 14.5 14.4 14.3

28.1 25.0 22.4 19.3

42.2 30.9 33.3 29.0

7430 6460 5820 5040

W40x593 x503 x431 x397

15.8 15.5 15.2 15.1 15.0 15.0 14.9 14) 14.9 14.8 . 14.7

53.9 45.3 38.2 35.4 33.0 32.2 28.8 26.1 25.0 22.4 19.3

76.3 64.9 55.4 ' 51,0 47.9 46.7 41.8 38.3 36.1 32.4 28.1

12700 10600 8980 8250

x249 x215

Q.406 0.406 0.406 0.407 0.406 0.406 G.406 0.406 0.406 0.406 o.406

W40x392 x331 x327 x294 x278 x264 x235 x211 x183 x167 x149

0.406 0.406 0.406 0.406 0.406 0.406 0.406 0.406 0.407 0.406 0.406

11.0 10.7 10.7 10.6 10.s 10.5 10.6 : · 10:4 ·10.4 . 9.98' 9.52

31.2 26.0 25.8 23.2 21.7 '\ 20.6 18.8 16.8 14.2 12.2 9.79

48.1 . 40.6 40.1 36.3 34.1 32.5 29.2 26.2 22.5 20.3 17.6

noo

I·

1·

I·

I

7520 6690 6100 5730 . 5130 4420

I l:;

7840

1,. I ·;

6550

6460 5820 545o . 5180 4630 4150 3550 3180 2740

l:

}l

I.....

.r: .J

, :~ ....

~-

R1 Mp

0.02M,C,

ldps

x2n

1640

!lO

UIFO

fl

x362 x324 x297

2000 1850

dz

In.

x3n

306()

Wz

-or-

I :h.;.\ .

,..

Ry= 1.1

,J

1' 11; J

··:(.

•1.1

I

t.

.. :~l AMEJUC;\N 1Nsmuni OF SrEa Co;-isnucno.'I

AMl!Rlo.N lNsnrtm! OF Sn!a. CONS1'RUCTIOH

rl

MVMcJ'l l r.!<.AMJ:..S

!

lJ~l\.Jl'f

U\,01,.. ~

~


,-~

Ry= 1.1

,.. ., ,,.

...

' .,..

. •l

~~

!•:-:j ,~

:!··;~ ·>:·

flI r:~

k" !~

.~-

~~.

:j: ~1:

Fy

=50 ksi

l

SM F Design Values

Shape

W36x652 x529 x487 X441 x395 x361 x330 x302 x282 x262 x247 x231

P,,W:U (U!FD)

i'l36x256 x232 x210

x194 x182 x170 x160 xJSO

2810 2290 1650 1240 805 506 262

1'133x387 x354 x318 x291 x263 x241

x221 x201 W33x169

x152 x141 x130

Panel Zone LRFD (t == UlO) ~pe

3650 3020 2500 2010

1160 777 477 245

Ry= 1.1

w-~ha pes

kips ,,.

..f~

=50 ksi

Panel Zone

•

(:"

Fy

W-Shapes

'

~


SMF Design Values

14700 11700 10700 9630 8620 7810 7110 6450 6000 5550 5190 4860

¢Rvi

'Ryz

0.75Pc

kips

kip-in.

kips

Wz dz -or-

90

90

Lateral Bracing UIFD OJYlM1 C4

Lt llJU

0.02F,b1t1

R1 Mp

ho

in.

ft

kips

0.378 0.378 0.377 0.378 0.378 0.378 0.378 0.377 0.377 0.378 0.378 0.378

17.0 16.6 16.5 16.3 16.1 16.0 15.9 15.9 15.8 . 15.6 15.5 15.4.

62.3 50.1 45.8 41.5 37.0 33.6 30.7 28.1 26.1 23.9 22.3 20.8

69.5 64.0 57.6 52.0 47.4 43.2 39.6 36.9 . 34.1 32.0

'

kips

klp·ft

85.1

13300 10700 9760 8750 7840

2430 1920 1770 1590 1410 1280 1150 1060 985 930 881 832

19900 7200 13100 5850 11100 5360 9110 4880 7320 4350 6070 3980 5110 3630 4240 3340 3680 3110 3100 . 2900 2710 2720 2360 2560

W36>t652 .x529 x487

5240 \ 4720 4200 3870 3620 3370 3150 2930

1080

2820 2550 2320 . 2140 2010 1880 1760 1660

W36x256 x232 x210 x194 .x182 x170 x160 x150

0.377

11.0

21.1

32.0

0.377

10.9 .

19.0

29.0

673

3290 2680 2030 1730 1520 1310 1120 954

0.378 0.378 0.377 0.378 0.377 0.378

10.7 10.6 10.6 . 10.5 - . 10.4 10.3

16.6 15.2 14.3 13.2 12.2 11.3

26.0 24.0 22.5 20.9 19.6 18.3

7870 7160 6400 5850 5240 4740 4320 3900

1360 1240 1100 1000 900 852 788 723

7580 6330 5140 4280 3510 2800 2330 1870

4280 3900 3510 3210 2900 2670 2450 2220

W33x387 :<35-4 5<318 x291 x263 'x241 '5221 x201

0.349 0.349 0.349 0.348 0.348 0.349 0.348 . 0.349

15.7 '15.5 15.4 15.3 15.2 15.0 14.9 14.8

36.9 33.6 30.2 27.5 24.8 22.3 20.2 18.1

50.9 46.6 42.0 38.5 34.8 31.5 28.9 26.1

7150 6510 5820 5320 4770 4310 3930 3540

3170 2820 2590 2350

679 638 604 576

1540 1170 954 757

1860 1680 1560 1440

W33x169 x152 x141 x130

0.348 0.349 0.349 0.349

10.4 10.3 10.1 9.93

14.0 12.3 11.0 9.83

21.2 19.0 17.5 16.0

2880 2560 2360 2140

.,

968 914 838 790 738 702

x~I

x395 x361 x330 x302 ; x282 x262 x247 x231

L

"

r f:

•:.

::

AMERlCAN lNsmtml OF STF..Ei:CONSTRlJCTJON

A.MSRJCAJll lNSTITUTE! OF STE!!L CONSTllU(,"llON

30.1

7foo 6460 ' 5870 ' 5450 5040 4720 4410 4770 4290 3820 3520 ·3290 3060 ··2s60 2660

4 •••v••tU°' 1 t".K.t\1'-U:~

DESIGN TABLES

SM F Design Values

Ry= 1.1

Fy

=50 ksi

W-Shap es Panel Zone

p•-

(l.RF1l)

Shape

\

kips WJ(b(391 x357 x326 x292 x261 x235 x21 1 x191 xl73 W30x14S x132 x 124 x116 xi OB

I

2260

t1tii,.l'

1670

~89t

~1~5f~ .4~

36\ <.; 242"

1350 982 720 5"2 364

x368 x336 x307 x281 x258 x235

t

I 1..J-

)(194 x178 x161 x146 W27x129 x114 x102 x94

klp·f1

W30x391 x357 x326 x292 x261 x235 x.211 x.191 x173

0.315 0.315 0.314 0.314 0.314 0.314 0.314 0.315 0.314

153 151 15.0 149 14.7 14.6 14.5 14.4 1'6 2

38.1 34.7 31.6 28.3 25.1 22.7 19.9 17.9 16.1

51.8 47.5 43.1 38.6 34.6 31.3 27.9 25.2 22.8

6650 6050

0315 031 4 0.315 0314 031 4

9.48 9.35 9.27 910 8.9"

12.4 105

18.6 16.4 15.3 142 13.1

2290

W30x148 x132 xt24 }(116 1<108

546 497

3310 2860 2260 1800 1470 1200

5960 4090 3720 3380 3120 2850 2600 2400 2140 1970 1790 1620

W27>'539 x368 ><336 x307 x281 x258 x235 x217 x194 x178 x161 x146

0282 0.283 0283 0.282 0.283 0.283 0.283 0.282 0.282 0.282 0.283 0.283

15.2 14.5 14.3 14.2 14.1 14.0 13.8 13.8 13.7 13.5 13.4 13.3

71 .7 48.9 4<19 412 37.6 34.S 31 .3 291 25.9 23.6 21 .4 19.3

8660 5680 5180 4720 4290 3910 3540 3260 2890 2610

505 467 419 395

1090 786 620 500

1420 1260 1130 1()40

W2.7X129 x114 x102

0.282 0.283 0.283 0.282

16.4 14.3 128 11 7

1810 1570 1400 1270

kips

7310

1350 1220 1110 979 882

2110 1570

2600

1340 965 527

1990 1730 1540

32'6

1400

597 599 559 530 509 "87

1320 945 817 683 546

n9 654

3580 3180 2870 2340

8360 7000

5820 4710 3720 3060 2370 1910 1550

718

3890

x217

kips

kip-in.

9530 6250 5700 5190 '720 4300

W27.x539

kips

kJps

1910 1740

f

ft

kip-ft

2060

R1M,

In.

0.75Pc

2520 2200

WO O.CYlM1 C. h.

Ltaw ·

•Rrt

. sfT, 6~ 545 . 4(5

d,

-90 or-90

•R~

5340 4750 4270 3790 3400 3060

w,

t

Lateral Bractng

Panel Zone

LRFD I+ UlO)

1.1R1M,

6660 6000

1513.

Ry= 1. 1 .

SMF. Design Values

Fy::: 50 k si

W-Shapes

I

\



l

1920 1260 1130 1030 932 853 784 707 632 605

17300 8140 6830

5660 4830 4030

4310 3940 3600 3230 2890

2600 2340 2100 1910 1640 1460

1370 1280 1190

Shape

x9'6

9.19 9.06 8.9" 8.81

9,n 8.93 7.98 54.2 36.5 33.3 301 Z78 25.3

22.9 212 18.8 168 • 15.1 13.7 11.0 9.39 8.30 7 45

5450 4860

4320 3880 3440 3090 2780

\

2000 1870 17~

1590

~\·

2360 2130

t·

\ '

:.._

Af.fEIUCAN lllmT\ITI! OF ST£EL CONSTIUICT'ION

...

..:.......

AMl:JuCAN L"IS'TT(UTE OF Sttl!L CONSTRUC110N

~

MOMENT FRAMES

4-130

r

i:'·

SMF Design Values

Ry= 1.1

Fy

=50 ksi1

""•:,

W-Shapes

i:' ·

Shape

i•

kips

r•.

I

" .::.

~·:·

., •.

:~d ~:··

...::.:>:·~ ..

:

:j;I J ;: 'r~ · !·

"'1

1ij

!~'.

...:.. 1;: :$,

...

~~:

~;: l'

~:

t.

W24x370 x335 x306 x279 x250 x229 x207 · x192 x176 .,x162 x146 x131

0.75Pc

kips

kip-in.

kips

x8_4 x76

1110 . 836 506 290

1410 1280 1130 1010

404 375 340 315

W24x62 x55

187 58.5

m

x94

Shape

$R112

1280 1140 1020 929 821 749 671 620 567 529 482 445

d, -or90 90

L11mu

in.

ft

W:

4090 3690 3360 3070 2760 2520 2280 2120 1940 1790 1610 1450

W24x370 x335 x306 x279 x250 x229 x207 x192 x176 x162 .x146 x131

0.251 0.250 0_250 0250 0.250 0250 0.251 0.251 0.250 0.251 0.250 0251

13.6 13.4 13.3 13.2 13.1 12.9 12.8 . 12.8. 12.6 · 12.7 12.5 12.3

ns -

1140

W24x103

8,27

625 481 374

1040 926 840

x94

x84 x76

0.250 0.251 0.251 0.250

221 161

683

608

\'/24x62 x55

0.250 0.251

9120 7470 6270 5230 4240 3530 2880 2490 2080 1740 1380 1070

~

.

-~

. --

LRFD

-r

":t~-rH -~ASO.~. ....·: ;-~~ ·

1)1Rv1

5700 5140 4650 4210 3750 . 3400 3060 . 2820 2580 2360 2110 1870

W24x103

._

LRFO (¢ =1.00)

(LRFD)

Lateral Bracing

Panel Zone

Panel Zone Pu mu

Ry= 1.1

SMF Design Values

Fy =50 ksi

W-Shapes

·~

I

4 - 131

DESIGN TABLES

Table .4-2 (continued)


I

~:

~

9:azF,1iftr - .::o.02M;cd

\.·M .,;. 1.5•,'11-h-:

~~'1'/r.~· ~: ••

D.02Fyb1tt

0.02M,Cd

R1 M,

h,

kips

kips

kip·ft

37.3 33.5 30.6 27.8 24.9 22.7 20.4 19.0 17.3 15.9 14.1 12.4

49.1 44.9 40.9 37.3 33 5 30.6

5180 4680 4230 3830 3410 3090 2780 2560 2340 2150 1920

27.7

25.6 23.5 21.6 19.5 17.3

1700

8.82

13.1

8.23 8.11 7.98

7.94 6.95 6.11

11.9 10.6 9.48

1280 1160 1030 917

5.74 s.~z:

4.15 3.54

7.29 6.38

701 614

20.5 18.5 16.9 14.4 12.9 11.9 10.8

27.2 24.7 22.5 f9.5 17.6 16.3 14.9

2430 2180 1980 1710 1530 1410 1280

H.7

676

306 280

W21x201 x182 x166 x147 x132 x122 x1 11

2670 2400 2180 1880 1680 1550 1410

628 565 506 4n 425 391 355

3010 2460 2060 1490 1210 1030 848

2220 2010 1830 1620 1460 1350 1220

W21x201 x182 x166 x147 x132 x122 x111

0.219 0.219 0.220 0.220 0219 0.220 0.219

W2lx93 x83 x73

1110

655 525 409 349 280

1020 915 806 750 686

· W21x93 x83 x73 . x68 x62

0.219 0.219 0.219 0.219 0.220

7.65 7.61 7.52 7.48 7.36

7.83 6.98 6.14 5.66 5.07

10.5 , 9.23 8.63 7.76

1010 898 788 733 660

n6

376 331 289 272 252

650 555 481

256 237 217

249

626 551 488

\Y21x57 x50 x44

0220 0.219 0.220

5.61 5.40 5.24

4.26 3.-19 2.93

6.99 5.99 5.17

591 504 437

x68

x62 W21x57 x50 x44

988

1060 685 521 330

867 807

326 176 57.6

168

118

12.6 12:5' 12.4 12.3 12.2 12.l 12.1

!:'

J

I

!

:.:.

:~ ' ·.~

I:I

,\1'!EIUCAN lNSTl'TVTE OF STEEL CoNsnuJ<:TlOl'i AME!uCN' INStmm; OF STEa. CONSTllUCOON

MOMENT FRAMES

oESlGN TABLES

4-1

Table 4-2 (c ontinued) Ry~

1.1

Tab le 4-2 (c ontinued)

SM F Design Values

Fy= 50 k si

SMF Design Values

Fy= 50 ksi

W-Shapes

Shape

W-Shapes Panel Zone

Pu max (!..RFD)

!..RFD (~ "' 1.
kips

- --

W18x311 x283 x258 x234 x211 x192 X17S x158 x143 x130 •x119 ··X106 x.97

3800 3410 3080

2no 2470 2230 2010 1790 1620 1460 1320 1160 1060 938

5<$6

W18x71 x65 x60

x55 x50 W18x40 'x40 .x35

1020 920 826 734 658 588

534 479 427 388 373 331 299

195 169 159

60.6

(16~

5620 4690 3810 3170 2590 2110 1760 1450 1140 891 756

451 384 329 269 219 . 200 149 97.5

457 395 335

427 224

8110

275

319 98.3 46.5

604

kip-in.

592

227 212 192

998 882 756

~R112

265

668 520 326

x 77

W16x31

kips

736 671 620 565 509

W16x100 x89 W16x57 xso x45 x40

kip-ft

Ry= 1.1

248

298

265 225

529 46-4 415 368

212 186 167

272

131

146

0.75P, kips

34«! 3120 2850 2570 2340 2110 1930 1740 1580 1440 1320 1170 1070 949

W18x311 x283 x258 x234 x211 x192 x175 x158 x143 x130 i<110 x106 x97

784 716 660 608 551

Wl8x71 x65

506 443 386

Wl8x4~

908 717 535

1100

328 253 202 161

630 551

96.4

Shape

983

a.ca 499 443

342

x86

x60

'555 xSO x40 x35

Wz

dz

90

90

-or-

}:·..

LRFD

o.02M;c,

Lbowt

R1 Mp

ho

In.

ft

kips

kips

kip·ft

0.187 0.188 0.188 0.188 0.188 0.188 0.187 0.187 0.187 0.188 0.188 0.187 0.187 0.187

12.3 12.1 . 12.0 11.8 11.7 11.6 11.5. 11.4. 11.3 11 .2 ' 11.2 11.1 11.0 10.9 .

32.9 29.8 27.1 24.7 22.2 20.1 18.1 16.3 14.8 13.4 12.0 10.5 9.66 8.55

42.3 38.3 35.0 31.8 28.7 26.0 23.8 : 21 .4 19.5 17.6 16.1 14.2 13.1 11 .6

3460 3100 2800 2520 2250 2030 1820 1630 1480 1330 1200 1050 967 853

0.188 0.188 0.187 0.187 0.187

7.07 7.02 6.98 6.94 6.86-

6.19 5.69 5.25 4.74 4.28

9.07 8.27 7.73 7.04 6.39

669 610 564 513 '453

0.188 0.187 0.187

s.36 5.28 5.07

3.67 3.16 2.55

5.70 4.96 4.23

416 359 305

0.167 0.167 0.166

W16x57 x50 x40

0.166 0.167 0.166 0.167

6.65 6.61 6.53 6.53

5.09 4.45 3.98 3.54

7.36 6.45 5.84 5.18

481 422 377 335

W16x31

0.167

4.86

2.43

3.83

248

x45

I

Lateral Bracing

W16x100 x89

xn

)"

10.4 10.4 10.3

10.2 9.10 7.83

13.6 12.1 10.5

908

802 688

r

I I ~:.;·

II. \..

I ~: ,,,.. , ... '.:

l

I

ht~

I

l

1 ··

l.·:

I

I.

"-'·~

AMillucv. lNST!TIJTE OF STEEL CONSTJtUCTION AMEluCAN

ll-tSTmTTl! OP STEEL CONSTIU.JCllON • lb~

I

.l

MOMENT FRAMES

4-134

''.~$1

i.f.-··

4-IJS

DESIGN TABLES

i~

Table .4-2 (continued)

.~/

SMF- Design Values

Ry= 1.1

Fy= 50 ksi

Table 4#2 (continued) W#Shapes

W~Shapes

Shape

LRFO (Ci> = 1.00)

(lRFO)

kips 8370 7460 6660

·..:~

\)t :·m11

« :: ) :: ,,

0.75Pc

kips

kip· In.

kips

x159 xl45

3040 2730 2460 2200 1970 1790 1610 1450 1310

W14x132

1180

284

1400

1460

701 635

665

. 560

5~0

219 192 174

467

' 900 818 750

W14x53 ·x48

439 395

154 141

316 . 256

585 . 529

W14x38

400

310

131

162

420

W14x26

116 .

203

106

5290 4720 4380 4040 3710

x426 x398 x370 x342 X311 x283 x257 x233 x211 x193

W14x82 x74 . x68

iil ·:

~Rt?

38800 32500 27100 22600 18700 15600 13900 12100 10500 9000 7450 6210 5140 4230 3460 2930 2420 1990 1660

~90

x11s

l~

41R,1

2060 1830 1630 1440 1290 1150 1050 972 891 809 723 646 581 514 462 414 378 335 302

I

i:::i

Shape

-8060 7350 6680 6080 5510 5030 4690 4390 4090 3790 3430 3120 2840 2570

59$0 :

-

Lateral Bracing

Panel Zone

Panel Zone Puma

79.9

ma

2130 1940 1750 1600

288

Ry= 1.1

SMF Desigr- Values

Fy = 50 ksi

dz -or90 90 W:

In. ..

Lb ,_

ft

LRFO 0.02MrCd

0.02F1bttt

87.9 80.0 72.4 65.7 59.5 53.9 50.8 47.3 43.9 40.5 36.6 33.3 30.2 27.3 24.6 22.6 20.6 18.6 16.9

104 95.2 86.9 79.l 71.7 65.2 60.9 56.8 53.3 49.3 44.8 40.8 . 36.9 33.S 3M 27.7 25.3 22.9 20.9

7610 6780 6050 5410 4810 4290 3980 3670 3370 3080 2760 2480 2230 2000 . 1790 1630 1470 1320 1190

15.1

18.8

1070

W14x730 x665 x605 x550 x500 x455 x426 x398 x370 ><342 x311 x283 x257 x233 x211 xl93 x1?6 x159 x145

0.140 0.140 0.140 0.140 0.140 0.140 \ 0.140 0.140 0.140 0.140 0.140 0.140 0.140 0.140 0.1,40 0.140 0.140 0.140. 0.140~

1S.5 19.2 18.9'" 18.7 :18.4 18.2 18.0 l7.9 17.7 17.6 17.5 17.3 17.2 17.0 16.9 15.B" · 16.7 16.6 16.5

W14x132

0.140

15.6

W14><82 x74 >C68

0.140 0.140 0.140

10.3 . 10.3· 10.2 .

8.64 7.93 7.20

11.4 10.3 9.51

637 578 527

W14x53 x48

0.140 0.140

7.98 7.94

5.32 4.78

7.26 6.53

399 359

0.145

6.44

3.4~

4.97

282

W14x38

0.145

4.49

2.11

3.28

184

W14x26

~~

'•

,,... .,'•'• {

1 I

kip-ft

kips

!•

AMEJtfCAN AMEJUCAN l.NSTTTUTR 01' Sre:a CO.NSTRUCTlON

ho kips

~·

II

Ry Mp

INS'J1TVJ1! ~ STEEL CONSTR•JC'l10N

. .,,

MOMENT FRAMES

_...•.JV

4-137

.·-

1:

l'

Table 4-2 {continued)

Table 4-2 (continued}

SMF Design Values

Ry= 1.1

l:.

pESIGN TABLES

Fy =50 ksi

Fy = 50 ksi

.c.

:. sMF Design Values

Ry= 1.1

W-Shapes

W-Shapes

r .,.

Panel Zone Ponwt

Shape

kips

W12x336 x305 x279 ><252 x230 x210 x190 x170 x1 52 x136 x120 x106 x96 W12x50 x45

Shape

~Rn

~R-2

kip-ft

kips

kip-in.

kips

3040 2710 2430 2160 1950 1750 1570 1390 1230 1080 938 827 741

897 797 730 647

10600 8720 7190 5920 4970 4160 3460 2760 2210 1740 1360 1080 889

584

520 458 403 358 318 279 236 210

3710 3360 3070 2780 2540 2320 2100 1880 1680 1500 1320 1170 1060

90

90

0.02M,C,

RyMp

-or-

hmu

In.

ft

kips

kiP.S._

kip-ft

o.12r 0.121 0.122 0.121 0.122 0.121 0.121 0.121 0.121 0.121 0.121 0.121 0.121

14.4 14.2 14.0 13.9 . 13.8 13.6 13.5 13.4 13.3 13.1 13 12.9 12.8

39.7

48.1 43.4 39.5 35.7 3.2.7 29.9 26.9 24.4 21.7 19.3 17.1 15.2 13.7

2760 2460 2200 . 1960

ho

~5.8

32.4 29.3 26.7 24.3 22.1 19.7 17.5 15.5 13.7 12.1 11 .0

\:

1no 1600 1430 1260 1110 981 853 752 674

6.82 6.14

330 294

135 122

298 240

548 491

W12x50 x45

0.121 0.122

8.15 8.11

160

386

W12x35

0.127

6AO

3.41

4.69

235

113

243 209

W12X22 x19

0.127 0.128

3.52 3.42

1.71 1.40

2.71 2.28

134 113

W10x112 x100 x88

11.1 11.0 10.9 10.8 10.8

13.0 11.5 10.2 8.87 7.78

15.9 14.3 12.7 11.0 9.74

674 596 518 447 391

x68

0.0989 0.09S4 0.098 0.0984 0.0984 0.0984

8.35

4.97

6.37

252

WlOx45 W10x30 x26

0.105 0.105

5.69 5.65

2.96

2.54

4.03 3-49

168 143

W10x19 x17

0.105 0.105

3.63 3.51

1.59 1.32

2.42 2.11

W12x22 x19

197 110

148 125

95.9 86.0

65.5 44.2

xS8

741 655 570 492 430

258 226 196 169 147

1460 1160 909 695 539

1230 1100 975 851 746

W10x45

2n

106

2n

499

W10x30

185

x26

158

94.S $).3

136 101

332 285

109 94.3

76.5 72.7

211

dt

362 324 258

W10x19 x1 7

W12x336 x305 x279 x252 x230 x210 x190 x170 x152 x136 x120 x106 x96

Wt

5.17 4.63

453

xn

i~

l.RFO

0.75P,

W1 2x35

W1 0x112 X100 x88

Panel Zone LRFO (~"' 1.00)

(UIFD)

Lateral Bracing

56.4 39.3

211 187

I

I

I' '-

xn

'1

99 85.7

'1

I

I; \

II \·" \

I•·:

11

r:

t

I

-:_,,

AMERICAN 1.Nsnnrm OJ' STJ;EL. CONSTROCTION

AMaucAN INsTmrr£ OF STEEL C0NSTR1.ICUON

..

~

5-1

MOMENT FRAMES

4-13&

PART 4 REFERENCES

PARTS

~'Swell.

...

B. (2011), "A Yield Line Component Method for Bolted A3llge Connec1ions;• Engineering Journal, American Institute of Steel Consll"Uction, Vol. 48, No. 2, 2nd Quarter, pp. 93-116.

Fisher. J.M. and Kloiber. L.A. (2010), Base Plate and Anchor Rod Design, Design Guide I. 2nd Ed., AJSC, Chicago, IL .

Gomez, I.. Smilh, C.; Deierlein, G. and Kam·inde, A. (2010). "Shear Transfer in faposed Column Base Pint~;· http://nees.or~resources/837.

BRACED FRAMES

5.1 SCOPE . . . . . . .

·· ········· ······· ·

· · · · · · · · · · · · · · .... .. .. .

5-3

- 2 ORDINARY CONCENTRICALLY BRACED FR.AMES (OCBF) : . . · ·. ·. • · · · 5-3

).

OCBF De~ign Example Plan and Ele\Jtion .............. . ....... · · · · · · · · · 5--4

Hamburger. R, Ktawinkler. H., Malley, J. and Adan, S. (2009), Seismic Design of Steel Special Moment Frames: A Guide for Practicing Engineers, NEHRP Seismic Design Technical Brief No. 2. National Institute of Standards and Technology.

Example 5.2.1 OCBF Diagonal Brace Design ......... . . . ..... · . · · · · · · · · · · 5-6

Murray, T.M. and Sumner, E.A. (2003), Extended End-Plate Momeni Ccnnecrions-Seismic and lVind Applications, Design Guide 4, 2nd Ed., AlSC, Chicago, IL.

Example 5 l.3 OCBF Beam Design F.xample 5.2.4 OCDF Brace-10-Beam/Column Connection Design .. ..... .... 5-25

Example 5.2.2 OCBF Column Design . . ....

....... . ............... 5-15 . ..... . .. 5-lS

Example 5.2.5 OCBF Ten.~ion-Only Diagonal Brace Design . . . . ......•. ·. 5-75

OSHA (2008), Occupational Safety and Health Regulation.~. Title 29. Code of Federal Regulations, U.S. Government Priming Office, Washington. DC.

5.3 SPECIAL CONCENTRICALLY BRACED FRAMES (SCBF) . . ...... · · • · · · 5-82

West, M.A. and Fisher, J.M. (2003), Serviceability Desig11 Considerations for Steel Buildings, Design Guide 3, 2nd Ed, AISC. Chicago, IL.

SCBF Design Example Plan and Elev3tioo . ..... · .. · · . · . · · · · · · · · · · · · · · · · 5-86 . . . . ......... - ... · .. · ...... · .. ...... 5-8'7 fa:unple 5.3. l SCBF Brace Design • 5-91• E:<:unple 5.3.2 SCBF An aJ ys1s ..............••.•• · • · •. · · · · · · · · · · · · · · ·

Example 5.3.3 SCBF Column Design .......•.. · . · .. · .... · · · · · · · · · · · · · · 5-98

111

faample 5.3.4 SCBF Beam Design ......... ·. · .. · · · · · · · · · · · · · · · · · · · · · 5-104 .

E.'
'.ii ~1 11

. ... · .... · · · · · · · · · · · · ·

. 5-119

Example 5.3.6 SCBF Column Splice Design . ................ · . · · · · · · · · · 5-129

,.

Example 5.3.7 SCBF Ma.-Umuro Force Limited by Foundation Uplift ....... 5-136

Example 5.3.8 SCBP Brace-to-Beam Connection Design ............... ·.· 5-140 Example 5.3.9 SCBPBrace-to-Beam Connection Design ................. · 5-178 Example 5.3.10 SCBF Brne»to-Bcam/Column Connection Design ........ · 5-2( · Example 5.3.11 SCBF Brace-10-Beam/Column Connection Design with Elliptical Clearance and Fixed Beam-lo-Column Connection .... · · . · · · · 5-269 Eitample 5.3.12 SCBF Brace-to-Beam/Column Connection DesignIn Plane Brace Buckling ....................... · .... · · · · · · · · · · · · · · · 5-299 5.4 ECCENTRICALLY BRACED FRAM6S (EBF) .............. ·. · ·. · · · · · · 5-334 EBF Design &le Plan and Elevation ................... · . · · · · · · · ·

5-33~.

Example 5.4.l EBF Story Drift Check ..... .... .. . ....... .. · . · · · · · • 5-3~' . 5-3~( Example 5.4.2 EBF Link· Des1gn ........ · ... · · . · · · · . · · . · · · · · · · · · · · · · · Ex.ample 5.4.3 EBF Be:im Outside of the Link Design .... · .. . · · . · · · · · · · · · 5-3'=

E:
II

4-138

5-1

MOMP.NT ?RAMES

PART 4 REFERENCES

PARTS

D~-swcll, B. (2011). "A Yield Line Component Method for Bolted fl~ge Connections." Eitginuring Joumal. Americ.ln Institute of Steel Cons!J"Ucooo, Vol. 48, No. 2, 2nd Quarter,

BRACED FRAMES

pp. 93 116. t"

Fisher, J.M. and Kloiber, L.A. (2010), Base Plate and Anchor Rod Design, Design Guide 1. 2nd Ed , AlSC. Chicago, IL. ·

5.1 SCOPE Gomez, I. Smith, C.. Deierlein, G. and Kam·inde, A. (2010). "Shear Transfer in Exposed Column Base Plates," h ttp://n ees.org/resources/837.

Hamburger, R., Krawinkler, H., Malley, J. aod Adan, S. (2009), Seismic Design of Steel

.

.. . .. . - .

. . · . · .. · · · . · ·

................ 5-3

5.2 ORDINARY CONCENTRICALLY BRACED FRAMES (OCBF) - .. · • · · · · · · · 5-3 OCBP Design Example Plan and Elevation ......... ••..... .... : · · · · · · · · · · 5-4

Special MomenJ Frames: A Guide for Practicing Engineers. NEHRP Seismic Design Technical Brief No. 2. National Institute of Standards and Technology.

Example 5.2.1 OCBF Diagonal Brace Design · .. - .. . . · . · · · · · · · · · · · · · · · · · · 5-6

Murray, T.M. and Sumner, E.A. (2003), Extended Encl-Plate Moment Connecrio11s-Seismic and 1Vi11d Applications, Design Guide 4. 2nd Ed , AISC, Chicago, IL.

Example 5.2.3 OCBF Beam Design ....................... . ... ·.······· 5-18

OSHA (2008), Occupauonal Safety and Health Regulations, Tille 29, Code of Federal Rcgulauons, U.S. Govenunent Printing Office, Washington, DC.

Example 5.2.5 OCBFTension·Only Diagonal Brace De$itn .... - .. · · · · · · · · · 5-75

West, M.A. and Fisher, J.M. (2003), Serviceability Design Considerations for Steel B11ildings, Design Guide 3, 2nd Ed., AISC, Chicago, IL.

Example 5.2.2 OCBF Column Design ............ ...... ·. ·. - · - · · · · · · · · · 5-15

EJtample 5.2.4 OCBF Brace to-Bc:im/Column Connection Design . . . . . . . . . . 5-25 5.3 SPECIAL CONCENTRICALLY BRACED FRAMES (SCBF) · · · · · · · · · · · · · · 5-82 SCBF Design Example Plan and Elevation ..... - ..... · · . · · . · · · · · · · · · · · · · 5-86 fa:imple 5.3.1 SCBF Brace Design ........ .. ....... · · · · · · · · · · · · · · · · · · - 5-87 fa:unple 5.3.2 SCBF Analysis ...... . · · · · · . · . · · · · · · · · · · · · · · · · · · · · · · · - 5-93

. Example 5.3.3 SCBF Column D es1gn ....•..• - • · . · · · · · · • · · · · · · · · · · · · · · · 5-98

. .............. · .. · . · · · · · · · · · · · · · · · · 5-104 E:tample 5.3.4 SCBF Beam Des1gn Example 5.3.5 SCBFBeam Design ................. ·. · · · ·. · · · · · · · · · · · 5-119

·0es·1gn .... · · · · · • · • · · · · · • · • · · · · · · • · 5-129 Example 5.3.6 SCBF Column S p tice Example 5.3.7 SCBF Ma;
fj

faample 5.3.8 SCBF Brace-lo-Beam Connection Design .. ···.··· - · · · · · · · · 5-140

Example 5.3.9 SCBP Brace-to-Beam Connection Design .... · .... · .. · · · · · · 5-178 Example 5.3.10 SCBF Brace-to-Beam/Column Connection Design ... . ... . ·· 5-202 Example 5.3.11 SCBF Brace-lo-Beam/Column Connection Design with Elliptical Clearance and Fixed Beam-lo-Column Connection ..... · · · · - · 5-269 Example 5.3.12 SCBF Brace·to-Beam/Column Connection Design--

In Plane Brace Buckling ......... · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-299 5.4 ECCENTRlCALLY BRACED FRAM~ (EBF) .......•.•...... · · · · · · · · · 5-334

EBF Design Example Plan and Elevation ........................ ·.. · · 5-338. Example 5.4.l EBF Story Drift Check ............. ...... ........ · · · · · · 5-339

.

.

'EJtample 5.4.2 EBF Link Design ....... · · · ... · . · . · · · · · · · · · · · · · · · · · · · ·

~~

Example 5.4.3 EBF Beam OulSide of the Link Design ....•...... · . · · · · · · 5-3~ Example 5.4.4 EBF Brace Design ..... · . · · ... · · · · · · · · · · · · - · · · · · · · · · - · 5-3

7

Example 5.4.5 EBP Column Design ..... ... ... . . . . . . . . . . . . . . . . . . . . . . . 5 .J67 Example 5.4.6 EBF Br3ce-to-Lin.k Connection Design ........... ......... _ 5 372 Example 5.4.7 EBF Brace-10-Be&n/Column Connectio·" D · .... cs1gn ... ...... . .. 5-379 5.5 BUCKLING-RESTRAINED BRACED FRAMEs (BRBF) ................ 5-413 BRBF Design Example Plan and Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-418

5.2 ORDL'lARY CONCENTRICALJ..Y DRACFD J=RA.'l\,ff'..S

s

1

5.1 SCOPE

\,

The AlSC Seismic Provisions requirements and other design considerations summarized in Ibis Part apply to the design of the members and connections in braced frames thnt require seismic detailing according to the AJSC Seismic ProvisWn.r.

'<

~..

Example 5.5.J BRBF Brnce Design .......... .

. . . . . . . . . . . . . . . . . . · • ···. 5-419 Example 5.5.2 BRBF Column Design ........... .

. . . . . . . . . . . . . • . . . ... . . 5-425 Example 5.5.3 BRBF Beam De.sign ................................... 5-4JO

5.6 NONBUlLDING STRUCTURES: A SPECIAL CASE ........... .... .... 5-443

k

5.2 ORDINARY CONCENTRICALLY BRACED FRAMES (OCBF) concentric~y br.lceJ frame (OCBF) systems. like other concentrically braced frame systems, resist lateral fon:es and displacements primanly through the ~ial strength and stiffness of lhe brace members. TI1e design of OCBF systems is :iddressed in AISC Seismic Provisio11s Section Fl. Concentrically braced frames are arranged such that the centerlines of the framing members (braces. columns nnd beams) coincide or nearly coincide, thus minimizing flexural behavior. While special concentrically braced frame (SCBP) sys· terns have numerous detailing requircmenis to ensure greater ductility, OCBF systems n.nticipate linle inelastic deformation and are designed usmg a higher seismic force level to account for their limited system ductility. OCBF systems, with their relativdy simple design and construction procedures, can be an attractive choice for sm:illcr buildings and nonbuilding structures. OCBF systems may be lc<.s desirable in larger buildings an
Ordinary

l:

I

l

I f

• Braces are moderately ductile members as given in Sccoon Fl .Sa • The required strength of bracing connections is given in Section Fl .6a • The brace slenderness limit of Kl Ir S 4JE I F1 for V or invencd-V configurations i~ given in Section Fl.Sb • The requirement.s for beruns in V or inverted-V frames nre given in Section Fl .4a

..

BRACB> FRAMES

The conne<:lion streoglh requirement of AlSC Sthmic Provisions Section Fl .6a is intended to en.~ure that lhe brace member acts as the ductile link (brace yielding) in the frame prior 10 the connections failing. lhus providing more relfabiHty to the system. The limit on the sJendemess in V-type and inverted V-type braced frames is intended to limit the unbalanced force that develops on the braced frame beam when the compression brace buckles and its strenglh degrades while the tension brace yields. The buckliJl8 of lhe compression . brace results in a significant reduc1ioo in the frame shear resistance. This slenderness limit does not apply to braces in two-story X-braced frames. because that configuration pre\'Cllts or reduces the magnitude of unbalanced forces on the beam. K-braced frames, as defined by the AISC Seismic Provisions Glossary, where a brace frames to a column at a location where there is no out-of-pbne ~upport. are not permjtted in OCBF systems. The definition of K-braced frames precludes the use of braces framing 10 columns between diaphrngm levels or locations of out-of-plnne lateral support for lhe columns This Jefinition als0- precludes multi-tiered concentric braced frames ~here there are two or mere levels of bracing between diaphragm levels or locations of ouc-of-pl:ine ln.teral support for the columns.

' '"r

I I

OCBF Design Example Plan and Elevation The following e>..:unples illustrate the design of an OCBP system based on the AISC Seismic Provisions Section Fl. TI1e pl311 3lld elevation are shown in Figure 5-1 and Figure 5-2.

o·+i·+·~-·

~

6

40'.0"

40'-0"

+---"-'-'--I----'-.;.....:;_

1

..

~

.~

~Open ~1teel joists

I

lters

H----- M

._ ____" ' . . F= at 6'-8"

II

~

If 111 111

f° \ •'

:-.;

::

\;,,,,

1X. . . . - - - - - D - - - - c-

---0---- D

f

=30 psf

. rtical load of the exterior wall is supported at grade. The seismic weight of the wall Th e \e f h b 'tdi . t The th t ·s trihutary to the roof level is 140 lb/ft on all four sides o t e w ng penme er.

Ja~e~I eanhquake force,£, acting at the roof level along grid I is 65.8 kips as calculated per

ASCEISEI 7 Section I2.8. . The applicable building code specifies I.he use of A~~SEI 7_ for calculauon of ~oa~:· From ASCEJSEI 7, lhe following parameters apply. Setsnuc Design ~ategory D. R - 3~. ilo = 2, le= 1.0, SDs = 0.528, and p = J.0. ASCEISEl 7 does not permit an ~ = 3. s~stem 10 Seismic Design Cat\!gory D; therefore, an OCBF system is used for ~1s. bu1ldmg and designed according 10 the AlSC Seismic Pnwision.~. ~e structural ~r~ng is regular and bas two bays of seismic force resisting perimeter framing on each side lll each orthogonal . · Th e'" ASCfJSEI 7 Section 12 .3.4 .2b perrru'ts the redundancy factor. p, to be direcuon. er 1ore. taken as 1.0. · · ASCEJSt:J "1 The vertical seismic load effect, E,,, based on LRFD load combinauons m ..... Section 12.4.2.3. is: (ASCEISEI 7 Eq. 12.4-4)

0.2SosD - 0.2(0.528)D

0.14Sosf) =O.l4(0.528)D = 0.0739D A

~

N-~~-1 B D

111 111 ,1, 111 111 111

,.

I

S

0

%- - 1 - - - l

I I I I I

c----•:-1 -

l

t---->.-L_ _._,. ____ ____ ____ ____

·!

'

l =Opsf

JT-1 Roof

:r.----c----c----c----c

I~

ts psf

for ASD load combinations in ASCE/SEI 7 Section 12.4.2.3, E, is:

II 11

D ..

q

(typ.)

Ix

l

TI1e gravity ((lading is as follows:

= 0.1060

5

4

5.2 ORDINARY CONCENTRIC \LLY BRACED l·R. \.\.fES

,.

"'

,.

C

-+--{ O

q

~~

Base

OCBF investigated in design examples.

For elevation, see Flgure 5-2. Fit. 5-1. OCBF roof plan.

Fig. 5-2. OCBF el~otiott.

=.

O.lOSo~D

= 0.10(0.528)D =0.0528D

Solution: From AISC Manual Table 2-4, tbe'~aterial properties

Note that according to ASCE/SEI 7 Table 12.2-1, buildings with OCBF frames in Seismic Design Categories D and E are only permitted up to a structural height of 35 ft. An cxccpuon applies for Seismic Design Categories 0, E and P that allows the maximum structural height to be increased to 60 ft for single-story buildings where the dead load of 1he roof does not exceed 20 psf, which is the case here. ~ume that the ends of the diagonal braces are pinned and braced against translation for both th.e x-x and y-y axes. The loads giYen for each example are from a first-order analysis. Assume that the elTecth'e length method of AISC Specijicarion Appendjx 7 is used for stability design. AJSC Specification Appendix 8 will be applied 10 approximate a .secoodorder analysis.

F1 =50 ksi F11 =65 ksi Required Strength Determine the required strength Tue load combinations that include seismic effects are: ASD

LRFD LRFD Load Combinations 5 and 6 from ASCE/SEI 7 Section 12.4.2.3 (including the 05 factor on L permitted in ASCfJSEI 7 Section 12.4.2.3)

Given: Refer to the roof plan shown in Figure 5-1 and che Brace BR-I shown in Figure 5-2. Select an ASTM A 992 \V-<;bape for the diagonal braces to resist the loads gi"en.

(1.2 + 0.2Sos)D + pQe + 0.5L + 0.2S

The axial loads and moments on the brace due to a first-order analysis are:

=5.54 kips

Ps= 6.70 ldps

The dead load bending moment indicated above is due lo the self-weight of the brace assuming a member chat weighs 33 lb/ft. Sometimes this self-weight lo3ding is ignored in the design of venical diagonal braces where judgment would indicate that the loading is minimal and only uses a small percentage of the member strength. Howc,·er, in this example, consjdering the relatively IOtlg length of the diagonal brace and that the self-weight moment is resisted by the wc:ik axis flexural strength of the brace, the dc:ld load moment is included in this design check. There arc no bending moments due to tiYe loads or snow loads.

(1.2+ 0 2Sos)D + pQe+0.5L + 0.2S

=l, 130 kips

(0.6 - 0.14SDS)D + 0.1pQe +II

\

I~

l f

force in the diagonal brace is:

,

L.....~~~~-=LRFD.:..:_~~~~'~~~-t-~~~~~-A-S_D~-:-~~~~I LRFD Lood Combination 5 from ASCE/SEI 7 Section 12.4.2.3

P. =[1.2+0.2(0.528))(5.54 lcips)

+ 1.0(22.3 kips)+0.5(0 kips)

ASCE/SEJ 7 Section 12.4.2.3 (including the 0.5 factor on L permitted in Section 12.4.2.3)

(1.0 + 0.14Sos)D + H + F + 0.1pQ£

Considering the load combinations given in ASCEISEI 7, the maximum compressive ax.iai

Psrery is the total vertical load on the story calculated using the foUowing governing load combination. From the analysis:

LRFD Load Combination 5 from

ASD Load Combinations 5 and 8 from ASCE/SEl 7 Section 12.4.2.3

(0.9 - 0.2Sos) D + pQ£ + l .6H

MD = 2.34 kip-ft

LR.FD

arc:

ASTMA992

Example 5.2. 1. OCBF Diagonal Brace Design

P, 14ry

l

tory shear from the analysis is 136 kips. The first order intcrstory drift due to thls shear Th es · · 00941 · force without the Cd factor applied from the analylils model 1s 1'1.H m.

and

PD

5-

5.2 ORDINARY CONC5NTRICAllY BRACfD FRAMl"'.S

BRACED FRAMES

L

ASD Lood Combination 5 from ASCFJSEI 7 Section 12.4.2.3

\

I"

Pa =[1.0+0.14(0.528))(5.54 kips)

+ O kips+O kips

I

~.::..::..+=0~.2=(6~·7~0 -ki-·p-s)~~~~~.L-~-+-0_.7_(_1.0-)-(2-2._3_k1-·p-s)~~~~j: . =21.6

ASD ASD Load Combination 5 from ASCE/SEI 7 Section 12.4.2.3

-30.9 kips

kips

. (LO+ 0.14Sos)D + H + F + 0.1pQe

-

Psrory :: 740 kips

.. AM£IUcAH J.NsmVn! Of STO!L CONSTIUJCTION

BRACED

FRAM~

The mrutimum bending moment in the brace concurrent wilh the above load combination is:

52 ORDlNARY CONCENTRICALLY BRAC£D FRAMES

5-9

Brace Slenderness

~· .,

ASD

LRfD Mu =l l.2+0.2(0.528))(2.34 kip-ft) + 1.0(0 lcip-ft)+0.5{0 kip-fl)

+ 0.2{0 kip-ft)

Check brace element width-to-thickness ratios

+ 0 kip-ft+ 0 kip-ft

According to AISC Seismic Provisions Sections Pl.5a. braces are required to satisfy lhe n.-quirement.S for moderately ducllle members. Elements in the brace members must not exceed AmJ width-to-thickness requirements given in Section DI.I.

+0.7(1.0)(0 kip-fl)

From Table Dl.I oft.heAISC Seismic Provisions:

M 0 =ll.0+0.14(0.528)](2.34 kip-ft)

=2.51 kip-ft

=3.06 kip-ft

'A.""'=0.38ff, The ASCEJSEI 7 load combination that results in the maximum axial tensile force in the diagonal brace is:

,. I

J

ASD

LRFD

LRFD Load Combination 6 from ASCEJSEI 7 Section 12.4.2.3

ASD Load Combination 8 from ASCFJSEI 7 Sectfon 12.4.2.3

·:::J

Pu = [0.9 - 0.2(0.528)](5.54 kips)

+ l.0{-22.3kips)+1 .6(0 kips) =-17.9 lcips

~I l i. •.• ~~ !~

P0 = [0.6-0.14(0.528))(5.54 kips)

-

Mw

LRFD

=(0.9-0.2(0.528))(2.34 kip-ft) + 1.0(0 kip-ft)+ 1.6{0 kip-ft)

ASD M0 =[0.6-0.14(0.528)](2.34 kip-ft)

+ 0 kip-ft+ 0 kip-ft + 0.7(1.0)(0 kip-ft}

= l .86 kip-ft

=1.23 kip-ft Try a W1 Ox33 with its flanges oriented parallel 10 the plane of the braced frame. From AlSC Ma1111al Table 2-4, the material propenies are as follows: ASTh1A992 :.i:. !":

:·

From AISC Manual Table l· I, the geomerric properties for lhe W10X33 are ns follows:

"=

0.435 in.

rx = 4.19 in.

from Table Dl. l of the AISC Seismic Provisiori.r for webs of rolled I-shaped sections used as diagonal braces:

ff,•

= 1.49

29,000 ksi 50 ksi

=35.9 Because /J/r,,,::;;

A...!. the web meets the requirements for moderately ductile members.

Altematively, Table l-3 can be used to "erify that the member satisfies the loc.11 width.-tothickne~s requirements for OCBF diagonal braces. Additionally, the W10X33 does not contain slender compression elements according to AJSC Specification Table B4. la. Available Compressive Strength Determine K As stated in the OCBF Design Example Plan and Elevation section, the cffecrive length

Fy =50ksi Fw = 65 ksi

A =9.7 1 in.1

Because btlZIJ ~ /....,,J, the flanges meet the requiremenll> for moderately ducole members.

/..,,..d=l.49

The maximum bending moment in the brace concurrent with the above load combination is:

50 ksi

:: 9.15

+0.7(1.0)(-22.3 kips)+O kips =-12.7 kips

29,000 ksi

= 0 ·38

b1=7.%in. k.ks = 0.935 in. ly = 36.6 in.'

d =9.73 in. b1121r9.15 ry =1.94 in.

t..,:: 0.290 in. hltw:: 27. I

method in AISC Specification Appendix 7 is used for stability design. According to AISC Specification Appendix 7, Section 7.2.3(a). for braced frame systems, the effective lengt!: factor, K, for members subject to compression is Ull:eo as 1.0. llllless a rational analysis ind:catcs that a lower value is appropriate. The length of the bnce diagonal in ench bay. based on the geometry in Figure 5-2, is:

L-:: J(40.0 ft}2 +(40.0 ft) 2 ::;56.6 ft

S-10

5.2 ORDINARY CONCENTRICAlJ..Y ORACl~ FRAMES

BRACl:D F'RAMLS

This length has been determined by calculating the distance between the work points based on the intersection of the centerlines of the brace, column and beams. Shorter unbraced lengths of the brace may be used if justified by the engine~ of record. By inspection, the laterally unbraced length of the diagonal brace in the in-plane (about the y-y aJtis) direction is half of the overall length. For buckling out-of-plane (about the x-x axis), if both of me diagonals :u-e continuous for their full Jenglh and are connected at the inte~cction poini. t~n the effective length factor, K, is 0.5 (EI-Tayem and Goel. 1986; Picard and Beaulieu, I987). Th.is requires a connection betwe.en tbe diagonal members :it their intersection that is rigid in flexure out-of-plane. The available axial compressive strength of diagonals in Xbracing where one of the diagonal braces is not continuous through the intersection can be detcnnined by an energy method (Nair, 1997).

L-~~~~~-LR~ro~~~~~~-1-~~~~~~A_s_o~~~~~- ' 1

Assume that the colUlection of the half brace sections at che X-brace intersection is rigid omof-plane. The braces are oriented such tha1 buckling :ibout the y-y a.xis of the brace occurs in the plane of the frame.

followrng.

~cFcr =7.38

Fer 91 k SJ. -=4.

ksi

Oc

~c~ =$c~rAg

!i_=(Fcr)A, 0., Uc

=7.38 ksi(9.71 in. 2 ) = 71.7 kjps

=4.9 1 k~i(9.71 in.2 ) = 47.7 kips

Secon~-order effects :ind interaction between axial force and fleiture are checked in I.hr

:

Available Flexural Strength

From AISC Manual Table 3-4, the available strength in the weak axis is:

=0.5(56.6 ft)

\.

L. -~-bM~n1_=_5_2_._s_k-ip--f-L~~~~~~--'~~-:_1_=_3_4_.9_~_·_p-f-i~~~~~~~~I t

Kx = 0.5 K1 = LO Kxl, 0.5(56.6 ft)(l2 in.lft) -= rz 4.19 in. --"---~---=-

Second-Order Effects Second-order effects are addressed using the procedure in AISC Specification Appendix 8 as follows:

= 81.l K1 L, = 1.0(28.3 ft)(12 in./ft)

M, = BtMni + JhM1J P, = P,., + B2P11

1.94 in.

=175

ASD

LRFO

= 28.3 ft

1

I~

Because there is no bending moment in the strong axis. Ma= 0.

Lx =56.6 fl L, =0.5L

r1

I

(governs)

\

\

'

(Sptc. Eq. A-8-1 (Spec. Eq. A-8-2

\.

Calculate 81

The slenderness, KL/r, ~ less lhan 200 and therefore meets the recommendation of the Usa Note in Section E2 of 1be AISC Specification.

Cm

=1.0 ns moment is due to self-weight applied between supports

a = 1.00 (LRFD); a = 1.60 (ASD)

=

Using AISC Specification Equation E3-l and AISC MOJtual Table 4-22 wilh KL/r 175, the available compressive strength is detennined as follows:

The elastic critical buckling strcnglh, Pt1. is calculated in the plane of bending. For this calculation, the plane of bending will be in the plane of me frame, about the brace's y-y ax.is.

K1Ly =J.0(28.3 ft)

=28.3 ft

1 '

l

I

·; I

!

...• l

-

5- 12

BRACED FRAMES

5.2 ORDINARY CONCENTRICALLY BRACED FRAMES

(Spec. Eq. A·8·5)

The required flexural scrength of lhe brace including second-order e1fects, using AlSC Specification Equation A-8-1, is:

2

~.

_ n E1; -(K1L)2

.

_ n2 (29,000 ksi)(36,6 in. 4 )

I ,,...

From AISC Specification Equation A-8-3:

M11

LRFD

~1

Cm

l-aPrffe1

B1

= 1-(1.00(30.9LO kips)/ 90.8 kips] =1.52:
=

Cm

;;;:: 1

1-aP,/ Pd

1.0 .

=1-(1.60(21.6 kips)/ 90.8 kips] =1.61 ~ l o.k.

'.

=2.5 I kip-ft =0 kip-ft

M11

Psraryis given as l,i30 kips (LRFD) and 74-0 kips (ASD) and His given as 136 kips.

HL Pt J/OYj ;; RM -

(Spec. E'J. A-8-7)

/:iH

= l.52(3.06 kip·ft)+J.00(0 kip-ft)

= t.61(2.s 1kip-ft)+1.oo(b kip-ft)

=4.65 kip-ft

::::: 4.04 kip-ft

;

Because 82 = l.00, the required axial compressive strength of the brace including secondorder effectS, based on AISC Specification Equation A-8-2, is: . ASD

136 kips (40.0 ft) . (0.0941 in.)(l ft/12 in.) ·= 694,000 kips

(l.2+ 0.2Sos )D+ B1 (PQE )+0.5L+0.2S , .(L 0+0.14Sos )D+ ij +.f + B, (0.7pQE)

B2 =

1 1- aP11~

~1

.

~

;·

,.J;

= 1.00

- + 0 kips+O kips + l.00(0-7)(1.0)(22.3. kips) = 21.6 kips

.

'

Bi=

...

Pe:no17

l ~ _ LOO(l,130 kips) 1 694,000 kips

Pa =(1.0+0.14(0'.528))(5.54 kips)

=30.9 !dps

Ui>ing AISC Specification Equation A-8-6:

Combined Loading (Compression and Ff~xure) '

1 l- a.Ps1ory

~l

i

:

"'\.

+ 0.2(6.70 kips)

ASD

I

ASCEIS.El 7 Section 12.4.2.3

+ 1.00(1.0)(22.3 kips)+0.5{0 kips

LRFD

I

ASD Load Combin-ation 5 f~om

LRFD Load Combination 5 from ASCEISEI 7 Section 12.4.2.3

Pu =[l.2+0.2(0.528)](5.54 kips)

=l.OO

l

Mr = B1M111 + BzM11

LRFD Calculate 8 2

I

I, I

Mnr =Mo

=3.06 kip-ft =0 kip-ft

M, ::: B1Mn1 + BzM1,

ASD

,.

ASD

,\Int= Mu

=90.8 kips

Bi=

'I

I...Rffi

[28.3 ft(J 2 in./fc)J 2

-

5-13

Check combined loading of the

W10x3~brace (::

Determine the applicable equation, using AIS,C Specification Section Hl:

...

Pu1ory

.

1

' I•

=I- 1.60(740 kips) 694,000 kips

=LOO

Because 82 ~ 1.5, !he effective lengl.b method is a valid way to check stability according to AISC Spccific01io11 Appendix 7. -

ASD

LRFD P, :::: 30.9 kips. 71.7 kips = 0.431

Pc

. P, = 21.6 kips

...,.

. ..

I

. Pc

47.7 kips =0.453

.

Because P,fPc~ 0.2. the brace design is controlled by the equation:

8(Mrx

P,.+ - - + -Mry) $LO Pc

9 Ma

Mey

. .

' ·.

.·

(Spec. Eq. Hl-!..ij

BRACED FRA.1',ffiS

S....14

.LRFD 30.9 kjps !(o - 4.65 kip-ft)-o 5 + +.5 . - . 10 71. 7 kips ~ .. 2.5 kip-fl

21.6 kips +!(o+ 4.04 kip-f')=o. 556 47.7 kips 9 34.9 kip-ft

o.k.

0.510<1.0

.

ASD

ASD

LRFD P, = 12.7 kips

P, = 17.9 kips Pc 437 kips

291 kips

Pc

=0.0436

=0.0410

o.k.

0.556<1.0

5-15

5.2 ORDrNARY CONCENTRICALLY BRACED FRAMES

Because P,IPc < 0.2. lhe brace design is controlled by lhe equation: Note that the weak axis bendjng moment from tbe self-weight of the diagonal br:ice utilizes about 8% of the member available strength.

Available Tf!n$[1e Strength From AISC Manual Table 5-1 •. the available strength of the W1 Ox33 brace in axial tension for yielding on the gross_section is: '

LRFO

'

$1Pn = 437 kips >P.9 kips

--

o.k.

Mey

(Spec. Eq. Hl-lb)

.

<1.0

Check combin~ldading of the W10x33 ,As previously ~et~rmined: •

".

,

'~

Mry=Mu

+(O+ l.86

kip· ft)= 0 _0559 52.5 kip-ft

12.7 kips +(o+ 1.23 kip-ft)=o.o 571 2(291 kips) 34.9 kip-ft

o.k.

< 1.0

o.k.

Mry=Mo

J

=17.9kips

=437 kips

The loads on Column CL-1 due to a ~l-
= 1.23 kip-ft

=T,,

Pc =cj>,P,,

Given: . ' Refer to Column CL-1 in Figure 5-2. Select a 40-ft-long ASTM A992 W-shape to .resist the loads given for the column.

ASD

= 1.86 kip--ft

.., •t.

Po= 16.4 !Ops

· Pr =Ta = 12.7 kips

P,.

'Pc =n,

'·

=291 kips Consider second-order effects per Appencfu 8 of the AISC Specification. As previously ~al culnted, 82 1.0. According to Appendix 8, Section 8.2 of the AISC Specification, B 1 shouEd be taken as 1.0 for members not subject to compression. Given that both 8 1 and 8 2 are equal to I, there is no amplification required for second-order effects for the loads on the member when I.be diagonal brace is ~n tension..

=

f

Example 5.2.2.,.0CBF Column Design

I,JU"D . >•

"·

ASD

i.RFD

The W1 Ox33 is adequate for lhe OCBF diagonal brace BR-I. The brace is oriented with Lhe flanges parallel to the plane of the braced frame.

·combined L~ading (fehsion and A~xure)

P,

Mex

... r,.

-

2Pc

17.9 kips 2(437 kips)

ASD

~", =291kips>12.7 k'ips

- o.k.

~+(Mrx + Mry)sl.O

~s =)9.9

kips

Pae= ±15.8 kips

Assume that the ends of the'columns are pinned and braced against translation for both the x-:c and y-y axes. The loading in the columns is from a first-order.analysis. Appendix 8 of the AlSC Specification can be appHed to approximate a second--0rder analysis. Solution: From AISC Manual Table 2-4, the material properties are:

ASTMA992

J•

L "

] l ...

l

.. ·:~{:

Fy =50 ksi Fa== 65 ksi

Required Strength AISC Seismic Provisions Section Dl.4a requires lllat the axial compressive and tensile \ strength be detennined using the ampl.i£ed seismic load; Lhat is, the seismic load multiplied by the overstrenglh factor, n.,. :' ....:;

!

BRACED FRAMES

:.-I()

The governing load combinations, including the overs1rength factor, for the required axiaJ compressive strength are:

LRFD

ASD

LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.3.2 (including the 0.5 fac1or on L pennjtted in Section 12.4.3.2)

P., =(l.2+0.2SDs)fb +n.,P(U +0.5Pi + 0.2Ps ={1.2+ 0.2(0.528)j(l 6.4 kips)

+ 2(15.8 kips)+0.5(0 kips) + 0.2(1~.9 kips)

P., =(1.0+0.14SDs)PD+ PH +Pp +0.70.,Pa.c

= [0.9- 0.2(0.528)j(l6.4 kips) +2(-15.8 kips)+l.6(0 kips) =-18.6 kips

Determine K According to AlSC Specification Appendix 7, Section 7.2.3(a), for braced frame systems, the effective length factor for members subject to compression shall be taken as I .0.

ASD Load Combination 8 from ASCFJSEI 7 Section 12.4.3.2

K1 =1.0

L.. =40.0 ft

Ly =40.0 ft

KxLx

--=

1.0(40.0 ft)(l2 in./ft) -US in.

=110

Pa =[0.6-0.14(0.528))(16.4 kips) + 0.7(2)(-15.8 kips)+O kips

K Ly

-1- = r1

1.0(40.0 ft )(12 in./ft) 2.54 in.

= 189 (governs)

,.. Use the procedure of AJSC Specification Appendix 8 to detennine the second-order effects on the required strengths, where the required flexural strength and required axial strength are given as:

~;

Kx= 1.0

+ 0.7U 0 PQ£ +PH

Second-Order Effects

:

Therefore:

Pa= (0.6-0.14SDs)Po

=-13.5 kips

..,,

Column Slenderness There are no specific requirements for member ductility for columns in OC.BF systems in Section Fl of the AISC Seismic Provisions. Therefore, check width-to-thickness ratios for element slenderness according to Table 84.la of the AJSC Specification. As indicated in AISC Manual Table 1-1, the W1 Ox49 section is not slender for compression.

+ 0.7(2)(15.8 kips)

ASD

P., = (0.9-0,2Svs)Po+O oP~ +l.6PH

b1= 10.0 in.

ry=2.54 in.

Available Compressive Strength

LRFD

Jl

CJ= 0.560 in.

I,..= 0.340 in.

d= 10.0 in. rt=4.35 in.

+ 0 kips +O kips

The governing load combinations, including lhe overstrength factor, for the required axial tensile strength is:

LRFD Load Combination 7 from ASCFJSEI 7 Section 12.4.3.2

From AlSC Manual Table 1-l, the geometric properties afc as follows:

=I L0+0.14(0.528)](16.4 kips)

= 39.7 kips

=57.0 kips

Try a W1 Ox49.

A= 14.4 in. 2


5-1.,


From AISC Manual Table .+-22 with KL/r = L89 and using AlSC Specification Equation E3-l, the available compressive strenglh is:

M,= B1M111 + ih.M11

(Spec. Eq. A-8-1)

9cFcr =6.32 ksi

Pr= Pn1 + B?/'11

(Spec. Eq. A-8-2)

~cPn =~cFc,Ai

There is nG bending moment in the column due to either vertical loading or lateral translation. Consequently there is no requirement 10 detennine multipliers for the required flexural strength due to second-order effects. The lateral drift is min1maJ. As calculated in Example 5.2.1, B2 = 1.0. Therefore there is no amplification of the axiaJ load in the column due to P-6. }Ji summary. no adjustments to the member forces calculated by a first-order anaJysis are required due to second-<:>rdcr effects. ~JCAN lJ-
ASD

LRFD

=6.32 ksi(l4.4

Fcr =4.21 ksi

. in.2)

=9 l.O kips> 57 .0 kips

o.k.

!le

Pn -(Fer )A - ' !le - f2c '

=4.21 ksi(l4.4 in. 2 ) =60.6.kips>39.7 ldps

I o.k.

I

!

5-18

BRACED FRAMES

I. ;,~ ~

Available Tensile Strength From AISC Manual Table 5· I, the available strength of the W1 Ox49 column in axial tension for yielding on the gross seccjon is:

ASD

LRFD ~,P,.

=648 kips >I 8.6 kips

o.k.

Pn = 431 kips> 13.5 kips

n,

o.k.

The W1 Ox49 for OCBF Column CL-I is adequate.

Example 5.2.3. OCBF Beam Design

S...19

5.2 ORDINARY CONCENTRICALJX BRACED rRAMES

The required axial compressive strength of the beam; with axial tension shown as negative,

r

is:

ASD

LR.FD

•

ASD Load Combinatio~ 5 from ASCE/SEI 7 Section 12.4.3.2

LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.3.2 (including lhe 0.5 factor on L permiued in Section 12.4.3.2)

P., =(1.2+0.2Sos)Po +OoPQ6

Pa =(l.0+0.14SDS)Po

+?,,+PF +0.1!laPi

+ 0.5P.L + 0.2Ps =(l.2 + 0.2(0.528))(-3.92 kips)

=[LO+ 0.14(0.528)](-3.92 kips)

+ 0 kips+ 0 ldps

+ 2(16.5 kips)+0.5(0 kips)

Given: Refer to Beam BM-I in Figure 5-2. Select a 40-ft-Iong ASTivi A992 W-shape to resist the loads shown below.

l

+ 0.7(2)(16.5 kips)

+ 0.2(-4.74 kips)

=18.9 kips

=26.9 kips

·~

The loads on the beam due 10 a first-order analysis are: Pv

=3.92 kips (tens.)

Mo= 72.0 kip-ft Vo= 7.20 kips

h::: 0 kips Ms= 120 kip-ft Vs= 12.0 kips

The required axial tensile strength of tbe beam is:

Ps = 4.74 kips (tens.)

Assume that che ends of the beam are pinned and braced against translation for boch the x-x and y-y axes. Solution: From AISC Manual Table 2-4, the material properties are:

ASTMA992 F1 50 ksi F.,=65 ksi

The beam is a collector element transferring diaphragm shear to che OCBF braces. According to Section 12.10.2.l of ASCE/SEI 7, the forces in the collector are calculated using the seismic load effects including the overstrength factor. The axial force in the beam from dead and snow load is in tension. The governing load combinations in ASCE/SEI 7 used for determining the required flexural strength of the beam are used to de1emrine the required axial strengths.

ASD ,

Pa =[1.0+0.14(0.5:8)j(-3.92 kips)

P11 =[l.2+0.2(0.528))(-3.92 kips)

· +0 kips+Okips + 0.7(2)(-16.5 kips) =-27.3 kips

+2(-16.5 kips)+0.5(0 kips)'

+ 0.2(-4.74 kips} = -39.l kips

..

. I

..

The required shear strength of the beam is:

:

\

=

Required Strength

..

LRFD

I

I.RFD v~ = [1.2 + 0.2(0.528)](7.20 kips)

.

· + 2(0 kips)+0.5(0 kips)

+ 0,2(12.0 kips) =11.8 kips

ASD

.

~ =[l.O.f0.14(0.528)](7.20 kips)

+ o'kip~+ o kips

t

,

·'

-.

0.7(2)(0 kips)

=7.73 ldps ..

---..

II

BRACED fRAM'.ES

;)-10

The governing load combinations, including the ovcrMrcngth factor, for the required a>;ia] comprc~sive

strength are:

ASCFJSEI 7 Section 12.4.3.2 (including the 0.5 factor on L permitted in Section 12.4.32)

Pu = (I 2+0.2Sos)Po +0 0 PQ&

+0.SPt + 0.2Ps

=(1.2 + 0.2(0.528)](16.4 kips) + 2(15.8 kips}+0.5(0 kips) + 0 .2( 19.9 kips)

ASD

. '

A== 14.4 in.2

ASD Load Combination 5 from ASCE/SEI 7 Section J2.4.3.2

Po =(1.0+0.I4Sos)Po+PH +Pp +0.7Q 0 Pa.

+ 0 kips+ 0 kips + 0.7(2)(15.8 kips)

!::J The go\'eming load combinations, incJuding the overstrength factor, for the required axial tensile Strengch is:

LRFD



ASCEJSEJ 7 Section 12.4.3.2

= !0.9- 0.2(0.528)]{16.4 kips) + 2(- 15.8kips)+1.6(0 kips) =- 18.6kips

·~

r: i. ·.

. l

t,.. r1

=0.340 in.

Pa= (0.6- 0.14Sos )Po

=2.54 in.

Available Compressive Strength Determine K According to AlSC Specification Appcndiit 7. Section 7 2.3(a), for braced frame ~ystems, the effective length faccor for mem~rs subjecl to compression i.hall be taken as 1.0.

Therefore: Ks = 1.0

K1 =1.0

Lx = .m.o r1

L:- = 40.0 ft

KxLx 1.0(40.0 ft)(l2 in./ft) --= 4 .35 io. = 110

+0.7!1 0 P0z +PH P0 =I0.6-0.14(0.528)](16.4 kips)

+ 0.7(2)(-15.8 ldps}+O kips

K1 Ly _ l.0(40.0 fc)(l2 in.In) -;;- 2.54 in.

=189 (governs) From AISC Manua l Table 4-22 with KL/r = 189 and using ATSC Specificatio11 Equation E3-l, lhe available compressive strength is:

Second~Order Effects

Use the procedure of AISC Specification Appendix 8 to determine the second-order effects on the requited strengths, where the required flexural strength and required axial strength are given as;

ASD

LRFD Fer =4.21.ksi

M, = B1Mn1 + B2M1t

(Spec. Eq. A -8-1)

~cFcr = 6.32 ksi

nc

=P,.1 + 8')}'11

(Spec. Eq. A-8-2)

9,_.P,,

~ =(~)A,

There is n~ bending moment in the column due to eiLher venkal loading or lateral translation. Consequently there is no requirement to determine multipliers for the required flexural strength due to second-order effects. The lateral drift is minimal. As calculated in Example 5.2. l. 82 1.0. Therefore there is no amplification of the axial load in the column due to P-t:... In summary. no adjtl$tmcnl.S to the membu forces calculated by a first-order ruW.ys.is are required due to second-order effecL~.

=

bt= 100 in.

Column Slenderness There are no ~pecific reqwrcincnts for member ductility for columns in OCBP systems in Section Fl of lhc A1SC Seismic J>m1 is1on.s. Therefore. check width-to-thickness ra1ios for element slenderness according to Table B4. la of the AISC Specification. As indicated iu t\ISC Manual Table 1-1, the W1 Ox49 section is not sJender for compression.

=- 13.5 kips

P, 1

ASD


Pu =(0.9- 0.2Sos )Po + n oPa. + 1.6PH

lJ = 0.560 in.

d= 10.0 in. rx=4.35 in.

=[J.0+0.14(0.528)J(l6.4 kips) =39.7 kips

=57.0 kips

Try a W1 Ox49.

From AJSC Ma1111al Table 1- 1, the geometric propenies are as follows:

LRfD


S-17

5.2 ORDINARY CONCENTRlCALLY BRACED FRAMES

:~cFcrA1

=6.32 ksi (14.4 in.2 ) =9 1.0 kips > 57 .0 kips

o.k.

i I

= 4 .2 J lcsi(14.4 in. 2 ) = 60.6 kips > 39.7 kips

o.k.

I'

DR.ACED FR.AMES

5-18

Available Tensile Strength From AISC Manual Table 5-1, the available strenglh of the W1 Ox49 column in axial tension for yielding on the gross section is:

S-19

5.2 ORDCNARY CONCENTRICALLY ORACED rR.AMES

The required axial compressive strength oft.he beam, with axial tension shown as negative, is:

ASD

LRFD

LRFD ~1Pn

ASD

=648 kips >18.6 kips

o.k.

Pn =431kips>13.5 kips

n,

o.k.

The W1 Ox49 for OCBF Column CL-I is adequate.

ASD Load Combination 5 from ASCEJSEl 7 Section 12.4.3.2

LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.3.2 (including the 0.5 factor on L permitted in Section 12.4.3.2) P., =(l.2+0.2Sos)fb +noPQ6

Pa =(l.0+0.14Sos)Po +PH+ 'PF+ 0.70 0 P~

+ O.SPr. + 0.2Ps =[1.2+ 0.2(0.528)](-3.92 kips)

Example 5.2.3. OCBF Beam Design

=[l.0+0.14(0.528)1(-3.92 kips)

+ 0 kips+O kips

+ 2 (16.5 kips)+0.5(0 kips) Given: Refer to Beam BM-1 in Figure 5-2. Select a 40-ft-long ASTM A992 W-shape to resist the loads shown below.

The loads on the beam due to a first~order analysis a,re: Po= 3.92 kips (tens.) Mo= 72.0 kip-ft Vo= 7.20 kips

PL= 0 kips

The required axial tensile strength of the beam is: ·

P.. =·[1.2 + 0.2(0.528))(-3.92 kips)

The beam is a collector element transferring diaphragm shear to the OCBF braces. According to Section 12.10.2.1 of ASCE/SEI 7, the forces in the collector are calculated! using the seismic load effects including the overstrength factor. The axial force in the beam from dead and snow load is in tension.

The governing load combinations in ASCE/SEI 7 used for detenninjng the required flexural strength of the beam are used to determine the required axial strengths.

Pa ={l.0+0.14(0.5~8)](-3.92 kips)

~

· +Okips+Okips

...

+ 0.7(2)(-16.5 kips)

+ 0.2(-4.74 kips)

=-27.3 kips

=-39.l kips

.

The required shear strength of the beam is:

ASTMA992 F1 =50ksi

Required Strength

ASD ,.

'

+2(-16.5 kips)+0.5(0 kip;)'

Solution:

Fu= 65 ksi

..

LRFD

Assume that the ends of the beam ace pinned and braced against translation for both the x-x and y-y axes.

From AISC Manual Table 2-4, the material properties are:

I·

= 18.9 kips.

=26.9 kips

Ps = 4.74 kips (tens.)

Ms== 120 kip-ft Vs= 12.0 kips

+ 0.7(2)(16.5 kips)

+ 0.2(-4.74 lcips)

. V11

' LRFD

=(1.2 + 0.2(0.528)](7 .20 kips) · + 2(0 .kips)+0.5(0 kips) + 0.2(12.0 kips) =11.8 kips

\

I

..

ASD

V,, =(1.0+0.14(0.528))(7.20 kips) :. +o'kips_+o kips

~ 0.7(2)(0 kip_s)_ = 7.73 kips , ,

-

, i

-··..

.I I

'"'~-·

11

BRACED FRAMES

S.2 ORDINARY CONCF..NTRICALLY BRACED FRA.VIES

K1 J.,,.

The required flexural strength of the beam is:

1.0(20.0 fl)(l2 in.lft)

-;:;- = LRFD M.

ASD

={J.2 + 0.2(0.528)j(72.0 kip-ft) + 2(0· kip-fl)+ o:s{o .kip-r1)

~

+ 0.2(120 kip-fl)

+ 0.7(2)(0 kip-ft)

0 kip-ft+ 0 kip-fl

=77 .3 kip- ft

=118 kip-fl

·· 1

M,, =(l.0+0. 14(0.528))(72.0 kip-ft)

Try a W18x50.

From AlSC Manual Table J-L the geometric properties are as follows: A::: 14.7 in. 2

d= 18.0 in.

=0.355 in. ry= 1.65 in.

kdu"' 0.972 in.

lw

Ir= 800 in.'

b1 = 7.50 in. hftw= 45.2

Sx = 88.9

in. 3

If = 0.570 in. rx = 7.38 in.

Zx = 101 in.3

Beam Slenderness

There are no specific requirements for member ductility for beams in OCBF systems in Section Fl of the AISC Seismic Provisions. Therefore, check widt.h~to-Lhic.kness ratios for element slenderness according to Table B4. la and Table B4. lb of lhe AISC Specification.

ll

As indicated in AISC Manuaj Tuble 1-1, the W18x50 is slender for co.m pression and com, pact for flexure. · ':·

1.65 in.

=145 (governs) The combination of the top flange bracing and the bottom flange bracing from the open web si.cel joist at midspan creates a torsional brace. This example uses a simplified calculation of lhe available compressive strength according to AISC Specification Section E7 that considers I.he limit sltlte of flexural buck.ling using the minor axis unbraced length of the member thilt is bl!:Sed on the bottom flange unbraced lenglh. A grearer compressive strength may be available due to the additional minor a.'tis coos1raint at the top flange. See Section 8.3 oft.hi ~ Manual for a method to deternUne 1he available torsional buckling strength considering constraint at the top flange.

B~ause the web is considered a slender element for axial compres&ion ( h/1,.. > l.49JE/ Fy

=l .49~29,000 ksi/50 ksi = 35.9) a reduction for slenderness is required for calculating Lbe available compressive strength per Section E7.2 of lbe AlSC Specification. This reduction is included in AJSC Manual Table 6- l; therefore, use AlSC Mamwl Table 6-1 to determine the available compressive strength of the W18x50. From Table 6-1. for K1 ly=20 ft:

LRFD 3

px10 = 6.37(kipsr

ASD

1

P x 103 = 9.ss(kipsr' I

J

Pn /Dc =-


p

Determine K

6.37x10-3 (kipsr 1

According to AISC Specification Appendlx 7, Section 7.2.3(a), fo~ braced frame systems, the effective length factor for memberS subject to compression shctll be taken as l.0. Consider the open web steel joists at ~ top flange of the beam to provide the strength and stiffness required by AISC Specification Appendix 6 to stabilize 1he top flange of the beam in the y-y axis at 6 ft 8 in. centers. Consider that the bottom flange 9f !he beam is stabilized in the y-y axis at midspan by a bottom chord extension from the open web steel joisL Consider the effective length of I.be beam in compression about Lhe y-y axis to be based on the unsupported length of the bottom flange.

Therefore:

K..= LO lx=40.0 fl

K1

=1.0

Ly =20.0 ft

7.38in.

=65 .0

· = 157 kips

9.58x10-3 (ltipsf 1 ::: 104 kips

Available Flexural Strength Because the beam is bending abour its major axis, and has both compact flanges and a compact web in iJexure, the available flexural strength is determined in accordance with AISC Specification Section F2.

The open web steel joisis provide lateral f;Upport of the compression flange ac 6 ft 8 in. centers.

KJClx l.0(40.0 ft)(l 2 in./ft) --=

rx

P

4=6.67 ft

According lo AISC ;Hmiu<1I Table 3-2: Lp=5.83 ft L,. =16.9 ft

AMERICAN iNSTITIJTli OF STEEL. C0l'ISTRIJCTION

5-'.lJ

BRACED FRAMES

5-22

Therefore Lp < La S 4 and the limit state of lateral-torSiooal buckling applies. Consen•ativety. use c,,= 1.0.

Calculate 82

,.- ' LRFD

.
;

n·z.

:

'

LRFD

Following rhe procedure of AISC Specification Appendix 8:

(Spec. Eq. A-8-1)

Calculate B1

(Spec. Eq. A-8-2)

Pu= (1.2 + 0.2SDs)PD + .BiOoPQe + 0.5PL + 0.2}\-

ex.:::: 1.00 (LRFD); ~ := 1.60 (ASD)

= [l.2+'0.2(0.528)J(-3.92

. K1Lx = 1.0(40.0 ft) = 40.0 ft

I'

' '

[40.0 ft(l2 in./ft)]

.

1.0 1.00(26.9 kips) 1 994 kips

= 1.03

..

=18.9 kips

l I

,..,

·~

LRFD

ASD

\ \

Mrx = B1M111 + 8zM1t

BI:;

.

=

. Cm 1-o.Pr/ P, 1

=122 kip-ft .'•

'= 1.03(77.'3kip-fi)71.00(0 kip-ft)

,.

.

= 79.6 kip-ft

..

.

. ..

•'

!

1.0 1.60(18.9 kips) 1994 kips

Mrx =B1Mn1 +.BiM11

= 1.03(118kii>-fi}+1.00(0 kip-ft)

ASD

'

=

+ 1.00(0.75{2)(16.5 kips)

·r ,

2

'·

B1= . Cm 1-o.Pr/ Pei .~

..

From AISC Specification Equation A-8-1, the required flexural strength is:

LRFD

'

=[LO+ 0.14(0.528)j(-3.92 kips) + 0 kips+ 0 kips

(Spec. Eq. A-8-5)

(49.000 ksi)(800 in. 4 )

=994 kips

Jdps)

=26.9 kips

:::: (K1L)2

' ·'

+ l1I +Pp+ Bi ( 0.74,P~)

'

+ 0.2(-4.74 !tips)

n Elx

:=:

Pa =(l.0 +0. 14Sos)PD

+ 1.00(2)(16.5 kips)+0.5(0 kips)

2

2

ASD Load Combination 5 from ASCEISEl 7 Section 12A.3.2

ASCEISEI 7 Section 12.4.3.2 (including the 0.5 factor oo L pemutted in Section 12.4.3.2)

.. .. •'. .. C,,, = 1.0 as the beam is subject to transverse loading between supports

1t

ASD


..

·

··}

From AISC Specification Equation ;\-8-2 and the applicable ASCF/SEI 7 load combination, the required axial compressive strength is:


..

1

Mn1

'

,

=0 kips

Fi1 = Pu or Pa as determined previously =Mu or M0 as determfoed previously M11 =0 kip-ft because there is oo monient due to seismic loading

·' . '

I

Mn :;245 kip-fl

Pru

..

ASD

t

Th = 1.00 as calculated in Example 5.2. 1

From AISC Manual Table 3-10. the available flexural streoglh o f the beam is:

l~

Combined Loading (Flexure 'and Compression) Determine tbe applicable equation in AlSC Specificarion Section Hl.1:

LRFD

=1.03

'ASD

26.9 kips -= Pc 157 kips

P, • 18.9 kjps -= Pc 104 kips

=0.171

=0.182

P,.

..J ,,

..

.

J

""' •i

\

...1

: .I

:l

BRACED FRAMES

Because P,!Pc < 0.2, the b~m design is controlled by 1be equation:

LRFD (Spec. Eq. Ht-lb)

!

: l;

ASD

LRFD

l

26.9 kips +(122 kip-ft +o)=0.4l 7 2(157 kips) 368 kip-re ·

·'

o.k.

0.417<1.0

0.416<1.0

Mrx= Mo

=118 k:ip-ft

=77.3 kip-fl

P, =Tu 39.1 kips

P, = Ta

Pc = 4>1Pn

Pc = Pn 10 1 440 kips

=

18.9 kips +(79.6 kip-fr +o):::: 0.4l 6

· 2(104 kips)

ASD

Mn=M,.

.,

r•

5-25

S.2 ORDINARY CONCENTRJC,\LLY BRACED FRAMES

245 kip-ft

=27.3 kips

=

= 662 kips

o.k. Detennine the applicable equation in AISC Specification Section Hl.l:


LRFD

From AISC Manual Table 3-6, the available shear strength of the W18x50 beam is: ·;

..'

!: --,

LRFD
=192kips>11.8 kips ...

Ill

l .

~ = 128 kips> 7.73 kips

o.k.

n.

•.

P,

39. l kips

Pc

662 ki ps =0.0591

-=

ASD

ASD P,

- = Pc

27.3 kips 440 kips

=0.0620

o.k. Since P,IPc < 0.2. the beam tle.~ign is controlled by tbe equation:

, ...

Available Tensile Strength

(Spec. Eq. Hl-Jb)

From AISC Mam~al Table 5-1, the available strengtb of the W18x50. beam in a."
.

'.

LRFD

ASD

ASD

._

cp 1P,. = 662 kips > 39. l kips

Pn = 440 kips> 27 .3 kips Q,

o.k.

2(440 kips)

245 kip-ft

'

+o)=o. 347 ..

I

0.350<1.0 Consider ~econd-order effects (tension loading) Consider second order effects according to Appendix 8 of the AJSC SpecificaJiQn. As previously calculated, Bi= 1.0. According to NSC Specification Appendix 8, Section 8.2, B1 is taken as 1.0 for members not subject to compression. Given that both B 1 and 82 are equal to 1.0, there is no amplification required for second-order effects for the loads on the mem· ber when the diagonal brace is in tension,

27.3 kips +(77.3 kip-ft

39.1 kips + ( l I8 kip-ft + O) = 0.:3SO 2(662 kips) 368 kip-ft

:

o.k.

''

0.347 < 1.0

o.k.

Note that the available flexural strength was conservatively based on Cb = 1.0. Derennining Cb and applying it would have resulted in a higher available flexural strength. The W18x50 is adequate for use as the OCBF Beam BM-~-

Example 5.2.4. OCBF Brace-to-Beam/Column Connection Design

Combi[Jed Loading (Flexure and Tension) Because the axial tensile force is greater than the :L"\ial compressive force, intet3ction will be checked. As previou~ly determined:

..... ii' A.MER.lCAN !NSTTTUTE OP Sn:a CONSTIUJCl10N

Given: Refer lo Joint JT-1 in Figure 5-2. Design the connection between the brace, beam and co' umo. Use a bolted connection for the brace-10-gusset connection. Use a single-pl:i• connection lo connect the beam and gusset to the column and a welded connection bctwce'l the beam and gusset plate. Use ASTM A36 for all plate and angle material. Assume tl.

AMERICAN hlsmvra OF

SlllEl. CoNS1'R\JCTION

BRACED FR.AMES

1 '

5

5.Z ORDrNARY CONCENTRICALLY BRACED FRAMES

--~~~~~~~~~~~~~-r-~~~~~~~~~~~~~---.

member siz.es are as determined in the previous OCBF examples. Use 3A-in.-diame1er ASTM A325-N bolts and 70-ksi weld electrodes. From Example 5.2. I, the loads on the connection from the brace based on a firs! order analysis are: Ps = 6.70 kips

PD = 5.54 kips

Poe= ±22.3 kips

From Example 5.2.3, the loads on the connection from the beam (collector elemcnr), base~ on a first-order analysis are: PD= 3.92 kips (tens.)

Pl= 0 kips

Ps =4.74 kips (tens.)

MD= 72.0 kip-ft

ML= 0 kip-fl

VD=7.20 kips

VL

Ms= 120 kip-ft Vs= 12.0 kips

=0 kips

PQr.

=±16.5 kips

Moe = 0 kip-ft

~~~~~-L_RFD ~~~~~~-1-~~~~~-A-SD~~~~~- 'i .: LRFD Load Combination 5 from ASCE/SEI 7 Section J2.4.3.2 (including

(1.2 + 0.2SDs)Po + fl 0 PQ1 +0.5P1., + 0.2Ps

l. .

(1.0 + 0.14SDs)P.o +PH+ PF +0.1fl 0 Pa1

I

I\

The required :axial compressive strength of !he collector at the beam-to-column connection · is, from the loads given in Example ?.2.3:

LRFD

ASD

Pu= II.2+ 0.2(0.528)j(Okips)

' 1:

P0 =(l.0+0.14(0.528)]{0kips}

+2(16.5 kips) +0.5{0k.ips)

ASTMA36 Fy =36 ksi F,,=58 ksi

+0 kips+O kips+0.7(2)(16.5 kips) = 23.1 kips

+ 0.2(0 kips)

1·

=33.0 !Ops

FromAISC Manual Table 1-1, the geometric propenies are as follows:

Beam d= 18.0 in. T= 15~ in.

b1=7.50 in.

'I= 0.570 in.

k.us = 0.972 in.

rx= 7.38 in.

Z;r =10 L in.3

Ix =z:800 in.' ry = 1.65 io.

;

t

Note: The above load results from tbe 1ransfer of tbe collector force from the beam in t. adjacenr bay. The axial components from snow and gravity axial loads used in Exampl 5.2.3 are transferred from the brace ~usset directly into the braced frame beam.

I

r·

According to AISC Seismic PrQVisions Section Fl.6a, the required strength of diagonal brace connections is the load effect based upon the amplified seismic load. Based on lh· /, loads given for me brace trom Example 5.2.1. the maximum a-ua1 tensile force in the rua 8 onal brace based upon the amplified seismic load, is: · · ·

I

I • •

LRFD

if= 0.560 in.

fw

= 0.340 in.

d= 9.73 in.

'I = 0.435 in.

Required Strength

The govei:ning load combinations for the colleccor force are:

• ASD

kw = 1.06 in.


Broce W10x33

A=9.71 in.1 bi.=1.96 in.

i'

VQE = O kips

From AISC _Manual Table 2-5, the material properties are as follows:

Column W10x49 d= 10.0 in.


the 0.5 fact0r on L penniued in Section 12.4.3.2)

Solution:

W18x50 A= 14.7 in. 2 t..., = 0.355 in. Sx = 88.9 in. 3

l.<

ASD Load Combination 8 from ASCF./SEI 7 Section· 12.4.3.2

(0.9 - 0.2SDS)PD + floPa. + l.6Pn

(~.6- 0.14SDs)Pq + .PH +P/i-:p'.1il.iPQ1

Pu = I0.9- 0.2(0.528)j(5.54 kips) + 2{~22.3 kips)+ 1.6(0 kips)

Pa =I0.6-0.14(0.528)J{5.54 kips)

=-40.2 kips

1

I! l

r

I

\i

+ 0 kips+O kips + 0.7(2)(-22.3 kips) =-28.3 kips

I

·~,

\:

"

BRACED FRAMES

5-28

, ..

•

.

' i\

According to the exception in AISC Seismic Pro~·isions Section FI.6a, Lbe required ax.ial tension strength need not ex'ceed the expected yield strength muhiplied by 1.00 (LRFD) or divided by 1.50 (ASP):-. ,,

5.2 ORDINARY CONCEN'TlUCALLY BRACED FRAMES

,.

AccordinJ; to 1he Excep1jon in AISC Seismic Provisions Section Fl.6a, the required axial strength of the brnce connection in compression need not exceed the lesser of the expected yield strength and l.14Fcl\' A8 , where Fcre is based on the expected yield siress. RyFy .

;

.' ~·

LRFD

"\

l

T,,, exp

I

=1.00(.R1F>'Ag) . =1.00(1.1)(50 ksi)(9.71 in.2 ) =534 ~dps

As determined in Example 5.2. 1, the available compressive strength of the brace is:

ASD

LRFD

Ta, txp = RyFyA8 /l.50

=u(5o ksi)(9.7t fo. 2 )/uo = 356 kips

Therefore, the required s~ngth of the brace connection in tension is Pu Pa :::;< 28.3 kips. ·

=40.2 kips and

The required shear strengch of the beam concurrent with axial tension in the brace is:

,

LRFD

ASD



ASCFJSEJ 7 Section 12.4.3.2

-

(0.6-0. 14Sns)Vo + VH+ VF+ 0.7~VQ£

(0.9-:0.2Sos)Vo + Q,,VQE+ 1.6VH

11

ASD

-

V,, =[0.9-0.2(0.528)}(7.20 kips)

Va = [0.6 - 0.14{0.528)j(7.20 kjps)

+ o kips+'o kips+o.7(2)(0 kips)

+ 2(0kips)+1.6(0 'kips)

= 5.72 kips

=3.79 kips

The available compressive strenglh is greater lhan the maximum compressive axial force calculated using the amplified seismfo load. Therefore, the exception limiting the required rodal compressive strength to the.expected yield strength and l.14Fm Ag will not govern. The required strength of the brace connection in compression is Pu = 53.2 kips and Pa 37.2 kips.

=

The required shear strength of the beam that is concurrent with maximum ax fol compression in the brace is, as calculated in R""
LRFD

I v.

=

ASD

Va = 7.73 kips

11.8 "'··

Brace-to-Gusset Connection Using AlSC Manual Table 7-1 for '!4-in.-diameter A325-N bolts (Group A) in double shear:

'

LRFD

The above shear force is concurrent with the maximum tension for<:e in the diagonal brace.

r1~ :·

l

;:·;·:: -I "...

Considering the lond combinations given in ASCPJSEl 7, the maximum compressive axial force in the diagonal brace based upon the amplified seismic load is:

LRFD

ASD

I

LRFD !,.pad Combination 5 from ASCF.iSEI 7 Section 12.4.3.2 (including the 0.5 factor on L from Section 12.4.3.2)

(1.0 + 0.14SD$)Po +PH +Pp

+0.2Ps

+0.7~ PQe

Pa =[l.0+0.14(0.528)J(5.54 lcips) ~ps+O kips

+ 2(22.3 kips)+0.5(0 kips)

+0

+ 0.2(6.70 kips)

+ 0.7(2)(22.3 kips)

=53.2 kips

=37.2 kips AMEJUC\N L>IS't1l\1l'E OP STEEL CoNsnu.1cnoN

\

\

I

~

=239 "'"'

For the limit Stale Of bolt shear, the minimum number Of bolts required in the brace-togusset connection is:

ASD Load Combination from ASCE/SEI 5 Section 12.4.3.2

(l.2 + 0.2Sos)Po + iloPQe + 0.5Pi

Pu= [l.2+0.2(0.528)](5.54 kips)

j .,. =35.8 kips

ASD

LRFD

ASD

Pu n=$rn

Pa n=-r11ln

= 53.2 kips 35.8 kips

_ 37.2 kips - 23.9 kips

= 1.49 bolts

=J.56 bolts

I

To facilitate erect.ion, use oversized holes in one ply of the connection as permitted in AI!::C Seismic Provisions Section 02.2(3).

AMERICAN lmTrTVT1l 01'

STEEi.. CONSTltUCTION

S.2 OIUJJNA.KY L:Ul\LI~ ll(IL'.ALLV ORACHO >-KAMJ:.!)

When oversized holes arc used in the diagonal brace connection, the required sttcnglh for the limit Slate of bolt slip need oot CJtceed the load effect calculated using the load combinations not including the amplified seismic load, according to AlSC Seismic Provuions Section Fl .6a(3). These correspond to the required strengths calculated for the member design in faample 5.2.1. Therefore, the required strength for I.he limit state of bolt slip need not exceed:

I'·"" =

3-0.9 kl"' LRFD

For short claw angle connections, eccentricity mny be an issue. For angles with the ratio Llg ~ 4, the eccenuicity effect of connections 10 opposite angle legs can safely be ignored (Thornton, 1996). l 1~ the distance between the centers of bolt groups on opposite legs of

the angle, and g is the bolt gage in lhe angle leg. Se.e Figure 5-3. Consider a 2.00-in. edge distance on the brace and che gusset, 11.?-in. space between the eod of the brace and the end of the gusset. and 4-in. spacing between bolts. •I

I

ASD

4.00 in. 0.500 in.) . L = 2 (---+ 2.00 m. + - - 2 2

=8.50 in.

P0 • • = 21.6kips

From AISC Manual Table 7-3 for '.l4-in.-diamcter A325-SC bolts (Group A) in double shear. Class A faying su1faccs, oversized holes in the diagonal brace web and standard holes in the gusset and angles:

g =2.00 in. L g

8.50 in. 2.00 in. = 4.25 > 4

LRFD

Check tensile yielding of the angles

=J0.8 kips

A1 = groi;s area of four :ingles

For the limit srnte of bolt slip, che minimum number of bolts required in the brace-to-gusset connection is:

LRFD

\.

=4A

=4(2. 10 in. 2 ) =8.40 in.2 I l. 1 •

Pa

= 30.9 kips

. .. ,, :

.

~

·'

=1.92 bol15

Use four claw angles 10 connect the brace to the gusset as shown in Figure 5-5. Try (4) L3 1hx3 1hx)/1e claw angles each connected to the gusset with (2) 'A-in.-diameter ASTM A325 bolls in double shear and to the brace web with (2) ~-in.-di:uneter ASTM A325 bolts in double shear. Therefore, the tot.al number of bolts at lhc brace-to-angle connection and at the angle-to-gusset connection, N,, = 4, is greater than che minimum number of bolts, n, calculated above.

..

l

l

FromAJSCMnnualTables 1-7 and l-7a:

Claw Angles L3 1hx3 1/2xs1ia A= 2.10 in.2

'

= 21.6 ldps 10.8 kips = 2.00 bolLS

16. l kips 1

ASD n=-r,./Q

~r,.

o.k.

ASD

~

P., n=-

·:

IJ =0.435 in.

x=0.979 in.

g = 2 in.

Fig. 5-3. Single claw angle dimt11Sion.r for check of eccentric effect.

- - - --<

:: r-1· i

S'-32

BRACED FRAMES

5.2 ORDINARY CONCENTRJ'CALLY BRACED FRAMES

S.-3..l

'

For tensile yielding of connecting elements, the nominal strength is:

- -·

R,. =Fy,Ag _ .

..

(Spec.,Eg. J4-I)

Rn 320 kips - =

~Rn = 0.75(320 kips)

= 36 ksi(8.40 in.2 )

=302.kips ·

r--~~~~~L_R_FD ~~~~~~-+-~~~~~~A_S~ D ~~~~~I

=240 kips > 40.2 kips

.. '

".

I

o.k.

= 160 kips> 28.3 kips

·.

The available tensile strength (yielding) of the four angles is:

2.00

Q

o.k.

Check block shear rupture of the angles

LRFD

ASD

~ = (302 kips) 11.67 =181 kips >.28.3 kips

$Rn= 0.90(302 kips)

o.k.

= 272 kips > 40.2 kips "

!·

. ;~

f~~

o.k.

The horiwmal edge distance ·along the tension plane, Leh, is calculated as the angle leg less the gage:

Check tensile rupture of the angl~s From AISC Specification Table D3.l, the shear lag factor is:

.

Leh

U=l-l

1

Use an edge distance, Lev. of I .SO in. at the ends of the ang_(es.

0.979.in. 4.00 in.

The nominal strength for the limit state of b1ock shear ruprure is:

=0.755 ,.

.'~ l~·

~:

Rn = UbsFuA'!r + mirl(0.60FyA8 v.0.60FuAnv)

Use standard holes in the angles. For calculation of net area, AISC Specification Section B4.3b defines the width of the bolt hole as Y\6 in. greater than the nominal dimension of the hole: where tlle nominal hole dimension is giv_e~_ i? Thble J~.3· · ~·· __ . Ai,

=Ag - 4tdh =8.40 in.2 -4(Sfi6 in.)( li6 in.+ =7.31 ln.2 13

•.. 1 ....... ,,•·.

•' ,,

=

3 'h in. - 2.00 in. ' =1.SOin.

x

·=

AISC Manual Tables 9-3a, 9-3b a.nd 9-3c for block shear may be used here for accurately calculating the rension rupture componenc. For the shear components, the values in the ta.hies are based on a bolt spacing of 3.00 in., whereas this conneetion uses 4.00-in. bolt spacing. For this reason, the tables are not used here for calculating shear components (but could haYe been used as a conservative check).

(from Spe9: Eq. J4-5)

Tension rupture comeo!1~nt _for one ang_(e: From AISC Manual Table 9-3a with Fu= 58' ksi, Len= 1.50 in., and Ubs LRFD

Yi6

in)

~f;,Ant 46.2 kipm. Ii -,-=

-..

=7.31 in.2 (0.755)

I

· FvA.tr = 30.8 kip/m. 10. . FuAruUbs = 30.8 Idp/fu.(S!i6 in.)(1.0)

= 14.4 kips

n

= S.52 in.2

Shear yielding componenl for one angle:

For tensile rupture of connecting elements, the nominal strength is:

R,, = F,,A,, = 58 ksi(5.S2 in.

(Spec. 2

Eq. 14-2)

o.66F1 Agv =0.60(36 ksl)(4.00 in.+ 1..50 io.)(-Yi~ in.) ::::: 37.l kips

)

= 320 kips

AMERICAN INsnruu; OF Sn;a CoNsnu;crroN

l

ASD \

(Spec. Eq. D3-l)

A,,z::AnU

=1.0:

.

=9.63 kips

.;:

(

"BRACED FRAMES

S-34

Effective net area:

ASD

LRFD ' .

$0.60FyAgv = 0.75(37. l kips) ..

u =1.0

0.60FyAgv = 37.1 kips

n

= 27.8.kips

5.2 ORDINARY CONC.ENTR.lCALLY BRACED FRAMES

2.00 = 18.6 lcips

. •.

. I.

An= (d-2d,,)t...,

=[9.73 in.- 2(1.00 in.)j(0.290 in.)

..

'

l·...~.

'

=2.24 in. 2

Shear ruprure component for one angle:

.~==AnU

0.60FuAnv:::: 0.60(58 ksi)[4.00in.+1.50 in:-'-1.5( 1 ~6 in.+ lt\6 in.)j(~6 in.)

(Spec. Eq. D3-

., . 2 .

= 2.24 m. (1.0)

== 45.5 kips

'.

= 2.24in.2 ASD

LRFD

0.60F.,AMv

$0.60F.,A;,v =Q.75(45.5 kips)

~

n

=34.1 kips

•"

For tensile rupture of the brace web, the nominal stre.ngrh is:

45.5 kips 2.00 = 22.8 kips

Rn= FuAe = 65 ksi(2.24

(Spec. Eq. J4-2_

I:.

in.2)

t·:·

=146 kips Shear yieldfog. governs over shear rupture. The available strength for the limit state of block shear rupture for the four angle~ is:

ASD

LRFD

$R,, :::·4(i4A .kips+27.81cips) = 169 kips> 40.2 kips

Rn =4(9.63kips+l8.6kips) o.k.

n

= 113 kips> 28.3 kips

o.k.

Check tension rupture of the brace The claw angles are .connected only to the web of lhe W1 Ox33 brace and not lO the flanges. Therefore shear Jag may reduce tl)e effective area. The bolt holes in the web of the brace are oversized for erection tolerance. Because the tension load is transferred only at rbe web of the wide flange brace, Case 2 of AISC Specification Table D3.1 is applicable. However to simplify calculation of the net section, consider the tensile rupture capacity of the web element only. This is similar to Case 3 of Table D3. l, which applies to members with transverse welds to some but not an ·of the cross-sectional elements. From AISC Specification Table J3.3, the diameter of an ove~ized hole for a '.!4-in.-diameter bolt is U/i6 in. From. AISC Specificarlon Section B4.3b, when computing the net area the width of the bolt bole is taken as Vi6 in. greater than the nominal dimension of the hole. d11

=15Ji6 in.+ 'li6 in.

The available tensile rupture str~ngth of the brace web is:

= 110 kips> 40.2 kips

o.k.

= 73.0 kips:> 28.3 kips

mem~~.

For this lightly loaded this conservative and simplified the available tensile rupture strength iS a_d~ua.te._·

c~uld

calci1~ted

indicates th..

I f;:

I

Alternatively, the effective net area be for the entire section as follow Calculate U, the shear lag factor, in accordance With Table D3.l, Case 2, of the AJS, Specification. AISC Specification Commentary Fi~e C-D3.l recommends treating half o.t the flange and a portion of rhe web as an angle. This is shown in Figure 5-4. ~-·

First, calculate ,'t of the angle, where xis measured from the centerline of the web (this ca, , cuJarion ignores che fillets): A= bJ (t1)+(%-t1)(';

J

=7.9~ in.(0.435 in.)+(9.7~ in. _ 0 _435 in.)f0.29; in.} =2.37 in. 2

=l.00 in.

AMERICAN lNSTrruTE OP STEa CONS'l'RUCl10f'I

·$\•.

cal~ulation

o.k.

l;::·

:·;: .......

1

S-36

BRACED FRAMES

_ t.X,Ai x=--

1

=(A-2dhtw )U

(0.2~in.)(0.2~in.)(9.7~in. _ 0 .4 3 Sin.)

=[9.71 in.2 -2(1.00 in.)(0.290 in.)j(0.669) = 6.11 in.2

- 2.37 in.2 +(3.9! in. )(3.98 io.)(0.435 in.)

,,,

(Spec. Eq. 03-1)

~ = AnU

1\

_

5-37

5.2 ORDlNARY CONCENTRICALLY BRACED FRAMES

For tensile rupture of the beam web, the nominJ1l strength is:

=1.47 in. AJSC Specification Commentary Section 03 states that 'i is the perpeodjcular distance from lhe connection plane to the centroid of the member section. Therefore, the used in the tension rupture calculation is the calculated i of l .47 in. minus half the web thickness. From AJSC Specification Table 03.l:

Rn =Fu~

x

(Spec. Eq. 14-2)

= 65 ksi(6.1 l io. 2 )

=397 kips The avajlable tensile rupture strength of the brace web is:

x

U=l-l

LRFD

=I 1.47 in. - ~(0.290 in.) 4.00 in.

¢Rn =0.75(397 kips)

=0.669

= 298 kips > 40.2 kips

=

ASD

o.k.

R11 397 kips - = n 2.00 = 199 kips > 28.3 kips

o.k.

2

For a W10x33 brace, with A 9.7J in. and using oversized boles in the brace web (dh:::: 1.00 in.), the effective net area is:

ll W1 Ox33 brace

-r

As shown, ttie available strength of the W-shape brace for the limit state of tensile rupture as calculated per the simplified caJ~lation (with only the brace web considered effective) is adequate for the applied loads. However, if additional capacity were required, lhe avaiiable strength as calculated per AlSC Specificario11 Table D3. l, Case 2, is much greater.

Check block shear rupture of the brace web The portion of the brace web between the bolt lines is checked for block shear. Assume a gusset plate thickness, lg, of'A in.

ubs =1.0 for unifonu tensile stress A111 =(2g +r8 -d11)c.., =[2(2.00 in.)+% in.-1.00 in.J(0.290 in.)

.

= 0.979 in. 2

;

' - =2.00 in. s

= 4.00 in.

A8• =2(.l.n. +s)tw =2(2.00 in.+ 4.00 in.)(0.290 in.) =3.48 in.2 Fig. 5-4. Tension rupnire on brace

A,,, =2( ~ +s-1.5d11)t,.,

=2[2.00 in.+ 4.00 in. = 2.61 in .2 AMERICAN lNST11V!1! OF

STEEl. CONSTRUCTION

1.5(1.00 in.)j{0.290 in.)

BRACED FRAMES

S-38

5-39

5.2 ORntNARY CONCENTRlCALLY BRACED FRAMES

L i

TI1e 11om.inal scrength for the limit state of block shear .rupnire is given by:

R,.

=0.60F Anv + UbsFuA.u S 0.60F,.Ap + Ub,F11Au

A.v = 2(Lev +s- l.5dh)c8 (Spec. Eq. J4-5)

11

AISC Specification F.quatio.o J4-5 can be expressed as follows to determine lhe available strength of the brace web for the limit state of block shear rupture:

+min(¢0.60F1 At", $0.60F.,A,.v)

=0.75(1.0)(65 ksi)

2.00

0.60FyAgv 2.00

=0.75(0.60)(50 ksi) x(3.48 in.2)

. 0.60F,,Anv

= 0.75(0.60)(65 k,si) 2

x(2.61 in.

AlSC Specificatio11 Equation 14-5 can be expressed as follows to determine the available strength of the gusset plate for the limit sl:ite of block shear rupture:

2.00

LRFD

9R,, =$UbsFuA..1

2.00

=(0.60)(65ksi)(2.61 in.

2.00

+min( ~0.60F1 Asv. ~0.60FuAnv) 2

2.00

~ =3l.8kips+50.9kips


o.k.

= 82.7 kips > 28.3 kips

2.00

x(I.28m.2)

~0.60FyA8 • = 0.75(0.60)(36 ksi) \

x(4.SO m.2)

With an assumed gusset thickness, d,,

* in., and standard .holes in tbe·gusset:

t, =

= ·~6 in.+!li6 in.

x( 3.52 in.

2.00

2.00 =48.6 kips

i

0.60F11 A,.. 2.00

= 0.75(0.60)(58 ksi) 2

(0.60)(36 ksi)(4.50 in. 2 )

'

=(0.60)(58 ksi)(3.52 in.2 )

)

$R,. = 55.7 kips+ n9 kips =129 kips > 40.2 kips

ub, =i.o

l

J

Rn = 37.1 kips+ 48.6 kips o.k.

n

=85.7 kips > 28.3 kips

o.k.

=(2g+t.,-d,,)r8

=[2(2.00 in.)+0.290 in. -0.875 in.J(~ in.) =1.28 in.2

Check the gusset plate for buckling on the Wh;tmore section

Lev

=2.00 in.

and Llni (2011 ), and is shown for this example in Figure 5-5.

s

=4.00 in. AMERJCAN

.t

~.00

= 61.2kips

= 91.9 kips

= 0.875 in.

Ant

~0.60FuAnv

)

2.00

0.60FyA.!" I

= 72.9 kips

Check block shear rupture of the gusset plate

2

= 37.l kips

=55.7 kips o.k.

2.00

Ub:Fu!int = (1.0)(58 ksi)(L28 in.

~Ub,F.,Ani = 0.75(1.0)(58 ksi)

.

47.7 kips+ 76.3 kips

. (0.60FyAzv , 0.60FuAnv) +mm

)

2.00

. -= 50.9 kips

)

I·

ASD

(0.60)(50 ksi)( 3.48 m.2)

=76.3 kips

.

(Spec. Eq. J4-5)

=52.2 kips

=78.3 kips

~Rn=

I

in.)

The nominal strength for the limit state of block shear rupture is g.ivcn by:

= 31.8 kips

=47.7 kips

~0.60F.,A,.,.

in.)(~

=4.50 in. 2

Ub,Fu.Ani -= n 2.00 . (0.60FyAgv 0.60FuAnv) +nun ' 2.00 2.00

u,,,FuA..i -= (L0)(65ksi)(0.979 in.2 )

x(0.?79 in.2 ) ~0.60F,Agv

}

Rn

$R,. = $Ub,F11An1

$Ub,FuAnt

l..:

Aiv=2(L.,.+s)t1 = 2(2.00 in.+4.00

ASD

LRFD

=2f2.00 in.+4.00 in.-1.5(0.875 in.)](~ in.) =3.52 in.2

J

}

The "Whhmore section" is discussed in AlSC Man:ual Part 9 (Figure 9-J) and in 'Thornton

INmwra Ol' STUl.. CoNsnu;cno.H

".

BRACED FRAMES

5-41

52 ORDINARY CONCENTRICALLY BRACED FRAMES

On the gusset plate, the space between the bolt lines of the angles is:

~column

I

2g+c.., = 2(2.00 in.)+0.290 in. = 4.29 in.

W18x50 beam

The Whitmore width is: W.P.

I..,= 2/tan30°+ s

- - - -~-----
=2(4.00 in.)tau30°+4.29 in.

beam

=8.91 in. r _..!J_

- Jli

.•

~: :

...

*in.

=-:m

~.
·'•

=0.108 in.

·>

- - -- -1

L:J W10x33 brace

Use rhe effective length factor, K, of 0.50 as established by full scale rests on bracing connections (Gross, 1990) and as referenced in theAfSC Design Examples VJ4.0. Note that this K value requires the gusset 10 be supported on both edges. Alternatively, the effective length factor for gusset buckling could be detennined according to DowsweIJ (2006). From Figure 5-5, the unbraced length of the gusset plate along the axis of the brace is

L W10x49

!; ,.'/ ,.v

L = 8.70 in. (Exam.pie 5.3.10 provides an equation for calculating che length of buckling; (6) ;i· dia. A325-N bolts in std. holes

here it is derennined graphically.)

KL

-

column

r

0.50(8.70 in.)

= -------'0.108 in.

=40.3 W10x33 brace

From AISC MarnJal Table 4-22 with F1\= 36 ksi and Kl

r

I

LRFD 1

4 - L3~3Yzxo/16 \;

:;· ...

~~19

=40.3: ASD ...

Therefore, from AISC Specificaticn Equation E3-l, the available compressive strength based on flexural buckliog is:

~~'

Fig. 5-5. As5wned initial geometry for £xample5 5.2.l through 5.2.4.

...,,

:;, 'r

AMERJ(".A}I

lNSTITUT!! OF STtD.. CONmuc:noN

=29.8 ksi(8.9 1 in.)(* in.) =99.6 kips> 53.2 kips

!

~=(~)Ag

cpP" =IJ>cFcrAg Section A-A

I

ASD

LRFO

o.k.

!

= 19.8 ksi (8.91 in.)(3,ii in.)

= 66.2 JOps > 37 .2 kips

o.k.

BRACED FRA,\ffiS

5-42

Note: An altema1ive is to use a reduced unbraced buck.ling length fo.r the gusset calculated from the ave.rage values from the end and center of the Whitmore section. See AISC Design Examples Vl4.0, Example II.C-2 (AISC, 2011). Because the absolute value of the required strength of the connection in tension is less than the required strength of the connection in compression, tension yielding on the Whitmore section will not control.

5.2 ORDINARY CONCENTRlCAf..LY 8.RACED FRAMES

ASD

LRFD ¢r,.

fn

= 0.75(23.8 kips)

23.8 kips 2.00 = 11.9 kips

-=

n

= 17.9kips

t.·:.. ·!

Considering four angles, each with one end bolt and one interior boll: Check bolt bearing on the angles

Standard holes are used in the angles. From AISC Specification Table J3.3, for a iliameter bolt, dh = 1Vi6 in.

~-in.

The bearing strength requirements per boll are given by AISC Specificarion Section 13. l 0. For the imerior bolt with a bolt spacing of 4.00 in., the bearing strength per bolt is: r11

=l.21,tF,, ~ 2AdtF.,

Therefore, no.ininal bearing strength for the interior bolt is rn =32.6 kips. The availabie bearing strength of the interior bolt is: ASD

LRFD

=170 kips > 53.2 kips

o.k.

4

[lbolt(l6.3 kips) +1

l o.k.

Note that AlSC Manual Table 7-4 could also have been used; however, it is based on smaller bolt spacing than 4.00 in. For the end bolt, with Lt= 1.50 in., the nominal bearing strength per bolt for each angle is:

(Spec. Eq. J3-6a)

~ 2.4d1F11

in.)](¥16 in.)(58 ksi)

=23.8 kips .S 32.6 kips

AMlllUCAN

ASD

LRFD

$rn = 0.75(33.9 kips) = 25.4 kips

rn

33.9 kips 2.00 = 17.0 lcips

-=

n

Note that AISC Manual Table 7-4 could !lave been usCd, but the table is based on smaller bolt spacing than the 4.00 in. used in this example.

in.)(Vt6 in.)(58 ksi)

The nominal bearing strength for the end bolt is rn strength of the end bolt is:

"

=1.2(4.00 in.- 1Vt6 in.)(0.290 in.)(65 ksi) =69.3 kips

Therefore, the nominal bearing strength of. the interior bolts is 33.9 kips. The available bear'i · ing strength of the interior bolts is:

= 16.3 kips

in. -1h(1¥i6

1.2.LctF.,

= ~3.8

)

=33.9 kips

n

=24.5 kips

(Spec. Eq. J3-6a)

rn = I .2LctFu < 2.4dtFu

2.4dtF., = 2.4{'A in.)(0.290 in.)(65 ksi)

rn = 32.6 kips 2.00

=0.75(32.6 kips)

$ 2.4(

R11

n= bolt(ll.9 kips) =113 kips > 37.2 kips

For the interior bolt with a bolt spacing of 4.00 in., the bearing strength per bolt is:

= 32.6 kips

3,4

I

Oversized holes are used in the brace. From AISC Specification Table 13.3, for a '.!A-in.diameter bolt, dh = 1Sft6 in.

2.4dtF,, =2.4(% in.)(Vt6 in.)(58 ksi)

::: l.2[1.50

bolt(2-t5 kips)

+ 1 bolt{l7.9 kips)

Check bolt bearing on brace web

=69.3 kips

rn ::: l.2lctF11

l

ASD

(Spec. Eq. J3-6a)

1.2/ctF,, =1.2(4.00 in. - 1Vl6 in.)(o/16 in.)(58 ksi)

~rn

¢R,. = 4

LRFD

kips. The available bearing

!J.IS1TIVJ"B OP SmEl. CONSTRUCTION

;(

BRACED FRAM.ES

'•

Use AISC Manual Taqle 7-5 for lhe end bolts. For L~ bolt is:

=2.00 in., the bearing strength per end

LRFD ~

Note that AISC Manual Table 7-4 could also have been used. However, it is based on smaller boll spacing than 4.00 in. Use AISC Manual Table 7-5 for end bolls. For Le = 2.00 in., the bearing strength per end bolt is:

ASD

G>rn = 87.8 kip/in.

5.2 ORDINARY CONCENT'RlC;\LLY BRACED FRAMES

=58.5 kip/in.

ASD r,. ? .. n : : : 5-.2 kip/m.

The :wailable strength of the end bolt is:

LRFD

ASD

Tue available strength of the end bolt is:

~ = 58.5 kip/in.(0.290 in.)

$r,, = 87.8 kip/in.(0.290 in.) = 25.5 kips

= 17.0 kips

LRFD

ASD

¢>rn : : : 78.3 kip/in.(* in.)

~ :::::: 52.2 kip/in.(% in.)

:::::: 29.4 kips

= 19.6 kips

Considering two interior bolts and two end bolts on the brace:

LRFD

$Rn= ' ·

ASD

l

[2 bolts(2S.4 kips)

R,.

n=

+ 2 bolts(25.5 kips)


l

. '

· LRFD

f2bolts(17.0kips) +2bolts(17.0kips)

=68.0 kips >-37.2 kips

o.k.

Considering two end bolts and two imerior bolts:

ASD

..

o.k.

¢Rn::::::

[2 bolts{29.4 kips) ] + 2 bolts(29.4 kips)


R11

n

=78.4 kips> 37.2 kips

o.k.

Check bolt bearing on the gusset Standard holes are used in the gusset. From AISC Specification Table J3.3, for a %-ill.diameter bolt, dh = 13/i6 in. For the interior bolt with a bolt spacing of 4.00 in., the bearing strength per bolt is:

r,. ::::. I.2LctFu < 2.4dtFu 1.2LctF,. =1.2(4.00 in. =83.2 kips

(Spec. Eq. J3-6a) 13/J6

2.4dtFu = 2.4(% in.)(% in.)(58 k:si)

=39.2 kips Therefore, !he nominal bearing strength of the interior bolt is 39.2 kips. The available bearing strength of the interior bolt is: ·

L.RFD $rn = 0.75(39.2 kips)

=29.4 kips

ASD

r,, = 39.2 kips Q

2.00 = 19.6 kips

..

·i o.k.

I

Use (4) ASTM A325-SC bolts in double shear to connect (4) L3 1hx3 1hx 5/1s lo the brace web. Use standard boles in the angles and gusset; and oversized holes in the brace web. Use (4) ASTM A325-N bolts in double shear to connect the (4) L31/2x3 1hx 5h6 to the gusset.

'

Connection Interface Forces

The forces the gusset-to-_beam aI!d gusseHo~cqj~~ interfac~s are detenni~ed using Uoifonn Force Method. The planes of unifo~ forces will be set at the column bolt line and !he gusset/berun interface. The assumption of a plane of uniform force at the column bolt line allows the bolts at the column connection to be designed for shear and ·wal load only (no eccentricity) and therefore simplifies the design.

the

at

in.)(* in.)(58 ksi)

I

[2 bol1$(l9.(i ~ips) "' + 2 bolts(19.6 kips)

It should be noted that this assumption is different lh~ that made for the typical cases of th-! Unifonn Force Method discussed in the AISC Manual where the unifonn force at the colum.ri is at the face of the column t1ange. Appropriate work point.s and uniform force planes er,:, often be selected conveniently to balance enginee.ring, fabcication and erection economy. As previously determined, the ma,mnum brace force according to ASCEtSEI 7 load corr:· nations is 53.2 kips (LRFD) or 37.2 kips (ASD) acting in coropre~sion. The maximum tm,(.,, force iu tension is 40.2 kips (LRFD) 28.3 kips· (ASD). Consider !he larger compress, . force to act in both directions in order to simplify calculations.

or

AM£J
JJ-ISTJTUTE OP STEEL CoNS"rR\JCnON

BRACED FRAMES

Assume an initfaJ connection geometry as shown in Figure 5-5. Using the analysis found in AISC Manual Part 13:

5.2 ORDINARY CONCENTRICALLY UM<.:a.D tAAMl:!S 5-4 1

t

the method described as "Analysis of Existing Djagonal Bracing C9nnections" in Part J3 of the A1SC Manual. I,. ;.

db

tb = -

2

18.0 in.

=- - 2

=9.00 in. tc

i

=

2

r = J(a+ec )2 +(J3+eb)

+2.50 in.

10.0 in. . = - - - + 2.50 10. 2 =7.50 in.

(Manual Eq. 13-6)

~ J(7.00 in.+ 7.50 in.)2 +(5.50 in.+9.00 in.)2 =20.5 in.

P

Set as the distance from the bottom of the beam to the center of the two bolts connecting the single plate lo the gussec.

The required shear force at the gusset-to-column connection is determined as:

(Ma11ual Eq. 13-2)

P=5.50 in. Use a shared single-plate connection to connect the beam and gusset 10 the column. Therefore, the bottom flange of the beam must be either coped or blocked flush 10 clear the .single-plate shear connection. Consider no weld between the gusset and the beam for 5 in. to allow for a 4 1h-in.-wide si.Ugle plate with a 1h-in. clearance between the plate and the start of the blocked beam flange. Assume a 17.0-in.-long gusset with a ~-in. clearance 10 the column flange. Consider the gusset-to-beam weld length as 12.5 in. Because the bolt line is used as the plan~ of uniform force, the distance to the center of the gusset-to-beam weld, Ci., must be set from the bolt line. . ·

_

12.5 in. . - + 4.50 in.+ 0.500 in. - 2.50 in. 2 =8.75 in.

LRFD

. 13

Vac--Pa r

r

= 5 · 5 ~ ~- (53.2 kips) 20.) 10. -

=S.SO in.(37.2 kips)

20.5 in. =9.98 kips

=14.3 lcips

I

\ I

LRFD

ASD

ec

Hae =-Pa r

J3 =~. 1he value of ex required for the uniform forces is:

=

(from Manual Eq. 13-1)

=9.00 in.(tan45~)-7.50 iil:+5.50 in.(tan45°) =7.00 in.

_p

V.,c =-Pu

Note: Alternatively, where the beam flange is blocked flush to lap the shear tab, the gusset could be welded to the beam with a one-sided fillet weld on the far side of the gusset, and a flush partial-joint-penetration groove weld on the near side. This would allow the full length of the gusse1 along the beam.to be included in the _design at this interface.

ex= eb tan9-ec +Ptan9

.

ASD

The required axial force at the gusset-to-column connection is determined as:

ct= -

Setting

t·

.

Because the a required for unifon'n forces does not equal ii based on this initial geometry, unifoon forces at the interfaces are not possible with the current configuration. The connection geometry can be adjusted by an iterative process to achieve the unifo~ distribution. Alternatively, th~ connection can be analyzed with an additional moment per

75

~ ~-(53.2 kips)

20..) ID.

= 19.5 kips

-.

=7·50 41·(37.2 kips) . 20.5 in. . =13.6 kip~ :_)

The required shear force at lbe gusset-to-Qeain connection is determined a~:

~

) t

-

BRACED FRAMES

r--1 ! ~

·~ ;

5.2 ORDINARY CONCENTR.lCALLY BRACED FRAMES

'

LRFD

I'"'

.

ASD

'I I

I·

t<

..:

I

a

ct_

column

a

Hub =-P.,

Hob =- Po r 7 00 0 · ~ '(37.2 kips) =20.5 J.n,

r

=7.00 - -in. -{53.2 k'lpS ) 20.5 in. 18.2 kips

=

=12.7 kips

The required axial force at the gusset-to-beam connoctioo is determined as: (Manual Eq. 13-4)

LRFD <:

··'· •)

- - -....

"·:~-:J

..,'·);~ , '·<•

ASD

tb

eb

Vab =-Pa r 9 = ·00 in. {37.2 kips) .20.5 in.

Vwb =-P,.

r

~ 9·00 in.(53.2 kips) 20.5 in.

=16.3 k.ips

=23.4 kips ·- .

ec

= 2de + ""2 '>V

The moment at the gusset-to-beam interface is: (Manual Eq. 13-17)

LRFD Mub = Vubla-aj

ASD

~

Mob= V.wla-Cij

= 23.4 kipsl7.00 in.-8.75 in~

=16.3 kipsl7.00 in.-8.75 in~

= 41.0 kii}-in.

=28.5 !Op-in.

WP~ \ I

These forces are illustrated symbolically in Figure 5-6.

Gusset-to-Beam Connection

.·

Design gusset-to-beam weld The gusset-to-beam weld will be determined by applying the Elastic Method discussed in

AISC Manual Pa.rt 8. To accommodate the bottom flange block, which extends ~ in. past lbe single plate, the ma.'timum length of weld a.long the gusset-to-beam interface is: l,..b = 17.0 in.+0.500 in. - 4.50 in.-0.500 in. = 12.5 in. Fig. 5-6. Free-body diagrams for Example S.2.4. AMSUCNI L"ITTJtVl"B OF STW. CoNSTRUCTION

5-50

BRACED FRAMES

5.2 UlUJINA.K'( l:UNLJ::.N I KlLl\U.Y

Treating the weld as a line:

Sw

LRFD

=(12.5 in.)2

fu, ~

6

=26.0 in.

3

LRFD

ASD

Hub

/av::: Hab

lwb

l...i,

!lllJ = "'"' lwb

= 23.4 kips 12.5 in. = 1.87 kip/in.

f,uJ>--_ Mub

Sw

= 41.0 kip·in. 26.0 in. 3 /in.

=1.58 kip/in.

+ (1.46)

2

-lh

2

lwb

·= 16.3 kips 12.5 in.

=1.30 kip/in.

+J(l.87+1.58)

2

'

l l

,,

+fa~ +JU,,, +lab )2 + fa~ JUoo - lab )

2

Jc1.30-1.10> 2 + c1 .02)2

=1.82 kip/in. !a.peak = 2.61 kip/in. fa, avg

1:

L82kip/in.

""f.43

O= ta:ri-1 ( fua + fub)

= 28.5 kip-in.

+(1.02)2

•,

+J(l .30 + 1.10)2 + (1.02) 2

=1.43

=tan

rm.

=)h

= 2.62 kip{m.

-1 ( 1.87

Sw

fa.avg =1h

+ (1.46)2

J.I\.

Mab fab=. - '

=J(I.30+ L.'10)

2

+ (1.46) 2

fu.ptaJc = 3.75 kip/in. 2.62 kip/in. fu,11'1!

aa -

~(Joa+ fob) +fa~

= 2.61 kip/in.

+~(fua + fub )2 + f.,; [,/(L87 - 1.58)

,,.,

},,

2

~(fua - J.b)2 + fu';

='h

/u,avg

12.5 in. =1.02 kip/in.

26.0 in.3

fa.peak=

= 3.75 kip/in.

=12.7 kips

/. _ Vab

ASD

+ fu;

=J(l .87+1.58)

The shear force, axial force, aod force due to flexure per linear illch of weld are:

. = 18.2 kips 12.5 in. = 1.46 kip/in.

= Ju.,,, +/kb )

2

2

/in.

fw=--

UKA\....l!U r~

kip/in.+ 1.58 kip/in.) 1.46 kip/in.

S=

tan-I( faafov+fob)

=tan-I ( 1.30 kip/in.+ l.lO kip/in.) 1.02 kip/in.

=67.0°

=67.1°

=1.10 kip/in.

The force on the weld due to bending is determine.d using elastic section properties as per the Elastic Method indicated in Part 8 of the AlSC Manual. Generally this method is considered conservative. The Instantaneous. Center of Rotation Method, also found in Part 8, often results in smaller requi.re4 weld sizes for welds subject to eccentricity. In the examples in this Manual employing special concentrically braced frame connections, a plastic stress distribution is used to determine the forces at the beam-to-gusset interface. This example will use the oiore conservative elastic method. Use a vector sum (square root of the sum of the' squares) to combine the shear, axial and bending stresses on the gusset-to-beam interface. Because the bending stress acts in opposite directions over each half of the length, tIµs creates both a maximum (peak) and a minimum stress. The average stress is detenniued based on the maximum (peak) stress and the minimum stress. AU stress un~ts below are in kip/in.

According to the AISC Manual Part 13, because the gusset is directly welded to the beam, the weld is designed for the larger of '11e peak stress and 1.25 times the average stress; Becausef~aklfavg > 1.25, the w~ld ductil,ity factor need not be applied . .For a discussion of the weld ductility factor of 1.25, see AISC Manual Part 13. ·

t·· :'.·

Therefore.fr= f f'«lk = 3.75 kip/in. (LRFD),:md 2-<51 kip/in. (ASD).

The strength of fillet welds defined in AISC Specification Section J2. can be simplified, as explained .in Part 8 of the AISC Manual, to AISC Manual Equations 8.-2a and 8-:?,b: LRFD

ASD

$R11 =(1.392 kiplin.)Dl

. Rn =(0.928 Jdptin.)Dl

n

l·

f

''

l.·". ...

:~

BRACl:!D FRAMES

~

2{1.392 kip/in.){ I + 0.50sinl.5 0) 3.75 kip/in.

2(1.392 kipfm.)[1+0.50sin1.S (67 .1°)j

=0.934 sixteenths

D~

~

2(0.928 ldp/in.)(1+0.50sin 15

a)

2.61 kipfm. 2(0.928 kipfm.)h + 0.50sin 1J (67.0°)J

=0.975 sixteenths

Use two-sided Yi6-in. fillet welds to connect the gusset plare

R. =V...

(M.) "" 1

r:r') (Mob) 1

=Ve1b+4 -

=16.3 kips+4( 28J_.S ·~ ki~in.) JO, =25.4 kips

=23.4 kips+-t( 41.0 kip-in.) 12.5 in.

=36.5 kips

ro 1he beam_ The beam is checked for the limit state of \\eb loc!\I yielding due Wl'lded to the beam flange.

10 the force

from the pl:t!.:

A conservati\'C method to determine the minimum gusset plate thickness required to lrallsfcr t11e sbear and tension forces is to set the shear rupture strength of the weld (based on the resultant force) equal to the shear ruprure strength of the gusset plate. Using AJSC Manual

The force is applied a distance a from the beam end. Because l'l
Equation 9-3:

For a force applied :it a distance less than the depth of the member:

LRFD

~

in. > 0.0077 in.

=(50 ks1){0355 in.)12.5(0.972sn.)+12.5 m.) =265 kips

F,,

58 ksi =0.0997 in.

(Spec. Eq. J 10-3)

R,, = Fy,.t,.(2.5k+lb)

lmv. = - -

=6.19 kiplin.(0.934) I•

ASD

6.L9D

6.19D f'"m=-F11

.,:i.,

Mw,

R,.~v,.+ (~f =Vub+4

Check gusset plate rupture at beam weld

;,·· 1

ASD

LRFD

!11.~(lk

From AlSC Specijicatkm Table 12.4, the minimum sii.e fillet weld allowed for the parts being connected is ¥16 in.

.,

rKAMI.:.'>

ASD

LR.FD D~

UKJ\l.l!U

portion of this stress distribution that acts JD the reverse direction, aoc.J considering the total force to be applied at the center of the bearing length, the resultant compre~ive force is:

The required weld size at the gusset-to-beam interface is:

fu, P,aJ:

520RDJNARV C.'ONCJ::.l'l'HUl...Al.l..t

=6.19 ldp/in.(0.975)

ASD

LRFD

58 ksi

=0.104 in. o.k..

*in.> 0.104 in.

¢Rn o.k.

Use a ~-io.-thick gusset plate to connect the brace lo the beam aod column. Alternatively, the required thickness of the gusset plate could be determined by cbeckiog ilie strength of gusset plate directly.

=1.00(265 kips) =265 kips > 36.5 kips

\

o.k.

R,. 265 kips -=

n

'

1.50


o.k. '

Alternatively, the available strength for web yielding can be determined from AlSC Manllal Table 9-4. · '

Check beam web local crippling Check gusset plate yielding at beam weld It can be shown that si~ce the gusset plate satisfies the minimum lbick.ncss criteria for rupture based on weld size, ii also satisfies the tension yielding criteria.

Check beam web local yielding The maxi.mum stress per unit lenglh on the gusse1-10-bealn interuce along the weld due to moment Mb is M~/2/4) assuming a plastic stress distribution. Conservati.,·ely neglecting the

A portion of the force is applied within d!l of the member cod; therefore, use AISC Specification Section J10.3(b). Check the length of beating relative to the beam depth: lb 12.5 in. -=--d 18.0 in.

=0.694 >0.2

tlKALtU t'KAMt:)


Therefore, use AJSC Specificarion Equation J 10-5b to determine the available strength, through use of AISC Manual Table 9-4. From AISC Manual Table 9-4 for the W18x50:

LRFD

ASD

R,,=JV~+HJc

LRFD

= Jo4.3 kips) +(J9.5 k.ips)

ASD

¢Rs

=52.0 kips

~ =34.7 kips

¢>Rt;

=6.30 kipfm.

~ = 4.20 kipfm.

Ra =Jv1.:+ H~ 2

=J(9.98 kips)2 + (13.6 Jcips)2

2

= 24.2 kips

ASD ~

Rs ~ -=-+lb-

= 52.0kips+12.5 in.(6.30 kip/in.) .

=131kips>36.5 k.ips

n

o.k.

n

f:.

l.:

Try two bolts connecting the gusset to a single plate. The required shear strength per bolt is:

LRFD

$Rn =Rs +lb ( i?Q)

t

= 16.9 kips

ASD


LRFD

I

.

n

Ra

V.u- R..., 2 24.2.kips = 2 =12. l kips/bolt

\..

Va=2

r

= 16.9 kips 2

=8.45 kipstbolt

; ;

:::: 34.7 kips+ 12.5 in.( 4.20 kip/in.)

=87.2 kips> 25.4 kips

o.k.

Beam and Gusset-to-Column Connection Use a single-plate connection lbat combines the connections of the beam and gusset to the column. Design the bolted connections of the iusset to the single pl:11e and of the beam to the single plate individually. Design the weld of the single plate to the column considering the combined plate length. The forces used to design the single-plate will be those derived per the Unifonn Force Method. Additional forces beyond those calculated by this method may occur in the connection of the beam/gusset connection to the column due 10 the rotation of the beam relative to the column._While forces in the connections due to rotation from seismic drift are opposite the forces determined by the Uniform Force Method, the beam and gusset connection to the column will be .designed following the single plate design philosophy in Part IO of tbeAISC Manual to provide additional rotational ductili1y to address both rotation from seismic drift and simple-beam end rotation. The eccentricity on the single plate due to the braced frame shear is addressed by the Uniform Poree Method which app}jes n couple based on the He a.xial forces applied at the center of the beam and the center of the .gusset-to-column connection.

~ =U.9 kips> 8.45 kips

I

.1. ,

'----------------~---------------

t

¢rn

=17.9 kips> 12.1 kips

o.k.

o.k.

I

From AISC Manual Table 7-4 with 3 in. bolt spacing, the bearing strength per inch of singleplate thickness is:

LRFD Qrn =78.3 kipfm.

ASD

"

-

~.

·-

~ =52.2 kipfm. I

Assume a Sfi6·in.-thick single plate.

~

For the interior bolt, lhe available bearing strength of the single plate is: Design gusset-to-column bolted connection The result~nt force

o~'tbe bolts in the gusset plate is:

LRFD

ASD

1 ·i·1

!----------------+--------------___, q>r,. = 78.3 kip/in.(¥!& in.)

=24.5 kips/bolt

~ :::·52.2 kipfm.{Vi6 in.)

=16.3 kips/bolt

I ~i

L--~~~~-L-~~~~--'

~ )

.,,3.

1n

BRACED FRAMES

5-56

The edge distances in Lhe single plate are l 1h in. vertically and 2 in. horizontally. Conscrv:itively, use the lesser of Lhese edge distances. A more refined cbeck would calculate the edge disrnnce in tbe direction of the force. For the end bolt, with L,, = 1'h in., the nominal bearing strength per bolt is:

,....

Yn

!!

~

J.2/"F,'

The nominal strength for the limit state of block shear rupture relative to the normal force

on the single plate is: (Spec. Eq. 14-5) where

=1.21,.Fu S 2.4dF,, t

(from Spec. Eq. J3-6a)

t

d 11

=13/16 in. + 1/16 in. =0.875 in.

=1.2[1.50 in. - 1h(1¥i6 in.)](58 ksi} = 76.1 kip/in.

A.iv= 2(~h -0.5dh)lp

2.4dF,, ::::: 2.4(~ in.)(58 ksi)

:::: 2[2.00 in. -0.5(0.875 in.)j(Vi6 in.)

t

=104 kip/in.

=0.977 in.

Therefore, the nomina.1 bearing sirenglh of the end bolt is rn bearing strength of the end bolt is:

=76. l kip/in. The available

LRFD rn

n

::; 57.1 kip/in.

2

A1 v =24Mp :::: 2(2.00 in.)(Vi6 in.)

=1.25 in. 2

ASD

¢rn:::: 0.75(76.1 kip/in.)

UI

5-57

5.2 ORDINARY CONCENTRICALLY BRACED f'RA1\.!ES

An1 =(s - dh)lp

76.l ldp/in. 2.00 = 38.1 kip/in.

= (3.00 in. - 0.875 in.)(~6 in.)

:::: 0.664 in.2 o.60FuA.-.v + ub~Fu,4..t = 0.60(58 ksi)(0.977in.2)+1.0(58 ksiX0.664 in.2)

For the end bolt, the available bearing strength of the single plate is:

=72-.5kips

LRFD ¢rn

f~-. -1 ...~

ASD

=57.1 k.iplin.(~6 in.)

~ = 38.l kip{m.(¥16 in.)

= l7.8 kips/bolt > 12.1 kips/bolt

0.60F1 A"" + UbsFuA.u

o.k.

= 11.9 kips/bolt > 8.45 kips/bolt

o.k.

Therefore, tbe nominal strength for the limit state of block shear rupture is Rn= 65.5 kips. The available strength for the limit state of block shear rupture on the single plate is:

Block shear rupture in the gusset-to-column single-plate connection Check block shear relative to nonnal force on the single plate.

According to A ISC Specification Section B4.3b. in compuling ne1 area for tension and shear, the width of a bolt hole is taken as 1/16 in. larger than the nominal dimension of the hole. The nominal diameter of the hole from Table 13.3 is 1¥26 in.

,I I

ASD

LRFD

The available bolt shear strength and the bearing strength for the end and interior bolts exceeds the required shear strength per bolt The gusset is tl·in.-thick and wiil have greater bearing strength than the o/16-in. single plate; therefore, the gusset plate is not checked for bearing strength.

=0.60(36 ksi)(l.25in.2)+1.0(58 ksiX0.664 in.2) ' =65.5 kips

~n

Rn

=0.75(65.5 kips)

-= Q

=49.l kips>19.5kips

o.k.

65.5 k,ips

2.00

=32.8 kips> 13.6 kips

o.k.

Check block shear relative to shear force on the single plate.

In thjs case, the AISC Manual tables will be used to dctennine the available strength for the limit state of block shear rupture, because the parameters fall within the limits of lhe table:;. provided. For the single plate at the gusset-to-eolumn connection:

A.'lEIOCAN {NSTTTUTP. OP STEEi, CONSTRUCTION

5- 58

BR.ACED FRAMES

=2 = 11h in. 411 =2.00in. Vbr = 1.0 n

5-59

5.2 ORDINARY CONCENT1UCALLY BRACED FRAMES

Combined shear and normal block shear design check using an elliptical equation For the single plate at !he gusset-to-column connection. the interaction of shear and normal bloc.k sbe~r is considered as follows:

L~

From AISC Specification Equation J4-5, the svailable strength for the limit state of block shear rupture can be written as:

LRFD

$R,, =$UbsF11An1 +min($0.60FyAgv. $0.60F11 A,,,,)

n

n

+IIll l

. (0.60f).A8 ,

Tension ruprure component from AISC Manual Table 9-3a:

$0.60F1 Agv =72.9 kip/in(SA6 in.)

Ub,F.,A.,,:::: 1.0(45.3 kip/in.)('lt6 in.}

n

in.)

0.60FyAg.

n

( . )( ) = 48.6 kip/in. ¥16 in.


0.60F.,Anv _ 55 5 Jdp/i {¥! . ) Q . ID. 16 Jn.

=17.3 kips

The av:tilable strength for the limit state of block sbc:ir rupture relative to the shear force on the single plate is:

$R,, = 21 .3 ldps + min(22.8 kips, 26.0 kips) o.k.

(~f +(~f $1.0

( 14.3 kips 44.lkips

( 9.98 lcips) 29.4 kips

2

19.5 kips 49.lkips

=0.263 $LO

=0.287 $ l.O

o.k.

n

2

,::: ..

~· •

o.k.

-~

'

Tensile rupture in the gusset-to-column single plate

(Spec; ~q. 14-2) where

d,,

= 0.875 in.

u

=1.0

+min(l5.2 kips, 17.3 kips) o.k.

)~ . ·:

A,, = (l-2d1t )tp

'.

=(6.00 in.- 2(0.875 in.)J('~6 in.)

j:

I

= 1.33 in.2

(Spec. Eq. D3-l)

=1.33 in.2 (1.0) = 1.33 in. 2

\i t;

..

Therefore:

=14.2 kips = 29.4 kips> 9.98 kips

.

Block shear rupture in the t1-in.-thick gusset plate is also adequate as tJ1e gusset is thicker than the single plate.

~=AnU

The available strength for the limit state of block shear rupture relative to the shear force on the single plate is:

R,,

+(32.8 13.6 kips) kips

Conservatively consider only a 6.00.in. length of single plate under axial tension from the gusset. The nominal tensile rupture strength is:

=15.2 kips

Shear rupture component from AJSC Manual Table 9-3c:

(~f +(~f $1.0

Shear yielding component from AISC Manual Table 9-3b:

:::: 22.8 kips

=44.1 kips> 14.3 ldps

n

= 14.2 lOps

Shear yielding component from AISC Manual Table 9·3b:

$0.60F.,A,,.:::: 83.2 ::::26.0 kips

·

0.60F11 A11 , )

Tension rupture component from AISC Manual Table 9-3a:

=21.3 kips

k:ipfm.( 5/16

n

ASD

LRFD

r+( r

ASD

l:..

t ....;-

R,, :::-58 ksi(i.33 in.2 )

=77.1 kips

\:.:

t"

,.!•

The available tensile rupture strength is:

f

S--60

BRACED FRAMES

LRFD

'

I

$Rn = 0."75(J7.1 kips)

=57.8 kips> 19.5 kips

j

R,.

77.1 kips

n

2.00 38.6 kips> 13.6 kips

-=

Rn

ASD

'

=

=0.60FuAnv =0.60(58 ksi)(l.33 in.2 )

(Spec. Eq. J4-4)

= 46.3 kips

LRFD

Tensile rupture in the Vs-in.-thick gusset is also okay because of its greater thickness.

Tensile yielding in the gusset-to-column single plate

S-61

5.2 ORDINARY CONCENTRJCALLY .BRACED FRAMES

ASD

14.3 kips

o.k. :

..

Rn 46.3 kips -= Q 2.00 = 23.2 kips> 9.98 kips

o.k,

Again, conservatively consider only a .6.00-in. length of single plate under ax.ial tension

from lhe gusset. The nominal tensile yielding strength is:

Shear rupture in the %-in.-tbick gusset is also okay because of its greater thickness.

Rn=FyAg

(Spec: Eq. J4-1)

where

Shear yielding in the gusset-to-column single plate Check the available shear yielding strength at the net section through_the bolt line.

Ag= ltp

Agv =ltp

= 6.00 in.(¥16 in.)

=6.00 in.(¥16 in.)

=1.88 in.2

=1.88 in.2

Therefore:

.(Spec. Eq. J4-3)

Rn = 0.60FyAgv

. R,, = ~6 ksi (J .88 in. 2 )

::: 0.60(36 ksi)( l.88

= 67.7 kips

in.2)

=40.6 kips The available tensile yielding strength is:

,.

LRFD LRFD

fl

ASD

ASD

Rn

$Rn= 0.90(67.7 kips) = 60.9 kips> 19.5 kips

.•

-=

o.k.

n

1.67 = 40.5 kips> 13.6 kips

..

$R,. =1.00(40.6 kips)

67.7 kips

=40.6kjps>14.3 kips

o.k. \

I

I

40.6 kips Q l.50 = 27.l kips> 9.98 kips

! . ...

Rn

-=

o.k•.

o.k.

Shear yielding in the ¥s-in.-tbick gusset _is also ?k.a!' becau~e of it~ greater thickness. Tensile yielding in the Vs-in.-thick gusset is also okay because of its greater thickness.

Shear rupture in the gusset-to-column single plate Check the avail.able shear rupture strength at the net section through the bolt line. Conservatively, consider only a 6.00-in. length of single plate.

Anv

=(l-2(fh)tp = 16.00 in.-2(0.875 in.)](¥16 in.)

=l.33 in.2

"

Use a ¥iirin.-tJlick single plate with (2)-'.}~-in.-diarneter ASTM A325-N bolts-in standard holes to connect the -%-in.-thick gusset to the column.

Design the beam-to-column single plate connection The beam-to-colU!lUI joint transfers both vertical shear and horizontal force. The horizontal forces acting at the beam-to-column interface are lhe uniform force component, H - fib He, and I.he collector force, Ab· For tbjs particular connection at this location ~n the structure. when the diagonal brace is in tension, lhe resultant horizontal force between the beam ant· the column is a compression force with a magnitude of He. However, when the diagon'2 brace is in compression, the collector force between the beam and the column will be in tension. Therefore the collector and He forces act in opposite directions. Conservatively, U· the greater of ~c and the collector force, Ab, for the design of the single piate.

=

~:

..,,?:

i\MEIUCAN lNS11T\1TS OF STEeJ:. CONSTRUCTION

S..-62

S.2 ORDINARY CONU.NTRICAl t Y BRACi;;D I RAMES

BRAC.li!) FRAMES

L.RFD P., =max

rl-Hu1> =ll.. ,} A..i.

:::max {19.5

=max {H

P0

kips}

The maxbnum shear at the beam-to-column interface will occu.r when I.he diagonal brace 1 in tension based on ASCEJSEI 7 Section 12.4.J.2 Load Combination 5 (LRFD and ASD). The beam rcacuon, V" or Va. is the concurrent force.

flob =Hd<"}

Aob

=max {13.6 kips} 23. I kips =23.J kips

33.0 kips

= 33.0 k.ips

LRFD

(1.2+0.2Sos)To+OoTa. +0.5ft

The vertical force on the beam web-to-column c~nnection is, as sho" n in Figure 5-6:

Rab = 7.73 k.ips

vub = 23.4 lops

vab

V"

=Rui, + V..b

=24.0 kips

LRFO

.

r.. v. V,,= R.,+-Mb ~

='"' + T.. vab D

~ps)(-23.4 kips)

=7.73 kips+(-25 ·3 ~ps)(-16.3 kips)

36 0 53.2 kips

37.2 lcips

= 27.6 lcips

\

~

= 18.8 kips

Combine the mwmum vertical force wilh the horizontal force at the beam-to-columo inter- J. face as follows: ...:

l

ASD '

R.,

=1.i3 kips+{-16.3 Jcips)

=-8.57 kips

I:.

Therefore.. the maximum vertical force in lhe beam-to-column connection is Vu= 27.6 kips ::I (LRFD) or V0 = 18.8 kips (ASD).

Va =Ra+ Vab

.

-

~

Ra =7.73 kips

=11.8 kips+ (-23.4 ldps) =-11.6 kips

V.a

= 11.8 k.ips+(- ·

ASD

Vab = -16.3 kips

\

.:i

1-------L_.RFD _ _ _ _ _ _--l----~~A_S_D~-~----:-' J

For the case where lhe brace is in compression:

v..

=-25.3 kips

Calculate v11 concurrent with tension in the brace by prorating the·rensile force in the brace calculated abo\'e to the m:i..'tilnum compressive force in the hr.Ice calculated at the beginning of this example.

Note tlm the vertical shear fon:e calculated above is conservame as lbe analysis has been simplified by considering the maximum brace force as equal in magnitude in either tension or compression. A more e.'tact analysis would include the actual tension and compression forces combmcd with the ~pective beam reaction.~ with considerntion of the dire(;tion of loading of each force component.. For this srrucrure, the larger diagonal brace force which acts in compression, and its resultant Vb component which acts upwards, would be counteracted by the beam reaction acting downwards. So to remedy the shortfall of this simplificatioo, the vertical force, V., (LRFD) and V0 (ASD). could be calculated for bolb the maximum force due to compression in the brace with its concurrent reaction and the maxjmum reaction resulting from tenSion force in the brace with the \'CrUcaJ beam reacuon.

-= -23.4 kips =Ru+V.,11

+ 0 kips+O kips + 0.7(2)(-22.3 kips)

=-36.0 kips

:::: 7.73 kips t-16.3 kips

VMb

T0 =[1.0+0.14(0.528)j(5.54 kips)

Va =Rab+ Vob

= 11.8 kips+ 23.4 kips

=11.8 kips

(1.0+0.l4Sru)To+1iJ +TF

+ 2(-22.3 kips)+ 0.5(0 kips) + 0.2(6.70 kips)

=35.2 kips

Ru

I

+0.10 0 To,

Tu= [1.2+ 0.2(0.528)j(5.54 kips)

= 16.3 kips

'


+ 0.2Ts

ASD

R~b = I l.8 kips

ASD

LRFD Load Combination 5 from ASCE/SEI 7 Section 12.4.3.2 (including tbc 0.5 factor on L pcmtitted by Sectton 12.4.3.2)

Note that the detennination of the relative directions of the collector force and II, forces at the column face may not alwa)s be as apparent as in this 5ingle-story structure. A conservative approach is to add the absolute values of the two components.

LRFD

I

For the case where the brace is in lcnsion:

ASD

..

·l

•

I

=Jv..,2 + Pu1

R.,

...~

= Jvl +Pal

= Jc216 kips}2 +(33.o kips) 2

=J(18.8 kips) +{23.l kips)

= 43.0 kips

=29.8 kips

1

2

I

.}

BRACED FRAMES

Try (4) ~-in.-diamcter A325-N bolts in the single plate connecting the beam and the

1

52 ORDINARY CONCENTRICALLY BRACED FRAMES

A., =[Js-(no. boll hole~)d11]tp

column.

= {3(3.00 m.)-(2 + 'h + l/i)(0.875 in )l(Vi6 in.)

=1.99 in.2

Available shear strength of the bolt group

From the check of lhe gusset-to-column single plate design, the available strength of tbc ~-in.-diameter ASTM A325-N bolt in the 'l'i6-in.-thick pfatc is 17.9 kips (LRFD) and J1. 9 kips (ASD) for bolt shear and 17.8 !0ps (LRFD) and 11.9 kips (ASD) for bolt bearing. The

0.60FuAnv + UbsFuAnt - 0.60(5$ ksi)(0.977 in.2) + l.0(58 ksiXl.99 in.

required number of bolts is:

0.60F1 A1 v + Ub,FuA..i

LRFD

Ru n,,,.,.=::::

¢r,. 43.0 kips 17.8 kips

=2.42

ASD

=0.60(36 ksi)(l.25 in.2 ) t =142 kips

1.0(58 ksiXl.99 in.

n-=-(r,.10) "'.29.8 kips 11.9 kips

ASD

LRFD

=2.50

~R~

=107 k.ips > 33.0 kips

n

o.k.

2.00

=7l.O kips> 23. l kips

=4

4 = l11l in. 411 =2.00 in. Ubs =1.0 I

From AJSC Specification Equation J4-5. the available sLrength for the limit state of block shear rupture can be written as:

The available strength for the limit state of block shear rupture is:

ASD

LRFD (Sp~c.

Eq. J4-5)

¢R..:::: ~UbsFuA,.i

+min(~0.60F1 A 1., ¢0.60FuA,,.,)

R., U,.,F,,A.u -=

..

= 2 (2.00 in.)(Y.4 in.) = 1.25 io. 2

n

n

. (0.60F.!'.A1,,

U0s =LO

Ap"' 241.tp

o.k.

Use lhe AJSC Manual tables to detennine the 3\'ailable scrength of the single plate for the limit !>Ute of block shear ruprure relative to the shear force on the single plate. For the single plate at the gusset·to-.:olumn connection:

Check block shear relative to the noanal force io Lbe single plate.

According to AlSC Specification Section B4.3b, in computing net area for tension and she.'lr, the width of a boh hole is taken as 1/16 in. larger than the nominal dimension of the bole. The nominal diameleT of the hole from Table J3.3 is 1¥16 in.

142 kips

R,,

-::----

=0.75(142 kips)

Block shear rupture in the beam-to-column single-plate connection

=2(2.00 in . ..: 0.5(0.875 in.)J(~6 in.) =0.977 in.2

)

=

n

A,.v =2(~h -0.5d11)tp

2

Therefore. the nominaJ strength for the limit state of block shear rupture is R,. 142 kips. The available strength for the limit state of block shear rupture on the "ingle rlate i:-.:

R,,

The beam web thickness is 0.355 in., which is slightly thicker than the single plate. Additionally. the beam specified minimum tensile strength, Fu. of 65 k.si is greater.man I.he F,, of the single rlate. Therefore, thc bolt available bearing strength on the beam web is greater than that of the ~ingle plate, and the bQlt be-ariog strength of lhe beam web is adequate.

where

)

- 149 kips

Use four bolts so thm the connection is at least haJf the depth of the beam.

1\

2

+mm

Tension ruprure component from AISC Manual T:sble 9-3a:

9u,,1 FuA.u

. 0.60~wAnv)

Tension ruprure component from AISC Manual Table 9-3n: Ub,FuA..1

=1.0(68.0 hipfm.){o/16 in.)

=21 3 kips

n

n •

1.0(45.3 kip/in.)(Yi4 in.) :::: 14.2 kips

I

:

BRACED FRAMES

LRFD

5-67


I

A1 =ftp

ASD

= (12.0 in.)('li6 in.)

She:ir yielding component from AISC Manual Table 9-3b:

Shear yielding component from AISC Manual Table 9-3b:

0.60F. A

. r{ " = (113 kip/in.)(~6 in.)

¢0.60FyA,.. =(170 ldp/in.)(~6 in.) = 53.1 IJps

=3.75 in.2 R,.

=35.3 kjps

)

The nominal strength clue to tensile yielding is: (S~c.

=F1A1

Eq. 02-1) "

=(36 ksi)(3.75 in.1)

She:ir rupmre component from AlSC Manual Table 9-3c: ~0.60F11 Anv

Shear nipture component from AJSC Manual Table 9-3c:

0.60FuA"" . )( 11& .In. ) . n - {l 29 k1p/in.

=(194 kip/in.)(~~ in.) =60.6 lops

=135 kips The available strength due to tensile yielding in the beam-to-column single plate is:

The 101al av:ulable block shear rupture strength of the single plate at the beamtO·column connection is:

The total available block shear rupture

strength of the single plate at the beamto-column connection is:

Rn . n-14.2 kjps

Mn =2 1.3 kips + m1n(53. l kips, 60.6 kips)

=74.4 IOps > 27.6 kips

+min(35.3 kips, 40.3 kips)

o.k.

= 49.5 kips> 18.8 kips

o.k.

Bl
$Rn =0.90(135 kips)

=122 kips > 33.0 ldps

-

1

is also adequ:ue. Tensile rupture in the beam-to-column single plate

Consider 12.0 in. of the plate to be effective.

r~r +(~rs l.O ( 27.6

~ps

74.4 kips

r+( r

0.233s1.0

33.0 kips 107 kips o.k. ,

= 0.233

r

(~ +(~r $1.0

23. l kips 71.0 k.ips

0.250s1.0

o.k.

=112.0 in.-4(0.875 in.)J('/16 in.)

=0.250

'

..

= 2.66 io. 2

. (Sptc. Eq. 03-1)

~=AnV

r+( r

( 18.8 kips 49.5 kips

Tensile yielding in the beam-to-column single plate· Consider 12.0 in. of the plnte to be effective.

= 0.875 in.

u =l.0

ASD

.

o.k.

A,, =(l-4d1i)tp

For the single--plate at the beam-to-column connection. the interaction of shear and normal block ~hear rupture is considered as foll~ws: LRFD

o.k.

R,. - 135 kips n l.67 = 80.8 kips> 23.1 kjps

The beam web bas a greater lhick.ness (0355 in.) and a higher specified minimum yield stress of F - 50 ksi; therefore, the av:.Ulable ten.qlc s1rength clue to yielding in the ~:im web

dh Combined shear and normal block shear design check using an elliptical equation l

ASD

LRFD

=40.3 kips

=(2.66 in.2 )(1.0)

.J

=2.66 in.2

·.~

Tue nominal strength clue to tensile rupture is:

(Sptc. Eq. J4-2)

Rn =F.,Ae

=(58 lsi)(2.66 in. = 154 kips

2

)

\

5-68

BRACED FRAMES

The available strength due to tensile rupture in the beam-to-column single plate is:

LRFD

= llp

Agv

= 12.0 in.(o/i6 in.)

ASD

Rn= 0.75(154 kips)

R,.

154 kips

n

2.00

-=

=11 6 kips> 33.0 kips

o.k.

S--6!t

5.2 ORDlNARY CONCENTRICALLY BRACED FRAMES

2

=3.75 in.

The nominal strength due to shear yielding is:

= 77.0 kips> 23.l kips

o.k.

The beam web has a greater thickness (0.355 in.) and a higher specified minimum rcnsile strength than the single plate, therefore, the available strength due to tensile rupture in I.he beam web is also adequate.

R,,

=0.6'0F,..A,..

(Spec. Eq. J4-3}

=0.60(36 ksi)(3.75 in. =81.0 kips

2

)

The available strength due to shear yielding is:

Shear rupture in the beam-to-column single plate

t:

-----~;-, ·.•.

f

1

t-:11

~11

·... \ .ii:':-,,. ·

$Rn = 1.00(81.0 kips) =81.0 kips> 27.6 kips

A,,v = (1-4dn) tp

=2.66 in.2 The nominal streogrh due to shear rupture is:

R,, = 0.60FuA...

(Spec. Eq. J4-4)

=0.60(58 k..~i)(2.66 in.

2

)

:~

;·: ~·;

:i ·

.....

·"· ·

..

•.. :~

f>

=54.0 kips> 18.8 kips

Use a minimum ¥t6·in.-thick single plate with (4) 3.4-in.-dfameter ASTM. A325-N bolts in standard boles to connect the beam to the column.

ASD

.R,.

92.6 kips

Q

2.00 46.3 IOps > 18.8 kips

-= o.Jc.

=

o.k.

When the collector force acts in tension on the column face, the He force on tbe gusset-tocolumn interface is also in tension. The collector force in the beam, Ab, acts 5.75 in. above the neutral a.us of the single plate, and the He force at the gusset-to-column interface acts 8.75 in. below the neutral a."
e14 = (23.5 in./ 2)- 1.5 in. - 3.0 in -1.5 in. I

o.k.

Design the weld of the combined single plate to the column face The weld of the single plate could be determined assuming two individual single plates. However this neglects the increased bending capacity of a 22-in.-long plate relative to the summation of bending capacities of a b.O-in.-long single plate and a 6.00-in.-1ong single plate. Therefore, design the weld based on a 23.5-in.-long single plate.

The available strength due to shear rupture is:

The beam web is lhicker (0.355 in.) and has a higher specified minimum tensile strength (65 ksi) than the single plate; therefore, the available strength of the beam web due to shear rupture is also adequate.

'~:

Q

= 92.6 kips

4>Rn =0.75(92.6 kips) ::: 69.5 kips> 27.6 kips

....,

o.k.

81.0 kips 1.50

The beam web is thicker (0.355 in.) with a higher specified minimum tensile strength (65 ksi) than the single plate; therefore, rhe available strength of .the beam web due . to shear yielding is also adequate.

LRFD

~:

R,.

--=

=[12.0 in.-4(0.875 in.)](¥16 in.)

~

·'

ASD

LRFD

Check the available shear rupture strength at the net section through the bolt line. Conservatively consider only a 12.0 in. length of .single plate.

=5.75 in.

Shear yielding in the beam-to-column single plate

I· Check the available stiear yielding strength at the

section through I.he bolt line. Conservatively consider only a 12.0 in. length of single plate. gTOSS

Eccentricity of He on the single plate: eH,

=(23.5 in./ 2)- J .5 in. - 1.5 in. =8.75 in.

Eccentricity of vettical shear on the column foce: e1: AMEIUCIJ'I

=2.50 in.

IN'STTTVn! OP STEEi.. Co!-ISTRUCTION

5.2 OR.DlNARY CONCENTRlCALLY BRACED FRAMES

5-70

.-~~~~~~~~~~~-r-:---:-~--:~~~-'-~~~~,

The total nonnal force at the column face is:

LRFD

H,,=Aub+H.,,

ASD

.I

Ha= Aab +Hae

=23.1kips+13.6 kips

=33.0kips+19.5 kips

.=52.5 kips

= 36.7 kips

Vu

=Rub + Vub + Vue =I 1.8 kips+ 23.4kips+14.3 kips

= 49.5 kips

. ASD

Y11 =Rab+ Vob +Vile =7.J3kips+16.3 kips+9.98 kips ='.34.0 kips

.

For moment on a weld group, sum moments about the mid-height centerline of the single plate at the face of the column:

LRFD M,. = V,.e, + AubeAa -HuceHc

=49.5 kips(2.50 in.)

=Vaec + AcbeA. - Hoc.eH, =34.0 kips(2.$0 in.)

+ 33.0 kips{5.75 in.)

+ 23.l kips{5.75 in.)

-19.5 kips(8.75 in.)

-13.6 kips(8.75 in.)

=143 kip-in.

=98.8 kip·in.

The stresses at the single plate-to-column interface are determined as follows: l

=23.5 in.

I

Ja - -, -

=36.7 kips

_ 52.5 kips 23.5 in. =2.23 ldpfm.

23.5 in.

= 1.56 kip/in. M;,a fab =-Z.., 98.8 kip-in. 138 in.2

/ub=Z,., 143 kip-in. 138 in.2

I

= 1.04 kip/in.

fur =

= 0.716 k.ipfm.

for= ~ja; +(/ca+ fab) 2

JJ,;; +(/ua + fub)2

1

_ / (2.11 kip/in/

~ + (2.23 kip/in.+ l.04 kip/in.)2

=(23.5 in.)2

Using the conservative solution (adding ; the flexural sLress), the angle of the 1 resultant load with respect to I.he weld. is:

e= un-1 (!uo + hb)

- \ +(1.56 kip/in.+0.716 kip/in.}2

Using !he conservative solution (adding the flexu..U stress), the angle of the resultant load -with respect to the weld is: 9 =tan-I

4

- 1 (2.23kipfm.+1.04

=57.2°

2

(1.45 k.ip/in.)

=~.70 kip/in.

= 3.89 kip/in.

=tan

,1

, _Hna

H,,

l

I

11

=1.45 kip/in.

Mu

1

l'

23.5 in.

f,.,,

lz Zw=4

I

ASD

=34.0I kips

/ua=1

ASD

Ma

/., =VOLi_

= 2.11 kip/in.

The total shear force at the column face is:

LRFD

LRFD

Vu 1 49.5 kips = 23.5 in.

f,,,,=-

2.11 kipfm.

kip/in.)

=

(faa +fa~)

I

!av

-i(l.56kip/in.+ 0.716 tan .. 1.45 kip/m.

=57.5°

=138 in.2

AME.RJC/\N ~Of STEEi.. CoJ-ISTRUCTION

kipfm.)

\

I

l:

J

f !

5-73 BRACED FR.AMES

5-72

S 2 ORDINARY CONCF.NTR.lCALLY BRACED FRAMES

~~:. . l

The weld size is determined from A1SC Mat111fll Equation 8-2a (LRFD) and 8-2b (ASD):

Check the plate for \he limit state of buckling using the doubJe--coped beam procedure given in AISC Ma1111.(ll Part 9.

LRFD

hr

D=

2{1.392 kip/in.)(1.0 +O.SOsin1.5 0) 3.89 kip/in. 2(1.392 kip/in.)

=

x

(Marlual Eq. 9-14)

ASD D= =

I

[t.O + 0.50sinl.S (57.2°)]

=J.01 sixteenths

Fer"' QFy

far 2(0.928 k:ipfm.)(1.0+0.50sin1.5 9)

ho.JP,

2.70 k:ipfm. 2 ( 0.928 kip/in.)

x

Calculate Q for the single plate: (Manual Eq. 9-18)

A.=----.=======::"

1 [t .0+0.50sinl.S (57.5°)]

10,p

475+28o(~Y

(23.5 in.)J36 ksi

:::~~..l:..:-7=~=======:;"

2

"" I .05 si:
10(¥16 in.) 475+280( Considering the C?lumn flange thickness and the single-plate lhickness, the minimum fillet weld size from AISC Specification Table J2.4 is Yi6 in. However, according to the AISC Manual Pa.rt 10 discussion of single-plate connections. the weld between a single plate and the support should be sized as: %rp

=0.284 Because A.~ 0.7, (Manual Eq. 9-15)

Q= l

=%(¥16 in.)

Fer= Fy; therefore, plate buckling does not control.

:::: 0.195 in. The use of the above minimum weld size combined with the single plate requirement for connection plate thicknesses to be less than db-l/i6 in. according to AlSC Manual Table 109 facilitates ductile behavior in the connection.

<

23.5 in.) in. 250

Use a o/16-in.·lhick single plate 23.5 in. long.

Use two-sided IA-in. fillet welds at the single plate to column connection.

Check column web local yielding The peak unit bending force./b. is less than the axial w1it bending force.fa · Therefore, ~~ bendin" forces do not affect the overall concentrated force on the gusset nor do ~ey aff'. the len~th of force applied on the interface. A portion of the concentrated force 1s applied

Check single-plate shear rupture at weld to column

within a dist.ance less

One method to detei:mine the IJUnimum single-plate thickness required to transfer the shear and :ension forces is to scl the weld strength (based on the resultant force) equal to the shear rupture strength of the .single plate. From AISC Manual Part 9, the minimum required single-plate thickness is:

For a force applied at a distance less ~an the depth of the member:

(Manual Eq. 9-3)

Eq. J 10·3)

6.19 kipfm.(1.0 1) 58 ksi

"" 0.108 in. < -'/16 in.

=445 kips

o.k.

6.19 kiplin.{l.05) r,,,;,, = 58 ksi 0. 112 in.< ¥16 in.

=

ASD

LRFD

ASD

LRFD lmin""

(Spec.

Rn= F)wlw(2.5k+lb)

= (50 ksi)(0.340 in.)!2.5(1.06 in.)+ 23.5 in.J

6. l 9D Fu

(milt=--

r":·:

than the depth of the column.

~R,, = 1.00(445

Rn

445 kips 1.50 = 297 kips > 23.J kips

-::::

kips)


o.k..

n

o.k.

o.k. AJtematively, the available strength for web yielding can be determined per Part 9 of t!le

..:·

,

;·

:·:, I:·

Check compression on the single plate When the brace force is in compression. the beam-to--column axial force is in compression. The unil force on the single plate in compression results from !l.."
AlSC Mamial, and Table 9-4.

AMEJUC!J'I [}'lSTITUTE OP STEEL CONSTRUcnON

5- 14

BRJ\CF.D FRAMES

S.2 ORDINARY CONCENTRICALLY BR>\CEO FRAMES

Check column web local cnppling

Cf. column

A portion of the concentrated force is applied at a disrnnce less thlln d12 from the end of the column; therefore, useAJSC Specificatwn Section JJ0.3(b). C~ck the length of bearing tel· ntive to the column depth: lb 23.5 in. -==d 10.0 in.

S-75

I

W18x50

beam

W.P.-

=2.35 > 0.2

--- -

---~-c:;_--

Therefore, use AISC Specification Equation J10-5b to determine the available scrength,

through use of AJSC Manual Table 9-4. From ATSC Manual Table 9-4 for the W1 Ox49:

LRFD ¢Rs =48.5 kips $~

~ .

ASD

co

(4) l3~>'nco/ll with (4) ~· dla. A325-N bolts to gusset in std. holes

Rs . n=J2.3 kips

=I0.1 kip/in.

~ =6.76 kip/in.

%"Pl (A36) - ll- -+---'

From AISC Manual Equations 9-48a and 9-48b:

(4) ~· dia. A325-SC bolls, std. holes in

LRFD ¢R,, =¢R, +lb (~Ro)

=48.S kips+23.5 in (10.1 kipfm.) == 186 kips > 33.0 kips o.k.

ASO

R,,

Rs n

-= -

n

Ro

W10x49

column

Hb-

n

=32.3 k:ips+23.5 in.(6.76 kipfm.) =191kips>23.1 kips o.k.

angles. ovs. holes

l

W10x33 brace

(6) ~·dis. A325-N bolts in std. holes I

\

'The final connection design and geome~ is shown in Figure 5-7.

in web of~

Fig 5·7. Connection desigMd in

Nole: 8Qlts indicated as Ntype are to be pretensioned with Class A Of' bettor raying

surfaces. E:campl~

5.2.4.

Example 5.2.5. OCBF Tension-Only Diagonal Brace Design Given: Unlike special systems, tension-only bracing is permitted in OCBP systems; therefore this example demonstrates a tension·only brace design for the same configuration a, Example 5.2.4. Refer to Brace BR-1 sbown in Pigure 5-2. Select an ASTM A36 singleangle section for the dfogonal brace to resist the_ loads sbown below as a tension-on!) br:icing contigurs.tion.

The applicable building code specifies the use of ASCEISEI 7 for calculation of loads. From n first-order analysis, the loads on the brace arc:

Po=O !Ops PH= Okips

Ps= 0 kips Pt=O kips

PQ«=±51.1 kips Mo= 1.13 kip-ft

J J

5-76

:'

BRACED F1V\MES

DESIGN OF PARTI.J\LLY-RESTRAlNE.D MOMENT CONNECTIONS

The dead load bending moment indicated above is due to the self-weight of the brace assuming a member r.hnt weighs l6 Jblft. Sometimes this self-weight loading is ignored in the desigo of vertical diagonal braces where judgment would indicate that the loading is minimal and only uses a small percentage of the available member strength. However, in this example, considering the relatively long length of the diagonal brace, the dead load moment is included jn this design check. There are no bending moments due to live loads or snow loads.

From AJSC Manual Table 1-7, the geometric properties :u-e as follo\.\s:

The story shear, H, from the first-order analysis 1s 136 kips and the first-<>rder intcrstory drift due to that load without the CJ factor applied from the analysis model is:

Check brace element width-to-thickness ratios

tlH=0.761 in. Solution:

5- 77

L5x5x1/2

A= 4.79 in.2

='1 =L53 LO. S.r =S1 =3.15 in.3

, :t

b

=5.()() in.

I"' 0.500

in.

d = 5.00 in. 'i

=0.980 in.

The braces must sntisfy I.he requuements for moderately ductile members. as slipulateJ in Sections F l .5n and 01.l of the AISC Seismic Provisions. Elements of the brnce members must not C:\ceed ~width-to-thickness ratios. From Table 1-4 o f this Manual, the L5x5x1/z satisfies width-to-thickness ratios for OCBF diagonal braces (moderately ducnle members).

From AJSC Ma11ual Tilble 2-5. the material properties lire: ASTMA36

Determine the effective slenderness ratio

F1 =36 ksi

Fu= 58 ksi Determine the required strength of the diagonal brace Considering the load combinauons given in ASCE/SEI 7, the governing load combination and resultant maximum axial tension and bending moment in the diagonal brace are:

LRFD

tl

LR.FD Load Combination 5 from


ASCEJSEJ 7 Section 12.4.2.3 (including the 0.5 factor on L penniued in Set.:tion

ASCE/SEI 7 Section l 2.4.2.3

l~.4.2.3)

(1.2+ 0.2Sos }D+pQ£ +0.5l+0.2S

(1.0+0.14Sos)D+H + F+0.7pQs

Pu = [ 1.2 + 0.2(0.528)j(O kips)

Pa

.. i.o(-51.1 kips)+0.5(0 kips)

+ 0.2{0 kips)

,.r:

,.,

'I .

I

I

=-51.1 kips

Mk =(l.2+0.2(0.528)j(l.13 k.ip-ft)

. I

i

l

l

+ 0 kips+ 0 kips t- 0.7(1.0)(-51.J kips)

= -35.8 lcips Ma= jt.0+0.14(0.52S)J(1.13 kip-ft) + 0 kip-ft+O kip·ft

+ 0.2{0 kip-ft)

+ 0.7(1.0)(0 kip-ft)

Try an l5x5x1'2 for the brace member.

..'• ·

=[l.0+0.14(0.528))(0 kips)

+ 1.0{0 kip-ft)+0.5(0 kip-ft)

= 1.48 kip-fl

.

ASD

= l.21 iip-ft

The available compressive strength of a tension-<>nly brace is ignored in the design of the bracing. Therefore in order to ensure the brace will buckle in compression under relatively minor loading, use a tension-only brace with a slendem~s ratio greater than the recommended maximum effective slenderness ratio, KL/r, of 200 as indicated in the User Note in Section E2 of the AISC Specification. According to the User Note in AlSC S1>ecijicario11 Section D l. K.L!r of members designed on the ba:;is of tension should preferably not excc!ed 300. Therefore the effecli\·e slenderness ratio, KL/r, is selected to be greater than 200, but less than

300.

Determine K According to AISC SpecificalWTI Appendix 7, Section 7 .2.3(a), for braced frame systems the effective length factor for members subject to compression shall be taken as 1.0, w1less a rational analysis indicates that a lower value is appropriate. The overall length of the brace diagonal in each bay is:

L = J(4-0.0 ft)2 +(40.0 ft) 2 =56.6 ft

This length lw been determined by calculating the distanee between the work points based on the intersection of the centcrHnes of the diagonal braces, columns and beam. Shorter lengths m;iy be used if justified by the enginur of record. Single angles in X·bracing are normally continuous for the full diagonal length of the bay ,1.;1h the orientation of each brace rcver~cd as s.hown in Figure 5-8, pcnnitting the brae~ to be coonecred to each other by bolling at mid-length. The effective length in 1his arrangement is 0.85 times the half diagonal length cons1dcring the radius of gyration in the z-a.."
S-78

BRACED FRAl-1F.S

S.2 ORDINARY CONCENTRICALLY BRACED FR.AMES

L: =0.5L

=0 .5(56.6 ft)

LRFD

ASD

= 28.3 fl

$1Pn

K%= 0.85 Ktlt

Pn

=0.90(17~ kips) = J 55 kips> 51.l ltips

, n, =

o.k.

=I03 kips > 35'.8 kips

= 0.85(28.3 ft){I2 in./ft)

r~

0.980 in.

o.k.

The limit state of tension rupture on the effective area should also be checked; however, by inspection, it would not control.

=295 The slenderness,

172 kips 1.61

X:-, is greater than 200, but Jess than 300, and therefore meets the desired

range based on I.he User Notes in Sections DJ and E2 of the AISC Specification. Note that ~e suggested slenderness limit of 300 does not apply to rod bracing, nor does the 0.85 effecuve length factor.

Determine the available tensile strength For tensile Y.ielding on tpe gross se.ction, the ~omJnaJ tensile strength is:

Pn = FyAg

(Spec. Eq. D2-J)

=36 ksi ( 4.79 in.2)

Determine the available flexural strength During the governing seismic lond conditions, the bracing is subject to significant axial tension with some minor flexure due to self-weight. The large axial tension loading provides'a stabilizing effect to the brace and negates the effect of lateral-torsional buckling due to flexure. Therefore, even though the member is not laterally restrained along the length, when consideration is given to the significant axial tension load in the member, flexural suenglh can be based on the limit state of yielding only. This assumes that the single-anglt· has continuous lateral restraint along the length; therefore, the lateral-torsional buckling limit state does not apply. Additionally, because the section is compact, the limit state of leg local buckling does not apply. The nominal tle."tural strenglh due to yielding is:

=172 kips

(Spec. Eq. FI0-1)

Mn= 1.5M1

I:. t

i

Mn= l.5SxF1

The available tensile strength is:

<>

= 1.5(3.15 in. 3 )(36 ksi)(l ft/12 in.) = 14.2 kip-ft The available flexural strength is:

I

\

LRFD High~strength

bolt with spacer plate

~11Mn

=0.90(14.2 kip-ft)

.

ASD '

= 12.8 kip-ft:> 1.48 kip-ft

Mn

14.2 ltip-ft 1.67 =8.50 kip-ft> 1.21 kip-ft

-= o.k.

Qb

o.k.

Consider second-order effects Follow I.he calculation procedure of AlSC Specification Appendix 8.

Fig. 5-&. Connt!ction of single-angle diagonol braces at mid-point.

M,=B1Mm+B2¥1r

(Sptc. Eq. A-8-1

P, = Pn1 + /hP11

(Sptc. Eq. A-8-21

l

Calculate 81

=

8 1 l.00 according to Section 8.2 of AlSC Sptcificarion Appendix 8, as the member is or , subject 10 compression. .; •:

·.,

BRACED FRJ\.C\1E8

...

S l ORDINARY C01'CLNTRJCALLY B~\CEO l'R,,\!>IES

.

Calculate B2

~

~:

a= LOO {I.RFD): a = 1.60 (ASD)

I,,.~

P"""' is lhe Lota! vertical load on the story calculated using the applicable load case. As cal·

Af,

culated in &le 5.2. 1:

~

I ...

I

~ps

P_, = l,130

=1.00(1.48kip-ft)+1.01(0 kip-ft)

=81M"' + /hM11 = l.OO(J.21kip-ft)+1.01(0 kip-fl)

=1.48 kip-ft

=1.21 kip-ft

= B1M,., + IhMtz

{

,

l~·

!.

LRFD

Ill

=R.11 D.H =l.O 136 kips(40.0 fl)

(Spec. Eq. A-8-7)

1 t- cx.Psrorz

~l

ASD

Ih =

~ 110'1

=

l l- oPJtcry

~l

=

Pi, = J5.8 kips

=1.01

Mtr.,. 0 kip-ft

=Piil +lhPiz = 0 kips+ 1.01(35.8 kips) =36.2 kips

=51.6 kips

.

P, _ 51.6 kips Pc 155 ldps

I

ASD

LRFD

'

I

36.2 ltips -::: Pc 103 kips 0.351 P,

I

=

=0.333

Because P,IPc
I.RFD

=1.48 kip-ft

P,

I

Check combined loading of the L5x5x'/z brace:

1

~JCst-ord~ be?<'ing moments with the strncture rcslr.\ined against !:Heral lr.lnslation (grav-

Mni =M,,

!

ASD

Pr =Pnr + B2Piz = 0 kips+ 1.01(51.l kips)

_ 1.60(740 kips) 1 85,800 kips

ity loads Ill this case), and due Lo lateral translation of the story are, respectively:

!i

Piil =O kips

=51.1 kips

P. ""'7

1

I_ l.00(1,130 kips) 85,800 lcips = 1.01

'

=0 kips

LRFD

LRFD

")'

P,,, fl,

Using AlSC Specification Equatjon A-8-6:

,..~

fh -

ASD

The required -;trength oftbe brace including second·ordcr effects is, from AISC Specification Equation A-8-2:

= 85,800 kips

I•·

·'

first-order ruual force:. wilh the strucrurc restrained ag:uaq lateral trani;lation
LRfD

(0.761 in.)(l fl/J 2 in.)

- - - ;:-:;:J

M,

ASD

RM= 1.0 (braced frame)

P, nory

..

ASO

LRFD

ASD Mm =Ma = 1.21 kip-ft M11 = 0 kip-ft

The required fle.'(ural screnglh of the brace including second-<:>rder effects is, from AJSC Specification Equation A-8-1: •

(Spec. Eq. Hl-1 :i)

LRFD

!(o+

51.6 kips .. 155 kips 9 0.436< 1.0

ASD

J.48 kip-ft)= 0.436 12.8 kip-ft

oi.

!(o +

36.2 k.ips + 103 kips 9 0.478< 1.0

kip-ft)== 0.478

1.21 8.50 kip-ft

o.k.

Note that I.he y-y _axis bending moment from the self-weight of the diagonal br.lce utih about 11 % of the member capacity. ;U1ERJCAl'I lNs'rm1r6 OF STEJlL O:lHs'nucnON

I

BRACED FRAMES

Use an L5x5x1h in the tension--only configuratfon for OCBF diagonal Brace BR- I

BraC:es must be continuous through and bolled to each other at the intersecung JOint as shown in Figure 5-8.

5.3. SPECIAL CONCENTRICALLY BRACED F~AMES (SCBF) Special concentrically braced frame (SCBF) systems, like other concentrically braced frai:nes, resist lateral forces and displacements primarily through the axial strength and stiffness of the brace members. In concentrically braced frames. the centerlines of the framing m~bers (bra~, columns, and beams) coincide or nearly coincide, eliminating or mini· mwng flexure m tbe system, The design of SCBF S}'stems is addressed in AJSC Seismic; Provisic11$ Section F2. Whlle the general layout of an SCBF is \'ety similar to that of an orilinary concentrically braced frame (OCBF), there are additional detailing requircmcntS to focus ductile behavior of the frames into the braces. These detailing requirements provide for greater energy dissipation anil duciility, allowing SCBF systems to be designed using a lower force level in comparison to that of OCBF systems. Concentrically braced frame systems tend to be more economical than moment resisting frames aitd eccentrically broced frames in te1ms of matcrfal, fabrication and erecrion costs. They .do, however, often have reduced flexibility in floor-plan layout, space planning, and clectncal and mechanical routing as a result of 1he presence of braces. In certain circum· stances, howe,·er, braced frames are exposed and fe:llurcd in the architeciure of the building. Braced frames typically are localed in walls lha! stack vcrticaJly between floor levels. In the typical office building. these walls generally occur in the core area around suiir and elc· vator shafts, cen1ral resirooms, and mechanical and electrical rooms. This generally allows for greater architectural flexibility in placement and configuration of exterior windows and cladding.

1

. ~ considering the configuration of a braced fr:imc system, both in plan and elevation, it is unportant to note the requirements for redundancy in the system. The AISC Sei$tniC Provisions require that a braced frame system balance the compression and tension braces. AISC Seismic Provisions Section F2.4a requires that along any line of bracing, the braces are oriented to resist a t least 30% but not more than 70% of the 1otal horiz.onts.l force in tension unless the exception in Section P2.4a is met . The Al~C Seismic. Pro_visio~. limit member slenderness, compressive strength, and WJdth-t~ckness rauos, m addiuoo to requiring special detailing for gusset plates. The cwnula1J,·e ~e£A of these ~uiremcnts is inleoded to result in braces that maintain a high level of ducuhty and bysterebc damping when subjected to severe seismic forces. Brsc.e slenderness is limited to ensure adequate compressive strength and resistance to the eyeUc degradation of the brace. The post-buckling performance of the brace is dependent on the compactness of Ille members used. Members with a higher width-to-thickness rntio are more susceptible to local buckling, which may lead to tearing of the brace material in the buckled areas prior to the dissipatfon of a significant amount of energy. This behavior results in a system with signHicantJy lower energy dissip:uion cap:ibility. . The la_st of the predominant issues relating to the bracing members is the spacing of mtenned1ate connecrors of double angle, double channel or similar built-up braces. AJSC Seismic Prtn:isicn.r Section P2.5b ootes that connectors should be placed such th:it the air,

5.:l SPECIAi.

CON('UNTRJCAU~Y

BAAl'W

t•KA1v11.:J

value for the individual components of the brace is less than 40% of the governing slcu demess of the built-up member. Addiuonally, 11 is required that the connectors have a ~bt strength that develops the tensile strength of individual components of the brace. The two provisions are intended to ensure that the brace buckles as a unit, thus allowing more reliable behavior. The connector requirements are reduced wben it can-be shO\\ n that 1'"~1 brace assembly can buckle as a single element without inducing shear forces in the co nectors between the individual members. In any case, no fewer than two connectors a. allowed with uniform spacing, and bolted connectors are not permitted in the middle ooefourth of the clear brace length. The limitation on the Jocati~n of bolted ~ttn~hme~ts included to gu:ud against premature fracture due to the formauon of a plasuc htnge in LI

l.

l

buckled brace. In order to increase ductility and energy dissipation of. the system the connection( l must be detailed to accommodate the effects of br.:ice bucklmg. Curren~y. there ar~ l\ approaches used in the design of these coonecuons; lh~e :ire smted m AlSC Se1sm. ~ Provisions Sections F2.6c(3)(a) anJ F2.6c(3)(b}. The first approach creates enough strengt'• and rigidity in the connections to force the brnce to form plastic hinges at the ends and mi \ die of the brace under compressive forces. The second appro:icb utilizes out-of-pla1 buckling of the gusset plate such that plastic hinges occur in the gusset plate a l the brae' ends with a hinge stlll occurring at the midpoint of the brace. This usually is accommodDIW in one o f two ways. As one opt.ion, the connection can. be detailed such 1hnt the end ~f ti brace is located a distance of at least two times the thickness of the gusset from the intc section of the gusset and the beam or column. This configuration is shov. n in Al SC Seismic Provisions Commentary Figure C-F2.9. The value.of two rim~ the thickn.es~ of th.e gus~ I bas been developed through research and analysis. Ahemauvely, an cllipucal yield b. ! approach can be u~d (Lehman et al., 2008). AISC Seismic PM is1ons Section F2.t.c addresses beam-to-column connection issues related to the accommodation of large seismic drifts associated with the yielding and buclcling of the braces. Tb.is provision is iliscussed gre:iter detail in the following. . The design requirements for most btiSic frnme configuratjons are covered hy Lhe conditions listed earlier in thls section. V-~yPe and in~ert~ V-ty~ frames,_ however, ~re requir1"' \ to meet additional criteria, as noted in AISC Se1sm1c Prov1sio1is Secuon F2.4b. The.~ requfrements are intended to reduce the effect of a loss in strength of tl1c comprc... ., sion brace relati"ve 10 the tension brace in the post-buckling f3Jlgc. as shown in Figure 5-9. A• the compression brace buckles under !~ad, its capab~lity to re~ist the \ertical load i~ climi ished relative to the strength of the tenStOn br.l<:e. This results ID an unblllanced verucal Jo; between the two members. which exens additional ,·ert.ical force on the beam. Braced framtconfigu:rotions utilizing zipper columns and two-story X configurations. as shown in Figures 5-9(b) and 5-9(c), distribute this unbalanced vertical load to other levels that are not expt encing b.igh seismic demands, providing for better overall frame performance. Another check covered in the AJSC Seismic Provisions relates to columns that are part or the SCBF system. Columns are required to meet the highly ductile width-to-thickness cri1 ria according to AlSC Seismic Provisions Section F2.5a. and have special considerations r their splices. According to AISC St!ismic Provisions Se.ction P2.6d, column splices mus:, develop :i required shear strength equal LO W pclHc for LRFD and rJ.1pcl(l.5llc) for ASD. This requirement is intended to accOODt for the possibility of the columns sbanng some the lateral force demand through frame action as the brace elements defoon inclastical deflecting the frnmes beyond what elastic calcul.uions might predict. Additionally. ·

I

l i

l

t

I

I

I

;I

5-84

BRACED FRAMEs

h.. ~ .

r I f I

noted I.bat the column splices m~st be located at least 4 ft from the beam-to-column flange connections in AISC Seismic Provisions Section D2.5a. ,

Design of Gusseted Beam-to-Column Connections to Accommodate Large Drifts

l ~ I 1::

AISC qeismic Provisions Section F2.6b requires that gusseted beam-to-column connections .!>e designed to accoffiinodate demands corresponding to large drifts. In the contex; of this provision, the connectiqi;i consjsts of the gusset plate, the affected parts of the beam a.nd c.otumn, and any other connectj1;m .ma~erial, such as angles and plates, interconnect-·

L.\ I

~

~

.:!:··

i

!.H ..

ing these elements.

Two methods of accommodating demands corresponding to large. drifts are provided. First, as described in AISC S,eismfc ProvisiQns Seccion F2.6b(a), the connection may be detailed to pro~idc sufficient rotation capacity .such that the bean1 and column are not constrained to rorate together ~ the. frame defonns. The provision defines this ~quired relative rotation as 0.025 rad. Connections similar to the simple connections prese~ted in Part 10 of

sJ ...

~- ·

':J; ,

tl ..,

.~.

¥

Yielding brace

Yielding brace ·

:·

;~

~;

(a) Inverted V.braced (chevron) fra{lle

t: l ~~

(b) Inverted V·brocedfram~ with zipper column

,,"... . g :~ :~

.....

'·· ~·

:;,

~; ~:

Yielding brace

I.

Buckled brace ~

t· ·

,.;;. (

~

.

the AISC Manual and meeting the rotational ductility checks described in Part 9 of the AISC Manual can be assumed to provide a minimum. of 0.03 rad and satisfy the intent of the AISC Specification Section B3.6a for simple connections. TI1e Part 9 rotational if~ctility che~ks are intended for use with connections between 6 in. and 36 in. deep and with gcometnes similar to those shown in che AISC Mo.nu.al. 'J;'he use of deeper connectio~, smaller.ser.:off distances ~tween the supported and supporting members, or smaller edge distances can affect the ability of connections to accommodate large rotations in a ductile manner. It is important to nore that these bounds apply to the connection as a whole. For example, if the colUlection at the column face consists of a dollble-angle connection from column flani>e-co-gusset and a double-angle connection from column flange-to-beam web, the two

dou~le-angle comiections should not be considered as separate; they should be considered

as rotating about a single point and the entire depth of the assembly should not exceed 36 in. in order for the roration requiremeocs to be deemed satisfied in the absence of further demonstration. Physical testS can also be used to demonstrate adequate rotation capacity. The second method of accommodating demands cotTesponding to large drifts is described inAJSC Seismic Provisions Secrion F2.6b(b). Rather than aUempting to detef11Une the actual d~mand placed on gusseted connections by seismic drifts, this method establishes an upper bound demand based on flexural yielding of either the beam or the column. It .is assumed that these members have sufficient rotationarductility to maintain their function aS bracedframe members when subjected to 'inelastic rotation. The connection is designed to re'.sist a moment corresponding to the lesser of 1.1 times the expected beam flexural strength and l. l times the sum of the expected column flexural strength above and below the connection. This moment is considered in conjunction with the brace forces corresponding to the brace expected strength. Connection assemblies may be designed to resist this moment i~ one of two ways. The enpre assembly may be analyzed wic~ the required moment and axial force applied and all connection elements designed for the correspon~ing forces. Conn~ct~g the beam itself to the column by a fully restrained moment connection capabl~ of resisting the expected flexural strength of the beam is.another option. Wirh this option the gusset plate and related connection elements may be designed for forces derived considering ~e brace \ . ·· connection required strength. · Thus, there are three methods of complying with AJSC Seismic Provisions SectJon F2.6b presented in this Manual. :gach of these m.etbods is presented in a different connectio~ example-Examples 5.3.10, 5.3.11 and 5.3.12. These examples also illustrate three d1fferent methods of accommodadng the rotation associated with brace buckling as required by Section F2.6c(3). There is no correlation between the inethod of accommodating frame drift and the method of accommodating brace rotation due to buckling, i.e., any method of com· plying with Section F2.6b may be used in conjunction witb. any method of complying with Section F2.6c(3). Examples 5.3.10, 5.3.11 ~nd 5.3.12 are configured as follows:

Example

5.3.!0 5.3.ll

(c) 1ko story X-bracedfrorne

5.3.12 Fig.'5-9. Assumed inel.astic defomiation. of various bracedfrwne co11jiguration.s. AM.ERICAN

lNsTrnrrn 01' Sn;a CONmucno.'i

S-85

5.3 SPECIAL CONCENTRICALLY BRACED FRAMES

Method of complying with AISC Seismic Provisions Section F2.6b

Method of complying with AISC Seismic Provisions Section F2.6c(3)

Detailed to provide rotation per Section F2.6b(a) Detailed as FR connection per Section F2.6b(b)(i) Designed to resist moments per Section F2.6b(b)

Linear hinge zone Elliptical hinge zone Hinge plate for in-plane brace buckling

BRACED FRA\.fF.S

E:
I'

Example 5.3.1. SCBF Brace Design Given:

Refer to Brace BR· l in Figure 5-11. Select an ASThl A500 Grade B round HSS to resist the following ;Wal lo3d~

SCBF Design Example Plan and Elevation The following examples illustrate lhe design of SCBF systems based on AlSC St.ismic Provisions Section F2. The plan and elevation are shown in Figure 5-10 and Figure 5-11. The lateral forces shown in Figure 5-1 l are the seismic forces from the equivalent lMeraJ force procedure of ASCE/SEI 7 Section 12.8 and apply to the entire frame. The code-specified gravity loading is as follows:

=85 psf Drocf =68 psf Dflcor

Po

=18.0 kips

The applicable building code specifies lhe use of ASCEISEI 7 for calculation of lo:ids. The

a..rjaJ force due to the snow load is negligible.

Relevant seismic design parameters were given in the SCBF Design Example Pl:in and Elevation section.

from an elastic analysis, the first-order inten.tory drift between the base and the second level is !J.H =0.200 in.

L/roor =80 psf (50 psf reduced) S :::: 20 psf Curtain w<\ll =175 lblft along building perimeter at every le..-el

~ 1-----=~-----'-t.

=

From ASCFJSEI 7, the Seismic Design Category is D, 0 0 2.0, R =6, p =J .3, and Sos= LO. Assume that the effective length method of AlSC Specific01ion Appendix 7 is u~ed for subitity design.

25'-0"

~oof

~~·

1

Pa1: =±197 kips

Pt= 9.50 kips

7·

3

2

30'-o·

•t-H•

5

4

~

.

~l+l

N'

-----1!1

~Ourth

I--~!!:.:.:.:=-~~~~~--!

Level

m: l

· · · ·----"'-"------------~~----~ ·-~- -· · ·- - --l ~~;~:estlgated l~ ..............

......

in Part 4.

SCBF investigated in Part 5

For elevation, see Figure 4-8.

Fig. 5-10. SCBF plan for SCBF membtr uamplu. AMEIUCAN lNSTTIVTt! Of! S11!a COl'IS'lllUCTION

Third Level

Fx,= 84 kips Column splice 48" above finished floor (typ.)

•CD c-,• .....

l-'------:l

= 91 kips

•CD

30·-0·

30'-0"

l l

.':? N

Second Level

• 5' ..... ""'

.....J

(.)

Base

Fig. 5-11. SCBF tfei:aricnfor SCBF mtmber aomplts.

I

(

,.,.

S-88

5.3 SPECIAL CONCENTRlCALLY BRACED ffiA.ME.S

Assume that the ends of the brace are pinned and braced against translation for boib the x-x and y-y axes.

~ f(

BRACED FRAMES

The required axial tensile strength of the brace is:

I

C::;

ii...

LRFD

Solution:

ASD

LRPD Load Combinntion 6 from

From AISC Manual Table 2-4, the material properties are as follows:

ASD Load Combination 8 from ASCEISEI 7 Section 12.4.2.3


ASTM A500 Grade B

Fy =42 ksi Fu= 58 ksi

Pu= [0.9-0.2(1.0)j(18.0 kips)

P0 =[0.6-0.14(1.0)](18.0 kips)

+ 1.3(-197kips)+1.6(0 kips)

+ 0.7(1.3)(-197 k.ips)+O kips

= -244 kips

:::::-171 kips

Required Strength The unbraced length of the brace from work point-to-work point is:

Determine the required strength

The governing load combinations that include seismic effects are:

LRFD

...

· :· r}, ··

LRFD Load Combinations 5 and 6 from ASCFJSEI 7 Section 12.4.2.3 (including the 0.5 factor on L permitted

= 18.8 ft

ASD

This length has been determined by calculating the distance between che work points base
ASD Load Combinations 5 and 8 from ASCEISEl 7 Section 12.4.2.3

'·. :--:-:

by Section 12.4.2.3)

~11 ·

(1.2 + 0.2Sos)D + pQE.+ 0.5L + 0.2S

(1.0 + 0.l4Svs)D

(0.9 - 0.2Sos)D + PQE + l.6H

(0.6 - 0.14Svs)D + 0.7pQE + H

~; ·

l= ~(14.0 ft)2 +(12.5 ft)2

AlSC Seismic Provisions Section F2.4a requires that between 30% and 70% of the tots! hor· izontal force is resfated by brace~ in tension. From analysis, the.total horizontal force in the

+ H + F + O)pQE

line of the braced frame is 91 kips + 84 kips + 57 kips + 30 kips =262 kips. The horizontal

component of the axial force due to earthquake force in Brace BR-1, when it is in tension is: 12 5 · ft )(l97 k.ips) =131 kips ( 18.8 ft .

The required axial compressive strength of the hrace is:

LRFD . LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.2.3

Pu= [l.2+ 0.2(1.0)j(lS.O kips)

- "..

· ASD


.

+O kips+O kips

+ 0.5(9.50 kips)+0.2(0 kips)

+ 0.7(1.3)(197 kips)

\

Try a round HSS8.625x0.500 for the brace.

From AISC Manual Table 1-13, the geometric properties are as follows:

P,, =[l.0+0.14(1.0))(18.0 kips)

+ 1.3(197 kips)

=286 kips

which is 50% of the total horizontal force in the line of the braced frame. Therefore, it meets the lateral force distribution requiremepts in AISC Seismic Provisions Section F2.4a.

D= 8.625 in. [-:::: 100 in.~

0.500 in. r= 2.89 in. lncm =

tdes

=0.465 in.

A :::: 11.9.in..-,•

.

:::200 kips

Width-to-Thickness Umitations

.I

According to AISC Seismic Pro'Visions Section F2.5a, braces must sa~sfy the requirements for highly ductile members. Elements .in the brace members must not ~xceed AmJ width· to-thickness ratios in AISC Seismic Provisions Table D 1.1.

From Table Dl.l:

,,

ASD

D

8.625 in. =0.465 - - in. Ide$

[l.2+0.2(1.0)]

+ 0.2(20 psf)

=0. 038 (29,000 ksi) 42 ksi

X(l kip/1,000 lb)

.

p .2+0.2(1.0)J

j

~26:2

Ides

=9,000 ft 2

l[L0+0.14(1.9)] x[68 psf+3(85 psf)]

i

I

x(l kip/1,000 lb)

·

l

[t.o+o.14ci.o)]

+

:S A.1i4 , tbe HSS8.625x0.500 satisfies the width-to-thickness limitation for highly

ductile members.

x[175 lb/ft(4)(. 390 ft)]

J:

I l!

x(l kip/l,000.Jb)

= 3,630 kips

x(l k:ip/1,000 lb)

.

I

I

+ 0 psf + 0 psf + 0 psf

+ xll75 lb/ft(4)(390 ft)]

D

Smee -

P.riory

+ 0 psf + 0.5(3)(50 psf)

E

A.ht! = 0.038.. F,

.

r

x(68 psf + 3(85 psf)]

= 18.5

1 ,,

= 5,160 kips . _ __ _ _ _ _ _ _ _ _ _ _ _ _......__ _ _ _ _ _ _ _ _ _ _ _ __ . , j

Alternatively, using Table 1-6, it can be seen that the HSS8.625x0.500 will satisfy the width-to-thickness requirements for an SCBF brace.

Brace Slenderness · Use K= I .0 for both. the x-x and y-y axes. According to AISC Seismic Provisions Section

F2.5b(l ), braces must have a slenderness ratio KL $ 200. ·

The total story shear, H, with t':VO bays of bracing in che direction under consideration. where each bra~ed.frame is designed to resist the seismic loads shown in Figure 5-11, i s determined as follows. From an elastic analysis, the first-order interstory drift is D.H ;, 0.200 in.

, ,.

l h

H =2(91 kips+84.k:ips+57,k:ips+30 kips). =524 kips

' ·

r

L =14.0 ft

KL _ 1.0(18.8 ft)(i2 i~.fft)

RM =1. 0 for a braced frame

2.89 in.

r

=78. l < 200

o.k.

HL

(Spec: Eq. A-8-7)

Pe.r1ory=R1t1-

6.H


the

Follow procedure of AISC Specification Ap~n
1

Becaus~ there are no momen~, (Spec. Eq. A-8-2)

....

= l.O - 52.4 kips(l 4.0 fl) (0.200 in.)(l ft/12 in.) \

=~40,000 kips

\

Using AISC Specification Equation A-8-6:

Calculaie 82 To detennine P~llJry• use an area of 9,000 ft2 on each floor and the gravity loads !riven in the SCBF Design Example Plan and Elevation section. Use load combinations that ;elude seismic effects; in this case, Load Combination 5 from ASCEJSEI 7 Section 12.4.2.3 for LR.FD and ASD governs.

LRFD

lh=---->1 l_

a.P11ory -

ASD

Bi=

1 l- aPstory

Pe s10ry 1 = _ 1.00(5,160 kips) 1 440,000 kips

~1

Pe·story

=-

l

-1. 6-0-(3-,6-30~ki-ps-)

1 ,

== 1.01 ~ l

1:

440,000 kips

=1.01~1

Because B2 S 1.5, 1he effective length method is a valid way 10 check stability according 10 AISC Specification Appendix 7.

yield strength oflhe brace in tension, a 13% decrease in brace area would reduce th~ require. connec1ion strength.

The required axial compressive Sl.J'Cllgth of the brace including second order effects is, from AISC Specification Equation A-8-2:

Example 5.3.2. SCBF Analysis

(Spec. Eq. A·8-2)

LRFD

ASD

Pu =(1.2 + 0.2Sos) Po + B2PQe

Pa =IL0+0.14(1.0)]Po

+ Pn +PF+ 0.7pBzPa,;

+0.5L+0.2S

=IJ.2 + 0.2(1.0)](18.0 ldps) + 1.01(1.3)(197 kips)

+ 0.5{9.~0 kips)+ 0.2(0 kips) = 289 kips

..

Give'n : Refer to the braced frame elevation and sizes shown in Figure 5-12. All braces' are ASTM A500 Grade B round HSS. Perform an analysis to determine the expected strengths in 1ension and compression of tl1e braces according to AISC Seismic Provisions Section F2.3. Some engineers may choose not to change the brace size at every level, but they are different a1 every level in these design examples to fully illustrate 1he AJSC Seismic Provisions

=!l.0+0.14(1.0)J(l8.0 kips) + 0 kips+O kips

requirements.

+ 0.7(1.3)(1.01)(197 kips) = 202 kips

Solution: From AJSC Manual Table 2-4, 1he material properties are as follows:

}


As stated previously, use L = 18.8 ft for the unbraced length of the brace. From AISC Manual Table 4-5 for !he HSS8.625x0.500 brace with KL= 18.8 ft (using interpolation), the available compressive strength is:

LRFD

Roof

o.k.

~ =206 kips > 202 lcips

·f

<'?

N ,-

o.k. Fourth Level

~c

•

Available Tensile Strength

'9

Prom AISC Manual Table 5-6 for the HSS8.625x0.500 brace, the available tensile yielding strength is:

LRFD

N

....

Third Level

ASD

cp,P,, == 450 kips> 244 kips

25'-0"

•

ASD

G>cPn =309 kips > 289 kips

"

o.k.

P.

nn, = 299 kips > 171 ldps

.

<.OI

N ,-

o.k. Second

i:: ~~·.

Level

Tensile rupture on the. net section must also be checked at the connection; see Examples.

5.3.8 and 5.3.10 for mustrntion of this check. Use an HSS8.625x0.500 for SCBF Brace BR-1.

"'Base

Comments:

f ,, ...::.

•'

The engineer of record may be able to justify a shorter unbraced length for the brace. In this ex.ample, if an unbraced length of 14 ft could be justified, an HSS7.500x0.500 could have been used for !he brace. Because the end connections may be designed to resist the expected

Fi8· 5 -12. SCBF elevatio11for Example 5.3.2.

J\Jl1E1UCA11 lNSTmm! OP STEa CONSTXOCTION

AMERICAN 1NS1Tl'Vl"I! OF Sn:a. CO~STR'UCTION

-

..

5.3 SPECIAL CONCF..NTRJCAllY BRACED FRAMES

F2 6c(3)(b)] by allowing 3 2 1 clearance between the end of the brace and the line of res.tr:iint. ll is likely that the actu3.l length from brnce end-to-brace_ end .between the con. ·11 be · ifi ti less than the work point-to-work point distance calcul:Hed necnons w1 sign can y . • • t I 12 reviously. Example 5.3.8 verifies that the actual lengtl' of the brace 1s appro~una e Y ~o 13 ft; therefore, use a length of 12 ft for determining the expected strength U1 compres-

ASTM A500 Grade B

0· =42 ksi Fu= 58 ksi Prom AISC Manual Table 1- 13, the geometric properties of the br:ices are:

. •'

sion for all braces.

r=·2.02 in.

HSS6.875x0.500 A= 9.36 in.2

r = 2.2,7 in..

The following Tubles 5-1 and 5-2 show the expected strengths in tension a~d ~e e~pected and post-buckling strengths in compression of all braces. A s~ple calculauon is given for the HSS6x0.312, and a similar procedure is used to detemune the strengths of the other braces. From AISC Seismic Provisions Table A3. l:

r= 2.49 in.

f .h b . t Ry= 1. From AISC Seismic Provisions Section F2.3, the expected strength o l c race m en-

HSS7.500x0.500 A= 10.3 in. 2

4

HSS8.625x0.500 A= 11.9 in. 2

\:

sion is:

r= 2.89 in.

Pr~n.sion =

According to AlSC Seismic Provisions Section F2.3, the required strenglhs of columns, beams and connections are based on the load combinations in the applicable building code. where the amplified seismic load, Emh. is based on the larger force determined from the following two analyses: (i) An analysis in which all braces arc assumed to resist forces corresponding to their

expected strength in compression or in tension (ii) An analysis in which all braces in tension are assumed to resist forces corresponding to their expected strength and all br:ices in compression are assumed to resist their expected post-buckling strength · In order to study the effects of analyses (i) and (ii) on the rest of the frame, the expected compres~ion the post-buckling strength in compression must be strengths in tension determined for all of the braces.

and

-1

\:

HSS6x0.312 A =5.22 in. 2

and

RyFyAg

=l.4(42 ksi)(5.22 in.2)

,• ..,i:

=307 kips · R .F, is used in lieu of Fy for the determination of Fcre according to ATSC In compresSion, y y AISC s ifi · Chapter Seismic Provisions Section F2.3, where Fcre is determined from peci canon E, using the equations for Fer·

KL l.0(12.0 ft)(l 2 in.lft) -= 2.02 in.. r =71.3

4.7 1~ RyFy E =4.7 1

29,000 ksi 1.4(42 ksj)

I

I \

For detennining the expected strength in compression, AJSC Seismic Provisions Section F2.3 requires that the brace length used shall not exceed the distance from brace end-to-brace end. The work poinHo-work point length of the typical brace above the base level is:

L=Jo2.5 ft)

2

= 105 Because 71.3 < 105, AISC Specification Equation .E3~2 applies,

an~

Fcre is determined as

I

follows:

..l

+ (12.5 ft)2

(Spec. .Eq. E3-4) ·.;;

= 17.7 ft The work point-to-work point length of the brace al the base level is: L

1t2 (29,000 ksi) 2

=J(l4.0 ft) 2 +(12.S ft) 2

=

: 18.8 ft

= 56.3 ksi

(71.3)

I •

The brace length will be less than lhis distance because of the column and beam depth and because I.he gusset will accommodate brace buckling [AISC Seismic Provisions Section

...

5.3 SPE.Cll\L CONCENTRICALLY BRACED FRAMES

S-96

Fett= 0.658

In Examples 5.3.3 through 5.3.6, the forces generated in this :inalysis wiU be considered in the dc~ign of the beam. column and colulTUI splice connection. The diagram in Figure 5-13 shows the forces imposed on the frame from buckJing and yielding of U1e braces. For the analysis provisions of AISC Seismic Provisions F2.3(ii), che expected strengths of the braces in compression shown in Figure 5-l3a nre multiplied by 0.3 (expected post-buckling brace

!!Li (from Spec. Eq. E3-2)

RyF1

F.

1.4(42 ksi)

= 0.658 <56·3 .ksi) =38.0 ksi

..·.

(1.4)(42 ksi)

strength) and shown in Figure 5-13b.

t

.

From AlSC Seismic Provisions Section F2.3, U1e expected strength of che brace in compression is:

l

.·. ;.:

=1.14(38.0 ksi)(5.22 in.2)

~·

·~:

Roof

.

=·226 kips 3~

N

.

Fourth Level

R1 F1 A9 kips

HSS6x0.312

5.22

307

Third

HSS6.875l<0.500

9.36

550

Level

HSS7.500x0.500

10.3

606

HSS8.625x0.500

11.9

700

Expected Strength

~..

·: . :>

:·

In Compression Brace Member

A=A1

'

Length

in.i

In.

ft

Kl.Jr

F.,.. ksl

HSS6l<0.312

5.22

2.02

12.0

71.3

38.0

63.4

41.6

1.14F-4, kl)ls

226

Expected Post·Buck/irig Strength in Compression

0.3(1.14F.,..Ag) kips 67.8

2.27

12.0

444

133

HSS7.500x0.500

10.3

2.49

12.0

57.8

44.1

518

155

HSS8.625x0.500

11.9

2.89

12.0

49.8

47.5

644

193

HSS6.875x0.500

9.36

. 0

Expected Brace Strength and Post.. Buckling · Brace Strength in Compression

!~

. I

~ ,....

Base

444 kips

"' ""'/ 518 kips

N

Table 5-2

307 kips

/

<9

1..

•I

550 kips

I

N

Second Level

/

r

/""

t:>

A ln.2

Brace Member

l ~I

226 kips

Table 5-1

Expected Brace Strength in Tension

;'·. 1

"' ""'/

<9

" - - -- y:;

25'-0"

I

I \

/"" .

700 kips

/

""'/

606 kips

644 kips

""

Fig. 5-13a. Forces imposed on frame from brace b11cklinglyielding according co AJSC Seismic Provisions Sec1ion F2.3(i).

..

---

BRACED FRA..~fES

.r · ~v

~ .

'.

Roof

(Cl

N'

Fourth Level

~ N

25'-0"

""'

550 kips

/

Third Level

~

N

Second l evel

Base

/

2(a) in Section F2.3 will also be considered. There are two additional Exceptions: 2(b) forces corresponding 10th~ resistance of the foundation to overturning uplift, and 2(c) force! determined from nonlinear anaJysis. Exception 2(b) will be considered in Example 5.3.6.

l

I;

Assume that the ends of the column are pi110ed and braced against translation for both the

x-x and y-y axes. 1.

Solutio n: From AJSC Manual Table 2-4, the material properties a.re as follows: ASTMA992 F_..,

=50 ksi

'·

Fu= 65 ksi

133 kips

"'/

606 kips

/""

700 kips

/

307 kips

""' "'/ 155 kips

9

~ ..-

"'/ /""

67.8 kips

f

s-9·

5.3 SPEClAL CONCENTIUCALLY BRACED FRAMES

Required Strength

i:

Determine the required strength of the column from A/SC Seismic Provisions Section F2.3 (Mechanism Analysis) According to AlSC Seismic Provisions Section F2.3, the required strengths of columns are I based on the load combinations in the applicable building code, where the amplified seis- f': mic load, Emh, is based on an analysis in which all braces are assumed to resist force~ corresponding to their expected strengths in compression or in tension. The analysis in which the compression braces are at their post-buckling strength does not govern here. \

193 kips

"'

"

Fig. 5-13b. Forces imposed on frame from brace bucJtling!yirlding according to AJSC Seismic Pruvisions Section F2.3(ii).

Figure 5- 14 shows the forces from the expected strengths of the braces :is detemuned ir. '. Example 5.3.2. These forces can be considered as applied loads acting on the columns and as applied loads on the beam, which :ire :shown here as beam shears acting on rhe column. b Because seismic forces must be considered in both directions, both columns in the frame must be designed both for the maximum tension, shown for the column on gridline B, and for the maximum compression, shown for i.he column on gridline C.

f

The axial compression force in the col'iunn frQm this analysis is, with forces that produce

compression in the column ·sh own as positive:

Example 5.3.3. SCBF Column Design

PE-.A

Given : Refer to Column CL- l in Figure 5-1 l. Select an ASTM A992 W-shape with the available strength required by the AISC Seismic Provisions. Relevant seismic parameters were given in the SCBF Design Example Plan and Elevation section. The column forces from gravity and snow loads are the following: •

Po= 147. kips

Pi= 60.0 kips

Ps = 7 .00 kips

The seismic force in Column CL-1 from tbe seismic forces stipulated by the app.licable building code using an equivalent lateral force analysis, n9t including lbe Q,, amplification, was determined from analysis to be PQr 248 kips.

=

The forces resulting from the expected strengths of the braces defined in AlSC Seismic Provisions Section F2.3 and calculated in Eltample 5.3.2 must be considered. The Exception

t

'.;:

= (307 kips+444 kips+606 k:ips)sin45°+(8.84 kips- 1,1.3 ·kips) = 957 kips (compression)

The axial tension forc.e in the' column from this analysis is, with forces that produce tension in the column shown as negative:

.

L

r

Ts.,. :::: (-226 kips-550 kips-518 kips)sin45°+ (8.84 kips-11.3 kips) ::::-917 kips (tension) Note tlult since the expected strength from the brace at the lowest level is not included, the forces in tension and compression are not exactly equal. Using the lo:ul combinations in ASCE/SEI 7 including the overstrcngth factor as requirec by AlSC Seismic Provisions Section F2.3 where the amplified seismic load is substituttr

~

BRACED FRAMES

~

with the. anaJysis described in Section F2.3, the required uial compres~ive ~rrength of lhe column 1s.

t

f

L,

LRFD LRFD Load Combination 5 from ASCf/SEI 7 Section 12.4.3.2 (including lhe 0.5 facror on l permitted in Se.ction 12.4.3.2)

ASD Load Combination 5 from ASCEJSEI 7 Section 12.4.3.2

+ 0 kips+ 0.7(957 kips)

..

.;. ._

- - -.... ~'.:":1 ..

l9

N .....

level

-fl < ...

I""' -·-,,

226 kips

18~-~~

Fourth

•
-· ..-

/

550 kips

N

Third

level t

~

/

"----~518 kips

N ..-

"

, 11.3 kip;' ,,/'

b

..,. -· Base

700 kips

/

i

-----.-- --

/

307 kips /

-~84 Id~_! '· 444 kips

j

-----~ /

606 kips

/

:'.!ldpsl

Pa =(0.6-0.14Svs)Po +O.?P1-:..,, +PH

=10.6-o.14{Lo)J(t47 kips)

+ 0.7(-917 k:ips)+O kips =-574 kjps

Determine the required strength of the column from A/SC Seismic Provisions Section F2.3 Exception (2)(a)

AISC Stismic Provisions Section F2.3 Exception l2)(a) sl.1tcs that the required strength of columns need not exceed t~ forces determined using load combinations stipularcd by the applicable building code including the amplified seismic load, applied to a building frame model in which all compression braces have been removed. For exterior columns (columns at lhe cods of a br:iced frame or at the ends of sevtra.I bays 0 1 bracing), forces determined using this exception may be lower lhan rho:.e required by AISC Seismic Provisions Sc:<:tion Dl.4a(2), in which case it might not be prudent to use this ex.ctption. In this example wit.h a 2-srory X configuration, the required st.reng
=248 ltips (compression)

Par= 248 kips (tension)

644 kips

""'

Fig. 5-14. SCBF opplied column forces for Example 5.3.3. A.MEllCA/'l lHs"tmml

+(-917 kips) =- 814 kips

ASD Load Combination 8 from ASCe/SEI 7 Section 12.4.3.2

=IJ.0+0.14(1.0)](147 kips)+O kips =837 kips

.

ASCEISEI 7 Section 12.4.3.2

Pa =(!0+0.14Sos)Po +PH+ Pr + 0.7Pr;.,.

= l,190l5ps

::

LR.FD Load Combination 1 from

='0.9-0.2(1.0)](147 kips)

+ 0.5(60.0 kips)+0.2(7.00 kips)

0-8-oof

ASD

LRFD

Pu =(0.9-0.2Sos)Po +~

=ll.2+0.2(1.0)](147 lcips)+957 kips

5-10!

The r«Juircd a:<1aJ tensile strength of the column 1s:

ASD

P,. =(1.2 +0.2Svs)Po +PE,,. + 0.5PL +0.2Ps

tll

.53 SPECIAl CONCEN11UCALLY BRAC.FO fRAMr.S

°" Srm.. ~

Using these forces in the full model which includes the compression braces as an approximation of Exception (2)(a) of AISC Seismic Prrwisions Section F23, the load combinations in ASCEISEl 7 give a requircJ axial compressive scrcngth for the coJumn as follows:

I

~.

LRFD

f--~~~~~-LRFO~~~~~~~-f-~~~~~~A-S_D~~~~~~ 'r

ASD


P., =(l.2+0.2SDs)PD + [hh 0 Po1

ASD Load Combination 5 from ASCFJSEl 7 Section J2.4.3.2

.

Pu= (l.2+0.2Sos )JD+ iloJ>G!t'+ 0.5PL

.

+ J.01(2.0)(248 kips)

+ 0.1Q 0 PQr

=fl.2+0.2(1.0)}(147 kips)

. +B2(0.?)!laPQ1

=[L2+0.2(1.0)j(l47 kips)

Pa =(l.0+0.14SDS )Po+ P11 +PF

+0.2Ps

Pa =(J.0+0.14Sos)Po +PH +PF

+0.5Pt+0.2Ps

+ 0kips+O1dps

+ 0.2(7.00 kips)

+ 0.7(2.0)(248 kips)

+ 0.2(7 .00 kips) = 738 JOps

\.

+ 0 k.ips + 0 kips + l.Ol(0.7){2.0)(Z48 kips)

+ 0.5(60.0 kips)

=!L0+0.14(1.0)](147 kips)

+ 2.0(248 kips)+ 0.5(60.0 kips)

=IJ.0+0.14(1.~)](147 kips)

= 518 kips

'\ 1 ·

~~~~~~~~~~~~~~~~~~~~~~~~~~~~-

= 733 kips

= 515 kips

I

For comparison, Table 5-3 provides a summary of the required :ix.ial strengths of the colum based on the cwo different analyses considered.

The required axial tensile strength of the column is:

Try a W12x96.

LRFD LRFD lp;id Combination 7 from AS_CFJsw.7 Section U.4.3.2

ASD

P., =(0.9-0)Sos )Po+ Q.,PQr + l.6f'H

P0

=[0.9-0.2(1.0))(147 k.ips)

+ 2.0(-248ldps)+1.6(0 kips) =- 393 kips

~

Use K = 1.0 for both the x-x and y-y axes. From AISC Manual Table 4- l, the avail.ab! strength in nial compression for a W12><96 with KL= 14 ft:

f

=(0.6-0.14SDS )Po +0.1QaPQt +PH =[0.6-0.14(1.0)](147 kips)

-

+ 0.7(2.0)(-248 kips)+ 0 kips

=- 280 kips

Because these required strengths are less than those determined from the mechanism analysis of AlSC Seismic Provisions Section P2.3, they will be used for lhe design of the col umil. :.


Because the column is designed for code-based forces rather than lhe mechanism analysis requirements of AISC Seismic Pn:wisions Section F2.3, second~rder effects should be considered. From Example 5.3. l for the brace nt this level. B2 = 1.01. Because the columD does not have.moments, I.here is no need to calculateB1 factors. Therefore, the h:quired axial Compressive strength of the column including second-order effects is, from AISC Specification Equation A-8-2:

Pr= P"' + Bi.f'tr


ASD Load CombinatioJl S from AScEtSEI 7 Section 12.4.3.2

(Spec. Eq. A-8-2)

. ,...

Available Tensile Strength · From AISC Marn1al Table 5- l, the avaijable strength of the W12><96 column in axial tension for yielding on lhe groi:s section i~;

$ 1 Pn

=1,270 kips> 393 kips

l'

ASD

LRFD

o.k.

Pn = 844 bps > 280 kips

n,

o.k.

I

Width-to- Thickness Umitations

According to AISC Seismic Provisions Section F2.5a, the stiffened and unstiffened elements of columns musl satisfy the requirement<; for highly ductile membCrs in Section D 1.1. From 1'able 1-3 of this Manual. it can be se.,~ thats W12X96 will satisfy lhe width-to-thickness limits for an SCBF column (note lhac any villue of Pu mat and Pa-· is pennissible, as shown in Table 1-3).

Use a W12x96

f9~

SCBF Column CJ....1.

l

BRACFD FRAMES

r: r,.:

~·

~.,.

Required Axial Strength of Column CL-1 According to the Requirements of AISC Seismic Provisions Section F2.3 and 01 .4a

-

Anal)'sis with code·specl11ed amplified setsmlc loads [AISC Sl!lsmic Pro'lisions Secllcn 0Ua(2))

\"

Compre~n

Tension

S.. llb

'lllese forces arc shown in Tables 5-1 and 5 ·2, and the forces acting on bearu BM-2 are sbown in Figure 5-15.

Table 5-3

Analysls with braces al expected strengths In tenslon and compression [AISC ~Jsmic PrOYis/OllS Section F2.3(1))

.5.3 SPECIAi. CONCENTRICALLY BRJ\CF.D FR.\MES

Required Strength Determine the required axial strength of the beam based on A/SC Seismic

Provisions Section F2..3(i) From AISC Seismic Provisions Section P2.3(i), lhe requfred axial strength of the beam is based on the braces at their e.~pected strengths in tension and compression. The "unbafanced., \crtica.l force is determined from the •atical component C'f all four brace fo~.

Temion

Corr.press!on

P1 = {307 kips - 226 kips+ 444 kips - 550 kips )sin 45° UIFD

ASD

LRFO

ASD

LRFD

ASD

UIFO

ASO

1,190

837

-a14

-574

738

518

-393

·280

~~: ~~·

-

Given: Refer to Be3m BM-2in Figure 5-11. Select an ASTM A992 W-shape with a maximum depth of 36 in. D~ign the bc:un as a noncomposite beam for slreogth, although the composite deck can be considered to brace the beam as discusse-0 later in this example. The applicable building code specifics the use of ASCEISEI 7 for calculation of loads. Assume the brace sizes are as shown in Figure 5- 12. Rclev31lt seismic paramerers w~re given in the SCBF Qe.-;ign Example Plan and Elevation section. The gravity i:hears and moments on the beam. assuming a simple span from column line B to C, :ire: Vo= 11.2 kips

V1., =8.50 lcips

,\.to= I20lcip-rt

This unbalanced ve111c:U force can be considered as a load acting at the midpoint of the beam, and produces the following shear and moment: Py =__._

Example 5.3.4. SCBF Beam Design

.7;....,,"11

=-17.7 kips

M1.,

=100 kip-fl

2 _ 17.7 kips 2 8.85 kips

=

PvL

Me,.,.=-·4

= 17.7 kips(25.0 ft) 4

= 111 kip-ft

~

Solution:

~

From AISC Manual Table 2-4. the matei-ial properties arc BS follows: ASTMA992

F1

.•.,,

'· ,,i:

\•

=50 ksi

Fu= 65 ksi As required by AJSC Sti.rmic Provisio11.s Section F2.3, lhe required strength of the beams shnll be based on the load combinations in the applicable builcling code, including the amplified seismic load. The runpl}fied seismic load is determined from the lt1rger of: (i) An analysis in which all br.ices a.re assumed 10 resist forces corresponding to their expected strength in compression or in tension

(ii) An analysis in which all braces in tension 3.re as:.umed to resist forces co~~ponding to lhe1r expected strengt.h anti all braces in compression arc assumed to resist 1hcir expected post-buckling strength

CJl>.!..»O!l.-- -

•

~

~ ~

25'-0"

r:;--------------;1 I ' I '

!226~ps

/

;

I I

3oi~psi

00,..~1!.u!.!.--l- l BM-~ / l / ""' : ~ l: ss91<1ps 444'k-!_ps l ..- T,' ', r ~~-.L ~~--- -- ------ -~ ~ ' -./' /1

(a) Forcts from AISC Seismic P10\·isioru

Stcrion F2.J(i)

25'-0" Roof

f

r:;------------ --:,1 ~

N

I ' I

'~

l 67.8_klps

~;

/

I I

30i-Kips:

~'-"-=.;'-'--1- ! BM-~/

l

/""' : ~ l: s501
', T

"""".LUJ'1.J
(b) ForctsfromAISC ~ismic Pro~ision.t S«tion F2.3(ii)

Fig. 5-J5. Forrts acting on Otam BM-2 from a mtcha11ism analysis of AJSC Stismic Provisii>ns Stction F1.J as carntd out in E.tamp/1! 5.J.2. AMEIUCAJ" bls'1Tnm! <:# Snn. Cossr!wcnoN

$'RACED FR.AMES

5-106

Note thaL the unbalanced vertical force from the braces is considered to act at a single point for the purpose of evaluating member limit sl.'.ltcs in the beam. In the connection design presented iu Example 5.3.8, beam local limit states arc evaluated using intemal forces detcnnined in the brace connection design. To deteonine the required axial force of the beam, the horizontal component of the difference between the sum of the expected strengths of the braces below the beam aod the sum of the expected strengths of the braces above the beam can be thought of as a "~tory force" which the beam must deliver to the braces. Since the braced frame is in I.be middle bay of a three-bay building, half of this story force can be considered to enter the br.iccs from each side, and is carried by Beam BM-2 to the braces connected to the beam midspan. This force could act in either direction and is shown as positive. P:i =cos4 50

=cos45 0

[.t(Braccs below be:un)- l(Braces above beam)] 2

5.3 SPECIAL CONCENTIUCAl.LY BRACED FRAMES

. J

ASD

LRFD

LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.3.2

ASD Load Combination 5 from ASCFJSEl 7 Section 12.4.3.2

V,, =(l.2+0.2SDS)Vo +Ve.,.

Va= (1.0+0.l4Sos)Vo + VH

+ 0.5Vl + 0.2Vs

+VF+0.7VE..t,

::: (1.2+ 0.2(1.0)j(ll 2 kips)

+ S.85 kips+ 0.5(8.50 kips) + 0.2(0 kips)

=(l.0+0.14(1.0))(11.2 kips)

+ 0 kips+ 0 kips+ 0.7(8.85 k.ips

= 19.0 kips

=28.8 kips The required Oexur:il strength of Berun BM-2 according to the analysjs rcquiremencs AISC Seismic Provisions Section F2.3(i) is:

1(550 kips+ 444 kips)-(226 kips+ 307 kips)! 2

LRFD

ASD

= 163 kips

LRFD Load Combination 5 from Using the load combinations in ASCFJSEI 7, the required axial strength of Beam BM-2 according to the analysis requirementS of AlSC Seismic Provisions Section F2.3(i) is:

LRFD LRFD Load Combination 5 from ASCFJSEl 7 Seccion 12.4.3.2 (including the 0.5 factor on l pemritted in Section 124.3.2) P,, =(1.2+0.2SDS )PD + %,,..

+ 0.5Pz. + 0.2Ps =[l.2+ 0.2(J.O)J(O k:ips)+163 kips + 0.5(0 .kips)+0.2(0 kips) = 163 kips

ASD ASD Load Combination 5 from ASCE/SEJ 7 Section 12.4.3.2

ASCEISEI 7 Section 12.4.J.2

Mu =(1.2+0.2Sos)Mo t-Me,,.,, +0.5Ml +0.2Ms

=ll.2+0.2(1.0)]{120 kip-ft) + 1 LJ kip-ft+0.5(100 kip-ft) + 0.2(0 kjp-ft)

=329 kip-ft

ASD Load Combination 5 from ASCE/SEI 7 Section 12.4.3.2 M~ =(1.0+0.14Sos)Mo+MH

+MF+0.1ME,...

=[l.0+0.14(1.0))(120 kip-ft) + 0 kip-ft+ 0 kip-ft + 0.7(111 kip-ft) = 215 lcip-ft

Pa = (l.0+0.14Sos )Po+ Pn

+ PF+0.7Pe,.. =(1.0+0.14(10))(0 ltips)+O kips

+ 0 kips+ 0.7(163 kips)

=114 ltips

The required shear strength of Beam BM-2 according to the analysis requirements of AISC Seismic Provisions Section F2.3(i) is:

Determine the required axial strength of the beam based on AISC Seismic Provisions Section F2.3Q1J • From AISC Seismic Provisions Section F2.3(ii), the required axial strength of the beam « based on the braces at their expccced strength in tension and post-buckling strengths in Ct I pression. For this analysis, the expected s1rengths of the braces in compression must multipUed by 0.3 to approximate their post-bockling strength as shown in Table 5-2.

1

The "unbalanced" vertical force is determined from the vertical component of all four br forces. ~ P1 = (307 kips - 67.8kips+133 kips-550 k.ips)sin45°

1

=-126 klps

....

AMUlcAl'I lNS'ITIVl"B Of' STEEi.. CONS'TllUC'llON

"t l

r

i·

5-108

I

This unbalanced vertical force can be considered as a load acting on the beam, and produces · the following shear and moment:

BRACED FRAMES

5- 1(>'

5.3 SPECIAL CONCENTRICALLY .BRACED FRAMES

L t

t

Py =-

LRFD

2 = 126 kips 2

~ I !'·

=IL2+ 0.2(1.0)](l l.2 kips)

'< !·

...

l :.

The required flexural strength of Beam BM-2 according to 1he analysis requirements of AISC Seismic Provisions Section F2.3(ii) is: LRFD

ASD


ASD Load Combi.nation 5 from ASCfJSEI 7 Section 12.4.3.2 Mo. =(1.0 +0.J4SDs).Mo +M11 +Mp+0.7Me,..1

Mu= (1.2+0.2Sos)Mo +Me,.. + 0.5Mt +0.2Ms

=[LO+ 0.14(1.0))(120 kip-ft) + 0 k.ip-ft+O kip-ft

+ 788 kip-ft+ 0.5(100 kip-ft)

Using the load combinations in ASCFJSEI 7, the required axial strength ofBM-2 according to the analysis requirements of AISC Seismic Pro\•i.sio11s Section F2.3(ii) is:

+ 0.2(0 kip-ft)

=1.010 kip-ft

+ 0.7(788 kip-ft)

I

I

=688 kip-ft

I

ASD


P., =(1.2+0.2SDs)Po +Pe... + 0.5Pr. + 0.2Ps [1.2 + 0.2(1.0)}(0kips)+109 !Ops

=

+ 0.5(0 kips)+0.2(0 kips) = 109 kips

I

=11.2 + 0.2(1 .0)}{120 kip-ft)

LRFD

I:

=56.9 kips

=82.9 kips

=109 ldps

~::

·1'0 kips+O kips+0.7(63.0 kips)

+ 0.2 (0 kips)

=(cos 450)[ (550kips + 133 kips)~(67 .8 kips+ 307 kips) 1

~·

=11.o+o.14(LO)J(1i.2 kips)

+ 63.0 kips+0.5(8.50 kips)

p" = (cos 450 )l L(Braces below beam); L(Braces above beam) l

·..-

r VF+0.1Ve..,..

+ 0.5Vt + 0.2Vs

P1 L ME= ..,. - 4

To determine the required axial force of the beam, the horizontal component of the difference between the sum of the expected strengths of the braces below the beam and the sum of the expected strengths of the braces above the beam can be thought of as a "story force" which the beam must deliver to the braces. Since the braced frame is in the middle bay of a three-bay building, half of this story force can be considered to enter the braces from each side.

··1

Va ={l.0+0.14Sos)Vo + V11

V11 = (1.2+0.2SDs)VD +VE..,

=788 k,ip--ft

~:

ASD Load Combination 5 from ASCEISEI 7 Section 12.4.3.2

ASCFJSEI 7 Section 12.4.3.2

_ 126 kips(25.0 ft) 4

••illlll

ASD


=63.0 kips

i

The required shear strength of BM-2 according to the analysis requirements of AlSC Seismic Proi:isions Section P'2.3(iJ) is:

.


Pa =(1.0+0.14SDs)Po +Pu

+PF +0.7Pe.,,, =[l.0+0.140.0)J(O k.ips)+O kips

Note that the analysis of AISC Seismic Provisions Section F2.3(ii), \Vith the braces acpostbuckling strength in compression, gives significantly higher required shear and moment for the beam, and a moderately lower required axial force. The shear and moment resulting from the analysis of Section F2.3(ii) do not act simultaneously with the axial force resulting from Section F2.3(i).

In summary, the required strength of Beam BM-2 determined by the analysis provisions of AISC Seismic Provisions Section F2.3(i) is:

+ 0 kips+0.7(109 kips)

=76.3 kips

-

LRFD

ASD

1.

,. '·

i

1 - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - --i' P., ::: 163 kips

Pt) = 114 kips

V., = 28.8 kips

Va

M., = 329 kip-fl

M0 =2 15 kip-ft

=19.0 kips

•.

·'i:·

I I

AM.EIUCAN 1Nsnnrra oP STl:EL CONST11ocnoN

S-JIO

BRACED FRAMES

The required strength of Beam BM-2 determined by the analysis provisions of AISC Stismic Provisions Section F2.3(ii) is:

LRFD Pu = 109 kips v. = 82.9 lcips JI.= 1,010 kip-ft

5.3 SPECIAL CONCENTRlCALLY BRACED FRAMES

S-1

Determine lateral bracing requirements Beam bracing requirements are given in AlSC Specificazion Appendb: 6. The required s1rcng1 l of lateral nodal bracing is: ~

ASD

..

Po == 76.3 kips Vo = 56.9 kips Mo = 688 kip-fl

(Spec. Eq. A-6-71 where

From AlSC Seismic Provisions Equation D l • l, the required flexural strength is:

Beam Size Selection The beam is subject 10 axial and flexural forces. The discussion in Part 8 and Table 8-1 of this Manual regarding the design of collector beams is applicable to the design of beams within a braced frame. Try a W27x114.

LR.FD

ASD

M,= R1 F1 Z

l

M, :::: R1 F1 Z I l.5

=1.1(50 ksi)(343 in.3)

___

. = 18,900 kip-in. .___

I

::::: 1.1(50 ksi)( 343 in.3) 11.5

l

_ __ _

_...__ ::::: 12,600 kip-in.

From AISC Manual Table 1-1, the geometric properties are as follows: From AISC Specificarion Equation A-6-7, the required strenglh of lateral nodal bracing is: . W27x114 A= 33.6 in. 2

d= 27.3 in.

If= 0.930 in.

kdu = 1.5'.3 in.

Sx =299 in. 3 r,.=2.18 in.

rx = 11.0 in. h0 =26.4 in.

lw = 0.570 in. hftw = 42.5

z.. =343 in.

3

J = 7.33 in.4

hr== 10.1 in. Ix.= 4,080 in. 4 11 =159 in.~ Cw= 27,600 in. 6

In order to determine which limit states apply, the beam bracing requirements must be investigated.

Bracing Requirements According to AISC Seismic Provisions Section F2.4b(2), beams in SCBF using V- and inverted-V configurations must satisfy the bracing requirements for moderately ductile members. This beam is considere,d part.of such a configuration because it is intersected by braces at its midspan. AISC Seismic Provisions Section DL2a requires that beam bracjng in moderately ductile members have !i maximum spacing of:

Li,= 0.17r1 EIF1

(Provisions Eq. DI-2)

=0.17(2.18 in.)(l ft/12 in:)(29,000 ksi) I (50 ksi) =17.9 ft The beam .span is 25 ft; therefore it is economical to provide bracing at midspan of the bea.m (lb= 12.5 ft).,

AISC Stismic Provisioiis Section Dl.2a(a)(I) requires L!iat both flanges of lhe beam be laterally braced or the cross section be rorsionilly braced. Assume the beam shown in Figure 5-10, spanning between column lines 1 and 2, at midspan of lhe SCBF frame will be used to provide lateral bracing.

Prb

=0.02(RyFyZ)Cd I ho = 0.02(18,900 kip-in.)(1.0)/26.4 in.

=14.3 kips

Prb = 0.02(R1 F1Z)Cd I h0

= 0.02(12,600 kip-in.)(1.0)/26.4 in. = 9.55 kips

'

The r~uired stiffness of l:lte!al nodal bracing is, according to AISC Specific,qtion_Equatio A-6-8:

1--A---'~'-.!.-(-IO_M_,_c_dL)_RFD _____'_, _ Q

t'br

_

lbho

l

1 10(18,900 kip-in.)(1.0) 0.75 (12.5 ft)(l2 m./ft)(26.4 in.)

=63.6 kip/in.

I

1

_.__A_=_ ·n_(.._l_O~-,-c-d_A)_so_ _;_·_·- - - ,'.!. t'br

L11ho

=2 _00 [ .

·

ki~-in.)(1.0)

10(12,600 (12.5 ft)(12 in./ftX26.4 in.)

l i .i;

1

:::: 63.6 kipfm.

l.. ...

The axial stiffness of lhe member providing bracing to the beam is:

•)

..

AE k=L

\

The required area of lhc brace is:

I·

k ~ ~br = 63.6 kip/in.

• AMti:klcAN lNsrmm! OF STEEi.. CONSTRUCTION

l

- - - --

5-112

A

BRACED FRAMES


,. · e"

Determine the critical buckling strength for flexural buckling about the x-x axis, assuming Q = 1

~~br(i.) > 63 _6 k.i

/in.[30.0 ft(l2 in./ft)J . P 29,000 ksi

-

:m

=0.790 in.2 Provide beam lateral bracing of both flanges at midspan of the beam ( 12.5 ft) with :i minimum of 0.790 in.2 and with an available axial co.mpressive strength of 14.3 kips (LRFD) and 9.55 kips (ASD).

area

Note: The gravicy beam shown (but not sized) in Figure 5-10 should be able to provide this lateral bracing, depending on the depth of the beam and the connection type.

Kx

= 1.0

l..x

=25.0 ft

K:rL:r J.0(25.0 ft)(12 in./ft) --= r:r 11.0 fo. =27.3 The elastic buck.ling stress is:

(Spec. Eq. E3-4)

,,"., tt--1

f:~

Available Flexural Strength Beam lateral bracing will be provided at 12.5 ft. However, the composite slab can be considered to continuously brace the beam, and therefore the limit state of la~eraHorsional buckling does not apply and the available flexural strength is based on the plastic moment of the beam. From AISC Manual Table 3-6, che available flexural strength of the beam is:

LRFD ·.

'lJ1>Mp = l,29p1kip-ft

...,,,

-;';.· .~.·

(.

ASD M

_]!_ =

856 kip-ft

Qb

_ ' 1t

-

2 {29,000

ksi)

(27.3)2

=384 ksi Tbe va)ue of Fer before local buckling effects are considered is determined as follows:

Fy

50 ksi

F.

384 ksi

-=--:::: 0.130 •

Available Compressive Strength In compr~si~n:·ihe beam is considered continuously braced by the slab so mi.Uor-axis flexural buckling about the y-y axis does not apply. For major-axis flexural buckling about the X· X axis; the beam is assumed unbraced (KL= 25 ft). As explained in Part 8 for collectors, torsioni.il buckling is considered because the torsional unbraced length is not the same as the minor-axis flexural buckling unbraced length. Because the top flange is constrqined by the composite slab, the applicable to~sionai limit state is constrained.-.ax.is flexural-torsional buckling, as discussed in Part 8 of this Manual.

.. .

For torsional buckling, the beam is considered unbraced between torsional brace points. In this exam.pie; the lateral braces of both flanges at midspan are assumea to .provide a torsional braced point. Therefore the unbraUd length for torsional buckling is taken as 12.5 ft. Tu summari.Ze:

4. =25.0 ft (flexural buckUng about x-x axis) Ly= 0 (t (flexural buckling about y-y axis does not apply) Lt= 12.5 ft (constra+ned-axis flexural-torsional buck.ling)

-

From AJSC Manual Table l -1 and AJSC Specificazion Table B4.l, the web is slender for compression. Therefore the reduction factor for slender stiffened elements, Q0 , roust be determined.

Because 0.130 < 2.25, use AlSC Specification Equation E3-2 ro detennine the critical buckling stress. I

F"+658t ]F,

i

(Spec. Eq. E3-2)

\

"[o.658'':. '::;;]so k~ .. •

i

... ·'

=47.3 ksi

Determine the critical buckling strength for constrain~d-axis · · flexuraHorsiona~ buckling, assuming Q 1 For the limit state of constrained-ax.is flexural~torsiooal buck.ling, the unbraced leugt.1? ls 12.5 ft and the top flange of the beam is considered continuously braced by the slab as described in Part 8 of this Manual.

=

AMEJUCAN lNSTmTrE 0'1 S11ln. CONSTRUcnON


(8-3)

b, = l.921

IIf

0 34 1- ·

fj

@j s. b

(bit) ~/ .

l

(Spec. Eq. E7-r )

= 1.92(0.570 in.) 1_2_9.:.....,0_00_ks_i [l- 0.34 29,000 ksi $ 24 .2 in. 38.l ksi 42.5 38.1 ksi

:::: 23.5

in.~ 24.2

in.

Q.,"' ~ . Ag

x

= Ag-tw(li-b,)

1 ---------------! 21 4 4 4,080 in. + 159 in. +( ·~ in.r (33.6 in.2)

Ag

· .33.6 in.2 - 0.570 in.(24.2 in.-23.5 in.)

The value of Fer before local buckling effects are considered is determined as follows:

F

50 ksi

~

77.2 ksi

= =0.988 Q, =1.0 Q

Because 0.648 < 2.25, use· Equation E3-2 to determine the critical buckling S!l'ess.

(Spec. Eq. E3-2)

· 1i

.

.

=77.2 ksi

-1=

(Spec. Eq. E7-ll'\)l

50ksi ·1

= 0.65877 ·2 ksi 50 ksi

33.6 in.

1

= Q,Q,, =1.0(0.988)

1.

I

·= 0.988 For the governing Jim.it state of constrained-a.xis flexural-torsional b~ckling, accounting fc. slender elements, the available strength is determined as follows from AISC Specificatio Section E7:

QFy 0.988(50 ksi) = F. (77.2 ~i)

.

· ')

k !

l ' •}

=0.640

= 38.1 ksi

I

\

Because 0.640 < 2.25, use AISC Specif;cation Equa~on F:J-2.

Because Fer is lower for constrained-axis flexural-torsional buckling, this limit state governs over major ax.is flexural buckling.

~

Fa-= Q 0.658 F. F1 Determine the reduction factor, Q, for slender elements To determine the reduction factor, Q, useAJSC Specification Section E7.2, with/= Fer, and the minimum Fer from !he two preceding limit states. The reduced effective width of the slender web is detennined as foll.ows:

._ I . I

Eq. E7-:

I;

(Spec. Eq. E7- 1

t

(Spec.

...

0.988(50 k!i)

=0.988 0.658 . n.2 ks!

(50 ksi),

= 37.8 ksi

b=h

;;, d-2kdcs

Pn = FcrAg 2

=27.3 in.-2(1.53' ill.)

=37.8 ksi(33.6in.

=24.2 in.

= 1,270 kips

J=F'cr = 38.1 ksi

)

1

S.3 SPEClr\L CONCENTR.ICALLY BRACED FRAMES

5-116

r:

I

LRFD

ASD

LRFD P,.

l,270 kips 1.67 = 760 kips

~

I~.....,, .,

~

brace strengths in compression and tension; instead, they may be thought of as contributing to the system reaching that state. P-8 effects do apply, however. The effective length method!

+ 111 kip-ft+ l.Ol(0.5)(100 kip-ft}

+ 0 lcip-ft+O kip-fl

+ 0.2(0 kip-ft)

+ 0.7(111 kip-ft)

=216 kip-ft

The required flexural strength of Beam BM-2 according to I.he analysis requirements of AJSC Seismic Provisions Section F2.3(ii) and including second-order effects is:

LRFD

is used.

Mu= B1 (1.2+0.2Sos)Mo+ ME..o

C,,, <'! l 1-o.P,/Pti

(Spec.

rtl £/.

(Spec.

(K1L)

=

Eq. A-8-3)

ASD

·-

+B10.5ML +0.2Ms

4

ksj)(4,080 in.

Eq. A-8-5}

.

= l.Oljl.0+0.14(1.0)](120 kip-ft)

+ 788!tip-ft+1.01(0.5)(100 kjp-ft)

+ 0 kip-ft+O kip-ft

+ 0.2(0 kip-ft)

+ 0.7(788 kip-ft)

: 1,010 kip-ft

)

Ma= B1(1.0+0.14Sos)Mo +MH +MF+0.1ME..i.

=LOl(l.2+ 0.2(1.0)!(120 kip-ft)

P.1--2 2 rt (29.000

=LOJ!L0+0.14(1.0))(1~0 kip-ft)

=331 kip-ft

Because the seismic component of the beam required strength comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on the expected strengths of the braces, P-6 effects need not be considered and B2 from AISC Specificario11 Appendix S need oot be applied. P-6 effects do no1 increase the forces corresponding to the expectedi

< -

+MF+0.7ME.,,.

=1.01(1.2+0.2(1.0)](129 ki!>""ft)


Bi =

Ma =B1(1.0+0.14SDS)Mv +MH

+B10.5ML +0.2Ms

f

.

ASD

M .. = Bi(1.2+0.2SDs)Mo+ME.,.

-=

nc

5-11 7

=690 kip-ft

2

jl.0(25.0 ft)(12 inJft)]

In summary, including second-order effects, the required strength of Beam BM-2 determined by lhe analysis provisions of AlSC Seismic Provisions Section F2.3(i) is:

= 13,000 kips

C,,. = LO, because lherc is transverse loading between supports

LRFD LRFD

LO Bi c-

l-[J.00(163 kips)/13,000 kips) =l.01

ASD B _ 1

-

1.0 l-[1.60(114 kips)/13,000 ldps]

•,•·

c. ~-"·

=163 kips

v,,

= 28.8 kips

.

Mu =331kip-ft

I

\

Po =114 kips Va ::::: 19.0 kips Ma= 216 kip-ft

1.

::::: 1.01

t

~

Pu

ASD

The B1 factor (P-
Including second-order effects, the required strength of Beam BM-2 determined by the analysis provisions of AISC SeiSmic Provisio11S Section F2.3(ii) is:

.

LRFD

Pu

=109 kips

Vu = 82.9 kips M., =1,010 kip-ft

ASD P,, =76.3 kips Va = 56.9 kips Ma = 690 ki!>""ft

I


Combined Loading

Check shear strength of the W27)(114 From AlSC Manual Table 3-2:

for the analysis provisions of AlSC Seismic Pro"Visions Section P2.3(i):

LRFD

Pr

-=

Pc

ASD P,

163 kips 1, 140 kips

-= Pc

= 0.143

LRFD

114 kips 760 kips

LRFD

I

o.k.

0.150 + 216 klp·f[ +0=0.327 2 856 kip-ft 0.327<1.0

o.k.

For the analysis provisions of AlSC Seismic Pro"Visions Section F2.3(ii):

LRFD

ASD

109 kips 1,140 kips =0.0956

P,

-=

o.k.

Pc

=76.3 kips 760 kips

=0.100

LRFD

o.k. ·

According to AISC Seismic Provisions Section F2.5a, beams in SCBF must satisfy lhe requirements for moderate! y ductile members. From Table 1-3 of this Manual, the W27x 114 satisfies the limiting width-to-thickness ratios and Pu and P0 are less than the maximum permitted.

ASD

=0.831

0.100 + 690kip-ft +0=0.856 2 856 kip-ft 0.856< 1.0

Example 5.3.5. SCBF Beam Design

J.

Given: Refer to Beam BM-1 in Figure 5-11. Select_an ASTM A992 W-shape with a maximum depth of 36 in. Design the beam as a noncomposite beam for strength, although the composite deck can be considered to brace the beam. The applicable building code specifies the use of ASCFJSEI 7 for calculation of loads.

1.~

VD= 11.2 kips MD= 120 kip-ft

(Spec. Eq. Hl- lb)

0.0956 + 1,010 kip-ft+ 0 2 1, 290 kip-ft

Check width-to-thickness limits of the W27x114

o.k.

J~:

Assume the brace sizes are llS shown in Figure 5-12. Relevant seismic design parameters were given in the SCBF Design Example Plan and Elevation section. The gravity shears and moments on the beam are:

Because P,IPc < 0.2, the beam-column design is controlled by the equation:

0.831<1,0

n"v = 311 kips> 56.9 kips

ASD

0.143 + 33lk.ip-ft +0=0.328 2 1,.290, kip-ft

Pc

v.

o.k.

=0.150

(Spec. Eq. Hl-lb)

P,

ASD

QvVn = 467 ldps > 82.9 kips

Because P,fPc< 0.2, t.he beam-column design is controlled by t.he equation:

0.328<1.0

5-119

VL

=8.50 kips

ML= 100 lqp-fc \

Note I.hat in Example 5.3.10, tbe bracing connections at the third level use a splice in the beam away from the gusset plate. Based on the connection configuration, a shorter length could have been used for the beam design, here. In lhis example, the full 25-ft bay width is used as the length of the beam. Solution:

From AISC Manual Table 24, the material properties are as follows: ASTMA992 Fy = 50 ksi F., = 65 ksi

1;

Seismic Provisions Section F2.3, the requfre.d strength of the beams are based on the load combinations in the applicable building code, including the amplified seismic loads. The amplified sejsmic loads are determ.ined from the larger of: As required by AJSC

(i) An analysis in which all braces are assumed to resist forces corresponding to thei r

expected strength in compression or in tension

~

f.;

t .. ~1

5-120

BRACED PRAMES

.,

(ii) An analysis in which alJ braces in tension are assumed Lo resist forces corresponding

t

to their expected strength and all braces in compression :ire assumed to resist their expected post-buck.ling strength

~

These forces are shown in Tables 5-1 and 5-2, and the forces ac1ing on Beam BM-1 are shown in Figure 5-16.

)

i. h

·:. Unlike Beam BM-2 designed in Example 5.3.4, these forces do not cause shears and moments oo the beam; the only shears arid moments are from gravity loads.

·~

;

:·:

Required Strength

•·.,,s:

Determine the required axial strength of the beam based on A/SC Seismic Provisions Section F2.3(i) ·

'·\"

,., :~

;: ::1 ·~ :

·~

~: ,. v

~ ~·

ftl

};

~ ~

-

~

i:.l !'-.·

>::

From AJSC Seismic Provisions Section P2.3(i), the required axial strength of the beam is based on the braces a1 their expected strengths in tension and compression. To determine the required axial force on the beam, the horizontal component of the difference berween the sum of the expected strengths of the braces below the beam and lhe sum of the expected strengths of the braces above lhe beam can be thought of as a "story force." The story for.cc for the analysis in AISC Seismic Provisions Section F2.3(i) with tension and compressio.n braces at their expected strengths is:

.

Px =(cos45°)[!(Braces below beam)-:E(Braces above beam)]

=(cos45°)[(518 kips+606 kips) - (550 kips+ 444 kips)J = 91.9 kips

~~

25'-0"

.,

5-121

S.3 SPECIAL CONCENTRlCAl..LY BRACED PR.AMES

Because the brace
For lhis analysis, the expected strength of the braces in compression must be multiplied by 0.3 co approximate Lheir post-buckling strenglb, as shown in Table 5-2. Figure 5-16(b) shows the forces corresponding to the tension braces at their expeccec strengths ::md che compression braces at their post-buckling strength. Similar to Beam BM2 in Example 5.3.4, an equivalent "!>tory force"' can be determined as:

P.t::: (cos45°)[I(Braces below beam)-r(Braces above beam)]

=(cos45")[(155 kips+606 k.ips) - (550kips+133 kips)]

=55.2 ldps Since the braced frame is in the middle bay of a three-bay building, half of this story foro. or 27.6 kips, can be considered to enter the braced bay from each side. From equilibriun the joints at each end of the beam, this resulu in a axial force in the beam of E>(lh = 307 kips. as shown in Figure 5-18. The analysis of AJSC Seismic Provisions Section F2.3(ii) governs, in which tension braces are at their expected strengths and compres~ion braces are at their post-buckling strengths.

~ ~

~=

I

r

I I I I

,.

~~;

46.0 klps

i:·

:..

.... ~~

t:

•:;:.

I

~~ :~. :; ~ ·!·

/'

'

I

'

I

r------~-~------,

~' <:.

~·;

',

I

!As.a

!""

lT

j. (a) Forces from A/SC Seismic Provisions Section F2.3(i)

(b) Forces from A/SC Seismic Provisions Section F2.J(ii)

Fig. 5-16. Forces on Beam BM-1 from a mechanism m1alysis ofA/SC Seismic Provisions Section F2.3 as carried out in Example 5.3.2.

/

/

559..t<1ps

'

'

444~ps

kips 68.6

51 S-kips ',

I

'

I

,'

I I I I

ki~i 46.0 kips

/il

606,Klps //

T

/

I

',

I

~ ------~-~--- -- -1

Fig. 5-17. Axial force in Beam BM-1 from the rr.i!chanism analysis of A/SC Seismic Proi·isions Section F2.3(i).

5- 122

BRACED FRAMES


The required shear and flexural ·strenglh of the beam comes from gravity loads only, and Ulerefore are the same for both analysis cases. Using the load comb.inations in ASCE/SEI 7, the requfred $hear strength of Beam BM-I according to the analysis requirements of AISC Seismic Provisions Section Fi.3(ii) is:

LRFD

ASD

LRFD Load Combination 5 from ASCE/SEI 7 Section 12.4.3.2 (including the 0.5 load factor on L permitted by Section 12.4.3.2)


LRFD Load Combination 5 from ASCEJSEI 7 Section 12.4.3.2 (including the 0.5 load factor on L permitted by Section 12.4.3.2)

Ma=(l.O+O.I4Sos)Mv+Mu

+ 0.5A'h + 02.Ms

+Mp+0.7ME.,.

Va:::: (l.0+0.14SDS)\'D + VH

+ Vp + O.?VeiM

=ll.2+0.2(1.0)](1 1.2 kips)+O kips

= [1.0+ 0.14(1.0)](120 kip-ft)

+ 0 kip-ft+0.5{100 kip-ft) + 0.2(0 kip-ft)

.

= 12.8 kips

The r~qp.ire~ flexural ·strength of Beam BM-1 according to the analysis requirements of AISC Seisnuc Provisions Sectfon F2.3(ii) is:

I

LRFD Load Combinati~n 5 from ASCE/SEI 7 Seetion 12.4.3.2 .


P,. =(l.2+0.2Sos)Po+PE...,,

Pa= (1.0 +0.14Sos)Pv +PH

+'PF+ 0.7P:e>M

=ll.2+0.2(1.0)J(O .kips~+307 kips

=[L0+0.14(1.0)J(O kips)+,0 kips

+ 0.5(0 kips)+ 0.2'co· kips)

~------~-~------i I 1

I

27.6 kips.,

'// .<

550-Kips .r

16"1

:, lT

kips

155'-kips '\

'

'>+ 13., -i..;ps ·~

307

.r/

I

'

r

//

',

r

.

--'l IL-- ----~-~---.r ,

Fig. 5·18. Axial force in Beam BM-1 from the mechanism analysis of A/SC Seismic Provisions F2.3(ii).

~ea.ms

frame.

I ..f~·· I I':,·: ~-·

within a braced

I

In flexure, the beam is coosider.ed continuously braced by the slab and Jateral-torsiona;. :,

buckling does not apply.

··

:

,

::

Jn compression, the beam is considered continuously braced by the slab in the y-y directio1 J·.· so minor-axis flexural buckling does not apply. For major-axis flexural buckling, the bean. ,'.? is assumed unbraced. As expl~ed in Part 8 for collectors, torsional buckling is considered ·"' because the torsional unbraced length is not equal to the minor-axis flexural bucklini unbraced length. For torsional buckling, the beam is considered braced by the gravity bean and its connection at midspan. Since the top flange is constrained by the composite slab, the , applicable torsional limit state is constrained-axis flexural-torsional buckling, as discussed in Part 8 of lhis Manual ]: :

I

Try a W24x68. AMERICAN lN~-rrrvn; OF ST£a CONSTJ\UCT'ION

fi:

~j

lT I

:·:

..

I

/

::::: 215 kips

for a discussion of collector beams, whlch also generally applies to

1

ki~f 27.6 kips

606A
j;i 1:·: .,

'-Th-e-bea-m-is-su-b-1ec. -t-to_a_)(_ia_l_a_n_d_fl_e_x_u-ra_l_fo_r,_c-es_._S_e_e_P_art_8_an_d_T:_a_b_le-8--1-o_f_th_i_s_M_an_u_a.

I I

/!

+ 0 ldps+0.7(307 kips)

=307 kips

f

b.

k:

ASD

LRFD

+ 0.5PL +o.iPs

//

,.

+O kip-ft.+O kip-ft+0.7(0 kip-ft)

The require-d axial strength of Beam BM-1 according to the analysis.requirements of AISC Seismic Provisions Section F23(ii) is:

"

f

I

= 137 kip-ft

= 21s kip-ft

+ 0 kips+0.7{0 kips)

',

J

= ll.0+0.14(1.0)](11.2 kips)+O kips

+ 0.5(8.50 kips)+0.2(0 kips) = 19.9 kips

I

I I;:

= jl.2 + 0.2(1.0)]{120 kip-ft)

Vu = (I.2+ 0.2Svs) Vo + Vi::...., + 0.5VL + 0.2Vs

I

ASD

LRFD

Mu= (1.2+ 0.2Svs )Mo+ Me,.io


5-1 .'

.;.,.: AMl;RJCAfl lNSTnUT:e OF STEEL CONSTRUCTION

5-124

BRACED FRAMES

5-1 2.5

5.3 SPECLo\L CONCENTRJC.'\LLY BRACED FRA..'1.1ES

Beam Size Selection

(Spec. Eq. E3-4)

From AISC Manual Table 1-1, the geometric properties are as follows:

W24x68

A= 20.l in.1

'1 =0.585 in. • 3 Sx = 154 10. r 1 =1.87 in.

{1=23.7 in. .

lw

=0.415 in.

b1 = 8.97 io.

kdu =1.09 in.

hltw= 52.0

Ix = 1,830 in.~

rx

=9.55 in.

Z.= 177 in.3

1, = 70.4 in.4

h0 = 23.1 in.

J = 1.87 in.4

Cw = 9,430 in. 6

Lateral Bracing Requirements Because this beam ~ not part of a V- or inverted-V-braced frame (there is no brace connection at the midspan of t11e ~m), there are no lateral bracing requirem~nts in the AlSC Seismic Provisioru, other than what may be required for strength. However, there is a gravity beam framiDg into the beam at midspan. The gravity beam at midspan and its connection will be conside~ed to provide a torsional brace.poi~t for the liiil.it.state of constrained-axis flexurru-torsion~ buckling.

=

2 (29,000

?i

(3 1.4)

ksi)

2

=290 ksi The value of Fer before local buckling effects are considered is determined as follows: F

50 ksi

1 -=--F, 290 ksi =0.172

Because 0.172 < 2.25, AISC Specijicario11 Equation E3-2 applies.

(Spec. Eq. E3-2) Available Flexural Strength The composite slab can be considered to co~tinuously brace the and therefore the limit state offateral-torsi~nal buckling doe~ not apply a'n d.the av~~l~~I.e flexuqt stre.ngVI, is based on the plastic moment.. From AISC Manual Table 3-6, th~ avaHable flexural strengtli of the beam is:· · · ·

beam,

..

LRFD
Mp

•

n.b

'

ASD

'

'' ·'


Determine the critical buckling strength for constrained-axis flexural-torsional buckling, assuming 0 1 . . For the limit state of constrained-axis flexural~torsional buckling, I.be unbrac~d length is 12.5 ft and the lop flange of the beam is considered continuously braced by the slab as described. in Part 8 of this Manual. \

.

L, =0 ft _Oateral movement is braced _by the slab)

l

2

it

F,=

4 =25.0ft

Lr. = 12.5 ft (torsio~ with top flange restrained by the slab) From AISC Manual T
=

. ' Kx Li

=I.O

= 25.0 ft

ftX12 inJft) - - = _1.0(25.0 ...;.__--'-'---KiLi

9.55 in.

rx

=31.4 AMERJCAN INS1TllJT£ OP S'Y:EEL COl'ISTR\JCTION

(50 ksi)

=46.5 ksi

The unbraced lengths for flexural buckling were ?iscussed previously. To summarize:

Determine the criticai buckling strength for flexural buckling about the x-x axis, assuming Q 1

l

[

=

-=442 kip-ft ;

50ksi

= 0.658290 k s•

2

j

]I l:~+I,+(d/2)2Agl.

E[Cw+.ly (d/2) (K4 L)2 +GJ

1t2 (29,000

=

l

I

2

4

6 ksi) 9,430 in. + 70.4 .m. (23.7 - -- in.) ]

z

2

ILO( l2.5 ft)(l2 inJft)j

I x

2·

4 . .2) 1,830 in.4 + 70.4 in. + (23.7 - - in.) (20· 1 m 2

=56.5 ksi

(8-3)

1-

, . . 4 + 11,200 ksi(l.87 in. ) '

BRACED FRAMES

The val~e of Fer before JocaJ buck.Jing effects are considered, wilh F.,

F,

Determine the available compressive strength for the governing limit state of constrained-axis flexural- torsional buckling, accounting for slender elements

s 2.25, is:

!z. Fer= 0.658'' F.,

~w = 0.65856.5 bi

I

(Spec. Eq. E3-2)

I .

'.,

QF1 0.942(50 bi) -= F, (56.5 m)

=0.834 Because 0.834 < 2.25. use AISC Specific01ion Equation E?-2.

50 ksi

= 34.5 ksi

Fa

=.+.6589f.']F, .

=

To detennine the reduction factor Q. use AISC Specification Section E7.2, wilh f Fen using the minimum Fe, from the two precedi11g limit states. Determine the effectjve width, be, M~~~

-

b=h

~

(Sp.c.

Eq. E7•2

(Sp
Eq. E7- I . '

...".,,,.,I

Because Fa is lower for constraioed-aJtis flexural-torsional buckling, this limit slate governs over major axis flexural buckling.

Determine the reduction factor, Q, for slender elements

,..

, ',

=33.2 ksi

P" =F;,,A1 =33.2 ksi(20.l

in.2)

'

=667 kips

=d-2kdes

The available compressive strength is:.

= 23.7 i:n.- 2(1.09 in.) = 21.5 in.

fil1. fj

b., = t.921

LRFD

ASD

Pn 661 kips -=-----

9cP,. = 0.90(667 kips) 0 34 · (b I

=1.92(0.415 in.)

IIj-;;, b 1)"-/t

(Spec. Eq. E7- 17)

l

nc .

=600 !tips'

1.67

=399 kips

.

I

'I

29,000 ksi [1- 0.34 29,000 ksi < 21 5 in 34.5 ksi (~2.0)' 34.5 ksi . .


=18.7 in.'5,21.5 in.

Q,,=Ae

(Spec. Eq. E7-16)

A,

=A, -tw(h-b~)

A, _ 20. l in. 2 -0.4 15 in.(21.5 in.-18.7 in.) 20.1 in. 2 = 0.942

as= i.o Q =QiQa

=1.0(0.942) =0.942

'

I~

(Spec. Eq. A-8-3)

IJ

5-128

BRACED FRAMES

-"

5-1 2•

5.3 SPECIAL CONCENTRICALLY BRACED !'RAMES

ti •.

rt 2 EJ • 2

=

LRFO

(Spec. Eq. A-8-5)

Pei "'"(K1L)2 4

1t (29.000ksi)(1,830 in. )

.,

o.s12+!( 231 ltip-ft +o)=o.s21

o.539+~( 145 kip-ft + o)"' o.831

0.821 < 1.0

0.831<1.0

9 664 kip-ft

[1.0{25.0 ft)(J2 inJfl)j·

I

ASD

o.k.

9 442kip-ft o.k.

=5,820 kips

Cm = 1.0 because 1here is transverse loading


LRFD B1 -

1.0 t -[1.00(307 kips)/5,820 kips]

From AISC Manual Tuble

ASD B1 -

=l.06

¢vV11

The B1 factor (P-5 effecc) need only be applied to the first-order momen1 with the structure restrained against translation. The required fle.xural strength of Beam BM-1 according to the analysis requirements of AlSC Seismic Provisions Section F2.3(ii) and including secondorder effeets is determined from ASCEJSEI 7 Section 12..4.3.2 Load Combination 5 for LRFD and ASD:

LRFD M,, = B1 (1.2+0.2Svs)Mo +Me,.

1

ASD

LRFD

1.0 I -[J.60(215 kips)/ 5.820 kipsJ

= 1.06

3-2, the available shear strength is:

=295kips>19.9 kips

o.k.

.!!!_ = 197 kips> 12.8 kips

nv

o.k

Width-to· Thickness Umitations According to AISC Seismic Provisions Section P2.5a, beams in SCBF shall satisfy the of this Manunl, the W24x68 requirements for moderately ductile members. From Table satisfies the limiting width-to-thickness ratios and P,, and Pa are less chan the maximuiy1 permitted.

1-3

ASD Mo= B1(1.0+0.I4Svs)Mo +MH

+ B1 0.5M l + 0.2.l'ds

+JfF+0.1Me.,,.

=1.06(1.0+ 0. 14(1.0)l(l20 kip-ft}

= 1.06[!.2+ 0.2(l.O)j(l20: ~p-fl)

+ 0kip-ft+1.06(0.5)(100 kip-ft)

+O kip-ft+O kip-fi+0.7(0 kip-ft)

=145 kip-ft

+ 0.2(0 kip-ft) = 23 I kip-ft

Example 5.3.6. SCBF Column Splice Design Given: Design a fully welded splice between the third and fourth levels for the SCBF columr: located on grid C in Figure 5-11. The column material is ASTM A992, the upper shaft is a W12x45 and the lower shaft is a W12x96. The applicable building code specifies the use of ASCE/SEI 7 for calculation of loads'.

The relevant seismic parameters were given in the SCBF Design Example Plan and Elevation section.

Combined Loading

;I

1'~.

LRFD 307 kips

P,

=215 kips

Pc

600 kips

Pc

399 kips

= 0.512

The required axial strengths of the columns due to dead (including curtain wall), live and snow loads at the splice location are:

ASD

P,

·

Pv

=66.3 kips

Pi= 18.8 kips

Ps =7.00 kips

The seismic component of Lhe required axial strength of the column due to code-specified seismic loads from the applicable .building code is:

=0.539

Because P,fPc~ 0.2., th~ beam-column design is C-Ontrolle:I by the equation:

Pal!.= 45.S kips

Assume that the ends of 1he C-Olumn are pinned and braced against translation for bolh l'-...

(Spec. Eq. Hl- Ja)

x-x and y-y axes and the column moment produced by the gravity framing connection., '

negHg.ible.

BRACFD FRAMP.S

5--130

Solution: From AJSC Manual Table 2-4, the material properties are as follows:

PE..J.

ASTh'f A992

=307 kips(sin 45 ') + 8.84 kips =226 kips (compression)

PE..= 226 kips(sin45 )-8.84 kips

F1 =50ksi F,, =65 ksi

= 151 kips (tension)

From AlSC Manual Table l·l, the geometric properties are as follows:

W12x45 A= 13.1 in. 2 lw

s. 131

.S.3 SPECIAL CONCENTRICALLY DRACED FRAMF.S

d= 12.1 in.

= 0.335 in.

br= S.05 in.

If= 0.575 in.

Zr - 64.2 in.3

At this level, Exception 2(:1) for the column in AISC Seismic Provisio'ns Section F2.3 can be shown not to result in reduced forces; therefore the exception is not used. For comparison, the seismic component of the required axial strength of the column due to code-specified seismic loads from the applicable building code is given as: PQr.

W12x96

=45.5 kips

Z;r= 147 in. 3

l ..

Required Strength

AlSC Seismic Proi;i.sions Section F2.6d requires that SCBF column splices comply with S~tion 02.5, which states that the required strength of column splices is the greater of (a) the required strength of tbe colunms, including that determined from Chapters E, F, G and H, and Section Dl.4a, or (b) the required strength determined using t.he load combinations stipulated in the applicable building code, including the amplified seismic load, but need not e:xceed the W:Ltimum loads I.hat can be transferred to the splice by the system. Also, for columns with net tension, three other specific conditions muse be satisfied, as stipulated jn

\ Roof &,

·' N

Section D2.5b. The required axial strength of columns in SCBF frames is based on the expected strength of the braces, as defined in AJSC Seismic Pro~·iswn.s Section F2.3. Example 5.3.2 provides a desqipcion of this analysis. For the column at the lowest story, Example 5.3.3 illustrates the determit)ation of the column force. For the splice location, only the braces at the top two sto· ries need to be considered. From Example 5.3.2, with brace forces shown in Figure S-13 and Tables 5-1 nnd 5-2, the expected tensile strength of the HSS6x0.312 brace between level 4 and the roof is: P1ouion = 307

Fourth Level

226 kips

.,

l8'~-~P.5; ,, 550 kips

Third Level

'/._______

307 kips /

~~~ ki£~~

"·

444 kips

""'

kips

From Example 5.3.2, in Tuble 5-2, the expected compressive scrength of the HSS6x0.312

brace berw~ level 4 and the roof is given as: Pcampf~-MiDn = 226

kips

The vertical components of these brace expected strengths are transferred to the column. J\l the fourth level, the brace forces at the beam midpoint connection arc carried across in beam shear. The forces acting on the columns due 10 Lhe expec1cd s11Cngths of the braces arc ns shown in Fig\Jre 5-19.

Base

Fig. 5-19. SCBF column forcu for splice duign from E.xomple 5.3.3. The axial force in the column u the splice location due to sei~mic load effeclS (including the nmplified seismic load) is:

\

.:·

I J t I

-;:'):'

I

Using amplified seismic forces, this becomes:

Required Flexural Strength

AISC Seismic Proviswns Section F2.6d requires the column splice to develop 50% of lhe lesser available Oexural strength of the connected members. For simplicity, use the plastic flexural strength, $1>.Mp (LRFD) or Mp/Qb (ASD).

PE..,,= n 0 PQ1

=2.0{45.5 kips) =91.0 kips

For the smaller column, W12x45, detennine the available flexural strength from AISC Ma11ual Table 3-6:

The seismic component of the required strength of the column using the analysis requirements of AJSC Seismic Proi:isic11S Sec~on F2.3 (226 kips compre.ssion and 151 !tips tension) is greater than that detennined from the code-specified loads (91.0 kips tension or compression). Therefore, use the analysis requirements of AISC Seismic Provisions Section F2.3 for design of the splice.

LRFD

LRFD

Pu =(l.2+0.2SDs)Pv +Ps,..

ASD

nb

The required flexural strength of the splice is:

ASD

LRFD

ASD Load Combination 5 from ASCE/SEJ 7 Section 12.4.3.2

ASD

Ma=

Mu= 0.50(
=

0.50(241 kip-ft) = 121 kip-ft +PF +0.1?,,,..

= [I.2+ 0.2(1.0)](66.3 Jtips)

=0.50(160 kip-ft) = 80.0 kip-ft

Assuming that the entire moment is taken through the flange splices, the required strength of each flange splice is:

=[l.0+0.14(1.0)](66.3 kips)

+ 226 kips+ 0.5(18.8 kips)

.

+ 0 kips+ 9_kips+0.7(226 kips)

..

LRFD

=234 kips

+ 0.2(7.00 kips) = 330 kips

ASD

R., = Mu d-t1

The required axial tensile strength of the column is:

Ra=~

I

d-11

\

= 121 kip-ft(l2 in./ft)

80.0 kip-ft(l2 in./fl) 12.l in. - 0.575 in.

12.1 in.-0.575 in.

LRFD

Pu = (0.9-0.2SDs)Pz> +PE..i. +1.6Py

=[0.9-0.2(1.0))(66.3 kips) +(-151kips)+1.6(0 kips) = - 105 kips

(

i, .

..

.•,

.·

o.so(M nov) .

P0 =(l.O+O. l4Svs)fi>+ PH

+ 0.5Pi +0.2Ps

LRFD Load Combination 7 from ASCEISEI 7 Section 12.4.3.2

.

Mp =160 kip-ft

bM P :::; 241 kip-ft

Using the load combinations in ASCE/SEI 7, the required axial compressive strength of the column is:

LRFD Load Combination 5 from ASCEISEI 7 Section 12.4.3.2 (including the 0.5 factor on L pem1itted in Section 12.4.3.2)

5-133

5.3 SPECIAL CONCENTRICALLY BRACl:.D FR.AMES

BRACED FRAMES

ASD

=126 kips


= [0.6-0.14(1.0)j(66.3 kips)

+ 0.7(- 151 k.ips)+O kips

.

\

Use CJP groove welds to splice the colwun flanges and web.

I

I

I

ASD

LRFD

-

As stated above, this splice is 10 be a welded splice. AISC Seismic Provisions Section F2.6d requires that groove welds must be complete-joint-penetration (OP) groove welds.

-

The available strength of each CJP groove welded flange splice is controlled by the base metal strength according to AISC Specification Table J2.5. Thus, based on tension yielding of the flange from AI.SC Specification Section D2(a), the available strength of the CJP groove weld is:

Pa =(0.6-0.14SDs)PD +0.1Pe,,.. +P1:1

=-75.2 kips

=83.3 kips

¢Rn= 0.90F>bflf = 0.90(50 ksi)(S.05 in.)(0.575 in.)

=208 kips> 126 kips

o.k.

Rn n=

FybJIJ

/1.67

=(50 ksi)(8.05 in.)(0.575 in.)/l .67 =139 kips> 83.3 kips

A.\fERJCAN .!NS1TIV1ll OF Srm. CON$Tl\l1CTTON

o.k.

BRACED FRAMES

5-134

Required Shear Strength AISC Seismic Provisions Section F2.6d defines lhe required shear strength of the splice as at least f.MpclHc (LRFD) or !Mpel( l.5Hc) (ASD), where !.Mpc is the sum of the nominal plastic Oexural strengths of the columns above and below the splice, and He is the clear height of.the column between beam connections. A CJP groove weld will be used. Assume that the 12.5-ft story height is from top of steel to top of steel. The beam at the story above the splice is a W27. Therefore, the approximate value for Ile is:

=12.5 ft ~ (27 in.)(l ft/12 in.) =l0.3 ft

He

1

(1) The available strength of partial-joint-pcnec.rntion (PJP) groove welded joints, if used, shall be at least equal to 200% of the required strength.

(2) The avaiJnble strength for each flange splice shall be . at le!15t equal t_p 0-.5RyFybf'f (LRFD) or (0.5/1.5) R1 Fybf'J (ASD). (3) Where butt joints in column splices are made with CJP groove welds, when the tension stress at any location in the smaJler flange exceeds 0.30F1 (LRFD) or 0.20Fy (ASD), . tapered mmsitions are required between flanges of unequal thickness or width.

. j {

Since there is net tension, the additional requirements must be met.

=50 .ksi(l47 in. 3 +64.2 in.3 )(1 ft/12

in.)

(1) AISC Seismic Provisions Section D2.5b{l) does not apply bec~use partial-joint-pene-

=880 kip-ft .

tration (PJP) welds are not used. (2) AISC Seismic Provisions Section D2.5b(2) requires that the available strength of each flange splice be at least 0.5RyFybJ1f (LRFD) or (0.5!1.5)RyF1 b1t1 (ASD). With a CJP groove weld, the available strength of the smaller flange can be developed, so this

The required shear strength of the splice is:

LRFD l..Mpc He

using the load combinations stipuJaccd in the applicable building code. includi~g 11ic a?'lplified seismic load. These additional requirements are: •

As detennined previously, the column is subjected to a net tensile load effect.

'ZMJX::::: Fy (Zx ~, .+ Zx rop)

--=

5-135

5.3 SPECL<\.L CONCF.NTRICALLY BRACED FR.AfJIES

ASD

r.lv/pc l.5Hc

880 kip-ft 10.3 ft

--=

=85.4 kips

requirement will be met. (3) AISC Seismic Provisions Section D2.5b(3) requires tapered transitions when the tension stress in the smaller flange exceeds 0.30F1 (LRFD) and 0.20Fy (ASD) for butt joints with CJP groove welds. The tension stress over the cross section is:

880 kip-ft l.5(10.3 ft)

\· ...:

1:

=57.0 kips

ASD

LRFD For the limit suite of shear yielding according to AISC Specification Section G2. the available shear strength of the W12x45 colwnn is:

T., Ag

LRFD

ASD

cj>R,. = $0.6F1 AwCv

R,.

0.6FyA,,.Cv

n

1.50

-=

= 1.00(0.6)(50 ksi) x(l2.l in.)(0.335 in.)(1.0)

= 122 kips> 85.4 kips

o.k.

. Ta Ag

13.l in.2 ::::: 8.02 ksi

0.3F1 =0.3(50 ksi)

·' - 75.2 kips = . 13.l in.2 =5.74 ksi

I

\

'

0.2F1 = 0.2(50 ksi)

=15.0 ksi

= (1/l.50)0.60(50 ksi) x(l 2.1 in.)(0.335 in.)(1.0)

= 81.l kips> 57.0 kips

=-105 kips

o.k.

,.

For the shear in the weak axis of the column, the column flanges of the smaller member will easily be able to meet the required shear strength, since the Mp values for the columns are smaller in this direction and the flange o.rea is sign.ificantJy larger than the web area jn

this case.

8.02ksj<15.0 ksi

=10.0 ksi 5.74 ksi < 10.0 ksi

Therefore, the requirements in AJSC Seismic ProvisioJ'!S Section D2.5b(3) need not be met.

Check Splice Location The splice location satisfies the requirement in AJSC Seismic Provisions Section 02.Sa that the splice be located 4 ft or more away from the beam-to-column Oange connection. The final connection design is shown in Figure 5-20.

Additional Requirements for Columns Subject to a Net Tensile Load Effect AISC Seismic Provisions Section 02.Sb has additional requirements for welded column splices in which any portion of the column is subjected to a net tensile load effect dccem:tlned

AMERICAN INSTmm! OP Snia CONS'raVCTIOH

·;·~

t~

5-136

BRACED FRAMES

5.3 Sl'F.ClAL CONCENTRICALLY BRACED FR.AMES

=4.00 ft(6.50 fl){35.0 ft)

ti

Example 5.3.7. SCBF Maximum Force Limited by Foundation Uplift

YnUll

= 910

·' .

.•, r

'

I

-A· =(.!. ft)(6.50 fl)(35.0 ft) 12 =152 ft3

Given:

, Vio•I o•a "-

Some of the sections in the AISC Seismic Pro~isions allow the required strength of certain members or components to be limited by the forces corresponding to a maximum force that can be delivered by the system. One example is AISC Seismic Provisions Section P'2.3, Exception (2)(b), which states that the required strength of the column need not exceed the forces corresponding to lhe resistance of the foundation to overturning uplift. The max.imum force that can be delivered is the force required to overturn the foundation. The use of Section P2.3 Exception (2)(b) will be illustrated in this example.

V,tob ow ltUll

the SCBF eleva1ion shown in Figure 5-21. Determine the maximum force Lh:u cam be delivered to (:olumn CL-1 based on the foundation uplift resistance of the system. The seismic loads at each floor are given in Figure 5-21. Assume a concrete density equal to 150 lb/ft3 and a soil density equal to 100 lb/ft. 3 As given in Example 5.3.3 for !he SCBF column design, the column fore~ at the base from gravity and snow loads are: PD= 147 kips, PL= 60.0 kips, Ps 7.00 kips. The relevant seismic parameters were given in the SCBF Design Example Plan and Elevation section.

rt3

=(~ n)(6.SO ft){35.0 ft) =75.8 fl3

Usipg the densities given, the weights of the mat, soil and slab are:

Refer to

W,,.a,

=910 ft 3

(1so lb/ft3)1(1,000 lb/kip)

= 137 ltips

=

~~~ ~ . ....:..----i~ 25'-0"

Solution:

Roof

Dead Load Resistance to Overturning

91 kips

The volumes of the mat, soil and slab are:

ct_ Upper and lower column shaft

f,.1

W12x45

Fourth Level

57 kips

Third Level -

30 kips

"I,; ~•.. l

·. {

(~ 1

Weld access hole per AJSC Specification Section J1 .6 (typ.) W12x96 25'-0" Note: Erection aids not shown for clarity. Fig. 5-20. SCBF coltu11n splice designed in Example 5.3.6.

fig. 5 .21. SCBF elevation and foundation. AMEJUC/\N ~STl"IVTS OF STEEL CONSTRUCTION

BRACED FRAMES

.5-138

3

3

Wsoll over 11111 1 = l 52 ft (100 lb/ft ) I (1,000 lb/kip)

S-139

..:

S.3 SPECl.AL CONCP.NTRICALLY BRACED FRAMES

"

The overturning momenl caused by the seismic loads given in Figure 5-21, and including ovcrstrength, is:

=15.2 kips Me,.,.

3 3 Wslab over""''= 75.8 ft ( 150 lb/ft ) I (1,000 lb/kip)

:dloL;./ih; _

l30.0 kips(l 4.0 ft)+ 57 .0 kips(26.5 ft)+ 84.0 kips(39.0 ft)l

20 - · + 91.0 kips(5 l.5 ft)

=11.4 kips Summing moments at the extreme lower right comer of the mat allows estimation of the maximum moment required to overturn the foundation.

·

= 19.800 kip-fl For convenience, use the concept of an effective oversirength factor, n~. determined as follows:

Dead Load kips

Element Cone. Mat Soil over Mat

Slab over Mat Column Cl-2 Column CL·l };

live Load

Moment

kips

Snow load kips

-

-

137 15.2 11.4 147 147

60.0 60.0

-

-

-

-

7.00 7.00

Ann

Resisting Moment (0)

Moment (L)

ft

kip-ft

kip-ft

17.5

-

30.0

2,400 266 200 735 4,410

300 1,800

35.0 210

-

8,010

2,100

245

17.5 17.5 5.00

-

Resisting

Resisting Moment (S) kip-ft

-

-

ASD

LRFD

n;=

Me Q no, =--0 Me_.

Me n o Me.,.

=20.200 kip-ft (2.0)

= 12,300 kip-ft (2.0) 19,800 k.ip-ft

19,800 kip-ft =2.04

=1.24

From Ex.ample 5.3.3. the seismic component of the required column streo~th .based. on the seismic loads is Pa 248 kips in tension or compression. Rather than amplifying this force by n = 2.0 as sh~\vo in Exnmple 5.3.3, it could instead be amplified by. 1.24 (LRFD) 0 or 2.04 (ASD) as allowed by AISC Seismic Provisions Section P2.3 Excepuon (2)(b). For determining the required ax.ial compressive strength, the controlling load combinations that include seismic load are ASCE/SEI 7 Section 12.4.3.2 Load Combination 5 for LRFD and

=

The (;Ont.rolling load combinations (for compression in the column) that include seismic load axe ASCFJSEI 7 Section 12.4.3.2 Load Combination 5 for LR.FD and Load Combination 6 . for ASD. Setting the ovenurn.ing moment, ME, equal to the resisting moment in these load combinations, the overturning moment required t0 cause uplift of the foundation is:

\

l

Load Combination S for ASD.

LRFD

ASD

LRFD (l.2+0.2Sos)Mo +Me +0.5ML

(1.0+ 0.105Sos )Mo +0.525M E

+ 0.2Ms =0

Me =1-[i.2+0.2(1.o)]MD·- o.5MLI -0.2Ms -(1.2+0.2(1.0))(8,010 kip-ft) =

- 0.5(2,100 kip-ft) - 0.2(245 kip-ft)

= 12,300 Jc.ip-ft

The required axial compressive strength

+0.75ML +0.75Ms =0

i'.fe=

1{-[L0+0.105(1.0)]Mv

I

- 0.15ML -0.75Ms }/0.525 {-1.105(8,010 k.ip·ft) ::: - 0.75(2,100 kip·ft) I -

0.75(245 kip-fi)}/0.525

= 20,200 kip-ft

The overturning moment required to cause uplift of the foundation, Me. should be compared ~o the overturning moment caused by the seismic loads including overstrength, ME.,..· If ME is less than Me_.. then the seismic component of the required column force in Example 5.3.3 could be reduced by the ratio of those moments.

ASD

I

of the column is:

Pu =(l.2+0.2Sos)PD + n~PQe _ + 0.5P,. +0.2P, =(1.2+0.2(1.0)](147 kips)

P0

=(1.0 + 0.105Sos)Po +0.5250~Pa.+ 0.75PL +0.75P,

.

"

= (1.0 + 0.105(1.0))(i 47 kips)

+ 1.24(248 kips)+ 0.5(60.0 kips)

+ 0.525 (2.04)(248 kips)

+ 0.2(7 .00 kips)

+ 0.75(60.0 kips)+ 0.75(7 .00 kips)

= 545 kips

!

The required axial compressive strength of the column is:

I

··!

=478 kips

For determining the required axial t.ensile strength of the column, ASCEJSEl 7 S~~on 12.4.3.2 Load Combination 7 for LRFD and Load Combination 8 for ASD apply. A suru.lar approach is used to calculate the maximum tension force in the column ~ue to foundauon uplift. Re-calcufating Me for the governing load combination for tension m the column:

.J

"··-'

5.3 SPECIAL CONCENTRICALLY BRACl!t> FR.AM-e5

BRACED FRAMES

l

...

Relevant seismic design parameters were given in lhe SCBF Design E."
LR.FD (0.9-0.2Sos) Mo +Mc= 0

I I.

Mc =l-I0.9-0.2(1.0)]Mol

ASD

Elevation section.

·~

The complete connection design is shown in Figure 5-22.

(0.6-0.14Sos)M 0 +0.1Me -0

ME =l-[0.6-0. 14(1.0)]Mo/0.71

=l-[0.9-0.2(1.0)j(S,010 kip-ft)!

=l-0.46(8,010 kip-ft)/0.71

= 5,610 kip-ft

=5,260 kip-fl

Solution: From AlSC Manual Tables 2-4 ansl 2-5. the material prop
ASTh1A36 F1 =36 ksi F., - 58 ksi

Use an effective over:.trength factor, similar to I.be compression case, calculated as:

LR.FD

n~Mc fl 0 0 -

Ms 0 0,.._ ME,..

ME.,. .

= 5,610 k.ip-fi (2.0) 19,800 kip-fl

=0.567

. .

·11

~.

ASD Q 0

= 5,260 kip-fl (2.0)

HSS6x0.312 brace

19,800 kip-fl

=0.531

LRFD

ASD

The required axial tensile strength

The required .Wal tensile strength

of the column is:

of the column is:

P., =(0.9-0.2So.))P.o + n; P
'

Pa= (0.6-D.14Sos)P.o +o.1n;PQ£ = [0.6-0.14(1 0)}(147 kips)

+ 0.7(0.531)(-248 kips) =-24.6 kips

As Stated in the Exception to AJSC SeiSmic Provisions Section F2.3, the required strength of the columns does not need to exceed the forces corresponding to the resistance of the foundation to overturning uplifl These forces are smaUer than. the required strengths of the column as determined in Ex:imple 5.3.3, and could have been used as the required strengths for tbe design of the column. I: t

..

Flat Bar 1!7"lt1~· (A572 Gt. 50) (1-NS. 1-FS)

Example 5.3.8. SCBF Brace-to-Beam Connection Design

~-:

Given: Refer to Joint IT- I in_Figure 5-11. Design the connection between the braces and the beam Use :m ASTM A36 welded gussel plate concentric to the .braces Md 70.ksi electrode:. to connect the bmces to the beam. Use ASTM A572 Grade '50 material for braec reinforcement. All bmces m ASTM A500 Grade B round HSS ao
Fig. 5.zz. Futal conru:ction tksignfor Example 5.3.8.

1

AJ.tEIUC~ 11'1~ OP Sn:J!l.. COH5lllUCTION

5-142

ASTM A500 Grade B

Therefore:

Fy =42 ksi F.., =58 ksi

P,,,.Jton

ASTMA992

Fy =50ksi

.)

- ; ,p.:

.

Fu= 65 ksi From AISC Manual Tables 1-1 and 1-13, the geometric properties are as follows:

=0.312 in.

HSS6.875x0.500 0.500 in.

=

"'

.•·

For the braces above the beam, the required strength of the bracing brace is in tension is:

tc1es

=0.291 in.

A= 5.22 in.2

r=2.02 in.

Ide:

=0.465 in.

A= 9.36 in.2

r = 2.27 in.

Ptmnon

=0.570 ln.

=RyFyAg = 1.4(42 ksi)(9.36 in. )

k.ks =. 1.53 in.

""550 kips

For the braces below the beam, the required strength of th~ ~m1ci.ng c~nnecti?ll wh~u the . ;· "·. · · ' . · ··. brace is in tension is:

factor (relative to the requirements of Section F2.3) applied to the required strength of Uie connection. · For these SCBF connection examples, the .requirements of AISC Seismic Provisions Sections B2 and F2.3 will: be used for both LRFD and ASD, except for the limit state of compression .buc~ing on the Whitmore section, "which will use the 1.1 factor specified in AISC Seismic Provisions Section F2.6c(2}. lbe required strength of the bracing connection due to seismic loading is based on ASCFJ SEI 7 ~ection 12.43.2 Load Combination 5 (LRFD and ASD) with 0 0 0£ = Em11, as discussed m AISC Seismic Prpvisions- Section P2.3.

Determine the expected tensile strength of the braces The brace connections must be designed to develop the larger force.s determined from the two analyses specified in .AISC Seismic Provisions Section F2.3. The required tensile strength of the connection ill based on the expected strength.

.

.

For the HSS6x0.312 brace above the beam: From AISC Sei~mic Provisio(IS Table A3. l:

Pa= 0.7Emh =0.7(307 kips) =215 kips

2

fJ = 0.930 in.

AISC Seismic Provisions Sections F2.3(i) and F2.3(ii) define the two mechanism analyses: · that must be considered in determining the required stren8th of beams, columns and connections. AISC Seismic Pr.ovisions Section F2.6c specifies the required strength of bracing connections. for the required compressive strength, Section F2.6c(2) has an additional 1.1

Ry= 1.4

when the

For the HSS6.875x0.500 b r ace below the beam:

W27x114 lw

c~nnection

ASD

P., =l.OE,,,Jt =LO (307 kips) =307 !Ops

Beam

d = 27.3 in.

~·

LRFD

Brace (below the beam) fnom

l

=RyFyAg =1.4(42 ksi)(s.22 in.1) =307 kips

-

Brace (above the beam) HSS6x0.312 fncm

5-143


.

ASD

LRFD Pw =l.OEmh =LO (550 kips) = 550 kips

-

Pa= 0.7£,,,h = 0.7(550 kips)

\

\

'~' • r

.

=385 kips

j

l

...

·'•

Determine the expected strength in compression of the braces · for detennining the expected strength of.the brace in coripr~~s~.on, RyFY. is ~s~d)n liyu of Fy-for the dete~tion o{ Fcre a~cording, t~ AJ;~C Seismic Provisi~tp .Sect_J.on F2.3. The brace length usep for the.detennination. ~f Fcremust notexcee? .tbe distance from brace end to brace end. Estimate that the length of the connections will reduce the brace length to approximately 12 ft. This will be verified once th.e connection is ~mplete. Th_erefore, a length- of 12 ft. will be used to detennine the brace expected strength m compressJon.

·.

1 . . .. J

For the HSS6x0.312 br3ce above the beam:

Use AlSC Specifica!Wn Chapter.E with F., = RyFy to determine Pere. as follows:

KL

-= r :=

1.0(12.0 ft)(12 in./ft) 2.02 in. 71.3

...

5-144

.... 1

~

BRACF-D FRAMES

4.71JR EF =4.71

29,000 ksi

If

1.4{42 ksi)

1 1

For the braces above the beam, the required st.renglh of the bracing connection when I.be brace is in compression at its post-buckling strength is:

=105

r

!

:I

_ 7t

-

2

(Spec. Eq. E3-4) For the HSSG.875x0.500 brace below the beam:

(29,000 ksi) (71.3)2

KL

:· ·:·

F.n"[0.658

T

¥. jn,F,

1.•1•l

f

(from Spec. Eq. E3-2)

••i))

As caJculatcd previously, 4.7lJ E RyFy

=105.

KL ~ When -~4.71 --: T R)Fy

= 0.658 sm,; (1.4)( 42 ksi )

=38.0 ksi The e~pected compressive strength of the braces above the beam is: Pco.,,,pns.rion =

1.0(J 2.0 ft){l 2 in.lft) 2.27 in . ::::63.4

-=

= 56.3 ksi

........

= =47.5 kips

=67.8 kips

1t2E

(~Lr

t ..:·:.

P,,=0.7Emh 0.7(67.8 kips)

Pu ==-1.0ErnJi =1.0 (67 .8 kips)

1 1

f't=--

;

ASD

LR.FD

.7JJR EF :

When: KL $; 4

s-1.;s

5.3 SPECTAL CONCENTRICALLY BRACED FRi\MES

1. 14 Fcr~Ag

rr.2E

(Spec.

F.---

e-(~Lr

Eq. E3-4)

n 2 (29,000 ksi) (63 .4)2

= 1.14(38.0 ksi)(5.22 in. 2 )

= 226 kips

=71.2 ksi

And the expected post-buckling strength is:

\

\

I

0.3?.:omprmion

=0.3(226 kips)


=67.8 kips ...{d ... ,

th:

For _braces abov~ th.e beam, the required strength of the bracing connection when the brace ism compression is based on Em1t equal to the lesser of R F. A and 1 l 4F: A d ing to AISC s · · p . . Y 1 g • ere 1 accor • . . e!S.m1c rovis1ons Section P2.3; therefore, use£,,,,.= 226 kips.

f

f..

= 0.658~ 1(1.4)(42 ksi) [

=41.6 ksi

The expected compressive strength of the braces below the beam is:

The required strength· is:

Pcompr~sslon

LRFD P,, - I.OE,,.,,

=LO (226 kips) =226 kips

~·

>!

...

~

•!

., I

l:·,•, '

('

J

ASD

Pa= 0.7£...J, =0.7(226 kjps) = 158 kips

= I. l4Fc,.Ag 2

= 1.14(41.6 ksi)(9.36 in.

)

=444 kips And the expected post-buckling strength is: 0.3Pto11iprmi<>1t::: 0.3(444 ldps)

=133 lcips

5- 146

BRACED FRAMES.

Por ihe braces below the be~, the required strength of the bracing connection when the brace is in compression is based on Ent11 equal to the lesser of R1 FyA1 and 1.14FcreA accord! 1 ing to AISC Seismic Provisions Section F2.3; therefore. use E,,.,, 444 kips.

=

LRFD

ASD

I',, = I .OEmJo = 1.0 (444 kips)

= 0.7(444 kips)

=311 kips

For the br~s below the beam, the required strength of the bracing connectfon when the brace is in compression at its post-buckling strength is:

LRFD

ASD

Pu= l.OEmh =1.0 (133 kips) = 133 kjps

Pa =0.1Emn = 0.7(133 kips) = 93. 1 kips

Top Brace-to-Beam Connection Tue required tensile strength of the connection is based upon RyFyAg of the braces as stipulated in AISC Seismic Provisions Section F2.6c(l). All limit states applicable to tension or compression in lhe brace must be checked.

The limit state of shear J\Jpwre in the brace wall is used to deternUne the minimum bracegusset lap length. Note that lhe expected brace rupture strength, R,F"' may be used in the determination of lhc available strength according to AISC Seimtic Provisions Section A3.2.

1

Using AJSC Specification Section 14.2, including R1 from AISC Seismic Provisions Table A3.1:

R,= l.3 (from Spec. Eq. J4-4) In this equation, Anv is taken as the cross-sectional area of the four walls of the brace, Anv 4lt.us. Therefore:

l

=

t

Rn= 0.60R,Fu(41t,us)

.....

The lwo sets of forces are shown in Figures 5-23 and 5-24.

226 kips (LRFD) 58Jcips(ASO) compression)

l

Determine the minimum length, I, required for the brace-gusset lap

Pa -:::.0.7EmA

=444 kips

'

5- 147


~

307 kips (LRFD) 215kips (ASD) ' / (tension) /

67.8 kips (LRFO) """

~ 7.5 kips (ASO)

"~)

i

307 kips (LRFrO)

215 kips (ASO) (tension)

..

l

··:

/.650

ki~s (l.RFD)

385 kips (ASD) · (tomion)

....,,, 444 klps (l.RFO""

311 kips (ASO)

(compression)

Fig. 5-23. Required strength of bracing connections according to A/SC Seismic Provisions Sectioa F2.3(i).

kips (IBFO) / ~50 iss kips (ASO) (tension)

133 kips

(LRFO~

93.1 kips (ASOl

(compresslon)

"""'

Fig. 5-24. Requirtd st~ngth of bracing con11eclicns according to A/SC Seismic Provisions Section F2.3(ii).

.

.... 5-148 ~=

BRACED FRAMES

S-149

5.3 SPECIAL coi-:cENTRJw\l.1.Y BRACED FRAMES

. Setting Lhe aV".i.ilable shear rupture strenglh equal to the required censile strenglh and sotv: ing for the minimum lap length, /:

. l.

.,.

\

t. ••

LRFD l~

~

:·

:.

Pu

l~

~

•,•·

•.· :·.

OPa 0.60RrF..(41deJ) 2.00(2 15 kips) 0.60(1.3)(58 ksi)(4)(0.291 in.)

~ 8.17

~7.77 in.

:.I

..

ASD

$(0.60)R,F;, (4tJu) 307 kjps 0.75(0.60)(1J)(58 ksi)(4)(0.291 in.)

Since the gross sheru- area, Agv. and the net sbenr area, A,,.,, are equal in this case, the shear yielding component, 0.60F_,A1,,, is smaller than the shear rupture component, 0.60FuAm.. and the right side of the ~untion controls.

0.60F1 Agv =0.60F1 (2)1tp

-

= 0.60(36 ksi){2)(15.0 in.)(tp) I

= 648/p

I

in.

=1.0F,.Dbraulp

UbsFuAnt

=l.0(58 ksi)(6.00 in.)(tp) =348/p

Note that this length is the minimum required for !he limit state of shear rupture in the brace wall. A longer length may be used when designing the fillec welds between the brace and the gusset plate, if desired, to allow a smaller fillet weld siz.e as is implemented in the following. Size the weld between the brace and the gusset plate

The s~en~th of fillet welds defined in AlSC Specijicarion Section J2 can be simplified, as explained in Pan 8 of the AISC Manual, to AISC 1\-lanual Equations 8-2a and 8-2b:

LRFD I

~

307 kips 0.75(648 kip/in.+348 kip/in.)

~0.411

Rn

n

=0.60FyAgv +UbsFuAnt <:::Pa n

2.00(215 kips)

Ip~ (648 kip/in.+348 kip/in.) ~ 0.432 in.

in.

•0.928DI

1

Try A-in. fillet welds for the four lines of weld, which can be made in a single pass:

LRFD 4(1.392)Dl <::: P,,

$R11 =0.75(0.60f'.vAgY+Ub,F.,,f\,i,) ~Pu tp ~

ASD

ASD

LRFD

ASD 4(0.928)D/ <::: P0

Check required gusset width and thickness based on the limit state of tensile yielding Tensile yielding is checked on a section of the gusset plate commonly ~ferred to as tJ~e Whitmore section. This section is explained in AISC Manual Part 9 (Figure 9-1) and m Thornton and Lini (2011). Because the'. widtb and thickness of the gusscl plate have not yet been chosen, the minimum area will be-. determined for this limit stale. The nominal tensile yielding strength is:

l~

307 kips 4(1.392 kjp/in.)(4 sixteenths)

<:::13.8 in.

t

215 kips l <::: 4(0.928 kip/in.)(4 sjxteenths) ~

14.5 in.

-Rn.Q

~P,.

QFy

~

Check block shear rupture of the gusset plate The available strength for the limh state of block shear rupture is: R,, = 0.60F11 A11 v +UbsFuAn.1~0.60F,,A1v +UbsFuAni

I

307 kips 0.90(36 ksi)

OPa

P,.

Use (4) 15-in. long. \4-in. fillet welds to connect the brace above the beam to the gusset plate.

i:. I• •

~: ;:: I..

QR.

fp\Vp~-

j;

ASD

LRFD

The designs in lRFD and ASD give slightly differenl required lengths of ~eld. For convenience, the more conservative result will be used in subsequent calcula1ions and in I.he final design. ln practi~, designers should consistently use one Jllethod or the other.

~-

(Spec. Eq. J4-l)

2

tpWp ~-F., ~ 1.67(215 kips)

.

36 ksi ;::. 9.97 in. 2

(Spec. Eq. 14-5) AMf.RlCJIH b-ISTllVTl! OP S'Jlll!l. CONSTRUCTION

.

I I

_J

5-150

A gmset plate IA-ill be chosen that has a width on the Whitmore section, wp. of 12 in. and a thickness, tp. of~ in. This meets the minimum required gusset plate thickness for the Ii niit

state of block shear rupture calculated previously. Check that the bracing connection can accommodate brace buckling according to A/SC Seismic Provisions Section F2.6c(3)

The requirements of AISC Stismic Provisions Section P2.6c(3) 3re met through the use of option (b): rotation capacity. As e.'tpl3ined in the U~r Note of that se~tion and in the Commentary Figure CF2.9, accommodation of inelastic rotation is accomplished with the bnice tenninating before the line of restraint. Figure 5-22 shows the 2r clearance beyond the end of the brace. The choice of a relatively small Whitmore ~ction resuJts m a tapered gu~~et, which i'I beneficial because it allows the brace to be located closer to the beam while stilJ accommodating brace rotation by providing a 2t clearance per AfSC Sejsmic Provisions Section F2.6c(3) and Commentary. Check the maximum Whitmore section

As explained in AISC Manual Part 9, the maximum width of the Whitmore section that can be considered effective is defined by a 30" spread to each side, but not exceeding the nctual width of the gusset plate. To make sure tbat the 12.0 in. width chosen previously can be cnnsidercd effective in tension, check the maximum Whitmore section. Wp

S Dbraa + 2L tan30°. S 6.00 io.+2(15.0 in.)tan30° = 23.3 in.

12.0 in.

~

23 .3 in.

o.k.

Therefore, tbe 12 in. width and acceptable.

* in. tluckness for the gusset plate chosen previously is

The actual angle of the gusset edge, measured relntive to the centerline of !he brace, is: ,,. - tan -l[~(ll'p-Dbrace)] ,.. _

I

=ran-i['h02.0 in.-6.00 in.)] 15.0 in.

=11.3° Note: I.his angle I.hat is smaller than the Whitmore section angle of 30" provides a more compnct gusseL

Using 3 gap of 1,1'6 in. on each side of the brace slot to alJ~v clearance for erection: A,, = 5.22 in.2 -2[* in.+2(Yi6 in.)j(0.291 in.)

=- 4 .64 in.2 From A tSC Specification Table 03.1, Case 5. because I> l.3D, U

= 1.0, and the effective

net area is:

~ =1.0(4.64 in.2 )

=4.64 in.2 race reinforcement is required. The approxilllate area of reinforcement Because A • < A g· b • · red u · d A · th area remoYe
Assuming a value of U = 0.80:

A,

Am =Q.80-A.,

=5.22 in.2 _ 4.6-i in.1 0.80

=l.89 in.2 · x 1 1·n nat bMS with 3 total area of 2.00 in.1 AlSC Seismic Provisions Section • • • be t F2.5b(J)(i) re~ that the specified .mini.mum yield strength of the reinforcement a lhat 1of the brace; f.herefore, use ASTM A572 Grade 50 material for the Oat bar. The cross-sectional geometry is shown in Figure 5-25.

Try two 1 10.

ie:st

Dbroc•

lui

r1 =-2-- l

,

\

6.00 in. 0.291 in. =~2

·~

=2.85 in. Dbrac• 1.00 in. r2=--+~

2

6.00 in. 1.00 in. =-i-+~

=3.50 in. The distance to tho centroid of a pnrtial circle is given by:

I

.:<

l

Check brace effective net area

From AISC Sti.rmic Provisions Section F2.5b(3), the br.ice effective net llJ"Ca, A., shall not be less than the brace gross area, A1 .

.... ,

BRACED FRAMES

where the total arc of the partial circle is 20 and 0 is meas ed · d. I · l"gh I I ' ur m ra 1ans. A though th~ 1 ce is s I Y ess th~ a ~I half-circle because of the slot :is shown io Figure 5-25, use : angle, 0, of rt/2 for s1mphc1ry. This is slightly unconservative for calculating the value of e shear lag factor, U. A more precise calculation could be perfonned using the exact angle,

bra

= l.81 in.

=4.64 in.2 + 2(1.00 in.)(1.00 in.)

xfor the composi1e cross section.

'

1?

=6.64 in. 2

x

A

xA

Part

in.

111.

in.

Half of brace One flat bar

1.81

2.32

3.50

1.00

4.20 3.50

.E

-

3.32

7.70

i

J

.

2

Ae =UAn

3

=0.845(6.64 in. 2 )

=5.61 in.2 > 5.22 in.2

o.k.

Design welds connecting (fat bars to brace According to AJSC Seismic Provisions Section F2.5b(3)(ii), the flat b:ir must be connected to the pipe brace to develop the exp~ted strength of the flat bar on each side of the reduced section (the expected yield strength, RyFy. is used here). The reduced section is the length of the HSS from the extent of the slot (dimension x of Figure 5-22) to the start of the HSSto-gusset weld. The required strength of the weld is based on the expected flat bar yield strength, using R7 from AISCSeismic ProvisionsTab1eA3.1 for ASTM A572 Grade SO bars. For ASD, use 1.0/1.5 of the expected strength of the flat bar reinforcement.

- I.xA x=-LA

=

x

An = An(broce) +Arn

=3.50 in.

f

From AJSC Specification Table 03.1, Ci:ise 2, which applies to round JJSS with reinforce-

.mot added:

=

{rc/2) rad

Detennine

. ~..

U=l-1 _ 2.32 in. 1 15.0 in. =0.845

=2. 85 ID. sin(tt/2} rad) . ( _......_.;.....,,'----

Xbrace


7.70 in. 3 3.32 io. 2

=-2.32 in.

ASD

LRFD I

RyFyAfl, =d.l(SO ksi)(t.oo in.2 )

-

.-

I

I

R1 FyAJb I 1.5 =1.1 (50 ksi )(1.00 in. 2 ) 11.5

=36.7 !Gps

= 55.0 kips

There is a small gap of approximately 0.041 in. between the face of the pipe brace ~d the edge of the Ont bar, as indicated in Figure 5-25. Since this is less than 1116 in., it can be neglected according to AWS Dl.l clause 5.22.1. A single-pass ¥16·in. fillet weld can be used.

;·:.

With two welds, the length of Y.6-in. fillet welds connecting the flat bar to the brace is determined from AJSC Manual Equations 8-2a and 8-2b as follows:

LR.FD 55.0 kips 1 _ "' - 2(1.392 kipfm.}(5 sixteenths) Fig. 5-25. Cross section of brace abo1·e ben. at ne1 sec11on. · ~·11 AMEIUCAN 1NSTITUT8 OF STEEL CONSTRUCTJON

ASD lw =

36.7 kips 2(0.928 kipfm.)(5 sixteenths)

J'

..__=_3_._9S_i_n._ _ _ _ _ _ _ _ _.__=_3_.9_s_m. _ _ _ _ _ _ _ _ __

.O~l\\.J;:)J

!•KAM.SS

Use a l in. x l in. flat bar with ¥16-in. fillet welds; the derail extends past both sides of lli~ reduced section of the brace. The flat bar fillet weld develops the expected strength of the bar on each side of lhe end of the brace slot. The brace slot may be longer than the slot length by a maximum erection clear.ince of x inches (see Figure 5-22), as detenni.ned by the fabricator. The length of the flat bar wilJ be 4.00 in. + 4.00 in. + x in. 8.00 in. + x in.

=

From Figure 5-22, the buckling length, which is taken along the brace centerline {Dows well. 2006), is lb 8.00 in. (Example 5.3.10 provides an equation for calculating the length of ~ck.ling; h:re it is detem1ined graphically.) AJSC Seismic Provisions Section F2.6c(2) spec1~es a required compressive strengrh for buckling limit states that is at least equal to J.1 times the expected brace strength in compression for LRFD. The stress over the \Vbitmore section, using the 'Whltmore width of 12.0 in., is:

=

= 23.7 ksi

=307 kips(cos45°)

=215 kips(cos45°)

I'

= 152 kips

=217 ldps

The nonnal (tension) force is: LRFD

ASD

Nu= 307 kips(sin45°)

Na= 215 kips(sin45°)

=152 kips

I

!s: LRFD

r=iii t

M,, =Nu(l.5 in.)

:.i in.

=m =0.253 in. Recommended values for the effective length factor, K, are given in DowsweU (2006). However, that paper doea not address t!1e case Of a single gusset plate with the 2t clearance to accommodate brace buckling [called an°extended" gusset plate io DowsweU (2006)]. Therefore, in this case, use K = 1.2 from AISC Specification Commentary Table C-A-7.1 assuming that the gusset plate is fixed at one end and free to translate but not rotate at ilbe other. With 1,, = L: ·

KL

Va

l.2(8.00 in.)

-=------', 0.253 in.

ASD

Ma-= Na (1.5 in,)

= 217 kips(l .5 in.)

= 152 k.ips(l.5 in.)

=326 kip-in.

= 228 kip-in.

Check the gusset and design the weld at the gusset-to-beam flange interface The forces are:

LRFD

ASD

Shear Vu

=217 kips

=152 kips

Normal Nu

=217 kips =326 kip-in.

Moment M.,

Normal Na

I

=152 kips

MomentMa=228 kip-.i_n.

=37.9

Interpolating from AlSC Manual Table 4-22:

LRFD $cFcr =30.0 ksi > 23.7 ksi

ASD

o.k.

Fer =20.0 ksi > 16.6 ksi nc

~

t

}i

12.0 in.(* in.)

= 16.6 ksi

The radius of gyration of the gusset plate

1--~~~-LRFD ~~~~--t~~~~-AS_D~~~~,. t

i· The contact length between the gusset plate and the beam top flange, as shown in Figure 5-22, is 21.0 in. and the brace line of action tnisses the centroid of the contact length by 1.5 in. due to the incre
f; _ 1.l (158 kips) aa -

Based on I.be required tensile strength of the bracing connection (which is larger than the required compressive strength), the shear force at tbe interface of lhe gussec with the beam flange is:

=217 kips

ASD

f; _ I. 1(226 kips) 0 " - 12.0 iu.('Vs in.)

Determine the forces at the gusset-to-beam interface

Vu

Check the gusset plate for buckling on the Whitmore section

LRFD

5.3 SPl:.L:lAL. l.UN(...J::.N 1Ki\..ALI...'X U.KA\..tlJ rK.AMi::.=>

o.k.

The momenl, Mu or Ma, and the nonnal force, N., or Na, can be combined to give an equivalent normal force, Nu,q11 tv or Na#qufv· This equivalent tension assumes a plastic stres~ distribution for the moment, Mu or M0 , which is similar to the stress distribution in the welt! assumed in the inelastic method of the AlSC Manual Part 8 eccentrically loaded weld group tables. On one half of the contact length, the srress due to the normal force, N., or Na. anc' the srress due to the moment are additive. On the other half, !he stresses are in oppositt

5-156 BR.ACED FRAMES

5.3 SPECIAL CONCENTRlCAU.Y BRACED FRAMES

directions. For convenience of calculations, one of the forces in lhe force couple (du t the moment, M~ or Ma) is i~agined reversed so the enti.re cont<1c1 surface is in uniform ~e~ion or compression. The equ1valent normal force is:

..

LRFD N,,,l/ldv

=N,, + 4M,, =217 kips+ 4(326 kip-in.)

~~ ·

=279 kips

.,

=21.6 ksi > 11.s ksi

'"

= 152 kips+ 4(228 kip-in.) 21.0 in . = 195 Jcips

21.0 in.

~~ ~-

LRFD

=

o~

.

.

n

\

o.k.

9=

_ Na;qui• aa---tplb

=

(~

195 kips in.)(2 1.0 in.)

-

=10.6ksi

The design tcn~ile yielding stress from AISC Specification Section J4.1 is:

The allowable tensile yielding stress from AISC Specification Section 14.1 is: F..,

q,Fy= 0.90(36 ksi)

Q

__

36 ksi 1.67 = 2 l.6 ksi > J0.6 ksi

-..:..::;:

o.k.

ASD

1

~:""')

S=tao

t:in - ( N..

-J(Natqui\•) --Va

/.

279.kips in.)(21.0 in.)

= 32.4 ksi > 15.2 k si

o.k.

LRFD

In cension

=15.2 ksi

I

.

0.60(36 ksi) 1.50 = 14.4 ksi > 8.27 ksi

Size gusset-to-beam weld

ASD

In tension

. tplb

0.601-~

--=

The angle of the resultant force can be calculated and used in the directional strength increase of fil1e1 welds according to AISC Specification Equation J2-5 as follows:

f: · The gusset stresses are:

f ua z:: NH9ui•

The allowable shear yielding stress from AlSC Specification Section 14.2 is:

¢0.60Fy= 1.00(0.60)(36 ksi)

Natquiv = N a + 4Mo --

.."..

~!

The design shear yielding stress from AlSC Specification Section J4.2 is:

ASD

ASD

lb ,

.

LRFD

o.k.

= tan _ 1 ( 279 kips) 217 kips

=Ian -I ( 195 kips) 152 kips

= 52.1°

=52.1°

AISC Specification Section J2.4 :illows an increase in lhe available strength of fillet welds when lhe angle of loading is not along the weld longitudinal axis, which is used in lhe following calculation. The weld ductility factor, equal to 1.25, which is explained in AlSC Mw1ual Part 13. is applied here. Using AlSC Manual Equations 8-2a and 8-2b, the m1mber of sixteenths of fillet weld required is: \

LRFD

LRFD In shear

JllY = v..

tplb

~-

" :i. :~;

.'(:...

..."

:~

217 kips =(~ in.)(21.0 in.) =11.8 ksi

ASD

ASD

D,~q·J

Drtq'd 2:

In shear

l.25~N;,9.,,.., +VJ

2(1.392kip/in.)(l + 0,5sin 1·s 9)(lb)

fav = Va t plb

=

L25~(279 kips)2 +(217 kips)2

152 kips Oi i.n.)(21.0 in.)

2(1.392 kip/in.)(l.35)(21.0 in.) = 5.60 sixtcenlhs

=8.27 ksi

2:

1.25~N';,quiv +

v;

2(0.928 kip/ in.)(1+0.5sinl.S 0)(lb) 2

2

;: l.25J(195 ldps) +{152 ldps) 2(0.928 kip/in.)(1.35)(2 l .O in.)

=5.87 sixteenths

'

An alternative fully plastic approach to Uie gusset-to-beam stresses is shown in the following cnJculations and presented in lhe !BC Sm1cturoVSeismic Design Manual (SEAOC' 2006), where lhe normal and bending stresses are assumed to act over separate portions of

AMERICAN lNSTlTVT!l OF STEa. CONSTRUCTION

tlKACCD f"RAMEs ~

.

.w;

/...,


tl~e ~on~ct length, lb, an.d are set equal to eacb other in order to result in a unifo -~ "'-! distnbuuon as shown in Figure 5.26. · rm strcs1 ~ From Figure 5-26,

M

th~ mom,enl about the center of th~ contacr length,

lb, is:

=F'[ •;'+•)(2)

l~ '~

:

p I

I

M0

N., =217 kips

N 0 =152.kips

kip-in-r +(10.5 in.)2 = (326 217 kips

e

so,

= ( 228 kip·inl+ (10.5 in.)2

e

152 kips

-( 326 kip-in.) 217 kips

F' =.!:!._

·a+e

..I.;

= 228 kip-in.

Mu= 326 kip-in.

I

= F' (a+. e) -

ASD

LRFD

-( 228 kip-in.) 152 lcips ::::: 9.11 in.

= 9.10 in.

and Therefore:

F'

lb=--(a-e)tp M

·-

00 -

=13.6 ksi

N

fub-

2etp

-

.

!c10.s in.)2- (9.10 infl(%in.)

J. ob -

e~~(~r +a2 -(~)

....

t •.'

-:-;

.-::;

228 kip-41. [c10.s in.)2-(9.11 m.)2 J(1i i~.)

l •:

=13.6 ksi

Setting/a =lb and solvlng for e:

...

152 kips 2(9.11 in.)(% in.)

= 9.53 ksi

326 kip-in.

la=-.·.

f. _

J. _ 217 kips "° - 2 (9.10 in.)(* in.)

Likewise, from Figure 5-26: .

ASD

LRFD

. :~}

= 9.56 ksi

As required, fa= fb = 13.6 ksi (LRFD) and approximately 9.53 (ASD).

l

Compare this to 15.2 ksi (LRFD) and ici.6 ksi (ASD) using the simpler. method. The sim- · · pier method is about 12% (LRFD) or :\1% (ASD) conservative.

For this _example:

Using !he plastic method to check (normal) force as:

a -21.0 - - 'i11. 2 =IO.Sin.

th~ requ~red weld size, define an equivalent tensile

,,;

·i\: I

ASD

LRFD

'l

1--~~~~~~~~--~~~.,..+-~~~~~~..,--~~~~~~-=-1

N~u;uiv = (13.6 ksi)(21.0 in.)(Ys

in.)

N~equiv =(9.53 ksi)(21.0 in.)(Ys in.) = 175 kips

= 250 kips

0 Gusset-to-beam interface

8

=

tan-1(Nu~~uw)

=tan- l (250 kips)

0

Lit

=tlll-J (175 kips)

''·'~ ·":\

152 kips

=49.0°

Fig. 5-26. Fully pl.astic stress distribuiion on gusser-10-bea.m interface. AME!u.CAN

lNsnnm; OF STEEL CONSTRUCTION

l l l.

=tan-l ( N~~=uiv)

217 kips

=49.0°

1·'.)

AMERICAN JNS'ITJ'\lTtl OP S'T'Elll.. CONS'l'l!UCTION

'!'.~)

1

5-160

LRFD

= L25J(250 k:ips)2 +(217 kips)

f,;.. l

2(21.0 in.)(L392 kip/in.)

x

'

ASD 2

Dreq'd

5- 161

5.3 SPECIAi.. CONCENTRICALLY BRACED FRAl\iES

1

(1.0 + 0.Ssinl.5 49.0°) = 5.33 sixteenths

Dru/d

= l.25J(175 kips) 2 +(152 kips)2 2(21.0 in.)(0.928 kip/in.)

x

II.

·080•~ 1+3(~ J(:; r]t:."' = 0.80(0.570

in.)2 lJ +3(

1

(i.o + 0.5sin1.s 49.0°)

x

=5.60 sixteenths

1

(Spec. Eq. 110-4)

0 570 0 2 1.0 '. ·)1.5 27.3 m. 0.930 in.

~·)( ·

j

29,000 ksi(50 ksi)(0.930 in.) 0.570 in.

f ~~~~"--~-'-!..~~--'-

=842 kips

This result is within 5% of lhe simpler method and both will require a * -in. fillet weld. The plastic method is slightly less conservative than rhe more co~runon simple method lt· can always be used for these calculations but will not be pursued further in tl1is Manual.. Use a "1bs-in. fillet weld on each side of tlle gusset at the gusset-10-beam connection for brace a ove 1he beam..

lb~

ASD

LRFD

Rn

¢Rn = 0.75(842 kips)

-

= 632 kips

> Nu t.qlliv = 279 kips

842 kips 2.00 = 421 K:ips

-=

o.k.

'

n

>Na equiv= 195

ldps

o.k.

Check beam web local yielding

For a force applied at a distance from !he end that is greater than the depth of the member:

Rn= Fy..-tw (5k+ lb) 1

11

!{::

.. (Spec. Eq. Jl0-2)"

=5.0 ~si(0;570 in.)[5(1.53 in.)+ 21.0 in.] =817.kips

·

LRFD

> Nuequw = 279 kips

l,,

"

For rhe HSS6.875x0.500 below ilie beam, the required strength of the bracing connections was determined at the beginning of this example.

ASD

=817.kips

o.k.

Bottom.Brace-to-Beam Connection

The required tensile strength of !he connection is base_d on RyFyAg of the braces as stipulated in AISC Seismic Provisions Section F2.6c(l). All limit states applicable lO tension or compression in the brace must be checked.

·

This completes the design of the top brace to the beam. Figure 5-22 shows the configuration.

Rn = 817 kips Q 1.50 = 545 kips

> Na•quiv =195 kips

Determine the minimum length, /, required for the brace-gusset lap The limit state of sh~ ~pture in the b\-ace wall is used to detennine thte mini.mum prace-

o.k.

Web. local yieldina applt"es t_o both tension · and compression loads. Web local .. cri lino . o _ 0 applies only to the compression loads, but the lan?er tension Load 1·5 used h · ,, pp · If d · · "" · ere 1or convenience. · _es~red, the compressive strength of the brace could be used for web local crippling_ Check beam web local crippling

gusset lap length. Note that the expe~ted brace rupture strength, R1Fu, may be used according to AISC Seismic Provisions Section A3.2.

Using AISC Specification Section J4.2, including R1 from .A.lSC Seismi~ Provisions Table A3.l: . : ' . . .

R, =1.3 (from Spec..Eq. J4-4)

For a force applied greater than a distance of d/2 from the beam end:

Jn this equation, Am, is taken as the cross-sectional area of the four walls of the brace, A,.,,= 4ltdes· Therefore: R,,

=0.60R,Fu(4ltd~s)

Setting the available shear rupture strength equal to U1e.required tensile strength and solv ing for the minimum lap Jeogth, l: ., :~

..%

AMERICAN .INS1TIVTE OP Sfi!EL CONSTIUJCJtON

AMElUCA.~ lJ'ISITJ1JTI) OF STEEL CONSTRIJC110N

LRFD 1'2:. ~ ~

ca A are equal in this case. the- shear Since the gross shear area, AH"' and the nets h ear ar • ""' yielding component, 0.60f).Ar• is smaller than the she:\t rupture component. 0.60F.,Anv,

ASD

P.,

I '2:.

t(0.60)R, F., (4ldcz) 550 kips

'2:.

0.75(0.60)(1.3)(58 ksi)(4)(0.465 in.)

~

8.71 in.

and the right side of the equation controls.

uPa 0.60R,Fu (4rdts)

Ubs

=LO

2.00(385 bps)

=

0.60F1 Ar 0.60F1 (2)1tp

0.60(1.3)(58 ksi){4)(0.465 in.) 9.15 in.

Note chat this length is lhe minimum required foe 1he limit stare of shear rupture in the brace wall. A longer length may be used when designing the fillet welds between the brace and the gusset plate. if desired, to allow a smaller fillet weld size as is implemented in lbc following.

U~F11 An1

=0.60(36 Jc.siX2X25.0 in.)tp =1,0&0rp =l.OFNDbructlp = 1.0(58 ksiX6.875 in.)tp

=399/p

Size the weld between the brace and the gusset plate The strength of fillet welds defined in AISC SpeciJiration Section J2 can be simplified, as explained in Part 8 of the AISC Manual, to Equations 8-2a and 8-2b:

LRFD

I

tR.. =139201

I

~

Ip

-0.928Dl

LRFD

/~ ~

550 kips

4(0.928)D/ ~ Ta [ ';?.

24.7 in.

-

385 kips

4(0.928 kip/in.)( 4 sixteenths)

\

I

I

Rn

-

n

=

Ip ~

0.6F1Ar +UbsF.,A111 '
n

2.00(385 kips) (1,080 kip/in.+ 399 kip/in )

~ 0.521

in.

in.

the limit state of tensile yielding I I eferred to as the Tensile yielding is checked on n section of the gusset p ate common Y r . Whltmore section. This section is e.'\plnined in AISC Manual Part 9 (Figure 9-1) and in · (201 l) B•..ause the width and thickness of the gusi;et plate have not yet · """ · al ii Thornton an d Liru been chosen, the minimum area will be ~etcrmined for this limit s~te. The nomm tens e yielding strength is:

(Spec. Eq. 14-1)

~R,.'
Ai

R,. =0.60F.A11v + UbsF.,A.u ~ 0.60F1 Ap t- U1>1 F.,A,.,

.

'2: P,.

$F, 550 k.ips '2: 0.90(36 ksi)

The available strength for the limit state of block sh~ rupture is:

(Spec. Eq. J4-5)

ASD

LRFD

Use (4) 25-in. long, 'A-in. fillet weld! to connect the brace below the beam to the gussei plate.

Check bloclc shear rupture of the gusset plate

.·

Check required gusset width and thickness based on

";?.25.9 in.

The designs in LRFD and ASD give slightly different required lengths of weld. Use the LRFD result in this example. In practice, designers should consistently use one method or the other.

I

~

550 kips 0.75(l,0&0 kip/in.+ 399 kip/in.)

~ 0.496

ASD

4(1.392 kipfm.)(4 sixleenlhs)

~R,, =0.15(0.60F1Agv + UbsF,.A,.,) ~ P,.

ASD

Using 1A-io. fillet welds for the four lines of weld so that they can be m:\de in a single pass:

4(1.392)DI '2:. T.,

ASD

LRFD

'2: 17.0 in.2

R,. '2:P.,

.

..

n

' .

UPo A,'2:T 1

l 67(385 lcips) '2: 36 ksi '2: 17.9 in.

2

}:.

BRACED FRAMES~

Choose a reduced Whitmore width, w1 , of approximately twice the brace width. This doe3 not exceed the ma.umum Whitmore width descn'bed in AISC Manual Part 9. Therefore, wp = 14.0 in. and the gusset plate thick:uess is: LRFD

loJl1•

5.3 SPECIAJ... CONCENTRICALLY BRACED FRAMES

5 - 165

. a tota1 are.'\ o f 4.50 in·l AJSC Seismic Pro1·isio11s · 11L · flat bars wuh Try lWO Jlh m. x.) n in.. that the • . ·mum y1·etd strength of the reinforcement spe ..-"'ed -u i n:uru ( Section F2.5b(3) l requires . ASTM A572 Grade 50 material for the flnt bar. be at least that of the brace; therefore, use Tue geomecry is shown in Figure 5-27.

ASD Dbraet

Ag

tp~-

ldu

r1::-2--2

>Ag

fp--

Wp

' wp 2

l 7.0 in. = 14.0 in. =l.21 in.

=

17.9 in.

6.875 in.

0.465 in.

2

2

2

=3.21 in.

14.0 in.

= 1.28 in.

Db>oce

1lh in.

6.875 in.

11h in. +-2-

r2=~+-2-

The minimum required gusset thickness for this limit state is higher than 1he minimum required for rb~ limit stste of block shear as calculated previously.

.,

Using the LRFD solution, a l ~-in.-1hick plate is selected for the gusset plate. below lhe

-----i~:

beam.

The distance 10 the centroid of a partial circle is given by:

Check brace effective

net area

From AISC Seismic Provisions Section F2.5b(3), the brace effective net area, At, should noi be less than the brace gross are:i, Ag. Tims:

~11

. '!••;"·

Using a gap of Yi6 in. on each side of the slot to allow clearance for erecrlon: 2

= 8.08 in.2

_ ri sin 0 x=--0

. . . 20 and 0 is measured in radians. Although the f the slot as ~hown in Figure 5-27, use where the total arc of the partial c1rc~c is be' . li h I less than a full balf-ctrCle cause o . brace 1s s g t Y . . 'ghll servntive A more prtCi~e calculal!on an angle, e, ofrc./2 for simplicity. This is sli y uncon .. could be perfonned using the ex:ict angle.

_

A,, = 9.36 in. - 2(1'.4 in.+ 2('1t6 in.) ](0.465 in.)

X/m1co

.

.

.

From AISC Specificarum Table 03. l, because l > l.3D, U =1.0, and 1he effective nee area i s: ~

= 2 =4.19 in.

. ( sin(it/2}rad)

""3.21 m.

"'2.04 in.

(1t/2)rad

I

I

I

=UA,,

=J,0(8.08 in.2 ) =8.08 io.2 Becaure A.,
Am = ~- A.. 0.80

' ;"

.;

I~

.

9.36 in. 2 -8.08 in.2 0.80 =3.62 in.2

, OJ·'the braet: below rite beam at rhe net sectitm. Fig. 5-27. Cross section AMEJUCAN }NS"JTttfTI! OF Stt.1!1. CONSTRUCTJO~

BRACED FRAMES .

Xrt

=r2

r

=4.19in. Derennine

:-d •)

;

A in. 2

Part

in.

Half of brace One flat bar

4.19

4.04 2.25

r

-

6.29

2.04

R1 F1 Afb

I

LRFD

ASO

=1.1(50 ks1)(2.25 in.2 ) =124 kips

R1 F1AJ1>11.5= 1.1(50 ksi)(2.25 in. 2 )11.s

?,

x for the composite cross section.

5-1611


::: 82.S kips

I

1·

XA in. 3 8.24 9.43 17.7

There is a smnll gap of approitimately 0.081 in. between the face of the brace nod the edge of the flat bar as shown in Figure 5-27. Since chis is more than 1/16 in., the fillet weld of the Oat bar to the brace would be increased by the fabricator by 'li6 in. (see AWS D 1.1 clause 5.22.1). Thus, to keep the weld as a single pass weld, '/.-in. fillet welds can be used and the Oat bar length on each side of the reduced section of the brace, x, is determined using AlSC Manual Equations 8-2a or 8-2b as follows:

_

:ExA

x=--

LRFD

rA

17.7 in.3

I _

=6.29 in.2 =2.81 in.

w-

124 kips 2(1.392 k.ip/in.)(4 sixteenths)

=l l.l in.

From AISC Specification Table D3. I, Case 2, which applies to round HSS with reinforcement added:

x

U=l--

l

=1_ 2.81 in. 26.0 in.

I _

82.5 kips

w-

2(0.928 kip/in.)(4 sixteenths)

.

=11.lin.

Use a 1lh in. x l 'h in. flat bar with 1A:in. fillet welds; the detail extends 11 \.1 in. past both sides of the reduced section of the brace. Figure 5-22 shows a 1A-in: fillet weld for the flat \ bar to HSS weld. Note that fabricators typically assume the weld given on detail dr.lwings ~· to be the weld required for strength. Therefore, the gap between the edge of the flat bar and the curved brace, which is greater than 1/i6 in., will cause the shop to increase the fillet weld size to ·'116 in. The flat bar fillet weld develops the expected yield s~ength of the bar on each side of the reduced section of the !)race. The brace slot may be longer than the slot length by an erection clearance of x ~ches (see Figure s,22).as determined by the fabricat!'.>T. The length of the flat bar will be a minimum of 11 'h iii. + l l 1h in. + x iJ1. = 23.0 in. + x in.

=0.892

A,, =An(brpa) +Am

=8.08 in.2 + 2(2.25 in.2)

=12.6 io.2 ~

ASD

Check the gusset plate for buckling on the Whitmore section .

=UA,,

=0.892(12.6 in. ) =11.2 in.2 >A,= 9.36 in.2 • 2

o.k.

Design welds connecting fist bars to brace According to AISC Seismic Provisions Section F2.5b(3)(ii), the flat bar must be connecLed to the brace co develop the expected strength of the flat bar on each side of the reduced section (the expected yield strength, RyFy, is used here). The reduced section is the Jenglh of the HSS from the extent of the slot (dimension x of Figure 5-22) to the strut of the HSSto-gusset weld. The required strength of the weld is based on the expected flat bar yield strength, using Ry from AJSC Seismic Provisions Table A3. l for ASTM A572 Grade 50 bars. For ASD, use 1.0/l.5 of the expected strength of the flat bar reinforcement.

From Figure 5-22, the buckling length, which is taken along the brace centerline (Dowswell, 2006), is lb = 10.0 in. (Example 5.3. JO provides an equation for calculating the length of buckling; here it is determined graphica!Jy.) AJSC Seismic Pro1:isions Section F2.6c(2) specifies a required compressive strength for buckling limit states that is at least equal to l.l times the expecte
LRFD

J ..:

~

J. _

1.1(311 kips) "" - 14.0 in.(l ~ in.)

= 14.0 in.(l v.. in.)

=27.9 ksi

..

~·~

ASD

l.1(444 kips)

f,,o

J.

.

=19.5 ksi

l:i

5-16ll

BRACED FRAMES

The radius of gyration of the gusset plate is: r-

5.3 SPECIAL CONCBNTRICAI l..Y URACPD T1lAMES

5-16<1

by I in. due to 1he increasing width of the gusset plate. Therefore, the moment on the contact surface is:

Ip

-Ji?_

.f··

LRFD

Iiµ

=m

,,;:.....

M., = N.. (1.0 in.)

=0.361 in. Recommended vaJues for the effective length factor, K. Ille given in Dowswell (2006). HoweYer, that p3per does not 3ddress the c3se of a single gusset plate with lhe 2J dear.me~ to accommodate brace budding {called an "extended" gusset in Dowswell (2006)]. Therefore, in !his case, use K = 1.2 from AISC Specification Commc:nlJ.r}' Table C-A-7.1 assuming that the gusset plate is fixed at one end, and free to translate but not rotate at the other. With 10 = l:

_____..

KL r

-=

.:,· ·-

ASD

N.,(l.O in.)

=389 kJps(J .0 in.)

= 272 kips(LO in.)

=389 kip-in.

= 272 kip-in.

Combining the moment. M 11 or M.,, and the normal force, N,, or N,,, into an equivalent normal force as explained for the dei.ign of the brace above the beam:

LRFD Nuft/ldv =

l.2(10_0 1n.) 0.361 in.

Jfa =

N,,

ASD

4M +-11

No<'qu;.,

lb

=389 kips+ 4(389 kjp-in.)

=33.2

= 272 kips+ 4(272 kip-in.) 24.0 in. 317 kips

24.0 in.

ln1erpol:11ing from AISC Manual Table 4-22:

9, 1''c, =30.6 ksi > 27 .9 ~i

~1 1 .1

~ f

'

ASD o.k.

~ = 20.41.:si > 19.5 k~i

....

~;

•.•

~,. · ~:

The gusset stresses are: o.k.

Determine th~ forces at the gusset-to-beam interface

Based on the required ten!>tlc strength of the bmcing connection (which is larger tlun lhc re-imrcd compressive strength) for the brace below the beam, the shear force at the interface of the gusset with the beam bottom flange is:

V.,

ASD

=550 kips(cos 45°) =389 kips

1

Va= 385 kips(cos45°) = 272 kips

ASD

J. -

NII !'f'I•

"" -

1plb

=550 !Ops(sin45°) =389 kips

.

ASD No = 385 k:ips(sin 45°)

=272 ltips

The contoct length bctwceo the gusset plate and the beam bottom na.oge. as shown io Figure 5-22, is 24 .0 m. and the brace line of action misses the cenlroid of the contact length

.hoo-- N.~ lplb

\

454 kips (l 1A in.)(24.0 io.)

=

=

317 ldps (1 ~ in.X24.0 in.)

= 10.6 ksi

=15.L ksi

The design tensile yielding stress from AISC Specification Section J4. l is:

=32.4 ksj > 15. l ksi

LRFD N,,

ln tension

The allowable tensile yjelding stre~s from AISC Sp~cification Secrion J4. l is:

F

36 ksi 1.67 = 2 l.6 ksi > 10.6 ksi

1 =-Q

~F1 = 0.90 ( 36 ksi)

The normal (tension) force is:

=::

I -

LRFD In tension

LRFD ~:

=

=454 kips

LRFD

4Ma =N.,+-lb

o.k.

o.k.

5-170

BRACED FR.Al\
LRFD In shear

J.w-..:. v..

=

=13.0 ksi

2(1.392

272 kips (1 lA in.)(24.0 in.)

1,

0.60Fy

$0.60F1 = 1.00(0.60)(36 ksi) = 21.6 ksi > 13.0 ksi

The allowable shear yielding stress from AISC Specification Section 14.2 is:

Q

o.k.

0.60(36 ksi) 1.50 = 14.4 ksi > 9.07 ksi

I'

o.k.

v:

•.

Z

i.25JN0 , 911 +

k.ip/in.)(1+0.5sin1•5 0)

1,

=9.07 ksi

The design shear yielding stress from AISC Specification Section J4.2 is:

Duq·d ~

l.25JNutqul~ +

lplb

389 kips (l IA in.)(24.0 in.)

ASD

D,~q'd ~

Va /av=-

tplb

5-171

LRFD

ASD

In shear

=

5.3 SPEC.IAL CONCENTRICAl.LY BRACED FRAMES

v;

2(0.928 kip/ in.)(J + 0.5sin1•5 0) (111 )

(lb)

= 1.2sJ(454 kips ) + (389 kips )2 2(1.392 kip/io.)(1.33)(24.0 in.)

=l.25J(317 kips}2 +(272 kips)2

= 8.41 sixteenths

=8.81 sixteenths

2

2(0.928 kip/in.)(1.33)(24.0 in.)

Use a o/16·in. fillet weld on each side of the gusset at the gusset-to-beam connection for the brace below the beam. · Check beam web local yielding

For a force applied at :i distance from the end that is greater than the depth of the member:

The angle of the resultant force can be calculated and used in the directional screngtb increase of fillet welds according to AISC Specification Equation 12-5.

LRFD

..

. 0 =tan-I ( Nu~:uiY)

'

0=

tan-1 [Na~:11iv)

= tan- 1 (3 17kips) 272kips

=49.4°

=49.4°

AISC Specijica1ion Section J2.4 allows 3.n mcrease in the available strength of fillet welds when the angle of loading js not along the weld longitudinal axis, which is used in the fol-

·:

l

=50 ksi{0.570 in.)!5(1.53 in.)+24.0 in.J =902 kips

ASD

=tan-• (454 kips) 389 kips

(Spec. Eq. Jl0-2)

Rn =Fywt.,..(Sk+lb)

Size gusset-to-beam weld

·:

LRFD

1.

ASD Rn

q>R,, = 1.00(902 kips)

-

Q

= 902 .kips > Nueq11iY =454 ldps

o.k.

.

902 kips 1.50 = 601 kips >No equiv= 317 kips

I.·. ,,

·o.k•


lowing calculation.

Web local yielding applies to both tension and compression loads. Web local crippling applies only to the compression loads, but the larger tension load i's used here for.cqnvenience. If desired, the compressive strength of the brace could be used web local crippllng: .

The weld ductility factor, equal to l.25, which is explained in AISC Manual Part 13, is applied here. Using AISC Manual Equations 8-2a and 8-2b, the number of sb\te~nths of fillet weld required is:

For a fo.rce applied greater than a distance of d/2 from lhe beam end:

for

r

R,, =0.80t! 1+3(; )( :; JE~:'I = o.soco.s10 in.)211+3(24.o

xJ29,000 ksi (50 ksi)(0.930 in.) =906 kips

(Spec. Eq. Jl0-4) · ·

~·)(o.510 ~-)I.SJ

27.3 10. 0.930 ID.

0.570 in.

\

I\

I~ ,,,

.

l

[

.. ~1

S-172

BRACED FRAMES

~R,.

= 0.75(906 kips) = 680 ldps > N,,,'I",. =454 kips

Cf. bay

ASD

LRFD R,,

906.ldps

n

2.00 = 453 kips

-=

o.k.

~upper gusset

l(f lower·gusset

,

'

5-1 73

S.3 SPEClAJ. CONCENTRlCN..LY BRACED FRAMES

,,

:! '

> Na
o.k.

Figure 5-22 shows lhe final configuration. Beam Web Available Shear Strength

,,

:·

Figure 5-28 shows the shear distribution in the beru.n web due to the gusset vertical cornpo-ncnts. The design of the top gusset shown earlier in this example was based on the expected. strength in tens!on, but this force is not simultaneous with tension in the bottom bra<:e (as shown in Figure 5-23). Therefore, for checking the beam web, I.he br:ice below the beam will be considered to be in tension and the brace above the beam will be considered to be in com: pression. For the brace. in tension below the beam, the forces .at the gusset-beam interface have already been calculated. For the brace in compression above the beam, the forces at the gusset-beam intefface are:

I 7.62 kip/in. I

: 2.18 kip/in.

W.P. '

1•

I

I 2'Y.2"

---===:i=~'=-==---

16.,2 kip/in. 2.70 kip/in.

~

ASD

LRFD NonnalN,,

Shear V.,

=226 k.ips(sin45°) =~60 kips =226 kips(cos~5°)

=160 kips MomentM., =Nu(l.50 in.) =160 kips(l.50 in.) =240 kip-in.

11

... . Normal Na "" 158 kips(sin 45°)

~pg kip-in ...... ...._-'-L._

=112 kips

::

Shear Va

= 158 k.ips(cos45°)

=112 kips

.

Moment Ma= N 0 (l.50 in.)

· =112 k.ips(l.50 in.)

.

I

,

ASD

Vu = (226 kjps+5SO kips)(siu45°)

=549kips

Vo =(158 kips+ 385 k.ips)(sin45°)

I I I I I I I I I

1 I I

11 11 11

The braces to the left of the beam centerline, where the brace below the beam is in tension as shown in Figure S-23, result in the hjgbest shear force. The total vertical shear at the beam centerline is: ·

' l~: 1 I

11

= 168 kip-in.

LRFD

389 kips

11 1I 1I 11 11 11 11

I 1

~

11 11

1 I 343 ki~ 1I

0 kips

Shear diagram

v

542 kips Fig. 5-28a. Beam shear due lo gusset forces (LRFD).

=384 kips

AMSIUCAN .INsrmJTS OP Sn;a CoNSTRVCTION

5-174

BRACED FRAMES ~ bay

~ upper gusset

•-

5.3 SPECIAL CONCENTRICALLY BRACT.l> FR.AMES

S-l i

From AISC Manual Table 3-6, the available shea:r strength of the W27x114 is:

, ~lower gusset

LRFD ~.vn

I 5:33 kip/in.

: 1.52 kip/in.

v.u (x') =34 3 kips +

11.3 kip/in.

ASD

10.5 in.

(for 0 :S x' $10.5 in.)

I

l I I I

l

I

'!~ I

:::: 240 kips+(13.2 kip/in.)x'

I :::

(for 0 $ x' $ 10.5 in.)

}'.:

-----11

,.....------LRFD ____ . ··- -. - -- ---A-S-D-.

I I I I I I

r

,

x =

Ii

Va (x') ::: 311 kips

V., (x')::::: 467 kips

I I I

467 kips - 343 kips 19.0 kip/in.

x

--~-----~

,

311 kips - 240 kips 13.2 kip/in.

=--~------

I

I·>

= 6.53 in. '. :::: 5.38 in. ..___ ______ ......__ _ _ _ _ ____,I }·:!

I

I I 1x l

l"l

"'·. {379 kips - 240 kips) I . x Va ( x ') :::: 24 0 NPS + . x' ) · · 10.5 m. ;;

Setting this shear equal to the available shear strength of the beam and solving for x' to find om where the beam available strength is adequate resUltS in:

I

I I

l·::

(542 kips - 343.kips) ,

=343 kips+(I9.0 lcip/in.)x'

1.89 kip/in.

I I I I I I

n.g.

< 384 kips I•

LRFD

I 2~"

~72 kip-in.

n..,

n.g. .

BecbauFse the beam avaifable shear strength is not adequate, a doubler plate is required on th{ 1.. we . com Figure 3-28a and 3-28b, measuring x' as shown, the equation for the shear, V, in the region of inter~st is:

I

11 .

I

-Vn= J 11 k.ips

= 467 kips

< 549 Jqps

,.........~,.......~~:!;::#::!;::!;::!;:~ · 1

ASD

okips v

· Shear diagram

384 kips Fig. 5-28b. Beam shear due to gusset forces (ASD ).

AMERJCAN INsmvre OP STEa CONSTRIJCnON

The distance from the beam centerline to this point is:

-12-.5-in-.-_-6-.5-3-in-.-~-5-.97-in-.

Ii-

A_?~-~2-in-.----1 1

------111-12-.5-in-.-_-5.3-8-in-.___

Use a 14 in. x 14 in. doubler plate centered on the web as shown in Figure 5-22.

J

5-176

Based on shear yielding and AJSC Specificarion Section J4.2, lhe plate ihickness required i~ determined as follows:

LRFD D

LRFD

ASD

=(LOOX0.60X36 ksi)(l4.0 in.}(rd) =302td kips

n

1.50

= 0.60(36 ksi)(l4.0 in.)(td)

The required doubler plllte shear

\ .

~6

549 kips - ~67 kips= 82.0 kips Setting lbe available strength equal to 1he required strength and solving for ftf:

~ ~I I .,

i}

The re-quired doubler plate shear strength is: 384 kips - 311 kips= 73.0 kips Setting the available strength equal to the required strength and solving for rd: ~

2! 82.0 kips Id

302 ]ti pl.in. =0.272 in.

Id

73.0 kips 202 kipfm.

= 0,3,61 in.

U sing the instantaneous center of rotation melhod of AlSC Manual Part 8, use Table 8-8 with 0 ::: 0° to determine the strength of welds on the doubler plate. For a channel-shaped weld on half of the doubler plate, the geometric variables are:

i•.

=7.00 in./14.0 in. :::::0.500 =0.125(14.0 in.)= l.75 in. :::5.25 in .

a =0.375

By interpolation, AlSC Manuol Thble 8-8 with 0 = 0° gives: C= 3.35

1:

..<:

=3.11

Use a Pl 3/e in. x 14 in. x 1 ft 2 in.. with IA-in. fillet welds. Comment: The length of the brace used to de1ennine the c~pectecl strength of bolh brdces was 12 ft. This length shouJd be verified once !he connection design is complete. For bo1h braces, the length of tbe brace with a 12.5-fl s1ory height :ind a 25-ft bay as shown in Figure 5-1 l is: 2

l = J(12.5 ft) + (25.0 ft 12)

2

= 17.7 ft

From Figure 5-22. with a pull-off dimension of 27 1h lit. at both ends of the 1op brace. the actual unbraced length of the hr.tee is: L= 17.7 ft -2(27 1h in.)(l ft/12 in.)

=13. l ft

end :is required by AJSC Seismic Provisions Section F2.3,

=7.00 in. - 1.75 in.

From AISC Manual Table 8-3. C1

=2.33

2.00(73.0 kips)

=(3.35)(1.00)(14.0 in.)

Therefore, the length of 12 ft used for 1he determination of the expected compressive strength of I.be brace is adequate because it does not exceed the actual length from brace end-to-brace

;•

~=

82.0 lcips 0.75(3.35)( l.00)(14.0 in.)

L ""' J7.7 ft- 2(30.0 io.)(I ftll 2 in.) =12.7 ft

e:r=of

..'..·

CC1/

unbraced length of the brace is:

kl= 7.00 in. ~l

~cc,1

Por the bottom brnce, with a pull-off dimension of 30 in. at both ends of the brace, the actual ·

l =14.0 in.

k

=

'

nvdoMbla 0,,,J,,=

1.50

= 202td kips strength is:

ASD

_ Vdc>ubter n1111-

i ~

~ _ 0.60F,Ar

~Rn= 1.00(0.60FyA,rv)

iI

5-I TI

S.3 SPEClAL CONCFNTRJCAU.Y f\RACEO FRAM ES

= 1.00. The fillet weld size required is:

The reduced Wh.iunore section used in this ex.ample greatly reduced I.be size of I.be gusset plates, at the e.x.pense of the gusset thickness. l1ris is usually B good trade-off, bm if a lighter beam were used it is possibJe that the beam web local yielding or local crippling checks would have failed. A beam web doubler plate would then be necessary for one or both of these limit states. This doubler requirement can usually be avoided by increasing the .gusset-U>-beam interface lcnglh by focreasfog I.he Whi1more section (the maximum width that can be considered effective.. as explained in AJSC Manual Pan 9, is limited to the width on a 30° spread). The rc3der should keep in mind that there is not just one way 10 design these connections. Any method that s:uisfies equilibrium and the applicable limit states is an acceptable method.

BRACED FRAMES

Example 5.3.9. SCBF Brace~to~Beam Connection Design Given:

An alternative design for Example 5.3.8 at Joint JT-1 of Figure 5-11 is presented here. Example 5.3.8 used separa\e gusset plates for eacb brace, while this example uses continuous "chevron type" gusset plates for !he top and bouom braces as shown in Figure 5-29. This is a common arrangement for this sin1ation, and the example provides an admissible internal force distribution that differs from the distribution used for the four separate gusset plates. All braces are ASTM A500 Grade B round HSS and lhe beam is an ASTM A992 W27x114. For the connection, ASTM A36 plate material and 70-ksi electrodes are used. Solution:

=

ldtz

=0.291 in.

fdn

Beam W27x114 d= 27.3 in.

11=0.930 in.

t,. = 0.570 in.

r = 2.27 in.

= 0.465 in.

kiUz = 1.53 in.

From A1SC Manual Table 2-4 and 2-5, the material properties are: ASTMA36

r

F1 =36 ksi

F., =58 ksi

j. I;

F1 =42ksi ,. . , =58 ksi

r= 2.02 in.

ASTMA992

F1 =50 ksi F., = 65 ksi

46"

For brace-t<>i)usset information not shown, see

HSS6.875x0.500 (brace below the beam) A =9.36 in.2 IM>n = 0.500 in.

ASTM A500 Grade B

From AISC Manual Table 1-1 and 1-13, the geometric properties are: HSS6x0.312 (brace above the beam) A= 5.22 in.2 lncm 0.312 in.

5-179

5.3 SPECIAL CONCENTRICALLY 'BRACED FRAMES

The complete connection design is shown in Figure 5-29.

~symmeby

AlSC Seismic Provisio11s Seciions F2.3(i) and F2.3(ii) define the two mechanism analy-

Figure 5-22 HSS6x0.312

HSS6x0.312

W27x114

beam

·- ~beam

ses lbat must be considered in determining the required strength of beams, columns and

l.

connections. For this example. only the mechanism analysis of Section F2.3(i) will be considered. AISC· Seismic Provisions Sections F2.6c specifies the required strength of bracing connections. For the required compressive strength, Section F2.6c(2) has an addjtional 1.1 factor (relative to the requirements of Section F2:3) applied to the required strength of 1he connection.

(

I '.

For these SCBF conne<:tion e.'<.amples~ tbe requirements of AISC Seismic Provisions Sections B2 and F2.3 will be used for bo~h LRFD and ASD. Determine the expected strengths of the braces

HSS6.875x0.500 brace

The calculations for brace expecte9 strengths w~re shown in Example 5.3.8 and are not repeated bere. The required strengths are g.i\•en in the following and shown in Figure 5-30. For the HSS6>.-0.312 brace above the beam: For the braces above the beam, the required strength of Lhe bracing connection when the brace is in tension is:

LRFD

51"

-

Fig. 5-29. Connection with chevron gusset plates designed in Exaample 5.3.9.

P., = 1.0Em11

=307 kips

ASD'

Pa =0.1Em1t =0 .7(307 kips) =215 kips

:

I ...

5-180

·~

BRACED FRAMES

307 kips (tension)

226 kips (compression)

t

~

..

For lhe braces above che beam, the required strength of the bracing connection when the brace is in compression is:

/

LRFD

Pu =l.OEmA =226 kips

...

;

/

550 kips (tension)

'.~

11 ·

.,.

I~

~


Fig. 5-30a. Required strength of bracing connecrians according to AI.SC Seismic Provisions SeCJion F2.3(i) for LRFD design.

;


215 kips (tension)

/

-

~.:

!: . "

:~

Pa=0.1£,,,h = 0.7(550 kips)

=550 kips

=385 kips

'

I

For the braces below the beam, the required strength of the bracing connection when the brace is in compression is:

LRFD

ASD

P., =l.OEm11

P0 =0.7Emh

= 0.7(444 kips)

'·

..

l

I

Pu= l.OEmh

=311 kips

Brace-to-gusset design

~; !:.

!i "!~·

ASD

=444 kips

J .

~I

LRFD

'·

.

!~

-

For the braces below the beam ~ the required strength of the bracing connection when the brace is io tension is:

p

•.

Pa= 0.1EmJt =0.7(226 kips) = 158 kips

For the HSS6.875x0.500 brace below the beani:

..

l

.'

ASD

.

.

~··

S-181


/

385 kips (tension)

~


Fig. 5-30b. Required strength of bracing connections according ro AJSC Seismic Provisions Secrion F2.3(i) for ASD design.

The brace-to-gusset design is exactly the same as for the design shown .in fjgure 5-22 and is n-01 repeated here. The gusset checks involving the Whitmore sections in Example 5.3.8 are conservative for the geometry in this example, as shown in Figure 5-29, because the gusset plates in this condition have a wider Whitmore width with the same plate thickness . Therefore, the gusset thicknesses previously chosen, ~-in.·thick plate for the top gusset and l 'A-in.·thick plate for the bottom gusset, are satisfactory. For the case of chevron gusset plates in this e.-
5-182

5.3 SPECIAL CONCENTRICALLY BRACED FRAM.ES

forces on section a-a. Subsequcn'ily, the gusset is cut :it its centerline at se.ction b-b. as shown in Figure 5-3lc, which also shows the forces on this interface. Horizontal and vertical force components and moments without a prime symbol act on section a-a. Components and moments with a prime symbol act on section b-b. Because there are four braces with four different loads and two gussets with different geometry, Figure 5-31 in11oduces a sign convention as a means. of keeping track of all the quantities. All of the force qu3ntities are shown in the positive directions in these figures. If a quantity calculates as negative, it acts in a dfrection opposite to chat shown. Alternatively, the designer can work with basic problem-specific free body diagrams. For lhe moments M1 and Mi, which act on section a-a, M1 is considered positive when it acts in a clockwise dir~tion, whereas M2 is considered P.<>Sitive when it acts in a counter-cloc~ise direction. Consequently, the total moment on seecfon a-a is the difference between those two moments rather lhan the sum, where

Plate thickness = t

L

Fig. 5-3Ja. Chevron brace gllSsetforcts.

Mi =H1e+Vi6 M1 = H2e-Vz6

D.

= h( L2 - L1)(Note: 6 1

is negative if L 2 < L1)

The moments M1. and M2 are due to the brace forces P1 and P2. respectively, and are taken abouc the midpoint of section a-a, with brace forces resolved at the common work point. The moments Ml and M2. also due to the brace forces P1 and P2, are taken at the midpoint of section b-b, as illustrated in Figure 5-3lc, where

Forces on section a-a Normal: N

=Vi + V2

Shear: V =Hi - H2 Moment: M

=M1 - M2

Ml= 1hLV.- 1!4hH1 - 1hM1 M2 = 1hLV2 - Y..hH2 - 1hM2 Fig. 5-3/b. Forces on section a-a (positive direction shown).

The derivation of M{ and M2 can be illustrated by considering half of the gusset plate, as shown .in Figure 5-3lc. Internal forces from both brace forces are considered evenly distributed across section a-a. The sign convention used in this example is as follows:

• Pi and P2 are positive for tension and_negative for compression • If P1 is positive, V1 and H1 are positive also • If Pi is negative, V1 and Hi are negative also • If P2 is positive, V2 and H2 are positive also • If P2 is negative, V2 and H2 are negative also

I

I

\

Forces on section b-b Normal: N' = 'h(Ht + H2)

= h(Vt -V2)-~M. L Moment: M' =M{ + M2.

Shear: V'

1

/

Fig. S-3/c. Forces on section b-b (positive directions s/U>wn).

J

~ lo'/

5-184

BRACED FRAM.ES

From Figure 5-31c, the forces on section b-b can be derived (note 1hat the brace force P2 and its components do not act direcOy on the half-gusset shown as the }'1 force does, but is shown for completeness). For horizontal equilibrium:

5.3 SPECIAL CONCF.NTRICALLY BRACED FR.AMES

S-IS5

M' =-Hi(e+ !:)-Vit.+~ Vh+.!.NL+.!..M 2

4

8

2

=-Hie- H1 (~)-Vit.+.!.h(H1 -H2)+.!.L(V1 + V2)+!(M1 -M2) 2 4 . 8 2 l I 1 1 l · =-L(Vi + V2)--hH1 +-hH1 --hH2 +-(M1 -M2)- H1e - V1.6 8 2 4 4 2

Therefore:

. v

=.!_L(Vi + V2)-_!_hH1 _.!._hH2 +.!.Mi _.!_M2 -(Hie+ V1.Ll)

N'=--+H1 2

I

=--(H1 -If2)+H1 2 .

8 . 4 4 2 2 l . l l 1 =-L(Vi + V2)--h(H1 +H2)+-M1 --M2 -M1 8 4 2 2

=Ml+Mi

For vertical equilibrium: V' + 2M + N _ Vj :::: O L 2 1

Design of gusset above the beam

Therefore:

TI1e required strengths shown in Figure 5-30 represent external loads acting in a left-to-right motion. With external Jqads reversed, the brace expected strengrhs in compression and tension will b.e .rever$e.d but the effect on the gusse.t plate will be equivalent. _ _

V'=- 2M _ N +Vi L .

2

2M

I

= - - - -(Vj +V2)+V1 L 2 2M· l l =-- --Vi--V2+Vi L 2 2 l 2M ='2(Vi-V2)-T

For the geometry shown in Figure 5"29 for the gusset plate above the beam for general terminology:

l1 =Li =23.0 in.

For moment equilioriurn, with moments taken abou't tbe midpoint of section b-b and brace forces acting at the work point: ·

I

I

\. ·.

L =Lt+Ui =46.0 in. e =d/2 =27.3 in.ti

Therefore:

=13..7 in. h =20.0 in.

AMERICAN lNSlTIVTE OF STEEL CONSTIUICTJON

,\.\tEUCAN L~STm.m! OP STI'.EL CoNSTRlJCTION

and Figure 5-30

S-186

URACEOFRAMES

·!'!.'!

For 1he forces given in Figures 5-30a and 5-30b:

LRFD

LRFD

Pi =-226 kips

ASD '

M2 =..!.Lvz _}_hH2 _.!_Mi 8

Pi =-158 kips

4

2

ASD

M2 =.!_LV2-.!_hH2-_!..M2

,.

8

=!(46.0 in.)(217 kips)

Iii =(-226 kips)(cos45°)

v.

_ .!.(20.0 in.)(217 kips) 4

=-112 kips

= (-226 kips )(sin 45°)

Vi

=(-158 kips)(sin45°)

=-160 kips

=-H2 kips

P2 = +307 kips

P2 = +215 kips

Hz= (307 kips)(cos45°)

H2 = (215 kips)(cos45°)

= 217 kips

Vi

= 217 kips

::o (215

4

2

.

=.!.(46.0 in:)(l52 kips) 8

.

-.!.(20.0 in.)(152 kips) 4 .

_.!.(2,970 kip-in.) 2 = - 1,320 kip-in.

_.!.(2,080 kip-iri.) 2 = - 926 kip-in.

For the gusset above the beam, the forces on section a-a are:

=IS2kips

V2 =(307 kips)(sin45°)

I

8

Hi =(- 158 kips)(cos45°)

=-I 60 kips

5- 187

5.3 SPECIAL CONCENTR.ICJ\l.LY BRACED FRAMES

ASD

LRFD

kips)(sin 45°)

Normal Na :::V1+V2

Nonna! Nu =Vi+ V2 = -160 kips+217 kips

= 152 kips

;

= 57.0 kips

=-112 kips+152 kips :::40.0 kips

The moments :lre:

. i..RFo M1

= Hie+ViLl

.

• '

ASD .~

=[-112 kips(l 3. 7 in.)]+

(-160 kips(O fo.)j

(-112 L.;ps(O in.)]

=-1,530 kip-in. Mi

=[152 kips(l3.7 in.)J

-{217 kips(O in.)J

-[152 kips(O in.)J

Ml= ..!.LVi-!_hH1 -.!..M1 8 4 2

= ..!.(46.0 in.)(-160 kips) 8 . _.:!_(20.0 in.)(-160 kips) 4

-~(-2,190 ki~-in.) = + 975 kip-in.

Shear V.,

=H1-H2

=H1-H2

=-160 kips-217 kips

=-112 kips-152 kips

=-377 kips

=-264 kips Moment Ma= Mi - Mi =-1,530 lip-in. -2,080 kip-in.

Moment Mu= Mi -M2 = - 2, 190 kip-in. -2,970 kip-in.

=- 5, 160 kip-in.

\

=H2e-V2D.

= [217 kips(13.7 in.)J = 2,970 kip-in.

.

Sliear VH ---

M1 =Hie+ \'iil

=[-160 kips(J3.7 in.)]+

=- 2,190 kip-in. "12 =Hie - V2Ll

.

= 2,080 kip-in.

M( =.!_LVi-..!.hH1 _ _!..M1 8 4 2 = ~( 46.0 in.)(-112 kips) _.!_(20.0 in .)(-112 kips) 4 -l(-1,530 kip-in.) 2 + 681 kip-in.

=

=- 3,610 kip-in. -

Check available strength of the gusset plate above the beam on section a-a Tue available shear strength of the gusset plate on sectio~ a-a is:

Vn =0.60FyAgv

(Spec. Eq. J4-3) '

1--~~~~~L_R_F_D~~--~~--i~~~~~~A_S_D~--~--~~i ~ = 0~60{36 ksi)(Ys

Fn = l.00(0.60)(36 ksi) x(% in.)( 46.0 in.)

=869 kips> 377 kips

o.k.

in.)

x(46.0in.)/l.50 = 580 kips> 264 kips

t l(

1 ··

t. o.k.

.. -.• 1

l---~--~------------------1~~~--------------------~

The normal force favolves both N and M. It is convenient to introduce an equivalent nonn:u 1· force as:

;l i \ b'•

BRACED FRAMES

S-188

;1

4

Nequiv

=INl+j

The equivalenc normal force is:

. -157 0 k.

------ii·....~

•

lpS

1 46 0 0.90(36 ksi)(* in/ · in.)

=

46.0 in.

4

::: 15,000 kip-in.

ASD

I+14(5.160 kip-in.)1 ·

M,.

¢Mn=QFyZ

n

= F1 Z n

2

36 ksi (* in.) ( 46·0 in.) 4 1.67

= =9, 980 kip-in.

Therefore, the interaction equation from plasticity lheory is:

LRFD utqu1v -

ASD

LRFD

2 This is determined as follows. Over half I.he gusset. the normal force is N + M • and over . . N 2M . . . . 2 L 2 the other half 1t JS - - . For s1mpliciry m calculations one of the moment fiorces M . 2. L . ' 'L' 1s i:v~rsed so that a. ~mfonn eqmvalent normal force exists over the entire gusset section a-a. ~1s JS also convenient for use in the beam web local yielding and web local crippling equauons of the AISC Specification that assume a uniform compression over the contact area.

N

5-189

S.3 SPECIAL CONCENTRICALLY BRACED FRAMES

LRFD

N atq111v . --1 40.0 ki psI+ 14(3.610 kip-in.)I 46.0 in.

= 506 kips

=354 kips

.The available ·strength of the gusset plate to resist this force js determined for the fanit state of tensile yielding:

( 5,160 kip-in. ) ( 57.0 kips 15.000 kip-in. + 1,300 kips +(377 kips 869 kips :::: 0.381 S l.O

r.

r

ASD

+(264 kips 580 kips

=0.407~1.0

o.k.

r

(3,610 kip-in.)+( 40.0 kips 9,980 kip-in. 868 kips

r

o.k.

(Spec. Eq. J4-l)

LRFD ~N,.

Design the weld at the gusset-to-beam flange interface

ASD Nn

FytpL

-=--

=$FytpL

= 0.90(36 ksi)(% in.)(46.0 in.) =1,300 kips> 506 kips o.k.

n

n

= 36 ksi ("~ in.)(46.0 in.) 1.67

=868 kips> 354 kips

o.k.

Th~ gusset sh~ and nonnal forces and streng~ calculated previously do not consider interaction. Interaction seldom controls at this location because the gusset thickness is usually controlled by the limit states associated with tbe brace-to-gusset connection. If interaction is to be considered here, the following interaction equation from plasticity theory is rccomniended (Astaneh, 1998): ·

The use of a plastic distribution for the moment is converuent for calculation as mentioned previously. but requires sufficient ductility. The gusset and the beam can be assumed to be sufficiently ductile, but the fillet welds or PIP groove welds generally used to connect the gusset to the beam are well-known to have less ductility when loaded at angles significantly different from the longitudinal ax.is, which often is the case with the moment forces, Therefore, it is prudent to use the weld ductility factor originally derived from Richard (i986) as a value of 1.4, and modified by Hewitt and Thornton (2004) to a 90% confidence litnit and the value of l.25. This value, which is explained in AJSC Manual Part 13, is used in these calculations. The original 1.4 factor is from Richard's work on corner gussets. Nevertheless, it is reasonable to use some "ductility factor" here because the weld is assumed to be uniformly loaded ove·r each half width, even lhough the actual distribution can vary. The use of a CJP groove weld avoids this issue, but likely at greater cost.

The resultant force on the weld is:

ASD

LRFD u + u + Vu (M)(Nf( $M,. $N,. ¢V,.

r

Sl

r r

(n::a J+(~a +( OV~a

Sl

ASD

LRFD

~ =JN:,quiv + Va2

R,, =JN;~quiv + V}. = J(506 ltipsf +(377 kips)

=J(354 kips)2 +(264 kips)2

=631 kips

=442 kips

1

For the present problem, the required strengths have been ~alculated in the preceding text, as have tbe ~vailable streng~s in sh ear ~d ten~ion. The available flexural strength of the gusset plate 1s calculated using the plasuc section modulus of the gusset plate :it section a-a:

. I

BRACED FRAMES

5- 190

5.3 SPECIAL CONCENTRJCALLY SRACED

The angle of the result.ant force can be calculated and used in the directional strength increa.c:e for fillet welds as follows:

-

LRFD

9=

tan:- 1 (

N,,~:,,;•)

= 1.00(1,530 kips) = 1,530 kips> 506 kips

Rn

-= o.k.

n

S = tan-i(Na~:vi•)

kips)

= tan -1 ( 506 377 kips

= tan -1(354 kips) 264 kips

=53.3°

=53.3°

Using AISC Manual Equations 8-2a and &-2b, the number of sixteemhs of fillet weld required is:

•.=aso.;!1·3[~)[:; x

1.25(631 kips)

1.25(442 kips) 2(0.928 kip/in.)(1.36)(46.0 in.)

= 2(1 :392 kip/in.)(1.36)(46.l) in.)

=

=4.53 sixteenths

= 4.76 sixteenths

=1,370 kips

~

I

ASD R,. -Q

G>Rn = 0.75(1,370 kips)

=1,030 kips> 506 kips

o.k.

I-

= =

o.k.

1

ASD

LRFD 1

Norma l N~ =-(Hi +Hz)

2-

-

1 . Nomia! N~ =-(Hi +H2) 2

=.!.(.: ll2kips+ 152 kips)

=.!.(- 160 kips+217 kips}° 2 = 28.5 kips

Check beam web local yielding For a force applied at a distance from the beam end that is greater 1han the depth of the member: (Spec. Eq. H0-2)

1;370 kips 2.00 685 kips> 354 kips

This completes cbe design of the top gusset for the forces on section a-a.

Tl}e forces on gusset section b-b are:

Use double-sided !Y16·in. filJet welds to connect the top gusset plate to the beam.

=(50 ksi)(0.570 in.)[5(1.53 in.)+46.0 in.J =1,530 kips

I:

29,000 ksi(SO ksi)(0.930 in.) . 0.570 JO,

Based on the thickness of the thinner c9nnected part, the minimum fillet weld size required by AlSC Specification Table J2.4 is ¥16 in.

R,. =F-ywrw(5k+lb)

I

1 - - - - _ _ . . . . : . . - - - + - - - - - 41

1.25R,, 2(0.928 kip/in.)(1.36)/

l

o.k.

(Spec. Eq. Jl0-4)

LRFD

Duq·d ~

l.25Ru 2(1 .392 kip/in.)(l .36)1

rr::''

0 570 0 =(0.80)(0.570 io.)211 +3( 46 · '.n·)( · ~"·)LS 27.3 m; 0.930 m.

ASD

' Dr~q'd ~

=

I

I

Check beam web local crippling For a force applied greater than a dist
1.0 + 0.50sinl.S53.3° = l.36

.

1,530 kips 1.50 1,020 kips >)54 kips

l.

AISC Specification Section 12.4 allows an i11crease in the available strength of fillet welds when the angle of loading is not along the weld longitudinal a~is. The directional strength increase is determined from the following portion of AISC Specification Equation 12-5:

LRFD

ASD

LRFD

¢R,,

ASD

5-J

FRAMES

Shear V,~

1 2 = 2(Vi -Vz)-L(M.)

=.!.(-160.kips-217 kips) 2 2(-5,160 kip-in.) 46.0 in. = ~5:8 kips

2 =20.0 kips

Shear V~

l 2 =-(Vi -Vz)--(Mo) 2 . L

I

I

I

I

;lt1

I

=.!..(-112 kips-152 kips) 2 2(-3,6 10 kip-in.) 46.0 in. =25.0 kips

.J

"' AM.ERJCAN lNSTITVl'S OP ST!!EL CONSTRUCTION

1:: !

LRFD .MomentM~

I•

Moment M~ = Mi+ M2

'l '•

=681 kip-in.

+(-1,320 lcip-in.)

!...

Design of gusset below the beam For the geometry shown in Figure 5-29 for the gusset plate above the beam and using Figure 5-3 l for the general lerminology:

ASD

= Mf +M2 =975 kip-in.

!

6. =0

+(-926 kip-in.)

.

=-245 kip-in.

= -345 kip-in.

Lt =L2 = 25.5 in.

'

L =L1 +L2

Check gusset available strength on section b-b The available shear strength of the gusset pla1e on section b·b is: V11

5-1 93

S.3 SPECIAL CONCENTRICALLY BR.ACED FRAMES

BRACED FRAMES

5-192

=51.0 in.

=0.60.F).Agv

(Spec. Eq. J4-3)

e =dl2 =27.3 in./2

<>V,,

>fl

!r1 '"

tl ~~·

v.

=1.00(0.60)(36 ksi)

h = 29.0 in.

~ = 0.60(36 ksi)(J1 in.)

x( ~ in.)(20.0 in.)

= 378 lcips > 35.8 kip

=13.7 in.

ASD

-LRFD

For the forces given in Figures 5-30a and 5-30b:

·x(20.0 in.)/ l .50

o.k.

o.k.

= 252 kips> 25.0 kips

The nonnal force involves both N and M. It is convenient to inttoduce an equivalent normal force, as before, using the governing condition where N and the component of M are additive. This can be written as:

ASD

LRFD

...

A =550 kips

f\ =385 kips

H 1 = (550 kips )(~os45")

H 1 = (385 kips)(cos45°) =272 kjps

= 389 kips

Vi = (385 kips )(sin 45°)

Vi =(550 kips)(sin45°)

=389 kips

~

LRFD

ASD

Pz. N'urq1m•. -128 - ki psI+14(-345 kip-in.)l .) . 20.0 in. . .

N'a equiv . -120 o·k.tps I+14(-245Okip-in.)' . . 20. in.

=97.5 ki_PS

(Spec. Eq. J4-l)

LRFD

..

~:..

·: =~

.. ~

i. ~.

$N,,=$FylpL

= 0.90(36 ksi)(Ji in.)(20.0 in.) o.k. =567 kips> 97 .5 kips

f)·tpl

n

n

H2

=(-311 kips)(cos45°)

=-220 kips

=-314 kips The moments are:

Mi

= 36 ksi(* in.)(20.0 in.) I.67

o.k.

I

V2 =(-311 kips)(sin45°)

ASD

LRFD

-=~

= 377 kips> 69.0 kjps

Pi =-311 kips

=-220 kips

V2 =(-444 k.ips)(sin45")

ASO Nn

\

=-314 kips

The aviµlable slrength of Lhe gusset plate to resist this force is determined for the limit state of tensile yielding:

:·:

I

= -444 kips

H2 = (-444 kips)(cos45°)

=69.0 kips

Nn=F.,,Ag

=272.kips

=H1e+Vi6

M1 =Hie+ Vi.6.

=(389 kips(l 3.7 in.)j

=(272 kips(l3.7 in.)]

+{389 k.ips(O in.)]

+1272 kips(O in.)]

=5,330 kip-in.

:::: 3, 730 kip-in.

I

S--194

S...1 9.

5.3 SPECIAL CONCENTRlCALLY BRACED fRAi\fES

LRFD

ASD

M2 = H it- V2D.

Mi

=H it -

V2D.

=l-3 14 lcips(13.7 in.)J

= l-220 kips(13.7 in.)}

-l-3 14 kips(O in.)J

-l-220 kips(O in.)]

=- 4.300 kip-in.

= - 3,010 kip-in.

M'I =l LVi --hH, 1 1 --M, 8 4 2

Ml =.!_L\'i-1_hH1 _.!_Mt

ics .o in.)

=

1

4

8

2

=i(51.0 in.)(272 kips)

_.!_(29.0 in.)(389 kips) 4

_ .!.(29.0 in.)(272 kips) 4

_..!.(5,330 kip-in.) 2 =- 3,010 kip-in.

_.!_(3, 730 kip-in.) 2 = - 2, I 00 kip-in.

, l l' l M2 =-LV2- - hH2 - - M2 8 4 2

M'2 =-LV2i 1M 2 -I J1H2 - -

8

4

2

=~(51.0 in.)(-220 kips)

=..!.(51.0 i.ri.) (-314 kips)

.

-~(29.0 in.)(-220 kips)

_.!,(29.0 in.)(-314 kips) 4

4

-.!.(-4,300 kip-in.)

_.!.(-3,010 kip-in.) 2 = 1, 700 kip-in.

2

= 2,420 lcip-in. ·

1·

(Spec. Eq. 14-3)

ASD

LRFD V,,

¢V,, = 1.00(0.60)(36 ksi)

(389 kips)

8

Check available strength of bottom gusset below the beam on section a-a The available shear st.cength of the gusset plate on section a-a is:

n

x(l 1A in.)(51.0 in.)

=l ,380 kips> 703 kips

=0.60(36ksi)(l 1.4 in.) x(5 l .O in.)/1 .50

o.k.

=918 kips> 492 kips

o.k.

The nonnal force involves both Nu or N0 and Mu or Ma. Tt is convenient to introduce ar

equivalent normal force, as before, as: ASD

LRFD Nu equiv

• . 14(9,630 .kjp-in.)l =17.).Q k1psl + · 0· 51. in.

Na equiv

.

=j52.0 kipsj+

l{

14(6,740 kip-in.)1 1 i

=581 kips

= 830 kips

O.

51 .

Jll .

' I

l

Tue availab.Je strength of the ~sset plate- to resist this force is determiiJed for the limit state ·· ·

of tensile yielding:

.

.

.

(Spec. Eq. 14-1) .·.

N,..= F1 A8

LRFD

1.;.

ASD

~~~~~~~~~~~~~~i--_N~,,-=--F.-~ tp~L ~~~~~~~~~--,,

For the bottom gusset, the forces on section a-a are:

¢Nn = ¢FytpL

LRFD

NormalN., = V1+V2

ASD Normal N 0 = Vi + v,,

=389 kips-314 kips = 75.0 kips

Shear Vu

=H1- H2

= 0.90(36 ksi)(l 'A io.)(51.0 in.) o.k .

=2,070 kips> 830 kips

Q

~

1Q

1

=36 ksi(l 'A in.)(S l.O in.)

.:·

1.67

=1,370 kips> 581 kips

o.k.

=272 kjps+(-220 kips}

Shear Va

=52.0 kips

Interaction as calculated for I.be top gusset above the beam, is not repeated here.

= H1 -H2 272 kips - (-220 kips) = 492 kips

Design the weld at the gusset-to-beam flange interface for the gusset below the beam As discus~ed for the gusset above lhe beam, the 1.25 ductility factor is used here.

=

= 389 kips-(-314 kips) = 703 kips

Moment Mu = Mi - M2 = 5,330 kip-in. -(- 4,300 kip-in.) = 9,630 kiP-in.

\

Moment Ma

=

M, - M2 = 3, 730 kip· in. -(-3,0 10 kip-in.) = 6. 740 kip-in.

1

1. :...

t

.....

L

S-196

,

l

i ..l

The resultant force on the weld is:

"···

.~·..

l

R" = ~NJcquiv + V,,2

(Spec. Eq. 110-2)

R,. =Fywt..,(5k+lb)

LRFD

~~·

,.i

5-197

5.3 SPEClAL CONCENTR1CALLY BR.ACEO FRAMES

ASD

=(50 ksi)(0.570 in.)[5(1.53 in.)+ 51.0 in.J = 1,670 kips

Ra= ~N1equiv + V}

= J(830 kips)2 +(703 kips)2

= )(581 kips) +(492 kips)2

= 1, 090 kips ·

= 761 kips

LRFD

ASD

2

Rn

$R,. = l.OO(l,670 kips) = 1,670 kips> 830 kips

l,670 kips 1.50 = 1,110 kips> 581 kips

-=

o.k.

n

o.k.

The angle of the result.ant force can be calculated and used in the dirnctional strength increase for fillet welds as follows: Check beam web local crippling

LRFD equiv 0 =tan -1 (Nu - -. · Vu .

J

ASD 0 = tan

-tVa;:uiv)

For a force applied greater than a distance of d/2 from the beam end:

R,. =O. 8Ot,.,21+.>~(/b)(1"')l.5 - d

=tan -

kips) 703 kips

l ( 830 .

. -i(5811cips) =tan 492 kips

=49.7°

=(0.80)(0.570

= 49.7°

lf

(Spec. Eq. Jl0-4) EF>wtf lw

in.)2 11+3(~~:~ :::)(~:!~~~:JS·]

29,000 ksi(5_0 ksi)(0.930 in.)

AISC Specificg.tion Section J2.4 allows an increase in the available strength of fillet ,welds when rhe angle of loading is not along the weld longitudinal axis. The directional strength increase is determined from the following ponion of AISC Specification F,quation 12-5:

XI--'---'----'-"-'--~--~

0.570 in. = l,470 kips

1.0 + 0.50sin1s49.7° = 1.33

LRFD

Using AISC Man~al. Equations 8-2a and 8-2b, the number of ~ixteenths of fillet weld required is:

Dreq'd~

.. l.25Ru 2(1.392 kip/in.)(l.33)l kips) - 2(1.3921.25(1,090 k.ip/in.)(1.33)(51.0 in.) "

= 7.22 sixteenths

j;

1,470 kips 2.00 0. :::: 735 kips> 581 kips

Rn

-=

Rn =0.75(1,470 kips)

= l,100 kips> 830 kips L~

ASD

o.ki

\

o.k.

ASD This completes the des.ign of the bottom gusset for the forces on section a-a

Dreq'd~

1.25.R.t 2(0.928 lcip/in.)(1.33)/ kips) - 2(0.928 1.25(761 kip/in.)(1.33)(5 LO in.) -=7.56 sixteenths

Use double-sidhd Yl-io. fillet welds to connect the bottom gusset plate to the beam.

The forces on gusset section b-b are:

},

NormalN~ =-(H1 +H2)

2

..!.[389 kips+(-314 kips)] 2

=37.5 kips

~:

Check beam web local yielding For a force applied at a djstance from lhe beam end that is greater than lhe depth of the

member:

AMF-lUCAN lNSTITVre OF Sn:a CoNSTlllJCnON

ASD

LRFD 1 2

NormalN~ = - (H1

+Hi)

-=.!.1212 kips+(-220 kips)] 2 • = 26.0 kips

I i

5-198

s


LRFD 1

Shear V~

2

Shear V~

=-(Vi-Vz)--(Mu) 2 L

1

ASD

LRFD

ASD 2

N~

-

~Nn = 9F>tPL

=2:(V.- V2)-L(Ma )

Q

::: 0.90(36 ksi)(l 'A in.)(29.0 in.)

. = .!.[389 kips -(-314 kips)]

=1.[272 kips-(-220 kips)]

2

: 1.170 ~ips > 119 kips

2

kip-in.) - 2(9,630 51.0 in.

F tpL

1 =-

n

36 ksi(l 'A in.)(29.0 in.) = 1.67

o.k.

=781kips>81.2 kips

740 .Jcip-in.) - 2(6, 51.0 in.

=-26.1 kips

t9 :J

o.k.

=-18.3 kips Check beam web shear at the centerline of the connection

MomentM~

MomentM~

= M( +M2 = -3,010 kip-in.

=Ml +Mi

From Figure 5-32:

t:

=-2,100 kip-in.

+2,420 kip-in.

+l,700 kip-in.

=- 590 kip-in.

~gusset

=-400 kip-in.

~Ltop

Check gusset available strength on section b-b

=0.60F,A8v

(Spec. Eq. J4-3)

LRFD

ASD

4>Vn = 1.00(0.60)(36 ksi) x(l 1.1.i in.)(29.0 in.)

=783 kips> 26. l kips

.

~ =0.60(36 ksi)(l 1.1.i in.)


I

o.k.

force~

as before, as:

I;.

(2M/L)top

l I

(N/2)top

•

r

-;

t

I

j VM•m •

I

The normal force invo(ves both·N and M. It is convenient to introduce an equivalent normal

.. II

t

l J

x(29.0 in.)11.so·

o.k.

t

I

'.The available shear strength of the gusset plate on section b-b is: V11

1•

i

I

\

t t

lI

I

1·

(N/2}oo1

(2MIL}ooi

LRFD N,'utqutv. -137 5 k.JPS I+14(-590 kip-in.)' • . 29.0 10.

=119 kips

ASD ,

NHquiv

l•

14(-400 kip-in.)' =126.0 kips!+ _ in. 29 0 .

=S J .2 kips

~Lbot

.. 1

l

>·:

[(N) - + (2M) - [(N) + (2M) 2 t>ot L bot 2 top L

Vi18am =

The available strength of the gusset plate to resist this force is detellllioed for the limit state of tensile yielding: (Spec. Eq. 14-1)

tcp

l

ca/cu/ate beam shear; V~. (forces are shown in 0$Swned positive direction).

Fig. 5-32. Free body diagram

r \'

I()

I

•.. ,, AM:EluCAN ~STITIJTE Ol' SlTilll. CONST1UlCllON

l:

5-200

BRACED FRAMES

S- 20!


·,

i,,..l

-----ln:J

LRFD v,

-[ 75.0 kips

b~a>n -

2

Startjng at rhe beam centerline, the shear per inch js:

ASD

+ 2(9,630 kip-in.)1

LRFD

v.beam --[ 52.0 kips + 2(6, 740 kip-in.)J

5l.O in.

-f

-[57.0 kips+ 2(:-5,160 kip-in.)J 2 46.0 in. ..=611 kips

2

5 1.0 in.

v(x )= 611 kips

40.0 kips+ 2(-3,610 kip-in.)) 2 .46.0 in.

l

v(x)= 427 kips -(5 .95kip/in.+1L4 kip/in.)x

- (8.52 kip/in.+ 16.3 kip/in.)x

=611 kips-(24.8 kip/in.)x

= 427 kips

From AISC Manual Table 3-6, the available shear strength of the W27x11 4 is:

ASD

=427 kips - (17.4

kip/in.)~

where x is measured from the beam centerline. Se«ing v(x) equal to tbe available strength of the beam and solving for x:

LRFD

ASD

(l>vVn = 467 kip~< 611 kips

LRFD

v.

n.g.

Qn

= 311 kips< 427 kips

n .g.

" :Oe av:ulab!e s?ear strength is less than the require.d shear strength. Thus, a web doubler plate is require.d, as m Example 5.3.8. The normal force per inch for the bottom gusset is:

LR.FD

2MJ ll(L/2) Poo1 =[(N) +( 2 bot L bot

2

=f(75.0 kips )+('2(9,630 ~p-in.) )] 2

=f(52.0 kips)+(2(6,740 k_Jp-in.))J 51.0 Jll. 2 /(51.012)

51.0 m.

/(51 .0/2)

=16.3 kip/in.

-

2

M)top Jt(l/2)

L

=[(57:02kips)+ (2(-5~:.~ ~~-in.))} = -8.52 kip/in.

x=5.81 in.

x°"'6.67 in.

Try a 14 in.xl4 in. doubler plate. Using the available shear strength of the beam and AISC Specification Equarion J4-3 and solving for t,u,ublu:

- . ASD

LRFD

1

$Vn (btom) +$Vn (doub/u) ~Vu

Vn (b..am) '/ n + V,,

467 kips+ l.OO(tdoubler )(14.0 in)

31 1 kips+ { 0.60(tdoubltr )(14.0, in)

x(0.60)(36 ksi) ~

(doubter)

I 0 :;:: V~

x(36 ksi)/1.50}

611 kips

~427

'··~' 2 0.476 ill.

kips

r.,,.b,., 2!0.575 in.

1\'Pically, one method should be chosen and used consistently throughout an entire design. In d~sign _by LRFD, a Y2-in. _doubler plate would be adequate. For this example, the ASD result will be used.

LRFD

/(46.0/2)

427 kips-(17.4 kip/in.)x= 311 kips

=11.4 kip/in.

The normal force per inch for the top gusset is:

Prop=[( ~Jtop +(

611 kips-(24.8 kip/in.)x=467 kips

ASD

Pbo1 =[(NJ +( LM)bor )1(L!2) 2 bor

ASD

ASD

(~J +(~) l'(L/2)

Ptop=f

top

L

top

=[(40.0 kips)+(2(-3.610 ~p~fo.)Jj 2 46.0 m. /(46.0/2) ::: -5.95 lcip/in.

Use a doubler plate~ ~~-X l4 in.xi '-2", near si_de onlfThe required shear strengih of the doubler plate is: LRFD Vb
ASD

=611 kips - 467 kips

l

Vb
=116l
= 144 kips

j

'------~~-~~-~~-,.-L-----~-~~~~~~~-'

,. '

AMEIUCAl'l l.NS'ITll.n"B OF STEEL CONSTRUCTION

... .

BRACED FRAMES

5-202

Using the instantaneous cen1er of rotation method of AJSC Manual Part 8, use Table 8-8 with 0 =0° to determine the strength of welds on the doubler plate. For a channel-shaped weld on half of the doubler plate, the geometric variables are:

l = 14.0 in.

.S.3 SPECIAL CONCENTRJCAU..Y BRACED FRAMES

Example 5.3.5. this connect.ion uses ASTM A572 Grade 50 splices in the beam away from the connection. ASTM A992 W24x146 beam stubs are used at the beam ends to meet the high shear demand from the braces over the connection. Use ASTM A325-X bolts and 70..ksi weld electrodes. The applicable building code specifies 1he use of ASCEISEI 7 for calculation of loads. The gravity shears and moments on the beam are: Vv

k = 7.00 in, /14.0 in.

=11.2 kips

Mv

Vt= 8.50 kips

=120.kip-ft

section.

xi= 0.125(14.0 in.)= 1.75 in.

Solution: This connection design uses splices in the beam to provide a simple beam-to-column con· nection satisfying AISC Seismic Provisions Section F2.6b(a).

ei =al =7.00 in. - 1.75 in.

From AISC Manual Tables 2-4 and 2-5, lhe material properties are as follows: ·

=5.25 in.

ASThiA36

a =0.315

F1 =36 ksi Fu= 58 ksi

By interpolation,AJSC Man(lal Table 8-8 withe= 9° gives: C=3.35

ASTMA572 Grade 50

From ~lSC Mam~al Table 8-3, C 1

=l .00. Tue fillet weld size reA)uired is:

LRFD D . _ Vb.,am $CC1l

144 kips 0. 75(3.35)(1.00)(14.0 in.)

= 4.09

.

ML = 100 kip-fl

.kl= 7.00 in.

=

fl

The relevant seismic parameters are given in the SCBF Design ~ample Plan and Eleva~ion

= 0.500

lllm -

l

ASD

om. m - nvb,_,,,, ---CC1l

2.00(116 kips) (3.35)(1.00)(14.0 in.) =4.95

Fy =50 ksi Fu= 65 ksi

··.I

ASTM A500 Grade B F1 :::42 ksi

Fu::: 58 ksi ASTMA992

F1 =50 ksi F,, = 65 ksi

I

\

From AlSC Manual Tables 1-1 and 1-13, the geornetric properties are as follows: Use a ¥16-in. all around fillet weld, as shown in Figure 5-29. All delAi.ls are shown in Figure 5-29.

Example 5.3.10. SCBF Brace-to-Beam/Column Connection Design Given: Refer to Joint IT-2 at level 3 in Figure 5-11. Design the connection between braces, beam nnd column using splices in the beam away ftom the gusset plates. The brace is designed to buckle out-of-plane. Use-ASTM A36 welded gusset plates concentric to the braces and 70ksi electrodes to connect the braces co the gusset plates and the gusset plates to the beam and column. As designed in Examples 5.3.1, 5.3.3 and 5.3.5, the braces are ASTM A500 Grade B round HSS sections, the column is an ASTM A992 W12x96, and the beam is an ASTM A992 W24x68. The brace reinforcing bars are ASTM A572 Grade 50 material. As noted io

Brace (above the beam)

HSS6.875x0.500 t,,_ =0.500 in.

t", =0.465 in.

=9.36 in.2

r=2.27 in.

A = 10.'.3 in.2

r= 2.49 in.

.A

Brace (below the beam)

HSS7 .500x0.500 1110,,.

=0.500 in.

Beam W24x68 d :::23.7 in.

Beam stub W24x146

ldu =

0.465 in.

r.

l·:

. lw=0.415 in.

y

=0.585 in.

kdu

= J .09 in.

,,._..

5-205

BRACED FRAMES·

5-204

I

A =43.0 in. 2

~

: kdu

1§:. I u • •.

= 1.59 in.

d= 24.7 in. T=20* in.

r.., =0.650 in. ry

IJ= 1.09 in.

= 3.01 in.

...

Column

S.3 SPEClAL CONCENTRICAilY BRACED FRAMES

The required strength of the bracing connection due to seismic lo~ding is i:ased o~ ASCE/SEl 7 Section 12.4.3.2 Load Combination 5 (LRFD and ASD) with 0.00: - Emh_• discussed in AISC Seismic Provisions Section F2.3. The required strength of the bracing connection when the brace is in tension is:

W12x96

d= 12.7 in.

t,.,

=0.550 in.

11

=0.900 in.

kdu

= I.50 in.

The comp,lete connection design is shown iu Figure 5-33. 'The connection geometry and member forces are as shown in Figures 5-34 and S-35. These were originally determined in E.xample 5.3.5. The calculations will be shown again here. See the discussion under "Solution" in Example 5.3.8 for a discussion of the analysis forces required by the AISC Seismic Provisio1ts and of the LRFD and ASD approaches.

Erection bolt -+---..

the

In Example 5.3.8, there were two braces above the beam and two braces below, so direction of loading d1d not affect the connection design. In this comer connection, since the braces above and below the beam are not the same size, the direction of loading affects the amount of force that must be considered in the connection design. Two design cases will be considered.

AISC Seismic Provisions Sections F2.3(i) and F2.3(ii) define the two mechanism analyses that must be considered in detem1ining the required strengch of beams, columns. and connections. AJSC Seismic Provisions Section F2.6c specifies the required strength of bracing c.onnections. For the required compressive strength based on buckling limit states, Section F2.6c(2) has an additional 1.1 factor (relative 10 the requirements of Section F2.3) applied to lhe required strength of the connection.

,rW24i<68

/

beam

For this SCBF connection example, the requirements of AlSC Seismic Provisions Section F2.3 will be used for both LRFD and ASD, except for the limit state of compression buckling on the Whitmore section, which will use the 1.1 factor specified in AlSC Seismic Provisions Section F2.6c(2). Design Case I

Design Case I shows brace strengths whiCb correspond to lateral forces applied in the positive x..
l

l

\:

'

brace Determine the expected tensile strength of the HSS6.875x0.500 brace above the beam for Design Case I From AtSC Seismic Provisions Table A3.l:

P,""""" =RyFyA8 ~: 1 ..

=1.4(42 ksi)(9.36 in.2)

i:

=550 kips

i;

HSS 7.500i<0.500

Note: A325-X bOIUI are to be pretensioned with slip-critical faying surfaces.

Fig. 5-3~. Geomerry and complmd design for Exampl115.3.JO.

BRACED FRAMES

5-203

LRFD P.

=l.OEm1i =1.0(518 kips)

'

ASD

F.

:t

=0.7(518 kips) =

=363 lcips

= 518 kips

And the expec ted post-buclding brace strength from AISC Seismic Proi:isioltS Section

F,,,

_ _ __,

(Spec. Eq. E3-4)

--

(~Lr

n2 (29,000 ksi) 2

(63.4)

I

= 0.658

I

The required strength due to seismic loading of the bradng connection when the brace is in compression, based on poM-buckling !>trenglh, is:

I

=71.2 ksi

F2.3 is:

0.3Pron.prtwon = 0.3(518 kips) == 155 kips

.

n2E

1

Po= 0.1Em11

S-209

5.3 SPFU/\L CO~(.b.'l"rRICAl.l.Y BRACED f'RA.\.IES

l


f!i_FL F, R1 Fy 1 4(4Zksi)

l

= 0.658 ?~ (1.4)(42 ksi) =41.6 ksi The eitpcctcd compressive strength of the brace nbove the beam, based on AlSC Seismic

Pro~·isions Section F2.3, is taken as the lesser of R>F1..\1 or l.14FmA::

·!. ·~":.;? ·

ASD

LRFD

Pu = l.OEh..., =1.0(155 kips) =155 kipli

Pa= 0.7Em>r

=0.7(155 kips) = 109 kips

The two sets of forc~s 10 be considered in Design Case I are shown in Figures 5-34 and 5-35. Detcnnination of the collec1or force from outside the frame and the axial forces in the beam are shown for lhe beam design in Example 5.3.5 (see Figures 5-17 and 5-18).

Pcvmprmion

=min{l.14FmAg, RyFyAg} =min{ll.14(41.6 ksi)(9.36 in.1)]. !1.4(42 lcsi)(9.36 in.2)1} =otin {444 kips, 550 kips) =444 kips

The required strength due to seismic loading of the bracing connection v. hco the brace is in

compression is:

ASD

LRFD

Design Case II

Design Case H shows brace strengths corresponding to lateral forces applied in the negative x-
P,. = LOE.,.,,

\

\

•

=1.0(444 k.Jps)

.

P0 =0.7£,,,,,

=0.7(444 kips) =3 11 kips

,,. 444 lcips

I

Determine the expected compressive strength of the HSS6.875x0.500 brace above the beam for Design Case II

:: I !i·

•....

?..,.

KL r

=J.0(12.0 ft)(l 2 inlft) 2.27 in.

And the expected post-buckling strength is:

0.3Prompr•.s.sfon = 0.3 (444 kips)

=133 kips The required strength due to seismic loading of.the bracing conncclion when the brace is in

=63.4

compression, based on post-bucl
29,000 ksi

4.71J E =4.7 1 1.4(42 lcsi) R1 F1 =105

I1 Witti -Kl ~4.11 ~ --: r

R1 F1

ASD

LRFD Pu= 1.0E,,111 "" 1.0(133 kips) =133 kips

P,. =0.7Em>i =0.7(133 !0ps)

=93. l lcips

BRACED FRAMES

5-210

Determine the expected tensile strength of the HSS7.500x0.500 brace below the beam for Design Case II

PR.AMES

For Design Case Il, this shear is:

•

From AISC Seismic Provisions Table A3. l:

l

ASD

LRFD

(444 kips+606 kips)sin45° =742 kips

R1 =1.4 I'tcnsiolt

5.3 SPECIAL CONCENTRICALLY BRACED

(31lkips+424 kips)sin45° = 520 kips

=R1 F1 A1

=1.4(42 ksi)(l0.3 in.2 )

311 kips


=606 kips

(compression)

/

/

The required strength of the bracing connection due to seismic loading when the brace is in tension is:

I :

r:. ASD

LRFD

32.2.kips

46.0 kips

P,, =0.1Em11

P" = 1.0E,,,11 = 1.0(606 kips)

=0.7(606 kips)

=606 kips

=424 kips

r

.


Vu =(1.2+0.2Sns)VD +Q0 V01:

v., =(1.0+ 0.14SDs )Vo+ VH

=1.4(11.2 kips)+ 2.0(0 kips)

I·

/

/

=l.14(11.2kips)+O kips+O kips

+ 0.7(2.0)(0 kips) =12.8 kips

+ 0.5(8.50 kips)+ 0.2(0 kips)

=19.9 kips

19.3 kips

27.6 kips

.'"

.

Considering Design Cases I and II, the total maximwn vertical shear is lhe sum of the vertic::1I components of the expected strength of the braces above and below the beam. For Design Case I, thls shear is:

(550 kips+518 kips)sin45°=755 kips

.,

(compression

(compression)

+Vp +0.7Q0 Vca

+ 0.5VL + 0.2Vs

93.1 kips

133 kips

t ~l

ASD

LRFD Load Combination 5 from ASCFJSEI 7 Section 12.4.3 ..Z -

LRFD

(b)ASD

Fig. 5-36. Required strength of bracing connections according to AJSC Seismic Pro,•ision.s Section F2.3(i)for Design. Case JI.

LRFD

":-'faln Member Design Considerations .

(tension)

(a) £.RFD

There is no shear in the beam due to seismic loads. The required shear'strength of the beam

due to gravity loads is:

424 kips

606 kips (tension)

The two sets of forces to be considered in Design Case II are shown in Figures 5-36 and 5-37 (also see Figures 5-17 and 5-18 ofExample5.3.5).

(a) lRFD

ASD (385 kips+363 kips)sin45°

=529 kips

424 kips (tension)

606 kips (tension) (b)ASD

Fig. 5-37. Requind strength of bracing connections according to AJSC Seismic Provisions Section F2.3(ii) for Design Case If.

.·', .

\

l

:.

S-212

BRACED FRAMES

1

l

L ,,

...... I

,, :~

"·

Design Case I controls. In the usual computer or manual analysis of this design problem where all members intersect at a common gravity axis work point, the beam does not participate in the carrying of this shear, and is designed for gravity loads and the axial load due to the mechanism analysis required by AISC Seismic Provisions Section F2.3. Jn reality. however, the beam pruticipates with lhe gusset plates as the principal carrier of the shear due lo the brace force vertical components. The total vertical shear in this case is 155 kips (LRFD) nnd 529 kips (ASD). As a ·'rule of lhumb," lbe beam should be able to carry one half or more of this shear, plus the specified gravity shear. to ayoid the need for doubler plates. The chosen W24x68 beam, with an available shear strength of 295 kips (tRFD) and 197 kips (ASD) from AJSC Manual Table 3-6, \Vill require doubler plates. To avoid the use of doubler plates, use a W24x146. This is an increase in weight of (I 4<5 lb/f1 - 68 lb/ft)(25 fl) =1,950 lb. Alternatively, the beam stubs shown in Figure 5-33 can use the heavier W24x146 section and the original W24x68 can be used betWe.en the splices. As yel another possibility, a continuous pl are can be used in lieu of 1he W24x146 stub, and the W24x68 can be connected to this plate. This option is shown in Figure 5-43 as an illustration, withoul calculations. The option using the W24x146 and the W24x68 in.till piece will be used here. Brace-to~Gusset Connection Design

The design approach used here will follow that of Example 5.3.8, with single pass, 'A-in. field welds between the brace and the gusset. The weld length required is determined using AISC.Manual Equacfons 8-2a and 8-2b. For the top gusset, the ma:umum force is 550 kips (LRFD) and 385 kips (ASD), thus: LRFD

Rn =0.928Dl

4 welds(l.392 kip/in.)D/ > P,,

4 welds(0.928 k:ip/'10.)Dl > P0

l=

P.. 606 kips

4 welds(l.392)D/ >

4 welds(0.928)Dl > P.,

l=

l

4 welds(l.392 k:ip(m.)(4 sixteenths}

= 27.2 in.

Use (4) 29-in.-long lfi·in. fillet welds to connect the brace below the beam to the gusset plate. Determine the minimum length, I, required for the brace-to-gusset lap The limjt state of shear rupture in the brace wall is used to determine the minimum braceto-gusset lap length. Note that 1he expected brace rupture strength, R,Fu, n:iay be used i'.1 tl'.e detennination of the available strength according to the User Note m AISC Seismic Provisio11S Section A3.2.

Using AJSC Specification Section J4.2, including R1 from AISC Seismic A3.l:

=24.7 in.

(from Spec. Eq. J4-4) In this equation, Anv is taken as the cross-sectional area of the four walls of the brace, Anv = 4lltJu. Therefore:

l 2!.

385 kips 4 welds(0.928 kipfrn.)(4 sixteenths) ..

Use (4) 26-in.-long A-in. fillet welds to conoecc the brace above the beam to the gussel plate. For the bottom gusset, the maxjmum force is 606 kips (LRFD) and 424 kips (ASD) and the required weld length is:

"~·

\

Pu

¢(0.60)R,F,. (4tw) 550 kips 2! 0.75(0.60)(1.3)(58 ksi)(4)(0.465 in.)

= 25.9 in.

Table

.

Solving for the minimum lap length, /, for che brace above the beam:

1

~·: 1

Provi:~i
R1 =1.3

LRFD I=

424 kips

=4 welds(0.928 kip/in.)(4 si.xcccn1hs) =28.6 in.

n .

550 kips 4 welds(l.392 kii>fio.)(4 sixteenths)

ASD

LRFD

Rn = 0.60R,F,. (4/td~s)

ASD

¢Rn =l.392Dl

5-213

S.3 SPECIAL CONCENTRICAU.Y BRACF..D FRAMES

2! 8.71 in.

ASD l~

ilPa

0.60R1 Fu (4tc1u)

~

2.00(385 l;ips) 0.60(1.3)(58 ksi)(4){0.465 in.)

~

9.15 in.

The 26 in. required for the Y..-in. fillet weld controls. Solving for the minimum lap length, l, for the brace below the beam:

.BRACED FRAMF.S

5.J Sl'J::,UAI. l...Vl~\..l!N I KJl...Al•.l..l

.

~

LRFD

ASD

l~ 606.k.ips(S.71 in.)

550 kips ~9.60

in.

'

~IO. J in.

DP.

J

The 29 in. length required for the 1,4-io. fillet welds controls.

Check tflst the bracing connection can accommodate brace buckling

according to AJSC Seismic Provisions Section F2.6c(3) The requirements of AlSC Seismic Provisions Section F2.6c(3) are met through the use of option (b}-rotation capacity. As explained in the User Note of tlut section and in tbe Commentary Figure C-F2.9, accommodation of inelastic ro1alion is ~mplished "'ith the brace terminating before the line of restraioL Figures 5-37 and 5-38 show the 21 cJearance beyond lhe end of the brace.

P

¢F1 wp

=

.

I~--

t~-

385 kip~

ASD

LRFD

P.,

I~ 424 kips(9 15 in)

-

.tSKJ\l...~U l'IV~JVIJ.;J

550 kips 0.90(36 ksi)(25.8 in.)

F1 w 1

= 1.67(385 kips) 36 ksi(25.8 in.)

.

=0.692 in.

= 0.658 in.

Use a ~-in.-thjck gusset plate for !he brace above the beam. For the brace below the beam, the width of the gusset on the Wbiunore section is: w p = Di,_.~ + 21 tan Q

=7.50 IO.+- 2(29.0 in.)(tan 20°) =28.6 in.

The choice of a rela1ively small Whitmore sec1ioo resuhs in a tapered gusset, which is ben· cficial because it allows 1he brace to be located closer 10 the beam while still accommodating brace rotation by providing a 2t clearance according to AlSC S~ismic Provisions S~tion F2.6c(3) and Commentary.

Determine gusset plate thickness for the limit state of tensile yielding on the Whitmore section fo keep the gussets compact, choose an angle!), as shown in Figure 5-38, of 20°. Ex:implc 5.3.8 used$::: 10°, but in this example ::i smaller angle will result in shorter gusset interfaces nnd larger welds and may resuh in concentrated forces th:ll cause yielding or crippling in the beam and column.

B

With cj> =20°, the gusset thickness can be estimated. For lhe top brnce, the width of the gusset. at the \Vbitmore section is: Wp

=

Dbraa

Face of beam flange

+ 21 tan c>

W.P.

=6.875 in.+ 2(26.0 in.)(tan 20°} =25.8 in.

~beam

Find the minimum gusset plate thickness based on the limit state of tensile yielding.

R,. =F.,.A1

+

tor determining Whitmore section is 30°.

Note: Maximum

(Spec. Eq. 14-- l )

= FylpWp Fi&. 5-38. Geometry of gusset to accommodate bending ume.

5-2l6

BRACEP FRAMES

5.3 SPECIAL CONCENTIUCALLY .BRACED FRAMES

Find tlie minimum gusset plate thickness based on t11e limit state of tensile yieldfog.

Rn =F1 A8

(Spec. Eq. J4-l)

= FytpWp

"(•f :

.~:

I

•,j,

~R,, =$(0.60F1 Agv ~ V1>:F11An1)

ASD

Pu

. Ip~--

tp > __ 0Pa _

Fywp

Fywp

606 kips 0.90(36 ksi)(28.6 in.)

,•,·. ,_.,

ASD

LRFD

.

R11 ~ 0.60FyA8v + VbsFuA~,

'

n

n

= 0.75(842 kips+299 kips)

LRFD

<\:.

5-217

= =0.654 in.

=856 kips> 550 kips

~:~

o.k.

=

o.k. -

For the gusset plate below the beam:

:::: 1.67(424 kips) 36 ksi(28.6 in.) =0.6S8 in.

842 kips+ 299 kips . 2.00 57 l kips > 385 kips.

:

Ani = 7.50 i.n.(v.i in.) Use a ~-in. -thick.gusset place for the brace below the beam.

:::: 5.63 in.2

A811 = An1

Check block shear rupture of the gusset plate

:::: 2(29.0 in. ) (~ in.)

The available strength for the limit state of block shear rupture is:

Rn= 0.60F;,Anv +U1>sFuAn1

$

0.60FyAgv +UbsFuAru

=43.~ in. 2 (Spec. Eq. 14-5)

For the gusset plate above the beam:

0.60Fy,<\.gv

=0.~0(36 ksi)(43..5 in:~) =940 kips ! .;

An1

= 6.875 in.(3,4 in.)

2

UbsF11.An1 , = l.0(58 ksi}(5.63 .in.

)

=327 klps

=:5.16in. 2

..

LRFD

Agv= Anv

=2(26.0 in.)(JA in.) =39.0 in. 2

R,.

~Rn=$( 0.60FyAgv + Ub,FuAm)

I

.,

'

=0.75(940 kips+327 kips)

area,

Since the gross shear A811 , and the qet shear area, Anv, are equal in I.his case, the shear yielding component, 0.60F1 Agv, is smaller tlJan the shear rupture component, 0.60F.,Anv:.'.

:::: 950 kips > 606 kips

-=

=842 kips

=L0(58ksi)(5.16 in.2 ) . = 299 kips

ASD

0.60FyAgv + Ub$FuA111

n

o.k.

0.60F1 A8 v= 0.60(36 ksi)(39.0 in.2 )

U1>~F;;A"'

•.

n

940 kips+ 327 kips 2.00 = 634 kips > 424 kips . .. - -..

o.k.

'

Determine .gusse.t geometry·

From Figure 5-38, the gusset geometry can be determined as foll~ws: L

=Jceb tan6+asin0tan0)1 +(eb +asin0)2

a =

d

2 + (lw + 2t) tanQ

a L6 = - - + t'b tan 0 - ~ cose L8

=(L+l..., +2c)ws0+%sin0-eb -l(L+l,.. +2t)sin0-%cos0-ec jtan(90°- 0Allle!UCAN

INSTIT\ITI! OP STEEL. CoNSTRUCTI.ON

5-218

BRACED FRAMES

For the gusset above the beam:

5.3 SPEClALCONCENTJUCAUY BRACED FRAM~

Ls= (L+l., +2r)cos0+%sin0-eb -l(L+lw

The width of the gusset edge, d, is 2.00 in. wider than the brace diameter to allow clearance the gusset comer, i.e., 1.00 in. on each side of the HSS. between the HSS

and

8 ·88 in. ( . 45°' =(32.1in.+26.0 in.+ 2.00 in.Xcos450\,+---i-sin r

d:: 6.875 in.+ 2.00 in.

-[(32.l in.+26.0 in.+2.00 in.)(sin45°)-

=8.88 in.

88

· ~ in. (cos45j-6.35 in.]

= 17 .8 in. Use Ls = 1 ft ili in.

2 = 12.4 in.

=atan0+2t

lb

= 14.6 in.(tan45°)+ 2.00 in.

12.7 in.

ec=-2

=16.6 in.

= 6.35 in.

For the bottom gusset:

0=45°

= 7.50 in.+ 2.00 in.

d

= 9.50 in.

=20°

AISC Seismic Provisions Section F2.6c(3) requires that the brace connection accommodate the flexural forces or rotation imposed by bmce buckJing. This can be achieved either by option (a) designing the connection to have an available flexural strength of the expected brace flexural strength, R1 Mpo multiplied by 1.1 (LR.FD) or by 1.1/1.5 (ASD) or option (b) providing rotation capacity to accommodate the required rouirion. This brace configuration satisfies option (b) as it pro,·ides rotation capacity by providing the minimum 2t offset distance recommended in AISC Seismic Provisions CommenlaJ')' Section F2.6c(3). Using a %-in.-thick gusset plate, 2t = 2(3A in.)= 1.50 in., but use 2.00 in. to allow for a possible gusset thickness increase as the calculations proceed. With !..., 26.0 in.:

I..,= 29.0 in.

a

=2+(lw +2t)tan$

l,

=~+(lw+2t)tan$ 2

= 9.SO in.+ (29.0 in.+ 2.00 in.)(tan 20°) 2 =16.0 in.

L = d

I

2t = 2.00 in.

=

Jce0 tan0+ asin0tan0)2 +(eb + asin0)2

= [12.4io.(1an45°)+16.0 _in. (si!l,45°)(tau45°)j2 +[12.4 io.:i-!_6.0 in.(sin45°)j2

8 88 in.+ (26.0 io. + 2.00 in.)( tan 20°)

= ·

12 4 . . in.

x tan(90° - 45° - 20°)

24.7 in. eb=-- -

a

+2t)sin0-~cos0-e,:jian(90°-0-$)

2

\

:: 33.5 in. Use L = 2 ft 9'h in.

.

=14.6 in.

a 9 LA•=--+eb tan -ec

l·"..:.

cos9

L

=J
=~12.4 in.(tan 45°)+ 14.6 in.(sin45~)(tan 45°)]2 +112.4in.+14.6 in.(sin45°)J = 32.l in. Use L

= 2 ft 8 h in. 1

a Ltt=-· +ebtan0-ec cose 14.6 io. =-+I 2 .4 .ui. ( tan 450) - 6 .35 .m. cos45 =26.7 .in. Use L,.. =2 ft 2~ in. 0

=16·0 in.+12.4 in.(tan45°)-6.35 in. cos45° =28.7 in. Use LA =2 ft 43.4 in. Ls= (L+l,.. +

2t)cos9+~sin0-eb -l(L+l,.. + 2t)sin0-%cos0-ec }tan(90°-9- ~)

=(33.5 io.+ 29.0 in.+ 2.00'in:J(cos45°)+ 9· 5~ in. (sin45°)-12.4 in.

I .

. . . "'

l

9.50 . - (33.5 m.+29.0 m.+2.00 m.)(sm45 r --in. (cos 45°'1- 6 · 35 m. 2 Xtan(90°-45°-20°) = 19.8 in. Use La =l ftlliin. AMEJUCAN lNSTO"IJTS 01' Sn;a CONSTIWCTJON

~:

BRACED FRAMES

5--220

The required compressive slreJtgth of the gussec plate is:

10 = atan0+2t = 16.0 in.( tan45")+2.00 in. = 18.0 in. t

l


ASD

LR.FD

This completes the gusset geometry, and the basic gusset geometry of Figure 5-33 can be generated.

P,,

=488 kips 56 l kips > 488 kips

(•

Pa = 1.1(311 kips) = 342 kips

= 1.1(444 kips) o.k

373 kips > 342 kips

o.k.

Top Brace-to-Gusset Connection i

.,,f

The design of the top brace-to-gusset connection in Example 5.3.8 is very similar. The gusset plate there is 11.4 in. thick wltlle it is ~ in. thick here due to the wider gusset plate used in this example. For the limit state of tensile rupture of the brace, the check in Example 5.3.S is adequnte and need not be repeated here. Because the gusset plate is thinner in this example, less :u-ea is removed from lhe brace to accommodate the gusset plate.

Check the top. gusset plate for buckling on the Whitmore section Because the gusset geometry is different from the gusset in Example 5.3.8, gusset plate buckling must be investigated. Determine the available compressive strength using an effective length factor, K = 0.6, for the extended comer gusset, from Dowswell (2006). As noted in the beginning of Example 5.3.8, the additional 1.1 factor specified in AlSC Seismic Provisions Section F2.6c(2) is applied to the expected brace strength for determining the required compressive strength based on buckling limit staces. Klb

A11 =Ag-2[tp+2(gap)]tt1u Using a gap of l/i6 in. on each side of the brace slot to allow clearance for erection:

An = 10.3 in.2 - 2[¥.t in.+ 2(1/16 in.)](0.465 in.)

=9.49 in.2 > 1.3(7.50 in.)

= 9.75 in.,

U = 1.0, thus:

=46.0

A.,= UA.,.

From AISC Manual Table 4-22, wich KL/r

•->.

Check the brace effective net area From AISC Seismic Provisions Section F2.5b(3). the brace effective net area, An(bra"J' should not be less than the brace gross area, Ag. Thus the net area is:

from AISC Specification Table 03.l, Case 5, if I= 29.0 in.

0.6(16.6 in.)

7 = :IA in./..Jfi

gl ~:-

Bottom Brace-to-Gusset Connection

=46.0, the available critkal stress is:

LRFD

ASD

~: =19.3 ksi

$cFcr = 29.0 ksi

=9.49 in.

Since A~< A.r, reinforcement is requir~d. The approximate area. of reinforcement required, Am. is the area removed, but the position of the reinforcement \\.111 reduce U to less than 1.0.

(A,. + A,.,.)U ~ A8

Try U = 0.80, then:

ASD A,,,=

4>cP11 =$cl'CrAg =4>cFcrtpWp

.

Pn =FcrAg --

nc

nc

FcrlpWp .O.c

=29.0 ksi(~ in.)(25.8 in.)

-

=561 kips

= 19.3 ksi{~ in.)(25.8 in.)

=373 kips

2

The required area of reinforcement can be obtained from:

From AISC Specification Equation E3-l . using the width at the Whitmore section, the available compressive strength of the top gusset plate is:

LRFD

2

= 1.0(9.49 in. )

10.3 in.l 0.80

9 49 . 2 . 1.ll.

= 3.39 in.2 Try two flat bars of ASTM A572 Grade 50 steel 1 112 in. x l 'h in., with. a tot~l area _of 2(1 'h in.)2 4.50 in.1 With Fy.,, 50 ksi, ASTM A572 Grade 50 matcnal sausfies 11. requirement in AISC Seismic Provisions Section P2.5b(3), that the yield strength ot ti.~

=

reinforcement be at least the specified minimum yield strength of the member. The arrangement is shown in Figure 5-39. AMmoCAN INSTTrvTI! oP STEEL CoNSTRocnoN

BRACED FRAMEs

From Figure 5-39: Dbraa

Determine

xfor the composite cross section.

tu 2

r i = - - - -1

2

7.50 in. :::---

i 2

in.

A in. 2

in. 3

Half of brace One Flat Bar

2.24 4.50

4.75 2.25

10.1

t·

-

7.00

20.7

Dbrac~ 1'l!i in. r?.::::--+--

2

2

7.50 in.

I~

in. =---+-2 2

x

= 4.50 in.

xA

Part

0.465 io.

2 ==3.52 in.

5-223


~-

10.6

.I:XA

=-IA 20.7 in.3

7.00 in.2

The distance to the centroid of a panial circle is given by:

=2.96 in.

_ r1sin0 x=--

FromAISC Specification Table D3.1, Case 2, which applies to HSS with reinforcement added:

0

where_ the_ total arc of the partial circle is 29, and 9 is measured in radians. Although the brace is slightly less than a full half-circle because of the slot as shown in Figure 5-39 use an angle, e, of 1tl2 for simplicity. '

I

x

U =I-. I

t;..

'··

= 1_ 2.96 in.

29.0 in.

=0.898

. --'--""sin(it/2) radJ •-xbroc~ -_ 3 . 52 10. -

{n/2) rad

I~

A,, = An(bn>e~) +Am

= 2.24 in.

2

=9.49 in. +4.50 in.

2

~-

= 14.0 in.2 =4.50 in.

Ae =UA., · =0.898(14.0 in. = 12.6 io.2

~·gusset

pla_ te

2

I

)

> 10.3 in.

\

2

\

o.k.

Design welds connecting flat bars ~o brace According to AISC Seismic Provisions Section F2.5b(3)(ii), the flat bar is connected to the HSS brace to develop the eitpected strength of the flat bai on each side of the reduced section (the eitpected yield strength, RyF.,. is used here). The reduced section is the length of the HSS from the extent of the slot (dimension x of Figure 5-33) to the start of the HSSto-gusset weld. The required strength of the weld is based on the expected flat bar yield

strength using Ry from AlSC Seismic Provisions Table A3.1 for ASTM A572 Grade 50 bars. For ASD, use 1.011 .5 of the expected su-ength of the flat bar reinforcement. ASD

LRFD

R1 F1 AJb = 1.1(50 ksi)(2.25 Fig. 5-39. Cross section of brace below the beam at net secticn.-

=124 kips

in.2)

R 1 FyAJbll.5

=l.1(50 ksi)(2.25 in.2 )11.5 =82.5 kips

S-224

BRACED FRM1ES

Usmg two ~ingle pass V...-in. fillet welds, from AJSC Manual weld lenglh required is:

Equarion~

8-23 and 8-2b, the

The requireJ compressive strength of the gusset plate is:

ASD

l.392D/ > P.,

1.

=

124 kips 2 welds{l.392 kipfm.){4 sixteenths)

I _

82.5 kips ,..- 2 welds(0.928 k.ip/in.)(4 sixreenlhs)

=11. l in.

Use (2) J l 1h-in.-long

v...in. fillet welds on each side of the reduced section of lhe brace.

Since !he gap between !he edge of the l ~ in. x 1~ in. flat bar and the brace is 0.037 in., as shown in Figure 5-39. and is less than V.6 in. (see AWS 01.l clause 5.22.J), lhe Y..-in. fillet welds are adcquaie. Note !hat the flac bar reinforcement need:. co e.."tend I 1'h in. on each side of the end of the actual slot, ~hich includes the dimension x that may be requjred for erection.

'..

..

Check the bottom gusset plate for buckling on the Whitmore section

:1'1

m .. 111 .,

Detennine the available compressive strength using an effective length factor, K =0.6, for 1he c:(tended corner gus~et, from DowswelJ (2006). As noted in !he beginning of Example 5.3 S, the additional l. l factor specified in AISC Seismic Provisions Section F2.6c(2) is applied to compression buclc.ling limit slates. K/11

7

P,,

= J.1(518 kips)

0.6(18.0 in.) = 3A in./ Jf.2

609 kips> 570 kips

.

=1.1(363 kips) = 399 kips

=570 kips

0.928Dl >Pu

=11.1 in. !

P.,

ASD

·!

LRFD LRFD

S-225

5.3 SPEOAL CONCENTRICALLY RR.ACED fRA.MES

o.k.

405 kips > 399 kips

'

I

o.k.

Connection Interface Forces Tue Unifonn force Method (UFM) requires that a consinunt on the locations of the inter(ace centroid~ be satisfied in order to eliminate moments on che gusset to-beam and gusset-to-column interfaces, M11 and Mc. respectively. When this constraint is not satisfied, moments will be introduced on the connection interfaces. This is diS<:USsed in Part 13 of the AISC ,\-fa1111al, and the tenninology used there is repc:sted here. Let (i and ~ represent 1he distance from the column flange 10 the actual centroids of 1hc gusset-to-beam and gus~t-to column connections, respectively. When the calculated a > & or the calculated ~ > ~. the additional shear mduced in the beam or column due to the moment may add to the shear, Vb. in the beam and He in the column. Thus, for the beam: When a>a:

When a< Ci:

=49.9 From AISC Manual Table 4-22, with KUr

LRFD

=49.9, rhe available critical stress is:

·

ASD

I,_ .

where

Rb =beam end reaction s =snip siz.c in the gusset where the top flange of the be:im connects to the column O:mge

18 .• J<.i For the column:

From AlSC Specification Equation E3-l, using the width at the Whitmore section, lbe available compre..~sive strength of the bottom gusset pl:11e is: (,

i3:

Total column

l. J

When !l >

LRFD

. ~,P,.

=~cFcrA1 =9cFcrtpWp =28.4 ksi(JA in.)(28.6 in.) =609 kips

ASD I

.!i_= F,.,A, n ,. ilc

~hear= mu {I~ +Ii~sl .IHcl}

When~<~:

= FcrlpWp

n ,.

= 18.9 ksi (~ in.)(28.6 in.) a:405 kips

In oonseismlc nnd low-seismic design, this is not ao issue because the brace forces are more closely matched to the beam and column sius and calculated loads are used. In some

·"

S- 226

BRACED FR.AMES

structures detailed for seismic. resistance, the connections are not designed for calculaled loads but rather must be designed for the expec!ed tens~le .strength of the brace, RyFyAg ~ This is normally larger than the actual design load from the applicable building code. For; instance, the HSS6.875x0.500 brace would normally be designed for poinr-to-point buckling with a length of ~(12.5 + (12.5 ft) 2 = 17.7 fr. The available compr~sive strength. of this brace is 207 kips (LRFD) and 137 kips (ASD) from AISC Manucil Table 4-5, and lhe actual brace load will ,be less th
ftf

_

26% in. -1.00 in.

2

"'

2

e=

6 35 == · in.(550 kips) 28.6 in.

=6.35 in. (385 kips)

""122 kips

= 85.5 kips

28.6 in.


e=

~given by AISC Manual Equatjon .

:::: 9.45in.(tan45°)+12.4 io.(tan.~5°) - 6.35 in.

=13.9 in. (550 kips)

r 13 :::::· ·9 in.(385 kips)

=267 kips

=·187 kips

28.6 in.


p

Vac =-Pa

r

7.85 ,,,, _ _inT _ .)50 ki 'PS)

""'7.85 in. (385 ki s) 28.6 in. . p

= 151 kips

=H!6kips

28.6 in.

= Vb(a..:. a) may add to the beam shear. Choose ex= Ci=

e" tan0-ec

I

(Manual Eq. 13-1)

=~(a+~ )2 +(~+eh )1

=~(13.9 in.+ 6.35 in.)2 +(7.85 in.+ 12.4 in.)2 =28.6 in: AMEIUCAN lNST11V11! OF SJ'Ea CoNS11UJCT10N

....

because

p S j3.

(Manual Eq. 13-6)

I!

=122 kips(9.45 in. -

=195 kip-in. .

et>

::::

12 .4 ~- (385 kips) 28.6m. .

-

' .

From AlSC Manual Equation 13-19:

Mac=Hac(~-P)

Mvc=Huc(~-~) - j3)

'

Vab=-Pa r

=167 kips

=238 kips From AISC Ma11ual Equation 13-19:

~ =. 7.85 in.< i3 = 9.45 in.

a=

\

28.6 in.

13.9 in. - ~(tan45°) =12.4 in.(tan45°)- 6.35 in.

The c-0lumn shear will not be increased by the momeot Mc = He ('13 Therefore; u~e Ct::::: 13.9 in. and~= 7.85 in. Then:

= 12 .4 in. (550 kips)

''

From AlSC Manual Equation 13-4: \

eb

Vu1>=-P.,

r

,;

Hab :z-Pa

H111>=-Pu r


=15.5 in. Since a> ii, the moment M1> 13.9 in., then:

l

a

a

V.,c:::: -~ Pu

a= ~tan0+ eb tan9-ec

...

Hoc =-Pa r

r

Choosing P= 'j3; 9.45 in., the constraint between a and eb tan ec, gives: 13-1, a - p tan

r

ec

ec P. Hue==-,. r


l OO . + . m.

::::: 9.45 in.

a-~tane::::


from AISC Manual Equation 13-3:

28.6 in.

+.LOO in.

= 13.9 in.

A =17% in. - 1.00 in.

1.

ASD

LRFD

I·

From the geometry show·n in Figure 5-33 and the Uniform Force Method variables inAISC Manual Part 13:

ex="

Tue controlling brace forces for the top gusset interface forces are:

From AJSC Manual Equation 13-5:

Top Gusset-Des,ign Case I

S-227

5.3 SPECIAL CONCENTRlCALLY BRACED FRAMF.S

7 .85 in.)

=85.5 k.ips(9.45 in.-7.85 in.)

=137 kip-in.

I I;

. al Note lhat the sum of the horizontal gusset forces must equaJhb t e race honzont compo- .. ... nenl The sum of the vertical gusset forces must equal the brace vertical component.

t

5-228

BRACED FRAMES


5-229

\.!t:

Gusset-Design Case I

Bottom

LRFD

From the geometry shown in Figure 5-33;

_

a--

From AISC Manual .Equation 13-2:

28.8 in. -1.00 in. · 2 . " + I .00.lll.

.

=152 kips

a= 14.9 in., then: (Manual Eq. 13-1)

14.9in.-J3(tan45°)=12.4 in.(tan45°)-6.35 in.

J3 = 8.85 in.<~= l 0.5 in. Use a= a= 14.9 in. and J3

LRFD

=12.4 in.(518 kips)

(Manual Eq. 13-6)

Muc

+ (8.85,in.+ 12.4 in.) 2

=~ 363kips . m.

~·

)

gusset-pesign Case II

s

I

•.(

The geometry is the same as Design Case I, only the loads have changed in magnitude and direction as shown in Figures ~-?6 and5-37.._ · ·


..

a

Hub=-P,,

'

Hab=-Pa

r

r

14.9 i.n. ( ) = 30.l'in. 518 kips

=256 kips

-l!fc I· 13 -

,.,., ;

Top

=76.6 kips


'.

'

r

6.35 in.(

=76.6 kips(l0.5 jn. - 8.8,5 in.) =126. kip-in.

In this example, the column. shear, He, is greater than the combined sh~ar; I~ 2 Therefore, Figures 5-~0,a and 5-40b show pnly the He forces. . . . . .

Hac =-Pa ec

= 109 kips

Mac::::: Hae (~-13)

Figures 5-40a and 5-40b show thi; force distribution for Design Case I. The total column shear when J3 < ~ is discussed in the previous Connection Interface Forces section.


=3Q.'ii; 518 kips)

""Hu~(~-13)

::

ASD

6.35 in.(

.4 in. {363 kips) 30.l in.


=109 kips(I0.5 in.-8.85 in.) =180 kip-in.

' .t

12

=150 kips


r

~

=

=213 kips

=8.85 in.

:

a

Vab=-Pa r

30.1 in.

From AISC Manual Equation i3-3:

"·'

eb

Vub= - Pu r

=30.l in. .•

.


eb

o.l<.

r = ~(a+ec )2 +(P.+eb)2 ·

=~(14.9 in.+ 6.35 in.)2

= 107 kips

Froni AISC Manual Equation 13-4:

a-J3~n6= eb ta.n0-ec

ec uc=-Pu

= 8.85 in. (% 3 kips) 30.l in.

30.l m.

=10.5 in.

H

r

=8·85 ~0 '{518 kips)

. + 1.00 ill.

2

.

Vac=~Pa

r

A_ 19.9 in. -1.00 in.

Choose a=

. From AISC Manual Equation 13-2:

V..c ::::~Pu

=14.9 in. "' -

ASD

14.9 in. (

= JO. l in. 363 kips I

= 180 .kips

, .

.

LRID From AISC Manual _Equation 13-3:

from AISC Ma11~al Equation 13-3:

) Hue= ec Pu r

= 6.35 in. ( 444 kips)

28.6 in.

= 98.6 kips

AMEIUCAN lNSTflUtt OF STEEi.. CONS'l'RUCTION

ASD

.,

H

ec ac=-Pa r

.

-

= 6.35 in. (311 ki~s) 28.6 in.

= 69.1 kips

I

S-230

BRACED FRAMES

LRFD


a Hub=-P.


Cl

Hab= - Pa r

r 39 0 = -8.6m. · '. · ( 444 ldps) =216 kips

!

,,

f3

28.6 in.

r

28.6 in.

=122 kips


= H.c(~-13)

Moc =H ac (j}- f3)

=69.1 kips(9.45 in.- 7.85 in.) =1l l kip-in.

=98.6 k.ips{9.45 in. - 7.85 in.) =158 kip-in.

85 =~·-8.610. ~-(31 J kips)

ps

28.6 in.

=135 kips

From AISC Manual Equation 13- I9: M.,,

r

)

= 12.4 in. (311 ~ps)

. ) kips

=193 kips

Vnc=~Po

Vuc=-Pu

eb

Vob=-Pa r

r

=12.4 in. (444


I:


eb V.,b =-P.

= 13.9 in.( 31Ikips) 28.6 in. = 151 kips


.ASD

LRFD

ASD .


= 7.85 in. ( 444 k.i


t

=85.4 kips

13.9' 137 kip-in,

195 kip-in.

!'"'~··

kips

)

r·~·ps

238 kips 238 kips 238 k i i s . . 19.9 kips . 238 k"tps 267 kips 122 kips 122 kips

t 46.0 kips

I

46.0klp~

i

109 kips

167 kips

1~.9 kips ___ .-------'-

t

46.0 kips

~ips

j 213 kips

180 kip-in. 180 kip-in.

F2klps )

(

213 kips

109 kips·

32.2 kips

' , 167 kips 85.5 kips 85~5 kips 32.2 kip~ 32.2ki'Ps" .

I t

I

t150 kips

·

i

~ 256 kips

152. kips

1so kips

1~.8 kips____ _.y__

F7klps \

kips)

_,__

1=~===1=ao=ki=.p=s~

r

J

(

76.~~s____J

\

.:__t__ 180 kips

"'

.

It)

- - ! - -- - . \ - -- - - "

c::i

1;-;J

6 .35. Fig. 5-40a. Design Case I gusset interface forces (LRFD).

_

50l
126 kip-in. 126 kip-in.

~

. ,,.J

187 kips

1so kips I

I

- - - 1 - -- ¥ - - - ' -

:

I

167 kips 167 kij__s

· 12.8 kips

76.6 kips 76.6 kips

213 kips 1=-.===2=56=ki=.p=s~

f213 kips

kips

\

kips)

J . J

Fig 5-40b. Design Case l gusset interface forces (ASD). AMERICAN

lNS'JTlVTI! OP STESL CONSTRUcnON

..

.

-Ii~ ~232

BRACED FRAMES

Gusset Below the Beam-Design Case If

LRFD ec

= 6.35 in. ( 606 kips)

= 6.35 in.(424 kips)

=128 kips

=89.4 kips

30.1 in.

AISC Seismic Provisions Section F2.6b and Commentary require that connections that involve a beam, a column and a brace satisfy option (a) or (b) h~ that section. This example wiU use option (a)-a simple beam-to-column connection.

30.l in.

FromAISC Manual Equation 13-5:

0.

To satisfy option (a), a splice can be provided in the beam just outside of the connection region as is done in this example. If che beam splice were a perfect pin, then (1.1 R1 Mp)splice = 0. As long as the splice can accommodate 0.025 rad of rotation without binding (i.e., no fouling of parts), AISC Seismic Provisions Section F2.6b(a) will be satisfied. The simple connections presented in Parts 9 and IO of the AlSC Manual are deemed to comply with

r

Section F2.6b(a).


a HiJJ=-Pu r

Hab=-Pa

49

= ~,,Q.1 · '."· (606 kips) m.

14.9 = - in.( - 424 ki ps) 30.l in. =210 kips

= 300 kips

Fro!11 AISC ManualEquation 13-2:

Jll

Ductility Requirements

H ac =-Pa r

r

6

.-


ec Huc= -Pu

From AISC Manual Equation 13-2: Yoe --

13 -Pa r 8 85 = · in. ( 424 kips) 30.l in. =125 kips

=8 ·85 in. (606 kips) 30.1 in.

:= 178

kips



--

,.

Vilb =-Pa

= 12.4 in. (606 kips)

30.1 in. = 250 kips

68.6 kips~ ~ 19.9 kips ~

30.1 in.

=175kips

From A.ISC Manual Equation 13-19:

Muc = Huc(~-13)

./:

=12.4 in.(424 kips)

, .

~

·. 46.0 kips

eb

t,, '

~233


Each of the Design Cases l aod II has a subsidiary case in which the compression brace postbuckJing strength is considered. This affects the design of the main members but not, in this case, the gusset connection.

ASD

FromAISC Manual Equation 13-3:

;; ,

From AISC Manual Equ~tion 13-19: Mac

~:)

=Hac(P-13)

=128 kips(I0.5 in. -8.85 in.)

= 89.4 kips(I0.5 in.-8.85 in.)

::::: 2 ll kip-in.

=148 kip-in.

211 kip-in.

Figures 5-41 a and 5-4 lb show the force distribution for Design Case II. The total column shear when f3 <~is discussed in che previous Connection Interface Forces section.

He:. is greater than the combined shear, I~ _,_Mc 2 Therefore, Figures 5-4la and 5-4lb show only the He forces. fl-s

In this example, the column shear,

AMERICAN lNSTTIVre Of STEEi.. CONSTRIJCnON

I

I

( ,~:.~::.1 ----_,,___. . ~ 211 kip-in.

I 6.35. Fig. 5-4/a. Design Case II gusset inrerface forces (LRFD).

A.\IERICAN l?>!STmntl OP STEl!L CONSTRucnoN

5-234


BRACED FRAMES

Design of Splice

5-23

LRFD

Since the beam splice is in a mairi member, the design of the member needs to be considered. 1n normal design practice, the beam will be considered to be continuous from column-to-column. in this example, a splice is inserted 2 ft 6~ in. from the face of the column. This splice must carry the loads thac would exist a1 this point in the continuous beam. There.fori:. the.splice must carry the beam shear, beam axial force, and a moment equal to the beam shear tii;nes 2 ft _6~ in. This moment is the moment that would exist in the beam as designed, withom the splice.

Shear: V.,

ASD

=19.9 kips (gravity)

Shear: V,, = 12.8 kips (gravity)

Axial: Pu= 307 kips (compression)

Axial: Pa= 215 kips (compression)

Figure 5-42 shows the beam splice (one plate on rhe near face and one on the far face). In order to prevent binding at a 0.025 rad story drift, the clearance between the .bea.~ and the beam stub at the splice must be at least 12.4 in.(0.025 rad) = 0.310 in., where 12.4 in. is half of the W24x146 beam stub depth. Use a 1.00 in. clearance as shown in Figure 5-33.

Tiie extended shear t;ib presented in Part 10 of the AISC Manual will be used for che splice ·

d~sign, The splice must be de~i~ed b~fore it can be checked for ductility.

The splice is on the beam cen terline~ Use ~-in.-diameter ASTM A325-X bolts.

From Ex~ple 5.3:5 the required strength of the beam, and therefore the splice connection, is as fol~ows. The~e forces are also shown in Figures 5-35 and 5-37.

For gravity load alone- the connection to the W24x68 is designed as follows: ·· · The gravity shear force needs to be delivered from the centroid of the W24x68 bolt group to the face of the column. Therefore: ex =30.5 in.+(1/2 in.+2 in. +l~ in.)

:::::34.5 in. Interpolating from ATSC Manual Table 7-7 for angle::::: 0° withs= 3 in., ex= 34.5 in., and n=6: ·

Us:;~:

=i-I 151 kips I135 kips

13s kips . 12.8 kips ~ips

32.2 kips

135

kips

t __l_151

69.1 kips

1_7;;:-

89.4 kips ~75 kips

J

fF======~

-r---

148 kip-in.

(

12~_st

89~

12.8

kips- ~!

Fill plate~.. each side

210 kips '

f

~ 175 kips

~~kips)

f

47.8 kips _&

175 kips

~s

ASTM A325-X (Group A) bolts in dou-

kips

32.2 l
32.2 kips 89.4 kips

7-1 for

Manual Table %-in.-diameter ble shear, the available shear strength is:

l

--L210ki s

4" 19.9 kips (LRFD) 12.8 kips (ASD)

.

c-.i

Bolts °?'$" dia. A32S.:x in std. holes

•

("')

c.,

II)

307 ~ips LRFD 215 kips (ASD)

---+----'<---' d .....

148 kip-in.

'·

Gravity · ~

plus seismic

13.9"

Fig. .5-41b. Design Case If gusset interface forces (ASD).

1·

2'-6~"

I

J ~ ,J.

c.,

Gravity only 19.9 kips (LRFD) 12.8 kips (ASD)

l

'-~

PL%x15x19 (A572 Gr. 50) (1-NS, 1FS)

End of W24x68 beam

Fig. .5-42. Beam splice.

J

S.3 SPP.CtAL CONCENTRICAI

LRFD

ASD

R.. =JP.} + v,}

n

.

~R~= C~r,.

=1.56(61.3 kips) = 95.6 kips> 19.9 kips

o.k.

~ =c(~) = 63.8 kips> 12.8 kips

o.k.

The gravity shear force needs to be deliYered from the centroid of the W24x146 bolt group to the face of the column. Therefore:

e, =30.5 in.-4.00 in. Intcrpolacing from AISC Manual Table 7.7 for angle= 0° witJ1 s

=3 in., t!t = 26.5 in.. and

n=6: C=2.02

LRFD

.

i

..

=215kips

y =tan =Un

·r~: l (19.9 kips)

y

_1

~07

=tan·(;:) =Ian - 1( 12.8 k.ips) 215 !Ops

kips

=3.71°

=3.41"

ex= 30.5 in. -13.9 in. -4.00 in. =12.6 in.

C= 8.06

~ =C(~) o.k.

. ,

= 308 kips

=

ASD

~R,.=C~rn

?-

=J(215 kips)~ +(12.S kips)2

Use AISC Manual Tnble 7-7 with the angle from the Yerticil equal to 90" - 3.71° = 86.3' (LRFD) and 90° - 3.41° =86.6°
The available shear strength of the W24x146 bolts is:

:-l

=r;;r;vJ

The distance from the gravity plus seismic resultant force to the centroid of the W24x146 boltS is:

=26.5 in.

=2.02(61.3 kips) =114 kip~> 19.9 kips

Ra

= J(307 lcips)2+(19.9 kips)z

=I .56(40.9 kips}

For gravity load aJone-the coWlection to lhe W24x146 is designed as follows:

'

ASD

lRFO

r,. - =40.9 lvps

=61 .J kip'

~rn

__, S ~··

r." BR;\CFD FRAMES

=2.02(40.9 kips) =82.6kips>12.8 kips o.k.

For gravity plus seismic forces: The majority of the horiz.ontal seismic force is resotved into lhe gussets and does not reach the column face. The average gusset-to-beam connection length, from the geometry of Figure 5-33 and subtracting l io. for the snip, is:

(25 3.4 in. + 27~ in.)n =26.8 in. Assume for calculation purposes n point (26.8 in.+ 1.00 in.)/2 = 13.9.in. from the column face, as shown in Figure .S-42, can be used as a reference point to check the splice under gravity plus seismk loading. The resultant of the beam shear aod aiti:1l forces and the load ;ingle from the horizontal :t.""
LRFD

ASD

..

¢Rn =C¢rn

= 8.06(61.3 kips)

=..t94 kips> 308 kips

o.k.

6=C(~) = 8.06(..t0.9 kips) = 330 kips> 215 kips o.k.

For the W24x68 bolts:

ex= 30.5 in.-13.9 in.+4.00 in . =20.6 in. Interpolating from AISC ,\-fanua/ Tub le 7.7 for au angle equal to 75° withs= 3 in., ex= 20.! in., and n =6: C=6.54

.:' I

I

5-238

BRAC."ED FRAMES

LRFD

LRFD

ASD

= 267 kips> 215 kips

I

Tearout: Gravity

-

$rn = 1.21,rFu

=6.54(40.9 kips)

o.k.

ASD

Tcarout: Gravity

~=c(~)

$R,, = C$rn

=6.54 (61.3 kips) =401kips>308 kips

5..3 SPECIAi.. CONCENTRICALLY tlKAl ·.cu 1-KAMl:.:S

rn 1.21,rF,, -=---

= 0.75(1.2)(2.00 in.- 1h( 15!t6 in.)]

o.k.

n

x(0.650 in.)(65 ksi)

=58.2 kips/bolt

Check bolt bearing on the W24x 146 and W24x68 Because the force is eccentric and the AISC Manual eccentrically loaded bolt group tables are used, the lowest tearout strength of the bolt group should be used; in this case, the edge bolt controls. The bearing and tearouc strength limit states are separated for clarity in the following. For . SCBF systems, where lsrge deformations are anticipated. it is appropriate to assume that defonnation at the bolt hole is not a design consideration for the seismic loading, and the tearollt strength is checked at the end bolt with the 2.00 in. edge distance using AISC ,Specification Equation J3-6b. AJSC Seismic Provisions Section D2.2(1) limits the nominal bearing strength at bolt holes to 2.4dtF,,; therefore the available bearing and tearout strengths for the W24x146 web are:

LRFD

=2.02(38.8 kips/bolt) =78.4 kips > 12.8 kips

o.k.

r,. = 38.8 kips/bolt(l.5 / 1.2)

n

=48.5 kips/bolt

~ =c(~) ..: 8.06(48.5 kips/bolt)

o.k.

= 391kips:>215 kips

2.4dtFu

o.k.

.J

-=---

:::: 0.75(2.4)0~ in.){0.650 in.)

n

Q

= 2.4(11 in.)(0.650 in.)(65 ksi)

x(65 ksi)

For the W24x68:

2.00 = 44.4 kips/bolt

=66.5 kips/bolt q>Rn =C$r11

=2.02(66.5 kips/bolt) =134 kips> 19,.9 kips

Rn=

n

f LRFD

'. '

Bearing: Gravity

c( nrn J

= 2.02(44.4 kips/bolt) = 89.7kips>12.8 kips

o.k.

¢r" o.k.

Bearing: Gravity plus seismic

ASD Bearing: Gravity

rn

=$2.4dtFu

2.4dtF,,

-=---

n

= 0.75(2.4)(* in.){0.415 in.)

n

2.4(* in.){0.415 in.)(65 ksi) 2.00 28.3 kips/bolt

=

x(65 ksi) Bearing: Gravity plus seismic

$rn

o.k.

Tearout: Gravity plus seismic

=58.2 kips/bolt(l.5 /1.2) =72.8 kips/bole

= 587 kips > 308 kips

rn

~ =c(~)

=C$r,, =2.02{58.2 kips/bolt) =118 kips> 19.9 kips

= 8.06(72.8 ki~/bolt)

Bearing: G;Jvity

$r11 :::: $2.4dtFu

=38.8 kips/bolt

Te;u-our: Gravity plus seismic r,.

Y.!(1¥16 in.)]

x(0.650 in.)(65 ksi)/2.00

.

¢R11 ::::Cq>r,,

ASD

Bearing: Gravity

4>R11

n

=1.2[2.00 in. -

= 42.5 kips/bolt •.

=66.5 kips/bolt

rn

n

o.k.

= l.56(42.5 kips/bolt) = 66.3 kips> 19.9 kips

=8.06(44.4 kips/bolt) = 358 kips> 215 kips

AMOUCAI' J.Nsnnrre OF Sn;a CONSTRUCTION

~ =c(~ )

4JR11 = C$rn

~ =C(~)

$R11 =C$rn

=8.06(66.5 kips/bolt) =536 kips > 308 kips

=44.4 kips/bolt

o.k..

= =

1.56(28.3 kips/bolt)

44. l kips > 12.8 kips

o.k.

o.k.

AMERICAN

INS1'1TUTI? OF STEl!l. CONSTRUCTION

I

..

--•"11\J

BRACED FRA..\llES

LRFD

LRFD

ASD

Bearing: Gravity plus seismic

=37.2 k.ips/b-Olt(l.5/J.2) =46.5 kips/bolt $f 308 kjps

...

~R,.

~ =c(~)

=C$rn = 6.54( 42.5 kips/boll) = 278 kips < 308 kips

1~ I;, ..•

<'.

-----.

;:;:---'

"'

""6.54(28.3 kips/bolt}

n.g.

=185 kips< 215 kips

n.g.

A web doubler can be used to increase the W24x68 web Lhickness. or a less approximate an:tlysis of 1he bolt group can be used. Entering Table 7-7 of lhe ATSC Manual at B = 75°

when the rrue angle is 86..3° (LRFD) and 86.6° (ASD) is very conservative. A computer program based on the i.nstanl3neous center of ro1a1ion method of Part 7 of the AISC Manual y1el
Bearing: Gr.ivity plus seismic

=9.76{42.5 kips/bolt) =415 kips> 308kips Tel!out: Gravity

"" 276 kips > 215 kips

From AlSC Manual Table 4-22 for F1

o.k.

r,. 1.2lctFu -=--Q

=0.75(1.2)

x(0.415 in.)(65 ksi)/2.00

x(0.415 ht.)(65 ksi)

=24.8 kips/bolt

= 37.2 kips/bolt

,-

LRFD

¢Rn =C$r11

.

= 1.56(37.2 kips/bolr)

.

=58.0kips>19.9 kips

o.k.

\

~ =C(~)

= 38.7 kips> 12.8 kips

,

The design compressive strength of the

two pl:nes is:

= 513 kips> 307 k.ips

o.k.

Fer

Oc

=23.9 ksi .

Tue allowable compress1ve strength of lhe rwo plates is:

R,. Pc,A1 -= - -

=36.0 ksi(% in.)(19.0 in.)(2)

=1.56(24.8 kips/bolt)

ASD

\

cllcR.. =¢cFcrA.r

'

i•

o.k.

=50 ksi, the available critical stress is:

n

=1.212.00 in. - 1h(IS/i6 in.)j

x[2.00 in.-1h{o/i6 in.)}

=303 kips> 215 kips

:; 55.4

Tearout: Gravity

=~l.2lctFu

~ =9.76(31.0 kips/bolt) oJ<.

¥s in/Jfj_

-

9r,.

= 31 .o lcips/boh

1.2(5.00 in.)

7=

= 9. 76(28.3 kips/bolt) o.k.

= 24.8 kips/ool!(t.5/1.2)

Q

Size splice plates Choose plates of ASTM A572 Grade 50 steel and a total thickness that exceeds the web thickness of the lighter beam. Try (2) %-in.-lh.ick plates. The length, /, is the horizoncal distance between t.he last boh on the W24x68 beam and the first bolt on the W24x146 beam stub, which is 5.00 in.

Kl

~ =C(~)

lf!R,. = Crn

r,,

Gravity plus seismic

Check axial compression of splice plates As the axial force in the beam due to seismic load:. is always in compression, nee tension is not a limit state. With K =l.2 from AISC Specification Commentary Table C-A-7.1:

ASD

Beru:ing: Gravity plus seismic

T~ut:

~r.

~ ::::: 28.3 kips/bolt

$rn "'42.5 kips/bolt

ASD

Tcarout: Gravity plus seis!Tllc

Bearing: Gravity plu" seismic

1

,J..

5.3 SPEOAL CONCENTRlCAU..Y BRACFD FRAME.5

o.k.

nc

n.,

=23.9 ksi(* in.)(19.0 in.)(2) =341kips>215 kips o..k.

S-242

BRACEP FRAMES

Check splice gross section foi shear and flexural yielding for gravity-only forces

LRFD

ASD

The required shear strength due to gravity load only is: (

ASD

I

$Rn= $0.60FuA"" =0.75(0.60)(65 k.si) '

Rn

'

n I-' ••

x(% in.)(2) Moment at critical sectjon:

= 285 kips> 19.9 kips

The critical section is at the first line of bolts in the W24x68 side of the splice; 33.0 in. from the column face. The required moment is:

ASD

LRFD Mu splice

Mo Splice=

12.8 kips(33.0 in.)

.-

R,r

q>R,. .,; $0.60FyA8 v x(l9.0 in.)(2) =428 kips> 19.9 kips

::::: 47.4

0.60FyAgv

From AISC Specification Section J4.5 and Section Fll, the available flexural strength is:

=0.90(50 ksi)(2) (% in.}_{~.O in:)~ :::: 3,050 kip-in.> 657 kip-in.

o.k.

ASD

Mn

-

=

Mn "°FyZ nb nb

= 2,310 kip-in.> 657 kip-in.

I

=65ksi(41.4in.3 )

o.k.

!

.. ;. ~ )

;

. ..... ; "·. :'

!• ~

~

j

o.k.

•

Check splice for shear and flexural yielding for gravity and seismic for_ces

ASD

o.k.

$Rn =428 kips> 19.9 kips

o.k.

~ = 285 kips > 12.8 kip~:-

I

o.k.

I..

,_____ ___,___ ___,___ ! Moment at critical section:

Check splice net section for shear and flexural rupture for gravity~only forces

From AISC Specification Equation 14-4, the available shear strength is:

I

I.

2.00

= 1,540 kip-in.> 422 kip-in.

l..RFD

=SO ksi(2) (% in.)(19.0 in.)2 (-1-) 4 1.67 = 2,030 kip-in.> 422 kip-in.

nb

0.15( 65 ksi)( 47.4 m.3)

I

FuZner

=-2.00

There is no shear in the splice due to sdisrnic loads. From previous calculations, for gravity loading, the available shear strength is as follows:

ASD

cl>bMn =cl>bFyZ

in.3

QbM'n ::::: $bFuZnet •

n

LRFD

o.k.

..."

LRFD

= 0.60(50 ksi)(% in.)(19.0 in.)(2) 1.50 = 285 kips> 12.8 kips o.k.

o.k.

:::o 190

4

ASD

-= Q

· ~ 1.00(0.60)(50 ksi)(% in.)

x(% in.)(2) I 2.00 kjps > 12.8 kips

o..k.

x(l.5 io.+4.5 in.+7.5 in.)(2)

From AISC Specification Equation J4-3, the available shear strength of bolh splice plates is: ..

in.+ Yi6 in.)]

- 2(% io.)(1.0 in.)

.·

LRFD

1¥!6

z - 2(% in.)(19.0 inf

= 422 kip-in.

. = 657. kip-ill.

xi 19.0 in. - 6(

From AlSC Manual Equatio~ 9-4, the available flexural strengih is deiennined ;as follows:

n#-

=19.9 kips(-33.0 in.)

'

n

::::: 0.60(65 ksi)

x( l9.0 in. - 6(1S!i6 in.+ \1\6 in.)J

Shear: Va= 12.8 kips

=0.60FuAnv

1

The critical section is at the first line of bolts in the W24x68 side of the sp"ifoe; 19 .1 in. from the gravity plus seismic resultant force. The required moment at the critical section is:

l=

r. h.

I LRFD M.

.. ;;

From AlSC Manual Table 7-7 for angle= 0 ° with s

ASD

·'

9Mn

LRFD o.k.

M....u

=6:

=~(A,,c')

(Manual Eq I 0-4)

0.90

= 68 ki.i [0.601 in.2(54.2 in.)j 0.90

n= 2,O''O kip-m.. > 244 k:ip-m.. ,\-fn

and n

The nominal flexural strength of the boll group is:

ASD

= 3,050 kip-m. > 380 kip-in.

=3 in

C' =54 ...:! in.

Ma 1pUu =12.S kips(19. l in.) =244 kip 10.

= 19.9 kJp~(l9.I in.) = 380 kjp-in.

From previous calculations, lhc available flexural strenglh is:

_it'.

5-245

5.3 SPFCb\L CONC'ENl'RICALLY BRACED FRAMES

.>

= 2.460 kip-in.

o.k.

6Mmo., 1:

=

j:

~

Check splice net section for shear and flexural rupture for gravity and seismic forces

_____, < L ...,

LRFD

.. ~·

'PRn

:ii

Jll ·'

·~u .;


¢M,. =2,3 10 kip-in.> 380 kip-in.

The

~plice

6(2,460 kip-in.)

=50 ksi(19.0 in.)2 =0.818 in.

ASD

~ =190 kips> 12.8 kips

o.k. o.k.

Since 21=2(~ in.)= 0.750 in.< t;111u

o.k.

~" =l,540 kip-in.> 244 kip-in.

o.k.

• plate thickness perntined is:

I

:r

~

.;.

I

6Mflt4)1, tmdX = - - F, d2

,

l:

. I'

~

Nounal:

Nonna!:

N,, =1109 kips-46.0 kips-122 kip~

Na =176.6 kips-32.2 kips-85.5 kips!

=59.0 kips (compression)

= 41 . 1 kips (compression)

(Manual Eq. 10-3)

= 431 kips

\

Shear: Va =167 k.ips+l50 kips-12.8 kips = 304 kips

where

,I t ,.

ASD

Shear: V,, =238 kips 1-213 kips-19.9 lcips

~

~l

0.818 in., the splice satisfies the ductility requirement.

LRFD

be used to check the ductility of the splice. From AISC Manual Part J0, the maximum splice

:1

=

Beam-to-Column Interface-Design Gase I The forces at the beam-to-rolumn mterface., shown in Figures 5-40a and S-40b, arc:

is satisfactory for the requirCil strengths.

,, I Check the ductility of the splice ii~ The procedure used for the extended single-plate connection in AISC Manual Part 10 can :i

F\d 2

(Manual Eq. 10-4)

Check beam stub gross section for shear and tension yielding From AISC Manual Table 3-6, the availilble shear strength of the W24x146 beam ~tub is:

LRFD

For the splice plate snd bolts, the nominal shear stress of ASTh1 A325-X bolts from AJSC Specification Table 13.2 is: F""= F\.= 68 ksi

The area of a 3ii-in.-di:uneter bolt, from AISC Manual Table 1-1, is: Ab= 0.601 in. 2

41 V.,

=482 kips > 431 lcips

ASD o.k.

~ =321 kips > 304 kips

o.k.

Check 1hc available compressive strength of lhe beam stub. Treating the beam stub ns a connecting clement, determine whether the available compressive strength can be detcml.ined using AISC Specificarion Section J4.4: KL l.0(30 in.) -= r 3.01 in.

The directional strength increase is calculated as follows: ASD

LRFD

Pn =F1 A1

=50 ksi(43.0 in.

8~2b: ~~~~~-L-RFD~~~~~~,.-~~~~~A-SD~~~~~-1

)

=2,150 kips

435 kips

The available compressive strength is:

Dreq'J =

LRFD Pn

-=

= 0.90(2,150 kips) =1,940 kips> 59.0 kips

n

o.k.

The nom1al force of 59.0 kips (LRFD) or 41. l kips (ASD) on the column indicates that wel local crippling and local yielding checks should be made on we.column as follows. Check column web local yielding

The resultant force to be resisted by the weld is:

From AJSC Specification Equation J l 0-2, because the load is applied greater than d from the ASD

Ra =JV}+Nt

= J(304 .kips)2 +(41.l kips)2

=307 kips

=435 ltips

ASD

LRFD

tan- 1 (~:)

9Rn

LRFD

ASD

=$F,,.,t,..(5k,u, +lb)

Rn F>wlw(5kw +111) -=

0= tan-I(~:)

kips) =13II- I ( 59.0 431 kips

= tan -t ( 41.l kips) 304 ldps

=7.79°

= 7.70°

n

\

\

= 1.00(50 ksi)(0.550 in.)

x(S(l.50 in.)+20~ in.]

The angle of the resultant force can be calculated and used in the directional strength increase of fillet welds according to AISC Specification Equation 12-5. The angle of the resultant with respect to the vertical along the column is:

9=

I: J,.::

end of the column, the available web local yielding s(!cngth of the column is:

LRFD

=Jv,,2 + N: =J< 431 kips )2 + (59.o kips)2

•

=7.82 sixteenths

Design of beam stub web-to-column weld

R,,

l

I

'h-in. double-sided fillet welds are required for Design Case I on rhe beam T-discance of 203A in.

2,150 kips 1.67

=1, 290 kips > 41.1 kips

o.k.

307 kips Dm/'d = 2(0.928 ldp/in.)(20* in.)(1.02)

=7.38 sixteenths

ASD

$Pn = Q>FyA8

2(1.392 kip/in.)(203/.i in.)(1.02)

~-

I

The required weld size is calculated as follows from AlSC Manual Equations 8-2a and

(Spec. Eq. 14-6) 2

I

l.0+0.5sinu7.70°= 1.02

L0+0.5sinu7.79°= l.02

=9.97 < 25; therefore, AJSCSpeciftcarion Section 14.4 is applicable ·

l

5-1.

5.3 SPECIALCONCENTRlCALLY BRACED FRAMES

= 777 kips> 59.0 kips

t

t

n =5~ ksi(0.550 in.)

x[5(1.50 in.)+203/.i in.] o.k.

x(l/l.50) =518k.ips>4Llkips

o.k.

Check column web local crippling I. FromAISC Specification Equation] 10-4, because the load is applied greater than d/2 frorr }" the end of the column, the available web local crippling strength of the colunm is:

AMERlcAN lNnTruTE OP STEEL CONSTIUICIJON

-- -

e.

•; ~ ..

~

I

S- 248

BRACED FRAMES

LRFD

1

~

~. =~oso1a[··'[~ l( :;

!.«..

n

~·

~"

"

IJ;

r

Rn =0.80r.,2

0

I,.,

'

= 0.75(0.80)(0.550 in.)2

i

x[ I + 3( 20* in.)( 0.550 in. 12.7 in. 0.900 in.

.4~

't'·

:::: 934 kips> 59.0 kips

0

~~

r

The available compressive strength detennined previously for Design Case I is:

r

o.k.

LRFD

x[ I+ 3( 2012.71" !n.)( 0.900 0.550 ~n. r~ 1

1

3

10.

The Jim.it state of column web compression buckling is not checked here because only I.be beam stub web is attached ro the column flange. Therefore, pinching of the column web would not occur, as it would if the beam stub flanges were also connecred. Beam-to-Column Interface-Design Case II

-l

The forces ar the beam-to-column interface, shown in Figures 5-4 la and 5-4 lb, are:

S:

L"lFD Nom1al:

"· i'•

Nu =198.6 kips-128 kips - 46.0 kips! =75.4 kips (compression)

Na= 169.1kips-32.2 k.ips-89.4 kips!

Shear:

Shear:

·~· ~

i:

Vu =193 kips+250 kips+19.9 kips

Va

=135kips+175kips+12.8 kips =323kips

Check beam stub for shear and tension yielding t•

l•

The avail:iblo shear yielding strength determined previously for Design Case I is:

j,;

.·.·

LRFD

:-., ~;

~Vn

=482 kips> 463 kips

ASD o.k.

V,

(; = 321 kips < 323 kips

n.g,

2

l

=JvJ+N; 2

= J(323 kips)2 +(52.5 kips)

= 327 kips

=469 kips

The beam stub web-10-column weld size is determined from AJSC Manual Equations 8-2a and 8-2b, including the directional strength increase of AISC Speclfication Equation J2-5, :lS follows:

9=

~;

'•'

J(463 k.ips)2 + (75.4 kips )

Load angle

= 52.5 kips (compression)

=463 kips

Ra

LRFD

NonnaI:

,,...

=

I

ASD

=~VJ +N~

ASD

~·

·:::

LRFD Ru

*

o.k.

Design of beam stub web-to-column weld

o.k.

(•

~~~

=1. 290 kips> 52.5 kips

Pn

n

The resultant force at the beam-10-column interface is:

x(2.~)

~

a· ··~

;l I

o.k.

0.550 in.

=623 kips> 41.1 kips '~

¢Pn = 1,940kips >15.4 kips

tn .

x /29,000 ksi(50 ksi)(0.900 in.)

~~~

'h

ASD

=0.80(0.550 in.)2

ksi)(0.900 in.) x/29,000 ksi(50 0.550 in.

{'

"

1+3(~ )( :;

Due 10 the different load combinations used for LRFD versus ASD, there is a slight discrepancy between the LRFD and ASD results for the required shear strength. Typically. one method should be chosen and used consistently throughout an entire design. For the purposes of this example, U1e LRFD result will be used here.

xJE~~IJ (~)

xJEF_w.IJ

'" r.

ASD

5.3 SPECIAL CONC.ENTRJCALLY DRACEO fRAMES

.

-

ASD

Load angle

I

0=Ian-t(Na) Vo.

~-1(~:)

kips)

-tS2.5 kips) 323 kips

= tan- 1 (75.4 463 kips

= tan

=9.25°

=9,23°

Directional strength increase


l.0+0.Ssinl.5 9.25°= l.03

1.0+ 0.5sinJ.S 9.23°=1.03

I :

I

II I I I

. BRACED FRAMf:S

5-250

LRFD

Dreq'd

=

5-

Although it seldom controls, interaction can be checked here using the interaction formu of Example 5.3.8.

ASD

Number of sixteenths inch of weld required

5.3 SPEClAL CONCENTRICALLY BR.ACED FRAMES

J'

Number of si.ueenths inch of weld

required

469 kips

·

D req'd

2(1.392 kip/in.)(20~ in.)(1.03)

Design of beam flange-to-fop gusset weld

327 kips

=

2(0.928 kip/jn.)(20~ in.)(1.03)

=8.24 sixlCC!lths

=7.88 sixteenths

The beam Oange-10-top gusset plate weld is detennincd as follows using the direction strength increase of AJSC Specification Equation 12-5, the I .25 ductili1y fac1or discussed AISC Manual Pan 13, and AlSC Manual Equations 8-2a and 8-2b:

ASD

lRFD Note that this Case controls (Desjgn Case In requiring double-sided o/i6-in. fillet welds. The c-0lumn must also be checked for web local crippling and web local yielcling. These limit states will not control here for Design Case IT. The calcul:ltions were shown for Design Case I.

R., =

Top GusseHo-Beam Interface-Design Case I

The forces at the top gusset-to-beam interface, shown in Figures 5-40'a and 5-40b, are: LRFD Normal: N,. =238 kips Shear: V.,

e

.. Nonnal: Na::::: 167 kips -

=267 kips

Jv., +N; 2

R0 =

=358 kips

=251 kips Load angle

=~-·(~~)

e

The available shear yielding strength of the gusset plate is determined from AISC Specification Equation J4-3, and the available tensile yielding strength is determined from AJSC Specificat_ion Equation 14-1 as follows:

LRFD 9Vn

ASD

=1.00(0.60)(36 ksi)('A in,)

Q

=417 lcips > 267 kips

x('A o.k.

in.)(26~ in.-1.00

=tPF1 A8

in.)

Use double-sided ~in. fillet welds.

FyA

Q

Q

o.k.

8 -=--

::::: 0.90(36 k.si)('A·in.} x(26'.4 in.-1.00 in.)

=626 kips > 238 kips

P,.

o.k.

in. - LOO in.)(1.27)

=4.92 sixieenths

x(l/1.50)

(26~

= 0.60(36 ksi)

x(26'A in.-1.00 in.)

. _ 1.25(358 kips) req d - 2{1.392 kipfm.) x~~~~~--,~~

Q

= 36 lcsi(1.4 in.)(26'.4 in.-1.00 in.) 1.67 = 416 kips> 167 kips o.k.

I

1.0 + 0.50sinl.5 41.8°=1.27

1.0 + 0.50sinl.S 41.7°::: l.27

l

V,. 0.60F1 Agv -=

=¢0.60F1 Agy

=tan-•(167 kips) Directional strength increase


D

-i(No) Vo

=tan

=41.8°

=41.7°

I

I

I

I

.};

187 kips

267 kips

Check top gusset for shear yielding and tension yielding along the beam flange

2

=Jc187 kips)2 +{16; kips)2

=tan-I (238 kips)

Shear: Y11 ::::: 187 kips

Jva +N;

::::: J(267 kips)2 +{238 ldps)2

Load angle

;

ASD

Resultant force

Resultant force

D . _ 1.25(251 kips) rtq d -

2(0.928 kipfm.)

1 x~~-~---(26~ in.- LOO in.)(1.27) =5.17 sixteenths

I

I

f::

l.

I

I

l

The 1.25 factor in the numerator is a ductility factor from the work of Richard (1986) ... modjfied by Hewitt nnd Thornton (2004). Richard found that lbe ratio of the maximum streSs to the average stress on corner gussets was 1.4, wb.ich was reduced to a 90% con den~e limit ·by Hewiu and Thornton resulting in the 1.25 factor. The UFM nssumes uniform distribution of stress on the gusset edge, but the actual distribution is not likely t be uniform; the 1.25 factor accounts for this.

I

S-252

'•' l

t;· j'

~:

!

'·

BRACED FRAMES

Beam stub strength.

Top Gusset-to-Beam Interface-Design Case II The forces at the top gusset-to-beam interface, shown in Figures 5-41a and 5-41 b, are:

Check web local yielding

From AISC Specification Equation Jl0-3, because lhe load is applied less than er equal to the beam.stub depth, d, from the end of the beam stub, the available web local yielding srrength of thy beam stub is: ASD

LRFD Q~1

=$Fywtw(2.5kdes +lb) =1.00(50 ksi)(0.650 in.) [2.5{1.59 in.)

Rn

F)'.,.,1,., (2.5kde$ + 11>)

n

n

-=

l

ASD

LRFD

=135 kips

Normal: Nu= 19'.3 kips

Normal: N0

Shear: Yu= 216 kips

Shear: V0 = 151 kips

.

Check top gusset gross section for shear and tension yielding

From Design Case I:

= 50 ksi (0.650 in.)

x[2.5(l .59 in.)+ (263.-~ in. -1.00 in.)]

x +(26~.in. -1.00 in.)


5.3 SPECIAi... CONCENTRICALLY BRACED FRAMES

LRFD

ASD

)((I/ l .50) o.k.

=644 kips> 167 kips

o.k.

~V,.::: 417

kips> 216 kips

Vn

o.k.

, Check web local crippling

n

=0.60(36 ksi) t

x(J,4 in.)(26% in.-!.00 in.)

..

x(l/l.50)

Because tl1e compressive force is applied. at the centroid of the beam stub-to-gusset interface, which is a distance from the beam stub end that is greater than d/2, the nominal web local crippling strength i~.:

=278kips>151 kips

.. ~Pn

Pn FyA8 -=-n Q

=q>FyAg x(26% in. - 1.00 in.) = 626 kips > 193 kips

,,

,

=36 ksi(~ in.)(26% in.-1.00 in.)

"'0.90(36 ksi)('.IA in.) (Spec. Eq. Jl0-4)

o.k.

l.67

o.k.

=4i6 ldps > 135 kips

o.k. ·

The available web local crippling strength is: · LRFD

ASD Rn =0.80(0.650 in/

$Rn= 0.75(0.80)(0.650 in.)2 I I x

1+ 3 (2631~ in.-1.00 24.7 in.

inl

x(0.650 1.09 in.

n

in.)

1+3(26~ in.-1.00 in.) 24.7 in.

x

5

-

l

Resultant force

>< /29,000 ksi{50 ksi)(l.09 in.)

"

Resultant force

R,, =~VJ+ N~

I

=~(216 kips) =290 kips

x(2.~o)

!

R,, :-::~Vi +N'! 2

0.650 in.

=643 kips> 167 kips

I

A$D

LRFD

1---~~~~~~~~~-t-~~~~~~~~~- ,1

x(0.650 in-r..s 1.09 in.

xJ29,000 ksi{SO ksi)(l.09 in.) 0.650 in. = 965 kips> 238 kips o.k.

Beam flange-to-top gusset weld , The beam flange-to-top gusset plate weld is determined as follows using the directional strength increase of AISC Specification Equation )2-5. the 1.25 duclility factor discussei;i in AlSC Ma11ual Prut 13. and AISC Manual Equations 8-2a and 8-2b:

2

+(193 kips)

=~(151 k.ips)2 +{135 ki~s) =203 kips

!'

2

I,

L____ _ _ _ _ _ _ _ _ _ _ _ __ . __ _ _ _ _ _ _ _ _ _ _ _ _ _.... :

o.k.

AMllRICAN INSTITU'ra Or STEEL CONSTRUCTION

5-254

BRACED FRAMES

LRFD

=tan- I

e

(193 kips J

Va

=41.8"


J.0+0.50sinJ. 5 41.8°:::: -.

Directional strenglb increase 1.0+ 0.50sin 1.s 41.8°=1.27

l.27

1.15(290 kips) 2(1.392 kip/in.)

=

l

x

(26% in. -1.00 in.)(1.27)

=3.98 sixteenths

1.25(203 kips) 2(0.928 kip/in.)

Dreq'd=

(26~

1 in. -1.00 io.)(1.27)

Nonnal: Na = 85.5 kips

Shear: Vu = 151 kips

Shear: Va= 106 kips

1

Combine the axial force and the moment by converting the moment into an equivalent axial force derived from !.he moment equation for a simply supported member with a concentrate. ! load at midspan (s is lhe snip dimension of lhe gusset and ~ is I.he distance to the centroi· l:: '.' of the column-to-gusset connection, detei;nined previously): ..

1-------I:.RFD-· --------+------A_S_D _ _ __ _ _ 4Muc

Nu t quiv

= 4.18 si-xteenths

'

Nonnal: Nu = 122 kips

l.-.M._o_m_.e_n_t:_M~uc-=~1-95~ki-·p-_i_n_.~~~~~'--M-o_m~en_t_:_M_a'__-_i_37~ki-·p-~in_.~~~~~ I~

151 kip_s

= 41.8°

x

_ -i(Na) -

-tan

=tan - 1(135 kips)

_ 216 kips

Dreq'd

The forces at the top gusset-to-column interface, shown in Figures 5-40a and 5-4-0b, are:

Load angle

e =tan_,(~:) -

Top Gusset-to-Column Interface-Design Case I

ASD

Load angle

5.3 SPECIAL CONCE.NTRICALLY BRACED FRAMES

This requires double-sided -'l'\6-in. fillet welds. Note that Design Case I controls, however, requiring a %-in. fillet weld.

= N,. + - ( -) 2 ~ -s =122 kips+

Na equiv= Na+-(-) 2 ~-s .

2(195 kip-in.) . . 9.45 m. - 1.00 in.

=_16_8_ki _·P_s_ _~ ;:.._·.:...·_· ...:.'-'_

L __ _

Beam stub strength

4Mac '

= 85.5 kips+

2(137 kip-in.) _. . 9.4) m.-1.00 m.

.I..

I. I:~:t:

l

=_1_1_s_ki.:..·p_s- -- -- - -

_:__:..i__ _ _

This i~ not a realJoad_but res.ult$ in. the, same demand on the gusset.and ,weld as working ·:; wi~ N and M; se~aiately and. all
Check beam stub web local yielding

Fro!n Design Case I calculation: Design of column flange-to-top gusset weld LRFD

.......

ASD

..

·R11 = 966 kips> 193 kips

o.k.

~ n

= 644 kip.s > 135 kips

.

o.k.

1 l

· .:··

The colu~ flange-to-top guss~t pl~te\weld i~ qetermined as (ollo"".s. using the ~irection~' strength mcrease of AlSC Speciji'ca11011·Equatton 12-5, the l.25 ductility factor discussed J AlSC Manual Part 13, and AISC Manual Equations 8-2a and 8-2b:

LRFD Check beam stub

web local crippling

Resultant force

From Design Case I calculati,on:

~ = JvJ + NJ(.q•"w

LRFD Rn

= 965' kips> 193 kips

ASD

o.k.

R,. = 643 kips > 135 kips

n

o.k.

Resultant force

Jv; + N} equiv

Ra =

= J(151 kips)2 +(168 lcips)2

=J(106 kips)2 + (118 kip&)2

=226 kips

= 159 kips

j:.

,,

..;.:~

: I l

BRACED FRAMES

S-256

LRFD

..

Load angle

=tan-I( Nw~:Mil')

S

Check column web local yielding From AISC Sptcification Equation J 10-2, bec3U'.te the lo3d is applied greater lh:in the col· umn depth, d, from the end of the column, the available \\eb local yielding strength of the column is:

ASD

Load angle

0 =tan

S-2.!51

S.3 SPEClAl. CONCE.NTRICA l LY SRACEn r'RAMES

•(Na~;rv)

LRFO =tan-1(I68kips)

=tan

=48. l"

=48.1°

151 kips


=__2_..{l_.3_9_2_k.i-.pli-1-n.-)-x

D,,~·;1

n

=1.00(50 ksi}(0.550 in.) x!S(l.50 m.)+(17J.S in. - J.00 in.)]

=670 kips> 168 kips

(17:.i in. - LOO in.)(1.32)

x

I

fywlw(5kJu +Ji,)

n

-50 ksi(0.550 in.)

o.k.

I

x[5(1.50 in.)+(17:~ in.-1.00 in.)]

x(l / l .50) = 447 kips> 118 kips

l.25(159 kips) =----"----'--'----2{0.928 ki~m.)

l

=4.56 sixteenths

Rn

-=

¢Rn= ~F>,.t,.,(5kdf.r +lb)

l.0+0.50sin 1.S48.l 0 = 1.32

l._25(226 kips)

Dteq"d

kips) 106 kips

Directio113l strength incre
1.0 + 050sinl.S 48.1" = 1.32

ASD

1 (118

o.k.

=4.81 sixteenlhs

ASD

Check top gusset for sJiear yielding and tension yielding along the column flange The available shear yielding strength of the gusset plate al the column flange interface is determined from AISC Specification Equation J4-3, and the available tensile yielding s1.rcngth at the column flange interface is determineJ from AISC Specification Equation J+ l as follows:

$R,,

=$0.SOr! l + 3( ~)( :; )

xJEFy-.. IJ lw

= 0. 75(0.80)(0.550

,. ,.

\

.;

l

..•

I ·

¢ Vn

=~0.60,r:.,.A,. =1.00(0.fi0)(36 ksi)(* in.}

0.60F>A!v

n

n

.


Pn

o.k.

= 0.90(36 ksi}(3A in.)

36 ksi(% in.)(17~ in. - 1.00 in.)

x(l7* in.- l.00 in.) o.k.

= 1.67 =273 kips> 118 kips

n

- 0.80(0.550 in.)2

12.7 in.

x(0.550

x(0.550 ~)t.s 0.900 UL

in.)•..s

0.900 in. x

/29,000 ksi(50 ksi)(0.900 in.) .

0.550 m.

= 812 Jdps > 168 kips

FA

1 1 -=-n n

9Pn =¢F>'A1

=410kips>168 kips

x

1.50

o.k.

in.)2

(j_)

(t'ffi in.-1.00 in.)

1+ 3

=o.60(36 1csi)('A m.xm~ in.- Loo in.}

x(l7* in.-1.00 in.) = 273 kips> 151 kips

~ •080•01•+3[~ tJ]

1.S

xj¥

ASD

v,.

I

Because the load is applied greater than d/2 from the tnd of the column, the a\'ailable web local crippling sirength of the column is determined from AISC Specifica1io11 Equation J10-4 as follows:

LRFD

LRFD

I

Check column web local crippling

( 17* in.-J.00 in.)(1.32)

Use a double-sided ¥16-in. fillet weld.

/

i

x /29,000 ksi{50 ksi)(0.900 in.) 0.550 in.

o.k.

=541kips>118 kips

o.k. /

o.k. Check column web shear strength From AlSC Man11al Table 3·6, for a W12x96, the available shear strength i&:

5-258

BRACED FRAMES

LRFD ~Vn

•r' > ' t

5.3 SPECJAL CONCENTRlCALLY BRACC!D FRAMES

LRFD

ASD

=210 kips> 122 kips

o.k.

~ =140 kips > 85.5 kips

oJc.

.

ASD

P,,

=0.90(36 ksi)()A in.) x(28~

Top Gusset-to-Column Interface - Design Case JI The forces at the top gusset-to-column interface, shown in Figures 5-41a and 5-4lb, are:

LRFD NonnaJ: Nu =98.6 kips

ASD ].

Shear: Va= 85.4 kips

Moment: Muc =158 kip-iu. ·

Momem: Mat= 111 kip-in. Resultant force

un

ASD

= 150 kips

LRFD

x(283A in.-1.00.in.) =450 kips > 256 kips

=tan

Load angle

-r(Nu) v..

:::: Lan-I

(213 kips)

=39.8° Directional strength increase J.0+0.50sin1.S39.8°= 1.26

Dreq'd

1.25(333 kips) =--2-(1-.3..:..92-k.i-.p-'/i......n.""")- -

ASD Q

=0.60(36 .ksi) x(l/f.50)

"'300 kips> 180 kips

1 (

~=)

= tan- 1 (150 kips)

180 kips I

\

=39.8° Directional strength increase l.0+0.50sin1.539.8°= 1.26 Drtq'd

1.25(234 kips) =___

__,__.....:~--

2(0.928 kipfm.)

o.k.

l

I !::

l

(283.4 in.-1.00 in.)(1.26)

=4.51 sixteentbs

Use a double-sided Yi6·in. fillet weld. Design Case ll must also be investigated.

x(3A in.)(283A in. - 1.00 in.)

o.k.

= tan-

x \283A in. -1.00 in.)(1.26) = 4.28 sixteenths

Vn 0.60FyAgv -= Q

a

-

256kips

Shear: Va= 180 kips

=cp0.60F1 A8 ,, =1.00(0.60)(36 ksi)(3A in.)

=234 kips

Load angle

Check bottom gus;.et for shear and tension yielding along the beam flange The available shear yielding strength of the gusset plate is detennined from AISC Specification Equation 14-3, and the available rensile yielding srrength is determined from AISC Specification Equation 14-1 as follows:

41Vn

~ ~(180 kips )2 + (150 kips )2

~(256 kips)2 +(213 kips)2

=333 kips

The forces at the bottom gusset-to-beam interface, shown in Figures 5·40a and 5-4-0b, are:

. l,

Ra=~V}+N;

R,, =~Vu +NJ

Bottom Gusset-to-Beam Interface-Design Case I

Shear: Vu =256 kips

1.

Resultant load

2

=

Normal: N0

o.k.

ASD

LRFD

This completes the top gusset design.

LRFD

1.67


The beam flange-to-bouom gusset plate weld is determined as follows using the directional strength increase of AJSC Specifi.cation Equation 12-5, Lhe 1.25 ductility factor discussed in AlSC Manual Part 13, and AJSC Manual Equations 8-2a and 8-2b:

Comparing these loads with those of Design Case 1, it can be seen that Design Case [ controls.

Nonna!: Nu= 213 kips

o.k.

Design of beam flange-to-bottom gusset weld

NonnaJ: Na= 69.l kips


36 ksi(~ in.)(283A in. -1.00 in.)

=

in.-1.00 in.)

=674 kips> 213 kips

F1 A8

n--=-n

¢Pn =¢FyA8

l. ,,l:

5-260

BRACED FRAMES

5.3 SPECIAL CONCENTRICAU.Y BRACCO FRAMES

5-261

Beam stub strength

Bottom Gusset-to-Beam Interface-Design Case fl

Check beam stub ·web local yielding

The forces at the bottom gusset-to-beam interface, shown in Figures 5-4la and 5-4lb, are:

Because the normal force acts at the centroid of the bottom gusset-Lo-beam interface, wb.ich is less than the depth of the beam stub, d, 1be available web local yielding strength of the beam stub is detennined from AISC Specification Equation J 10-3 as follows:

LR.FD Rn

-=

=1.00(50 ksi)(0.650 in.)

LRFD

x(l/1.50) o.k.

The norm~! force acts at the centroid of the bottom gusset-to-beam interface, which is greater than d/2 from the. end of the beam. The available web local crippling strength of the .beam stub is detem1ined from AISC Specification Equaiion Jl0-4: LR.FD

x

ASD Rn= 0.80r~.

n

tw

1+ 3 (28314 in.-l.00 24.7 in.

in.)

in.r

x

x(0.650 1.09 in.

x( 0.650 iti. . 1.09 in.

x~29,000 ksi(50 ksi)(l.09 in.) 0.650 in.

... tr

"!:

,.

t

I

=1,0.10 kips> 213 kips

o..k.

o.k.

P,.

=449 kips> 175 kips

o.k.

$Vn:::: 450 kips> 300 kips

o.k.

V,,


o.k.

Q

ASD

in.)

r.s

\

o.k.

=J(210 kips)2 ;(175 kips)2

2 '.•

=391.kips

:d 273 kips

Load angle

e :::::tan- 1 (~:) =tan -

x(2.~)

Ra=~V}+NJ

I

= ~(300 kips)2 +(250 kips)

Load angle

/29,000 ksi(50 ksi)(l.09 in.) x ·~ 0.650 in.

Resultant force

\

Ru= Jv}+NJ

= 673bps>150 kips

Q

I

Beam flange-to-bottom gusset weld

Resultant force

Q

1+3(283-4 in.-1.00 24.7 in.

i

674 kips> 250 kips

~P11 ::::

LRFD

= 0.80(0.650 in.)2

= 0.75(0.80)(0.650 in.)2

Ii I

r

xE~wtf - - (-

w

x

1+3(~ )(~;

!

ASD

The beam flange-to-bottom gusset plate weld is detennined as follows using the directional strength increase of AISC Specification Equation 12-5, !,he 1.25 ductility facto.t; discussed i1~ AISC Manual Part 13, ~d AlSCManual_ ~quations 8-2a and 8-2b:

l)

[¥·

Shear. Va= 210 kips

x[2.5(1.59 in-)+(28~ in.-J.00 in.)]

o.k.

f5

Normal: Na= 175 kips

Check bottom gusset for shear and tension yielding along the beam f~ange

Check beam stub web local crippling

='1>0.80t;_ 1+3(~J(:;

.'

From previous calculatiou.s for Design Case I:


$R11

=250 kips

+lb)

n

=50 k:si(0.650 in.)

x[2.5(1.59 in.)+(28¥.t in. -1.00 in.)}

=1,030 kips> 213 kips

Fywt,.,(2.5kd~s

n

Normal: Nu

ASD


ASD

$Rn::::: 'PF)wtw(2.5kdes +lb)

LRFD

I (

=39.8°

250

e =ran- 1 (~:)

kips)

300 kips

= t:an- 1(175 kips) 210 kips = 39.8'o

LRFD

ASD

Dire.ctional sirength increase

q5(391 kips)

=

D,.q'd

2(1.392 kip/in.)

x

"

1.0+ 0.50sin ..s 39.8°= 1.26

l (28* in. -1.00 in.)(1.26)

I

x

=109 kips+

Norqui•=Ta+ 2(J3-s)

2(180 ki~in.! 10.5

= 16.6 kips+ 2(1~6 kip·in.~

10.5 10. - 1.00 tn.

in. -1.00 lfl.

The column flange-to-bottom gusset plate weld is determined as follows using the direc· tional strength increase of AISC Sptcification Equation 12-5, !.he 1.25 ductility facto1 discussed in AISC Manual Part 13, and AISC Manual Equations 8-2a and 8-2b:

._~_sn______----;; I;

Check beam stub web focal yielding

1--------L_RFD _______________

The available web local yielding strength of rhe beam is (from previous calculations):

Re.~ultant

ASD o.k.

$Rn:::: 1,030 kips> 250 kips

Rn :::::687kips>175 kips

n

Ru= ~V11 + NJ,qui• o.k.

$R,. = 1,010 kips> 250 kips

l

=21lkips

=149 kips

o.k.

Rn

n

=673kips>175 kips

Load angle

Load angle

0

=tan-1(N"~:u1v)

0

o.k.

- -kips) 152 kips

=tan-I (103 kips) 107 kips

:::::44.0°

=43.9°


1.0 + Dreq'd

ASD

Normal: N11. = 109 kips

Normal: N" =76.6 kips

Shear: Y,.._= 152 kips

Shear: V0 = 107 kips

Moment: Muc = 180 kip· in.

Moment: Moc= 126 kip-in.

=tan-1 ( Na;:im.)

!' lfl

I.

I I. l , !

_ 1 (147

Bottom Gusset-to-Column Interface-Design Case I The forces at the bottom gusset-to-column interlace, shown in Figures 5-4-0a and 5-4-0b, are: LRFD

=~Vo2 +NJ equi• = J(107 kips)2 +(103 kips) 2

=tan

~;

Ra

""~(152 kips)2 +(147 kips)2

ASD '

Resultam force

force 2

Check beam stub web focal crippling The available web local crippling strength o(the beam is (from previous calculations):

LRFD

1 '

Column flange-to-bottom gusset plate weld

Use a double-sided ti-in. fillet weld. Design Case ll controls.

LRFD

1

t.\

'--~~=~l4_7_k_iv_s~~~~~~~--'~~~=~I0_3_ki_.P_S~~~~~~~- j:

I (283,4 in. -1.()() in.)(1.26)

=5.26 sixteenths

;, 5.02 sixteenths

4Moc

Nutqu;.=Tu+ 2{P-s)

I

l.25(273 .ldps) 2(0.928 kip/in.)

= I

I

I

ASD

4Muc

1

l.0+0.50sin ..s39.8°= l.26 Dreq'd

LRFD


1

5--26

5.3 SPEClAL CONCENTRICALLY BRACED FRAMES

BRACED FRAMES

5-262

0.50sin1..S 44.0° =


1.29

1.25(211 kips) =----"----''--"-2(1.392 kip/in.)

--1.~-in-.

x -(1_9_*_in-.

!

)(-1-.2-9)

l.0+0.50sin1..s 43.9°=1.29 1.25(149 kips) 2(0.928 k:ipfm.)

Dr~fJ=-----.;.--~--

1 x -(1_9_71s_in-.---t_oo_i-n.-)(-J.-29-)

.:·

t·

IJ I '=

,

1

=3.89 sixteenlhs = 4.J 2 sixteenths ....____ __......__--=-------' }· Use a double-sided Yit.-in. fillet weld. Design Case Il must also be investigated.

Combine the axial force and the moment by converting the moment into an equivalent axi:tl force derived from lhe moment equation for a simply suppo'!_Ni member with a concentrated load at midspan (sis the snip dimension of the gusset and P is lite distance to the centroid of the column-to-gusset connection, detennined previously):

...

1

l.

~ .. (

I

..

r

''·· 1 :;

"~

BRACED FR.A1\.fES

5-264

Check bottom gusset plate for shear and tensile yielding along the column flange The available shear yieldjng strength of the gusset plate :it the column flange interface is determined from AISC Specification Equation J4-3, and the available tensile yielding strength at the column flange interface is determined from AISC Specijicarion Equation J4I as follows:

Check column web local crippling Because the nonnal force is applied at a distance from the column end that is greater than or equal to d/2, the available web local crippling strength of the column from AlSC Specification Equation J10-4 is:

ASD

Shear: Y11

V,,

=$0.60FyAgv

-=

x(l9*jn.=-l.OO in.) 306 kips> 152 kips

=

f

x(~

o.k..

··~ ?~

.,_•'

..

~ll

Normal: $Pn

in.)(19311 in.-1.00 in.)

Pn

:;;; 36 ksi(~ in.)(19* in.- l.00 in.) 1.67

x (l 9J.t in. -1.00 in.)

=459 kips> 147 kips

x

o.k.


LR.FD R,,

$Rn= ¢Fywfw(5kdu +11>)

-=

n

= 1.00{50 ksi){0.550 in.) x[5{1.50 in.)+(19}i in.-1.00

=725 kips> 147 kips l·

): '·

o.k.

in.)("

l + 3 (19}i in. - LOO in.) 12.7 in.

:::: 875 kips > 147 kips

n x[5(1.50 i.n.)+(19}i in.-1.00 in.)]

i:

x

in.)

5

/29,000 ksi(50 ksi)(0.900 in.) 0.550 in.

x(i.~o)

o.k..

o.k.

Check column web shear.strength From AISC 1\.fanual Table 3-6, the available shear strength of the W12x96 column is: I

I

'

LR.FD 210 kips> 109 kips

o.k.

.

ASD

~ = 140 kips> 76.6 lOps

o.k.

Bottom Gusset to Column Interface-Design Case II The forces at the bouom gusset-to-column interface, shown in Figures 5-4 la and 5-41 b, are:

x(l / t.50)

LRFD

o.k.

in.r

=583 kips> 103 kips

~v,, =

= 50 ksi(0.550 in.)

I + ( 19* in.-l.00 3 12.7 in. ,

x(0.550 0.900 in.

/29,000 ksi(50 ksi}(0.900 in.) 0.550 in.

ASD

Normal: Nu= 128 kips Shear: V,.

l·

x

inl5

Fywt,..(54s +11>)

=484 kips> 103 kips

=0.80(0.550 in.)2

o.k.

ASD

l+3(~)(:;r

x)E;:'J (ii)

x( 0.550 0.900 in.

FyAg

Check column web local yielding Because the normal· force is applied at a distance from the column end that is greater than or equal to the column depth, d, the available web local yielding strength of the column from AJSC Specification Equation 110-2 is:

; .,

x

o.k.

-n=n-

=0.90(36 ksi)(% in.)

n

=0.75(0.80)(0.550 in.)2

Nonna!:

=q>FyAg

Rn= 0.801;.

lw

=204 kips> 107 kips

:'··

il:;r

x ---

x(l/l.50)

- - - -...... !!::J

,+3[~ 1

EF>"''J

0.60FyAgv

.,n n ' =0.60(36 ksi)

=l.00(0.60)(36ksi)(3A in.) !"

911. =¢•so.;

Shear:

ASD

LR.FD

~.

LRFD

S- 26.S


= 178 kips

Moment: M uc =21 l kip-in.

Normal: Na: 89.4 kips I

Shear: Va = J25 kips

I

Moment: Mtic =148 kip-in.

I

'

5-266

BRACED FRAMES

Similar to previous calculations, the axial force and moment are combined by converting 1he moment into an equivalent axial force:

LRFD

4Moc Na,'l"iv=Na+n 2 ~-s

= N,. + (- } 2 ~-s lei

= l 28 ps+

=172 kips

Check bottom gusset shear and tensile yielding along the column flange Prom previous calculations for Design Case I, the available shear yielding and available ten· sile yielding strengths of the bo«om gusset are:

ASD

4Muc

N1uqwv

5-267


2(211 kip-in.) •. . 10..) m.-1.00 m.

=

89

.4

kl 2(148 lcip-in.) 'J'S+ . . 10.5 In. - l.00 m.

= 121 kips

Shear:

Shear:

$V,, = 306 bps> 178 bps

Vn = 204 bps> 125 ldps

o.k.

n

Normal:

The column flange-co-bot tom gusset plate weld is determined as follows using the directional strength increase of AISC Specification Equation J2-5, the 1.25 ductility factor discussed in AISC Manual Pan 13, and AISC Manual Equations S-2a and 8-2b:

ASD

o.k.

Nonnal:

¢N,, = 459kips>172 kips

Design of column flange-to-bottom gusset weld

LRFD

ASD

LRFD

N,,

o.k.

n

=305kips>121 kips

o.k.

Check column web local yielding From previous calcuJations for Design Case I, the available column web local yielding streng1h is:

\

Resultant force

Jv} +NJ tquiv =J(11s kips)2 +(172 kips)2

Ru=

Ra = Jva2 +NJ tqiciv

Niuqun. Vu

.

-1(172 kips) 178 kips

=44.0"

n

=484 kips> 121 kips

o.k.

Check column web local crippling From previous calculations for Design Case I, 1be available column web local crippling strength is:

e

= latl-1

(Na~:ui\>)

=tan-I ( 121

kips) 125 kips

=44.1°


1.0+ 0.50sinl.S 44.0°=1.29 1.25 (248 kips) 2(1.392 kip/in.)

x

Rn

o.k.

= J(125 kips) +(121 kips)2

Load angle

_ - 1( -tan - - -J

Dr«i'd-

kips

= 174 kips

Load angle

=tan

~Rn= 725kips>172

2

= 248 kips

e

ASD

LRFD

Resultant force

I

(l9* in.-1.00 in.)(1.29) = 4.57 sixteenths Use a double-sided 51i6-io. fillet weld.

\

LRFD $Rn= 875 kips> 172 kips

ASD

I

o.k.

R,.

n

=583 kips> 121 kips .

o.k.


l.0 + 0.50sin1.5 44.1° = 1.29 1.25(174 kips) 2(0.928 kipfm.)

Dreq'd=

x

1 (19}i in. -1.00 in.)(1.29)

~ 4.81

sixteenths

Check column web shear strength From previous calculations for Design Case I, the available shear strength of the W12x96 column is:

$Vn = 210 kips> 128 kips

I

ASD

LRFD o.J<.

Vn

n


o.k.

I I

1·

5-268

BRACED FRAMES

5.3 SJ>ECI '1. CONCENTRICALLY BRACED FRAMES

5-26?

The complete
Alternate Detail Using a Continuous Gusset Piste

An aJLemate detail using a continuous gusset plate instead of a beam stub is shown in Figure 5-43. This aJLemate uses :.i v...in.-thick gusset plate with plate reinforcement in lieu of the W24x146 beam stub and diminares many welds. Nore that the horizontal dimension 2a is used to set 1he gusset horizontal dimension.

~.

It.

I

\

HSS 6.875>t0.500

Example 5.3.11. SCBF Brace-to-Beam/Column Connection Design with Elliptical Clearance and Fixed Beam-to-Column Connection Given:

Refer to Joint JT-1 at the thlfd level in Figure 5-44 (the pJan 1s given jn Fig~ 5-10). Design the connection between brace, beam and column. Use an ASTM A36 welded gusset plate concentric to the braces and 70-ksi electrodes 10 connect the brace ·to lhe gu$SCl plate and the gusset plate to lhe beam and column. Use ASTM A572 Grade 50 contim111y plates. The bl3Ce is An ASTM A500 Grade B round HSS, the beam is an ·\STM A992 W24x68, and the column 1s a W12x96. The applicable building code specifies the use of ASCE/SEI 7 for calculation of loads. The gravity shear forces at the end of the beam are:

brace

Vo= 4.50 kips

., ;:

;

W12xS6 ...._

VL

column

;~

~

-~-~

Pl~x4>t2'-4" (typ.) (A36)

!:.

W2 x68 4

(1-NS, 1-FS)

...jI

=3.00 kips

W.P.

r ~m

2s·-0·

0-Roo_ f

Fills as roqvired

Third

,

j;

Second

HSS 7.SOO>t0.500 brace

Noe ad dimer\$ION .,. shown. See Flgure S.33 fof addibOnal connection details.

Note:

·'..

Fig. 5-43. Alternate design using collJilwous gusset plate.

Fig. S-44. Frame

ef~arion.

5--270

BRACED FRAMES

This ex.ample illustrates an alternative method for gusset plate design to that provided jn the AlSC Seismic Provisioru CommentMy Figure C-F2.9, proposed by Lehman et .al. (2008), acco~odate brace buck.ling as required by·AlSC Seismic Provisions Section F2.6c(3). In lieu of the 2tp linear brace offset. an Srp ellipticaJ offset may be used. In p::u:: ticular, for rectangular gusset plates, the 8tp elliptical offset offers a more compact gusset plate with equivalent defonnation capacity to accommodate the out--0f-plane brace movement. However, for gusset plates that have significant taper, as is the case in Example 5.3.10, the 8tp elliptical offset and the 2rp linear offset offer similar results. This example, as shown in Figure 5-45, illustrates a connection design using the elliptical offset method applied to a rectangular gusset plate.

to

In addition to illustrating the application of the elliptical clearance methodology, this example uses a fixed beam-to-column connection to satisfy the requirements of item (b) of AISC Seismic Provisions Section F2.6b. ln the design, the beam web and flanges are welded to the column flange with CJP groove welds. The flange weld requires a substantfal comer clip in the gusset plate for access. This clip, is detailed as 1.5 in. In this example, the clip is considered for ruprure limit states, but it )s ignored for yielding limit states.

Some features of this example, including the ellipt.ical clearance, I.he fixed beam-to-column connection, and the sizing of welds at the gusset plate interfaces are provided as an alternative to Example 5.3.10. Tbe brace-to-gusset calculations are not shown in this exampJc because they are similar t? Example 5.3.10.

5--27 l


Solution: From AISC Manual Tables 2-4 and 2-5 and AlSC Seismic Provisions Table A3.l, the material propenies are as follows: ASTMA36 Fy =36 ksi Fu= 58 ksi ASTM A572 Grade 50 Fy = 50 ksi Fu= 65 ksi ASThl A500 Grade B Fy::: 42 ksi F., =58 ksi Ry = 1.4 R, = 1.3 AST.MA992 F> =50 ksi FM= 65 ksi


./

~

f.

Brace (above the beam) HSS 6.875x0.500 tnom

=0.500 in.

fdts

A= 9.36 in.z

r= 2.27 in.

A= 10.3 in.2

r= 2.49

in.

b1= 8.97 in.

1l =0.585 in.

0.550 in.

b1= 12.2 in.

1f =0.900 in.

=0.465 in.

Brace (below the beam) HSS 7.50x0.500

1~·x1 ~· dip in

t,,_ = 0.500 jn.

gusset plate

\

fcf€s

=0.465 in. \

in.

Beam

PL )4" x 4~· (A572 Gr. 50) Both sides of web at beam flanges

W24x68beam

W24x68 d= 23.7 in. . kdes

t,., = 0.415

=1.09 in.

Column W12x96

d

=12.7 in.

lw =

kdts ::::: 1.50 in. W12x96 column Notes: Welds of web and doubler/shear plate

to column fiange are demand critical.

Fig. 5-45. Rectangular gusstt plaJe with 8tp elliptical brace offset addressed in Example 5.3.J J.

Required Strength For the HSS6.875x 0.500 brace above the beam

According to AJSC Seismic Provisions Section F2.3(i), lhe amplified seismic load is determined from !he expected strengths of the brace in compression and in tension. The expected tensile strength of the brace is detennined as follows. AMER.SCAN JHS111Vl1l 01' S1'El!I.. CONSTRUCTION

5-272

.

~ l L

BRACED FRAMES

From AISC Seismic Provisions Section Pl.3 and Table A3. I:

5.3 SPEClAL CONCENTRICALLY BRACED FR.AMES

The exp.!cted compressive strength of the brace is:

R1 =1.4

Pcomprtt.
P1t1uton = R1 FyAg

=I .14FmAg =l.14(41.6 ksi)(9.36 in.2)

=444 kips

=1.4(42 ksi)(9.36 in. 2) =550 kips

The rcquued compressive strength due to seismic looding is:

The required tensile strength due to seismic loading is:

LR.FD P0

=550 kips {•

=0.1Em11 =0.7(550 k.ips) =385 kips

0.3 P~omprtSJuin

I !

Pa=0.7Emh

I

=0.7(444 kips)

The expected strenglh of the brace in compression (using L strength is:

The expected strength of the brace in compression (using L = 12 ft as the actual length of the brace) is detennined as follows:

I

= 12 ft) at its post-buckling

=0.3 ( 444 kips) =133 kips

KL 1.0(12.0 ft)(12 in./ft) -=

2.27 in.

r

ASD

=311 kips

I

~::::J

•.•.

Pu= 1.0Emh =444 kips

ASD

Pu= 1.0£,.,,i,

_ ____. t:·

LRFD

The required compressive strength based on pose-buckling ~trength is:

=63.4

4.71~

··~

.,ih' "

r

t

= 133 kips

~4.71J

E

RyF1

Fe

:

For the HSS7.500x0.500 brace below, the beam.

(Spec. Eq. E3-4)

From AlSC Seismic Prov~ions Table A3. l:

(63.4)2

=71.2 k:si

R1

Fera = [0.658 r. R1 F1 IA(42bi)

=[ 0.658 ll..llcu =41.6 ksi ,.

i:. =~

I

The connection of the brace below the beam is not designed as part of this example for Joint JT-1, but the brace member size is important when considering the analysis provisions of AISC Seismic Provisions Section Fl.3. The e.«tpected strength of the brace in tension is determined as follows.

- n 2 (29,000 ksi)

!!i!r.J

=0.7(133 kips)

I

=(K:r -

Pa =0.7Emh =93.l kips

rt 2 E

(: >.

Pu= l.OEm1i

=105

With KL

ASD

LRFD 29,000 ksi E = 4.71 RyF), 1.4(42 ksi)

I

{1.4)( 42 ksi)

:::

1.4

PUn.11011


= R1 FyA1 =1.4(42 ksi){I0.3 in.2) =606 kips

5-274

SR.ACED FRAMES

5.3 SPECW. CONCENTRJCALI..Y J3RACED FRAMES

The required tensile srrength due to seismic loading is:

LRFD

LRFD Pu= 1.0Em1i 606 kips

ASD

Pu= l.OEmn

=424 kips

The expected strength of the brace in compression (using L

=12 fl) is detennined as follows:

0.3P1;omprtssio11

Kl= 1.0(12.0 ft)(l2 in./ft) r 2.49 in. =57.8

=0.3(518 kips) =155 kips

Pu= 1.0£m1r = 155 kips

[Rf

Po =0.1Emh

-

(Spec. Eq. E3-4)

=85.7 ksi

Gusset Plate Design

Ferr= 0.658 F. R1 F1 1.4(42 Jtsi)

l

= [ 0.658 SS.7kSJ (1.4)(42 ksi)

=44.1.ksi The expected compressive strength of the brace below I.be beam is: P1;()mprrssio11

The brace-to-gusset connection and brace reinforcement wil~ not be addressed in this example. As in Example 5.3.10, lhe brace-to-gus.sec weld will be !A-in. fillet welds I.bat are 26 in long.

For reference. the final design using these methodol_ogies is shown in Figure 5-45. The symbols used are shown in Figure 5-46.

(29,000 ksi) (57.8)2

[ !Li..j

=0.7(155 kips) = 109 kips

1t2E

2

1.

ASD

With-s;4,71 --: KL r . R1 F1

_ 7t

l

=12 ft) at its post-buckling

LRfD

=105

F~ =(~f

I

The required compressive strength based on post-buck.ling strength is:

29,000 ksi 1.4(42 ksi)

=4.71

4.7 lJ E R.,Fy

The expected strength of the brace in compression (using L strength is:

I l

Pa =0.1E""' =0.7(518 kips) =363 kips

=518 kips

Po =0.?E""' =0.7(606 kips)

=

ASD

= 1.14FcrcAg =1.14(44.1 ksi)(l0.3 in. 2 ) =518kips

The required compressive strength is:


l

The geometry of the gusset place and t~tion of the end of the brace are established using the approach described in Lehman et al. (2008). The calculations for the brace connectio are shown in the following. The horizontal gusset dimension, a, has been chosen. as 40 in .; and the vertical dimension is calculated. These values result in an ~onomical gusset plate thickness and weld sizes. The value of a is based on iterations using the method outlined i Lehman et al. and allows for a brace--to-gusset weld length of 26 in. From the geometry in Figure 5-46 and based on the choice of a along lhe column flange is:

=40 in., the gussec length

"

I.

b =(a+ ec) tan r-e,,

= [40 in.+ 1A(12.7 in.)]tan45°- 1A(23.7 in.) =>34.5 in.

Where b is the vertical gusset dimension, r= 45° is the angle between the brace and the horizontal as shown in Figure 5-46 and determined from the elevation geometry in Figure 5-4and ec and e,, are the eccentricities of the gusset edges from the column and beam cente lines, respectively (that is, half the member depth).

L

5-276

"BRACED FRAMCiS

s. 2?/


Half of tbe lengths of the major and minor axis of the ellipse are 1hen calculated using 3 gusset plate thickness of 7l in. based on yielding on lhe Whitmore s~tion.

LRFD

ASD

Setting this equal to the required tensile strength of the brace connection, and with Ag =cpwp. the gusset plate thickness is:

Seuing this equal to the required tensile srrength of the brace connection, and with Ag= tpwp, the gusset plare thickness is:

". Check required gusset plate thickness based on the limit state of tensile yielding

Tension yielding is checked on a section of the gusset plate commonly referred to as the Whitmore section. This section is explained in AISC Ma11ual Part 9 (Figure 9-1) and in Thornton and Lini (2011). The width of the Whitmore section is determined based on a 30° spread.

p~

QPa

lp=--

Ip=--

Wp

~FyWp

=2/..,tan30° + DbraCt = 2(26 in.)(tan30°h 6.875 in.

=36.9 in.

·'.j

.

"

= 0.460 in.

i

A . 1 r.~ '"

... I ,~

!~

...

:~

l.67(385 kips)

=(36 ksiX36.9 in.) =0.484 in.

T1y a %-in.-thick gusset plate.

! ec (•

550 kips =---------0.90(36 ksi)(36.9 in.)

From AISC Specification Equation 14-1, the available tensile yielding strength is:

\·

~11

FyWp

a'

This calculation does not include any reduction considering that the Whitmore width e,"{teuds into the web of the column or beam. lf the Whitmore width enters into a beam or column web that is subst3ntially thinner than the gusset, there is a potential for ~vcb local yielding.

In ihe configuration selected. the Whitmore width does not intrude into the beam or column

I I

web. This can be demonstrated by a geometric evaluation.

Determine geometry of the gusset plate

!~

The determination of the location_ of the end of the br:ice, as determfoed in the following, is based on the methodology described in Leh!Jlan et al. (2008); the equations in the following are updated from the reference. The location may also be determined from Kotulka (2007). Note that the determination of the finlil dimensions of the gusset plate based on either method is iterative.

I l

.· ·: ·:•'

b'=b-Stp

..

=34.5 in.-8(* in.) =29.5 in.

a'= a-Srp

= 40.0 in.-8(~ in.) 35.0 in.

=

Fig. 5-46. Illustration of symbols used for lengths and angles.

AMERICAN 11-lsmvtll Of' STEU. CONSTJUJCl10N

AMl!IUCAN l.!'isTITUTI? Ol' STE.El. CoNSTRUcnoN

.tlML'.l::.JJ J·KAMl:S

The aspect ratio of the ellipse is:

In the preceding equation. Dbrace12 is expressed as c in Lehman et al. (2008), and is defined as the d1i.u1nce from the brace ccntroidal (D/2 in this case).

3.'(iS 10

the extreme fiber of the brace

The maximum Jist~e from the theoretical gus.~t comer 10 the end of the brace is/':

35.0 in. =--29.5in. =1.19

t'

=Jc l''f + (y')

2 -

co"

The dimension )1 defines the )~coordinate of 1he intersection of the brace axis wirh the

= Jc22.6 in.)2 +(22.5 in.)2 -0.588 in.

ellipse:

= 31.3 in.

The brace length overlapping the gusset plate must then be checked to ¢nsufe lhat there is adequate length for the required weld: l f =35.0 in. I--=---'--~ 2 2

cot 45°+(l.l9)

=22.5 in. The x-coordinace of the clljpsc is lheo found from:

x' a)1-(:T

l:V=

I'-( Db;aa

+s)coty

875 -- 31 . 3.m. - ( 6· in. + I .00.m. ) cot 45° 2 =26.9 in. wheres is the

"~houlder"

=

= 35.0 in. 1-(

225 29.5

iin.) n.

2

=22.6 in.

is shifted from the x nnd y' coordinates using the correction factor, Corr, calculated in che following:

22.6in.

(225 in.)(1.19}2

1

=35.3° Dbro.·, Corr"" - -ian(90° -

fied for the lillllt states of block shear ruprore and compression buckling.

Check compression buckling on the Whitmore section

The limit state of compression buckling is checked using AlSC Specificatio11 Se~tion J4.4. First detcnnine Kllr :is follows. '

~=tan-I(_..::__) y'pl -•[

This is greater than the 26 in. required for the 1A-in. fillet welds (determined in fa.:imple 5.3.10). Therefore, the geometry of the gusset pl:11e is now set. lf /~.were Jess than 26 in., I.hen the gusset plate height and width would have to be increased.

The rhick.ncss of the gusset plate was tentatively assumed 10 be ~ in. and needs to be veri-

!<> e~sure that the entire brace cross section remains clear of the elliptical zone, rhc brace

: tan

of the gusset at !he brace as shown in Figures 5-45 and 5-46.

The length of the brace ~terline from the theoretical gusset comer to the inte~tion with lhe bcnm flange is cruculated :i.s:

b L=siny

3.t.5 in.

~ -r)

2 6.875 in. = 2 tan(90° - 35.3°- 45.0°)

=--sin450 =48.8 in. The centerline lcng1h of buck.ling, l1, is:

= 0.588

l1=l-l' =.t8.8in. 31.3in.

r

= 17.5 in.

r

S-280

BRACED FRAMES

:. .,,.

The r:idius of gyration of the gusset plate is: r

4.• ..

.. ,

S-281


Check block shear rupture of the gusset plate (Spec Eq. J4-5)

=.!..e._ Jl2

Because the gross shear area, Agv, and the net shear area, Anv, are equal in this ca~e. the shear yielding component, 0.60F1 A1v. governs over the shear n1ptu.re component, 0.60F.An1··

5i-lin.

=7i2

=0.180 in.

R,, = 0.60F1 (2)l...,tp +U,,,FuDbroulp = 0.60(36 ksi)(2)(26.0in.)tP+1.0(58 ksi)(6.875 in.)tp

The elliptical clearance provided in this example results in an extended corner gusset plate, therefore, from Dowswell (2006), use K =0.6.

= 1,520 kip/in.(rp)

:•.

.. ~ •.•

~= ·;·

_ _____, "~;:J

KL 0.6(17.5 in.) -= r

t > P

From AISC Manual Table..A-Z2 with Fy

=36 ksi and

KL = 58.3:

~

r

LRFD Fer = 18.0 ksi QC

Therefore, the required compressive st!ength of the bracing connection is based on the expected compressive strength of the brace due to seisrnk loading as detennined previously, with the 1.1 factor applied. From AISC Specification Equation E3-l, I.be available compressive strength at the Whitmore section, based on flexural buckling, is:

...!;

Pn =(Fer )A

= 27.1 ksi(36.9 in.)(% in.)

=615 kips 625 Jcips > J.1 ( 444 )9ps)

=488 kips

nc '

Q

.

= 18.0 k.si(36.9 in.)(o/a in.)

o.k.

~

550 kips 0.75(1.520 kip/in.)

OP0 1,520 kip/in. 2.00(385 kips) 1,520 kip/in.

=0.507 in.

=415 kips 415kips>1.1 (311kips)=342 kips

Gusset Analysis

In order to perfonn the gusset plate checks at vertical and horizontal sections at the interfaces with the beam and e<>lumn and to perform checks of local limit states within the beam and column. it is necessary to obtain design forces by performing an analysis or"the gusset.

For the desig.n method illustrated in this example, the checks of the gusset plate at these vertical and horizontal sections will necessarily be satisfied as a consequence of satisfying the check of yielding of the Whitmore section and of designing the fillet welds at the gussetbeam and gusset-column interfaces to b~ stronger thnn the gusset plate. Nevertheless, il is necessary to derive the forces on these interfaces in order to obtain forces for the web local yielding and web local crippling checks on the beam and column. In this example, the Parallel Force Method (also known as the Ricker method) will be used for simplicity (Thornton, 1991). ·

Note: AJternatively, the Uniform Force Method is also applicable to this connection. Because of the proportioning of the gusset plate in this example, the Uniform Force Method will ~ult in moments being assigned to the vertical and horizontal interfaces. The forces used tO evaluate the limit slates of web local yielding and web local crippling would then be adjusted to include these moments as illustrated in Example 5.3.10.

ASD

$Pn = 4'cFcrAg

fp ~

Use a ?S-io.-thick gusset plate.

AISC Seismic Prm isio11s Sections F2.3(i) and F2.3(ii) define the rwo mechanism analyses that must be considered in determining the required strength of connections. AISC Seismic Provisions Section F2.6c specifies the required strength of bracing connections, in p:micular. For the required compressive strength, Seetion F2.6c(2) has an additional 1.1 factor (relative to the requirements of Section F2.3) applied to the required suength of the connection. The requirements of AlSC Sei~mic Provisions Section F2.3 will be used for both LRFD and ASD, except for the limit state of comp.ression buckling on the \Vhitmore section, which will use the 1.1 factor specified in AISC Seismic Provisions Section F2.6c(2).

LRFD

Pu ¢(1,520 kip/in.)

= 0.482 in.

ASD

¢cFcr =27. l ksi

·~· •i

ASD

LRFD

0.180 in . =58.3

o.k.

The Par.lllel Force Method has a disadvantage relative to the Uniform Poree Method in that minor momenrs result at lhe column face. However, the use of a rigid beam-to-column connection is generally sufficient to resist such moments and they may be disregarded under these conditions.

Therefore, the ~-in.-lhick gusset plate is acceptable. J\.l.!EJUCAN INs1TIVTll OF S-n;a CoNSTRVCnoN

1n the Parallel Force Method, eccentridties are calculated from the brace centerline to the centroids of the gusset plate welds at the .beam and column faces. The gusset-to-beam connection is designed for the tequired shear force, H1>, and the required .normal force, Vb. The gusset-to-column connection .i,s designed for the required shear force, VC> and the required normal force, He. As shown in Figure 5-47, a line perpendicular ro lhe brace axjs which passes through the centroid of the gusset-to-column-flange interface may be used to find eccentricity. (This is also done for the gusset-to-beam fl;uige interface.) As discussed previously, total gusset lengths are used for evaluating yielding limit states; local effects due 10 the corner clip are considered only for rupture limit states.

Xec

( tany)yc +Xe tan2')'+1 (tan 45°)(29.1 in.)+ 6.35 in.

(tan45°)2 + l

the

At the column flange, ihe gusset-to-column flange centroid is located at this point, relative to the working point:

=

:;::: 17.7 in.

.~

' '

Ytc = ( tanr )xu =(tan45°)17.7 in. :::: 17.7 in. The eccentricity between the centroid of the gusset-to-column interlace and the brace cen-

J

terline is therefore:

= (12.7 in. 23.7 2 • 2

in.; 34.5 in.) 2

=(6.35 in., 29.l in.) The point on the brace centerline that is the intersect.ion of a line through this point perpendicular to the brace centerline is given by these e.quations (as shown in Figure 5~7), with the working point taken as the origin:

ec

=~(Xec - Xe )2 +(Yee - Ye ) 2 ::::)(17.7 in. -

6.35 in.)2+(17.7 in.-29.1 in.)2

=16.l in. At the beam flange, the gusset-to-beam flange centroid is located at this point, relative to the

working point:

(xb,Jb) "' (

d; +~, d;)

=(12.7 in.+ 40.0 in. 2

2

23.7 in.)

'

2

=(26.4 in., 11.9 in.) The point on the brace centerline that is the intersection of a line through this point perpendicular to the brace centerline is given working point:

these equations (see Figure 5-47), relalive.to the

I

' .

{tawy )yb + Xb Xeb""

tly

t l f ·:

can1 y+1 (tan45°)1 l.9 in.+26.4 in.

==

(tan45°)2 +1

= 19.2 in. Yeb

=(tanr)x<1>

=(!an45°)19.2 in.

j

""19.2 in.

The eccentricity between the centroid of the gusset-to-beam interface and the centerline of the brace is therefore: ,,, Fig. S-47. Geometric method of esrabUshing eccentriciry from brace cemerline. AMElllCAN It;srmrra OP STl$L CONSTRUCTION

BRACED FRAMf.S

t'I>

=

J< X~b - .fb ) 2 + (.Vtb -

)°b )

S.3 Sl'EClAl, CONCF.Ni"RJCALLY BR,\CI D FRAMJ~S

1

ASD

LRFD ~

JCt9.2 in.-26.4 in.)2 +(l9.2 in.-1 l.9

in.}2

!', _ P,.ec w1>-(tc+t1>)

=10.3 in.

·\

Tak.ing moments about point (Xb, Yb). the di:lgonal force, parallel to the brace force, at 'the column flange correspond~g to !he expecled strength of 1he brace in tension is:

LRFD P. _

"" -

ASD

P,..eb (ee +eb)

P,

(550 kips)(l0.3 in.)

f:I

II

til

(385 kips}(l0.3 in.) (16.1 in.+10.3 in.)

The corresponding shear on the beam face is:

LRFD

ASD

=335 kips(cos45°) =237 kips

Hab = P""cosy = 235 kips(cos45°) = 166 kips

The corresponding shear on the column face is:

The corresponding normal force on the beam foce. is:

ASD

LRFD V.i,

=P,.,.siny =335 kips(~n45°)

v"" = P..,.qn·f = 235 kips(sin45°)

=166 kips

=237 kips

LRFD

ASD

=215 k.ips(sin45°)

=Pacsin1 =150 kips(sin45°) . =106 kips Vac

= 152 kips

H..i. = P.bcos"(

- 150 kips

Note lhat sumnUng moments as described will result in a Pc force in the opposite clirection to the column flange force as shown in Figure 5-47. Because Figure 5-47 is not ac1ually a free-body diagram of the gusse1. forces Pc and Pb are shown as they act on lhe beam and column. When resolving 1hese forces in10 components, forces denoted I/ :ic1 in the horizontal direction and forces \.'act in the 'enical direction. Depending on whether th<: interface is a beam or a column, Hor V might be either a shear or a normal force.

v.,., =P..., sin"(

.·t1

(16.1in.+10.3 in.)

=335 kips

-~

=

(tc +e,.) {385 kips)(l6.l in.) ::: (16.1 in.+10.3 in.) = 235 kips

= (550 k.ips)(l6.l in.)

ac - (ee+t1>)

= (16.l in.+ 10.3 in.) =215 kips

The beam-to column connection is designed for a moment based on the nonn:il nnd shear forces at the gusset-to-beam interface. Taking momenlS about the work point. the resulting moment at the beam-to-column connection due to the brace force is: LRfl)

.

\

ASD

}'

The corresponding nonnal force on I.be column face is:

",,~ ..,,

t·

Mu =!Hub (d; )- vub(%)1

LRFD

ASD

H..c =PwCOSY = 215 kips(cos45°) = l52 lcips

Hoc= Poerosr =150 kips{cos45°) =106 kips

Taking moments about point (x,, Ye), the diagonal force at the berun flange corresponcling to the expected strength of the brace in tension is:

I~

P0 tr:

Pab=

Ma

=IHab(d; )-vob(%)l

. (23.7 in.)

237kips

=

-237

166 kips(

~

kips(40.~ in.)

= 1,930 kip-in.

=

23

·~ in.)

-166 lcips( 40.~

in.)

=1,350 kip-in.

The horizontnl force at the connection of the beam to the column _i~ affected by bo~ tt:e force entering the frame (defined by the mech:ullsm analysis prov1Stons of AJSC Sewmc Provisions Section F2.3) and the horiz.ontal force transferred from lhe gusset to th~ column (He or Hae). The to1aJ force entering the frame can be computed based on lhe dif'1:e~~ between Lhe total expected frame shear strength above and below the be:\n1, ns explained m

Example 5.3.5. These l>hear strengths are calculated based oo the horiiontal components of the brace expected strengths. The total force entering the frame is the difference between 1he expected srrengths of the braces above the th.iro level :md the braces belO\\ the tlurd IC\el:

Hu.rol/«tor

-IL(Bracc expected strengths below beam) cosy I Px-

P,, =cos45°

1(606 k.ips+5l8 kips)

ASD

I

P =cos45°

-(550 kips+444 kips)

'

= 91.9 kips

l

Hu. c()M«tio11

:

Since the braced frame is in the middle bay of a three-bay building, the collector force (half of this story force) can be considered to ent<'r the braced frame from each side. These forces are shown in Figures 5-48a and 5-48b.

I

= 32.2 kips

ASD

=Hw, collatt>r + ffw:

Ho. -N.:Do~ = Ho. C'c>lkdar + H ac

=46.0 kips+ 152 kips

=32.2kips+106 IJps

=198 kips

= 138 kips

Thi~ force may be resii.ted in the beam Oange-10-colunm welds. the beam web-to colun~ weld or shared between the two. In this example the available strength of the flanges will

be c~culated, and nny excess demand wiU be assigned to the web. For this comparison the re{juired strength of each beam flange is taken as:

© vi,'

/

'

I I

r

l

'

'' '

'

'

f

~'-------,+,-------'1 I

I I

46.0 kip$

// s59-t0ps

fI //435

! .. '

:

/ I '

I

i

I

:

360 kips '

I

"'

I

1 /

'

1

I //

I

L'----- -

I I I I I

518-~ps

I

: I

I

-+------'J /I' I

// I ', / I , /

/

',

I 46.0 kips

I I I

'

"'

't,.

I

I I I

I I

44~s

'

- - - -'i

f

',

"'* / .. :'\: .. :---'---

IOps

60§.tlps

I

1

LRFD

1(424 kips+363 kips) -(385 kips+ 3 I I kips)

Similar 10 what was illustrated in Example 5.3.5, the mechruusm analysis with the compression braces at their post-bud.ling strengths will not result in a higher force entering the frame in this case.

I / I·' / I /

= h(64.3 kips)

Ha, ""f:.td.,r

Tue force at the beam-to-column connection within the frame must also include Hue (LRFD) and Hae (ASD):

= 64.3 kips

9

=1h(91.9 kips) =46.0 kips

-I(Bracc expected screngths above beam)cos y

LRFD

ASD

I RFD

1 T 32-2 kips

:- ;-: 421' l{ips / I / /

i 363-"!ps

1 1 II

'

L'-------+---I

,/1',

I I

1

, ,/

/

I I

32.2 kips

' ',

1 I ', I

--~

I I I

'/'----'_,.___ _.I_

I

Fig. 54&. Collecror and frame forces for the rh1rd ln.·el (U?F'D ).

Fi•g. 5-48b. Co"'lecror andframefiorcts for the third level (ASD ).

Ai-IERICA.,. l.NsTnVrB Of' STEEL CoNSlllucno.,.

5-288

BRACED FRAMES

LRFD d-t1

'sj

Ra =--+ Ml) Hl) C~ .

2

1,930 kip-in. = 23.7 in. - 0.585 in. + 1982kips = 182 kips

. ..

d-r1 2 1,350 kip-in. 138 kips = + 23.7 in. ":' 0.585 in. ·2 =127 kips

..

LRFD ~F1

ASD

Fy

=0. 90(36 ksi) = 32.4 ksi > 14.l ksi

The available strength of each beam flange for ~he limit state of tensile yielding is calculated as:

R,. = F1 Ag

'[

Hue

' cp(b-clip)

rlI

ASD

n

o.k.

1.67 = 157 kips> 127 kips

Gusset Plate at Column Flange

The combined effects of shear and tension at the gusset-to-column interface may be calculated using von Mises interaction (as shown in tcnn.s of stresses in AISC Manual Equation 9-1):

Hue

,,

,,!:

~: ·

'•

'

r (r +

tpb

3

f

=

152 kips (_% io.)(34.5 in.)

' +3[

152 kips

{~

152 kips in.)(34.5 in. -

I~

:

r

(1'!! in.)(34:5 in.)

r

r r

'!

H ac \ lp(b-clip)

-

in.)

r

+ 3[

l ~

+3

i

'I =

~:

AMERICAN

I 1h in.)

r

I I I'

The stress from the voo Mises interaction is compared to the strength of the gusset plate, which is taken as ~Fw (LRFD) and Fu!Q (ASD) for the limit state of tensile rupture, from AISC Specification Equation J4-2.

LR.FD ¢F,,

ASD

Fu

=0.75(58 ksi) o.k.

58 ksi

-=-n 2.00

=29.0 ksi > 10.3 ksi

o.k.

I

I

tpb

106 kips

($h in.)(34.5 in.)

I +3{

106 kips

r r

Gusset Plate at Beam Flange

.

.

Similar to lhe gusset at the column face, the combined effects of shear and tension on tl'gussct at the beam flange may be calculated using von Mises interaction:

(* in.)(34.5 ill.)

'·' I'

r

106 kips

(% in.)(34.5 in. -

Hoer + 3[Vocf tpb

r

106 kips (~ in.)(34.5 in. -1 ~in.)

=9.83 ksi

= 14.J ksi

Vee

tp(b -clip)

=10.3 ksi

""43.5 ksi > l4.7 ksi

Vue

fpb

Vue

tp(b -clip)

=14.7 ksi

•• !

ASD

+ 31

r

1 +31

o.k.

Thus, the entire force can be assigned to che beam flanges, and none need be assigned to the beam web in this case.

LRFD

r

=

('

o.k.

ASD

152 kips r(3h in.)(34.5 in.. - l 1h in.) .

=262 kips

Rn

=21.6 ksi > 9.83 ksi

LRFD

= 50 ksi(8.97 in.)(0.585 in.)

<;>R,, = 0.90(262 kips) = 236kips>1 82 kips

o.k.

A similar check for rupture oo this plane is made, considering the l 1h-in. comer clip:

(Spec. Eq. 14-1)

= 262 kips

36 ksi

-=-n l.67

-

= F1 b1r1.

LRFD

5 -289

The stress from the ,·on Mises interaction is compared to the strength of the gusset plate, whi.:h is taken as ~Fy (LRFD) and Fyl0. (ASD) for the limit state of tensile yielding from AISC Specificatio11 Equ3tion J4-l. '

ASD

Ru _ -Mu + H.,,Ct.'nnu-non --

5.3 SPECIAi.- CONCENTRICALLY BRACED FRAMES

1NsTrJvre 01' S'rEa CONSTRl.IC110N

AM6RJCAN

WSTl'\'\ITS OF STEEL CONS1"RUC'OON

5-290

BRACED 'FRAMES

ASD

LRFD

'

Vub tpa

r H~r + 3(

tpa

237 kips

r(* in.)(40.0 . in.)

= 1+3!

d

3 Hab tpa) + (-;;;

I Vab 2

r r

I

=

1+31

237 kips (-* in.){40.0 in.)

=19.0 ksi < q>Fy =32.4 ksi

9Rn

166 kips

r

166 kips (* in.)(40.0 in.)

'1r1b

\ 1tp(a-clip)

i =

r

+

3

o.k.

ASD

llub

r r

237 kips

{* in.)(40.0in.-l'h in.)

1 +3[

l

1tp(a-clip) '

237 kips (~ in.)(40.0 in. -1 'h in.)

= 19.7 ksi <Fu= 43.5 ksi

r( r r +3

Vab

' tp(a-clip)

Hob

166 kips

r

o.k.

=

1 +3(

166 kips

l.50

o.k.

= 773 kips> Hae= 106 kips

l 3(~ )(:;

R" =0.80ra +

r)

r (Spec. Eq. Jl0-4)

EF:::rI 5

2 :::: (0.80)(0.550 .LO.) {l + 3(34.5 - - .in.)(0.550 9()() in.)._ . 12.7 Jn. 0. tn.

1

J

=1,820 kips

r

This value is not compared to the value of Hue or Hae calculated previously, which is based on tension in the brace, as crippling is a compression limit state. Because the Hue and Hae forces calculated previously are directly proportional to the broce force, they can be scaled down based on the ratio of the brace force in compression to the brace force in tension. The maximum compression force at the gusset-to-column interface is: ·

= 13.8 ksi < F,,IO. = 29.0 ksi

ASD

LRFD

o.k.

444

{144

H ( kips)= 152 ki kips) "" 550 kips P 550 kips

At the gusset-to-column interface and guf!set-to-beam interface, the column and beam webs, respectively, must be checked for the limit states of web local yielding aod web local crippling. The length of bearing, lb, is taken as the height of the gusset plate, b.

I

\.

H (311 kips)= 106 ki cc

385 kips

=123 kips '·

Therefore:

Check column web local yielding

(Spec. Eq. 110-2)

kips)

.,

ASD Rn

l,820 kips 2.00 = 910 ~ps > 85.6 ltips

-=

~Rn= 0.75(1,820

kips) = 1,370 kips> 123 kips

8 (311

P 385 kips

=85.6 kips

LRFD

For a force applied at a disunce less than the depth of the member from the member end, the available web local yielcling strength is determined as follows:

o.k.

n

o.k.

Beam Web at Gusset-to-Beam Interface

t"..

Check beam web focal yielding Consider th:it the jnterface force, Vb, acts at the centroid of Lhe gusset-to-beam interface, a distance of a/2 40.0 io.12 = 20.0 in. from the face of the column.

./,,

=(50 ksi)(0.550 io,)[5(1.50 in.)+ 34.5 in.J = 1,160 kips

I:

(* in.)(40.0 in. -1 'h in.) .

Column Web at Gusset-to-Column Interlace

Rn = Fywtw(Skdes +lb )

o.k.

1,160 kips

n

(29,000 ksi)(50 ksi)(0.900 in.) x 0.550 in.

tp(a-clip)

{-% fn.)(40.0 in.-l'h in.)

-=

For a fon:e applied greater than a distance of d/2 from the member end:

A similar check for rupture on this plane is made, considering the l 'h-in. comer clip:

LRFD

Rn

=1.00(1, 160 kips) =1,160 kips> H.,,, =152 kips

Check column web local crippling

r

=13.3 ksi < p;.10. =21.6 ksi

o.k.

ASD

LR.FD

r

(* in.)(40.0 in.)

S-291


.,

=

BRACED FllAMES

For a f~rce applied at a distance greater than the depth of the member from the member end, the ava1lable strength is determined as follows: · ~..

,

Rn= Fy..,t..,(2.Skdu +lb)

(Spec.

l

J· LRFD

4>Rn

"·

~. I

ASD

=1.0(887 kips) =887 kips> vl
Rn 887 kips -= o.k.

n

1.50

=591 kips>

v.,b =166 kips

o.k.

~-·


The resultant force al the centroid of lhe gusset-10-beam interface is greater than d/2 from the member end. 11JUs, AlSC Specification Equacion J 10-4 is :ipplicable.

R. •080'!11

II

w

i

=887 kips

.

LRFD

Eq. JJ0-3)' '

=(50 .ksi)(0.415 in.)[2.5(l.C'9 in.)+ 40.0 in.J

+3[ ~ lf:;

6Rn = 0.75(793 kips) = 595 kips> 191 kips

ASD Rn

-=

...."~~,.

I

n

o.k.

2.00

== 397 kips> 134 kips

o.k.

2(1.5)~(0.60)Fexx(0.707)w ~ RyFytp

where ~ = Q.75. fn order to comply with the AISC Specification., use$:;= 0.75 instead of ~ =0.75.

rir::'J

(Spec. Eq. Jl0-4)

=(0.80)(0.415in.)2f1+3( 40·~ ~n·J( 0·~ 1 5 in:JJ.SJ 23.1 m. 0.)85 m.

This expression, which is based on AISC Specificarion Equations 12-4 and J2-5, may be rearranged to solve for the fillet weld size, w, for the given material strengths (the required strength for ASD is taken to be RyFyll.5). From AISC Seismic Provisions Table A3. l, for ASTM A36 plate material. R1 = 1.3.

x (29,000 ksi)(SO ksi)(0.585 in.)

LRFD

=793 kips

\ •"

793 kips

Interface Welds B3$ed on experiments and simulations, Roeder et al. (2011) recommend designing che welds at the gusset-to-beam and gusset-co-column interfaces for the expected tensile strength of the gusset plnte in order to increase che deformation and ductility capacity of the system and limit che weld damage. The recommended expression for the size of a pair of fillet welds, where w is the weld size and the 1.5 represents the directional strength increase for transversely loaded fillet welds, is:

0.415 in.

il

5-293

S.3 SPECIAL CONCENTRICALLY 'BRACED FRAMES

This v~ue ~s not compared to the value of V.,b or V.,b calculated previously, which is based on tension in the brace, as crippling is a compression limit state. Compression in the beam web occurs when the brace is in compression, not when it is in tension, so new Vub and vob f~rces need co ~ determined. Because· the Vub and Vab forces calculated previously are directly pro~rtional to .the brace force, they can be scaled down based on the r:itio of the brace force in compression to tl-,e bcace force in tension. The maximum compression force at the gusset-to-beam interface is calculated as;

LRFD

550 kips

ps

=191 kips Therefore:

Y -

RyFy

2{1.5)~(0.60) Fexx {0.707)

l

I

w-

l

I

QR.,Fy - 2(1.5)(1.5)(0.60).fE:u (0.707)

(

P

j

I

II

p

= 2(1.5)(0.75)(0.60)(70 ksi)(0.707) Ip

[ (2.00)(1.3)(36 ksi) = 2(1.5)(1.5)(0.60)(70 ksi)(0.7?7)

=0.100lp

=0.700tp

{1.3)(36 ksi)

Ip

I

For the *-in.-thick gussec plate, the weld size required is:

w= 0.100(5h in.)

ASD

kips)-- 237. kips . [444 Jdps) . 550

V.ub [ 444 ki

l ·- [

ASD

=0.438 io. Va11[ 311 kips)= 166 kips( 3 11 kips}

385 kips .

385 kips

:: 134 kips

Use a Ys6·in. fillel weld on both sides of the gusset pl:ite to connect the gusset to the beam and column.

BeanHo-Column Connection Tue beam-to-column connection must comply with tbe requirements of AISC Seismic Provisions Section F2.6b. For I.his example, Section F2.6b(b), the moment-resisting beani end connection option, is chosen. Titis example utilizes a moment connection with OF

BRACED FRAMt;S

groo"e welds of the beam nanges and web to the column flange, wluch will be adequate to, re~1st a moment corresponding to the expected beam flexural strength multiplied by I.I (LRFD) or 1.1/1.5 (ASD). lhcreby meetiog AISC Seismic Provisions Section F2.6b(bXi). An altcmath"e method of providing a moment connection at lhe beanHo-column connection and meeting AISC Seismic Prcwisions Section .F2.6b(b), which explicitly considers fTam~ rotational forces, is prtsentcd in Example 5.3.12. A connection with a simple beam-to-colunm connection meeting AISC Seismic Proi•isions Section F2.6b(a) was presented in farunple 5.3.10. Any of these approaches is ~atisfoctory. u~ CJP groo,:e welds at

lhe beam flanges-t<>-eolUITUl and beam web-to-column connection~.

S.3 SPECIAL CONCE.NTRlCAl l.Y BRACED FRAMES

Check web local crippling of the column

For a force applied greater than a distance of d/2 from the member end, the avail3blc web local crippling ~trengtb of the column is determined 3S follow~. where the length of bearing, lb, is taken as the beam nangc thickness:

•· •osoi![• •3( ~ J[ '.; .,I

= (0.80)(0.550 in.)" I+ 3

To de1cnn.ine whether continuity plates are required, check whether lhe limit states of web local yielding, web local crippling, ru°id flange loc:il bending of the column are adequate for the required strength. The required strength mu!;t be detennined. AISC Seismic Provi..sions Scc1ion F2.6b(b) requires that lhe conneaion be designed to resist a moment equal to the expected beam flexural strength multiplied b) I. I (LRFD) or I l/ 1.5 (ASD). Tn this case, the beam web has a CJP groove weld to the column flange and therefore can develop the full expected flexural ~trength of the beam web. Therefore, for the local column limit states of web local yielding and web local crippling, the demand at the column face will be taken as 1hc expected, st:ram·hardened strength of the beam flange using a strain-hardening fac· tor of I.I:

r\t;.'

x

Ruftmitt = 1.1R1 F1 Aft>1igt

R,,fl011gt

=1.1(1.1)(50 ksi) x(8.97 in.)(0.585 in.)

=(1.J I 1.5)Ryf',•Ajlong< =(I.J / 1.5)(1.1)(50 ksi)

in.)uj

l0.585 in.)(0.550 _ in. 0.900 io. 12 7

(29,000 ksi)(50 ksi)(0.900 in.) 0.550 in

=397 kips

ASD

LRFD

Rn

-=

~Rn= 0.75(397 kips)

=298 kips < 317 kips

n

n.g.

397 kips

2.00

=199 kips< 212 kips

n.g.

Check flange local bending of the column

j

The available strength of the column due to flange local bending is determined as follows:

::

(Spec. Eq. 110-1)

R,, = 6.25F,ttJ

x(8.97 in.)(0.585 in.)

=317 kips

=6.25(50 ksiX0.900 in.)2

""212 kips

=253 kips For a force applied at n distance greater than the depth of the member from the member end, the av:ulnble web Joc.'ll yielding strength of the column )s detennined as follows, where the length of bearing, Ip, is taken as lhe beaID flange thickness. (Spec. Eq. 110-2)

R,. = F,...t..,(5/c.us +lb) =222 kips

LRFD

ASD R,.

-=

n

\

ASD

!pR,. =0.90(253 ki~) = 228 kips< 317 kips

Rn

n.g.

n=

I ..

253 kips

I

i.61

=151 kips< 212 kips

l,

n.g.

.

L-~~~~~~~~~~~~..l.._...~~~~~~~~~~~~-''

I

Ba.se.d 00 the chec.ks of web Jocol yielding, web local crippling, and flange local bending the column requires continuity plates. The continuity plates mus~"be desifgnthcd to resisl thb( .. difference between the flange force, Ru~tor Rofi=ic• and the 1esser o e co1umn we local yielding, web local crippling, and Oange local bending strengths:

=(50 ksi)(0.550 in.)[5(1.50 in.)+0.585 in.J

n.g.

\ LRFD

Check web local yielding of the column

=1.00(222 !tips) =222 kips< 317 kips

(Spec. Eq. JI 0-4) }:

ASD

LRFD

$R,.

1

.

222 kips · 1.50

=148 lcips<212 kips

~R,, .. 317 kips- 222 kips

R.. = R., Jltmtt ll.&-

l Il

.--~~~~-LRF~-D~~~~~.-~-=-~~~AS -:-;::D:--~~~~~1

=95.0 lops

Ro= R,,Jbnl~ -R.1n

=212 kips-148 kips =64.o kips

I~

L--~~~~-'-~~~~~l

AMU1CV4 lNsTrnrn! "' STED... Cot'IS'TlltlC'TlON

BR.ACED FRAMES

5-296

5-297

5.3 SPECIAL CONCEN1 RICALl.Y BRACED FRAMES

For the •A-in.-thick continuity plate, the required weld size is:

Using a continuity plate width that closely matches the beam flange width:

'

I

I

2 2 . 8.97 in. 0.550 in. 4 2 lm. ---=. 2 2 Select 4.50 in. as the plate width.

= 0.674( .4 an.) ::: 0_169 in 1

sure that this plate width fits within the column

flange:

Use y16.jn. fillet welds between the continuity plate and the column flange (both sides of the

12.2 in. 0.550 in. - -- 2 2

. . =5.83 in.> 4.50 111.

o.k.

The required thickness for the two continuity plates, based on the limit state of tensile yielding from AJSC Specification Equation 14-1, is:

LRFb

(2 plates)Fybr/.Q >Ra

t>~

t>--

1

l

1.67 (64.0 kips) > (2)(50 ksiX4.50 in.)

> 0.235 in.

ASD

60.60F1 wt - 2{0.60)Fax (0.707)

(2)F>b

95.0 kips > 0.9-0(2)(50 ksiX4.50 in.)

this connection is not required to comply with SMF requirements.

LRFD

ORa

cp(2)Fyb

plate), For the welds between the continuity plate and the column web, a weld size will be chosen chat is stronger than the available shear strength of the continuity plate contact area with the web. This design approach meets AISC Seismic Provisions Section E3.6f(3)(b), although

Deriving the weld size as was done previously for the gusset plate in tension:

ASD

R,,

~

> 0.238 in.

l

1.00(0.60)(50 ksi)

l

2(0.75)(0.60)(70 ksi){0.707) t

1:herefore ~-in.-thick continuity plates wiU be used.

Design the welds between the continuity plates and column

w

0.90(50 icsj) 2(1.5)(0.75)(0.60)(70 ksi)(0.707)

= 0.674t

:: '••

]1

2.00(0.60)(50 ksi)

1

= [2(1.50)(0.60)(70 ksi){0.707) t

I I

I -l

l

1 t .QF. 2(1.59)0 (0.6)FEXX {0.707)

2.00(50 ksi) 2(1.50)(1 .67)(0.60)(70 ksi)(0.707)

=0.612t

=0.674( A in.) 1

= 0.169 in. Use ¥16-in. fillet welds between the continuity plate and the column web (both sides of the plate)_

·

Check beam web~to-cotumn connection The beam web is subject to gravity forces from beam shear in addition to forces from th~ brace. The required shear strength of the beam for the case of tension in the brace is calculated a~ follows. The gravity shears from the beam act in the opposite direction-as ~e brace fore<

ASD

LRFD

w=

l

For the 'A-in.-thick continuity plate, the weld size required is:

There are several design considerations that could be used to detemline the required weld size. For the welds between the continuity plates and column, lhe welds will be designed to be at least as strong as the available strength of the contact area of the continuity plate with the flange. This design approach meets the exception in AISC Seismic Provisions Section El.6b(c)(4); although this connection is ~ot required to comply with OMF requirements. Using the expression for the required weld size to develop a plate in tension discussed previously for the gusset plate, the fillet welds at the continuity plate to column flange are sized as follows:

w=j 2(1.5)¢(0.60) Fy j, Fexx {0.707)

l

.Q0.60F1 w= 2n(0.60)FEXX(0.707)]c

=0.674t

:::: 0.674t

=[

'

w=0.612t = 0.672(1.4 in.) =0. 168 in.

w = 0.674!

M~e

I

ASD

LRFD

with.Sos= 1.0:

l,

S-298

BRACED FRAMES

LRFD

LRFD


v# =(0.9-0.2SDs}VD +V,E,M

Vo =(0.6-0.14SDS }vo +O.?VEmh

Vu =0.7(-4.50 kips)+237 kips

Vo= 0.46(-4.50kips)+166 kips

¢vVn

ASD V,,

=1.00(249 kips)

249 kips 1.50 =166 kips> 164 ldps

-=

= 249 kips > 234 kips

nv

o.k.

The required shear strength of the beam for the case of compression in the brace is based on a brace expected strength of 444 kips (LRFD) and 31 l kips (ASD). As calculated previously for Vub (LR.FD) and V;,b (ASD):

LRFD

=237 ki

ASD

s( 444 kips)

p 550 kips

Vab('311 kips) :::!66 kips(311 kips) 385 kips 385 kips

=134 kips

= 191 kips

LRFD . LRFD Loud Combipation 5 from ASCFJSEl 7 Section 12.4.3.2

ASD ASD Load Combination 5 from ASCE/SEI 7 Section 12.4.3.2

v., = (l.2+ 0.2SDs }Vo+ VEmlr +0.5VL

Va =(l.0+0.14Sos )VD +0.?VEmh

Vu= 1.4(4.50kips)+191 kips

Va= 1.14(4.50 kips)+ 134 kips

= 139 kips

+ 0.5(3.00 kips)

f

The final design is sho"'n in Figure 5-45.

Example 5.3.12. SCBF Brace-to-Beam/ Column Connection Design-ln· Plane Brace Buckling Given: Refer to Figure 5-49. Design the brnce..to-beam connection at Joint JT-1 shown schematically in Figure 5-49. The brace orientation, connection type, transfer force, and beam shear _due to gravity loads are shown in Figure 5-50. The conneetion con.figuration shown in Figure 5-51, which makes use of a "hinge plate," allows large inelastic rotations for in-plane brace buckling with small flexural demand on the connection and supporting members. In this configuration, large inelastic rotations are accommodated with the advantage of having a compact connection (Thornton and Fortney, 2012). This is different from t.he approach shown in Examples 5.3.10 and 5.3.ll, where the brace is expected to buckle out of the plane of the frame. The round HSS brace is ASTM A500 Grade B and the beam and column are ASTM A992. Use ASTh1 A572 Grade 50 plate material. The bolts are AST!v1 A490-X.

The completed design shown in Figure 5-51 will be verified in this example.

P~rtnwn

=444 kips

1

=295 kips> 234 kips

ASD

o.k.

nv

l '

The strength of the beam in shear is, from AlSC Mamwl Table 3-6:

v. _ n = 197 kips> 164 kips

r

= 550 kips

F2.3ii)

LRFD

I.

From Example 5.3. l l, the e.xpected strengths of the HSS6.875x0.500 brace are:

0.3P°""PIUSitm = 133 kips (post-buckling strength from AISC Seismic Provisions Section

= 199 kips

v Vn

o.k.

= 164 kips

=234 kips

ub 550 kips


ASD


V: ( 444 kips)

'•'

W12x96 column

o.k.

At the column face, the available shear strength is reduced by the material re.moved for lhe weld access holes. From Table 1-1 and Table 1-3, weld access bole type B applies to the W24x68 and the (3) and (4) dimensions are ~ in. sud ~ in., respectively. The available shear strength is determined from AISC Specification Section G2.

W12J<96 column

W24x68 beam

V,, ={(0.6X50 ksi)[23.7 in.-2(0.585 in.+~ in.+'h in.)J}(0.415 in.)

= 249 kips Fig. 5·49. Beam-columnjoin1for Example 5.3.12.

The required strength of the connection froan ASCE/SEI 7 Section 12.4.3.2 Load Combination 5 (LRFD) and Load Combination 5 (ASD) is based on the horizontal seismiJ effect including the over)trcogth factor, E,,,h = Uo'2E (ASCE/SEI 7 Section 12.4.3.1). Jn thi; case, Emh is the expected strength given previously for the brace as stipulated in AIS~ Seismic Provisio11s Section F2.3. The required strength of the connection when the brace is in tension is:

LRFD

Pu= l.OEmh

·i!

ASD

LRFD

'

Pa= 0.1E,...n

P,. = l.OEm1i

=0.7(133 kips) =93.1 kips

Pa =0.1Em1i

=l.0{550 kips)

~... I

i

The required strength of the bracing connection when the brace is in compression at ils postbuckling strength is:

=1.0(133 kips) =133 kips

ASD

S-301

S3 SPECIAL CONCc"NTRICALLY BRACED FAAl->1ES

BRACED FRAMES

S-300

=0.7(550 kips) =385 kips

=550 kips

.-

Solution: From AISC Manual Tables 2-4 and 2-5, the material properties are as follows:

{,

The required strellgth of the bracing connection when the brace is in compression is:

;:

LRFD

::-, ».

...

P,,

ASD

=l.OEmh

PL114'x7Wx2'-3" (A572 Gr. 50) with 1" dia.

Po =0.1Emh

=1.0(444 kips) = .444 lips

-

=0.7(444 kips)

A400.X bOlts

in std. holes

=311 kips

:

HSS6.875x0.50-')

brace W12x96"-.

cclumn Pu = 550 kips (T)

:I·illlI

/

444 kips (C)

·-

P. z 385 kips (T) 311 kips (C)

Hinge PLrn•x11•x4·~s·

;i,

(A572 Gr. 50) slotted onto gusset

!.•

v. • 19.9 kips (LRFD) V, • 12.8 kllls CASO)

£Hinge reglon

Pll4" (A572 Gr. 50) dovbler plate, one side of web PL~"x7~"x1'-9"

W24x68 beam

(A572 Gr. 50) with

1" dia. A490-X bolts in std. holes

....

Note: M90-X bolts are to be pretensioned with slip-critical faying surfaces.

'

~~

Fig. 5-50. Bmce coiu1ection

10

be designed for Example 5.3.12.

Fig. 5-51. Completed connecrion desigt1for Example 5.3.12.

J - .JVI,,

BRACED FRAMES

"t

Hinge Plate Assume the width of the hinge plntc is limited by the column Oangc width of 12.2 in. Th liJ:njt is an orchitecturcll consideration to ensure that the connection does not affect lhe fa~J1 or in~I partition width. It is not an engineering requirement.

ASTM A500 Grade B

F1 =42 ksi F,, =58 ksi ASThf A572 Grade 50

Choose a hinge plate width, bp, of 11.0 in. This protrudes beyond the beam flange widt1 but is less than the column flange width and is sufficient to accommodate the 6.875 in dian ctcr HSS brace.

F1 =50 ksi Fu =65 ksi

ASTMA992 r'., =65 ksi

Brace HSS 6 .875x0.500

r,_. = 0.500 in.

A= 9.36 in. 2

·

(Spec. Eq. J-t-1 ' J::

From AISC Manual Tables 1-1 and 1-13, the geometric properties are as follows:

D =6.875 in. r= 2.21 in.

l~

To size the hinge plate for the lirrut state of tension yielding, where tp is the thickness of th hinge plate:

F1 =50 ksi

The 11.0-in.-wide hinge plnte is well within the maximum allowable Whitmore sectioi. according 10 AlSC Manual Pan 9, and therefore the entire hinge plate width can be consh ere.d effective in this limit state.

I

Beam W24x68

=23.7 in. =1.09 in.

=0.415 in.

A ::: 20.1 in. 2

d

t1= 0.585 in.

kdu

z.. =

d= 12.7 in.

I,.. = 0.550 in.

b1= 12.2 in.

k.Jr1 = 1.50 in.

k4,,

lw

1>1= 8.97 in.

177 in. 3

,, >OPa -- F>bP

Column W12x96

1.67(385 k.ips)

= I 1~o in.

Z:r =

147

in.'

tr= 0.900 m.

A ISC Seismic Provisions Sections F2.3(i) and F2.3(ii) define the two mechanism anal:)'ses that must be considered in determining the required strength of beams, columns and connections. AISC Seismic Provisions Section F2.6c specifies the required strength of bracing connections. For the required compressi~e sirength based on buckling limit states, Section F2 6c(2) has an additional 1.1 factor (relative to the requirements of Section F2 3) applied to the required strength of the connection. For lhese SCBF connection examples, the requirements of AISC Seismic Provisions Section F2.3 will be used for both LRFD and ASD, e~ccpt for the limit state of compression buckling on the Whitmore section, which will use the l.l factor specified in AISC Seismic Provisions Section F2.6c(2).

Brace-to-Hinge Plate Connection Design Example 5.3.10 showed.the full brace.to-gusset connection design for the same size brnce as used in this exrunple. The calculations for the brace side of the brnce-to-gusset connection arc not repeated here.

AMu!cAN INsTrnm; OF STEEL CotUTRl!CT!Ot<

2: 0.90(50ksi}(l1.0 in.)

2: (50 ksiXI 1.0 io.)

2: 1.11 in.

2: 1.17 in.

J

\

Use a 1\4-in.-thick hinge plate.

\

\

Check hinge plate net section for tensile rupture strength Assume the gusset plate thickness is I IA io. and verify this assumption later. The_lunge plat is slotted over the gusset plate with an additional 1/16 in. increase in slot width on either sid of the gusset plate. For the hinge plate:

An= [11.0 in. - PA in. - 2('t16 in.)J(I !A in.)

.l.

= 12.0 in.2

=

According to AISC Specification Table 03. l Case I, U LO because the teosfon load i .\· transmitted directly 10 the cross-section elemcnL From AISC Specification Equation J4- , ,_

!

5 3 SPFCIAL CONCENTRICAU.Y liRACED FRAMES

LRFD ¢R,. =~F..~

R,. = F,,~

n

- 0.75(65 ksi)(12.o in. 2 ) == 585 kips > 550 kips

Because KUr < 25, buckling is not 1:cns1dere
ASD

n 65 ksi(l2.0 in. 2 )

o.k.

From AlSC Ma1111al Table 4-22·

2.00

=390 kips> 385 ldps Hinge Plate-to-HSS Brace Connection Design

.... ~

!,

)

I;::, '

·~

1· i

111

Check hinr;e plate for compression buckling The minimum recommended lunge leng!h for this connection configuration measured berw~cn th~ end of the brace and the gusset, is 3tp. Refer to Thornton and Fortney (2012) for d1scuss1on on the recommended 3tp hinge length.

=3.75 in. Use 4.00 in. for the hinge length.

. ··... .. ~:

..'·

~lodeling the binge plate as foed at one end and free to route a1 the other end, the cffecuve length facLOr from AISC Specification Commentary Table C-A-7.1 is 1.2. The effective length of the hinge plate is:

·

KL= l 2(4.00 in.) =4.80 io. The radius of gyration of the hinge pl:11e is: t r==t.i

~r -= 29.6 kJ.i

.,

The limit sime of shear rupture in the brace wall was used in Example 5.3. LO to determine the length of tbc brae~· lo-gusset plate connection. Because the brace i;ize in this example is the same as that us~ in &le 5.3.10, determination of the weld size and length between tbe brace and tb.e hinge plate are not repe~ted here. Similarly, the 11:11 bar reinforcement on the brace is kept the ~me as Example 5.3. IO. For the limit :.late of block shear rupture on the. hinge plate. the lunge plate io this example is thicker ( l'A in.} than the gusset plate (~ in.) m Example 5.3. l 0 and is also a material with n higher yield sLrcngth. Therefore, from Example 5.3.10, block shear on the hinge plate wiU be adequa1e and need not be checked.

3tp =3(1'.4 in.)

ASD

LR.FD

o.k.

H e

TI1e available comprei;sive strength of the hinge plate is:

LRFD

ASD P" F.::rAi = -Q n

¢Per = 6Fc,1\1 = 44.4 ksi(l l.O in.)(l 1A in.)

=29.6 ksi (l J.0 in.)(!~ in.) =407 kips

= 611 kips

611 kips> 1.1(444 kips)= 4$8 kips o.k.

..tO? kips> 1.1(31Ikips)=342 kips o.k.

AlSC Seismic Provisions Section F2.6c(3) requires 1hat the brace connection accommodate the t1exural forces or rotation imposet1 by brace budding. This can be achieved either by option (a) design.mg the connecuon to have an av:iilable flexural ~aength of the expected brace flexural strength. RyM,,. multiplied by J.I (LRFD) or by 1.1/1.5 (ASD) or option (b) providing rotation capacity to accC>mmodate the required rotation. Eumplcs 5.3.8 through 5.3.11 used option (b) 10 sab:;fy lhis requiremenr. This brace configuration also satisfies option (b) becau~e the 31,, length of the hinge plate provides rotation c:ipacity (Thornton and Fortney, 2012).

The hinge ph11e allows the brace 10 buckle in the plane of the gusset plate by means of introducing a perpendicular hinge plate. The connection thus accommodates brace rotation according to AISC Seismic Provi.sions Section F2.6c(3)(b); lbe rcquiremeo1 10 withstand flexural forces im(Xl-~ by brace buckling according to Section P2.6c{3Xa) is not applicable. Note that the commentary to this section implies that budiling in the pl;uie of the gusset is fixed-end buckling (thus requmng applic:ition of Section F2.6c(3)(a)): in IM cooteXt of this connection, the hinge plate rakes the place of lhc gusset for purposes of determining end fi:
l ~in.

To ensure that rotation of the hmge plate can occur without damage to olher parts of the assembly, m this example the expec1ed tlexur.U 5trength of the hinge plate is u~ed to determine maximum forces on the hinge-pl3te welds. This ensures that the hinge pl:ue-to-gus~ct

:: 0.361in.

welds are sufficient to allow Lhe hinge plate 10 achieve its e.'tpectcd flexural strength mul tiplied by I. I.

'"=-:Ji2. KL r

4.80 in. 0361 in.

=13.3

Determine the c.'tpected flexural strcnglh of t.bc binge plate (mulriplkd by I I ): Mh111¥~

=l.1R1 FyZh AM~ 11.ICA>I

INSTTl'UT1! OP Sn.a CONSTRIX..'TION

S-306

BRACED FRAMES

~ ~.

The width of the maximum Whitmore section on lhe gusset plate at 30° is:

where

Ry =1.1 from AJSC Seismic Provisions Table A3. l Zh =plastic section modulus of the hinge plate about the weak axis

I,.. =2(26.0in.)(tan30°)+PA in. =31.3 in.

bpr;

=--

Part of this Whitmore section lies outside of the gusset plate. Approximately 12.0 in. of this width remains in the gusset at the gusset-to-column interface. In order to avoid accounting for Whitmore width within the bolted joint, a 12.0 in. width will be used on the column side and 15.0 in. on the beam side. On the beam side, approximately 5.00 in. are in the gusset and 10.0 in. are in !he beam web (I.be 10.0 in. within the beam web is included in the Whitm0re section area). Try a l !.4-in.-thick gusset. The Whiunore area is:

4

=11.0 in.(!IA in.)2 4

=4.30 in.3 M11;,,ge

= 1.1(1.1)(50 ksi)(4.30 in.3)

A,..= (12.0 in.+ 5.00 in.)(l'A in.)+ (10.0 in.)(0.415 in.)

= 260 kip-in.

=25.4 in. 2

This moment can be replaced by two equal and opposite forces, F, acting on the welds between the hinge plate and the brace.

From ATSC Specification Equation J4-l, the available tensile strength is:

ASD

LRFD

F= Mhinge Ip

= 260 kip-in. )I;.\

1!>P11

in.

P" FyAw -::::-Q n

=
=208 kips

"'1,140 kips> 550 kips

50 ksi(25.4

=

().k.

The weld required to carry the force, F, from AISC Manual Equ:uions 8-2a and 8-2b is:

LRFD D-

1.67

= 760 kips > 385 kips

o.k.

I

ASD

F

D=

2(1.392 kip/in.)/ 208 kips 2(1 .392 kipfm.)(26.0 in.)

= =2.87 sixteenths < 4 si~teenths

'

in.2 )

=

o.k:

Check shear yielding on the gusset plate From AISC Specification Equation 14-3, the available shear strength due to yielding on th<

F 11.5 2(0.928 kipfm.)J

gusset plate is:

(208 kips/ 1.5) 2{0.928 kipfm.)(26.0 in.)

= 2.87 sixteenths < 4 sixteenths

o.k.

l-----LRFD _ _ _ _ _+----~A_s_n_ _ _ _ R.,.::;; 0.60Fyltp(2)

¢R,. =
Check tensile yielding of the gusset plate on the Whitmore section Tension yielding is checked on a section of the gusset plate commonly referred to ns the ··Whitmore section." This section is explained in AISC Manual Part 9 (Figure 9·1) and in Thornton and Lini (2011).

Q

= 1.00(0.60)(50 ksi}(26.0 in.) x(l1A in.)(2) = 1,950 kips> 550 kips

Q

=0.60(50 ksi)(26.0in.)(l1A in.)(2) 1.50

o.k.

= l,300 kips> 385 kips

o.k.

Therefore, a l 1A-in.-lhiek: gusset plate is adequate.

ll.

I

I

.

r ...

Check buckling of the gusset plate The gusset buckling length is 5.00 in., and by inspection buckling will not control.

t

5-308

BRACED FRAMES

.,,, r,;;

s..::::

5.3 SPECIAL CONCENTRJCALLY 'BRACED FRAMES

Gusset Interface Forces

f I (

L

Use the Uniform Force Method presented in AJSC Manual Part 13. From the geometry of FJgurc 5-51:


de

r

.

~·

,..

ec Hoc=-Po

Hue =-Pu

12.7 in. :i:--2 =6.35 in.

'"

From AlSC Manual Equatio n 13-3.

ec

ec=2

.

ASD

LRFD

db eb =2 23.7 in. =--2 11.9 in.

r

"'6.35 in. (550 kips) 38.1 in.

=6.35 in.(385 kips)

=91.7 kips

"'64.2 kips

38. l in.

From AISC Maiwal Equation 13-5:


a

,.

Hub=-P.,

=

Hob

24.0 in. m.+--2

OQ .

" =3. =15.0 in.

=20.6 in. ( 385 kips)

= 297 kips

=208 kips

Vue

For the force distribution to remain free of moments on the connection interfaces. choose a value of a to satisfy the following expression. (Ma111~al Eq.

13-1)

= (15.0in.+ 11.9 in.Xl)-6.35 in. = 20.6 in.

2

r"' J(a+ec )2 +(P+eb)

=Jc20.6 in. +6.35 in.)2 +(1s.o in.+ 11.9 in.)1 =38.1 in.

I

\\ ~·

r 15 0 · in.(550 kips)

=

=15.0 - -in. - (38-=> ki ps) 38.1 in. = 152 kips

38. l in.

=217 kips


Vab =-Pa r

r

=l I.9 in. (550 kips) 38.l in.

\

\

=172 .kips

I

!

eb

V""= -Pu

(Manual Eq. 13-6)

I

=11.9 - -in. - (38=>_ ki ps)

II

. 38.l in.

=120 kips

;

These forces are shown in Figures 5-52a and 5-52b.

Beam-to-Column Connection

.:.

The beam-to-column con!le(;tion will be designed to satisfy the requirements of AJSC Seismic Provisions Section F2.6b(b). The following exemplifies the detcnnination of the required moment and forces on the connection.

~

I ~.

Vac --~ -Pa r

=~Pu

el>

The required axial and shear forces on the connection due to lbe tensile load on !he brace are derennined from AISC Manual Equations 13-2 through 13-5.• where:

?


From AISC Manual E.quation 13-4:

a= (P +et-)( tan 45°)- ec

" ..

38. 1 in.


e =45°

r

20.6 in. ( _ ki ) = - - - 5 =>0 ps 38.1 in.

A

a

=- Po

I

In this cxnmple, lhe required flexural strength is resisted through the entire connection including the gusset plate. The moment resistance is noc confined co lhe beam-to-coluir· portion of the connection. Alternatively, as shown in Example 5.3.l l, AlSC Seisir ' Provisions Section F2.6b(b) could also be satisfied by provicling a fixed beam-to-colun~ connection.

AMEJOCAN ~STmJT£ 01' STEEL CONSTRUCTION

:>-,)lV

BRACED FRAMF.S

• .

5.3 SPECIAL CONCENTRICALl Y BRACED FRAMES

The required flexural strength is based on r.he lesser of the expected flexural strengths of tl" column and beam multiplied by 1.1 (LRFD) or 1.1/l.5 (ASD) as required by AISC Seism. Provisions Section F2.6b(b):

389 kips

2.75"

tti ....

~

N

;.,

..

@ co

q

(7k'"'jl~~... ...

_.

I

't::::;L-_ _ ___J

97 kips /

Mb~am

I .L::

-

r· ·- ·- · ~. .---. .389 kips -46.0 kips

.

172 kips :: :

'•

)

= (1.1/1.5)(1.1)(50 ksi)(l77

= 10,700 kip-in.

... J :: :

I

Mbeom = (l.1/l.5)RyFyZx

=l.l(l.1)(50ksi)(177 in.

2972_

46.0 kips 91 .7 kips

= J .1R1F1Z., 3

1172 kips

~

389 kips.

I

l

20.6"

= l:(L l/l.5)R~F1 Zx

=2(1.J/ l.5)(1.1)(50 ksi)(l47 in.3 ) I =11,900 kip-in.

= 17,800 kip-in.

172 kips

@) W.P.

M eo/

= 2(1.1)(1.l)(SO ksi)(l47 in.3 )

• ••

."'

ASD

M" 1 = I:t.lRyFyZ.t

:• •

II)

1

LRFD

•••

j.

in.3)

= 7,140 kip-in .

I.

The lesser of these expected fle,xuraJ strengths is MR= Mbeam = 10,700 kip-in. (LRFD) an 7,140 kip-in. (ASD). The subscript R is used to denote "rotational" forces and momenu; because this moment is due to fram.e action.·Refer to Thornton and Muir (2009) for more discussion.

I I;

From Figures 5-53a and 5-53b: Fig. 5-52a. Gusset interface forces due ro brace expected strength (I.RFD).

LRFD

ASD

MR HR=--

MR HR = - -

P+eb

272 kips

2.75"

=

385 kips

10, 700 kip-in. 15.0in.+11.9 in.

= 398 kips

272 kips

VR

=HR~ 20.6 in.

=290 kips

r.n

...

1120 klps

272 kips

I

~L ::

.:2~8~ I --- --- :..:

32.2 kips 64.2 kips

120 kips

,___.-

1: :. '•.

__ ---

...............

272 kips 32.2 kips

Fig. 5-52b. Gusset inrtrfaceforr:es due to brace e.:rpected strength (ASD).

..

I

I

7,140 kip-in. 15.0 in.+ 11.9 in.

1·.

= 265 kips

1"

\.

0.

=398 kips(l5.0 in.) W.P.

I

~+eo

HR~ VR = - -

0.

~

=

v

=265 ldps(l5.0.in.) 20.6 in.

=193 kips

j

..

1·

These rotational forces due to frame action are shown in Figures 5-54a and 5-5Application of moment in the figure is consistent with the angle between the beam and Cl umn closing as the brace goes into tension. In addition to the admissible force distributk due to the brace expected strength shown in Figures 5-52a and 5-52b, and the adro.is~il force distribution due to frame action shown in Figures 5-54n and 5-54b, an admissible gr... ity force distribution must also be detennined. Note that the gravity forces always exist :ind therefore, must be added lO the brace ex pee• strength shown in Figures 5-52a and 5-52b and the rotational forces shown in Figures 5-5

and 5-54b.

....

AMEIUCAN INSlTtunl OP ST£EL. CorlsTR\JenON AMl!IUCAN lNSTllUll! OP STEJ!L CONSTRUCTION

5-312

BRACED FRAMES

AlSC Seismic Provisions Section F2.6b requires that the rotational forces c:ilculated from tbe., Jesser·of the column moment so:ength or the beam moment sirengtb be "considered in combination with the required strength of the brace connection and beam connection, ~!!duding amplified_dfophragm <;~Hector forces."

~,350

I

kip-in.

6.35"

.

2.75"

~

-~-SMR

I'

'• 398 kips . - 1•• q 290 kips :.••••

N

II

f

(.)

.

2.75"

..... I:.. ,,

~

6.35"

5-3 13


I••

I,/)

~

(!)

~!·=·=--------' 398 kip-;---1 290 kips

Co W.P. ~

II

c.,

20.6"

@)

-I

(!)

290 kips

~

&,[

I I

398 kips

290 kips Ii•

10,700 kip-in.

~ 39'8i-)

\......:_../ 5,350 kip-ii).

~=

i.

·~!

;;; ··11 ., ·'-'

Fig. 5-54a. Rotational force distribwion due to frame action (lRFD).

o.sM°}-J ~.570 kip-in.

Fig. 5-53a. Rotational forces due to frame action, MR.

6.35'

., 2.15·

tn

.. I:.. ,,

~ n

N

265 kips

{-

h
~

'• .

1.::. I• •

't::::::::::..-...,.....===----'

&> ..... W.P.

265 kips

~

20.6"

@) IO

193 l
~ Face

of column _)"-- -a - ---i '-J

3,570 kip-in.

Fig. 5-53b. Gusset plate free body diagram due to rotational forces.

m[

::

1193 kips.

I

26Skips

193 kips ,. •

7, 140 kip-in.

2~11~~~·-·-·-·--~~) •'•. ••

Fig. 5-54b. RotaJionalforce distribution due to frame action (ASD). AMERICAN lNSTTIVre OI' STEEL CONSTRUCTION

.

5-314

5.3 SPECJAL CONCENTRICALLY BRACED f'RAM.l:S

Figures 5-55a and 5-55b show the combined brace, rotational, and gravity interface forces as required by AJSC Seismic Provisions Section F2.6b.

Use l-in.-diame1er bolts.

5-31

From AISC Manrwl Table 7-1 I.be available shear strength of l-in.-diameter ASTM A490-> (Group B) bolts in standard holes is:

Gusset-to-Column Single-Plate Connection Design

Figures 5-55a and 5-55b show the interface forces for this connection. Note that shear forces from the brace expected strength are additive with shears from the rotational forces, but normal forces from the brace e:
Qrn

=49.5 kips/boll

LRFD

N0 = 201 kips

R,, =JV]+N:

R,, =~V} +N;

=J(507 kips)2 + (306 kips)

2

e= tan- I (306 kips)

=345 kips

Nu =306 kips

B= ian- 1(201 kips·)

_.__~--3-4_ =30.2° 5_ki_·p_s~---~~-~' tl~

_ =__ 31.l 0_s_0_7_ki_·p_s_ _ _ _ _ _ _ L

2

2

=J(345 kips) +(201 kips)

=592 kips

ASD

LRFD

ASD V0

rn = 33.0 kips/bolt

n

The angle from the vertical is:

From Figures 5-55a and 5-S5b, the total ·required s1rengths are:

V,, = 507 kips

ASD

LRFD

The eccentricity from the centerline of the two rows of bolts to the column face is:

3.00 in. . 2.75 m.+---= 4.25 in. 2

=399 kips

I

l

L

Pa

Pu

r:

~,570 kip-in.

~,350 kip-in.

I

6.3s·

I

s.3s· 272 kips

389 kips

2.75"

[

.

306 kips

-Cl t,()

......

118 kips

t===ll=:i:::::::Jl!!...!:l--19.9 kips

iJ-i

5,350

(gravity)

kip-in.~ 389 kips

507 kips

I

)4,"'' .. I::: / - ··· .,l•...• /./ . '• .. 2.75"

;sokips

...,'•... /~kips I:...'•... / / l. • '• .

,

I• •

201 kips

/r ~ !"·~

:=?'--=----__J

I 9 < ~ i;; I•• •

19.9 kips

73 kips

/ '.i===li=:j=l\l!-!:I 12.8 kips

~

·-·-·

I

12.8kips1 ••

10.100 kip-in.

kl~~

___ 46.0 46.0 kips 306 kips l • • 118 kips ...•· ·- - - - - - - - - - 1 1 9 . 9 kips P., +19.9 kips

Pig. 5-55a. Combined brace, rotational and gravity forces (LRFD).

20.6" 73.0 kips

(gravity)

695 kips

~

272 kips

345 kips

.

I • •

118klps l

t.

.

3,570 kip-in.~ 272 kips

(gravity)

I• •

I I

73.0 kips

473 kips

~

7,140§kip-ln.

- - :·· I: :

I• • ·-·-· 32.2 kips 272 k' 32.2 kips 201 kips 73.0 kips ...•·- ·- - - - - - - - ' 1 2 . 8 kips Pe +12.8 kips

I

Fig. 5-55b. Combined brace, rotational and gravity forces (ASD ).

5-316

BRAcr;o FRAMES

Using AlSC Manual Table 7-7 for an angle of 30" wilh e.t = 4.25 in., n =9, ands = 3 in.:

c - 14.9 The available shear strength of the bolt group is: )

LRFD

=23.6 in. 2

~ =c(~)

=14.9(49.5 kips/bolt) = 738 kips> 592 kips

A,,,,= j29.0 in. -9(P/:6 in.+~& in.)j{l'.l.i in.)

ASD

¢R,. =C$r,.

From AlSC Specification Equation 14·4, the plate is:

14.9(33.0 kips/bolt}

o.k.


av:iil~1ble

shear rupture strength of the gusset

o.k.

Check gusset gross section for she
=0.75(0.60)(65 ksi)( 23.6 in. 2) =690 kips> 507 kips o.k.

=29.0 in.(1 \4 in.)

Rn

0.60FwA..v

n

n

-=

6>R,, = $0.60F.,:\~,

From th!.! geometry 3Jld edge distances shown in Figure 5·51: A1

Check gusset net section for shear rupture strength

Based on the required hole size for a l-in.-di3.meter boll in )ca.ndard h
>.'

~

5-3! 7

S.3 SPl:Cll\L CONCENTRICALLY BRACED FRAMES

""36.3 in. 2

=

0.60(65 ks1)(2J.6

in_2)

2.00

=460 kips> 345 kips

From AJSC Specifica1io11 Equation J4-3, the available shear yielding strength of the gusset plate IS:

LRFD R~

0.60F1 A1

.n

n

-:::

=1.00(0.60)(50 ksi)(36.3 in.2 ) = 1,090 kips> 507 kips

-

o.k.

0.60(50 ksi)(36.3

Check gusset net section for tensile rupture strength

The net tension area is:

ASD

¢R,, = $0.60F1A1

from AISC Specificazion F.quatfon 14-2, \vitb A,.= A..,, the available tensile rupture strength is:

in. 2 )

1.50 ::: 726 kips> 345 kips

LRFD

Check gusset gross section for tensile yielding strength

From ATSC SpecijicclJion Equ:uion 14-1, the available tensile yielding strength of the gusser pJate lS"

Rnr F..~ -=-n n

=0.75(65 ksi)(23.6 in.2) =l,150 kips> 306 kips

65 ksi(23.6

o..k.

in.2)

= 2.00 =767 kips> 201 kips

o.k.

ASD Rn

'>R,. >= <>F1 A,

n

=0.90(50ksi){36.3 in. 2 ) = 1,630 kips> 306 kips

ASD

\

o.k.

cl>Rm =4>F11Ac

LRFD

o.k.

o.k.

;i

Check net tension and sheur rupture interaction

F1 A1

n =so i.:s;_(36.J 10.2 ) 1.67 = 1,090 lcips > 201 kips

LRFD 2

o.k.

ASD

k.ips) +(345 kips)

2

306 lcips ) (507 !cips) ( 1,150 kips + 690 kips

=0.611
201 ( 767 kips o.k.

2

2

400 kips = 0.631 < J.0

o.k.

5- 318

BR/ICED FRAMES

5.3 SPECIAL CONCENTIUCAl.LY ORACED FRAMES

Check block shear rupture on gusset at gusset-to column interface The failure path shown in figure 5-56 controls lhe block shear .rupture Slrength on !he gusset pl:ue relative to the shear force. BCC
=

Section J4.3:

ubs =o.s A,,, =[4.75 in. -1.5(l1/i6 in.+ 11\6 in.)j(l ~ in.} =3.83 in.2 Agv =26.0 in.(1 /.t in.}

LRFD ~R,,

ASD Rn

=0.75(924 kips)

-=

= 693 kips > 507 kips

n

o.k..

924 k.ips 2.00

=462 k.ips > 345 kips

Check block shear relative to Lhe normal force on the gussel plale using the failure path shown in Figure 5-56:

Ubs =1.0

1

=32.5 in. 2 A,,.,= !26.0 in. - 8.5(1V.6in.+1Ji6 in.)](I ~in.)

= 20.5 in.

S-3"

An1

=!26.0 in. -8.5(!1116 in.+ Yi6 in.)](1 \ii in.) =20.5 in.2

Ap

=4.75 in.(11.4 in.)

2

=5.94 in.2

The available strength for the limit state of block shear rupture relarive lO the shear force on

A,,.= [4.75 in.-1.5(!1116 in.+ 1/i6 .in.)l(l1A in.)

the gusset plate is:

=3.83 in.2 (Spec. Eq. J4-5) 0.60FuA..v +UbsFuAni =0.60(65 ksi)(20.5 in.2)+0.5(65 ksi)(3.83 in.2)

(Spec. Eq. J4-5)

R,. = 0.60F,,A,,y + UbsFwA111 !:: 0.60FyAgv +Ub,FuA.11

l.

0.60FuAnv + Ui...FuA.u =0.60(65 ksi)( 3.83fo.2 )+1.0(65 ksi)(20.5 in.2 }

=924 kips 0.60FyA8., +UbsFuA.u =0.60(50 ksi)(32.5 in.2 )+ 0.5(65 ksi)(3.83 in. 2) =1,100 kips

=1,480 kips 0.60FyAp +UbsF..A.u =0.60(50 ksi)( 5.94 in.2 )+ 1.0(65 ksi)(20.5 in. 2 ) =l,510 kips

=

Therefore, the nominal strength for the limit state of block shear rupture is R,. 924 kips. The available strength for the limit state of block shear rupture on the gusset plate is:

Therefore, the nominal strength for tbelimit state of block shear rupture is R,. = 1.4_8~ kip~ The available strength for the limit state of bl~k shear rupture on the gusset plate 1s.

LRFD

I

ASD

L - - - = - = - - - - - t - - - - - - ~~ Rn l,480 kips f "'R,. =0.75(1,480 kips) -= n 2.OO =1,110 kips> 306 kips o.k. = 740 kips> 201 kips o.k. 'f

Check shear and tension interaction due to block shear

ASD

LRFD ( Fig. 5-56. Controlling block shear failure pa1h in gusset plate.

l~J 10 ~s 06 ki

2

)

2

2

kips)

= 0.611<1.0

2

kips)

201 kips) +(345 ( 740 kips 462 kips

(507 + 693 kips

o.k.

=0.631<1.0

o.k. '

IJRAC.:EO HlA.MliS

Check bolt bearing and tearout on the gusset plate The gusset vertical edge distance to the end boll is 2 00 m. at the top nnd 3.00 in. at the bot· tom. The gusset horiz.ontal edge dimension is 1.75 in. The resultant force per bolt., ba~ed on the C value taken from AJSC Manual Table 7-7 previously, is:

LRFD ru =

ASD

592 ldps

ra

14.9 bolts

= 39.7 kips/bolt

399 kips =14.9 bolts

Check bolt bearing and tearout on the single plate Assume the single plate is I 'A m. thick- the same as the gusset plate. The bearing and tearout strength limit ~tates are separate.! for clarity m the follo""ing. For SCBF systems. \\here large defomlations are anticipated, il is appropriate to assume that deformation at the bolt hole is not a design consideration for the seismic lo~ding, and the tearout strength is checked at the end bolt using AJSC Specification Equation J3-6b. A!SC Seismic Prm;isions Secuon 02.2(1) limits the nominal beanng strength to 2.4drFu. therefore the available ~ari.ng sucoglh of the single plate is:

= 26.8 kips/bolt

ASD

LRFD

TI1e edge distance along the line of action of the boll force may be calculated from the line of action of the given shear and tension. For simplicity, use a conservative value for the bolt edge distance of 1.75 m. lr this conservative assumption reijuires a thicker gusset plate, the aforementioned line of action method \l,·jll be used

The bearing and tearout strength limit :.tates nre separated for clarity in the following. For SCBF systems, where large defonnations are anticipated, it is appropriate to assume Lhat deformstion at the boll hole is not a design consideration for the seismic loading, and the tearout strength is checked at the end bolt with the 1.75 in. edge dist:mce using AISC Specification Equation J3-6b. AlSC Seismic Prol'isions Section 02.2(1) limits the nominal be3ring stn:ngth of the gus~et plate to 2.4dtF.,, therefore the 3vaiJable bearing strength is:

-- -

S.3 SPECIAL CONCENTRICAU.V n~ACl.'0 FRAMES

!!_ _ 2.4dt e.Fu

$rn::; ~2.4dtpFu

n

n

::;0.75(2.4)(1.00 in.)(1 1,4 in.)(65 ksi) ::; 146 kips/bolt> 39.7 kips/bolt

=

o.k.

2.4(1.00 in.)(! 'A in.)(65 ksi) 2.00

-= 97.5 lops/bolt> 26.8 kips/bolt o.k. The sing.Jc plate has top and bottom edge disrancteS of 1.50 in. and a horizontal edge distance of 1.75 in.

From AISC Sp
" \1

LRFD $rn

r1

ASD

ASD

LRFO 2.4dtpFu

r"

=$2.4dtp Fw -= n n =0.75(2.4)(1.00 in.)(l 'A in.)(65 ksi) =2.4(1.00in.)(l1,4 in.){65 ksi) =146 kips/bolt> 39.7 kips/bolt o.k. 2.00 =91 5 kips/bolt > 26.8 k.Jpsfboll

r,.

¢rn =~l.5lct p.F;,

=0.75(1.5)[!.50 in.-0.5(l'A6 in.)} o.k.

n-

..

..

,.

in.)jl

= x(l'A io.)(65 ksi)

o.k.

2.00

=59.0 kips/bolt> 26.8 kips/bolt

rrom the lefthand side of AISC Specification Equa11on J3-6b, the availo:ible tea.rout strenglh .,

n {1.5[1.50 in.-0.5(P/i6

x(l 1A in.)(65 ki;i)


l.5lcf pfu

o.k.

is:

+r,. = ~1.5lctpF•

r~

l.5lctpFi.

n

n

-=

=0.75(1.5)!1.75 in.-0.5(1'116 in.)J

. {1.5[1.75 in. - O.S(Jl/1& in.)]}

x(l 1A in.)(65 ksi) ::; 111 kips/bolt> 3?.7 kips/bolt

Check gross and net shear and tension on the single plate From Figure 5-51, the single plate is 27.0 in. long. From AlSC Specification Equation J4-3, the available shear yielding strength of the single plate is:

ASD

LRFD

o.k.

= x(l~ in.)(65 ksi) ¢R,,

2.00

- 74.'.l kips/bolt> 26.8 kips/bolt

o.k.

Rn

=Q0.60F7 Ap =1.00(0.60)(50 ksi)(27 .0 in.) x(l 'A in.)

= l,010 kips> 507 kips

I

ASD

LRFD

o.k.

n

'

0.60F1 A,,

n

0.60(50 ksi){27.0 in.)(11/. in.)

= 1.50 =675 kips> 345 kips

o.k.

5-322

BRACED FRAMES

From AISC SpecificallOn Equation J4-J, the available tensile yielding strength of the sing.le plate 1s:

S.3 SPECIAL CONCENTRICALLY BRACED FRAMf'!S

Check net tension and shear rupture interaction

ASD

LRFD

LRFD

ASD ( 306 kips J,030 kips

Rn F1 A8 - = --

¢Rn=~F1 A1

=1,520 kips> 306 kips

n·

n

=0.90(50 ksi)(27.0 io.)(1 ~in.)

=0.763<1.0

1

o.k.

The a\'ailable shear rupture strength of the single plate is detennined from AISC Specification Equation J4-4. where:

=0.790<1.0

o.k.

a~ tan

ASD

Rn

0.60F,.A 0 ~

n

n

-=

Load angle

o.k.

I ( 306

:3.i5 kips

507 kips

=30.2"

=41 J kips> 345 kips

'fr 2(1.392 kip/in.)(t+0.50sin1..50)(1)

Ra D,,,, = 2(0.928 kip/in.)(l + 0.50~inl..5 0)Cl)

592 kips =2(1.392 kip/in.)(1.19)(27.0 in.)

=2(0.928 kipfm.)(l .l 8)(27.0 in.}

=6.62 s1'tteenlhs

=6.75 sh:tee.nths

D -

2.00

I

a=tan-1(20lkips) ---

kips)

=3 1.10

=0.60(65 ksi)(21.l in.2)

ASD

.

LRFD

LR.FD


o.k.

flange weld is:

Load angle

"'-0.75(0.60)(65 ksi)(21.1 in.2 )

+ (345 kips 411 kips

Single piste-to-column flange weld From /\!SC Manual Equations 8-2a and 8-2b, including the increased strength due to the load angle given by AlSC Specifi~atio11 Equation J2-5, the required single plate-to-column

in.)

= 21.l in.2

=¢0.60F.,A,.,

r r

1.67

=1,010 kips> 201 kips

¢R~

( 201 kips 686 kips

507 kjps

+ 617 lops

=50 ksi(27.0 in.}{1 A in.}

o.k.

.4,,. = 127.0 in. -9(11/16 in.+ 'Ao in.)j(l 1..4

r( r

o.k.

The ;wa1lable tensile rupture strength on the single plate is determined from AJSC Specification Equation 14-2. with A, =Ani. where·

R.

399 kips

I l I

~

\

I

A.it= A,,,.

Use a Yirin. fillet weld.

=21.J in.2

Gusset-to-Beam Interface

LRFD ¢R,"

ASD

R,.,

F..A,.,

n

n

Tue length of the weld is:

-=--

= ¢F.,A,., 2

= 0.15(65 ksi)(21.1 in. )

= 1,030 kips> 306 kips

lb= (a-1.00)(2)

=(20.6 in. -1.00 in.)(2)

= 65 ksi(21.1 in.2) o.k.

2.00 = 686 lcips > 201 kips

I

= 39.2 in. o.k.

Tue required strengths at the gusset-to-beam interface from Figures 5-55a and 5-55b are:

1--~~~~~LRFD~~~~~~--t~~~~~~A_s_o~~~~~-f V., =695 kips

Nw

=118 kips

Va =473 kips

Na=13.0 kips

.. AMUUCAN lHSTITIJTll OF Sna. CONSTRUCTION

1

Gusset-to-beam weld

Check beam web local yielding

From AISC Manual Equations 8-2a and 8-2b, including lhc increased strength due to lhc load angle. and the 1 25 weld ductility factor di$Cussed in Part 13 of the A ISC Manual. lhe required gusset plate to-beam flange weld is:

For the W24x68. the available web local yielding strength 1s determined from Al~(. Specification Equation 110-3 for a force apphcd from the mem~r end that is less than th: member depth as follows·

LRFD Load angle

Load angle

kips}

0= lall-1(118 695 kips

0

_

( 1.0 + o.sosin

.

rtq -

= 871 kips > l 18 kips

. s o)en

{1.0 +0.50 sin LS 0

)
= i.25J(47J kips)2 +(73.0 kips)2

2(1 .392 kip/in.){l .03)(39.2 in.)

2(0.928 kip/in.)(1.0J){39.2 in.)

The available ~trcnglh due 10 web local crippling is:

=1.00(0.60)(50 k.tj)(l '.4 in.) x(391A in.) =1,470 kips> 695 kips

= 0.90(50 ksi)(PA in.)(391.4 in.)

~

\ ..

o.k.

1

l

/29,000 ksi(50 ksiX0.585 in.) 0.415 in.

::; 586 kips> 1 l8 kips

=(l/2.00)(0.80)(0.415 in.)2

xll + 3(39Y. )(0.415 in.)t.51 23.7 in. 0.585 in. in.

x

29,000 ksi(50 ksi)(0.585 iii.) . 0.415 in.

=391kips>73.0kips

The required strengths from Figures 5-55a and 5-55b are:

FA

_ 50 ksi{I IA in.)(39~ in.) -

n

Beam-to-Column Connection

1 1 -=-n n

1.67

= 1,470 kips> 73.0 kips

o.k. ....

\

o.k.

R,.

oJc.

Tension yielding on gross section, from Al.SC Specification Equation 14-1:

R,.

~R..=¢F1 A1

i1


3(39 A in.)(0.415 in.)'..sl. x I+ 23.7 in. 0.585 in.

x

n

= 0.60(50 ksi)(I ~ in.)(391A in.) 1.50

o.k.

Tension yielding on gross section, from AJSC SpecijicaJion Equation )4-1:

=2,210 kips> 118 kips

She.tr yjelding on gross section, from AJSC Spuijica1ion Equation J4-3:

n-

.

~R~ =0.75(0.80)(0.415 in.)1

V,. _ 0.60F1 A1•

¢V,. =~0.60FyAgv

ASD

LRFD ASD

Shear yielding on gross section, from AJSC Specification Equation J4-3:

,."

o.k.

(Spec. Eq. JlC-1)

= 7.98 si:
LRFD

;,

581 kips> 73.0 kips

inal strength due to web local crippling.

Check gusset plate for shear yielding and tension yielding

=-··

xp.5(1.09 in.)+39 14 in.]

o.k.

Check beam web local crippling The resultant load on the heam from the gusset plate is applied at ~0.6 in. from the column face. which 1s greater than d/2; therefore, use lhe folio\\ ing equation to detcmline the nom-

I

U!>e a 1h-m. fillet weld, 391..4 in. long.

t...., \

n

=- (1/ 1.50)(50 ksi)(OA I 5 in.)

x[2.5(1.09 in.)+ 39 1 ~ in.]

""1.25J(695 kips)2.+(118 kips) 2

·~

m.)

F>t..,(2.5/c,:a +lb)

2(0.928 k.iplin.) x

1

=7.84 si:
''

n"'

D _ J.2s,,/V} + N]

"" - 2(1.392 kip/in.) l

R,.

=~F1 t,.,(2.5kd~s + 111) = J.00(50 ksi){0.415

"'8.77°

1.2s,Jv,.2 + N; x

~R~

0 =tan -I ( 73.0 lcips) 473 kips

=9.64°

ASD

LRFD

ASD

-·- .

o.k.

URAC.:F.D FRAMES

LRFD

Check beam shear strength

ASD

From AJSC Manual Table 3-6. lhex-x a"
=73.0 kips+ 12.8 kips

V,. :::: 118 kips+l9.9 kips =138 kips

Va

.V. = 306 kips+ 46.0 kips = 352 kips

Na= 201 kips+ 32.2 kips

5.3 Sl'l!ClAL CONCENTRICAl LY BRACED .FRAMES

=85.8 kips

ASD

LRFD

c>Vn =295 kips> 138 kips

=233 kips

Check bolt strength

R,, =

2

=Jens

Ra 2

=378 kips

2

~Pn 2

+(233 kips}

2

Pn

50 ksi (20.1 in. 2 )

o.k.

1.67 =602 kips > 233 kips

There are 14 ASTht M9Q.X bolts in standard holes as shown in Figure 5-51. From AlSC Manual Table 7-1, the available shear strength per boil is:

r,, n

The limit state of block shear rupture due to the shear load on the beam web is not applicable because lbe remaining bcrun flange will prevent net section rupture However, the limit slate of block she.'lt rupture must be checked for the tension load on the beam web as follows.

=33.o kips/bolt

The angle of the resultant with respect to the vertical is:

LRFD

I

A,., =[18.0 in.-6(1~6 in.+ Y\6 in.)j(0.415 in.)

ASD

S= tan- I (352 lcipsJ 138 kips

=4.67 in.2 A1v =4.75 in.(0.415 in.)(2)

S= tan-'( 233 laps) 85.8 kips

=68.6°

2

=3.94 in.

=69.8°

Using AISC ManutJl Table 7-7 with 60°, n

o.k.

Check block shear ropture on beam web

ASD

¢r. =4 9 .5 kips/ bolt

F Ag

1 -=-n n

== ¢F1 Ag

=0.90(50 ksi)(20.l in.2 ) =905 kips> 352 kips

= 248 kips

LRFD

o.k.

ASD

LRFD

=JVa +NJ =J(85.81Jps)

kips) +(352 kipsf

=197 kips > 85.8 kips

From AJSC Specification Equation D2- I, the 3vailable tensile strength due to yielding is:

ASD

Jvu +NJ

~

Check beam tensile yielding strength

The required bolt srrength due to the resultant loading is:

LRFD

v.

o.k.

.

=7, ex= 4.25 in., ands= 3 in.:

A.... =(4.75 in.-1.5(l'!t6 in.+ 'A6 in.)j(0.415 in.)(2)

I

:::2.54 in.2

J

C== 11.4

(~ec.

LR.FD

.

0.60F.,A,,-. + U,.,,FuA..i

R,, =Cr"

¢R,. =C9r,.

n

= 11.4(49.5 !dps/bolt)


ASD

o.k.

== 403 .kips

n

== 11.4(33.0 kips/bolt} :: 376 kips> 248 kips

=0.60(65 ksi)(2.54in.2 )+1 .0(65 ksi)(4.67 in.2)

0.60FyAgv +U1>s1';,A,,,:::: 0.60(50 ksi)(3.94 in.2)+ 1 0(65 ksi)(4.67 in.2) o.k.

=422 kips

Eq. J4-5)

5-328

,,,

DRACED FRAMES

Therefore, the nominal block shear rupture strength is 403 !Ops and lhe available block shear rupture strenglh is:

.

,l

¢R~

LRFD

=0.75(403 kips) =302 kips < 352 kips

Assuming that defonmuion at the boll hole is nol a design consideration, the tearom strength is checked at the end boll with the I 75 in. edge dist.ancc. The a\·ailable tearout M.rength i~·

R,, 403 kips -=

n.g.

ASD

LRFD

ASD

n

l .5F.,U

'~ = - - -

¢in = ¢l.5F.,I, t

2.00

= 202 kips < 233 kips

n.g.

=0.75(1.5)(65 ksi)

= (l/2.00)(1.5)(65 ksi) x[l.75 in.-0.5(1 1'i6 in.)J

1

x(0.415 io.+ .4 in.)

Therefore, a web doubler plate is required. The required thickness of the doubler plate is:

=59.3 kipStboll > 33.2 kips/boll

r=( 352 kips-)(0.415 in.)-0.415 in. 302 kips

233 kips )(0.4 15 in.)-0.4 15 in. 202 kips

=0.0637 in.

=0.0687 in.

x(0.415 in.+ 'A in.) o.k.


ASD t= (

n

n

x!l75 in.-0.5( 1 ~6 in.;]

LRFD

S-329

5.3 SPECIAL C'ONC'E..'

o.k.

·-

As previously discussed, this is a conservative tr~unent of te.arout. If the check failed, the edge distance along the line of action of the bolt force would be evaluated before declaring lhe design inadequate. Beam-to-column single-plate connection

Use a 1.4·in.-thick doubler plate wilh 1A-in. fillet welds.

Determine the require-0 thickness of the 7.50 in. x 21.0 in. single plate connecting the beam web to lhe column flange. Try a ~"· in.-thick plate.

Check bolt bearing and tearout on the beam

The result:int load per bolt based on the C-value taken from A!SC Manual Table 7-7 pre-

From AISC Specification Equation 14-3. the available shear yieldfog strength of the plate is:

\'iously. is:

LRFO

:~

.,

....•: ::

LRFD

~R,.

378 !...ips =11.4 bolts = 332 kips/boll I r,,

248 kips 11.4 bolts = 21.8 !Ops/boll

x(n in.)

= 394 kips > l 38 ~ps

ASD

LRFD

=0.75(2.4)(1.00 in.)(0.415 in.+~ in.) x(65 ksi)

= 77.8 k:ips/bolt > 33.2 Jcips/bolt o.k.

lb

2.4d1F,,

n

n

R. 0.60F7 Agv -=

= ¢0.60F>A,,,

o.k.

'.

0.60(50 ksi)(21.0 in.)(~ in.) 1 50 =263 kips > 85.8 kips o.k.

=

From AISC Specification Equation J4- l, the a•-ailable tensile yielding strength of lhe plate is:

ASD

LRFD ~R,.

=0.90(50 ksi)(21.0 in.)(% in.)

=591 kips> 352 kips

Rn F-,A -=-n n 1

=c>F1 A1 o.k.

=50 ksi (21.0 in.)(~ in.) 1.67


-= - - {2.4(1.00 in ){0.415 in.+\4 in.)} x(65 k.si} = 2.00 =5 J.9 kips/boll > 21.8 .kips/boll o.k.

n

n

= 1.00(0.60)(50 ksi)(21.0 in.)

ra =

The bearing and tearout srrength limit states are separated for clarity in the foJJowing. For SCBF systems, where large defonn::uions ~ anticipated, it is 3ppropriate to assume that defonn:uion al lhe bolt hole is not a design consideration. and lhe tearou1 strength is checked al the end bolt with Lhe 1.75 in. edge distance using AlSC Specification Equation J3-6b. AISC Seismic Provisions Section D2.2(1) limits the nominal bearing strenglh IO 2.4dtFu; therefore the available bearing strength of the beam and doubler plnte is:

$r,. =$2.4dtF,,

ASD

ASD

o.k.

Single plate-to-column flange weld

Detenuine the fillet weld size required to connect the single pla1e on the beam to tl:c column flange. Using AISC Man11al Equations 8-2a and 8-2b. including the increai;eti

s 330

BRACED FRAMES

5j SPEOALCONCE.NTRICAU.Y BRAC'PD FRAMES

strength due 10 tbc load angle gh·en by AISC Specification Equa1ion 12·5. the required single plate-to-column flange weld is determined as follows:

ASD

LRFD Resultant load R,, =378 kips

Resultant load

LooJ angle

Load angle

0 =Un-

I(

= 2.4(100 in.)(~ in.)(65 ksi)

o.k.

2.00

=48.8 kipslbolt > 21.8 kips/bolt

e]

[1.0+ 0.50sin 1..s

LRFD

ASD

=Ii .O+O..S0sin ..s 69.8°J 1

[1.0 +0.50sin 1·5 68.6°J

r,. 1.5/ctF. -=--n n

¢rn =~I .SlctF..

a]

=1.45

=0.75(1.5)[1.75 in. -0.5( 11Ji6 in.)]

J.5!1.75 in.-0.5{1 1A6 in.)]}

x(% in.)(65 ksi) = 55.7 kips/boll > 33.2 kips/bolt o.k.

x(~

=

D _

378 kips 2(21.0 in.){1.392 kip/in.)(1.45)

rtq -

248 kips 2(2l.O in.)(0.928 kip/in.)(1.45)

= 4.39 silltc~nths

= 4.46 :;ixtecnths

in.)(65 ksi)

= 2.00 =37.1 kips/bolt > 21.8 kips/boll

ASD

LRFD

o.k.

The tearout strength is checked at the end bolt with the 1.75 in. edge distance using the left side of AISC Spuijica11on Equation J3-6b. The a>.ulable tcarout strength is:


"" l.45

rtq

::::: 0.75(2.4 )(1.00 in.)(~ in.}(6.S ksi)

:::;: 69.8°

Directional srrcngth increase

D

2.4dtF,, -r,. =-n n

=t2.4dtF., =73. I kips/bolt> 33.2 kips/bolt

9 =Un- I ( 233 kips} 85.8 kips

= 68.6°

"'

~rn

Ra = 248 kips

352 kips) 138 kips

11.0+ 0.50sin 1·5

ASD

LRFD

o.k.

Check block shear rupture on single plate at beam-to-column interface For the shear force The nominal block shear rupture strength due follows:

10

shear on the single pls1e is dctennincd as

Use ~ ¥i6·in. fillet weld. \

\ ~ =[4.75 in.-l.5{1'1i6 in.+'A, in.)](~ in.)

Check bolt bearing and tearout on the single plate The resultant load per bolt determined previously is:

1,.

= 33.2

kips/bo~

I

. =1.91 in.2 ASD

" =21.8 kips/ boll

The bearing and tearout strength limit states are separ.ited for clarity in the following. For SCBF systems, where large defonnations are anticipated, it is appropriate to assume that defonnation at the bolt bole is not a design consideration, and the tearout strength is checked at the end bolt using AJSC Specification Equation J3-6b. Aisc Seismic Provisions Section 02.2(1) limits the nominal bearing. strength to 2.4dtF.,; therefore the available bearing strength of the gusset plate is:

Ap ={19.5 in.)('A in.) = 12.2 in. 2

Am>= [19.5 in. -6.5(11/16 in.+ 1A6 io.)j(~ in.)

r

=7.62 in.2 ·

Rn:: 0.60F.,A,w + U0sF.,A111 ~ 9.60F1 A1 v t- Ub,F.,A,,,

(Spec. Eq. J4-5)

0.60F..A..v + Ub,FuA.. 1 =0.60(65 ksi)(7.62 in.2) + 0.5(65 ksi)( 1.91 in.2 ) =359 kips 2

0.60F1 A1v +UbsF.,A,,1 =0.60(501csi){l2.2 in.2)+0.5(65 ksi )(t.9 1 in. )

= 428 kips

r

J

5- 332

Therefore, the nominal block shear rupture strength is 359 kips and the available block shea7. rupture strength is: ] ~-

LR.FD

= 269 kips > 138 kips

.,.

ASD R,. = 359 kips n 2.00 = rno kips> 85.8 kips

¢Rn= 0.75(359 kips)

!.._ , ,

o.k.

..

I

____ ___, ~;;J

.,> ;~

I

~( 352 kips 428 kips

r

LRFD

+ ( I 38 kips 269 kips

o.k.

( .r (8 8~ r 233 kips 285 kips

5.

ps

+ 180 kips

o.k.

= 0.896< 1.0

o.k.

Use a Ys-in..thick plate.

For the tension force

Check shear rupture on the single plate

The nominal block she.ar rupture strength due to the tension force on lhe single plate is:

From AISC Specification Equation J4-4, the available snear rupture strength of

Agv =

LRFD .
ASP

. ...

-

..

~ =(112.00)(0.60)(65 ksi)

=0.75(0.60)(65 ksi) xl21.0 in. - 7(l1/\6 in.+ Y\6 in.)]

4.75 in.(S/s in.)

'·

x{Ys in.)

= 2.97 in.2

I

x[21.0 ~. -7(lVi6 in. +iii~ in.)]

x(% in.)

""240 kips > 138 kips Anv

the single

plate is:

Am = [19.5 in. -6.5(Jlli& in.+ lfi6 in.)J(* in.) =7.62 in. 2

?:

Jl

..

ASD

r

= 0.940 <1.0

Uus =1.0

l

5-333

5.3 SPEClAL CONCENTRICAUY BRACED FRAMES

o.k.

=[4.75 in. - l.5(l1116 in.+ \116 in.)J(Y3 in.)

· = 160 kips> 85.8 kips

o.k;

'

=l.9lin.2 Check tensile rupture on the single pfate

0.60FuAnv.+ UbsFu1'1n1

From AISC Specification Equation J4-2,' the available tensile rupture stre~~i:h.of the single plate is: '

=0.60(65 ksi)(l.91 in.2 )+1.0(65 ksi)(7.62 in.2 )

·

=570 kips 0.60FyAgv + U1>~FuA111 =0.60(50 ksi)( 2.97 in. 2 )+ 1.0(65 ksi)(7.62 in. 2 ) =584 kips

I

Therefore, the nominal block shear rupture strength is 570 kips and the available block shear rupture strength is:

\· $R11 = 0.75(65 k~) .. x[21.0 in. - 7(1Vi6 in.+ \116 in.)}

x(* in.) lRFD

Rn

¢R,, = 0.75(570 kips)

=428 kips> 352 kips


ASD 570 kips 2.00 = 285 kips > 233 kips

o.k.

Rm;, 65

n·

ksi

x[i~.O in. -7(1V16iq/ 1/\6 in.)l .::<(% in.){112,00)

o.k.

I

"


o.k.

..

-= .Q

..

AS°D

LRFD

-

o.k.

Check tension·shear interaction (tensile and shear rupture)

LRFD

Check tension-shear interaction (bfock shear rupture)

The interaction of tension and shear based on the block shear rupture limit stare is checked as follows:

( 352 kips 400 kips

ASD

r r

r r

'

+ ( 138 kips

( 233 kips 267 kips

240 kips

=l.11 :>I.O

n.g.

A.'AERICN'I

+(85.8 kips 160 kips

=1.05> LO

lNSTl'lVT6 OF S"rea CONSTRIJCTJON

.'n.g.

I

5-334

BRACED FRAMES.

\Vith a *·in.·thick plate: -,

LRFD

i.11(~~ ~n-r::::: 0.771<1.0 11).

ASD

o.k.

* inJ =o.729 < 1.0

1.05( ~.

. ~ m. .

. o.k.

Use a ~-in.-tbick plate. Note: Shear yielding and tensile yielding limit states should also be checked, but were assumed to not co_n trol this design. The final connection design is shown in Figure 5-51.

5.4 ECCENTRICALLY BRACED FRAMES (EBF) Tn eccentrically braced frame (EBF) systems, lateral forces are resisted by a combination of flexure, s~ear ~nd axial forces in the framing members. An EBF is essentially a hybrid system, offenng lateral stiffness approaching that of a concentrically braced frame system and ductility a~ro~ching that of a moment frame system. The design provisions for EBF s.ys~ems are gi\'en m AJSC Seismic Proviswns Section F3 and typical configurations are shown m AISC Seismic; Provisions Figure C-F3.l. Section F3.1 describes EBF systems as "braced frames for which ~ne end of each brace intersects a beam at an eccentricity from the inter~ectio~ of the centerlines of the beam and an adjacent brace or column, forming a link that ~s, subJect to shear and _flexure." The Ii~ becomes the focal point. in the design and detailing of an EBP system, as it is intended to be the primary location for the inelastic behavior in the ~me. The rem~inder of the members and connections are intended to remain essentially elastic and are requrreg to have sufficient strenglh to withstand forces corresponding to the expected strength of the link, including strain hardening. Designers can often fit eccentrically l;>raced frames in locations within the arclritectura! floor plan where concentrically braced frames cannot be located, due 10 the space limitations presented by doors a.n~ windows. Additionally, !he system is generally considered to be stiff enough to efficiently limit nonstructural, drift-related damage, as c-0mparcd to the relatively flexible ~ature of moment frames. An EBF system may be more complex for design and construcuon than other common systems. As with all systems, the choice of an EBF as the lateral system requires balancing lhe needs of lhe builcling owner and architect with the proj· ect budget Co~iderati~n should be given to "first-costs" of the project versus the life-cycle costs and pot~nt.Jal reparr costs following a major earthquake. First-cost benefits of using an EBF system wclude a reduction in the seismic base shear force due to !he hjgber R factor l~an other braced frame systems, which may result in savings in the construction of the diaphragm and foundation. · While EBF systems ~ombine many concepts of both concentrically braced frames and moment frames, the technology of eccentricaJly braced frames is relatively new. The system was first developed in Japan in lhe early 1970s. Research and development in the United States followed later that decade, continuing through the 1980s, \\ith the first codified

5.4 ECCENTRICALLY BRACED F'RAMC.S

5-335

design procedure appearing in the 1988 Uniform Building Code (UBC). As noted previously, the focal point of the design of an EBF system is the link. The link design procedures put fonh in the AISC Seismic Provisions are quite C.'\tensive and arc intended to provide reliable and ductile performance of the link under seismic loading. The first of these provisions relates to width·to-rhickness limits in SeGtion D1. 1 of the AlSC Seismic Provisions. For EBF systems, I.he link muse satisfy the width-to-thickness requirements for highly ductile members. There is an exception for the flanges of shon, ~hear dominated links with I-shaped sections. For link lengths less than J.6Mp1Vp• the flanges need only satisfy the width-totbickness requirements for moderately ductile members. Additional limitations on the web include a ma: 2.6Mp1Yp the link rotation angle is limited to 0.02 rad. For values between these limits, the link rotation angle should be interpolated. This is illustrated in Figwe 5-58. Additional link design considerotions apply when providing stiffener plates in the link ) · zone. The AISC Seismic Provisions specify that links of all lengths require stiffeners at each end. Additionally. spncing of intermediate stiffeners varies with link length. Note that when e > 5.0Mp/Vp, no intermediate web stiffeners are required.

l

L

\ .'• •

IJ

BRACED FRAMES

When· the frame is configured such that the link 1s directly adjacent to a column. there arc special requirements for the connection between the link :ind the column as required by AISC Seismic Provuions Section F3.6e. The link·t<>-colurnn connection must be capable

20

3

16

~
€

..,, 12

~

«>

E

~ 0

..

::.;:J

-~

8

lii

a;

er 4

::I ·.~

0

0.0

0.2

0.4

0.6

0.8

1.0

e/L

~l

Fig. 5-57. Frame stiffness 1·ersus link lengrh (Engelhardt and Popov, 1989).

.,

-

"· .•

i

Ya (rad)

0.081-----

~.

;.

::

....

·:

f f

e::: 1.6MPIVP

e::: 2.6M"/VP

Link length, e Fig. 5-58. Maximum allowed link rotation tJngle versus link l1!llgth.

5.4 l'CC't.'lfl"RlCAl LY BRACED FRAM.l.:.S

of sustaining lhc link rotation an&le as prescribed by the AISC Seismic Prodsions bas.:u on link length. Additionally. the connection must be 11ble to develop the full value of the ~pccttd link sh~ strength., R., Vn, at such a rotauon angle. Furthennore., the link to column connection must meet lhe re1)uiremcm.s of moment connections consistent with tbose as pre· scribed under lhe provisions for special moment frames; in other words; 3 qualified or prequalified connection must be used. The e.~cepcioo to this occurs when the connections are adeqwtely reinforced ruch lh:'lt beam yielding is forced 10 a lo.:llion away from the face of the column, and \.\hen !be length of the link is less lhan I 6Mpli'j,. In this case, the link length is defined as the length from the end of the beam remforcing co the end of lhe brace member. If the link-to-column connection meets these requirements, prcqualification or qualification of the co~tion is not required. Full-depth suffener plates are st.ill required :rt the end of the link adjsun1 to the reinforced beam section, however. AlSC Seismic Proi·isions Section F3.4b requires l:uer:.il bracing of both the top and bottom flanges at the ends of I-shaped links. These braces mus1 be designed to S3ti~fy the strength and stiffne~s requirements of AJSC St~mic Pro~·isicms Section D 1 2c for ~pedal braces :11 plastic hinge Joc:ttions. Once tbe design of the link is complete. the remaining r~u1rements address 1he design of the diagonal brncc and bezm segments away from the link, the connections of the beams to the columns, and the ~ttength of 1he columns and 1he column base attachmenl 10 the foundation. Due to the nature of EBF sy~tems, the brace members may be subject to large axial and flexural forces resulting from the rotations amicipated in the link segment Therefore. the diagonal brace is required to have a combined a.'tial and flexural strength due to seismic loading equaJ to the forces g,enenued by the adjusted link shear strength. The adjusted link shear strength is defined as the expected shear strength of !he link, RyVn. mulliplied by a factor to account for strain h.'lrdcning. This strain hardening factor is equal to l .25 for l·l.haped Jinks and 1.4 for buill-up box links. Braces must also satisfy lhe width-to-thickness requirements of AISC Seismic Prm·isions Section D l. l for moderately ductile members. The design of the beam outside of the link is similar, bu1 differs slightly from I.be design requirements for braces. It is also designed for lhe forces due 10 the adjusted shear strength of the linlc. However, the ~justed :.hear strength of the link 1s allowed to be taken equal to 0.88 times the value used in the design of the braces. This accounts for the increasc-0 member strength realized by having a concrete slab C(lmposite wilh the beam ouuide of the link and recognizes the fact that limited yielding in the be.am is not likely to be detrimental to EBF perfonnance. as lO!lg as stability of the beam is assured. If there is not n concrete slab composite with the beam outside of the link. a strain hardening factor of l.25 &hould be used (for additional inform.aricn see the Commentary to AlSC Seismic Provisions Scc1ion F3.3). Additional lateral bracing along the length of the beam, if required, is designed per AISC Specijicfllion Appendu 6. If I.be beam outside of the link is a differenc section lhan the link. then it must also sati~fy the width-to-thickness requirements of AISC Seismic Provisions Section DJ. l for moderately ductile members.. The connection of the brace 10 the beam is 1equired to me~• the same strength requirements as the brace member. The AlSC Seimiic Provisions require this conncc1ion to be collSidcred fully restr.lined (FR) if the connection is detailed such that the brace resists an} portion or the link end moment Because it was considered to be overly conser•ative in pre vious editions, the 2010 AlSC Seismic Provisions no longer require that the connection als.' be de.signed for l.IR1 P,. of the br:ice and no longer prohibit the brace connection fror:•

5-338

BRACED FRAMES

extending into I.he link zone. There is a discussion of !hese changes in I.he Commentary to Sections F3.6c and F3.5b, respectively. The beam-to-column connection: where a brace connects to both members has design and. detailing ·considerations in addition to the preceding requirements for the brace--to· beam connection. AISC Seismic Provisions Section F3.6b requires that these connections either be a simple connection meeting the requirements of AlSC Specification Section B3.6a with a required rotation of 0.025 rad, or they must be designed as a moment con, · nection. If the latter is chosen, !he required strength of the connection is equal to the lesser of the expected beam flexural strength and the sum of the expected flexural strengths of the column ab-Ove and below the joint. The columns of the EBF system must satisfy the width-to-thickness requirements of AISC Seismic Provisions Section Dl.1 for highly ductile members. Additionally, the columns must be designed to resist the forces due to the adjusted shear strengths of all links above the level of the column (as discussed previously for brace design). For columns in frames with three or more stories of bracing; the adjusted shear strength of the link is allowed to be taken equal .to 0.88 times the value used in the design of the braces, which recognizes !hat it is unlikely for all links to be fully strain-hardened at lhe same time. ·

5.4 ECCENTRJCALLY BRACED FRAMES

5-3.i

Example 5.4.1. EBF S~ory D rift Check

' Given: Refer to the EBF elevation shown in Figure 5-59. The applicable building code specifies the use of ASCEISEI 7 for drift requirements. Determine if the third level of the frame satisfie: the drift requirements. From an elastic analysis of the strocture usfog an equivalent lateral force analysis, the story drift between the second and third levels is: . o~. =

l

0.175 in.

c

B

30'-0"

l

EBF Design Example Plan and Efevation The following section consists of seven design examples for an EBF system. See Figure 5-59 for me elevation of the EBF. Example 5.4.l checks st0ry drift. Examples 5.4.2 through 5.45 illustrate. a link design, a beam outside of the link design, a brace design, and a column design,: respectively. ~xa.mples 5.4.6-and 5.4.7 show. the design of a brace-to-link connection and a brace-to-beam/column connection. From ASCFJSEI 7, the following parameters apply: Seismic Design Category D, R 8, .Q.a 2, Cd= 4; le= 1.0, Sos= LO, and p =l.3, '...The total floor area js 9,000 ft2, the perimeter is 390 ft, and the code-specified gravity loading is as follows: .

=

=

. PJWor =:= 85 psf

=68 psf Lftoo,, =80 psf (50 psf reduced) .

, DtrJOf

.

fu N

Fourth Level

t

fu

N'

Third Level· '.

S =20psf Curtain wall= 175 lb/ft along building perimeter at every level The loads given in each design example are from a first-order analysis. Assume the effective length method of AISC Specification Appe.ndix 7 is used for tbe st.ability design. _ When designing EBP systems, several design iterations are usually required to obtain the best combination ofcompau'ble frame-member sizes. Optimized designs are often difficult to obtain, due to member local buckling requirements, geometric constraints, th~ resisrapce of tbe beam o.utside of the link to flexure combined with axial effects, and architectural constraints that commonly occur throughout the design process. Nonetheless, EBF systems. can be used to provide ductile and cost-effective solutions for seismic load resistance.

.l

Roof

.

•
Second eve!

.

•

0 ~

......

Base

Fig. 5-59. EBF elevation.

5-340

~

..'

.. '··

BRACED FRAM.ES

Solution: According to AISC Seismic Provisions S~tion B 1, the design story drift and the story drift liuUts are ihose ~tipulated by the applicable building code. From ASCEJSEI 7 Table 12.12-1. the allowable story drift, ~. is 0.025h.u. where hJX is the story height below level x.

6a =0.025hsx

Fy = 36 ksi F. = 58 ksi ASTMA992

=0.025(12.5 ft)(l2 in./ft)

=3.75 in.

Ry= I.I

;'.

..,,

:~

(ASCEJSEI 7 Eq. 12.8-15)

From AlSC Manual Table 1-1, the geometric properties are as follows: W16x77 A =2Z.6 in. 2

d= 16.5 in.

1,.. =

'I= 0.760 in.

kae1= 1% io.

k1 = l

Zx=

4

Ix= 1.110 in.

hit.,.= 31.2

Therefore, the design story drift at le\'el 3 is:

ii ...~

ASThfA36

F, = 50 ksi Fk =65 ksi

ASCE/SEJ 7 defines the design story drift as b., the difference of the deflections at level 2 and level 3 at the centers of mass. The deflection at level x, Ox, is:

s ·.341

5.4 ECCENTRICALLY BRACED FRAl\iES

0.455 in. 1lt6

in.

150 in.l

b1= 10.3 in. b112t1= 6.77

h0

=15.7 in.

Required Strength

ox= 63 Cdo.r3

Considering the load combinations given in ASCE/SEI 7 that include seismic effects, it was detenn.ined that the governing load combination for the link is:

= - - -Cdox2 -!,

le

=Cd (ox3 - o..2)

ASD

LRFD

le

;~ ~~

=4(0.175 in.)

•'

·;~

1.0 = 0.700 in.< 3.75 in.

LRFD Load Combination 5 from ASCEJSEI 7 Section 12.4.2.3 (including the O.S factor on l permitted in Section

o.k.


12.4.2.3) (1.2 + 0.2Sos)D + pQE + 0.5L + 0.2S

Example 5.4.2 EBF Link Design

(1.0 + 0.l4SDs)D + H + F + 0.7pQ£

\

\

Given:

..

..·:.

{ ,'

,"

Refer to Beam BM-1 in Figure 5-59. Determine the adequacy of anASTM A992 W 16xn as the link segment for the following loading. The stiffener material is ASTM A36 plate. The applicable building cooe specifies the use of ASCEJSEI 7 for calculation of loads. From a first-order analysis: Po

=7.40 kips

PL= 5.30 kips

PQE::::

5.50 kips

=1.30 kips

VQi; =

84.0 kips

Vo= 1.80 kips

VL

Mo= 14.4 kip-ft •

ML= 9.60 kip-ft

MQE= 168 Jcip-ft

Assume the brace-to-beam connection will be that shown in AJSC Seismic Provisions Figure C-F3.7. The brace will ~ detailed as fixed to the link in order to decrease the flexural demand on the beam .outside of the link. Assume the brace will be an ASTM A992 W10x112. Solutio n: From AJSC Manual Tables 2·4 and 2-5, and AJSC Seismic Provisions Table A3. l, the material properties a.re as follows:

Determine the required shear strength of the link

The required shear s1rength of tJ1e link is: ASD

LRFD Vu = (1.2+0.2SDs )Vo +pVae

+ 0.5VL +0.2Vs =IL2+0.2(t.0)](1.so kips)

+ 1.3(84.0 k:ips)+0.5(1.30 kips) + 0.2(0 kips) = 112 kips

Va =(l.O+O.l4Sos)Vo + VH +VF

+ 0.7pV!ll = [l.O + 0.14(1.0))(1.80 kips) + 0 kips+O kips + 0.7(1.3)(84.0 kips)

.

= 78.5 kips t

.·

DRACED FRAi'vlES

5-342

5.4 ECCENTRICALLY BRACED FRAM!i.S

BL

Determine the required axial and flexural strengths of the link Consider second-order effects

=LO 199 kips(J50 in.) 0.175 in. = 171,000 kips

Second-order effects are addressed using AlSC Specification Appendix 8 as follow!l:

(Spec. Eq. A-8-1) (Spec. Eq. A-8-2)

C,,,

1--'

P,,

=1.00 I

Bz=

1

o.P.

1 -~

(Spec. Eq. A-8-6)

:
'

ex = 1.60

Bi= _ 1.00(3,680 kips) 1

I

ASD

LRFD (X

Since the calculation of B1 requires P,, 8 2 will be calculated first, although r\JSC Specijicatio11 Appendix 8, Section 8.1 permits the use of a first-order estimate of P,.

r

Using AISC Specification Equation A-8·6:

(Spec. Eq. A-8-3)

81 =--o:Jf~l

(Spec. Eq. A-8-7)

PeJJDry =RM C.u

171,000 kips

l

82 =

l.60(2.600 kips) 1 171,000 kips = i.02

= i.02 I L-~~~~~~~~~~~~...L-~~~~~~~~~~~~-' P-6 effects, approximated through the 82 factor, apply only to axial forces and moments du{

P, S101)'

to lateral translation. Thus, the required axial strength of the link including second-order . ., '· · effects is:

l

Ga/cu/ate Pstory

From the given loading, the total vertical load at the third level is: ASD

LRFD

P.,

x[68 psf + 2{85 psf)J l'trory = 9, 000 ft

+O psf + 0.5(2)(50 psf)

+0.2(20 psf)

f

x(l kip/1,000 lb)

I

.2+ 0.2(1.0)J + [175 lb/ft(2)(390 ft)]

=(l.2 + 0.2Sos ~ Po+ B2PPQE + 0.5Pz. +0.2Ps

[1.2+ 0.2(1.0)J 2

= {1.2+ 0.2(1.0)}(7.40 kips)

r0+0.14(LO)J PJtDry

=9,000 ft

2

+1.02(1.3)(5.50 kips)

x[68 psf+2{85 psf)}

+ 0 psf + O psf + 0 psf

1

x(l kip/1.000 lb)

{!t.0+0.14(1.0)J } + ll75 lb/ft(2)(390 ft)J x(l kip/l.000 lb)

+ 0.5(5-30 kips)+ 0.2(0 kips) = 20.3 kips

=!LO+ 0.14(1.0))(7.40 kips) + 0 kips+ 0 kips

+ 0.7(1.02)(1.3)(5.50 kips) =13.5 kips

Calculate B 1

Conservatively assume Cm= 1.0 and the effective length method is used for stability desigr f: From Figure 5-59, the link length is 48.0 in. I

=3,680 kips

(Spec. Eq. A-8-'.:

The rota! story shear. H, is shown in Figure 5-59 as V3 = 199 kips. From Example 5.4.l, an elastic analysis determined that first-order interstory drift i~ t:.11 0.175 io.

the

RM

Pa =(l.0+0.14SDs)Po +Pn +PF + 0.7fhpPQs

=2,600 kips

x(l kip/1,000 lb)

.l

ASD

LRFD

=12.5 ft(J2.0 inlft)

=

rt2EJ" P.1--t - (K1L)2

(Spec. Eq. A-8-5'

t

rc 2 {29.000 ksi)(l,110 in. 4 )

=150 in.

=

"" 1 for bra~ frame systems

=138,000 kips

[ 1.0(48.0 in.) j2

J I.

BRACED FRAMES

5.4 ECCENTRJCAJ...LY BRACED FRAMES

11., ,

LRFD Ct

=l.00

81=

1-

ex

1.0 ~l 1.00(20.3 k.ips)

!•o1 ••

138,000 k.ips

LRFD

ASD

=1.60

= l.00, the required flexural strength need no1 be amplified to occount for P·o

LRFD

"

~

ll

=1,130 kips

= 1.00

M., =(l .1+0.2SDs) Mo + BzPM
Pr

20.3 kips 1,130 kips

Pc

-= Pc:

=0.0180

13.5 kips 753 kips

=0.0179

\\}th P,IPc: ~ 0.15. the A1SC Sti
ASD

Vp

i•

..:~·

1.5

1.5 = 753 k.ips

The required flc.'wral strength of the link including second-order effects is:

- - --b ...

c -

= 1,130 kips

Pr Since 81 effects.

P. _ !J_

Pc= P1

1.0 ~I 81= 1.60( 13.5 kips) 1138.000 kips

=1.00

ASD

=0.6FyA1w

(Provisions Eq. F3-2)

Ma =(l.0+0.14Sos)Mo +MH +MF

+ .0.5Mr +0.2Ms

=[1.2+ 0.2(1.0)](14.4 kip-ft)

Where A1w for I-shaped link sections is defined as:

+ O.?B1PMQe =[l.0+0.14(1.0)}(14.4 kip-ft)

+ 1.02(1.3)(168 kip-ft)

+ 0 kips+ 0 kips

+ 0.5(9.60 k.ip-ft)+0.2(0 kip-ft)

+ 0.7(1.02)(1.3)(168 kip

= 248 k.ip-ft


Arw=(d-2t1)t..,

=(16.5 in.- 2(0.760 in.)](OA55 in.)

ft)

=6.82 in.2

= 172 kip-ft

The link shear strength is:

\

Second-order effects arc not required to be applied to the required .Jiear strength. VP= 0.6(50 ksi)(6.82 in.

-

According to AISC Seismic Provisions Section F35b(l). the stiffened and unstiffcoed elements of linls shall comply \\ilh AISC Seismic Proli.sions Section Dl.l for highly ductile members. There is an exception given in AISC Seismic Provisions Section F3.5b(l) that allows flanges of I-shaped links with lenglb e ~ l.6Mp1Vp to satisfy the requirements of modemtely ductile membcn. Determine whether the link length satisfies this limit.

Py= FyA 1

=50 ksi(22.6 in.2)

=1,130 Jcips

)

=205 kips


'i ·

2

Mp


=F1 Z =50 lcsi(150 in.3 )

=7,500 l.Jp-in.

(Provisions Eq. P3-6)

1.6Me _ 1.6(7,500 kip-in.)

Vp

-

205 kips

= 58.5 in.

From AISC Seismic Provisions Section F3.5b(2):

Because e =48.0 in. < 58.5 in., link flanges are permincd to comply with the require~enlS for moderately ducule members. From Table l-3 of this Manual, a W16x77 satisfies the requirements for modcrutcly ducule link beam nangcs. Table 1-3 of this Manual also shows that a W16xn satisfies the requirements for o highly ductile link beam web.

..

l

Available Shear Strength AJSC Seismic Provisions Section F3.5b(2) defines the shear strength of the link as the Jesse(: of that detennined based on the limit states of flexural yielding and shear yielding. ·: .

I

For the limit srate of shear yielding AISC Seismic Provisions Equation F3-l defines the shear strength as follows, where VP was previously calculated:

'•

-;· r

~

A value of the ratio, Vpe/Mp. less than 1.6 indicates that the link behavior will be dominated by shear yielding. The corresponding limit on the link rotation angle for this type of expected link behavior is 0.08 rlld according to AlSC Seismic Provisions Section F3.4a. AJSC Seismic Provisions Figure C-F3.4 defines the link rotation angle for this configura-

1

tion as:

Vn =Vp

=205 kips

where

For the limit state of flexural yielding AlSC Seismic Provisions Equation F3-7 defines the shear strength as follows, where Mp was previously calculated:

Vn

=2Mp

AISC Seismic Prol-isions Section F3.3 requires that the inelastic link rotation angle be determined from the inelastic ponion of the design story drift. From Example 5.4.1, the inebstic

e

_ 2(7,500 kip-in.)

-

portion of the s tory drift is:

48.0in.

=313 kips

6.p=8.t-8.u

Because 205 kips< 313 kips, the limit state of shear yielding from Al SC Seismic Provisions Equation F3-2 controls:

LRFD

=185 kips> \1 =112 kips 11

o.k.

eP =12.s ft(12 in.lft)

~= n,. 205 kips/1.67 = 123 kips> Va = 78.5 kips

=0.525 in. 0.525 in.

ASD

9vVn = 0.90(205 kips)

= 0.700 in. -0. 175 in.

=0.00350 rad o.k.

'Yp = 30.0 ft(l~ in./ft)(0.00350 rad) 48.0 m. =0.0263 rad

Unk Rotation Angle AISC Seismic Provisions Section F3.4a specifies a max.imum link rot:nion angle based on the expected behavior of the link. The expected link behavior is detemtined by solving for the coefficient in front of Mp/Vp based on the given link length.

'Y P < 0.08 rad

o.k.

\

Note that the plastic story drift could. have been conservatively assumed to equal the design story drift (0.700 in.). Using lhe design story drift determined in Example 5.4.1, 'Yp

=0.0350 rad. Available Compressive Strength

Solving for the coefficient X:

Use K= 1.0 for both the x-:c and y-y axis. UseAlSC Manual Table 6-1, where interpolating

appr~ximblale becaubs~ ~~ail

co~presfisivaeWstr1e6ng7th7d~tbsnKLotvary4 flit·~·

between values is the able early with KL. Tue availa e strengt m axiru compression or For the link being inves6gated: ~- 205 kips(48.0 in.)

Mp -

7,500 kip-in.

=1.31<1.6

x

w1

= .

l.

S-348

LRFD

. I

...... ;

Lateral Bracing Requirements AlSC Seismic Provisions Section F3.4b requires thafboth flanges at each end of the link be braced. Bracing is required to have strength and,.stiffness as specified by AISC Seismic Provisions Section D l .2c for e:xpe.cted plastic hinge locations. This design uses lateral bracing of the flanges. From AlSC Seismic Provisions Equations Dl -4a and Dl-4b, the required lateral brace strength, with Ry= l.J from·AISC Seismic Provisions Table A3. l , is:

ASD

I

I

Oc Pn

p = $~Pn

p=:-

= 1.03x10- 3

::::: J.54xl0" 3

$cP11 = 97 1 kips > 20.3 kips

o.k.

P. Qnc

=649 kips> 13.5 kips P., =

From.AISC Manual Table 3-2, Lp = 8.72 ft. Since Lb~ Lp, the limil state of lateral-torsional bu~kling d9es not apply according to AISC Specification Section F2.2. Therefore, the available flexural stre_n&th is, from AlSC. Manual Table 3-2:

0.06R7 FyZ

-.;

LRFD

ho

0.06(1.1)(50 ksi)(150 in. =

~l>&Mp

=563 kip-ft> 248 kip-ft

11 i·

!'..-

t:.,

)

o.k.

n: =

M

374 kip-ft> I 72 kip-ft

15.7 in.

=21.0 kips

o.k.

The required brace sciffoess according to AISC Seismic Provisions Section D1.2c(3) is calculated in accordance with AISC Specification Appendix 6 with Cd= 1.0 and with the value of Mr specified in AISC Seismic Provisions Equation Dl-6 as:

LRFD

P,

=20.3 .kips 971 kips

ASD

=

Pr = 13.5 kip~ Pc 649 kips :: 0.0208

=0.0209

Mr =.RyFyZ/L5

2~c +(Z: + ~:Jsi.o LRFD 0.0209 248 kip-ft -2-+ 563kip:ft +0=0.45 I o.451 < ~.o

o.k. ·

-

1.1(50 ksi)(150 in.

= 1.1(50ksi)(150 in.3

)

)/1.5 ·

=5,500 kip-in.

This required flexural strength can be used in AJSC Specification Appendix 6 to detennine the requited stiffuess of 1be lateral bracing. Use nodal bracjng aod Equation A-6-8 to calculate 1he required stiffness, where Lb is th~ length of the link, 48 in., as: ASD

LRFD

(Spec. Eq. Hl-lb)

f)

"•I "

3

= 8,250 kip-in.

Because Pr/Pc < _o::· the beam-col~'.~n desi~ is controlled by the equation:

l

ASD

Mr =RyFyZ LRFD Pc

= (0.06/1.5)(1.1)(50ksi)(150 in.3)

15.7 in.

Combined Loading

-1f1"1. I

3

ASD

1~-..J

. ~

Pa= (0.06/1.5)RyF7 Z

ho

= 31.5 kips

____.....,. ·11~

L'l. •••

ASD

LRFD

Available Flexural Strength

..

5- 3<19

.5.4 ECCENTRJCALLY BRACED FRAMES

-

br

'

0.470<1.0

c\l

ASD

=

0.0208 172 kip-ft --+ +0=0.470 2 374 kip-ft

~ =n(lOM,CJ)

=.!.( lOMrCd)

_l_( 0.75

10(8,250 kip-in.)(1.0)) (48 in.)(15.7 in.)

= 1:t6 kip/in.

Lb ho

br

Lblto

=2

-

.oo( 10(5,500 kip-i.n.)(l .0)) (48 in_.)Q.5.7 in.)

=146 kip/in.

o.k. .

l'be W16x77 is adequate to resist the loads given for the link segment of Beam BM-1.

AMERICAN lNSTTJVrE OF S-raa.. CONSTRUCnoN

Top and bottom flange bracing will be provided in accordance with AISC Specification Appendix 6 with the strength and stiffness required by these calculiitions.

AMERICAN lNsnruT!l Of STl!EL CoNSTRVC'TION

5-350

BRACED F'RAMES({~~

5.4 ECCENTRICAU...Y BRACED FRAMES

~~~

~

Stiffener Requirements

'.;;

.;}'.t?:--':

AJSC Seismic Pro~isions Section F3.5b(4) requires double-sided, full-depth web stiffener~ ·" at each end of.the lmk._The minimum required combined width of the stiffeners is (bi-2t~Y.; .:.. Thus, the rrummum w1dtb of each stiffener is: · -: '

;1 = 10.3 in.-2(0.455 in.) 2 = 4.70 in.

. :;

The ininimum required thickness is the larger of 0.75tw and~ in.: lmi>1

l,,,;n

=lw

=0.455 in.~ '.Ml in.

Therefore, 1,.,;,, = 0.455 in. The required width of intennediate stiffeners on one side only is:

b1 2

w,,,;11 =--tw

10·3 in. 0 45·5 . =---. Ill. 2 =4.70 in. Full depth 1h in. x 4 3A in. intennediate web stiffeners will be provided within the link segment., on one side of the web only and at a maximum spacing of 19.4 in. With the link length of 48 in. given in Figure 5-59, choose to use two intermediate link stiffenerS with a spacing

= 0.75tw ""0.75(0.455 in.)

=0.341 in. < % in.

of 16.0 in. on center.

Therefore, tmm. =3/s in. Full depth :win. x 4% in. stiffeners will be provided on both sides of the web at each end of I.be link segment. . .. AISC Seismic Provisions Section F3.5b(4) also requires full depth intennediate web stiff· ener~ (i1~tennediate stiffeners ~i·e stiffeners within the link segment). Because che length of the link is less than l .6Mp1Vp. the spacing requirements for intermediate web stiffeners .are .determined based on the link rotation angle. .· ·

Note tbat it may be beneficial to also· use 1h-in.-thick material for the link end stiffeners in order to simplify the detailing and fabrication of the link. This simplification wiU be made

in this example.

. .

AJSC Seismic Provisions Section F3.5b(4) also specifies that.the required strength of the fillet welds connecting the link stiffeners to the iink web FyAs1 (LRFD) or FyAs111.5 (ASD) and of the welds connecting the little stiffeners to the link flanges is F;yA~114 (LRFD) or FyAsr14(1.5) (ASD), where As1 is the horizontal cross-sectional area of the stiffener. For the 'h· in.-thlck stiffener, the cross-sectional area of tlie stiffener is:

is

For a link rotation angle equal to 0.08 rad, the required spacing is:

Ast = 1h in.(4% in.) 6

30tw -~ = 30(0.4S5in.)-(1 ·~ in.)

=2.38 in.2 I

= 10.4 in. For a link rotation angle equal to 0.02 rad or less, the required spacing is:

52tw -

~= 52(0.455 ln.)-( 16 ·~ in.) =70.4 ~-

Interpol~ting betw~eri these limits using the calculated link rotation angle ofrp =0.0263 rad,

The Commentary to AISC Seismic Provisions Section F3.5b(4) suggests that welding in the k-area of the beam be avoi~ed, To acco~plish this, the stiffener clips will be ~zed to comply with the requirements of AWS Dl.8 clause 4.1 .l Based on AWS Dl.8 clause 4.1.l, the clip along the web must extend at least l 1h in. beyond the published k.a,,1 dimension for the rolled shape. This corresponds to a clip length measured from the edge of the stiffener of at least:

Ph in.+ kae1 -ti:= l'h in.+ 1% in.-0.760 in.

=2.37 in.

.the maximum spacmg betwee.n web stiffeners is 19.4 in.

~ron:1 AIS
:.:

Use a clip length of 2% in. along the web. The length of the stiffener along the web is thus: L,1 =d-2r1-2(2%in.)

=16.5 in. -2(0.760 in.)- 2(2% in.) ;::: 10.2 in.

,,..-.

AMERICAN lNsmvra OF STIOEL Col-ISTRUCTIO.N

r

r·

r

S-353

5.4 ECCENTRICAl l.Y BRACED FRA>,.U;s

5-352 \

From AISC Manual Equations 8-2a and 8-2b, the double-sided !iJlet weld required to con- ~ nect the link stiffeners to the link web is:

.I

LRFD D=

ASD

D ::::

F1 A...1 2(1.392 kip!in.)(L..,) 2

=

36ksi(2.38in.

_ 136 ksi(2.38 in.2)]/1.5

)

= 3.02 sixteenths

:l

Checking AISC Specificario11 Table J2.4, wi1h the 0.455 in. link web thickness, the minimum fillet weld size is 3/i6 in.

Use double-sided 1A-in. fillet welds 10 connect the link stiffeners to the link web. Based on AWS Dl.8 clause 4 .1.2, the clip along the flanges must not exceed a distance of 1h in. beyond the published k detail dimension for the rolled shape. The maximum clip 1 length measured from the edge of the plaie is therefore:

ll

2

Use a 1.00-in. c)jp along the flange to allow the stiffeners to clear the fillets. The width of the stiffener along the flange is:

- 1~

. (bf- ----1. lw OO m., • 4~ • .m.-1.00 in.) =IIU1l 2

.

=min(3.92 in., Jl4 in.)

PD:::::

1.00 kips

Vo= 6.80 kips Mo= 17.0 kip-ft

PQs= 105 kips VQE = 8.70 kips MQE= 113kip-ft

Pt= 0.700 kips VL =4.80 kips Ah= 11.3 kip-ft

Relevant seismic parameters are given in !he EBF Design Example Plan and Elevation

Solution: From AlSC Manual Table 2-4 and AlSC Seismic Provisions Table A3.l, the material properties are as follows:

Ry= 1.1

=33A in.

From AISC Manual Table 1-1, !he geometric properties are as follows:

From AISC Manual Equations 8-2a and 8-2b, the double-sided fillet weld size required co connect the link stiffeners to the link flanges is: '

ASD

LRFD

D=

loads. From a firsc-ordcr analysis:

ASTMA992 F1 =50 ksi Fu ::65 ksi

J

. . _ . (10.3 io.-0.455 in. 1. m., JL • - rmn 4 ,,. m.-1. 00 m. 00

...~

Given: Refer to Beam BM-1 in Figure 5-59. Determine the adequacy of the ASTM A992 W16x77 link segment selected in Example 5.4.2 as the beam outside of the link for the following loading. The applicable building code specifies the use of ASCE/SEI 7 for calculation of

Assume the braces are ASTM A992 W1 Ox112, the colunIDS are W12 wide-flange sections and that the flanges of Beam BM- I are braced at the columns.

= 1.34 in.

2

Example 5.4.3. EBF Beam Outside of the Link Design

section.

fw )IL • JllL • 0:455 in: . k·1--+n.m.= ;r1610.+1hm.

w.ir

Note th:ll it may be beneficial to also use double-sided 1.4-in. fillet welds to conned the link stiffeners 10 the link flanges in order co simplify the detailing and fabrication of the link.

- 2(0.928 kip/in.)(10.2 in.)

:::: 3.02 sixteenths

2

Use double-sided ~6-in. fillet welds to connect the link stiffeners to the link flanges.

2(0.928 kip/in.)(L11)

2(1.392 k.ip/in.)(10.2 in.)

;. I

(FyA.11 )/1.5

Checking AISC Specijication Table J2.4, with the 1h-io. stiffener plate thickness, the minimum fillet weld size is ¥16 in.

F1 A,,14

D=

2(1.392 kip/in.).(111.11)

= 136.ksi(2.38in.2 )]/4 2(1.392 kipfm.)(3=!4 in.) = 2.05 sixteenths

(F1 Asr)Al.5(4)j 2(0.928 kip/in.)(w.11)

Beam W16x77 A= 22.6 in. 2

r1

=2.47 in.

Brace W10x112 ix= 716 in.4

_ j36 ksi(2.38 in.Z)j/{1.5(4)) -

2(0.928 kip/in.)(33,4 in.)

=2.05 sixteenths AMERICN'I

lNSTI'IV11l Of STI!EI.. CONSTRUCl'ION

...

S-354

BRACED~.·

Required Strength

d

ACC-Ording 10 AISC Seismic Provisions Section F3.3, the required strength of the be:lm out• side o'. the li~k is n combination of the factored gravicy forces plus the forces generated b_y the adjusted hnk shear strength. From Example 5.4.2, the nominal shear strength of 1be lirilc'.! Vn, was determined to be 205 kips. According to AlSC Seismic Provisions Section P3.3, the adjusted link shear strength for an I-shaped section (using Exception (l)(n) from Section F3.3) is:

S.4 ECCENTIUCALLY BRACED FRAMES

S-3.S5

As given in Example 5.4.2, the brace-to-beam connection will be detailed as a fixed connection; therefore, the moment at lhc end of Lhe link will be distributed between the brace and the beam outside of the link. One way to detennine the poJ1ion of this moment resisted by the beam outside of the link is based on relative member stiffness. Since the modulus of elasticity is the same for both members, it can be neglected in !he stiffness cakul:itioo. Using relative member stiffness to distribute the link end moment, the portion of the moment taken by the beam outside of the link (bol) is:

0.88(1.25)RyVn =0.88.(1.25)(1.1)(205 Jcjps)

=248 kips The geometry of the column, brace, half-beam and half-link is shown in Figure 5-60: The a.~ial force in the beam outside of the link based on the adjusted shear strenglh of the

link is:

·

30.0 ft - 4.00 ft

L1>o1 - - -

p F..,.

_ 0.88(1.25)RyVnL 2H

----

2

=13.0 ft

_ 248 kips(30.0 ft) 2(12.5 ft)

=Jc12.s ft)2 +(13.o ft) 2 =18.0 ft

Lb,

=298 kips The resulting link end moment based on the adjusted shear strength of the link is:

I11o1

1,110 in:*

L1>o1

13.0 ft

--=

r

=85.4 in:* I ft

Miw = 0.88(1.25)RyVne 2

= 248 kips(48.0 in.)

716 in.4 =---

2 =5,950 kip-in.

=39.8 in.4 /ft

18.n ft

lbol

4

85.4 in. /ft ---------t- ~ - 85.4 in. /ft+ 39.8 in. /ft

r- 1 '-/)()

0.88(1.l5)RyVn

/ bol

Lbo1

4

4

Lbr

=0.682

f

Using this method, the beam outside of the link is assumed to take 68.2% of the link end moment. The moment in the beam outside of the link i_s then:

«>

-·

N ..-

M£..i.

II

::i::: ~of frame

U2=15'-0"

Fig. 5-60. Diagram/or E:cample 5.4.J.

= Mbol =0.682MunJi

= 0.682(5,950 kip-in.)/(12 in.I ft) =338 lc:ip-ft Alternatively, a method based on the calculation of an amplification factor can be used. In this method, the adjusted Link shear strength is divided by the link shear generated by the code-specified eanhquake forcts. The resulting amplification factor is used to amplify tbl!

r

..f

5-356

5-357

S.4 ECCENTRICALLY BRACED FRAMES

:.

rcrnainjng member end forces generated by the analysis using the code-specified earthquake loading. From Example 5.4.2. the link shear force obtained from a computer analysis using the code-specified seismic forces was given as: VQe =

''·

84.0 kips

'The resulting overstrength factor is:

_0.88(1.25)R _..;.._..;_,__= 1 V~ 248 kips V
t"

i

...

LR.FD Load Combination 5 from ASCEJSEI 7 Section 12.4.3.2 (including the 0.5 factor on L pennitted in Section

=2.95MQe =2.95(113 kip-ft) =333 kip-ft

(1.0 + 0.14Svs)D + H + F+ 0.1E,,.,.

(l.2 + 0.2SDs)D + EmJi + 0.5l + 0.2S

Tue required axial scrength of the beam outside the link is:

ASD .

LRFD

Pd= (LO+ 0.14SDs )PD+ PH+ Pp

Pu= {l.2 + 0.2Svs )Po+ PE.,. + 0.5Pi. + 0.2Ps =[1.2 + 0.2(1.0)J(t.OO kips)

+ 0.7Pe.,.. = [1.0 + 0.14(1.0)](1.00 kips)

+ 0 kips+O kips

+310 kips+0.5(0.700 kips)

§I ~JI

The axial force in the beam outside of tJ1e link due to the link mechanism based on 1he expected sbear strength of the link is:

=2.95PQ.e .=2.95(105 kips) =310 kips

ASD Load Combinatjon 5 from ASCEJSEI 7 Section 12.4.3.2

12.4.3.2)

The moment in the beam outside of the link due to the link mechanism based on the expected she:ir strength of the link is:

ME...i.

ASD

LRFD

+ 0.7(310 kips)

+ 0.2(0 kips)

=312 kips

= 218 kips

PE.-

11 ..

The shear in the beam outside of the link due to the link mechanism based on 1he expected shear strength of the link is: VE.,.

l~ : ,

I

=2.95V<2E = 2.95(8.70 kips) = 25.7 kips

Note that the moments generated by lbe two methods are very similar. Since the beam outside of the link shear has already been determined, the forces generated using the amplification factor method will be used in the calculation of the required strengths. Considering the load combinations given in ASCE/SEJ 7 that include the amplified sefamic loads, it was determined that the goveming load combination for the beam outside lhe link, with 0.0 Q~ Em11, is:

=

The required flexural streng1h of the beam outside the link is:

M,,

=(l.2+0.2SDS).\.fo +ME"""

Md =(l.0+0.14Sos)MD +MH +MF

+0.7ME"" = [1.0+0.14(1.0))(17.0 kip-ft)

+ 0.5Mt +0.2Ms =IL2+0.2(l.O)j(l7.0 kip-ft) + 333 kip-ft+ 0.5(11.3 kip-ft)

I \

+ 0.2(0 kip-ft)

+ 0 kip-ft+O kip--ft + 0.7(333 kip-ft) = 252 kip-fl

=362 kip--ft

The required shear strenglh of the beam outside the link is:

ASD

LRFD Vu= (1.2+ 0.2Svs )Vv +Ve....,+ 0.5V£.

+0.2Vs = [l.2+ 0.2(1.0)j{6.80 kips)

" ""... }!

ASD

LRFD

V0 =(1.0 +0.14SDs)Vv+VH ·t- Vp

+ O.?Ve,.. =[LO +0.14(1.0)](6.80 kips)

+ 25.7 ldps+0.5{4.80 kips)

+ 0 kips+O kips

+ 0.2(0 kips)

+ 0.7(25.7 kips)

=37.6 kips

= 25.7 kips

i

'

l

....

5-358

S.4 ECCENTRICALLY BRACED FRA.Jl.1ES

Width-to-Thickness Limitations

wbere

Since the beam outside of lbe Jjnk is the same section as the link, no addition:il local buck~ , Jjog checks are required.

i

,

Unbraced Length

.! . I

n.2 E(

P,1

(Spec. .Eq. A-8-5)

= ( K1l)2 n 2 (29,000ksi)(l.l 10 in. 4 )

As established in Ex:imple 5.4.2, each end of 1he link will be br:iced. A nominal column depth of 12 in. will be assumed. Therefore, the unbraced length of the beam outside of 1he

=

link to the face of the column is:

=14,100 kips

Lb=

!--~- 2 (dc) 2

!J .0(150 in.)J2

From AISC Specificatio11 Equation A-8-3:

2 ::: 30.0 ft(12 inlft)-48.0 in. -12.0 in.

=150 in.

ASD

LRFD

a = 1.60

ex =LOO

2

l.0

81=

or

l-11.00(312 kips) 14,100 kips Lb= 150 in. /(J2 in./ ft)

l

LO

81=

l,.;

1_ [1.60(218 kips)] 14,lOO kips

=1.02

=12.5 ft

l'..

= l.03

According to AISC Specification Equation A--8-1, the B1 factor (P-o effect) need only be applied to the first-order moment with the structure restrained against translation.


From AJSC Specification Appendix 8, the required flexural and axi:ll s1.renglh including second-order etfectS are detemlined as follows: (Spec. Eq. A-8-1) (Spec. Eq. A-8-2)

The multiplier that accounts for P-6 effects, B2, is LO because lhe.iateral load effect is based on the adjusted link shear str~ngth. P-D. effects do not increase lhe forces corresponding to the fully-yielded, strain-hardened link; ipstead they may be thought of as contributing to the system reaching that state.

=

S-359

Because B2 1.0, the required C<>mpression and flexural strengths will not be amplified to account for P-D. effects. Conservatively use C,,. 1.0 and the effective length method is used for stability design.

=

Calculate 8 1

(Spec. F.q. A-8-3)

l

ASD

LRFD M0

Mu= B1 (1.2+0.2Sos)Mo +ME.J,

+0.1Me,.,,,

+Bi (0.5Ml)+ B1 (0.2Ms)

=1.0211.2+0.2(1.0)](17.0 kip-ft) + 1.02(0.5)(11.3 kip-ft) + 1.02(0.2)(0 kip-ft)

"'

I~

=i.?3[1.0 + 0.14(1.0)](17 .0 kip-ft) I

I

+333 kip-ft

=B1(1.0+0.14SDS)Mo +MH +MF + 0 .kip-ft+ 0 kip-ft + 0.7(333 kip-ft) =253 kip-ft

= 363 kip-ft

,

Combined Loading 1 Because the beam outside of the link is the same member as the link, AISC Seismic Pravisio11s Section A3.2 pennits the use of R1 F1 in lieu of Fy when determining lhe :ivailable strengths of the beam outside of the link.

l .;

I

determine available compressive strength of the W16x77 '• Use AJSC Specification Section E3 to determine the available compressive strength. Note lhat using AJSC Manual tables to determine the available compressive strenglh and multiplying this strength by R1 may not give accurate values, as the compressive strength does 1w

AME!UC/\H lNS'l'J1VTll OF Stta. CONSTRUcnON

5-361

5.4 ECCENTRICALLY BRACED FRAMES

vary linearly with F1 . The applicable critical stress equation can be detennined by I.he ratio of RyF1 1Fe. The elastic buckljng stress, Fe. is:

Mn

¢b."1n = l.1(521 kip-ft)

nb

=573 kip-ft

(Spec. Eq. E3-4)

-

2

(29,000 ksi)

( 150 in. )

_t

RyFy _ 1.1(50 ksi) F, - 77.6 ksi

(!

= 0.709

- - ----. rb ;~.

Check combined flexure and compression of the W16xn

Ill

J.1(50 ksi)

=0.658 n.6 m

!lePr -=-P,.

P, P, -= - -

Pc

Because

(Spec. Eq. E3-2)

I

=218 kips 553 kips

=0.394

~ ~ 0.2, AISC Specification Equation Hl-la applies.

P,

Mry)

8(M•x lO -+- - + - <. Pc 9 Mex Mey

(1.1)(50 ksi)

"~:

...

l

-

The available compressive strength is I.hen decermined from AISC Specification Equation E3-l:

.,~l !

>

•'

:.

l

=~cFcrA1 =0.90(40.9 ksi)(22.6 in.2 ) = 832 kips

P,.

FaA

nc

Oc

8( Mr.r.

!(9

ASD

= (40.9 ksi)(22.6 in. 2 }

..

= 553 kips

,

ilcPr 8( QbMrx Q bMry) - + - -- - + - P,. 9 Mru; M,.,

M,., )

+ QbMny

363 kip-ft +0) 573 kip-ft

=0.938<1.0

1 -=--

1.67

.-

P,

9cPn + 9 ¢bMIU 0.375 +

ASD

LRFD ¢cPn

(Spec. Eq. HJ-la)

LRFD

=40.9 ksi l,.

P,,

Pt:

q,cPn 312kips ::::: 832 kips =0.375

=[0.658!!Lr] P. R Fy 1

ASD

LRFD

Because R1 F1 1Fe S 2.25. the critical stress, Fer. is:

Fer

I

\ I

o.394+!(253 ~p~ft +o) 9 382 kip-ft

= 0.983<1.0

o.k.

Determine available flexural strength of the W16xn • . From AlSC Manual Table 3-2, for a W16x77, Lp 8.72 ft and 4 27 .8 ft. 1lmefore, with Cb= 1.0 and 4 12.5 ft (Lp < 4 ~ 4), lateral-torsional buck.ling applies. Using AISC Manual Table 3-10 and adjusting by R1 , the available flexural streaglh is:

,'~·

=

=

o.k.

Available Shear Strength From AISC Manual Table 3-6, the available shear strength is:

LRFD

=

.

2

2.47 in. = 77.6 ksi

r

=l.1(347 kip-ft) = 382 kip-ft

;. .• ,, .,,, _ 1t

'

ASD

LRFD

QvVn = 225 kips > 37 .6 kips

ASD·

o.k.

~ =150 kips> 25.7 kips

nv

o.k.

The W16x77 is adequate to resist the loads given for the beam outside of the link seg1w: of Beam BM- 1. Additional Oange bracing is not required.

5-363

5:4 ECCENTRICALLY BRACED FRAMES

5-362

l

M £,.,,, = 3.36MQE

Example 5.4.4. EBF Brac_e Design

== 3.36(54.5 kip-ft)

=183 kip·:ft

Given:

I

Refer ro Brace BR-1 in Figure 5-59. Select an ASTM A992 wide-flange section to resist tti~ following loads. 'J1le applicable building code specifies the use of ASCFJSEI 7 for calcula.i tion of loads. From a fi.rsc-order analysis:

Po= 11.8 kips

PL= 8.30 kips

Vo= 0.200 kips

VL

Mo= 3.20 kip-ft

l>h = 2.20 kip-ft

=0.120 kips

The axjal force in the brace due to the link mechanism is: PE..i. = 3.36Pas

= 3.36(136 kips)

PQ 8 = 136 kips VQE =J.Q2 kipS MQE

=54.5 kip-ft

_R elevant seismic parameters are given in the EBF Design Example Plan and Elevation section. Assume that the link segment and beam outside of the link segments are those selected in Examples 5.4.2 and 5.4.~, and lh~t the column-end of the brace is pinned and braced against translation for both the x-x and y-y axes.

Solution:

=457 kips The shear in the brace

VE..,,.

due to the link mechanism is:

=3.36VQ£ = 3.36(3.02 kips)

=10.1 kips

l:

Considering the load combinations given in ASCE/SEI 7 that include the amplified seismic load, with .Q0 QE = Emh· it was determined that the governing load combination for the brace is:

From AISC Manual Table 2-4 and AISC Seismic Provisio11s Table A3. l, the material properties are as follows: ASTMA992

Fy =50ksi Fu= 65 ksi R1 -= 1.1

t

ASD

LRFD LRFD Load Combin~tion 5 from ASCE/SEI 7 Section 12.4.3.2 (including the 0.5 factor on L permitted in Section c 12.4.3.2) .. (1.2 + 0.2SDs)D + Emh·+ O,SL + 0 .2S .

.)

ASD Load Combination 5 from · ASCE/SEI 7 Section 12.4.3.2

(1.0 + 0.14SDs)D + H + F + 0.1EmJ1

I

I

Required Strengths According to AISC Seismic Provisions Section F3.3, the required strength of the brace is a combination of the factpred gravity forces plus the forces generated by the adjusted link .shear strength, using the load combinations that include the amplified seismic load. Fro~ Example 5.4.2, the noininal shear strength of the link, Vm is 205 kips.

The required axial strength of the brace.,is:

'_+-----A~s_n_____~Ji

1-------LRFD ______

Pu::::(l.2+0.2Svs)PD·+PE..i.+0.5PL· l.25R1Vn = 1.25(1.1)(205 kips)

=282kips Using the overstrength factor method described in Example 5.4.3 w!th the link s4ear force, VQ£• given in Example.5.4.2, che overstrength factor is: l.25RyV,.

YQs

=282 kips 84.0 kips

Pa=(1.0+0.14Sos)Po+PH+Pp

+ 0.7PE-1i

+ 0.2Ps =[l.2+0.2(1.0)](11.8 kips)

··

·•

;[i.o+0.14(1.0)j(ll.8 klps)

+ 457 kips+ 0.5(8.30 kips)

+ 0 kips+ 0 kips

+0.2(0kips)

+0.7{457kips)

I ~. f

1 ··j::

L-~=-47_s_ki_·p_s~~~~~~~~--l~-~-3_3_3_ki_·p_s~~~~~-'--~~-I I

=3.36 TI1e moment in the brace due to the link mechanism is:

AMEruCAN !Nsmunl.OF Srea CONSTRUCTION

5-364

5-36!.'


DR.ACED FR.AMES

,•' The required flexural strength of the brace is:

LRFD M., = (1.2+0.2Sos )Mo +Me.,... +0.SML +0.2Ms

ASD Ma = (1.0+0.l4Sos )Mo +MH +Mp +0.1Me.,,.

= IL2 +0.2(1.0)j(3.20 kip-ft) + 183 kip-ft+ 0.5(2.20 kip-ft)

+ 0.2(0 kip-ft)

=189 kip-ft

=[L0+0.14(1.0)J(3.20 kip-ft) + 0 kip-ft+ 0 kip-ft + 0.7(183 kip-fr)

'·

I!:'

The required shear strength of the brace is:

..

-----<

v;, =(1.2+0.2S.os)Vo +VE.,. +0.5Vi =ll.2+0.2(1.0))(0.200 kips) +10.l .ldps+0.5(0.120 kips)

(Spec.

-:: : (LO+ 0.14(1.0)](0.200 kips) + 0 kips+O kips

Pe1 = (K1L)2

n2 (29,000 ksi)(716 in.4 )

=

As assumed in Examples 5.4.2 and 5.4.3, uy a W1 Ox112 for the brace. From AISC Manual Table 1-1. the geometric properties are as follows:

fj

l ,. l 5.

J:I ~~

... :~

,. -:-

A= 32.9 in. 2

d= 11.4 in.

br:::.10.4 in.

11= l .25 in.

According to AISC Seismic Provisions Section F3.5a, the stiffened and unstiffened elements of EBF braces shall comply with the requirements of Section Dl.l for moderately ductile members. From Table 1-3 of this Manual, the W10x112 satisfies these limits for EBF braces.

l

Lb= J(l2.5 ft)2 +(13.0 ft) 2

=18.0 ft i'

or

'Where there is no transverse loading oo the brace, Cm is determined from AISC Specification Equation A-8-t For both LRFD and ASD: Cri =0.6-0.4(M1/M2)

=0.6-0.4(0)

L,, ::::(18.0 ft){l2 iolft) =216 in.

• '

(Spec. Eq. A-8-4)

=0.6 Therefore: LRFD

a

~ 1.00

B1 =

_l 1

ASD Ct

0.6 ~ l.O l.00(478 kips) l 4,390 kips l

=0.673

>·

{

2

lt.0(216 in.)J

= 4,390 kips


Determine unbraced length

1.

t,., = 0.755 in. Ix= 716 in.4

(Sp'e c. Eq. A-8-5)

rr.2Et

=7.30 kips

=10.4 kips

Eq. A-8-3)

where

+ 0.7(10.1 kips)

+ 0.2(0 kips)

a,

v., =(l.O+O.l4Sos)Vo +Vu+ VF + 0.7Ve.,,.

+ 0.2Vs

=

ASD

:$::)

'*·

Second-order effects are addressed using AJSC Sptcificarion Appendix 8. Since the lateral load effect is based on the adju~ted link shear strength, B2 = 1.0. P-tl dfects do not increase the forces corresponding to the fully yielded, strain-hardened link; instead they may be thought of as contributing to the system reaching that state.

Calculate

LRFD

~

-


Because 8 2 1.0. the required compressive and flexural strengths will not be amplified to account for P-~ effects. The effective length method is used for stability design.

= 132 kip-ft

"'·/,

'$;

Note that the unbraced length is based on the work point-to-work point dist.1nce. Shorter lengths may be used provided lhe lateral support is adequate at each end of the assumed unbraced length.

= l.60

81=

l

0.6 ~LO 1-[1.60(333 kips) 4,390 kips

=0.683

I

I

Bcc3use 81
I.

The W10x 11 2 is adequa1e to re.~ist lhe loads given for Br:ice BR-1.

Since 81 = 82"' 1.0. the required tle.xural strength calculaled previously need noL be amplified to account for P-o or P-t::. effects.

Example 5.4.5. EBF Column Design

Combined Loading

Given:

Using AISC Manual Table 6-1 for combined ioading with KLy

LRFD p

ASD

=1.09x10-3 kips·•

b_, = 1.12 x io-3 (kip-ftf

=Lt>x =18.0 ft:

p 1

= J.63x 10- 3 kips- 1

LRFD

= l.09 x10-3 (47S kips)

= 1.63x!O 3 (333 lcips)

=0.521

=0.543

Because

P1.=46 0 kips

PQr= 172 kips

,>,.f u

=9 00 kip-ft M 1.y =6.00 kip-ft

.~le_= O.kip-ft

Mg,.,,, = 0 1tip-ft

Assume that the ends of I.he column arc pinned and braced against 1.ranslation for botli the x-x and y-y axes and that the beam at the third level and brace between the second and 1hir• levels are as designed 10 Examples 5.4.2, 5.4.3 and 5.4.4.

P, Pc

-=pPr

Pc

Po= 151 kips

Mm.= 15.0 kip-ft

Relevant seisrrtlc parame1crs arc given in 1he EBF Design Ex.ample Plan and Eleva1io1 secrion.

ASD

P, -=pP,

Refer to Column CL- I in Figure 5-59 Sclcet an ASTivt A992 wide-flange section to resis1 the followmg loading bc~-ccn lhc base :uid ~ond level. The applicable bu1lding code specifies the use of ASCFJSEI 7 for calculauon of load!!. From a first-order analysis:

Mo, = l0.0 kip-ft

b_,:::: 2.59x10- ] (kip-ftf1

l

Solution: From AlSC Manual Table 2-4 and AlSC Seismic Provisions Table A3. l, the material properties are as follows:

~ ~ 0.2, AISC Specification Equstion HI - la spplies:

8(M"

P, --· +--L. M,..,)
(Spec. Eq. Ill-13)

ASTMA992 F1 =50 ksi F. =65 ks i R,= 1.1

Or, in terms of AISC Manual Equstion 6-1: Required Strength LRFD

pP,+b.rMn +b1 M,, 3

pP, +b.rMrx + b1 Mry 1

0.521+1.72x 10- (k.ip-ftf (189 kip-ft)

1

0.543+ 2.59x10-3 (ldp-fif (132 kip-ft)

+O

=0.846 $

Using the load combinations in ASCFJSEI 7 1hat include the amplified seismic load. wit !l,,QE = Em11, it was detcnnined that the governing load combination for the column , compres~ion is·

ASD

ASD

+O l .O

=0.885~ 1.0

o.k.

I.RFD Load Combination 5 from

o.k.

ASCFJSEI 7 Section 12.4.3.2 (including the 0.5 factor on l pennitted in Section 12.4.3.2)


From AlSC Manual Thble 3-6:

(1.2 + 0.2Sos)D + E,,.,. + 0.5L + 0.2S'

LRFD

,,.v,, =258 Jtips > l0.4 kips

ASD Lood Combination 5 from ASCEJSEI 7 Section 12.4.3.2

ASD o.k.

2- =172 kips> 7.30 kips

n.

o.k.

( l.0 +0.14Sos)D + H + F+ 0.1Em1i

I

l I l

' I

)

!.• .

And the goveming load combination for the column in rension i~: -

LRFD LRFD Load Combination 7 from ASCEISEI 7 Sectfon 12.4.3.2 (0.9- 0.2Sos)D + E..,,. + l.6H '

: '

..;: ..... :.

~

- --

:;:J

l~ "

:t" l !~

.•'•,

ASD

LRFD

ASD

.

+0.1Me_

+0.5Mit +0.2Ms

ASD Load Combination 8 from ASCE/SEJ 7 Section J2.4.3.2

=p.o + o.14(LO)J(1s.o k:ip-fl)

=ll.2+0.2(1 0))(15.0 kip-ft)

(0.6- 0.14Sru)D + 0.1EmJr +Ii

AISC Seismic Provisions Section F3.3 requires the column to have Ille strength to resist the forces generated by lhc sum of the adjusted link shear sirengths of the Unks above the level of the column top in 3Jd1tion to the fac1ored gra\ity forces. From faample 5.4.2. the nominaJ shear strength of the hnk at the third le'.-el is 205 kips. By calculations not shown here, it was determined that the sum of the nominal shear strengths of the links at the fourth level and the roof is 318 kips. There is also a small axial load due to the shear from the beam outside of the link at level 2. It is neglected in the following calculation due to its negligible effect on the result ~rcfore, accounting for the exception allowed in AISC Seismic Provisions Section F3.3( l Xb), lhe sum of che adjusted link yield ~trcngths of the links at the third level, foui'th level :ind roof is:

M, (l.0+0.14Sos)MD + ,\.fH + ,\fI

M .... = (1.2+0 2Sos) \f 0 +ME..,.

+0 kip-ft+ 0.5(9.00 kip-ft)

+ 0 kip-ft+ 0 kip-ft

+ 0.2(0 kip-fl)

+ 0.7(0 kip-ft)

=25.5 kip-ft

- 17.l kip-fl

M,_., = (l .0+0. 14Sru)Mo +Mn +MF

i\f•-r =(1.2+ 0.2Sos )Mo+.\!£.,...

+0.7;\.fE...,

+0.5Mty ... 0.2.\-fs

11 0+0.14(1.0)](10.0 kip ft)

=ll.2+0.2(1.0)j(lO.O kip-ft)

+ 0 kip-ft+ 0 kip-ft + 0.7(0 kip-ft}

+ 0 kip-ft+ 0.5(6.0 kip-ft) + 0.2(0 kJp-ft}

= 11.4 !Up-ft

= 17.0 kip-ft

Using the governing load combination for the column in tension, the required axial tensile strength of the column is:

0.88(l.25)R1 LV,, = 0.88(1.25)(1.1)(318 kips+ 205 kips) - 633 kips

Usmg the govemiug looJ combination for the column in compression. the required axial compressive strength of the column is:

LRFD

ASD

ASD

LRFD

Pa= (0.6-0.14Sos)Pv +0.?PE.,. +PH

P,. = (0.9-0.2Sos) Po+ PE... + l.6P11

=I0.6-o.14<1.o>JOs1 kips)

=(0.9-0.2(1.0)](151 kips)

+ 0.7(-633 k.ips)+ 0 kips

+(-633 kips)+ t.6(0 kips)

P., ={1.2+0.2Sos )Po+ PE,.,.+ 0.5Pt +0.2Ps =ll.2+ 0.2(1.0)J(l5 I kips)

+ 633 kips+ 0.5(46.0 kips) + 0.2(0 kips) =867 kips

Pa= (1.0+ 0.14Sos)Pv + P11 +Pp

=-374 kips

=-527 kips

+0.7%,.. = p.o +0.14(1.0)](151 kips)

\

The required flexural strength of the column simult:mcous with the rocial tension is:

r 0 kips+ 0 kips + 0.7(633 k.ips) - 615 kips

M.... =(0.9-0.2Sos).W0x +M4 + 1.6MH

The required flexural strength of the column simultaneous .with the o.x.ial compress.ion is:

ASD

LR.FD

.

=10.9- 0.20 .0>](15.o kip-ft) + 0 kip-ft .. 1.6(0 ki~ft)

= 10.5 kip-ft

M.u

=(0.6-0.14Sns)Mo.r +0.1Mt+MH

={0.6-0.140.0))(15.0 kip-ft) + 0.7(0 ki~ft)+O kip-ft

=6.90 kip-ft

.

,BRACEO 'FRAMES.

>-JIU

.~~

ASD

LRFD

May = (0.6-0.14Sru)MDy +0.7 ME1"17 '~•

Muy = (0.9-0.2Sos)MDy +ME...,

+M11 = (0.6-0.14(1 .0}](10.0 kip-ft)

+l.6M11

= [0.9- 0.2(1.0)J(I0.0 kip-ft)

+ 0kip-ft+1.6(0 kip-fl)

1t2El;

Pds ~.

2 rt (29,000

.~

=4.60 kip-ft

ksi)(833 in.

4

)

= [i.0(14.0 ft)(12 inJft)f

•

=8,450 kips

+ 0.7(0 kip-ft)+O kip-ft

=7 .00 lcip-ft

(Spec. Eq. A-8-5)

=(KiL)2

ly P.11 = P~is Ix

The load combination that will govern the design of the column is chat for compression. The resulting required strengths are: '

LRFD Pu

= 8,450

Pa

Max= 17.l kip-ft

M,.y = 17.0 kip-ft

May = 11.4 kip-ft

l

The columns are assumed 10 be pinned at the base, so Mi in AlSC Specification Equation A-8-4 is zero. Because the column is not subject to 1.ransvcrse (perpendicular to the axis of the member) loading, Cm is detennined for both LRFD and ASD as follows:

= 615 kips

Mux = 25.5 kip-ft

in.

=2,740 kips

ASD

= 867 kips

kips(270 ~n·: ) 833

Cm

.

(Spec. F.,q. A-8-4)

=0.6-0A(M1/M2) ::: 0.6-0.4(0)

Try a W12x96.

:::0.6

From A1SC Manual Table 1-1, the geometric properties are as follows:

A =28.2 in.2 4

Ix= 833 in.

=12.7 in. 11 =270 in. d

4

1f =0.900 in.

= 0.550 in. bJl21f= 6.76 lw

hit..,= 17.7

Width-to-Thickness Umitations According to ATSC Seismic Provisions Section F3.5a, the column must comply with the requirements of Section D 1.1 for highly ductile members. From Table 1-3 of chis Manual; these requirements are satisfied for a W12x96 column (both flanges and web). Consider second-order effects From AlSC Specification Appendix 8, the required flexural and axfal strength including second-order effects

are determfoed as follows:

..

(Spec. Eq. A-8-1)

(Spec. Eq. A-8-2)

=

Since !he lateral load effect is based on the adjusted link shear strength, B2 1.0. P-6 effects do not increase the forces corresponwng to the fully yielded. strain-hardened link; instead they may be thought of ~s contributing to the system reaching that state.

Because B2 = I .0, the required compressive and flexural strengths will not be amplified to account for P-A effects. Determine B1 as follows from AISC Specification Appendix 8. The effective length method is used for stability design.

j::

(Spec. Eq. A-8-3)

1.~

Therefore:

LRFD Cl

=1.00

B1x

=

0.6 > 1:0 1.00(867 kips) l8,450 kips

=0.669 Bi,=

ASD

\

0.6 ~ 1.0 1.00(867 kips) l2,740 kips

=0.878

I

Cl

= 1.60

B1x =

0.6 . ::!: LO 1.60(615 kips) 18,450 kips

Bty= ~-

0.6 l0 1.60(615 kips)::!: · 2,740kips

..

I

=0.936

Because the calcuJated Bix and Biy ru:e less than 1.0, B1x= B1y amplify the .required flexural strengths.

I

=0.679

=1.0, and there is no need to

.J'

r.

S.4 ECCE.NTRlCALl..Y BRACED FRAMES

Combined Loading

Solution: From AISC .\fm111al Table 2~5. the material prorenies are as follows:

Using AlSC Manual Table 6-1 for combined loading wi1h

i:

4y = 4x = 14 fl:

.'

~:.1.

ASD

LRFD p =0.978xl0-3

kips-1

bx= I .67 x I 0-3{kip-fl f by= 3.s1x10- 3 (kip-ft

r

j'

p ::: 1.47X10- 3 kips-I 1

bx= 2.50x 10- 3 {kip-ftf

1

b1

lj

.

1

=5.28 x I 0-3 {kip-ftr'

ASTMA36

F1 =36 ksi Fu =58 ksi From AISC Manual Table J-1 lhe geometric properties are as foUows: Brace

W10x112

A= 32.9 in. 2

/T:::o7J6in.

ASD

LRFD P, -=pPr P,.

-----~:~ ....

=0.978 x 10-3 (867 kips)

= 1.47x10-3 (615 kips)

=0.848

:::: 0.904

8(M"'

ASD

pP, +bxMrx + byMry S 1.0

0.455 in.

bt = 10.3 in.

fJ =0.760 in.

ASD

1

o.904+2.sox10-3 (kip-ftr (11.1 kip-ft)

1

+5.28x10-3 (kip-ftf (11.4 kip-ft)

+3.51x10-3 (kip-ftf (17.0 kip-ft) o.k.

P., =478 kips

Pa = 333 kips

v,.

Va =7.30 kips

= 10.4 kips I

Mu= 189 kip-ft

pP, + bxMrx +b1 Mry S 1.0

0.848+1.67x10-3 (kip-ftf (25.5 kip-ft)

Ma= 132 kip-ft

1

1

=LOOS 1.0

o.k.

Determine the brace flange force Assuming the axial force is resisted entirely by the flanges, the force in each flange due to axfal load is:

The W12x96 is adequate to resist the loads given for Column CL-1 between the base and second level.

EBF Brace-to-Link Connection {)esign

Refer to Joint JT-1 in Figure 5-59. Design tbe connec(ion between Brace BR-1 and Beam BM-l assuming the brace is oriented with the web in Lhe plane of I.be frame. Use ASTM A36 material for all plate material and 70-ksi electrodes for all welds. Assume 1he Hnk, beam outside of the link, and brace are as designed in Examples 5.4.2, 5.4.3 and 5.4.4, respectively.

ASD

LRFD P., P1a=-

Given:

I

lw=

LRFD

LRFD

;; j Example 5.4.6.

=1.75 in.

lf = 1.25 in.

(Spec. Eq. HI-l a)

Mey

Or, in terms of AlSC Mo.nual Equation 6-1:

= 0.950 < 1.0

kJ,s

bi= 10.4 in.

Determine the brace connection forces According to AlSC Seismic Provisions Section F3.3. brace connections must consider the forces generated by the adjusted link shear strength. From Example 5.4.4 for the design of the brace, the required strengths of the brace ba.~ on the adjusted link shear strength are:

Pr ry )<1.0 -+- +M 9 Mex

d = 11.4 in.

kus = 1.16 in.

P.

Pc

4

Beam W16x77 d= 16.5 in.

P, - ==pP, Pc

Because ~ ~ 0.2,AISC Specification Equation Hl-Ia applies:

·.

5 373

S-372

2 478 kips 2 =239 kips

Pa 2

Pfo = -

=

33~

kips 2 167 kips

=

S-375

5.4 ECCENTRlCALLY BRACED FR.AMES

Assuming the entire moment will be takeo by the flanges. the force in each flange due to the moment is:

LRFD

ASD

Mu Pf!=--

LRFD

= 189 kip-ft(l2 in./ft) =223 kips

= 239 kips+ 223 kips 462 kips

=

2.00

=423 kips> Pa/ =323 kips

Check concentrated forces at brace flange connection

=156 kips

The venical component of the flange force is:

LRFD

v. =P.

ASD ..

845 kips

=

LRFD

=P1a +Pff

o.k.

n

uf

P.v = Pta +Pg

=167kips+156 kips =323 kips

ASD

ft)

ft)

18.0 ft

V, -::P. (12.5 a/ of 18.0 ft

=4Q2 ki ps(l2.5 ft) 18.0 ft

= 323 ki

=321 kips.

=224 '9ps

Mf

( 12.5

s( ft)

12 5 · p 18.0ft

It will be assumed that the entire shear force will be taken by the web. ·

(Spec. Eq. Jl0-2)

R,. = Fywlw(5kcu +lb)

LRFD

= 10.4 kips

= {50 ksi)(0.455 in.)!5(1.16in.)+1.25 in.]

ASD V..,= Va

= 7.30 kips

I.RFD

Try a complete-joint-penetration (CJP) groove weld to connect the brace flanges to the beam flange. From AlSC Specification Table J2.5, the strength of the CJP groove weld in tension is based on the strength of the base material. The tensile rupture strength of each brace flange, wit.h

'\

(Spec. Eq. 14-2)

I

n..g.

= 160 kips < Viif = 321 k.ip~

"

ASb

-·

R,, 160 kips -= 1.50 n :::::)07 kips< Va/= 224 kips

n.g.

Because the concentrated force is appplied at a distance greater than or equal to. d/2 from the beam end. the beam web locitl crippling strength at the brace flange connection is:

R. =0.801!

1+3(~ l[:; r)t::''

A.. =A8 , is:

(Spec. Eq. JI0-4)

25

x ,______ .___ ksi)(0.760 .........._ _in.) _ 29,000 ksi(50 0.455 in.

=285 kips

1··

~:i

:•

55 ~·)( o.4 ~-)I.SJ 16.5 m. 0.760 m.

= co.so)(0.455 in.)'211+ 3(1.

= 65 ksi(l0.4 in.)(1.25 in.)

= 845 k.ips

-.. -

<9Rn = l.00(160 kips)

From faample 5.4.2, because the brace. was designed to resist a portion of the link end moment, AlSC Seismic Provisions Section F3.6c requires that this connection be designed as fully restrained. Use a fully welded connection.

=F.,b111

).

= 160 kips

Brace Flange Connection

R,. =FuA.

Ii

;

Because the concentrated force is applied at a distance greater than d, the beam depth, from the beam end; the. beam web local yielding srrengih_at the brace flange connection is:

Determine the brace web force

Vw = Vu

o.k.

• ,,,i·.

The maximum resultant force in each flange is:

P.,f

-=

=634 kips> Pu/ =462 kips

132 kip-ft{l2 inJft) 11.4 in. -1.25 in.

11.4 in. -1.25 in.

Rn

¢Rn =0.75(845 kips)

Ma Pg=-d-11

~-11

ASD

,·

5--377

5.4 ECCENTRICALLYBRACE'.D FRAMES

5-376

LRFD

f: I

strength of the stiffeners is the difference between the venical component of lbe f1.ange force, Vuf or Vaj, and the available strength of the beam web due to web, local yielding.

ASD

!'.(;.. '

$Rn= 0.75(285 kips) =214 kips< vzif..=321 kips

n.g.

R,, 285 kips -= n 2.00 k 143 kips< Vaf = 22A kips

.. n.g.

Size beam web stiffeners Using one stiffener on each side of the beam web, the portion of the vertical component of the brace flange force to be resisted by e:ich stiffener is:

The flange local bending strength is:

LRPD (Spec. Eq. 110~1)

Rn =6.25F)1t}

=6.25(50 ksi)(0.760 in.)2 ASD

LRFD -.-

$Rn= 0.90(181 kips) =163 kips< Vut = 321 kips

n.g.

Rn 18lkips -= - - n l.67 =·108 kips< Vaf

=224 kips

n.g.

Beam web stiffe~c~s.are ;equi~ed adjacen~ to the brace flanges as shown in figure 5-61. nie controlling limit state for concentrated loading is bea~ weh local .yielding, at;d the require.d

·>~ :~

.

W16x77.beam \

2

= 224 kips -107 kips

¢Rn

·.,.9 ,.

2

ASD

P,

>

---=---ct_ link

P,

tmin ; ? : - - -

FyWs1

J

.; ~;

PL %"x4"x0'..fi!!.---->~ (A36) with bolts ·

Rn

;::p,

~Fywntmin ;:::

~!·

I

= 58.5 kips

LRFD

J

....

Ps-

For convenience, use the same stiffener geometry as used in Example 5.4.2 for the link stiffeners. Try a 4%-in. stiffener width with l in. x 2~ in. comer clips. From Example 5.4.2, aceounting for the comer clips, the length of stiffener in contact with the flange is ws1 =VA in. and the length of stiffener in contact with the web is L,1 = 10.2 in. The stiffener rhickness necessary to develop the required strength, based on the limit state of tensile yielding from Al.SC Specification Equation J4-l, is:

Full depth PL %"x4%" (A36) each side of web

::

",.~ ....,

_Va1-(~)

Vu1 -
Ps =

· = 181 kips

·'

ASD

;::p,

n '\

Fywntmin > R

n

tmin

,

;<: QP,

Fywsr

80.5 kips ;::: 0.90(36 ksi)(33,~ io.)

;::: 1.67(58.5 kips) 36 ksi(33A in.)

~0.663

;::: 0.724 in.

in.

Note that one flange of each brace frames into the beam at the end of the link segment. In Example 5.4.2, the AISC Seismic Provisions requirements resulted in a ¥s in. minimum thickness for the stiffeners at the end of the link.

as required for erection loads

w1ox112 brace Fig. S-61. Connection as designed in E.romple S.4.6.

Use 3,4 in. x 4¥1 in. full-depth stiffeners on each side of the beam at the locations where a brace flange intersects the beam flange. These will replace the link end stiffeners designe. in Example 5.4.2.

Design stiffener welds

Using the increased strength allowed for transversely loaded fillet welds according to AISC! I ' Specijicaticn Equation 12-5, (I .0 + 0.50 sin 1s 9) ( 1.0 + 0.50 sin 13 90°) = 1.5, the minimum f · • double-sided fillet weld size required to tran:.fer lhe required stiffener load from the beam 1 ~ flange to the stiffener is: ·'

=

.. ' -~;n

.

LRFD Dm;,.=

Ps 2(1.5)(1.392 kip/in.)wst

ASD Dmin

=2(1.5)(0.928Ps kipfm.)w,

80.5 kips

58.5 kips

=2(1.5)(0.928 kiplin.)(3~ in.) =5.60 si.xteembs

The minimum double-sided fillet weld size required to transfer the stiffener force to the web is:

LRFD

ASD

. Ps 2(1.392 kip/in.)L11 80.5 kips :::: 2(1.392 kipfm.)(10.2 in.) = 2.83 sixteenths

l

Example 5.4.7. EBF Brace-to-Beam/ Column Connection Design

,

Given: Refer to Joint JT·2 in Figure 5-59. Design lhe connection between brace, beam and colum1 Use ASTM A572 Grnde ·50 for all plate material and 70-ksi electrodes for all welds. U. AS™-A325-N bolts. Assume that the beam is as designed in Example 5.4.3, the brace sizt! is !he same as that determined in Example 5.4.4 and the column is as designed in E.xamp' 5.4.5. The applicable building code specifies the use of ASCEJSEI 7 for calculation of load .

I

1

=2(1.5)(1 .392 Jcip/in.){3% in.) =5.14 sixteenths

D,..;,,

s

5.4 ECCENTRICALLY BRACED FR.AMES

5-378

D,,,;n

=2(0.928 l'skip/in.)L.,

Relevant seismic paramecers are given in the EBF Design Example Plan and Elevation seccion. The brace will be connected to the beam-to-column joint through a gusset plate. The co: , nection of the brace to the gusset plate will consist of WT sections with flanges bolted co each side of the brace web and gusset plate. The gusset plate and beam will be connectt ·1 to the column using a bolted end piste. Figure 5-62 is a sch~matic drawing showing the rt .. evant forces on the conne<:tfon. This is not a realistic drawing of the connection and show:-. ·. only minimal detail. S olut ion: From AISC Ma1111al Tables 2-4 and 2-5. the material properties are as follows:

58.5 kips

=2(0.928 kip!m.)_(10.2 in.) =3.09 sixteenths

l

Note that per AISC Specification Table J2.4, lhe minimum stiffener-to-web weld is Vi6 in. based on the thinner part joined, tw =0.455 in. The minimum stiffener-to-flange weld is 1A in. based on the ~-in. stiffener, which is the thinner p:u1 joined. Use double-sided ~-in. fillet welds to connect the stiffener to the beam flanges and doublesided ~-in. fillet welds to connect the stiffener to lhe beam web. Design the brace web connection

Use a% in. x 4 in. x 0 fl 6 in. single-plate connection with ¥16-in. fillet welds to connect the brace to the beam. This connection will be adequate for the small required shear strenglb. The final connection design and geometry is shown in Figure 5-61.

Po= 1.30 kips PL= 1.00 kips

P0

.v----1-1--

e = 46.1 °

,= 105 kips

7iV0 VL

70.0 kips

L ·.·.

=4 .10 kips =3.00 kips

W.P.

v0 .= ...S.70 kips

).

Fig. 5-62. Connection forces for E.:cample 5.4.7.

...I

S.:.380

BRACED FRAMES

ASTM A572 Grade 50 I

..!;.,

5-3!1 1

5.4 ECCENTRICALLY BRACH> f'RAMfS

ASD

LRFD

F1 -50 ksi

LRFD Load Combina1ion 5 from ASCE/SEI 7 Section 12.4 3 2 (including lhe 0.5 factor on L pennitted in Section 12A.3.2)

Fu= 65 ksi

ASTMA992 F1 =50 ksi

F., = 65 ksi

(I .2 + 0.2Sos)D + E,,.~ + 0.5L + 0.2S

ASD Load Combination 5 from ASCEISEI 7 Section 12.4 .3.2

(1.0 +O.l4S.os)D + H + F +0.1Em>t

From AJSC Manual Table l • l, the geometric properties are as follows: ~

•:

Beam outside of the link

,·

.'\ =22.6 in.= 1j =0.760 in.

., •7·

,.

The governing seismic load case causes compression in !he brace. Assume lhe connection forces are as shown in Figure 5-62.

W16xn d= 16.5 in. kdu

= 1.16 in.

1..., = 0.455 io.

bt= 10.3 in.

T= J3'A in.

Brace

W10x112

= 11.-1 in.

A = 32.9 in.1

d

'J =l.25 in.

T= 71h in.

lw

=0.755 in.

Determine the load from the beam outside of the link (considered in both Conditions 1 and 2) The adjusted link yield strength used m 1be design of the beam outside of the link was allowed to be reduced by 0.88 according to faception (l)(a) in AISC Seismic Provisions Section F3.3. This reduction is not allowed for connec1ions. From Example 5.4.4, lhe overstrength factor for the link at the third level is 3.36. The factored forces ut the connection due 10 the beam outside of the link are:

Column

W12x96 A -28.2 in. 2 ken

=1.50 in.

d= 12.7 in.

1,.

= 0.550 in.

ti=0.900 in.

In order 10 envelope t.he design, 1wo condi1ions should be examined. Forces from bolh con· ditions are shown in Figure 5-62.

~-1

~

.:

··.~:

ASD

LRFD

Condi lion 1: The brace force required 10 develop the adjusted link yield sirength al tbe fourth level must be transferred through 1he connection and in10 t.he column and beam oulSide of the link. The :idditional collector force required to de~elop lhe adjusled link yield strength at the third level must be transferred from the collector element through the beam-to-column connection. This collector force need not C.'(ceed tbat de1errnined using the amplified seismic I03d. The shear in I.be beam outside of me link must be transferred in10 the column. Condition 2: The amplified collector force must be transferred into I.he be:im ourside of I.be link. The adclitional brace force required to develop the adjus1ed link yield strength :it the third level must be transferred through the conneclion and into the column and beam ouiside of lhe link. The brace force need not exceed 1hat required to develop the adjusted link yield strength ,at the fourth level. 1l1e shear in lhe beam outside of \he link must be ttan~ferrcd into lhe column.

P., =(1.2+ 0.2SDs)PD +Pr·... + 0.5P1. +0.2Ps = !I.2 + 0.2(1.0)j( l.30 kips) + 3.36(105 kips)+0.5( 1 00 kips)

+ 0.2(0 kips)

P0 =( l.0+0.14Sos)Po +Pn +PF

+0.1PE.,,. =!LO+ 0.14(1.0))(1.30 kips)

+ 0 kips + 0 kips + 0.7(3.36)(105 kips) =248 kips

=355 kips

ASD

LRFD

v., = ( l.2+0.2Sos)Vo +Ve""+ 0.5V1. +0.2Vs

"'[l.2+0.2(1.0)](4.IO kips)

v.. =(1.0+0.14SDs)VD+Vu+VF +0.1Vs,..

=[LO+ 0.14(1.0))(4.10 kips)

+ 3.36(8.70 kips)+0.5(3.00 kips)

+Okips+O kips

+ 0.2(0 kips)

+ 0.7(3.36)(8.70 kips)

=36.5 kips

=25.1 kips

:·;

Required Strength The govemjng load rombinstion, with !l,,Qe = Em1r. is:

I

Determine the load from the brace (Condition 1) AISC S~ismic Provisions Section F3.3 requires thst the brace connections have sufficiC' srrength to develop the adjusled link yield srrength. Use the overstrength factor mell. described in Example 5.4.3 and assume that the oversuenglh factor is 3.36, the same as L),

.

5-382

BR.ACED F'RAMES


used in Example 5.4.4 for the design of the brace. The required strengths of the connect.io!li from the brace, based on the forces shown in Figure 5-62, are: LRFD

Pu= (I.2+ 0.2SDs )Po+ %..1+0.5P1,

= 2.0(70.0 kips)

0.7Q 0 Pa.t

=140 kips

+ 0 .7 PE.,.

=[l.0+0.14(1.0)](12.3 lcips)

+3.36(105 kips)+0.5(8.70 kips)

+ 0 kips+O kips

+ 0.2(0 kips)

+ 0.7(3.36)(105 kips)

798.0 kips

.. To achieve equilibrium at the joint, the force from I.he brace must be adjusted accordingly. The net horizontal force due to the coJlector force and the axial force in the beam oucside of the link is:

ASD

LRFD

=-215kips

V., = (1.0+0.14SDs)Vn + \IH +VF

+0.2Vs

LRFD

:::: [1.0 +0.14(1.0))(0.200 kips)

+3.36(2.30 kips)+ 0.5(0.100 kips)

+ 0 kips + 0 kips

+ 0.2(0 kips)

+ 0.7(3.36)(2.30 kips)

=8.06 kips

u

=5.64 kips

kip•[ ~(13 ft)

2

ft +(12.5 ft) 2

l

- 355 kips+ Pdrag = 0

Pdrag

=355 kips [ x

:;Jo 3

13 ft

~(13 ft)2 +(12.5 ft)2

l

-248 kips+ Parag = 0

Therefore:

13 ft + 02.5 ft)2

ft.)2

1 x

[

Jo 3 tt)

13ft

2

+ 02.s ttf

]

=59.9 kips

=85.4 .lcips

Determine the load from the brace (Condition 2) Petermine the coUector force based on th.e amplified seismic load. The amplified collector force is: AMERICAN

lNSTm1J:1! OP Sraa CONSTRUCTION

ft)']

L .: •

= 208 kips

example, these forces will be assumed to be e}ualhbut oppos~te tbeor.thedco~rutiod~ oftht~e brace in tension. This is a conservative assumption 1or t e connection mg es1gne 111 1s exam~ pie. However, this may not be a conservative assumption fo,r all .c onnection geometries and loading coi:iditious. ·

Determine the required strength of the brace--to·gusset connection (Condition 1) Using the required strength of the brace'(Condition 1), ~e resultant force on the connec· tion is:

ASD

LRFD

Pdrag = 248 kips- 261 kips

c12.s

13 ft

Force diagrams for Conditions 1 and 2 are· shown in Figure 5-63. For the purposes of this

Therefore: 374 kips

. [Jen ft)'+

Pa= 150 kips

l3 ft

=298 kips

ASD 261 "'"'[

ASD

. [J0 3 •J' +(12.5 ft)']

P. = 215 kips

The resulting collector force in Condition 1 is what is needed to achieve horizontal equilibrium. Ignoring the small contribution to borizontal forces from the brace shear, the collector force in Conrution 1 is: ·

374

=-150 kips

Thus, the force from the brace to achieve equilibrium is:

+ 0.7VE..A

=IL2 + 0.2(1.0)J(0.200 kips)

13

(

ASD

V., = (1.2 + 0.2SDs) Vo+ VE~..1 + 0.5VL

LRFD

[·.

Fh = 98.0- 248 kips

Fh ::::: 140 kips - 355 kips

LRFD

=0.7(2.0)(70.0 kips)

.

=261 kips

::: 374 kips

ASD

Pa= (l.0+0.14Sos )fb +PH+ Pp

+0.2Ps

=IL2+ 0.2(1.0))(12.3 kips)

LRFD Q 0 Pa.t

ASD

S-383

R,, =JPJ+VJ

Ru =JPJ+vJ ::: ~(374 kips ) + (8.06 kips ) 2

=374 kips

=

2

.

= ~(261 k:ips)2 +(5.64 kips)2

-

= 261 kips

Because this is greater than P,. 298 kips (LRFD) and Pa = 208 kips viously for Conrution 2, use Condjtion 1 values.

(ASD) calculated pre-

1.,:

f

~.·:.'. l.

:BRACEPFRAMES ~.

5-384

' .. ~,

'· !·

5-385

w

l

:...,, I

"(

..!;

5.4 ECCENTRICALLY :BRACED FRAMES

}'ffJ.

X

I

"'.:0 ..

'·

8.06 k'rp s

374 kips

~12.5

\

t

,.. ·~

.•."

25.1 kips I

,,.,

...

r

36.5 kips

355 k;ps

5.64 k'ps .I

· ·x~2,

13

::

,"

261 kips

I

'"'

· ll

---t-4-----

85.4 kips

....

y'

248 k;ps

·l

--+-4'-----

59.9 kips

;~ I

;~~

.t

t

Condition 1

(~

~ I ~-

36.5 kips I

355 kips---+

"'

' ~

25.1 kips

4.--~--

..

~;

Condition 1 .. .': ..

140 kips

248 kips

:__f

1

u

JI

98.0 kips

4 - - --

Yr::

II.,...;~

lL ~;

t:

f: . r::

t Condition 2

t Condition 2

:~:

"

·'

>'

(a) Si;:hematic of LRFD force diagram for Example 5.4. 7 · Fig. 5-63.. Schematic force diagrams for Example 5.4:7.

~·:

(b) Schemaric of ASD force diagram for faa.mp/e 5.4. 7 Fig. 5-63. Schematic force diagrams for Example 5.4.7.(cominued)

g AMERICAN INsnrvm.oF STEa CONSTRVC'nON

A.MEJUCAN !NS11l"UTE OF Stsa CoNSTRUCOON

5-386

BRACED FRAMES· f,


5-387

Connection Design

LRFD

ASD

Determine the required number of bolts Using AISC Manual Table 7-1, the minimum number of 1-in.-cliameter ASTM A325-N bolts in double shear required co develop the required strength is:

LRFD

ASD

Ru nm;;,=-

nun

374 ldps = 63.6 kips/bolt

= 5.88 bolts

LRFD ¢R,. =6{84.8 kips)+ 2(64.4 kips)

=6.16 bolts

Check bearing strength of gusset plate

Try an initial gusset plate thickness of 3,4 in. Using AISC Manual Table 7-4 for I -in.diameter bolts in standard holes and ASTM A572 Grade 50 plate material, the available bearing strength of the plate at each of che interior bolts is:

=113 kipfm.(3,~ in.) =84.8 kips

~

R,.

n

o.k.

=6{56.7 kips)+2(43.0 kips) =426 kips> 261 kips o.k.

Check block shear strength of gusset plate

Assume tbac the brace force Pu (LRFD) or Pa (ASD) can act as a censile force and check t~e block shear rupture strength using AISC Specification Equ~tion 14-5. A~ assumed ~re:1ously, use bolt spacing of 3.00 in. aud edge distance o~ 2.~0 1~. The gage 1s equal to 3 Y.i in. and from AISC Specification Table 13.3, the bolt hole is 1 ili6 m. Ubs

LRFD

ASD


Try eight bolts in standard holes wich 3-in. spacing and 2-in. edge distance as shown in Figure 5-64.

ASD

Agv

=75.6 kip/in.('A in.) =56.7 kips

A""

=1.0 =2[2.00 in.+ 3(3.00 in.)](3A in.) =16.5 in.2 ::: 16.5 in.2 -2(31/i)(!l/16in.+1/J6 in.)(~ in.)

= 10.6 in.2 Using AISC Manual Table 7-5 for 1-in.-diameter boHs in standard holes wilh 2-in. edge distance, the available bearing strength of th~ plate at each of the edge bolts is:

.

=43.0 kips

Therefore, the total available bearing strength of the gusset plate is:

Ra r" In

261 kips = 42.4 kips/bolt

I

n

=64.4 kips

n. = - -

cprn

!"!!. = 57.3 kip/in.(~ in.)

¢r,. = 85.9 kips/in.(~ in.)

Agr

=3 h 1

}.

l.

t

t

'\

in.(3A in.)

'

= 2.63 in.2 A"'

= 2.63 in. 2 -(1~6 in.+ Yi6 in.)(~ in.) =1.79 in.2

F,,A111 =65 ksi{t.79

in.2)

=116 kips 0.60F.,A,,,,

l

'•·

=0.60(65 ksi)(l0.6 in.2 ) =413 kips

0.60F1 Aiv = 0.60(50 .ksi)(l 6.5 in. 2 )

=495 kips Fig. 5-64. Initial bolt conjig11ro1ion. AMl!RICAN lJ.ISTT!lJTB 01' ST!'.!a COHS'ffiUCTION

BRACED FRAMES

5--388

L,., =

Because 0.60F11 A11v < 0.60FyAgv, from AISC Specification Equation J4-5: -..!

LRFD

"'

ASD

$Rn =¢(0.60FuA.i• + UbsF.,A,,,) =0.75[413 kips+ (l.0)(116 kips)] =397 kips> 374 kips o.k.

Rn

-=

'

5-65, is:

n

= [413l 261 kips

31/2 in.+ 2(3)(3 in.)tan30°

= 13.9 in.

The average unbraced length of the gusset plate, using the dimensions given in Figure

(0.6F.,A11v + u1>sF11An1)

n

S-389


10* in.+5 1h in.+rn in.

L=-------3 =6.04 in.

o.k.

"

Continuing with the assumed ~ in. thickness, the radius of gyration of the gusset plate is:

See Figure 5-65 for initial connection geometry.

l

r=

Check compre~ion buckling strength of the gusset

Jfi

3A in.

As can be seen in Figure 5-65, the width of the Whitmore section is:

=

I

..i~

.Jfi

= 0.217 in.

Using a column effective Jenglh fa~tor of 0.65 from AlSC Specification Commentary Table

C-A-7.1:

KL 0.65(6.04 in.) = r 0.217 in.

-

11

=18.1

,.

With KL/r ~ 25, AlSC Specification Section J4.4(a) applies and Fer = F1 . The design strength of the gusset is determined as follows:

~

.

·.·

brace

(Spec. Eq. J4-6)

Pn =Fc,Ag ::::: SO ksi(l3.9 in.)(-'.A in.)

~

I/)

I

\

=521 kips

I

;...

ASD

LRFD :=

¢Pn = 0.90(521 kips) 1'-10"


o.lc.

R,. 521 kips -= 1.67 n

=312 kips> 261 kips

o.k.

Use a 3,4-in.-thick gusset plate.

...·" ~-

W16x77

beam

W12x96 column

Select trial connection between gusset and brace Use a pair of bolted \VT-sections to connect the brace to the gusset plate. The flange width of the WT-sections must be less than or equal to the T·dimension of the W1 Ox112 brace (T

=7 h 1

in.). Try (2) WT8x28.5.

Fig. 5-65. Initial connection geometry for Exampl~ 5.4. 7. AMERICJ.N WS1TJV111 OP Sl'EL CONSTitUcnON

5-390

BRACED FRAMEs

A=< 8.39 in. fw::::

0.430 in.

d= 8.22 in.

b1=7.12 in.

=1.60 in.

y = 1.94 in.

ry

bi= 7.12 in.< Tbroa:::: 7 1h in.

=10.7 in.2 ~14.3 in.

2

=10.7 in.2

o.k.

The tensile rupture streng1b of the two WT-sections is:

From AISC Specification Equation 14-1, the tensile yielding strength of the two WT-

=65 ksi(l0.1 in.

2

)

=696 kips

(Spec. Eq. J4-l)

Rn =FyAg

(Spec. Eq. J+2)

R,.=F.,~

sections is:

I"

= 50 ksi(2)(8.39 in. 2 )

ASD

LRFD

= 839 kips

Rn 696 kips - =

~Rn= 0.75(696 kips)

LRFD

=522 kips> 374 kips

ASD

n

o.k.

2.00 348 kips> 261 kips

=

o.k.

R,, 839 kips -=

~Rn = 0.90(839 kips)

I

= 0.784( l.3.6'in. 2 ) s 0.85(2)(8.39 in. 2 )

9" = 0.715 in.

Check tensile yielding strength of WT~sections (for the required strength of the brace considered as a tension force)


5-391

"' =UAn S 0.85A1

From AISC Manual Table 1-8, the geometric properties of a Wf8x28.5 are: 2

5.4 ECCENTRICA.UY BRACED FRAMES

Q

o.k.

~.

1.67


o.k.

Check tensile rupture strength of the WT-sections

Check compressive strength of the WT-sections Tue unbraced length of each WT is 5 1h in., measured from the last bolt on the brace to the first bolt on the gusset plate, as shown in Figure 5-65. The effective slenderness rati? is:

KL

Assume that all bolts will be 1-in.-diameter A325-N bolts. The net area of the two WTsections is:

1~:

0.65(5'h in.)

- = - -- --'-

r,

1.60 in.

=2.23

A,,= 2(A8 -2dhff)

=218.39 in.

2

Wilh KL/r S 25, AJSC Specification Section J4.4(a) applies and Fer= Fy. The nominal com-

' is: pressive strength of the two WT-section~

-2(JIJ\6 in.+ IJ\6 in.)(0.715 in.)j

= 13.6 in.2

P,,

Because the WT webs are not connected to the brace, an effective area of the WT-sections needs to be detennined. From AISC Specification Table D3. l with y for the WT-section, the shear lag factor is:

x::::

= FyAg =50 ksi(2)(8.39 in.2)

(Spec. Eq. J+6)

=839 kips ASD

LRFD

u =1--x 1

= 1-1.94 in. 3(3 in.)

'P" =0.90(839 kips) = 755 kips> 374 kips

P

839 kips l.67 = 502 kips > 261 kips

.

11 -=

o.k.

n

o.k.

= 0.784 Check bearing strength of the WT-sections Because the specified minimum tensile strength o f the WT-sections is equal to the specified minimum tensile strenglh of the gusset plate and the sum of the WT flange thicknesses is greater than the gusset plate thickness, the bearing strength of the WT~sections is adequate. ' AMERICAN l.HSTIT\TTll OP STEEL CoNSTIUJC'TlON

I'

:r

5-392

BRACED FRAMES

4'· ··

Check block shear rupture strength of the WT-sections Because the specified minimum tensile strength of the WT-sections js equal to the specified minimum tensile strength of the gusset plate and the shear and tensile areas of the WT flanges in block shear are each greater than the corresponding gusset areas, the block shear rupture scrength of the \VT-sections is adequate.

..

~

~·

:I -:. ·

5.4 ECCE.'ITRICALLY BRACED FRAMES

From AISC Specification Table 03.1, Case 2:

l

=1-~ 9.00 in.

Use (2) Wf8X28.5 co connect the brace web 10 the gusset plate. Use (8) 1-in.-diameter ASTM A325-N bolts in standard holes to connect the WT-sections to the gusset plate. Use a 3-in. spacing, 2-in. edge distance and 3'h-in. gage for the bolts.

=0.767 A,.= UA,,

=0.767(31.2 in.

Check bearing strength at bolt holes in the brace web Because the specified minimum tensile strength of the brace is equal to the specified minimum tensile strength of the gusset place and the brace web thickness is grea1er than the gusset plate thickness. the bearing strength of the brace web is adequate.

=23.9 in.

it'

Check tensile rupture strength of the brace

·!)....I •/

·::;

in.2)

= 1,550 kips

LRFD ¢Pn

Pn

=0.75(1,550 kips) = 1,160 kips> 374 kips

=32.9 in.2 -

I

ASD

-= o.k.

n

1,550 kips

2.00

=775 kips> 261 kips

o.k.

I

Use (8) 1-in.-diameter ASTM A325-N bolts in standard holes to connect the \VT-sections to the brace web. Use a 3-in. spacing, 2-in. edge distance and 31h-in. gage for the bolts.

A,,= A8 - 2(d,, + 1/16 in.)t,..

'"

(Spec. Eq. 02-2)

The iiei area of the brace is:

~·

~;,

)

2

=65 ksi(23.9

Check block shear rupture strength of the brace web Because the material strength of the brace is e.qual to the material strength of the gusset plate and the brace web thickness is greater than the gusset plate thickness, the block shear rupture strength of the brace web is adequate.

2

Pn = FuAr

"

ib ...

.

u =1--x

2(Jl/i6 in.+ 1/i6 in.)(0.755 in.)

::: 31.2 iu.2 To detennine lhe connection eccentricity for shear lag in a W-sbape connected by the web only, AISC Specification Commentary Figure C-03.1 reconunends !hat half of the flange and a portion of the web be treated as angle.

an

Conservatively ignoring the fillets, the distance from the web centerline to the centroid of the effective section is:

Determine gusset-to-beam and column connection interface forces · The forces at the gusset-to-beam and gusset-to-column interfaces are detennined using the geometry shown in Figure 5-65 and tli~ Uniform Force Method. It will be assumed th:u a 1-in. clip in the comer of the gusset will be necessary to clear a fillet weld on the top flange of the beam, and a ~-in.-thick bolted end-plate will be used to connect the gusset and beam to the column.

eb=8.25 in.

ec =6.35 in.

0=46.1°

a= Yi(22.0 in.-1 in.-* in.)+l in.+% in. = 11.8 in.

~ =lh(l7.5 in.-1 in.)+ Un. =9.25 in.

Using~=~. (from Manual Eq. 12- ·

ex=(~ +13)tan0-ec 0

=(8.25 jn. +9.25 in.)tan46.J -6.35 in.

=11.8 in.

BRACED FRAMES

5-394


Because
=J(o.+ec )2 + (13 +eb ) 2

(Manual Eq. 13-6)

:::)(1 1.8 in.+ 6.35 in.)2 + (9.25 in.+ 8.25 in} =25.2 in. The forces on the gusset-to-beam and gusset-to-column interface are: LRFD From AISC Manual Equation 13-4: Vkb

eb

=-P.,

r 8 25 · '.n.(374 kips) 25.2 ill.

ASD

=

= 122 kips

=85.4 kips

13 Vue =-P., r

From AISC Manual Equation 13-5: a Hut> =-P,;

From AISC Manual Equation 13-2: Vac

9 25 = · '."· {374 kips) 25.2m. == 137 kips

=~Po r

=1.1.8 in. (374 lcips) 25.2in. =175 kips From AISC Manual Equation 13-3:

e,, r

Huc=-Pu

6 35 = · in. (374 kips) 25.2 in. = 94.2 kips

137 kips

I. +175kips 122 kips (a) Connection interface forces for Example 5.4.7 (LRFD)

9 = ·25 in. (261 kips) 25.2in. 95.8 bps

=


a

'

r

+ 9 4.2kips

eb Vab =-Pa

r 8 25 = · in.(261 kips) 25.2in.


l:


Hab =-Po

r

=~(261ki s) 25.2 in. p r

=122 kips

1.


+65.Skips

ec

95.8 kips

Hoc =-P0

r

6 35 = · ~·(261 kips) 25.2m.. 65.8 kips

=

The connection interface forces are shown in Figure 5-66. It should be noted that lbe forces are for the brace in compression. For the purposes of this example, equal and opposite forces have been assumed for the brace in tension.

+122klps

85.4 kips (b) ConMction interface forces for Example 5.4.7 {ASDJ Fig. 5--06. Cor1J1ection interface forces for Example 5.4. 7.

5-396

BRACED FRAMES

5.4 ECCEN1RlCALLY BRACED fRAMES

Design the weld at the gusset-to-beam interface ~

....,,'• . . ...

Assuming a ·~-m.-thick eod-pla1c :i.nd 1-in. comer clip, the length of the weld connecting the gusset plate 10 the beam flange is: l..,

=22.0 in. - I in. -

~

ASD

LRFD

-1( Hob VIiii) (85.4 kips) =tan

0 =tan - i(V~b) -

0 = t3Jl

fi;J>

in.

=20.4 in.

=l3n

_1

1 (l22kips)

122 kips

175 kips

The s1resses al lhe gussel-t<>-beam interface arc:

= 35.0°

=34.9°

LRFD

fov=-

I,.,

I..,

_ 175 kips 20.4 in.

,,'·

= 8.58 kip/in.

Vw1> .fua=I.,

filler weld !'i7c for two lines of weld is:

= 122 kips 20.4 m. = 5.98 kiprw.

LRFD

Vab

Dm;,,=

loo=/,.,

= 122 kips 20.4 in.

85.4 kips 20.4 in.

= 5.98 kip/in.

::: 4.19 kip/in.

J,,, = J1;., +I~

far=

,\lSC Specification Section J2A allows an increase in !he available strength of fillet weld' when the angle of loading is not along the weld longitudinal axis. Using AISC Manuc. ' Equations 8·2a and 8-2b in conjunction with AJSC Specification Equation 12-5. the requireo

Hab

f,,.,=H""

" ----. «~::::J

ASD

-

ASD

13.1 kipfm. 2(1.392 kip/in.)

x( I .0+0.50sin

15

I

9.13 kip/in.

D,.,,, = 2(0.928 kip/in.)

x(1.0 + 0.50sin

34.9°)

1

i j

35.0°)

.... 4.04 sixteenths

= 3.87 sixtet>nths

From AJSC Specification Table 12.4, the minimum weld size is •A in.

Jf;,, +/}a

Use double sided Yi<>-in. fillet welds to connect the gusset plate to the beam.

=J(8.58 kiplin.)2 + (5.98 kiplin.)2

= J(5.98 kiplin.}2 +(4.19 lcipfin.)2

= 10.5 kip/in.

= 7.30 kip/in.

Check gusset rupture at weld The shear rupture strength of the gusset is:

Multiplying by the weld ductility factor of 1.25 discussed in Pan 13 of the AISC Mon11al, the required strength per inch of weld is:

LRFD fur= 1.25{10.5 kip/in.) = 13.l kipflll.

h.:l·· I~

$

<·

;

;.:

...,. :~

1

\

Rn

=0.60(65 ksi)('A in.)

for= 1.25(7.30 kip/in.}

The resultant load angle with respect to the JongjtudinaJ ax.is of the weld group is:

(Spec. Eq. J4.

= 29 .3 kiplin.

ASD

=9.13 kip/in.

=0.60F.,A,,.

LRFD ¢R,, =0.75(29.3 k:ipfm.) = 22.0 kip/in.> 13.l kip/in.

ASD

R"

29.3 kipfm.

-=--~-

o.k.

n

2.00

=14.7 kip/in.> 9. 13 lcipfm.

o.k.

Check yielding of the gusset The sberu- yielding ~trength of the gusset plate is:

R,.

=0.6F1 Ar -0.6F1 d..,

(Spec. Eq.;

5-398

BRACED FRA..\fES

I..

~

R,,/l...,::: 0.6(50 .ksi)(3A in.)

=22.5 kip/in. LRFD Rn

o.k.

22.5 kip/in.

n

1.50 15.0 kipfID. > 9.13 kip/in.

=

..

.

o.k.

With the 'centrold of the compressive force applied less than d (the beam depth) from the member end, and lb is the length of bearing, the web local yielding available strength is detennined as follows:

(Spec. Eq. Jt0-3)

aa -

=94.2 kips

-

=1.00(530 kips) = 530 kips > Vuq

R

530 kips

11 -:;;;;

=122 kips

Q

o.k.

16.5 in. ::::3.99 kip/in.

= J(8.30 k.ip/in.)2 +(5.71 kip/in.)

=Jf ;.,, +/!, =J(5.Sl kip/io.)2 +(3.99 kiplin.)2

=10.1 lcipfm.

= 7.05 kip/in.

for

=85.4 kips

o.k.

r::·'

(Spec. Eq. Jt0-4)

0 55 20 = (0.80)(0.455 in.)2[1+3( .4 16.5 m. 0.760 m..

~)( .4 ~·Ju]

29,000(50 ksi)(0.760 in.) 0.455 in.

LRFD

ASD

::::: 526 kips>

vub =122 kips

o.k.

n

l

f..,. = 1.25(10.l kip/in.)

701 kips 2.00 351 kips > Vob

=

=85.4 kips

I

I

o.k.

.;.

t

far= 1.25(7.05 kip/in.)

=8.81 kip/in.

The load angle with respect to the longitudinal axis of the weld group is:

~-----L-RFD-.------...------;~-S-D-----~I I

(#oc). (65.8 kips) 95.8 kips

0= tafl~l . Voe .

.

t

ASD

LRFD

=701 kips

$R,. =0.75(701 kips) ·

..·.·

Multiplying by the weld ductility factor of 1.25 discussed in Part 13 of the AISC Manual, the required strength per inch of weld is: ·

= 12. 6 lcip/in.

R..

I

1.50

= 353 kips> Vab

Check beam web local crippling With the centroid of rhe compressive force applied greater than d/2 .from the beam end. the web local crippling available strength is detennined as follows:

,r~ tJ

l..,. 65.8.kips

:::::.

16.5 in.

2

ASD

!

f;. _Hae

HM<:

!110=l..,

fur= )fJv + JJa

LRFD

R, = oso.; l+

-

=5.71 k:ip/in.

=530 kips

$R11

VM

fav=lw 95.8 kips 16.5 in. =5.81 kip/in.

137 kips 16.5 in. = 8.30 kip/in.

.

=Fy.,.,,t!V(2.5kdes +lb) =50 ksi(0.4S5 in.)[2.5(1.16 in.)+ 20.4 in.J

..

Vue I....,

fuv=-

Check beam web local yielding ·

R,.

ASD

LR.FD

R,,

-=

= 22.5 kip/in.> 13.1 ldp/in. ..

Design the weld between the gusset and the end plate fTom Figure 5-65, the length of weld is L7.5 in. Subtracting the 1-in. clip in the gu~set plate, the length of weld is 16.5 in. The forces on the gusset per unit length arc:

ASD

=1.00(22.5 kip/jn.)

5"-39

5.4 ECCENTRlCALLY BRACED FRAMES

=tan-1

=34.5°

(94.2 kips)

=tan- I

137 kips

=34.5°

!

IJ;

l

AISC Specification Sectfon 12.4 allows an increase in the available strength of fillet welu when the angle of loading is not along the weld longitudinal axis. Us.ing AISC Manur :.

-

11 BRACED FRAMES

f

~

s..

Equations 8-2a and 8-2b in conjunction with AJSC Specification Equation 12·5, lhe required fillet weld size for two lines of weld is:

LRFD D . =

-

'

J

12.6 kip/in.

The minimum double-sided fillet weld size required to develop the vertical force through the

beam web T -dimension is:

r

2(1.392 kipfm.)

D~

- -12(0.928 kiplio.) = 3.91 sixteenths

From AISC Specification Table 12.4, the minimum weld size is 'A in. Therefore, a doubl~ sided IA-in. fillet weld js required at the gusset-to-end plate connection. For ease of fabrication, use the maximum required weld size of che gusseHo·end plate connection and the beam-to-end plate connection.

Use the gusset shear rupture strength previously determined for the gusse t-to-beam interface.

o.k.

si.x~nths

:::: 4.51 sixteenths

Use a ¥!G·in. double-sided fillet weld to connect the beam web to I.he end plate. Also use a ~6-in. double-sided fillet weld to connect the gusset to the end plate.

Check beam web rupture strength at weld

~ = 14.7 kip/in.> 8.81 kip/in.

(Spec.

Rn ""0.60FuA..v =0.60(65 ksi)(0.455 in.){13 A in.) =235 kips

l -:·l ·

ASD

Rn =22.5 lcipfm. > 12.6 Jcip/jn.

o.k.

~ =15.0 kip/in. > 8.81 kip/in.

o.k.

n

2.00

::::: 118 kips > 111 kips

Design the weld between the beam flanges and the end plate The horizontal force com'ponent is the m:Wmum of tbe following three load conditions~

1. The amplified collector force from Figure 5-63 (Conditipn I). o.k.

Design the weld between the beam and the end plate Frorn Figures 5-63 and 5-66, lhe vertical force component at the beam-to-end plate inter· face is: ·

.

Vub + vub
=122 lcips + 36.5 kips

=159 kips

ASD Vob+Va1>eam =85.4 k.ips+25.1 kips = 111 kips

o..k.

'

LRFD

LRF.D

I

.

Rn= 235 kips

=176 kips> 159 kips

u~e the gusset shear yielding strength previously determined for the gusset-to-beam interface.

I

ASD ..

LRFD

o.k.

Check yielding of the gusset at gusset-to-end plate

LRFD

Eq. J4-4)

1

$Rn =0.75(235 kips)

~i

l ll kips 2(0.928 kip/in.){J3 1A in.)

A o/i11-in. weld size is the minimum required by AISC Specification Table J2.4 for the W16xn web and %-in.-lhick gusset plate.

ASD

¢R., =22.5 kip/in.> 12.6 kip/in.

D "?:.

2(1.392 kiplin.)(13\4 in.)

The shear rupture strength of the beam web is:

Check gusset rupture at gusset-to-end plate weld

LRFD

159 kips

=4.31

x(t.o+ 0.50sinu 34.5°)

= 3.73 si.xteenlhs

ASD

LRFD

8.81 kip/in.

D . _

.>40J

5..1 ECCENTRJCALLY BRACED FRAMES

ASD

x{t.0+0.50sinu 34.5°)

·1:1 s.~II

7

HJ)

ASD

=85.4 kips

2. The axial force in the beam outside the link corresponding to 1.25RyVn - H 0 , where lhe force in lhe beam outside the link corresponding to l.25RyVn is shown in Figur~ 5-63.

ASD

LRFD H,, =355 kips-175 kips =180 kips

Ha =248 kips-122 kips

=126 kips

I

BRACED FRAMES

3. Hue or lfuc: The hori.wntal component at the gusscf.lo-colurnn rntcrface from the Uniform Force Method, calculated previously for Condition l. LRFD

ASO

5.4 r:CCENTIUCAJ..LY BIV\CED FRM'1ES

Design end-plate bolts Try seven rows of two 1-in.-diameter ASTM A32S-N bolts at 3 51h-io. gage. Use four bolls adjacent to each beam flange and an additional three b.,-,hs on each side of the gusset platr as shown in Figwc 5-67. Assuming the total shear is shared equally among all bolts (refer to Figure 5-63), the required shear force per boll is:

Hu= 94.2 kips

LRFD

ASD

137 kips+l22 kips-36.5 kip~ 14 bolts

95.8 kips+ 85.4 kips - 25. 1 kips = 14 bolts

=

Therefore, the required horizontal strength of the beam-to--column connection is H., I80 ldps and H,, 126 kips. as provided by the second condition. Assuming that the horizontal force is transferred by the be4lm flanges, the force in each flruige is:

=

I.RFD

Ra

if:::::

=

ASD

2

2

=63.0 kips

= 90.0 kips

Using the full beam flange width and the direcrional strength increase for a transversely loaded fillet weld. the minimum required single-sided fillet weld size to develop the tlange force is: LRFD D~

=I I .2 kips/bolt

=15.9 kips/bolt

Rat = 126 kips

180 kips

n1>

n1>

ct, brace

ASD

90.0 kips 1.5(1.392 iciplin.)(L0.3 in.)

D~

=4.18 sixteenths

63.0 kips 1.5(0.928 kiplin.)(10.3 in.)

= 4.39 sixteenths brace

A ~-i n. weld size is the minimum required by AJSC Specification Table J2.4 for the thinner part joined-the 'ti-in. end plate.

Use single-sided

~6-in.

fillet welds to C?nnect the be3m flanges to the end plate.

Check beam flange rupture at weld

1·-10·

The tension rupture strength of the beam flange is: (Spec. Eq. 14-2)

Rn= FMA, =FMbflf

= 65 ksi(0.760 in.)(10.3 in.) =509 lc.ips

W12x96

w1sxn

LR.fD

ASD R,, = 509 kips

~Rn= 0.75(509

kips) = 382 kips > 90.0 kips

beam

o.k.

n

2.00

= 255 kips> 63.0 kips

o.k.

Fig. 5-67. End-plate geometry for Example 5.4.7.

column

..

If

BRACED FRMIE.S

S.4 ECCENTRICAU. Y BRACRJ) FRAMES

~~

I

From AISC Specification Table J 3.2 for Group A bolts with the threads not excluded, F,,, = 90 lsi and FlfV 54 ksi. From AISC Manual T:ible 7-1, the area of a l -in.-diameter bolt 1s 0.785 in. 2 Based on the required shear force per bolt, the nominal tensile strength of each bolt subject to combined tension and shear rupture, from AISC Specification Equation J3-3, is:

~

1 ·~ ~.

It;lL

~·.

LRFD

.;-·

ASD

~

F;, =J 3F111 -

~

~'

Fru

~F,.v

Irv $Fru

F.' ,.,

OF111 =1.3F"' ---Irv $ F,,,

(.

_ fa•

126 kip~

ISO kips

r"'=--· 8 bolts = 15.8 kips/bolt

r. - - - ~I - 8 bo)ts

=22.5 kips/bolt < ¢r.:i

=4U kips

o.k.

7 < ~1

n

-

27 .2 kips

I o.k.

I I

I

When the brace is in tension. a tensile force is transmitted across the gussel to column interface. Assuming the four rows of bolts adjacent to the gusset plate transfer the tensile load,

I l;

I J!· ~.

.

JN =!:::!.

•

Ab

,,.- Al>

=15.9 kips/bolt

-

0.185 in.2

t;

::a ·:... ,.;. ~

t

Fn¥

ASD

LRFD

=

~·

,.;: <'

=20.3 ksi

l) .2 kips/boll

F,;, ;

!

[JM<

r.,, = n 94.2 kips

1.3(90 ksi) 2.00(90 ksi) 04 _3 ksi) 54 ksi 69.3 ksi s 90 ksi

90 ksi (20.3 ksi) 0.75(54 ksi)

=

=71.9 hi $ 90 ksi

= 8 bolts =11 .8 kipqj)olt < ¢r/, =42.3 kips 1

111 ...... t ..~ =i· !·

Use F,;,

~

f:..

The available tensile strength of each bolt is, from AlSC Specification Equation J3-2:

LRFD

....

.. I

~r,., - ~F.:,Ao

•I

H. & ~

,...

. ;; ~4

~

1:

=0.75(7 1.9 ksj)(0.785

=42.3 kips

_ 65.8 kjps - 8 bolts

o.k.

=8.23 kip!'Jbolt < r;,,1n =27.2 kips

o.k.

Use F.:, = 69.3 ksi .

71.9 ksi.

-,·

ASD

LRFD

0.785 in.2

=14.3 ksi

F;, " l.3(90 ksi) -

the required ten~ile force per boh is:

ASD

in.2)

.

'

Tnr F,:,Ao -:&-n n

= (69.3 ksi)(0.785 in . 2 ) 2.00 =27.2 kips

Select end-plate thickness Part 9 of the AISC Manual will be used to account for lhe effects of prying :iction on the bolts. Since the bolts are used to resist combined shear and tension, the available tensile s trength per bolt used in the prying action calculations will be taken as calculated previously. with a reduction to include tlle effects of shear streSs . The two locations that need to be investigated for prying :iction :\re at the bolls adjacent to the gusset plate and the bolts adjacent to each beam flange. The controlling condition for prying action in tllis case is for the bolts adjacent to the beam flanges when the brace is in compress.ion. Using lhe dimensions shown in Figure 5-67, ao 11-in. end-plate width, and smn
When tl1e brace is in compression, a tensile force is transmitted across lhe beam-to-column interface. Assuming the four bolts adjacent to each beam flange transfer the tensile load. the required tensiJe force per bolt is:

b = S'hin.-'A in. 2 = 2.38 in. b'=b- d& 2

2 38 .tn. -LOO in. .... --2-

=1.88 in.

5.4 ECCENTRlCALLY BRACED FRAMES DRACEP FRAMES

a=

11.0

in.-5~

2

=2.75 in.

a'=a+ ~

t1nm

~(l.25b+ d;)

(Maual Eq. 9 -27)

= 2 .75 10.+ · LOO in. < · ) + l .OO in. _ l .25(2.38 m. 2 2 3.25 in.!> 3.48

= =

[ !l4r41 b'

4r"'b' $pF., (1+00')

lttrin

= pF., (1+ &t') = / 1.67(4)(12.5 kips}(l.88 in.) 4.32 in.(65 ksi)lt + o.754 (1.0)J

4(17.8 kjps}( l.88 in.) {°.90(4.32 in.)(65 ksi)}

\ x{l + 0.754( 1.0)]

= Use a =3.25 in.

=0.565 in.

::;0.550 in. Try a 'h-in.-thick end plate.

The 1riburazy length, p, as shown in AISC Manual Figure 9-4, for the bollS adjacent to the flanges will be limited by b. For the lower flange, edge distance will also affect the tributary length for the bottom bolls. The average value for pat the lower flange is: p=

ASD

LRFD

in.

Check bearing strength of end plate From AISC Manual Table 7-4, the minimum spacing required to achieve full bearin ' strength for 1-in.-diameter bolts is 3Yi6 in. Using.1he small~st bolt spacing on t~e cn_d pl (4'h in.) and ASTM A572 Grade 50 plate, the available be.anng strength at each mtenor b , is (given in the row noted as s ~ S/111/ ): "·

l:·

2(2.38 in.)+2.38 in.+I.5 in.

2

= 4.32 in.

'-------L_RFD _ _ _ _ _ _-+-______ A_so_ __ _ __ I·;

d'= 11116 in. d' 0 = 1- p =1_ Jl.116 in. 4.32 in.

(Maual Eq. 9-24)

~ = 78.0 kip/in.(% in.)

¢r11 =117 kipfm.(* in.) = 73.1 Jcips > 15.9 kips/bolt

=0.754

= 48.8 kips > 11.2 kips/bolt

f:

Conservatively using AISC Manual Table 7-5 with an edge distance equal to I \4 in .. available bearing strength at each edge bolt is:

b'

(Maual Eq. 9-26)

p =a'

LRFD

ASD

1.88 in.

=-3.25 in. =0.578

~

¢r11 = 42.0 kipfm.(* in.) = 26.3 kips> 15.9 kips/bolt

=28.0 kip/in.(% in.) =17 .5 kips> 1l.2 kips/bolt


LRFD

~= '

·~,

!(

I

0,

( 42.3 lcips 17.8 kips.

=2.38 Because ~ > 1, a: Equation 9-23:

i)

1 ( 27.2 ·kips 0.578 12.5 kips

=

... I

Because the available strength of each boll is greater than the required shear strength pc.": bolt, the bearing strength of the end plate is adequate. ·

",•:

~ =_l_(~-1) P Or

$r,;, - 1)

P rut

=0.578

ASD

1)

=2.03

=1.0. The minimum required end-plate thickness is, from AlSC Manual

Check bearing strength of column flange Since the column flange thickness is greater than the end-plate thicknes~ and the end pfr ·I. and column have the same specified minimum censile strength, the bearing strength of column flange is adequate. ·:

f.

Use seven rows of two 1-in.·di:.uneter ASTM A325-N bolts at a Slh in. gage. Use four be' adjacent to e:icb beam flange and an additional ch.rec bolrs on each side of the gusset p as shown in Figure 5-68. •.1 A.'JEIUCAN

1"'smVrn OF

STEEL C ONSTI\UCltON

.......-,vu

v

':· ~~'

5.4 E
'~

Check shear yielding strength of the end plate

=2(0.60)FyAgv Rnll =2(0.60)F)'t Rn

ASD

LRFD

111e available shear yielding strength of the end plate is determined as follows:

(from Spec. Eq. J4-3)

= 2(0.60)(50 ksi)(Ys in.)

Rn

37.!'i kip/in. 1.50 ::: 25.0 kip/in.

-=

¢Rn = 1.00(37.5 kip/in.) =37 .5 Jcipfm.

n

This is greater than the required strength at both the beam and gusset connections to the em~ plate. Therefore, the available end plate shear yielding strength is adequate.

=37.5 kip/in.

Check end plate rupture at beam web weld (16) 1" dia. A32S...N bolts in std. holes @3Wgage

....., ..

..."

WT8x28.5 A992 each side of brace web

Th~ available shear ruprure strength of the end plate at the beam web weld is detennin~

as follows:

•,'

(from Spec. Eq. 14-4)

R,.. = 2{0.60) Fu An• = 2(0.60)FuT1>tamt = 2(0.60)(65 ksi)(l3 1A in.)(~ in.)

=646 kips i:I

f•.. J .,

W10x112 brace

ASD

LRFD R.,

¢R1t =0.75(646 kips)

n

=485 kips > Vub + V~ =159 kips

PL~·

646kips 2.00 =323 kips

-=

> Vab + V<>beam = 111 kips

o.k.

o.k.

(A572 Gr. 50)

Check end-plate rupture at beam flange weld The tensile rupture strength of the end plate at each beam flange weld is: (fiom Spec. Eq. J4.;•

R1t =FuA.: =F..,tb1

= 65 ksi(* in.)(I0.3 in.) W12x96 W16x77 beam

= 418 kips

column (14) 1"dia.A325-N bolts .@ 517" gage

Fig. 5-68. Connection designed in Example 5.4.7.

i

ASD

~R,. = 0.75(418

icorumn PL %"x11 "X3'-2" (A572 Gr. 50)

LRFD

!----------------!---------------, ' R,. 418 kips kips) = 314 kips > 90.0 kips

-=

o.k.

n

. 2.00 = 209 kips > 63.0 kips

o.k.

BRACED FRAMES

5-410

~,

5.4 ECCENTRICALLY BRACED FRAMES·

This available strength can conservatively be applied to check concentrated forces from ti gusset plate, since 1his gusset has.a longer beating length.

Check end-plate shear rupture at bolt line The total height of the end plate is 38.0 in., as shown in Figure 5-68. The available shear rupture strength of the end plate at the bolt li.ne is detennined as follows:

t

=37.7 in.2 R,, ::::: 0.60FuAn

0

I

o.k.

>Hoc

(Spec. Eq. 14-4)

=0.60(65 ksi)(37.7

in.

2

Check column web local crippling . ,.. With the centroid of the compressive force applied greater than d/2 from the column e1 where d is the column depth, the column web local crippling available strength adjacent !

)

=1,470 kips Rn

0.75(1,470 kips)

= l,470 kips

=1,100 kips

2

(lt>)(tw). d CJ

Rn ::=0.80tw 1+3

2.00

Q

determi~:d as fo~lows:

each beam flan,ge is

ASD

LRFD ~R,, =

R11

o.k.

'

..

· ASD

LRFD A,.= 2(% in.)[38.0 in. - 7(1Yi6in.+ 1/\6 in.)]

=735 kips

~~

JEF,...,t1 -,,.,-

(Spec.

in.)(0.550 in.)i.s] )2l1+3 (0.760 12.7 in. 0.900 in.

= 0.80(0.550 in.

The total required shear strength of the end plate is:

Eq. JlO--" Iii

29,000 ksi(50)(0.9.00 in.) 0.550 in.

=405kips

LRFD Vu

..

=V,,c + Vub - Vubeotn =137 kips+ 122 kips =223 kips ..

1,100 kips >223 kips

ASD

36.5 kips

=


735 kips> 156 kips

(Spec. Eq. Il0-2)

R,, = Fywtw(Skt1t$+lt>)

o.k.

1''1

=227 kips

ASD

LRFD R,.

=1.00(227 kips)

-= o.k.

Q

OOD

·\

I

ASD

227 kips l.50 151 kips> 63.0 kips

=

I

ljR.

> H~

oJ<.

.

~ > H~

..

I.

o.!L '

Check prying action on column flange Tue prying action model found in theAISC Manual be.used to deteonine roinii: column flange thickness required to prevent flexural yielding of the flange. This flanf,... . ,; thicker than the end plale, which was previously determined to have adequate thickness .

fJ= 0.900 in.

th~

t

h

Therefore:

o.k.

t

~-----------+-------------:-

c~

=(50 ksi)(0.550 in.)[5(1.50 in.)+ 0.760 in.]

=227 kips > 90.0 kips

= 203 kips> 63.0 kips

This available strength can conservatively be applied t6 check concentrated forces from gusset plate, since this gusset has a-l~nger bearing length. .

Check.column web local yielding . The centroid of the compressive force is applied at a distance greater than the column depth, d. Therefore, adjacent to each beam flange, the column web local yielding available strength, with Zt> taken as the beam flange thickness, is detemlined as follows:

~R,,

oJt.

o.k.

Use a % in. x 11 in. end plate.

..

t

R,. 405 kips -= Q 2.00

~Rn= 0.75(405 kips)

= 156 kips .

o.k.

ASD

LRFD

Va = Vac + Vab - Vat>cam 95.8 kips+ 85.4 kips- 25.l kips

o.k.

J'

l,,, l

5-412

BRACED FRAMES

5.5 BUCKLING-RESTRAINED BRACED FRAMES

Check column web panel zone shear •.\ I •.

!•

... . :. (

I

The maximum shear in the column is equal to the gusset-to-column force, Hue (LRFD) or Hae (ASD). Using lhe required axial compressive strength of the column based on I.he sum of !be strain-hardened expected yield strengths of the liol-s ac the third and fourth le\·efs as determined in Example 5.4.5, Pr= 867 kips (LRFD) or P, 615 kips (ASD).

=

'::· ~

LRFD P, - =

Pc

ASD

867 kips

P, 615 kips - = Pc 0.60(50 ksi)(28.2

50 ksi(28.2 in.2)

=0.615

~)

(Spec. Eq. Jl()..10)

LRFD

ASD

$Rn= 0.90(0.60)(5Q.ksi)(l2.7 in.)

x(0.550 in.)(1.4- 0.615)


~ = 0.60(50 k.si)(l2.7 in.) x(0.550 ui.)(1.4 -0.727)11.67

o.k.

= 8-t.4 kips > 65.8 kips

o.k.

Check rotational ductility of the beam-to-column connection

~1 ~-

,

AlSC Seismic Provisions Section F3.6b includes requirements for beam-to-column connectio~ a~ the location of a brace connection. This example uses option (a), a simple connection whi~ ts capable of providing the reqµired rotation. The method for determining rotational du~ty of a tee stub connection presented by Thomron (1997) will be used. This is :i gen· eralized fonn of the rot11tional ductility check fot a tee stub connection found in Part 9 of !he A!SC Manual. Thornton (1997) presents the minimum bolt dfameter, db, required to develop the si-?1ple beam end rotation as: 2

dt> =0.8921 F-,s[b

Fib L2

+2)

where · t =end-plate thickness =~ in. F, = specified rnirlimum yield stress of the end plate = 50 .ksi P, =tensile strength of the bolt 120 ksi s bolt spacing= 38 in./7 rows= 5.43 in. (average) b = 2.38 in., as previously dete1mined for prying action L = depth of connection element= 38 in.

=

=

J20 ksi(2.38 in.) (38.0 in)2

=0.769 in. The 1-in.-d.iameter bolts use.
5.5 BUCKLING-RESTRAINED BRACED FRAMES (BRBF)

in.2)

=0.727

Rn =0.60Fydctw[l.4-

2

in..) 50 ksi(5.43 in.) f(2.38 in.) + 2 ]

The final connection design and geometry is shown in Figure 5·68.

Fro~ AISC S~ecificaJi.on Section Jl0.6 wilh ~ > 0.4:

------.ti:?

db::: 0 _892('n

Buckling-restrained braced frame (BRBF) systems are a special class of concentrically braced frames addressed in AISC Seismic Provisions Section F4. Like other concentrically braced frames, BRBF systems resist laceral forces and displacements primarily through the axial sttcngth and stiffness of the brace members. The centerlines of BRBP framing members which meet at a common joint (braces, columns and beams) coincide or nearly coincide, forming a vertical truss capable of being derailed to minimize the effects of flexure. BRBP systems have more ductility and energy dissipation capability than other types of concentrically braced frames [?ecause overall buckling of the buckling-restrained brace (BRB) is preclude.d at forces and, deformations corresponding to the design story drift. Buckling-resrrained braces are characterized by their ability to yield in compression as well as in tension. This is accomplished by separating the actions ofresisring ax.ial loads an-J resiscing global buckling. AISC Seismic; Provisions Commentary Figure C-F4. l illustrates the components of a BRB. Global buckling of the brace is resisted by the BRB casing, which is typically a square or round HSS section, and can be sized as needed for th.is requirement. Axial te11sion and compression loads in the brace are resisted by the BR:B core which con· sists of a shaped plate, in either a flat or crocifonn section, sized as required by the AISC Seismic Provisions. Because both the casing and I.be core are sized° independently, che brae< strength can be fine-tuned, eliminating much of the overstrength that other braced frame systems impart to I.be structure. Because buckling of the BRB c~re is restrained to very small amplitudes, I.be core achieves the same, or greater, · strength in compression as in tension. This behavior is repeatable throughout multiple loading cycles without the occurrence of brace bucklin~ (and the consequent degradation associated with it), dissi pating high levels of energy and resulting in a highly ductile system. This uniform. predictable behavior eJ.im.lnates the lateral-force-distribution reqµ.irement that exists for SCBF systems (AlSC Seismi, Provisions Section F2.4a) where the percentage of braces in a given line that 'm ay be in tension at one time is limited. Buckling-restrained braced frame systems tend to be cost-competitive and often mor~ economical than SMF, EBF and SCBF systems in terms of material, fabrication and erection costs. Similar to SCBF systems, BRBF systems may have reduced flex.ibHity in floor-pl:in Lilyout, space planning, and electrical and mechanical routing as a result of thtprescncc of braces. In certain circumst3Jlces, however, the frames arc exposed and featun in the architecture of the building. AlSC Seismic Provisio11s Section F4.5a requires that btlam and column members BRBF systems satisfy the requirements for highly ductile me~bers. Section F4.6c ~! requires that BRB connections be designed for 1.1 times the adjusted brace sttcng:'

BRACED FRAMES

5-414

compression to ensure that they can withstand the maximum forces that the braces can deliver, including the effec!S of s1rain-harderung beyond the degree corresponding to lhe calculated drift. These requirements are intended ro re.suit in a system wilh braces that maintain a high level of ductility and hysteretic damping when subjected to severe seismic forces while ensuring that the connecting elements remain essentially elastic allowing the BRB to be the energy dissipating member in the system. V-type and inverted V-type BRBF systems are required to meet the additional cri1eria given in AISC Seismic Provisions Section F4.4a. These requirements include: (1)

B~~.

connections and _their supporting members must be designed for gravity dead and live loads, assuming the bracing proVides no 'support. (2) Beams intersected by braces must be designed for the vertical and horizontal u.nbalanced loads resulting fro.m the effects of adjusted grace strengths in compre~siom and tension. (3) Beams must be continuous between columns. (4) Beams must be braced to satisfy the requirements fo( moder.u.ely ductile mernbers in accordance with AISC Seismic Provisions Section D l .2(a).

•.

'·

Because the adjusted brace compression and tension forces are nearly equal, the verticai unbalanced load on the beam is minimal. The available compressive strength of the BRB is greater than the available ten~ile strength by an amount equal io (~ - 1) times the adjusted brace strength; where · ~ is the compression strength adjustmenr factor d1scussed in AJSC Sei~mic Provisio{1s Secti.o n F4.2. The vertical cgmponent of this difference in force is the Un.b alanced foad tbat will be developed. Brace configurations tbatutilize a two-story X-configurari9n may tiii've even lower vnbalanced forces at the beam. Coli.lmns in BRBF systems, like beams, are required to meet the requirements for h:ighly ductile members. Accordiflg to AlSC Seismic Provisions Section F4.6d, column splices are · requi,red to develop at least 50% of the lesser available flexural strength of the connected members and to have a reqmred. shear strength equal to LMpcfHc (LRFD) or LMpcf(l.5Hc) (ASD). This requirement is identical ·to that for SCBF systems and is intended to account for the possibility of the columns sharing some of the lateral force demand through frame action -as lhe brace elements deform inelastically, deflecting the frames beyond what elastic calculations might predict. . Buckling-restrained braces are required to be deSigned based upon results from qualifying cyclic tests in accordance with the requirements of AISC Sei.rmic Provisions Sei;tion K3. Qualifying tests must consist of at least two successful cyclic tests. One of these tests must be a suba.sSemblage test that 1ncludes rotational demandi at the ends of the BRB. The second test may be either a UDiaxial test or a subassemblage test. Qualifying tests may be done specifically for a project or may consist of previous tests documented elsewhere. Contract documents should include requirements for testing of tl:ie ·braces ronforming to the AISC Seismic ProvisiOns. .'Tiris reqliirement demonstrates to the contractor that this is a specialty item an~ cannot simply be fabricated by a typical steel contra<-:tor, but must be procured by a company that has conducted the necessary testing lO qualify the braces. Testing of each brace type is required to confirm !hat the brace design concept meets the requirements ro be considered a buckljng-restrained brace. It is also performed to determine the load ranges acceptable for a g~ven brace design: In most systems, member sizes are selected from a labJe of discrete values. Io this way lhe yielding members are selected to meet the minimum strength requirements, and material AM!:l\JCAN lNsTITUTS OF S-rea Col"STRUCTION

T'

5.5 BUCKUNG-RE.STRAlNEO BRACED FRAMES

variability is addressed through use of the Ry factor for the design of conneelions and adj

I

cent members. Buckling-restrained braces, however, are manufactured to match the project requiremeri and the yielding area can be precisely de.fined. The details of the br:ice design, such as tJ., area and·tenglh of the yielding zone, can be runed considering the yield stress of the core ma1erial. However, during the design phase the yield stress ·of the core material is not .knov precisely, although an acceptable range ma::r be specified. This range should be st1fficieni wide 10 perm:i1 a reasonable procurement process for brace manufacturers. The ;:<1nge of to 46 ksi is the de facto industry standard; typically the engineer defines this range by spe ifying the minimum and maximum core material yield stress (Fymin and Fymax)- Complian with these limits is verified by the brace manufacturer through coupon tests of the materi to be used in cbe fabrication of the brace. The engineer may account for this material variability in one of two ways: the area-based or the strength-based approach. The area-based approach is the more common approach for designing BRBF systems. ::: the area-based approach, the engineer defines the core area; the brace strength is define by the core area and yield stress. The engineer uses the lower bound yield stress, Fy mi•,, f, choosing the core area of the brace. Once this area is established, the upper bound yi t J. stress, FymP1sc llJ Py,JQ, or the nominal strength, Pysc·) The engineer should spe~ify an acceptable range (e._ ·· for LRFD, ~Pysc = 500 kips+ 25 kips/- 0 kips) and should use the upper bound for desi. of connections and adjacent members (factoring up _as de~~ribed previo~sl>: to account. strain hardening and compression overstrength). ThJS 25 Kips tolerance is roughly equ1 Jent to the ~.; in.l tolerance recommended for the area-based approach. Tili.s method allc the manufacturer to set the brace area provided to adjust for the measured yield stress of · core material so that Pysc is obtained as the yield capacity of the brace. If Pysc is establisl J using yield stress determined from a coupon test, the Ry factor is not applied. Brace stiffo js estimated in the design based on the area from an assumed yield stress in the middle 1 the specified range and the applicable adjustment factor as described previously. Wit,. strength-based approach, sliffness must be specified explicitly (in kip/in.) on the der drawings with a specified tolerance. Tb.is 1olerance is typica.lly ± 10%. That range, bowe

I

l

I

j

AMERJCAN lNS11TUTB OF STE.EL CONSTRUcnOI"

.'r \.

..'

i l

I,

,," H !~:

·-'..d :~

<

~-1 '•

~

5-416

DRACEO FRAMES

is insufficient to cover both' the adjustments implied by the range of core yield stress (± 10%) and the differing details and proportioning used by different manufacturers. Thus for material stress at lhe extremes of the permitted range, lhe manufacturer may need to make adjustments in the core length (along with other derails such as the core area outside lhe yieldin g zone) in order 10 maintain stiffness in the specified range of± I 0%. The details so configured must comply with the range of lhe brace tests. (For example. core strains must be calculated using the detailed core length and compared to values in the tests.) Such adjustments in the brace details would not be necessary if the specified range were increased to ± 20%, but this is not typical practice. In the strength-based approach, therefore, the material variability becomes a variability in stiffness and may also limit the applicabili ty of tests to a smaller range. Ths is a consequence Of the overall variability implied by the tolerances commonly used in this method. While it is theoretically possible to specify precisely the strength required in the strength-based approach, it is nonetheless preferable to allow a reasonable tolerance (rypically 25 kips) in order to permit the manufacturer to use ~-in. dimensions; precision beyond this is not warranted given the methods used lo establish yield stress. Table 5-4 s ummarizes how the area-based and strength-based approaches address the effect of material variability on the strength and ·Stiffness of buckling-restrained braces. It should be noted that both the elastic stiffness and the first yield strength (both necessary properties for use in code-based seismic design) are transient propertjes in lhe actual seismic response of systems; these properties change significantly as drifts exceed the drift corresponding to first yield. Designers should not perform bounding analyses or otherwise place undue emphasis on the effects of variability beyond accounting for maximum brace forces in the design of connections, beams and columns. Such variability in stiffness is r outinely (and ju~tly) neglected in the seismic desigi.J. of many systems and is minimal in the context of the use of elastic methods to represent inelastic response. Brace strength is_ controlled by brace core area, but the use of this core area in the structural model without any adjustment will not correctly capture the stiffness of the brace. Overall brace stiffness includes contnoutions from not only the yielding core, but also from the nonyielding portions of the brace and connection materials. This stiffness is usually captured in the model through the use of a stiffness modification factor, K.F. The modeled brace stiffness would then be represented by the following equation:

!·

'

(5-1)

.,...

where Ase is the steel core area, Eis the modulus of elasticity, and L,.p•.,p is the work pointto-work point distance along .the axis of the brace. The modeled brace stiffness can also be represented as a sprin.g with a defined stiffness, Km<>
•,

~·

:~

..;,, ., J


I

Table 5-4

1

Summary of Variability in the Area-Based and Strength-Based Approaches

iI

Method

Strength Valiability

Stiffness variability

Implicit, 48 ksi/38 ksl 1.2 (+20%/--0%)

Engine!:r·specified,

Engineer-specified, typically s 5% (+5%/-0%)

Engineer-specified, lypicalty ±10%

I

I I

I I

Area-based appcoach

Strength-based approach

I

typicatty :!:1()%

'

I ..)

As buckling-restrained braces are typically provided by a specialty manufacturer who designs the details of the brace (such as sizing the casing, determining the details of the tr:msitions between yielding and nonyielding zones, etc.), the design proce;;s may be slightly different from that of other systems in that it idea~y involves input from brace manufacru::ers during the design process. The manufacturer typically proposes certain details of lhe brace connection. It is ofte-: com·enient for the engineer to delegate certain parts of the connection design to the manufacturer, such as the connection of the brace to !he gusset plate. Tue engineer must explicitl y identify :my such delegated design, and review !he corresponding calculations with the brace submittal. The following design process illus~tes the inferactioa-betw,een the engineer of recorr~ ('EOR) and the manufacrurer. I. Preliminary design phase.

(a) EOR determines base shear, frame layout, etc. (b} EOR sizes braces (required core :trea or required strength).

(c) EOR assumes brace stiffness factors, KF, and overstreogth factors, p and ro. preliminary consultation with the manufacturer may be helpful at this stage.)

(

(d) EOR sizes beams and columns. (e) EOR checks drift.

(f) EOR estimates brace deformations. 2. Consulration with manufacrurer(s). EOR consults with manufacturer for: (a) Sufficient applicable testing the brace sizes proposed

for

(b) Stiffness of braces or stiffness factors; KF, ·used in the EOR's analysis (c) Overstrength factors ~ and

(I)

used in the EOR's design of beams and columns.

3. Design iteration. EOR reanalyzes (as required by change in member size or change : · stiffness factors, etc.). (a) EOR finalizes br.lcc sizes, benm and column sizes, brace stiffness factors and b:~ defonnations. (b) EOR consults wit.b the brace manufacturer if the brace sizes or defonnation , substantially different than the preJjmi.nary design.

5-418

BRACED FRAMES

4. Specification. EOR specifies: (a) Required brace sizes (C-Ore area or required strength), with tolerance (b}'Miniriium and maximum core material yield stress (c) Overstrepgth factors ~and
5. Brace submittal. (a) "':Manufacturer submits: i. Brace shop drawings ii. Supporting documentation

stability design. AISC Specification Appendix 8 will be applied to apprdx.imate a secoodorder analysis. ·

Example 5.5.1. BRBF Brace Design Given: I:: Refer to Brace BRB-1 in Figure 5-70. Frame configuratjons and preliminary loads have been sent tu a BRB manufacturer and the elastic stiffness of the brae~ ~ave been found to 1.5 times higher than the stiffness of the yielding t;ote area alone, if lt were extended frc work point to work point (KF =Kaciua1IKc1>re =1.28). These stiffness factors may be used ·' : derenni.ne the horizomal load distribution on each story. Design a buckling-restrained brat:.: to resist the resulting axial loading, PQ. = 113 kips. The appl~cable building code specifies t use of ASCFJSEI 7 for calculation of loads. According to AJSC Seismic Provisions Secti 1: F4.3, buckling-restrained braces should ~ot ~ considered as resisting gravity forces.

'· -I

USing the area-based approach described previously~ allow for material variability of 42 J

± 4 ksi. Fysc min =

Fysc "!"" = 46 ksi

38 ksi

From an elastic analysis, the first-order interstory drift is /).H

=85 psf =68 psf

Lfowr

=80 psf (50 psf reduced)

S

=20 psf

3

2

The following examples illustrate the design of a BRBF based on AISC Seismic Provisions Section F4. The plan and elevation are shown in Figure 5-69 and Figure 5-70. · The lateral forces shown in Figure 5-70 are the seismic forces from an equivalent lateral force procedure of ASCEJSEI 7 Section 12.8 and apply to the entire frame. The code-specified gravity loading is as follows: .

30·-0·

30'-0"

=0.223 in. 5

4

1··

30'-0" ---...

30·-o·

'ill-:!

~~~------~~~~:I?l~~~~~~m

Curtain wall= I 75 lb/ft along building perimeter at every level

I :

BRBF Design Example Plan· and Elevation-

Dfloor

j·

L;

(a) Justifying ·appUcable tests (in tem1s of brace size, strain at rhe specified · displacements) . (b) Ov~rstrength factors, P and w (based on specffied displacements) (c) Brace stiffness ~lculations (d), Connecti_on design~ where delegated to brace manufacturer (b) Test reports.for sµbmitt,ed brace types and s4.es ., .. (c) EOR verifies compliance. with specification

Dn:x>f

~ I.

S.S BUCKLING-RESTRA1NED .BRACED FRAMES

f;J

· ,

I j,

t

The applicable build4ig code specifies. the use of ASCEJSEI 7 .for calculation of loads. = 1.3, fe 1.0, Svs= 1.0, and Cd=5.0. The v~cal seismic load effect, Ev, according to ASCEJSEI 7 is:

From, ASC~SEI .7, the Seismic Design Category is D, p

0.2SvsD = 0.2(1.0)D =0.2D .

=


Assume that the ends of the diagopal braces are pinned and braced against translation for both the x-x and y-y axes. Th.e loads given for each exarople are from a first-order analysis. Assume that the effective length method of AISC Specificnrum Appendix 7 is used for the

BRBF investigated in Part 5.5 For elevatlon see Figure 5-70.

SMF investigated in Part 4. For elevation, see Figure 4-8.

Fi~; 5-69., Floor plan/or BRBF Examples,

J

5--420

Assume that the ends of the brace are pinned and braced against rranslatjon for bolh the x-x and y-y a;ces.

~

'• ~

"· ··

BRACED FRAME3

5-421

5.5 l>UCKLlNG-RESTRAJNED BRACED FRAMES

The required compressive and tensile strengths of the brace are:

I

f

' ' ~.

'•'•

ASD

LRFD

Solution: The governing load combiualions in ASCE/SEI 7 including seisrruc effec1s are:

.]

Pa =Ta =0.1pPQe

Pu =Tu =pPa,.

~RFD

LRFD Load C
ASD ASD Load Combinations 5 and 8 from ASCPJSEI 7 Section 12..4.2.3

=0.7(1.3)(113 kips) =J03 kips

=

1.3(113 kips) = 147 kips

Required Strength

( 1.2 + 0.2SDS)D + pQ~ + 0.5l + 0.2S

(1.0 + 0.14SDs)D + H + F + 0.1pQE

(0.9·- 0.2SDs)D + PQE + l.6H

(0.6 - 0.I4SDs)D + 0.1pQE + H

Consider second-order effects AJSC Specification Appendix 8 is used 10 address second-order effects. The required second-order a.tial strength is:

(Spec. ·Eq. A-~-2) For the calculation of Bz: &-

~..' J .

_ CJ.P,,r>ry 1 P4,,cry

(Spec. Eq. A-8·6)

i!I

To determine Ps10,,., use an area of 9.000 ft2 on each floor and the swtade gravity loads given in the BRBF Design faample Plan and Elevation section. Use load combinations that include seismic effects.

...,. ~ ~:

~;

~

'

LRFD Colu.mn splice 48"

[1.2 +0.2(1.0)l ..

above finished floor

(typ.)

I

r0+0.14(!.0)j

I,

•

x[68 psf + 3(~5 psf)J

PS1ory

P~=9,000 ft 2 +O psf + 0.5(3)(50 psf) .

r2+02(1.0)j + x(175 lb/ft(4)(390

.

x (l k:ipll,000 lb) = 5,160 kips

. ft)] 1

=9,000 ft

2

x[68 psf +_3_(85 psf)J + 0 psf + 0 psf + 0 psf

1I

-

.

r0+0.14(1.0)j

• + x{175 lb/ft(4){390 ft}] ' X(l kip/1,000 lb)

=3,630 kips

!•

..

1 ,•

'

AASJUCAN ~smvra OF S'l'l>& C~S'l"lcVCTI<>N

I

. ·I

The total story shear, H, with two bays of bracing in the direction under consideration wh each braced frame is designed to resist the seismic loads shown in Figure 5-70, is determ. in the following. From an elastic analysis, the fiISt-order interstory drift is An= 0.223 i.u.

Fig. 5-70. Frame elevation for BRBF examples.

i

i I

x(l lcip/1,000 lb)

+ 0.2(20 psf) x(l kip/1,000 lb)

..

ASD

5-422

S.S BUCKUNG-RFSrRAINED SRJ\O· n FRAMES

II = 2(54.0 kips+ 49.0 kips+ 32.0 kips+ I 6.0 kips) = 302 kips

LRFD

=14.0 ft R,, =l.O for braced frames

P,ll
.'\,c """ :;: ¢F,

=

LRFD

ASD Ct = 1.60

B2 =

P,!JU>ry

=

I I- 1.00(5,160 kips)

228,000 kips

I I- O.Psro2• Peno7

=

1

;:;:: J

I 1.60(3,630 ldps)

228,000 ldps

.

=1.03

= 1.02

Considering second-order effects, the required compressive and tensile sueng1hs of the brace are:

LRFD P11 =T,.

= 1.02(147 kips)

=150 lcips

38 ksi

= 4.66 in.2

Try a BRB with a core nrea, AK, of 4.50 in.1

Using AlSC Spwfication Equation A-8-6:

~ I

0 .90(38 ksi}

In design practice, either LRFD or ASD de~ign should be used consistently. The two methods give slightly different r~ulls here. In order not to show two separate designs. lhe LRFD result will be used.

=228,000 kips

I =I- a.Psro7

= 1.67(106 kips)

150 kips

= 4.39 in.2

(Spec. Eq. A-8-7)

0.223 in.{l ft/12 io.)

B2

Fy~"""

)'JC "")l

Hl =RJ.toH =l.O 302 kips(l4.0 ft)

ex = 1.00

'

nP. Ai.:..,.,,=---

P.

l

.

ASD

ASD

P,, =Ta

=1.03(103 kips) =106 kips

Determination of the brace area required 10 res.ist the required brnce strenglh must use the minimum yield of I.he e<>re material, F>·sc mm· For I.he limit stn1e of tensile or compressive yielding, set the required strength equal to AlSC Seismic Provisions Equation F4-l and solve for A..., min:

Note that while BRB manufacture.rs cun fabricate a BRB with the accuracy to which the core can be cut (generally± 118 in. in width) it is common to round the required core area up to standard increments. Generally. it is good practice to specify core areas in 0.25 in. 2 increments for 0 in.2 20.0 in, 2 (or mnin1aining increment amounts in the range of 5% to I0% of the total amoun1) When specifying BRB area greater than required. the EOR must account for the increased demand that I.be specified area will place on I.he structure, because the beams and columns

;:r::~~: ::1::~::: :::g:j;:;::eb~:t 0

::t:g:.tensile or compression

I;

~eldinl

':

is:

9Pn mu. =QF)sc """Ase

(Spec. Eq. D2- I 2

=0.90(38 ksi}(4.50 in. )

= 154 kips < 150 lups

o.k.

Verify with the brace manufacturer that the stiffness factor KF = 1.28 is acceptable for 4.50 in. 2 brace of this length. The remainder of the brace design is pe.rfonned by the BRB manufacturer. Overstrcngtb factors, and (J), along wirb the maximum defom.ialion capa bility of rhe brace, must be provided by the brace manufacturer in order 10 design th• 1 columns and beams of I.he BRBF and to detcnnine the BRB applicability to the design.

p

1·:

The final pan of the brace design is establishing the expected deformation of the brace an using this deformation to detemline forces that the brace imposes on the columns, beam and connections. AJSC Stismic Provisions S«:tion F4.2 requires considerntion of defonnations at the greater of 2% drift or two times the design story drift. ). The design story drift is defined in the AlSC Seismic Provisions Glossary as the calculate story drift including the effect of expected inelastic ac1ion. As given, the firstrorder interstory drift is liH = 0.223 in Thi! drift docs not include the redundancy factor, p. Nole th:-'

I

..

' ..-\;·

5-424

L

BRACED FRAMES

ASCE/SEI 7 Section 12.3.4.1 perm.its p to be taken equal to I for drift calculations. The design story drift including inelastic action is:

=5.0(0.223 in.)

'

=1.12 in.

,.:, .

I

I

(ASCE/SEI 7 Eq. 12.8- 15)

le

i; ...

i

1

A= Cdb.H

.

5-425

5.5 BUCJ
Determination of lhe strain and the yield length is typically performed by the brace manufacturer and is shown here for illustrative purposes only.

Consulting with the brace manufacturer, the ~ and ro factor~ corresponding to this level of strain are determined

10

be:

co= 1.36

1.0

~

Twice the story drift including inelastic action is: (I

·~

.

2A = 2(i.J2 in.) =2.24 in.

:

=1.1

Alternatively, according to AISC Seismic Provisions Section F4.3 and ASCE/SEI 7 Chapter 16, brace deformation is pennltted to be deicnnfoed from a nonlinear analysis in lieu of the expected deformation requirements in AISC Seismic Provisions Section F4.2 illustrated here.

2% drift corresponds to a deflection of:

i! ---.. $'t;-::i

Example 5.5.2. BRBF Column Design

!::>. =0.02H

=0.02(14.0 ft)

=0.280 ft !::>. =0.280 ft ( 12 in.II ft)

~11 >·

=: 3.36 in.

PD= 147 kips

In this case, 2% drift governs. The brace spans 14.0 ft vertically and 12.5 ft horiz.ontally. The brace deformation can be calculated to be: D.b,

=[J(14.0 ft) 2 +(12.5 ft+0.280 ft)2 -J(l4.0 ft) 2 +(12.5 ft) 2 J(l2 in.fl It) = 2.25 in.

PL= 60.0 kips

Ps = 7 .00 kips

Relevant seismic parameters are given in the BRBF Design Example Plan and Elevation Section.

The brace core areas are as indicated in Figure 5-71 (BR.B X.X indicates a brace with a core area of X.X in.') AJlow for BRB core material variability of 42 ksi ± 4 ksi (Fysc min = 38 ksi. F}-sc nuu 46 ksi). The brace manufacturer bas provided the given oversttength factors. From AJSC Seismic Provisions Section F4.2~ the factor Ry need not be _applied if P)sc(= F1$c:) i!' determined from a coupon test, as is \ he ca'se here. Therefore, Ry wiU not be shown in the examples in Section 5.5.

=

Consulting with the brace manufacturer, the yield length for this brace is determined to be 70% of the work-point length.

..L.,

Given: Refer to Column CL-1 in the frnme shown in Figure 5·70. Select an ASTM A992 wide· flange section to resist the following axial loading between lhe base and the second level The applicable building code, specifies the use of ASCE/SEI 7 for calcul:ition of loads.

"?.·o.n

(() = 1.36

~ = 1.1

==o.1J(14.o n)2+(12.s ft)2 (1.2 m.11 ft) Solution:

=158 in.

From AlSC Manual Table 2-4, the material properties are as follows: The strain is. therefore:

ASTMA992 F-, = 50 ksi F,, 65 ksi

6br

(,

> \•

..

~:

e=L.,

=

2.25 in. 158 in. = 1.42%

=---

According to AISC Seismic Provisions Section F4.3, the required strength of columns dl lo the applied seismic load, P£.,, is based on the adjusted strengths of the braces i:i · frame, where adjusted strength is defined in AISC Seismic Provisions Section F4.2a. Use t'" specified Ase and Fymax to determine the brace forces in the design of the column to aeco1~·

AMERICAJ'f JJ.IS1TIVT6 OF S'rm. CoNSTIUJCTlON

BRACED FRAMES


5-42. I.

for material variability. Starting at the lower· braces, the adjusted brace strengths for the braces contributing to the load on Column CL-1 in compression are:

=l3coA.sc2 Fysc ma.:c =1.1(1.36)(3.75 in.2 )(46 ksi) =258 kips ~roPysc max3 =13
- '.J

'The a.xia.I compressive force,

PE,,.,., is then determined from the force diagrain of the column,

as shown in Figure 5-72. 'The vertical force on the column fron~ the braces' adjusted strength is:

} )
f.

=401 kips

(

The vertical component of the force from the tension brace on the beam will be I· ©Pysc max sin 0 and the vertical component of the force from the compression brace on ~: the beam will be ro!3Py.rc max sin 0. The net sum of these forces, whjch act in opposite ., directions, is wBPysc ma.:c sin El - roPysc max sin El Cl3- l) roPysc max sin El, with half of this force reacting at each end of the beam. Thus the force due to beam shears resulting frorc unbalanced brace-induced vertical forces is:

= l.1~1.36)(3.o~·in. )(46 ksi) 2

=

=.206 kips , ~ffiPysc max4 = 13roAsc4 Fysc max

= 1.1 (l.36)(1.50 in.2 J(~6 ksi) = 103 kips

t ~(j3-1)wPysc-maxJ>1nS4

Yi(~ -1 )(J)P,_max 4sin0,

~

.

'~ ~··

. .;:

Roof

12·-e· · 1·

.; .. .·· !

Yi-.c-mex3 sin03

· 1

co
~

><

.... N

1 •;;_

T

. '<

0

~

Yil> -1}©Py~in0 2

Fourth Level .•".· ~

....~

...·~·

}'2(13 -1 )o>P~-mllltisin01

Third Level :;.

~ N

~

~p~,

P•P~~,

YiH~ - 1~roPyso-max3sinOa

~(13 - 1 )roP ysc.max2sin02

~

~P,_,0,

/

~

1

..

~

,~ ~roP~

Secood

'•

/ 1~· / ,~ / \

~(13 - 1)~P~·xiSinO..

j3roP~~rl ~

Level

..,.-·b

~·

~.;l'

Fig. 5-72. BRBF cp/umn forces for _Example 5.5.2.

Base

Fig. 5-71. Frame elevation for BRBF examples with member sizes. AMmlJCAN

lNSJTIVT2 OP Sms., CONSTkllCTlON

AMERICAN I Nsrrnm; OF Sn;a CONSTRUCTION

.l ;:

..

f

5-428

I

1·0

5.5 Ot:C KUNG-RESTRAINED BRACED FRAMES

..

L 'h(JJ-l)CllP~...,... sin9 = 'h(~ - l}roF;x-.. L, A.., ~in0 ='h(l.1 -1)(1.36)(46 ksi) (1.so in.2 )(sin45.0°) +(3.00 in. 2 )(i:in45.0°) x

.

l.

ll

.

+(3.75 in. 2 )(sin45.0°) +(4.50 in.2 )(sin48.2°)

•.

::-.

Using the load combinations in A SCEJSEJ 7 th:11 include the amplified seism.1c load. v.h.rre the 1.unphficd seismic load is ~ubsliluted \\-ith the analysis described in AlSC Seisi·•ic Provisions Section F4.3, the required compresshe force in lhe column is: LR.FD

LRfD Load Combination 5 from ASCEJSEI 7 Section 12.4.3.2 (including the 0.5 factor on L pennitted in Section 12.4.3.2)

= 28.7 kips P11

Sec Example 5.5.3 for calculation of vertical unbalanced forces from 1he braces on the beam.

ASD ASD Lo3d Combination S from ASCE/SEI 7Se.:tion 12.4.3.2

=(l .2 + 0.2SDs )PD+ Pe.+ O.SPL_

P{j =(l.0+0.J4SDS)Po +Pt1 +Pp

+ 0.2Ps

+ 0.1Pe""

=1.14(147 kips)+ 0 kips+ 0 kips

={12+0.2(1.0)j(l47 kips)+372 kips

! i,,..J '·

The rota! axial rompression in the column due to the braces is: f>F....,.

=401kips-28.7 kips

'

+ 0.5(60.0 kips)+ 0.2(700 kips)

I

+ 0_7(372 kips)

=428 kips

-= 609 kips

= 372 kips

The required a:.d on Column CL-I in lcn~ion :>.re:

2

=1.36(3.75 in. )(46 ksi)

=235 kips

LRFD Load Combmation 7 from ASCEJSEI 7 Section 12A.3.2

lllDA

1

=1.36(1.50 in.2 )C46 ksi)

!;

=93.8 kips

,l

.

.. ., "

The force doe to the adjusted brace strength is:

LCl>~·scmar sin9 =(235 kips+ 188 kips+ 93.8 .lcips)(sin45°) = 365 k:ips

:•

ASD Load Combination 8 from ASCEJSEI 7 Section 12.4.3.2

From lbe calculktion for !he c-0lumn in compression, the force on the column due to brnceinduced beam shear Is 28.7 kips. The tocal axial iension in I.be column due to the braces is: Te.,.::: 365 kips+ 28.7 kips c 394 kips

Po =(0.6-0. l4Svs)Pv t-0.7PeM\ +Pu

=[0.9-0-2(1.0)](147 kips)

=[0.6-0.14(1.0))(147 kips)

+(-394kips)+1.6(0 kips) ::: -29 1 kips

=-208 kips

= 188 kips

=OlA1c'4F.>1c

-

Pu-. (0.9-0.2Sos )PD+ Pe... -+ l.6PH

=l.36(3.00 in.2 )(46 ksi) Pyzc mox4

ASD

LR.FD

+ 0.7(-394 kips)-+ 0 kips

'

Consider second-order effects Because the seismic component of the beam required strength comes from the mechanism analysis of AISC Seismic Provisions Section F4.3 and is based on the expected strengths of the braces, P-tl effects need not be e-0nsjdeml and 8 2 from AISC Specification Appeodh need not be applied. P-t. effect.S llo not ~ the forces ~ponding to the expcclet. brace strengths in compression and lenSiQJl; instead, Ibey may be thought of as contributin;~ to the system reaching that state. P-S effeels do apply; but because the column does 001 haw moments, there is no need co calculate 8 1 factors. Try a W10x68.

From AlSC Manual Table 1-1, the geometric properties are as follows: A"" 19.9 in.2

1f =0.770 in. Sx "'75.7 in.3

d"' 10.4 in. rx::: 4.44 in. hit,.,-= 16.7

1.,.::: 0.470 in.

r1

=2.59 in.

b112fJ= 6.58

l>f = 10.l in. Z. = 85.3 in. 3

5.5 13UCKLlNG·RESTRAINED BRACED FRAMES

5-430

Width-to-Thickness Limitations According to AJSC Seismic Provisions Section F4.5a, the stiffened and unstitTencd e!Cmeni~ of columns must comply with the width-t
From Table 1-3 in th.is Manual, the W10x68 satisfies the width-to-thickness requirements for a BRBF column.

Mo= 120 ki(>'"ft

The brace core areas are as indicated on Figure 5- 71. (BRB X.X indicates a brace with a C• area of X.X in.2) Allow for BRB co.re material variability of 42 ksi ± 4 ksi (Fy;c min= 38 ~ Fysc max= 46 ksi). The brace manufacrurer has provided the given oversrrength factors: (I)::::

~=I.I

1.36

Solution: From AlSC Manual Table 2-4, lhe material properties are:

\


From AISC Specification Section Cl.2 and Appendix 7, Sectjon 7.2.I, the effective length method is limited to conditions in which lhe strucrure supports gravity loads primarily through nominally vertical columns, walls or frames and the ratio of maximum second-order drift to maximum first-order drift in all stories is equal to or less than 1.5. Assume both conditions are met for BRBF systems. K LOfor both the x-x and y-y axes. Since the unbraced length is the same for boih axes, use the least radius of gyration. From AISC Manual Table 4-1, the available compressive strength for a W1 Ox68 with KL 14 fl is:

=

=

LRFD

4>cP,, : : : 658 kips > 609 kips

Vt= 8.50 kips

Vo= l l.2 kips

~:::: 438 kips> 428 kips f.1.c

F1 =50 ksi Fu"" 65 ksi

t·

Use the specified A:c and Fysc ma< to determine the brace forces in the design of the beam 1 account for material variability. Required Strength

ASD o.k.

ASTMA992

o.k.

betermire the adjusted brace strength of the tensipn : . ' . ,·Brace BRB-1 .. ;

(l)i\,cF1scmox

=1.36(4.50 io.2 )(46 ksi)

· =282 kips Available Tensile Strength

From AJSC Manual Table 5-1, the av:UJable strength of the W1 Ox68 column in a:
91Pn

=896 kips> 291 kips

Determine the adjusted brace strength of the compression Brace BRB-1

~roAscFyscmax = l.l(l.36)(4.50 in.2 )(46 ksi)

ASD o.k..

P,, = 596 ldps > 208 kips

n,

=310kips o.k.

Use a W1 Ox68 for Column CL-L Verify with 1he BRB manufacturer that the stiffness and overstrength factors are still applicable for the final bay geometry. Verify that the ratio of second-order drift to first-order driftjs less than or equal to 1.5.

Example 5.5.3. BRBF Beam Design t

'

..

Given:

Refer to Beam BM-1 in Figure 5-70. Select a ooocoroposite ASTM A992 wide-flange section (the beam may ~constructed as a composite member, but for simplicity it is designed as a noncomposite beam). Assume that lbe bottom flange of the beam is latera.lly hr.iced at its qunrter points. The applicable building code specifies the use of ASCEJSEI 7 for calculation of loi!ds. Relevant seismic parameters were given in the BRBF Design Example Plan and Elevation section. The gravity sb~ and moments on the beam are:

Determine the unbalanced vertical load on the beam The difference between the vertical components of the brace forces is: P1

={310 kips-282 kips)(sin 48.2°) =20.9 kips

Consequently, there is a 20.9-kip force acting upward on the beam. Determine the shear and moment in the beam due to the brace analysis

Assuming a simply supported beam:

-Py

=2 -20.9 kips 2 -10.5 kips

= =

t.

l·

·...r

5-432

BRACED FRAMES


~

..

-P L

1 ,\lfe,.,.=--

LRFD

4

-20.9 kips(25.0 ft)

:. I

4

=-13 1 kip-ft

ii

..

'

ASD



M., =(12+0.2Sos)Mo+ME..i, +0.5ML

Determine the axial force in the beam

The horizontal components of the _brace forces are:

Prx =282 kips( cos 48.2°)

= 188 kips Per= 310 kips( cos 48.2°) =207 kips

S-433

+0.2Ms

Ma= (1.0+0.l4Sos )Mo+ MH +MF +0.1ME"".

=1.4(120 kip-ft)+(-131 k.ip-ft) + 0.5(100 kip-ft)+ 0.2(0 kip-ft)

=87 .0 kip-ft

= 1.14(120 kip-ft)+O kip-ft

+ 0 kip·ft+0.7(-131 kip-ft) =45.l kip-ft

This required flexural strength is concurrent with the following required axial strength:

LRFD

f!·~· '

O,

f1 '·

These forces are delivered to the brace through axial forces in the beam-tension in the segment of lhe beam on one side of the midspan connection (braces-to-beam) and compression in tbe olher segment. The distribution of the toral horizontal force between tension and compression depends oi;i the load path and .tributary mass. Forces from collectors on each side of the frame may differ significantly based on the collector length and tributary width. The method presented for SCBF provides guidance. In this example, with a symmetrical brace configuration and symmetrical colJe.ctor conditions, the horizontal force may be assumed to be distributed evenly between the two segments of ~? ~.eam. •• R

E..i,:::

=__ 188 kips+ .:..___ 207 kips _,_

.

., ~

''·


Pu =(l.2+0.2Sos)Po +PE,.. +0.5PL +0.2Ps

=1..t(O kips)+ 198 kips

P,, =(1.0+0.l4SDS)Po+~1 t-P1.+ 0.1PE...

I

! l

=1.14(0 kips)+O kips+O kips

+ 0.5(0 kips)+ 0.2{0 kips) ::::198 kips

+ 0.7(198 kips}

=139 kips

The required flexuml strength according. to the analysis requirements of AISC Seismic Provisions Section F4.3 is also determined as/ollows:

2

LRFD

BR.BF beams and columns must be designed to resist all gravity loads. Using the load combinations in ASCE/SEI 7 that include the anlplified seismic load, where the amplified seismic load is substituted with the analysis described in AISC Seismic Pro~·isions Section F4.3, the required flexural strength of Beam BM-1 is:

'

l l


'

Pzx +Per 2

=198 kips

ASD

.

.

ASD

I I

LRFD Load Combination 7 from. ASCE/SEI 7 Section 12.4.3.2 M. =(0.9-0.2SDS}Mo+ME.,. +1.6MH

=0.7(120 kip-ft)+(-l31.kip-ft)+O =-47.0 kip-ft

!


Mo =(0.6-0.14Sos)Mo +0.1M£M +MH

=0.46(120 kip-ft) + 0.7(-131 kip-ft)+O = - 36.5 kip-ft

!

BRACED FR.AM.ES

5-434

5.5 BUCK.Ll.Nv·K.,t;) \KAIN ti.I

This required flexural s1reng1h is concurrent with the following required axial sttenglh:

.Ul'V\\...CLJ

rlV\;Vtc..)

.

ASD

LRFD _.l

ASD

LRFD

'

ASD Load Combination 8 from ASCE/SET 7 Seccion 12.4.3.2


Pu= (0.9-0.2SDs )PD+ Pe,..+ l.6P11

P,,

= 0.7(0kips)+198 k.ips+O kips

=(0.6-0.14Sos )Pv + 0.7 Pe,.,, +PH =0.46(0 kips)+0.7(198 kips) + 0 kips

= 198 kips

=139 lcips

Because the moment due 10 sejsmic forces counteracts the moment due to gravity load, it is important to also consider load combinations that do not include the seismic load. The required flexural strength of the beam for the governing load combination that does not include seismic load is:

ASD

LRFD Load Combination 2· from ASCFJSEI 7 Section 2.3.2

M.

. .

-

ASD Load Combination 2 from ASCFJSEI 7 Section 2.4. l

-

ASCFJSEI 7 Section 2.3.2 V.,

=l.2Vo + 1.6VL + 0.5(VL, or Vs or VR) =1.2(11.2 kips)+ 1.6(8.50 kips)

V0 =VD+VL

-

=11.2 kips+ 8.50 kips =l9.7 kips

+(O kip-ft)

·'

=27.0 kips Try a W16x50.

It is wonb noting lb at the unbalanced load resulting from the adjusted brace strength in tension and compression imparts an upward point load on the beam, acting in opposition 10 gravity forces. This is true regardless of the direction of eanhquake loading for an invertedV brace configuration, because the adjusted brace strength in compression is higher than the adjusted brace stTenglh in tension.

LRFD

ASD Load Combination 2 from ASCE/SEJ 7 Section 2.4.1


l:

From AISC Manual Table 1-1, the geometric properties are as follows: .4 = 14.7 in.2

c1 =0.630 in.

d= 16.3 in..

r...

k,u1 =1.03 in.

b112fJ= 5.61

b1 = 7.07 in. hit,.,= 37.4

rx= 6.68 in.

Z; = 92.0 in.3

=

Sx 81 .0 in.3 r1 =1.59 in.

4

Ix= 659 io.

ly = 37.2 in.'

=0.380 in .

f·

h0

=15.7 in.

J

=J .5'.~. in.

4

I

·

:~

•.

v

C,,. = 2,270 in.6 Width-to-Thickness Umitatioris According to AlSC Seismic Provisions Section F4.5a, beam members must satisfy the

requirements for highly ductile members stipulated in f\.ISC Seismic Proiisions Table DI. I

t;

From Table 1-3 of this Manual, a W16x50 satisfies the ductility requirements for beams in · BRBF systems.

.

= l.2Mv + 1.6ML

M.=MD+Mi

+0.5(Mi.. orM~ or MR)

=1.2(120 kip-ft)+l.6{100kip-ft)

=120kip-ft+100 kip-ft =220 kip-ft

+ 0.5(0 kip--ft) = 304 k.ip--ft

Available Flexural Strength (negative flexure) For negative flexure (bottom flange in compression), consider the bottom flange of the beam to be laterally braced at

L,,

_qu~er points.

1

I

=25.0 ft 4 =6.25 ft

Because dead and Jive loads do not result in axial forces in the beam, there is no axial load acting concurrently with this moment.

From AISC Manual Table 3-2, for a W16x50:

The required shear strength of the beam is shown in lbe following calculation. By inspection, because the unbalanced load from the braces always acts upward on the beam, tbe seismic component of the requi.red shear strength will always counteract the gravity shears. Therefore, the governing load combination is one that does not mclude seismic effects:

Therefore, lp < L11 ~ Lr, and lateral-torsional buck.hog applies. Conservauvely use C11 From AISC Manual Table 3-10, the available flexural strength (negative flexure) is:

Lp =5.62 ft

Lr:::: 17.2 ft

.

.

.

ASD

LRFD

t

=l.(J.. ·

~9-,,M-,.-=-33_S_k:i-.p--ft_>_l-4-7.-0-ki-.p--ft_l_o-.k.-r-~-:-==_2_2_5_ki_.p-_ft_>_l--3-6-.5-ki-.p---ft-1-o-.k.-

l:

JI

L_~~~~~~~~~~~~~~.L-~~~~~~~~~~~~~~ ~·

AMERICAN lJ.>SlITUT6 OF

STW.. CONST!l\JCTION

AMERICAN

lNS1'l1V11i OF S1"SE1. CoNSTJUJC'DON

I

l:

I

BRACE.O FRAMES

Available Flexural Strength (positive flexure)

::-·

'

LRFD

For posjtive flexure (top flange in compression), the beam can be considered fully braced by the slab. and therefore the limit state oflateral-torsiooal buckling docs not apply. From AJSC Manual Thble 3-6, the available flexural strength of a W16x50 is:

I

LRFD

ASD

=¢bMp

=345 k.ip-ft > 304 kip-ft ,> ~:,, •)

- - -- l r ·~~

o.k.

Mn M" -=n,, n,, =230 kip-ft> 220 kip-ft

=0.75

~br =n( 8~)

o.k.

The minimum BRB axial strength is:

LRFD

Available Compressive Strength As explained in Part 8 for collecto~. torsional buckling is considered because the torsional unbraced length 1s not the same as the minor-axis De'
For this puipose, assume first that the beam buckles and its midpoint moves upwards. Displacement compatibility will cause an increase in the demand on the BRB resisting tension due to lateral forces, while the load in the BRB resisting compression wilJ be reduced. Conversely, if the beam buckles and the mid1'oint moves downwards, lhe BRB in compression will experience a load increase while the BRB in tension will be relieved of some of its original load. lo both cases the BRB that is relieved of load will rebound along the path of its elastic stiffness.

If the strength and stiffness of the unloaded BR.B in e;icb of the 3forementioned cases meet lhe requirements of AlSC Specificarion Appeodut 6. Section 6.2.2., then the beam can be considered to be braced by the BRB at midspan. From AJSC Specification Equation A-6-3, the requjred sircnglb of nodal bracing is:

ASD

I.RFD Prb = O.OJP.,

Pri>=O.OIP,.

=0.01(198 kips) =1.98 ki~

=0.01(139 kips)

6Pn

=0.90(38 ksi)(4.50 m.2 )

_ 38 ksi( 4.50 in. 2 )

= 154 kips> 1.98 kips

-

A.'dElllCAN INsmvre OP Sn.a CoNSTRvcn<>N

!

1.67

=102!Ops>1.39 kips The elastic stiffne~s of the BRB adjusted by the ang.le of inclination. '"here KF = KocllWl• KC<'rw l .28 as gi\'en in Example is:

5.5. I,

=

J3.,.., =(KF)(

i" )sin0

29,000 ksi(4.50 in.2)

=l.28

1

(

)

sin48.2°

18.8 ft{l2 in./ft)

=552 kip/in.

'I

Nodal brncing requirements are met; tbcrcfurc, for the beam, KLi

=12.5 ft.

For flexural buckling about the y-y axis, lbc sfab braces the beam continuously, so KL,= 0 ft. For constrained-axis flc.~ural-torsional buckling. the unbraced length is the distance between bottom-flange braces, i.e., Kl-z = 6.25 0.

KLx

--= rx

1.0(12.5 ft)(l2 in./ft)

6.68 in.

= 22.5

KL,

=

ASD

=~F>teno,.AA.

:::: 1.39 kips

If the braces act as a braced point, the required stiffness of nodal br.tcing, from AlSC Specification Equation A-6-4 with L,, 12.5 ft, is:

I

=2. 8(139 kips) 001 (12.5 ft)(12 in./ft) =14.8 kip/in.

(12.5 ft)(12 in./ft)

;; 14.1 kip/in.

To determine lhe unbraced length for flexural buckling about the x-x axjs, it is necessary to verify whelher the BRB provide a brace.d point for the beam al midspan.

i.....ll

ASD

~br =i(8~) I l 8(198 kips) 1

~ ··

~i,M,.

5--1.

5.5 BUCKLING RESTRAINED BRACED fRA.1>,'IES

-;;=

1.0(0 ft)(l2 inJft) 1.59 in.

=O

5.5 BUCKLING-RESTRAINED BRACED f'RA!vfES

KL; = 1.0(6.25 f1){12 inJft)

r,

2

2

l.59 in.

F. '

=47.2

=!7t £!Cw+fy(d/ 2) 2 (K:L)

I

From AlSC Manual Table l-1 and AISC Specification Table B4.l, I.he web is slender for compression with Fy 50 Jcsi. Therefore, rhe reduction factor for slender stiffened elements.' Qa, must be detennined. Fust, determine the governing limit state.

=

=

Determine the critic81 buckling strength for flexural buckling about the x-x axis, assuming Q 1

=

j+GJ]I

I

6 n2{29 000 ksi)l2..270 in. +37.2

!

•

-

2

I,, +11 +(d/ 2) A1

l

(8·3)

2 in:'2 (16.3 in./2) ] ·( . 4)1 ' + 11,200 ksi 1.52 tn.

0.o(6.25 ft)(12 in./ft)J

x[ 659 in.'+ 37.2 in.' +;16.3 in./2)1 (14. 1 in.')I

The elastic buckling stress is:

=154 ksi (Spec. Eq. E3-4)

The value of F,, before locnl buckling effects are considered is detennined as foUows:

1

F1 - n 2 (29,000 ksi}

-

= 0.325

(22.5)2

=565 ksi The value of Fer before local buck.ling effects are considered is detemuned as follows: F1 F,

50 ksi

~ = ·154 ksi

= 50 ksi

I

(Sp«. Eq. E3·2'

565 ksi = 0.0885

Because 0.0885 < 2.25, use AISC Specification Equation E3-2 to determine the critical buckling stress.

(Spec. .Eq. E3-2)

.50 ksi =[ 0.658S6$ kli

l

Because 0.325 < 2.25, use AISC Specification Equation E3-2 to determine the critical buckling stress.

l

.so ksi. =[0.6581~ ksi

l

50 ks1

= 43.6 Ksi Because Fe~ is.lower for cons~ed-ax\s fle.'tural-Lorsional buckling, this limit state govern-.; over major ax1s flexural buckling. · Determine the reduction factor, Q, for slender elements To determine the reduction factor, Q. use.AJSC Specification Section E7.2;witb/=Fer an the minimum Fer from the two preceding limit st.ates. The reduced effective width of tl slender web is detennined as follows:

50 ksi

= 48.2 ks:i Determine the critical buckling strength for constrained-axis flexuraf-t9rslonal buckfing, assuming Q 1

=

For the. limit srotc of constrained-axis flexural-torsional buckling, lbe unbraced li:ngth is 6.25 ft and the top ~ge of the beam is considered continuously braced by the slab as described in Pnrt 8 of lhis Mnnual.

b=h

=d-2ki1u =16.3 in.-2(1.03 in.} =14.2 in.

1

I

l;:

I. "

BRACED FRAM[)$ ~

S-4-JI

5.5 Bl!Cl
.. f =Fer -= 43.6 ksi b,

I.RFD

=i.92,/f[1-cm~Jsb = 1. 92(0.380 in.) /29.000 ksi 43.6 ksi 14.4 in.

v

=

...

~~

'··'...

Because b, > b, use b,

(Spec. Eq. E7-17)

/i- 0.34

37.4

r.

345 kip-ft

Mrx -15. l kip-ft --= Ma 230 kip-ft =0.196

29.000 ksi I 43.6 ksi

For negati\'e moments (bottom flange in compreso:ion) due to .;eismic effects:

Therefore, from AlSC SpectjicaJion Equation E3-I, the available compressive strength of a W16x50 is:

LR.FD

Mn

47.0 kip-ft

Ma

338 kip-ft

Mn;

- = - ----'--

tle.~ure

Ma

values for interaction.

LRFD

ASD

ASD

8

,.,,

=577 kips

.:

~I i..

8

0.362+. (0.196+0) = 0.536

0.343 +-(0.252+0);::: 0.567

Pn 43.6ksi(l4.7in.2 ) -= 0.:1.67 =384 kips

+cP,. = 0.90(43.6 ksi)( l..S.7 in 2)

36.5 kip-ft 225 kip-fl =0.162

--=

=0.139 Use the positive

9

9

0.567<1.0

I

ASD

LRFD

= 14.2 in.

=

....'•

87.0 kip-ft

:0.252

Since b, h, there is no need to calculate the reduction factor and Fer is the minimum calculated for the two preceding limit states. Constrained-axis flexuraJ-ton;ional buckling governs .

f.:

Mn:

Ma

-o::

ASD

0.536 < LO

o.k.

o.k.

Available Shear Strength Combined Loading

From AISC Manual Table 3-2, th&available shear strength of lhe W16x50 is:

LRFD

,.. l

t.

;: (?

P,

ASO

\

198 Jcips 577 kips =0.343

P, = 139 kips Pc 384 kips

-= Pc

-

.,•J

:i.·.

~. V,.

8(M,, M,,)

P, -+- - + - S 1.0 Pc 9 M 0 Mey

I

1

I

o.lc.

~ =124 kjps > 19.7 lcips

nv

o.k.

Use a W16x50 for Beam BM-1. Verify with the BRB manufacturer that the stiffness and overstrcngth factors are still valid with the final bay geometry.

(Spec.

Eq. Hl-la)

Note that the maximum moment results from a load combination I.hat does not include seismic effects. This mornenl is not concurrent with axial force in the beam, because the ax.iaJ force is from seismic effeclS. Therefore, the maximum moment need no1 be considered in I.he combined loading check.

11 ,.

=186 kips > 27 .0 kips

= 0.362

Because P,IP, ~ 0.2, the beam-column design is contr0lled by the equation:

!'•

ASD

LRFD

Oetcnnine the moment ratio. For positive moments (lop flange in compression) due to sejsmic crrects:

Beam Bracing Requirements

From ATSC Seismic Provisions Section F4.4a(2), beams in V- wd invened V-braced frames should be braced to satisfy the requirements for moderately ductile members in Section Dl.2(a). AJSC Seismic Provisions Section Dl.2a(3) requires thal beam bracing in moder31ely ductile members have a maximwn spacing o f: lb= O. I 7r1 E/F1

=0. 17(1.59 in.)(29,000 ksi/50 ksi) =157 in.

(Provisions Eq. D 1-~

5--442

BRACED FRAMES

5.6 NONBlJILDtNG STRUCTURES: A SPECIAL CASE

5.6 NONBUILDING STRUCTURES: A SPECIAL CASE

Lb= 157 in.(l ft/12 in.)

=13.1 ft The bracing of the bottom flange at the quarter points of the beam (6.25 ft) satisfies th.is requirement.

Beam bracing requirements are given in AlSC Specifica1ion Appendix 6. The required strength of lateral nodal bracing is: (Spec. Eq. A-6-7)

Typical building structures have both in-plane and out-of-plane support at lhe location < bracing connections to columns. Jn nonbuilding structures, however, it is common to ha• ' multistory planar braced frames with in-plane support but no out-of-phlne support at intermediate locations where braces connect ·to 1he column. The AISC Seismic Provisi01 classifies this configuration as K-bracing due to the lack of out-of-plane support. Altboug K-bracing is not pennined for systems in the AISC Seismic Provisions, the steel ordinary concentrically braced frame designed to satisfy the AlSC Specification (using R l 1h per ASCE/SEI 7 Table 15.4-1) is pennitted.

=

where h0 15.7 in. Cd= 1.0

=

From Al SC Seismic Provisions Equation D1-1 , the required flexural strength to be used in AISC Specificacion Appendix 6 equations is:

LRFD M,

ASD

=R1F1 Z =1.1(50 ksi)(92.0 in.3 ) =5,060 kip-in.

M,

~

=RyF_.Z/1.5

=1.1(50 k-si)(92.0 in.3 )tJ.5 =3.370 kip-in.

From AlSC Specification Equation A--0-7, the required brace strengch is:

LRFD Pfb

ASD

=0.02M,C4 I h =0.02(5,060 kip-in.)( 1.0)/15.7 in.

1·

P,b = 0.02M,Cdlho

0

..

= 0.02(3,370 lcip-io.)(I .0)/15.7 in. = 4.29 kips

= 6.45 kips

'

I

1·

..~ From AJSC Sp.ecification Equation A-6-8, the required brace stiffness is:

LRFD

p = .!.( lOM,Cd) br ~ 4 h,,. _ 1 [ . 10(5,060 k:ip-in.)(1.0) - o.75 (6.25 ft.Xt2 ioJft)(l5.7 in.)

=57.3 kip/in.

,.

ASD

-

l

J3 =(IOM,Cd) br 4ho

=2.00[

10(3,370 lcip-in.)(1.0)° (6.25 ftX12 in./ft)(l5.7 in.)

.•.

t.

l

·'" 1·

::: 57 .2 kip/in.

i~·~·

Provide top and bottom flange beam bracing with these minimum strengths and stiffnesses at quaner points of the beam.

Ii:

... Al.WUCAN lNS1IIVIE OF S'tliEL CO.NS11\UCTION

....... !J

l l f

~

'

Thornton, WA. (1996), "The Effect of Eccentricity on Brace-to-Gusset Angle~ ... Engineering Jo11mal, AISC. Vol 33. No. 4, 4th Quarter, pp. 123-128.

PART 5 REFERENCES Ashaneh-Asl, A. (1998), "Seism.ic Behavior 31ld De.sign of Gusset Plates for Braced Frames;' Steel 1ips, Strucrural Steel Education Council, Moraga, CA.

AJSC (2011). Design Examples, VJ 4.0, American Institute of Steel Construction, Chicago: IL,

~v.aisc.org.

Dowswell, B. (2006), ''Effective Length Factors for Gusse1 Plate Buckling," Engineering Journal, AlSC, Vol. 43, No. 2, 2nd Quarter, pp. 91-101.

Dowswell, B. (2012), "Effective Length

"

Frames.~

Facto~

for

Gu~set

Plates in Che\'t'on BrawJ

Engineering Journal, AlSC, Vol 49, No. 3, 3rd Quarter, pp. 115-117.

El-Tayem, A. and Goel, S. (1986), ··Effective Length Factor for the Design of X-bracing Systems,~ E11gi11eering Journal. AISC, Vol. 23, No. l. lst Quarter, pp. 41-45. l

l~ ..

PART S RFFERF.NCf,5

BRACED Flv\MF.S

...

Thornton, W.A. (1997), "Strength and Ductility Requirements for Simple She:ir Connections With Shear and Axial Load:' NarioM.l Steel Construction Co11fcrenrt•

Proceedings, AISC, Chicago, IL Thomlon, W.A. and Muir, L.S. (2009), "Design of Vertical Bracing Connc<:tions for High· Seismic Drift," National Sreel Construction Conference Proceedings, AlSC, Chicago, U... Thornton, W.A. 3.Dd Fortney, P. (2012), "Satisfying Inelastic Rolation RequirementS for InPlane Critical Axis Brace Buckling for High-Seismic Design," Engineering Journal, AISC, Vol. 49, No. 3, 3rd Quarter, pp. 99-108. Thornton, W.A. and Lini, C. (2011), "How to Use I.he Wh.itrnore }.lelhod for Tension and Compression Strength Checks," .'>fodem Steel Cons1ructio11, July.

Engelhardi. MD. and Popov, E.P. (1989), ··Behavior of Long Links in Eccentrically Braced Frames," UCBIEERC - 89!01, Earthquake Engineering Research Center, University of California, Berkeley. CA . Gross, J.L (1990), "E.xperiment3l Study of Gus~e1ed Connections," Engineering Jounu1l, AJSC, Vol. 27, No. 3, 3rd Quarter, pp. 89-97.

Hewiu. C.~l. and Thornton, W.A. (2004), "Rationale Behind and Proper Applicalion of lhc DuctiHly Factor for Bracing Connections Subjected lO She:1r :ind Transver:oe Lo:iJing," Engineering Journal, AlSC, Vol. 41. No. I, Isl Quarter, pp. 3-6. Kotulka, B.A. (2007), "Analysis for a Design Guide on Gusset Plates Used in Special Concen1rically Braced Frames," M.S. Thesis, Department of Civil Engineering, University of Washington, SC
Lehman, D..E, Roeder, C.W., Hennan, D., Johnson S. and Kotulka, B. (2008), "Jmproved Seismic Performance of Gusset Plate Connections," Jounwl of Scmctural Engineering, Vol. 134, No. 6, pp. 890-901. ~·

Nair, S. (1997), "Practical Application of.Energy Methods 10 Structural Stability Problems." Engineering Journal, AlSC, Vol. 34. No. 4. 4lh Quarter, pp. 126-134.

Picard, A. and Beaulieu, 0. ( I 987), "Design of Diagonal Cross Bracings Part I: Theorelicsl Study." Engineering Journal, AlSC, Vol. 24, No. 3, 3rd Quarter, pp. 122-126. Richard, RM. (1986), "Analysis of Large Bracing Connection Designs for Heavy ConStruction.·· National Steel Con.rrruction Conference P1oceedings, AISC, pp. 31.13 1.24, Chicago, IL.

,,

,

)

I.

Roeder, C. W., Lumpkin, EJ. and Lehman, D.E. (2011 ), "A Balanced Design Procedure for Special Concentrically Braced· Frame Connections," Jo11mal of Omstructional Steel. Research, VoL 67, pp. 1,760-1,772.

SEAOC (2006), fBC S1ructural/Seim1ic Design Manual, Structurnl Engineers Association of California. S:icramento, CA Thornton, WA. (199 1), "On lhe Analysis and Design of Brocing Coooections," Na1iorn1/ Steel Construction Conference Procudings, AJSC, pp. 26.1-26.33, Chicago, IL

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PART6

I ' ~

COMP.OSITE .MOMENT. FRAMES

:

,. !

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. . ·.i· ... -.. : ··n

I'

6.1 SCOPE .............. . ........ : ................. . .......... : : ..... 6-2

~

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·:

1·

6.2 COMPOSITE ORDINARY MOMENT FRAMES (C-OMF) · · · · · · · ·.· · · · · · · · · 6Overview of Applicabl: ~esign Provisions ....... : ..... . ....... . ..... ... . 66.3 COMPOSITE INTERMEDIATE MOMENT FRAMES (C-IMF) ............. 6-

.:

~

' ':.

,..

Overview of Applicable Design ~~visions ..... ·..... . .. . . .. ·_. . .· : ... ..... .. 66.4 COMPOSITE SPECIAL MOMENT FRAMES (C-SMF) ... ...... .. .. . .. .. ... 6-

.

6.5 ::;:::::~~s:;;:·~~~;~~· · ··: ;:····· 6 I {C-PIUvIF) ........-.-.. , ....... ·" . .... . ........................ -'· ..... 6-11 Overvi.e{v of Applicable Desi~l>rovisions , . :·: -~:. :: ..... .. .... : . : ....... 6-P j 6.6 CONNECTION DESIGN '.. .· d ~

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6-.

Reinforced Concrete Column-to-Steel Beam Connections ......... , .... . .. . 6-1 Round Filled Com·posiie Colum.1Ho~Steel Beam Connections . . .. . . . ........ 6-

j

Rectangular FiUed Comp;site.Column-to-Steel Be_am Connections ......... ·: 6-'.

PART 6 REFERENCES .-.......... • ,,, ... . . .. . .. . ... " ... . .... .... : .. . ..... 6-::.

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•• "••I ,. AMERICAN lN$mVrE Of STE!?L CoNSTRUCTION

COMPOSrrE MOMENT FRAMES

6.1 SCOPE

f.

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..

The following 1ypes of composite moment fulmes are addressed in this Part: compo:<.lle ordinary moment frames, composite imennediate momenr frames, composite special moment frames, and composite partially restrained moment frameq, The AISC Sti.smic Provision-1 and other design considerations summarized in lhi~ Part apply to lhe design of the members and conn«tions in composite moment frames that require seismic detailing. AJSC Seismic Provisions Sections Al and B2 state that systems with reinforced concrete elementS that must be designed according to ACI 318 should be designed only by lhe load and resistan~ factor design (LRFD) method because AO 318 does not addre~s allowable strength design (ASD) .

FRAMES (C-OMF)

.,

.. ~· ,.

:·

Item

Note In Over.iew

1

Referenced Standards'

Se/$mic Prov.

Materials

Sects.~. I ,

A3.4 &A3.5

2

Struc;tsrat d8sigll drawings and speciflcations

Seismic Prov. Sects. M 1,

3

Loads 2lld toed comb«lations

StiSmie Prov. Sect 82

4

Required s1reng'Jl for structural memoors and connections

Seismic Prov. Seel 83.l

5

S1ructlnl anal'jSls

Seismic Prov. Ch. C

(a)

Elastic strlfneu or concrete/composite membefs

Commentary to Seismic Prov. Ch. C

6

ColutM membeB

AC! 318 (excl Cll. 21)

7

Beam memOOl's

ASCfJSEI 7 permits lhe use of C-OMF systems in Seismic Design Categories A and B only, as is the case for ordinary reinforced concrete moment frames. The u~e of C-OMF systems is limited because they can potentially invoh e the use of reinforced concrete columns or beams that are not designed or derailed to meet the seismic requfrementS of ACJ 318 Chapter 21.

8

Beam-to·CCllumn coonectloos

Seismic Prov. Seel 02

9

Column sprees

Seismic Prov. Seel 02.5

10

Column ba$eS

Seismic Prov. Sect. 02.6

11

Steel ~ stlJd anchofs oc ,;,-elded relnforciog bar anchors

Seismic Prov. Sect. 02 .S

12

Com~te slab diaphragms

Seismic Prov. Sect. 01 .5

Because C-OMF systems are limited ro Seismic Design C:uegories A and B, they are expected 10 withstand minimal inelastic drift through inelastic behavior of the composite beams, columns and panel zones. As a result, there are no requirements for: (i) ~tructural analysis; (ii) sysrcm configuration; and (iii) designing steel or compos11e members other tl1an those given in the AISC Specification and the applicable building code. There are no additional requirements for designing reinforced concrete members besides those provided in ACI 318, excluding Chapter 21.

Overview of Applicable Design Provisions An O\'erview of the applicable provisions of the AISC Seismic Provisions for the design of C-OMP systems follows and is presented in a simplified fonnal i n Table 6-1. All requiremenrs of the AlSC Specifi.ca1ion apply, unless stated otherwise in the AISC Seismic

No1e I. The structural sreel material used for C-OMF systems is limited by the requirements of AISC Seismic Prol'isions Section A3.l wllh the cxccprfon that 1he specified minimum yield stress of rhe steel for members in which inelastic behavior is expected is not to exceed 55 ksi. Thfa specified minimum yield srress can be exceeded when the suitability of the material is derennined by resting or 01her rational cri1eria. The concre1e and srecl rcinforccmenr is selec1ed to satisfy the requirements of AJSC Seismic ProvisioM Section A3.5. The weld filler metal

'

Simplified Overview of Provisions for C-OMF Systems

Compoime ordinary moment frame (C-OMF) systems consist of: (i) composite or reinforced concrete columns; (ii) structural steel. concrete-encased composite, or composite beams; and (iii) fully restrained connections. C-OMF systems a.re designed and detailed according 10 AISC Seismic Provisions Section GI. They MC expected 10 provide minimal inelastic deformation capaci1y in !heir members and connections.

ProYision.v.

..:-

Table 6-1

A42 &M.3

6.2. COMPOSITE ORDINARY MOMENT

·-

6.2 COMPOSITE ORDINARY MOMENT l·RAMES (C OMF,I

I

-

'The 11fereoce1 ~ llsted ift .. ~to Ille~~ \

used 10 the members and connections of seismic force resisting syi.tems is selected to meet the requirements of AlSC Seismic Provisions Section A3.4a. For C-OMF systems. rhcre are no welds desigruued as demand critical welds. Note 2. The structural design drawings and specifications for C-OMF syslems arc ro m~t

lhe requirements of AlSC Seismic Pro1•iSio11s Sections A4. l, A4.2 and A4.3. Note 3. Loads and load combinations as defined by the applicable building code arc to be followed 3S indicared in AISC Seismic ProYisions Section B2. C-OMF systems including reinforced concrete components are to be designed using load nnd resii:tance fac;ror design (LRFD) because allowable strength design (ASD) is not addressed in ACI 318. Note 4. The required strength for s tructural members and connections is de1crmineJ according to AISC Seismic ProYision.s Section B3. I . Note S. Strucrurnl analysis for the appropriate load combinations is to be perfonncJ accordance with the requirements of AJSC Seismic Provisions Chapter C.

;~

COMPOSl'TE MOMENT FRAMES'.~ 1·~

6.3 COMPOSITE INTERMEDIATE MOMENT fRAMBS (C-lMF)

,~: ;~ I

h~.

(a) Fo.r elastic analysis, the stiffness of composite members· includes the effects o{ :;l; cracked sections. Additional guidelines for estimating the stiffness of concrete ~~{ be:im 3J!d coltJmn members, conerete-encased and concrete-filled membeclJ :.p~ and steel.be~~ ';i~ _com(l9.~ite,slabs are provided in the Commentary to tli~ ·r_~ AJSC Seismic Provisions Chapter C. These concrete and composite rnembet properties reflect the effective stiffness at the onset of significant yielding the members. · ·

[

I

Note 8. The beam-to-column connections are designed in accordance with the AISC Specification and AISC Seismic Provisions Section D2.

Note l. The structural steel material used for C-IMF. systems is limited by the requirements of AlSC Seismic Provisions Section A3.1 with the exception that tl specified minimum yield stress of tbe steel for .members in. which inelastic beha · ior is expected is not to exceed 50 ksi. This specified minimum yield stress can be exceeded when the s'"uitability of the material is detennined by testing or other rational criteria. Expected material strength is discussed in _AISC Seism · Provisions Section A3.2 and values of R1 and R1 required to calculate the expect• yield and tensile strength of steel are provided in AISC Seismic Provisions Table A3.1. The concrete and steel reinforcement is selected to satisfy the requiremer •· of AISC Seismic Provisions Section A3.5. The weld filler metal used in the me1 bers and connections of seismic force resisting systems is selected to meet t111.. requirements of AISC Seismic Provisions Section A3.4a. For C-IMF systt!ms, there are no welds designated as demand critical welds. .

Note 9. Column splices are de$igned in accordance with the AISC Specification and AISC Seismic Provisions Section 02.5. ,

Note 2. The structural design drawings and specifications for C-IMF systems are to me ~ the requirements of AJSC Seismic Provisions Sections !-4.l, A4.2 and A4.3.

Note 10. Column bases are designed in acpordan<;e with the AISC Specification and AlSC Seismic Provisions Section D2.6.

Note 3. Loads and load combinations as defined by the applicable building code are be followed as' indicated in AISC Seismic Provision; Section B2. C-IMF s~ tems includJng reinforced concrete ~~IT1ponents are t~ be designed using loa and r~sistance fa~tor deslgn (LRFD) because allowable strength design (ASfl 1· is not addressed m ACI 318. . . . J Note 4. The general provisions for the required strength for strUctural members and co · nections is determined according to AISC Seismic Provisions Section B3.1. T required strength of columns is detennined according to AlSC Seismic Provisit Section Dl.4a. . .., Structural analysis for the appropriate load combinations is to be performed ; Note5. accordance with the requirements of AISC Seismic Provisions Chapter C.

m

Note 6. Columns of C-OMF systems are designed in accordance with AJSC Specification Chapter I or ACI 318 (excluding Chapter 21). Nore 7. Bemns of C·OMF systems are designed in accordance with I.be AJSC Specification.

Note 11. Steel headed stud anchors and welded reinforcing bar anchors are designed id accordance with the AJSC Specifica'ticm and AJSC Seismic Provisions Section 02.8. Note 12. Composite slab diaphragms are to satisfy the requirements of A1SC Seismic Provisions Section Dl.5.

6.3 COMPOSITE INTERMEDIATE MOMENT FRAMES (C~l"'JF) Composite intermediate moment frame (C-IMF) systems consist of: (i) composite or reinforced concrete columns; (ii) Structural steel, concrete-encased or composite beams; and {iii) fully restrained connections. C-IMF systems are designed and detailed according to AISC Seismic Provisions Section G2. ASCFJSEI 7 limits the use of C-Th1F systems to Seismic Design Categories A, B and C. The provisions for C-IMF systems as well as the associated R and Cd values in ASCE/SEI 7 comparable to those required for reinforced concrete IMF systems. · C-IMF systems are expected to proviae limited inelastic deformation capacity through flexural yielding of the C-IMP beams and columns and shear yielding of the column panel zones. The inelastic drift capability of C-IMF systems is permitted to be obtained from inelastic defonnations of beams, columns and panel zones. The C-IMF system connection is based on a tested design with a qualifying story drift.angle of 0.02 rad.

are

Overview of Applicable Design Provisions An overview of the applicable provisions of the AISC Seismic Provisions for the design of C-IMF systems follows and is presented in a simplified format in Table 6-2. All requirements of the AISC Specification apply, unl~ss stated otherwise in the AISC Seismic Provisions.

i

j

I

(a) For elastic analysis, the stiffness of composite members mcludes the effecL< ·cracked sections. Additional guidelines for estimating the stiffness of concn.. beam and column memqers.,_ concrete-~nc~d an~ concrete-filled memb~~ I and steel beams with composite slabs are provided m the Commentary to A Seismic Provisions Chapter C. These concrete and composite member pror ties reflect the effective stiffness at the onset of si¢ficant yielding in t'

I I

members. . . · As stipulated in AISC Seismic Provisions Section G2.5a, steel and compo Note 6. columns of C-Ilvf.F systems arc required to meet the moderately ductile memb· requirementS of AJSC Seismic Provisions Section DLl. ·

(a) Encased composite c9lumns must s~tisfy the. requireme~ts of AISC Seis Provisions Section Dl.4b(l). The width-to-thickness r;attos of steel comp1 .. sion elements must not exceed the limiting width-to-thickness ratios, '4.J, fror . AJSC Seismic Provisions Table D 1.1. . . (b) Filled composite columns must satisfy the requirements ·of AlSC; Se1~ J , Provisions Section D l.4c. The width-to-thickness ·ratios of steel compress' · elements must not exceed the limiting width-to-thickness··ratios, A.,,.d. f 1· AlSC Seismic Provisions Table D 1.1. (c) Concrete columns roust satisfy the requirements of AC! ·31s S~tio~ 21.3.

I

~ INsmvre of ST£EL CONSTRUCTION

COMPOSITE MOMENT FRAMES·

6.-4 COMl'OSITB SPECIAL MOMENT FRAMES
6 7

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Note 7

Table 6-2 }:

Simplified Overview of Provisions for C-IMF Systems

..

Note In Overview

.

Item

(a) The \\ idth-to-lhickncss ratios of steel compression clements arc not to e:i:cc.::d the limJling width-to-thickness ratios, A,,,i1, from AISC Seismic Provisions

Table 01.1.

Referenced Standard$j

(b) The lateral bracing for beams is to be designed according to the requirements llf AISC Seismic Provisions Secuon DI .2a.

Seismic Prov. Sects. A3.1, A3.2', A3.4 &A3.S

1

Steel and concrete materials

2

Structural design drawings and specificalJOn

(c) Special bracing at plastic binge IOC3tions required by AISC Seismic Provisions Section G2..ta mu~t meet the requiremenlS of AISC Seismic Provisions Section

Seismic Prov. Sects. M. l , A4.2&A43

Dl.2c.

Seismic ,"tov. Sect 82

3

loads and load combinaw-.s

4

Required 6trenglh fOI' stnWal members and comec'.ielns

SelSITlic Prov. Sects. 83.1 &01.43

5

Structutal analysis

Seismic Prov. Ch C

(a)

E~ $1Tffness of concrete/comPoSite

Note 8. Beam-to-<:olumn connections are to be Jesigncd according to AJSC Seismic Pro1·isio11s Sections D2 :md G2.6.

•.

(a) The perfonnance requirements for beam-to-column co1ulections are gi\·cn in

AlSC Seismic Prcrdsions Section G2.6b.

Commeo!aly to Sel$/TllC

members

(b) The methodology for coofonn:ince dcmonsLCation is given in AISC' Seismic

Prov. Ch. C

6

Moderate!'/ ductile column members

(a)

Encatcd COmPoSrte columns

Provisions Se-ction G2.6c.

Seismic Prov. Sects. O1.1 & G2.5a

(b)

' ·~

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~

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(c) The required shear strength for cllnncctioos is based on AlSC Seismic Pro\ isrons Section G2.6d.

Se1Smic Prov. Sect. 01.4b(1) & Table 011

,, Filled composite columns

in A1SC Seismic Prol'i..~i,ms SC(;tion G2.5a, ste~J and compo~Jte I.MF systems are required to meet lhe mt'dcrately Juctile memb.:r reqwremcnts of AJSC Seismic Pro1 ision.r SecCJon D 1.1.

As stipulated

beam.~ of C

:

Note 9. Connection diaphragm plates and continuit) plates are designed according to the requirements of AISC Seismic Prol-·tsions Section G2.6e.

Se1Smic Prov. Sect. 01.4c &Table 01 I

the requirements of AJSC Seismic

ACI 318 Seel 21 3

Note 10. Column i>phccs .lte designed according Provisions Sections 02.5 and G2.6f.

Seismic Pr
Note 11. Column bases are to satisfy lhe requirements of AISC Stismic Provisions Section 02.6.

Lifllltiog width-to-thiclule$S ratios

Seismic Prov. Table 01.1

Lateral bracing ot moderately ductile beam members

SeiSmic Prov. ~L 01 2a

Note 12. Steel headed stuJ anchors or welded reinforcing bar anchors are designed to meet lhe requirements of AlSC Seismic Provisions Section 02.8.

(c)

l.a1eral bracing at plastie hinge locationS

Seismic Prov. Secis. 01 2c &G2.4a

Note 13. Composite slab diaphragms ore to S.ltisfy the requirements of AlSC Seismic Provisions Section 01.S.

8

Beam·lo-column connections

{c)

Reinlorced concrete COiumns

7

Moderately ducille beam members

(a)

(b)

I

10

5eismic Prov. Sects. 02 &G2.6

~ I

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6.4 COMPOSITE SPECIAL MOMENT FRAMES (C-SMF)

Seismic Prov. Seel G2.6b

(a)

Beam-to-column conneciioo perlormance requirements

(b)

Beam-llKolumn conformance dtmoostrallon

Seismic Prov. Sect G2.Sc:

(C)

Beam-to-<:Olumn requlftd shear strength

Seismic Prov. Sect G2.6d

9

Connection diaphragm plates and continuity plates

Seismic Prov. Sect G2.6e

10

Cdumn gpices

Seismic PrCJIK Sects. 02. 5 & 62.61

11

CollJIM bases


12

Steet'headed ~tud anc.hOfs or welded reinforcing

Seismic Prov. Sect 02.8

j


f

;-

bar anchof 13

Compo$4te 5lab diaphragms

"The rNtnced ~ lll:led 1111 In lldd~.JOn IO !ht NS/:. ~

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I·

I

Composite special moment frame (C-SMF) systerru consL~t of: {i) composite or reinforced concrete columns; (ii) structural steel~ concrete-encased composite, or composite beams; and (iii) fully restrained connections. C-SMF systems arc designed and detailed according to AlSC Seismic Provisions Section G3. ASCFJSEl 7 pennilS C-SMF systems in any seismic design ~ategory but they are primarily intended for use in Seismic Design Categories D, E and F. Design and det:liling provisions for C-SMF systems are compMable to those required for steel and reinforced concrete SMF systems. C-SMF systems are generally expected to experience significant inelastic dcfonnaifons during a large seisrruc event It is expected thllt most of lhe inelastic deformation will take pl:ice as rotation in beam "hinges" with limited inelastic defom1ntion in the panel zone o f the column. The bc:im 1o-column connections for these systems arc required 10 be qu3.IJfied based on tests that demonstrate that the connection can sustain a story drift angle of at AMDUCAN INS'TlTIJTE Of' Stm. CONS'Til.IJCTIOl>I

6-8

6.4 COMPOSfrE SPECIAL MOl\11.ENT FR.AMES (C·SMF)

COMPOSITE MOr. tENT FRAMES

least 0.04 rad based on the loading protocol specified jn AISC Seismic Provisions Chaplet

'

K. The connection configuration and design procedures are based on the results of these

Table 6-3

l.

Simplified Overview of Provisions for C-SMF Systems

qualifying 1ests. Other provisions are intended to limit or prevent excessive panel wne disiortion, failure of connectivity plates or diaphragms, column hinging, and local buckling tha1 may lead to inadequate system performance in spite of good connection performance.

Note In Overview

Referenced Standards'

Item

Overview of Applicable DE;?sign Provisions

1

Materials

Seismic Prov. Sects. f.J.1, A3.2, f.J.4 & A3.5

An overview of the AISC Seismic Provisions for the design of C-SMF systems follows and is presented in a simplified format in Table 6-3. All requirements of the AISC Specijica1ion apply._ unless stated otherwise in 1be AISC Seismic Provisions.

2

Slnlctural design drawings and specificatlon

Seismie Prov. Sects. A4 .1, A4.2 &A4.3

3

Loads and load Clllllbinations

Seismic Prov. Sect. 82

4

Required strength tor structural members and connections

Seismic Prov. Sects. 83.1 & D1.4a

s

Structural analysis

(a)

Bastic stiffness.of CQOCrete/composlte members

Nore 1. The stnictural steel material used for the C-SMF systems is limited by 1he requirements of AISC Specification Section A3. I and AJSC Seismic Pro1·isio11s Section A3. l with the exception that the specified minimum yield stress of the steel for members in which inelastic behavior is expec1ed is not to exceed 50 ksi, as stipulated in AISC Seismic Provisions Section A3. l. This specified minimum yield stress can be exceeded when lhe suitability of the material is determined by testing or other rational criteria. For columns in C-SMF systems, the specified minimum yield stress is not to exceed 65 ksi. Expected material strength is discussed in AlSC Seismic Provisions Se~tion A3.2 and values of Ry and R, required to calculate the expected yield and tensile strength qf steel are provided in AISC

Seismic Prov. Ch. C ,

~

Highly cluctlle column members

Seismic Prov. Sects. 01 .1 & G3.5a

(a)

Encased composite columns

Seismic Prov. Sect. 01 .4b(2) & Table 01.1

(b}

Filled composite columns

(c}

Reinforced concrete columns

AC! 318 Seel. 21.6

Highly ductile beam members

Seisn1ic Prov. Sects. 01 .1 &G3.5a

(a}

Width·l
Seismic Prov. Table 01.1

(b)

Lateral bracing of highly ductile beam members

Seismic Prov. Sect. 01 .2b

(c)

Lateral bracing at plastic hinge localions

. 7

.

I

Note 2. The structural design drawings and specifications for C-SMF systems are to meet of AISC Seismic Provisions Sections A4.l, A4.2 and A4.3. .the requirements ·, Note 3. Loads and load combinations as defined by the applicable building code are to be followed as indicated in AISC Seismic Provisions Section B2. C-SMF systems including reinforced concrete components roust be designed using load and resistance factor design (LRFD) because allowable strength design (ASD) is tJOt addressed inACI 318. ~

Note 4. The required strenglh for structural members aod connections is deteml.ined according to AJSC Seismic Provisions Section B3.I. The required strength of columns is d~tennined according to AISC Seismic Provision~ Section DJ .4a.

-

.

Seismic Prov. Sects. 01 .2c

Seismic Prov. Seel G3.4a S¢smic Prov. Sect GJ.6

9

Beam-to-column connections

(a)

Demand critical welds

Seismic Prov. Seel G3.6a

(b)

Beam·to-column connection perfonnance requirements

Seismic Prov. Sect. G3.6b

(c)

Beam-to-column confonnance demonstralion

Seismic Prov. Sect. G3.6c

(cl)

Beam-to-column required shear strength

Seismic Prov. Sect G3.6d

10

Connection diaphragm plates and conUnuity plates

SeiSmlc Prov. Sect G3.6e

11

Column Splicas

Sei$mlc Prov. Sects. 02.s &G3.6f

-

Column bases


13

Steel headed stud an<:hors or welded reinforcing bar ancllO<


14

Composite $lab diaphragms

Seismic Prov. Sect 01 .5

AMElUC:AN WSTTTVrS OF STEEL CO!OSTRUCTION

l

&G3.4b

Prol)ortionilg of columns and beams at joints

• The referenced sbndards Isled ... In adclUon IO lllt AISC Spoa1fcll/ion.

I

Seismic Prov. Sect. 01.4c &Table 01.1

8

12

Note 5. Structural analysis for the appropriate load combinations is to be performed in accordance with the requirements of AISC Seismic Provisions Chapter C.

Commentary to Seismic Prov. Ch. c

6

Seismic Provisions Table A3.l. This specified minimum yield stress can be exceeded when the suitability of the material is determined by testing or other rational criteria. The concrete and steel reinforcement is selected to meet lhe requirements of AJSC Seismic Provisions Section A3.5. The weld filler metal used in the members and connections of seismic force resisting systems is selected to meet the requirements of AISC SeiSmic Provisions Section A3.4a. Filler metals used in welds designated ss demand critical welds in AISC Seismic Provisions Section G3.6a are ex~~ted to meet the requirements of AISC Seismic Provisions Section A3.4b.

!·

1.

•\

I

6-10

COMPOSITE MOMENT FRAMES.

(a) For elastic analysis, the stiffness of composite members includes the effects of cracked sections. AdditionaJ gwdeljnes for estimating the stiffness of concrete beam and column members, concrete-encased and concrete-filled members, and steel beams with composite slabs are provi
::.

(~) Encased composite columns must satisfy the requirements of AJSC Seismic Provisions Section DJ.4b(2). The width-to-thickness ratios of steel compres~ sion elements must not exCU
(b) Filled composite columns must satisfy the requirements of AISC Seismic Provisions Section Dl.4<:. The width-to-thickness ratios of steel compression elements must not exceed the limiting width-to-thickness ratios, AJid, from AISC .Seismic Provisions Table D 1. l.

_ _____, "L.., ·1_, '. :·.

,_(c) Concrei~ columns must satisfy the requirements of AC! 318 Section 21,6.

Ill

Note 7., ~stipulated in AISC Seismic Provisions Section G3.5a, beams of C-SMF systems ;'lfe required to meet the highly ductile member requirements of AISC Seismic Provisions Section D 1.1. (a) Th_e width-to-thickness ratios of steel compression elements must not exceed the limiting width-to-thickness ratios, AJuJ, from AISC Seismic Provisions Table Dl.l.

·-·

: · (b) Tile' lateral bracing for beams is designed according to the · AlSC Seismic Provisions Section Dl.2b.

r~l!iremeots of

(c) Special bracing at plastic hinge locations required by AISC Seismic Provisions Section G3.4b must meet the requirements of AISC Seismic Provisions Section DJ..2c. Note 8~ Coluµms and beams of C-SMF systems are proportioned to meet the strong-column weak-beam requirements of AISC Seismic Provisions Section G3.4a. Note 9. Beam-t~oJurnn connections are designed according to AISC Seismic Provisions Section G3.6. ·'

(a) Welds designated as demand critical are stipulated in AISC Seismic Provisions Section G3.~a.

· (b) The perfonnance requirements for beam-to-column connections are given in · AlSC Seismic Provisions Section G3.6b.

..

;-:.

I

(c) The methodology fur conformance demonstration is based on AISC Seismic Provisio11s'Seclion G3.6c. (d) The required shear strength for connections is based on AISC Seismic Provisio11s Section G3.6d.

~·

6.5 COMPOSITE PARTIALLY RESTRA.tNED MOMENT FRAMES (C-PRMF)

'

Note 10. Connection diaphragm plates and continuity plates are designed according requirements of AISC Seismic Pr0\•isio11s Section G3.6e. Note 11. Column splices are designed according Provisions Sections 02.5 and G3.6f.

10

6-11

10

the

the requirements of AlSC Seismic

Note 12. ColW1Ul bases are to satisfy the requirements of AISC Seismic Provisions Section

D2.6. Note 13. Steel headed stud anchors or welded reinforcing bar anchors are de,signed to meet . the requirements of AISC Seismic Provisions Section 02.8. ' Note 14. Composite slab diaphragms are to satisfy the requirements of AISC Seismic Prorisions Section Dl.5.

6.5 COMPOSITE PARTIALLY RESTRAINED MOMENT FRAMES (C-PRMF) Composite partially restrained moment frame (C-PRMF) syscems consist of structural steel columns and composite beams that are connected with partially rcsrrained moment connections. C-PRMF systems are designed and detailed accordfog to AJSC Seismic Provisions Section 04. C-PRMF systems resist lateral forces and displacements through the flexural and shear strengths of the beams and columns·simil!U' to other moment frame systems. The primary difference between C-PRMF systems and the other moment frame systems is that the beam-

to-column connections in C-PRMF are .not designed for the full flexural strenglh of the beam. Consequently, hinging is. forced to occ.u r in lhe partially restrained composite connections (PRCC) rather than the beam ends and column panel zone. The beams and columns in a properly designed C-PRMF will typically remain elastic with low ductility demands with the exception of expected hinging at the base of the columns. .. The design of a C.PRMF is different.from the .design of a more traditional steel moment frame in three important ways. First,. PR;CC are not designed to be stronger than the beam it is connecting. Consequently, the lateral ~~ystem typically will hinge. within the connections and not within the associated' beams or columns. Second, because the connections are neither pinned nor fixed, their stiffness must be accounted for in the frame analysis. Third, because the connections are weaker than folly restrained moi;ient corwecrions, the lateral force resisting system requires more frames with more connections, resulting _in a highly redundant system. Tue work that fonns the basi_s of many of the recommendations for the C-PRMF has been summarized in Partially Restrained Composite Connections, Design Guide 8 (Leon et aJ., 1996) and ASCE (1998). The type of C·PRMF system envisioned under the current AISC Seismic Provisions is one using bare steel W-shape columns and'composite steel beam framing. Most research addressing C.PRMF systems bas investigated systems with a reinforced composite slab, a double-angle bolted web connection, and a bolted sear angle. With the magnirudc of the seismic response modification coefficient., R, between those of the f.}..lF and SMP systems, the C-PRMF system is expected to experience significau inelastic behavior during a seismic event and the PRCC must be capable of providing St3bk moment-rotation behavior up 10 o'. 02. rad. The PRCC must also e..'\bibit moment Streng.:.

a

6-12

COMPOSITE MOMENT FRAMES

of at least 50% of the nominal flexural sirength of lhe steel beam at a connection rotation of 0.02 rad. The AJSC Stismic Provisions do not provide an upper bound on lhe characteri~tic connection moment strength; however, 100% of the nominal plastic flaxural strength of the bare steel beam is recommended. The design concept of "strong column-weak beam" is not specifically required by th~ AJSC Stismic Provisions for C-PRMF systems; however, it is recommended for C-l?R.f\.1F systems in Seismic Provisions Commentary Section G4.4. Similar to the special moment frame, this provision is not intended 10 eliminate aJl yielding in the columns. Rather, it is intended to result in framing systems that have disuibu1ed inelasticity in large seismic events and diS<:ourage story mechanisms. I

Overview of Applicable Design Provisions An overview of lhe AISC Seismic Provisions requirements for the design of C-PRMF sysrems follows and is presented graphically in Figure 6-1 and in a simplified format in Table 6-4. All requirements of the AISC Specification apply, unless stated otherwise in the AISC

Seismic Provi.sio11s. Note l. The structural steel material used for the C.PRMF systems is limited by the requirements of AISC Specification Section A3.l and AJSC Seismic Provisions Section A3.l with the exception that the specified minimum yield stress of the steel for members in which inelastic behavior is expected is not to exceed 50 ksi, as stipulated in AISC Seismic Provisions Section A3.l. This spe~ified minimum · yield stress can be exceeded when the suitability of the material is determined by testing or other rational criteria. Expected material strength is discussed in AISC Seismic Provisions Section A3.2 and values of R., and R, required to calculate I.he expected yield and tensile strength of steel are provided in AlSC Seismic Provision.s Table A3.l. The concrete and steel reinforcement is selected to meet the requirements of ATSC Seismic Provisions Section A3.5. The weld filler metal used in the members and connections of seismic force resisting systems is selected 10 meet the requirements of AISC Seismic Provisions Section A3.4a. Welds designated as demand critical welds in AISC Seismic Provisions Section G4.6a are expected to meet the requrrements of AISC Seismic Provisions Section A3.4b.

6.5 COMPOSITE PARTIALLY RESTRAINED MOMENT FRAMES (C-PRJ..IF)

Provisions Chapter C. These composite member properties reflect the effecfr stiffness at the onset of significant yielding in I.he members. Note 6. As stipulated in AISC Seismic l'rovision.s Section G4.5a, colwnns of C-PRMF sy terns are required to meet the highly ductile member requirements of AISC Seisr11 ProvisiQns Section D l.J. Note 7. As stipulated in AlSC Seismic Provisions Section G4.5b, beams of C-PRMF sy terns are required to meet the highly ductile member requfremen1s of AISC Sei:sm .. Provisions Section D1.1. I·: (a) The width-to-thickness ratios of steel compression elements must not exce1 I:·: the limiting width-to-thickness ratios, 'Nut. from AISC Seismic Provisions Tab ·: Dl.l. (b) The lateral bracing for beams is designed according to the requirements AlSC Seismic Provisions Section Dl.2b. (c) A solid slab is to be provided as stipulated in AISC Seismic Provisions Sectk

~fu

Note 8. Beam-to-column connections are designed according to AlSC Seismic Provisic Sect.ions D2 and G4.6. Specifically, steel reinforcement must be designed to sa, isfy tbe requirements of AISC Seismic Provisions Section D2.7(5).

~

l:

02.6.

Note 3. Loads and load combinations as defined by lbe applicable building code are to be followed as indicated in AlSC Seismic Provisions Section B2. Note 4. The required strength for structural members and connections is detennined according lo AJSC Seismic, Provisions Section B3.l. The required strength of columns is determined according to AJSC Seismic Provisions Section DJ .4a. Note5. StructuraJ analysis for the appropriate load combinations is to be performed in accordance with the requirements of AlSC Seismic Provisions Chapter C :ind Section G4.3. (a) For elastic analysis, the stiffness of composile members includes rhe effects of cracked sections. Additional guMelines for estimating the stiffness of :.1ecl beams with composite slabs are provided in the commentruy to AISC Seismic

I

Note9. Column splices are to satisfy the requirements of AlSC Seismic Provisic Sections 02.5, G4.6a(l) and G4.6f. Note 10. Co!Umn bases are to satisfy the requirements of AISC Seismic Provisions Section

Note 2. The structural design drawings and specifications for C-PRMF systems are to meet the requirements of AJSC Seismic Provisions Sections A4.l, A4.2 and A4.3.

i

6

Fig. 6·1. Notes key for Table 6-4 for C-PRMF systems. A.'ID!.ICAl'I lNSTtTUTll 01' STEEL CONSTJWCTJON

I

ii

6-1 5

6.6 CONNECTION DESIGN

6-14

"

·-~~

I

'

~

I

?

I

.!_..

·Notes to Figure 6-1: C-PRMF Systems ,,

Note In

a _ _ ___, ib !~

"~

!; "'·

""

'

Table 6-4 ;

Note in Overview

-

1

Matelials

Sects.AJ.1, A3.2, A3.4 &A3.5

-

2

Structural design drawing$ and specification

Sects.A4.1,A4.2 &M.3

-

3

Loads and load combinations

SectB2

-

4

Required and available strength for structural members and connections

Sects. B3.1 & D1.4a

-

5

Structural analysis

Chapter C, Seel. G4.3

A

(a)

Composite member stiffness

Comm. to Ch. C

B

6

Highly ducble column members

Sects. 01.1 & G4' 5a

7

Beam members

Sects. 01.1 &G4.5b

(a}

WldtlHo-thickness ratios of highly ductile members

c

./

;

Ag. 6-1

AISC Se/$/TllC Provfs/ons Reference

ttem

-

Reinforced Concrete Column-to-Steel Beam Connections During the 1980s and 1990s, more than 400 RCS connections were tested in Japan and _36 in !he UnHed States (Deierlein and Noguchi, 2004). Through the U.S.-Japan Cooperattve Research Program, 56 more connection subassemblics were tested to fill knowledge gaps for certain connection con.figur3tions and force-cransfer mechanisms (U.S.-Japan, 1983). Examples of the wide variety of RCS connection details tested in Japan and the U.S. are shown in Figures 6-2a and 6-2b, which are raken from Deierlein and Noguchi (2004).

Long. Reinf.

Long. Reinf.

Hoops

Table 01.1

G

(b)

Lateral bracing of highly ductile beam members

Seel 01.2b

D

(c)

Sol!d slab zone

Sect G4.5b

F, I, J

8

Beam·lo·column connections 6nduding composite partially restrained connections)

Sects. 02 & G4.6

B:

9

Column splices

Sects. 02.5, G4.6a(1) &G4.6f

B E

10

Column bases

Sect. 02.6

11

Steel headed stud oochors

Seel 02.8

H

12

Composite slab diaphragm

Sect Ot.5

Steel Beam (1) Cover Plate Type

Face Bearing Plates (FBP) (2} Face Bearing Plate Type Rib Plate

' - - - - Hoops Steel. 8_eam FBP (3) Extended Face Bearing Plate Type

Band Plates Stiffeners (4) Steel Band Type

Note l l. Steel headed stud anchors are to satisfy the requirements of AISC Seismic Provisions Section D2.8. Note 12. Composite slab diaphragms are to satisfy the requirements of AISC Seismic Provisions Section Dl.5.

6.6 CONNECTION DESIGN Unlilce steel moment resisting frames, were currently are no prequalified connections available for use in composite moment resisting frames. Therefore, the following sum.marii.es the results of testing and evaluation of selected types of connections for composite moment resisting frames. The discussion focuses on reinforced concrete column-to-steel beam connections (RCS), round filled composite column-to-steel beam connections, and rectangular filled composite column-to-steel beam connections.

Hoops

Hoops

Steel Beam

Confinement Plates Steel Beam FBP (5) Cross Anchoring Plate Type (6)'Headed Stud Type

Fig. 6-2o. &Ampk details 1 1hro11gh 6 of reinforced concrete column·to-steel beam connections te.sttd in the U.S. and Japan (from Deierlein and Noguch~ 2004). Reprinted wi1h permission from ASCE:.

AMER.ICAN l:NST1TVT6 OF STEJ!L CoNSTRVCTION

COMPOSITE MOMEITT FRAMES

t~

?"'

6-1


~~

~~

In Figures 6-2a and 6-2b, details 1 through 7 are.through-beam type connections where ~~·· the beam is continuous through the joint. By not interrupting (splicing) the be.am at lbe poi,nt r of maximum moment at the column face, the through-beam details provide the ductility th~ is generally desirable in conventional steel construction. Details 8 through 11 are througli• column type connections where the beam flanges are interrupted to minimize the impact on the column reinforcing bar arrangement and to facilitate concrere placement in the joint Detail 12 is an example of a hybrid detail, combining conventional reinforced concrete concepts by encasing the steel beam ends connecting to the concrete column. Til.rOugh-bcam-type connections have been the preferred derail in the U.S., however, both types have be.en used in Japan. The primary differences between the detaiJs in Figures 6-2a

Vertical Sti ener Transverse Stiffeners

Table 6-5

Summary of Reinforced Concrete Column-to-Steel Beam Connection Tests References

OrganlutiOn

Building Contractors Society

Nishiyama e1 al. (1998, 2000) Kuramoto and Nishiyama (2004)

six tllree:-Oi~ensional, through-column joints

Kuramoto,and Noguchi (1997) Noguchi ·and Kim (1997, 1998)

siX planal: through-beam joints

Chi~a Univ.

five planar !hro·ugh-column jolnts

Osaka lnsl of

I

Hoops Steel Beam FBP · {7) B~arin.Q _Steel Column Type

Techno!Ogy Univ. of Michigan

_(8) Transverse Stiffener Type

six planar through-beam joints, investigation of specific internal force transfer mechanisms

Baba and Nislliinura (2000)"• •

15 ttu:cugh-beam joints (nine exterior configura~ons, four ~ittl comp0site slab, and h\10 poSt.-eaithquake repairs) ·

Parra·Montesinos et al. 2000b, 2001 a,

~

Texas A & M _,

B~am-J

-

(9). Inner Diaphragm Type · Long. Reinf.

zocn t>; ·2003)

Liang and Parra-

'-

Steel

'(2opoa,

il, (

I j;· i.: ~~

t'

l l;:

Montesinos (2004) -

'

Bugeja et ·at (1999, 2000) Bracci etal. (1999) Esche et al. (1999) 11.'

siX lllree-dlmensional 1hrough-beam joints, .with composite slab.

U.C. San Diego

two planar t~ of steel beams to compo$ite column with redui:,ed beam sections

Chou and Uang (2002)

Cornell Univ.

19 thraugh·beam jbints

Kanno arid Deierlein (1993, 1997)

UniV. of Texas

17 ltrrollgh-beam Joints

Sheikh et al. (1989) Deierlein et al. (1989)

J.

ffom DEie!IM and tloguctri (2004). Reprinted Wilh pennission from ASCE.

' ..

att~c~ents vario~s

Steel Beam End Plate (11) PC Bolt Type

PC Bolts

artial SRC Beam (12) Partial SRC Beam Type

Fig. 6-2b. Example ckcails. 7 rhrough J2 of reinforced concrere column·co-sreel beam connections tested in the U.S. and Japan (from Deierlein and Noguchi, 2004). Reprinted with pennission from ASCE.

I•.

covetipl~tes

bearin~ plat~s.

and 6-2b lie in of stiffener plates, and whi· l:. act together with reinforcing bars to t:ffect force transfer between the steel and concrete. •· .: A sununary of test results avaiJa~le in lhe literature is presented in Table 6-5. The test specimens were approxun:itely on~-half to two-thirds of full scale, with typical reinforc J concrete column sizes ranging from 10 to 18 in. deep. The tests were generally conduct. under cyclic loading, and several of the tests included axfal loading of the reinforced coo~ crete columns to represent gravity loading and eartbquake--induced overturning. The typk"'l yield strength of the steel beams was 50 ksi,. and lhe con~~te comp:e~sive s~r~ngth wa~ ksi minimum. Most connection test assemblies were designed to fSJ.1 m tbe JOiot to all,

6-18

,

:·

,... !

"'·

?

...~:...

...... "

COMPOSITP MOMFNT FRAMES

study of the inrcmal force tran5fer mechanisms. This is counter to de~ign practice. u. here the' Joints arc t)pically designed to be :.trooger th:1.11 the beams. This should be kept in mind wl1en reviewing test results from literature. OveraJJ, the tests show that, when properly detailed to mobilize in1ema1 force transfet mechanisms. RCS connections provide reliable strength and ductility for seismic design. /II. limited suite of details (face bearing plates, vertical joint reinforcement, web doubler plates, etc.) have been tested and shown to enhance sliffness antl strength of the connection. Other det:1.tls adjusted 10 suit design and fabrication that provide similar levels of confinement and force transfer nuy be suitable but would need engineering evaluation. Models to calcuJate lhe stiffness and strength of RCS joinls have been synthesized imo guidelines (ASCE, 1994). TI1e ASCE guidelines have been validated for seismic design using lhe tests noted in Table 6-5. Several proposals have been made to improve them (e.g., Parra-Montesinos and Wight, 2001a; Parra-Montesinos et al .. 2001; Kuramoto and Nishiyama, 2004). In particular. through-beam type connections eliminate the need for field weldfog of the beam flanges and are generally not susceptible 10 rupture behavior. Tests have sho"-n 1hat, of the many possjble ways of strengthening the joint, face be3ring plaies and steel band pl3tC;S auachcd to the beam are very effective for both mobilizing the joint shear strength of reinforced concrete:.: and providing confinement to lhe concrete. Further information on design methods and equations for these composite connections is available in published guideUnes, e.g.• Niiliiyama et al. (1990) and l>arra-Montesinos and Wight t200Ja). 1..iang and Parra~.Mont~inos (2004) have demonstrated the experimental beha11ior of the~e connections by te:.ting two interior :md tWt'l exterior RCS subas:1cmblics under cyclic load reversals. The test specimens included reinforced concrete columns o r RCS columns and composite beams with the steel beam running continuously through the columns and a reinforced concre1.e ~fab cast upon metal decks supported by the sleel beams. Strong column-weak beam design philosophy was implemented by designing the interior ~pecimens to have a column-to-beam moment strength ratio of 1.3, and the exterior spe<:imens to have a ratio of 2.2. Figure 6-3 shows the cwo types of composite joint details used for the interior and exterior RCS connection subassemblies. As shown in Figure 6-3(a). one of the details consisted of overlapping U -sbaped stirrups passing through h
,.

•'

t

(bl RCS joint With $teel bond pla1tl Fig. 6-3. RCS connection.J tested by Liang mu/ Parra-Monusinos (2004) and

thmon.stroted ro achiew 0.04 rad intl.'rstory drift.

(i.6 CONNl.:CTION DESIGN

6-19

assumed to frame in to the main beam some d.htancc away from the connection. Al~o c 1 osel~ spaced stirrups were placed in 1hc column regions directly above and below the Mccl be.;ims to provide confinement to regio11s susceptible to beating f:ulure and to mobilize concre11: regions outside the width of the steel beam flanges. The second detail shown in Figure 6-3(b) features :.tecl band plates wrapping around the column regkins just above and below the steel be3ffis. The U-shaped stirrups that pass through the steel web panel were eliminated because of the confinement provided by th.e ~ted band plates. This funber aJJO\l.S transverse beams to frame into the main beam !lt the conoecl:lon region. In order to pre\ent outward buckling of longitudinal bars 1hrougb the joint region, ~mall ties that do not penetrate the steel web panel v.ere provided over the joint depth. E."tperimental results indicated excellent performance and only moderate damage in the connecMnS. Plastic hinges fonned m the beam regions adjacent 10 the connections and dissipated energy under cyclic loading to achieve story drift angles greater than 0.04 rad, which is requiretl for C-SMF S}Stems.

Round Filled Composite Column-to-Steel · Beam Connections The behavior of different cypes of round filled column-10-~tccl beam connections for composite frames has been investigated in the U.S. (Aziz.inamini and Schneider, 2004). Six different types of comp<>site connccoons \\ere t~1ed; these te~t configurations :lfc pre~ented

m Figure 6-4 Each tested connection consisted of a round filled composite column conncc1cJ to an ASTM A992 W14x38 beam. The composite column was an ASTM A500 Grade B round hollow slnJclural section (HSS) that was 14 in. in diameter, 0.25 in. thick. and filleJ with/~ 5 ksi concrete. The test setup conmted of an exterior .;ubasscmbly (girder on only one side of 1be column) thal was subjected to cyclic deformations on the tip of the cantilever girder at a distance of 9 ft from the face of the column. The cyclic deformation history followed ATC-24 (ATC, 1992) guidelin~. When the steel beam is welded directly to the round HSS of lhc comp<>siie column, as shown in connection type J, large distortions of the HSS wnlls occurred. and the connection was susccpuble to weld, flange or HSS wall rupture. This type of connection had a rotation capacity less than 0.02 rad and is acceptable only for C-OMP systems. Connection types ll and m, with external diaphragm anJ continuous web details, rcspecti\ely, bad better ineJas.. tic behavior, but the flexural strength of these connections deteriorsted early in the imposed deformation history after reaching a roUltion capacity of 0.02 rad, which is not acceptable for C..St.iF systems. Connection type IV was similar to type I with the addition of four No. 6 rebars that were welded to tho girder 11:\nges and a11Chored into the concrete infil! of the composite column. The behavior of this connection was better. but lberc was some local te3ring of the st~I HSS at a rotauon of 0.03 rad. and rupru~ of the deformed bars :u a rotation of 0.037 5 rad. As a resuJt, this connection type is ruso not acceptable for C-SMF systclllS. Connection type V with the girder flange through the comp<>site column bad rupture failures :u the flange welc!s and is not recommended for any of the systems. Connection type VI. the through be
=

,

'


Connection types Il, ill and IV are acceptable for C-lMF systems where !he required rota, tion capacity is 0.02 rad. ,1 . Elremaily and Azizioamini (2000) conducted additional research to develop desjgn guide: Imes for through-beam-type connections for systems with round filled composite columnst They c~nducted seven two-thirds sc.ale tests on· connection systems consisting of a round compoSJte column and a steel beam passing through the column representing an interior

.i: i • '

!

. .J

Table 6-6

Matrix of Specimens Tested (Ricles et al., 2004)

I·

Connection Detail

Specimen

I

lntel'iOr dlaphragms (lour-sided CJP weld), weak beam

2

lnteflor Cfiaphragms (t!Jree-slded CJP weld), weak lleam

1R

krterior dlaplvagms (four-sided CJP weld), weak panel zone

2R 3

lntenor diaphragms {lhree·slcled CJP weld), weak panel rone

3R

Extended tee with taper, \veak beam

4 5

Bolted split-tee connectlon with shear tab, weak beam aOited split-tee connection witllout shear tab, weak beam

I·

Extende
6

~lded split·tee connection withou~shear tab, weak beam

7

Wclded splft-tee con~ection without shear t~~· weak beam

.· 1

L

l\ejlMled with permission rrom A.See.

subassembly. The specimens were designed to investigate different possible failure mode and develop connection strength equations. The maio test variables were the column-I beam flexural slreogth ratio (moment ratio) and the type of weld used to attach the beam 1 the HSS. The ASTM ASOO Grade B sreel HSS varied from 12 to 16 in. in diameter wjth 0.1: in. wall thickness, and the ASTM A992 steel beams varied from W16x31 to W18x50.

\

"l .

~Ill: ~WM> ~ii'~ --

~M Er:tb«lded Ol/om»dBM~

. ,.

Rectangular Filled Composite Column-to-Steel Beam Connections I

I

Extensive research has been conducted in Japan to study the behavior of moment conm tioos between filled composite columns and wide flange beams under seismic loadiP · conditions (Ricles et ii., 2004). Research on welded beam-to-filled composite col11r connections having interior or exterior diaphragms has shQwn that these elements • susceptible to buckling or shear yielding of the steel HSS within the panel zone of 1 connection. Rides et aL (2004) conducted (ull-scale tests representative of the interior subassembl; in the middle to upper floors of moment frames with six to 12 stories. A ~otal of 10 full-sc J tests were conducted. Each test specimen consisted of two W24x62 beam sections m«v from ASTM A36 steel attached to an HSS16x16x'h rectangular filled column made from ASTM A500 Grade B steel and filled with concr~te wi~ a measured compressive slren 1·· of 7 to 8.5 ksi. Tue test specimens are as defined in Table 6-6. Specimens 1, 2, 3, 4, 5, 6 and 7 in lhiS rest were designed us.ing the strong column-we::. beam principle, where the connection elements were designed to resist I.50 limes lhe non inal plastic moment strength of lhe beam. The details of lhese connections are showo Figure 6-5 and described as follows:

J.:

'·

0

@f'"""·~=I -I ,,.,. ··.. ~ \I': ~

Rltttflll ~

Fig. 6-4. Round.filled composite column-10-sreel beam connection test ccnjigurations (Azizinamini and Schneider; 2()()4). Reprinted with ptmnissionfrom ASCE.

I

6-22


• Figure 6-5(a) shows the detail of connection specimens I and 2 tha1 consisted of int~ rior diaphra~ms and welded details for the filled composite column-io-steel ~ connection. The only difference: between the two specimens was that lbe intmo~ diaphragms of specime.n 2 were welded o~ only lhree sides. The comple1e-join1-,

I

.,

.... I·

penetration groove weld on the nonh side adjacent to the panel zone (i.e., web of HSS) was omitted. • Specimen 3 had an cxteoded-1ec moment connection detail as shown in Figure 6-S(b). As sho,rn, the extended tee was an ST7.5x25 section th.at was attached to the beam flanges and column by complete-joint-penetration groove welds.

i

I

11mmDl1.x114 mm SMar Stud (typ.)

1

I I

• I;

'

Ll

W24X62

'

Sfru'C;fural

Tut>. 44>6x408x12

i

0

Umm Ola. x 114 mm

\;.

Sh.ar Stud (typ.)

Q

44mm

~

Tep & &ttom Dfeplttagml (Full P~ ~ omfttltd 011 Hortll Side ror Spec, 2)

11

3srruuJ L-lJ 7tmm 4@ 67mm

(a) Details of specimens J and 2 in Table 6-6

~ I

3&1mm

Section A·A

-

Structural Tube "°6x406ltf 2 16mmDia.x114 mm Shew Stud (typ.)

E71T-8

Section A-A (c) Derails of specimens 4 and 5 in Table 6,6

t •.- .

~~-,

!

!~

12mm

~

,,

I

W24xS2

·..

t

381mm

t 260

E7018, 'l'jp.

Section A-A

I ~1am"J I

Sectfon A-A

(b) Details of spromen 3 ;,, Table 6-6

(d) Details of speci~ns 6 and 7 in Table 6-6

Fig. 6 -5. Detai/,s of rectangular filled composite column-ro-steel beam connection (Ricles er al., 2004). Reprirsled w ith penni.ssion from ASCE.

Fig. 6-5 (conr'd). DerailJ (Jf rectangular jiUed composite colwnn-co-steel beam co11Mcrio11 res red by Ricles et al. (2004 ). Reprinted with pennission from ASCE.

6-24

COMPOSITE MOMENT FRAMEs

6.6 CONNL~L' I !UN Ut.:511..JN

• Specimens 4, 5, 6 and 7 had split-tee moment connection details as shown in Figure 6-5(c) and (d). The split-tee connections were designed to activate a diagonal concrete compression strut wilhin the connection's panel zone under the action of overturning moment. This was achieved by the use of ASTM A490 bolts to develop a horizontal tension force through the joint. These bolts were passed through lhe column with tbe use of PVC conduits placed prior to casting concrete and tensioned after curing of the concrete. The split-rec detail was designed to avoid prying action in the ASTM A490 bolts. • In specimens 4 and 5 the stem of the tees were attached to the beam flanges using nio.-diameter ASTM A325 bolts with 1h-fo. oversiwi bolt holes, whereas in specimens 6 and 7 a 'll:in. fillet weld was used. The structural tees in all specimens were cut from a W24x146 section of ASTM A572 Grade 50 steel chat bad a measured yjeld strength of 49.6 ksi. Specimen 1 achieved a maximum story drift of about 0.04 rad when a rupture irritiatt.-d at the fusion line of the beam flange and the weld. Prior to rupture, the beams de,·elopcd appreciable yielding in the flanges and web. This type of connectjoo detail is not accept· able for C-SMP systems, but it can be used for C-IMF systems thal require only 0.02 rad story drift angle. Specimen 3 developed a rupture in lhe beam tension flange, adjacent to an extended tee at lhe end of the connection during the first half cycle of 0.03 rad story drift. An ex:unina· tion of the beam flange in the ruprured area revealed that the material had necked at the crack, indicating that a significant amount of strain had develoJ?.ed. This type of connection detail is not acceprable for C·S~fF systems, but it can be used for C-1).fF systems that require only 0.02 rad of imemory drift. Specimens 4, 5, 6 and 7 developed sigrrificant yielding al the base of tee stem during cbe inelastic displacemem cycles during the test. These specimens also developed full plastic flexural hinges in the beams at the end of the connection, where pronounced flange and web yieliling occurred and was followed by local flange and web buckling. Each test was stopped after a story drift of 0.06 rad was iml>osed to the top of the colunm of these specimens. Figure 6-6 shows lhe moment-plastic rotation behavior of these connections. All of these connection details are acceptable for C-$MF systems !hat require 0.04 rad of interstory drift As shown in Figure 6-6, pinching occurred in the cyclic behavior of specimen 4 due to the bolt hole elongation and resulting slippage between tbe beam and the connection under cyclic loading. At the end of the test. a .!let section rupture QCCUrted in the flange bolt line, leading to deterioration in strength. The welding of the washer plates in specimen 5 and tee stems to the beam flanges in specimens 6 and 7 served to reinforce the bearing strength and increase the net area in the beam flanges. This avoided hole elongation and subsequent problems from developing. Figure 6-7 shows the inelastic story drift capacity of tested specimens, and the required inelastic story drift for design basis and maximum considered earthquakes. As shown, the split-tee moment connections (specimens 4 through 7) have acceptable behavior for use with C-SMF systems. The rMuired story drifts were calculated by conducting nonlinear time history nnaJysis of several CFf moment resisting frames, subjecting them each to several ground motion records. The panel zone shear strength of the spUt-tee moment connections can be estimated using the Kanntani et al. (1991) model developed based on I.he Japanese test results. Detailed seismic design gwdelines for the split-tee moment connections are included in Peng (200 l).

~

GOO

i~..L-~~..t-.1-1<1+++4~-W-.f-1-.,_~__,

(c)~4

(h) SpeG 7

• 1 ~.c• .o.o4 -o.u -0.02

o

0.01

Pl~~-~n

l

o.04 o.c. o.oa

•p*-

·~

fig. 6-6. .\1omenr-plastic beam rotation behavior of tested split· tee moment connecrions (Ric/es et al., 2004). Reprinted with permissionfromASCE.

0.08

[ f2I Seam eJ CoMnn 0

0.07

~

0.08

~

0.06

.g. "C Q

I

o.o,

E

!

i

P~nol Zor.o

II Conncdon

.

l

MCE

- _\__

J

0.03 0.02 0.01

0.00

1

1R

tR

3

3R

4

&pectmen

..

I

J

Fig. 6-7. Inelastic story drift capacity of connection ttst speci~ns (Ricles et al., 2004). Reprinud wilh permission from ASCE.

J AMERICAN INS1TTl111! OF STEEL CONSTROC110N

~. l

6-26

COMPOSITE MOMENT FRAMES \

PART 6 REFERENCES ASCE (1994), '·Guidelines for Design of Joints becw~n Steel Beams and Reinforced Concrete ColllJ11lls;• ASCE Task Commiuee on Design Criteria for Composite Structure{ in Steel and Coocrete, Journal of Strucrural Engineering, ASCE, Vol. 20, No. 8, pp. 2,330-2,357. ASCE ( 1998), "Design Guide for Panially Restrained Composite Connections," ASCE Task Committee on Design Criteria for Composite Structures in Steel and Concrete, Journal of Strucrural Engineering, ASCE, Vol. 124, No. 10, pp. l,009-1, 114. ATC (1992), "Guidelines for Cyclic Seismic Testing of Components of Steel Structures," ATC-24, Applied Technology Council, Redwood City, CA.

.,

!:

----~ ~;;:i

Azizinarnini, A. and Schneider, S.P. (2004), "Moment Connections to Circular ConcreceFilled Steet Tube Columns," Journal of Structural Engineering, ASCE, Vol. 130, No. 2, pp. 213-222.

6-27

PART 6 REFFRJ:!NCES

Kanatani, H.• Tabuchi, !111., l
-----

Kuramoto, H. and Noguchi, H. (1997), "An Overview of fapanese Research on RCS Systems," Proceedings, ASCE Strucrures Cfngress XV, ASCE, Res1on, VA, pp. 7 I6-720.

Baba, N. and Nishimura, Y. (2000), "Stress Transfer on Through Beam Type Steel Beaui~ Reinforced Concrete Column Joints," Proceedings of the 6th ASCCS lnremarional Conference on Sreel-Concrere Composite Srructu,res, Y. Xiao and S. Mahin, eds., pp. 753-760.

Leon. R., Hoffman, J. and Staeger, T. (1996), Partially Restrained Composite Connections, Design Guide 8, AISC, Chicago, 11.. ,

Bracci, J.M., Moore, W.P., Jr. and Bugeja, .M.N. (1999). "Seismic Design and Construccability of RCS Special Moment Frames:· Jounuil of Stmctura/ Engineering, Vol. 25, No. 4, pp. 385-392.

Liang, X. and Parra-Montesinos, G. (2004), "Seismic Behavior of RCS Beam-Column-Slab Subassemblies and Frame Systems," Journal of Structural Engi11eering, ASCE, Vol. 130, No. 2, pp. 310-319.

Bugeja, M., Bracci, J.M. and Moore, WP. (1999), "Seismic Behavior of Composite Moment Resisting Frame Systems," Technical Report No. CBDC-99..()J, Dept. of Civil Engineering, Texas A&M University.

Nishiyama, I., Hasegawa, T. and Yamanouchi, H. (1990), "Strength and Deformation Capacity of Reinforced Concrete Column to Steel Beam Joint Panels," Building Research Institute Report 71, Ministry of Construction, Tsulruba, Japan.

Bugeja, M., Bracci, J.M. and Moore, W.P. (2000), "Seismic Behavior of Composite RCS Frame Systems," Journal of Srmctural Engineering, Vol. 126, No. 4, pp. 429-436.

Nishiyama, I. It:idani, H. and Suginiro, K.. (1998), "Bidirectional Seismic Response of Reinforced Concrete Column and Structural Steel Beam Subassemblies;' Proceedings, Structural Engineers l\~rld Congres_s, ASCE, Paper Ref. T/77-2, Reston, VA.

Chou, C.C. and Uang, C.M. (2002), "Cyclic Performance of a Type of Steel Beam to SteeJEncased Reinforced Concrete Column Moment Connection," Journal of Consrructional Steel Researfh,, ,Vol. 58, No. 5- 8, pp: 637-663.

Nishiyama, I., Kuramoto, H., Itadani, H. and Sugihiro, K. (2000), "Biilirectiooal Behavior of Interior, Exterior and Comer Joints of RCS System," Proceedings, 12 WCEE, Paper No. 1911/6/A.

Deierlein, G.G., Sheikh, T.M., Yura, JA. and Jirsa, J.0. (1989), "Beam-Coltunn Moment Connections for Composite Frame.s: Pan 2," Journal of Structural Engineering, VoJ. 115, No. 11, pp. 2,877-2,896. .

.Noguchi, H. and Kim, K. (1997), "Analysis of Beam-Column Joints in Hybrid Structures," Proceedu1gs, ASCE Structures Congress XV. ASCE, Reston, VA, pp. 726-730.

Deierlein, G.G. and Noguchi, H. (2004), "Overview ofU.S.-fapan Research on the Seismic Design of Composite Reinforced Concrete and Steel Moment Frame Structures," journal of Structural- Engineering, ASCE, Vol. 130,. No. 2, February, pp. 361-367.

Noguchi, H. and Kim, K. ( l 998), "Shear Strength of Beam-to-Column Connections in RCS System," Proceedings, Structural Engineers World Congress, ASCE, Reston, VA, Paper Ref. Tl77-3.

Elremaily, A. and Azizinamini, A. (2000), "faperimental Behavior of Steel Beam to CFf Column Connections:· Journal of Construccional Sreel Rtsearr:h. Vol. 57, No. JO, pp. 1,099-J ,119.

Parra-Montesinos, G. and Wight, J.K. (2000a), "Seismic Behavior, Strength, and Retrofit of Exterior RC Column-to Steel Beam Connections,'' UMCEE 00-09, Department of Civil and Environmental Engineering, University of Michigan.

Esche, C.D., Bracci, J.M. and Moote, W.P. (1999), "Joint Strength in RCS Fram.es;• Technical Report No. CBDC-99-02, Department of Civil Engiueering, Texas A&M University.

P3ITa·Montesinos, G. and Wight, J.K. (2000b), "Seismic Response of Exterior RC Coh.unnto-Steel Beam Connections," Journal of Structural Engineering, Vol. 126. No. W, pp. I,! 13- 1,12L

Parra-Montesinos, G. and Wight, J.K. (2001a), "Modeling Shear Behavior of Hybrid RCS Beam-Column Connections." Journal ofStructural Engineering, Vol. 127, No. 1, pp. 3-1 I.

PART7

Parra-Mon1esinos, G. and Wight, J.K. (200Jb}, "Seismic Repair of Hybrid RCS BeamColumn Connections," AC! Stn1ctural Journal, Vol. 98, No. 5, pp. 762-770.

COMPOSITE BRACED FRAMES AND SHEAR WALLS

Parra-Montesinos, G., Liang, X. and Wight. J.K. (2003). "Towards Deformation-Based Capacity Design of RCS Beam-Column Connections," Engineering Structures, Vol. 25, No. 5, pp. 681-690. . Peng, S.W. (2001), "Full Scale Testing of Seismically Resistant Moment Connections for Concrete Filled Tube Column to WP Beam Hybrid Systems," Composite and Hybrid Structu~s: Proceedings of the Sixth ASCCS International Conference on Steel-Concrete Composite Structures, Vol. I. Ricles J., Peng, S. and Lu, L. (2004), "Seismic Behavior of Composite Concrete Filled Steel Tube Column-Wide Flange Beam Moment Connections," Journal of Structural Engineering, ASCE, Vol. J 30, No. 2, pp. 223-243.

Sheikh, T.M., Deierlein, G.G., Yura, 1.A. and Jirsa, J.O. (1989), "Beam-Column Moment Connections for Composite Frames: Part 1," Journal of Structural Engineering, ASCE, Vol. 115, No. 11 , pp. 2,858-2,876.

U.S.-Japan (1983), "U.S.-Japan Cooperative Research Program: Construction of the Full Scale Reinforced Concrete Test Structure," Technical Report UMEE 83R2, Department of 1 Engineering, Universicy of Michigan, AugusL

7.1 SCOPE . .. ....... . ........ . ................... . ............... .... 7-3

7.2 COMPOSITE ORDINARY BRACED FRA..\1ES (C-OBF) ........ .... ...... 7-3 Overview of Applicable Design Provisions ............................... 7-3 7.3 COMPOSITE SPECIAL CONCENTRlCALLY BRACED FRAMES (C-SCBF) .......................... .. .......•..................... 7-5 Overview of Applicable Design Provisions ............................... 7-5 7.4 COMPOSITE ECCENTRICALLY BRACED FRAMES (C-EBF) .... .. ....... 7-7

]·

Overview of Applicable Design Provisions ........... .. ......... .. ..... . . 7-7 7.5 COMPOSITE SHEAR WALLS ..................... . ......... : ....... 7-JO General System Behavior ........ .... .... . ........... . ...... . . . . : .... 7-10 Shear Wall Coupling .... .............. ....... ....... ...... . ...... 7- 10 Degree of Coupling ............................ ... ........ . . ..... 7- 11

t.·

Steel Coupling Beam Design ............................... . ...... 7- 11

,•

Beam Embcdment Length (Connection) .............................. 7- 14 Detailing Requirements in the Embedded Region .. .. .................. 7-14

Wall Oversuength .................. . .............. . ...... . ...... 7-15

Composite Ordinary Shes.r Walls (O?SW} .............................. 7-l6 Overview of Applicable Design ftovisions .................. .... ..... 7-16 Steel Coupling Beam Design ......................... : . ... ....... . 7-19

..

Beam Embcdment Length . .... ................................... · 7-19 Composite Coupling Beams ............... .-:-. ..................... 7-19 Expected Plastic Moment . .............. ... .................... . 7-19

I•

Shear Strength ............................................... 7-21

Embcdmcnt Length ... ..... .. . . .... ........ ... ..... .... . .. .... 7-21 E~amplc 7.5. l.

C-OSW Slee! Coupling Beam Design .......... .. ....... 7-21

Example 7.5.2. C-OSW Composite Coupling Beam Oesi&n .. ...... : ..... 7-30 Composite Special Shear Walls (C·SSW) ............................... 7-36 Overview of Applicable Design Provisions ........ . .................. 7-36 Steel Coupling Bemt Design ..............•....................... 7-39 AMl?Jl.ICAl'I INs'!nVre 01' STEEi.. CONSTRUCTION

l

7.2 COMPOSITE ORDINARY il!V\<.:~I) t-.KAM~

Wall Overstrength ............... ; ................................ 7-40

~

S:·••

I

•1(

7.1 SCOPE

Beam Embedmenr Length ..................... ............. ....... 7-4Q

::< ............. :.. .... .... 7-40

Intenn¢iatc Web Stiffeners '. ....... :· .'..

Face Bearing Plates ................... : .......................... 7-4l Stiffeners within the Embedded Region ......... . ..... : .............. 7-41 Vertical Transfer Bars ................................ . ..... . ..... 7-4 I Example 7.5.3. C-SSW Steel Coupling Beam D~ign ................... 7-41

7.6 DESIGN TABLE DISCUSSION ...................................... 7-51 DESIGN TABLES ..... .......... ......... : ...... ...... ... ...... ... 7-~~ Table 7-IOA. Plastic Capaci.ties for Rectangular Encased W-Shapes Bene About the X·X Axis ................................... . .... . ... 7-52 Table 7-1 OB. Plastic Capacities for Rectangular Encased W-Shapes Bene About the Y-Y Axis ". ..... ... ·: ........................ ·.... ....... 7-53 Table 7-1 l A. Plastic Capacities for Composite Filled HSS Bent Abour Either Axis .......................·.............. . ........ 7-54 Table 7-1 IB. Plastic Catyacities for Composite. Filled Round HSS Bent About Any Axis ................ .... ........................... 7-55

PART 7 REFERENCES .................................................. 7-56

The following types of composite braced frame and shear wall syscero~ are' addressed in th.is Part: composite ordinary braced frames, coml>osite special concentrically braced frames, composite eccentrically braced frames, composite ordinary shear walls, and composite special shear walls. The AlSC Seismic Provisions and other design considerations summarized in this Part apply to the design of the members and connections in composite braced frame and shear wall systems that require seismic detailing. Where these sysiems utilize reinforced concrete elements. these elements are to be designed in accordance with ACI 318. Reinforced concrete elements are pemtitted tO be used in Section Hl (C-OBF), Section H4 (C-OSW), and Section H5 (C-SSW). However, the requirements of ACI 318 Chapter 21 are applicable only in the design of the reinforced concrete walls used in Section HS (C-SSW). AISC Seismic Provisions Sections Al and B2 state that systems with reinforced concrete elemenlS that must be designed according to ACI 318 should be designed only by the load and resistance factor design' (tRFD) method because ACI 318 does not :iddress allowable strength design (ASD). The design e,i:amples in this Part are limited to the LRFD method since in each example there is a concrece elemem that must be designed according to ACI 318.

7.2 COMPOSITE ORDINARY BRACEP_FRAMES (C- OBF) Composite ordinary braced frame (C-OBF) syscems consist of structural steel, composite or reinforced concrete columns; stro~tural S!~l o_r composit~ ~llms; and structural steel or filled composite brace members, provided at least one element is either cQmposite or reinforced concrete. Concentrically connected members are required; howeve'r, .eccentricities less than the beam depth are permine.d if accounted for in the. member design: C-OBF systems are ~igned and detaile:d a_ccording to AJSC Seismic Provi!ions Section Hl. They are expected to provide minimal inelastic deformation capacity in the membe~ and connections.

Overview of Applicable D esign Provisions

.

, ' ,.

An oveiview of the AISC Seismic Provisions applicable for design of C-OBF systems follows and is presented in a simplified format in Table 7-1. :

Note 1. The stnictural steel material used for C-OaF systems is limited by the requirements of AISC St!,ismic Provisions Section A3. l, where the specified minimum yield stress is not to exceed 55 ksi for mernbe~ in which foelastic behavior is expected. These specified minimum yield stresses can be exceeded when the suitability of the material is determined by testing or other rational criteria. For columns in C-OBF systems, the specified minimum yield stress i!i not to e.'
7-4

COMPOSITE 'BRACED FRA.\.iES AND SHEAR WALLS

i

Table 7-1

Simplified Overview of Provisions for C-OBF Systems

i "·'

;i

J

Note

l

i

.

Item

1

Steel end concrete nia~rials

2

OesJgn drawings and specifications

Referenced Standard'*

Seismic Prov. Sects. A.3.1. A3.4&A3.5 Seismic Prov. Sects. M .1, A4.2&A4.3

3



4

Required strength for members and connections

Seismic Prov. Seel 83.1

5

Structural anafy-sis

Seismic Prov. Ch. C

Bastic stiffness of concrete/composite members

Seismic Prov. Ch. C. See Seismic Prov. Commentary to< discussion.

S(a)

\

.. '

6

. Column member$

7

Beam members

None

8

Brace members

None

9

. COOnectiOflS

'.-

,

'

AC1 318 (exci. Ch. 21}

7.3 COMPOSITE SPECIAL CONCENTIUCALLY BRACED FRAMES

Note 6. Columns of C-OBF systems are designed in accordance with the AISC Specijicarion or ACl 318 (excluding Chapter 21). Note 7. Beams of C-OBP systems are designed in accordance with the AISC Specifica1i.on. Note 8. Diagonal braces of C-OBF systems are designed in accordance with the AlSC

Specification. Sei.rmic Provisions Section 02.7. Note 10. Splic~.s in stnJ.ctural steel or composite columns are designed in accordance with the AISC Seismic Provisions Section D2.S. Note 11. Column bases are designed in accord_ance with the AISC Specification and AISC {· Seismic Provisions Section 02.6. ..

Discussion ASCEISEI 7 permits the use of COBF systems in Seismic Design Categories A, B and C only. This is in contrast to steel on:linary concentricaJly braced frame (OCBF) systems that are also pennitted in Seismic Design Categories D, E and F with height limitations and roof load restric1ions for Seismic Design Category F. Because C-OBF systems are limited co Seismic Design Categories A, B and C, tl1ey are expected to withstand minimal inelastic drift through inelastic behavior of composite beams columns or braces. There are no additional requirements for designing reinforced concrdt columns beyond those provided in ACJ 318, excluding Chapter 21.

7.3 COMPOSITE SPECIAL CONCENTRICALLY BRACED FRAMES (C~SCBF}

Column spnces

Seismic Prov. Sect 02.5

11

Column bases

Seismic Prov. S5Ct. 02.6

'The rererenced standard$ are in addliion to lhe requirements of the AISC ~!in

Note3. Loads and lo~d ~ombination~ as defined by the applicable building code are to be ~ollow~d as. md1cated in AISC Seismic Provisions Section B2. C-OBF systems mcluding reinforced concrete components are to be designed using LRFD because ASD is not addressed in ACI 318. Notc4. The required strength for structural members and connections is determined according to AlSC Seismic Provisions Section B3. L · Note5. Structuial analysis for the appropriate load combinations is to be performed in accordance ~ith lhe r:equire~eots of AISC Seismic Provisions Chapter C. (a) For el ~tic analysis, the stiffness of composite members includes I.he effects of •· cracked sections. Additional guidelines for estimating I.he stiffness of concrete beam and column members, concrete-encased and concrete-filled members and sted .be~ wi~ composite slabs are provided in the Commenuuy to th~ AISC ~eism1c Provisions Chapter C. These concrete and composiie member propernes reflect the effective stiffness at the onset of Siinifi cam vielding in the members. ·

'

Note 9. Connections are designed in accordance with the AISC Specification and AlSC

Seismic Prov. Sect. 02. 7

10

7-:

f'

f:

t· Jj .:.

l

Composite special concentricaJJy braced frame (C-SCBF) systems consist of either encase1 or filled composite columns; structural steel or composite beams; and structural steel o filled composite brac.e members. Concentrically connected members are required; however, • · members connected with an eccentrid\y less than the depth of the beam are permitted provided the eccentricity is included in the 'analysis. C-SCBF systems are designed and detaile• according to AISC Seismic Provisions Section H2. They are expected to provide signjf1car inelastic deformation capacity primarily through brace buckling in ~ompression and yiel
t·

ing in tension.

Overview of Applicable Design Provisions An overview of the AISC Seismic Provisions requirements appli<::able for design of C SCBF systems follows and is presented in a simplified format in Table 7-2.

l

?. :

Note 1. The structural steel material used for C-SCBF systems is Hmited by the requirements of the AlSC Stismic Provisions Section A3. l, where the specified mi.nimu i·· yield stress is not to exceed SO ksi for members in which inelastic behavior expected. This specified minimum yield stress can be CJtcecded when the suitabil icy of the material is determined by testing or other rational criteria. For columr·· in C-SCBF systems, the specified minimum yield stress is oot to exceed 65 k

t

AMEIUCAN lNS1JlVI13 OF S1"E!!L CoNSTRVCtlOl'I

1.

7-6

COMPOSITE BRACED FR.A.'AJ',S AND SJ !EAR WAu.:li

,..

Table 7-2

Simplified Overview of Provisions for C-SCBF Systems

.. Note

Item

:.. _,, i

..

.:l·. .. :~

Steel and conerete materials

Sects. A3.1 & A3.5

2

Oe$ign drawings and specifications

Sects. A4.1, A4.2 & M.3

3


Sect 82

4

Required streng1h for members ReQuired streng1h tor connections

Sects. 83.1 , H2.3 & H2.S Sects. H2.3 & H2.6

5

Structural analysis

Ch. C &Sect. H2.3

Elastic s1iffness ol concrete/composite members

Commentary to Seismic Pr(J'f. Cit C

·~·

...

·',, ---~~~:J

5(a)

'·

.

.,

.

6

Column members

7

Beam members

8

Brace members

Sects. H2.5a & H2.Sb

9

Connections

Secis. 02 & H2.6

10

Column splices

Sects. G2.61 & H2.6d

11

Column bases

Sect. 02.6

12

Demand critX:al welds

Sects. A3.4b, H2.6a &12.3

Sects. 01.1 & H2.5a Sects. 01.1 &H2.5a

'The referenced st.ridards are in additioo to tJle requirements of the AlSC Specllic;ition.

Nace 2. Note 3. Note 4. Note 5.

7.4 COMPOSITE ECCENTRICALLY BRACED FRAMES

7-7

beam and column members, concrete-encased :1t1d concrete-filled members, and steel beams with composite slabs are provided in the Commentary to the A ISC Seismic Provisions Chapter C. These concrete and composite member properties reflect the effective stiffoes.s at t.he onset of significant yielding in the

members. Note 6. Columns of C-SCBF systems are designed in accordance with AISC Specification Chapter I and lhe requirements of AlSC Seismic Provisions Section H2.5a. Composite columns are required to satisfy the highly ductile member requirements

AISC Seismic ProYislon!I Reference•

1

,

The concrete and steel reinfbrcing materials used in composite components are to satisfy the requirements of AJSC Seismic Pro~·isions Section A3.5. The weld filler melal used in lhe members and connections of seismic force resisting systems is sele<:led to meet the requirements of AISC Seismic Provisio11S Section A3.4a. The structural design drawings and spec.ifications for C-SCBF systems are to satisfy the requirements of AISC Seismic Provisions Sections A4.l, A4.2 and A4.3. Loads and load combinations as defined by the applicable building code are to be followed as indicated in AISC Seismic Provisions Section B2. The required strength for structul)l.I members and connections is detennined according to AJSC Seismic Provisions Sections B3.l, H2.3, H2.5 and H2.6. Structural analysis for the appropriate load combinations is to be performed in accordance with the requirements in AISC Seismic Provisions Chapter C and Section H2.3. (a) For elastic analysis, the stiffness of composite members includes the effects o f cracked sections. Additional guidelines for estimating the stiffness of concrete

of AISC Seismic Provisions Section D l. l . Note 7. Beams of C-SCBF systems are designed in accordance with the AISC Specificarion and the requirements of ATSC Seismic Provisions Section H2.5a. Composite beams are requireJ to satisfy the moderately ductile member requfrements of AISC Seismic Proi·isions Section D l. l . Note 8. Diagonal braces of C-SC.BF systems are designed in accordance with AISC Seismic Provisions Section H2.5a and b. The radius of gyration for filled composite braces is taken as that of the steel section alone . Note 9. Connections are designed in accordance with the J\1SC Specification and AISC Seismic Pro11isions Sections D2 and H2.6. Note lO. Column splices are designed in accor
Note 12. Delll3nd critical welds are designed in accordance with AISC Seismic Provis:~ Sections A3.4b, H2.6a and 12.3.

Discussion ASCEJSEI 7 permits the use of C -SCBF systems in Seismic Design Categories A, B and C witbout height limitations and in Seismic Design Categories D, E and F with height limitations. These limitations are lbe same as those applied to steel concentrically braced frame systems. Tb.is system is expected to resist inelastic drift through inelastic behavior of com· posite beams, columns and braces.

7.4. COMPOSITE ECCENTRICALLY BRACED fRAM.~S {C-EBF) Composite eccentrically broced frame (C-EBF) systems consist of encased or filled composite columns; strocturaJ steel or composite beams; ·structural steel links; and strUctur:!l steel or filled composite broces. C-EBF systems are designed and detailed in accordanc{ with AISC Seismic Provisions Section H3. They are expected to provide significant inelastic deformation capacity primarily through shear or flexural yielding in the links.

Overview of Applicable Design Pr~visions An oYerview of the AISC Seismic ProviJions requirements applicable for design of C -f. systems follows and is presented i:n simplified format in Thble 7-3.

COMPOSITE BRACED FRAM~ND SHE.AR WALLS

7- 8

7.4 COMPOSITE ECCEN'TRICALLY DRACED FRAM.ES

Table 7-3

Simplified Overview of Provisions for C-EBF Systems AISC Se/$mlc Prov;sions Rtrerence•

!rem

Note

1

Steel and cof'lCfete materials

Sects. A3.1 &A3.5

2

Design drawings and spedfications

Sects.M.1,M.2 &M.3

3

.Loads and load combinations

Sect. 82

4

Required strength for membel1; Required strength for cor.nections

Sects. 83.1 & H3.6

structural analysis

Ch.C

Elastic stiffness of concrete/romposlte members

Commentary to Seismic

5 S(a)

Sects. 83.1 & H3.5

Prov. Ch. C 6

Additional analy~is _ and system requirements

Sect. H3.4

7

Column members

Sect. H3.5

8

Beam members

Sect. H3.5

.

9

Braces

10

C-Onnectlons

11

Column splices

Sects. 02.5 & H3.6

12

Column bases

Sect. 02.6

13

Protected zones

14


Sect. H3.5

Sect. H3.6

Sects. 01.3 & H3.5

,.

Sects. A3.4b, H3.6 & 12.3

'The referenced standan!s an in tdclition to the requiremenls of 1he AJSt Spedficatkn

Note 1. The structural steel material used for C-EBF systems is limited by the require-ments of AISC Seismic ProvisWns Section A3.l where the specified minimum yield stress of the steel is not to e..~ceed 50 ksj for members in which inelastic behavior is expected. This. sped.lied minjmum yield stress can be exceeded when the suita9ility of the material i.s determined by testing or other rational criteria. For columns o.f C-EBF, tl1e specified minimum yield stress is not to exceed 65 ksi. The concrete and steel reinforcing materials used in composite components should satisfy tbe requirements of AISC Seismic Provisions Section A3.5. The weld filler metal used in the members and connections of seismic force resisting systems is selected to nieet the requirements of AISC Seismic Provisions Section A3.4s. Note 2. The structural design drawings and specifications for C-EBF systems arc to satisfy the requirements of AlSC Seismic Provisions Sections A4.1, A4.2 and A4.3. Note 3. Loads and load combinations as defined by the applicable building code are to be followed as indicated in AISC Seismic Provisions Section B2.

ASCE/SEI 7 permits lhe use of composite eccentrically braced frame systems in Seismit: Design Categories A, B and C without height limitations and Seismic Design Categories D, E and F with height limitations. This system is CJtpected to re.sist inelastic drift through inelastic behavior of sttuctural steel links.

AMl!JuCAN lNS1't'J'1.TJ'E Of STI$L CONSTRUCTION

r

7- JO


~.· .,

)

I

l

I

"'·

7.5. COMPOSITE SHEAR WALLS

Composite shear wall systems are addressed in AISC . Seismic Previsions Sections H4, ~

t.· · ·

,,

r

~

t•:

l

7- Jl

Degree of Coupling

General System Behavior H5 and H6. The composite shear walls addressed are those that include Steel or composite boundary elements and/or sreel or composite coupling beams and walls consisting of steel pJate encased in concrete. Since all co~posite shear waU systems incorporate a reinforced

!

1.5 COMPOSITE SHEAR WAU.S

concrete waU that will be designed according 10 ACI 318, rhe discussion and examples lbat follow will only co~sider design by LRFD. ·

Shear Wall Coupling

The efficiency of c.oupled wall systems is generally measured by the degree .to w~cb the coupling action participates in the overall overturning res.istance to lateral load.s. !his measurement is referred to as the degree of coupling. Con.sider a wall system ~µrular 10 that shown in Figure 7-1. If the system has no couplingJ~eams. the degree of coup,ling would. be zero. As the fle.xural and shear stiffness of coupling beruns increase, the degree of coupling increases. TI1e d~gi:ee-of coupling is meas~red as the ratio of overturning resist;mce d~e to lhe coupling effect to the total qvei-tuming resistance, as shown in Equaci.on. 7: ~. In Figure 7-1, and Tare the accumulation Qf beam shears over the height of the building m the~c9~ pression and tension waUs, r~spectively. -.

c

{!

(;

):

~~:-

.,•{~ :$ :~,

,,Ii~

11 •:. ·i

The benefits of coupl~n·g shear walls are well recognized and understo'od. The coupitn·g beams provide transfer of vertical forces between adjacent walls, which ·c reate a frame-like coupling actioii that resists a portion of the totiil overturning moment induced by the seismic action. Figure 7-1 shows the overturning resisting mechanisms· formed in a coupled system. The tot.ill overturning resistance is a combination ·of the flexural resistance of'the · individuai' wall piers (M1 and M1), an(J the resistance provided by the coupling action (Mc!X =TL or Cl). ' The coupling beam action has three desirable effects: ( 1) the required flexural sirength of the wall piers is· ·reduced; (2) steel and composil~ coupling beams dissipate energy; and (3) lateral stiffness of the coupled system is greater than the sum of the individual wall piers. When the beams are proportioned properly, beam yielding over the height of the building can ·occur, providing desirable distribution of energy dissipation over the height of the building. A coinprehensive discussion of coupled wall system behavior is presented in Recommendari.on for Seismic Design of Hybrid Coupled Wall Syscems (El-Tawil et al.,

a

2009).

:;

. .. -

.

.; · ~

..

;~ :~

l

Lateral load

. ..

~·

!~

:~ ~~'

,,

Degree of coupling= · · . Mcpl · · Mcpl +(Mi+ MiJ

' (7-1)

J The degree of coupling can be measured at any stage of loading and at any floor le".el. However, it is generally measured at the base of the building and at the stage of loading where mechanisms have fonned in the coupling beams. Designers should be aware that the degree of coupling has an impact on the total lateral stiffness, wall pier. r~ui~ed strength, and economy of construction among other things. Compromises between bu1ldrng performance and construction costs must be made. The degree of coupling also has an impact on the total wall ·p ier axial forces. As the degree of coupJjng increases, the wall pi~r required moment ~trength d~qe~e§. However, the wall pier axial forces simultaneous_Jy increase as tlie degree of co~1pling incr~a~es~ Most model codes have upper limits. on. the required axial strength of reinforced co.~sret~~vall piers. \Vhen rhe wall pier required axial stre~gth e~ceeds prescri~e
1:

Steel Coupling Beam Design

~~ .::: ~ B .,

an

I

~" t

.. ~~

Fig. 7-1. Ovenuming mechanisms ill a coupled wall system.

.. r

Steel coupling beams are designed in a manner similar to shear I.i.nkS in eccentrically braced frame. Cross-sectional proportioning is. depende\'.it ~n the desired performance of the beams. flexure-<.:ritical beams will have cross-sectional properties · that e~~ure inelastic deformations are resisted through flexural yieldiog. Shear-critical beams will have crosssectional properties that ensure inelastic deformations are resisted thro\lgh shear yielding. AISC Seismic Provisio11s Sections H4 and H5 pennit either shear-critical or flexurccritical coupling beams. Shear-critical and flexure-critical coupling beams h~ve lengths (~!; .• than or equal to 1.6MpNp or greater than or equal to 2.6MpNp. respectively. Coupling

~:·

A.\f15RJCAN lf'IS1Tl1JTE OP S'ra;L CONST'RUCTION

AMEIUCAN

lNS'tn'UTE OF STEEL CONSTRUcnON

7-12

COMl'OSJTE BRACED FRAMES AND SHEAR WALLS

beuilt-up shapes provide more fleXibility for prOJ;>Ortioning cross sections to satisfy design requirements. Flanges and webs of the: beams must satisfy seismic ductility requirements regardless of whether built-up di rolled shapes are used. Coupling beams in ordinary systems are required to be moderately ductile. Coupling beams in special systems are required to be highly ductile. The required shear strength of a coupling beam is the shear corresponding to the required flexural strength, assuming the required flexural strength acrs as equal moments at the ends of the beam bending in reverse curvature, as shown in Equation 7-2.

7- 13

7.S COMPOSITE SHEAR WALLS

Using Equation 7. 3 for a shear-critical coupling beam and substituting Equations 7-5 and 7-6 gives the relationship between the required plastic section modulus, Z... and length of the bc3Ill, L, as~uming a homogeneous member. as follows:

l.6Mp l.6F1 Zx l.6Zx L'S.--= =-Vp 0.6F1 A,., 0.6Aw

Solving Equation 7. 7 for the required plastic section modulus yields, for a shear-critical coupling beam:

z

>I.A..,

For an ordinary system. the area of the web is calculaccd as A.., = dt,.. Therefore, for a shear-critical beam in an ordinary system:

z

>Ult,.,

.:t -

(7-9)

2.67

where d depth of beam t,.. = thickness of beam web For a special system, the area of the web is calculated as Aiw a shear-critical beam in a special system:

=

~~ discussed previously, steel coupling beams are treated similar tO steel links in eccentrically braced frame systems. For a given beam~ a relationship between the beam length, plastic section modulus, and web area can be written using the relationship between length, plistic ·frex~~ strength, and shear strength. Thus, for a shear-critical coupling beam:

L-.;l.6Mp -

Yp

Z:r ~ 11 ""

L(d-2t1)t,.,

(7-10)

2.67

thickness of beam flange

Using Equation 7-4 for a flexure-critic~ coupling beam and substituting Equations 7-5 and 7-6 gives the relationship between the.required plastic section modulus and length of the beam. assuming a homogeneous member, as follows: (7-4)

For an ordinary system, according to AISC Seismic Provisions Section H4.Sb, the shear strength of the beam is calculated using AISC Specification Chapter G where the area of the web is calculated as dr..,. For a special system, according to AISC Seismic Provisions Se.ction H5.5c, the shear strength of the beam is calculated according to AISC Seismic Provisions Equation B-2. Note tbat there is tyP,icauy little, if any, axial load demand on a coupling beam. Therefore, the area of the web is calculated as (d-211)1.... The plastic flex.ural strength and shear strength of the beam are given as:

lNsTmrre OF STSa Cotm11ucnoN

=(d-2y) 1...,. Therefore, for

where (7·3)

and for a flexure-critical coupling beam:

AMIWCAN

(7-8)

x - 2.67

(7-2)

where L ~ lepgth of beam Mu= jequired flexural strength Vu =required shear strength

(7-7)

2.6Mp

2.6F Zx

1 L>---=-......<..- V, 0.6F1 A..,

2.62.:r

(7-11)

0.6A,..

Solving Equation 7-11 for the required plastic section modulus yields, for a Oexurecritical coupling beam: (7-12)

(7-5)

For an ordinary system, the area oflhe web is calculated as A.,,,=dt,... Therefore, for a flex· ure-critic:il beam in an ordinary system:

(7-6)

(7- L3)

AMERJCAN

lNsTrTvnl OF STEEL CONSTRUCTION

I·

~

I


">.: ~ ..

7- 14

:l L.

For a speciaJ sys1em, the area of the web is calculated as Aiw a flexure-critical beam in a special system:

=(d- 2y)t,.,. Therefore, for (7-14)

Using a model of three rectangles for an I-shaped coupling beam. the plastic section modulus can be taken as:

t

,,

I:;

I

(7-15)

" ..!~··,

,_.-

·::.:

-----~:•...-,

··~

.,...

~:.

where

bf= width of beam flange Equations 7-9, 7-10, 7-13, 7-14 and 7-15 can then be used to establish the cross-sectional dimensions of the beam. Maldng further assumptions regarding beam depth, flange size or web size, the remaining cross-sectional dimensions can be calculated. For example, assuming a beam depth, d, a Oange thickness, fJ, and web thickness, 1,.., the required flange width, bf, can be calculated. There are other considerations to address in the detailing of the coupling beam. The embedment length into the wall pier, intermediate web stiffeners, face bearing plates, and connection detailing all also need to be determined. These considerations vary depending on the type of system (i.e., ordinary or special systems), and are discussed in separate sections of this Part of the Manual.

Beam Embedment Length (Connection)

~.

.. •·t: 1 (~·

.....

The required beam embedment length is detemlined based on the expected shear strength of the coupling beams. The AlSC Seismic Provisions require the embedded length to be me:is· ured from pie location of the first reinforcement layer of the confining reinforcement steel in the boundary element of the wali. The expected shear strength of the beam is detennined using a fonn of Equation 7-2, where ·the expected plaslic flexural strength of the bea.ni, RyMp. is substituted for Mu. This is the sta~c shear associated with a required flexw:al strength equal to the expected plastic flexural strength of the beam. For special systems, the shear calculated based on the expected plastic flexural strength must be amplified by a factor of 1.1 when computing embedment length, as required by AISC Seismic Provisions Section H5.5c. This is to account for strain hardening. The embedment length can be determined th.r ough AlSC Seismic Provisions Equation H4-2 or H4-2M. The coupling beam clear span is identified as g in Equation H4-2.

the Manual, further discussion of detailing requirements is provided in the Commentary to AJSC Seismic Provisums Sections H4 and H5. Face bearing plates (link stiffeners) are provided on both sides of the beam web, and located at the face of the wall pier. These plates should meet the requirements of stiffeners in links at the diagonal brace ends in an EBF as required in AISC Seismic Provisions·Section F3.5b(4). The web of the beam. over the clear span, must be supported with web stiffeners meeting the requirements for intermediate link stiffeners in Section F3.5b(4). From AJSC Seismic Provisions Section H5.5c, the beams in special systems are to have inelastic deformation capacities equal to 0.08 rad. Smaller rotations are pennitted if justified by a rational analysis of the inelastic defonnations expected under design story drift.

Wall Overstrength The beam required shear and flexural strengths delivered to the wall piers as an ax.ial force and moment, respectively, mus t be accounted for in the design axial and flexural demands on the wall piers. In ordinary systems, lhe required axial strength from the coupling action is based on an accumulation of expected beam shear strengths (i.e.i LVn)- ln special systen;is, the expected beam shear strength must be amplified by a factor of 1.1 to account for strain hardening [i.e.• 2:(1.lVn)J. These amplified axial loads are generally referred to as wall overstrength. The proportioning of beam shear strengths can ha,·e a significant impact on the required a,~ial strength of the wall piers. To minimize. the waJl overstrcngth, beam sizes can be grouped over the height of the building to minimize the ratio of nominal beam shear strength to required beam shear strength at each floor.lev~. Figure 7-2(a) shm~s a representative plot of che beam required shear strengths over the tieight of the building when the same coupling beam size is used over the entire height of the structure. When the same beam size is used, the beam size is proportioned based on the maximum required beam shear strength. Beam

1 i---.;:z;~~'7)7,:~~~)?,i ~

Detailing Requirements in the Embedded Region For ordinary seismic force resisting systems, there are no special detailiog requirements in the embedded region. For special systems, the embedded region must be detailed to provide resistance against connection strength and stiffness degradation. and to ensure proper distribution of bearing stresses within the embedded region. Face bearing plates, web stiffeners, and vertical transfer bars are required. In addition ro the discussion presented in !his Part of

....

7- 15

7.5 COMPOSJTE SHEAR WALLS

Beam shear

(a)

(b)

Fig. 7-2. Beam shears/or (41) same size beam over the entire height and (b) three groups of different sizes.

7-16

COMPOSITE BRACED FRAMES AND SHEA.R WALLS


7-17

I

strenglhs at all other floors, other than the floor corresponding to maximum required strength, will be relatively stronger lhan required. This effect is amplified in the upper and lower floors. In Figure 7-2(a), the hatched region bounded by the nominal streogch and required strength is a gr.iphical representation of the magnitude of the wall overstreogth required. At the floor level of maximum required strength, the design strength-to-required strength ratio approaches one, wilh that ratio increasing at floors above or below that floor. Even at the floor level of maximum required strength, some deg.rec of overstrength will exist when the shear strength resistance factor, 9'·. is less than 1.00. When wall overstrengtb is based on e.,"l'.pecr.ed beam shear strengths, wall overstrengtl1 requirements increase further. Although proportioning a system in this manner is advanta· geous for drift-controlled systems, it represents tho worst case for wall overstrength requirements. Considering that coupled systems rarely are drift-controlled. proportioning be.un sizes by groups over the heigh1 of the building will reduce 1he wall overstrength required for the wall piers without compromising drift limits. Figure 7-2(b) represents beam required shear strengths and available strengths varied over the height of the building. In the representation shown in figure 7-2(b), three groups of different size beams are used. This type of proportioning alters the distribution of required shear strength over the height as a result of the varying beam stiffness and reduces the aesign strength-to-required strength ratios at each of the floor levels relative to the case where the same beam size is used over the entire heigbL Th.is type of proportioning is referred to as tuning the beam shear strengths. The extent of tuning performed is up to the designer based on the level of efficiency desired. Further information regarding runing and wall overstrength can be found in Fortne)' et al. (2008) and Harries :md McNeice (2006).

Note 3. Loads and load combinations as delioed by the applic:ibJc building code are to be followed as indicated in AISC Seismic Provi.rions Section 82. Note 4. The required strength for structural members and connections is dctennincd according 10 AISC Seismic Provisions Seccfons B3.1 and H4.5. Noce 5. Structural analysis for the appropriace load combinations is Lo be perfooned in accordance with the requirements of AISC Seismic Provisions Chapter C and Section H4.3. (a) For elastic analysis, the stiffness of composice members includes the effects of cracked sections. Additional guidelines for estimating the stiffness of concrete beam and column members. concrete-encased and concrete-filled members, and steel beams with composite sJabs are provided in lhe Commemary to lhe AJSC Seismic Provisions Chapter C. These concrete and composite member properties reflect the effective stiffness at the onset of .significant yielding in the members. Note 6. System requirements are as given in AJSC Seismic Provisions Section H4.4. Note 7. Boundary members of C-OSW systems are designed in accordance with the AlSC Specification and AISC Seismic Pro~·isions Section H4.5a. Note 8. Coupling beams of C-OSW systems are designed in accordance with the AISC Specification and AJSC Seismic Provisions Section H4.5b. Structural steel links must satisfy the requiremem for moderately ductile members. (a) J'he beam flange must meet the width-to-thickness requirements for a moderately ductile element giveo in AISC Seismic Pr
Composite Ordinary Shear Walls (C-OSW) Composite ordinary shear wall (C-OSW) systems are d~igned in accordance with AISC Seismic Provisions Section H4. Face of wall

Overview of Applicable Design Provisions A

An overview of the AlSC Seismic P~ions requiremerus for the design of C-OSW systems follows. Figure 7-3 illustrates an embe-Oded steel coupling beam in an ordinary system.

Cf.beam B

Areas of the figure are labeled to identify peninent design considerations that correspond to the "Notes in figure 7-3" listed in Table 7-4. Table 7-4 also provides a simplified overv1ew of the design requirements that follow. Note l. The structural steel material used for C-OSW systems is limited by the require· ments of AlSC Seismic Provisions Section A3.l, where the specified minimum yield stress of the steel for members in which inelastic behavior is C)tpected is oot co e."(eeed 55 ksi. These specified minimum yield stresses can be e..'\ceeded when lhe scitability of the material is determined by testing or other rational criteria. The weld filler rnctaJ used in the members ;:ind connections of the seismic force resist· ing system is s~lected to meet the requirements of AISC Seismic Proyisions Section A3.4a. The concrete and steel reinforcing mat.erials used in composite component<> should satisfy the requiremen~ of AJSC Seismic Provisions Section A3.5. Note 2. The structurnl design drawings :10d specifications for C-OSW systems are to mw,, the requirements of AJSC Seismic Provisions Sections A4.1, A4.2 and A4.3.

4

•

•
c D

E

Fig. 7-3. lllusiration of1U1 embedded sreel coupling beam for a C~OSW system. Nares

are keyed to Thble 74.

I'

l.

'.

t

7- 18

COMPOSITE BRACED FRAMES AND SHEAR WAU.S

Notes in Figure 7-3 and Simplified Overview of C-OSW Requirements

..

i::J ...

~1 1

7- 19

Steel Coupling Beam Design

Table 7-4

. ·'

Note in Flg. 7.3

Note in Overview

-

1

Mater1als

Seismic Prov. Sects. AJ. J, A3.2, A3.4a & A3.5

-

2

Structural design drawings and specificatio(ls

Seismic Prov. Sects. M.1, A4.2&M.3

Refefenced

Item

standard•

-

3



4

Required strength for structural members and cormections

Seismic Prov. Sects. 83.1 & H4.S

-

5

Structural analysis

Seismic Prov. Cli. C& Sect. H4.3

-

5(a)

Composite member stiffness

Seismic Prov. Comm. to Ch.C

-

6

System requrrements

Seismic Prov. Sect H4.4

-

7

Boundary members

Seismic Prov. Sect H4.5a

-

8

Coupling beams

Selsmfc Prov. Sect H4.5b

A

S{a)

Beam flange local buckling

Seismic Prov. Sect H4.5b(1)(1) &Table 01.1

8

S(b)

Web local bLickling

Seismic Prov. Sect. H4.5b(1Xl) & Table 01.1

c

8(c)

calculated embedment length

•.

75 COMPOSITE SHEAR WALLS

Seismic Pr(JV, Sect

The steel coupung beams used in C-OSW systems do not require special detailing. The proportioning of the beam cross sections over the height of the building need only satisfy the requfred shear and moment strengths determined from a linear elastic analysis (e.g., equivalent lateral force analysis). Flexural and shear strengths are determined using AlSC Specification Chapters F and G. However, AISC Seismic Provisions Section H4 requires the beam-to-waU connection to transfer the expected beam shear strength. Therefore, it is ldvantageous to consider grouping beam strengths over the height of the building in an effort to minimize the required embedment lengths at each level. Flanges and webs must satisfy the ductility requirements of AlSC Seismic Provisions Section D1.1 for moder!ltely ductile members. For these checks, the value of Ca in Table D1. l can be taken as zero because these coupling benms have litlle or no required axial strength.

Beam Embedment Length The required length of the beam embedded into the wall pier is determined using AISC Seismic Pr(]Visions Equation H4-2 or B4-2M. The Vn teon in this equation is the expe.cted beam shear strength. In this equation, the tenn g is the clear span of the coupling beam. However, the acrual embedment length is measured from the first line of boundary element wall reinforcement. So. the actual embedment length of the beam, from the face of the wall, is the length calculated using Equation H4-2 plus 1be concrete cover of the boundary elemem reinforcement as illustrated in Figure 7-4.

Composite Coupling Beams Expected Plastic Moment AJSC Specification Section 13.3(c) permits the use of the plastic stress distribution or straincompatibility methods for determination of tlexural strength on the composite section when

H4.5b(l )(3)

D E

F

Total embedment length Beam cJear·span, t0< calculation ol embe
Reinforced concrete walls

reinforcement

Boundary steel

ACl 318 Sect. 11.9 &

Face or wall

Cit 14

-

wan pier axial load due to coupring actioo

~beam

•4

Undefined in lt.e SeiSmiC PrrwisJons. Sa! this Part al tile Manual for guidance.

'The refereoced stan
j; ~; '.•

... j: r:

r:·

(c) The embedment length is determined from AISC Seismic Provisions Equation H4-2 or H4-2M, and is considered to begin inside the outer layer of confining reinforcement in the wall boundary layer. Note 9. Reinforced concrete walls ore designed in accordance with ACI 318 Section 11.9 and Chapter 14.

Outer layer of confining relnfOf'cement Note: Horizontal wall reinforcement not shown

L. Total embedment length

Concrete cover

'f2

Fig. 7-4. Total embedmenr length of beam. A/.tEJIJCAN 1.NSTTIV11! OP Sn:E.. CONSTl\\JC110.'(

7-20

COMPOSTTE BRACED FRAMES AND SHEARWALLs

l'

o.asrcr

..:.

G

21.0H.-W

~ ·

"ti

i---

Tb

.

I j:

Shear Strength

'T'; Concrete stress

7-21

cf the structural steel coincide with the elevation of the upper and lower reinforrement, respectively. an emirely new set of geometries exists. Additional configurations are possible, depending on the placement of the steel member and the reinforcing. Figure 7-5 shows three possibilities for the location of the plastic neutral axis in a cross section where the structural steel does not extend into the elevations of the steel reinforcemenL For Case I, the plastic neutral axis is above the top of the steel shape. Although it is possible, it is unlikely that the reinforcing steel in thjs region would be below the plastic neutral ax.is, so that possible arrangement is not illustrated. For Cases 2 and 3, the plastic neutral axis e:i:tends imo the structural section. Regardless of the position of the elements, the plastic moment strength can be determined using either the plastic s tress distribution method or the strain compatibility method of AJSC Specification Section 13, as appropriate. The challenge is in determimng the location of the plil~tic neutral axis. One approach would be to use the equations for pure bending given for composite beam-columns in Tables 7-IOA, 7- JOB, 7-llA and 7-1 lB in this Part of the Manual.

steel ~c~ors are provided. At the expected plastic moment strength of a composite coupling beam, it 1s reasonable to assume that the concrete in tension has cracked. To calculate plastic moment strength, the location of the plastic neu tral axis of the cracked section must be determined. Depending on the p0sition within the cross section of the constituent elements there are· many different locations of the plastic neutral axis that can be conceived when detennining the internal forces acting on the section. For example, assume that the structural steel section does not extend up to the top layer or below the bottom layer of longitudinal reinforcement as shown in Figure 7-5. lf the centroids of the top and bottom flange

PNA

7J COMPOSITE SHl:.AR WALLS

The limiting expected shear strength of a composite coupling beam is calculated using A ISC Seismic Provisions Equations H4·4 or H4-4M and js based on the expected strength of the steel shape. The total expected shear strength is the sum of the resistances provided by the strucrural steel section, the concrete, and the transverse reinforcement. Of the three material contributions to the total shear resistance of the beam, expected material strength is considered only for the structural steel. From the ACI 318 requirements for shear reinforcement, the size and spacing of transverse reinforcement depends on the ma&•Ttitude of shear stress being resisted. However, regardless of the magnitude of shear stress, at least the minimum shear reinforcement requirements must be provided. The Commentary toAISC Seismic Provisions Sections H4.2 and H5.2 provides funher cliscussion on this topic.

Forces

Case 1: Plastic Neµtral Axis a bove Steel Shape

,:

Embedment Length

Concrete stress

As with steel coupling beams, the embedment length of the steel section of the composite

beam is considered to begin within the outer layer of confining reinforcement. Similar

Case 2: Plaptic Neutral Axis in Flange

to steel coupling beams, the embedment length is determined through ATSC Seismic

Provisions Equation H4-2. but is based on the nominal shear strength defined by Equation ll4-3. As discussed previously, it is permitted co have a composite beam detailed to be shear- or flexure-critical.

PNA

Example 7.5.1. C-OSW Steel Coupling Beam Design Given: Concrete stress

The siJ.:th floor core plan of a 15-story core wall system is shown in Figure 7-6. The com-

Forces

~ite ordinary shear wall system is coupled

Case 3: Plastic Neutral Axis in Web Fig. 7-5. Possible internal forces based on the plastic stress distribwion. AMERICAN .INSTITIJTS OF STEtil.. CONSTllUCllOl'I

..

I ,

~-

with steel coupling beams. Coupling beam sizes are grouped such that different beam sizes are used at floor levels 1-5, 6-10, and 11-15. Table 7. 5 tabulates the maximum LRFD beam required shear strength for each group Of beams. A modal response spectrum analysis procedure according lo ASCE/SEI 7 was AMERICAN I NSTl1Vll! OF STEEL CoNSTRUcnON

t

....

l

7-22


7.5 COMPOSITE SHE.AR WAUS

7-23

•t..,

"·

used to detennjne the seismic loading, wbkb was theu combined with gravity loads using the basic seismic load combinations of ASCEISEl 7 Section I 2.4.23 (not using the ampli· fied seismic load). The analysis meets AISC Seismic Provisions Section H4.3 requirements; I) uncracked elJcctive stiffness ralues were used, and 2) flexibility of the connea:ion between coupling beams and wall piers was taken into account. Second order effects were also considered in the ruialysis.

From ASCEJSEI 7, lhe following parameters apply: R = 5, Cd= 4.5, Design Category C, and le = 1.0.

~:::

Table 7-5

LRFD Beam Required Shear Strength

2.5, Seismic

The compressive strength of the wall pier concrete is 8 ksi, the steel reinforcement is ASTh1 Grade 60. and the steel beams are built-up I-shapes of ASTM A572 G.ttide 50 plate material. The clear cover from foce of wall co boundary reinforcement is 0.750 in. The maximum beam depth permined is 30.0 in. Assume a maximum rotation of 0.08 rad and no a.."tfaJ load in the coupling beam.

FlOOf Level

v•. kips

11-15

295

6-10

486

1-5

380

Table 7-6

Expected Beam Shear Strengths, Vn

Perform the following: 1. Specify lhe cross-sectional dimensions of the coupling beruns on levels 6-10 assuming that lhe beam will be shear-critical. 2. For the beam sized in Part l of this problem, compute the required embedmenl length of lhe beam into the wall pier. ·· 3. Given tbe LR.FD beam required s™:ar strengths over !he height of ~e building provided in Table 7-5, determine the LRFD required axial s1rength al tb.e base of !he wnll piers due to coupling action only.

FlOO' Level

Vn. kips

11-15

325

6-10

To be detennined

1- 5

429

Solution:

Part 1: Coupling Beam Design From AISC Manual Table 2-4, the material properties are as follows:

!IHllll

~

;·,,

.

AS'Thl A572 Grade 50 Fy =50 ksi F.,=65 ksi

Stiffener

Ill HJ

plate (typ.)

A

Local Buckling

en ...-

For a C-OSW system, the flanges and webs of the steel coupling beam are to satisfy the requirements for moderately ductile members. Referring 10TableD1 .1 of the AlSC Seismic Prvvisions, the limiting widrh-to-thickness ratio for a built-up member is given.

t·

lllHI 12'-0" (a)

..

..

j (b)

From AISC Seismic Pl'()Vision.s TabJe Dl.l, the limiting widLb-to-lhickness ratio for the Oanges of the beam is:

b

-$/. f

Fig. 7-6. (a) Core planar six1hjloor and (b) Section A-A-beam cross section. ;,

,,.

.. ;

·~ii

:: -l 1

d

'"

7-24

COMPOSJTE BRACED FRAMES AND SHEAR WALLS

'Arru1 =0.38 =

75 COMPOSITE SHEAR WALLS

Determine Lhe required nange thickness to satisfy flange local buckling based on the litniriog width-10-thick.ness ratio derermincd previously.

fK

vF;

~ ~9.15

_ 29,000 ksi 0 38 50 ksi

t

= 9.15

b b1 -=2t1

The limiting width-lo-thickness rario for the beam web is also detemtined from Table DL l as follows:

"'9.15 11

> 15.0 in.= 0 820 . - 2(9.15)

·

'"·

Assume y = 1.00 in.

Because there is no axial load on the beam, P,. =O; therefore, C0 = 0.

Knowing the depth (d = 30.0 in.) and flange thickness (lj value, d - 2lj. can be calculated.

Ama=3.76 ([(l-2.75C,,)

'JF,

=3 .76

7-2.5

=1.00 in.) of the cross section, the

d-2c1 ==30.0 in. -2(1.00 in.)

29,000 ksi (l-O) 50 ksi

= 28.0 in.

=90.6

Using rbe trial values for the flsnge and web dimensions, the thickness of the web can be determined. The thickness required to satisfy the link length equation is used to compute the required 1hickness and A..,= dt,., :iccording to AISC Specification Section G2. Solving for c,,.:

Link Length Requirement

The problem stAtement requires a chord rotation of O.OS rad and a shear-critical coupling beam. Using Equations 7-9 and 7-15:

> Ldt...,

b1t1(d-t1 )+

c,., ( d-21 4

I

l

Ult.., 2.67

)

=--

· )(J .00 rn. · )(30.0 ·in. _ 1.00 rn. . ) +--------t..., (28.0 jn.)2 _ 72.0 in.(30.0 in.)r; (15 .o m.

- 2.67

4

I,.. ::: 0. 710

2.67

in.

Use 1,., = 0.625 in.

Assume the beam depth, d, is the ma.'timum permitted of 30.0 in. The maximum flange width that can fit within the steel reinforcement in the wall piers is (assuming No. 8 bori· zontal and vertical reinforcing bars):

= 24.0 in. - 2(0.75 in.)- 2(1.00 in.)-2(1.00 in.)

I

'

The following trial section dimensions can be used to check the requirements.for the design of the beam. b1::: 15.0 in. d=30.0 in.

11 = l.00 in. lw =

0.625 in.

A =47.5 in. 2 11 =563 in:'

'1=3.44 in.

=18.5 in. Check web local buckling

where c~

= concrete cov~r

db,v

=diameter of vertical reinforcement bar dfameter of horizontal reinforcement bar

db,h

=

Use b1= 15.0 in.

h

-$90.6 I

h

28.0 in. 0.625 in.

==44.8 <90.6

o.k. AMEIUCAN

lNsJTnml OP S1EllL Cot
.l

1 ,.. t

7-26

COMPOSITE BRACED FRAMES ANO SHEAR Wi;us

Check flange local buckling

l .,.,

')".-~ i

,, 1:- .•

~--1

~$9.15


7-27

Aexural Strength The required flexural strength at levels 6-10, from Equation 7-2 wilh

v,, from Table 7-5, is:

./

t

Mu= V.,L

f!._ .!!i_

2

=486 kips(72.0 in.)

- 2t1

=

2 =17,500 kip-in.

15.0 in. 2(1.00 in.)

Because !he shape is compact according to the AJSC Specijicorion, determine whether the limit state ot lateral-torsional buckling applies.

o.k.

=7.50<9.15

Maximum Unk Length

For a shear-critical beam in an ordinat)' system. the maximum link lcnglh is determined from Equation 1-3 as follows:

Lp = l .76r1

[f

(Spec. Eq. F2-5)

'J.F_~

29.000 ksi -50 ksi

"'1.76(3.44 in.)•-S l.6Mp Vp

L

(7-3)

l.6Mp _ l.6F7 Zi Vp - 0.6FyA1,,.

"'146 in. Because 72 in. < 146 in., lateral-torsional buckling does not apply, and the:. design flexural strenglb based on flexural yielding is detenn.ined in acco.rdru1ce with AJSC Specification Section F2.l:

where

)2 Z;,: = b1t1 ( d-c1 ) +-'----';..:._ t,.. ( d - 2t1

(7-15)

4

= (15.0 in.)(1.00 in.)(30.0 in. -

2 1.00 in.)+ 0 ·625 ia.( S.O in.)2

$Mn=tVMp =0.90(27,900 lcip-in.)

=25,100 kip-in. 25,100kip-in.>17,500 kip-in.

4

o.k.

1

=558 in.

1:~ ...

Shear Strength

(7-5)

Mp= F1 Zx = 50 k.si(558 in.3)

For a built-up member:

=27,900 kip-in. ' I'

(7-6)

VP :::: 0.6F1 A,,,,

=0.6(50 ksiX30.0 in.X0.625 in.) =563 kips

,... :·

For a beam without stiffeners, k..,

uot·E =uo

=5, and

5(29,000 ksi) 50 ksi

=59.2 > 44.8

L $ 1.6(27,900 kip-in.) 563 k:ips

\

Therefore:

S79.3 in. 72.0 in. S 79.3 in.

~::::0.90

Fy

Therefore:

......"

The available shear strength frorn AlSC SpecijicaJio11 Section 02 is determined as follows.

(Spec. Eq. 02-3) o.k .

The given link length of 6 ft meets this rcqui.remenl.

COMPOSJTE .GRACED FRAMES AND SHEAR WAU.S

7-28

7- 29

Use Vn = 619 kips.

lbe available shear strength is: (from Spec. Eq. G2-1)

=0.90(0.6)(50 ksi)(0.625 in.)(30.0 in.)(1.0) =506 kips> 486 kips o.k.

Detenn.ine the cmbcdmcm length by solving for L. in Equation H4-2:

24 0 in 619 = l.54.J8 ksi ( · . · 15.0 JO. 619=

Part 2: Beam Embedment Length From Prut l of this solution, Vn

7.5 CO!'v!POSI fE SHEAR WAU..S

=563 kips and M.,. =27,900 kip-in.

)o.66

(0.65)(15.0 in.)L.

0.58- (0.22)(0.65)1 72.0 0.88+ -

.

2L,

25.3L. 0.88+ 36.0

L.

From AJSC Seismic Provisions Section H4.5b(l )(3):

L. = 42.3 in. The toral embcdment length, from the face of the wall, is:

(Provision.s Eq. H+2)

\.:

L.+Cc =42.3 in.+0.750 in. =43. 1 in. where b,.,=24 in.

Therefore, each end of the beam will be embedded a minimum of 44.0 in. from the face of the wall.

fJ =8 ksi ~l

=0.65 from ACI 318 Section 10.2.7.3

Part 3: Wall Pier Required Axial Strength

g =L=72.0in.

In AISC Seismic Provisions Equation H4-2, g could be replaced with 8eff• an effective clear span to account for spalling at the face of che walJ, but this is not required by the AISC Seismic Provisions and will have very fatle impact on lhe final design. This would require the clear span to be increased by the concrete cover over the first reinforcing bar at each side.

AISC Seismic Proi:isions Section H4.5b(1)(4) requires that vertical wall reinforcement with a no~inal strength equal to the expected shear strength. Vn, of the steel coupling beam be provided over the embedded length of the coupling beam. The axial load resultin<> from the coupling action on the base wall piers is the ac~umulation of the expected i:am shear strengths over the height of the building.

For the given core wall system, two coupling beams frame into each shear wall.

The expected shear strength of the steel coupling beam is:

(Provisions Eq. H4-l)

~ased on the nominal shear strengths ·given in, Table 7-6, the required wall pier axial strength 1s determined as follows. \

Expected beam shear strength at levels 11-15, from Table 7-6: From AISC Seismic Provisions Table A3.l, for ASTM A572 Grade 50 material:

=(325 kips/floor/beam) (l::V,. )1 1-1s =(5 floors)(325 k.ips/floor/beam}(2 beams) (V,. )11_ 15

Ry= 1.1 V,.

=2R1 Mp

=3,250 kips

g

=2(1.1)(27,900 kip-in.)

Expected beam shear strengths at levels 6-10 from previous calculations:

72.0 in, =853 kips V,. =R1 Vp

=1.1(563 kips) =619 kips

(Vn.)6-io =(619 kips/floor/beam) ',I

(.tV,, )6--10

=(5 floors)(6 I 9 kips/floor/beam)(2 beams)

I~

= 6,190 kips

I

..

LI

7-3-0

COMPOSITE BR.ACFO FRAMES AND SHEARWA!LS

Expected beam shear strength at levels 1-5, from Table 7-6:

..

(V" )1_5 = ( 429 k1ps/Ooor/beam)

(LV,,)1_ 5 ~· •, •,

..

=(5 floors)(429 kips/floor/beam)(2 beams) = 4. 290 kips

~

7 - ll

75COMPOSITESHFAR WAI IS

AST\1 A992 material is used for the structural i.recl. ASTM \615 Grade 60 matenal i.; used fOf all steel reinforcement, :ind the concrete compre~sivc \lrength 1s 4 ksi. 1 Specify the required spacing of the transverse rcinforcemenL 2. Calculate the expected plastic moment strength of the composite beam. 3. Calculate the required cmbedmenl length of the structural i.tcel seccion into the \\all pier. Assurne !he sp~m length of the beam •~ 5.00 ft between wall faces .

The total axial load effect due to coupling below level 1 is: P~. wall, coupling=

3,250 kips t-6, 190 kips+4,290 kips

Solutio n: From AISC Manual Table 2-4, lhe material properties are as follows:

= 13,700 kips The required axial strength of the wall piers in upper floors is calculated in a similar manner. Jn such a case, the total axial load due to coupling, al a given floor level, is an accumulation of ~e beam shear strengths for the beam at the floor being considrrcd 3Jld

ASTMA992 Fy = 50 ksi F. = 65 ks1 From AISC Manual Table 1- 1. the geometric propenies .ire a:.

beams above.

follow~:

W14x53

Exampfe 7 .5.2. C-OSW Composite Coupling Beam Design

..:~

-

' •

Given: A composite coupling beam is used to couple the 16-in. thick shear walls of a com~1tc ordinary shear wall system. A cross section of the coupling beam is shown in Figure 7-7. A mod:il response spectrum analysis procedure according to 1\SCE/SEl 7 was used 10 deter· nune the seism.ic looding. ''hich was then combined with gravity loads using the basic seismic load combinations of ASCE/SEI 7 Section 12.4.2.3 (not using the amplified seisJnJc load). The analysis meets AISC Seismic Previsions Section 114.3 requirements: I) uncrackcd effective stiffness values were used, and 2) flexibility of the connection between coupling beams and wall piers was taken into account. Second-order effeccs were also considered in the analysis. The LRFD required shear and flexural strengths are:

r11• = 0.370 in.

d:::: 13.9 in.

Z= 87.1 in.

=S.06 in.

If

=0.660 in.

Part 1: Specify Transverse Reinforcement Spacing .\ccorc.ling to AISC Specifica1io11 Section 14. l, the sh~ar ~trcngth of the composite beam can lit 13ken as the sum of that contributed by the steel ~ape and that comnbuted by the rein· forcing. with¢= 0.75. With the required shear strength gl\en :is 232 kips, the nominal shear strength of the composite coupling beam must be .11 le~t the following:

9 k'l pS

232

v,.~--=30

11

0.75

For the rolled steel :.hape with ltrength of the steel is:

Vu =232 kips M11 = 6.960 kip-in.

bt

3

Ii/ r.., ~ 2.24.JE/ Fy • c. =1.0; therefore, the nominal shear (S~c.

V•,s1u1=0.6F.A,.C, = 0.6(50 ksi)(J 3.9 in.)(0.370 in.)(1.0)

=154 kips

Comer bal'$, #8

The rei nforcing steel must provide the following nominal shear stteogrh:

W1 4x53

v...

Stirrups,#5

Jr

~ 309

kips - 154 kips= 155 kips

For No. 5 stirrups, the maximum spacing can be clctem1incd usi ng:

~:

"" ''·

V,.,,,

=A,f,.d 1

16.0"

Fig. 7.7, Composi1e coupling beam su11on.

..

Eq. G2-I)

Therefore, solving for s, the required stirrup spacing is:

(AO 318 Eq. 1 l -15)

7-32

COMPOSJTI.: BRACED FRAMES AND SHEAR WAilS

=

Avhd s=--

=

ASThf A992: R>F1 1.1(50 ksi) 55 ksi ASTM A615: R}F1 = 1.25(60 ksi) =75 ksi

V,.,,,

=

7- 33

7.5 COMPOSITE SHEAR WAL.LS

4-k..~i

2(0.31 in.2)(60 ksi)(J 7 .5 in.)

..

154 kips

=4.23 in.

concrete: 1.50/c' =I 50(4 ksi) = 6 ksi

From Table 7- lOA, ai;~uming that the plastic neutral axis is io the flange, the variable hn c:m be determined. This is 1he distance from the centroid of the section to the location of the plastic neutral axis. Th\ls:

Maximum Transverse Spacing Requirements

0.85//(Ac +As - db1 )-2F1 (As -db1) hn = 2[0.S5/:(h1 -bi)+ 2F1 b1]

The maximum spacing of the transverse reinforcement is determined from ACl 318 Se<:tion l 1.4.5.l and solving for sin lhe equations for Aw. m1,, gh•en in Section l l.4.6.3. With the concrete strength taken in psi for use in ACJ 318 equ:uions: d_l7.5in. _

- -

2

2

-

Note there is no term for the reinforcing s1eel because there is no reinforcing steel at the midpoint of the section. Determine the area of the steel shape using the same geometry used in the derivation of the equations, which is the model of three rectangles.

.

875 . In.

24 in. ..\1

2

smax $min AvFy = 2(0.31 in. )(60,000 psi)= _ in. 46 5 50b,,, 50(16.0 in.) 2

:::: 2(0.3 l in. )(60,000 psi) 0.75fjlb,., 0.75-/4,000 psi(l6.0 in.) AvFy

Therefo~.

I·

=2(8.06 in.)(0.660 in.)+!J 3.9 io. -

2(0.660 in.))(0.370 in.)

=15.3 in.2

=49 _0 in.

The area of the concrete is:

Ac= 16.0 in.(20.0 in.)-15.3 in.2 -4(0.79 io.2)

the maximum spa_cing is 8.75 in.

=302 in.2

The spacing requirements based on shear strength were determined as 4.23 in. Thus. use No. 5 closed stirrups at 4.00 in. on-center spacing.

Thus: 0.85(6 ksi)l302 in. 2 +15.3 in.2-13.9 in.(8.06 in.)]- 2(55 ksi)

Part 2: Expected Flexural Strength of Composite Beam

x[l5.3 in.2 -..13.9 in.(8.06 in.)] 2[0.85(6 ksi)(J 6.0 in. - 8.06 in.)+ 2(55 k si)(8.06 in.)}

h,, =~~~---!.-~--~--'-~--'-~---,....-

It may take several iterations to identify the case (see Figure 7-5) that applies to the cross section in any given problem. For lhis problem il is assumed that the plastic neutral axis is in the flange of the steel shape-Case 2 in Figure 7-5. The plastic flexural strength may be determined by application of equjJjbrium principles or by the equations provided for pure bending of encased composite beani-columns given in Table 7- lOA of this Part of !he Manual (Geschwindner, 2010). Because these equations :ire somewhat more straigbtfoc· ward, they will be illusu-ated here. · AISC Seismic Provisions Section H4.5b(2) requires lhe use of the expected strength of the steel shape, the reinforcing steel, and the concrete. As for other expected streoglh calculations, AISC Seismic Provision.s Table A3.l gives R1 1.1 for ASTM A992 steel and Ry= 1.25 for ASTM A615 reinforcing steel.

=

The User Note in .AISC Seismic Provisions Section A3.2 states that to dete.nnine the expected strength of reinforced concrete, reference should be made to Seismic Rehabilitation of 5.xisring Buildings. ASCE/SEI 41-06 (ASCE, 2006). The expected strength can be determined by applying lhe factor provided in ASCEJSEI 41-06 Table 6-4 for concrete compressive strength, where a value of 1.50 is given. Thus, the expected yi~ strengths used in determining the expected plastic flexural strength are:

AMERICAN L~ OF Sn:a CO>ISTllucnON

=6.30 in. Because this dimension is greater than the distance from the cenler of the section to the under· side of lhe flange and Jess lban haJf of the steel beam depth, the assumpti?" that the plastic neutral axis is in the flange is correct.

.

I )

::

Using the series of equatfons given in Table 7- lOA in this Part of the ManuaJ for Point B, for h,. within the flange, and Point D:

Zsn =Z, -bf (%-Jin)(i+hn) =871' . an. 3 -806' . m. (

13 9 · in. 2

6.30in.)(

13 9 · in.+6.30in.) 2

=17.7 in.3

t

I·

7-34

COMl'OSITE BRACED FRAMES AND SHEAR WAUS

7-15

7.5 COMPOSrTE SllEAR WALLS

~·'

7...:,.=h1~-z,,.

The clear span, g, for l.hjs composite coupling beam is 5.00 fl.

=16.0 in.(6.30 in.)

2

-17.7

in. 3

The expected shear slrength, V11,W11p• lS determined from AISC Seismic ProvisioJts Equation as follows:

H4~3

=6 17in.3

Z,

..

=(Au-A,,,)(h;-c)

V•. comp =

f

= 262 kips< Vcomp

=23.7 io. 3

:::.;

Zc

~

:··

where

h1h~

=- - -z, - z,

Vc.,,,,p

4

= 1.6.0 in.{20.0 in.)2 _ 8 4

~\:::J

. _2 . 7 • 1 in.3 3. 7 in. 3

r;; A3F..,,,.d, ) =R1 Vp + (0.0632-.jfcb ..-cdc + ~ =1.1(0.6)(50 ksi)(l 3.9 in.)(0.370 in.)

(from Provisions Eq. H~)

+ 0.0632J4 ksi (16.0 in.){! 7 .5 in.)

=l,490 in.3

~!·

(Provisions Eq. H4-3)

2(654 kjp-fl) 5.00 fl

=[4(0.79 in.2)-o in.2 ]( 20 ·~ in. -2.5 in.)

!. .•.

2Mp, exp 5 Vcomp g

2(0.31 in. 2 )(60 ksi)(l7.5 in.)

+-'-~~~...;._~....:..;~~-'-

·:·~

•'·

.;. ~::

,,,.~·1 ,",...

4.00 in.

Mo = ZsFy + Z7 Fyr + Zc (0.85/:) 2

=87 .1 in. 3 (55 ksi) + 23. 7 in.3(75 ksi) + 1•490 in.

l

2

=10.400 kip-in.

=368 kips

3

[0.85(6 ksi)]

Therefore, V11,comp

Note thrit the equation used here for Vromp includes a conversion factor so that/~ can be applied in ksi units.

Ms = Mo-Zrn F1 - Zen (0.85/:) 2

i" ~:~=l ~..

,,

~

=10,400 kip-in.-17.7 in .(55 ksi)

The cmbedmem length can then be determined from AJSC Seismic Provisions Equation H4-2 as follows:

3

617 in. [0.85(6 ksi)] 2

8.06 in.

Thus:

x

M p,up = 7,850 kip-in.1{12 in./ft)

262-

·-

'·...'·

~·:

~~· •'

::

.

",;

!\•

I

~:

Part 3: Beam Embedment Length From AlSC Seismic Provisions Section H4.5b(l)(3), modified according

in.)

L. 0.58-0.22(0.85) _ + 60.0 in. 0 88

= 654 kip-ft

.·..:·

~~: •.:,

0 66 . (0.85)(8.06

262:::: 1.54J4 ksi ( 16 ·0 in.)

=7,850 kip-in.

l:

(·

=262 kips.

24

13.04 0.88+ 30.0

to

Secrion

Le

=35.0 in.

4

H4.5b(2)(2):

The total embedded lenglh from the face of the wall is: b,

Vn, comp = 1.54.fjf(2

.b1

f/=4 ksi p, =0.85

)0.66 J}ib;l,

0.58-0.2213'11 0.88+-L

24


L. 1-Cc =3S.0 in.+ 0.75 in. =35.8 in. Each end of the beam will be embedded a minimum of 36 in. beyond lhe face of the wall.

7-36

COMPOSJT.e BRACED FRAMES AND SRF.AR WAJ..1.S

Composite Special Shear Walls (C-SSW)

I

Composite special shear wall (C-SSW) systems are designed in accordance with AJSC Seismic Provisions HS. C-SSW systems are reinforced concrete walls composite wuh structural steel, including steel or composite boundary members and steel or composite coupling beams.

Overview of Applicable Design Provisions An overview of the AJSC Seismic Provisions and ACT 318 requirements for lhe design of C· SSW systems follows. Figure 7-8 illustrates an embedded steel coupling beam in a composite special shear wall system. Areas of I.he figure are labeled to identify pertinent design considerations. Table 7-7 identifies specific requirements of the AISC Seismic Provisions that correspond to lhe areas labeled in the figure and pro,·ides a simplified summary of the design requirements. Note 1. The structural steel material used for C-SSW systems is limited by the requirements of AISC Seismic Provisions Section A3. l, where the specified minimum yield stress of lhe sreel is not to exceed 50 ksi for members in which inelastic behavior is expecred. This specified mjnimum yield stress can be exceeded when the suitability of the material is determined by testing or oilier rational criteria. The weld filler metal used in the members and connecrions of the seismic !force resisting system is selected to meet lhe requirements of AJSC Seismic Provisions Section A3.4a. The concrete and steel reinforcing materials used in composite components should satisfy the requirements of ATSC Seismic Provisions Swion A3.5. Note 2. The structural design drawings and specifications for C-SS\V systems are to meet the requiremenrs of AISC Seismic Proi•isions Sections A4.l, A4.2 and A4.3. Note 3. Loads and load combinations as defined by the applicable building code are to be followed as indicated in AISC Seismic Provisions Section B2. Note 4. The required strength for structural members and connections is determined according to AISC Seismic Provisions Sections B3. l and HS.5. Note 5. Structural analysis for the l\ppropriate load combinations is to be performed in accordance with the requirements of AISC Seismic Provisions Chapter C and Section HS.3. (a) For elastic analysis, the stiffness of composite members shall include the effects of cracked sections. Additional guidelines for estimating the stiffness of concrete beam and column members, concrete-encased and concrete-filled members, and steel ~earns with composite slabs are provid~d in the Commentary to the AlSC Seismic Provisions Chapter C. These concrete and composite member properties reflect 1he effective stiffness at the onset of significant yielding in the members. Note 6. System requirements are as given in AISC Seismic Provisions Section H5.4. Note 7. Boundary members ofC-SSW systems are designed in accordance with theAJSC Specification and AlSC Seismic Provisions Section H5.5b. Note 8. Steel coupling beams of C-SSW systems are designed in accordance with the A.ISC Specification and AISC Seismic Provisions Secrions HS.Sa, H5.5c and H5.5
..

7- 37

7J COMPOSITE SHr~ WAL.LS

(a) As s tipulated in AJSC Seismic Provisions Section H5.5c by reference to Section F3.5b, for I-shaped beams, with link lengths ~ 1.6,\lfp/Vp. the steel beam flange may meet the width-to-thickness requirements for a moderately ductile element given in AISC Seismic Pro,·isio11s Table Dl.l; otherwise the requirements for highly ductile elements must be met. (b) As stipulated in AlSC Seismic Provisio11s Section H5.5c, the steel beam web must meet the width-to-lhick11ess requirements for a highly ductile element given in AISC Seismic Provisions Table DI. J. (c) As stipulated in AISC Seismic Provisions Seciion HS.5c by reference to Section F3.5b, for links made of built-up cross sections. complete-joint-penc· tration groo,·e welds are used to connect the web to the flanges. (d) Intermediate web stiffeners are designed in accordance with AISC Seismic Proi:ision.r Sections H5.5a by reference to Section F3.5b(4), and Section H5.5c. which also references Section H4.5b. (e) Face bearing plates are designed in accordance with AlSC Seismic Prodsions Sections H5.5c and F3.5b by reference. (f) Vertical transfer bars are designed in accordance with AISC Seismic Provisio11s Sect.ion HS.5c. (g) The embcdment length is detennined from AlSC Seismic Provisio11s Equation H4-2 or H4-2M with modifications given in Section H5.5c and is considered to begin inside the first layer of confining reinforcement in rhe wall boundary layer. (h) The link length is detennined in accordance with AISC Seismic Provisions Section H5.5c, by reference to Sections F3.5b and H4.5b.

Face of wall

K G

Outer layer of boundary steel H

J

Fig. 7-8. Notes key for AISC Seismic Provisions design requiremems for a coupling beam in a C-SSW system (see Table 7-7).

1.

\·

-,,.m.... COMPOSITE BRACED ~"iES AND SHEAR WAU.S

7-38

:. J

""'

i~

1 )9

7j COMPOSITE SHEAR WALLS

F:ti.1 Table

:I

7~7

Notes in Figure 7-8 and Overview of Requirements for C-SSW Systems

,,,

Note in Fig. 7·8

Note In Summary

-

1

item

Materials

·.~


~

Notes in Figure 7-8 and Overview of Requirements for C-SSW Systems

I

Referenced Standard•

llote in Fig. 7-8

Note In Summary

Seismic Prov. Sects. A3. t,

J

8(h}

A3.4 &A3.5

-

2

Structural design drawings and specifications

3

load and load combinations

Seismic Prov. Seel 82

-

4

.Required strength for structural ~mbers and connecti-Ons

Selsmlc Prov. Sects. 83.1 & HS.5

-

5

Structural analysis

Seismic Prov. Seel HS.3

-

S(a)

Elastic stiffness of concrete/composite

Seismic Prov. Comm.

members

to Ch.C

System requirements

Seismic Prov. Sect HS.4

-

6

-

7

Boundary members

Seismic Prov. Sect. HS.Sb

-

8

S1eel coupnng beams

Seismic Prov. Secls. H5.5a & HS.Sc

A

8(a)

Beam flange local buckling

Seismic Prov. Sects. HS.Sc, F3.Sb(1) (Exception) & Table 01.1

B

8(b)

Web local flucl
Seismic Prov. Seel HS.SC &Table 01.1

c

8{c)

Flange-web weld (built-up I-shape)

Seismic Prov. sect. F3.5b(1}

0

8(d}

Intermediate \Yeb stiffeners

Seismic F'rov. sects. F3.5b(4), H4.Sb & HS.Sc

E

8(e)

Face bearing plates

Seismk Prov. Sects.

Clear span of beam: link length

Referenced Standard•

Seismic Prov. Sect. F3.5b(3)

Seismic Prov. Sects. A4.1, A4.2 &A4.3

-

Item

For calculation of embedmem (definition of fh

Seismic Prov. Sect. H4.5b(1)

-

Stilfener welds

l

-

Wall pier axial load Clue to coupling action

SelsnliC Prov. Seel. HS.Sc

-

9

Composite coupling beams

Seismic Prov. Sect H5.5d

-

10


Seismic Prov. Sect. H5.6a

-

11

Column spfices

Seismic Prov. Sect. H5.6b

12

Reinforced concrete walls

ACI 318 Sect. 11.9. Ch. 14 & Sect 21.9

K

-

Seismic Prov. Sect. F3.5b(4)

'The relerenceel $.dards llJ'e in addition 10 the AlSC Specification.

Note 9. Composite coupling beams are designed in nccordance with AISC Seismic Provisions Section H5.5d. Note 10. Demand critical welds are required as defined in AISC Seismic Provisions Section HS.6a. Note JI. Column splices are de.~igned in nccordance with the AISC Specificarion and AISC Seismic Provisions Section H5.6b. Note 12. Reinforced concrete walls are designed in accordnnce with ACI 318 Section 11.9 and Chapter 14, in addition to Section 21.9.

F3.5b(4) & HS.Sc F

8(~

G H

8(g)

Vertical transfer bars localion of end vertical transfer bar and stiffener Embedment lenglh: caJculated embed length Magnitude or shear used lo calculate

embed length I

Total embedment length

Seismic Prov. Seel HS.Sc Seismic Prov. Seel HS.Sc

Seismic Prov. Seel H4.Sb(1)(3) Seismic Prov. Seel.

Seel HS.Sc Seismic Prov. Sect. H4.5b(1)(3)

Steel Coupling Beam Design The steel coupling be.ams used in C-SSW systems require special detailing as outlined in AISC Seismic Provisions Section H5.Sc. The propo1tions of the beam cross sections must meet the requirements of Sections H4.5b nnd F3.5 where the coupling beam is treated as a link in an eccentrically braced fr:\me. The anticipated roLational demand of the beams in special systems is equal to or larger than 0.08 rad. • Moment and shear strength is determined using AISC Specification Ch:ip1ers r and G. The requirements of AJSC Semnic Provisions Section HS stipulate the transfer of the ex~cted beam shear strength, amplified by a factor of I. l, to the wall piers. Therefore,

AMEIUCAC'I INSTITVT£ OJ' Sn:a CONSTRUCOON

7-40

COMPOSITE BRACED !-'RAM.ES AND SHEAR WALLS

it is advantageous to consider grouping beam strengths over the height of the building in an effort to reduce the wall overstrength ·requiremenras was discussed for C-OSW systems. , , ·, Flange and web: width-to-thickness ratios ~ust satisfy the requirements of AISC Sei..rmic Provisions Section Dl.I for highly ductiJe members. :

....

Wall Overstrength From AISC Seismic Provisions H5.4(2), lhe expected shear strength of the coupling beams amplified by a factor of 1.1, must be considered as the shear required to be transferred to th~ wall piers; fo_add~tio_n, when computing the required embedment length for steel coupling beams, the Vn calculated using Equation H4- l must be amplified by l. J as indicated in AISC Seismic Provisions Section H5.5c.

7-.JJ

7j COMPOSITE SHEAR WAL.LS

Face Bearing Plates From AISC Seismic Provisions Section HS.Sc, face hearing plates (link stiffeners) are provided on both sides of the beam web and located at the face of the wall pier. These plates should meet the requirements of stiffeners in links at "the diagonal br:1ce ends" as required in AlSC Seismic Provisions Section F3.5b(4). Figure 7-9 illustrales the placement of face bearing plates.

Stiffeners within the Embedded Region Although not specifically required by the AISC Seismic Provisions, stiffeners on both sides of the web, aligned with the outennost pair of vertical transfer bars, provide significantly higher cotmection ductility than when these stiffeners are not present. The same size stiffener specified for the face bearing plate should be used and placed as shown in Figure 7-9. TI1e AISC Seismic Provisions Commentary Section H5 discusses this further.

Beam Embedment Length The length of the steel coupling b~ embedded into the wall pier is computed using AISC

Vertical Transfer Bars

Seismic Provisions Equation H4-2. The Vn tenn in this equation is the same expected beam · shear strength used to determine wall overstrength for the C-SSW system. In this equation, the term g is the clear. span of the beam. However, the embedmem length, Le. is measured from the .o uter layer of boundary element wall reinforcement. Thus, the embedment length .of the beam, from the face of the wall, is che length calculated using Equation H4-2 plus the concrete cover o~ the boundary element reinforcement as illustrated in Figure 7-9.

In C-SSW systems, reinforcing bars are attached to the flanges within the embedded region to improve the ductility and general hysteretic behavior of the connection region. The requirements for size
Intermediate Web Stiffeners

The AISC Seismic Provisions permit the attachment and development of these bars to be done mechanically. When mechanical devices are not used, weldable grade reinforcing bars (e.g., ASTM A706) may be welded directly to the flanges of che beam, and the development length is computed using the provisions of ACI 318 for the development length of straight reinforcement bars in tension. It should be noted that, depending on the diameter of the reinforcing bar used, I.he development length might be significant. Where geommy is tight, mechanical anchorage will reduce the space required for these bars.

From AlSC Seismic Provisions Section HS.5c, web stiffeners musr meet the requirements for intennediate link stiffeners given in AlSC Seismic Provisions Section F3.5b(4).

Vertical transfer bar (fyp.)

I:.

I' :.

·stiffener same as face bearing plate;

Example 7 .5.3. C-SSW Steel Coupling Beam Design

Cf.beam

both sides of web

Given: :.,

..

: ,!. -,

>d/2

t-----L.=-----1-1~Concrete cover

Total embedment length

Aligned With outer layer of wall boundary steel

Fig. 7-9. Placement of vertical transfer bars and face bearing plaies.

-~

The sixth floor core plan of a 15-story core wall system is shown in Figure 7-10. The composite special shear wall system includes steel coupling beams. Table 7-8 tabuJates the LRFD required shear strengths and Table 7-9 tabulates the nominal beam shear strengths over the height of the building. At the sixth floor level, the LRFD required shear and moment strengths (determined using the equivalent lateral force procedure) on the coupLing beams are 795 kips and 2,390 kip-ft, respectively. There is no axial load on the.beams. The applicable ASCE/SEI 7 parameters are: R = 6, C4 ::: 5, Q 0 2.5, Seismic Design Category C, and J,, LO.

=

=

l ,,.

);: >•

The compressive strength of the wall pier concrete is 8 ksi, the steel reinforcement is ASTM A61S Grade 60, and the steel beams a.re built-up I-shapes of ASThi A572 Grade 50

i

7-42

COMPOSITE BRACED FRAMFS AJ'l.'D SHE.AR WAU.S

pla1e material. The sllffener material is also ASTM A572 Grade 50 plate. The beam chord roration demands are expected to be equal to or greater thal\ 0.08 rad. The clear cover from the face of I.be wall to the reinforcement is 0.75 in. The coupling beam
.n

Table 7-8

LRFD Beam Required Shear Strengths

Perform the following for the coupling beam at lhe sixth floor: I. Cbeck the width-to-thickness rcquircmenL<1 for the flanges and web of the C-OUpling beam gh'en in Figure 7-IOl.b). 2. Determine if the clear ~pan length of tJ:ie beam is sufficient gjven the expected chord rotation demands. 3. Determine the size and spacing of the web stiffeners over the clear span region of 11Jc beam. 4. Compute lbe required embedment length of the beam into the wall pier. 5. Specify the diameter, quantity and location of Yect.ical transfer bars needed at lhc flanges within the embedded regions of the beam. 6. Detail the fai;e bearing plates required at the face of the wall and ~liffcncr near the end of the embedded regfon. 7. Given the LRFD beam required shenr strengths over the height of the buifding provided in Table 7-8, detennine the LRfD required axial strength at the base of the wall piers due to coupling action.

1

7.5 COMPOSITE .Sl!EAR WALLS

Floor Level

Vu, kips

11-15

340

6-10

795

1-5

318

Table 7-9

Nominal Beam Shear Strengths, Vn Floor Lewi

V,, kips

11-15

404

6-10

To be determined

1-5

462

~·

Solution:

tl l

The geometric properties of lhe buih-up .)Ct:tion are:

From AISC Manual Table 2-4, the material properties are as follows: ASThi A572 Grade 50

A= 91.5 in.

Fl= 50 ksi

11= 2.00 in.

F,,

=65 ksi

1

= J.25 in.

d=26 in.

1.,.

ry= 3.87 in.

Zx=9J9 in. 3

br= 16.o in.

Pan 1: Local Buclding Check member ductility

il...

From AISC S~isn11c Prr:Jl'isioll.S Table DI. I, the limiting ""idth-to-lhickness ratio for the Oanges of a highly ducule member is:

.-

' IHllll

Stiffener plate (typ.)

m 111

=o.3o fllltl

., "

12'-0· {a)

J

:: _ 29, 000 ksi 0 30 50 ksi ::7.22

Transfer~

bar (typ.)

(b)

----

Fig. 7-10. (a) Core plan and (b) Stction A-A-beam cross stctiDIL

II

~F,

'• .irr .1i'.~

..

t.f

COMPOSITE BRACED FRAM~S AND SHEAR WALLS

7-44

!?_

·.

7-4S

1.5 COMPOSITE SHEAR WALLS

from AlSC Seismic Provisions Section F3.5b(2). noting that the area of the web in the beam of a special system is calculated as A1w (d-211)1.,.:

=.!!.L

=

2t1

VP= 0.6P,AJ,.. 0.6(50 ksi)(22.0 in.)(1.25 in.)

16.0 in. =---2(2.00 in.) =4.00<7.22

=825 kips

o.k.

From AJSC Seismic Provisions Table D LI, rhe limiting widt!Ho-thickness ratio for the web of a highly ductile member is:

For a shear-critical beam in a special system, Equation 7-3 can be used to check the length of the beam: l.6Mp l5--

~::; 2.45 fI(l-0.93C,,) ' yiy

vp

=

"" 2 .45 29.000 ksi {l -O) 50 ksi ::::59.0

1.6(3,830 kip-fl) 825 kips

=7.43 ft L= 6.00 ft< 7.43 ft

h

22.0 in. t l.25 in. ::::17.6<59.0

(Provisioru Eq. F3-2)

=

o.k.

-=~--

Part 3; Size and Spacing of Web Stiffeners

o.k.

AISC Seismic Provisiolls Section F3.5b(4) addresses provisions for stiffener thickness and This member also meets the compact limils according 10 AlSC Specification Table B4. lb.

Part 2: Beam Length Determine whether lhe limit state of lateral-torsional buckling applies. Because the beiun is comp5ct, according to AlSC Specification Section F2. Equation F2-5 gives the ma.icimum unbraced length pennined for the beam to reach lbe plastic moment. Thus:

Lp = i.16r1

Stiffener Spacing

:::: 30(1.25 in.)- 26.0 in.

5

29 000 ksi • 50 ksi

==32.3 in.

::: 13.7 ft

Because the depth of the beam is 26 in. ~ 25.0 in.), stiffeners are required on both sides of the web.

4 =6.00 fl 6.00fi<13.7 ft; therefore, 1he limit state of lateral-torsfonal buckling does not apply and yielding controls.

Stiffener Thickness

> '• - ma.x

From AISC Specification Section P2.l. the nominal flexural strength is:

= (50 ksi)(919in. _____:3 ),. 12 inJft

spacing requjrements as well as requirements for one- or two-sided stiffeners. Since the length of the beam is Jess than l.6Mp/Vp. and the e,"'(pec1ed chord rotation is greater than or equal lo 0.08 rad, part (a) of AISC Seismic Provisions Section F3.5b{4) is used to detennine the stiffener requirements.

5

vF;

Mn= Mp= Fyl,x

f

;

d s530t..,--

II

=(1 ft/12 in.)(1.76)(3.87 in.)

1

(Spec. Eq. F2-l)

{r,.. =1.25 in.

1.

*in.

~e 11 = 1.25 in.

~-...:....;

=3,830 kip-fi

1..

j

COMPOSITE BRACED FRAM.ES AND SHEAR WAU.S

Provide l.25-in. x 6.75-in. full depth stiffeners on each side of the web spaced no farther apart than 32 in. See Figure 7- 1 I for final beam detailing.

Single Stiffener Width I

7-t7

7J COMPOSITE SHEAR WALLS

~

b1

b,:2::2-'"'

Part 4: Beam Embedment Length

16.0 in. . 1 25 ID. =----. 2

"

from AlSC Seismic Prodsions Section H4.5b( I)(3). Le is detennined from:

=6.75 in.


Sriffener-to-Flange Weld According to AISC Seismic Provisions Section F3.5b(4), the required strength of lhe stiffener-10-flange weld is decermined as follows:

J:= 8 ksi

"'~ FyAsr ,.., 4 .

~1

l>

=0.65 from ACI 318 Section 10.2.7.3 g =L=12.0 in.

(50 ksi)(l.25 in.)(6.75 in.)

;.

'

b.,. ~I

ll ,,.

ill

=105 kips

where

4

The expected she:ir strength of the steel coupling beam is:

(f>rovisio11.s Eq. H4- l)

Assuming a I-in. comer clip, the weld size is determined from AISCManual Equation &-Za as follows:

Ry= l. l (from AISC Seismic Provisions Table A3. l)

=(J .392 kip/in.)DL

~w

vn = 2(1. 1)(3,830 kip-ft)(l 2 in./ft)

105 kips= (1.392 kip/in.)D(5.75 in.)(2)

.~·

~\I

~:I ~,

72.0 in.

=6.56 sixteenths

D

= l.~00 kips

Use Yi6-in. fillet weld on both sides of the stiffener.

v. = R1 VP

=1.1(0.6)(50 ksi)(22.0 in.)(I. 25 in.)

Stiffener-to-Web Weld

According lo AJSC Seismic Provi"sions Section F3.5b(4), the required strength of I.he stiffener-lo-web weld is detennined as follows:

=(1.392 kip/in.)DL

422 kips = (1.392 .k ip/in. )0(20.0 in.)(2) D

=7.58 sixteenths

h

!!

i. (,

i.

.. I'

Use !h-in. fillet welds on both sides of the stiffener.

=908 kips

As a C-SSW system, in accordance with AISC Seismi"c Provisions Section H5.5c, the expected shear strength of lhe beam for which embedment length is calculated must be increa..~ by a factor of l.l to account for strain hardening. Therefore:

Assuming a 1-in. x 1-in. comer clip at the flange-to-web comer of the stiffener, the ":e.Jd size is detennined from AJSC Manual Equation 8-2a as follows: .

=908 kjps Use Y-i

Ruw :1: F,Asr =(50 ksi)(l .25 in.)(6. 75 in.) =422 kips

R1'W

:: l.1(825 kips)

v. == 1.1(908 kips) ==999 kips

...

and AJSC Seismic Provisions Equation H4-2 gives:

7-48

COMPOSITE BRACED FRAMF.S ANO SHEAR WAU.s

999 kips=J.54J8 ksi (

Note that the transfer bars must be developed in a manner consistent with AISC Seismic frtJ\·is1oru Section H5.5c. Also no1e th:H AISC Seismic Provisions Equation H5-2 provides an upper limit on Aib· Assume the longitudinal wall reinforcemen1 ratio is 0.0025. Therefore, ihe area of longitudinal wall reinforcement along the emb
24 0 . )0.66 10.58- 0.22(0.65) · '.n. (0.65)(16.0 in.)4 _ +~ 16.0 m.

0 88

24

25.94

=o.ss+ 36.o

A, = 0.0025b,.cl~

Le

4

=0.0025(24.0 in){60.0 in.} =3.60 in. 2

=57.9 in.

The total embe
4 +Cc =57.9 in.+0.75

7-49

7J COMPOSlle SHEAR WALLS

UseAJSC Seismic Provisions Equation HS-2

10 check

the limit on A1b·

in.

0.08L,b.., - As= 0.08(60.0 in.)(24.0 in.}-3.60 in. 2

=58.7 in.

= 112 in.'

Each end of the beam wm be embedded a mjnimum of 60 in. beyond the face of th~ wall.

The pro,idcd A,b is 4.00 in.= [(4) No. 9 bars mechanically attached to the flanges) or 4.34 in.2 if (7) No. 5 U-shaped hairpins are provided. Either of these values is well below the limit of 112 in. 2

Part 5: Vertical Transfer Bars

From AlSC Seismic Provisions Section H5.5c, the required cross-sectional area of verti· cal lransfer reinforcement, attached to the top and bottom Oanges of the beam is determined using Equation H5-l. As calculated previously, the embedment length is 60.0 in. Jess the cover on the reinforcing. Here the embedment length will conser vatively be taken as 60.0 in.

Part 6: Face Bearing Plates

AJSC Seismic Pro1·isio11s Se.ction H5.5c, requires bearing plates at the face of the wall pier. These face bearing plates must meet the detailing requirements of AISC Seismic Provisions Section F3.5b(4). and must be placed on both sides of the web regardless of beam depth according to Section H5.5c.

(Provisions Eq. H5-l)

..

A > 0.03(8 ksi)(60.0 in.)(16.0 in.) 60 ksi

rb -

rn· stiffener plate; full

2

= 3.84 in.

depth, both sides of web

From requirements of AISC Seismic Provisions Section H5.5c, Arb is the area of vertical transfer reinforcement required at the top and bottom flanges in each region of the embed· ded length. Assuming four bars will 'be used in each of the fow- required locations, 2 A, - "84. -'· m. eq4

'· 72"

=0.960 in.2 t Jocation Thus, provide (4) No. 9 vertkal transfer bars on each flange at each of the four regions of the embedroent length. See Figure 7-11 for de1ails of transfer bar arr.mgemenlS. Another option is to use alternating U-shaped hairpins (see AISC Seismic ProvisionS Fig~~ C-HS-3). The hairpins extending above (or below) the flange need to provide A 1b = 3.84 JJJ. Limit the bar size to No. 5 in order to ensure reasonable bend radii U-shaped hairpins 113~-t two legs, and the area of a No. 5 bar is 0.31 in.1 Therefore:

N (number of No. 5 hair pins)= {3.84 in. 212)/0.31 in.2

60" t..+ Cc Note: The left end is deta~.ed the same as the right end.

1• stiffener plate; full depth, both

sides of web

~N

PL1 ~·x6'.4"x1'-10" with 1·x1• corner clip (A572 Gr. 50)

=6.19; therefore use 7 Fig. 7-1 J. Steel coupling beam detail for Example 7.5.3. A.\.IEIUCAN JNSTITVlll OF STEEi. CONSTRUCTION

~

..J ~

~. l

7 5-0

COMPOSITE BRACED FRAMJ:.S ANO SHEAR WAU..s

The foce bearing plate is located at the beam-wall interface, and therefore requiremen
~hould sathfy

the

Suffrners are rcquued at two locations: one pair at the beam-wall interface and one pair at the location of vertical transfer bars nearest the end of the embedded region. · Stiffeners in the embedded region and at the beam-wall interface must be two-sided stiffeners.

J.

Suffc:ner Th.ick.ness Is~

0.751,. ==(0.75)(1.25 in.) =0.938 in. max { ~in.

bJ, combined~ bf - 2t,..

= 16.0 in.-2(1.25 in.)

=lJ.5 in.

..

=~ .,

-

~

...::

.1•

..

at

lc\el~

6- 10:

=999 kip
noors)(999 kips/Ooor/beam)(2 beams)

=9,990 kips Amplified i;hears at !e"
= 1.1(462 kips) = 508 kip~floor/beam

L(J.1 Vn ) 1_ 5

= (5 floors)(508 lips/lloor/beam}(2 beams)

The total a,"(ial load effect due to coupling is: P.....,11.
= l 9,500 kips Thus. the 19,500 kjps will be :idded to the force in the wall due to other loads.

Part 7: Wall Pier Axial Load

7.6 DESIGN TABLE DISCUSSION

As di~cussed in AlSC Seismic Provisions Section H5.5c, the embedded regions of the beams mu~t iransfer UV,, of beam shear strength in a composite special shear wall system. This expected shear strength, increased to account for strain hardening, must be accounted for in the calculated waU pier required axial strengths. The required axfal strength resulting from the coupling action on the base wall piers is the accumulation of the :unplified shear strengths over lhe height of the building. For the given core wall system, two coupling beams frame into each shear wall. B:ised on the nominal beam shear strengths provided in Table 7-9. the total wall pier required uxial strength is determined as follows.

(I.IV,. )11_ 15

t•.

shear~

Provide 1 in. x 6.75 in. full depth stiffeners on each side of the web at the beam-wall interface and at the location of the vertical tranSfer bars nearest the end of the embedded region. See Figure 7·I l for final beam detailing.

Amplified shears at levels l l- 15:

.r:.

Amplified

7-51

=5.080 kips

Stiffener Width

r11 '·'

7 6 DESIGN TABLE DISCUSSION

=1.1(404 kips) =444 kips/floor/beam

i:(l.1Vn)11_ 15 =(5 fioors)(444 kips/tloor/beam)(2 benms) = 4,440 kips

The final coupling beam w11J1 transfer bars tmd stiffeners is sbm.vn in Figure 7-1 I.

Design Tables 7- IOA, 7-1 OB, 7-11 A and 7-1 IB present equations applicable to !he design of members subject to combmcd comprcs.;;ion anJ bending (Gescbwindner, 2010). The nominal axial and flexural strengths are given for rectangular encased W-shapes bent about lhex-x aris and y-y a.'tis in Tables 7-IOA :ind 7- IOB, respectively. depending on where the pruuc neutral axis is located in the member. Equations for the pertinen1 properties are also included. Tables 7-1 IA and 7- 11 B provide ~imilar equations for composite filled HSS bent about either pnncipal axis and composite filled round HSS bent about any axis, respectively. The given equ:itfons may be U$Cd with the simplified inter.let ion di3gram discussed in AISC Specification Commentary Section l5 (see Method 2).

7- 52

COMPOSITE BRACED FRAMES AND SHEAR WAU.S

Table 7-10A

Plastic Capacities for Rectangular Encased W-Shapes ~c Bent About the Y-Y Axis

·LJ

.c 0

. Defining Equations

Pl

7- 53

Table 7-108

b'·

Plastic Capacities for Rectangular Encased W-Shapes Bent About the X-X Axis , Stress Distnllution

oESJON TA OLES

..

Section

Stress Distribution

M,,. •O • area or steel st>ape

A A1

H

C

I

?,; • . .. • .-

A.,

Pc •0851~.Ac Mc -Als

Pe

E

A

A, - As,

~ A,Fy +(0.851~}[A,,-~("2-b, )+ ~]

ME: Mo-Z,EFy

z,

l.£~7 -z,E

4

-Av.-~-~--c-)_ __

C

___, E

Pc =0.85f~Ac Mc=Ma

2

*"'o-Z,.F, - ~(0.851;,)

D

IAo = z,Fy + Z,F.,

Z,

4

c

o.s5f~(Ac +A,,.)-2Fr..~.,.

h 0 •

zA,,(1--c:) %

!!fI _z, -z, 4

I

la. -h,~ - z,,,

0.851~(.4,, +A,-db, +J\,,)-2F,(A,-db,) -2F,,-~

8

z.,, -z.-1>,(i-11,,)(%+ho)

B

OW,(,o\+J4.+Aw.)-2F,.,,,-2F,..A... 2(0.851~)

I

0.85f~ (Ac+ 1\-21,b, }-2Fy(A.

2(0.ss1~(hi-b,)+2Fy1>.]

z.,, .z,

·5f(o.W<)

1 Ma - Mo -Z.,,Fy - ; (0.851<)

D

h,. •

l

Pa ~o

2[0.85l~(h,-t,..)+2F,t.. ]

z.,, •t.,,h:

h~ •

- ¥(0.85fc)

lull Y·lilldS plastic sec;tiOn modulus of steel shape

Po = 0.85fc'\

P11 •O Ma

~

11itl.

"full x·alds plastic seGlion modulus of steel sllape

z... ~-z..

h.t-[!-/Ir. - . ·--- ---: . .

hihz -

Z,E =Zs

't 1-+-z-, z. ·_{A,,-2 •!!fi. _z. -z,

c

steel shape

or continuous reinl0
Mo • Z,Fy •Z,FY' +3j-(0.851~)

D A,,.. area of continuous reinf(J(clng bafS ~I d'oe ~nterlre

~-

~ area of ~area

A,, •

Po • 0.851~..S., 2

A

h~F

A A,

r. ' -+A_.,_·_a-re-a o_r_.u_con_rln_uou_s_r_ein-rom-·ng-b-ais-----1 'I. ~ Ac •hi"2-~-A.r

h2

Defining Equalio11$

Pl

z.. . z, -21,(%+h

0

h+-e--tttPNA 't .

. --- - -

B

)(%-hn)

For h,. above the flange ( tt,. >

<(

-21,b,)

2(4t1F1 +(ti,-2t,)0.85t
ho•

o.asr< (Ac •A.)- 2F1 A. ho •

2(0.851(h,J

z.,, - z. AMEIUCAN !NS'rrruTl! OF STEEL CONSTR\J<:'flON

!})

I..

C0~1POSITE 8RACED FRAM!oS

AND SHEAR WAUS

D

Table 7-11A

Plastic Capacities for Composite Filled HSS Bent Abol.1t Either Principal Axis ,.

7 55

[li;.
Table 7-118

Plastic Capacities for Composite Filled Round HSS ~c Bent About Any Axis

. •c

"L_j_

0

.

.. Stress Olstril:utloo

Defining Equations

Pt.

P,. .; F1A• ; M,.. ..

-". •

'...

~

..

(·

~a

ot st.HI shape

w1r2

"' • 4

--
PE • Pr Y.[F,.(d2 -h~)• 0 ~ h1)<~ -son~)

H-21

095/'Z

Mf • F,1.6£+~ 2

b,

·~

ll

A A. • a(dl-t2)

o

" .,

~--,

,.~ ..

Defining Eqaz:lons 1.1,. .. 0

0.85/~A,,

A ~ • b,~ - 08581! ~ • 8-21

H L

'

A

E

A

0851'~

Pc • -'-t0.8510 ~1'E •4F1 tht

2

"·ti~-~

Fz o.asr,;zd'. o-,11£2 E L,c; •b,t>~ M

£

M

ZI£

2t~

h£ •

!!c.. !i 2 4

E

--
z,f · ~s1n (.f) Z.e _(
hE

,.!lJ.+~ 2

'

e, ~ · -211a11(~) C Pc • O95/~A,, Mc •Ms

~ (•

~l •\

:I \

"·t-~~c

"t-f:j}-·•

8

c

2

---

Pe •O

z, • llJJI x-axis pla:5tc sedlon modulus ol tiSS

~

Pe .o

0 h,. •

•

2 0 8Sf~bt • '"''

Ii.

~ 2

Eque~ ~ ~

hlM\'(~)

z.a·-e8

•

I

,fl

~I

N Dend.ng d !he t:t"PO U>oot its ll·X axl• (when H :lo 8) OI elJO&'

nt Y·Y a> H).

(d3 -h3) . (e)

Zss•-s-"" 2

0

o;zm

8 z.,,-21~ z.,. ~~

Ms •F,Z..+ 095~Zs1

v-

z. • rl ' -0.1-nr,

Ms • Mo -F1z,,, -

0

.

Po• 0851~'\ 085/'Z

~~

~·

'i. -FNA

O M0 .F1 Z,t~

(

l·

0

P,. • F1 A. + 0 951.iJlc

.,,

t

~

'

B

6

• 00200K0 -2K. 0.08481<~

~:

7- 56

8-1

COMPOSl'l'E BRACED FRAMES AND SH'EAR WAU,S

PART 7 REFERENCES ASCE (2006), Seismic Rehabilitation of Existing Buildings, ASCE/SEI 41-06, American Society of Civil Engineers, Reston, VA.

PARTS DIAPHRAGMS, COLLECTORS AND CHORDS

El-Tawil,$., Harries, K.A., Fortney, P.J., Shahrooz, B.M., Kurama, Y., Hassan, M. and Tong, X. (2009). Recommendation for Seismic Design of Hybrid Coupled Wall Systems, ASCE Special Publication, American Society of Civil Engineers, Reston, VA. Fortney, PJ., Shahrooz, B.M. and Rassati. G.A. (2008). "Seismic Perfonnance Evaluation of Coupled Core WaJls with Concrete and Steel Coupling Beams," Steel and Composite Structures Journal, Vol. 7, No. 4, pp. 279-301. Geschwindner, L.F. (2010), "Discussion of Limit State Response of Composite Columns and Beam-ColuJlllls Part II: Application of Design Provisions for the 2005 AISC Specification,'· Engineering Journal, AISC, Vol. 47, No.2, 2nd Quarter, pp.131 -140. Harries, K.A. and McNeice, D.S. (2006). "Performance-Based Design of High-Rise Coupled Wall Systems," The Structural Design of Tall and Special Structures, VoL 15, No. 3, pp. 289-306.

8.1 SCOPE .............................. . ........ .... ................ 8-2

82 GENERAL DISCUSSION ............................................ 8-2 8.3 R.,EXURAL AND TORSIONAL BUCKLING OF

COLLECTOR ELEMENTS ....... . .......... ............ ........ .... . 8-4 Br:icing and Compressive Strength of Collectors ................ .. ... ..... 8-4 Major Axis Buckling ............ . ... ............................... . 8-5 Minor Axis and Torsional Buckling ..................................... 8-5

8.4 DESlGN EXAMPLES ............................................... 8-8 Example 8.4.1 . Diaphragm Chord and Collector Design ........ . ....... . .... 8-8 Example 8.4.2. Collector Connection Design ................... ......... 8-22 PART 8 REFERENCES .. . .............................................. 8-37

\

\

I

J:

1 t

."' AMEIUCAN JNS'TlTIJTE OP STEEL CONS'IR\K."TION

:.I ·..

8- 2

OlAPtfR.A\.MS, COi l.EC.,-ORS AND CHORDS

8.1 SCOPE The requirements :ind other design considerations summariLed in this Pan apply to elemenu and connections of buildings and of frame.<: th:u are o:pec11ically dct:uled for se1sntic resist· ance (or other lateral loads) but are not covered in Parts 4, 5, 6 or 7.

(•

8.2 GENERAL DISCUSSION Seismic design requires that components of the structure be connected or tied togccher in such a manner that they behave as a uniL Diaphragms :1te an important ~tructural element for creaung this interconnection. Diaphragm clements' • connect the distnbuted ma.<;s of the building to the vertical elements of the lateral force res1~hng S)Stem (braced frames. momen1 frames or ~hear wall<;); • in1er(onnect the vcnical clements of the lateral force resisting ~y~1cm, thus completing the system for resistance 10 building torsion; • provide lateral stabiliry ro columns and beams including nonlalcral force resbting system columns :ind beams; and • provide out-of-plane support for waJJs and cladding.

.." ::

-

i,. l ...

t..

r..

The clements that make up a diaphragm are generally aJready present in :1 building to cnrry other loads, such as gravity loads. Floors, roofs. and other membrane or bracing systems are generally used as diaphragm elements. Di:iphragms are typically horizontally spanning members, analogous to deep beams, which distribute the seismic loads from their origin to the venically oriented laleral force resii.iing frames (braced frames, momem frames. etc.). Diaphragms are idealized as ~imple-span or continuous horizontally spanning deep beams. and hence are subject to shear, moment and axial forces, and the associated deformations. Figure S·l shows typical loading, ~hear and moment diagrams for the analysis and design of a diaphragm. The floorer roof-deck system is usually designed as the shear-resbunt clement (an3.logous to the web of a beam) and lbe beruns or supplemental deck reinforcing at the boundaric.~ of the diaphragm are designed to resist axial force (analogous to the flanges of a beam). Diaphr;igms act as be~ on elastic ·snpports, with the diaphragm acting as the beam 3lld the vertic:il clemenis of the lateral force resisting system acting as the suppons. The relative rigidity of the diaphragm and the vertical elements is used to classify diaphragms into one of three calCgories: rigid., flexible or semi-rigid. Rigid diaphragms arc those in which the Ouibility of the supports is far gtc3ter ihan the in-plane flexibility of the diaphragm. Tuey also possess the strength and suffness to distribute the lateral forces to the lnleral forte resisting frnmes in proponion to the relative stiffness of the indjvidual frames, without significant deformation in 1.he diaphragm. Where the in-plane flexibility of the diaphragm is far greater lhan that of 1he venical clements, ihe diaphragm is classified a.s Oexible. A llt:Xiblc dinphragm distributes the lateral forces co the lateral force resisting frames in a manner anal· ogous to i\ simple beam spanning between the lateral force resisting elements. The distribution of the latcrot forces through a flexible diaphragm is independent of the relative )liffness of I.he later:tl force resisting frames. Where the flcx1bility of the diaphragm and it$ supports (the vertic~ clements) is similar (or where the dinphragm cannot be unifonnly cal· egoriz.ed as either rigid or flexible in a.11 spans io each direction) the diaphragm is considered

f

g2GENF..RAL DISCUSSION

semi-rigid. A scnu rigid diaphragm distributes lateral forces in proportion to the stiffness of ibc J1aphragm and the rclali\'c Stiffnc!>S of 1he lat~rnl force res1Ming frames. Sem1-ng1d diaphr:tgros arc often analyzed 11$ing rhc analogy of ti beam on cla)tic suppottS. where the t;cam represents 1hc suffne\~ of the diaphragm and the elastic supports represent the stih· !)(SS of the laterJ I force rc~isung framci; Jn a buildin~ with tlexible diaphragms. lbe diaphragm is analy1ed first (for diaphragm for.:es}: the effect of the rc.Ktions on the ~upport~ is u~ed in the design of the 'crtical clc· mcnls of the lateral force resisting system. These reactions may need to t>e adjusted to be wnsi>teot with the base ~hear. la buildings \\Cith rigid or semi-rigid diaphragms, a full building analysis is done
1111111111111 111111111111111111n111111111111111111111111111111

~

t~

j

~

Diaphragm loading diagram

(~ ' Shear diagram

'X:QIIIUI 11 i111 IJllllllY

'
Moment diagram

'_ - - - -~ - - - - ~- - - _)Y_ -- - -

Chord 5

typ

• Lateral force resisting frame -~'--~~~~

~

t

1------::r:__ -- - -----

-~---_.!,

con ec tor typ

x--~~--

Lateral force resisting frame

---------

____ __:!; _ _ _ _ _ I

fig. 8 I. Diaphragmfol'{'e clistriburion.

Chord typ.

DIAPHRAGMS. C()LLfCTORS A!'
lateral force resisting frames. A redistribution of collector forces can occur as ductile design mechanisms form in lhe lareral force resbring frames. When horizontal truss bracing is used as a diaphragm, the chords should be regarded nnd designed as collectors using lhe appropriate load combinations. The diagonal and cross brace members can also be regarded and designed as collectors to ensure that they will not buck.le or hinge before they deliver forces to the vertical lateral force resisting frame. Alternatively, diagonal diaphragm braces can be allowed to buckle or hinge and be a source of additional energy absorption. Neither ASCEJSEI 7 nor the AISC Seismic Pro\·isions provide prescriptive direcrion on how 10 consider horizontal truss bracing. f-Or recommendations on rhe design of diaphragms, see Sabelli et al. (2011).

8.3 FLEXURAL AND TORSlONAL BUCKUNG O F COLLECTOR ELEMENTS Bracing and Compressive Strength of Collectors In buildings, collectors are typically floor or roof framing members that transfer loads to the seismic force resisting system. In nonbuilding strucrures, collectors may be connected to horizontal bracing. In many of these conditions the effective lengths may be djfferent for major axis flexural buckling, minor axis flexural buckling, and torsional buckling. Additionally, the torsional buckling strength determined in AlSC Specijicarion Section E4 is no1 applic.ible to members constrained to twist about an a,"'l.is other than the centroidal axis. This is the case for beams with the top flange laterally braced continuously at the top flange by the d,eck or slab and the bottom flange unbraced between lateral brace points. This condi1ion is termed constrained a«is flexural-torsional buckling. For W-shapes the constrained axis flexural-torsional buckling strength will be greater than the flexural buck.ling strength if the unbraced lengths are equal. The constrained a.'liS flexural-torsional buck.ling length is taken as the bottom-flange unbraced length. This buck· ling strength will be less than the torsional buckling strength for lhe same unbraced length. Thus, when constrained ax.is flexural-torsional buckling is an applicable limit state in wideflange members, torsional buckling typically need not be evaluated. Designers often simplify the determination of the compressive strength of collectors witll conservative assumptions and methods, such as neglecting the continuous bracing of the top flange and tiling the minor axis unbraced length as lhe distance between bortom-ffange lateral supports so I.hat t0rsional and constrained axis flexural-torsional buckling m:iy be neglected. While such approaches are" acceptable, they often indicate the need for additional braces or increases in beam size well beyond what is actually required. Note that Appendix 6 of the AISC Specification does not provide requirements for torsional bracing of compressive members. Criteria for torsional bracing of columns can be found in Helwig and Yura (1999). The following discussion provides guidance for a more explicit derenni"nation ofthc governing limit states and a more efficient design approach. Once Ute available axial compressive strength of t.he collector is determined. che com· bined effects of flexural and axial forces are evaluated per Chapter H of the Af~C Specification. In many C3SCS, a more detailed stability analysis than the foUowiJlgwill ~ mil even greater efficiency. Such approaches can include explicit consideration of rJie torsional bracing provided by the steel or composire deck, or a beam-column stabili!Y

SJ FLEXURAL ANO rORS!ONAl.. BUCKLING OF COLLECTOR ELEMENTS

8- 5

analysis considering both flexure and a'ial forces simulraneously in lieu of the Chaprer H inreraction merhod.

Major Axis Buckling For collectors, the major axis flexural buckling lengrh is rypically raken as the full member length as described in AJSC Specification Commentary Section 17, assuming webs are orienred vertically. Exceptions to rhis include certain cases in ~hich braces may be considered to provide in-plane bracing under design conditions. For ~eismic loads, such cases include beams in eccenrrically braced frames and beams in V- and inverted V-configur:uion braced fr:imes not sp«;ifically detailed for seismic resistance; ihe diagonal braces in these .systems provide a braced poinr.

Minor Axis and Torsional Buckling Steel deck with ribs parallel to the beam is generally assumed nor to provide lateral bracing. Lateral and iorsional br:icing may be provided by transverse members at points along 1he length of the be.im because typically the connection lo lhe transverse member is designed to provide bot.h torsional and lateral restraint. For this case the minor axis flexural buckling lengths and torsional buck.Ung lengths are the same and equal to the distance between these bracing poinrs; thus. the minor axis flexural buckling strength will be lower than the tor~iooal buckling strength. Steel deck with ribs perpendicular to the beam is generally assumed to provide continuous lateral bracing bm not torsional bracing. Torsional bracing may be provided at points along the beam length. For this case the compression strength may be governed by consirained axis flexural- iorsional buckling. Figure 8-2 shows minor axis flexural buckling, torsional buckling, and constrained axis flexural-torsional buckling about rhe top flange. Colle~tor beams with composite deck or slabs are likewise continuously braced for minor axis flexural buckling as noted in AISC Specification Commentary Sec1ioo 17. The composite deck or sl;1b also provide~ significant continuous torsional bracing. This continuous lorsional bracing is often sufficient 10 preclude torsional buckling altogelher. This can be

r-,~------.--, ~--.....----'"-J

\I 11 11 11 11 11

11 11

---- - -~

\..-,,..----

~-------,I

I I I

1 I

'

I I

I I

I I

11

I 1 I I I I

11 11 I I

--------'--J

(a) Minor axis flaural buck/mg

I

'I ' I I

I

11

rr-..........~~'~'--.... -,

I'

---

____ ,......

_I------ ,,.-----· I

L ·''

I\__ -----)

------ ---- --\----:

\-----(bJ Torsional buckling

(c) Cons/rained axis jlexural1orsional buckling about 1he top flange

Fig. 8·2. Types of collector buckling.

A."ll!JIJCAN lNSTITIJTE OF STEEi. Col'ISTRVCTJON

1

. "' f'

l

DIAPHRAGMS. COUl!CfORS AND CHORDS

8-6

verified using methods developed by Helwig and Yura ( 1999). For simplicity, designers can conservathely compute the constrained aJtis tlexural~torsional buckling ~trcngth about the top flange and neglect the effect of the continuous torsional bracing. For collectors in diaphragms with horizontal diagonal bracing, if the brace connccuons provide torsional bracing such that both minor a.'l:is flexural buckling and torsional buckling Ieng~ are equal, I.be compresm-e strenglh is likely governed by fle.'l:ural buclding. Where the torsional and minor axis flexural budding Ieng~ are equal, the torsional buckling strength "Will e.'l:cced the minor axis flexural buckling strength for doubly symmetric I· shaped members. If the brace connections do not pro"ide torsional brncing (for example, bracing only one flange), the minor axis flexural buckling and torsional buckling lenglhs arc not equal and both limit staie~. in addition to major axis buckling, must be considered. t.lcthods for computing lhe compressive strength of members governed by 1orsiO!lll buckling about the centroidal a.-,;is are presented in the AlSC Specificatit>n Section E4 F
Table 8-1

Summary of Unbraced Lengths and Restraint Conditions for Collector Beams {Compressive Strength) Major Axis

Sleel deck

Length

Lfllgth

Bucldiog l..el19tti

T
Ribs parallel to beam

Full length

Between lateral brace points

Not applicable

Between l0tslonal

Ribs

Fu!l lenglh

Hot applleable (continuously braced)

Bct.,.;een torsional

riot applicable

Be1ween tooional brace points1

riot applicable•

Not appfie<:b!e

Between torsional

perpendicular

to beam Full length

(continuously

Constrained-Axis

braCe points I-lot applicable

brace p!iints

braced)

(S.I) ~

Minor Axis

Rexural Buckling Rexunl Buckling Rmnl-Torslonal

Condition

Composite deck or slab

..·:·.·:·~

8-7

SJ Flf-'\URAL ANI'> TORSIONAi BL'CKI l;>;G OF COl.LfCTOR !!I b\1ENTS

Full length Horizontal diagon;il bracing

Between lateral brace paints

where

~t

braced al

-

brace paints

centroid)

P,y=

1

1t2'tf/ y --2-

Lr

-

The com;>oSlle deck°' 'b.b provides somo witlouous 1oitiollal !ltacino In some cases llloS torsional mcttg is sufflelcnl 10 ~ flexurat. ~i«l.ll bucldino. Melllods '°' cMerm/tllr.g ~ ol SUCh ~ ate noc presented In !his ~1atal
E - modulus of elasticity. ksi

G =shear modulus, ksi

11

:::

minor axis moment of inertia, in.

4

4

L\ .

;:

..

:·

J == torsional constant. in. Lr ::: torsional unbraced length, in. Pr =torsional buckling strength. kips a == distance from centroid to faternl restraint on the member minor axis, in. d == member depth, in. rx =radius of gyration about the major axis, in. r1 =radius of gyration about the minor axis, in. 't

~here

A1 =gross cross sectional area of member, in. 2 I, =major axis moment of inertia, tn.'

C,.. = w:irping constant, 1n.6 K, = effeclive lcnglh factor for to~1onal buckling For a == d/2, the case for restraint at the top flange, Equation 8-2 simplifies to:

(8-3)

=umget modulus stiffness reduction factor

use \\ilh AlSC Specification equations, this can be expressed in a fonn sim.il;i.r to AJSC Specification Equation E4-4, in which the elastic wrsional buckling stress, F,, is co:nputetl as follows: FQr

AMDJCA.~

INSTrTVre OI' Sn:a. CONS11U)C'l'10H

The value of F, is used in AISC Specification Equation E3-2 for F1 JF, S 2.25 and AISC Specification Equation E3-3 for F1 1Fe > 2.25. A summary of the buckling lengths mid this discussion is provided in T:ible 8-1.

I

DIAPHRAGMS. COLLECTORS AND CH OROS

8.4 DESIGN EXAMPLES

8.4 OESJGN EXAMPUiS

Mo:::: 123 kip-fl

ML = 96.2 kip-ft

Example 8.4.1. Diaphragm Chord and Collector Design

The gravity shear loads are:

=11.8 kips

Given:

Vo

Refer to Figure 8-3a for 1he plan and Figure 8-3b for r.he braced frame elevations called out on the plan. Assume the braced frames are special concentrically braced frames (SCBF). Based on the following information given for a north-south morion, determine the required strengths of a collector and a chord at !he third level and design the chord. (A similar calculation must be perfonned for east-west loading; this is not illustrated here.) Design lhe collector on grid 1 between grids C and Dusing ASTM A992 material. The diaphragm consists of 2-in. metal deck with 2~-in. normal weight concrete topping (total slab thickness-:: 4~ in.) with ~-in.-diameter s teel headed stud anchors spaced every 12 in. along the beam. The specified compressive strength of the concrete is 4.000 psi and rbe metal-deck span is north-south. The applicable building code specifies the use of ASCEJSEI 7 for calculation of loads. Assume surface loads of D = 85 psf and L = 80 psf (Lreduced = 50 psf) on typical levels, and D, 85 psf and L, = 20 psf on the roof. Due to seismic forces from an equivalent lateral force analysis (ASCE/SEI 7 Section 12.8), the first-order interstory drift at level 3, liH, is 0.375 in.

VL = 8.29 kips

From ASCE/SEI 7, tltis strucmre is assigned 10 Seismic Design C·uegory D, Q 0 "" 2.0, p =1.3, I, 1.0, R 6, SDs"" 1.0, k 1.0 and C1 "" 0.167. The seismic base shear is:

=

=

=

V=C3 W

{ASCE/SEI 7 Eq. 12.8· 1)

=0.167(4)(765 kips)

=51 l kips where W is the effective seismic weight including the total dead load of the building as required by ASCE/SEI 7 Section 12.7.2 (assuming no other loading applies). The seismic

=

For the collector beam at the third level along gridline 1 and berween gridlines C and D, the gravjty moments are:

3

2 30'-0"

30'-0"

30'..()"

Roof

30'-0"

J

t· ·.>

.. I

(o

5

4

~

25'-0"

!·

N'

Fourth ~, N

t:,

Third

.. .....
N

Second

9~ .....

Base Braced frames

Fig. 8-3a. Floor plan for Example 8.4.J.

Fig. 8-3b. SCBF elevation.

...

(I i

8 10

DlAPHRAGMS, COU.1-CTORS AN'O CHORDS

SA DESIGN EXAMPLES

8--1 I

..

~

.

forces in I.he nonh-south direction using 1he equivalent !Jlleral force procedure of ASCEI SEI 7 arc:

L

i~ .. ~

~··

Level

Story Height H, ft

Seismic We.ight w;, kips

Force F11 kips

Roof

12.5

201

4 3

12.5 12.5

2

14.0

765 765 765 765

152

wL2 8

M=I 28 kip/fi(J20 ft) 2 = ---'---'----8 = 2,300 kip-ft The reactions at the braced frames ~hould be consistent with the force distribution from the lateral analysis. In Ibis case, due 10 symmetry, the ma:
10)

55 w

..

1

- - -"'1 ~:__.

;~,...i

:~ ....··~ ~,

-,

;,.

fll..

FPJ = i~•

However. ASCE/SEI 7 requires lhnt this force must be greater than or equal to 0.2Sosf,wp>• but need not exceed 0.4Soslewpx· Values of Fp• arc calculated in the table below. Shade<.! val· ues iodic:i1e 1he governing force, no1 including n.,.

Roof

-

(ASCFJSEl 7 &j. 12.10.1)

Wpx

2:,w;

Level

4

3 2

w1=wp~

LW{

F;

'f.F;

n.,,Fpx

0.1.SnsJ,wpx

kips

kips

kips

kips

kips

kips

765 765 765 765

765

201 152

201

402

353 456 511

354

153 153

1,530

2.295 3,060

103 55

152

306

128

256

0.4Sosf,w1, kips

~1111111111111111Wl1J1JJJII1ID1I M = 2,300 kip-ft

Moment diagram

306

306 306 306

The governing require.d strength for the diaphragm at the lhird level is 153 kips. Analyze the diaphr.s&m as a uniformly loaded beam with a length, L., equn1 to 120 ft (Ibis is the disUDCC

:::

= 76.5 kips

Shear diagram

cp

er

er

between lhe braced frame aloog grid 1 and 1he braced frame aloog grid 5). The distributed load is C
er

typ.

typ.


~~-_,,~---~---U<==;l~=-----~


w=fe..

L = 153 kips 120 fl 1.28 k.ip/ft

=

As shown in Figure 8-4, lhe maximum moment in the diaphragm :it the third level is:

Fig. 8-4. Diaphragm load, shear and moment diagram

, i

> '•

er

@- ~·•----cf:i-----41-:i ..IJl -C-h-or_d_ _cr.1 Collector11:f

Chord Force at the Third Level

•··t

1

Rs

Diaphragm loading diagram

l:F;

}:

=153 kips/120 ft =1.28 kip/ft

r~ 111111111111111111111111111111111111111111111111111111111111

Solution: The diaphr:igm force is:

aJ

1he 1hird le\'tL

~

DIAPHRAGMS. COJ..LECTORS AN'O CHORDS·

8-J2

g,J

DESIGN EXAMPLES

2 I 53 .kips 2 = 76.5 kips

Jess than 0.2//. Because the deck span is perpendicul;ir 10 the chord span, assume that only

!ht concrete above the top of Lhc metal deck is effective in resisting the chord force. The

J.

plastic section modulus of the diaphragm is: bd2 Z=4

For unsymmetric cases with rigid or semi-rigid diaphragms the distribution should be determined from the lateral analysis. For more informatjon, see Sabelli (20 l l ).

21h in.(75.0 ft) 2 4(12 in./fl)

Assuming lhe diaphragm depth, d, is equal to 75.0 ft (the distance between grids A and D) and the moment is resisted by chord members aJong grid lines A and D. the maximum tension and compression force in the chords along gridlines A and D is:

=293 fl 3 The extreme compressi\e fiber stress at the chord is:

T=C M

=d

M

=-

J~

z

2,300 kip-ft :::; 75.0 ft =30.7 kips

=

0.2/c"=0.2(4,000 psi) =800 psi

fc < 0.2//: therefore. additional transverse reinforcing is not required at the diaphragm chord. Provide two No. 6 continuous reinforcing bars at the edges of lhe concrete floor. Per Section 12.2.2 of ACI 318, lhe development length, Id, is computed as: Jd-:::.

(1.2 + 0.2SDs)D + pQE + L + 0.2S

:: 28.4 in.

Tu =pQs

Per Section 12.15.1 of ACI 318. the minimum lap length for a Class B lap splice is calcu-

=1.3(30.7 kips)

lated as:

= 39.9 kips

=1.3(28.4 in.) =36.9 in.

T,.

= 0.739 in.2 Two No. 6 bars (A, = 0.88 in.2) can provide thls supplemental slab reinforceroeot .11.t ~ chord locations for the tension force in the chord. Per ACl 318 Section 21.ll.7.5, addJUO~ 00 transverse reinforcement to confine the concrete and reinforcement under coropreSSJ

I=

lap length ~ 1.3/d

The required area of slab reinforcement is:

=

37.9db

:::: 37.9(0.750 in.)

Therefore, the required tension force in the chord is:

=$Fy 39.9 kips 0.90(60 ksi)

2,300 kip-ft(l ,000 lb/kip) 293 ft 3 (12 in./f1 )1

=54.5 psi

A chord member with adequate tensile strength to resist this force can be provided by the addition of supplemental slab rein(orcement such as ASTM A615 Grade 60 deformed reinforcing bars, or the fore~ cou Id be assumed to be carried by the steel members alone. II the concrete slab is utilized as .the collector, the concrete chord must be designed using the strength design provisions of ACI 318, whether the structural Slee! is designc~ using LRFD or ASD. The governing load combination is LR.FD Load Combination 5 (the load factor on Lis permitted to equal 0.5 since the Jive load is less Lhan 100 psf) fromASCE/SEI 7 Section 12.4.2.3:

Asnq

1.

forces is not required if the extreme compressive fiber stress in the concrete is equaJ to or

V= Fp

•·.

8 13

'

Lap all splices a minimum of 37 in.

The maximum she:u- in the diaphragm occurs at each end; therefore the total shear force along grid I is 76.5 kips. This shear is considered to be uniformly distributed along the depth of lhe diaphragm (grid I). This :issumption is a simple and rational approach to de1enninc _. •he required strength of the collector beam. Other assumptions about shear transfer through ~diaphragm may also be \'aJid bm are not considered here since lhe focus of thls example 15 . collector beam design. Assuming a uniform distribution of shear along the depth of the diaphragm, the shear demand on the diaphragm is: AMUJ<:,\N JNSTITIJ'Tll Ol' STEa CONSTRUCTlON

~...I r

i: .

DIAPHRAGMS.

v=

cot LFCTORS A.ND ClJORDS

v

&.4 DESIGN F_XAMPLF..S

11 - 15

governing LRFD load combination is Load Comtiination 5 (the load factor on Lis pemuued 10 equal 0 5 s~e the hve lood •~ lt-ss than l 00 psi) and lhe governing ASD lcond combm3tion is Load Combination 6 35 follow~:

d

=76.5 ._,ips 75.0 ft

=1.02 kip/ft

... ..;. -:·',.

: ;·

i;;:J

LRFD

As noted previously. ASCE/SEI 7 requires that collector clements in structures assigned to Seism1c Design Category C through F be designed 10 resist the amplified seismic loads (flo-level loads). The required strength ~r foot is:

v.. =2.0(1.02 kip/ft)

(1.2 +0.2Sos )D+ O.,Qe + 0.51. t- 0.2S

ASD (l.0+0.105Sos )D+ H + F +0.5250,,QE

+0.75L+0.75S The required fle:tural strenglh is:

=2.04 kip/ft

LRFD

A diaphragm should be sele.cted that has a shear strength greater than 2.04 .k.iplft Ir ~tcel headed stud anchors are used, they must resist this shear strength. The dfaphrogm should be attached to the collector in order to transfer this shear. TI1is rn:iy be accomplished by using puddle welds between the collector and metal deck or headed shear studs welded to lhe col· lector. Gravity loads should also be consid.e.red.

Mu= 1.4(123 kip-fi) t- 2.0(0 kip ft)

ASD M,.

+ 0.5(96.2 kip-ft)+ 0.2(0 kip-ft) =220 kip-ft

=1.J05(123 kip-ft)+ 0 kip-ft+ 0 kip-ft + 0.525(2.0)(0 kip-ft) + 0.75(96.2 k.ip-ft)+0.75(0 J.,.1p-f1) = 208 kip-ft

Wide-Flange Collector Beam Between Grids C and D Along Gridline 1

The collector axial force diagram is shown iD Figure 8-5. ASCE/SEI 7 Section J2.J0.2.I s1ipulates lhe load combination 10 use for collector elcmentS in structures assigned 10 Seismic Design Category D. In lb.is case, the load combination including the runplificd scis· mie loads (0.,-Jevel loads) controls: therefore, from ASCFJSEI 7 Section J2.4.3.2, the

Using the shear streng1h along griJ I, the axial force in the collector, due to the seismic load, at the inte~ction of gnds C and I is:

=25.0 ft (l.02 kip/ft)

PQ,

== 25.5 kips (tension or compression)

Therefore. from ASCE/SEI 7 Secuon 12.4.3.2, the governing LRFD load combin:iuon is Load Combination 5 and the governing ASD load combinalion is Load Combination 5, and the required first order a."
cp

0-~====1

LRFD Pu ::::: (1.2 + 0.2Sos) Po + OoPQ6

~>;!-----

JJolaphragm T shear, V

+ 0.5Pl + 0.2f>s

~~~- , ,·

::: 1.4(0 kips)+ 2.0(25.5 kips) + 0.5(0 kips)+ 0.2(0 kips) = 51.0 kips (tension or compression)

Collector

ASD P.

=(l.O + 0. l.tSDS)Po +PH+ PF +0.7fl 0 PQc

= 1.14(0 kips)+o kips+O kips + 0.7(2.0)(25.5 kips)

=35.7 kips (tension or compression)

force,£ i

I

1'

1

Try a Wl 8><50. From AJSC Mam10/ Table 2-4, the gcomelrie pmpt:rties are as follows:

®--~=== Fig. 8-5. Collector a.rial load dia.gram for Exnmple 8.4. 1.

AST.M A992 50 ksi P.::::: 65 k.si F'y:::

From AJSC Manual Tables 1- 1 and 6-1, the gcomc1ric proi:)enies are as follows:

... DIAPHRAGMS, COlJ.ECTORS AND CHORDS

8-16

W18x50 A= 14.7 in.2

d=l8.0in.

tw

.r:x =7 .38 in.

r1 =1.65 in .

l:x:::: 800 in.4

=0.355 in.

~

8-17

8.4 DESIGN EXAMPLES

Di is calculated from AJSC Specification Equation A-8-6: hltw= 45.2

J = 1.24 in.4

11 =40.l in. 4

Cw= 3,040 in. 6

LRFD

r:xlr1 =4.47

ASD

a:: 1.00

a= l.60

Required Second Order Axial Strength

82=

Consider second-order effects with L = 12.5 ft using AlSC Specification Appendix 8.

1

l-

t

(I.}',

'

story

Pe srory

B2 is calculated based on an elastic analysis of the structure. Alternatively, a maximum pennitted drift can be used to calculate B2. Note that B2 and 0 0 apply to the forces derived from the base shear..They do not apply to the minimum diaphragm force from ASCEISEJ 7

=I-

Equation 12.10-2.

=1.02

1 1.00(3, 750 kips) 182,000 kips

:::: _ 1.60(2,620 kips) 1 182,000 kips

=1.02

Calculate B?, with a first7.order interstory
H

=201 kips+ 152 kips+ 103 kips

L RM

= 456 kips = 12.5 ft = 1.0 for braced frames

Detennine the required second-order axial force, Pr, using AISC Specification Equation A-8-2, with P1, equal to P,, and P0 for LRFD and ASD, respectively, as detennined previously.

LRFD

HL

(Spec. Eq. A-8-7)

Pe story = RM -

456 kips(l2.5 ft) (0.375 in.)(l ft/12 in.)

=182,000 kips

and

Roof

D= 85 psf Dr= 85 psf

LRFD

.. $.

=(1/1,000 lb/kip)(9,000 ft 2 ) •

·x ( [1.2 +0.2(1.0))

x {[LO+ 0.14(1.0)]

x [85 psf + 2(85 psf)) + 2.0(0 pst)

x (85 psf + 2(85 psf)) + 0 psf

=3,750 kips

,

1

I

+O psf + 0.7(2.0)(0 psf)} ::2,620 kips

AMeRICAN l!'lsttlVJ'I! OP Sim.. CONSTRUCTION

,,.

(KL)t

~

I

ASCFJSEl 7 Section .12.4.2.3 . .

+ 0.5(20 psr"+ 2(50 psf)) + 0.2(0 psf)}

l

...•

=25.0 ft I

(KL)1 =0 ft (assume lateral movement is braced by the slab)

For ASD, use Load Combination 5.

Psiory

= 36.4 kips

{KL)x

ASD

= (1/ 1,000 lb/kipX9,000 ft2 )

=52.0 kips

Assume that the W18x50 collector beam has the following unbraced lengths in compression:

Lr= 20 psf

Using the ASCE/SET 7 Section 12.4.2.3, the goveming load combinations are as follows:

f'srory

=0 kips + 1.02(35.7 kips)

Compressive Strength of the W18x50

Lredu«d "" 50 psf

For LRFD, use Load.Combination. 5, with the 0.5 factor on L permitted by

= 0 kips+ 1.02(51 .0 kips)

Note: The amplification calculated here is for the lateral system and the force it delivers through the diaphragm to the collector beam.

2

Calculate P,10'>' the total vertical load supported by the story. Use a surface area of 9,000 ft on each floor the following surface loads: . .

Floor

Pr= Pnr + B2P11

P, = Pnt + B'lP11

D.H

= l.O

ASD

= 12.5 ft

J

For the compressive strength based on the limit state of flexural buckling, assume the composite slab fully braces the beam in the weak axis but not in the strong a.'tis. Calculate the strong axis compressive strength using AlSC Manual Table 6- L Enter the table using (KL)1 , 9:

, ·:

.

-,

::(KL):x

(KL) yeq

(Manual Eq. 4-1)

r:x/ r1 25.0 ft 4.47 5.59 ft

=--

=

AMEIUCAN lNS11TUTE OF STEEL CoNSTRUCMON

j

8-18

DIAPHRAGMS, COLI CCTORS ANO CllOROs

fnterpolating p from AJSC Manual Table 6-1, the compressive ::.trength due axis flexural buckling is: LRFD

10

strong

ASD

S-19

8.A DESIGN f_XAMPLES

With f = F,,, check that hit,.~ I -49 vElf - 45.0 as gt\'f'n m AISC Specificmio11 Sec lion E7.2(a}. Because hit...,"" 45.2 .. 45.0, there is negligible reduction in the gross cross section based on AISC Spec1ficot1on Section E7 2. The available axial strength is detemunet.1

•IS

follo\\.'s: (Spec. Eq. EJ-1)

Pn = f'c,A,

=31.S ks1(t4.7 in.2 ) '• ~·

- 0.00180 kips-I

- 0.00270 kips'1

=556 k.ips

= 370 kips

=467 lops

LRFD Weak ms comprcssi\'C strength due lo (Kl= 0).

fle.~ural

buckling wilJ not go'-em by inspecuon

The W18x50 has a slender web in compression, as indicated in Table 1-1 of tl1e AISC Manual. To dctem1ine the reduction factor, Qa, for slender stiffened elemenrs, use AlSC Specification Section E7.2, with/= Fa computed with Q 1.0.

=

~-11 . ...

' f.

Pc= =

n 2E[c... +I1 (d 12)

l

2

(KtL)

l

]

+Gl

1

=0.90(467 kips)

=280 kips The foUowing is a summary of the limit s1a1es in compression on the collector. StrQngAxis 1'1exural Buckling

J1_.+1 1 +(d/2) A8

ln (29,000 ks.i)!{3,040 in. )+(40.1 in.' )(18.0in.12) ]+ 11, 200 ksi{1.24 in.'' }I 2

(KLh

2

6

¢cP11 =420 kips

1

~= 370 l;ips

800 in.' +40.1 in.4 +(18.0 inJ2)2 (14.7 in.2)

QF

1 -=

~

The available axial compressive strength of the seclion is governed by constrainf'tl axis ClcxuraI-tonional buckling.

J.0(50 0 ksi) 46.2Xsi 1.08S 2.25

Required Flexural Strength

=

Calcul:He 8 1 from AlSC Specification Appendix 8, Section 8.2.1.

Therefore:

1tl£J. P,1=-~

!:

P. =280 kips n,

n.,

::::46.2 ksi

Constrained Axis F le..niral-Torsional Buckling

(KL'h = 12.5 ft

2

x~~~~~~~~~~~~~~

.:j:

=25.0 ft

ILO(J2.5 ft)(12 inJft)J

t

P,

1.61

= 467 kips 1.67

=420 kips

(8-3)

2

P,.

n..

-=-

9cPn = 0.90Pn

For the limit state of constrained axis torsional buckling, I.he unbraced length is J2.5 ft. Use Equntion 8-3 for Fe.

2

ASD

F., =Q 0.658 ,, F,

~:

= LO 0.658 ~, 44.ltit 50 ksi

I

=3 1.8 ksi

(Spec. Eq. A-8-5)

(K1L)2

(Spec. Eq. E7-2)

2

7t

(29,000

ksi)(soo in.~)

= lt.0(25.0 ft)(l2

io./fl)j

1

=2.540 kips

Because !he beam is subjccr 10 transverse loading between supporu: C.,= 1.0

DIAPHRAGMS, COLLECTORS AND CHORDS

8-20

Bec:iuse the member does not require composite action, the studs are only required to resi'st

ASD

LRFD (Spec. Eq. A-8-3)

C~r ~ l

81 =

ihe diaphragm shear transfer. Where composite flexural action is required, the shear studs m3y be considered fuUy effective for both flexural shear tr:insfcr and diaphragm shear trans-

(Spec. Eq. A-8-3)

PeJ

Use a W18x50 for 1he collector.

LO

= ~- l.60(36.4 kips) 2.5~

2,540 kips

Alternatively, :i colJector with adequate tensile strength co resist the diaphragm she9r can be provided by the addition of supplemental slab reinforcement, such as ASTM A6 l 5 Grade 60 deformed reinforcing bars. In this case, the required area of slab reinforcement is:

kips

=1.02

=1.02

Tu

Asr~q=-

From AISC Specification Equation A-8-1, the required second-order flexural strength is:

¢F.,

ASD

LRFD Mrx = B1Mn1 + B2M11

Mrx

=

=B1M111 +lhMu

= 1.02(0kip-ft)+1.02(220 kips)

= J.02(0kip-ft)+1.02(208 kips)

= 224 kip-ft

= 212 kip-f1

The composit~ fle:<~ral strength may be used for collectors. The following demonstrates !hat the noncompo~ite beam is· adequate. Assuming it is fully braced and using AISC Manual Table 3-2 for a W18x50, the available flexural strength is:

ASD

LRffi

OM. =379 Jcip-ft

I ':; = 252 Jcip-ft

Check combined loading of the W1 8>s50 using AISC Specification Section HI .1.

52.0 kips

0.90(60 ksi)

= 0.963 in.2

Available Aexural Strength of the W18x50 Beam

I

j

Four No. 5 bars (As= l .24 in. 2) can be used 10 provide this supplemental slab reinforcement al lhe collector location. Per ACI 318 Section 21.11.7.5, additional transverse reinforcement is not required if the cxrrcme fiber stress in the concrete is kept below 0.2//. Because the deck span is parallel to the collector axis, the concrete above and below the 1op of the metal deck will be effective in resisting the collector force. Assuming the met:il deck profile is such that one-half of the area below the top of the metal deck is filled with concrete, tl1e effective chick.Dess of the concrete collector is 3Yz in. The minimum wjdcJ1 of slab required to resist the collector force is, b. __P._._ nun - 0.2/Jc

=

Pr

Pr 36.4 kips -=---'P., 280 kips =0.130

52.0 kips 420kips

Pc

=0.124

0.2( 4.00 ksi)(3 1h in.)

=18.6 in.

Using the 0.2/J compression limitation set forth in ACl 318 Section 21.11.7.5 in conjunc-

as limiting compressive strains in the concrete collector co 0.003 (which is analogous to the

Because Pr/Pc< 0.2, use AISC Specification Equation H 1-1 b.

0.124 + 224 lcip-ft + 0 = 0.653

0.130 + 212 kip-ft +O = 0 _906 2 252 kip-ft

2

379 kip-ft

0.653 <1.0

o.k.

0.906< 1.0

needs to be provided to transfer the force from the slab reinforcement into the structure. tion with 0 0 -level forces may be conservative. Alternate approaches can also be used such

Because P,IPc < 0.2, use AISC Specification Equation HI-lb.

I.-

I.

I.

52.0 kips

This collector width can be easily accommodated a.long grid A. Note .that a mechanism ASD

LRFD

j,

fer as descnbed in Burmeister and Jacobs (2008).

1--

1.0 =------..,.. 1.00(52.0 kips)

8 21

strain limits for unconfined conc~ete resisting seismic loads), treating the collector as a short compression member, or any other rational design method that provides a load path between the inertial mass and the seismic force resisting system.

o.k.

AME.RICAN lNS'ITl'UTE OF STEEL CONSTRUCTION

DIAPHRAGMS. COl l.J:.C'TORS A-ND CHORDS

Given: Refer to Figure 8-6. Check the adequacy of lhe ASTM A36 single-plnte connection shown to rcsi~t the collector forces determined m Example 8.4. l, where \'o == I l .8 kips, Vi= 8.29 IJ~. and Po,= 25.5 kips as determined in Example $.4.1. The beam is ASTM A992 material.

'

LRFD R,.., = (1 2+ 0.2Sns )D + n ..QE .... 0.SL+0.2S

ASTMA36 F1 36 ksi

Fu= 58 ksi

= 1.14(0 k.ip<>)+O kips+O kips + 0.7(2.0)(25.5 kips) = 35.7 k.ips (tension or compression)

i~:

ASD

R.. =~(20.7 kips)2 +(51.0 kips) 2

W18x50 1..., = 0.355 in.

R., = ~(13.5 kips) +(35.7 kips) 2

2

=38.2 kips

=55.0 kips

As noted in Example 8.4.1, ASCPJSEI 7 requires that collector clements in structures assigned to Seismic Design Categories C through F be designed to resist the amplified seismic loads (n.,..Jevel loads).

Design the connection in accordance with lhe proce.dure for extended single-plate shear connections in Part I 0 of the AISC M anual. modified for the pre::ence of an a."
From ASCFJSEI 7 Section 12.4.3.2, lhe required shear strength is de1ennined from the g<>v· eming Load Combination 5 for LRFD and Load Combination 5 for ASD. These load combinations govern based on the resultant required strength de1emuned in the following.

LRFD

iI

0.70. Qt

LRFD

From AISC Manual Table 1-1, the geometric propeo ies are as follows:

i>.

t

=1.4(0 kip!>)+ 2.0(25 5 kips)

The resultant required strength

=

.-

R;;a=(l.O+O 14Sos)D+H+F

=51.0 kips (tension or compression)

From AISC Manual Table 2-4, the plate material properties are as follows:

~

ASD

+ o.s(o kips)+o.2(0 k1ps)

Solution:

~11

8-2J

The requircJ a."
ExamPte 8.4.2. Collector Connection Design

i

SA OESJGN F.XAMPLF.S

R.,., =( I 2+0.2Sos}D+f2oQE + 0.5L+0.2S

== 1.4(11.8 kips)+2.0(0) + 0.5(8.29 kips)+ 0.2(0) 20.7 kips

=

(includes 0.5 factor on l permitted by ASCE/SEI 7 Section 12.4.3.2)

Available Shear Strength of the Bolt Group

The angle of the resultant load with respect to lhe longitudinal axis of lhe bolt group is:

ASD

LRFD

R,,., ={l.0+0.14Sos )D+ H + F

0=tan-t(R..a) R,;,.

+0.7f2oQE

=1.14(11.8 kips)+O ldps + 0 kips + 0.7(2.0)(0)

=13.5 kips ,,,,t

ASD

0= tan

· (::)

=ran-I (51.0 kips) 20.7 kips

=un- •(35.7 kips}

=67.9°

=69.3°

13.5 kips

t '"'"'

,;, rm..: •• 1JJ.• it ; I' 1(1:.·"'J

... _,, ·j

~J rt

The calculated load angle, 67.9°, is between the tabulated values for 60° and 75° in A1SC Manual Table 7-6. The eccentricity of the shear load is determined by the mclhod used for extended single-plate connections.

The calculated load angle, 69.3°, is between the tabulated values for 60° and 75° in AISC Mamwl Table 7.0. The eccentricity of the shear load is determined by the method used for extendeJ single-plate connections.

Interpolating from AISC Manual 'foble 7-6 with 0 = 67.9°, a= ex= 2'h in.. s,,. 3 in. and using n =4 bolls,

lnterpolnting from AISC Manual Tuble 7-6 with e 69.3°, a= ~z = 2'h in.. .r =3 in. and using n =4 bolts,

C=3.29

C=3.3 1

=

8.4 DESIGN EXAMPLES

DIAPHRAGMS, COLLECTORS AND OIORDS

8-24

8-25

'

~

Try a ~-in. single plate.

From AJSC ,\if011ual Table 7-1. for a Jii-in.-diarneter ASTM A325-N (Group A) bolt with the lhreads included in single shear, the available sh.ear strength of one bolt is:

I~,.

I ~=162kips

LRFD

= 24.3 "'"'

55.0 kips< 79.9 kips

'• ~ 2.4 (11 in.)(* in.)(58 ksi) =45.7 kips

User'•= 26.9 kips.

LRFD

=3.31(16.2 kips)

= 79.9 kips

=53.6 k.ips 38.2 kips< 53 .6 kips

o.k.

l

= 26.9 ldps

~ =c(~)

=3.29(24.3 kips)

Eq. J3-6a)

'• = 1.2[1~ in.-0.5( 1Vi6 in.)](* in.)(58 bi)

ASD

$Rn= Cc~r,,

(Spec.

where le is conservatively taken as the least dimension to the edge in ei1her the horitomal or vertical direction (the vertical edge distance of l 1h in. governs).

ASD

The available shear strength of the bolt group is:

LRFD

Bearing on the Plate At lhc plme edge:

R,, =

$R., =C~r,, o.k.

I.

ASD

"'3.29(0.75)(26.9 kips)

=66.4 kips

n

c(!!!.) n

= 3 _31 (26.9 kips)

2.00 =44.5 kips

W12x96

55.0 kips< 66.4 kips

W18x50 with std. holes

D L

=11.8 kips =8.29 kips

o.k.

38.2 kips < 44.5 kips

o.k.

Bearing on the Beam web 2)2" 2·

The beam web is nearly as !hick as and stronger than I.he plaic. The beam web has sufficient be.aring streng1h by inspection.

I.

Maximum Permissible Plate Thickness As discussed in AISC Manual Part JO, the connection wilJ be proponioned such that bolt shear failure cannot occur prior to plate 0.exur.\l yielding. Th.is proportioning ensures sufficient ductility to permit boch beam end rotation and rotational defonnntions corresponding to lateral drift.

P 0 •::: 25.5 kips

In order to achieve this proportioning of limit stat.es, I.he flexural srrenglh of the bolt group is computed, and the maximum shear plate thickness is determined using the plate )ield stress and depth (which is alrendy J...'llown). From AlSC Manual Tobie 7-6 (for 0 = 0° in this c:ise), C' = 11.3 in. From AISC Specificotitm Table J3.2, F,,,, = 54 ksi for A325-N bolts (Group A).

PL%" with $ld:holes (A36)

rs·

(4) dia. A325-N bolts

_J

Fig. 8·6. Collector connecrion investigated in Exompk 8.4.2.

.}

8-16


MfffllX=~(AbC')

(Manual Eq. 10-I)

0.90

8 ~ OESlG~ E.'CA.'.fPLES

Therefore, lhe minimum required plate thickness is:

LRFD

=~.~i (0.601 in.2 )(I J.3 in.) I

=407 kip-in.

'=

6M,,,,,x = Fyd 1

=

(Manual Eq. 10-3)

_ 6(407 kip-in.) - 36 ksi(l2.0 in.) 2 = 0.471 in. > 0.375 in.

2

1,,,.;., =v(rpvoon)

ASD

+(rpa,..,.)2

Ip min= J(tpvmin)2 +(tpanun)

Jco.0199 in.)2 + (0.131 in.)2

=

2

~(0.0781 in.)2 +(0.138 in.)2

=0.159 in.

=0.153 in. 0.375 in. > 0. 153 in.

o.k.

0.375 in.> 0.159 in.

o.k.

o.k. Net Section Rupture of the Plate under Combined Shear and Tension

Yieldf!lg of the Plate under Combined Shear and Tension

In evaluating this limit state, the minimum plate thickness is calculated independently for each force and the resulting thicknesses are combined for lhe interaction of forces usfog an elliptical approximation. The elliptical approximation is not required by the AISC Specification, but it is a rational approach for detei:mining the minimum plate thickness.

Jn evaluating this limit state, !he minimum plate thickness is calculated independently for each force and the resulting thicknesses are combined for the interaction of forces using an elliptical approximation.

=Lr~1lp

For shear yielding, the nominal strength is:

=[12.0 in. -4( 1¥16 in.+ 1/J6 in.))rp (Spec. Eq. J4-3)

Rn= 0.60FyAgv = 0.60F1 dtp

=8.00rp in.2 For shear rupture, the nominal strength is:

ASD

LRFD

(

~-1 '

..

:~

. R,,,, pv mm - $0.60Fyd

1

pv mm

Rn= 0.60F.,Anv

=(0.60F).d1n)

20.7 kips =-----...::---1.00(0.60)(36 ksi)(l2.0 in.)

=~~~-l3_.5_b_-~ps~~__.

= 0.0799 in.

=0.0781 in.

t

Rav =0.60Fu{8.00 in.)/ Q

---~---

20.7 kips =------------

=

=0.0991 in.

=0.0970 in.

0.75(0.60)(58 ksi){8.00 io.)

13.5 kips (0.60)(58 .ksi)(8.00 in.)/2.00

For tensile rupture, the nominal strength is:

~=

LRFD t

f pv min

(Spec. IJ.Cf: 14-1)

Rn= F1 A8 =F1 dtp

...~;

R,,,,

. -

"'""" - ¢0.60Fu (8.00 in.)

(0.60)(36 ksi)(l2.0 in.)/1.50

For tension yielding, the nominal strength is:

I

ASD

LRFD

••.-'

~!

(Spec. Eq. 14-4)

ASD

R,,,, . --¢F>d

(

pamtn -

51.0'kips 0.90(36 ksi)(l2.0 in.) =0. 13lin.

35.7 kips 36 ksi (12.0 in.)/1.67 = 0.138 in.

=-----'----

R,.=F11At

,, .. , ~.

=F,,Ant .;:.\.h

(Spec. Eq. J4-2)

8.4 DESIGN EXAMPLES

OtAPHRAGMS, COLLECTORS AND CHORDS

t

.

pa mrn

---=-- $F.,(8.00 in.) =__5_1_.0_ki_·p,_s_ _

f pa min

0.75(58 ksi)(8.00 in.) = 0.147 in.

F.,(8.00 in.) I 0. 35.7 kips (58 ksi)(8.00 in.)/2.00

'=

=244tp kips

Ip min

= J(0.0991 in.)2 +(0.147 in.)2 o.k.

From AJSC Specification Equation 14-5:

Therefore, the minimum required plate thickness is:

=~(tpvmin)

2

7.00tp in. 2

0.60FuA,,,, =0.60(58 ksi)(7.00rp in. 2 )

= 0.154 in.

Therefore, lhe minimum required plate thickness is:

-~-

= 10.5rp -3.50( 1S1i6 in.+ l/idn.)/p

Anv

Rua

=0.177 in.< 0.375 in.

Shear Rupture

ASD

LRFD

8-29

LRFD

ASD

2

+(tpamm)

= O.J82 in.< 0.375 in.

Rn

$Rn =9[0.60F,,Anv+Ub,f~AniJ

=~(0.0970 in.)2 + (0.154 in.)2

-=

s 9(0.60Fy.-\gv + Ub,FuA..1 J

o.k.

~I0.60FuAnv + UbsFuilnr J

0.60FuAnv + UbsPuAnt

Ip

0..tp

= 244kip/in.+116 kip/in.

=0.75(244 kip/in.+ 116 kip/in.)

2.00

'

= 270 kip/in.

tp

Agr

=2.50rp in.2

Anr

=2.50zp-0.50( 1S/J6 in.+'lt6in.)zp

•

= 227 kip/in. + 116 kipfm. 2.00

= 257 kip/in.

= 2.501p ..., 0.5001p

\

Use $R.. I Ip;: 257 kip/in.

=2.00rp in.2

R.,, r,,..,,,;,,=--¢Rn I tp

=1.0

U1>sFuA..r = 1.0(58 ksi)(2.00tp in.2 ) = 116tp kips

=

Shear Yielding

'---

=(12.0 ·in. -1.50 in.)tp in.2 =10.5tP. in.2

0.60FyAgv ;:Q.60(36 ksi)(IO.Stp

=227rp kips

w.2)

=172 kip/in. Use Rn I 0.. tp =172 kip/in. I

= 20.7 kips 257 kip/in. 0.0805 in. < 0.375 in.

I~

0..tp

== 0.75(227 kip/in.+ 116 kipfm.) j

\.

0.60FyAgv +Ub1 F.A111

9j0.60F,A1v + UbsFuAw)

Tensile Rupnire

I

= 180 kip/in.

Investigate the failure path 1-2-3-4 in Figure 8-7(b) for the shear force.

Agv

n s; 0:60F1 AI" + Ubs F11An1

n

Block Shear Rupture of the Plate In evaluating this limit state, lhe minimum plate thickness is calculated independently for each force, and the resulting thicknesses aJe combined for the interaction of forces using an elliptical approximation.

U1>s

0.60.F,,A,,v +UbsF.,Anr

n

. -

I

o.k.

R.,.,

pvm;n - (Rn /0..)/tp 13.5 kips

= 172 k:ipfm.

=0.0785 in.< 0.375 in.

o.k.

~4

DIAPHRAGMS. COl..LECTORS AND CHORDS

8-30

DESlGN EXAMPLF,.S

S-'.31

\ Investigate the failure path 1-2-3-4 in Figure 8-1(b) for the axial force.

0.60FuAnv =0.60(58 ksi)(2.00fp in. 2 )

=69.61, kips

Tensile Rupture

Ag1

=(12.0 in. - 1.50 in.)tP =IO.Stp

From AISC Specification Equation J4-5:

in.2

"

LRFD

.

ASD

= 10.5tp -3.50( 1Ys6 in.+ Yi6 in.)t p

Rn

¢Rn= ¢[0.60FuAr.v + UbsFuAm]

=7.00tp in.2

$

-=

4>[0.60FyAgv +UbsFuAnr]

-

UbsFuA..1 =1.0(58 ksi)(7.00tp in.)

Shear Yielding

0.60F.,A,,v + UbsFuA..1

Ip

fltp 69.6 kip/in.+ 406 kip/in.

= 0.75(69.6 kip/in. + 406 kip/in.)

2.00

=357 kip/in.

= 2.50tp in. i

= 238 kip/in.

~10.60F,Agv + Ul>sFuAnr j

0.60FyAgy = 0.60(36 ksi)(2.50rp in. 2 )

0.60F1 A1v + UbsFuAni

n

tp

= 54.0tp kips

54.0 kip/in.+ 406 kip/in.

"' 0.75(54.0 kip/in. t-406 kip/in.) Shear Rupture

=--.:....._-~-"'----

2.00

= 345 kip/in.

=2.50tp-0.50( 15/i6 in. + 1/i6in.)tp

n

9I0.60FuAnv +UbsFuA111J

=.4-06tp kips

Anv

n < 0.60FyAgv +UbsFuAnr

=1.0 .

Agv

0.60F.,A,,v +UbsFuAn1

n

= 230 kipftn.

Therefore, use $Rnltp = 345 kip/in.

Therefore, use Rnl!lrp = 230 kip/in.

= 2.50tp -0.500tp

=2.00tp in.2

lpamin

Rua $Rn I tp

=---

t

= 51.0 kips 345 kip/in.

2·

Raa

. ----

pa1tun - Rn/0. tp

35.7 kips

\

=--~-

230 kip/in.

=0. 148 in. ,

'i ;,

.

= 0. 155in.

The minimum requir~d plate thickness due to bolh forces is:

}

Ip,.,;,,

2

= J(lpv min } +(tpo min )2

Ip mbt

2

= J(0.0805 in.) +(0.148 in.) 2

·:·.

The minimum required plate thickness due to both forces is:

=0.168 in. < 0.375 in.

o.k.

=~(r,,., min ) 2 +(r,.,. ,,,;,.}2 =Jco.0785 in.)2 +(0.155 in.)2 = 0.174 in.< 0.375 in. o.k.

-I'

rvestjg:ne the failure path 1-2-3-5 on Figure 8.7(b) for the shear force.

f:ot the shear force conservatively use the minimum thickness determined from path 1-2-3-4.

I

•.

::

..

s:

$:

I:

(a) Beam web

(b) Single plate

Fig. 8-7. Block shear failure paths for Example 8.4.2 .

~jj

l)JAPHKA(.;M:S, CUU...tc.:roRS ANO CHORDS

LRFD t/1" ml•

ASD

= 0.0805 in.

t pv min

=0 .0785 in.

l

LRFD

ASD

¢!0.60F;,A,,,, + Ub~FuA..1) Ip

0.60F.,A,.v +UbJFvAn1

Jnyestigate the failure palh 1-2-3-5 in Figure 8-7(b) for the axial force.

=0.75(139 kip/io.+ 348 lcipfm.)

Tensile Rupture A8 ,

= 365 k.ip/in.

=(12.0 in.-3.00 in.)tp

¢[0.60~'"Agv + U~nFuA..r J

= 9.00tp io.2 A1t1

ubs

= 6.001 P in.2

:: 342 kip/in. Therefore. use R,, 2

_ 108 kip/in.+ 348 kip/in.

-

2.00

= 228 kip/in.

=LO

=342 kip/in.

'Therefore. use

)

Shear Yielding

=2(2.50 in.)tp 2

Rua =$Rn I Ip

=35.7 kips = 0.157 in.

Ip,,..,, =

~(1pnnin)2 +(tpo ,...;,)2

=j(0.0805 in.)2 +(0.149 in.)2 =0.169 in. < 0.375 in. o.k.

=5.001P -(1o/16 in.+ Y\6 jn.)rP

Roa

= _(_R_n_ Jf...-.l.,...}_/_Ip

342 kip/in. = 0. 149 in.

=108rp kips Shear Rupture

I po min

= 51.0 kips The minimum required plate thickness due to both forces is:

0.60FyAgv = 0.60(36 ksi)(5.001p in. 2 )

~ = 228 kipfm. n ip

fp

lpamin

= 5.00tp in.

0.60F1 Agv +UbsF.,A,., flc p

=0.75(108 k.ip/io.+ 348 kip/in.)

=348tp kips A8 ,

_ 139 kip{Jn. + 348 l
lp

=9.00tp-3(1S/111 jn. +11\6 in.)tp

Ub,F.,A,,1 =1.0(58 ksi)( 6.00tp in.

Otp

\

228 kips

The minimum required plate thickness

due lo both forces is: 2

Ip - .

=J(rP" mln) +(t""..,;,,)

2

=Jco.on5 in.)2 + (0.157 m.)2 =0.176 in. < 0.375 in. o.k.

=5.00tp-lp

=4.00tp in.2

Block Shear Rupture and Shear Rupture of the Beam Web

In evaluating these limit states, the minimum beam web lhjckness is calculated independently for each force, and the resulting thicknesses are combined for the interaction of forces using an elliptical approximation.

0.60F.,A,,,, = 0.60(58 ksi )( 4.00tP in.2 ) ==l39tp kips From AlSC Specijicotion Equation 14-5:

LRFD ~R,, =

'(0.60F.,A,,, + UbsFuA..1} ~ $[0.60F1 A1 v+UbsF..At.1]

Block shear rupture can occur on the beam web due to lhe axial load on the beam (block shear rupture cannoc occur due to shear on an uncoped beam). Por the block shear calculations, investigate lhe failure path 1-2-3-4 as shown in Figure 8-7(a). A beam underrun of

ASD R,,

-

n

=

~ rn. will be assumed.

0.60F11 A11v + Ub,FuA,.,

n ~

::.

• ro..

0.60FyAgv +Ub:rFuA111

n

•

j

Tensile Rupture

A11

= 3(3.00 io.)r,..

= 9.00tw Ln. 2

I

.....

.

-···--····-- -- - - - --

~

'

t

8-34

A111


= 9.001.,. in. 2 - 3(1Yi6 in.+ V.6 in.)tw

=6.00t,. in. U1>s

8.4 DESIGN EXAMPLES

LRFD

ASD

2

Therefore, use ¢R,,

=366 kip/in.

Therefore, use

=I 0

R..,, 1....,,,....=---

F.,A,,,:::: Ub3(65 ksi)(6.00t,. io. 1 }

I

¢R,,. I Ip

= 3901.., kips

R,,. --1<.>"'"' - R,,!Otp

51.0 kips

35.7 kips

366 kipfm. = 0.139 in. < 0.355

Shear Yielding

~ = 244 k.iplin.

=244 kip/in. =0.146 in.< 0.355 in.

o.k.

in.

o.k.

- 2(2.00 in. - A in.)t,. 1

=3.501.,. in.2

Also check shear rupture of the beam \\cb according to AISC Specification Section 14 2. a:. foUows:

0.60FyAgv =0.60(50 ~i)(3.50t.., in. 2 )

LRFD

Shear Rupture

Anv

I

=3.50tw in.2 =2.50tw in.2

2(0.50)(t5/J6

in.+ 1~6

Ruv

. ---'-'-I..,

Ruv =-----

in.)r,,.

0.75(0.60)(65 ksi}

x

ASD R 0.60F.,A,.. + Uh.tF,.A"' -11=

o

;.

..,,'

., ::

..

.. ;

). )

i-..

n

< 0.60FyAgv +Ub,FuA..1

)'

.....

= 0.75(97.5 kip/in.+ 390 kip/in.) =366 kip/in.

0.60F.,Anv +U,,,FuAnl

x =0.0495 in.

=J(t....,min)2 +(11<-omin)2 =

,.., ,,.;,, =J<1....., ,,,.,. )2 +(1.. ...m)2 =Jco.0495 m.)2 +co.146 in.)2 0

Jc0.0505 in.)2 + (0.139 in.)1

= 0.148 in.< 0.355 in.

I

[18.0 in.-4( 1.V.6 in.+ 1116 in.)]

=0.154 in. < 0.355 in.

o.k.

o.k.

Plate Required Flexural Strength

flt..,

LRFD

97.5 Jdpfm. + 390 kip/in .

2.00 :: 244 kip/in.

0.60F1 Ap + U~F,,A.u

lw

flt,.

"" 37 l ltiplin .

-

n

cl>[0.60F1 A1, +U""F,,A,.,] • 0.75(105 kip/in.+ 390 kip/in.)

I

[ 18.0 in. - 4 ( 1-'li6 in.+ 1/i6 in.)]

=0.0505 in.

-

¢[0.60F,,A,,, + Ub,F.,A,,i) t.,

13.5 kips =---:-,---..,---=----=--[(0.60)(65 ksi)/ 2.00]

=-------=----~

fwmiJs

"'·

[{0.60)F,./fl)dn~t

20.7 kips

LRFD

i:,

Rav

$(0.60)F,,dn(I

From AJSC Specification Equation 14-5:

S ¢(0.60F1 Ar +Ub,FuAm]

r,... min= (R,./Q)/ t,,..

"''mm - $Rn I

0.60Fut1,,., =060(65 k~i )( 2.50tw in.2) "'91.51.., k.ips

lt/R,,. =~[0.60F.A,,. + U.,F.A.u l

ASD

105 kip/in.+ 390 kip/in. 2.00 =248 kipfm.

:::s

M.=R,,.,e =20.7 k.ips(2.50 in.)

=51.8 kip-in.

ASD Alu a R,,,,e

=13.5 kips(2.50 in.) :: 33.S kip-in.

Plate Available Flexural Strength

The Von Mises criterion will be used to reduce the pcrmined bending strength for the shear stress pre..o;;ent. The a."l:ial tension

St:re.S!

lo account pre...<:eot is deducted dircct1y from the

If' . S-36

OIAPHR-\GMS, COLl..ECTORS AND CHORDS

PART 8 REFERENCES

S-37

)

bending stress. Rearranging ATSC Manual Equation 9-1 to solve for f~. elimin:iting the perpendicular axial component (f, = 0), setting/,,.= Fer.le= Fy, and/xy =fv, and subrracting the ax.fol cension stress, results in the following equations. A factor, Ct, has been incorporated imo the equation. This is the factor used in the AlSC Specification when calculating loads or stresses at the ultimate strength level.

LRFD

ASD

Ct=].()()

J

Frr = FJ -

=

<:t=l.60

Fer =JF/-3a/J -of,

3o./J -of,

(36 ksi) 2 - 3(1.00)(

20 7 · kips ) 12.0 in.(!.\ in.)

2

=

1.00(51.0 kips) 12.0 in.(3h in.)

PART 8 REFERENCES Bunneister, S. and Jacobs, W.P. (2008), "Under Foot: Horizontal Floor Diaphragm Load Effects on Composite Beam Design," Modem Steel Construction, AISC, December.

f.

Helwig, T.A. and Yura, J.A. (l 999), ''Torsional Bracing of Columns," Journal of Structural Engineering, ASCE, Vol. 125, No. 5, pp. 547-555. Sabelli, R., Sabol, T.A. and Easterling, S.W. (2011), NEHRP Seismic Design Technical Brief No. 5 Seismic Design of Composite Steel Deck and Com:rere-filled Diaphragms: A Guide for Practicing Engineers, NIST GCR 11 -917-10, NEHRP Consultants Joint Venture, partnership of the Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering, National Ins1itute of Standards :ind Technology, Gaithersburg, MD.

I,

i

1.60(35.7 kips) 12.0 in.(lh in.) = 22.7 ksi

= 23.8 ksi

2

(36 ksi)2 - 3(1.60)( 13.5 kips J·1 12.0 in.(3h in.)

t

=% in.(12.0 in.)2 4

=13.5 in.3 LRFD ~Mn

"'·

ASD

=$FcrZ

Mn

-

= 0.90(23.8 ksi)(13.5 in.3 ) = 289 kip-in.> 51.8 kip-in.

o.k.

n

Fc,Z

=--

n

(22.7 ksi)( 13.5 in. 3) J.67 = 184 kip-in.> 33.8 ldp-in.

\

o.k.

\

I "

The selected *-in.-thick plate is acceptable.

Weld Strength

The welds are sized as AISC Manual.

*'P to develop the strength of the plate as discussed in Part 10 oftbe ..

*'p =¥s <*in.) =0.234 in.

..

.

' .

Use a \4-in. fiUet weld to connect the single plate to the column flange. The single-plate connection shown in Figure 8-6 is adequate to resist the collector fo~ determined in Example 8.4. I . .. · -~

rl·

••!

(1

'

~

'.

~1.,..2-158

10-J

REFERENCES

ii

iarlson, K.D., Lin, Z., Hardin, R.A., Beckermann, C., Mazurkevich. G. and Schneider M.C. (2003), "Modeling of Porosity Formation and Feeding Flow in Steel Casting,': Proceedings of Modeling of Cnsring, Welding and Advanced Solidification Processes X, ,; · May 25- 30, Destin, FL.

PART 10

t

ENGINEERED DAMPING SYSTEMS

&

~: fardin R.A., Ou, S., Carlson, K. and Beckermann, C. (1999), "Relationship between

Casting Simulation and Radiographic Testing: Results from the SFSA Plate Casting ' Trials," Proceedings of the 1999 SFSA Technical and Operating Conference, November ~ 4-6, Chicago, IL. ~

10.l SCOPE ... . ........................ . ............................ l0-2

.

~

10.2 INTRODUCTION TO ENGINEERED DAMPING SYSTEMS ............. 10-2

v Niyama E., Nchida T., Marikawa M. and Shigeki, S. (1982), "A Method of Shrinkage

~

10.3 VISCOUS DAMPERS ...... ·.. . ... . .................... . ..' .. : ..... . 1~2

l

. Prediction and its Application to Steel Castings Practice," paper presenced at 49th lmernatio,nal Foundry Congress, Chicago, IL. .

10.4 VISCOELASTIC DAMPERS ......................... . .... . ..... : .. 10-4 10.5 FRJCTION DAMPERS . . .......... .. . . .. . ....... . ........ .. ....... 10-5

·>.

10.6 YfELDJNG METALLIC DAMPERS . ... ... . .. . ............. . ...... . . 10-5 ~

10.7 APPLICATION TO ANALYSIS AND DESfGN . ............ . .. .. ... . ... 10-6

- - - --
PART 10 REFERENCES .... . ....... . . . ... . ..... . ........ . ............ .. 10-7

-. >

. Prequalified Connections for Special and ltllenMdi.ale Steel Momeni Fram.t!s for Seismic Applications, 2010. incl. Suppleme1tt No. l AMERJCAt< INSTI1Vll! 01' ST.Ea CONSTRUCTION

I

i

AMEIUCN'I !Nsmvra OP STE.EL CONSTRUC'ttON

.

..: I "·

10-2

ENGINEERED DAMPING SYSTEMS

10.1 SCOPE Although not covered in theAISC Seismic Provisions, damping can be used to reduce seismic response and is lhus an important methodology that may be utilized in the design of steel structures. Tiris discussion provides an overview of types of engineered damping systems. but does 001 provide design guidance. A more thorough trea1ment may be found in Constantinou et al. (1998), Hanson and Soong (2001). Liang et al. (20 11), Ramirez et al. (2002), and Whittaker et al. (2003).

. !

l;

.,..~ l'

....:·:~

~ ~· •I. .:;·,,

10.2 INTRODUCTION TO ENGINEERED DAMPING SYSTEMS Damping provides a means of dissipating a segment of input seismic energy. The inherent damping from strUctural and nonstructural sources is approximated as an equivalent viscous effect. For steel structures, the bare framing typically provides 1 to 2% equivalent viscous damping. The origin of this struc1ural damping is from sources such as slip of bolls, minor yielding of members, and rocking of base plates. When nonstructural componenrs such as partitions and other tenant improvements are added, the equivalent viscous damping can be as high as 5%. This additional damping is from tbe interaction of various nonstructuraJ components and slip of componenlS. The magnitude of damping is highly dependent on type and extent of nonstructural elements. Such inherem damping is difficult to estimate and is too small to provide an effective means for energy disi;ip:Hion. By contrast, supplementary damping can be incorporated in bolh new consr.ruction and seismic retrofit applications to produce much larger equivalent damping, typically in the range of 10 to 40%. Th.is supplementary damping is more reliable and readily predictable. Supplementary damping can be counted on to dissipate significant seismic energy and thus reduce demand on the structural system. This reduction of drift, acceleration and inelastic behavior will provide significantly higher performance than !hat of conventional construction which relies heavily on inelastic energy dissipation by the frame elements. Foor design, lhe expected level of damage is approximately proportional to the seismic input intensity. This implies acceptance of a certain level of damage based on the seismic input intensity. Research.has shown (lvtiyl!-JllOlo et al., 2011) that steel moment frame buildings designed per the applicable building code and using supplementnry damping will ha,·e a significantly lower collapse rate than a building designed without supplementary damping. Supplementary damping devices used for seismic design fall into four broad calegories: viscous dampers, viscoelastic dampers, friction dampers and metallic dampers. Each of these four brood groups of damper devices also includes subsets. For example, both solid viscoelastic dampers and fluid viscoelastic dampers are available. Damping devices are manufactured by a number of vendors; see Figure 10-1 for examples of the dampers. The various damper types bave distinc1 force-defonnation (F-u) constitutive relations as shown in Figure 10-2.

10.3 VISCOUS OAMPERS 1 Viscous dampers are velocity-proportional devices. Figure t().2(a) illustrales the force-d.is-

placement relationship of a viscous damper. The constitutive force-velocicy relationship for viscous dampers can be wrincn as:

10.4 VlSCOELASTIC DAMPERS

(a) When ri

~

IO-

0

F=Ci/l (b) Whe.n

(10-l .

u< 0 F=-Cluf

where

C =damping constant

u :: velocity

a=\ elocity exponent The choice of the parameters C and a depends on the structural system. 1n general, for buildings with higher story stiffnes!', larger values of C would be required. For viscoi
(a} Wsco1t.r damper

(bJ Viscoelrutic dampu

(c) Priction damp?.r

Fig. 10-1. Tmages of viscous, viscoelastic, friction and yiefdi11g metallic dampers. (a) New medical office comp/a (Miyamoto lnrema1io11a/) {b) Retrofa of an alsring commucia/ building (Miyamoto lnremational) (c) RetJ'O/it of an alsring commen:ial l>uilding (Miyommo lnteTMtionol) ( d) Retrofit of an existing building 011 campus of University of California Berkeley (NISEE e•library, Pacific Earthquake Engineering Research Ctnter)

ENGINEERED DAMPlNG SYSTEMS

I0.6Ylat>1NO METALLIC DAMPERS

dampers, the brace used to con·nect lhe damper to the structural members must be sli.ff enough to ensure 1hat the nearly pure viscous behavior is reproduc.cd io the damper. In commercially available structural analysis programs, viscous dampers are modeled as Maxwell's model of a dashpot in series with a spring. A vfllue of CL equal to 1 denotes a purely viscous response. This type of damper is referred to as a linear damper. Dampers with o: of smaller lhan unity are corrunonly referred to as nonlinear dampers. In general, viscous dampers do not increase stiffness or strength of the strucrural system and serve as purely damping elements. In other words, if the static pushover curves for a system with and without dampers are plotted, the curves will be identical so Jong as the demand on the viscous damper is within its operational capacity. Viscous dampers are ideal for structures with longer periods, such as moment frame buildings. They have been used extensively in new construction and for retrofitting steel moment frame buildings, resulting in reduced inelastic demand o.n me members and beam-to.column connections. The most common type of viscous damper is the fluid viscous damper which is similar to the shock absorbers used in automobiles. Figure .10-l(a) shows a typkal viscous damper.

where K = effective stiffness of Lhe device u displacement

=

Tbe damper's effective stiffness, K. and damping constant, C, depend on both the amplitude of excitation and its frequency. Viscoelastic dampers increase both the stiffness and strength of I.he structural 'system. In other words, if the suitic pushover curve for a system with and withour damp~rs is plotted, the curve with a viscoelastfo damper will have a higher capacity and a lar2er stiffness. Viscoelastic dampers are ideal for structures for which an increase in both damping and ~; stiffness is desired. For example, they can be used to mitigate torsional resP<>nse and increase damping for vulnerable structures or to reduce soft story response in buildings. An example of the viscoela5tic damper is ,illustrated in Fig~re 10-l(b). 1, 1 In commercially available structural analysis programs, solid viscous dampers can be ::. modeled as Kelvin's model of a dashpot in parallel with a spring .

I

1·~.4· V1sc·oELAsric ~~MPERS .·. .~

·-..·,

-,

10.5 FRICTION DAMPERS

~

Friction dampers exhibit elastic-perfectly-plastic response . .Figure 10-2(c) illustrates the force-displacement relationship of°a friction damper. They are displacemen t-proportional devices and increase the strength of the stru~tural system. The constitutive force~d.isplacement relation for friction dampers can be written as: · · ··

~~codastic dampers are displacement- .and vel<:>eit)'.-proportional devices. Figure ~~~(b) i!J~strates ~~.. force~displacement r!!lationship of a viscoelastic damper. The constitutive :-.:!· ........ '·' ·" ..... .t .·'?~ ~ '?' • .. •• ~o~c.e;dtsplacement r.el~t1on for v1scoelasti<:; dampers can be written as: ·. . . --:. .·~ : ..: ·.F= Ku+ Cu (10..:3) _!- . • .

: •• • • •• -· . •

•

•

: ...

~

.. : ·..>

:·~·

10-:

.....~ ".-;

(a) When u <

Us/ip

.

F=Ku

(10-4)

F=O

(10-5)

I n

t

(b) When u ~ Us!ip

where K llslip

(a) :·

v~~oiis damper '

l.

=initial stiffness of the device

= displacement at which the slip initiates

Friction dampers are ideal for structures for which damping and an increase in initial stiffness is desired. They can also be used to limit the force that is delivered to a structural member placed in series with them. Figure 10-l(c) shows a typical friction damper. .,-. _ In commercially available structural analysis programs, friction dampers are mo
I

(b) Viscoelastic damper

"':·•.'·

1· ·"

10.6 YIELDING METALLIC DAMPERS

( c) Fri.crion damper

(d) Yielding metallic damper I

Yielding met.a.Ilic dampers exhibit multi-linear force displacement response. Figure 10-2(d) illustrates the force-d.isplacemeut relationship of a yielding metallic damper. They are displacement-dependent devices. The constitutive force-displacement relation for I.he yiefdjng metallic dampers can be written as:

I·

Fig. 10-2. Idealized force-displacemenr relarion for l!arious types of dampers.

;.

t

F=f(u)

j:.

J

AMERICAN )NST111JTI; OF STllEL CONSTRUCTION

(10-6)

I·

J()-6

-

FNGINlillREO OAMPlNG SYS1T>MS

,

where f(u) denotes the nonlinear dependence of the de' ice force on its displacement. Yielding metal Uc dampers increase both stiffness and strenglh of the srrucrural sysiem. In other words, if the static pushover curves for a syMem with and without dampers are plotted, the curve with dampers will have a higher capacity and larger stiffness. Yielding dampers are ideal for structures for which both damping and stiffness increases are desired. In U.S, practice, yielding metallic elementS such as buckling-restrained braces are not typically treated us dampers, but as primary lateral Jo:id resisting elements. See Figure 10-l(d): In coinmercially available srructural analysis programs, yielding metallic dampers are modeled as multi-linear one-dimensional dements.

11 .~ .

=•!9

PART 10 REFERENCES

10. 7

PART 10 REFERENCES ASCE (2006), Stismic Reltabilization of faisting B11ildi11gs, ASCE 41-06, American Soeiety of Civil Engineers, Rcston, VA. Constantinou. M.C., Soong, T.T. and Dargush, G.F. (1998), Passivl! Energy 1Jissipa1ion Systems for Stmctuml Design and Retrofit, Monograph No. I, Multidisciplin"ary Center for Eanbquake Engineering Research, University of Buffalo, State University of New York. Buffalo, NY. FEMA (2009), NEHRP Recommended Seismic Provisions For New Buildings And Other Srructures, FEMA P-750, Federal Emergency Management Agency, Washington, DC.

10.7 APPLICATION TO ANALYSIS AND DESIGN

Hanson, R.O. and Soong, T.T. (2001), Seismic Design with Supplemental Energy Dissipation Devices, MN0-8, Earthquake Engineering Research Institute. Oakland. CA.

Each type of damper has specific characteristics, advantages and disadvantages for strucrural applications, and each type is made by several different manufacturers. To design with dampers, it is critical to caprure the dynamic characteristics and the nonlinear behavior of the srnicture. TI1is perm.its the designer to determine the amoun t of additional damping and stiffness required to achieve the desired performance. The equivalent viscous damping ratio can be estimated by computing the area of the force-displacement curve for one full cycle of loadi~g. · EngineerCci damping systems inhere"ntly require a performance-based design approach. Engineere-0 damping systems are effective for abnost all but the most rigid buildings. A thorough discussion of engineered, supplemental damping system design is beyond the scope of this l\fanual, but ASCE/SEI 41-06 (ASCE, 2006) is considered srate-of-the-art for existing srructures, and FEMA P-750 (FEMA. 2009) and ASCE/SEI 7-10 provide infom1atioo for new siructures.

Liang, Z, Lee, G.C., Dargush, G.F. and Song, J. (2011), Structural Damping: Applications ill Seismic Response Modification, CRC Press. Miyamoto, H.K., Gilnni, A.SJ ., Wada, A. and Ariyaratana, C. (2011), "Identifying the Collapse Haz:trd of Steel Special Moment-Frame Buildings with Viscous Dampers Using the FEMA P695 Me1hodology," Earthquake Spectra, Earthquake Engineering Research Institute, Vol. 27, rssue 4, pp. 1,147-1,168. Ramirez, 0.~t.. Conscantinou. M.C., Whittaker, A.S., Kircher, C.A. and Chrysosotomou, C.Z. (2002). '"Elastic and Inelastic Seismic Response of Buildings with Damping Systems," Earthquake Specrra. Earthquake Engineering Research Institute, Vol. 18, Issue 3. pp. 531-547. Wbitlaker, A.S., Constantinou, M .C., Ramirez, O.M., Johnson, M.W. and Chrysostomou, C .Z. (2003), "Equivalent Lateral Force and Modal Analysis Procedures of the 2000 NEHRP Provisions for Buildings with Damping Systems.'" Earthquake Spectrn., Earthquake Engineering Research Institute, Vol. 19, Issue 4, pp. 959-980.

..~

: .1

... ••'; ' '

I

..

I

)

":

A>.ffilUCAN }Nsmvn; OF STEEL CONSTRUCllON

J

pill4911•MRffilW'*#*lfWU~llPB&i'W¥MWMW9tik1¢Mi"fkWM~ 10-8

~

.ENGINEERED DAMPING SYSTEMS

INDEX

Analysis ....................................................... : 2-2, 9.1-10 Applic:ible building code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J-6 ASCE/SEI 7

Analysis methods ... .. ................................. ....... . ... ... 2-6 Design coefficients and factors for SFRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i-1 O Beam design Buckling-restrained braced frame ....... . .. .... . ...................... 5-430 Collectors and chords...•. . ........................... .... ............ 8-l Composite ordinary shear wall steel coupling beam ................. ·... . . .• 7-21 Composite ordinary sbe:ir wall composite coupling beam ................... 7-30 Composite special sbe:ir wall steel coupling beam ............. . .. . ... 7- 39, 7-41

Eccentrically braced frame .... . ............... . : ............ . . ·. . . . . . 5-353 EmbedmentJength ............ .. .......... .... . ........... .. ........ 7-14 Moment frame (R::: 3) .............................. ·.... . .. ......... . 3-10 Ordinary concentrically bmced fr:imes .... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5- l 8 Ordinary moment frames ................... . ........ .. -. . . . . . . . . . . . . . . 4-12 Speci:il concentrically braced frames ........... . . . ........ ... ... 5-104. 5-119 Special moment frames ............. .. .......................... _ . . . . 4-46 Beam embedment length .............................. _ . . . . . . . . . . . . . . . . . 7-14 Bolted Oange plate moment connection ................................. .. 9.2-39 Bolted joints .. .. ........................................ . .......... . 9.1-20 Bracing connection Braced frames (R::: 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-25 Eccentrically braced frames .................................... 5-372, 5-379 Ordinary concentrically braced frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-25 Special concentrically braced frames .......... 5-140, 5-178; 5-202, 5-269, 5-299 Brace design Braced frames (R :::: 3) .... ......... . .............. ..... . . , . . . . . . . . . . . 3-22 I

I•

~

I

.J

Buckling-restrained braced frllJlleS ...................•......•........• 5-419 Eccentrically braced frames ................... ..... ·.. ... .. .. . ...... .. 5-362 Ordinary concentrically braced frames .... ........ ... . . . .... . ..... .. 5-6, 5-75 Special concentric3Uy braced frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-87 Braced frame sys1erns R = 3 syste.ll\S ............. : . ........................•.•...•.. . ....• 3-21 R > 3 systems .......•..........................•....... .. ........... 5-1

l,i

2

Buckling-restrained braced frames ........................... 5-413, 9.1-65

Gravity column splice ...... _..................... _...... _........... 4- , -

Composite braced frames ................. .................. . 7-3, 9.1-88

Special concentrically braced frames ....... .. ...................... .. . 5-l:

Eccentrically br:iced frames . .. .... .................. ... .... 5-334, 9.1-57

Special moment frames .................·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-'

CoroposjteeccentricaUy braced frames ............... . ..... ... ....... 7-7. 9.1- 9! Analysis ................... _....... ........................... ... 9.1-92 Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 .1-9~

Ordinary concentrically braced frames ........................ - 5-3, 9.1-50

Special concentrically braced frames ... _ ... _. . . . . . . . . . . . . . . . . . 5-82, 9.1-52 BuckJiog-restrained braced frames ................................. 5-413, 9.J-{)5 Adjusted brace strength .....................................·. . . . . . . 9 .1-65

Connections . ..................................... _............... 9. J-92

Analysis ........................ . ................................ 9.1-66

Composite inrermediatc moment frames .............................. 6-4, 9.J-78 Analysis ......................................................... 9.1- 78

Beam design ............................................... 5-430. 9.1-67 Bracing connections ......... : .................. . ........ . ...... . .. 9.1-{)9 Brace design ............................................... 5-419, 9.1-67 Column design .. ... ........ ....... . .. ... .................. . 5-425, 9. 1-67

·;~

Bean1 fl:inges .... ... ......................... .................. . .. 9.1-7<.Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . • . . . . . . . . . . . . . . . . 9.1-79 Connections ..... .... ............... ........ . ..... _....... _.. _.... 9.1-'')

ColuJllJl splices_ ..... . ............................................. 9.1-70

Beam-to-column connec1jons ................ _.................... 9.1-79

Connections...................................................... 9.1-69

Confonnance demonstration................... _..............· .... 9.1-79

Beam-to-column connecrions .............. . .................... ·- 9.1-69

Connection diaphragm plates ..................................... 9. 1-Stl

Demand critical weJds .......................................... 9.1-69

Column splices ............................................... . 9. l

Diagonal brace connections ...... . ..... . .. . .. .... ........ . ....... 9.J-69

Dernaud critical welds ............................. .. ........... 9.1-

Required shear slrcngth ......................................... 9. l Protected zones_ ............ .. ..... . ........ _.. _..... ... .......... 9.1-. _ Composite ordinary braced frames ............. . ..................... 7-3, 9.1-83 Analysis ........... .. ...... ... ... ... ............................. 9. l-89

Column splices ................ . ............................... 9.J-70

=!

:<

·:.

Protected rooe .... ........................ ............ ... ... .... . . 9.J--09 Qualifying cyclic testing . ............. , ......; ......... •. ... . ....... 9.1-129•

~~..:1 1

System requfrements ........ _...................................... 9. l-67

V-and inrertcd V-braced frames ..............•........... - . . . . • . . . 9.1-67 K-braced frames .. _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1--07

Beams .......................................................... 9. 1-89

Width-to-thickness lim.i1ations ......................................... 1-36

ColllIIllls .......... ... ............ ..... .. ... ........... . ......... 9.1-t,

Braces ..... .. .... .. ............ .......... ....................... 9.1-89 Connections ... ...... ...... . ......................... .......... .. .

Building separations . . ... ........................................ ....... 1-17

Demand Critical Welds_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. l-S9

Capacity design .....•. ... _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

Protected zones ................... ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1-S'.>

Chord design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2, 8-8

Composite ordinary moment frames .................................. 6-2. 9.1-77

Classification of sections for local buckling: ........ : .. .... _. . . . . . . . . . 1-25, 9.1-11

Analysis ................................................ _........ 9.1-77

Collector design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-4, 8-8

Connections................. _........................ .. .......... 9.1-78

Column design ......... ........... .... ............ .. ................ 9.1-16

Demand critical welds ........................ .... ...... . .. ...... . : 9.1-78

=

Br:iced fr.unes (R 3) ................................ _.............. 3-24 Buckling-restrained braced frames .................................•.. S-425

Members . . ..... _... _... _.. _.. _.......... _.................. _.... 9. I-78

Protected zones ................................................... 9.1-78 Composite ordinary shear walls ................... _............. _......... 7-16 Analysis..... .. ................... . ............................ ·. . 9. 1-93 Beam embedment length ................................. 7-19, 7-21. 9.1-:...

Eccentrically braced frames .......................................... 5-367 Ordinary concentrically braced frames ................................... 5-13 Ordinary momenl frames ........... __ . .............. _................. 4-1

=

Moment fr.:imes (R 3) . ......................... - ......... · · . · · · · · · · · 3-6 Special concentricnlly braced frames ............................ - . . . . . . 5-98

:.

r~:

9.1-~9

Building drift ........... _....... . ............ _....... . ......... .... ... 1- 18

Special moment frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42

I

Column splice desig·n .... . .......... •. ................................ 9.1-21

Boundary members .....................................•.......... 9.1-1:' I'

Composite coupling beam design ........................... 7-19, 7-30, 9.1-7

f. ~

Demand critical welds ... .... ................... . ........ . ... : . . . . . 9 .1-' ,.·

J

Connections ...................................................... 9.1-'.:::z

Protected zones .................. ... .............................. 9 1-96 Steel coupling beam design ............ . ...........•... . .. 7-19, 7-21, 9

Beam-to-column cormet·11ons.

1-9~

Compo~Jte

partially restrained moment frames . . . . . . . . . . . . . . . . . . . . . . . 6-J 1. 9.1-85 Analysis............ . .......... . ......... . ... . .... . ........... . . 9.1-85 Columns .................... . .............. . ..... . ..... . ........ 9.1-85 Beams .......................................................... 9.1-86 Protected Zones .. ... . . • ...... • .................... . .. . ... . . . ...... 9.1-86

Syslem requirements . .. . ... .. . .. ... . . . . . ... ... . ... . ................ 9.1-S ~foment ratio .•. • .. .. .•.. •. .. . . ... .... ... .................... 9.1-8

Demand Critical Welds .. .. ...................................... 9.l-86 Required Strength .................••............ •... ... ·"'· .•.... 9.1-86

Required strength of brace connections ............................. 9.1-91 Protected zones ... ........................................... . .... 9. 1-90 Composite special moment frames ................................... 6-7, 9.1-8 1 Analysis ............. : .......................................... 9.1-8 1 Beam flanges ........ '. ............................................ 9. 1-83 Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. 1-82 Connections ............................................. . ........ 9.1-83

I

Column splices. . . . . . .......... • •. . ........•............ • .. 9.1-85 Demand criucal \!.el
Connections... . ..... • .............. . .............. .. ... . ...•.... 9.1-86

Beam-to-Column Connections. . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . 9 .1-86 Conformance Oemo1btration . . ....................• . ............. 9.1-86 Column Splices. . ..............•......•......• .. ..... . ...... 9 1-87 Composite plate ~hear walls .. .... .... ... .......... ..... •.............. 9.1-99 Analysis. . . . . . . . . . . . .......................•...... . ......•.... . 9. 1-99 ' Boundary members ............................................... 9.1-101 Column splices ....................... . ........... .. ............. 9. L- 102 Concrete stiffening elements ..... . .. .. .............................. 9. 1-101 Connections ..................................................... 9.1-101 Demand critical welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1-l 0 I Prote<.tcd ~ones....... . .............. . ............ •. ............ 9.1-101 Webs .................... ........... ... ... ................... . . 9.1-100 Compo$ite she:i.r wall~ ................................ . ................. 7-10 Composite ~lab diaphragms ..... .. ..... ... ............................. 9.1-19 Composite special concenirically braced frames .............. . ......... 7-5. 9.1-89 Analysis................................................. . ....... 9.1-90 'Seams •.•.........• .••..•.. •••...••......•......•............... 9.1-90 .Br:ices ......................................•.... • .............. 9.1-90 Columns . . . . ....................... . .......................... 9.1-90 Connections...................................................... 9.1-90 Beam-to-column connections........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1-91 Column splices ... .......... ........ ......... . ................. 9.1-91 Demand critical welds .......................................... 9.1-90

. ...... .. ......................... 9.1 1:1..,

Conformance dcmonstra1ion. . • .. •.... . ................... · ·. · · · 9.1 Connection diaphragm plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. I->

St:ibility br:icing of beams . .

...... .

. . . . . . ..................

..

. .. .. ..

'

9.1-8 ~

~t:ibilit~ bracing at beam 10-columo connections ...... ...... ...... ·~. 9.1-8"'

Composite i;pec1ru shear \\alls ..

1· I·

.. ..... . ............ 7-.>6. 9.1 - 9 ~

Analysis. . . . . . . . . . . . . .. ... ..... ..... .. ..... . .......... ... ..... 9. J-9( Beam embedment length ........ . ............ . ................ 7-40, 9.1-9 .., Boundary members .... ... .. ... . .• . ..• .•......... .. ............. 9.1-
l· r:

Composite coupling beams . .......... . .............................. 9.J-9X \ Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. l -9 Demand critical welds ................... . ... ................. .... . 9.1-99 : Ductile elements .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . 9 .1-9 ,

Face bearing places ...... . ...... • ...... . . . ... . ............... 7-41, 9.1-9' S1eel coupling beams ............................... , .... 7-39, 7-41, 9.1-91 Vertic:ll lr:!nsfer bars ..... .. •.. . .............................. 7-41, 9.1-98 Wall

o~ersrrength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7-41

t

\Vcb stiffeners.......................... . ......... .................. 7-4l, Composite structural ~tecl and reinforced concrete buildings ....... 1-23, 9.1-77, 9.1-88 (also see individual composite sys1ems) Composite connecoons .... . . . .................................. 9. 1-Z· Composite members

t

t

I •

Composite slab diaphragms ...................................... 9.1-1 ' Encased composite columns ...... • ......... . ..................... 9.1-1 i Filled composite columns ........................................ 9.1- 19 Composite moment fromes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1 Composite shear walls ....................... ..................... ... 7-1< Connection design

..·

Bolted joints: see Bolted joints Braced frame (R

=3) . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-25

Column b!'ISCs ................. . .................................. 9.1-22 Column splice design ............ •. ....... . ...•............... 4-67, 9.1-21 Collector connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.. ,;

I

.

6

• > ~: "

&.

Composite connections ............... ...... ... . ....... ·.... · . · ..... . 9.1-24 Continuity plates and stiffeners .............. . ....................... 9.1-21 Eccentrically braced frames . ....... . ............... .. ... .. ...•. 5-372, 5-379

Diagonal brace connectioni. .............. . ................. 5-379. 9.l -, · Link-to-column connections ... . .. ............................. . .. 9. 1-•

Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-340. 9.'Pro1ected zone. . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . 9.•. i.:.:

Moment frames (R = 3) ................ . .......................... . .. 3-13 Ordinary concentrically braced frames .......... ... ..................... 5-2.5

Story drift ..............•..................................•.. • ... 5-3<1

Ordinary moment frames. . . . . . . . . . . . . . . . . . . . . . . . • . . . . .. . . . . . . . . . . . . . . . 4- l 6

System requirements ......... .. ...... . ...... . ......... ...... .. ..... 9_ 1

PrcquaJified ....................................................... 9.2- i

Link rotation angle ........................... ........ ........ .. 9.1 - ...

Rectangular filled coroposi1e column-to-steel beam .......... .... .......... 6-21

Bracing of link ......... ..... ... ..•... ......................... 9.1-S ...

Reinforced concrete column-10-steel beam ................ ..... ....... . .. 6-15

Width-to-thickness limitations .............. .. ........... 1-36, 5-338, 9.J. "" Effective length method ............. . ..... ...... . . ....................... /.-. Encased W-shapes, plastic c::apacicies ....•....................... .. ......... 7-::._ End-pla1e moment connection....................................•...... 9.?-1 Engineered damping systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : ;J-.;

Round filled composite column-10-ste.el beam .............. .. ............ 6-19 Special concenuically braced frames .......... 5-140, 5-178, 5-202. 5-269. 5-299

Special moment frames .............................................. 4-57 Steel anchors, .................................................. .. 9.1-26

:;.· ,,,..

-----t~.::l

Analysis and design .................. .... ...... . ........ . ......... . . ~·~-: Friction dan1_pers ..... ... ... . .............. .. ............... _,........ ....... '"" Viscous dampen; .... .. . . .... . . . '-.: ................................. . Viscoelastic dampers .. .. .....•.. .... .. . .... ... ........ ...... ..... ... JU-Yielding metallic dampers ......... ...... . . .. . ................. . .. .. .. 10-:! Equivalent lateral force analysis ...... ....... . . ....................... ... .. 2-t' Erection drawings . . ................. . ........ ... .................... 9.1-

Welded joincs; see Welded joints Continui1y places and stiffeners ....... ........... . ............... . ....... 9.1-21 ConXtech ConXL moment connection ......... . .......................... 9.2-64 Coupling beams ........................... . .. 7-11. 7-19, 7-21, 7-30, 7- 39, 7-41 Damping systems; see Engineered damping systems Deflection amplification factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Deflection compatibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18

.......··~ ,,

':;·.

:·

Deformation compat1bility ..... . .. ...... .... . ..•. . •.. , ....... . ........ . 9.1-26 Dema1ld critical welds ....... . ... ....................................... 1-21

Expansion joints . .................. .. ............................ .- ... ·.. 1-J ..

Design basis earthquake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10

Fi.lled HSS, plastic capacities ...... . .. . •... ........................ . ...... 7-.1 First-order analysis method ......................... ... . ... .... ...... ... .. 2 -..f Friction dampers ....................................................... JO-" H-piJc .. . .......•................. . .................... .. .... . ...... 9.1-~ t Battered H--piles ..... ....... ...... ...... . . ..... ................... 9.I-~~ Protected zone ................... . ....................... ......... 9.J -21 Tension in H·pilcs ..... . ........... .. ...... .... ....... ..... ........ 9.1-Heavy section CVN requirements.......................... . .............. 9.1 _ Inspection Inspection of bolting .............................................. 9.1-1 L Inspection of composite structures . .... ........ .. ......... .. ......... 9.1-11 ~ Inspection of H-piles............. .. ............................... 9.1-1 Inspection of welding ............ . ................ ..... ........... 9.1-1' ~spection tasks. . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 9. 1- If'' Olher steel structure inspections ..... . .............................. . 9. · Personnel. ...... .. ........ .... ........ ............... ........... 9.llntermedinte momeot frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33. 9. 1 • Analysis.. . ............... , . .......... . ...................... . . . . 9

E.xpectcd material s1rength ...................................... ..... ... 9

Design drawings ... . .............. .... . .. ............... .... 1-21, 1-22, 9.1--0 Diaphragm design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . .. . . 8-2, 8-8

Direct analysis n1ethod. . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Drift limits ..... ... ........ ...... ................ 1-18, 2-19; see also Swry drift Ductile design mecha.nisin ................................................. 2-2 Ductility requirements................. ·...................... 1-25, 1-34, 9.1-11

Earthquake ground motion ......................... : . . . . . . . . . . . . . . . . . . . . . . 1-7 Eccentrically braced frames .................................. . ... 5-334, 9.1-57 Analysis...... .... .... ........ .... .................... . ........ .. 9. J-58 Beam outside of Link desigii ...•................... , ........... 5-353, 9.1-59 Brace design .................................... .... .... . .. 5-362, 9.1-59

If I

Brace.to-link connections ................. ...... .................. . . 5-372 Column design ............................................. 5-367, 9.1-59 Connections......... . ......... .. .............................. . .. 9.1- 62 Beam-to-colu~ connections ........ . ............... .. .... . ...... 9.1-63 Column splice design ........................................... 9.1-63 Demand critical welds ........ .. ................................ 9.J-62 ~·

f

_j

1-

Beam nanges .................... .... ............................. 9.1- '.3 I Comparison to SMP and OMF................................... . . 4-122 Connections. . . . . ............................................ .... 9.1-32 Beam- to-column connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 .1-3 2 Column splices ............... . ................................ 9.1-34 Conformance demonstration.............................•. .. ..... 9.1-33 Conunuity plates .............................. ..... ... .... ...•. 9.1-34 Demand cnucal welds .......................................... 9.1-32 Required sheM strength ......................... . ....... ... ..... 9.1-33

Intermediate moment frames ... ...... ... ...... .............. 4-33, 9 1 Ordinary moment frames . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2, 9 Special moment frnrnes ................................... . .r.JJ. 9. Nonbuilding st.ructures. . . . . . . . ......... ......................... .... 5 Ordinary cantilever column systems ......................... ........ ..... 9. Ordinary concentrically braced frames ................................ 5-3. 9. Above Seisllllc Isolation Systems ............. ...... . ................. 9.1- •. Analysis ... ...................................................... 9. J

Brace connections . .. ........ ...... ........................... 5-25, 9.1-~

Pnncl zone ........... .... ... .... .............................. 9.1-33 Stability bracing of beams .................................. ... ..... 9.1-31

Beam design .................................. . .................... ~

9.1-32 Protected zone. Width-to-thickness limitations .................................. 1-36, 9.1-31

Column design . . .

Y-braced anti invencd V-braccd frames ............................ · 9.1 K-braced fr:imes .......................... ............... 5-443, 9. I

K·br:iced frnmes ............................................... 5-443, 9.1-54

Link design .............................................. . .... . ...... 5-340 Load combinations .......................................... • ......... 9.1-8 Local buck.ling ................................ • .......... . ...... l-25, 9.1-11 Pipe ...................... . ..........•..................... 1-29, 1-57 Rectangular I JSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 28, 1-53 Round HSS . . . . ........................................ . .... 1-29, 1-55

Nonbuilding structures ......................... ... .................. 5-4 Width-to-thickness limitations ................................. . 1-36, 9.1

l:

Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Beasn design .................... . ........................... 4-12, 9.1 Be:im to-column connections ................................... 4-16, 9.1 Column design ................ .. ..... .. ................... 4 7. 9.1

Square HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 28, t -54 \V-Shap.:s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . 1-26, 1-36 Lowest anuc1pated service temperature ............................... 1-18, 9.J-7 Low-seismic design (R = 3) ............. , .............. ..... ..... ... . 1- 13, 3-2 Material specifications . .. ........... . ............................ 1-21. 9.1-2 Maximum considered earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1- lO Maximum force delivered by system ... .'............................. 1-16, 5-136 Modal response spectrum analysis .......................................... 2-7

Comparison to IMF :ind SMF ........................... .. .... .. ..... 4- 1

weld~

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 FR moment connections ............................... . ............ 9.1 Dem:llld critical

I..

I

PR moment connection~ ............•.... . ........•................. 9.1 Story drift and stability check ............ ... .•......... .......... ...... Overstrength factor ............................................... l- 14, 9.,

Moment connections Composite moment frames ........................................... 6-14 Moment frame (R 3) ............ ... ..... . ...... :. . . . . . . . . . . . . . . . . . . . 3-13

=

Moment frames R = 3 systeIU.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4 R > 3 systems ..................................................•.... 4-1

rf

Ordinary moment frames .... ... ................ .............. .. : .. 4-2, 9.1

Single angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........•.. I 27, l-52

Qualification of. ................................................. 9. 1-121 Special moment frames ................ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-57

. ............................................ .

Sys1em requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. J -~·

KaiStr bolled bracket moment connection .. ............................... 9.2-52

Ordinary moment frames ............................................. 4-16 PrequnJjfied ................................................ 9.1- l I 8, 9.2-i

f

Brace members .......•....•......•.•....•............... 5-6, 5-75. 9.1

I•

i i

f

_J

Performance goals .................................................... . Period ................................................ .. ..... . ....... . Prequalified connection standard ...•...................................... 9.Prequalificarion ........................... ....... ................... 9. 1-1 • Beam-to-column connections .................................. 9.1-11 8, 9 I Llnk-10-<;olumn connections ........................................ 9.1- J Protected zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22, 9. J- 1 Qualificatio~

Buclding-restrnined braced frames ..... .... .......................... Beam-ro--column connections ....................................... Link-t
9.19.1 I 9.19.1-J

Conformance demonstration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s·. Required shear strength ....................... . . ......... ......... 'J. • Panel zone ..... ....... ...... ...................... .... ... . .... 9. ! Continuity plates. . .................. .. . ... . ................... 9.'

Quality control ............... . . . .. ... ......................... 1- 19. 9. 1- 106 Reduced beam section moment connection . .......................... 4-57, 9.2-11 Redundancy factor ................. . . . . . ........ .. ..................... l- 15 Response modification coefficient ........ ..... . ..................... l- 12, 9. 1- 1 R :::; 3 applications .......................................... . ... 1- 13. 3-2

R-factor (see Response modification coefficient) Risk category ........ .. .... ... . .... . . ...... . ........................... 1-7

Column splices ............................. . ............. 4-90, 9.. Stability bracing at beam-to-colulTUl conne<:tions ....... ,·........ : .... 9.1 Stability bracing of beams ........................ .. ................ 9. Protected zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q. 1 _

Seismic design category .. . ......... ...... .. . ............................. 1-7

Story drift and sl3bility check ........... .. ..... . ...................... .:

Seismic joints ..... .. ..... .. ... .. .. ..... ............................... 1-l 7 Seismic Provisions fo r S1ructural Sreel Buildings .... .... ..... . ............... 9. 1-i

Width-to-thickness l.imjtations ..... . ............... .. .. . ......... 1-36, ._, Special plate shear walls ... .. ..................... .. ........ ........ ... 9.1 -

Shear wall coupling ................... . ................... .... . . ....... 7-10

Analysis ............... ..... .... . ................................ 9.1·-

Shop drawings ...... ............... . . .. ... ~ .......... . ......... ..... 9.l-103

Connections..... . .......................... ....... ... ....... .·. . . . 9. j Column splices..... ........ ....... . ... ........ .. ........ . ...... 9.1 -

Response spectra .......... ... ... ... ................. .......... . ... ..... 1-7

Special cantilever column systems ................... ......... . .......... 9.1-48 Width-to-thickness limitations ....... . .... ............... . .. .. . ... .. ... 1-36

Connectfons of webs to boundary clements ..... .... . .. ....... . ...... 9. ' Demand critical welds .. .. .. ....... .... ......... ..... ............ ~· HBE-to-VBE connections ..................... .. .. ......... .... . 9 .1·Perforated webs ... .. ......... . ................. .................. . 9. ]-

Special concentrically braced frames .......... . .......... .. .. . ... ... 5-82, 9.1-52 . Analysis.... .. ................................... : ........ . .. 5-93, 9. 1-52 .· Beam design ... ......... . ........... ..... ............ 5-104, 5- 119, 9.J-54 Brace design ................. ...... . . . ... .. .... .. . .. . .. 5- 83, 5-87, 9.1-54 Column design ... .. ......................................... 5-98, 9.1-54

Protected zone ............•................ . .. ................ .. . ... 9.1 System requirements .... .... ... ..... .. . ... ............ .. : ...... : .. . 9. •

Column splice design . . . . .... . .......... . ......... .. ......... 5- 129, 9.1-57 Connection design ... ... ... ....... .. 5-140, 5-178. 5-202, 5-269, 5-299, 9.1-55 Demand critical welds .. . ... .. ...... ... . . ... ....................... 9.1-55 System requirements ............................................... 9.1-53 Lateral force distribution ........ .. .... ........................... 9.1-53 V-braced and inverted V-braced frames ........................ 5-83, 9.1-53 K-braced frames ......................................... 5-443, 9. 1-54 Tension-onl y frames ........... .- ................................ 9.1-54 Width-to-thickness limitations ............................ . 1-36, 5-82, 9.1- 54 Special moment frame ...................................... 4-33, 4-76, 9. 1-34 Analysis ..... ... ............................ ..................... 9. 1-34 Beam design .... .. .... ........... .... ..... . . ............... .. 4-46, 9.1-38 Beain flanges......... . ................ .. ....... .......... . .. .. ... 9.1-38

Stiffness of boundary elements .......................... .' ........ 9. 1 HBE-to-VBE connection moment ratio .... ..... ............. .. ..... 9.1Bracing ..... .. ................. . .... ............... : ......... 9.; Openings in webs ............. ... ..... ............ - · ...... . ... . 9.' Webs ................................... . . . ..................... 9 Width-to-thickness limitations ................. . : . . . . . . . . . . 1-26, 1-36, 9. Special truss moment frames ..................... ..... ...... ... . ...... . 9.1Analysis....................................................... . . 9. ·

S_pe,cial segment ............ ..... ..... ............. ..... . ..... ..... ~ Nonspecial. segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.. Built-up chord members ........................... ......... . .. . .... 9. i Connections ..... ................. ..... . ...................... . ... ~Demand critical welds .... ...................................... 9. Connections of diagonal web members in the special segment ........... o Column splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......... . Protected zones .................................. .. ...... . ...... . Strength of special segment members ............. ~ ...... . ....... .... . System requirements ............... . ........ ....... ...... ..... .... . Special segment ........ . ..................................... . Stability bracing of trusses .............. .. ...................... .

Column base ............... .. ...... . .. . ~ . . . . . . . . . . . . . . . . . . . . 4-94, 4-11 3 Column design ... , ................... ..... ..... . . ........... 4-42, 9.1-38 Column,beam momenr ratio ... . ............ ·.. .. .. ............... .' .. . 9.1-34 Comparison to OMF and IMF ... .. ................................... 4-122 Conneclions ....... ·. ... .................. ... ... .......... ... ...... 9.1-38 Demand critical welds ............ ... .. .... . ..•................. 9.1-38 Beam-to-column connections .. . .......... .. ... .............. 4-57, 9.1~39 AM~

WSTJTVT6 OF STEEL C0NSTR.UC110N

_j

Stability bracing of truss-to-column connections ...................... 9.1-45 Stiffness of stability bracing ...................................... 9.1-45 Widlh-co-t.IUckness limitations ......... ...... .... .......... ..... 1-36, 9.1--46 SpecificM.ions, codes
Stability bracing ........ .. ........................................... 9. l-14 Stability design methods ..........•...•....................... .... ....... 2-5 Steel beaded stud anchors .................. . .... .......•... .. ...... 1-30, J-58 Steel plate shear walls; see Special plate shear walls

Stiffeners; see Contioufry plates and stiffeners Story drift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18, 3-5, 4-36

;.

Structural modeling .............. .. ..................................... 2-7

I·

Gravity Joads ...................................................... 2-13 Stiffness of strucmral elements ..... ... . ................................. 2-8

·'

Strength of structural elements .... . .................................... 2-7 Viscoelastic dan1pers ................................................... 10-4

VJscous dampers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L0-2 Wall overstrenglh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-15 Weld access hole ..... ..... ................. ..... ..... • ........... 1-25, 1-33 Welded joints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. J-21 Welded unreinforced flange-welded web moment connection . ......... ....... . 9.2--46 Welding provisions ............................................... 9.1-5, 9.2-7

AWS Dl.8 .......................... ....... .. ............ . ........ 1-23 Demand critical welds ......................................... 1-21, 9.1-5 Inspection ................. .. ................................... 9. l-109 Notch toughness verification Widlh-to-tbickness limitations;

t~t

se~

...................................... 9.1- 5

Local bucklfag and specific systems

\

Yielding metaUic dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-5

' ..

;:

AMEIUCAN

l.NS'T'1'nml 01' STEa C0.'1S!"l\UC1101'1

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AISC Seismic Design Manual 2nd Edition (7civil.com)

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