Design Guide 13_ Wide-Flange Column Stiffening at Moment Connections (See Errata Listed at End of File.)

© 2003 by American Institute of Steel Construction, Inc. All rights reserved.

13

Steel Design Guide Series

Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications Charles J. Carter, PE American Institute of Steel Construction, Inc. Chicago, IL

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

Copyright © 1999 by American Institute of Steel Steel Construction, Inc.

All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher. The information presented in this publication has been prepared in accordance with recognized engineering principles and is is for general information information only. only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitablility, and applicability by a licensed professional engineer, designer, or architect. The publication of the material contained herein is not intended as a representation or w arran ty o n th e pa rt o f th e America n In stitute of Steel Steel Constr Constructio uction n or of any other other person named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon other 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 this editio edition. n. 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 this edition. Printed in the United States of America Revision:

October 2003


TABLE OF CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Column Stiffening . . . . . . . . . . . . . . . . . . . 1.3 References Specifications . . . . . . . . . . . . . . 1.4 Definitions of Wind, Low-Seismic, and High-Seismic Applications. . . . . . . . . . . . . 1.5 Acknowledgements. . . . . . . . . . . . . . . . . . .

1 1 2 2 2 2

2. Strong-Axis Moment Connections to Unreinforced Columns . . . . . . . . . . . . . . . 3 2.1 Force Transfer in Unreinf orced C olumns . . . . 3 2.2 Determining the Design Strength of an Unreinforced C olumn . . . . . . . . . . . . . . . . 5 2.3 Column Cross-Secti onal Stiffness Considerations . . . . . . . . . . . . . . . . . . . . 11 2.4 Design Aids. . . . . . . . . . . . . . . . . . . . . . . 11 3. Economical Selection of Columns . . . . . . . . . 3.1 Achieving Balance Between Increases in Material Co st and Reductio ns in Labor Cost. . . . . . . . . . . . . . . . . . . . . . . 3.2 Eliminating Column Stiffening. . . . . . . . . . 3.3 Minimizing the Econ omic Impact of C olumn Stiffening Requirements in Wind and L owSeismic Applications. . . . . . . . . . . . . . . . 3.4 Minimizing the Econ omic Impact of C olumn Stiffening Requirements in High-Seismic Applicatio ns. . . . . . . . . . . . . . . . . . . . . . 4. Strong-Axis Moment Connections to Stiffened Columns . . . . . . . . . . . . . 4.1 Determining the Column Stiffening Requirements . . . . . . . . . . . . . . . . . 4.2 Force Transfer in Stiffened C olumns . . 4.3 Design of Transverse Stiffeners . . . . . 4.4 Design of Web D oubler Plates . . . . . .

13

13 14

15

16

....

17

. . . .

. . . .

18 20 22 27

5. Special Considerations . . . . . . . . . . . . . . . . . 5.1 Column Stiffening f or Beams of Differing Depth and/or Top of Steel. . . . . . . . . . . . .

33

.. .. .. ..

5.2 C olumn Stiffening f or Weak-Axis M oment Connections . . . . . . . . . . . . . . . . . . . . . . 5.3 Column Stiffening for C oncurrent Str ong- and Weak-Axis Moment C onnections . . . . . . . 5.4 Web Doubler Plates as Reinforcement f or Local Web Yielding, Web Crippling, and/or Compression Buckling of the Web. . . . . . . 5.5 Web Doubler Plates at Locations of Weak-Axis Connections . . . . . . . . . . . . . . . . . . . . . . 5.6 Diagonal Stiffeners. . . . . . . . . . . . . . . . . .

33 34

35 35 36

6. Design Examples . . . . . . . . . . . . . . . . . . . . . Example 6-1. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-2. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-3. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-4. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-5. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-6. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-7. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-8. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-9. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-10. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-11. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-12. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-13. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-14. . . . . . . . . . . . . . . . . . . . . . . . .

39 39 40 41 45 47 47 50 52 52 54 55 58 59 61

APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . .

67

APPENDIX B. . . . . . . . . . . . . . . . . . . . . . . . . .

75

APPENDIX C . . . . . . . . . . . . . . . . . . . . . . . . .

83

APPENDIX D . . . . . . . . . . . . . . . . . . . . . . . . . Special C onsiderati ons. . . . . . . . . . . . . . . . . . . M oment C onnecti ons t o C olumn Webs. . . . . . . .

95 95 99

33


Chapter 1 INTRODUCTION in Chapter 2. Econ omical considerations for unreinf orced columns and c olumns with reinf orcement are given in Chapter 3. Force transfer and design strength of reinf orced columns with strong-axis m oment c onnecti ons, as well as the design of transverse stiffeners and web d oubler plates, is covered in Chapter 4. Special considerations in c olumn stiffening, such as stiffening f or weak-axis m oment c onnections and framing arrangements with offsets, are c overed in Chapter 5. Design examples that illustrate the application of these pr ovisi ons are pr ovided in Chapter 6, with design aids for wind and low-seismic applications in Appendices A, B, and C.

1.1 Scope

The design of columns for axial load, c oncurrent axial l oad and flexure, and drift c onsiderati ons is well established. However, the c onsideration of stiffening requirements f or wide-flange co lumns at moment connections as a r outine criterion in the selection of the components of the structural frame is not as well established. Thus, the econ omic benefit of selecting c olumns with flange and web thicknesses that do not require stiffening is n ot widely pursued, in spite of the eff orts of other authors who have addressed this topic previously (Th ornton, 1991; Th ornton, 1992; Barger, 1992; Dyker, 1992; and Ricker, 1992). This Design Guide is written with the intent of changing that trend and its contents are focused in tw o areas:

1.2 Column Stiffening Transverse stiffeners are used t o increase the strength and/or stiffness of the column flange and/ or web at the l ocation of a concentrated f orce, such as the flange f orce inducedby the flange or flange-plate of a m oment-c onnected beam. Web doubler plates are used to increase the shear strength and stiffness of the c olumn panel-zone between the pair of flange forces from a m oment-c onnected beam. The panel-zone is the area of the c olumn that is bounded by the c olumn flanges and the pr ojecti ons of the beam flanges as illustrated in Figure 1-1. If transverse stiffeners and/or web d oubler plates carry loads from members that frame t o the weak-axis of the

1. The determination of design strength and stiffness for unreinf orced wide-flange columns at l ocati ons of strong-axis beam-to-c olumn m oment c onnecti ons; and, 2. The design of c olumn stiffening elements, such as transversestiffeners (also known as c ontinuity plates) and web d oubler plates, when the unreinf orced c olumn strength and/or stiffness is inadequate. Recommendations for econ omyare includedin b othcases. Force transfer and design strength of unreinf orced columns with strong-axis m oment c onnections are c overed

Projection of beam flanges, or transverse stiffeners, if present

Column panel-zone

Figure 1-1 Illustration of column panel-zone.

1


column, the recommendations herein must be adjusted as discussed in Sections 5.2, 5.3, and 5.5. As discussed in Section 5.4, if web doubler plates are required t o increase the panel-zone shear strength, they can also be used t o resist local web yielding, web crippling, and/or compressi on buckling of the web per LRFD Specification Secti on K1. As discussed in Section 5.6, diag onal stiffening can be used in lieu of web d oubler plates if it d oes n ot interfere with the weak-axis framing.

High-seismic applications are those f or whichinelastic behavi or is expected in the beams or panel-z ones as a means of dissipating the energy induced during str ong gr ound m oti ons. Such buildings are designed t o meet the requirements in b oth the LRFD Specification and the AISC Seismic Provisi ons and a resp onse m odificati on fact or R that is appr opriate f or the level of detailing required f or the m oment-frame system selected is used in the determination of seismic f orces. 1 Additi onally, the m oment c onnections used in high-seismic applications have special seismic detailing that is appropriate for the moment-frame system selected.

1.3 References Specifications

This Design Guide is generally based upon the requirements in the AISC LRFD Specification for Structural Steel Buildings (AISC, 1993), hereinafter referred to as the LRFD Specificatio n, and the AISC Seismic Provisions for Structural Steel Buildings (AISC, 1997a), hereinafter referred to as the AISC Seismic Provisi ons. Although direct reference t o the AISC Specification for Structural

1.5 Acknowledgements

This Design Guide resulted partially from w ork that was done as part of the Design Office Pr oblems activity of the ASCE Committee on Design of Steel Building Structures. Chapter 3 is based in large part up on this previ ous work. Additi onally, the AISC C ommittee on Manuals and Textbooks has enhanced this Design Guide thr ough careful scrutiny, discussion, and suggestions f or impr ovement. The author thanks the members of these AISC and ASCE Committees for their invaluable input and guidance. In particular, Lawrence A. Kloiber, James O. Malley, and David T. Ricker contributed significantly to the development of Chapters 3 and 4 and William C. Minchin and Thomas M. Murray pr ovided helpful c omments and suggestions throughout the text of this Design Guide.

Steel Buildings—Allowable Stress Design and Plastic Design (AISC, 1989) is n ot included, the principles herein

remain generally applicable. 1.4 Definitions of Wind, Low-Seismic, and HighSeismic Applications

For the purposes of this Design Guide, wind, l ow-seismic and high-seismic applications are defined as f ollows. Wind and low-seismic applications are th ose f or which the structure is designed to meet the requirements in the LRFD Specification with n o special seismic detailing. This includes all applications for which the structural response is intended to remain in the nominally elastic range and the response modification factor R used inthe determination of seismic forces, if any, is n ot taken greater than 3.

1

From AISCSeismic Provisi ons Commentary Table I-C4-1, R-values of 8,6, and 4 are commonlyusedf or Special MomentFrames(SMF),Intermediate Moment Frames (IMF), and Ordinary M oment Frames (OMF), respectively.

2


Chapter 2 STRONG-AXIS MOMENT CONNECTIONS TO UNREINFORCED COLUMNS In wind and l ow-seismic applications, it is often p ossible to use wide-flange columns without transverse stiffeners and web d oubler plates at m oment-connected beams. T o use an unreinforced column, the f oll owing criteria must be met:

c ouple in the beam flanges or flange plates. The c orresp onding flange f orce Puf is calculated as: P uf 

Mu d m



Pu

2

(2.1-1)

where

1. The required strength (Section 2.1) must be less than or equal to the design strength (Secti on 2.2); and, 2. The stiffness of the column cross-secti on must be adequate to resist the bending deformati ons in the c olumn flange (Section 2.3).

factored beam flange force, tensile or c ompressive, kips M u  factored beam end moment, kip-in. d m  moment arm between the flange forces,2 in. Pu  factored beam axial force, kips Puf

If these criteria cannot be met, c olumn stiffening is required. In high-seismic applications, transverse stiffeners are normally required, as discussed in Secti on 2.3. However, it remains possible in many cases to use wide-flange columns in high-seismic applications without web doubler plates at moment-connected beams.



The formulation of Equation 2.1-1 is such that the c ombined effect of the moment and axial force is transmitted through the flange c onnections, ign oring any strength c ontribution from the web c onnection, which is usually m ore flexible. When the moment to be developed is less than the full flexural strength of the beam, as is c ommonly the case when a drift criterion g overns the design, and the axial force is relatively small, this calculatio n is fairly straightforward. However, when the full flexural strength of the beam must be developed, or when the axial f orce is large, such a model seems to guarantee an overstress in the beam flange, particularly for a directly welded flange m oment connection. N onetheless, the above f orce transfer m odel remains acceptable because inelastic actio n into the range of strain hardening all ows the devel opment of the design flexural strength of the beam in the c onnection (Huang et al., 1973). Such self-limiting inelastic action is permitted in LRFD Specification Secti on B9. Alternatively, a web connection with a stiffness that is compatible with that of the connections of the beam flanges can be used t o activate the full beam cross-section and reduce the p orti on carried by the flanges. Note that, if a composite m oment c onnection is used between the beam and column, the calculations in Equations 2.1-1and 2.1-2mustbe adjustedbasedup on theappr opriate

2.1 Force Transfer in Unreinforced Columns

In an unreinforced c olumn, c oncentrated f orces fr om the beam flanges or flange plates are transferred locally int o the column flanges. These c oncentrated f orces spread through the column flange and flange-t o-web fillet regi on into the web as illustrated in Figure 2-1a. Shear is dispersed between them in the c olumn web (panel-zone) as illustrated in Figure 2-1b. Ultimately, axial f orces in the column flanges balance this shear as illustrated in Figure 2-1c. 2.1.1 Required Strength for Local Flange and Web Limit States

In wind and low-seismic applications, beam end moments, shears, and axial forces are determined by analysis f or the loads and l oad c mbinati o o ns in LRFD Specificati on Section A4.1. Note that the t otal design m oment is seldom equal to the flexural strength of the beam(s). A rational approach such as that illustrated in Example 6-4 or similar to that proposed by Disque (1975) can be used in conjunction with these loads and l oad c ombinati ons. Different load combinations may be critical f or different local-strength limit states. For the general case, the beam end moment is res olved at the column face into an effective tension-compressi on

2

The actual moment arm can be readily calculated as the distance between the centers of the flanges or flange plates as illustrated in Figure 2-1a. Alternatively, as stated in LRFD Specification C ommentary Section K1.7, 0.95 times the beam depth has been conservatively used for d m in the past.

3


m

d

(a) Beam flange forces distributed through column flange and fillet

(b) Free-body diagram illustrating shear and axial force transfer through column panelzone

(c) Free-body diagram illustrating resulting column axial forces and flange forces (moments)

Note: beam shear and axial f orce (if any) omitted for clarity. Figure 2-1 Force transfer in unreinforced columns.

detailing and forcetransfer m odel. Some p ossible c omp osite connections are illustrated in AISC (1997a), Leon et al. (1996), and Viest et al. (1998). In high-seismic applications, the moments, shears, and axial forces are determined by analysis for the l oads and load combinations in LRFD Specification Secti on A4.1 and AISC Seismic Provisions Section 4.1. The resulting flange force Pu f is then determined using Equation 2.1-1. Note that the corresponding c onnecti on details have special seismic detailing to pro vide for c ontrolled inelastic deformations during strong gr ound m oti on as a means of dissipating the input energy from an earthquake. 3 For Ordinary M oment Frames (OMF), a cyclic inelastic ro tation capability of 1 percent is required. Moment connections such as those discussed in AISC Seismic Provisions Commentary Section C11.2 and illustrated in

Figure C-11.1 can be used. Fr om AISC Seismic Pr ovisions Section 11.2a, the flange f orces in Ordinary M oment Frames (OMF) need n ot be taken greater than th ose that c orresp ond t o a m oment M u equal t o 1 .1 R y F y Z x or the maximum m oment that can be delivered by the system, whichever is less. F or Special M oment Frames (SMF) and Intermediate M oment Frames (IMF), a cyclic inelastic r otati on capability of 3 and 2 percent, respectively, is required. Several alternative connection details using reinf orcement, such as c overplates, ribs, or haunches, or using reduced beam secti ons (d ogb ones), have been successfully tested and used. Such c onnecti ons shift the l ocati on of the plastic hinge int o the beam by a distance a fr om the c olumn face as illustrated in Figure 2-2. Fr om AISC Seismic Pr ovisi ons Section 9.3a, the flange f orces in Special M oment Frames (SMF) and Intermediate Moment Frames (IMF) need n ot be taken greater than:

3

With stro ngpanel-zo nes and fully restrained(FR) constructio n, the primarys ource of inelasticity is commonly hinging in the beamitself.If the panel-zone is a significant so urce of inelasticity, or if partially restrained (PR) construction is used, the flange-force calculati on in Equation 2.1-2 should be adjusted based upon the actual force transfer model.

Pu f



M u dm



4


1.1 R y F y Z  V u a d m

(2.1-2)

where 1.1 is an adjustment factor that n ominally accounts for the effects of strain hardening, and R y

F y Z Vu a

Seismic Pr ovisi ons L oad C ombinati ons 4-1 and 4-2 and Equati on 2.1-1, the t otal panel-z one shear f orce is calculated with Equation 2.1-3. As a w orst case, h owever, the total panel-zone shear force V u need n ot be taken greater than:

an adjustment factor that nominally accounts f or material yield overstrength per AISC Seismic Provisi ons Secti on 6.2  1.5 for ASTM A36 wide-flange beams  1.3 for ASTM A572 grade 42 wide-flange beams  1.1 for wide-flange beams in other material grades (e.g., ASTM A992 or A572 grade 50)  beam specified minimum yield strength, ksi  plastic sectio n modulus of beam cr oss-secti on at hinge location (distance a from c olumnface), in.3  shear in beam at hinge l ocation (distance a fr om column face), kips  distance from face of c olumn flange t o plastic hinge location, in. 

Vu

Vu

As illustrated in Figure 2-3, the total panel-zone shear force V u at an interior c olumn results fr om the c ombined effects of two m oment-connected beams and the st ory shear V us . In wind and l ow-seismic applications, the total panel-zone shear force V u is calculated as: ( Pu f )1  ( Pu f ) 2  V us



Pu f



V us

(2.1-5)

2.2 Determining the Design Strength of an Unreinforced Column

An unreinforced column must have sufficient strength l ocally in the flange(s) and web to resist the resulting flangeforce couple(s). Moment c onnecti ons are termed “d ouble concentrated forces” in LRFD Specification Section K1 because there is one tensile flange force and one c ompressive flange force acting on the same side of the c olumn as illustrated in Figure 2-4a. When opposing m oment-

(2.1-3)

In high-seismic applications, when the flange forces have been calculated using the m oment resulting fr om AISC

Reinforced zone or zone between beam end connection and reduced beam section (RBS)

a

(2.1-4)

Note that gravity-load reduction, as used f or high-seismic applications in Equation 2.1-4, is not appr opriate in Equation 2.1-5 f or a column with only one m oment-c onnected beam.

2.1.2 Required Strength for Panel-Zone Shear



0 .8[( Pu f )1  ( Pu f ) 2]  V us

The factor 0.8 in Equation 2.1-4 is fr om AISC Seismic Provisions Section 9.3a. It rec ognizes that the effect of the gravity loads will counteract s ome p ortion of the effect of the lateral loads on one side of an interi or c olumn and thereby inhibit the development of the full plastic m oment in the beam on that side. In wind, low-seismic, and high-seismic applications, for a column with only one m oment-c onnected beam, Equation 2.1-3 can be reduced to:

The axial force effect is neglected in Equation 2.1-2, since the model is already based c onservatively up on the fully yielded and strain-hardened beam flange at the critical section.

Vu



Plastic hinge location

Figure 2-2 Schematic illustration of moment connection for high-seismic applications. 5


connected beams coincide, a pair of double c oncentrated forces results as illustrated in Figures 2-4b (the gravity load case) and 2-4c (the lateral load case). The design strength of the panel-z one in shear must be checked for all c olumns with m oment c onnected beams. For a tensile flange f orce, the design strength of the flange in local flange bending and the design strength of the web in local yielding must also be checked. F or a c ompressive flange f orce, the design strength of the web in l ocal yielding, crippling, and compressi on buckling must be checked. Note that the c ompressi on buckling limit state is applicable only when the compressive c omponents of a pair of double c oncentrated f orcesc oincide as illustrated in Figure 2-4b (i.e., at the bott om flanges). If the magnitudes of these opposing flange f orces are n ot equal, the c ompression buckling limit state is checked for the smaller flange force, since only this portion of the larger flange f orce must be resisted. Each of these limit states is discussed below.

F or P u

0.4 P y,



 Rv





0 .9  0 .6 F y dc tw 1 .4

In wind and l ow-seismic applicati ons and high-seismic applications involving Ordinary M oment Frames (OMF), the design shear strength of the panel-z one  Rv is determined with the provisi ons of LRFD Specificati on Section K1.7, which allows two alternative assumptions. The first assumption is that, f or calculation purposes, the behavior of the panel-zone remains n ominally within the elastic range. The resulting design strength given in Equations 2.2-1 and 2.2-2 is then determined fr om LRFD Specification Equations K1-9 or K1-10 with c onsideration of the magnitude of the axial l oad Pu in the c olumn: 0.4 P y,

 Rv



0 .9  0 .6 F y dc tw



In the second assumption, it is rec ognized that significant post-yield panel-zone strength is ign ored by limiting the calculated panel-zone shear strength to that in the nominally elastic range. At the same time, it must be realized that inelastic deformations of the panel-z one can significantly impact the strength and stability of the frame. Accordingly, a higher strength can generally be utilized as long as the effect of inelastic panel-zone def ormati on on frame stability is considered in the analysis. When this option is selected, the resulting design strength given in Equations 2.2-3 and 2.2-4 is determined from LRFD Specification Equations K1-11 and K1-12 with c onsideration of the magnitude of the axial load Pu in the c olumn: 

0.75 P y,

2.2.1 Panel-Zone Shear Strength



Pu P y

(2.2-2)

F or P u

For P u



 Rv





0.9  0.6 F y d c t w 1 

F or P u



0.75 P y,

 Rv



0.9  0.6 F y d c tw 1 



3b f t 2f dbd ctw

3b f t 2f d b d c t w





1 .9 

(2.2-3)

1.2 Pu Py



(2.2-4)

For F y equal t o or less than 50 ksi, all W-shapes listed in ASTM A6 except a W30  90 and a W16  31 have a web thickness that is adequate to prevent buckling

(2.2-1)

V us (P u ) f 1

(P u ) f 1 V u

(M u ) 2

(M u ) 1

(P u ) f 1

(P u ) f 1 V us

Note: shear forces in beams and moments and axial forces in column omitted for clarity.

Figure 2-3 Panel-zone web shear at an interior column (with moment-connected beams bending in reverse curvature). 6


1 ) f u P (

1 ) f u P (

2 ) f u P (

2 ) f u P (

±

±

±

1 ) f u P (

2 ) f u P (

2 ) f u P (

f u

f u

±

P ±

) c (

±

1 ) f u P (

±

, s e c r o f d e t a r t n e c n o c e e l s b a u c o d d a f o o l r l i a a r e p t a A l

, s e c r o f d e t a r t n e c n o c e e s l b a u c o d d a o f l o y r i t i a v p a r A g ) b (

±

±

s e c r o f d e t a r t n e c n o c e l b u o D ) a (

P ±

7

. y g o l o n i m r e t e c r o f e g n a fl n o i t c e n n o c t n e m o M 4 2 e r u g i F

. r e h s i l b u p e h t f . o d n o e i v r s s e i s m e r r e s p t t h g u i r o l t l h i A w . c m n r I o , f n y o n i t c a u n r i t s d n e o c C u l d e o e r p t e S r f o e b e t t u o t i n t s t n s u I n m a f c o i r r e e e m h t A t y r b a p 3 y 0 n 0 a 2 r © o n o i t a c i l b u p s i h T

under panel-zone web shear per LRFD Specification Section F2. For F y  50 ksi, these two shapes exceed the limit on h/t w by 1.9 and 1.5 percent, respectively. Thus, for all practical purposes, in wind and low-seismic applications, shear buckling of the c olumn web need n ot be checked for c olumns with F y equal t o or less than 50 ksi. 4 In high-seismic applications involving Special Moment Frames (SMF) or Intermediate Moment Frames (IMF), the effect of inelastic panel-zone deformation on frame stability must be c onsidered in the analysis. The design shear strength of the panel-z one  Rv given in Equati ons 2.2-5 and 2.2-6 is determined fr om AISC Seismic Pr ovisi ons Section 9.3a: For P u



 Rv





2.2.2 Local Flange Bending

When a directly welded flange or flange-plated m oment connection is used, differential stiffness across the width of an unstiffened c olumn flange results in a stress c oncentration in the weld adjacent t o the c olumn web as illustrated in Figure 2-5 that must be limited f or tensile flange forces. The design l ocal flange bending strength  Rn given in Equation 2.2-8 is determined from LRFD Specification Equation K1.1 with considerati on of the proximity of the c oncentrated flange f orce t o the end of the c olumn:

0.75 P y,

 Rv

For P u

N ote that Equation 2.2-7 is in a f orm that has been adapted from that which appears in the AISC Seismic Pr ovisi ons.



 R n



3b f t 2f

0.75  0.6 F y d c t w 1 

d b d c t w



(2.2-5)



3b f t 2f dbd ctw



1 .9 

1.2 Pu Py



(2.2-6)  R n

These provisi ons are identical to those in LRFD Specification Equations K1-11 and K1-12, except that a l ower resistance factor is used to provide an added margin against excessive panel-zone yielding. Additionally, t o prevent shear buckling under the higher inelastic demand ass ociated with high-seismic loading, the minimum thickness of the unreinforced column web given in Equation 2.2-7 is determined from AISC Seismic Provisions Secti on 9.3b: t w min



d m  d c  2t f

90

0.9  6.25t 2 f F y  C t



0.9 

 

bs t f 2 F y  C t  m pe

(2.2-9)

where t f F y

(2.2-7)

 

column flange thickness, in. column specified minimum yield strength, ksi. No te that Equatio n 2.2-9 was developed fr om research that considered only ASTM A36 material (Curtis and Murray, 1989). If c olumn material with higher yield strength is used, it is recommended that F y be taken conservatively as 36 ksi in Equation 2.2-9.

where t w b f t f d b d c F y Pu P y A d m

(2.2-8)

When an extended end-plate moment connection is used, flange bending must be limited to prevent yielding of the column flange under tensile flange forces. The design l ocal flange bending strength  Rn given in Equati on 2.2-9 is determined from Murray (1990) with c onsiderati on of the proximity of the c oncentratedflange f orce t o the end of the column as:

0.75 P y, 0.75  0.6 F y d c tw 1 



column web thickness, in.  column flange width, in.  column flange thickness, in.  beam depth, in.  column depth, in.  column minimum specified yield strength, ksi  column required axial strength, in.  F y A, c olumn axial yield strength, in. 2  column cross-secti onal area, in.  moment arm between concentrated flange f orces, in. 

Figure 2-5 Concentration of stress in flange or flange-plate weld for a column with thin flanges and no transverse stiffeners.

4

If using all owable stress design, the shear buckling limit is slightly more conservative and the foll owing W-shapes must be checked for shear buckling: W44230, W40215, W40199, W40183, W40174, W40167, W40149, W36150, W36135, W33130, W33118, W3 099, W3 090, W27 84, W24 68, W24 55, W2144, W1835, W1631, W16 26, W14 22, and W12 14. 8


0.5 if the distance from the column end t o the closer face of the beam tension flange is less than 10t f  1 otherwise bs  2.5(2 p f t f b ), in., f or a f our-b olt unstiffened extended end plate; see Figure 2-6a  2 p f t f b 3.5 pb , in., f or an eight-b olt stiffened extended end plate; see Figure 2-6b p f  distance from centerline of b olt t o nearer surface 1 of the tension flange, in; d b plus /2 in. is generally enough t o pr ovide wrench clearance; 2 in. is a comm on fabricat or standard t f b  beam flange thickness, in. pb  vertical pitch of bolt group ab ove and b olt gr oup below tension flange, in. C t

m

When an extended end-plate m oment c onnecti on is used, the concentrated f orce is distributed t o the c olumn web as illustrated in Figure 2-7b. The design l ocal web yielding strength  Rn given in Equation 2.2-11 is determined fr om Murray (1990) with c onsiderati on of the pr oximity of the concentrated flange force t o the end of the c olumn:





1.36

t w F y k N C t

for a f our-b olt unstiffened extended

end plate

w

1/4

 

pe  1.13 d b

f or an eight-b olt stiffened extended t p d c

end plate pe



g



d b



k 1

2 4 g  bolt gage, in. d b  bolt diameter, in. k 1  distance from beam web centerline to flange toe of flange-t o-web fillet, in.

1.0  [Ct (5 k)  N ] F y t w

column web thickness, in.  column specified minimum yield strength, ksi  distance fro m outside face of c olumn flange t o the web toe of the flange-t o-web fillet, in.  beam flange or flange plate thickness plus 2 w, in.  0.5 if the distance from the c olumn end t o the closer face of the beam flange is less than d c  1 otherwise  leg size of fillet weld or groove weld reinf orcement, if used, in.  end-plate thickness, in.  column depth, in. 

The design l ocal web crippling strength  Rn given in Equation 2.2-12 is determined fr om LRFD Specificati on Equations K1-4, K1-5, or K1-6 with c onsiderati on of the proximity of the c oncentratedflange f orce t o the end of the column:

When a directly welded flange or flange-plated m oment connection is used, the c oncentrated f orce is distributed to the column web as illustrated in Figure 2-7a. The design local web yielding strength  Rn given in Equation 2.2-10 is determined from LRFD Specification Equati ons K1-2 or K1-3 with c onsideration of the pr oximity of the concentrated flange force t o the end of the c olumn: 

 R n



2

0.75  135 Ct tw 1  N d

1.5

 t w t f

 Ft t

y f w

(2.2-12) where 0.5 if the distance from the c olumn end t o the closer face of the beam compression flange is less than d c /2  1 otherwise t w  column web thickness, in. Nd  3 N / d c if the distance from the c olumn end t o the closer face of the beam tension flange is either: (1) greater than or equal t o d c/2; or, (2) less than d c /2 and N / d c is less than or equal t o 0.2. 4 N  0.2 otherwise  C t

(2.2-10)





(a) Four-bolt unstiffened

1.0  [Ct (6 k  2 t p)  N] Fy t w (2.2-11)

2.2.4 Web Crippling

2.2.3 Local Web Yielding

 Rn



where

1/4

  pe d b

 R n

t f F y N

(b) Eight-bolt stiffened

Figure 2-6 Configuration of extended end-plate moment connections.

d c



column flange thickness, in.  column specified minimum yield strength, ksi  beam flange or flange plate thickness plus 2 w f or directly welded flange or flange-plated moment connecti on, in.  beam flange thickness plus (2 w  2 t p) for extended end-plate moment c onnections, in. 

9


leg size of fillet weld or gr oove weld reinf orcement, if used, in. t p  end-plate thickness, in. d c  column depth, in. w

web c ompressi on buckling strength  Rn given in Equation 2.2-13 is determined fr om LRFD Specificati on Equations K1-8 with c onsiderati on of the pr oximity of the concentrated flange force t o the end of the c olumn:



Note that, fr om LRFD Specification C ommentary Section K1.4, f or the r olled shapes listed in ASTM A6, the limit state o f web crippling will not govern the design of transverse stiffening for a m oment connecti on, except t o a W1250 or W1033 c olumn. That is, if transverse stiffening is required, another limit state, such as local web yielding or l ocal flange bending, will be m ore critical in all except the aforementioned two cases.

 R n

0.90 



4 ,100Ct tw3  F y h

where C t

t w F y h d c k

2.2.5 Compression Buckling of the Web

When a pair of c ompressive flange f orces c oincide as illustrated in Figure 2-4b, the c olumn web is subject t o outof-plane buckling as illustrated in Figure 2-8. The design

0.5 if the distance from the column end t o the closer face of the compression flanges is less than d c /2  1 otherwise  column web thickness, in.  column specified minimum yield strength, ksi  d c  2 k , in.  column depth, in.  distance from outside face of c olumn flange t o the web toe of the flange-t o-web fillet, in. 

k

k

t p

1:1 slope N + k 5

p t 2 + N + k 6

± Pu f

N

± Pu f

N

2.5

± F y

3

1

± F y

(a) Directly welded flange or flangeplated moment connection

1

(b) Extended end-plate moment connection

Figure 2-7 Local force transfer for local web yielding limit state.

Zone of column web subject to compression buckling (out-of-plane) (P u ) f 2

(P u ) f 1

k

h

(2.2-13)

k

Figure 2-8 Compression buckling of the column web. 10


if testing demonstrates that the intended inelastic rotation can be achieved without their use.

2.3 Column Cross-Sectional Stiffness Considerations

In addition to satisfying the strength requirements given in Section 2.2, the supp orting c olumn must als o have sufficient stiffness to resist local deformations of the crosssection under the tensile and compressive flange f orces. In wind and low-seismic applications, design for the strength criteria in Section 2.2 has historically resulted in columns with suitable stiffness as well as strength. In high-seismic applications, however, the associated higher inelastic demand necessitates a more explicit consideratio n of flange stiffness to limit the variation in stress distribution across the width of the c onnected flange or flange plate. AISC Seismic Provisions Sections 9.5 and 11.3 indicate that transverse stiffeners that match the configuration of th ose used in the qualifying cyclic tests (see AISC Seismic Provisions Appendix S) f or the m oment c onnecti on t o be used are required. Notethat transversestiffenersare not required

2.4 Design Aids

F or wind and l ow-seismic applicati ons, the determinati on of the design strength of unreinf orced wide-flange shapes used as columns is simplified with the tables in Appendices A, B, and C. In Appendix A, the design c olumn panel-zone shear strength is tabulated. In Appendix B, the design l ocal c olumn strength at l ocati ons of c oncentrated flange f orces is tabulated assuming that the c oncentrated f orce is n ot at a c olumn-end l ocati on. In Appendix C, the design l ocal c olumn strength at l ocati ons of c oncentrated flange f orces is tabulated assuming that the c oncentrated f orce is at a c olumn-end l ocati on. The use of these tables is illustrated in several of the example pr oblems in Chapter 6.

11



Chapter 3 ECONOMICAL SELECTION OF COLUMNS Transverse stiffeners and web d oubler plates are extremely labor-intensive detail materials due primarily to the fit-up and welding that is associated with their use. Additionally, issues such as restraint, lamellar tearing and welding sequence must be addressed when transverse stiffeners and/or web doubler plates are used. As such, they add considerable c ost in spite of their dispr op orti onately low material cost. If transverse stiffeners and web doubler plates can be eliminated and an unreinf orced c olumn can be used, significant c ost savings can often be realized. Additionally, the elimination of column stiffening will simplify (and thereby economize) connecti ons that are made to the weak axis of the c olumn. In wind and l ow-seismic applications, the specification of c olumn sizes that eliminate transverse stiffeners is encouraged. In high-seismic applications, h owever, transverse stiffeners will normally be required, as discussed previously in Section 2.3. In wind, low-seismic, and high-seismic applications, the specification of column sizes that eliminate web doubler plates is encouraged. Web d oubler plates require significantwelding into the columnflange-to-webfillet region (k-area), which is an area of p otentially l ower n otch toughness (AISC, 1997b). The shrinkage that acc ompanies the cooling of these welds typically can dist ort the cross-section and overwelding in this regi on carries the potential for cracking. Additionally, the weld joint may require the use of a n on-prequalified detail as discussed in Section 4.4.3.

welding transverse stiffeners and web d oubler plates that is predominant in their c ost. An equivalent c olumn weight change is tabulated fr om these estimated costs based upon a mill price of $425 per t on, which is a median value in the c omm on range of fr om $400 t o $450 per t on FOB, 6 ,7 and a 14-ft fl oor-t ofl oor height. The tabulated values are calculated as the estimated c ost times 2000 lb per t on divided by $425 per t on divided by the 14-ft length. The resulting value is the estimated maximum per-f oot c olumn-weight increase that c ould be made t o eliminate that element of the c olumn stiffening with out increasing c ost. In fact, because the tabulated values d o n ot c onsider other intangible ec on omic benefits, such as the simplificati on of c onnecti ons that are made t o the weak axis of the c olumn, the tabulated value sh ould be c onsidered c onservative. As an example, c onsider a W14 90 c olumn with fulldepth transverse stiffeners (Case 5, Table 3.1) at each beam flange (2 pairs t otal) and one web d oubler plate (Case 8, Table 3.1). The total of the tabulated c olumnweight-change values f or this c olumn stiffening arrangement is 40 lb/ft  82 lb/ft  122 lb/ft. Thus, if any heavier W14 up t o and including a W14 211 c olumn c ould be used with out transverse stiffeners and a web d oubler plate, it w ould likely be m ore ec on omical than the W14 90. In m ost cases, the actual increase in c olumn weight required t o eliminate column stiffening will be much less than the maximum calculated and a significant economic benefit can be realized. When the required c olumn-weight change exceeds the sum of the tabulated values, some engineering judgment must be used. If the comparis on is unfav orable, but still close, the use of a heavier column might still be justified by the af orementi oned intangibles. Alternatively, the designer may still find it advantageous to investigate the possibility of eliminating the web doubler plate only ( or transverse stiffeners only in some cases). As an example, consider again the W14 90 c olumn with full-depth transverse stiffeners (Case 5, Table 3.1) at each beam flange (two pairs t otal) and one web d oubler plate (Case 8, Table 3.1). If any heavier W14 up t o

3.1 Achieving Balance Between Increases in Material Cost and Reductions in Labor Cost

In Table 3.1, estimated costs are given for s ome arbitrarily selected transverse stiffener and web doubler plate details as illustrated in Figure 3-1. These estimated costs were determined by averaging the c ost estimates5 provided by several fabricators and r ounding the result t o the nearest five-dollar increment. When comparing these typical details to actual details, it sho uld be no ted that the co mparative weld types and sizes are of much greater significance than the thicknesses or overall dimensions of the plate materials. It is the labor inv olved in cutting, pr ofiling, and

6

FOB stands for “free on board,” which indicates that the quoted price assumes delivery to the indicated location. In the above case, the indicated location is the mill itself; subsequent shipping wo uld incur additional cost.

5

The estimated costs are predicated upon the material and labor c osts that existedat the time thisDesignGuide waswritten (circaearly1999). Because it is anticipated that labor costs will co ntinue to rise at a faster rate than material costs,the user mayfind it advantageous to periodically inquire with local fabricators to determine a more current estimate of these costs.

7

Because mill prices fluctuate, the designer may find it advantageo us to periodicallyinquire with fabricators, steelmills, or other shapesuppliers to determine the current range of mill prices. 13


and including a W14 159 c olumn c ould be used without a web d oubler plate, but with the transverse stiffeners, it would be m ore economical than the W14 90. Similarly, if any heavier W14 up to and including a W14120 c olumn c ould be used with out transverse stiffeners, but with a web d oubler plate, it w ould be m ore ec onomical than the W1490.

the design strength of the c olumn, yet there will be little or n o impact on the material c ost. Mill grade extras f or 50-ksi wide-flange material are largely n onexistent in shapes that weigh as much as 150 lb per ft of length. 8 Evenf or W-shapesin weight ranges that havegrade extras, these n ominal c ost differences of tw o or three pennies per p ound are negligible when compared to the advantage gained in detail material savings. Column material with even higher yield strength, such as ASTM A913 grade 65 material, is also available; however, the associated material cost differential is greater. 2. Consider a different c olumn secti on that has a thicker flange and/or web, as appr opriate. This increase in material cost, given t oday’s typical FOB mill price for c ommon grades9 of steel of appr oximately $400 to $450 per t on, is in m ost cases

3.2 Eliminating Column Stiffening

From Section 3.1, it is clear that there is significant potential for ec onomic benefit when transverse stiffeners and web doubler plates can be eliminated. Therefore, the designer should consider alternatives that eliminate the need for c olumn stiffening, when p ossible. The design aids in Appendices A, B, and C provide f or the rapid identification of c olumn strength and stiffening requirements in wind and low-seismic applications. Some additi onal suggestions follow.

8

Inquire with steel mills to determine the current range of shapes for which a grade extra applies.

1. Specify c olumn material with yield strength of 50 ksi, such as ASTM A992 or A572 grade 50 steel. The increased minimum yield strength will increase

9

Comm on grades include ASTM A992, ASTM A572 grade 50, and A36.

Table 3.1 Estimated Cost of Various Column Stiffening Details (as illustrated in Figure 3-1)

Case

Thickness

Attachment to Column Flange

Attachment to Column Web

Estimated Cost

Equivalent Column Weight (lb/ft) if WideFlange Steel Costs $425 per Ton from Rolling Mill3

Partial-Depth Transverse Stiffeners (Two Pairs) 4 PL 41/2  0’-10 (ASTM A36) with one 3 /4  3 /4 corner clip each 1 2 3 4

1

/2 in. 1 in. 1 /2 in. 1 in.

fitted to bear fitted to bear 1 /4 -in. fillet welds 1 /2 -in. fillet welds1

3

/16 -in. fillet welds /16 -in. fillet welds 3 /16 -in. fillet welds 5 /16 -in. fillet welds 5

$80 $120 $90 $140

27 40 30 47

Full-Depth Transverse Stiffeners (Two Pairs) 4 PL 4 1/2  1’-09/16 (ASTM A36) with two 3 /4  3 /4 corner clips each 5 6 7

1

/2 in. 1 in. 1 1/2 in.

1

/4 -in. fillet welds /2 -in. fillet welds CJP groove weld 1

3

/16 -in. fillet welds /16 -in. fillet welds 1 /2 -in. fillet welds1 5

$120 $210 $470

40 71 158

$245 $370 $215 $305

82 124 72 103

Web Doubler Plate (One) 1 PL 125/8  2’-0 (ASTM A36) 8 9 10 11

1

/2 in. /4 in. 3 /4 in. 1 in. 3

CJP groove weld CJP groove weld 5 /8 -in. fillet weld2 7 /8 -in. fillet weld2

3

/16 -in. fillet welds /16 -in. fillet welds 5 /16 -in. fillet welds 5 /16 -in. fillet welds 5

1

The consulted fabricators were asked if they would instead prefer a CJP-groove-welded detail in place of this larger-size fillet-welded detail. In all cases, the answer was no. 2 A 3/4 -in. by 3/4-in. bevel on the column-flange edges of the web doubler plate is used to clear the column flange-to-web fillet. It should be noted that the fillet-welded web doubler plate detail in Case 10 is not suitable for high seismic applications because the weld size does not develop the strength of the full thickness of the web doubler plate. 3 A floor-to-floor height of 14 ft has been used in this tabulation.

14


easily offset by the savings in labor c osts, as illustrated previously in Secti on 3.1. 3. Consider a deeper cross-sectio n f or the beam that is connected to the column. Increasing the depth of the beam decreases the flange force delivered due t o the increase in moment arm between the flange-force couple. If it were p ossible t o replace a W1650 with a W1850,thematerial costw ould not be increased; if a lighter, deeper shape were suitable, the material cost w ould in fact be decreased. Even if there were an increase in material cost, it would in most cases be easily offset by the savings in labor c osts. N ote that this suggestion may insteadbe punitive when the moment connection is designed to devel op the strength of the beam. 4. Increase the number of m oment-resisting c onnections and/or frames to reduce the magnitude of the moment delivered to a given c onnection t o a level that is within the local design strength of the c olumn section.

in wind and l ow-seismic applications: 1. Where allowed by governing building c odes, design column stiffening in response t o the actual moments and resulting flange f orces rather than the full flexural strength of the cross-secti on; the latter simply wastes m oney in the majority of cases. When the Engineer of Record (EOR) delegates the determination of the column stiffening requirements, the design forces and moments should also be provided. 2. If designing in all owable stress design, take advantage of the allowable stress increase in windload applicatio ns (load c ombinations in LRFD inherently account for such c oncurrent occurrence of transient loads). 3. Properly address reduced design strength at c olumn-end applicatio ns. The typical beam depth is usually such that the reduced design strength provisions f or c olumn-end applicati ons apply only at the nearer flange f orce. 4. Increase the number of m oment-resisting c onnections and/or frames to reduce the magnitude of the moment delivered to a given c onnection t o a level that allows a more econ omical stiffening detail. 5. Give preference to the use of fillet welds instead of groove welds when their strength is adequate and the application is appr opriate (see Chapter 4).

3.3 Minimizing the Economic Impact of Column Stiffening Requirements in Wind and LowSeismic Applications

In some cases, the need for c olumn stiffening may n ot be avoidable. When this is the case, the foll owing suggestions may help minimize the cost impact for building structures

(a) Partial-depth transverse stiffeners (Cases 1, 2, 3 and 4

(b) Full-depth transverse stiffeners (Cases 5, 6 and 7

(c) Web doubler plate (Cases 8, 9, 10 and 11)

Note: dimensions and edge connections for the above column stiffening elements are as given in Table 3.1, based upon a W 14 column. Figure 3-1 Column stiffening arrangements for cost estimates in Table 3.1. 15


This is particularly true for the welds c onnecting transverse stiffeners to the column. 6. When p ossible, use a partial-depth transverse stiffener, which is mo re econ omical than a fulldepth transverse stiffener because it need not be fitted between the column flanges. Select the partial-depth transverse stiffener length t o minimize the required fillet-weld size for the transverse-stiffener-to-column-web weld. 7. While transverse stiffeners are required in pairs when the limit states of local flange bending or l o cal web yielding are less than the required strength, a single transverse stiffener is permitted and should be c onsidered when the limit states of web crippling and/or c ompressi on buckling of the web only are/is less than the required strength. 8. In cases when the flange f orce is only c ompressive, allow the option to weld the transverse stiffener end or t o finish it t o bear on the inside flange. In m ost lateral l oad resisting frames, h owever, moments are reversible and the design flange force may be either tensile or compressive. 9. Use a single web doubler plate up t o a required thickness of 1/2 in. If thicker web reinf orcement is required, consider the use of two plates, one on each side of the column web. This practice may be more econ omical and is likely to reduce heat input, weld shrinkage, and member distortion. 10. Select the web doublerplate thickness so that plug welding between the column web and web d oubler plate is not required.

11. Recognize that, in the c oncentrated-flange-f orce design pr ovisi ons in LRFD Specificati on Secti on K1, it is assumed that the connection is a directly welded flange or flange-plated m oment c onnection, n ot an extended end-plate moment c onnection. Appr opriate design strength equati ons are given in Chapter 2 based upon the rec ommendations in Murray (1990). 12. Limit the number of different thicknesses that are used throughout a given pr oject f or transverse stiffeners and web d oubler plates. Pr oduction econ omy is achieved when many repetitive elements can be used. 3.4 Minimizing the Economic Impact of Column Stiffening Requirements in High-Seismic Applications

In high-seismic applicatio ns, eco nomy suggestions 4, 5, 6,10 9, 10,11 11, and 12 in Section 3.3 remain applicable. Additionally, economy suggesti on 1 remains applicable for web d oubler plates, when the flange f orce(s) are determined from LRFD Specification Secti on A4.1, AISC Seismic Provisions Section 4.1, and Equation 2.1-1.

10

Applicable when a moment connection is made to one flange only.

11

Note that this may not be possible in high-seismic applicatio ns if the column web thickness itself does not meet the seismic shear buckling criteria given in Equation 4.4-6.

16


Chapter 4 STRONG-AXIS MOMENT CONNECTIONS TO STIFFENED COLUMNS When the required strength (Section 2.1) exceeds the design strength of the c olumn f or the c oncentrated f orces (Section 2.2), or when the stiffness of the c olumn cr osssection is inadequate to resist the bending def ormati ons in the column flange (Section 2.3), column stiffening is required. Several comm on stiffening arrangements are illustrated in Figures 4-1 thr ough 4-6 with c omm on welding options f or the attachments of the stiffening elements to the column. In Figures 4-1 and 4-2, a c olumn with partial-depth transverse stiffeners only and a c olumn with full-depth transverse stiffeners only are illustrated, respectively. In Figure 4-3, a c olumn with web d oubler plate(s) only is illustrated. In Figures 4-4, 4-5, and 4-6, c olumns with b oth transverse stiffeners and web doubler plates(s) are illustrated. In Figures 4-4 and 4-5, the web d oubler plate(s)

extend past the partial-depth and full-depth transverse stiffeners, respectively. In Figure 4-6, the web d oubler plate(s) extend t o but n ot past the full-depth transverse stiffeners. As illustrated in Figures 4-4, 4-5 and 4-6 the web d oubler plates that are fillet welded t o the c olumn flanges are sh own thicker than th ose that are gr oove welded t othe c olumn flanges are. This is intended t o visually highlight the increased thickness that is often required t o facilitate the use of a fillet-welded edge detail (see Secti on 4.4.2). Fillet-welded and gr oove-welded details are illustrated generally in all cases. Fillet-welded details will be preferable in the maj ority of cases alth ough partial-j ointpenetrati on or c omplete-j oint-penetrati on gr oove welds may be the best ch oice in s ome cases. Ultimately, preference sh ould be given t o the use of details that require the

Section A-A

B

A

transverse stiffeners fillet welded to column flanges

transverse stiffeners fillet welded to column web

transverse stiffeners groove welded to column flanges A

transverse stiffeners groove welded to column web

B

Section B-B Figure 4-1 Column with partial-depth transverse stiffeners.

17


least amount of weld metal with due c onsideration of the material preparation requirements.

4.1.2 Local Flange Bending

When the column flange thickness is inadequate t o resist the tensile flange force, a pair of transverse stiffeners extending at least one-half the depth of the column web is required. They must be welded t o the loaded c olumn flange t o devel op the strength of the welded p orti on of the transverse stiffener. The weld t o the c olumn web must be sized t o devel op the unbalanced f orce in the transverse stiffener t o the web.

4.1 Determining the Column Stiffening Requirements

In wind and l ow-seismic applications, various alternative stiffening details utilizing transverse stiffeners, web doubler plates, or a combination there of, are permitted in LRFD Specification Section K1, depending upon the limit state(s) for which column stiffening is required. The welding requirements are also specified for each case therein. In high-seismic applications, the required placement and welding of transverse stiffeners and web d oubler plates is given in LRFD Specification Section K1 and AISC Seismic Provisions Sections 9.3c, 9.5 and 11.3. These c olumnstiffening requirements and alternatives are summarized in Sections 4.1.1 through 4.1.6.

4.1.3 Local Web Yielding

When the column web thickness is inadequate t o resist the tensile or compressive flange force, either a pair of transverse stiffeners or a web d o ubler plate,13 extending at least one-half the depth of the c olumn web is required. In wind and l ow-seismic applications, when required for a tensile flange f orce, and in high-seismic applicatio ns, the transverse stiffener must be welded to the loaded

4.1.1 Panel-Zone Web Shear

When the column web thickness is inadequate t o resist the required panel-zone shear strength, a web d oubler plate is required.12 The welding requirements for web d oubler plates are as summarized in Section 4.4.3 and 4.4.4.

12

Alternatively, diagonal stiffening can be used if it do es not interfere with the weak-axis framing; see Section 5.6. 13

See Section 5.4.

Section A-A

B

A


transverse stiffeners fillet welded to column web


transverse stiffeners groove welded to column web

B

Section B-B Figure 4-2 Column with full-depth transverse stiffeners. 18


column flange to devel op the strength of the welded p ortion of the transverse stiffener. In wind and l ow-seismic applications when required for a c ompressive flange f orce, the transverse stiffener must either bear on or be welded to the loaded flange t o devel op the f orce transmitted t o the transverse stiffener. The weld to the column web must be sized t o devel op the unbalanced force in the transverse stiffener int o the column panel-zone.

flange t o devel op the f orce transmitted t o the transverse stiffener. In high-seismic applicati ons, the transverse stiffener must be welded t o the l oaded flange t o devel op the strength of the welded p orti on of the transverse stiffener. The weld t o the c olumn web must be sized t o devel op the unbalanced f orce in the transverse stiffener int o the c olumn panel-z one. 4.1.5 Compression Buckling of the Web

When the column web thickness is inadequate t o resist the opposing c o mpressive flange f orces, either a transverse stiffener, a pair of transverse stiffeners or a web d oubler plate,15 extending the full depth of the c olumn web, is required. In wind and l ow-seismic applicati ons, the transverse stiffener must either bear on or be welded t o the l oaded flange t o devel op the f orce transmitted t o the transverse

4.1.4 Web Crippling

When the column web thickness is inadequate t o resist the compressive flange force, either a transverse stiffener, a pair of transverse stiffeners or a web d oubler plate,14 extending at least one-half the depth of the c olumn web, is required. In wind and low-seismic applications, the transverse stiffener must either bear on or be welded to the l oaded 14

15

See Section 5.4.

See Secti on 5.4.

web doubler plate beveled and fillet welded to column flanges web doubler plate groove welded to column flanges Section A-A

B See note below web doubler plates fillet welded to column web (top and bottom) A

A B

Section B-B Note: 2.5k minimum for directly welded flange and flange-plated moment connections, 3k + t p minimum for extended end-plate moment connections (top and bottom) Figure 4-3 Column with web doubler plate(s). 19


stiffener. In high-seismic applications, the transverse stiffener must be welded to the loaded flange to devel op the strength of the welded p orti on of the transverse stiffener. The weld to the column web must be sized to devel op the unbalanced force in the transverse stiffener into the column panel-zone.

transferred locally into the c olumn flanges. These c oncentrated f orces spread thr ough the c olumn flange and flanget o-web fillet regi on int o the web, transverse stiffener(s), if used, and web d oubler plate(s), if used. Shear is dispersed between them in the c olumn panel-z one. Ultimately, axial f orces in the c olumn flanges balance this shear.

4.1.6 Flange Stiffness

4.2.1 Required Strength for Transverse Stiffeners

In wind and l ow-seismic applications, flange stiffness is addressed by the local flange bending limit state (Secti on 4.1.2). In high-seismic applications, transverse stiffeners will normally be required (see Section 2.3) in pairs with welding as described in Sections 4.3.4 and 4.3.5.

The following discussion is applicable t o the required strength of the ends of the transverse stiffener in tensi on and/or c ompression. The required strength of the transverse stiffener in shear to transmit an unbalanced l oad t o the column panel-zone is covered in Secti on 4.3.2. In wind and l ow-seismic applications, transverse stiffeners are required only when the c oncentrated flange f orce (Section 2.1.1) exceeds the design strength of the c olumn flange or web (Secti ons 2.2.2 thr ough 2.2.5). In an exact solution, this f orce w ould be app orti ned between o the web and transverse stiffeners on the basis of relative

4.2 Force Transfer in Stiffened Columns

In a stiffened column, the l oad path is similar t o that described in Section 2.1, except that the added stiffening elements share in a portion of the f orce transfer. C oncentrated forces from the beam flanges or flange plates are


B


transverse stiffeners fillet welded to web doubler plate

See note below transverse stiffeners groove welded to column flanges A

web doubler plates fillet welded to column web (top and bottom)

A B

transverse stiffeners groove welded to web doubler plate Section B-B

Note: 2.5k minimum for directly welded flange and flange-plated moment connections, 3k + t p minimum for extended end-plate moment connections (top and bottom) Figure 4-4 Column with partial-depth transverse stiffeners and web doubler plate(s) (extended). 20


stiffness and effective area. Ho wever, AISC has l ong allo wed a simplified appr oach whereby only the f orce in excess of the governing c olumn flange or web limit-state is assumed to be transmitted to the transverse stiffener end in tension or c ompressi on. Because minimum transverse stiffener width and thickness pr ovisi ons are also included (see Sections 4.3.1 and 4.3.2), this rati onal method has historically pr ovided a safe result. Acc ordingly, the required strength of the transverse stiffener(s) in tensi on and/or c ompressi on is:

crippling, and c ompressi on buckling (if applicable) at l ocati ons of c ompressive flange f orces, kips

(4.2-1)

Ru st  Puf   R n min

where Puf

 R n min

factored beam flange force, tensile or c ompressive (Section 2.1), kips  the lesser of the design strengths in flange bending and web yielding at l ocations of tensile flanges forces, or the lesser of the design strengths in local web yielding, web 

If Ru st is negative, transverse stiffeningis not required and its value is set equal to zero in subsequent calculations. Note that the flange force against which each limit state must be checked may vary. For example, the c ompressi on buckling limit-state will usually be applicable for a pair of opp osing c ompressive flange f orces induced by maximum concurrent negative moments due t o gravity l oad at a c olumn with beams that are m oment c onnected t o both flanges. At the same time, the tensile or c ompressive flange forces induced by the maximum m oments due to lateral loads may be more critical for the other limitstates. In high-seismic applications, transverse stiffeners that match the configuration of th ose used in the qualifying cyclic tests (AISC Seismic Pro visions Appendix S) for the moment connecti on to be used are required as discussed previously in Sectio n 2.3.


B


transverse stiffeners fillet welded to web doubler plate

See note below transverse stiffeners groove welded to column flanges A

web doubler plates fillet welded to column web (top and bottom)

A B

transverse stiffeners groove welded to web doubler plate Section B-B

Note: 2.5k minimum for directly welded flange and flange-plated moment connections, 3k + t p minimum for extended end-plate moment connections (top and bottom) Figure 4-5 Column with full-depth transverse stiffeners and web doubler plate(s) (extended). 21


where

4.2.2 Required Strength Strength for Web Web Doubler Plates

Ru st  transverse transverse stiffener stiffener required required strength (Secti on

Web doubler plate(s) plate(s) are required required only when when the c olumn web shear shear (Secti (Section 2.1.2) 2.1.2) exceeds exceeds the design design strength strength of the column web (Secti (Section 2.2.1). 2.2.1). The requir required ed strength strength of the web doubler plate(s) plate(s) is: is: V u dp



V u   Rv

F y st



(4.2-2)

cw

When Wh en beams beams are are moment ment c onnec nnecte ted d t o b oth c olumn lumn flanges flanges and share share transv transvers ersee stiffen stiffeners ers,, the transv transvers ersee stiffstiffener end area is selected f or the maximum individual flange flange force, rce, n ot the c ombined mbined f orce fr om b oth transve transverse rse stiffen stiffener er ends. ends. The combined mbined f orce fr om b oth transve transverse rse stiffen stiffener er ends ends is of interes interest, t, h owever wever,, f or the design design of the column-web lumn-web edge of the transverse transverse stiffener stiffener and may impact the required required thickness; thickness; see Section 4.3.2.

where V u

 Rv cw

4.2.1), kips transverse transverse stiffener stiffener specified specified minimum minimum yield strength, ksi  0.9 

fact factored red pane panell-zzone shea shearr f orce (Sec (Secti tion 2.1.2), kips  column web design shear strength (Section 2.2.1), kips 

If V u dp is nega negati tive ve,, web web d oubler ubler plat platin ing g is n ot requ requir ired ed..

4.3.1 Width of Transverse Transverse Stiffeners

4.3 Design of Transverse Stiffeners

In wind and low-seismic w-seismic applicati applications, from LRFD SpecSpecification Section K1.9, the minimum minimum width of each transverse verse stiffen stiffener er bs min, as illustr illustrated ated in Figure Figure 4-7, 4-7, is

Transver Transverse se stiffeners stiffeners are sized to provide a cross-secti ss-secti onal area Ast , where Ast min



R u st  F y st

(4.3-1)

bs min



b

3



t pz


B


transverse stiffener and web doubler plate fillet welded transverse stiffener fillet welded, web doubler plate groove welded


transverse stiffener and web doubler plate groove welded

A B

Section B-B

transverse stiffener groove welded, web doubler plate fillet welded

Figure 4-6 Column with full-depth full-depth transverse stiffeners and web doubler plate(s) (flush). 22


2

(4.3-2)

where b t pz

the transverse stiffeners extend t o the full width of the c olumn flange.

widt width h of beam beam flang flangee (  b f ) or flang flangee plat plate, e, in. in.  column web web thickness, thickness, in., in., if a web doubler plate plate is not used used or if the web web d ouble ublerr plate plate exten extends ds to (but (but n ot past) past) the transv transvers ersee stiffen stiffeners ers;; t otal pane panell-zzone thic thickn kness ess,, in., in., if the the web web doublerplat ublerplatee extends past the transverse stiffeners.



The specified width should be selected with c onsideration of the the thick thickne ness ss requi require remen ments ts in Sect Sectii on 4.3.2, 4.3.2, t o satis tisfy the the minimum area Ast min (Secti ction 4.3). Area reducti reduction due due to c orner rner clips clips that that are are requi required red t o clear clear the the column flange-to-web fillets should be c onsidered when sizing the transverse stiffener and its welds. As discussed in the AISC AISC LRFD Manual Manual (page (page 8-117) 8-117) a 3/4-in. -in. diag onal corner clip will generally generally be dimensi dimensionally adequate adequate to clear clear most column lumn flange flange-t -to-web -web fillets, fillets, but the clip clip didimensi mension can can be be adjus adjusted ted up or d own as requ require ired d t o suit suit the the various conditions. In high-se high-seism ismic ic applicat applicatiions, the width width of each transtransverse stiffener stiffener should be c onsistent nsistent with that used in the tested tested assemblie assembliess (see Sectio n 2.3). To date, date, qualifyi qualifying ng cyclic cyclic tests have utilized utilized transver transverse se stiffene stiffeners rs of width width such such that the total stiffen stiffened ed width width equals equals or slightly slightly exceeds ceeds the beam beam flang flangee or flangeflange-plat platee width width or such such that that

t w w

4.3.2 Thickness of Transverse Stiffeners

In wind and l ow-seismic applicati applicati ons, fr om LRFD Specificati ificatio n Secti Sectio n K1.9, K1.9, the minimu minimum m thickn thickness ess of each each tran transv sver erse se stif stiffe fene nerr t s min when when tran transv sver erse se stif stiffe fene ners rs are are rerequired is: t s min



t

2



bs  F y st

95

(4.3-3)

where t  beam flange flange or flange plate thicknes thickness, s, in. bs  actual transverse stiffener width, in.

The The speci specifie fied d thick thickne ness ss should uld be selec selected ted with with consid nsider eraation of the length length requir requireme ements nts in Secti Secti on 4.3.3, 4.3.3, t o satisfy satisfy the shear strength strength that is required required t o transmit transmit the unbalance anced d force rce in the the tran transv sver erse se stiff stiffen ener er t o the the column lumn pane panellzone. For a pair of partial-depth partial-depth transverse transverse stiffeners, stiffeners, the thickness thickness required required for shear strength strength is: t s

b s s



Ru st 0.9  0.6 F y st ( l  clip)  2

for flange plate) b f f (b for

b s s

(a) Partial-depth transverse stiffeners

t w w

b s s

for flange plate) b f f (b for

b s s

(b) Full-depth transverse transverse stiffeners

Note: for flange-plated moment connections, use the flangeplate width b in in place of the beam-flange width b f f

Figure 4-7 Illustration of transverse stiffener width bs (wind and low-seismic applications). 23


(4.3-4)

For a pair of full-d full-dept epth h transv transvers ersee stiffen stiffeners ers,, the thickn thickness ess required for shear strength is: t s



( R u st) 1  ( Ru st ) 2 0.9  0.6F y st ( l  2  clip)  2

j oint penetr penetrati ati on gr oove welds welds with with fillet-w fillet-weld eld reinf reinf orcement, or c omplete-j oint-penetrati on gr oove welds. When using double-sided uble-sided fillet welds, the weld size required required is:

(4.3-5) wmin



where Ru st  requir required ed streng strength th of the transve transverse rse stiffen stiffener er (see (see

0.9F y st ts 0.75(1.5  0 .6 F EX X )  2



0 .943 F y st ts F EX X

(4.3-6)

where

Section 4.2.1), kips; the subscripts 1 and 2 in Equati Equation 4.3-5 indicat indicatee the f orces rces at each end end of the transverse stiffener F y st  transverse transverse stiffener stiffener specified specified minimum minimum yield strength, ksi l  transverse stiffener length, in. clip  transverse transverse stiffener stiffener corner clip clip dimensi dimensi on, in.

transverse transverse stiffener stiffener specified specified minimum minimum yield strength, ksi t s  transverse stiffener thickness, in. F EX X  welding welding electrode specified specified minimum minimum strength, ksi F y st



The The 1.5 1.5 fact factor in the the den denomina minatt or of the the sec sec ond ter term m in Equation 4.3-6 4.3-6 is the weld strength strength increase increase factor f or the 90-degree 90-degree angle of l oading determined determined fr om LRFD Specification Appendix Appendix J2.4. When the transverse transverse stiffener stiffener is required required f or a c ompressive sive flang flangee force rce only nly (due (due t o l ocal cal web web yiel yieldi ding ng,, web web crip crippl plin ing, g, or c ompress mpressii on buck bucklin ling g of the the web) web),, it must must eith eitherbe erbear ar on or be weld weldedt edt o the the c olumnfla lumnflan nget o deve devell op the force transmitted transmitted to the transverse transverse stiffener stiffener.. F or pr oper force rce tran transf sfer er in bear bearin ing, g, Ru st must must be equa equall t o or less less than than  R n as given in LRFD Specificati Specification Section J8(a). J8(a). Fr om this secti section, it can be be derived derived that, for a pair pair of transver transverse se stif stiffe fene ners rs,, the the widt width h bs and and thic thickn knes esss t s of each each of the the tran transsverse stiffeners must be such that:

In Equ Equati ation 4.3-5 .3-5,, ( Ru st) 1 and and ( Ru st) 2 can can add add, as f or latlateral eral moments, ments, or subtr subtrac act, t, as f or gravi gravity ty m oment ments. s. The The most critical case f or transverse stiffener thickness will usually usually result for the case wherein they add. add. In high high-s -seis eismi micc appl applica icati tions, the the thick thickne ness ss of each each transverse stiffener sho uld be c onsistent with that used in the tested tested assemblies assemblies.. To date, date, m ost qualifyi qualifying ng cyclic cyclic tests have utilized utilized transverse transverse stiffener stiffenerss of thickness thickness equal to that that of the the beam beam flang flangee or flan flange ge plate plate t o meet meet the the recrec16 mmendati tion of FEMA FEMA (1995) (1995).. ommenda 4.3.3 Length of Transverse Stiffeners

When full-depth transverse stiffeners are used, the length is selected selected f or the distanc distancee between between the column lumn flanges, flanges, with with due due c onsid nsider erati ation of c olumn lumn cr oss-sec ss-secti ti onal t olerlerance ancess and and the the weld welded ed joint int that that is to be used used.. Wh When en part partia ialldepth transverse stiffeners are used, the length is selected to minimize the transvers transversee stiffener stiffener thicknes thicknesss and, more importantly rtantly, the size of double-sided uble-sided fillet weld weld that that is required quired for the the c onnecti nnection of the the trans transver verse se stif stiffen fener er t o the column web; see Sections 4.3.2 and 4.3.5. Note that the minimum minimum length f or partial-depth partial-depth transverse transverse stiffeners stiffeners is one-half ne-half the column depth. depth.

(bs  clip)ts



0.370 Ru st F y st

(4.3-7)

Alternatively Alternatively,, when when using d ouble-sided uble-sided fillet welds, the weld size required is: wmin





4.3.4 Connecting Transverse Transverse Stiffeners Stiffeners to Column Flanges

R u st

0.75(1.5  0 .6 F EX X)( bs  clip)(2)  2

(4.3-8)

0.524 Ru st F EX X (bs  clip)

where transverse transverse stiffener stiffener corner clip clip dimensi dimensi on, in.  transv transvers ersee stiffen stiffener er requir required ed streng strength th (see (see SecSection 4.2.1), 4.2.1), kips kips F y st  transverse stiffener specified minimum yield, ksi F EX X  welding welding electrode specified specified minimum strength, ksi

clip Ru st

In wind wind and and low-se w-seis ismic mic appl applica icati tions, ns, when when the the tran transv sver erse se stiffen stiffener er is requ require ired d for a tensile tensile flange flange force (due (due t o l ocal web yielding yielding or local flange flange bending), bending), it must be welded welded to deve devellop the the stre streng ngth th of the the weld welded ed p orti rti on of the the tra trans ns-verse stiffener. As illustrated in Figure 4-8, this can be done with double-sided uble-sided fillet fillet welds, welds, d ouble-sided uble-sided partialpartial16

Subsequent Subsequent research (El Tawil et al., 1998) indicates that transverse transverse stiffness stiffness with with thickness thickness equal to o r greater greater than 60 percent percent o f the beam flange flange or flange-pla flange-plate te thicknes thicknesss can pr ovide vide f or the required required cr osssecti sectional stiffne stiffness ss when when a beam beam is moment-c ment-connected nnected to one column flange flange only. nly.



The The 1.5 1.5 fact factor in the the den denomina minatt or of the the sec sec ond ter term m in Equation 4.3-8 4.3-8 is the weld strength strength increase increase factor f or the 90-degree 90-degree angle of loading determined determined fr om LRFD LRFD SpecSpecificatio n Appendix Appendix J2.4. J2.4. 24


In high-seismic applications, the transverse stiffener must be welded to devel op the strength of the welded p ortion of the transverse stiffener. As illustrated in Figure 4-8, this can be done with d ouble-sided fillet welds, d oublesided partial-joint penetration groove welds with filletweld reinforcement, or c omplete-j oint-penetrati on gr oove welds. When using double-sided fillet welds, the weld size required can be determined as given previ ously in Equation 4.3-6.

transverse stiffeners.17 Welding t o the c olumn panel-z one will always be required when:

4.3.5 Connecting Transverse Stiffeners to Column Panel-Zones

The latter case is oc mmo n for moment connecti ons, especially in high-seismic applicatio ns, and results in a tensile force on one end of the transverse stiffener c ombined with a compressive force on the other end of the transverse stiffener. The sum of these forces is equilibrated by shear

1. Partial-depth transverse stiffeners are used (see Figure 4-9a); 2. A beam is moment-connected to one flange of the column only; or, 3. Beams are moment-connected t o b oth c olumn flanges and reverse-curvature bending is anticipated (see Figure 4-9c).

In wind, low-seismic and high-seismic applications, the transverse stiffener is welded to transmit the unbalanced force, if any, in the transverse stiffener t o the c olumn panel-zone. As illustrated in Figure 4-9b, welding t o the column panel-zone is not required if the opp osing beam flange forces are equal and opp osite, except when c ompression buckling of the web g overns or t o stabilize the

17

In such cases, minimum-size fillet welds per LRFD Specification Table J2.4 are commonly used.

Column flange

Column web

w t s

Transverse stiffener

w

(a) Double-sided fillet welds

(c) Complete-joint-penetration groove weld (single-sided preparation with backing bar shown)

(b) Double-sided partial-joint-penetration groove welds with fillet-weld reinforcement

Figure 4-8 Welded joint details for transverse stiffener ends (welding to column flange). 25


that is distributed along the column-web edge of the transverse stiffener as illustrated in Figure 4-10. For a pair of partial-depth transverse stiffeners, the fillet-weld size required for shear strength (with d oublesided fillet welds on each transverse stiffener) is: w



w



( Ru st) 1  ( Ru st) 2 0.75  0 .6 F EX X ( l  2  clip)  2

0.75  0.6 F EX X ( l  clip)  2   2

 2

(4.3-10)

where Ru st

R u st



(4.3-9)

Fo r a pair of full-depth transverse stiffeners, the fillet-weld size required for shear strength (with d ouble-sided fillet welds on each transverse stiffener) is:



transverse stiffener required strength (see Section 4.2.1), kips; the subscripts 1 and 2 in Equation 4.3-10 indicate the forces at each end of the transverse stiffener as illustrated in Figure 4-10

Web welds always required for partial-depth transverse stiffeners

P uf

(a) Partial-depth transverse stiffeners Web welds not required for full-depth transverse stiffeners if (P u ) f 1=(P u ) f 2, except for compression buckling of the web and to stabilize the transverse stiffeners (P u ) f 2

(P u ) f 1

(b) Full-depth transverse stiffeners with opposing flange forces Web welds always required for fulldepth transverse stiffeners with reverse-curvature bending

(P u ) f 2

(P u ) f 1

(c) Full-depth transverse stiffeners with reverse-curvature bending Figure 4-9 Web welding requirements for transverse stiffeners. 26


F EX X  weld electrode specified minimum strength, l clip

where

ksi transverse stiffener length, in.  transverse stiffener corner clip dimensi on, in.

 R n max



In Equation 4.3-10, ( Ru st) 1 and ( Ru st) 2 can add, as f or lateral moments, or subtract, as f or gravity m oments. The most critical case for weld size will usually result f or the case wherein they add. However, the welds need not be sized to develop a force that is larger than that due t o any of the f oll owing criteria:

F y st bs clip t s l F y

1. The sum of the design strengths at the c onnections of the transverse stiffener to the column flanges (see Equations 4.3-11 and 4.3-14 or 4.3-17); 2. The design shear strength of the c ontact area of the transverse stiffener with the column panel-zone (see Equations 4.3-12 and 4.3-15); n or 3. The shear yield strength of the c olumn panel-z one (see Equations 4.3-13 and 4.3-16).

t pz

N ote that, if a pair of full-depth transverse stiffeners is used, but a beam is m oment c onnected t o one c olumn flange only, Equation 4.3-17 sh ould be used in lieu of Equation 4.3-14, where:

Note that the second and third criteria should not g overn unless the transverse stiffener was provided f or stiffness rather than strength. Thus, fo r a pair of partial-depth transverse stiffeners, the design shear strength of the welds  Rn need n ot exceed any of the f oll owing three f orces:  R n max



0.9F y st(2)( bs

 R n max



0.9  0.6F y st ( l  clip)  2 t s

(4.3-12)

 R n max



0.9  0.6F y d c  t pz

(4.3-13)



clip)  t s

maximum force for which the welds c onnecting the transverse stiffeners to the column panel-zone must be designed, kips  transverse stiffener specified minimum yield strength, ksi  transverse stiffener width, in.  transverse stiffener c orner clip dimensi on, in.  transverse stiffener thickness, in.  transverse stiffener length, in.  panel-zone specified minimum yield strength (column web and/or web d oubler plate), in.  panel-zone material thickness (column web and/or web d oubler plate), in. 

 R n max



0.9F y st (2)( bs  clip)  t s (4.3-17)

When transverse stiffeners transmit an unbalanced l oad to both the column web and the web d oubler plate simultaneously, the welded detail must be configured for pr oper force transfer from the transverse stiffener t o the c olumn web and web d oubler plate. See Section 4.4.4.

(4.3-11)

4.4 Design of Web Doubler Plates

Similarly, for a pair of full-depth transverse stiffeners, the design shear strength of the welds  Rn need n ot exceed any of the f ollowing three f orces:  R n max



0.9F y st (4)( bs  clip)  t s

(4.3-14)

 R n max



0.9  0.6F y st ( l  2  cl i p)  2 t s

(4.3-15)

 R n max



0.9  0.6F y d c  t pz

(4.3-16)

4.4.1 Width and Depth of Web Doubler Plates

In wind, low-seismic and high-seismic applications, the width and depth of web d oubler plates are selected based upon the dimensi ons of the panel-z one, with due c onsideration of the details to be used t o c onnect the web d oubler plate.

P uf – φR nmin 2 2

P uf – φR nmin 1 2

P uf – φR nmin 1+ P uf – φR nmin 2

P uf – φR nmin 2

P uf – φR nmin 1

2

2

Figure 4-10 Force transfer for transverse stiffeners (reverse curvature moment case). 27


If full-depth transverse stiffeners are present, the web doubler plate(s) can be extended t o the transverse stiffeners and one of the weld details illustrated in Figures 4-11 and 4-12 can be used. Alternatively, the web d oubler plate may be extended past the transverse stiffener to clear the zone of the c olumn web subject t o crippling and buckling. As a minimum, this distance is 2.5 times the column k -distance for a directly welded flange or flange-plated moment connecti on and 3 times the column k -distance plus the end-plate plate thickness f or an extended endplate moment connection. The choice between these stiffening alternatives should be an econ omic one made by the fabricator with the approval of the Engineer of Rec ord. Extending the web doubler plate past the transverse stiffener may be desirable in some cases because the top and bott om edges of the web doubler plate can be square-cut and the corners of transverse stiffeners may n ot need t o be clipped to clear the column flange-to-web fillets.18 Additionally,

this detail may be preferable when partial-depth transverse stiffeners are used. H owever, if a web d oubler plate is extended bey ond the transverse stiffener, its thickness must be sufficient t o transmit the full unbalanced f orce in the transverse stiffener, if any, into the panel-z one. If transverse stiffeners are n ot present, the web d oubler plate should extend bey ond the beam flange or m omentc onnecti on flange plate t o clear the z one of the c olumn web subject to crippling and buckling. As a minimum, this distance is 2.5 times the c olumn k -distance f or a directly welded flange or flange-plated m oment c onnecti on and 3 times the c olumn k -distance plus the end-plate plate thickness f or an extended end-plate m oment c onnecti on. 4.4.2 Thickness of Web Doubler Plates

The web d oubler plate thickness is selected t o provide that required in excess of the c olumn web thickness t o resist panel-zone web shear. F or strength, the required web doubler plate thickness is

18 o

A corner clip may still be desirable to separate and simplify the welds n the ends and edge of the transverse stiffener.

Column web Transverse stiffener

Web doubler plate (a)

(c)

Fillet weld made first, remaining gap filled (b)

(d)

Figure 4-11 Common welded joint details at top and bottom edges with one web doubler plate and a pair of transverse stiffeners. 28


t p



V u d p 0.9  0 .6F y d c

For a full-depth transverse stiffener,

(4.4-1)

t p min

where V u dp F y d c

that portion of the t otal panel-z one shear that is carried by the web doubler plate, kips  web d oubler plate specified minimum yield strength, ksi  column depth, in. 





Rust 0.9  0.6F y( l  clip)  4



( Rust )1  ( Rust) 2 0.9  0 .6F y( l  2  clip)  4

(4.4-3)

( Rust )1  ( Rust) 2 0.9  0 .6 F y d c  2

where Ru st  required strength

f the transverse stiffeners (see Section 4.2.1), kips; the subscripts 1 and 2 in Equation 4.4-3 indicate the f orces at each end of the transverse stiffener as illustrated in Figure 4-10 F y  web d oubler plate specified minimum yield strength, in. l  transverse stiffener length, in. clip  transverse stiffener corner clip dimension, in. d c  c olumn depth, in.

When the web doubler plate extends past the transverse stiffener, it must be of sufficient thickness to resist the shear force that is transmitted to the column panel-zone through the transverse stiffener. F or a partial-depth transverse stiffener, t p min



Rust 0 .9  0 .6 F y dc  2

(4.4-2)

o

Column web Transverse stiffener

Web doubler plates (a)

(c)

Fillet welds made first, remaining gaps filled (b)

(d)

Figure 4-12 Common welded joint details at top and bottom edges with two web doubler plates and a pair of transverse stiffeners. 29


In Equations 4.4-2 and 4.4-3, the first term after the equal sign represents the design shear strength per in. of thickness of the web d oubler plate on two shear planes with a length equal to that of the transverse stiffener fillet welds. The second term represents the design shear strength per in. of thickness of the web d oubler plate on oneshear plane with a length equal to the column depth. When a single web doubler plate is used, the column web thickness must also be checked using Equations 4.4-2 and 4.4-3. When a fillet-welded edge detail is used, the minimum web doubler plate thickness t p min t o all o w f or pr oper beveling of the plate19 to clear the column flange-t o-web fillet is: t p min



r  re

 k  t f  re

h d c k

In wind and l ow-seismic applicati ons, to prevent shear buckling of the web doubler plate, the minimum thickness t p min per LRFD Specificatio n Section F2 should be: h F y

(4.4-5)

418

Alternatively, the web d oubler plate can be designed f or shear buckling in accordance with LRFD Specification Appendix F2.2. In high-seismic applications, to prevent shear buckling of the web doubler plate without the use of plug welds between the web doubler plate and the c olumn web, the minimum thickness of both the c olumn web and web d oubler plate per AISC Seismic Provisions Secti on 9.3b and LRFD Specification Section F2 sh ould be: t min



d m  ts  d c  2t f

90



h  F y

418

(4.4-6)

where moment arm between concentrated flange forces, in. t s  transverse stiffener thickness, in. d c  column depth, in. t f  column flange thickness, in. d m

19

c olumn depth, in. distance fr om outside face of c olumn flange t othe web t oe of the flange-t o-web fillet, in.



In wind and l ow-seismic applicati ons and high-seismic applicatio ns involving Ordinary M oment Frames (OMF), web doubler plates are welded al ong their c olumn-flange edges to develop the required shear strength of the web doubler plate; that is, V u dp as used in Equation 4.4-1. In high-seismic applications inv olving Special M oment Frames (SMF) and Intermediate M oment Frames (IMF), web doubler plates are welded al ong their c olumn-flange edges to develop the shear strength of the full webdoubler-plate thickness. Either fillet welds or groove welds can be used; see Figure 4-13. The preferred detail is usually the one that minimizes the amount of weld metal required with due c onsideration of the ass ociated material preparation requirements. It is rec ognized that welding in the flange-t o-web fillet region of wide-flange c olumns carries the p otential f or shrinkage distortions and subsequent cracking due t o restraint and low n otch t ughness (AISC, 1997b). This is o primarily of concern f or the gr oove-welded detail in Figure 4-13a. N onetheless, fabricators may prefer that alternative, which can be combined with g ood quality and process control, inspection, and repair when necessary to maximize efficiency. As another alternative, the detail shown in AISC Seismic Provisi ons Commentary Figure C-9.3c with a pair of web d oubler plates placed symmetrically away from the column web and used integrally with transverse stiffeners top and b ott om can be used. The use of a fillet-welded detail requires a beveled edge to clear the flange-to-web fillet radius and a web d oubler plate thickness that is at least equal to the required bevel. Allowing a slight plate encroachment into the flange-t oweb fillet radius, as illustrated in LRFD Manual Table 9-1 (page 9-12), reduces the required bevel and increases the net section that remains after beveling. Because the flange-to-web fillet region is a sm ooth transition, such slight encroachment does n ot n rmally affect fit-up. The o flange-to-web fillet radius can be estimated by subtracting the flange thickness from the k -distance and rounding the result to the nearest 1/16-in. increment. The reduction in plate thickness due t o beveling must be considered when selecting the plate thickness (Section

(4.4-4)

column flange-to-web fillet radius, which can be estimated by subtracting the flange thickness from the k -distance and r ounding the result t o the nearest 1/16-in. increment, in. r e  permissible encroachment from LRFD Manual Table 9-1 (page 9-12), in. k  distance from outside face of c olumn flange t o the web toe of the flange-t o-web fillet, in. t f  column flange thickness, in.





4.4.3 Connecting Web Doubler Plates to Columns Along the Column-Flange Edges



t p min

d c  2 k , in.

Alternatively, the web doubler plate and the c olumn web can be interconnected with plug welds (see AISC Seismic Provisions C ommentary Section C9.3 and Figure C-9.2) and the total thickness must satisfy the above equati on.

where r





This assumes a 45-degree level. 30


k

Encroachment of web doubler plate into column fillet per LRFD Manual Table 9-1 CJP groove weld may be a non-prequalified detail (see Section 4.4.3)

Bevel, if required

(a) CJP groove-welded detail

k

Encroachment of web doubler plate into column fillet per LRFD Manual Table 9-1

(b) Fillet-welded detail with plate bevel e ual to plate thickness

k

Encroachment of web doubler plate into column fillet per LRFD Manual Table 9-1

(c) Fillet-welded detail with plate bevel less than plate thickness Figure 4-13 Common welded joint details at column-flange edges of web doubler plates.

31


between the top and bottom edges of the web doubler plate and the column web. This is also the case when transverse stiffeners are used and the web doubler plate is extended past the transverse stiffeners as illustrated in Figures 4-4 and 4-5. In these cases, a minimum-size fillet weld per LRFD Specification Table J2.4 is used, except that the minimum size need not exceed the web doubler plate thickness minus When transverse stiffeners are used and the web dou bler plate extends to (but not past) the transvers e stiffener, the joint between the transverse stiffener, column we b and web doubler plate must be detailed consistently with the load path for the unbalanced force in the transverse stiffeners. Several common details are illustrated in Figures 4-11 and 4-12. The strength ch ecks required for each of these details are illustrated in Examples 6-13 and 6-14. In Figures 4-11a and 4-12a, a CJP groove welded joint detail is used at the top and bottom edges of the web dou bler plate(s). In Figures 4-11b and 4-12b, the join t details are essentially the same, except a fillet weld is first made connecting the transverse stiffene r to the column web and the remaining gap to the web doubler plate is subsequently filled with weld metal. In each of these cases, the resulting joint can be used successfully on the thinner range of web doubler plates, say up to thick. Beyond this thickness it is advisable to bevel the edge of the plate. Although this adds to the fabrication costs, it will benefit the welder and increase the probability of making a sound weld. In each of the details illustrated in Figures 4-11a, 4-11b, 4-12a, and 4-12b, one-quarter of the unbalanced force in the transverse stiffeners is transferred at each weld. In Figure 4-11c, a CJP groove weld is used to connect one transverse stiffener to the column web. The web dou bler plate extends to contact the transverse stiffener and is fillet welded to it. In Figure 4-12c, a similar detail is used with web doubler plates on both sides of the column web. If the column web thickness is sufficient to transmit the full unbalanced force from the transverse stiffeners (Equations 4.4-2 and 4.4-3 can be used for this check), the fillet weld between the transverse stiffener and the web doubler plate is selected as a minimum-size fillet weld per LRFD Specification Table J2.4. Otherwise, the joint detail must be configured to transmit the portion of the un balanced force in excess of the column web strength to the web doubler plate. In Figure 4-11d, the fillet welds on the right side connect one side of the transverse stiffener to the column web and the other side to the web doubler plate. In Figure 4-12d, a similar detail is used with web doubler plates on both sides of the column web. In each of these details, one-quarter of the unbalanced force in the transverse stiffeners is transferred at each weld.

4.4.2) and fillet-weld size. There is both a strength and geometric relationship that must be satisfied. When the bevel dimension and plate thickness are equal, as illustrated in Figure 4-13b, the minimu m fillet-weld size to develop the required effective throat in the web doubler plate is: Rev. 3/1/03

( 2) (4.4-7)

When the bevel dimension is less than the plate thickness, as illustrated in Figure 4-13c, the minimum filletweld size to develop the required effective throat in the web doubler plate is: (4.4-8)

where web doubler plate specified minimum yield strength, ksi minimum web doubler plate thickness required for strength per Equation 4.4-1, in. welding electrode specified minimum strength, ksi If a complete-joint-penetration groove weld is used, this joint is generally not an AWS prequalified weld joint, but can be successfully made with slight modification to the following AWS prequalified weld joint designations: (a) C-L1a or C-L1a-GF for web doubler plates that meet the thickness limitation ( ) and plate edges cut square (b) TC-U4a (series) for plate thicknesses exceeding the qualifications of (a) with beveled plate edges The two primary deviations from the prequalified joints are: (1) the root opening will exceed the maximum tolerance, assuming the plate width is selected to match the T -dimension of the column; and, (2) the weld throat will be slightly reduced, due to the flange-to-web fill et radius. As with a fillet weld, however, allowing a slight encroachment into the flange-to-web fillet radius reduces the shop labor required to make the weld by reduci ng the volume to be filled. The above practices are therefore recommended. 4.4.4 Connecting Web Doubler Plates Along the Top and Bottom Edges

When transverse stiffeners are not used and the web doubler plate is extended past the beam flange or flange plate as recommended in Section 4.4.1, there is no force to transfer

32


Chapter 5 SPECIAL CONSIDERATIONS 5.1 Column Stiffening for Beams of Differing Depth and/or Top of Steel

Frequently, beams of differing depths are c onnected with moment connections t o opposite flanges of a c olumn at the same location as illustrated in Figure 5-1a. In other cases, the tops of steel for such beams may be offset as illustrated in Figures 5-1b and 5-1c. For panel-zone web shear, the details illustrated in Figure 5-1 have multiple regions that must be investigated. Region 1 will be critical f ro reverse-curvature bending, while region 2 or 3 will be critical f or opposing m oments. For local strength of the c olumn flanges and/ or web t o resist the concentrated flange f orces, several options exist if transverse stiffening is required. As illustrated in Figures 5-1 and 5-2a, partial-depth transverse stiffeners can be used. H owever, since it is generally advantageous to use as few transverse stiffeners as p ossible, pairs of partial-depth transverse stiffeners can be replaced with sloping full-depth transverse stiffeners as illustrated in Figure 5-2b. The design of sl oping transverse stiffeners is similar to that for diagonal stiffeners. See Section 5.6. Alternatively, it may be possible t o use eccentric fulldepth transverse stiffeners as illustrated in Figure 5-2c. In full-scale tests, Graham, et al. (1959) sh owed that transverse stiffeners with 2-in. eccentricity e provided 65 percent of the strength of identical concentric transverse stiffeners and rapidly declined in effectiveness at greater spacing. It was thus recommended that “f or design purposes it would probably be advisable t o neglect the resistance of stiffeners having eccentricities greater than two inches.” Otherwise, the required transverse stiffener area, width, and thickness can be established by the same criteria as for concentric transverse stiffeners, pr ovided the strength is reduced linearly from 100 percent at zer o eccentricity to 65 percent at 2-in. eccentricity.

1

2

(a)

3 1 2

(b)

3 1

5.2 Column Stiffening for Weak-Axis Moment Connections

2

In s ome cases, m oment c onnections must be made for beams that frame to the webs of wide-flange c olumns. While the mechanics of analysis and design do n ot differ significantly, the details of the force transfer and connection design as well as the ductility considerations required are significantly different. Normally, the connection is configured s o that the field c onnecti on is outside

(c) Figure 5-1 Columns with beams of differing depths and/or tops of steel.

33


f the column flanges. Although this requires that transverse stiffeners (or weak-axis flange c onnecti on plates in this case) be used, it greatly simplifies the erection of the beam, permits the use of an impact wrench t o install all bolts, and increases accessibility and clearance for welding.

In wind and l ow-seismic applicati ons, as indicated in LRFD Manual Part 10 (pages 10-61 thr ough 10-65), weak-axis m oment c onnecti ons t o wide-flange c olumns require special detailing to achieve an acceptable level of ductility (Driscoll and Beedle, 1982; Drisc oll et al., 1983). Several rec ommendati ons are given therein f or the prop orti oning of c olumn stiffening and c onnecti on plates for weak-axis moment c onnecti ons. Additi onally, refer t o Ferrell (1998). Pages 10-61 through 10-65 of the 2nd edition LRFD Manual of Steel Construction and the reference Ferrell (1998) have been reprinted in Appendix D f or ease of reference. In high-seismic applications, column stiffening f or weak-axis moment connections must be c onsistent with that used in the qualifying cyclic testing.

o

5.3 Column Stiffening for Concurrent Strong- and Weak-Axis Moment Connections

(a) Two partial-depth transverse stiffeners

When weak-axis framing is present, the f orce transfer models described in Section 4.2 and c olumn stiffening sizing procedures described in Sections 4.3 and 4.4 must be adjusted for the additi onal f orces induced. Additi onally, the geometry of the transverse stiffeners that may also serve as weak-axis connection plates must be adjusted to provide f or the required ductility as discussed in Section 5.2. Consider the strong-axis m oment c onnection transverse stiffeners that also serve as weak-axis moment c onnection plates illustrated in Figure 5-3 for a “f our-way” m oment connection assembly. The transverse stiffener sizing and connection to the column flanges must be selected t o

(b) One sloped full-depth transverse stiffener ± (P u ) f 4

e

± (P u ) f 2

e

± (P u ) f 1

See Section 5.1 for discussion of eccentricity e . ± (P u ) f 3

(c) One eccentric full-depth transverse stiffener Figure 5-2 Transverse stiffening options at flange offsets.

Figure 5-3 Flange forces from multiple moment connections to one column. 34


transfer the portion of the flange f orces fr om the str ongaxis moment connections ( Pu f ) 1 and ( Pu f ) 2 in excess of the column strength, as well as the flange forces fr om the weak-axis moment connections (Pu f )3 and ( Pu f ) 4 . The transverse stiffener connection t o the column web must be selected to transfer the unbalanced force resulting fr om the flange forces from the strong-axis m oment c onnections ( Pu f )1 and ( Pu f ) 2 . Tamb oli (1999) treats this complex subject in greater depth. When multiple transverse stiffeners and weak-axis flange connection plates are required f or beams of varying nominal depth, adequate clearance must be pr ovided to install the transverse stiffeners. It is recommended that the vertical spacing of transverse stiffeners located on the same side of a c olumn web be n o less than three inches to ensure adequate clearance for welding. A detail such as that in Figure 5-4b may pro vide an eco nomical soluti on. However, a m ore ec on mical arrangement w ould likely o result if the beam sizes were of similar depth as illustrated in Figure 5-4c. In high-seismic applications, column stiffening f or concurrent strong- and weak-axis m oment c onnecti ons must be consistent with that used in the qualifying cyclic testing.

transverse stiffeners t o transmit the f orces t o the c olumn. In any case, eliminating the need f or a web d oubler plate thr ough the selecti on of a c olumn with a thicker web may be the m ost reas onable and ec on omical alternative.

(a)

5.4 Web Doubler Plates as Reinforcement for Local Web Yielding, Web Crippling, and/or Compression Buckling of the Web

e

From LRFD Specification Section K1.10, when required for l ocal web yielding or c ompressi on buckling of the web, the thickness and extent of the web d oubler plate must provide the additional panel-z one thickness necessary t o equal or exceed the required strength and distribute the flange force int o the column web. Additi onally, the web doubler plate must be welded t o devel op the pr op orti on of the total flange force that is transmitted t o the web d oubler plate.

e

See Section 5.1 for discussion of eccentricity e . (b)

5.5 Web Doubler Plates at Locations of Weak-Axis Connections

Sometimes, provision must be made for the attachment of a weak-axis connection to the web of the c olumn thr ough the web doubler plate. The load path illustrated in Figure 5-5 can be used when the edge c onnecti ons of the web doubler plate are adequate t o carry the l oads (Tamb oli, 1999). Otherwise, the shear from the end reacti on of the supported beam must be added algebraicallyt o the vertical shear in the web d oubler plate t o determine the required thickness and weld size. If the beam also were subjected to a small axial tension and/or moment, localized bending would be a major consideration in sizing the web d oubler plate. If the axial tension and/or m oment were significant, however, these components might better be res olved using

(c) Figure 5-4 Transverse stiffening at concurrent strongand weak-axis framing. 35


H = Rx/d m

One shear plane taken in web doubler plate for weak-axis connection shear R u

P uf

R u R u

V

m

d

V = P uf dm /x 1 x x 1 P uf H

Figure 5-5 Force transfer in web doubler plate with weak-axis shear connection.

V us

P uf θ

C s

m

d

M u

P uf

V us

Note: beam shear and column forces not shown above for clarity.

Figure 5-6 Diagonal stiffening.

36


and the diagonal stiffener c ompressive f orce C s is

5.6 Diagonal Stiffeners

A pair of diagonal stiffeners may be used as an alternative to a web doubler plate to reinf orce a c olumn web that has inadequate design panel-zone shear strength. However, the designer should be aware of the increased fabrication costs incurred by the addition of diag onal stiffeners t o a c olumn. As with web d oubler plates, it frequently is less costly to select a member with a thicker web than it is to add the diagonal stiffening. When specified, diagonal stiffeners are sized for the strength that is required in excess of the design shear strength of the column web. The full force in the diag onal stiffener must be develo ped at each end, as for any truss diagonal, using either fillet welds20 or groove welds. The diagonal stiffeners will prevent column web buckling with only a nominal attachment t o the web. From Figure 5-6, the combined h oriz ontal and vertical shear forces may be resolved as a diag onal c ompressive stress in the column web. Thus, a diagonal stiffener may be used to “truss” the column as a c ompression strut. For static equilibrium, the panel-zone shear must be resisted by shear in the column web and the horiz ontal c omponent of the diagonal stiffener design strength. Thus,

 Fu   Rv  Pu f c

o

s( )

Cs

Assuming d m

M u 0.9 d b



V us

 c Pn



(5.6-3)

 c Fcr As

0.9 d b and substituting terms,



V us



 Rv   c Fcr As co s( )

(5.6-4)

Solving for the required diag onal stiffener area, As req





Mu 1 co s( ) (0 .9 d b)   c Fcr



V us  c Fcr





 Rv  c Fcr

(5.6-5) where MuL  M uG , the sum of the factored m oments due to lateral load and gravity l oad, kip-in. d b  beam depth, in. F  c cr  design compressive strength as given in LRFD Specification Section E2, kips  Rv  design shear strength (see Secti on 2.2.1), kips V us  factored story shear due t o the lateral l oad, kips Mu



Letting  Fcr  0.85F y (assumes for diag onal stiffener K l / r  0) and  Rv  0 .90(0 .60 F y d c tw),

(5.6-1)

where, for a connection t o one side of a c olumn, M u  Fu  d m





As req

(5.6-2)





1 1.31 M u cos( ) d b F y



V us  0.64 tw d c 0.85 F y



(5.6-6) 20

Note that it is not always possible to use fillet welds because the roo t angle with diagonal stiffeners may not meet the limitations specified for fillet welds in AWS D1.1.

For a more detailed treatment of diagonal stiffeners, refer to Blodgett (1967).

37



Chapter 6 DESIGN EXAMPLES Neglecting the effects of story shear, the panel-z one web shear force is determined fr om Equati on 2.1-5 as

Example 6-1 Given:

Vu

Determine if transverse stiffeners and/o r a web doubler plate will be required for the directly welded flange m oment connection illustrated in Figure 6-1. The m oment transferred at the connection is 250 ft-kips. The axial compression in the column is 300 kips. The c onnecti on is part of a frame in a wind or l ow-seismic applicati on. Neglect the effects of story shear for calculation purp oses. W1850, F y  50 ksi d  17.99 in. b f  7.495 in. tw  0.355 in. t f  0 .570 in. W1453, F y  50 ksi d  13.92 in. b f  8.060 in. k1  15 /16 in. tw  0.370 in. T  11 in. A  15.6 in. 2

0 .660 in.





Fy A

Pu P y



300 kips 780 kips

250 ft-kips(12 in./ft) 17.99 in.  0.570 in.









780 kips

0.385



0.9  0.6 F y d c t w



0.9  0.6(50 ksi)(13.92 in.)(0.370 in.)



139 kips



V u



172 kips

n.g.

Therefore, the web of the W1453 is inadequate t o resist the panel-zone web shear without reinf orcement.

From Equation 2.1-1, the f orce at each flange is M u d  t f

(50 ksi)(15.6 in. 2)

P y

 Rv

Calculate the flange forces and panel-zone shear force:



172 kips

Since this ratio is less than 0.4, Equation 2.2-1 is applicable.

Solution:

Puf



Assuming the behavior of the panel-z one remains n ominally within the elastic range,

7/16 in. 1 

Puf

Determine the design panel-zone web shear strength:

k t f



Determine the design strength of the flange and web to resist the flange forces in tension:

172 kips

For a tensile flange force, the limit states of local flange bending and l ocal web yieldingmust be checked. F or l ocal flange bending, from Equati on 2.2-8,  R n

W14x53, F y = 50 ksi W18x50, F y = 50 ksi



0.9  6.25 t f 2 F y  C t



0.9  6.25(0.660 in.)2(50 ksi)  1



123 kips



Puf



172 kips

n.g.

For local web yielding, from Equati on 2.2-10,  Rn



1.0  [Ct(5 k)  N] F y t w



1.0  [1(5)(17/16 in.) 



0.570 in.](50 ksi)(0.370 in.)

144 kips



Puf



172 kips

n.g.

Therefore, the flange and web of the W1453 are inadequate to resist the tensile flange force without reinforcement.

Check if column stiffening is required

Determine the design strength of the web to resist the flange forces in compression:

For a c ompressive flange f orce, the limit states of l ocal web yielding, web crippling, and c ompressi on buckling

Figure 6-1 Framing arrangement for Example 6-1. 39


f the web must be checked. In this case, the c ompressi on buckling limit state does not apply because there is a m omentc onnection to oneflange only. F or l ocal web yielding, as determined previously,

by interp olati on between the values that are tabulated f or N  1/2 in. and N  3/4 in.

o

 R n



144 kips

Puf





172 kips

Example 6-2

n.g.

Given:

For web crippling, fr om Equati on 2.2-12, N d 

 R n







3 N d c



3(0.570 in.) 13.92 in.



For the framing arrangement given in Example 6-1, reselect the column size to eliminate the need for stiffening.

0.123

0.75  135Ct tw2 1  N d

1.5

 t w t f

Solution:

 Ft t

y f

Try a W1474 with F y

w

0.75  135(1)(0.370 in.) 2 







1  (0.123)



0.370 in. 0.660 in.

 1.5



Puf





Fy A

Pu P y



300 kips 1,090 kips

Therefore, the web of the W1453 is inadequate to resist the compressive flange f orce without reinf orcement.

1,090 kips

0 .4,

V u

Fro m Table B-1, with N



0.570 in.,

 R n

n.g.









0.275

172 kips

 Rv

172 kips



From Table A-1, with Pu/ P y

(50 ksi)(0.660 in.) 0.370 in.

138 kips

50 ksi:

(50 ksi)(21.8 in. 2)

P y







172 kips

o.k.



173 kips ( T)



Puf



172 kips

o.k.



189 kips ( C)



Puf



172 kips

o.k.

by interpo lation between the values that are tabulated f or N  1 /2 in. and N  3/4 in.

Summary:

Summary:

As illustrated in Figure 6-1, the W1453 is inadequate to resist the local forces that are induced without column stiffening. For the selection of a c olumn that is adequate without stiffening, refer t o Example 6-2. For the design of stiffening for the W14 53, refer to Example 6-3.

As illustrated in Figure 6-2, a W14 74 c olumn ( F y  50 ksi) can be used without stiffening. This c olumn-weight increase of 21 lb/ft ( 74  53) is well within the range

Comments:

The foreg oing s oluti on can be determined m ore expediently using the design aids in Appendices A and B. The design panel-zone web shear strength is determined fr om Table A-1 where, for a W14 53 with Pu/ P y  0 .4,  Rv



139 kips



V u

172 kips



W14x74, F y = 50 ksi W18x50, F y = 50 ksi

n.g.

The design strength of the flange and web t o resist the flange force in tensi on is determined from Table B-1 where, for a W1453, with N  0 .570 in. and reading from the T (tension) c olumn,  R n



123 kips



Puf



172 kips

n.g.

Column stiffening is not required

by interpolation between the values that are tabulated f or N  1 /2 in. and N  3/4 in. The design strength of the web to resist the flange force in compressi on is als o determined from Table B-1 where, for a W14 53, with N  0 .570 in. and reading from the C (compressi on) c olumn,  R n



138 kips



Puf



172 kips

Figure 6-2 Framing arrangement for Example 6-2.

n.g. 40


identified aseconomical in Chapter 3 for the elimination of two pairs of partial-depth transverse stiffeners and a web doubler plate.

t p min



Example 6-3

For the framing arrangement given in Example 6-1 (a wind or l ow-seismic application), design the transverse stiffeners and web d oubler plate that are required t o increase the local column strength of the W1453 c olumn. Use a stiffening detail with a pair of partial-depth transverse stiffeners at each beam flange and a web d oubler plate on one side only that extends past the transverse stiffeners by 2.5 k (nominally). Use ASTM A36 material f or the stiffening elements, transverse stiffeners with filletwelded joint details and two alternative solutions as follows:

t p min

Solution A: Calculate the transverse stiffener forces and web doubler plate shear force:

From Equation 4.2-1, the required strength f or the transverse stiffeners is 

Vu

  Rv cw 

172 kips  139 kips



33 kips

For strength, from Equation 4.4-1, V u dp 0.9  0.6F y d c



0.122 in.



0.528 in.





re  1 7/16 in.  0.660 in.  1/4 in.



1.70 F y t eff F EX X



t eff  2



1.70(36 ksi)(0.122 in.) 70 ksi



0.107 in.





(0.122 in.)  2

0.172 in.

where t eff is the web doubler plate thickness required f or strength per Equation 4.4-1. From LRFD Specification Table J2.4, with a 5/8-in.-thick web d oubler plate and 0.660in.-thick column flange, the minimum fillet-weld size is 1 / in. Use 1/ -in. fillet welds to connect the web doubler 4 4 plate to the column flanges. The top and bott om edges of the web d oubler plate are welded to the column web with minimum-size fillet welds per LRFD Specification Table J2.4. From LRFD Specification Table J2.4, with a 5/8-in.-thick web d oubler plate and 0.370-in.-thick c olumn web, the minimum fillet-weld size is 1/4 in. Use 1/4-in. fillet welds to connectthe top and bottom edges of the web doubler plate to the column web.

Design the web doubler plate and its associated welding:



k  t f

172 kips  123 kips  49 kips

Check that the unbalanced load from the transverse stiffener that attaches directly to the web doubler plate is not more critical than the panel-zone web shear. F or this case, the unbalanced load in one transverse stiffener is one-half of R u st or 24.5 kips. Thus, the panel-z one web shear f orce is more critical than the unbalanced load fr om the transverse stiffener.

t p min



wmin

From Equati on 4.2-2, the required strength f or the web doubler plate is 

0.181 in.

The thickness required for c onstructability g overns. The web d oubler plate width and depth are selected based upon the dimensions of the panel-z one and the edge details. Transverse to the axis of the column, the web d oubler plate dimension is selected equal to the clear distance between the column flanges, which is 12 9/16 in. Parallel t o the axis of the column, the web d oubler plate dimensi on is selected equal to the beam depth plus two times 2.5 k , which is nominally 25 1/4 in. Use PL 5/8 in.  12 9/16 in.  2’-1 1/4. Note that, once the transverse stiffeners are designed, the web d oubler plate will have to be checked for shear strength t o carry the reaction from one transverse stiffener at each flange int o the column panel-zone. The column-flange edges are to be fillet welded. Therefore, the web doubler plate must have a 5/8-in.  5/8-in. bevel along each of these edges. F or adequate weld and plate strength at the bevel, from Equation 4.4-7,

A) fillet-welded joint details between the web doubler plate and the column flanges and web. B) a groove-welded j oint detail between the web d oubler plate and the column flanges and a fillet-welded joint detail t o the c olumn web.

V u dp

418

[13.92 in.  2(0.660 in.)]  36 ksi 418



Check minimum thickness required to facilitate the filletwelded joint detail between the web doubler plate and the column flange (for c onstructability). From Equati on 4.4-4,

Given:

Ru st  Puf   R n min

h  F y



33 kips 0.9  0.6(36 ksi)(13.92 in.)

Design the transverse stiffeners and their associated welding:

Check minimum thickness required to prevent shear buckling of the web d oubler plate. From Equation 4.4-5,

From Equation 4.3-1, the minimum required cr oss41


F or weld shear strength with 1/4-in. fillet welds, using a rearranged form of Equati on 4.3-9,

sectional area for the transverse stiffeners at each flange is Ast min



R ust  F yst



49 kips 0.9(36 ksi)



1.51 in.2 lmin

From Equation 4.3-2, the minimum width of each transverse stiffener, checking the side without the web doubler plate as the worst case, is bs min

b



3



t pz

2



7.495 in. 3



0.370 in. 2





2.31 in.









Try a

3/ -in. 8

t



bs  F yst

2 95 0.570 in. (3 in.)  36 ksi  2 95 0.285 in.



lmin

Ast  2(3/8 in.)(3 in.  3/4 in.)

1.69 in.2



Ast min



1.51 in. 2

o.k.

wmin





F EX X



49 kips 0.75  0.6(70

Rust  clip 4(0.9  0 .6 F y t)



49 kips 4[0.9  0.6(50 ksi)(0.370 in.)]



1.23 in.

0.182 in.  3/16 in.

R ust 0.9  0.6 F yst ts  2



49 kips 0.9  0.6(36 ksi)( 3/8 in.)  2

 34

/ in.

Rust 0.9  0 .6 F y d c  2



49 kips 0.9  0.6(50 ksi)(13.92 in.)  2



0.0652 in.

 tw 

0 .370 in.

lmin





d

2t f 2



6.30 in.



o.k.

13.92 in.  2(0.660 in.) 2

governs

Use 2 PL 3/8-in.  3 in.  0’-6 1/2 with one 3/4-in.  3/4in. corner clip each and 1/4 -in. double-sided fillet welds to connect the transverse stiffeners to the column web and web doubler plate. Solution B: Calculate the transverse stiffener forces and web doubler plate shear force: R u st  49 kips



/ in.



From S oluti on A, in.

 34

The minimum transverse stiffener length, from LRFD Specification Section K1 (as summarized in Sections 4.1.2 through 4.1.5), is

 clip

 3 /4

 2



0.943(36 ksi)( 3/8 in.) 70 ksi



ksi)( 1/4 in.)  2 

2.95 in.

t min

From LRFD Specification Table J2.4, with a 3/8-in.-thick transverse stiffener and 0.660-in.-thick column flange, the minimum weld size is 1/4 in. Use 1/4 -in. double-sided fillet welds to connect the transverse stiffeners to the column flange. The length of the transverse stiffeners and the d oublesided fillet welds connecting them to the c olumn web or web doubler plate are selected to transmit the force in the transverse stiffener and minimize the required fillet weld size. From LRFD Specification Table J2.4, with a 3/8-in.thick transverse stiffener, 5/8-in-thick web d oubler plate and 0.370-in.-thick c olumn web, the minimum weld size is 1/4 in. Try 1/4 -in. fillet welds. For shear strength in the transverse stiffener, using a rearranged form of Equati on 4.3-4, lmin

 clip

Checking the second term after the equal sign in Equation 4.4-2,

The d ouble-sided fillet welds c onnecting the transverse stiffeners to the column flanges are sized to devel op the strength of the welded p ortion of the transverse stiffener. From Equation 4.3-6, the weld size required f or strength is 0.943F yst t s

0.75  0.6 F EX X w  2   2

0.189 in.

transverse stiffener thickness.



Rust

For shear strength in the column web and web d oubler plate with each element checked against one-half of Ru st , the 0.370-in.-thick column web with F y  50 ksi is m ore critical than the 5/8-in.-thick web doubler plate with F y  36 ksi. Using a rearranged f orm of the first term after the equal sign in Equation 4.4-2,

Try a pair of 3-in.-wide transverse stiffeners at each beam flange with 3/4-in.  3/4-in. c orner clips. Fr om Equati on 4.3-3, the minimum thickness is t s min



4.11 in.

V u dp 42




33 kips

Try a pair of 3-in.-wide transverse stiffeners at each beam flange with 3/4-in.  3/4-in. corner clips. Fr om Equati on 4.3-3, the minimum thickness is

Design the web doubler plate and its associated welding:

For strength, fr om Equation 4.4-1, t p





V u dp 0.9  0.6F y d c



33 kips 0.9  0.6(36 ksi)(13.92 in.)

t s min

0.122 in. 

Check minimum thickness required to prevent shear buckling of the web doubler plate. From Equation 4.4-5, t p min





h  F y



418



[13.92 in.  2(0.660 in.)]  36 ksi 418



wmin

3



R ust  F yst

t pz

2



0.189 in.



49 kips 0.9(36 ksi)





7.495 in. 3





lmin



1 .51 in. 2

F EX X



o.k.

0.943(36 ksi)( 3/8 in.) 70 ksi

0.182 in.  3/16 in.



Rust 0.9  0.6F yst ts  2



49 kips 0.9  0.6(36 ksi)( 3/8 in.)  2

 clip

 34

/ in.  4.11 in.

For weld shear strength with 3/16-in. fillet welds, using a rearranged form of Equati on 4.3-9, lmin



Ast min

0.943F yst t s

1.51 in.2

0.370 in. 2



From LRFD Specification Table J2.4, with a 3/8-in.-thick transverse stiffener and 0.660-in.-thick column flange, the minimum weld size is 1/4 in. Use 1/4 -in. double-sided fillet welds to connect the transverse stiffeners to the column flange. The length of the transverse stiffeners and the d oublesided fillet welds connecting them to the column web or web doubler plate are selected to transmit the force in the transverse stiffener and minimize the required fillet weld size. From LRFD Specification Table J2.4, with a 3/8-in.thick transverse stiffener, 1/4-in-thick web d oubler plate and 0.370-in.-thick c olumn web, the minimum weld size is 3/16-in. Try 3/16-in. fillet welds. For shear strength in the transverse stiffener, using a rearranged form of Equati on 4.3-4,

From Equation 4.3-2, the minimum width of each transverse stiffener, checking the side without the web doubler plate as the worst case, is b

0.285 in.

1.69 in.2



From Equation 4.3-1, the minimum required crosssectional area for the transverse stiffeners at each flange is



2 95 0.570 in. (3 in.)  36 ksi  2 95

The double-sided fillet welds c onnecting the transverse stiffeners to the column flanges are sized t o devel op the strength of the welded p ortion of the transverse stiffener. From Equation 4.3-6, the weld size required f or strength is




bs  F yst



Ast  2(3/8 in.)(3 in.  3/4 in.)

0.181 in.

Ast min

t

Try a 3/8-in. transverse stiffener thickness.

The thickness required to prevent shear buckling of the web doubler plate governs. The web d oubler plate width and depth are selected based upon the dimensions of the panel-z one and the edge details. Transverse to the axis of the column, the web d oubler plate dimension is selected equal to the T-dimension of the c olumn, plus twice the permissible encr oachment from LRFD Manual Table 9-1 (page 9-12), which is 11 in.  2( 1/4 in.)  11 1/2 in. Parallel t o the axis of the c olumn, the web doubler plate dimensi on is selected equal t o the beam depth plus two times 2.5 k , which is nominally 251/4 in. Use PL 1/4 in.  11 1/2 in.  2’-1 1/4. Note that, once the transverse stiffeners are designed, the web d oubler plate will have to be checked for shear strength t o carry the reaction from one transverse stiffener at each flange into the column panel-zone. The column-flange edges are t o be CJP gr oove welded. Use 1/4 -in. CJP groove welds to connect the web doubler plate to the column flanges. The top and bottom edges of the web d oubler plate are welded to the column web with minimum-size fillet welds per LRFD Specification Table J2.4. Fr om LRFD Specification Table J2.4, with a 1/4 -in.-thick web d oubler plate and 0.370-in.-thick c olumn web, the minimum fillet-weld size is 3/16 in. Use 3/16-in. fillet welds to connect the top and bottom edges of the web doubler plate to the column web.

bs min







2.31 in.



R ust

0.75  0.6 F EX X w  2   2

 clip

49 kips 0.75  0.6(70

ksi)( 3/16 in.)  2 

3.68 in.

43


 2

 34

/ in.

For shear strength in the column web and web d oubler plate with each element checked against o ne-half of Ru st , the 1/4-in.-thick web doubler plate with F y  36 ksi is more critical than the 0.370-in.-thick column web with F y  50 ksi. Using a rearranged form of the first term after the equal sign in Equation 4.4-2, lmin



R ust  clip 4(0.9  0 .6 F y t)



49 kips 4[0.9  0.6(36 ksi)( 1/4 in.)]

34

/ in.



to connect the transverse stiffeners to the column web and web doubler plate. Summary A:

The use of a W14 53 c olumn requires the use of a web doubler plate and a pair of transverse stiffeners at the l ocation of each beam flange. The web d oubler plate required is a PL 5/8 in.  12 9/16 in.  2’-1 1/4 with 5/8-in.  5 / -in. bevels on the c olumn-flanges edges. It is welded t o 8 the column flanges along the column-flange edges and t o the column web al ong the top and b ott om edges with 1/4in. single-sided fillet welds. The partial-depth transverse stiffeners required are 4 PL 3/8-in.  3 in.  0’-6 1/2 with 3 3 one /4 -in.  /4 -in. c orner clip each. Each transverse stiffener is welded to the column flange and the c olumn web 1 or web d oubler plate with /4-in. d ouble-sided fillet welds. This column-stiffening c onfigurati on is illustrated in Figure 6-3.

3.27 in.

Checking the second term after the equal sign in Equation 4.4-2, t min



R ust 0.9  0 .6F y d c  2



49 kips 0.9  0.6(36 ksi)(13.92 in.)  2



0.0905 in.

 t p 

1/ in. 4

Summary B:

o.k.

The use of a W14 53 c olumn requires the use of a web doubler plate and a pair of transverse stiffeners at the l ocation of each beam flange. The web d oubler plate required is a PL 1/4 in.  11 1/2 in.  2’-1 1/4. It is welded t o the column flanges along the c olumn-flange edges with 1/4-in. CJP groove welds and t o the c olumn web al ong the t op and bottom edges with 3/16-in. single-sided fillet welds. The partial-depth transverse stiffeners required are 4 PL 3/8in.  3 in.  0’-6 1/2 with one 3/4-in.  3/4-in. c orner clip each. Each transverse stiffener is welded to the c olumn

The minimum transverse stiffener length, from LRFD Specification Section K1 (as summarized in Sections 4.1.2 through 4.1.5), is lmin





d

2t f 2



6.30 in.



13.92 in.  2(0.660 in.) 2

governs

Use 2 PL 3/8-in.  3 in.  0’-6 1/2 with one 3/4-in.  3/4in. corner clip each and 3/16 -in. double-sided fillet welds

W14x53, F y = 50 ksi typ.

typ.

1

/ 4

W18x50, F y = 50 ksi

1

/ 4

1

typ.

/ 4

1

/ 4 1

3

2 PL / 8 × 3 × 0’-6 / 2, F y = 36 ksi, 3 at each beam flange with one / 4 3 × / 4 corner clip each

1

typ.

/ 4

1

/ 4

5

9

3

PL / 8 × 12 / 16 × 2’-1 / 4, F y = 36 5 5 ksi, with / 8 × / 8 bevels on vertical edges Figure 6-3 Framing arrangement for Example 6-3 (Solution A). 44


flange with 1/4-in. double-sided fillet welds and t o the c olumn web or web d oubler plate with 3/16-in. d ouble-sided fillet welds. This column-stiffening configuration is illustrated in Figure 6-4.

at each c onnecti on are: 250 ft-kips due t o lateral l oad, 100 ft-kips due t o t otal gravity l oad and 45 ft-kips due t o dead l oad only. The axial c ompressi on in the c olumn is 500 kips. The c onnecti ons are part of a frame in a wind or low-seismic applicatio n. Neglect the effects of story shear for calculation purposes.

Example 6-4 Given:

W1850, F y

Determine if transverse stiffeners and/o r a web doubler plate will be required f or the flange-plated m oment c onnection illustrated in Figure 6-5. The moments transferred

d tw

 



50 ksi

17.99 in.

b f

0.355 in.

t f

 

7.495 in.

0 .570 in.

W14x53, F y = 50 ksi typ.

typ.

3

/ 16

W18x50, F y = 50 ksi

1

/ 4 / 16

3

typ.

3

/ 16 1

3

2 PL / 8 × 3 × 0’-6 / 2, F y = 36 ksi, 3 at each beam flange with one / 4 3 × / 4 corner clip each

1

typ.

/ 4 / 4

1

1

1

1

PL / 4 × 11 / 2 × 2’-1 / 4, F y = 36 ksi Figure 6-4 Framing arrangement for Example 6-3 (Solution B).

W14x90, F y = 50 ksi W18x50, F y = 50 ksi

3

W18x50, F y = 50 ksi

1

/ 4 -in.-thick × 7 / 2 - in.-wide flange plate (typ.)




W1490, F y  50 ksi d  14.02 in. b f  14.520 in. k1  7 /8 in. tw  0.440 in. 1 T  11 /4 in. A  26.5 in.2

Vu k t f

3/8 in. 1 

0 .710 in.



( Puf )1  ( Puf ) 2






355 kips

Use 3/4-in.-thick by 7 1/2-in.-wide flange plates.


Solution:

Assuming the behavior of the panel-z one remains n ominally within the elastic range,


The worst-case flange force for all limit states except compression buckling of the web and panel-z one web shear is that due to the c ombined effects of the 250 ft-kip m oment due to lateral load and the 100 ft-kip moment due t o t otal gravity load. From Equation 2.1-1, the c orresp onding flange force is Puf  

M u d  t pl





Fy A

Pu P y



500 kips 1,330 kips

 Rv

(250 ft-kips  100 ft-kips)(12 in./ft) (17.99 in.  3/4 in.)

The w orst-case flange fo rce for the web c ompressi on buckling limit state is that due to the combined effects of the opposing 100 ft-kip m oments due t o t otal gravity l oad. From Equati on 2.1-1, the c orresp onding flange f orce is 



M u d  t pl



( Puf )2





0.9  0.6F y d c t w



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)



167 kips

V u





355 kips

n.g.



0.9  6.25t f 2 F y  C t



0.9  6.25(0.710 in.)2(50 ksi)  1



142 kips



Puf



224 kips

n.g.

For local web yielding, from Equati on 2.2-10,  R n

d  t pl

224 kips



 R n

( M u )1



0.376

For a tensile flange f orce, the limit states of local flange bending and local web yieldingmust be checked. F or l ocal flange bending, from Equati on 2.2-8,

64.0 kips



1,330 kips


(100 ft-kips)(12 in./ft) (17.99 in.  3/4 in.)

(250 ft-kips  100 ft-kips)(12 in./ft) (17.99 in.  3/4 in.)





Therefore, the web of the W1490 is inadequate t o resist the panel-zone web shear without reinforcement.

Neglecting the effects of story shear, the worst-case panelzone web shear f orce is that due t o the c ombined effects of the two 250 ft-kip m oment due t o lateral l oad (in reverse curvature), the 100 ft-kip m oment due t o t otal gravity l oad on one side (adding) and the 45 ft-kip m oment due t o dead load only on the other side (subtracting). Fr om Equati on 2.1-1, the c orresponding flange f orces are ( Puf )1




224 kips

Puf 

(50 ksi)(26.5 in. 2)

P y



1.0  [Ct (5 k)  N] F y t w



1.0  [1(5)(1 3/8 in.)  3/4 in.](50 ksi)(0.440 in.)



168 kips



Puf



224 kips

n.g.

Therefore, the flange and web of the W1490 are inadequate to resist the tensile flange force without reinforcement.

( M u )2


d  t pl



250 ft-kips  45 ft-kips)(12 in./ft) (17.99 in.  3/4 in.)



131 kips

For a c ompressive flange f orce, the limit states of l ocal web yielding, web crippling, and c ompressi on buckling of the web must be checked. F or l ocal web yielding, as determined previously,  R n

The corresponding panel-zone web shear f orce is determined from Equation 2.1-5 as



168 kips



Puf



224 kips

For web crippling, fr om Equati on 2.2-12, 46


n.g.

N d 

 R n



d



3( 3/4 in.) 14.02 in.



0.75  135Ct tw2 1  N d





3 N



1.5

 t w t f

 Ft t

y f

 Rn

w



190 kips



Puf



(50 ksi)(0.710 in.) 0.440 in.

224 kips



0.90 

n.g.

Try a W14193 with F y 

Fy A

h

Pu P y



500 kips 2,840 kips

4,100(1)(0.440 in.)3  50 ksi 14.02 in.  2(1 3/8 in.)



197 kips





Puf



64 .0 kips

 Rv

o.k.



 R n

The W1490 is inadequate t o resist the l ocal f orces that are induced without c olumn stiffening. F or the selection lumn that is adequate with out stiffening, refer t o of a c o Example 6-5. For the design of stiffeningf or the W14 90, refer to Example 6-6.

V u



355 kips



142 kips



Puf



224 kips



168 kips



Puf



224 kips

0.176





V u

0 .4,



355 kips

o.k.



506 kips(T)



Puf



224 kips

o.k.



506 kips(C)



Puf



224 kips

o.k.



1,640 kips ( compression buckling)



Puf  64.0 kips

o.k.

Given:

For the framing arrangement given in Example 6-4 (a wind or l ow-seismic application), design the transverse stiffeners and web doubler plates that are required t o increase the local column strength. Use a stiffening detail with a pair of full-depth transverse stiffeners at each flange plate and a pair of web doubler plates that extend t o the transverse stiffeners (Figure 4-12a). Use ASTM A36 material for the stiffening elements, transverse stiffeners with fillet-welded joint details and groove-welded web d oubler plate edge details.

n.g.

The design strength of the web t o resist the flange f orce in compressi on is also determined from Table B-1 where, for a W14 90, with N  3/4 in. and reading fr om the C column,  R n

372 kips

2,840 kips

Example 6-6

n.g.

The design strength of the flange and web t o resist the flange force in tension is determined fr om Table B-1 where, for a W1490, with N  3/4 in. and reading fr om the T column,  R n





As illustrated in Figure 6-6, a W14193 column ( F y  50 ksi) can be used without stiffening. This c olumnweightincrease of 103 lb/ft ( 193 90) is well withinthe range identified as econ omical in Chapter 3 f or the elimination of tw o pairs of full-depth transverse stiffeners and a web doubler plate.

The foreg oing s oluti on can be determined m ore expediently using the design aids in Appendices A and B. The design panel-zone web shear strength is determined fr om Table A-1 where, for a W14 90 with Pu/ P y  0 .4, 

50 ksi:

Summary:

Comments:

167 kips

o.k.

From Table B-1, with N  3/4 in.,

Summary:







From Table A-1, with Pu/ P y

Therefore, the web of the W14 90 is inadequate t o resist the compressive flange force without reinf orcement, except for the web compressi on buckling limit state.

 Rv

64 .0 kips

(50 ksi)(56.8 in. 2)

P y

0.90 



Solution:

4,100Ct tw3  F y



Puf



For the framing arrangement given in Example 6-4, reselect the column size to eliminate the need for stiffening.

For compressi on buckling of the web, fr om Equati on 2.213,  R n

197 kips

Given:

   1.5



Example 6-5

0.75  135(1)(0.440 in.) 2

0.440 in. 1  (0.160) 0.710 in. 

The design strength of the web t o resist c ompressi on buckling is also determined from Table B-1 where, f or a W1490,

0.160

n.g. 47


The thickness required for strength g overns. The web d oubler plate width and depth are selected based upon the dimensi ons of the panel-z one and the edge details. Transverse t o the axis of the c olumn, the web doubler plate dimensi on is selected equal t o the Tdimension of the c olumn, plus twice the permissible encroachment from LRFD Manual Table 9-1 (page 9-12), which is 11 1/4 in.  2( 1/4 in.)  11 3/4 in. Parallel t o the axis of the column, the web d oubler plate dimensi on is selected equal to the beam depth plus two times the flangeplate thickness minus two times the transverse stiffener thickness minus two times the root opening f or the CJP groove weld that will be used t o c onnect the web d oubler plate along the top and bottom edges. Assuming 1/2-in. transverse stiffener thickness and a 3/8-in. r oot opening f or the CJP groove weld, 17.99 in.  2( 3/4-in.)  2( 1/2-in.)  2(3/8-in.)  173/4 in., n ominally. Use 2 PL 3/8 in.  11 3/4 in.  1’-5 3/4. The column-flange edges are t o be CJP gr oove welded. Use 3/8 -in. CJP groove welds to connect the web doubler plates to the column flanges. The top and bott om edges of the web d oubler plates are welded to the column web and transverse stiffeners with CJP groove welds. Use 3/8-in. CJP groove welds to connect the top and bottom edges of the web doubler plate to the column web.

Solution: Calculate the transverse stiffener forces and web doubler plate shear force:

From Equation 4.2-1, the required strength f or the transverse stiffeners is R u st  Puf   R n min 




82 kips

From Equation 4.2-2, the required strength f or the tw o web doubler plates is V u dp



V u   Rv



188 kips


cw 

Design the web doubler plates and their associated welding:

For strength, fr om Equation 4.4-1, the t otal thickness of web doubler plates required is t p



V udp 0.9  0.6F y d c



188 kips 0.9  0.6(36 ksi)(14.02 in.)



0.690 in. ( or 0.345 in. per plate)

Check minimum thickness required to prevent shear buckling of the web doubler plate. From Equati on 4.4-5, t p min





h  F y

418




From Equation 4.3-1, the minimum required crosssectional area for the transverse stiffeners at each flange is

[14.02 in.  2(0.710 in.)]  36 ksi 418

Ast min

0.181 in.



R ust  F yst



82 kips 0.9(36 ksi)

W14x193, F y = 50 ksi W18x50, F y = 50 ksi

3

W18x50, F y = 50 ksi

1

/ 4 -in.-thick × 7 / 2 - in.-wide flange plate (typ.)






2.53 in.2

From Equati on 4.3-2, the minimum width of each transverse stiffener is bs min



b

3

t pz





2

7 1/2 in. 3



0.440 in. 2



strength of the welded p orti on of the transverse stiffener. From Equati on 4.3-6, the weld size required f or strength is

2.28 in. wmin

Try a pair of 3 1/2-in.-wide transverse stiffeners at each beam flange with 3/4-in.  3/4-in. corner clips. From Equation 4.3-3, the minimum thickness is t s min







t



2 3 / 4

in. 2



95

0.375 in.

(3 1/2 in.)  36 ksi 95 

0.221 in.

Try a 1/2-in. transverse stiffener thickness. Ast  2( 1/2 in.)(3 1/2 in.  3/4 in.) 

2.75 in.2



Ast min



2.53 in. 2

o.k.

w

The length of the transverse stiffeners is selected equal t o the depth of the column minus two times the c olumn flange thickness, which is 14.02 in.  2(0.710 in.)  12 5/8 in. Check the shear strength of the transverse stiffener to transmit the unbalance force in the transverse stiffener to the column panel-zone. Neglecting the effects of st ory shear, the worst-case unbalanced force in the transverse stiffener is that due to the combined effects of the tw o 250 ft-kip moment due to lateral load (in reverse curvature), the 100 ft-kip m oment due t o t otal gravity l oad on one side (adding) and the 45 ft-kip m oment due t o dead l oad only on the other side (subtracting). The unbalanced f orce in the transverse stiffener is ( Rust )1  ( Rust ) 2



( Puf



(224 kips  142 kips) 

  R n min

)1  ( Puf

  R n min





F EX X

0.943(36 ksi)( 1/2 in.) 70 ksi

0.242 in.  1/4 in.

( Rust )1  ( Rust ) 2



0.75  0.6 F EX X ( l  2  clip)  2





 2

82 kips



0.75  0.6(70 ksi)(12.6 in.



2  3/4 in.)



2



 2

0.0829 in.

From LRFD Specification Table J2.4, the minimum weld size for the 1/2-in.-thick transverse stiffener, 3/8-in-thick web doubler plate and 0.440-in.-thick column web is 3/ 16 in. Use 3/16-in. fillet welds. Each 3/8-in. CJP groove weld must transmit one-quarter of the 82-kip unbalanced f orce in the transverse stiffeners (20.5 kips). From LRFD Specificati on Table J2.5, the shear strength is the lesser of that on the effective area in the transverse stiffener base metal and that in the weld itself. For the transverse stiffener base metal,

)2

 R n

(131 kips  168 kips)





0.9  0.6F yst w ( l  2  clip)



82 kips  0 kips



0.9  0.6(36 ksi)( 3/8 in.)(12.6 in.  2



82 kips



80.9 kips  20.5 kips

From Equati on 4.3-5, t s

0.943 F yst t s

From LRFD Specification Table J2.4, with 1/2-in.-thick transverse stiffeners and 0.710-in.-thick c olumn flanges, the minimum weld size is 1/4 in. Use 1/4 -in. double-sided fillet welds to connect the transverse stiffeners to the column flange. The transverse stiffeners are to be c onnected t o the c olumn panel zonewith a detail thatc ombinestwo fillet welds and two CJP groove weld as illustrated in Figure 4-12a. From Equati on 4.3-10, the fillet weld size required for strength is

bs  F yst







3/ in.) 4



3/ in.) 4

o.k.

For the weld metal,  R n

( Rust )1  ( Rust) 2 0.9  0 .6 F yst ( l  2  clip)  2)



82 kips 0.9  0.6(36 ksi)(12.6 in.  2  3/4 in.)



0.190 in.



2





0.8  0.6FEXX w ( l  2



0.8  0.6(70 ksi)( 3/8 in.)(12.6 in.  2



140 kips  20.5 kips



clip)

o.k.

The c olumn web and web d oubler plate thicknesses must also be checked f or shear strength t o transmit the unbalanced fo rce in the transverse stiffeners t o the panelzone. For this detail, one-half of the unbalanced f orce (41 kips, the shear transmitted by the fillet welds) can be assigned to the c olumn web with one-quarter (20.5 kips, the shear transmitted by each CJP groove weld) assigned t o

Therefore, a 1/2-in. transverse stiffener thickness is o.k. Use 2 PL 1/2-in.  3 1/2 in.  1’-0 9/16 with two 3/4-in.  3 /4-in. corner clips each at each flange plate. The double-sided fillet welds connecting the transverse stiffeners to the column flanges are sized to devel op the 49


each web doubler plate. For the c olumn web, the design shear strength is  R n



0.9  0.6F y d c t w



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)



167 kips  41 kips

at the l ocati on of each beam flange plate. The web d oubler plates required are 2 PL 3/8 in.  11 3/4 in.  1’-5 3/4. They are welded to the column flanges along the c olumnflange edges and to the column web and transverse stiffeners along the top and bott om edges with 3/8-in. CJP gr oove welds. The transverse stiffeners required are 4 PL 1/2-in.  3 1/2 in.  1’-0 9/16 with tw o 3/4-in.  3/4-in. c orner clip each. Each transverse stiffener is welded to the column flange with 1/4-in. double-sided fillet welds and t o the c olumn web and web d oubler plates with a c ombinati on of a 3 / -in. single-sided fillet weld and 3/ -in. CJP groove weld. 16 8 This column-stiffening c onfigurati on is illustrated in Figure 6-7.

o.k.

For the web doubler plate, the design shear strength is  R n



0.9  0.6F ydp d c t pl



0.9  0.6(36 ksi)(14.02 in.)( 3/8 in.)




o.k.

Therefore, the column web and web d oubler plates are of adequate thickness to provide for pr oper f orce transfer of the unbalance force in the transverse stiffener to the panelzone. If either the c olumn web or the web d oubler plate thickness were inadequate in the above calculations, shear transfer between these elements on the effective area of the CJP groove weld r oot area can be utilized as a l oad path. Note, however, that if f orce is to be transferred fr om the column web to the web d oubler plate in this manner, the maximum f orce transfer may be limited by the design shearstrength on the effective area at the juncture between the CJP groove weld and the web d oubler plate.

Example 6-7 Given:

Repeat Example 6-1 using a f our-b olt extended end-plate moment connection as illustrated in Figure 6-8 instead of a directly welded flange moment c onnection. For the endplate thickness, use 3/4 in. For the beam-flange-to-endplate welds, use 1/2-in. fillet welds on both sides of the beam flange. Use the following end-plate parameters in the calculations (see Section 2.2.2): p f

Summary:



1 1/2 in.

g  5 1/2 in.

The use of a W14 90 c olumn requires the use of a pair of web d oubler plates and a pair of transverse stiffeners

d b



1 in.

1

typ.

/ 4

1

/ 4 / 8

3

typ.

W14x90, F y = 50 ksi

3

/ 16

W18x50, F y = 50 ksi

W18x50, F y = 50 ksi

1

3

1

/ 4 -in.-thick × 7 / 2 -in.-wide flange plate (typ.) typ.

9

1

2 PL / 2 × 3 / 2 × 1’-0 / 16 , F y = 36 ksi, at each beam flange with 3 3 two / 4 × / 4 corner clips each 3

3

3

2 PL / 8 × 11 / 4 × 1’-5 / 4, F y = 36 ksi, one on each side of column web

3

/ 8



Solution:

 R n



0.9 



53.2 kips

From Example 6-1,

V u



172 kips

Determine the design panel-zone web shear strength: 

139 kips



V u



172 kips

n.g.


 R n

pe

m

2.5(2 p f



2.5(2  1 1/2 in.  0.570 in.)



8.93 in.



g

2





1.36

172 kips

n.g.

1.0  [(1)(6  1 7/16 in.  2  3/4 in.) 0.570 in.](50 ksi)(0.370 in.)

198 kips



Puf



172 kips

o.k.

Therefore, while the web thickness is adequate, the flange of the W1453 is inadequate t o resist the tensile flange force without reinf orcement.

)

Determine the design strength of the web to resist the flange forces in compression: 

4

5 1/2 in. 2







 t f b

d b



Puf

1.0  [Ct (6 k  2 t p)  N] F y t w



For a tensile flange force, the limit states of l ocal flange bending and local web yieldingmust be checked. F or l ocal flange bending, from Equati on 2.2-9, 






bs



8.93 in. (0.660 in.) 2(36 ksi)  1 (1.52)(1.56 in.)

Notethat F y has beenc onservatively taken as36 ksi asrecommended in Section 2.2.2. For l ocal web yielding, fr om Equation 2.2-11,

From Example 6-1,  Rv

bs t f 2 F y  C t  m pe

0.9 

Calculate the flange forces and panel-zone shear force: Puf  172 kips

  





1 in. 4



15 / 16

1/4

  pe d b

For a c ompressive flange f orce, the limit states of l ocal web yielding, web crippling, and c ompressi on buckling of the web must be checked. In this case, the c ompressi on buckling limit state does not apply because there is a m oment connection to oneflange only. F or l ocal web yielding, as determined previously,

k 1



1.36



in.  1.56 in.

1.56 in. 1 in.

1/4





1.52

 R n



198 kips



Puf

W14x53, F y = 50 ksi W18x50, F y = 50 ksi

/ 2 typ. / 2 3/4-in.-thick end plate with 1-in.-diameter bolts






172 kips

o.k.

For web crippling, fr om Equati on 2.2-12, N



N d 

 R n



2w  2t p 3 N d c



2( 1/2 in.)  2( 3/4 in.)

3(2.50 in.) 13.92 in.





2.50 in.

 R n

 Ft t





1  (0.539)

161 kips

3(0.570 in.  2  1/2 in.  2  3/4 in.) 14.98 in.

0.615 2

0.75  135 Ct tw 1  N d



0.75  135(1)(0.745 in.) 2



Puf



0.370 in. 0.660 in.





   1.5

172 kips

(50 ksi)(0.660 in.) 0.370 in.



n.g.

0.745 in. 1  (0.615) 1.19 in.

655 kips



Puf



t w t f



F y t f t w

   1.5

172 kips

(50 ksi)(1.19 in.) 0.745 in.

o.k.

Check the web thickness of the W14159 f or panel-z one web shear. Assuming the behavi or of the panel-z one remains nominally within the elastic range,

Therefore, the web of the W1453 is inadequate t o resist the compressive flange f orce without reinf orcement. Summary:

The W1453 is inadequate t o resist the l ocal f orces that are induced without c olumn stiffening. F or the selection lumn that is adequate with out stiffening, refer t o of a c o Example 6-8. Although the design of stiffening f or the W1453 is not illustrated with an example pr oblem f or this case, it can be accomplished in a manner that is similar to that illustrated in Example 6-3.





1.5





0.75  135(1)(0.370 in.) 2 



y f w



d



1.5

 t w t f

3 N

N d 

0.539

0.75  135Ct tw2 1  N d 



Check the web thickness of the W14 159 f or web crippling. From Equation 2.2-12,

(50 ksi)(46.7 in. 2)

P y



Fy A

Pu P y



300 kips 2,340 kips







2,340 kips

0.128

Since this ratio is less than 0.4, Equation 2.2-1 is applicable.  Rv

Example 6-8



0.9  0.6F y d c t w



0.9  0.6(50 ksi)(14.98 in.)(0.745 in.)



301 kips

V u





172 kips

o.k.

Given:

Summary:

For the framing arrangement given in Example 6-7, reselect a column size that will eliminate the need for stiffening.

As illustrated in Figure 6-9, a W14159 column ( F y  50 ksi) can be used without stiffening. This c olumnweight increase of 106 lb/ft ( 159  53) is within the range identified as econ omical in Chapter 3 f or the elimination of tw o pairs of partial-depth transverse stiffeners and a web doubler plate.

Solution:

As determined in Example 6-7, the flange thickness must be increased to increase the local flange bending strength and the web thickness must be increased to increase the web crippling strength and the panel-z one web shear strength. The required flange thickness is determined using a rearranged form of Equati on 2.2-9 as t f req







1.19 in.

Puf pe m  F y bs C t



Example 6-9 Given:

Repeat Example 6-1, except with a column that ends 2 in. above the top of the beam as illustrated in Figure 6-10.



(172 kips)(1.56 in.)(1.52) 0.9(36 ksi)(8.93 in.)(1.0)

Solution: Calculate the flange forces and panel-zone shear force:

From Example 6-1,

Note that F y has been c onservatively taken as 36 ksi as recommended in Section 2.2.2. A W14159 has a flange thickness equal to 1.19 in.

Puf  172 kips V u



52


172 kips

Determine which column-end criteria apply and if they apply at the near flange only or at both flanges of the beam:


The c olumn-end criteria apply for l ocal flange bending within 10t f  6.60 in.; f or l ocal web yielding, within d c  13.92 in.; and f or web crippling and c ompressi on bucking of the web within d c/2  6 .96 in. Thus, f or a W1850 beam, with d  17.99 in., the c olumn-end criteria apply for all limit states at the near (top) flange only.


F or a tensile flange f orce, the limit states of l ocal flange bending and l ocal web yielding must be checked. At the b ott om flange f orce, fr om Example 6-1, f or l ocal flange bending,  Rn


From Example 6-1,  Rv



139 kips



123 kips



Puf



172 kips

n.g.

Puf



172 kips

n.g.

and for l ocal web yielding, 

V u



172 kips

 Rn

n.g.



144 kips



W14x159, F y = 50 ksi W18x50, F y = 50 ksi

1

/ 2 typ. / 2 3 / 4 -in.-thick end plate with 1-in.-diameter bolts


1

Figure 6-9 Framing arrangement for Example 6-8.

W14x53, F y = 50 ksi 2”

W18x50, F y = 50 ksi




At the t op flange f orce, f or l cal flange bending, fr om o Equation 2.2-8,  R n

Summary:

The W1453 is inadequate t o resist the l ocal f orces that are induced witho ut column stiffening. For the selection of a c o lumn that is adequate with out stiffening, refer t o Example 6-10.

2



0.9  6.25t f F y  C t



0.9  6.25(0.660 in.)2(50 ksi)  0.5



61.3 kips

Puf



172 kips



n.g.

Comments:

and for local web yielding, fr om Equati on 2.2-10,  Rn



1.0  [Ct(5 k)  N ] F y t w



1.0  [0.5(5)(1 7/16 in.) 



The foreg oing s oluti on can be determined m ore expediently using the design aids in Appendices A, B, and C. The design panel-zone web shear strength is determined from Table A-1 where, f or a W14 53 with Pu/ P y  0 .4,

0.570 in.](50 ksi)(0.370 in.)

77.0 kips

Puf





172 kips

 Rv n.g.

 R n


144 kips



Puf



172 kips

n.g.



Puf



172 kips

n.g.

 R n



138 kips





77.0 kips



Puf



172 kips

 R n

 R n



 R n

n.g.



d c



3(0.570 in.) 13.92 in.



2

0.75  135Ct tw 1  N d

1.5





1  (0.123)

68.8 kips





Puf

0.370 in. 0.660 in. 

Puf  172 kips

n.g.

Puf  172 kips

n.g.



Puf  172 kips

n.g.

69.3 kips at the top flange21 (Table C-1) Puf  172 kips

n.g.



Example 6-10

F y t f t w

Given:

For the framing arrangement given in Example 6-9, reselect the column size to eliminate the need for stiffening:

(50 ksi)(0.660 in.)    0.370 in. 1.5

172 kips

n.g.

by interpolation between the values that are tabulated for N  1 /2 in. and N  3/4 in.

0.123 t w t f

172 kips

138 kips at the bott om flange (Table B-1)



0.75  135(0.5)(0.370 in.) 2 





3 N



61.3 kips at the t op flange (Table C-1)



and for web crippling, fr om Equati on 2.2-12, N d 

V u

by interpolation between the values that are tabulated for N  1 /2 in. and N  3/4 in. The design strength of the web to resist the flange force in compressi on is als o determined from Tables B-1 and C-1 where,f or a W14 53, with N  0.570 in. and reading fr om the C c olumn,

At the top flange f orce, f or l cal web yielding, as detero mined previously,  R n



123 kips at the bott om flange (Table B-1)



and for web crippling,  R n





For a c ompressive flange f orce, the limit states of l ocal web yielding, web crippling, and c ompressi on buckling of the web must be checked. In this case, the compressi on buckling limit state does not apply because there is a moment connection to one flange only. At the b ott om flange force, as determined previously, f or l ocal web yielding, 

139 kips

The design strength of the flange and web t o resist the flange force in tensi on is determined fr om Tables B-1 and C-1 where, for a W14 53, with N  0 .570 in. and reading from the T c olumn,

Therefore, the flange and web of the W1453 are inadequate to resist the tensile flange force without reinf orcement at both the top and bott om flanges.

 R n



A) entirely. B) except the transverse stiffeners at the top flange force (near the column end).

n.g.

Therefore, the web of the W14 53 is inadequate t o resist the compressive flange f orce with out reinf orcement at both the top and b ott om flanges.

21

The slight discrepancy between the calculated value (68.8 kips) and the value determined by linear interpolation (69.3 kips) results because the equations used to generate the tabulated values are not linear. 54


Solution A:

Summary A:

Try a W14159 with F y P y





F y A  (50 ksi)(46.7 in. 2)



300 kips 2,340 kips





301 kips



2,340 kips

0.128

From Table A-1, with Pu/ P y  Rv

50 As illustrated in Figure 6-11 W14 159 c olumn ( F y  ksi) can be used without stiffening. This c olumn-weight increase of 106 lb/ft (  159  53) is within the range identified as econ omical inChapter 3 for the elimination of two pairs of partial-depth transverse stiffeners and a web doubler plate.

50 ksi:





V u

0 .4,



172 kips

Summary B:

o.k.

A W1474 c olumn ( F y  50 ksi) can be used with out stiffening, except the transverse stiffeners at the top flange force (near the column end). This column-weight increase of 21 lb/ft (  74  53) is well within the range identified as economical in Chapter 3 f or the elimination of one pair of partial-depth transverse stiffeners and a web d oubler plate.

At the bott om flange f orce (away fr om the c olumn end), fro m Table B-1, with N  0 .570 in.,  R n



371 kips(T)



Puf



172 kips

o.k.



371 kips(C)



Puf



172 kips

o.k.

by interpolation between the values that are tabulated for  1 /2 in. and N  3/4 in. At the t op flange f orce (near the column end), from Table C-1, with N  0 .570 in.,

N

 R n

Example 6-11



194 kips( T)



Puf



172 kips

o.k.

Given:



195 kips( C)



Puf



172 kips

o.k.

For a pair of 1/2-in.-thick full-depth transverse stiffeners (F y  36 ksi) that transmit anunbalancedf orce of 82 kips to a 0.440-in.-thick c olumn web ( F y  50 ksi) with a single 3/8-in.-thick web doubler plate ( F y  36 ksi), pr op ortion the welds and check shear in the c olumn web and web doubler plate. The transverse stiffeners are 1’-0 9/16in. long and have two 3/4-in.  3/4-in. c orner clips each. They are used with a W1490 column. Use a j oint detail as illustrated in:

by interpolation between the values that are tabulated for N  1 /2 in. and N  3/4 in. Solution B:

From Example 6-2, a W14 74 can be used with out a web doubler plate and without transverse stiffeners at the b ottom flange f orce. At the t op flange f orce (near the c olumn end), either a pair of partial-depth transverse stiffeners can be provided or a detail such as that illustrated in Figure 6-12 can be used.

A) Figure 4-11a. B) Figure 4-11b. C) Figure 4-11c. D) Figure 4-11d. Solution A:

W14x159, F y = 50 ksi

The transverse stiffeners are to be connected to the c olumn panel zone with a detail that c ombines three fillet welds and one CJP gr oove weld as illustrated in Figure 4-11a. From Equation 4.3-10, the fillet weld size required for strength is

2”

W18x50, F y = 50 ksi

w








( Ru st) 1  ( Ru st ) 2 0.75  0 .6 F EX X ( l  2  clip)  2



 2

82 kips 0.75  0.6(70 ksi)(12.6 in.



2  3/4 in.)



2



 2

0.0829 in.

From LRFD Specification Table J2.4, the minimum weld size for the 1/2 -in.-thick transverse stiffener, 3/8 -in-thick web d oubler plate, and 0.440-in.-thick column web is 3 / in. Use 3/ -in. fillet welds. 16 16

Figure 6-11 Framing arrangement for Example 6-10 (Solution A). 55


The 3/8-in. CJP groove weld must transmit one-quarter of the 82-kip unbalanced f orce in the transverse stiffeners (20.5 kips). From LRFD Specificati on Table J2.5, the shear strength is the lesser of that on the effective area in the transverse stiffener base metal and that in the weld itself. For the transverse stiffener base metal,  R n



weld) assigned t o the web d oubler plate. F or the c olumn web, the design shear strength is  R n



0.9  0.6 F yst w ( l  2  clip) ksi)(3/8



0.9  0.6(36

in.)(12.6 in.



80.9 kips  20.5 kips



2



0.8  0.6 FEXX w ( l  2



0.8  0.6(70 ksi)(3/8 in.)(12.6 in.








0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)




 R n

o.k.



0.9  0.6F y d c t w

o.k.

For the web doubler plate, the design shear strength is  3/4 in.)




clip) 

2





0.9  0.6 F ydp d ct pl



0.9  0.6(36 ksi)(14.02 in.)( 3/8 in.)




o.k.

Therefore, the column web and web d oubler plate are of adequate thickness to provide f or pr oper f orce transfer of the unbalance f orce in the transverse stiffeners t o the panel-zone. If either the column web or the web d oubler plate thickness were inadequate in the above calculations, shear transfer between these elements on the effective area of the CJP groove weld r oot area can be utilized as a l oad path. Note, h owever, that if f orce is t o be transferred fr om the column web t o the web d oubler plate in this manner, the maximum force transfer may be limited by the design shear strength on the effective area at the juncture between the CJP groove weld and the web d oubler plate.

3/ in.) 4

o.k.

The c olumn web and web d oubler plate thicknesses must also be checked for shear strength t o transmit the unbalanced force in the transverse stiffeners t o the panelzone. For this detail, three-quarters of the unbalanced force (61.5 kips, the shear transmitted by the fillet welds) can be assigned to the column web with the remaining onequarter (20.5 kips, the shear transmitted by the CJP groove

W14x74, F y = 50 ksi W18x50, F y = 50 ksi


Note: column top extends past transverse stiffener to provide ade uate shelf for fillet welds. Figure 6-12 Framing arrangement for Example 6-10 (Solution B). 56


Table J2.4 (3/16-in.). For the c olumn web, the design shear strength is

Solution B:

The soluti on f ro this example and the j int o detail illustrated in Figure 4-11b is identical t o S olution A.



0.9  0 .6 F y d c t w

Solution C:



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)

The transverse stiffeners are to be connected to the column panel zone with a detail that c ombines three fillet welds and one CJP groove weld as illustrated in Figure 4-11c. For the fillet welds on the side of the web with out a web doubler plate, fr om Equati on 4.3-10, the fillet weld size required for strength is




w

0.75  0 .6 F EX X ( l  2  clip)  2



 2

Solution D:

82 kips



0.75  0.6(70 ksi)(12.6 in.



2



3/ in.)  2  4

The transverse stiffeners are to be connected t o the column panel zone with a detail that combines three fillet welds to the column web and one fillet weld t o the web d oubler plate as illustrated in Figure 4-11d. From Equation 4.3-10, the fillet weld size required for strength is

 2

0.0829 in.

From LRFD Specification Table J2.4, the minimum weld size for the 1/2-in.-thick transverse stiffener, 3/8-in-thick web doubler plate, and 0.440-in.-thick column web is 3/ 16 in. Use 3/16-in. fillet welds. The 1/2-in. CJP groove weld must transmit one-half of the 82-kip unbalanced f orce in the transverse stiffeners (41 kips). From LRFD Specification Table J2.5, the shear strength is the lesser of that on the effective area in the transverse stiffener base metal and that in the weld itself. For the transverse stiffener base metal,  R n

w

0.9  0.6F yst w ( l  2  clip)



0.9  0.6(36 ksi)( 1/2 in.)(12.6 in.






2





3/ in.) 4

o.k.





0.8  0.6FEXX w ( l  2



0.8  0.6(70 ksi)( 1/2 in.)(12.6 in.






2



0.75  0.6 F EX X ( l  2  clip)  2



 2

82 kips 0.75  0.6(70 ksi)(12.6 in.



2  3/4 in.)



2



 2

0.0829 in.

The column web and web d oubler plate thicknesses must also be checked for shear strength to transmit the unbalanced force in the transverse stiffeners to the panel-zone. For this detail, three-quarters of the unbalanced force (61.5 kips, the shear transmitted by the fillet welds) can be assigned to the c olumn web with the remaining one-quarter (20.5 kips, the shear transmitted by the CJP gr oove weld) assigned to the web doubler plate. For the c olumn web, the design shear strength is

clip) 

( Ru st) 1  ( Ru st ) 2

From LRFD Specification Table J2.4, the minimum weld size for the 1/2 -in.-thick transverse stiffener, 3/8 -in-thick web doubler plate, and 0.440-in.-thick column web is 3/ 16 in. Use 3/16-in. fillet welds.










o.k.

Therefore, the column web is adequate t o transfer the entire unbalanced load to the panel zone without additional strength from the web d oubler plate. The fillet weld between the web doubler plate and the transverse stiffener is selected as minimum size per LRFD Specification Sectio n J2.4. Use a 3/16-in. fillet weld.

( Ru st) 1  ( Ru st) 2





 Rn

3/ in.) 4

o.k.

For this detail, either the entire unbalanced force can be transmitted t o the c olumn web (thr ough the tw o fillet welds on the side of the c olumn web without a web d oubler plate and the CJP groove weld) or the fillet weld between the web d oubler plate and transverse stiffener can be sized to transmit a porti on of this f orce t o the web d oubler plate.22 In the former case, the fillet weld between the web doubler plate and the transverse stiffener is selected as a minimum-size fillet weld per LRFD Specification

 Rn



0.9  0 .6 F y d c t w



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)




o.k.

For the web doubler plate, the design shear strength is  R n

22

As in Solution A, the shear strength of the effective area at the root of the CJP groove weld can be used for f orce transfer t o the web d oubler plate, if necessary.



0.9  0.6 F ydp d c t pl



0.9  0.6(36 ksi)(14.02 in.)( 3/8 in.)




57


o.k.

Therefore, the column web and web d oubler plate are of adequate thickness to provide for pr oper f orce transfer of the unbalance force in the transverse stiffener to the panelzone.

 R n





0.8  0.6 FEXX w ( l  2  clip)



0.8  0.6(70 ksi)( 3/8 in.)(12.6 in.






2  3/4 in.)

o.k.

The c olumn web and web d oubler plate thicknesses must also be checked f or shear strength t o transmit the unbalanced force in the transverse stiffeners to the panelzone. For this detail, one-half of the unbalanced force (41 kips, the shear transmitted by the fillet welds) can be assigned to the column web with one-quarter (20.5 kips, the shear transmitted by each CJP groove weld) assigned t o each web doubler plate. For the c olumn web, the design shear strength is

Example 6-12 Given:

For a pair of 1/2-in.-thick full-depth transverse stiffeners (F y  36 ksi) that transmitan unbalanced force of82 kips to a 0.440-in.-thick c olumn web ( F y  50 ksi) with tw o 3 / -in.-thick web d oubler plates ( F  36 ksi), pr op orti on 8 y the welds and check shear inthe columnwebandweb d oubler plates. The transverse stiffeners are 1’-0 9/16-in. l ong and have two 3/4-in.  3/4-in. c orner clips each. They are used with a W14 90 column. Use a j oint detail as illustrated in:

 R n

A) Figure 4-12a. B) Figure 4-12b. C) Figure 4-12c. D) Figure 4-12d.



0.9  0.6F y d c t w



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)




o.k.

For the web doubler plate, the design shear strength is 

0.9  0 .6 F ydp d ct pl

Solution A:



0.9  0.6(36 ksi)(14.02 in.)( 3/8 in.)

Each transverse stiffener is to be c onnected t o the c olumn panel zone with a detail that combines one fillet weld and one CJP groove weld as illustrated in Figure 4-12a. Fr om Equation 4.3-10, the fillet weld size required f or strength is




w

0.75  0.6 F EX X ( l  2  clip)  2



 2

82 kips



0.75  0.6(70 ksi)(12.6 in.  2



3/ in.)  2  4

 2

0.0829 in.

From LRFD Specification Table J2.4, the minimum weld size for the 1/2-in.-thick transverse stiffener, 3/8-in-thick web doubler plate, and 0.440-in.-thick column web is 3/ 16 in. Use 3/16-in. fillet welds. The 3/8-in. CJP groove weld must transmit one-quarter of the 82-kip unbalanced f orce in the transverse stiffeners (20.5 kips). From LRFD Specificati on Table J2.5, the shear strength is the lesser of that on the effective area in the transverse stiffener base metal and that in the weld itself. For the transverse stiffener base metal,  R n

Solution B:

The solution f or this example and the j oint detail illustrated in Figure 4-12b is identical t o S oluti on A. Solution C:

Each transverse stiffener is to be connected t o the c olumn panel zone with a detail that combines one fillet weld and one CJP groove weld as illustrated in Figure 4-12c. The 1/ -in. CJP groove weld must transmit one-half of the 822 kip unbalanced force in the transverse stiffeners (41 kips). From LRFD Specification Table J2.5, the shear strength is the lesser of that on the effective area in the transverse stiffener base metal and that in the weld itself. For the transverse stiffener base metal,





0.9  0.6 F yst w ( l  2  clip)



0.9  0.6(36 ksi)( 3/8 in.)(12.6 in.



80.9 kips  20.5 kips



2



o.k.

Therefore, the c olumn web and web d oubler plates are of adequate thickness to provide f or pr oper f orce transfer of the unbalance f orce in the transverse stiffeners t o the panel-zone. If either the column web or the web d oubler plate thickness were inadequate in the above calculations, shear transfer between these elements on the effective area of the CJP groove weld r oot area can be utilized as a l oad path. Note, h owever, that if f orce is t o be transferred fr om the column web to the web d oubler plate(s) in this manner, the maximum force transfer may be limited by the design shear strength on the effective area at the juncture between the CJP groove weld and the web doubler plate.

( Ru st) 1  ( Ru st) 2





 R n

3/ in.) 4

o.k.

For the weld metal, 58


 R n





0.9  0.6F yst w ( l  2  clip)



0.9  0.6(36 ksi)( 1/2 in.)(12.6 in.






2



3/ in.) 4



2



3/ in.) 4

From LRFD Specification Table J2.4, the minimum weld size for the 1/2 -in.-thick transverse stiffener, 3/8 -in-thick web doubler plate, and 0.440-in.-thick column web is 3/ 16 in. Use 3/16-in. fillet welds. The c olumn web and web d oubler plate thicknesses must also be checked f or shear strength t o transmit the unbalanced force in the transverse stiffeners t o the panelzone. For this detail, one-half of the unbalanced f orce (41 kips, the shear transmitted by the fillet welds t o the column web) can be assigned to the column web with the remaining one-quarter (20.5 kips, the shear transmitted by the fillet weld to each web doubler plate) assigned t o each web doubler plate. For the c olumn web, the design shear strength is

o.k.






0.8  0.6FEXX w ( l  2



0.8  0.6(70 ksi)( 1/2 in.)(12.6 in.






clip)

o.k.

For this detail, either the entire unbalanced f orce can be transmitted to the column web (thr ough the tw o CJP groove welds) or the fillet welds between the web doubler plates and transverse stiffeners can be sized to transmit a portion of this f orce t o the web d oubler plates. 23 In the f ormer case, the fillet welds between the web doubler plates and the transverse stiffeners are selected as minimum-size fillet welds per LRFD Specification Table J2.4 ( 3/16-in.). For the column web, the design shear strength is  R n

 Rn



0.9  0.6 F y d c t w



0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)




o.k.

For the web doubler plate, the design shear strength is 

0.9  0.6 F ydp d c t pl

0.9  0.6(50 ksi)(14.02 in.)(0.440 in.)



0.9  0.6(36 ksi)(14.02 in.)( 3/8 in.)







0.9  0.6F y d c t w

 

 R n

o.k.

o.k.

Therefore, the column web is adequate t o transfer the entire unbalanced load to the panel zone without additi onal strength from the web doubler plates. The fillet welds between the web doubler plates and the transverse stiffener are selectedas minimum size per LRFD Specificatio n Section J2.4. Use a 3/16-in. fillet weld.

Therefore, the c olumn web and web d oubler plates are of adequate thickness to provide f or pr oper f orce transfer of the unbalance force in the transverse stiffener t o the panelzone.

Solution D:

Given:

The transverse stiffeners are to be connected to the column panel zone with a detail that combines two fillet welds t o the columnweb and one fillet weldt o each of the web d oubler plates as illustrated in Figure 4-12d. From Equation 4.3-10, the fillet weld size required f or strength is

Determine the transverse stiffener requirements and if a web doubler plate will be required for the high-seismic reducedbeam section (RBS) connection illustrated in Figure 6-13 in a Special Moment Frame (SMF) or Intermediate Moment Frame (IMF). The axial compression in the c olumn is 1,000 kips. The shear at the plastic hinge location is 150 kips. Neglect the effects of story shear f or calculation purposes.

w







Example 6-13

( Ru st) 1  ( Ru st) 2 0.75  0 .6 F EX X ( l  2  clip)  2



 2

82 kips 0.75  0.6(70 ksi)(12.6 in.



2

 3/4 in.)  2 

W36150, F y  50 ksi d  35.85 in. b f  11 .975 in. a  22.5 in. t w  0.625 in.

 2

0.0829 in.

W14426, F y  50 ksi d  18.67 in. b f  16 .695 in. k1  1 9/16 in. tw  1.875 in. T  11 1/4 in. A  125 in. 2

Z x  581 in. 3 t f  0 .940 in. k 3 11/16 in. t f  3 .035 in.

23

As in Solution A, the shear strength of the effective area at the root of the CJP groove weld can be used for f orce transfer t o the web d oubler plate, if necessary.

Use an RBS detail with a plastic section m odulus Z  356 in.3 (at RBS). 59


Solution:

 Rv


From Equation 2.1-2, the f orce at each flange need n ot be taken greater than Puf



d

0.75  0 .6 F y d c t w 1 



0.75  0.6(50 ksi)(18.67 in.)(1.875 in.) 

 t f



1.1(1.1)(50 ksi)(356 in. 3)  (150 kips)(22.5 in.) (35.85 in.  0.940 in.)



714 kips





1.1 R y F y Z  V u a



3b f t 2f





1

d b d c t w

3(16.695 in.)(3.035 in.) 2 (35.85 in.)(18.67 in.)(1.875 in.)

1,080 kips



V u



714 kips



o.k.

To prevent seismic shear buckling in the panel-z one, from Equation 2.2-7,

Neglecting the effects of story shear, the panel-z one web shear force is determined fr om Equati on 2.1-5 as Vu



Puf



t w min

714 kips


In a high-seismic application, either Equation 2.2-5 or Equation 2.2-6 is used. 

Fy A

Pu P y



1,000 kips 6,250 kips



2

(50 ksi)(125 in. )

P y







6,250 kips

d m  d c  2t f

90



(35.85 in.  0.940 in.)  18.67 in. 90



0.528 in.

 tw 

1 .875 in.



2(3.035 in.)

o.k.

Therefore, the web of the W14426 is adequate t o resist the panel-zone web shear without reinf orcement.

0.160 Determine the transverse stiffener requirements:

As indicated in Section 2.3, transverse stiffeners are required to match the configurati on used in the qualifying


W14x426, F y = 50 ksi W36x150, F y = 50 ksi

Centerline of radiuscut RBS (location of plastic hinge)

22.5”

Check if column stiffening is required Figure 6-13 Framing arrangement for Example 6-13 (problem statement).

60


cyclic tests. From Engelhardt et al. (1998), a pair of full-depth transverse stiffeners at each flange with 1-in. thickness and 5-in. width is adequate. These transverse stiffeners are required f or cr oss-secti onal stiffness only, as the design strengths of the c olumn flange and web t o resist both tensile and compressive flange f orces (see Table B-1) are well in excess of the required strength of 714 kips. The transverse stiffener length is selected as the c olumn depth minus twice the flange thickness, which equals 1’-0 9/16 in. Use 2 PL 1 in.  5 in.  1’-0 9/16 with two 3 / -in.  3/ -in. corner clips each. 4 4 Determine the welding requirements for the transverse stiffeners:

w







0.9F yst (2)( bs  clip)  t s



0.9(36 ksi)(2)(5 in.  3/4 in.)(1 in.)



275 kips



0.9  0.6F yst ( l  2  clip)  2 t s



0.9  0.6(36 ksi)(12.6 in.  2  3/4 in.) 





0.9  0.6(50 ksi)(18.67 in.)(1.875 in.)



945 kips

275 kips 0.75  0.6(70 ksi)(12.6 in.



2  3/4 in.)



2



 2

0.278 in.

Summary:

Determine the transverse stiffener requirements and if a web d oubler plate will be required f or the high-seismic reduced beam section (RBS) c onnecti ons illustrated in Figure 6-15 in a Special M oment Frame (SMF) or Intermediate Moment Frame (IMF). The axial compressi on in the column is 1,200 kips. The shear at the plastic hinge location is 150 kips. Neglect the effects of story shear f or calculation purposes. W36150, F y  50 ksi d  35.85 in. b f  11 .975 in. Z x  581 in.3 a  22.5 in. tw  0.625 in. t f  0 .940 in.

432 kips

0.9  0.6 F y d c  t pz

 2

Given:

2(1 in.)





Example 6-14

W14500, F y  50 ksi d  19.60 in. b f  17 .010 in. k  4 3/16 in. k 1  1 3/4 in. tw  2.190 in. t f  3 .500 in. T  11 1/4 in. A  147 in. 2

From Equation 4.3-16 (limit based upon shear in the c olumn web, one shear plane used because the entire f orce must be transmitted into the panel-zone),  Rn max

0.75  0 .6 F EX X ( l  2  clip)  2

The W14426 is adequate without a web d oubler plate but requires the use of a pair of transverse stiffeners at the location of each beam flange. Use 4 PL 1 in.  5 in.  1’-09/16 with two 3/4-in.  3/4-in. c orner clips each, 1-in. CJP groove welds t o c onnect the transverse stiffeners t o the column flanges, and 5/16-in. d ouble-sided fillet welds to connect the transverse stiffeners to the c olumn web. This column-stiffening c onfiguration is illustrated in Figure 6-14.

From Equation 4.3-15 (limit based upon shear in the transverse stiffeners),  R n max

( Rust )1  ( Rust) 2

The minimum size fillet weld per LRFD Specification Table J2.4 is 5/16 in. Use 5/16-in. double-sided fillet welds to connect the transverse stiffeners to the column web.

Complete-joint-penetration groove welds are used t o c onnect the transverse stiffeners to the column flanges. Use 1-in. CJP groove welds to connect the transverse stiffeners to the column flange. In lieu of calculating the force that must be transmitted from the transverse stiffeners t o the c olumn web, the d ouble-sided fillet welds c onnecting the transverse stiffeners to the column web can be sized f or the maximum force provisions given in Secti on 4.3. Fr om Equati on 4.3-17 (limit based up on the strength of the transverse stiffener ends in tension),  R n max



Use an RBS detail with a plastic section m odulus Z  356 in.3 (at RBS). Solution:

Thus, the limit based upon the strength of the transverse stiffener ends in tensio n governs. Fr om Equati on 4.3-10 with the quantity ( Ru st )1  ( Ru st ) 2 set equal t o 275 kips,


From Equation 2.1-2, the f orce at each flange need n ot be 61


taken greater than Puf



Neglecting the effects of story shear, the panel-z one web shear force is determined fr om Equati on 2.1-4 as

1.1 R y F y Z  V u a d

 t f

Vu



1.1(1.1)(50 ksi)(356 in. 3)  (150 kips)(22.5 in.) (35.85 in.  0.940 in.)



714 kips



0.8[( Puf )1  ( Puf ) 2 ]



0.8[714 kips  714 kips]



1,140 kips

W14x426, F y = 50 ksi W36x150, F y = 50 ksi

5

typ.

/ 16

5

/ 16

9

typ.

2 PL 1 × 5 × 1’-0 / 16, F y = 36 ksi, 3 at each beam flange with two / 4 3 × / 4 corner clip each

1

Figure 6-14 Framing arrangement for Example 6-13 (solution).

W14x500, F y = 50 ksi W36x150, F y = 50 ksi

W36x150, F y = 50 ksi

Centerline of radiuscut RBS (location of plastic hinge), typ.

22.5”

22.5”

Check if column stiffening is required Figure 6-15 Framing arrangement for Example 6-14 (problem statement).

62


1-in. CJP groove welds to connect the transverse stiffeners to the column flange. In lieu of calculating the force that must be transmitted from the transverse stiffeners t o the c olumn web, the d ouble-sided fillet welds c onnecting the transverse stiffeners t o the c olumn web can be sized for the maximum force provisions given in Secti on 4.3. Fr om Equati on 4.3-14 (limit based upon the strength of the transverse stiffener ends in tension),


In a high-seismic application, either Equation 2.2-5 or Equation 2.2-6 is used. P y



F y A  (50 ksi)(147 in. 2)

Pu P y



1,200 kips 7,350 kips





7,350 kips

0.163

Since this ratio is less than 0.75, Equation 2.2-5 is applicable.  Rv







0.75  0 .6 F y d c t w 1 

d b d c t w





1

3(17.010 in.)(3.500 in.) 2 (35.85 in.)(19.60 in.)(2.190 in.)

1,360 kips



V u



1,140 kips



 R n max







0.9(36 ksi)(4)(5 in.  3/4 in.)(1 in.)



551 kips

0.9  0.6F yst ( l  2  clip)  2 t s



0.9  0.6(36 ksi)(12.6 in.  2  3 3/4 in.)



2(1 in.)

432 kips

From Equati on 4.3-16 (limit based upon shear in the column web, one shear plane used because the entire f orce must be transmitted into the panel-z one),

90 (35.85 in.  0.940 in.)  19.60 in. 90  tw 





d m  d c  2t f

0.528 in.

0.9F yst (4)( bs  clip)  t s



o.k.

To prevent seismic shear buckling in the panel-zone, fr om Equation 2.2-7, t w min



From Equation 4.3-15 (limit based upon shear in the transverse stiffeners),

0.75  0.6(50 ksi)(19.60 in.)(2.190 in.) 



3b f t 2f

 Rn max

2 .190 in.



2(3.500 in.)

 R n max

o.k.

Therefore, the web of the W14500 is adequate t o resist the panel-zone web shear without reinf orcement.



0.9  0.6 F y d c  t pz



0.9  0.6(50 ksi)(19.60 in.)(1.875 in.)



992 kips

Thus, the limit based upon shear in the transverse stiffeners governs. Fr om Equati on 4.3-10 with the quantity ( Ru st )1  ( Ru st ) 2 set equal t o 432 kips,

Determine the transverse stiffener requirements:

As indicated in Section 2.3, transverse stiffeners are required to match the configurati on used in the qualifying cyclic tests. From Engelhardt et al. (1998), a pair of fulldepth transverse stiffeners at each flange with 1-in. thickness and 5-in. width is adequate (see Figure 6-7b). These transverse stiffeners are required for cr oss-secti onal stiffness only as the design strengths of the c olumn flange and web to resist both tensile and compressive flange f orces (see Table B-1) are well in excess of the required strength of 714 kips. The transverse stiffener length is selected as the column depth minus twice the flange thickness, which equals 1’-09/16 in. Use 2 PL 1 in.  5 in.  1’-0 9/16 with two 3/4-in.  3/4-in. corner clips each.

w







( Rust )1  ( Rust ) 2 0.75  0 .6 F EX X ( l  2  clip)  2



 2

432 kips 0.75  0.6(70 ksi)(12.6 in.



2  3/4 in.)



2



 2

0.437 in.  7/16 in.

The minimum size fillet weld per LRFD Specification Table J2.4 is 5/16 in. Use 7/16-in. double-sided fillet welds to connect the transverse stiffeners to the column web. Summary:

The W14500 is adequate without a web d oubler plate but requires the use of a pair of transverse stiffeners at the location of each beam flange. Use 4 PL 1 in.  5 in.  1’-09/16 with two 3/4-in.  3/4-in. c orner clips each, 1-in. CJP groove welds to c onnect the transverse stiffeners t o

Determine the welding requirements for the transverse stiffeners:

Complete-joint-penetration groove welds are used t o c onnect the transverse stiffeners to the column flanges. Use 63


the the co lumn lumn flang flanges es,, and and 7/16-in. -in. d oubl ublee-si side ded d fille fillett weld weldss t o connect nnect the the tran transv sver erse se stif stiffe fene ners rs to the the c olumn lumn web. web. This This

c olumn lumn-s -sti tiff ffen enin ing g c onfig nfigur urat atii on is is illu illust stra rate ted d in Figu Figure re 6-16 6-16..

W14x500, F y y = 50 ksi W36x150, F y y = 50 ksi

W36x150, F y y = 50 ksi

7

typ.

/ 16 16

7

/ 16 16

9

typ.

2 PL 1 × 5 × 1’-0 / 16 16, F y y = 36 ksi, 3 at each beam flange fl ange with two / 4 3 × / 4 corner clip each

1

Figure 6-16 Framing arrangement for for Example 6-14 (solution).

64


REFERENCES American Institute of Steel Construction, 1997a, Seismic Provisions for Structural Steel Buildings, AISC, ISC, ChiChicago, IL.

D ogb one C onnecti ons,” Engineering Journal, Vol. 35, No. 4, pp. 128128-13 139 9, AISC, ISC, Chic Chicag ag o, IL. Federal Emergency Management Agency, 1995, FEMA Repair, Modifi267 Interim Guidelines: Evaluation, Repair, cation and Design of Steel Moment Moment Frames, Frames, FEMA, Washingt ashington, D.C. Note that this d ocument cument is intended intended to be upd updat ated ed per perii odica dicall lly y. To date date,, one upd updat atee has has been issued: Federal Emergency Management Agency, 1998 1998,, FEMA FEMA 267A 267A Interim Guidelines Advisory No. 1—Suppl 1—Suppleme ement nt t o FEMA FEMA 267, FEMA, FEMA, Wash Washing ing-ton, D.C.

American American Institute Institute of Steel Steel Constructi nstruction, 1997b, 1997b, “k-area “k-area Advisory Statement,” Modern Steel Construction, February, ruary, AISC, Chicag Chicago, IL. Americ American an Institu Institute te of Steel C onstruc nstructi tion, 1994, 1994, LRFD Manual of Steel Construction, AISC, Chicago, IL. Americ American an Institu Institute te of Steel C onstruc nstructi tion, 1993, 1993, LRFD Specifi Specificati cation on for Struct Structura urall Steel Steel Buildin Buildings, gs, AISC, Chicago, IL.

Ferr Ferrel ell, l, M.T., M.T., 1998, 1998, “Moment C onnec nnecti tions t o C olumn lumn Webs,” Proceedings of the 1998 AISC National Steel Construction Conference, pp. 13.1-13.8, AISC, Chicago, IL.

Americ American an Institu Institute te of Steel Steel C onstruc nstructi tion, 1989, 1989, Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design, AISC, Chicago, IL.

Barger, Barger, B.L., B.L., 1992, “What “What Design Design Engineers Engineers Can Do t o Reduce Reduce Fabrica Fabricati tion Costs,” Modern Steel Construction, February, February, pp. 31-32, AISC, Chicago, IL.

Graham Graham,, J.D., J.D., Sherb Sherbourne, A.N., A.N., Khabba Khabbaz, z, R.N., R.N., and Jensen, Jensen, C.D., 1959, 1959, “W “Welded Interi Interior Beam-t Beam-t o-C olumn f or AISC, AISC, Chicago, IL. Connections,” Report for

Blodgett, O.W., 1967, Design of Welded Structures, The Lincoln Electric Electric Company, mpany, Cleveland, Cleveland, OH.

Huang, J. S., W. F. Chen, and L. S. Beedle, 1973, “Behavi havior and and Desig Design n of Steel Steel Beam Beam-t -to-Column lumn M oment ment Connections,” Bulletin 188, Oct ober, Welding Research Council, New York, NY. NY.

Curtis, L.E. and Murray, T.M., 1989, “C olumn Flange Streng Strength th at Moment End-Pl End-Plate ate Connecti nnections,” Engineering neering Journal, Journal, Vo l. 26, N o. 2, pp. 41-50, AISC, Chicago, IL. Disque, Disque, R.O., R.O., 1975, 1975, “Directi “Directional M oment C onnections— APr op osedDesignMeth odf rUnbracedSteelFrames,” o Engineering Journal, Vol. 12, N o. 1, pp. 14-18, 14-18, AISC, AISC, Chicago, IL IL. Driscoll, G.C. and Beedle, L.S., 1982, “Suggestio ns for Avoiding Beam-to-Column Web Connection Failures Failures,” ,” Engineering Journal, Vol. 19, N o. 1, pp. 16-19, 16-19, AISC, AISC, Chicago, IL. Drisc Driscoll, G.C., G.C., Pourb urbohloul, A., A., and and Wang, ang, X., X., 1983 1983,, “Fra “Fractu cture re of M oment ment C onnecti nnections— ns—T Tests ests on SimuSimulated Beam-to -Column Web Moment Connection Details,” Fritz Engineering Laboratory Report No. 469.7, Lehigh University, Bethlehem, PA.

Leon, R.T., R.T., Hoffman, J.J., and Staeger, T., T., 1996, Partially Restrained Composite Connections, AISC,Chicago ,IL. Murray, T.M., 1990, Extended End-Plate Moment Connections, AISC, Chicago, IL. Ricker, D.T., 1992, “Value Engineering and Steel Ec onomy,” Modern Steel Construction, February, pp. 22-26, AISC, Chicago, IL. Handbook of Structural Structural Steel ConTamboli, A., 1999, 1999, Handbook nection Design and Details, McGraw-Hill, McGraw-Hill, New York, NY.; see Chapter 2 by W. A. Thornton and T. Kane, pp. 128-143.

Thornton, W.A., .A., 1992 1992,, “Des “Desig igni ning ng f or C ost Effici Efficien entt Fabrication,” Modern Steel Construction, February, pp. 12-20, 12-20, AISC, Chicag Chicag o, IL.

Dyker, Dyker, W.G., W.G., 1992, 1992, “What Design Engineer Engineerss Can D o t o Reduce Reduce Fabrica Fabricati tion Costs,” Modern Steel Construction, February, February, pp. 28-29, AISC, Chicago, IL.

Thornton, W.A., W.A., 1991, 1991, “Structur “Structural al Arrangement Arrangement f or C ost Proceedings gs of Effecti Effective ve Fabric Fabricati ation and Erecti Erection,” Proceedin the 1991 1991 AISC AISC Nationa Nationall Steel Steel Constr Constructi uction on Confer Conferenc ence, e,

El Taw Tawil, il, S., S., Mik Mikes esell ell,, T., T., Vidar idarss sson, E., E., and and Kunn Kunnat ath, h, Strength th and Ductili Ductility ty of FR Weldedelded-Bol Bolted ted S.K., S.K., 1998, 1998, Streng Connections, Report N o. SAC/BD-98/01

pp. pp. 27.1 27.1-2 -27. 7.16 16,, AISC AISC,, Chic Chicag ag o, IL. IL. Viest, iest, I.M., I.M., Colaco, J.P., J.P., Furl Furlong, R.W., R.W., Griffi Griffis, s, L.G., L.G., Composite ConLeon, R.T., and Wylie, L.A., 1998, Composite struction: Design for Buildings, McGraw-Hill/ASCE, Reston, VA.

Engelhardt, Engelhardt, M.D., Winneber Winneberger ger,, T., Zekany Zekany, A.J., and Potyraj, tyraj, T.J., .J., 1998 1998,, “Exp “Exper erime iment ntal al Inve Invest stig igati ation of 65



Appendix A COLUMN PANEL-ZONE WEB SHEAR STRENGTH For wind and l ow-seismic applicati ons, Table A-1 aids in the determinatio n of the panel-z one web shear strength for wide-flange c olumns with str ong-axis directly welded flange, flange plated, and extended end-plate m oment connections. F or high-seismic applications, see AISC (1997a). All values are given to three significant figures. For a given W-shape, the table is entered under the appropriate values of Pu/(F y Ag) t o determine the design shear strength of the c olumn web. The tabulated values are fo r material with F y  50 ksi. For values o f Pu/(F y Ag) that are less than orequal t o 0.4, the tabulated design strength is determined from LRFD Specification Equation K1-9, where:  Rv



The design strength at intermediate values of Pu/(F y Ag) can be determined by linear interp olati on. 24 In the ab ove discussi on and equati ons, Pu F y A g d t w

The tabulated design strengths are based up on the “firstyield” strength pr ovisi ons in LRFD Specificati on Sectio n K1.7(a) and will be c onservative f or the “p ostyield” strength provisions in LRFD Specification Section K1.7(b). Alternatively, a higher design strength can be determined by calculation with the latter provisions.

0.9  0.6 F y dt w

For values of Pu/(F y Ag) that are greater than 0.4, the tabulated design strength is determined fr om LRFD Specification Equation K1-10, where:  Rv





0.9  0.6 F y dt w 1 .4 

Pu F y Ag

column fact ored axial f orce, kips  column specified minimum yield strength, ksi ss area, in. 2  column gr o  column depth, in.  column web thickness, in. 

24

Note that the value determined by linear interpolations between tabulated values will be approximate, since the equations used to generate the tabulated values are n ot necessarily linear.



67


Table A-1 Panel-Zone Web Shear Strength for Wide-Flange Columns, F y  50 ksi (Wind and Low-Seismic Applications, see Section 1.4) Design Panel-Zone Shear Strength  R v , kips Pu /(Fy A)

Shape

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

W44335 290 262 230

1210 1020 924 823

1150 973 878 781

1090 922 831 740

1030 871 785 699

970 820 739 658

909 768 693 617

849 717 647 576

788 666 600 535

727 615 554 494

667 564 508 452

606 512 462 411

546 461 416 370

485 410 370 329

W40593 503 431 372 321 297 277 249 215 199 174

2080 1750 1490 1270 1080 1000 889 797 684 679 670

1970 1660 1420 1210 1030 950 845 758 650 645 637

1870 1570 1340 1150 974 900 801 718 616 611 603

1770 1490 1270 1080 920 850 756 678 581 577 570

1660 1400 1190 1020 866 800 712 638 547 543 536

1560 1310 1120 954 812 750 667 598 513 509 503

1450 1220 1050 891 758 700 623 558 479 475 469

1350 1140 970 827 703 650 578 518 445 441 436

1250 1050 896 764 649 600 534 478 410 407 402

1140 962 821 700 595 550 489 439 376 373 369

1040 874 746 636 541 500 445 399 342 339 335

935 787 672 573 487 450 400 359 308 305 302

831 699 597 509 433 400 356 319 274 271 268

W40466 392 331 278 264 235 211 183 167 149

1910 1590 1340 1110 1040 889 797 684 677 650

1820 1510 1280 1050 985 845 757 650 643 617

1720 1430 1210 995 933 801 718 616 610 585

1630 1360 1140 940 881 756 678 581 576 552

1530 1280 1080 885 829 712 638 547 542 520

1440 1200 1010 830 778 667 598 513 508 487

1340 1120 941 774 726 623 558 479 474 455

1240 1040 873 719 674 578 518 445 440 422

1150 956 806 664 622 534 478 410 406 390

1050 877 739 608 570 489 438 376 372 357

957 797 672 553 518 445 399 342 339 325

861 717 605 498 467 400 359 308 305 292

765 638 537 442 415 356 319 274 271 260

W36848 798 650 527 439 393 359 328 300 280 260 245 230

2890 2700 2150 1700 1410 1250 1130 1020 937 873 822 779 737

2740 2560 2050 1620 1340 1180 1070 970 891 829 781 740 700

2600 2430 1940 1530 1260 1120 1020 919 844 785 740 701 663

2460 2290 1830 1450 1190 1060 961 868 797 742 699 662 626

2310 2160 1720 1360 1120 996 905 817 750 698 658 623 589

2170 2020 1610 1280 1050 934 848 766 703 654 617 584 553

2020 1890 1510 1190 983 872 792 715 656 611 576 546 516

1880 1750 1400 1110 913 809 735 664 609 567 535 507 479

1730 1620 1290 1020 843 747 679 613 562 524 493 468 442

1590 1480 1180 937 773 685 622 562 516 480 452 429 405

1440 1350 1080 852 702 623 565 511 469 436 411 390 368

1300 1210 969 767 632 560 509 460 422 393 370 351 332

1160 1080 861 682 562 498 452 409 375 349 329 312 295

W36256 232 210 194 182 170 160 150 135

970 872 822 754 711 664 632 605 576

922 828 781 716 676 631 600 575 547

873 785 740 678 640 598 569 544 518

825 741 699 641 604 564 537 514 490

776 698 658 603 569 531 506 484 461

728 654 617 565 533 498 474 454 432

679 610 576 528 498 465 442 423 403

631 567 534 490 462 432 411 393 374

582 523 493 452 427 398 379 363 346

534 480 452 415 391 365 348 333 317

485 436 411 377 356 332 316 302 288

437 392 370 339 320 299 284 272 259

388 349 329 301 284 266 253 242 230



68


Table A-1 (cont’d) Panel-Zone Web Shear Strength for Wide-Flange Columns, F y  50 ksi (Wind and Low-Seismic Applications, see Section 1.4) Design Panel-Zone Shear Strength  R v , kips Pu /(Fy A)

Shape W33354 318 291 263 241 221 201



0.4

0.45

0.5

1110 1 060 1 000 987 938 889 903 858 813 811 771 730 766 728 689 710 674 639 650 618 585

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

946 839 768 689 651 603 553

891 790 722 649 613 568 520

835 740 677 608 574 532 488

779 691 632 568 536 497 455

724 642 587 527 498 461 423

668 592 542 487 460 426 390

612 557 543 494 497 452 446 406 421 383 390 355 358 325

501 445 444 395 406 361 365 324 345 306 319 284 293 260

W33169 152 141 130 118

612 574 544 518 488

581 545 517 492 464

551 517 490 466 439

520 488 462 440 415

489 459 435 415 390

459 431 408 389 366

428 402 381 363 342

398 373 354 337 317

367 345 326 311 293

336 316 299 285 268

306 287 272 259 244

275 258 245 233 220

245 230 218 207 195

W30477 391 326 292 261 235 211 191 173

1510 1220 997 882 794 701 647 588 538

1430 1160 947 837 754 666 615 559 511

1360 1100 898 793 714 631 583 529 484

1280 1040 848 749 675 596 550 500 458

1200 975 798 705 635 561 518 471 431

1130 914 748 661 595 526 486 441 404

1050 853 698 617 556 491 453 412 377

979 792 648 573 516 456 421 382 350

903 731 598 529 476 421 388 353 323

828 670 548 485 437 386 356 323 296

753 609 499 441 397 351 324 294 269

678 548 449 397 357 316 291 265 242

602 487 399 353 317 281 259 235 215

W30148 132 124 116 108 99 90

538 503 477 458 439 416 375

511 478 453 435 417 395 356

484 453 429 412 395 375 337

458 428 405 389 373 354 319

431 403 381 366 351 333 300

404 377 357 343 329 312 281

377 352 334 320 307 291 262

350 327 310 298 285 271 244

323 302 286 275 263 250 225

296 277 262 252 241 229 206

269 252 238 229 219 208 187

242 226 214 206 198 187 169

215 201 191 183 176 167 150

1730 1640 1560 1400 1330 1260 1130 1 080 1 020 927 881 835 767 728 690 704 669 634 637 605 573 569 541 512 544 517 490 492 467 442 447 425 403

1470 1190 962 788 652 599 542 484 463 418 380

1380 1120 906 742 613 563 510 455 436 393 358

1300 1050 849 696 575 528 478 427 408 369 335

1210 980 793 649 537 493 446 398 381 344 313

1120 910 736 603 498 458 414 370 354 320 291

1040 840 679 556 460 423 382 342 327 295 268

387 357 320 303 282

364 336 301 285 265

341 315 283 267 249

319 294 264 249 232

296 273 245 231 216

273 252 226 214 199

W27539 448 368 307 258 235 217 194 178 161 146 W27129 114 102 94 84

455 420 377 356 332

432 399 358 338 315

410 378 339 321 299

951 865 770 700 623 566 510 464 422 383 387 352 350 319 313 285 299 272 270 246 246 224

778 692 630 560 510 453 417 371 345 307 317 282 287 255 256 228 245 218 221 197 201 179

250 231 207 196 182

205 189 170 160 149

69


228 210 188 178 166

182 168 151 142 133


Shape

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

W24492 408 335 279 250 229 207 192 176 162 146 131 117 104

1580 1270 1030 837 740 674 604 557 511 476 434 400 360 325

1500 1210 974 795 703 641 574 529 486 452 412 380 342 309

1420 1140 923 753 666 607 544 501 460 428 391 360 324 292

1340 1080 872 712 629 573 513 473 434 404 369 340 306 276

1260 1020 820 670 592 540 483 446 409 381 347 320 288 260

1180 954 769 628 555 506 453 418 383 357 326 300 270 244

1100 890 718 586 518 472 423 390 358 333 304 280 252 227

1030 826 667 544 481 438 393 362 332 309 282 260 234 211

946 763 615 502 444 405 362 334 307 286 261 240 216 195

867 699 564 460 407 371 332 306 281 262 239 220 198 179

789 636 513 419 370 337 302 279 256 238 217 200 180 162

710 572 461 377 333 303 272 251 230 214 195 180 162 146

631 509 410 335 296 270 242 223 204 190 174 160 144 130

W24103 94 84 76 68

364 338 306 284 266

346 321 291 270 253

328 304 275 256 239

310 287 260 242 226

291 270 245 227 213

273 254 229 213 199

255 237 214 199 186

237 220 199 185 173

219 203 183 171 160

200 186 168 156 146

182 169 153 142 133

164 152 138 128 120

146 135 122 114 106

W2462 55

276 251

262 239

248 226

234 214

220 201

207 189

193 176

179 163

165 151

152 138

138 126

124 113

110 101

W21201 182 166 147 132 122 111 101

566 509 455 429 383 351 319 288

538 484 432 407 364 334 303 274

509 458 410 386 345 316 287 260

481 433 387 365 326 299 272 245

453 407 364 343 306 281 256 231

424 382 341 322 287 263 240 216

396 356 319 300 268 246 224 202

368 331 296 279 249 228 208 187

340 305 273 257 230 211 192 173

311 280 250 236 211 193 176 159

283 255 228 214 192 176 160 144

255 229 205 193 172 158 144 130

226 204 182 172 153 140 128 115

W2193 83 73 68 62

339 298 261 245 227

322 283 248 233 215

305 268 235 221 204

288 253 222 209 193

271 238 209 196 181

254 223 196 184 170

237 209 183 172 159

220 194 170 159 147

203 179 157 147 136

186 164 144 135 125

169 149 130 123 113

152 134 117 110 102

135 119 104 98.1 90.7

W2157 50 44

230 214 195

219 203 185

207 192 176

196 182 166

184 171 156

173 160 146

161 150 137

150 139 127

138 128 117

127 118 107

115 107 98

104 96 88

92 85 78

W18311 283 258 234 211 192 175 158 143 130

916 826 742 660 592 527 482 431 384 348

870 785 705 627 562 501 457 410 365 331

824 743 667 594 532 475 433 388 346 313

779 702 630 561 503 448 409 367 327 296

733 661 593 528 473 422 385 345 307 279

687 619 556 495 444 396 361 323 288 261

641 578 519 462 414 369 337 302 269 244

595 537 482 429 385 343 313 280 250 226

550 496 445 396 355 316 289 259 230 209

504 454 408 363 325 290 265 237 211 192

458 413 371 330 296 264 241 216 192 174

412 372 334 297 266 237 217 194 173 157

366 330 297 264 237 211 193 173 154 139



70



Shape

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

W18119 106 97 86 76

335 298 269 238 209

319 283 255 226 199

302 269 242 215 188

285 254 228 203 178

268 239 215 191 167

252 224 201 179 157

235 209 188 167 146

218 194 175 155 136

201 179 161 143 125

185 164 148 131 115

168 149 134 119 104

151 134 121 107 94.0

134 119 107 95.3 83.6

W1871 65 60 55 50

247 223 204 191 172

235 212 194 181 164

222 201 184 172 155

210 190 174 162 147

197 178 164 153 138

185 167 153 143 129

173 156 143 133 121

160 145 133 124 112

148 134 123 114 103

136 123 112 105 94.8

123 111 102 95.3 86.2

111 100 92.0 85.8 77.6

98.7 89.2 81.8 76.3 69.0

W1846 40 35

176 152 143

167 145 136

158 137 129

149 129 122

140 122 115

132 114 108

123 107 100

114 99 93

105 91 86

97 84 79

88 76 72

79 69 65

70 61 57

W16100 89 77 67

268 237 203 174

255 226 193 165

241 214 183 157

228 202 173 148

214 190 162 139

201 178 152 131

188 166 142 122

174 154 132 113

161 142 122 104

147 131 112 95.8

134 119 101 87.1

121 107 91.3 78.4

107 95.0 81.2 69.7

W1657 50 45 40 36

191 167 150 132 126

181 158 143 125 120

172 150 135 119 114

162 142 128 112 107

153 133 120 105 101

143 125 113 98.9 94.7

134 117 105 92.3 88.4

124 108 97.7 85.7 82.1

114 100 90.2 79.1 75.8

105 91.8 82.6 72.5 69.5

95.4 83.4 75.1 65.9 63.2

85.8 75.1 67.6 59.3 56.8

76.3 66.7 60.1 52.7 50.5

W1631 26

118 106

112 101

106 95.3

100 90.0

94.3 84.7

88.4 79.4

82.5 74.1

76.6 68.8

70.7 63.5

64.8 58.2

59.0 53.0

53.1 4 7.2 47.7 42.4

2310 2190 2080 1960 1850 1860 1770 1670 1580 1490 1650 1570 1490 1410 1320 1470 1390 1320 1250 1170 1300 1240 1170 1110 1 040 1160 1100 1040 985 927 1030 983 931 880 828

1730 1390 1240 1100 975 869 776

1610 1500 1380 1270 1150 1040 1300 1210 1120 1020 929 836 1160 1080 992 909 827 744 1030 953 879 806 733 660 910 845 780 715 650 585 811 753 695 637 579 522 724 673 621 569 517 466

W14808 730 665 605 550 500 455 W14426 398 370 342 311 283 257 233 211 193 176 159 145



945 874 801 729 652 583 520 463 416 372 341 301 271

898 830 761 693 619 554 494 440 395 353 324 286 258

851 787 721 656 587 525 468 417 374 335 307 271 244

803 743 681 620 554 496 442 394 354 316 290 256 231

756 699 641 583 521 466 416 371 333 298 273 241 217

709 656 601 547 489 437 390 348 312 279 256 226 204

662 612 561 511 456 408 364 324 291 260 239 211 190

614 568 520 474 424 379 338 301 270 242 222 196 176

567 524 480 438 391 350 312 278 250 223 205 181 163

520 481 440 401 358 321 286 255 229 205 188 166 149

71


473 437 400 365 326 292 260 232 208 186 171 151 136

425 393 360 328 293 262 234 209 187 167 153 136 122

923 743 661 586 520 464 414 378 350 320 292 261 233 208 185 166 149 136 121 109


Shape

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

W14132 120 109 99 90

255 231 203 185 167

243 219 193 176 158

230 208 183 167 150

217 196 173 158 142

204 185 162 148 133

191 173 152 139 125

179 161 142 130 117

166 150 132 121 108

153 138 122 111 100

140 127 112 102 91.6

128 115 101 92.7 83.3

115 104 91.3 83.4 75.0

102 92.3 81.2 74.2 66.6

W1482 74 68 61

197 172 157 141

187 164 149 134

177 155 142 127

167 146 134 120

158 138 126 113

148 129 118 105

138 121 110 98.4

128 112 102 91.4

118 103 94.4 84.4

108 94.7 86.5 77.3

98.5 86.1 78.7 70.3

88.7 77.5 70.8 63.3

78.8 68.9 62.9 56.3

W1453 48 43

139 127 112

132 120 107

125 114 101

118 108 95.6

111 101 90.0

104 94.9 84.4

97.3 90.4 88.6 82.3 78. 7 73.1

83.4 76.0 67.5

76.5 69.5 69.6 63.3 61. 9 56.2

62.6 57.0 50.6

55.6 50.6 45.0

W1438 34 30

118 108 101

112 106 100 102 96. 8 91.4 95.8 90.8 85.8

94.4 88.5 82. 6 76.7 86.1 80.7 75. 3 69.9 80.7 75.7 70.6 65.6

70.8 64. 9 59.0 53.1 64.5 59. 2 53.8 48.4 60.5 55.5 50.4 45.4

47.2 43.0 40.4

W1426 22

95.8 85.3

91.0 86.2 81.4 81.1 76.8 72.5

76.6 71.8 67.0 62.3 68.3 64.0 59.7 55.5

57.5 52.7 47.9 43.1 51.2 46.9 42.7 38.4

38.3 34.1

W12336 305 279 252 230 210 190 170 152 136 120 106 96 87 79 72 65

806 716 655 580 522 469 412 364 322 286 252 212 189 174 157 142 128

766 680 622 551 496 445 391 345 306 272 239 202 179 166 149 135 121

725 644 589 522 470 422 370 327 290 257 226 191 170 157 141 128 115

685 609 557 493 444 398 350 309 274 243 214 180 160 148 134 121 108

645 573 524 464 418 375 329 291 258 229 201 170 151 139 126 114 102

605 537 491 435 392 351 309 273 242 215 189 159 142 131 118 107 95.7

564 501 458 406 366 328 288 255 225 200 176 149 132 122 110 100 89.3

524 465 426 377 339 305 268 236 209 186 163 138 123 113 102 92.4 83.0

484 430 393 348 313 281 247 218 193 172 151 127 113 105 94.3 85.3 76.6

443 394 360 319 287 258 226 200 177 157 138 117 104 95.8 86.4 78.2 70.2

403 358 327 290 261 234 206 182 161 143 126 106 94.4 87.1 78.6 71.1 63.8

363 322 295 261 235 211 185 164 145 129 113 95.5 84.9 78.4 70.7 64.0 57.4

322 286 262 232 209 187 165 145 129 114 101 84.9 75.5 69.7 62.8 56.9 51.0

W1258 53

118 112

113 107

107 101

101 95.5

94.8 89.9

88.9 84.3

82. 9 77.0 78. 6 73.0

71.1 67.4

65. 2 59.2 61. 8 56.2

53.3 50.6

47.4 44.9

W1250 45 40

122 109 95.1

116 110 104 104 98. 2 92.7 90.3 85.6 80.8

97.4 91.3 85. 2 79.2 87.3 81.8 76. 4 70.9 76.1 71.3 66.6 61.8

73.1 67. 0 60.9 54.8 65.4 60. 0 54.5 49.1 57.1 52.3 47.6 42.8

48.7 43.6 38.0

W1235 30 26

101 86.6 75.9

96.2 91.1 86.1 82.3 78.0 73.6 72.1 68.3 64.5

81.0 75.9 70.9 65.8 69.3 65.0 60.6 56.3 60.7 56.9 53.1 49.3

60.8 55.7 50.6 45.6 52.0 47.6 43.3 39.0 45.5 41.7 37.9 34.1

40.5 34.7 30.4

W1222 19 16 14

86.4 77.2 71.2 64.3

82.1 73.3 67.7 61.1

69.1 61.7 57.0 51.5

51.8 46.3 42.7 38.6

34.6 30.9 28.5 25.7



77.8 69.4 64.1 57.9

73.5 65.6 60.5 54.7

64.8 57.9 53.4 48.2

60.5 54.0 49.9 45.0

56.2 50.2 46.3 41.8

47.5 42.4 39.2 35.4

43.2 38.6 35.6 32.2

72


38.9 34.7 32.0 28.9


Shape



0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

162 143 124 106 92. 4 81. 1 70.6 64.1

151 132 115 98.6 85.8 75.3 65.5 59.6

0.8

0.85

0.9

0.95

1

W10112 100 88 77 68 60 54 49

232 204 177 152 132 116 101 91.6

220 208 197 185 194 183 173 163 168 159 151 142 144 137 129 121 125 119 112 106 110 104 98. 5 92.7 95.8 90.7 85.7 80.6 87.0 82.5 77.9 73.3

174 153 133 114 99.0 86.9 75.6 68.7

W1045 39 33

95.4 84.4 76.2

90.7 85.9 81.1 76.4 80.2 75.9 71.7 67.5 72.4 68.6 64.8 60.9

71.6 66.8 62.0 57.3 63.3 59.1 54.8 50.6 57.1 53.3 49.5 45.7

52.5 47.7 43.0 46.4 42.2 38.0 41.9 38.1 34.3

38.2 33.7 30.5

W1030 26 22

84.8 72.5 65.9

80.6 76.3 72.1 67.8 68.9 65.3 61.6 58.0 62.6 59.3 56.0 52.7

63.6 59.4 55.1 50.9 54.4 50.8 47.1 43.5 49.4 46.1 42.8 39.5

46.6 42.4 38.2 39.9 36.3 32.6 36.2 33.0 29.7

33.9 29.0 26.4

W1019 17 15 12

69.1 65.5 62.0 50.6

65.7 62.2 58.9 48.1

62.2 59.0 55.8 45.6

58.8 55.7 52.7 43.0

55.3 52.4 49.6 40.5

51.8 49.1 46.5 38.0

48.4 45.9 43.4 35.4

44.9 42.6 40.3 32.9

41.5 39.3 37.2 30.4

38.0 36.0 34.1 27.8

34.6 32.8 31.0 25.3

31.1 29.5 27.9 22.8

27.6 26.2 24.8 20.3

W867 58 48 40 35 31

139 120 91.8 80.2 68.0 61.6

132 114 87.2 76.2 64.6 58.5

125 108 82.6 72.2 61.2 55.4

118 102 78.0 68.2 57.8 52.3

111 96.4 73.4 64.2 54.4 49.2

104 90.4 68.9 60.1 51.0 46.2

97.0 84. 3 64.3 56.1 47.6 43.1

90.0 78.3 59.7 52.1 44.2 40.0

83.1 72.3 55.1 48.1 40.8 36.9

76.2 66.3 50.5 44.1 37.4 33.9

69.3 60. 2 45.9 40.1 34.0 30.8

62.3 54.2 41.3 36.1 30.6 27.7

55.4 48.2 36.7 32.1 27.2 24.6

W828 24

62.0 52.5

58.9 55.8 52.7 49.6 49.8 47.2 44.6 42.0

46.5 43.4 40.3 37.2 39.3 36.7 34.1 31.5

34.1 31.0 27.9 28.9 26.2 23.6

24.8 21.0

W821 18

55.9 50.5

53.1 50.3 47.5 44.7 48.0 45.5 43.0 40.4

41.9 39.1 36.3 33.5 37.9 35.4 32.9 30.3

30.7 27.9 25.2 27.8 25.3 22.7

22.4 20.2

W815 13 10

53.6 49.6 36.2

51.0 48.3 45.6 42.9 47.1 44.7 42.2 39.7 34.4 32.6 30.8 29.0

40.2 37.6 34.9 32.2 37.2 34.7 32.3 29.8 27.2 25.4 23.5 21.7

29.5 26.8 24.1 27.3 24.8 22.3 19.9 18.1 16.3

21.5 19.8 14.5

W625 20 15

55.1 43.5 37.2

52.4 49.6 46.9 44.1 41.3 39.2 37.0 34.8 35.3 33.5 31.6 29.8

41.3 38.6 35.8 33.1 32.6 30.5 28.3 26.1 27.9 26.0 24.2 22.3

30.3 27.6 24.8 23.9 21.8 19.6 20.5 18.6 16.7

22.0 17.4 14.9

W616 12 9

44.1 37.4 27.1

41.9 39.7 37.5 35.3 35.6 33.7 31.8 30.0 25.7 24.4 23.0 21.7

33.1 30.9 28.7 26.5 28.1 26.2 24.3 22.5 20.3 19.0 17.6 16.2

24.2 22.0 19.8 20.6 18.7 16.9 14.9 13.5 12.2

17.6 15.0 10.8

W519 16

37.5 32.5

35.7 33.8 31.9 30.0 30.8 29.2 27.6 26.0

28.2 26.3 24.4 22.5 24.3 22.7 21.1 19.5

20.6 18.8 16.9 17.9 16.2 14.6

15.0 13.0

W413

31.4

29.9 28.3 26.7 25.2

23.6 22.0 20.4 18.9

17.3 15.7 14.2

12.6

139 127 122 112 106 97.4 91.0 83.4 79.2 72.6 69.5 63.7 60.5 55.4 55.0 50.4

116 102 88.5 75.8 66. 0 57. 9 50.4 45.8

73


104 92.6 91.7 81.5 79.7 70.8 68.3 60.7 59.4 52.8 52.2 46.4 45.4 40.3 41.2 36.6


Appendix B LOCAL COLUMN STRENGTH AT AN INTERMEDIATE LOCATION ALONG A WIDE-FLANGE COLUMN For wind and l ow-seismic applications, Table B-1 aids in the determination of the l ocal c olumn strength at intermediate column locations 25 for wide-flange c olumns with strong-axis directly welded flange and flange plated m oment connections. Table B-1 is f or c olumns with F y = 50 ksi. For high-seismic applications, see AISC (1997a). All values are given to three significant figures. For wide-flange columns with extended end-plate moment connections, the design strength equati ons given in Chapter 2 differ. F or a c ompressive flange f orce, the designer can either calculate the design strength from the Equations in Chapter 2 or conservatively use the tabulated values. However, for a tensile flange force, the l ocal flange bending limit state is significantly more conservative for extended end-plate moment connections and the designer must calculate the design strength from the Equations in Chapter 2. A flange force is considered to be applied at an intermediate location when it is applied equal to or greater than the distance shown below fr om the end of the c olumn.

K1-1, where  R n



0.90  6.25 t f 2 F y

For the limit state of local web yielding, the design strength is determined from LRFD Specification Equati on K1-2, where  R n



1.0  5 k  N  F y t w

The design strength at intermediate values of N can be determined by linear interpolation.26 In the ab ove discussi on and equations, column flange thickness, in.  column depth, in.  thickness of beam flange or flange plate that delivers the concentrated force, in. F y  column specified minimum yield strength, ksi k  distance from outer face of flange t o web t oe of flange-to-web fillet, in. t w  column web thickness, in.

t f d c N

INTERMEDIATE LOCATION CRITERIA Apply when flange force is applied Limit State at least: Local flange bending 10t f from the c olumn end Lo cal web yielding d c fro m the c olumn end Web crippling d c /2 from the c olumn end Compression buckling d c/2 from the c olumn end of the web



Compressive Flange Forces

The tabulated local column strength is determined as the lesser value from the limit states of local web yielding and web crippling. For a given W-shape, the table is entered under the appropriate value of N and the design strength is determined from the c orresponding c ompressi on ( C) column. When designing for tw o opp osing c ompressive flange f orces, the l ocal c olumn strength is determined as the lesser value from the limit states of local web yielding, web crippling, and compression buckling of the web. F or a given W-shape, the table is entered under the appr opriate value of N and the design strength is determined f or l ocal web yielding and web crippling from the c orresp onding compression (C) c olumn. The lesser of this value and that tabulated for compression buckling of the web is taken as the design strength. For the limit state of l ocal web yielding, the design strength is determined from LRFD Specification Equati on

Tensile Flange Forces

The tabulated local column strength is determined as the lesser value from the limit states of local flange bending and local web yielding. For a given W-shape, the table is entered under the appr opriate values of N and the design strength is determined from the c orresponding tensi on ( T) column. For the limit state of local flange bending, the design strength is determined from LRFD Specification Equati on 25

An intermediate column location is one that is far enough from the column end that thereductio nsf or column-end locations in AISC LRFD Specification Section K1 do not apply. See the discussion in Appendix C for Table C-1 f or further inf ormati on.

26

Note that the value determined by linear interpolation between tabulated values will be appro ximate, since the equations used to generate the tabulated values are n ot necessarily linear.

75


K1-2, where  Rn



The design strength at intermediate values of N can be determined by linear interpolation.27 In the ab ove discussi on and equations,

1.0  5 k  N  F y t w

N

For the limit state of web crippling, the design strength is determined from LRFD Specification Equation K1-4, where  R n



2

0.75  135 t w

1.5

F y k

   

N 1 3 dc

t w t f

F y t f t w

t w t f d c h

For the limit state of compression buckling of the web, the design strength is determined fr om LRFD Specification Equation K1-8, where  Rn



0.90 

thickness of beam flange or flange plate that delivers the concentrated force, in.  column specified minimum yield strength, ksi  distance from outer face of c olumn flange t o web toe of flange-t o-web fillet, in.  column web thickness, in.  column flange thickness, in.  column depth, in.  d c  2 k , in. 

27

Note that the value determined by linear interpolation between tabulated values will be approximate, since the equations used to generate the tabulated values are n ot necessarily linear.

4,100tw3  F y h

76


Table B-1 Local Column Strength at Intermediate Location Along Wide-Flange Column, F y  50 ksi (Wind and Low-Seismic Applications, see Section 1.4) Least Design Strength for Local Flange Bending, Local Web Yielding, and Web Crippling R n , kips N , in. 1

1

/4

3

/2

/4

11/4

1

11/2

13/4

2

Web Compr. Buckling  R n , kips

Shape

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

C only

W44335 290 262 230

666 527 442 364

666 527 442 364

679 538 452 373

679 538 452 373

692 549 462 382

692 549 462 382

704 560 472 391

704 560 472 391

717 571 481 399

717 571 481 399

730 582 491 408

730 582 491 408

743 593 501 417

743 593 501 417

755 604 511 419

755 604 511 426

712 442 330 240

W40593 503 431 372 321 297 277 249 215 199 174

2010 1540 1210 957 747 724 581 502 394 319 194

2010 1540 1210 957 747 724 581 502 394 374 333

2030 1550 1230 972 759 735 591 511 402 319 194

2030 1550 1230 972 759 735 591 511 402 382 341

2050 1574 1240 986 772 747 602 520 410 319 194

2050 1574 1240 986 772 747 602 520 410 390 349

2080 1593 1260 1000 784 759 612 530 418 319 194

2080 1593 1260 1000 784 759 612 530 418 398 358

2100 1612 1280 1020 797 766 623 539 419 319 194

2100 1612 1280 1020 797 770 623 539 427 405 365

2120 1631 1290 1030 809 766 633 548 419 319 194

2120 1631 1290 1030 809 782 633 548 433 409 370

2140 1651 1310 1040 822 766 643 558 419 319 194

2140 1651 1310 1040 822 793 643 558 436 412 374

2170 1670 1330 1060 834 766 654 567 419 319 194

2170 1670 1330 1060 834 805 654 567 439 416 379

4390 2790 1840 1190 763 622 436 323 209 210 210

W40466 392 331 278 264 235 211 183 167 149

1740 1330 1030 778 717 581 502 394 295 194

1740 1330 1030 778 717 581 502 394 364 323

1760 1350 1040 791 729 591 511 402 295 194

1760 1350 1040 791 729 591 511 402 372 331

1790 1360 1060 803 741 602 520 410 295 194

1790 1360 1060 803 741 602 520 410 380 339

1810 1380 1070 816 753 612 530 418 295 194

1810 1380 1070 816 753 612 530 418 388 343

1830 1400 1090 829 765 623 539 419 295 194

1830 1400 1090 829 765 623 539 427 396 347

1850 1420 1100 842 777 633 548 419 295 194

1850 1420 1100 842 777 633 548 433 402 352

1870 1430 1120 854 789 643 558 419 295 194

1870 1430 1120 854 789 643 558 436 406 356

1890 1450 1130 867 801 654 563 419 295 194

1890 1450 1130 867 801 654 567 439 410 360

3550 2190 1390 811 676 436 323 209 209 191

W36848 798 650 527 439 393 359 328 300 280 260 245 230

3620 3270 2330 1660 1230 1030 889 778 676 606 549 510 447

3620 3270 2330 1660 1230 1030 889 778 676 606 549 510 461

3650 3300 2360 1680 1250 1040 903 791 688 617 559 513 447

3650 3300 2360 1680 1250 1040 903 791 688 617 559 520 470

3680 3330 2380 1700 1260 1060 917 803 700 628 570 513 447

3680 3330 2380 1700 1260 1060 917 803 700 628 570 530 480

3710 3350 2410 1720 1280 1070 931 816 712 639 580 513 447

3710 3350 2410 1720 1280 1070 931 816 712 639 580 540 489

3740 3380 2430 1740 1300 1090 945 829 724 650 583 513 447

3740 3380 2430 1740 1300 1090 945 829 724 650 591 550 499

3770 3410 2460 1760 1310 1100 959 842 735 661 583 513 447

3770 3410 2460 1760 1310 1100 959 842 735 661 601 560 508

3800 3440 2480 1780 1330 1120 973 854 747 672 583 513 447

3800 3440 2480 1780 1330 1120 973 854 747 672 612 570 518

3840 3470 2510 1800 1350 1130 987 867 759 683 583 513 447

3840 3470 2510 1800 1350 1130 987 867 759 683 622 580 527

13400 11300 6420 3500 2110 1520 1180 891 708 581 497 430 368

W36256 232 210 194 182 170 160 150 135

642 555 490 428 392 340 293 249 176

642 555 490 428 394 349 323 301 261

654 566 501 437 392 340 293 249 176

654 566 501 437 403 357 331 309 268

666 576 511 447 392 340 293 249 176

666 576 511 447 412 366 339 316 276

678 587 520 447 392 340 293 249 176

678 587 521 457 421 374 347 324 283

690 598 520 447 392 340 293 249 176

690 598 532 466 430 383 355 332 291

702 609 520 447 392 340 293 249 176

702 609 542 476 440 391 364 340 298

714 620 520 447 392 340 293 249 176

714 620 552 485 449 400 372 348 306

726 631 520 447 392 340 293 249 176

726 631 563 495 458 408 380 355 313

717 535 465 364 310 255 223 198 175

77


Table B-1 (cont’d) Local Column Strength at Intermediate Location Along Wide-Flange Column, F y  50 ksi (Wind and Low-Seismic Applications, see Section 1.4) Least Design Strength for Local Flange Bending, Local Web Yielding, and Web Crippling R n , kips N , in. 1

1

/4

3

/2

/4

11/4

1

11/2

13/4

2


Shape

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

C only

W33354 318 291 263 241 221 201

848 712 627 527 464 409 355

848 712 627 527 464 409 355

863 725 639 538 475 419 364

863 725 639 538 475 419 364

877 738 651 549 485 429 372

877 738 651 549 485 429 373

892 751 663 560 495 438 372

892 751 663 560 495 438 382

906 764 675 571 506 448 372

906 764 675 571 506 448 391

921 777 687 582 516 457 372

921 777 687 582 516 458 400

935 790 699 593 527 457 372

935 790 699 593 527 467 409

950 803 711 604 537 457 372

950 803 711 604 537 477 418

1370 985 777 577 501 407 320

W33169 152 141 130 118

354 306 259 206 154

354 306 272 252 222

362 313 259 206 154

362 314 280 259 229

371 313 259 206 154

371 321 287 266 235

379 313 259 206 154

379 329 295 274 242

387 313 259 206 154

387 337 303 281 249

396 313 259 206 154

396 345 310 288 256

404 313 259 206 154

404 353 318 295 263

412 313 259 206 154

412 361 325 303 270

264 225 194 171 146

W30477 391 326 292 261 235 211 191 173

1550 1120 816 682 578 477 421 353 315

1550 1120 816 682 578 477 421 353 315

1570 1140 830 695 590 488 431 362 319

1570 1140 830 695 590 488 431 362 323

1590 1160 844 708 602 498 441 371 319

1590 1160 844 708 602 498 441 371 332

1610 1170 859 720 613 508 450 379 319

1610 1170 859 720 613 508 450 379 340

1630 1190 873 733 625 519 460 388 319

1630 1190 873 733 625 519 460 388 348

1650 1210 887 746 636 529 470 395 319

1650 1210 887 746 636 529 470 397 356

1670 1220 901 759 648 540 480 395 319

1670 1220 901 759 648 540 480 406 364

1690 1240 916 771 660 550 486 395 319

1690 1240 916 771 660 550 489 415 373

4230 2460 1440 1030 785 557 455 348 275

W30148 132 124 116 108 99 90

333 277 243 203 162 126 105

333 277 254 237 220 193 160

341 281 243 203 162 126 105

341 284 261 244 227 200 166

349 281 243 203 162 126 105

349 292 269 251 233 206 172

358 281 243 203 162 126 105

358 300 276 258 240 213 178

366 281 243 203 162 126 105

366 308 283 265 247 219 184

374 281 243 203 162 126 105

374 315 291 272 254 226 189

382 281 243 203 162 126 105

382 323 298 279 261 232 195

390 281 243 203 162 126 105

390 331 305 286 267 239 201

269 226 195 176 158 137 101

W27539 448 368 307 258 235 217 194 178 161 146

2120 1540 1120 830 625 537 464 396 349 307 263

2120 1540 1120 830 625 537 464 396 349 307 263

2140 1560 1130 845 637 549 475 405 358 316 267

2140 1560 1130 845 637 549 475 405 358 316 270

2170 1580 1150 859 649 560 485 415 367 324 267

2170 1580 1150 859 649 560 485 415 367 324 278

2190 1600 1170 874 662 572 495 424 376 328 267

2190 1600 1170 874 662 572 495 424 376 332 285

2220 1620 1190 888 674 583 506 434 385 328 267

2220 1620 1190 888 674 583 506 434 385 340 293

2240 1650 1200 903 686 594 516 443 394 328 267

2240 1650 1200 903 686 594 516 443 394 349 301

2270 1670 1220 917 698 606 527 452 398 328 267

2270 1670 1220 917 698 606 527 452 403 357 308

2290 1690 1240 932 711 617 537 462 398 328 267

2290 1690 1240 932 711 617 537 462 412 365 316

8310 4880 2860 1700 1020 818 620 459 413 313 241

W27129 114 102 94 84

284 239 194 156 115

284 239 208 182 164

292 243 194 156 115

292 246 214 188 170

299 243 194 156 115

299 253 220 194 175

307 243 194 156 115

307 260 227 201 181

315 243 194 156 115

315 267 233 207 187

322 243 194 156 115

322 274 240 213 193

330 243 194 156 115

330 281 246 219 198

337 243 194 156 115

337 289 253 225 203

247 201 149 128 106

78



1

/4

3

/2

/4

11/4

1

11/2

13/4

2


Shape

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

C only

W24492 408 335 279 250 229 207 192 176 162 146 131 117 104

2150 1570 1140 848 712 612 527 466 408 361 313 259 203 158

2150 1570 1140 848 712 612 527 466 408 361 313 272 230 194

2170 1590 1160 863 725 624 538 476 417 370 321 259 203 158

2170 1590 1160 863 725 624 538 476 417 370 321 280 237 200

2200 1610 1170 877 738 636 549 486 427 379 329 259 203 158

2200 1610 1170 877 738 636 549 486 427 379 329 287 244 206

2220 1630 1190 892 751 648 560 496 436 388 334 259 203 158

2220 1630 1190 892 751 648 560 496 436 388 337 295 251 213

2250 1650 1210 906 764 660 571 506 445 397 334 259 203 158

2250 1650 1210 906 764 660 571 506 445 397 345 303 258 219

2270 1670 1230 921 777 672 582 516 455 405 334 259 203 158

2270 1670 1230 921 777 672 582 516 455 405 353 310 265 225

2300 1690 1240 935 790 684 593 527 464 414 334 259 203 158

2300 1690 1240 935 790 684 593 527 464 414 362 318 272 231

2320 1710 1260 950 803 696 604 537 473 419 334 259 203 158

2320 1710 1260 950 803 696 604 537 473 423 370 325 278 238

9490 5570 3260 1940 1400 1100 820 661 524 435 341 275 207 155

W24103 94 84 76 68

248 215 167 130 96.3

248 216 189 164 148

254 215 167 130 96.3

254 222 195 169 152

261 215 167 130 96.3

261 229 201 175 155

268 215 167 130 96.3

268 235 207 180 157

270 215 167 130 96.3

275 241 213 186 160

270 215 167 130 96.3

282 248 219 189 163

270 215 167 130 96.3

289 254 223 192 166

270 215 167 130 96.3

296 261 226 195 169

206 169 129 106 88.9

W2462 55

97.9 71.7

153 129

97.9 71.7

159 132

97.9 71.7

164 135

97.9 71.7

167 137

97.9 71.7

170 140

97.9 71.7

173 143

97.9 71.7

176 146

97.9 71.7

179 149

98.8 76.8

W21201 182 166 147 132 122 111 101

552 477 408 347 301 259 215 180

552 477 408 347 303 261 230 202

563 488 417 356 301 259 215 180

563 488 417 356 311 268 237 208

574 498 427 365 301 259 215 180

574 498 427 365 319 276 244 214

586 508 436 372 301 259 215 180

586 508 436 374 327 283 251 220

597 519 445 372 301 259 215 180

597 519 445 383 335 291 258 227

609 529 455 372 301 259 215 180

609 529 455 392 343 298 265 233

620 540 464 372 301 259 215 180

620 540 464 401 351 306 272 239

631 550 473 372 301 259 215 180

631 550 473 410 360 313 278 245

1080 819 604 532 394 308 238 179

W2193 83 73 68 62

243 196 154 132 106

252 208 176 160 143

243 196 154 132 106

259 214 182 165 147

243 196 154 132 106

266 220 188 171 150

243 196 154 132 106

274 227 193 176 153

243 196 154 132 106

281 233 199 181 155

243 196 154 132 106

288 240 205 185 158

243 196 154 132 106

295 246 210 188 161

243 196 154 132 106

303 253 215 191 163

279 195 135 114 91.6

W2157 50 44

119 80.5 57.0

144 125 102

119 80.5 57.0

149 128 104

119 80.5 57.0

154 131 107

119 80.5 57.0

159 133 109

119 80.5 57.0

162 136 112

119 80.5 57.0

164 139 114

119 80.5 57.0

167 141 117

119 80.5 57.0

170 144 119

94.7 78.6 61.2

W18311 283 258 234 211 192 175 158 143 130

1330 1130 976 812 692 597 512 440 374 322

1330 1130 976 812 692 597 512 440 374 322

1340 1150 992 827 706 609 523 451 383 331

1340 1150 992 827 706 609 523 451 383 331

1360 1170 1010 841 719 621 534 461 392 339

1360 1170 1010 841 719 621 534 461 392 339

1380 1190 1020 856 732 633 545 471 402 348

1380 1190 1020 856 732 633 545 471 402 348

1400 1200 1040 870 745 645 556 481 411 356

1400 1200 1040 870 745 645 556 481 411 356

1420 1220 1060 885 759 657 567 491 420 364

1420 1220 1060 885 759 657 567 491 420 364

1440 1240 1070 899 772 669 579 501 429 373

1440 1240 1070 899 772 669 579 501 429 373

1460 1260 1090 914 785 681 590 511 438 381

1460 1260 1090 914 785 681 590 511 438 381

5930 4630 3540 2620 2000 1490 1180 896 655 506

79



1

/4

3

/2

/4

11/4

1

11/2

13/4

2


Shape

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

C only

W18119 106 97 86 76

295 247 213 167 130

295 247 216 179 151

303 249 213 167 130

303 254 222 185 157

311 249 213 167 130

311 262 229 191 162

316 249 213 167 130

319 269 236 197 167

316 249 213 167 130

328 277 242 203 173

316 249 213 167 130

336 284 249 209 178

316 249 213 167 130

344 291 256 215 183

316 249 213 167 130

352 299 262 221 189

474 346 258 186 130

W1871 65 60 55 50

185 158 136 112 91.4

192 167 148 133 115

185 158 136 112 91.4

198 173 153 138 119

185 158 136 112 91.4

204 179 158 143 121

185 158 136 112 91.4

210 184 163 147 124

185 158 136 112 91.4

217 190 169 152 126

185 158 136 112 91.4

223 195 174 155 128

185 158 136 112 91.4

229 201 179 158 131

185 158 136 112 91.4

235 207 184 161 133

205 154 120 100 75.4

W1846 40 35

103 77.5 50.8

117 93.5 78.6

103 77.5 50.8

122 95.3 80.5

103 77.5 50.8

126 97.1 82.5

103 77.5 50.8

129 98.9 84.4

103 77.5 50.8

132 101 86.3

103 77.5 50.8

134 102 88.3

103 77.5 50.8

136 104 90.2

103 77.5 50.8

139 106 92.1

78.2 52.5 45.6

W16100 89 77 67

254 212 162 124

254 212 169 141

261 215 162 124

261 218 175 146

269 215 162 124

269 225 181 151

273 215 162 124

276 231 186 156

273 215 162 124

283 238 192 160

273 215 162 124

291 244 198 163

273 215 162 124

298 251 203 166

273 215 162 124

305 258 209 169

384 277 180 118

W1657 50 45 40 36

144 112 89.8 71.7 52.0

153 129 111 87.6 77.2

144 112 89.8 71.7 52.0

159 134 114 89.5 79.3

144 112 89.8 71.7 52.0

164 139 116 91.4 81.3

144 112 89.8 71.7 52.0

169 144 119 93.2 83.3

144 112 89.8 71.7 52.0

175 147 121 95.1 85.3

144 112 89.8 71.7 52.0

180 150 124 97.0 87.4

144 112 89.8 71.7 52.0

185 153 126 99 89.4

144 112 89.8 71.7 52.0

191 156 128 101 91.4

152 105 78.6 54.3 49.2

W1631 26

54.5 33.5

70.1 54.1

54.5 33.5

71.7 55.7

54.5 33.5

73.3 57.2

54.5 33.5

74.9 58.8

54.5 33.5

76.5 60.3

54.5 33.5

78.1 61.9

54.5 33.5

79.7 63.4

54.5 33.5

81.3 65.0

39.8 30.1

W14808 730 665 605 550 500 455

5480 4310 3710 3160 2710 2320 1980

5480 4310 3710 3160 2710 2320 1980

5530 4350 3740 3190 2740 2350 2000

5530 4350 3740 3190 2740 2350 2000

5580 4380 3780 3220 2770 2380 2030

5580 4380 3780 3220 2770 2380 2030

5620 4420 3810 3250 2800 2400 2050

5620 4420 3810 3250 2800 2400 2050

5670 4460 3850 3280 2830 2430 2080

5670 4460 3850 3280 2830 2430 2080

5720 4500 3880 3320 2860 2460 2100

5720 4500 3880 3320 2860 2460 2100

5760 4540 3920 3350 2890 2480 2130

5760 4540 3920 3350 2890 2480 2130

5810 4580 3950 3380 2920 2510 2150

5810 4580 3950 3380 2920 2510 2150

122000 66800 52500 40400 31300 24400 18900

W14426 398 370 342 311 283 257 233 211 193 176 159 145

1750 1570 1390 1220 1050 903 767 649 564 484 425 359 306

1750 1570 1390 1220 1050 903 767 649 564 484 425 359 306

1780 1590 1410 1240 1070 919 782 662 576 495 436 368 315

1780 1590 1410 1240 1070 919 782 662 576 495 436 368 315

1800 1620 1430 1260 1090 935 797 675 588 506 446 377 323

1800 1620 1430 1260 1090 935 797 675 588 506 446 377 323

1820 1640 1450 1280 1110 951 811 689 600 517 457 386 332

1820 1640 1450 1280 1110 951 811 689 600 517 457 386 332

1850 1660 1470 1300 1120 968 826 702 613 528 467 396 334

1850 1660 1470 1300 1120 968 826 702 613 528 467 396 340

1870 1680 1500 1320 1140 984 841 716 625 540 477 398 334

1870 1680 1500 1320 1140 984 841 716 625 540 477 405 349

1890 1700 1520 1340 1160 1000 856 729 637 551 483 398 334

1890 1700 1520 1340 1160 1000 856 729 637 551 488 414 357

1920 1730 1540 1360 1180 1020 870 742 649 562 483 398 334

1920 1730 1540 1360 1180 1020 870 742 649 562 498 424 366

15200 12800 10500 8440 6500 4980 3760 2830 2190 1640 1330 961 727

80



1

/4

3

/2

/4

11/4

1

11/2

Shape

T

C

T

C

T

C

T

C

T

C

T

W14132 120 109 99 90

280 247 208 171 142

280 247 212 180 157

288 249 208 171 142

288 254 218 186 162

296 249 208 171 142

296 262 225 192 168

298 249 208 171 142

304 269 231 199 173

298 249 208 171 142

312 277 238 205 179

298 249 208 171 142

W1482 74 68 61

206 173 146 117

214 181 161 135

206 173 146 117

220 187 166 138

206 173 146 117

226 193 171 142

206 173 146 117

233 198 176 145

206 173 146 117

239 204 181 148

W1453 48 43

123 100 79.0

134 112 89.9

123 99.6 79.0

137 115 92.0

123 100 79.0

140 117 94.1

123 99.6 79.0

143 120 96.2

123 100 79.0

W1438 34 30

74.6 58.2 41.7

86.2 74.8 64.3

74.6 58.2 41.7

90.1 77.4 66.3

74.6 58.2 41.7

94.0 79.3 68.3

74.6 58.2 41.7

97.5 81.3 70.3

W1426 22

49.6 31.6

61.3 47.1

49.6 31.6

62.8 48.5

49.6 31.6

64.3 50.0

49.6 31.6

W12336 305 279 252 230 210 190 170 152 136 120 106 96 87 79 72 65

1660 1420 1240 1040 900 789 659 552 473 393 331 265 228 185 152 126 103

1660 1420 1240 1040 900 789 659 552 473 393 331 265 230 200 175 153 133

1680 1440 1260 1060 916 804 672 564 484 402 339 273 228 185 152 126 103

1680 1440 1260 1060 916 804 672 564 484 402 339 273 237 206 181 159 138

1700 1460 1280 1080 932 819 686 576 495 412 343 276 228 185 152 126 103

1700 1460 1280 1080 932 819 686 576 495 412 348 280 244 212 187 164 143

W1258 53

115 93.0

127 112

115 93.0

130 116

115 93.0

W1250 45 40

115 93.0 74.6

132 108 84.6

115 93.0 74.6

136 111 86.8

W1235 30 26

76.1 54.5 40.6

78.8 64.2 50.1

76.1 54.5 40.6

82.5 66.4 51.5

13/4 C

2


T

C

T

C

C only

320 284 244 211 184

298 249 208 171 142

329 291 251 217 190

298 249 208 171 142

337 299 258 223 195

620 477 337 264 197

206 173 146 117

245 210 185 151

206 173 146 117

252 215 189 154

206 173 146 117

258 221 193 157

313 215 169 125

146 122 98

123 99.6 79.0

149 125 100

123 100 79.0

152 127 103

123 99.6 79.0

155 130 105

120 92.9 67.1

74.6 58.2 41.7

100 83.2 72.2

74.6 58.2 41.7

102 85.2 74.2

74.6 58.2 41.7

104 87.2 76.2

74.6 58.2 41.7

106 89.1 78.2

64.9 50.4 42.9

65.8 51.4

49.6 31.6

67.4 52.8

49.6 31.6

68.9 54.2

49.6 31.6

70.4 55.6

49.6 31.6

71.9 57.1

35.9 26.5

1730 1480 1300 1090 948 833 699 588 506 422 343 276 228 185 152 126 103

1730 1480 1300 1090 948 833 699 588 506 422 357 288 251 219 192 169 147

1750 1500 1320 1110 964 848 712 600 517 432 343 276 228 185 152 126 103

1750 1500 1320 1110 964 848 712 600 517 432 366 295 258 225 198 175 152

1770 1520 1330 1130 980 863 725 612 527 439 343 276 228 185 152 126 103

1770 1520 1330 1130 980 863 725 612 527 442 375 303 265 232 204 180 157

1790 1540 1350 1150 996 878 739 624 538 439 343 276 228 185 152 126 103

1790 1540 1350 1150 996 878 739 624 538 452 384 311 272 238 210 185 162

1810 1560 1370 1160 1010 892 752 636 549 439 343 276 228 185 152 126 103

1810 1560 1370 1160 1010 892 752 636 549 462 393 318 278 245 216 191 167

15500 11900 9860 7430 5800 4530 3270 2420 1820 1350 984 622 459 374 285 218 163

133 120

115 93.0

137 123

115 93.0

140 126

115 93.0

143 129.1

115 93.0

146 132

115 93.0

149 135

129 112

115 93.0 74.6

139 114 89.0

115 93.0 74.6

143 117 91.3

115 93.0 74.6

146 120 93.5

115 93.0 74.6

150 123 95.8

115 93.0 74.6

153 126 98

115 93.0 74.6

157 129 100

140 103 71.0

76.1 54.5 40.6

86.3 68.2 52.9

76.1 54.5 40.6

90.0 69.9 54.3

76.1 54.5 40.6

93.8 71.7 55.7

76.1 54.5 40.6

97.5 73.4 57.1

76.1 54.5 40.6

100 75.1 58.5

76.1 54.5 40.6

103 76.9 59.9

67.1 43.8 30.3

81


Table B-1 (cont’d) Local Column Strength at Intermediate Location Along Wide-Flange Column, F y  50 ksi (Wind and Low-Seismic Applications, see Section 1.4) Web Compr. Buckling  R n , kips

Least Design Strength for Local Flange Bending, Local Web Yielding, and Web Crippling R n , kips N , in. 1

1

/4

Shape

3

/2

/4

11/4

1

11/2

13/4

2

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

C only

W1222 19 16 14

50.8 34.5 19.8 14.2

60. 1 49. 9 39. 8 32. 0

50.8 34.5 19.8 14.2

63.4 51.5 41.6 33.6

50.8 34.5 19.8 14.2

66. 6 53. 2 43. 4 35. 2

50.8 34.5 19.8 14.2

69.1 54.8 45.2 36.8

50. 8 34. 5 19. 8 14. 2

70.9 56.4 47.0 38.4

50.8 34.5 19.8 14.2

72.7 58.1 48.8 40.0

50. 8 34. 5 19. 8 14. 2

74.5 59.7 50.6 41.6

50.8 34.5 19.8 14.2

76.3 61.4 52.4 43.2

43.4 32.1 26.5 19.8

W10112 100 88 77 68 60 54 49

363 306 253 205 167 130 106 88.2

363 306 253 205 167 143 120 105

373 315 261 212 167 130 106 88.2

373 315 261 212 173 148 125 109

382 323 268 213 167 130 106 88.2

382 323 268 219 179 154 130 114

392 332 276 213 167 130 106 88.2

392 332 276 225 185 159 134 118

401 340 276 213 167 130 106 88.2

401 340 284 232 191 164 139 122

411 349 276 213 167 130 106 88.2

411 349 291 239 197 169 143 126

420 353 276 213 167 130 106 88.2

420 357 299 245 203 175 148 131

429 353 276 213 167 130 106 88.2

429 366 306 252 209 180 153 135

1476 1080 761 511 354 255 174 135

W1045 108 39 79.0 53.2 33

114 108 92.5 79.0 76. 8 53.2

118 96.5 79.9

108 79.0 53.2

123 108 100 79.0 83. 0 53.2

127 104 86.1

108 131 79.0 108 53. 2 89.2

108 79.0 53.2

136 111 92.3

108 140 79.0 114 53. 2 95.4

108 79.0 53.2

144 118 98.5

147 106 83.7

W1030 73.2 26 54.5 36.5 22

74. 1 73.2 60. 1 54.5 48. 0 36.5

77.8 63.4 51.0

73.2 54.5 36.5

81. 6 73.2 66. 6 54.5 54. 0 36.5

85.3 69.9 57.0

73. 2 89.1 54. 5 73.1 36. 5 60.0

73.2 54.5 36.5

92.8 75.4 62.7

73. 2 96.6 54. 5 77.5 36. 5 64.7

73.2 54.5 36.5

100 79.6 66.7

82.0 53.4 41.6

W1019 17 15 12

43.9 30.6 20.5 12.4

53. 9 48. 0 42. 4 28. 9

43.9 30.6 20.5 12.4

57.0 51.0 45.3 30.7

43.9 30.6 20.5 12.4

60. 2 54. 0 48. 2 32. 5

43.9 30.6 20.5 12.4

63.3 57.0 50.7 34.3

43. 9 30. 6 20. 5 12. 4

66.4 59.5 53.1 36.1

43.9 30.6 20.5 12.4

68.7 61.7 55.6 37.8

43. 9 30. 6 20. 5 12. 4

70.8 63.9 58.0 39.6

43.9 30.6 20.5 12.4

72.8 66.2 60.4 41.4

47.3 41.9 36.9 20.8

W867 58 48 40 35 31

212 174 124 88.2 68.9 53.2

212 219 174 180 124 129 100 88.2 81.4 68.9 70. 4 53.2

219 180 129 105 85.3 73.9

226 185 132 88.2 68.9 53.2

226 233 186 185 134 132 109 88.2 89.1 68.9 77. 5 53.2

233 193 139 114 93.0 81.0

240 240 185 199 132 144 88.2 118 68.9 96.9 53. 2 84.6

246 185 132 88.2 68.9 53.2

248 206 149 123 101 88.2

246 255 185 212 132 154 88.2 127 68.9 105 53. 2 91.7

246 185 132 88.2 68.9 53.2

262 218 159 132 109 95.3

789 565 273 199 127 98.6

W828 24

60.8 45.0

70. 4 60.8 56. 7 45.0

73.9 59.7

60.8 45.0

77. 5 60.8 62. 4 45.0

81.0 64.9

60. 8 84.6 45. 0 67.4

60.8 45.0

88.2 69.8

60. 8 91.7 45. 0 72.3

60.8 45.0

95.3 74.8

97.7 62.1

W821 18

45.0 30.6

53. 9 45.0 46. 0 30.6

57.0 48.9

45.0 30.6

60. 2 45.0 51. 8 30.6

63.3 54.6

45. 0 66.4 30. 6 57.5

45.0 30.6

69.5 60.0

45. 0 72.7 30. 6 62.4

45.0 30.6

75.8 64.8

61.3 47.8

W815 13 10

27.9 18.3 11.8

49. 0 27.9 42. 4 18.3 24. 4 11.8

52.1 45.3 26.0

27.9 18.3 11.8

55. 1 27.9 48. 2 18.3 27. 6 11.8

58.2 51.0 29.2

27. 9 61.3 18. 3 53.9 11. 8 30.9

27.9 18.3 11.8

64.3 56.8 32.5

27. 9 67.4 18. 3 59.7 11. 8 34.1

27.9 18.3 11.8

70.4 62.5 35.8

58.1 48.0 19.3

W625 20 15

58.2 37.5 19.0

69. 0 58.2 52. 0 37.5 38. 8 19.0

73.0 55.3 41.7

58.2 37.5 19.0

77. 0 58.2 58. 5 37.5 44. 6 19.0

81.0 61.8 47.4

58. 2 85.0 37. 5 65.0 19. 0 50.3

58.2 37.5 19.0

89.0 68.3 53.2

58. 2 93.0 37. 5 71.5 19. 0 56.1

58.2 37.5 19.0

97.0 74.8 58.9

180 98 67

W616 12 9

46.1 22.1 13.0

52. 0 46.1 38. 8 22.1 25. 3 13.0

55.3 41.7 27.4

46.1 22.1 13.0

58. 5 46.1 44. 6 22.1 29. 5 13.0

61.8 47.4 31.6

46. 1 65.0 22. 1 50.3 13. 0 33.7

46.1 22.1 13.0

68.3 53.2 35.7

46. 1 71.5 22. 1 56.1 13. 0 37.8

46.1 22.1 13.0

74.8 58.9 39.9

96 66 26.8

W519 16

52.0 36.5

58. 2 52.0 48. 0 36.5

61.6 51.0

52.0 36.5

65. 0 52.0 54. 0 36.5

68.3 57.0

52. 0 71.7 36. 5 60.0

52.0 36.5

75.1 63.0

52. 0 78.5 36. 5 66.0

52.0 36.5

81.8 69.0

146 103

W413

33.5

51. 6 33.5

55.1

33.5

58. 6 33.5

62.1

33. 5 65.6

33.5

69.1

33. 5 72.6

33.5

76.1

206

82


Appendix C LOCAL COLUMN STRENGTH AT A WIDE-FLANGE COLUMN-END LOCATION For wind and l ow-seismic applications, Table C-1 aids in the determination of the l ocal c olumn strength at c olumnend locations for wide-flange c olumns with str ong-axis directly welded flange and flange plated m oment c onnections. Table C-1 is for c olumns with F y = 50 ksi. F or highseismic applications, see AISC (1997a). All values are given to three significant figures. For wide-flange columns with extended end-plate moment connections, the design strength equati ons given in Chapter 2 differ. F or a c ompressive flange f orce, the designer can either calculate the design strength from the Equations in Chapter 2 or conservatively use the tabulated values. However, for a tensile flange force, the l ocal flange bending limit state is significantly more conservative for extended end-plate moment connections and the designer must calculate the design strength from the Equations in Chapter 2. A flange force is considered to be applied at a c olumnend l ocati on when it is applied less than the distance shown bel ow fr om the end of the c olumn.

entered under the appr opriate value of N and the design strength is determined fr om the c orresp onding tensi on ( T) c olumn. F or the limit state of l ocal flange bending, the design strength is determined fr om LRFD Specificati on Equati on K1-1 with a 50-percent reducti on, where  R n



0.90



6.25 t f 2 F y 2

For the limit state of local web yielding, the design strength is determined from LRFD Specification Equati on K1-3, where  Rn



1.0  (2.5 k  N) F y t w

The design strength at intermediate values of N can be determined by linear interpolation.28 In the above discussion and equations, column flange thickness, in.  column depth, in.  thickness of beam flange or flange plate that delivers the concentrated force, in. F y  column specified minimum yield strength, ksi k  distance from outer face of c olumn flange t o web toe of flange-t o-web fillet, in. t w  column web thickness, in.

t f d c N

COLUMN-END CRITERIA Apply when flange force is applied Limit State less than: Local flange bending 10t f from the c olumn end d c fro m the c olumn end Lo cal web yielding d c /2 from the c olumn end Web crippling Compression buckling d c/2 from the c olumn end of the web



Compressive Flange Forces

The tabulated local column strength is determined as the lesser value from the limit states of local web yielding and web crippling. For a given W-shape, the table is entered under the appr opriate value of N and the design strength is determined from the c orresponding c ompressi on ( C) column. When designing f or tw o opp osing c ompressive flange forces, the l ocal c olumn strength is determined as the lesser value from the limit states of l ocal web yielding, web crippling, and c ompressi on buckling ofthe web. F or a given W-shape, the table is entered under the appropriate value of N and the design strength is determined f or l ocal web yielding and web crippling from the c orresp onding

The values in Tables C-1 and C-2 are calculated assuming the flange force is applied at a distance from the c olumn end that is less than all four of the f oreg oing c olumn-end criteria. When the flange force is appliedat a distance fro m the column end that is less than one or m ore, but n ot all of the foregoing c olumn-end criteria, the tabulated values will be conservative. The user may find it advantageous t o calculate the individual design strengths in lieu of using the tabulated values. Tensile Flange Forces

The tabulated local column strength is determined as the lesser value from the limit states of l ocal flange bending and local web yielding. For a given W-shape, the table is

28


83


compression (C) c olumn. The lesser of this value and that tabulated for compressi on buckling of the web is taken as the design strength. For the limit state of l ocal web yielding, the design strength is determined from LRFD Specification Equati on K1-3, where  R n



Equati on K1-8 with a 50-percent reducti on, where  R n

N

For the limit state of web crippling, the design strength is determined from LRFD Specification Equati ons K1-5a and K1-5b, where if N/ d is less than or equal t o 0.2:  R n



0.75  68 t w

1.5

  

N 1 3 dc

t w t f

F y k

 Ft t

y f

d c t w t f h

w

and if N / d is greater than 0.2:  R n



2

0.75  68 tw 1 



4 N dc



0 .2

1.5

0.90 

4 , 100tw3  F y 2h

The design strength at intermediate values of N can be determined by linear interpolation.29 In the above discussion and equations,

1.0  (2.5 k  N ) F y t w

2



thickness of beam flange or flange plate that delivers the concentrated force, in.  column specified minimum yield strength, ksi  distance from outer face of c olumn flange t o web toe of flange-t o-web fillet, in.  column depth, in.  column web thickness, in. 2  column flange thickness, in.  d c  2 k , in. 

   t w t f

F y t f t w 29


For the limit state of compression buckling of the web, the design strength is determined fr om LRFD Specification

84


. g r y n n , s l b p i e m l p n k R i o W o c u  k C C B

6 1 5 0 5 2 6 2 3 2 1 1

0 0 0 7 1 1 8 1 5 5 5 9 9 2 9 8 1 1 6 0 0 0 1 3 9 5 3 3 2 1 1 1 1 2 1

4 . 0 0 3 5 8 8 1 5 5 5 8 9 9 0 3 1 6 0 0 9 7 0 6 4 3 2 1 1 1 1 1

C

9 5 5 9 2 4 9 4 4 3 2 2

0 2 1 7 7 2 2 5 1 9 1 7 1 3 8 6 4 6 9 2 0 9 1 9 7 5 4 4 3 2 2 2 1 1

0 7 7 5 9 2 5 1 6 1 3 9 2 8 4 6 9 2 0 8 0 7 6 4 4 3 2 2 2 1 1

9 5 4 9 2 4 8 0 4 3 2 2

9 . 0 2 1 7 1 3 9 4 9 0 6 7 1 3 8 4 8 4 8 0 6 9 1 9 7 5 4 3 3 2 2 1 1

9 . 0 7 7 1 1 9 2 9 8 6 3 9 2 6 2 4 8 0 4 9 0 7 6 4 4 3 2 2 1 1

6 4 5 0 1 3 8 4 4 3 2 2

0 3 4 3 5 7 8 3 0 8 9 5 9 1 7 5 3 5 9 2 0 8 1 8 7 5 4 4 3 2 2 2 1 1

0 9 2 2 7 8 3 0 4 9 1 7 1 7 3 5 9 2 0 7 0 7 6 4 4 3 2 2 2 1 1

6 4 4 9 1 3 8 0 4 3 2 2

9 . 0 3 4 3 1 3 9 4 9 0 6 5 9 1 7 4 8 4 8 0 6 9 1 8 7 5 4 3 3 2 2 1 1

9 . 0 9 2 1 1 9 2 9 8 6 1 7 1 6 2 4 8 0 4 9 0 7 6 4 4 3 2 2 1 1

3 4 5 1 0 2 7 3 4 3 2 2

0 3 7 8 2 6 8 1 8 6 6 3 7 9 5 4 2 4 9 1 0 8 1 8 6 5 4 4 3 2 2 2 1 1

6 1 7 9 5 8 1 8 3 7 8 6 9 5 2 4 9 1 0 7 9 7 5 4 4 3 2 2 2 1

3 4 5 9 0 2 7 0 4 3 2 2

9 . 0 3 7 8 1 3 8 4 9 0 6 3 7 9 5 4 8 4 8 0 6 9 1 8 6 5 4 3 3 2 2 1 1

9 . 6 1 7 9 1 8 2 9 8 6 8 6 9 5 2 4 8 0 4 9 9 7 5 4 4 3 2 2 1

0 3 5 2 9 1 6 2 3 3 2 2

0 4 0 4 0 4 7 9 7 4 4 1 5 8 4 3 1 3 8 1 0 8 1 8 6 5 4 4 3 2 2 2 1 1

5 3 1 6 3 7 9 7 1 5 6 4 8 4 1 3 8 1 0 7 9 7 5 4 4 3 2 2 2 1

0 3 5 9 9 1 6 0 3 3 2 2

9 . 0 4 0 4 0 3 7 4 9 0 6 1 5 8 4 3 8 3 8 0 6 9 1 8 6 5 4 3 3 2 2 1 1

9 . 5 3 1 6 3 7 2 9 8 6 6 4 8 4 1 3 8 0 4 9 9 7 5 4 4 3 2 2 1

8 2 6 3 7 0 5 1 3 3 2 2

0 5 4 9 7 3 7 4 5 2 2 8 3 6 2 1 0 2 8 1 0 8 0 8 6 5 4 4 3 2 2 2 1 1

5 6 6 4 1 7 4 5 9 3 4 2 6 3 0 2 8 1 9 7 9 7 5 4 4 3 2 2 1 1

8 2 6 9 7 0 5 0 3 3 2 2

9 . 0 5 4 9 7 3 7 4 9 0 6 8 3 6 2 1 8 2 8 0 6 9 0 8 6 5 4 3 3 2 2 1 1

9 . 5 6 6 4 1 7 2 9 8 6 4 2 6 3 0 2 8 0 4 9 9 7 5 4 4 3 2 2 1

5 1 6 4 6 9 4 0 3 2 2 2

0 6 7 5 5 1 6 4 3 0 9 6 1 4 1 0 9 1 7 1 0 7 0 8 6 5 4 3 3 2 2 2 1 1

4 8 1 1 9 6 4 3 7 1 2 0 5 2 8 1 7 1 9 7 9 7 5 4 3 3 2 2 1 1

5 1 6 4 6 9 4 0 3 2 2 2

9 . 0 6 7 5 5 3 6 4 9 0 6 6 1 4 1 0 8 1 7 0 6 9 0 8 6 5 4 3 3 2 2 1 1

9 . 4 8 1 1 9 6 4 9 8 6 2 0 5 2 8 1 7 0 4 9 9 7 5 4 3 3 2 2 1

2 0 6 5 5 8 3 9 3 2 2 1

0 6 0 0 2 9 6 5 9 9 7 4 9 3 0 9 7 0 6 0 9 7 0 7 6 5 3 3 3 2 2 1 1 1

3 0 6 8 7 6 5 9 4 9 0 9 3 0 7 0 6 0 9 6 9 6 5 4 3 3 2 2 1 1

2 0 6 5 5 8 3 9 3 2 2 1

9 . 0 6 0 0 2 9 6 5 9 0 6 4 9 3 0 9 7 0 6 0 6 9 0 7 6 5 3 3 3 2 2 1 1

9 . 3 0 6 8 7 6 5 9 8 6 0 9 3 0 7 0 6 0 4 9 9 6 5 4 3 3 2 2 1

9 9 6 6 3 6 2 8 3 2 2 1

0 7 3 6 0 8 6 5 1 1 1 2 7 1 8 8 6 9 5 0 9 7 0 7 6 4 3 3 2 2 2 1 1 1

2 2 0 5 5 6 5 1 6 5 8 7 2 9 6 9 5 0 8 6 8 6 5 3 3 2 2 2 1 1

9 9 6 6 3 6 2 8 3 2 2 1

9 . 0 7 3 6 0 8 6 5 1 0 6 2 7 1 8 8 6 9 5 0 6 9 0 7 6 4 3 3 2 2 2 1 1

9 . 2 2 0 5 5 6 5 1 8 6 8 7 2 9 6 9 5 0 4 9 8 6 5 3 3 2 2 2 1

5 0 2 0 3 9 6 3 3 2 2 2     4 4 W

3 3 1 2 1 7 7 9 5 9 4 9 0 3 7 2 9 7 4 1 9 7 5 5 4 3 3 2 2 2 2 1 1            0 4 W

6 2 1 8 4 5 1 3 7 9 6 9 3 7 6 3 1 8 6 4 4 3 3 2 2 2 2 1 1 1           0 4 W

2 T

i s k 0 5 

) . , 1 n o n i t o i a t c c o e L S d e n e E s , n s n m o u i l t o a 1 - C i c C e l e g p l p b n a A a l c T F - i e m d i s i e W t S a w o h t L g n d e r n a t S d n n i m W u ( l o C l a c o L y

F 4

s p i k , n

C

R 

4 / 3 g 1 n i l T p p i r C b C e W 2 / 1 d 1 n a , T g n i d l e i C Y b 4 / e 1 1 W l a T c . o n L i , , g N n i C d n e 1 B e T g n a l F l a C c o L 4 / 3 r o f T h t g n e r t C S n g 2 / i 1 s e T D t s a e L C 4 / 1

T

e p a h S

85


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4 3 1 2 1 3 0 8 6 4 2 2 1 1 1

8 . 1 7 0 3 6 0 6 4 7 1 4 6 2 9 7 4 2 8 4 3 2 2 1 1 1 1

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9 8 3 6 6 7 5 6 4 9 4 1 7 5 2 0 8 6 3 3 3 2 2 2 2 1 1

8 0 2 4 0 8 6 1 4 9 3 0 6 3 5 4 3 3 3 2 2

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8 0 2 4 6 9 6 1 4 9 3 7 2 8 5 4 3 3 2 2 1

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7 7 2 7 7 1 3 5 1 8 3 0 6 4 2 0 8 6 3 3 3 2 2 2 2 1 1

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2 . 1 . 3 . 6 1 2 2 1 3 2 9 4 2 0 8 6 5 1 1 1 1

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6 8 2 8 1 5 4 6 4 6 3 7 9 4 8 5 1 9 8 6 4 3 3 2 2 2 1

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6 8 2 8 1 5 3 7 0 6 3 7 9 4 8 4 9 6 8 6 4 3 3 2 2 1 1

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4 / 1

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87

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0 8 9 3 3 6 5 9 4 7 7 7 3 5 6 3 9 3 5 9 4 0 7 4 1 8 5 2 2 9 6 5 4 3 3 3 2 2 2 1 1 1 1 1 . 0 8 9 3 3 6 5 0 3 9 7 0 2 9 6 3 9 3 5 9 4 0 5 0 6 3 0 7 2 9 6 5 4 3 3 3 2 2 1 1 1 1 0 8 1 8 0 4 4 9 5 8 9 4 1 4 3 1 8 1 4 8 3 9 6 3 0 8 5 2 2 9 6 5 4 3 3 2 2 2 2 1 1 1 1 1 . 0 8 1 8 0 4 4 9 3 9 7 0 2 9 3 1 8 1 4 8 3 9 5 0 6 3 0 7 2 9 6 5 4 3 3 2 2 2 1 1 1 1 0 7 4 4 7 2 4 9 5 9 1 8 9 2 1 9 6 0 2 7 2 8 5 2 0 7 4 2 2 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 . 0 7 4 4 7 2 4 9 3 9 7 0 2 9 1 9 6 0 2 7 2 8 5 0 6 3 0 7 2 8 6 5 4 3 3 2 2 2 1 1 1 1 0 7 7 9 4 0 3 8 6 0 3 0 6 0 9 7 4 8 1 6 1 7 4 2 9 7 4 2 1 8 6 4 4 3 3 2 2 2 1 1 1 1 1 1 . 0 7 7 9 4 0 3 8 6 9 7 0 2 9 9 7 4 8 1 6 1 7 4 0 6 3 0 7 1 8 6 4 4 3 3 2 2 2 1 1 1 1 0 6 0 5 1 8 2 8 7 2 5 3 9 8 6 5 3 7 0 4 0 6 3 1 8 6 3 1 1 8 6 4 4 3 3 2 2 2 1 1 1 1 1 1 . 0 6 0 5 1 8 2 8 7 9 7 0 2 9 6 5 3 7 0 4 0 6 3 0 6 3 0 7 1 8 6 4 4 3 3 2 2 2 1 1 1 1 0 5 2 0 8 6 1 8 7 3 7 5 2 3 4 3 1 6 8 3 9 5 2 0 7 5 3 1 1 8 6 4 3 3 2 2 2 2 1 1 1 1 1 1 . 0 5 2 0 8 6 1 8 7 3 7 0 2 9 4 3 1 6 8 3 9 5 2 0 6 3 0 7 1 8 6 4 3 3 2 2 2 2 1 1 1 1 0 5 5 6 5 4 0 8 8 4 9 7 5 6 1 1 9 4 7 2 8 4 1 9 6 4 2 0 1 8 5 4 3 3 2 2 2 1 1 1 1 1 1 1 . 0 5 5 6 5 4 0 8 8 4 7 0 2 9 1 1 9 4 7 2 8 4 1 9 6 3 0 7 1 8 5 4 3 3 2 2 2 1 1 1 1 1 0 4 8 1 2 2 9 8 9 5 0 0 9 0 9 9 7 3 6 1 6 3 0 8 6 4 1 0 0 7 5 4 3 3 2 2 2 1 1 1 1 1 1

6 . 6 . 8 . 4 . 3 4 4 2 4 0 8 6 5 4 1

4 . 4 . 9 8 4 3

1 . 9 . 1 9 4 8 4 6 3 1 9 8 1 1 1

4 . 8 . 0 4 9 7

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

7 . 5 . 9 7 3 6 3 5 3 1 9 8 1 1 1

9 . 4 . 8 3 8 7

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

3 . 1 . 7 5 1 5 2 5 3 1 9 8 1 1 1

3 . 0 . 7 2 8 7

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

9 . 7 . 5 3 0 3 0 5 3 1 9 8 1 1 1

8 . 6 . 5 0 8 7

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

5 . 3 . 8 0 8 2 9 4 3 0 9 7 1 1 1

2 . 2 . 4 9 8 6

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

0 . 9 . 1 4 7 1 7 4 2 0 9 7 1 1 1

7 . 8 . 2 7 8 6

4 . 0 . 1 . 5 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

6 . 5 . 4 7 4 9 6 3 1 0 8 7 1 1 1

2 . 4 . 1 6 8 6

4 . 0 . 1 . 4 8 3 5 8 3 0 8 6 4 1 1

0 . 9 . 9 5 4 3

7 . 6 . 1 . 7 1 7 4 5 2 1 9 8 7 1 1

3 . 0 . 9 5 7 6

4 . 8 9 2 6 7 4 9 9 3 0 0 6 9 5 1 8 5 4 3 2 1 1 1

3 . 4 . 8 . 8 . 0 7 7 6 5 4 9 6 5 4 1

1 6 4 1 2 7 7 0 6 1 7 4 1 8 5 3 3 3 2 2 2 1 1 1

0 . 3 . 5 8 8 6 2 7 3 0 9 8 1 1 1

0 . 1 8 0 6 1 0 8 0 6 0 6 8 5 3 0 9 3 3 2 1 1 1 1

0 . 0 . 0 . 2 . 2 8 7 6 3 2 9 7 6 5 1

0 6 5 2 4 9 4 8 5 0 6 3 0 7 5 2 3 3 2 2 2 1 1 1

6 . 9 . 2 6 7 4 0 7 3 0 9 8 1 1 1

0 . 0 6 0 6 1 0 8 0 5 0 6 8 5 3 0 9 3 3 2 1 1 1 1

0 . 0 . 0 . 2 . 2 8 7 6 3 2 9 7 6 5 1

8 6 5 3 6 2 2 6 3 9 5 2 9 7 5 2 3 2 2 2 1 1 1 1

1 . 6 . 6 4 5 3 9 6 3 0 9 7 1 1 1

0 . 8 6 5 6 1 0 8 0 3 9 5 8 5 3 0 9 3 2 2 1 1 1 1

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6 . 3 . 9 2 3 1 8 5 3 0 9 7 1 1 1

0 . 7 5 6 6 1 0 8 0 2 8 4 8 5 3 0 9 3 2 2 1 1 1 1

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0 . 0 . 0 . 2 . 2 8 7 6 3 2 9 7 6 5 1

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3 3 3 8 2 9 8 7 6 6      1 2 W

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6 0 2 0 2 7 8 6 6 6 8 8 9 0 3 7 2 8 4 1 7 6 5 5 4 3 3 2 2 2

1 . 1 1 0 0 4 0 7 5 2 9 2 1 1 1

0 . 6 . 8 . 8 7 1 9 5 2 0 9 7 6 1 1

7 . 5 . 4 . 8 2 5 6 5 4

8 . 5 7 1 3 7 4 1 8 1 1 1

6 0 2 0 2 7 8 6 5 3 8 8 9 0 3 7 2 8 4 0 7 6 5 5 4 3 3 2 2 2

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

7 3 6 6 9 5 7 6 7 7 6 6 7 8 1 6 1 7 3 0 7 6 5 4 4 3 3 2 2 2

5 . 2 4 5 8 2 9 6 4 1 9 1 1 1 1

5 . 2 . 7 . 6 5 9 8 4 2 0 8 7 6 1 1

5 . 6 . 5 . 7 1 4 6 5 4

2 . 7 2 9 2 6 4 0 8 1 1 1

7 3 6 6 9 5 7 6 7 3 6 6 7 8 1 6 1 7 3 0 7 6 5 4 4 3 3 2 2 2

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

8 5 0 1 6 3 6 6 8 9 4 4 6 7 0 5 0 6 2 9 7 6 5 4 4 3 3 2 2 1

8 . 4 7 8 6 0 8 5 3 1 9 1 1 1 1

0 . 7 . 5 . 4 3 8 6 3 2 0 8 7 6 1 1

4 . 7 . 5 . 6 0 3 6 5 4

7 . 0 5 7 0 6 3 0 8 1 1 1

8 5 0 1 6 3 6 6 8 9 4 4 6 7 0 5 0 6 2 9 7 6 5 4 4 3 3 2 2 1

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

9 8 4 7 3 1 5 6 9 1 2 2 4 5 9 4 9 5 1 9 7 6 5 4 3 3 2 2 2 1

1 . 6 9 1 0 9 7 4 3 1 8 1 1 1 1

5 . 3 . 3 . 8 1 6 5 2 1 0 8 7 6 1 1

2 . 8 . 5 . 5 9 2 6 4 4

1 . 3 9 5 9 5 2 0 7 1 1 1

9 8 4 7 3 1 5 6 9 1 2 2 4 5 9 4 9 5 1 9 7 6 5 4 3 3 2 2 2 1

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

0 0 8 2 9 9 4 6 0 2 1 1 2 4 7 2 8 4 1 8 7 6 5 4 3 3 2 2 2 1

4 . 8 2 5 4 7 6 4 2 0 8 1 1 1 1

7 . 9 . 9 . 1 . 1 7 4 3 1 1 9 8 7 6 1

1 . 9 . 5 . 4 8 1 6 4 4

8 . 6 . 5 2 8 7 4 2 9 7 1 1

0 0 8 2 9 9 4 6 0 2 1 1 2 4 7 2 8 4 1 8 7 6 5 4 3 3 2 2 2 1

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

1 3 2 8 6 7 3 5 1 4 9 9 1 2 6 1 7 3 0 7 6 5 5 4 3 3 2 2 2 1

3 . 7 . 0 5 8 8 3 6 3 1 9 8 1 1 1

1 . 7 . 5 . 9 . 5 2 1 2 9 0 9 8 7 5 1

9 . 0 . 6 . 2 8 0 6 4 4

1 . 1 . 8 6 3 6 3 1 9 7 1 1

1 3 2 8 6 7 3 5 1 4 9 9 1 2 6 1 7 3 0 7 6 5 5 4 3 3 2 2 2 1

4 . 0 . 8 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 6 8 1 2 3 0 8 6 1 1

2 5 6 3 3 5 1 5 2 5 7 7 9 1 5 0 6 2 9 6 6 5 4 4 3 3 2 2 1 1

3 . 4 . 1 7 1 2 8 5 2 1 9 7 1 1 1

0 . 5 . 5 . 9 . 8 . 9 6 6 8 8 9 8 7 6 5

8 . 1 . 6 . 0 7 9 6 4 3

4 . 8 . 1 9 7 2 3 0 8 7 1 1

2 5 6 3 3 5 1 5 2 5 7 7 9 1 5 0 6 2 9 6 6 5 4 4 3 3 2 2 1 1

4 . 0 . 1 4 6 3 5 5 2 0 8 6 1 1 1

3 . 1 . 9 . 8 . 7 . 2 9 7 5 5 9 7 6 5 4

5 . 8 . 4 . 1 8 5 5 3 2

2 . 2 . 1 8 1 2 3 0 8 6 1 1

1 3 8 4 1 2 5 8 3 0 1 8 5 3 1 9 7 5 4 3 3 2 2 2 2 1 1 1 1 1          8 1 W

9 6 7 6 6 1 0 9 8 7 1 1      8 1 W

1 5 0 5 0 7 6 6 5 5      8 1 W

6 0 5 4 4 3    8 1 W

0 9 7 7 0 8 7 6 1     6 1 W

0 0 0 0 0 6 2 8 8 3 7 1 7 1 0 4 9 4 2 5 9 3 7 3 0 7 5 4 3 2 2 2 1 1 1

89



8 . 5 . 3 . 1 . 6 . 5 2 9 7 4 7 5 3 2 2

9 . 0 . 9 5 1 1

6 . 7 . 8 . 0 . 1 8 4 0 6 0 7 6 5 4 1

9 . 7 . 0 2 4 3

T

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

C

8 . 2 . 5 . 8 . 0 . 8 7 3 9 5 9 7 6 4 4

1 . 9 . 0 1 4 3

T

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

0 . 7 . 2 . 9 . 0 . 7 5 2 8 4 9 7 6 4 4

3 . 2 . 9 1 3 3

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

1 . 3 . 0 . 9 . 0 . 5 4 1 7 3 9 7 6 4 4

5 . 4 . 8 0 3 3

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

3 . 8 . 8 . 0 . 0 . 3 2 9 7 2 9 7 5 4 4

7 . 6 . 7 9 3 2

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

0 . 4 . 6 . 0 . 9 . 0 1 8 6 0 9 7 5 4 4

9 . 8 . 6 8 3 2

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

7 . 9 . 4 . 1 . 9 . 4 9 7 5 9 8 6 5 4 3

1 . 0 . 6 8 3 2

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

C

3 . 1 . 1 . 1 . 9 . 9 7 6 4 8 7 6 5 4 3

3 . 3 . 5 7 3 2

T

9 . 8 . 9 . 9 . 0 . 1 5 4 5 6 7 5 4 3 2

2 . 7 . 7 6 2 1

e p a h S

7 0 5 0 6 5 5 4 4 3      6 1 W

1 6 3 2   6 1 W

C 2

i s k 0 5 

) . , 1 n o n i t i o a t c c o e L S d e n e E s , s ) n m n d ’ o u i t l n o t o C a c c i ( e l p 1 p - g n C l a A c e F l - i b e a i m s i T d e W t S a w o h t L g n d e r n a t S d n n i m W u ( l o C l a c o L y

F 4

s p i k , n

R 

4 / 3

1


4 / 1

0 0 0 0 0 0 0 0 0 0 0 0 0 7 9 4 2 2 6 2 4 0 3 6 0 5 2 9 6 3 2 2 1 1

0 0 0 0 0 0 0 0 0 9 5 0 4 1 1 4 2 5 9 8 2 9 1 6 8 6 6 4 2 2 2 4 8 4 0 8 6 4 3 7 6 5 4 3 2 1 1 1

0 0 0 0 0 0 0 9 4 2 2 8 7 8 0 4 1 8 5 3 1 3 2 2 1 1 1 1

0 1 1 6 9 2 4 5 4 5 1 9 7 5 5 5 5 5 7 9 2 7 2 9 4 1 0 9 8 7 6 5 4 4 3 3 2 2 2 1

0 0 0 0 0 0 0 9 4 2 2 8 7 8 0 4 1 8 5 3 1 3 2 2 1 1 1 1

0 1 1 6 9 2 4 6 2 2 1 9 7 5 5 5 5 5 7 9 1 4 9 4 9 6 0 9 8 7 6 5 4 4 3 2 2 1 1 1

0 0 0 0 0 0 0 5 0 8 9 5 4 5 0 4 0 7 5 3 1 3 2 2 1 1 1 1

0 9 0 6 1 6 9 1 1 4 0 0 8 3 2 3 3 4 5 7 1 6 1 8 4 0 0 9 8 7 6 5 4 4 3 3 2 2 2 1

0 0 0 0 0 0 0 5 0 8 9 5 4 5 0 4 0 7 5 3 1 3 2 2 1 1 1 1

0 9 0 6 1 6 9 1 2 2 1 9 7 3 2 3 3 4 5 7 1 4 9 4 9 6 0 9 8 7 6 5 4 4 3 2 2 1 1 1

0 0 0 0 0 0 0 0 7 5 6 2 1 3 0 3 0 7 5 3 1 3 2 2 1 1 1 1

0 7 9 7 3 0 4 8 9 3 0 0 0 0 0 0 1 2 4 6 9 4 0 7 3 0 0 9 8 7 6 5 4 3 3 3 2 2 2 1

0 0 0 0 0 0 0 0 7 5 6 2 1 3 0 3 0 7 5 3 1 3 2 2 1 1 1 1

0 7 9 7 3 0 4 8 2 2 1 9 7 0 0 0 1 2 4 6 9 4 9 4 9 6 0 9 8 7 6 5 4 3 3 2 2 1 1 1

0 0 0 0 0 0 0 5 3 1 2 9 8 0 9 3 0 7 4 2 1 2 2 2 1 1 1 1

1 5 9 8 6 4 0 5 7 2 9 1 1 8 8 8 9 0 2 5 8 3 9 5 2 9 9 8 7 6 6 5 4 3 3 2 2 2 1

0 0 0 0 0 0 0 5 3 1 2 9 8 0 9 3 0 7 4 2 1 2 2 2 1 1 1 1

1 5 9 8 6 4 0 5 7 2 1 9 7 8 8 8 9 0 2 5 8 3 9 4 9 6 9 8 7 6 6 5 4 3 3 2 2 1 1

0 0 0 0 0 0 0 0 9 8 9 6 6 8 9 2 9 6 4 2 0 2 2 1 1 1 1 1

8 3 8 9 8 8 5 1 5 1 9 2 3 5 6 6 7 8 0 3 7 2 8 4 1 8 9 8 7 6 5 5 4 3 3 2 2 2 1

0 0 0 0 0 0 0 0 9 8 9 6 6 8 9 2 9 6 4 2 0 2 2 1 1 1 1 1

8 3 8 9 8 8 5 1 5 1 1 9 7 5 6 6 7 8 0 3 7 2 8 4 9 6 9 8 7 6 5 5 4 3 3 2 2 1 1

0 0 0 0 0 0 0 6 5 4 6 3 3 5 8 2 9 6 4 2 0 2 2 1 1 1 1 1

5 1 7 9 1 2 0 8 2 0 9 3 4 3 4 4 5 7 9 2 5 1 7 3 0 7 9 8 7 6 5 4 4 3 3 2 2 2 1

0 0 0 0 0 0 0 6 5 4 6 3 3 5 8 2 9 6 4 2 0 2 2 1 1 1 1 1

5 1 7 9 1 2 0 8 2 0 9 9 7 3 4 4 5 7 9 2 5 1 7 3 9 6 9 8 7 6 5 4 4 3 3 2 2 1 1

0 0 0 0 0 0 0 1 1 1 3 0 0 3 8 2 9 6 4 2 0 2 2 1 1 1 1 1

1 9 7 0 3 6 6 4 0 9 8 3 6 1 1 2 4 5 7 0 4 0 5 2 9 6 9 8 7 6 5 4 4 3 3 2 2 1 1

0 0 0 0 0 0 0 1 1 1 3 0 0 3 8 2 9 6 4 2 0 2 2 1 1 1 1 1

1 9 7 0 3 6 6 4 0 9 8 3 6 1 1 2 4 5 7 0 4 0 5 2 9 6 9 8 7 6 5 4 4 3 3 2 2 1 1

0 0 0 0 0 0 0 6 7 7 9 7 7 0 7 1 8 5 3 1 0 2 2 1 1 1 1 1

8 7 6 1 5 0 1 1 8 8 8 4 7 8 9 0 2 3 6 9 3 8 4 1 8 5 8 7 7 6 5 4 3 3 2 2 2 1 1

0 0 0 0 0 0 0 6 7 7 9 7 7 0 7 1 8 5 3 1 0 2 2 1 1 1 1 1

8 7 6 1 5 0 1 1 8 8 8 4 7 8 9 0 2 3 6 9 3 8 4 1 8 5 8 7 7 6 5 4 3 3 2 2 2 1 1

8 0 5 5 0 0 5 0 3 6 0 5 0 5 8 7 6 6 5 5 4        4 1 W

6 8 0 2 1 3 7 3 1 3 6 9 5 2 9 7 4 1 8 5 3 1 9 7 5 4 4 3 3 3 3 2 2 2 2 1 1 1 1              4 1 W

90


. g r y n n , s l b p i e m l p n k R i o W o c u  k C C B C 2 T

i s k 0 5 

) . , 1 n o n i t i o a t c c o e L S d e n e E s , s ) n n m d ’ o u i t l n o t o C a c c i ( e l p 1 p - g n C l a A c e F l - i b e a i m s i T d e W t S a w h o t L g n d e r n a t S d n n i m W u ( l o C l a c o L y

F 4

s p i k , n

R 

g n i l p p i r C b e W d n a , g n i d l e i Y b e W l a c . o n L i , , g N n i d n e B e g n a l F l a c o L r o f h t g n e r t S n g i s e D t s a e L

C 4 / 3

1 T

C 2 / 1

1 T

C 4 / 1

1 T

C 1 T

C 4 / 3

T

C 2 / 1

T

C 4 / 1

T e p a h S

4 . 5 . 3 . 4 3 6 9 3 9 9 8 3 9 6 4 3 2 1

8 . 0 . 8 1 4 3

6 . 9 . 0 3 3 2

5 0 . 0 . 6 . 9 4 9 2 2

9 . 8 . 5 . 9 8 3 8 4 3

0 . 2 . 4 . 8 3 3 4 3 1

8 . 4 . 2 1 7 5

4 . 4 . 8 . 5 . 9 5 9 1 0 1 5 3 9 8 6 5 1 1

6 . 4 . 1 8 5 3

3 . 3 . 9 3 3 3

8 . 9 . 5 . 7 3 8 3 3 1

5 . 8 . 4 . 4 7 9 6 4 3

2 . 7 . 2 . 7 8 1 4 3 2

4 . 8 . 4 4 5 4

1 . 2 5

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 8 . 2 . 1 . 2 8 4 7 8 9 5 2 9 7 5 4 1 1

4 . 7 . 9 6 4 3

6 . 6 . 7 1 3 3

7 . 7 . 4 . 5 1 7 3 3 1

5 . 0 . 6 . 0 5 6 6 4 3

7 . 1 . 8 . 4 6 9 4 3 1

0 . 0 . 1 2 5 4

6 . 8 4

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 7 . 8 . 0 . 5 2 9 4 5 7 4 2 8 7 5 4 1 1

4 . 2 . 7 5 4 3

2 . 2 . 6 0 3 3

9 . 8 . 4 . 3 9 6 3 2 1

5 . 2 . 8 . 6 2 3 5 4 3

2 . 5 . 5 . 2 3 8 4 3 1

7 . 3 . 7 9 4 3

1 . 5 4

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 3 . 8 . 2 . 8 6 4 0 3 5 3 1 8 7 5 4 1 1

8 . 9 . 5 3 4 3

9 . 0 . 4 9 3 2

3 . 2 . 6 . 2 8 5 3 2 1

5 . 4 . 0 . 2 9 1 5 3 3

8 . 9 . 1 . 9 0 7 3 3 1

3 . 5 . 4 6 4 3

6 . 1 4

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 8 . 8 . 4 . 1 9 9 5 1 3 3 0 7 6 5 4 1 1

1 . 7 . 4 2 4 3

6 . 8 . 3 7 3 2

8 . 5 . 7 . 0 6 4 3 2 1

5 . 3 . 7 . 8 7 8 4 3 2

4 . 8 . 9 . 7 8 5 3 2 1

9 . 7 . 0 3 4 3

1 . 8 3

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 3 . 8 . 6 . 4 3 4 1 9 1 2 0 7 6 4 4 1 1

4 . 4 . 2 1 4 3

3 . 5 . 2 6 3 2

2 . 9 . 9 . 9 4 3 2 2 1

5 . 1 . 6 . 4 4 6 4 3 2

1 . 6 . 9 . 4 6 4 3 2 1

5 . 5 . 7 1 3 3

6 . 4 3

3 . 0 . 1 . 5 . 6 . 3 2 6 4 4 6 2 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

4 . 4 . 8 . 5 . 8 . 7 6 9 6 6 9 1 9 6 5 4 3 1

5 . 2 . 0 0 4 3

1 . 3 . 1 5 3 2

7 . 3 . 1 . 7 3 3 2 2 1

5 . 9 . 7 . 0 0 3 4 3 2

9 . 7 . 8 . 0 3 3 3 2 1

2 . 5 . 4 8 3 2

1 . 1 3

3 . 0 . 1 . 5 . 6 . 7 2 6 4 4 6 1 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

0 . 4 . 3 . 6 . 0 . 0 0 4 2 2 7 1 9 6 5 4 3 1

0 . 9 . 7 8 3 2

5 . 1 . 8 4 2 2

0 . 7 . 3 . 6 1 2 2 2 1

5 . 6 . 8 . 6 7 0 3 2 2

6 . 8 . 8 . 7 0 2 2 2 1

8 . 5 . 0 5 3 2

6 . 7 2

0 . 4 . 1 . 5 . 6 . 0 0 4 4 4 6 1 9 6 4 3 2 1

4 . 5 . 0 2 3 2

5 . 3 . 2 5 2 1

4 1 0 . 1 . 9 . 4 9 5 1

1 1 . 7 . 5 . 9 8 9 2 1

0 1 . 0 . 5 . 3 1 6 2 1

0 . 2 . 6 8 2 1

7 . 6 1

7 8 8 0 5 1 6 5 4 4 3 3       8 W

8 4 2 2   8 W

1 8 2 1   8 W

5 3 0 1 1 1    8 W

5 0 5 2 2 1    6 W

6 2 9 9 6 1 1  1 1     6 5 W W

93

3 0 1

3 1  4 W



Appendix D COLUMN STIFFENING CONSIDERATIONS FOR WEAK-AXIS MOMENT CONNECTIONS Pages 10-61thr o ugh 10-65 of the 2ndediti on of the LRFD Manual of Steel Construction and the reference Ferrell (1998) have been reprinted in this appendix f or ease of reference.

“Figure 10-26 illustrates the distributi on of l ongitudinal stress across the width of the c onnecti on plate and the c oncentrati on of stress in the plate at the c olumn flange tips. It also illustrates the uniform l ongitudinal stress distribution in the connection plate at s ome distance away fr om the c onnecti on. The stress distribution shown represents schematically the values measured during the l oad tests and th ose obtained fr om finite element analysis. ( o is a nominal stress in the elastic range.) The results of the analyses are valid up to the loading that causes the combined stress t o equal the yield point. Furthermore, the analyses indicate that localized yielding could begin when the applied uniform stress is less than one-third of the yield p oint. Another contribution of the non-unif ormity is the fact that there is no back-up stiffener. This means that the welds to the web near its center are not fully effective. “The longitudinal stresses in the moment c onnection plate introduce strains in the transverse and the throughthickness directions (the Poisson effect). Because of the attachment of the connectio n platet o the column flanges, restraint is introduced; this causes tensile stresses in the transverse and the thr ough-thickness directions. Thus, referring to Figure 10-26, tri-axial tensile stresses are present al ong Section A-A, and they are at their maximum values at the intersections of Sections A-A and C-C. In such a situation, and when the magnitudes of the stresses are sufficiently high, materials that are otherwise ductile may fail by premature brittle fracture.” The results of nine simulated weak-axis FR m oment connecti on tests perf ormed by Drisc oll et al. (1983) are summarized in Figure 10-27. In these tests, the beam flange was simulated by a plate measuring either 1 in.  10 in. or 1 1/8 in.  9 in. The fracture strength exceeds the yield strength in every case, and sufficient ductility is provided in all cases except for that of Specimen D. Als o, if the rolling direction in the first five specimens (A, B, C, D, and E) were parallel to the l oading directi on, which w ould more closely approximate an actual beam flange, the ductility ratio s for these w ould be higher. The c onnecti ons with extended connection plates (i.e., projecti on of three inches), with extensions either rectangular or tapered, appeared equally suitable for the static loads of the tests. Based on the tests, Driscoll et al. (1983)report that those specimens with extended connection plates have better toughness and ductility and are preferred in design for

FROM AISC (1994): Special Considerations FR Moment Connections to Column-Web Supports

It is frequently required that FR m oment c onnecti ons be made t o column web supp orts. While the mechanics of analysis and design d o n ot differ fr om FR m oment connection to c olumn flange supp orts, the details of the connecti on design as well as the ductility considerations required are significantly different. Recommended Details. When an FR moment c onnection is make to a column web, it is n ormal practice to st op the beam short and locate all bolts outside of the c olumn flanges . . . . This simplifies the erection of the beam and permits the use of an impact wrench to tighten all b olts. It is also preferable to l ocate welds outside the column flanges to provide adequate clearance. Ductility Considerations. Driscoll and Beedle (1982) discuss the testing and failure of two FR movement c onnections to column-web supports: a directly welded flange connection and a b olted flange-plated connecti on, sh own respectively in Figures 10-25a and 10-25b. Alth ough the connections in these tests were prop orti oned t o be “critical,”they wereexpectedto provideinelasticrotationsat full plastic load. Failure occurred unexpectedly, however, on the first cycle of loading;brittlefracture occurredin the tension connection plate atthel oadc orresponding t o the plastic moment before significant inelastic rotation had occurred. Examination and testing after the unexpected failure revealed that the welds were of proper size and quality and that the plate had normal strength and ductility. The f ollowing is quoted, with min or edit orial changes relative t o figure numbers, directly fr om Driscoll and Beedle (1982). “Calculatio ns indicate that the failures o ccurred due to high strain c oncentrations. These concentrations are: (1) at the junction of the c onnecti on plate and the c olumn flange tip and (2) at the edge of the butt weld j oining the beam flange and the connection plate. 95


seismic loads, even though the other c onnecti on types (exceptD) may bedeemedadequatet o meet the requirements of many design situati ons. In accordance with the preceding discussion, the f oll owing suggestions are made regarding the design of this type of c onnecti on:

beam flange. This greater area acc ounts f or shear lag and also provides f or misalignment t olerances. AWS D1.1, Secti on 3.3.3 restricts the misalignment of abutting partssuch as this t o 10 percent of the thickness, with 1/8 in. maximum f or a part restrained against bending due t o eccentricity of alignment. Considering the vario us t olerances in mill r olling ( 1/8 in. for W-shapes), fabricati on, and erecti on, it is prudent design t o call f or the stiffener thickness

1. For directly welded (butt) flange-t o-plate c onnections, the connection plate sh ould be thicker than the

Figure 10-25 Test specimens used by Driscoll and Beedle (1982).

Figure 10-26 Stress distributions in test specimens used by Driscoll and Beedle (1982). 96


to be increased to accommodate these t olerances and avo id the subsequent problems enc ountered at erection. An increase of 1/8 in. t o 1/4 in. generally is used. Frequently, this connection plate also serves as the stiffener for a strong-axis FR or PR m oment c onnection. The welds which attach the plate/stiffener to the column flange may then be subjected t o c ombined tensile and shearing or c ompressi on and shearing fo rces. Vect or analysis is c omm only used t o determine weld size and stress. Itis good practicet o use fillet welds wheneverp ossible. Welds should n ot be made in the c olumn fillet area for strength.

The extension should als o pr ovide adequate r oom f or run out bars when required. 3. Tapering an extended c onnecti on plate is only necessary when the c onnecti on plate is n ot welded t o the c olumn web (Specimen E, Figure 10-27). Tapering is not necessary if the flange f orce is always c ompressive (e.g., at the b ott om flange of a cantilevered beam). 4. T opr ovide f orincreased ductilityunder seismic l oading, a tapered connection plate sh ould extend three inches. Alternatively, a backup stiffener and an untapered c onnecti on plate with 3-in. extensi on c ould be used.

2. The connection plate should extend at least 3/4 in. beyond the column flange to av oid intersecting welds and t o provide f or strain el ongati on of the plate.

N ormal and acceptable quality of w orkmanship f or c onnections inv olving gravity and wind l oading in building c onstructi on w ould t olerate the f oll owing:

Figure 10-27a Results of weak-axis FR connection ductility tests performed by Driscoll et al. (1983). 97


Figure 10-27b Results of weak-axis FR connection ductility tests performed by Driscoll et al. (1983).

98


1. Runoff bars and backing bars may be left in place f or Groups 4 and 5 beams (subject t o tensile stress only) where they are welded to c olumns or used as tensi on members in a truss. 2. Welds need not be gr ound, except as required f or nondestructive testing. 3. C onnection plates that are made thicker or wider f or control of t olerances, tensile stress, and shearlag need not be ground or cut t o a transiti on thickness or width to match the beam flange to which they connect. 4. Connection plate edges may be sheared or plasma or gas cut. 5. Intersectio ns and transitions may be made with out fillets or radii. 6. Burned edges may have reas onable r oughness and notches within AWS tolerances. If a structure is subjected to loads other than gravity and wind l oads, such as seismic, dynamic, or fatigue l oading, more stringent control of the quality of fabricati on and erection with regard t o stress risers, notches, transiti on geometry, welding, and testing may be necessary; refer t o AISC’s Seismic Provisions for Structural Steel Buildings. FROM FERRELL (1998): Moment Connections to Column Webs

(M. Thomas Ferrell, Ferrell Engineering, Inc.) Introduction

accommodate t olerances f or fabrication and beam flange tilt. Note that the bottom of this connection plate is aligned with the bottom of the beam t op flange. 4. The bottom connection plate thickness is equal t o t f plus 3/8 in. This is necessary to accomm odate t olerances for fabrication and beam flange tilt plus p ossible overrun/underrun in the beam depth. N ote that the centerline of this connection plate is aligned with the centerline of the bottom flange of the beam. 5. The welds for c onnection plates t o the c olumn flanges must be designed for shear f orces. These welds may also be subjected t o tensile/compression and shear f orces when these plates serve as stiffener plates for a strong-axis moment beam. Use fillet welds where possible. It is good practice t o deduct twice the weld size from the length of plate available for welding so that the welds d o n ot terminate at the edges of the plate or c olumn flange. If calculated stresses are transferred through the welds at the c olumn web, then backup stiffeners must be provided. 6. Bolts for the shear plate t o beam web are n ormally located outside of the column flanges. This practice simplifies beam erection and allows access to tighten

Details for momentco nnecti onst o c olumnwebs mustc onsider mill and shop t olerances of the structural members and provide for material ductility. This paper will present details which will accommodate these requirements and present limit state strength oc nsiderati f r both m oo ns o ment connections with field welded beam flanges and field bolted flange plates. Moment Connection with Field Welded Beam Flanges

Figure 1 illustrates a field welded flange m oment connection. 1. The connection plates must be the same grade of material as the weak-axis moment beam. 2. The connection plate has been extended 3/4 in. minimum beyond the column flange t o pr ovide better toughness and ductility. AISC L oad and Resistance Factor Design [Manual] Volume II, pages 10-60 through 10-65, has summarized results of nine simulated weak-axis FR moment connecti on tests performed by Driscoll et al. t o aid in selection of details to ensure ductility. 3. The top c onnecti on plate thickness is equal t o t f plus 1/4 in. This additional thickness is necessary to 99


the bolts with use of an impact wrench. Short slots should be used in the plate and standard h oles in the beam web. Flange welds should be c ompleted bef ore the bolts are tightened. The sho rt slots will “hold” top of beam elevati on and all ow for weld shrinkage to occur at the flange welds. The b olts are designed for shear f orces only (no eccentricity). The welds f or the shear plate to column web are designed f or shear only. The welds f or the shear plate to c onnecti on plates must be designed for shear stresses due to the eccentricity fro m the neutral axis of the b olt gr oup t o the edge of the c olumn flange. If a c olumn web d oubler is required due t o a str ong-axis m oment beam, then the additional stresses from the shear plate must be considered in determining the thickness of the web doubler plate.

These c onnecti ons with oversized h oles must be designed as slip critical. If tensi on c ontr ol b olts are used, if p ossible, use a b olt gage which will all ow b olts at the b ott om flange t o be tightened fr om the inside of the beam flange. In many cases this is n ot p ossible due t o beam flange widths and beam depths. 3. Shims must be pr ovided at the t op or b ott om flanges t o acc omm odate fabricati on and mill t olerances f or flange tilt plus p ossible overrun/underrun in beam depths. Fabricators n ormally prefer the shims t o be at the b ott om flange due t o restricti ons on pr ogramming of sh op equipment. If shims are pr ovided at the t op flange, the detail can be pr ovided t o serve as a deck support (Figure 3). 4. The flange plates must be designed f or tensi on yielding, tensi on rupture, and c ompressi on strength. 5. The flange bolts must be designed f or shear strength. 6. The beam design flexural strength with regard t o net section must be determined t o assure that the net beam section is adequate without reinforcing. 7. The welds for the flange plates t o the c olumn flanges/webs are designed using the same criteria used for the c onnecti on plates f or the field welded flange moment beams in Figure 1. 8. Theweb shear plate designis the same as for the field welded flange moment beams.

Moment Connections with Beam Flange Plates

Figure 2 illustrates a field bolted flange plate moment connection. 1. It is not necessary f or the flange plates t o be the same grade of material as the weak-axis moment beam. 2. Oversized h oles should be used in the flange plates to allow for mill t olerances in the c olumn and beam.

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Design Guide 13_ Wide-Flange Column Stiffening at Moment Connections (See Errata Listed at End of File.)

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