Steel+Construction+Manual+Design+Examples,+V14.0+part+4+of+4

DESIGN EXAMPLES Version 14.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ii Copyright © 2011 by American Institute of Steel Construction All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. The AISC logo is a registered trademark of AISC. The information presented in this publication has been prepared in accordance with recognized engineering principles and is for general information 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, suitability, and applicability by a licensed professional engineer, designer, or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction or of any other person named herein, that this information is suitable for any general or particular use or of freedom from infringement of any 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 edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial publication of this edition. Printed in the United States of America First Printing, October 2011

Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

iii

PREFACE The primary objective of these design examples is to provide illustrations of the use of the 2010 AISC Specification for Structural Steel Buildings (ANSI/AISC 360-10) and the 14th Edition of the AISC Steel Construction Manual. The design examples provide coverage of all applicable limit states whether or not a particular limit state controls the design of the member or connection. In addition to the examples which demonstrate the use of the Manual tables, design examples are provided for connection designs beyond the scope of the tables in the Manual. These design examples are intended to demonstrate an approach to the design, and are not intended to suggest that the approach presented is the only approach. The committee responsible for the development of these design examples recognizes that designers have alternate approaches that work best for them and their projects. Design approaches that differ from those presented in these examples are considered viable as long as the Specification, sound engineering, and project specific requirements are satisfied. Part I of these examples is organized to correspond with the organization of the Specification. The Chapter titles match the corresponding chapters in the Specification. Part II is devoted primarily to connection examples that draw on the tables from the Manual, recommended design procedures, and the breadth of the Specification. The chapters of Part II are labeled II-A, II-B, II-C, etc. Part III addresses aspects of design that are linked to the performance of a building as a whole. This includes coverage of lateral stability and second order analysis, illustrated through a four-story braced-frame and momentframe building. The Design Examples are arranged with LRFD and ASD designs presented side by side, for consistency with the AISC Manual. Design with ASD and LRFD are based on the same nominal strength for each element so that the only differences between the approaches are which set of load combinations from ASCE/SEI 7-10 are used for design and whether the resistance factor for LRFD or the safety factor for ASD is used. CONVENTIONS The following conventions are used throughout these examples: 1.

The 2010 AISC Specification for Structural Steel Buildings is referred to as the AISC Specification and the 14th Edition AISC Steel Construction Manual, is referred to as the AISC Manual.

2.

The source of equations or tabulated values taken from the AISC Specification or AISC Manual is noted along the right-hand edge of the page.

3.

When the design process differs between LRFD and ASD, the designs equations are presented side-by-side. This rarely occurs, except when the resistance factor, φ, and the safety factor, Ω, are applied.

4.

The results of design equations are presented to three significant figures throughout these calculations.

ACKNOWLEDGMENTS The AISC Committee on Manuals reviewed and approved V14.0 of the AISC Design Examples: William A. Thornton, Chairman Mark V. Holland, Vice Chairman Abbas Aminmansour Charles J. Carter Harry A. Cole

Douglas B. Davis Robert O. Disque Bo Dowswell Edward M. Egan Marshall T. Ferrell Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

iv Lanny J. Flynn Patrick J. Fortney Louis F. Geschwindner W. Scott Goodrich Christopher M. Hewitt W. Steven Hofmeister Bill R. Lindley, II Ronald L. Meng Larry S. Muir Thomas M. Murray Charles R. Page

Davis G. Parsons, II Rafael Sabelli Clifford W. Schwinger William N. Scott William T. Segui Victor Shneur Marc L. Sorenson Gary C. Violette Michael A. West Ronald G. Yeager Cynthia J. Duncan, Secretary

The AISC Committee on Manuals gratefully acknowledges the contributions of the following individuals who assisted in the development of this document: Leigh Arber, Eric Bolin, Janet Cummins, Thomas Dehlin, William Jacobs, Richard C. Kaehler, Margaret Matthew, Heath Mitchell, Thomas J. Schlafly, and Sriramulu Vinnakota.


v

TABLE OF CONTENTS PART I.

EXAMPLES BASED ON THE AISC SPECIFICATION

CHAPTER A Chapter A References

GENERAL PROVISIONS.........................................................................................................A-1

CHAPTER B Chapter B References

DESIGN REQUIREMENTS ..................................................................................................... B-1

CHAPTER C Example C.1A Example C.1B Example C.1C

DESIGN FOR STABILITY .......................................................................................................C-1 Design of a Moment Frame by the Direct Analysis Method ........................................................ C-2 Design of a Moment Frame by the Effective Length Method ...................................................... C-6 Design of a Moment Frame by the First-Order Method ............................................................. C-11

CHAPTER D

DESIGN OF MEMBERS FOR TENSION...............................................................................D-1

Example D.1 Example D.2 Example D.3 Example D.4 Example D.5 Example D.6 Example D.7 Example D.8 Example D.9

W-Shape Tension Member ..........................................................................................................D-2 Single Angle Tension Member ....................................................................................................D-5 WT-Shape Tension Member ........................................................................................................D-8 Rectangular HSS Tension Member ............................................................................................D-11 Round HSS Tension Member ....................................................................................................D-14 Double Angle Tension Member .................................................................................................D-17 Pin-Connected Tension Member ...............................................................................................D-20 Eyebar Tension Member ............................................................................................................D-23 Plate with Staggered Bolts .........................................................................................................D-25

CHAPTER E

DESIGN OF MEMBERS FOR COMPRESSION ................................................................... E-1

Example E.1A Example E.1B Example E.1C Example E.1D Example E.2 Example E.3 Example E.4A Example E.4B Example E.5 Example E.6 Example E.7 Example E.8 Example E.9 Example E.10 Example E.11 Example E.12 Example E.13

W-Shape Column Design with Pinned Ends ............................................................................... E-4 W-Shape Column Design with Intermediate Bracing.................................................................. E-6 W-Shape Available Strength Calculation .................................................................................... E-8 W-Shape Available Strength Calculation .................................................................................... E-9 Built-up Column with a Slender Web........................................................................................ E-11 Built-up Column with Slender Flanges ...................................................................................... E-16 W-Shape Compression Member (Moment Frame) .................................................................... E-21 W-Shape Compression Member (Moment Frame) .................................................................... E-25 Double Angle Compression Member without Slender Elements ............................................... E-26 Double Angle Compression Member with Slender Elements .................................................... E-31 WT Compression Member without Slender Elements ............................................................... E-37 WT Compression Member with Slender Elements .................................................................... E-42 Rectangular HSS Compression Member without Slender Elements ......................................... E-47 Rectangular HSS Compression Member with Slender Elements ............................................... E-50 Pipe Compression Member ........................................................................................................ E-54 Built-up I-Shaped Member with Different Flange Sizes ............................................................ E-57 Double WT Compression Member ............................................................................................. E-63

CHAPTER F

DESIGN OF MEMBERS FOR FLEXURE.............................................................................. F-1

Example F.1-1A Example F.1-1B Example F.1-2A Example F.1-2B

W-Shape Flexural Member Design in Strong-Axis Bending, Continuously Braced ................... F-6 W-Shape Flexural Member Design in Strong-Axis Bending, Continuously Braced ................... F-8 W-Shape Flexural Member Design in Strong-Axis Bending, Braced at Third Points ................. F-9 W-Shape Flexural Member Design in Strong-Axis Bending, Braced at Third Points............... F-10

......................................................................................................................................................A-2

...................................................................................................................................................... B-2


vi Example F.1-3A Example F.1-3B Example F.2-1A Example F.2-1B Example F.2-2A Example F.2-2B Example F.3A Example F.3B Example F.4 Example F.5 Example F.6 Example F.7A Example F.7B Example F.8A Example F.8B Example F.9A Example F.9B Example F.10 Example F.11A Example F.11B Example F.11C Example F.12 Example F.13 Example F.14 Chapter F Design Example References

W-Shape Flexural Member Design in Strong-Axis Bending, Braced at Midspan..................... F-12 W-Shape Flexural Member Design in Strong-Axis Bending, Braced at Midspan..................... F-14 Compact Channel Flexural Member, Continuously Braced ...................................................... F-16 Compact Channel Flexural Member, Continuously Braced ...................................................... F-18 Compact Channel Flexural Member with Bracing at Ends and Fifth Points ............................. F-19 Compact Channel Flexural Member with Bracing at End and Fifth Points ............................... F-20 W-Shape Flexural Member with Noncompact Flanges in Strong-Axis Bending ...................... F-22 W-Shape Flexural Member with Noncompact Flanges in Strong-Axis Bending ...................... F-24 W-Shape Flexural Member, Selection by Moment of Inertia for Strong-Axis Bending ............ F-26 I-Shaped Flexural Member in Minor-Axis Bending .................................................................. F-28 HSS Flexural Member with Compact Flanges ........................................................................... F-30 HSS Flexural Member with Noncompact Flanges ..................................................................... F-32 HSS Flexural Member with Noncompact Flanges ..................................................................... F-34 HSS Flexural Member with Slender Flanges ............................................................................. F-36 HSS Flexural Member with Slender Flanges ............................................................................. F-38 Pipe Flexural Member ................................................................................................................ F-41 Pipe Flexural Member ................................................................................................................ F-42 WT-Shape Flexural Member ..................................................................................................... F-44 Single Angle Flexural Member .................................................................................................. F-47 Single Angle Flexural Member .................................................................................................. F-50 Single Angle Flexural Member .................................................................................................. F-53 Rectangular Bar in Strong-Axis Bending .................................................................................. F-59 Round Bar in Bending ............................................................................................................... F-61 Point-Symmetrical Z-shape in Strong-Axis Bending................................................................. F-63

CHAPTER G

DESIGN OF MEMBERS FOR SHEAR ...................................................................................G-1

Example G.1A Example G.1B Example G.2A Example G.2B Example G.3 Example G.4 Example G.5 Example G.6 Example G.7 Example G.8A Example G.8B Chapter G Design Example References

W-Shape in Strong-Axis Shear ....................................................................................................G-3 W-Shape in Strong-Axis Shear ....................................................................................................G-4 C-Shape in Strong-Axis Shear .....................................................................................................G-5 C-Shape in Strong-Axis Shear .....................................................................................................G-6 Angle in Shear .............................................................................................................................G-7 Rectangular HSS in Shear ............................................................................................................G-9 Round HSS in Shear ..................................................................................................................G-11 Doubly Symmetric Shape in Weak-Axis Shear .........................................................................G-13 Singly Symmetric Shape in Weak-Axis Shear ...........................................................................G-15 Built-up Girder with Transverse Stiffeners ................................................................................G-17 Built-up Girder with Transverse Stiffeners ................................................................................G-21

CHAPTER H

DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION ............................H-1

Example H.1A

W-shape Subject to Combined Compression and Bending About Both Axes (Braced Frame) ...............................................................................................H-2 W-shape Subject to Combined Compression and Bending Moment About Both Axes (Braced Frame) ................................................................................................H-4 W-Shape Subject to Combined Compression and Bending Moment About Both Axes (By AISC Specification Section H2) ..............................................................H-5 W-Shape Subject to Combined Axial Tension and Flexure......................................................... H-8 W-Shape Subject to Combined Axial Compression and Flexure ..............................................H-12 Rectangular HSS Torsional Strength .........................................................................................H-16

Example H.1B Example H.2 Example H.3 Example H.4 Example H.5A

.................................................................................................................................................... F-69

....................................................................................................................................................G-24


vii Example H.5B Example H.5C Example H.6 Chapter H Design Example References

Round HSS Torsional Strength ..................................................................................................H-17 HSS Combined Torsional and Flexural Strength .......................................................................H-19 W-Shape Torsional Strength ......................................................................................................H-23

CHAPTER I

DESIGN OF COMPOSITE MEMBERS................................................................................... I-1

Example I.1 Example I.2 Example I.3 Example I.4 Example I.5 Example I.6 Example I.7 Example I.8 Example I.9 Example I.10 Example I.11 Example I.12 Chapter I Design Example References

Composite Beam Design ............................................................................................................... I-8 Composite Girder Design ........................................................................................................... I-18 Concrete Filled Tube (CFT) Force Allocation and Load Transfer .............................................. I-35 Concrete Filled Tube (CFT) in Axial Compression .................................................................... I-45 Concrete Filled Tube (CFT) in Axial Tension ............................................................................ I-50 Concrete Filled Tube (CFT) in Combined Axial Compression, Flexure and Shear ................... I-52 Concrete Filled Box Column with Noncompact/Slender Elements ............................................ I-66 Encased Composite Member Force Allocation and Load Transfer ............................................ I-80 Encased Composite Member in Axial Compression ................................................................... I-93 Encased Composite Member in Axial Tension ......................................................................... I-100 Encased Composite Member in Combined Axial Compression, Flexure and Shear ................ I-103 Steel Anchors in Composite Components ................................................................................. I-119

CHAPTER J

DESIGN OF CONNECTIONS ...................................................................................................J-1

Example J.1 Example J.2 Example J.3 Example J.4A Example J.4B Example J.5 Example J.6 Example J.7

Fillet Weld in Longitudinal Shear ................................................................................................. J-2 Fillet Weld Loaded at an Angle .................................................................................................... J-4 Combined Tension and Shear in Bearing Type Connections........................................................ J-6 Slip-Critical Connection with Short-Slotted Holes ....................................................................... J-8 Slip-Critical Connection with Long-Slotted Holes ................................................. J-10 Combined Tension and Shear in a Slip-Critical Connection ................................................. J-12 Bearing Strength of a Pin in a Drilled Hole ................................................................................ J-15 Base Plate Bearing on Concrete................................................................................................... J-16

CHAPTER K

DESIGN OF HSS AND BOX MEMBER CONNECTIONS ...................................................K-1

Example K.1 Example K.2 Example K.3 Example K.4 Example K.5 Example K.6 Example K.7 Example K.8 Example K.9 Example K.10 Example K.11 Example K.12 Example K.13 Chapter K Design Example References

Welded/Bolted Wide Tee Connection to an HSS Column ...........................................................K-2 Welded/Bolted Narrow Tee Connection to an HSS Column .....................................................K-10 Double Angle Connection to an HSS Column ...........................................................................K-13 Unstiffened Seated Connection to an HSS Column ...................................................................K-16 Stiffened Seated Connection to an HSS Column .......................................................................K-19 Single-Plate Connection to Rectangular HSS Column ..............................................................K-24 Through-Plate Connection .........................................................................................................K-27 Transverse Plate Loaded Perpendicular to the HSS Axis on a Rectangular HSS .......................K-31 Longitudinal Plate Loaded Perpendicular to the HSS Axis on a Round HSS ............................K-34 HSS Brace Connection to a W-Shape Column ...........................................................................K-36 Rectangular HSS Column with a Cap Plate, Supporting a Continuous Beam ...........................K-39 Rectangular HSS Column Base Plate ........................................................................................K-42 Rectangular HSS Strut End Plate ...............................................................................................K-45

....................................................................................................................................................H-30

................................................................................................................................................... I-123

....................................................................................................................................................K-49


viii

PART II.

EXAMPLES BASED ON THE AISC STEEL CONSTRUCTION MANUAL

CHAPTER IIA SIMPLE SHEAR CONNECTIONS.......................................................................................IIA-1 Example II.A-1 Example II.A-2 Example II.A-3 Example II.A-4 Example II.A-5 Example II.A-6 Example II.A-7 Example II.A-8 Example II.A-9 Example II.A-10 Example II.A-11 Example II.A-12 Example II.A-13 Example II.A-14 Example II.A-15 Example II.A-16 Example II.A-17 Example II.A-18 Example II.A-19 Example II.A-20 Example II.A-21 Example II.A-22 Example II.A-23 Example II.A-24 Example II.A-25 Example II.A-26 Example II.A-27 Example II.A-28 Example II.A-29 Example II.A-30 Example II.A-31

All-Bolted Double-Angle Connection ...................................................................................... IIA-2 Bolted/Welded Double-Angle Connection ............................................................................... IIA-4 All-Welded Double-Angle Connection .................................................................................... IIA-6 All-Bolted Double-Angle Connection in a Coped Beam .......................................................... IIA-9 Welded/ Bolted Double-Angle Connection (Beam-to-Girder Web). ...................................... IIA-13 Beam End Coped at the Top Flange Only .............................................................................. IIA-16 Beam End Coped at the Top and Bottom Flanges.................................................................. IIA-23 All-Bolted Double-Angle Connections (Beams-to-Girder Web) ........................................... IIA-26 Offset All-Bolted Double-Angle Connections (Beams-to-Girder Web) ................................ IIA-34 Skewed Double Bent-Plate Connection (Beam-to-Girder Web)............................................. IIA-37 Shear End-Plate Connection (Beam to Girder Web). ............................................................. IIA-43 All-Bolted Unstiffened Seated Connection (Beam-to-Column Web) ..................................... IIA-45 Bolted/Welded Unstiffened Seated Connection (Beam-to-Column Flange) .......................... IIA-48 Stiffened Seated Connection (Beam-to-Column Flange) ........................................................ IIA-51 Stiffened Seated Connection (Beam-to-Column Web) ........................................................... IIA-54 Offset Unstiffened Seated Connection (Beam-to-Column Flange)......................................... IIA-57 Single-Plate Connection (Conventional – Beam-to-Column Flange) ..................................... IIA-60 Single-Plate Connection (Beam-to-Girder Web) .................................................................... IIA-62 Extended Single-Plate Connection (Beam-to-Column Web) .................................................. IIA-64 All-Bolted Single-Plate Shear Splice ...................................................................................... IIA-70 Bolted/Welded Single-Plate Shear Splice ............................................................................... IIA-75 Bolted Bracket Plate Design ................................................................................................... IIA-80 Welded Bracket Plate Design. ................................................................................................ IIA-86 Eccentrically Loaded Bolt Group (IC Method) ....................................................................... IIA-91 Eccentrically Loaded Bolt Group (Elastic Method)................................................................ IIA-93 Eccentrically Loaded Weld Group (IC Method)..................................................................... IIA-95 Eccentrically Loaded Weld Group (Elastic Method) .............................................................. IIA-98 All-Bolted Single-Angle Connection (Beam-to-Girder Web) .............................................. IIA-100 Bolted/Welded Single-Angle Connection (Beam-to-Column Flange).................................. IIA-105 All-Bolted Tee Connection (Beam-to-Column Flange) ........................................................ IIA-108 Bolted/Welded Tee Connection (Beam-to-Column Flange) ................................................. IIA-115

CHAPTER IIB FULLY RESTRAINED (FR) MOMENT CONNECTIONS............................................... IIB-1 Example II.B-1 Example II.B-2 Example II.B-3 Example II.B-4

Bolted Flange-Plate FR Moment Connection (Beam-to-Column Flange) ............................... IIB-2 Welded Flange-Plated FR Moment Connection (Beam-to-Column Flange) ......................... IIB-14 Directly Welded Flange FR Moment Connection (Beam-to-Column Flange). ..................... IIB-20 Four-Bolt Unstiffened Extended End-Plate FR Moment Connection (Beam-to-Column Flange) ............................................................. IIB-22

Chapter IIB Design Example References ................................................................................................................................................. IIB-33 CHAPTER IIC BRACING AND TRUSS CONNECTIONS.......................................................................... IIC-1 Example II.C-1 Example II.C-2 Example II.C-3 Example II.C-4 Example II.C-5 Example II.C-6

Truss Support Connection........................................................................................................ IIC-2 Bracing Connection ............................................................................................................... IIC-13 Bracing Connection ............................................................................................................... IIC-41 Truss Support Connection...................................................................................................... IIC-50 HSS Chevron Brace Connection ............................................................................................ IIC-57 Heavy Wide Flange Compression Connection (Flanges on the Outside) .............................. IIC-69

CHAPTER IID MISCELLANEOUS CONNECTIONS .................................................................................. ,ID-1 Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ix Example II.D-1 Example II.D-2 Example II.D-3

Prying Action in Tees and in Single Angles ............................................................................ IID-2 Beam Bearing Plate ................................................................................................................. IID-9 Slip-Critical Connection with Oversized Holes...................................................................... IID-15

PART III. SYSTEM DESIGN EXAMPLES ................................................................. III-1 Example III-1

Design of Selected Members and Lateral Analysis of a Four-Story Building .............................III-2 Introduction..................................................................................................................................III-2 Conventions .................................................................................................................................III-2 Design Sequence..........................................................................................................................III-3 General Description of the Building ............................................................................................III-4 Roof Member Design and Selection ...........................................................................................III-5 Floor Member Design and Selection ........................................................................................III-17 Column Design and Selection for Gravity Loads ..................................................................... III-38 Wind Load Determination ........................................................................................................III-46 Seismic Load Determination .....................................................................................................III-49 Moment Frame Model ...............................................................................................................III-61 Calculation of Required Strength—Three Methods ..................................................................III-67 Beam Analysis in the Moment Frame........................................................................................III-77 Braced Frame Analysis ..............................................................................................................III-80 Analysis of Drag Struts..............................................................................................................III-84

Part III Example References ...................................................................................................................................................III-87

PART IV. ADDITIONAL RESOURCES ..................................................................... IV-1 Table 4-1 Table 4-1 Table 6-1 Table 6-1

Discussion................................................................................................................................... IV-2 W-Shapes in Axial Compressions, Fy = 65 ksi ........................................................................... IV-5 Discussion................................................................................................................................. IV-17 Combined Flexure and Axial Force, W-Shapes, Fy = 65 ksi .................................................... IV-19


Return to Table of Contents

IID-1

Chapter IID Miscellaneous Connections This section contains design examples on connections in the AISC Steel Construction Manual that are not covered in other sections of the AISC Design Examples.



IID-2

EXAMPLE II.D-1 PRYING ACTION IN TEES AND IN SINGLE ANGLES Given: Design an ASTM A992 WT hanger connection between an ASTM A36 2L3×3×c tension member and an ASTM A992 W24×94 beam to support the following loads: PD = 13.5 kips PL = 40 kips Use w-in.-diameter ASTM A325-N or F1852-N bolts and 70-ksi electrodes.

Solution: From AISC Manual Table 2-4, the material properties are as follows: Hanger WT ASTM A992 Fy = 50 ksi Fu = 65 ksi Beam W24×94 ASTM A992 Fy = 50 ksi Fu = 65 ksi Angles 2L3×3×c ASTM A36 Fy = 36 ksi Fu = 58 ksi



IID-3

From AISC Manual Tables 1-1, 1-7 and 1-15, the geometric properties are as follows: Beam W24×94 d = 24.3 in. tw = 0.515 in. bf = 9.07 in. tf = 0.875 in. Angles 2L3×3×c A = 3.56 in.2 x = 0.860 in. for single angle From Chapter 2 of ASCE/SEI 7, the required strength is: ASD

LRFD Pu = 1.2(13.5 kips) + 1.6(40 kips) = 80.2 kips

Pa = 13.5 kips + 40 kips = 53.5 kips

Tensile Yielding of Angles Pn = Fy Ag

(

2

= 36 ksi 3.56 in.

(Spec. Eq. D2-1)

)

= 128 kips φ = 0.90

LRFD

φPn = 0.90(128 kips) = 115 kips > 80.2 kips

o.k.

ASD Ω = 1.67 Pn 128 kips = Ω 1.67 = 76.6 kips > 53.5 kips

o.k.

From AISC Specification Table J2.4, the minimum size of fillet weld based on a material thickness of c in. is x in. From AISC Specification Section J2.2b, the maximum size of fillet weld is: wmax = thickness − z in. = c in. − z in. = 4 in.

Try 4-in. fillet welds.



IID-4

From AISC Manual Part 8, Equations 8-2: ASD

LRFD Pu 1.392 D 80.2 kips = 1.392(4 sixteenths) = 14.4 in.

Pa 0.928D 53.5 kips = 0.928(4 sixteenths) = 14.4 in.

lmin =

lmin =

Use four 4-in. welds (16 in. total), one at the toe and heel of each angle. Tensile Rupture Strength of Angles x from AISC Specification Table D3.1 case 2 L 0.860 in. = 1− 4.00 in. = 0.785

U = 1−

Ae = AnU

(Spec. Eq. D3-1)

= 3.56 in. ( 0.785 ) 2

= 2.79 in.2 Pn = Fu Ae

(

= 58 ksi 2.79 in.2

(Spec. Eq. D2-2)

)

= 162 kips LRFD φt = 0.75 φt Pn = 0.75 (162 kips )

= 122 kips > 80.2 kips

o.k.

ASD Ωt = 2.00 Pn 162 kips = Ωt 2.00 = 81.0 kips > 53.5 kips

o.k.

Preliminary WT Selection Using Beam Gage g = 4 in. Try four w-in.-diameter ASTM A325-N bolts. From AISC Manual Table 7-2: ASD

LRFD P T = rut = u n 80.2 kips = 4 = 20.1 kips/bolt B = φrn = 29.8 kips > 20.1 kips

P T = rat = a n 53.5 kips = 4 = 13.4 kips/bolt o.k.

B = rn / Ω = 19.9 kips > 13.4 kips


o.k.


IID-5

Determine tributary length per pair of bolts, p, using AISC Manual Figure 9-4 and assuming a 2-in. web thickness. 4.00 in. − 2 in. 8.00 in. − 42 in. + 2 2 = 3.50 in. ≤ 42 in.

p=

LRFD 2 bolts(20.1 kips/bolt) = 11.5 kips/in. 3.50 in.

ASD 2 bolts(13.4 kips/bolt) = 7.66 kips/in. 3.50 in.

From AISC Manual Table 15-2b, with an assumed b = (4.00 in. – 2 in.)/2 = 1.75 in., the flange thickness, t = tf, of the WT hanger should be approximately s in. The minimum depth WT that can be used is equal to the sum of the weld length plus the weld size plus the kdimension for the selected section. From AISC Manual Table 1-8 with an assumed b = 1.75 in., t f ≈ s in., and d min = 4 in. + 4 in. + k ≈ 6 in., appropriate selections include: WT6×25 WT7×26.5 WT8×25 WT9×27.5

Try a WT6×25. From AISC Manual Table 1-8, the geometric properties are as follows: bf = 8.08 in. tf = 0.640 in. tw = 0.370 in. Prying Action Using AISC Manual Part 9 The beam flange is thicker than the WT flange; therefore, prying in the tee flange will control over prying in the beam flange. g − tw 2 4.00 in. − 0.370 in. = 2 = 1.82 in. > 14-in. entering and tightening clearance, and the fillet toe is cleared

b=

bf − g 2 8.08 in. − 4.00 in. = 2 = 2.04 in.

a=

b′ = b −

db 2

(Manual Eq. 9-21)



IID-6

⎛ w in. ⎞ = 1.82 in. − ⎜ ⎟ ⎝ 2 ⎠ = 1.45 in. db ⎛ a′ = ⎜ a + 2 ⎝

db ⎞ ⎞ ⎛ ⎟ ≤ ⎜ 1.25b + ⎟ 2 ⎠ ⎠ ⎝ w in. ⎛ w in. ⎞ = 2.04 in. + ⎜ ⎟ ≤ 1.25(1.82 in.)+ 2 2 ⎝ ⎠ = 2.42 in. ≤ 2.65 in.

(Manual Eq. 9-27)

b′ a′ 1.45 in. = 2.42 in. = 0.599

ρ=

(Manual Eq. 9-26)

ASD

LRFD 1⎛B ⎞ β = ⎜ − 1⎟ ρ⎝T ⎠

(Manual Eq. 9-25)

1 ⎛ 29.8 kips/bolt ⎞ − 1⎟ ⎜ 0.599 ⎝ 20.1 kips/bolt ⎠ = 0.806

(Manual Eq. 9-25)

1 ⎛ 19.9 kips/bolt ⎞ − 1⎟ ⎜ 0.599 ⎝ 13.4 kips/bolt ⎠ = 0.810

=

δ = 1−

1⎛B ⎞ β = ⎜ − 1⎟ ρ⎝T ⎠

=

d′ p

(Manual Eq. 9-24)

w in. + z in. 3.50 in. = 0.768

=1−

Since β < 1.0, LRFD

ASD 1⎛ β ⎞ α′ = ⎜ ⎟ ≤ 1.0 δ ⎝1− β ⎠ 1 ⎛ 0.810 ⎞ = ⎜ ⎟ 0.768 ⎝ 1 − 0.810 ⎠ = 5.55, therefore, α ′ = 1.0 Ω = 1.67

1⎛ β ⎞ α′ = ⎜ ⎟ ≤ 1.0 δ ⎝1− β ⎠ 1 ⎛ 0.806 ⎞ = ⎜ ⎟ 0.768 ⎝ 1 − 0.806 ⎠ = 5.41, therefore, α ′ = 1.0 φ = 0.90 tmin = =

4Tb′ φpFu (1 + δα ′)

(Manual Eq. 9-23a)

4 ( 20.1 kips/bolt )(1.45 in.)

=

0.90 ( 3.50 in.)( 65 ksi ) ⎡⎣1 + ( 0.768 )(1.0 ) ⎤⎦

= 0.567 in. < t f = 0.640 in.

tmin =

o.k.

Ω 4Tb′ pFu (1 + δα ′)

(Manual Eq. 9-23b)

1.67 ( 4 )(13.4 kips/bolt )(1.45 in.)

3.50 in. ( 65 ksi ) ⎡⎣1 + ( 0.768 )(1.0 ) ⎤⎦

= 0.568 in. < t f = 0.640 in.


o.k.


IID-7

Tensile Yielding of the WT Stem on the Whitmore Section Using AISC Manual Part 9 The effective width of the WT stem (which cannot exceed the actual width of 8 in.) is: lw = 3.00 in. + 2(4.00 in.)(tan 30D ) ≤ 8.00 in. = 7.62 in.

The nominal strength is determined as: Rn = Fy Ag

(Spec. Eq. J4-1)

= 50 ksi(7.62 in.)(0.370 in.) = 141 kips LRFD

φ = 0.90

Ω = 1.67

φRn = 0.90(141 kips) = 127 kips > 80.2 kips

o.k.

ASD

Rn 141 kips = 1.67 Ω = 84.4 kips > 53.5 kips

o.k.

Shear Rupture of the WT Stem Base Metal 6.19D Fu ⎛ 4 sixteenths ⎞ = 6.19 ⎜ ⎟ ⎝ 65 ksi ⎠ = 0.381 in. > 0.370 in.

(Manual Eq. 9-3)

tmin =

shear rupture strength of WT stem controls over weld rupture strength

Block Shear Rupture of the WT Stem Agv = ( 2 shear planes )( 4.00 in.)( 0.370 in.)

= 2.96 in.2 Tension stress is uniform, therefore Ubs = 1.0. Ant = Agt = 3.00 in. ( 0.370 in.)

= 1.11 in.2

Rn = 0.60FuAnv+UbsFuAnt ≤ 0.60FyAgv+UbsFuAnt

(Spec. Eq. J4-5)

Because the angles are welded to the WT-hanger, shear yielding on the gross area will control (that is, the portion of the block shear rupture equation that addresses shear rupture on the net area does not control). Rn = 0.60 Fy Agv + U bs Fu Ant

(

)

(

= 0.60 ( 50 ksi ) 2.96 in.2 + 1.0 ( 65 ksi ) 1.11 in.2

)

= 161 kips



IID-8

LRFD

φ = 0.75


Ω = 2.00

o.k.

ASD

Rn 161 kips = Ω 2.00 = 80.5 kips > 53.5 kips

o.k.

Note: As an alternative to the preceding calculations, the designer can use a simplified procedure to select a WT hanger with a flange thick enough to reduce the effect of prying action to an insignificant amount, i.e., q ≈ 0. Assuming b ' = 1.45 in. From AISC Manual Part 9: LRFD

φ = 0.90

tmin =

4Tb′ φpFu

4(20.1 kips/bolt)(1.45 in.) 0.90(3.50 in./bolt)(65 ksi) = 0.755 in.

=

Ω = 1.67

(Manual Eq. 9-20a)

tmin =

=

ASD

Ω 4Tb′ pFu

(Manual Eq. 9-20b)

1.67 ( 4 ) (13.4 kips/bolt)(1.45 in.)

(3.50 in./bolt)(65 ksi) = 0.755 in.

A WT6×25, with tf = 0.640 in. < 0.755 in., does not have a sufficient flange thickness to reduce the effect of prying action to an insignificant amount. In this case, the simplified approach requires a WT section with a thicker flange.



IID-9

EXAMPLE II.D-2 BEAM BEARING PLATE Given:

An ASTM A992 W18×50 beam with a dead load end reaction of 15 kips and a live load end reaction of 45 kips is supported by a 10-in.-thick concrete wall. Assuming the concrete has f c′ = 3 ksi, and the bearing plate is ASTM A36 material determine the following: a. If a bearing plate is required if the beam is supported by the full wall thickness b. The bearing plate required if lb = 10 in. (the full wall thickness) c. The bearing plate required if lb = 62 in. and the bearing plate is centered on the thickness of the wall

Solution:

From AISC Manual Tables 2-4 and 2-5, the material properties are as follows: Beam W18×50 ASTM A992 Fy = 50 ksi Fu = 65 ksi Bearing Plate (if required) ASTM A36 Fy = 36 ksi Fu = 58 ksi Concrete Wall f c′ = 3 ksi From AISC Manual Table 1-1, the geometric properties are as follows: Beam W18×50 d = 18.0 in. tw = 0.355 in. bf = 7.50 in. tf = 0.570 in. kdes = 0.972 in. k1 = m in.



IID-10

Concrete Wall h = 10.0 in. Solution a:

LRFD Calculate required strength.

ASD Calculate required strength.

Ru = 1.2(15 kips) + 1.6(45 kips) = 90.0 kips

Ra = 15 kips + 45 kips = 60.0 kips

Check web local yielding using AISC Manual Table 9-4 and Manual Equation 9-45a.

Check web local yielding using AISC Manual Table 9-4 and Manual Equation 9-45b.

Ru − φR1 ≥ kdes φR2 90.0 kips − 43.1 kips = ≥ 0.972 in. 17.8 kips/in. = 2.63 in. < 10.0 in.

lb req =

Ra − R1 / Ω ≥ kdes R2 / Ω 60.0 kips − 28.8 kips = ≥ 0.972 in. 11.8 kips/in. = 2.64 in. < 10.0 in.

lb req =

o.k.

o.k.

Check web local crippling using AISC Manual Table 9-4.

Check web local crippling using AISC Manual Table 9-4.

lb 10.0 in. = d 18.0 in. = 0.556

lb 10.0 in. = d 18.0 in. = 0.556

Since

lb > 0.2, use Manual Equation 9-48a. d

Ru − φR5 φR6 90.0 kips − 52.0 kips = 6.30 kips/in. = 6.03 in. < 10.0 in.

Since

lb req =

Verify

lb > 0.2, use Manual Equation 9-48b. d

Ra − R5 / Ω R6 / Ω 60.0 kips − 34.7 kips = 4.20 kips/in. = 6.02 in. < 10.0 in.

lb req =

o.k.

lb > 0.2, d

Verify

lb 6.03 in. = d 18.0 in. = 0.335 > 0.2

o.k.

o.k.

lb > 0.2, d

lb 6.02 in. = d 18.0 in. = 0.334 > 0.2

o.k.

Check the bearing strength of concrete.

Check the bearing strength of concrete.

Note that AISC Specification Equation J8-1 is used because A2 is not larger than A1 in this case.

Note that AISC Specification Equation J8-1 is used because A2 is not larger than A1 in this case.

Pp = 0.85fc′ A1

Pp = 0.85fc′ A1

(Spec. Eq. J8-1)


(Spec. Eq. J8-1)


IID-11

LRFD

ASD Ωc = 2.31

φc = 0.65

φcPp = φc0.85fc′A1 = 0.65(0.85)(3 ksi)(7.50 in.)(10.0 in.) = 124 kips > 90.0 kips

Pp 0.85 f c'A1 = Ωc Ωc 0.85 ( 3 ksi )( 7.50 in.)(10.0 in.) = 2.31 = 82.8 kips > 60.0 kips

o.k.

o.k.

Beam Flange Thickness Check Using AISC Manual Part 14 LRFD Determine the cantilever length from Manual Equation 14-1.

ASD Determine the cantilever length from Manual Equation 14-1. bf − kdes 2 7.50 in. = − 0.972 in. 2 = 2.78 in.

bf − kdes 2 7.50 in. = − 0.972 in. 2 = 2.78 in.

n=

n=

Determine bearing pressure.

Determine bearing pressure.

fp =

Ru A1

fp =

Determine the minimum beam flange thickness required if no bearing plate is provided. The beam flanges along the length, n, are assumed to be fixed end cantilevers with a minimum thickness determined using the limit state of flexural yielding. Mu =

f p n 2 Ru n 2 = 2 2 A1

Ra A1

Determine the minimum beam flange thickness required if no bearing plate is provided. The beam flanges along the length, n, are assumed to be fixed end cantilevers with a minimum thickness determined using the limit state of flexural yielding. Ma =

f p n 2 Ra n 2 = 2 2 A1

Z = 4t 2

Z = 4t 2

⎛ t2 ⎞ M u ≤ φFy Z = φFy ⎜⎜ ⎟⎟ ⎝4⎠

Ma ≤

Fy Z Fy ⎛ t 2 = ⎜ Ω Ω ⎜⎝ 4

tmin =

Ω4M a Ω 2 Ra n 2 = Fy A1 Fy

tmin =

4M u 2 Ru n 2 = φFy φA 1 Fy

φ = 0.90

tmin =

2 Ru n 2 φA 1 Fy

Ω = 1.67

tmin =

Ω 2 Ra n 2 A1 Fy


⎞ ⎟⎟ ⎠


IID-12

LRFD

ASD

2(90.0 kips)(2.78 in.)2 0.90(7.50 in.)(10.0 in.)(50 ksi) = 0.642 in. > 0.570 in.

=

1.67 ( 2 ) (60.0 kips)(2.78 in.) 2

=

(7.50 in.)(10.0 in.)(50 ksi) = 0.643 in. > 0.570 in.

n.g.

A bearing plate is required. See note following.

n.g.

A bearing plate is required. See note following.

Note: The designer may assume a bearing width narrower than the beam flange in order to justify a thinner flange. In this case, if 5.44 in. ≤ bearing width ≤ 6.56 in., a 0.570 in. flange thickness is ok and the concrete has adequate bearing strength. Solution b:

lb = 10 in. From Solution a, web local yielding and web local crippling are o.k. LRFD Calculate the required bearing-plate width using AISC Specification Equation J8-1.

ASD Calculate the required bearing-plate width using AISC Specification Equation J8-1.

φc = 0.65

Ωc = 2.31

A1 req =

Ru φc 0.85 f c ′

A1 req =

60.0 kips(2.31) (0.85)(3 ksi) = 54.4 in.2

90.0 kips 0.65(0.85)(3 ksi) = 54.3 in.2

=

=

B req =

Ra Ωc 0.85 f c ′

A1 req N

B req =

A 1 req N

54.4 in.2 10.0 in. = 5.44 in.

54.3 in.2 10.0 in. = 5.43 in.

=

=

Use B = 8 in. (selected as the least whole-inch dimension that exceeds bf).

Use B = 8 in. (selected as the least whole-inch dimension that exceeds bf).

Calculate the required bearing-plate thickness using AISC Manual Part 14.

Calculate the required bearing-plate thickness using AISC Manual Part 14.

B − kdes 2 8.00 in. = − 0.972 in. 2 = 3.03 in.

n=

tmin =

2 Ru n 2 φA1 Fy

(Manual Eq. 14-1)

B − kdes 2 8.00 in. = − 0.972 in. 2 = 3.03 in.

n=

tmin =

Ω 2 Ra n 2 A1 Fy


(Manual Eq. 14-1)


IID-13

2(90.0 kips)(3.03 in.)2 0.90(10.0 in.)(8.00 in.)(36 ksi) = 0.798 in.

=

=

1.67 ( 2 ) (60.0 kips)(3.03 in.) 2

(10.0 in.)(8.00 in.)(36 ksi) = 0.799 in.

Use PL d in.×10 in.×0 ft 8 in.

Use PL d in.×10 in.×0 ft 8 in.

Note: The calculations for tmin are conservative. Taking the strength of the beam flange into consideration results in a thinner required bearing plate or no bearing plate at all. Solution c:

lb = N = 6.50 in. From Solution a, web local yielding and web local crippling are o.k. Try B = 8 in.

A1 = BN = 8.00 in.(6.50 in.) = 52.0 in.2 To determine the dimensions of the area A2, the load is spread into the concrete until an edge or the maximum condition A 2 / A1 = 2 is met. There is also a requirement that the area, A2, be geometrically similar to A1 or, in other words, have the same aspect ratio as A1.

N1 = 6.50 in. + 2(1.75 in.) = 10.0 in. B 8.00in. = N 6.50 in. = 1.23 B1 = 1.23(10.0 in.) = 12.3 in. A2 = B1N1 = 12.3 in. (10.0 in.) = 123 in.2 Check

A2 123 in.2 = A1 52.0 in.2 o.k. = 1.54 ≤ 2

Pp = 0.85 f c ′ A1 A2 A1 ≤ 1.7 f c ′ A1

(

)

(Spec. Eq. J8-2)

(

= 0.85 ( 3 ksi ) 52.0 in.2 (1.54 ) ≤ 1.7 ( 3 ksi ) 52.0 in.2

)

= 204 kips ≤ 265 kips



IID-14

LRFD

ASD

φc = 0.65

Ωc = 2.31

φc Pp = 0.65(204 kips) = 133 kips

Pp 204 kips = 2.31 Ω = 88.3 kips

o.k.

133 kips > 90.0 kips

Calculate the required bearing-plate thickness using AISC Manual Part 14. B −k 2 8.00 in. − 0.972 in. = 2 = 3.03 in.

n=

tmin = =

(Manual Eq. 14-1)

Calculate the required bearing-plate thickness using AISC Manual Part 14. n=

B B −k −k 2 2

(Manual Eq. 14-1)

8.00 in. − 0.972 in. 2 = 3.03 in.

=

2 Ru n 2 φA1 Fy

tmin =

2(90.0 kips)(3.03 in.)2 0.90 ( 6.50 in.)( 8.00 in.) (36 ksi)

= 0.990 in.

o.k.

88.3 kips > 60.0 kips

=

Ω 2 Ra n 2 A1 Fy

1.67 ( 2 ) (60.0 kips)(3.03 in.) 2

( 6.50 in.)(8.00 in.) (36 ksi)

= 0.991 in. Use PL 1 in.× 62 in.× 0 ft 8 in.

Use PL 1 in.× 62 in.× 0 ft 8 in.

Note: The calculations for tmin are conservative. Taking the strength of the beam flange into consideration results in a thinner required bearing plate or no bearing plate at all.



IID-15

EXAMPLE II.D-3 SLIP-CRITICAL CONNECTION WITH OVERSIZED HOLES Given:

Design the connection of an ASTM A36 2L3×3×c tension member to an ASTM A36 plate welded to an ASTM A992 beam as shown in Figure II.D-3-1 for a dead load of 15 kips and a live load of 45 kips. The angles have standard holes and the plate has oversized holes per AISC Specification Table J3.3. Use w-in.-diameter ASTM A325-SC bolts with Class A surfaces. PD = 15 kips PL = 45 kips

Fig. II.D-3-1. Connection Configuration for Example II.D-3. Solution:

From AISC Manual Tables 2-4 and 2-5, the material properties are as follows: Beam W16×26 ASTM A992 Fy = 50 ksi Fu = 65 ksi Hanger 2L3×3×c ASTM A36 Fy = 36 ksi Fu = 58 ksi



IID-16

Plate ASTM A36 Fy = 36 ksi Fu = 58 ksi From AISC Manual Tables 1-1, 1-7 and 1-15, the geometric properties are as follows: Beam W16×26 tf = 0.345 in. tw = 0.250 in. kdes = 0.747 in. Hanger 2L3×3×c A = 3.56 in.2 x = 0.860 in. for single angle Plate tp = 0.500 in. LRFD Calculate required strength.

ASD Calculate required strength.

Ru = (1.2)(15 kips) + (1.6)(45 kips) = 90.0 kips

Ra = 15 kips + 45 kips = 60.0 kips

Check the available slip resistance of the bolts using AISC Manual Table 7-3.

Check the available slip resistance of the bolts using AISC Manual Table 7-3.

For w-in.-diameter ASTM A325-SC bolts with Class A faying surfaces in oversized holes and double shear:

For w-in.-diameter ASTM A325-SC bolts with Class A faying surfaces in oversized holes and double shear:

φrn = 16.1 kips/bolt

rn = 10.8 kips/bolt Ω

n=

Ru 90.0 kips = φrn 16.1 kips/bolt

n=

= 5.59 → 6 bolts

= 5.56 → 6 bolts

Slip-critical connections must also be designed for the limit states of bearing-type connections. Check bolt shear strength using AISC Manual Table 7-1. φrn = φFv Ab = 35.8 kips/bolt

φRn = φrn n = (35.8 kips/bolt)(6 bolts) = 215 kips > 90.0 kips

Ra 60.0 kips = ( rn / Ω ) 10.8 kips/bolt

o.k.

Slip-critical connections must also be designed for the limit states of bearing-type connections. Check bolt shear strength using AISC Manual Table 7-1. rn Fv Ab = = 23.9 kips/bolt Ω Ω Rn rn = n Ω Ω = (23.9 kips/bolt)(6 bolts) = 143 kips > 60.0 kips


o.k.


IID-17

Tensile Yielding Strength of the Angles Pn = Fy Ag

(

= 36 ksi 3.56 in.2

(Spec. Eq. D2-1)

)

= 128 kips LRFD

ASD

φt = 0.90

Ωt = 1.67

φt Pn = 0.90 (128 kips ) = 115 kips > 90.0 kips

o.k.

Pn 128 kips = 1.67 Ω = 76.6 kips > 60.0 kips

o.k.

Tensile Rupture Strength of the Angles x from AISC Specification Table D3.1 Case 2 l 0.860 in. = 1− 15.0 in. = 0.943

U = 1−

Ae = AnU

(Spec. Eq. D3-1)

= ⎡⎣3.56 in. − 2(c in.)(m in. + z in.) ⎤⎦ ( 0.943) = 2.84 in.2 2

Pn = Fu Ae

(Spec. Eq. D2-2) 2

= 58 ksi(2.84 in. ) = 165 kips LRFD φt = 0.75 φt Pn = 0.75(165 kips) = 124 kips > 90.0 kips

o.k.

ASD Ωt = 2.00 Pn 165 kips = 2.00 Ωt = 82.5 kips > 60.0 kips

o.k.

Block Shear Rupture Strength of the Angles

Use a single vertical row of bolts. U bs = 1, n = 6, Lev = 12 in., and Leh = 14 in.

Rn = 0.60 Fu Anv + U bs Fu Ant ≤ 0.60 Fy Agv + U bs Fu Ant

Shear Yielding Component Agv = ⎣⎡5 ( 3.00 in.) +1.50 in.⎦⎤ ( c in.)

= 5.16 in.2 per angle


(Spec. Eq. J4-5)


IID-18

(

0.60 Fy Agv = 0.60 ( 36 ksi ) 5.16 in.2

)

= 111 kips per angle Shear Rupture Component Anv = 5.16 in.2 − 5.5 (m in. + z in.)( c in.)

= 3.66 in.2 per angle

(

0.60 Fu Anv = 0.60 ( 58 ksi ) 3.66 in.2

)

= 127 kips per angle Shear yielding controls over shear rupture. Tension Rupture Component Ant = ⎣⎡1.25 in. − 0.5 (m in. + z in.) ⎦⎤ ( c in.) = 0.254 in.2 per angle

(

U bs Fu Ant = 1.0 ( 58 ksi ) 0.254 in.2

)

= 14.7 kips per angle φ = 0.75

LRFD

Ω = 2.00

φRn = 0.75 ( 2 )(111 kips + 14.7 kips ) = 189 kips > 90.0 kips

o.k.

ASD

Rn 2 (111kips + 14.7 kips ) = 2.00 Ω = 126 kips > 60.0 kips

o.k.

Bearing / Tear Out Strength of the Angles Holes are standard m-in. diameter. Check strength for edge bolt. lc = 1.50 in. −

w in. + z in. 2

= 1.09 in. rn = 1.2lc tFu ≤ 2.4dtFu = 1.2(1.09 in.)(c in.)(2)(58 ksi) ≤ 2.4(w in.)(c in.)(2)(58 ksi)

(Spec. Eq. J3-6a)

= 47.4 kips ≤ 65.3 kips

Check strength for interior bolts. lc = 3.00 in. − ( w in. + z in.)

= 2.19 in. rn = 1.2lc tFu ≤ 2.4dtFu = 1.2(2.19 in.)(c in.)(2)(58 ksi) ≤ 2.4(w in.)(c in.)(2)(58 ksi)


(Spec. Eq. J3-6a)


IID-19

= 95.3 kips ≤ 65.3 kips

Total strength for all bolts. rn = 1(47.4 kips) + 5(65.3 kips) = 374 kips LRFD

φ = 0.75

φrn = 0.75(374 kips) = 281 kips > 90.0 kips

o.k.

ASD Ω = 2.00 rn 374 kips = 2.00 Ω = 187 kips > 60.0 kips

o.k.

Tensile Yielding Strength of the 2-in. Plate By inspection, the Whitmore section includes the entire width of the 2-in. plate. Rn = Fy Ag = 36 ksi(2 in.)(6.00 in.) = 108 kips

(Spec. Eq. J4-1)

LRFD φt = 0.90 φRn = 0.90(108 kips) = 97.2 kips > 90.0 kips

o.k.

ASD Ωt = 1.67 Rn 108 kips = 1.67 Ωt = 64.7 kips > 60.0 kips

o.k.

Tensile Rupture Strength of the 2-in. Plate Holes are oversized ,-in. diameter. Calculate the effective net area. Ae = An ≤ 0.85 Ag from AISC Specification Section J4.1

(

≤ 0.85 3.00 in.2

)

2

≤ 2.55 in.

An = 3.00 in.2 − (2 in.)(, in. + z in.)

= 2.50in.2 ≤ 2.55in.2 Ae = AnU

(Spec. Eq. D3-1)

= 2.50in. (1.0 ) 2

= 2.50 in.2 Rn = Fu Ae

(Spec. Eq. J4-2) 2

= 58 ksi(2.50 in. ) = 145 kips



IID-20

LRFD φ = 0.75 φRn = 0.75(145 kips) = 109 kips > 90.0 kips

o.k.

ASD Ω = 2.00 Rn 145 kips = Ω 2.00 = 72.5 kips > 60.0 kips

o.k.

Block Shear Rupture Strength of the 2-in. Plate Use a single vertical row of bolts. U bs = 1.0, n = 6, Lev = 12 in., and Leh = 3 in. Rn = 0.60 Fu Anv + U bs Fu Ant ≤ 0.60 Fy Agv + U bs Fu Ant

(Spec. Eq. J4-5)

Shear Yielding Component Agv = ⎡⎣5 ( 3.00 in.) + 1.50 in.⎤⎦ (2 in.) = 8.25 in.2

(

0.60 Fy Agv = 0.60 ( 36 ksi ) 8.25 in.2

)

= 178 kips Shear Rupture Component Anv = 8.25 in.2 − 5.5 (, in. + z in.)(2 in.)

= 5.50 in.2

(

0.60 Fu Anv = 0.60 ( 58 ksi ) 5.50 in.2

)

= 191 kips Shear yielding controls over shear rupture. Tension Rupture Component Ant = ⎡⎣3.00 in. − 0.5 (, in. + z in.) ⎤⎦ (2 in.) = 1.25 in.2

(

U bs Fu Ant = 1.0 ( 58 ksi ) 1.25 in.2

)

= 72.5 kips φ = 0.75

LRFD

Ω = 2.00

φRn = 0.75 (178 kips + 72.5 kips ) = 188 kips > 90.0 kips

o.k.

ASD

Rn (178 kips + 72.5 kips ) = Ω 2.00 = 125 kips > 60.0 kips


o.k.


IID-21

Bearing/Tear Out Strength of the 2-in. Plate Holes are oversized ,-in. diameter. Check strength for edge bolt. lc = 1.50 in. −

, in. 2

= 1.03 in. rn = 1.2lc tFu ≤ 2.4dtFu = 1.2(1.03 in.)(2 in.)(58 ksi) ≤ 2.4(w)(2 in.)(58 ksi)

(Spec. Eq. J3-6a)

= 35.8 kips ≤ 52.2 kips

Check strength for interior bolts. lc = 3.00 in. − , in. = 2.06 in. rn = 1.2lc tFu ≤ 2.4dtFu = 1.2(2.06 in.)(2 in.)(58 ksi) ≤ 2.4(w in.)(2 in.)(58 ksi) = 71.7 kips ≤ 52.2 kips

(Spec. Eq. J3-6a)

Total strength for all bolts. rn = 1(35.8 kips) + 5(52.2 kips) = 297 kips LRFD φ = 0.75 φrn = 0.75(297 kips) = 223 kips > 90.0 kips

o.k.

ASD Ω = 2.00 rn 297 kips = 2.00 Ω = 149 kips > 60.0 kips

o.k.

Fillet Weld Required for the 2-in. Plate to the W-Shape Beam Because the angle of the force relative to the axis of the weld is 90°, the strength of the weld can be increased by the following factor from AISC Specification Section J2.4. (1.0 + 0.50sin1.5 θ) = (1.0 + 0.50sin1.5 90°) = 1.50

From AISC Manual Equations 8-2, LRFD Ru Dreq = 1.50(1.392l ) 90.0 kips = 1.50(1.392)(2)(6.00 in.) = 3.59 sixteenths

ASD Pa Dreq = 1.50(0.928l ) 60.0 kips = 1.50(0.928)(2)(6.00 in.) = 3.59 sixteenths



IID-22

From AISC Manual Table J2.4, the minimum fillet weld size is x in. Use a 4-in. fillet weld on both sides of the plate. Beam Flange Base Metal Check 3.09 D Fu 3.09(3.59 sixteenths) = 65 ksi = 0.171 in. < 0.345 in.

tmin =

(Manual Eq. 9-2)

o.k.

Concentrated Forces Check for W16x26 Beam Check web local yielding. (Assume the connection is at a distance from the member end greater than the depth of the member, d.) Rn = Fywtw (5kdes + lb )

(Spec. Eq. J10-2)

= 50 ksi (4 in.) ⎡⎣5 ( 0.747 in.) + 6.00 in.⎤⎦ = 122 kips φ = 1.00

LRFD


o.k.

ASD Ω = 1.50 Rn 122 kips = Ω 1.50 = 81.3 kips > 60.0 kips


o.k.


III-1

Chapter III System Design Examples



III-2 EXAMPLE III-1

Design of Selected Members and Lateral Analysis of a Four-Story Building

INTRODUCTION This section illustrates the load determination and selection of representative members that are part of the gravity and lateral frame of a typical four-story building. The design is completed in accordance with the 2010 AISC Specification for Structural Steel Buildings and the 14th Edition AISC Steel Construction Manual. Loading criteria are based on ASCE/SEI 7-10 (ASCE, 2010). This section includes: • Analysis and design of a typical steel frame for gravity loads • Analysis and design of a typical steel frame for lateral loads • Examples illustrating three methods for satisfying the stability provisions of AISC Specification Chapter C The building being analyzed in this design example is located in a Midwestern city with moderate wind and seismic loads. The loads are given in the description of the design example. All members are ASTM A992 steel. CONVENTIONS The following conventions are used throughout this example: 1.

Beams or columns that have similar, but not necessarily identical, loads are grouped together. This is done because such grouping is generally a more economical practice for design, fabrication and erection.

2.

Certain calculations, such as design loads for snow drift, which might typically be determined using a spreadsheet or structural analysis program, are summarized and then incorporated into the analysis. This simplifying feature allows the design example to illustrate concepts relevant to the member selection process.

3.

Two commonly used deflection calculations, for uniform loads, have been rearranged so that the conventional units in the problem can be directly inserted into the equation for steel design. They are as follows: Simple Beam:

Beam Fixed at both Ends:

Δ=

Δ=

5 w kip/in. ( L in.)

4

384 ( 29,000 ksi ) ( I in.4 ) w kip/in. ( L in.)

=

w kip/ft ( L ft )

4

384 ( 29,000 ksi ) ( I in.4 )

=


4

1,290 ( I in.4 )

w kip/ft ( L ft )

4

6,440 ( I in.4 )


III-3 DESIGN SEQUENCE The design sequence is presented as follows: 1. General description of the building including geometry, gravity loads and lateral loads 2. Roof member design and selection 3. Floor member design and selection 4. Column design and selection for gravity loads 5. Wind load determination 6. Seismic load determination 7. Horizontal force distribution to the lateral frames 8. Preliminary column selection for the moment frames and braced frames 9. Seismic load application to lateral systems 10. Stability (P-Δ) analysis



III-4 GENERAL DESCRIPTION OF THE BUILDING Geometry The design example is a four-story building, comprised of seven bays at 30 ft in the East-West (numbered grids) direction and bays of 45 ft, 30 ft and 45 ft in the North-South (lettered grids) direction. The floor-to-floor height for the four floors is 13 ft 6 in. and the height from the fourth floor to the roof (at the edge of the building) is 14 ft 6 in. Based on discussions with fabricators, the same column size will be used for the whole height of the building.

Basic Building Layout The plans of these floors and the roof are shown on Sheets S2.1 thru S2.3, found at the end of this Chapter. The exterior of the building is a ribbon window system with brick spandrels supported and back-braced with steel and infilled with metal studs. The spandrel wall extends 2 ft above the elevation of the edge of the roof. The window and spandrel system is shown on design drawing Sheet S4.1. The roof system is 12-in. metal deck on bar joists. These bar joists are supported on steel beams as shown on Sheet S2.3. The roof slopes to interior drains. The middle 3 bays have a 6 ft tall screen wall around them and house the mechanical equipment and the elevator over run. This area has steel beams, in place of steel bar joists, to support the mechanical equipment. The three elevated floors have 3 in. of normal weight concrete over 3-in. composite deck for a total slab thickness of 6 in. The supporting beams are spaced at 10 ft on center. These beams are carried by composite girders in the East-West direction to the columns. There is a 30 ft by 29 ft opening in the second floor, to create a two-story atrium at the entrance. These floor layouts are shown on Sheets S2.1 and S2.2. The first floor is a slab on grade and the foundation consists of conventional spread footings. The building includes both moment frames and braced frames for lateral resistance. The lateral system in the North-South direction consists of chevron braces at the end of the building, located adjacent to the stairways. In



III-5 the East-West direction there are no locations in which chevron braces can be concealed; consequently, the lateral system in the East-West direction is composed of moment frames at the North and South faces of the building. This building is sprinklered and has large open spaces around it, and consequently does not require fireproofing for the floors. Wind Forces The Basic Wind Speed is 90 miles per hour (3 second gust). Because it is sited in an open, rural area, it will be analyzed as Wind Exposure Category C. Because it is an ordinary (Risk Category II) office occupancy, the wind importance factor is 1.0. Seismic Forces The sub-soil has been evaluated and the site class has been determined to be Category D. The area has a short period Ss = 0.121g and a one-second period S1 = 0.060g. The seismic importance factor is 1.0, that of an ordinary office occupancy (Risk Category II). Roof and Floor Loads Roof loads: The ground snow load (pg) is 20 psf. The slope of the roof is 4 in./ft or more at all locations, but not exceeding 2 in./ft; consequently, 5 psf rain-on-snow surcharge is to be considered, but ponding instability design calculations are not required. This roof can be designed as a fully exposed roof, but, per ASCE/SEI 7 Section 7.3, cannot be designed for less than pf = (I)pg = 20 psf uniform snow load. Snow drift will be applied at the edges of the roof and at the screen wall around the mechanical area. The roof live load for this building is 20 psf, but may be reduced per ASCE/SEI 7 Section 4.8 where applicable. Floor Loads: The basic live load for the floor is 50 psf. An additional partition live load of 20 psf is specified. Because the locations of partitions and, consequently, corridors are not known, and will be subject to change, the entire floor will be designed for a live load of 80 psf. This live load will be reduced, based on type of member and area per the ASCE provisions for live-load reduction. Wall Loads: A wall load of 55 psf will be used for the brick spandrels, supporting steel, and metal stud back-up. A wall load of 15 psf will be used for the ribbon window glazing system. ROOF MEMBER DESIGN AND SELECTION Calculate dead load and snow load. Dead Load Roofing Insulation Deck Beams Joists Misc. Total

= 5 psf = 2 psf = 2 psf = 3 psf = 3 psf = 5 psf = 20 psf



III-6 Snow Load from ASCE/SEI 7 Section 7.3 and 7.10 Snow = 20 psf Rain on Snow = 5 psf Total = 25 psf Note: In this design, the rain and snow load is greater than the roof live load The deck is 1½ in., wide rib, 22 gage, painted roof deck, placed in a pattern of three continuous spans minimum. The typical joist spacing is 6 ft on center. At 6 ft on center, this deck has an allowable total load capacity of 89 psf. The roof diaphragm and roof loads extend 6 in. past the centerline of grid as shown on Sheet S4.1. From Section 7.7 of ASCE/SEI 7, the following drift loads are calculated: Flat roof snow load = 20 psf, Density γ = 16.6 lbs/ft3, hb = 1.20 ft Summary of Drifts

Side Parapet End Parapet Screen Wall

Upwind Roof Length (lu) 121 ft 211 ft 60.5 ft

Proj. Height 2 ft 2 ft 6 ft

Max. Drift Load 13.2 psf 13.2 psf 30.5 psf

Max Drift Width (W) 6.36 ft 6.36 ft 7.35 ft

The snow drift at the penthouse was calculated for the maximum effect, using the East-West wind and an upwind fetch from the parapet to the centerline of the columns at the penthouse. This same drift is conservatively used for wind in the North-South direction. The precise location of the drift will depend upon the details of the penthouse construction, but will not affect the final design in this case. SELECT ROOF JOISTS Layout loads and size joists. User Note: Joists may be specified using ASD or LRFD but are most commonly specified by ASD as shown here. The 45-ft side joist with the heaviest loads is shown below along with its end reactions and maximum moment:

Because the load is not uniform, select a 24KCS4 joist from the Steel Joist Institute load tables (SJI, 2005). This joist has an allowable moment of 92.3 kip-ft, an allowable shear of 8.40 kips, a gross moment of inertia of 453 in.4 and weighs 16.6 plf. The first joist away from the end of the building is loaded with snow drift along the length of the member. Based on analysis, a 24KCS4 joist is also acceptable for this uniform load case. Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-7

As an alternative to directly specifying the joist sizes on the design document, as done in this example, loading diagrams can be included on the design documents to allow the joist manufacturer to economically design the joists. The typical 30-ft joist in the middle bay will have a uniform load of w = (20 psf + 25 psf)(6 ft) = 270 plf wSL = (25 psf)(6 ft) = 150 plf From the Steel Joist Institute load tables, select an 18K5 joist which weighs approximately 7.7 plf and satisfies both strength and deflection requirements. Note: the first joist away from the screen wall and the first joist away from the end of the building carry snow drift. Based on analysis, an 18K7 joist will be used in these locations.



III-8 SELECT ROOF BEAMS Calculate loads and select beams in the mechanical area. For the beams in the mechanical area, the mechanical units could weigh as much as 60 psf. Use 40 psf additional dead load, which will account for the mechanical units and the screen wall around the mechanical area. Use 15 psf additional snow load, which will account for any snow drift which could occur in the mechanical area. The beams in the mechanical area are spaced at 6 ft on center. Per AISC Design Guide 3 (West et al., 2003), calculate the minimum Ix to limit deflection to l/360 = 1.00 in. because a plaster ceiling will be used in the lobby area. Use 40 psf as an estimate of the snow load, including some drifting that could occur in this area, for deflection calculations. Note: The beams and supporting girders in this area should be rechecked when the final weights and locations for the mechanical units have been determined. Ireq (Live Load) =

0.240 kip/ft ( 30.0 ft )

4

1,290 (1.00 in.)

= 151 in.4

Calculate the required strengths from Chapter 2 of ASCE/SEI 7 and select the beams in the mechanical area. LRFD

wu = 6.00 ft[1.2 (0.020 kip/ft2 + 0.040 kip/ft2) +1.6(0.025 kip/ft2 + 0.015 kip/ft2)] = 0.816 kip/ft

30.0 ft ( 0.600 kip/ft ) 2 = 9.00 kips

30.0 ft ( 0.816 kip/ft ) 2 = 12.2 kips

Ru =

Mu =

0.816 kip/ft ( 30.0 ft )

ASD wa = 6.00 ft[0.020 kip/ft2 + 0.040 kip/ft2 + 0.025 kip/ft2 + 0.015 kip/ft2] = 0.600 kip/ft Ra =

2

Ma =

8

= 91.8 kip-ft

0.600 kip/ft ( 30.0 ft )

2

8

= 67.5 kip-ft

Assuming the beam has full lateral support, use Manual Table 3-2, select an ASTM A992 W14×22, which has a design flexural strength of 125 kip-ft, a design shear strength of 94.5 kips, and an Ix of 199 in.4

Assuming the beam has full lateral support, use Manual Table 3-2, select an ASTM A992 W14×22, which has an allowable flexural strength of 82.8 kipft, an allowable shear strength of 63.0 kips and an Ix of 199 in.4



III-9

SELECT ROOF BEAMS AT THE END (EAST & WEST) OF THE BUILDING

The beams at the ends of the building carry the brick spandrel panel and a small portion of roof load. For these beams, the cladding weight exceeds 25% of the total dead load on the beam. Therefore, per AISC Design Guide 3, limit the vertical deflection due to cladding and initial dead load to L/600 or a in. maximum. In addition, because these beams are supporting brick above and there is continuous glass below, limit the superimposed dead and live load deflection to L/600 or 0.3 in. max to accommodate the brick and L/360 or 4 in. max to accommodate the glass. Therefore, combining the two limitations, limit the superimposed dead and live load deflection to L/600 or 4 in. The superimposed dead load includes all of the dead load that is applied after the cladding has been installed. In calculating the wall loads, the spandrel panel weight is taken as 55 psf. The spandrel panel weight is approximately: wD = 7.50 ft(0.055 kip/ft2) = 0.413 kip/ft

The dead load from the roof is equal to: wD = 3.50 ft(0.020 kip/ft2) = 0.070 kip/ft

Use 8 psf for the initial dead load. wD(initial) = 3.50 ft(0.008 kip/ft2) = 0.0280 kip/ft

Use 12 psf for the superimposed dead load. wD(super) = 3.50 ft(0.012 kip/ft2) = 0.0420 kip/ft

The snow load from the roof can be conservatively taken as: wS = 3.50 ft(0.025 kip/ft2 + 0.0132 kip/ft2) = 0.134 kip/ft

to account for the maximum snow drift as a uniform load. Assume the beams are simple spans of 22.5 ft. Calculate minimum Ix to limit the superimposed dead and live load deflection to ¼ in. Ireq =

0.176 kip/ft ( 22.5 ft )

4

1,290 (4 in.)

=140 in.4

Calculate minimum Ix to limit the cladding and initial dead load deflection to a in. Ireq =

0.441 kip/ft ( 22.5 ft ) 1,290 ( a in.)

4

= 234 in.4

The beams are full supported by the deck as shown in Detail 4 on Sheet S4.1. The loading diagram is as follows:



III-10

Calculate the required strengths from Chapter 2 of ASCE/SEI 7 and select the beams for the roof ends. LRFD

wu =1.2(0.070 kip/ft + 0.413 kip/ft) + 1.6(0.134 kip/ft) = 0.794 kip/ft 22.5 ft ( 0.794 kip/ft ) 2 = 8.93 kips

22.5 ft ( 0.617 kip/ft ) 2 = 6.94 kips

Ru =

Mu =

0.794 kip/ft ( 22.5 ft )

ASD wa = (0.070 kip/ft + 0.413 kip/ft) + 0.134 kip/ft = 0.617 kip/ft Ra =

2

Ma =

8

= 50.2 kip-ft

0.617 kip/ft ( 22.5 ft )

2

8

= 39.0 kip-ft

Assuming the beam has full lateral support, use Manual Table 3-2, select an ASTM A992 W16×26, which has a design flexural strength of 166 kip-ft, a design shear strength of 106 kips, and an Ix of 301 in.4

Assuming the beam has full lateral support, use Manual Table 3-2, select an ASTM A992 W16×26, which has an allowable flexural strength of 110 kipft, an allowable shear strength of 70.5 kips, and an Ix of 301 in.4



III-11

SELECT ROOF BEAMS ALONG THE SIDE (NORTH & SOUTH) OF THE BUILDING

The beams along the side of the building carry the spandrel panel and a substantial roof dead load and live load. For these beams, the cladding weight exceeds 25% of the total dead load on the beam. Therefore, per AISC Design Guide 3, limit the vertical deflection due to cladding and initial dead load to L/600 or a in. maximum. In addition, because these beams are supporting brick above and there is continuous glass below, limit the superimposed dead and live load deflection to L/600 or 0.3 in. max to accommodate the brick and L/360 or 4 in. max to accommodate the glass. Therefore, combining the two limitations, limit the superimposed dead and live load deflection to L/600 or 4 in. The superimposed dead load includes all of the dead load that is applied after the cladding has been installed. These beams will be part of the moment frames on the side of the building and therefore will be designed as fixed at both ends. The roof dead load and snow load on this edge beam is equal to the joist end dead load and snow load reaction. Treating this as a uniform load, divide this by the joist spacing. wD = 2.76 kips/6.00 ft = 0.460 kip/ft wS = 3.73 kips/6.00 ft = 0.622 kip/ft wD(initial) = 23.0 ft (0.008 kip/ft2) = 0.184 kip/ft wD(super) = 23.0 ft (0.012 kip/ft2) = 0.276 kip/ft

Calculate the minimum Ix to limit the superimposed dead and live load deflection to 4 in. Ireq =

( 0.898 kip/ft )( 30.0 ft ) 6,440 (4 in.)

4

= 452 in.4 Calculate the minimum Ix to limit the cladding and initial dead load deflection to a in. Ireq =

( 0.597 kip/ft )( 30.0 ft ) 6,440 ( a in.)

4

= 200 in.4



III-12

Calculate the required strengths from Chapter 2 of ASCE/SEI 7 and select the beams for the roof sides. LRFD

wu = 1.2(0.460 kip/ft + 0.413 kip/ft) +1.6(0.622 kip/ft) = 2.04 kip/ft 30.0 ft ( 2.04 kip/ft ) 2 = 30.6 kips

ASD wa = (0.460 kip/ft + 0.413 kip/ft) + 0.622 kip/ft = 1.50 kip/ft 30.0 ft (1.50 kip/ft ) 2 = 22.5 kips

Ru =

Ra =

Calculate Cb for compression in the bottom flange braced at the midpoint and supports using AISC Specification Equation F1-1.

Calculate Cb for compression in the bottom flange braced at the midpoint and supports using AISC Specification Equation F1-1.

MuMax =

2.04 kip/ft ( 30.0 ft )

2

MaMax =

12 = 153 kip-ft at supports

Mu =

2.04 kip/ft ( 30.0 ft )

2

Ma =

2

From AISC Manual Table 3-23,

⎞ 2.04 kip/ft ⎛ 6 ( 30.0 ft )( 3.75 ft ) ⎜ ⎟ 2 2 ⎜ − ( 30.0 ft ) − 6 ( 3.75 ft ) ⎟ 12 ⎝ ⎠

= 52.6 kip-ft at quarter point of unbraced segment

⎞ 2.04 kip/ft ⎛ 6 ( 30.0 ft )( 7.50 ft ) ⎜ ⎟ 2 2 ⎜ − ( 30.0 ft ) − 6 ( 7.50 ft ) ⎟ 12 ⎝ ⎠

= 19.1 kip-ft at midpoint of unbraced segment M uC =

1.50 kip/ft ( 30.0 ft )

24 = 56.3 kip-ft at midpoint


M uB =

2

12 = 113 kip-ft at supports

24 = 76.5 kip-ft at midpoint

M uA =

1.50 kip/ft ( 30.0 ft )

⎞ 2.04 kip/ft ⎛ 6 ( 30.0 ft )(11.3 ft ) ⎜ ⎟ 2 2 ⎜ − ( 30.0 ft ) − 6 (11.3 ft ) ⎟ 12 ⎝ ⎠

= 62.5 kip-ft at three quarter point of unbraced segment

M aA =

⎞ 1.50 kip/ft ⎛ 6 ( 30.0 ft )( 3.75 ft ) ⎜ ⎟ ⎜ − ( 30.0 ft )2 − 6 ( 3.75 ft )2 ⎟ 12 ⎝ ⎠

= 38.7 kip-ft at quarter point of unbraced segment

M aB =

⎞ 1.50 kip/ft ⎛ 6 ( 30.0 ft )( 7.50 ft ) ⎜ ⎟ 2 2 ⎜ − ( 30.0 ft ) − 6 ( 7.50 ft ) ⎟ 12 ⎝ ⎠

= 14.1 kip-ft at midpoint of unbraced segment M aC =

⎞ 1.50 kip/ft ⎛ 6 ( 30.0 ft )(11.3 ft ) ⎜ ⎟ 2 2 ⎜ − ( 30.0 ft ) − 6 (11.3 ft ) ⎟ 12 ⎝ ⎠

= 46.0 kip-ft at three quarter point of unbraced segment



III-13

LRFD

Using AISC Specification Equation F1-1, 12.5M max Cb = 2.5M max + 3M A + 4 M B + 3M C 12.5 (153 kip-ft ) = ⎡ 2.5 (153 kip-ft ) + 3 ( 52.6 kip-ft ) ⎤ ⎢ ⎥ ⎣⎢ +4 (19.1 kip-ft ) + 3 ( 62.5 kip-ft ) ⎦⎥ = 2.38

ASD Using AISC Specification Equation F1-1, 12.5M max Cb = 2.5M max + 3M A + 4 M B + 3M C 12.5 (113 kip-ft ) = ⎡ 2.5 (113 kip-ft ) + 3 ( 38.7 kip-ft ) ⎤ ⎢ ⎥ ⎣⎢ +4 (14.1 kip-ft ) + 3 ( 46.0 kip-ft ) ⎦⎥ = 2.38

From AISC Manual Table 3-10, select W18×35.

From AISC Manual Table 3-10, select W18×35.

For Lb = 6 ft and Cb = 1.0 φbMn = 229 kip-ft > 76.5 kip-ft

For Lb = 6 ft and Cb = 1.0 Mn / Ω b = 152 kip-ft > 56.3 kip-ft

o.k.

For Lb = 15 ft and Cb = 2.38, Mn / Ω b = (72.7 kip-ft)2.38 = 173 kip-ft ≤ Mp / Ωb Ωb / Mp = 166 kip-ft > 113 kip-ft

o.k.

For Lb = 15 ft and Cb = 2.38, φbMn = (109 kip-ft)2.38 = 259 kip-ft ≤ φbMp φbMp = 249 kip-ft > 153 kip-ft

o.k.

o.k.

From AISC Manual Table 3-2, a W18×35 has a design shear strength of 159 kips and an Ix of 510 in.4 o.k.

From AISC Manual Table 3-2, a W18×35 has an allowable shear strength of 106 kips and an Ix of 510 in.4 o.k.

Note: This roof beam may need to be upsized during the lateral load analysis to increase the stiffness and strength of the member and improve lateral frame drift performance.



III-14

SELECT THE ROOF BEAMS ALONG THE INTERIOR LINES OF THE BUILDING

There are three individual beam loadings that occur along grids C and D. The beams from 1 to 2 and 7 to 8 have a uniform snow load except for the snow drift at the end at the parapet. The snow drift from the far ends of the 45-ft joists is negligible. The beams from 2 to 3 and 6 to 7 are the same as the first group, except they have snow drift at the screen wall. The loading diagrams are shown below. A summary of the moments, left and right reactions, and required Ix to keep the live load deflection to equal or less than the span divided by 240 (or 1.50 in.) is given below.

Calculate required strengths from Chapter 2 of ASCE/SEI 7 and required moment of inertia. LRFD

Grids 1 to 2 and 7 to 8 (opposite hand)

ASD Grids 1 to 2 and 7 to 8 (opposite hand)

Ru (left) = 1.2(11.6 kips) + 1.6(16.0 kips) = 39.5 kips

Ra (left) = 11.6 kips + 16.0 kips = 27.6 kips

Ru (right) = 1.2(11.2 kips) + 1.6(14.2 kips) = 36.2 kips

Ra (right) = 11.2 kips + 14.2 kips = 25.4 kips

Mu = 1.2(84.3 kip-ft) + 1.6(107 kip-ft) = 272 kip-ft

Ma = 84.3 kip-ft + 107 kip-ft = 191 kip-ft



III-15

LRFD

Ix req’d =

( 0.938 kip/ft )( 30.0 ft ) 1,290 (1.50 in.)

ASD 4

Ix req’d =

= 393 in.4

( 0.938 kip/ft )( 30.0 ft ) 1,290 (1.50 in.)

4

= 393 in.4

From AISC Manual Table 3-10, for Lb = 6 ft and Cb = 1.0, select W21×44 which has a design flexural strength of 332 kip-ft, a design shear strength of 217 kips, and Ix = 843 in.4

From AISC Manual Table 3-10, for Lb = 6 ft and Cb = 1.0, select W21×44 which has an allowable flexural strength of 221 kip-ft, an allowable shear strength of 145 kips, and Ix = 843 in.4

Grids 2 to 3 and 6 to 7(opposite hand)

Grids 2 to 3 and 6 to 7(opposite hand)

Ru (left) = 1.2(11.3 kips) + 1.6(14.4 kips) = 36.6 kips

Ra (left) = 11.3 kips + 14.4 kips = 25.7 kips

Ru (right) = 1.2(11.3 kips) + 1.6(17.9) kips) = 42.2 kips

Ra (right) = 11.3 kips + 17.9 kips = 29.2 kips

Mu = 1.2(84.4 kip-ft) + 1.6(111 kip-ft) = 279 kip-ft

Ma = 84.4 kip-ft + 111 kip-ft = 195 kip-ft

Ix req’d =

( 0.938 kip/ft )( 30.0 ft ) 1,290 (1.50 in.)

4

Ix req’d =

= 393 in.4

( 0.938 kip/ft )( 30.0 ft ) 1,290 (1.50 in.)

4

= 393 in.4

From AISC Manual Table 3-10, for Lb = 6 ft and Cb = 1.0, select W21×44 which has a design flexural strength of 332 kip-ft, a design shear strength of 217 kips and Ix = 843 in.4

From AISC Manual Table 3-10, for Lb = 6 ft and Cb = 1.0, select W21×44 which has an allowable flexural strength of 221 kip-ft, an allowable shear strength of 145 kips, and Ix = 843 in.4

The third individual beam loading occurs at the beams from 3 to 4, 4 to 5, and 5 to 6. This is the heaviest load.



III-16

SELECT THE ROOF BEAMS ALONG THE SIDES OF THE MECHANICAL AREA

The beams from 3 to 4, 4 to 5, and 5 to 6 have a uniform snow load outside the screen walled area, except for the snow drift at the parapet ends and the screen wall ends of the 45-ft joists. Inside the screen walled area the beams support the mechanical equipment. A summary of the moments, left and right reactions, and required Ix to keep the live load deflection to equal or less than the span divided by 240 (or 1.50 in.) is given below.

LRFD

wu =1.2 (1.35 kip/ft) +1.6(1.27 kip/ft) = 3.65 kip/ft Mu =

3.65 kip/ft ( 30.0 ft )

2

Ma =

8

= 411 kip-ft 30.0 ft ( 3.65 kip/ft ) 2 = 54.8 kips

1.27 kip/ft ( 30.0 ft )

2

8

30.0 ft ( 2.62 kip/ft ) 2 = 39.3 kips

Ra =

4

Ix req’d =

1,290 (1.50 in.)

= 532 in.

2.62 kip/ft ( 30.0 ft )

= 295 kip-ft

Ru =

Ix req’d =

ASD wa = 1.35 kip/ft + 1.27 kip/ft2 = 2.62 kip/ft

4

1.27 kip/ft ( 30.0 ft )

4

1,290 (1.50 in.)

= 532 in.4

From AISC Manual Table 3-2, for Lb = 6 ft and Cb = 1.0, select W21×55, which has a design flexural strength of 473 kip-ft, a design shear strength of 234 kips, and an Ix of 1,140 in.4

From AISC Manual Table 3-2, for Lb = 6 ft and Cb = 1.0, select W21×55, which has an allowable flexural strength of 314 kip-ft, an allowable shear strength of 156 kips, and an Ix of 1,140 in.4



III-17 FLOOR MEMBER DESIGN AND SELECTION

Calculate dead load and live load. Dead Load Slab and Deck Beams (est.) Misc. ( ceiling, mechanical, etc.) Total

= 57 psf = 8 psf = 10 psf = 75 psf

Note: The weight of the floor slab and deck was obtained from the manufacturer’s literature. Live Load Total (can be reduced for area per ASCE/SEI 7)

= 80 psf

The floor and deck will be 3 in. of normal weight concrete, f c ′ = 4 ksi, on 3-in. 20 gage, galvanized, composite deck, laid in a pattern of three or more continuous spans. The total depth of the slab is 6 in. The Steel Deck Institute maximum unshored span for construction with this deck and a three-span condition is 10 ft 11 in. The general layout for the floor beams is 10 ft on center; therefore, the deck does not need to be shored during construction. At 10 ft on center, this deck has an allowable superimposed live load capacity of 143 psf. In addition, it can be shown that this deck can carry a 2,000 pound load over an area of 2.5 ft by 2.5 ft as required by Section 4.4 of ASCE/SEI 7. The floor diaphragm and the floor loads extend 6 in. past the centerline of grid as shown on Sheet S4.1.



III-18 SELECT FLOOR BEAMS (composite and noncomposite)

Note: There are two early and important checks in the design of composite beams. First, select a beam that either does not require camber, or establish a target camber and moment of inertia at the start of the design process. A reasonable approximation of the camber is between L/300 minimum and L/180 maximum (or a maximum of 12 to 2 in.). Second, check that the beam is strong enough to safely carry the wet concrete and a 20 psf construction live load (per ASCE 37-05), when designed by the ASCE/SEI 7 load combinations and the provisions of Chapter F of the AISC Specification. SELECT TYPICAL 45-FT INTERIOR COMPOSITE BEAM (10 FT ON CENTER)

Find a target moment of inertia for an unshored beam. Hold deflection to around 2 in. maximum to facilitate concrete placement. wD = (0.057 kip/ft2 + 0.008 kip/ft2)(10.0 ft) = 0.650 kip/ft I req ≈

0.650 kip/ft ( 45.0 ft )

4

1,290 ( 2.00 in.)

= 1,030 in.4 Determine the required strength to carry wet concrete and construction live load. wDL = 0.065 kip/ft2(10.0 ft) = 0.650 kip/ft wLL = 0.020 kip/ft2(10.0 ft) = 0.200 kip/ft Determine the required flexural strength due to wet concrete only. LRFD

ASD wa = 0.650 kip/ft

wu = 1.4(0.650 kip/ft) = 0.910 kip/ft Mu =

0.910 kip/ft ( 45.0 ft )

Ma =

2

8

0.650 kip/ft ( 45.0 ft )

2

8

= 165 kip-ft

= 230 kip-ft Determine the required flexural strength due to wet concrete and construction live load. LRFD

ASD wa = 0.650 kip/ft + 0.200 kip/ft = 0.850 kip/ft

wu = 1.2(0.650 kip/ft) + 1.6(0.200 kip/ft) = 1.10 kip/ft Mu =

1.10 kip/ft ( 45.0 ft )

= 278 kip-ft

2

Ma =

8 controls

0.850 kip/ft ( 45.0 ft )

2

8

= 215 kip-ft

controls

Use AISC Manual Table 3-2 to select a beam with Ix ≥ 1,030 in.4. Select W21×50, which has Ix = 984 in.4, close to our target value, and has available flexural strengths of 413 kip-ft (LRFD) and 274 kip-ft (ASD). Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-19

Check for possible live load reduction due to area in accordance with Section 4.7.2 of ASCE/SEI 7. For interior beams, KLL = 2 The beams are at 10.0 ft on center, therefore the area AT = ( 45.0 ft )(10.0 ft ) = 450 ft2. Since K LL AT = 2 ( 450 ft 2 ) = 900 ft2 > 400 ft2, a reduced live load can be used. From ASCE/SEI 7, Equation 4.7-1: ⎛ 15 ⎞ L = Lo ⎜⎜ 0.25 + ⎟ K LL AT ⎟⎠ ⎝ ⎛ ⎞ 15 = 80.0 psf ⎜⎜ 0.25 + ⎟ 2 ⎟ 900 ft ⎠ ⎝ = 60.0 psf ≥ 0.50Lo = 40.0 psf Therefore, use 60.0 psf. The beam is continuously braced by the deck. The beams are at 10 ft on center, therefore the loading diagram is as shown below.

Calculate the required flexural strength from Chapter 2 of ASCE/SEI 7. LRFD


1.86 kip/ft ( 45.0 ft )


2

8

= 471 kip-ft

Ma =

1.35 kip/ft ( 45.0 ft )

2

8

= 342 kip-ft

Assume initially a = 1.00 in. Y2 = Ycon – a / 2 = 6.00 in. – 1.00 in. / 2 = 5.50 in. Use AISC Manual Table 3-19 to check W21×50 selected above. Using required strengths of 471 kip-ft (LRFD) or 342 kip-ft (ASD) and a Y2 value of 5.50 in.



III-20

LRFD

Select W21×50 beam, where

ASD Select W21×50 beam, where

PNA = Location 7 and ΣQn = 184 kips

PNA = Location 7 and ΣQn = 184 kips

φbMn = 598 kip-ft > 471 kip-ft

o.k.

Mp / Ωn = 398 kip-ft > 342 kip-ft

o.k.

Determine the effective width, beff. Per Specification AISC Section I3.1a, the effective width of the concrete slab is the sum of the effective widths for each side of the beam centerline, which shall not exceed: (1) one-eighth of the span of the beam, center-to-center of supports

45.0 ft ( 2 sides ) = 11.3 ft 8 (2) one-half the distance to the centerline of the adjacent beam 10.0 ft ( 2 sides ) = 10.0 ft controls 2

(3) the distance to the edge of the slab Not applicable Determine the height of the compression block, a. a=

=

∑ Qn 0.85 f c ′b

(Manual Eq. 3-7)

184 kips 0.85 ( 4 ksi )(10.0 ft )(12 in./ft )

= 0.451 in. < 1.00 in.

o.k.

Check the W21×50 end shear strength. LRFD

ASD

45.0 ft (1.86 kip/ft ) 2 = 41.9 kips

45.0 ft (1.35 kip/ft ) 2 = 30.4 kips

Ru =

Ra =



φvVn = 237 kips > 41.9 kips

o.k.

Vn / Ωv = 158 kips > 30.4 kips

Check live load deflection. Δ LL = l 360 = (45.0 ft)(12 in./ft)/360 = 1.50 in.

For a W21×50, from AISC Manual Table 3-20, Y2 = 5.50 in.


o.k.


III-21

PNA Location 7 ILB = 1,730 in.4 Δ LL =

=

wLL l 4 1, 290 I LB 0.600 kip/ft ( 45.0 ft )

4

1, 290 (1, 730 in.4 )

= 1.10 in. < 1.50 in.

o.k.

Based on AISC Design Guide 3 (West, Fisher and Griffis, 2003) limit the live load deflection, using 50% of the (unreduced) design live load, to L / 360 with a maximum absolute value of 1.0 in. across the bay. ΔLL =

0.400 kip/ft ( 45.0 ft )

4

1, 290 (1, 730 in.4 )

= 0.735 in. < 1.00 in.

o.k.

1.00 in. – 0.735 in. = 0.265 in. Note: Limit the supporting girders to 0.265 in. deflection under the same load case at the connection point of the beam. Determine the required number of shear stud connectors. From AISC Manual Table 3-21, using perpendicular deck with one w-in.-diameter stud per rib in normal weight, 4 ksi concrete, in weak position; Qn = 17.2 kips/stud. ∑ Qn 184 kips = Qn 17.2 kips/stud = 10.7 studs / side

Therefore use 22 studs. Based on AISC Design Guide 3, limit the wet concrete deflection in a bay to L / 360, not to exceed 1.00 in. Camber the beam for 80% of the calculated wet deflection. Δ DL ( wet conc ) =

0.650 kip/ft ( 45.0 ft )

4

1, 290 ( 984 in.4 )

= 2.10 in.

Camber = 0.80(2.10 in.) = 1.68 in. Round the calculated value down to the nearest 4 in; therefore, specify 1.50 in. of camber. 2.10 in. – 1.50 in. = 0.600 in. 1.00 in. – 0.600 in. = 0.400 in. Note: Limit the supporting girders to 0.400 in. deflection under the same load combination at the connection point of the beam. Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-22

SELECT TYPICAL 30-FT INTERIOR COMPOSITE (OR NONCOMPOSITE) BEAM (10 FT ON CENTER)

Find a target moment of inertia for an unshored beam. Hold deflection to around 1.50 in. maximum to facilitate concrete placement. I req ≈

0.650 kip/ft ( 30.0 ft )

4

1,290 (1.50 in.)

= 272 in.4 Determine the required strength to carry wet concrete and construction live load. wDL = 0.065 kip/ft2(10.0 ft) = 0.650 kip/ft wLL = 0.020 kip/ft2(10.0 ft) = 0.200 kip/ft

Determine the required flexural strength due to wet concrete only. LRFD

ASD

wu = 1.4(0.650 kip/ft) = 0.910 kip/ft Mu =

wa = 0.650 kip/ft

0.910 kip/ft ( 30.0 ft )

Ma =

2

8

0.650 kip/ft ( 30.0 ft )

2

8

= 73.1 kip-ft

= 102 kip-ft Determine the required flexural strength due to wet concrete and construction live load. LRFD


1.10 kip/ft ( 30.0 ft )


2

Ma =

8

= 124 kip-ft

controls

0.850 kip/ft ( 30.0 ft )

2

8

= 95.6 kip-ft

controls

Use AISC Manual Table 3-2 to find a beam with an Ix ≥ 272 in.4 Select W16×26, which has an Ix = 301 in.4 which exceeds our target value, and has available flexural strengths of 166 kip-ft (LRFD) and 110 kip-ft (ASD). Check for possible live load reduction due to area in accordance with Section 4.7.2 of ASCE/SEI 7. For interior beams, KLL = 2. The beams are at 10 ft on center, therefore the area AT = 30.0 ft × 10.0 ft = 300 ft2. Since KLLAT = 2(300 ft2) = 600 ft2 > 400 ft2, a reduced live load can be used. From ASCE/SEI 7, Equation 4.7-1: Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-23

⎛ 15 ⎞ L = Lo ⎜⎜ 0.25 + ⎟ K LL AT ⎟⎠ ⎝ ⎛ ⎞ 15 = 80.0 psf ⎜⎜ 0.25 + ⎟⎟ 600 ft 2 ⎠ ⎝ = 69.0 psf ≥ 0.50 Lo = 40.0 psf

Therefore, use 69.0 psf. The beams are at 10 ft on center, therefore the loading diagram is as shown below.

From Chapter 2 of ASCE/SEI 7, calculate the required strength. LRFD

wu = 1.2(0.750 kip/ft) + 1.6 (0.690 kip/ft) = 2.00 kip/ft Mu =

2.00 kip/ft ( 30.0 ft )


2

Ma =

8

= 225 kip-ft

1.44 kip/ft ( 30.0 ft )

2

8

= 162 kip-ft

Assume initially a = 1.00 1.00 in. Y 2 = 6.00 in. − 2 = 5.50 in. Use AISC Manual Table 3-19 to check the W16×26 selected above. Using required strengths of 225 kip-ft (LRFD) or 162 kip-ft (ASD) and a Y2 value of 5.50 in. LRFD

Select W16×26 beam, where

ASD Select W16×26 beam, where

PNA Location 7 and ∑ Qn = 96.0 kips

PNA Location 7 and ∑ Qn = 96.0 kips


o.k.

Mn / Ωn = 165 kip-ft > 162 kip-ft

o.k.

Determine the effective width, beff. From AISC Specification Section I3.1a, the effective width of the concrete slab is the sum of the effective widths for each side of the beam centerline, which shall not exceed: (1) one-eighth of the span of the beam, center-to-center of supports Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-24

30.0 ft ( 2 sides ) = 7.50 ft controls 8 (2) one-half the distance to the centerline of the adjacent beam 10.0 ft ( 2 sides ) = 10.0 ft 2

(3) the distance to the edge of the slab Not applicable Determine the height of the compression block, a. a=

=

∑ Qn 0.85 f c ′b

(Manual Eq. 3-7)

96.0 kips 0.85 ( 4 ksi )( 7.50 ft )(12 in./ft )

= 0.314 in. < 1.00 in.

o.k.

Check the W16×26 end shear strength. LRFD

ASD

30.0 ft Ru = ( 2.00 kip/ft ) 2 = 30.0 kips

30.0 ft Ra = (1.44 kip/ft ) 2 = 21.6 kips



φvVn = 106 kips > 30.0 kips

o.k.

Vn / Ωv = 70.5 kips > 21.6 kips


For a W16×26, from AISC Manual Table 3-20, Y2 = 5.50 in. PNA Location 7 ILB = 575 in.4 Δ LL =

=

wLL l 4 1, 290 I LB

0.690 kip/ft ( 30.0 ft )

4

1, 290 ( 575 in.4 )

= 0.753 in. < 1.00 in.

o.k.


o.k.


III-25

Based on AISC Design Guide 3, limit the live load deflection, using 50% of the (unreduced) design live load, to L/360 with a maximum absolute value of 1.0 in. across the bay. ΔLL =

0.400 kip/ft ( 30.0 ft )

4

1, 290 ( 575 in.4 )

= 0.437 in. < 1.00 in.

o.k.

1.00 in. – 0.437 in. = 0.563 in. Note: Limit the supporting girders to 0.563 in. deflection under the same load combination at the connection point of the beam. Determine the required number of shear stud connectors. From AISC Manual Table 3-21, using perpendicular deck with one w-in.-diameter stud per rib in normal weight, 4 ksi concrete, in the weak position; Qn = 17.2 kips/stud ∑ Qn 96.0 kips = 17.2 kips/stud Qn = 5.58 studs/side

Use 12 studs Note: Per AISC Specification Section I8.2d, there is a maximum spacing limit of 8(6 in.) = 4 ft not to exceed 36 in. between studs. Therefore use 12 studs, uniformly spaced at no more than 36 in. on center. Note: Although the studs may be placed up to 36 in. o.c. the steel deck must still be anchored to the supporting member at a spacing not to exceed 18 in. per AISC Specification Section I3.2c. Based on AISC Design Guide 3, limit the wet concrete deflection in a bay to L/360, not to exceed 1.00 in. Camber the beam for 80% of the calculated wet dead load deflection. Δ DL ( wet conc ) =

0.650 kip/ft ( 30.0 ft )

4

1, 290 ( 301 in.4 )

= 1.36 in.

Camber = 0.800(1.36 in.) = 1.09 in. Round the calculated value down to the nearest 4 in. Therefore, specify 1.00 in. of camber. 1.36 in. – 1.00 in. = 0.360 in. 1.00 in. – 0.360 in. = 0.640 in. Note: Limit the supporting girders to 0.640 in. deflection under the same load combination at the connection point of the beam. This beam could also be designed as a noncomposite beam. Use AISC Manual Table 3-2 with previous moments and shears: Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-26

LRFD

ASD

Select W18×35

Select W18×35



φbMn = φbMp

Mn/Ωb = Mp/Ωb

= 249 kip-ft > 225 kip-ft

= 166 kip-ft > 162 kip-ft

o.k.

φvVn = 159 > 30.0 kips

o.k.


o.k. o.k.

Check beam deflections. Check live load deflection of the W18×35 with an Ix = 510 in.4, from AISC Manual Table 3-2. Δ LL =

0.690 kip/ft ( 30.0 ft )

4

1, 290 ( 510 in.4 )

= 0.850 in. < 1.00 in.

o.k.

Based on AISC Design Guide 3, limit the live load deflection, using 50% of the (unreduced) design live load, to L/360 with a maximum absolute value of 1.0 in. across the bay. 4 0.400 kip/ft ( 30.0 ft ) Δ LL = 1, 290 ( 510 in.4 ) = 0.492 in. < 1.00 in.

o.k.

1.00 in. – 0.492 in. = 0.508 in. Note: Limit the supporting girders to 0.508 in. deflection under the same load combination at the connection point of the beam. Note: Because this beam is stronger than the W16×26 composite beam, no wet concrete strength checks are required in this example. Based on AISC Design Guide 3, limit the wet concrete deflection in a bay to L/360, not to exceed 1.00 in. Camber the beam for 80% of the calculated wet deflection. Δ DL ( wet conc ) =

0.650 kip/ft ( 30.0 ft )

4

1, 290 ( 510 in.4 )

= 0.800 in. < 1.50 in.

o.k.

Camber = 0.800(0.800 in.) = 0.640 in. < 0.750 in. A good break point to eliminate camber is w in.; therefore, do not specify a camber for this beam. 1.00 in. – 0.800 in. = 0.200 in. Note: Limit the supporting girders to 0.200 in. deflection under the same load case at the connection point of the beam.



III-27

Therefore, selecting a W18×35 will eliminate both shear studs and cambering. The cost of the extra steel weight may be offset by the elimination of studs and cambering. Local labor and material costs should be checked to make this determination.



III-28

SELECT TYPICAL NORTH-SOUTH EDGE BEAM

The influence area (KLLAT) for these beams is less than 400 ft2, therefore no live load reduction can be taken. These beams carry 5.50 ft of dead load and live load as well as a wall load. The floor dead load is: w = 5.50 ft(0.075 kips/ft2) = 0.413 kip/ft

Use 65 psf for the initial dead load. wD(initial) = 5.50 ft(0.065 kips/ft2) = 0.358 kips/ft

Use 10 psf for the superimposed dead load. wD(super) = 5.50 ft(0.010 kips/ft2) = 0.055 kips/ft

The dead load of the wall system at the floor is: w = 7.50 ft ( 0.055 kip / ft 2 ) + 6.00 ft ( 0.015 kip / ft 2 )

= 0.413 kip/ft + 0.090 kip/ft = 0.503 kip/ft The total dead load is wDL = 0.413 kip/ft + 0.503 kip/ft = 0.916 kip/ft The live load is wLL = 5.5 ft(0.080 kip/ft2) = 0.440 kip/ft The loading diagram is as follows.

Calculate the required strengths from Chapter 2 of ASCE/SEI 7. LRFD

ASD

wu = 1.2(0.916 kip/ft) + 1.6 (0.440 kip/ft) = 1.80 kip/ft Mu =

1.80 kip/ft ( 22.5 ft ) 8

wa = 0.916 kip/ft + 0.440 kip/ft = 1.36 kip/ft

2

Ma =

1.36 kip/ft ( 22.5 ft ) 8


2


III-29

= 86.1 kip-ft 22.5 ft Ra = (1.36 kip/ft ) 2 = 15.3 kips

= 114 kip-ft 22.5 ft Ru = (1.80 kip/ft ) 2 = 20.3 kips

Because these beams are less than 25 ft long, they will be most efficient as noncomposite beams. The beams at the edges of the building carry a brick spandrel panel. For these beams, the cladding weight exceeds 25% of the total dead load on the beam. Therefore, per AISC Design Guide 3, limit the vertical deflection due to cladding and initial dead load to L/600 or a in. maximum. In addition, because these beams are supporting brick above and there is continuous glass below, limit the superimposed dead and live load deflection to L/600 or 0.3 in. max to accommodate the brick and L/360 or 0.25 in. max to accommodate the glass. Therefore, combining the two limitations, limit the superimposed dead and live load deflection to L/600 or 0.25 in. The superimposed dead load includes all of the dead load that is applied after the cladding has been installed. Note that it is typically not recommended to camber beams supporting spandrel panels. Calculate minimum Ix to limit the superimposed dead and live load deflection to 4 in. Ireq =

0.495 kip/ft ( 22.5 ft )

4

1,290 (4 in.)

= 393 in.4 controls Calculate minimum Ix to limit the cladding and initial dead load deflection to a in. Ireq =

0.861 kip/ft ( 22.5 ft )

4

1,290 ( a in.)

= 456 in.4 Select beam from AISC Manual Table 3-2. LRFD

ASD

Select W18×35 with Ix = 510 in.4

Select W18×35 with Ix = 510 in.4

φbMn = φbMp = 249 kip-ft > 114 kip-ft

o.k.

Mn / Ωb = Mp / Ωb = 166 kip-ft > 86.1 kip-ft

o.k.

φvVn = 159 > 20.3 kips

o.k.


o.k.



III-30

SELECT TYPICAL EAST-WEST SIDE GIRDER

The beams along the sides of the building carry the spandrel panel and glass, and dead load and live load from the intermediate floor beams. For these beams, the cladding weight exceeds 25% of the total dead load on the beam. Therefore, per AISC Design Guide 3, limit the vertical deflection due to cladding and initial dead load to L/600 or a in. maximum. In addition, because these beams are supporting brick above and there is continuous glass below, limit the superimposed dead and live load deflection to L/600 or 0.3 in. max to accommodate the brick and L/360 or 0.25 in. max to accommodate the glass. Therefore, combining the two limitations, limit the superimposed dead and live load deflection to L/600 or 0.25 in. The superimposed dead load includes all of the dead load that is applied after the cladding has been installed. These beams will be part of the moment frames on the North and South sides of the building and therefore will be designed as fixed at both ends. Establish the loading. The dead load reaction from the floor beams is: PD = 0.750 kip/ft(45.0 ft / 2) = 16.9 kips PD(initial) = 0.650 kip/ft(45.0 ft / 2) = 14.6 kips PD(super) = 0.100 kip/ft(45.0 ft / 2) = 2.25 kips

The uniform dead load along the beam is: wD = 0.500 ft(0.075 kip/ft2) + 0.503 kip/ft = 0.541 kip/ft wD(initial) = 0.500 ft(0.065 kip/ft2) = 0.033 kip/ft wD(super) = 0.500 ft(0.010 kip/ft2) = 0.005 kip/ft

Select typical 30-ft composite (or noncomposite) girders. Check for possible live load reduction in accordance with Section 4.7.2 of ASCE/SEI 7. For edge beams with cantilevered slabs, KLL = 1, per ASCE/SEI 7, Table 4-2. However, it is also permissible to calculate the value of KLL based upon influence area. Because the cantilever dimension is small, KLL will be closer to 2 than 1. The calculated value of KLL based upon the influence area is KLL =

( 45.5 ft )( 30.0 ft )

⎛ 45.0 ft ⎞ + 0.500 ft ⎟ ( 30.0 ft ) ⎜ 2 ⎝ ⎠ = 1.98

The area AT = (30.0 ft)(22.5 ft + 0.500 ft) = 690 ft2 Using Equation 4.7-1 of ASCE/SEI 7



III-31

⎛ 15 ⎞ L = Lo ⎜⎜ 0.25 + ⎟ K LL AT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ = 80.0 psf ⎜ 0.25 + ⎜⎜ 2 ⎟ (1.98 ) ( 690 ft ) ⎟⎠ ⎝ = 52.5 psf ≥ 0.50 Lo = 40.0 psf

Therefore, use 52.5 psf. The live load from the floor beams is PLL = 0.525 kip/ft(45.0 ft / 2) = 11.8 kips The uniform live load along the beam is wLL = 0.500 ft(0.0525 kip/ft2) = 0.026 kip/ft The loading diagram is shown below.

A summary of the moments, reactions and required moments of inertia, determined from a structural analysis of a fixed-end beam, is as follows: Calculate the required strengths and select the beams for the floor side beams. LRFD

ASD

Typical side beam

Typical side beam

Ru = 49.5 kips Mu at ends =313 kip-ft Mu at ctr. =156 kip-ft

Ra = 37.2 kips Ma at ends = 234 kip-ft Ma at ctr. = 117 kip-ft

The maximum moment occurs at the support with compression in the bottom flange. The bottom laterally braced at 10 ft o.c. by the intermediate beams. Note: During concrete placement, because the deck is parallel to the beam, the beam will not have continuous lateral support. It will be braced at 10 ft o.c. by the intermediate beams. By inspection, this condition will not control because the maximum moment under full loading causes compression in the bottom flange, which is braced at 10 ft o.c. LRFD

ASD

Calculate Cb = for compression in the bottom flange braced at 10 ft o.c.

Calculate Cb = for compression in the bottom flange braced at 10 ft o.c.



III-32

LRFD

ASD

Cb = 2.21 (from computer output)

Cb = 2.22 (from computer output)

Select W21×44

Select W21×44

With continuous bracing, from AISC Manual Table 3-2,

With continuous bracing, from AISC Manual Table 3-2,

φbMn = φbMp = 358 kip-ft > 156 kip-ft

Mn / Ω b = Mp / Ω b = 238 kip-ft > 117 kip-ft

o.k.

o.k.

For Lb = 10 ft and Cb = 2.21, from AISC Manual Table 3-10,

For Lb = 10 ft and Cb = 2.22, from AISC Manual Table 3-10,

φM n = ( 265 kip-ft )( 2.21)

M n Ω = (176 kip-ft )( 2.22 ) = 391 kip-ft

= 586 kip-ft

According to AISC Specification Section F2.2, the nominal flexural strength is limited Mp, therefore φbMn = φbMp = 358 kip-ft.

According to AISC Specification Section F2.2, the nominal flexural strength is limited Mp, therefore Mn/Ωb = Mp/Ωb = 238 kip-ft.

358 kip-ft > 313 kip-ft

238 kip-ft > 234 kip-ft

o.k.

o.k.

From AISC Manual Table 3-2, a W21×44 has a design shear strength of 217 kips. From Table 1-1, Ix = 843 in.4

From AISC Manual Table 3-2, a W21×44 has an allowable shear strength of 145 kips. From Table 11, Ix = 843 in.4

Check deflection due to cladding and initial dead load.

Check deflection due to cladding and initial dead load.

Δ = 0.295 in. < a in.

Δ = 0.295 in. < a in.

o.k.

o.k.

Check deflection due to superimposed dead and live loads.

Check deflection due to superimposed dead and live loads.

Δ = 0.212 in. < 0.250 in.

Δ = 0.212 in. < 0.250 in.

o.k.

o.k.

Note that both of the deflection criteria stated previously for the girder and for the locations on the girder where the floor beams are supported have also been met. Also noted previously, it is not typically recommended to camber beams supporting spandrel panels. The W21×44 is adequate for strength and deflection, but may be increased in size to help with moment frame strength or drift control.



III-33

SELECT TYPICAL EAST-WEST INTERIOR GIRDER

Establish loads

The dead load reaction from the floor beams is PDL = 0.750 kip/ft(45.0 ft + 30.0 ft)/2 = 28.1 kips

Check for live load reduction due to area in accordance with Section 4.7.2 of ASCE/SEI 7. For interior beams, KLL = 2 The area AT = ( 30.0 ft )( 37.5 ft ) = 1,130 ft2 Using ASCE/SEI 7, Equation 4.7-1: ⎛ 15 ⎞ L = Lo ⎜⎜ 0.25 + ⎟ K LL AT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ = 80.0 psf ⎜ 0.25 + ⎜⎜ 2 ⎟ ( 2 ) (1,130 ft ) ⎟⎠ ⎝ = 45.2 psf ≥ 0.50 Lo = 40.0 psf Therefore, use 45.2 psf. The live load from the floor beams is PLL = 0.0452 kip/ft2(10.0 ft)(37.5 ft) = 17.0 kips

Note: The dead load for this beam is included in the assumed overall dead load. A summary of the simple moments and reactions is shown below: Calculate the required strengths and select the size for the interior beams. LRFD

ASD

Typical interior beam


Ru = 60.9 kips Mu = 609 kip-ft

Ra = 45.1 kips Ma = 451 kip-ft

Check for beam requirements when carrying wet concrete.



III-34

Note: During concrete placement, because the deck is parallel to the beam, the beam will not have continuous lateral support. It will be braced at 10 ft on center by the intermediate beams. Also, during concrete placement, a construction live load of 20 psf will be present. This load pattern and a summary of the moments, reactions, and deflection requirements is shown below. Limit wet concrete deflection to 1.5 in.

LRFD

ASD

Typical interior beam with wet concrete only

Typical interior beam with wet concrete only

Ru = 34.2 kips Mu = 342 kip-ft

Ra = 24.4 kips Ma = 244 kip-ft

Assume Ix ≥ 935 in.4, where 935 in.4 is determined based on a wet concrete deflection of 1.5 in. LRFD

ASD

Typical interior beam with wet concrete and construction load

Typical interior beam with wet concrete and construction load

Ru = 41.3 kips Mu (midspan) = 413 kip-ft

Ra = 31.9 kips Ma (midspan) = 319 kip-ft

Select a beam with an unbraced length of 10.0 ft and a conservative Cb = 1.0.

Select a beam with an unbraced length of 10.0 ft and a conservative Cb = 1.0.

From AISC Manual Tables 3-2 and 3-10, select a W21×68, which has a design flexural strength of 532 kip-ft, a design shear strength of 272 kips, and from Table 1-1, an Ix of 1,480 in.4

From AISC Manual Tables 3-2 and 3-10, select a W21×68, which has an allowable flexural strength of 354 kip-ft, an allowable shear strength of 181 kips, and from Table 1-1 an Ix of 1,480 in.4

φbMp = 532 kip-ft > 413 kip-ft

Mp / Ωb = 354 kip-ft > 319 kip-ft

o.k.

o.k.

Check W21×68 as a composite beam. From previous calculations: LRFD

ASD

Typical interior Beam


Ru = 60.9 kips Mu (midspan) = 609 kip-ft

Ra = 45.1 kips Ma (midspan) = 451 kip-ft

Y2 (from previous calculations, assuming an initial a = 1.00 in.) = 5.50 in.

Using AISC Manual Table 3-19, check a W21×68, using required flexural strengths of 609 kip-ft (LRFD) and 451 kip-ft (ASD) and Y2 value of 5.5 in. Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-35

LRFD

ASD

Select a W21×68

Select a W21×68

At PNA Location 7, ∑ Qn = 250 kips

At PNA Location 7, ∑ Qn = 250 kips


o.k.

Mn / Ωb = 561 kip-ft > 461 kip-ft

o.k.

Based on AISC Design Guide 3, limit the wet concrete deflection in a bay to L/360, not to exceed 1.00 in. Camber the beam for 80% of the calculated wet deflection. 24.4 kips ( 30.0 ft ) (12 in./ft ) 3

Δ DL ( wet conc ) =

3

28 ( 29, 000 ksi ) (1, 480 in.4 )

= 0.947 in.

Camber = 0.80(0.947 in.) = 0.758 in. Round the calculated value down to the nearest 4 in. Therefore, specify w in. of camber. 0.947 in. – w in. = 0.197 in. < 0.200 in. Therefore, the total deflection limit of 1.00 in. for the bay has been met. Determine the effective width, beff. Per AISC Specification Section I3.1a, the effective width of the concrete slab is the sum of the effective widths for each side of the beam centerline, which shall not exceed: (1) one-eighth of the span of the beam, center-to-center of supports 30.0 ft ( 2 sides ) = 7.50 ft controls 8

(2) one-half the distance to the centerline of the adjacent beam ⎛ 45.0 ft 30.0 ft ⎞ + ⎜ ⎟ = 37.5 ft 2 ⎠ ⎝ 2

(3) the distance to the edge of the slab Not applicable. Determine the height of the compression block. a=

=

∑ Qn 0.85 f c ′b

250 kips 0.85 ( 4 ksi )( 7.50 ft )(12 in./ft )

= 0.817 in. < 1.00 in.

o.k.



III-36

Check end shear strength. LRFD

ASD

Ru = 60.9 kips

Ra = 45.1 kips

From AISC Manual Table 3-2, φvVn = 272 kips > 60.9 kips

o.k.

From AISC Manual Table 3-2, Vn / Ωv = 181 kips > 45.1 kips

o.k.


From AISC Manual Table 3-20, W21×68: Y2 = 5.50 in., PNA Location 7

ILB = 2,510 in.4 Δ LL =

Pl 3 28 EI LB

17.0 kips ( 30.0 ft ) (12 in./ft ) 3

=

3

28 ( 29, 000 ksi ) ( 2,510 in.4 )

= 0.389 in. < 1.00 in.

o.k.

Based on AISC Design Guide 3, limit the live load deflection, using 50% of the (unreduced) design live load, to L/360 with a maximum absolute value of 1.00 in. across the bay. The maximum deflection is, 15.0 kips ( 30.0 ft ) (12 in./ft ) 3

Δ LL =

3

28 ( 29, 000 ksi ) ( 2,510 in.4 )

= 0.343 in. < 1.00 in. o.k. Check the deflection at the location where the floor beams are supported. Δ LL =

15.0 kips (120 in.)

⎡3 ( 360 in.)(120 in.) − 4 (120 in.)2 ⎤ ⎦ 6 ( 29, 000 ksi ) ( 2,510 in.4 ) ⎣

= 0.297 in. > 0.265 in. o.k. Therefore, the total deflection in the bay is 0.297 in. + 0.735 in. = 1.03 in., which is acceptably close to the limit of 1.00 in, where ΔLL = 0.735 in. is from the 45 ft interior composite beam running north-south. Determine the required shear stud connectors. Using Manual Table 3-21, for parallel deck with, wr / hr > 1.5, one w-in.-diameter stud in normal weight, 4-ksi concrete and Qn = 21.5 kips/stud. ∑ Qn 250 kips = 21.5 kips/stud Qn = 11.6 studs/side



III-37

Therefore, use a minimum 24 studs for horizontal shear. Per AISC Specification Section I8.2d, the maximum stud spacing is 36 in. Since the load is concentrated at 3 points, the studs are to be arranged as follows: Use 12 studs between supports and supported beams at 3 points. Between supported beams (middle 3 of span), use 4 studs to satisfy minimum spacing requirements. Thus, 28 studs are required in a 12:4:12 arrangement. Notes: Although the studs may be placed up to 3'-0" o.c. the steel deck must still be anchored to be the supporting member at a spacing not to exceed 18 in. in accordance with AISC Specification Section I3.2c. This W21×68 beam, with full lateral support, is very close to having sufficient available strength to support the imposed loads without composite action. A larger noncomposite beam might be a better solution.



III-38 COLUMN DESIGN AND SELECTION FOR GRAVITY COLUMNS Estimate column loads Roof

(from previous calculations) Dead Load Live (Snow) Total

20 psf 25 psf 45 psf

Snow drift loads at the perimeter of the roof and at the mechanical screen wall from previous calculations Reaction to column (side parapet): w = (3.73 kips / 6.00 ft) − (0.025 ksf)(23.0 ft) = 0.0467 kip/ft

Reaction to column (end parapet): w = (16.0 kips / 37.5 ft) − (0.025 ksf)(15.5 ft) = 0.0392 kip/ft

Reaction to column (screen wall along lines C & D): w = (4.02 kips / 6.00 ft) − (0.025 ksf)(22.5 ft) = 0.108 kip/ft

Mechanical equipment and screen wall (average): w = 40 psf



III-39

Column

2A, 2F, 3A, 3F, 4A, 4F 5A, 5F, 6A, 6F, 7A, 7F snow drifting side exterior wall 1B, 1E, 8B, 8E snow drifting end exterior wall 1A, 1F, 8A, 8F

Loading Width Length ft ft

23.0

PD

SL

PS

ft2

kip/ft2

kips

kip/ft2

kips

690

0.020

13.8

30.0 30.0 3.50

23.0

snow drifting end snow drifting side exterior wall 1C, 1D, 8C, 8D

30.0

DL

Area

22.5 22.5 22.5 15.5

snow-drifting end exterior wall

15.5

17.3

0.0467 klf 1.40 0.413 klf 12.4 26.2 78.8

0.020

1.58

18.7

0.025 1.97 0.0418 klf 0.941

0.413 klf 9.29 10.9 357 0.020 (78.8 ft 2 ) − 2 = 318

11.8 15.5 27.3 37.5

0.025

6.36

2.91

0.025

7.95

0.0418 klf 0.493 0.0467 klf 0.724 0.413 klf 11.3 17.7 581 0.020 (78.8 ft 2 ) − 2 = 542

26.3 26.3

10.8

9.17

0.025

13.6

0.0418 klf 1.10 0.413 klf 10.9 21.7

14.7

2C, 2D, 7C, 7D

37.5

30.0

1,125

0.020

22.5

0.025

28.1

3C, 3D, 4C, 4D 5C, 5D, 6C, 6D snow-drifting mechanical area

22.5

30.0

675

0.020

13.5

0.025

16.9

15.0

30.0 30.0

450

0.060

27.0 40.5

0.108 klf 0.040 klf

3.24 18.0 38.1



III-40 Floor Loads (from previous calculations) Dead load Live load Total load

75 psf 80 psf 155 psf

Calculate reduction in live loads, analyzed at the base of three floors using Section 4.7.2 of ASCE/SEI 7. Note: The 6-in. cantilever of the floor slab has been ignored for the calculation of KLL for columns in this building because it has a negligible effect. Columns:

2A, 2F, 3A, 3F, 4A, 4F, 5A, 5F, 6A, 6F, 7A, 7F Exterior column without cantilever slabs KLL = 4 Lo = 80.0 psf n=3

AT = ( 23.0 ft )( 30.0 ft ) = 690 ft 2

Using ASCE/SEI 7 Equation 4.7-1 ⎛ ⎞ 15 L = Lo ⎜⎜ 0.25 + ⎟ K LL nAT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ = 80.0 psf ⎜ 0.25+ ⎜⎜ ⎟ 4 )( 3) ( 690 ft 2 ) ⎟ ( ⎝ ⎠ = 33.2 psf ≥ 0.4 Lo = 32.0 psf Use L = 33.2 psf. Columns:

1B, 1E, 8B, 8E Exterior column without cantilever slabs KLL = 4 Lo = 80.0 psf n=3

AT = ( 5.50 ft )( 22.5 ft )

= 124 ft 2 ⎛ ⎞ 15 L = Lo ⎜⎜ 0.25 + ⎟ K LL nAT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ = 80.0 psf ⎜ 0.25+ ⎜⎜ 2 ⎟ ( 4 )( 3) (124 ft ) ⎟⎠ ⎝ = 51.1 psf ≥ 0.4 Lo = 32.0 psf Use L = 51.1 psf

Columns: KLL = 4

1A, 1F, 8A, 8F Corner column without cantilever slabs Lo = 80.0 psf

n=3



III-41 AT = (15.5 ft )( 23.0 ft ) − (124 ft 2 / 2 )

= 295 ft 2 ⎛ ⎞ 15 L = Lo ⎜⎜ 0.25 + ⎟ ≥ 0.4 Lo K LL nAT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ ≥ 0.4 ( 80.0 psf ) = 80.0 psf ⎜ 0.25+ ⎜⎜ 2 ⎟ ( 4 )( 3) ( 295 ft ) ⎟⎠ ⎝ = 40.2 psf ≥ 32.0 psf

Use L = 40.2 psf. Columns:

1C, 1D, 8C, 8D Exterior column without cantilever slabs KLL = 4 Lo = 80.0 psf n=3

AT = (15.5 ft )( 37.5 ft ) – (124 ft 2 / 2 )

= 519 ft 2 ⎛ ⎞ 15 L = Lo ⎜⎜ 0.25 + ⎟ ≥ 0.4 Lo K LL nAT ⎟⎠ ⎝ ⎛ ⎞ 15 ⎟ ≥ 0.4 ( 80.0 psf ) = 80.0 psf ⎜ 0.25+ ⎜⎜ 2 ⎟ ( 4 )( 3) ( 519 ft ) ⎟⎠ ⎝ = 35.2 psf ≥ 32.0 psf Use L = 35.2 psf.

Columns:

2C, 2D, 3C, 3D, 4C, 4D, 5C, 5D, 6C, 6D, 7C, 7D Interior column KLL = 4 Lo = 80.0 psf n=3

AT = ( 37.5 ft )( 30.0 ft ) = 1,125 ft 2 ⎛ 15 L = Lo ⎜⎜ 0.25 + K LL nAT ⎝

⎞ ⎟⎟ ≥ 0.4 Lo ⎠

⎛ ⎞ 15 ⎜ ⎟ ≥ 0.4 ( 80.0 psf ) = 80.0 psf 0.25+ ⎜⎜ 2 ⎟ 4 3 1,125 ft ( )( ) ( ) ⎟⎠ ⎝ = 30.3 psf ≤ 32.0 psf Use L= 32.0 psf.



III-42 Column

2A, 2F, 3A, 3F, 4A, 4F 5A, 5F, 6A, 6F, 7A, 7F exterior wall 1B, 1E, 8B, 8E exterior wall 1A, 1F, 8A, 8F

Loading Width Length ft ft

23.0

5.50

23.0

22.5 22.5 15.5

27.3 37.5

exterior wall

2C, 2D, 3C, 3D, 4C, 4D 5C, 5D, 6C, 6D, 7C, 7D

DL

PD

LL

kip/ft2

kips

kip/ft2

690

0.075

51.8

0.0332 22.9

0.503 klf

15.1 66.9

22.9

30.0

exterior wall 1C, 1D, 8C, 8D

30.0

Tributary Area ft2

15.5

26.3

37.5

30.0

124

0.075 0.503 klf

357 0.075 2 (124 in. ) − 2 = 295 0.503 klf 581 0.075 2 124 in. ( ) − 2 = 519 0.503 klf

1,125

0.075


PL kips

9.30 11.3 20.6

0.0511 6.34

22.1

0.0402 11.9

13.7 35.8

11.9

38.9

0.0352 18.3

6.34

13.2 52.1

18.3

84.4

0.0320 36.0


III-43 Column load summary Column

Floor

PD

PL

kips

kips

2A, 2F, 3A, 3F, 4A, 4F 5A, 5F, 6A, 6F, 7A, 7F

Roof 4th 3rd 2nd Total

26.2 66.9 66.9 66.9 227

18.7 22.9 22.9 22.9 87.4

1B, 1E, 8B, 8E


10.9 20.6 20.6 20.6 72.7

2.91 6.34 6.34 6.34 21.9

1A, 1F, 8A, 8F


17.7 35.8 35.8 35.8 125

9.14 11.9 11.9 11.9 44.8

1C, 1D, 8C, 8D


21.7 52.1 52.1 52.1 178

14.6 18.3 18.3 18.3 69.5

2C, 2D, 7C, 7D


22.5 84.4 84.4 84.4 276

28.1 36.0 36.0 36.0 136

3C, 3D, 4C, 4D 5C, 5D, 6C, 6D


40.5 84.4 84.4 84.4 294

38.1 36.0 36.0 36.0 146



III-44 SELECT TYPICAL INTERIOR LEANING COLUMNS Columns: 3C, 3D, 4C, 4D, 5C, 5D, 6C, 6D

Elevation of second floor slab: Elevation of first floor slab: Column unbraced length:

113.5 ft 100 ft KxLx = KyLy = 13.5 ft

From ASCE/SEI 7, determine the required strength, LRFD

ASD

Pu = 1.2(294 kips) + 1.6(3)(36.0 kips) + 0.5(38.1 kips) = 545 kips

Pa = 294 kips + 0.75(3)(36.0 kips) + 0.75(38.1 kips) = 404 kips

Using AISC Manual Table 4-1, enter with the effective length of 13.5 ft, and proceed across the table until reaching the lightest size that has sufficient available strength at the required unbraced length. LRFD

ASD

W12×65

W12×65

φcPn = 696 kips > 545 kips

o.k.

Pn / Ωc = 463 kips > 404 kips

o.k.

W14×68

W14×68


o.k.


o.k.

Columns: 2C, 2D, 7C, 7D

Elevation of second floor slab: 113.5 ft Elevation of first floor slab: 100.0 ft KxLx = KyLy = 13.5 ft Column unbraced length: LRFD

ASD

Pu = 1.2(276 kips) + 1.6(3)(36.0 kips) + 0.5(28.1 kips) = 518 kips

Pa = 276 kips + 0.75(3)(36.0 kips) + 0.75(28.1 kips) = 378 kips


ASD

W12×65


W12×65 o.k.

o.k.

W14×61

W14×61



o.k.



o.k.


III-45 SELECT TYPICAL EXTERIOR LEANING COLUMNS Columns: 1B, 1E, 8B, 8E

Elevation of second floor slab: 113.5 ft Elevation of first floor slab: 100.0 ft KxLx = KyLy = 13.5 ft Column unbraced length: LRFD

ASD

Pu = 1.2(72.7 kips) + 1.6(3)(6.34 kips) + 0.5(2.91 kips) = 119 kips

Pa = 72.7 kips + 0.75(3)(6.34 kips) + 0.75(2.91 kips) = 89.1 kips


ASD

W12×40


W12×40 o.k.

Pn / Ωc = 210 kips > 89.1 kips

Note: A 12 in. column was selected above for ease of erection of framing beams. (Bolted double-angle connections can be used without bolt staggering.)


o.k.


III-46 WIND LOAD DETERMINATION

Use the Envelope Procedure for simple diaphragm buildings from ASCE/SEI 7, Chapter 28, Part 2. To qualify for the simplified wind load method for low-rise buildings, per ASCE/SEI 7, Section 26.2, the following must be true. 1. 2. 3. 4. 5. 6. 7. 8.

Simple diaphragm building o.k. Low-rise building <= 60 ft o.k. Enclosed o.k. Regular-shaped o.k. Not a flexible building o.k. Does not have response characteristics requiring special considerations o.k. Symmetrical shape o.k. Torsional load cases from ASCE/SEI 7, Figure 28.4-1 do not control design of MWFRS o.k.

Define input parameters

1.

Risk category:

II from ASCE/SEI 7, Table 1.5-1

2.

Basic wind speed V: 115 mph (3-s) from ASCE/SEI 7, Figure 26.5-1A

3.

Exposure category:

4.

Topographic factor, Kzt : 1.0 from ASCE/SEI 7, Section 26.8.2

5.

Mean roof height:

6.

Height and exposure adjustment, λ: 1.59 from ASCE/SEI 7, Figure 28.6-1

7.

Roof angle: 0°

C from ASCE/SEI 7, Section 26.7.3

55' - 0"

ps = λ Kzt ps30 = (1.59)(1.0)(21.0 psf) = 33.4 psf = (1.59)(1.0)(13.9 psf) = 22.1 psf = (1.59)(1.0)(-25.2 psf) = -40.1 psf = (1.59)(1.0)(-14.3 psf) = -22.7 psf = (1.59)(1.0)(-17.5 psf) = -27.8 psf = (1.59)(1.0)(-11.1 psf) = -17.6 psf

(ASCE 7 Eq. 28.6-7) Horizontal pressure zone A Horizontal pressure zone C Vertical pressure zone E Vertical pressure zone F Vertical pressure zone G Vertical pressure zone H

a = 10% of least horizontal dimension or 0.4h, whichever is smaller, but not less than either 4% of least horizontal dimension or 3 ft a = the lesser of:

10% of least horizontal dimension 40% of eave height

12.3 ft 22.0 ft

but not less than

4% of least horizontal dimension or 3 ft

4.92 ft

a = 12.3 ft 2a = 24.6 ft

Zone A – End zone of wall (width = 2a) Zone C – Interior zone of wall Zone E – End zone of windward roof (width = 2a) Zone F – End zone of leeward roof (width = 2a)



III-47

Zone G – Interior zone of windward roof Zone H – Interior zone of leeward roof Calculate load to roof diaphragm

Mechanical screen wall height:

6 ft

Wall height:

2 ⎣⎡55.0 ft – 3 (13.5 ft ) ⎦⎤ = 7.25 ft

Parapet wall height:

2 ft

Total wall height at roof at screen wall:

6 ft + 7.25 ft = 13.3 ft

Total wall height at roof at parapet:

2 ft + 7.25 ft = 9.25 ft

Calculate load to fourth floor diaphragm

Wall height:

2 (55.0 ft – 40.5 ft) = 7.25 ft 2 (40.5 ft – 27.0 ft) = 6.75 ft

Total wall height at floor:

6.75 ft + 7.25 ft = 14.0 ft

Calculate load to third floor diaphragm

Wall height:

2 (40.5 ft – 27.0 ft) = 6.75 ft 2 (27.0 ft – 13.5 ft) = 6.75 ft


6.75 ft + 6.75 ft = 13.5 ft

Calculate load to second floor diaphragm

Wall height:

2 (27.0 ft – 13.5 ft) = 6.75 ft 2 (13.5 ft – 0.0 ft) = 6.75 ft


6.75 ft + 6.75 ft = 13.5 ft

Total load to diaphragm:

ws(A) = (33.4 psf)(9.25 ft) = 309 plf

Load to diaphragm at roof:

ws(C) = (22.1 psf)(9.25 ft) = 204 plf at parapet ws(C) = (22.1 psf)(13.3 ft) = 294 plf at screenwall

Load to diaphragm at fourth floor:

ws(A) = (33.4 psf)(14.0 ft) = 468 plf ws(C) = (22.1 psf)(14.0 ft) = 309 plf

Load to diaphragm at second and third: floors

ws(A) = (33.4 psf)(13.5 ft) = 451 plf ws(C) = (22.1 psf)(13.5 ft) = 298 plf



III-48

l = length of structure, ft b = width of structure, ft h = height of wall at building element, ft

Determine the wind load to each frame at each level. Conservatively apply the end zone pressures on both ends of the building simultaneously. Wind from a north or south direction: Total load to each frame:

PW ( n − s ) = ws ( A) ( 2a ) + ws (C ) ( l 2 − 2a )

Shear in diaphragm:

v( n − s ) = PW ( n − s ) 120 ft for roof v( n − s ) = PW ( n − s ) 90 ft for floors (deduction for stair openings)

Wind from an east or west direction: Total load to each frame:

PW ( e − w) = ws ( A) ( 2a ) + ws ( C ) ( b 2 − 2a )

Shear in diaphragm:

v( e − w) = PW ( e − w) 210 ft for roof and floors

l ft Screen 93.0 Roof 120 4th 213 3rd 213 2nd 213 Base of Frame

b ft 33.0 90.0 123 123 123

2a ft 0 24.6 24.6 24.6 24.6

h ft 13.3 9.25 14.0 13.5 13.5

ps(A) psf 0 33.4 33.4 33.4 33.4

ps(C) psf 22.1 22.1 22.1 22.1 22.1

ws(A) plf 0 309 468 451 451

ws(C) plf 294 204 309 298 298

PW(n-s) kips 13.7 14.8 36.8 35.5 35.5 136

PW(e-w) kips 4.85 11.8 22.9 22.1 22.1 83.8

v(n-s) plf − 238 409 394 394

v(e-w) plf − 79 109 105 105

Note: The table above indicates the total wind load in each direction acting on a steel frame at each level. The wind load at the ground level has not been included in the chart because it does not affect the steel frame.



III-49 SEISMIC LOAD DETERMINATION

The floor plan area: 120 ft, column center line to column center line, by 210 ft, column centerline to column center line, with the edge of floor slab or roof deck 6 in. beyond the column center line. Area = (121 ft)(211 ft) = 25,500 ft2 The perimeter cladding system length: Length = (2)(123 ft) + (2)(213 ft) = 672 ft The perimeter cladding weight at floors: Brick spandrel panel with metal stud backup Window wall system Total

(7.50 ft)(0.055 ksf) = 0.413 klf (6.00 ft)(0.015 ksf) = 0.090 klf 0.503 klf

Typical roof dead load (from previous calculations): Although 40 psf was used to account for the mechanical units and screen wall for the beam and column design, the entire mechanical area will not be uniformly loaded. Use 30% of the uniform 40 psf mechanical area load to determine the total weight of all of the mechanical equipment and screen wall for the seismic load determination. Roof Area = (25,500 ft2)(0.020 ksf) = Wall perimeter = (672 ft)(0.413 klf) = Mechanical Area = (2,700 ft2)(0.300)(0.040 ksf) = Total

510 kips 278 kips 32.4 kips 820 kips

Typical third and fourth floor dead load: Note: An additional 10 psf has been added to the floor dead load to account for partitions per Section 12.7.2.2 of ASCE/SEI 7. Floor Area = (25,500 ft2)(0.085 ksf) = Wall perimeter = (672 ft)(0.503 klf) = Total

2,170 kips 338 kips 2,510 kips

Second floor dead load: the floor area is reduced because of the open atrium Floor Area = (24,700 ft2)(0.085 ksf) = Wall perimeter = (672 ft)(0.503 klf) = Total Total dead load of the building: Roof Fourth floor Third floor Second floor Total

2,100 kips 338 kips 2,440 kips 820 kips 2,510 kips 2,510 kips 2,440 kips 8,280 kips



III-50

Calculate the seismic forces. Determine the seismic risk category and importance factors. Office Building: Risk Category II from ASCE/SEI 7 Table 1.5-1 Seismic Importance Factor: Ie = 1.00 from ASCE/SEI 7 Table 1.5-2 The site coefficients are given in this example. SS and S1 can also be determined from ASCE/SEI 7, Figures 22-1 and 22-2, respectively. SS = 0.121g S1 = 0.060g Soil, site class D (given) Fa @ SS M 0.25 = 1.6 from ASCE/SEI 7, Table 11.4-1 Fv @ S1 M 0.1 = 2.4 from ASCE/SEI 7, Table 11.4-2 Determine the maximum considered earthquake accelerations. SMS = Fa SS = (1.6)(0.121g) = 0.194g from ASCE/SEI 7, Equation 11.4-1 SM1 = Fv S1 = (2.4)(0.060g) = 0.144g from ASCE/SEI 7, Equation 11.4-2 Determine the design earthquake accelerations. SDS = q SMS = q (0.194g) = 0.129g from ASCE/SEI 7, Equation 11.4-3 SD1 = q SM1 = q (0.144g) = 0.096g from ASCE/SEI 7, Equation 11.4-4 Determine the seismic design category. SDS < 0.167g, Seismic Risk Category II:

Seismic Design Category: A from ASCE/SEI 7, Table 11.6-1

0.067g M SD1 < 0.133g, Seismic Risk Category II: Seismic Design Category: B from ASCE/SEI 7, Table 11.6-2 Select the seismic force resisting system. Seismic Design Category B may be used and it is therefore permissible to select a structural steel system not specifically detailed for seismic resistance, for which the seismic response modification coefficient, R = 3 Determine the approximate fundamental period. Building Height, hn = 55.0 ft Ct = 0.02:

x = 0.75 from ASCE/SEI 7, Table 12.8-2

Ta = Ct (hn)x = (0.02)(55.0 ft)0.75 = 0.404 sec from ASCE/SEI 7, Equation 12.8-7 Determine the redundancy factor from ASCE/SEI 7, Section 12.3.4.1. ρ = 1.0 because the Seismic Design Category = B



III-51

Determine the vertical seismic effect term. Ev = 0.2SDSD = 0.2(0.129g)D = 0.0258D

(ASCE 7 Eq. 12.4-4)

The following seismic load combinations are as specified in ASCE/SEI 7, Section 12.4.2.3. LRFD

ASD 1.0 + 0.14 S D + H + F + 0.7 ρQE ( DS )

(1.2 + 0.2S DS ) D + ρQE + L + 0.2S = ⎡⎣1.2 + 0.2 ( 0.129 ) ⎤⎦ D + 1.0QE + L + 0.2S

= ⎡⎣1.0 + 0.14 ( 0.129 ) ⎤⎦ D + 0.0 + 0.0 + 0.7 (1.0 ) QE

= 1.23D + 1.0QE + L + 0.2 S

= 1.02 D + 0.7QE

( 0.9 − 0.2S DS ) D + ρQE + 1.6 H = ⎡⎣0.9 − 0.2 ( 0.129 ) ⎤⎦ D + 1.0QE + 0.0

(1.0 + 0.10S DS ) D + H + F + 0.525ρQE + 0.75L + 0.75 ( Lr or S or R ) = ⎡⎣1.0 + 0.10 ( 0.129 ) ⎤⎦ D + 0.0 + 0.0 + 0.525 (1.0 ) QE + 0.75 L + 0.75S

= 0.874 D + 1.0QE

= 1.01D + 0.525QE + 0.75L + 0.75S

( 0.6 − 0.14S DS ) D + 0.7ρQE + H = ⎡⎣0.6 − 0.14 ( 0.129 ) ⎤⎦ D + 0.7 (1.0 ) QE + 0 = 0.582 D + 0.7QE

Note: ρQE = effect of horizontal seismic (earthquake induced) forces Overstrength Factor: Ωo = 3 for steel systems not specifically detailed for seismic resistance, excluding cantilever column systems, per ASCE/SEI 7, Table 12.2-1. Calculate the seismic base shear using ASCE/SEI 7, Section 12.8.1. Determine the seismic response coefficient from ASCE/SEI 7, Equation 12.8-2 S DS ⎛R⎞ ⎜I ⎟ ⎝ e⎠ 0.129 = ⎛3⎞ ⎜ ⎟ ⎝1⎠ = 0.0430

Cs =

controls

Let Ta = T. From ASCE/SEI 7 Figure 22-12, TL = 12 > T (midwestern city); therefore use ASCE/SEI 7, Equation 12.8-3 to determine the upper limit of Cs. S D1 ⎛R⎞ T⎜ ⎟ ⎝ Ie ⎠ 0.096 = ⎛ 3⎞ 0.404 ⎜ ⎟ ⎝1⎠ = 0.0792

Cs =



III-52

From ASCE/SEI 7, Equation 12.8-5, Cs shall not be taken less than: Cs = 0.044SDSIe ≥ 0.01 = 0.044(0.129)(1.0) = 0.00568 Therefore, Cs = 0.0430. Calculate the seismic base shear from ASCE/SEI 7 Equation 12.8-1 V = CsW = 0.0430 ( 8, 280 kips ) = 356 kips

Calculate vertical distribution of seismic forces from ASCE/SEI 7, Section 12.8.3. Fx = CvxV

(ASCE Eq. 12.8-11)

= Cvx ( 356 kips )

Cvx =

wx hx k n

∑ wi hi k

Fx = CvxV

(ASCE Eq. 12.8-12)

i =1

For structures having a period of 0.5 s or less, k = 1. Calculate horizontal shear distribution at each level per ASCE/SEI 7, Section 12.8.4. n

Vx = ∑ Fi

(ASCE Eq. 12.8-13)

i=x

Calculate the overturning moment at each level per ASCE/SEI 7, Section 12.8.5. n

M x = ∑ Fi (hi − hx ) i=x

Roof Fourth Third Second Base

wx kips 820 2,510 2,510 2,440 8,280

hxk ft 55.0 40.5 27.0 13.5

wxhxk kip-ft 45,100 102,000 67,800 32,900 248,000

Cvx kips 0.182 0.411 0.273 0.133

Fx kips 64.8 146 97.2 47.3 355

Vx kips 64.8 211 308 355

Calculate strength and determine rigidity of diaphragms. Determine the diaphragm design forces from Section 12.10.1.1 of ASCE/SEI 7. Fpx is the largest of: 1.

The force Fx at each level determined by the vertical distribution above Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Mx k-ft

940 3,790 7,940 12,700


III-53

n

∑F

i

2.

Fpx =

i=x n

∑w

w px ≤ 0.4S DS I e w px from ASCE/SEI 7, Equation 12.10-1 and 12.10-3

i

i=x

≤ 0.4 ( 0.129 )(1.0 ) w px ≤ 0.0516 w px

3.

Fpx = 0.2 S DS I e w px from ASCE/SEI 7, Equation 12.10-2 = 0.2 ( 0.129 )(1.0 ) wpx = 0.0258w px

Roof Fourth Third Second

wpx kips 820 2,510 2,510 2,440

A kips 64.8 146 97.2 47.3

B kips 42.3 130 130 105

C kips 21.2 64.8 64.8 63.0

Fpx kips 64.8 146 130 105

v(n-s) plf 297 892 791 641

v(e-w) plf 170 382 339 275

where A = force at a level based on the vertical distribution of seismic forces n

∑F

i

B = Fpx =

i=x n

∑ wi

w px ≤ 0.4S DS I e w px

i=x

C = 0.2 S DS I e w px Fpx = max(A, B, C) Note: The diaphragm shear loads include the effects of openings in the diaphragm and a 10% increase to account for accidental torsion.



III-54

Roof Roof deck: 12 in. deep, 22 gage, wide rib Support fasteners: s in. puddle welds in 36 / 5 pattern Sidelap fasteners: 3 #10 TEK screws Joist spacing = s = 6.0 ft Diaphragm length = 210 ft Diaphragm width = lv =120 ft By inspection, the critical condition for the diaphragm is loading from the north or south directions. Calculate the required diaphragm strength, including a 10% increase for accidental torsion. LRFD From the ASCE/SEI 7 load combinations for strength design, the earthquake load is, Q vr = 1.0 E lv Fpx = 1.0 ( 0.55 ) lv ( 64.8 kips ) = 1.0 ( 0.55 ) (120 ft )

ASD From the ASCE/SEI 7 load combinations for allowable stress design, the earthquake load is, Q vr = 0.7 E lv Fpx = 0.7 ( 0.55 ) lv ( 64.8 kips ) = 0.7 ( 0.55 ) (120 ft )

= 0.297 klf

= 0.208 klf

The wind load is, vr = 1.0W


= 1.0 ( 0.238 klf )

= 0.6 ( 0.238 klf )

= 0.238 klf

= 0.143klf

Note: The 0.55 factor in the earthquake load accounts for half the shear to each braced frame plus the 10% increase for accidental torsion. From the SDI Diaphragm Design Manual (SDI, 2004), the nominal shear strengths are: 1. 2.

For panel buckling strength, vn = 1.425 klf For connection strength, vn = 0.820 klf

Calculate the available strengths. LRFD Panel Buckling Strength (SDI, 2004) va = φvn

Connection Strength (SDI, 2004)

ASD Panel Buckling Strength (SDI, 2004) v va = n Ω 1.425 klf = 2.00 = 0.713 klf > 0.208 klf Connection Strength (SDI, 2004)

Earthquake

Earthquake

= 0.80 (1.425 klf ) = 1.14 klf > 0.297 klf

o.k.


o.k.


III-55

LRFD va = φvn = 0.55 ( 0.820 klf ) = 0.451 klf > 0.297 klf

o.k.

Wind (SDI, 2004) va = φvn = 0.70 ( 0.820 klf ) = 0.574 klf > 0.238 klf

o.k.

ASD vn va = Ω 0.820 klf = 3.00 = 0.273 klf > 0.208 klf Wind (SDI, 2004) v va = n Ω 0.820 klf = 2.35 = 0.349 klf > 0.143 klf

o.k.

o.k.

Check diaphragm flexibility. From the Steel Deck Institute Diaphragm Design Manual, Dxx = 758 ft

K1 = 0.286 ft-1

K2 = 870 kip/in.

K4 = 3.78

K2 0.3Dxx K4 + + 3K1 s s 870 kips/in. = 0.3 ( 758 ft ) ⎛ 0.286 ⎞ 3.78 + + 3⎜ ⎟ ( 6.00 ft ) 6.00 ft ⎝ ft ⎠ = 18.6 kips/in.

G' =

Seismic loading to diaphragm. w = ( 64.8 kips ) ( 210 ft ) = 0.309 klf

Calculate the maximum diaphragm deflection. Δ=

wL2 8lv G '

( 0.309 klf )( 210 ft ) 8 (120 ft )(18.6 kips/in.) 2

=

= 0.763 in.

Story drift = 0.141 in. (from computer output) The diaphragm deflection exceeds two times the story drift; therefore, the diaphragm may be considered to be flexible in accordance with ASCE/SEI 7, Section 12.3.1.3 The roof diaphragm is flexible in the N-S direction, but using a rigid diaphragm distribution is more conservative for the analysis of this building. By similar reasoning, the roof diaphragm will also be treated as a rigid diaphragm in the E-W direction. Third and Fourth floors Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-56

Floor deck: 3 in. deep, 22 gage, composite deck with normal weight concrete, Support fasteners; s in. puddle welds in a 36 / 4 pattern Sidelap fasteners: 1 button punched fastener Beam spacing = s = 10.0 ft Diaphragm length = 210 ft Diaphragm width = 120 ft lv = 120 ft − 30 ft = 90 ft to account for the stairwell By inspection, the critical condition for the diaphragm is loading from the north or south directions Calculate the required diaphragm strength, including a 10% increase for accidental torsion. LRFD From the ASCE/SEI 7 load combinations for strength design, the earthquake load for the fourth floor is, Q vr = 1.0 E lv Fpx = 1.0 ( 0.55 ) lv (146 kips ) = 1.0 ( 0.55 ) ( 90 ft ) = 0.892 klf

ASD From the ASCE/SEI 7 load combinations for strength design, the earthquake load is, Q vr = 0.7 E lv Fpx = 0.7 ( 0.55 ) lv (146 kips ) = 0.7 ( 0.55 ) ( 90 ft ) = 0.625 klf

For the fourth floor, the wind load is, vr = 1.0W

For the fourth floor, the wind load is, vr = 0.6W

= 1.0 ( 0.409 klf )

= 0.6 ( 0.409 klf )

= 0.409 klf

= 0.245 klf

From the ASCI/SEI 7 load combinations for strength design, the earthquake load for the third floor is, QE vr = 1.0 lv Fpx = 1.0 ( 0.55 ) lv (130 kips ) = 1.0 ( 0.55 ) ( 90 ft ) = 0.794 klf

From the ASCI/SEI 7 load combinations for strength design, the earthquake load for the third floor is, QE vr = 0.7 lv Fpx = 0.7 ( 0.55 ) lv (130 kips ) = 0.7 ( 0.55 ) ( 90 ft ) = 0.556 klf

For the third floor, the wind load is, vr = 1.0W

For the third floor, the wind load is, vr = 0.6W

= 1.0 ( 0.394 klf )

= 0.6 ( 0.394 klf )

= 0.394 klf

= 0.236 klf

From the SDI Diaphragm Design Manual, the nominal shear strengths are: For connection strength, vn = 5.16 klf Calculate the available strengths.



III-57

LRFD

ASD

Connection Strength (same for earthquake or wind) (SDI, 2004) va = φvn = 0.5 ( 5.16 klf ) = 2.58 klf > 0.892 klf

o.k.

Connection Strength (same for earthquake or wind) (SDI, 2004) v va = n Ω 5.16 klf = 3.25 = 1.59 klf > 0.625 klf o.k.

Check diaphragm flexibility. From the Steel Deck Institute Diaphragm Design Manual, K1 = 0.729 ft-1

K2 = 870 kip/in.

K3 = 2,380 kip/in.

K4 = 3.78

K2 ⎛ ⎞ G' = ⎜ ⎟ + K3 ⎝ K 4 + 3K1 s ⎠ 870 kip/in. ⎛ ⎞ =⎜ ⎟ + 2,380 kip/in. 0.729 ⎞ ⎛ ⎜⎜ 3.78 + 3 ⎜ ⎟ (10.0 ft ) ⎟⎟ ⎝ ft ⎠ ⎝ ⎠ = 2, 410 kips/in.

Fourth Floor Calculate seismic loading to diaphragm based on the fourth floor seismic load. w = (146 kips ) ( 210 ft ) = 0.695 klf Calculate the maximum diaphragm deflection on the fourth floor. Δ=

wL2 8lv G '

( 0.695 klf )( 210 ft ) = 8 ( 90 ft )( 2, 410 kips/in.) 2

= 0.0177 in.

Third Floor Calculate seismic loading to diaphragm based on the third floor seismic load. w = (130 kips ) ( 210 ft ) = 0.619 klf Calculate the maximum diaphragm deflection on the third floor.



III-58

Δ=

wL2 8lv G '

( 0.619 klf )( 210 ft ) 8 ( 90 ft )( 2, 410 kips/in.) 2

=

= 0.0157 in.

The diaphragm deflection at the third and fourth floors is less than two times the story drift (story drift = 0.245 in. from computer output); therefore, the diaphragm is considered rigid in accordance with ASCE/SEI 7, Section 12.3.1.3. By inspection, the floor diaphragm will also be rigid in the E-W direction. Second floor Floor deck: 3 in. deep, 22 gage, composite deck with normal weight concrete, Support fasteners: s in. puddle welds in a 36 / 4 pattern Sidelap fasteners: 1 button punched fasteners Beam spacing = s = 10.0 ft Diaphragm length = 210 ft Diaphragm width = 120 ft Because of the atrium opening in the floor diaphragm, an effective diaphragm depth of 75 ft will be used for the deflection calculations. By inspection, the critical condition for the diaphragm is loading from the north or south directions. Calculate the required diaphragm strength, including a 10% increase for accidental torsion. LRFD From the ASCE/SEI 7 load combinations for strength design, the earthquake load is, Q vr = 1.0 E lv Fpx = 1.0 ( 0.55 ) lv 105 ( kips ) = 1.0 ( 0.55 ) ( 90 ft )

ASD From the ASCE/SEI 7 load combinations for strength design, the earthquake load is, Q vr = 0.7 E lv Fpx = 0.7 ( 0.55 ) lv 105 ( kips ) = 0.7 ( 0.55 ) ( 90 ft )

= 0.642 klf

= 0.449 klf



= 1.0 ( 0.395 klf )

= 0.6 ( 0.395 klf )

= 0.395 klf

= 0.237 klf

From the SDI Diaphragm Design Manual, the nominal shear strengths are: For connection strength, vn = 5.16 klf Calculate the available strengths.



III-59

LRFD Connection Strength (same for earthquake or wind) (SDI, 2004) va = φvn = 0.50 ( 5.16 klf ) = 2.58 klf > 0.642 klf

o.k.

ASD Connection Strength (same for earthquake or wind) (SDI, 2004) v va = n Ω 5.16 klf = 3.25 = 1.59 klf > 0.449 klf o.k.

Check diaphragm flexibility. From the Steel Deck Institute Diaphragm Design Manual, K1 = 0.729 ft-1

K2 = 870 kip/in.

K3 = 2,380 kip/in.

K4 = 3.78

K2 ⎛ ⎞ G' = ⎜ ⎟ + K3 ⎝ K 4 + 3K1 s ⎠ 870 kip/in. ⎛ ⎞ =⎜ ⎟ + 2,380 kip/in. 0.729 ⎞ ⎛ ⎜⎜ 3.78 + 3 ⎜ ⎟ (10.0 ft ) ⎟⎟ ⎝ ft ⎠ ⎝ ⎠ = 2, 410 kip/in.

Calculate seismic loading to diaphragm. w = (105 kips ) ( 210 ft ) = 0.500 klf

Calculate the maximum diaphragm deflection. Δ=

wL2 8bG '

( 0.500 klf )( 210 ft ) = 8 ( 75 ft )( 2, 410 kip/in.) 2

= 0.0152 in.

Story drift = 0.228 in. (from computer output) The diaphragm deflection is less than two times the story drift; therefore, the diaphragm is considered rigid in accordance with ASCE/SEI 7, Section 12.3.1.3. By inspection, the floor diaphragm will also be rigid in the E-W direction. Horizontal shear distribution and torsion: Calculate the seismic forces to be applied in the frame analysis in each direction, including the effect of accidental torsion, in accordance with ASCE/SEI 7, Section 12.8.4.



III-60



Fy kips 64.8 146 97.2 47.3

Load to Frame % kips 50 32.4 50 73.0 50 48.6 50 23.7

Load to Grids 1 and 8 Accidental Torsion % kips 5 3.24 5 7.30 5 4.86 5 2.37

Fx kips 64.8 146 97.2 47.3

Load to Frame % kips 50 32.4 50 73.0 50 48.6 50.8(1) 24.0

Load to Grids A and F Accidental Torsion % kips 5 3.24 5 7.30 5 4.86 5 2.37

(1)

Total kips 35.6 80.3 53.5 26.1 196 Total kips 35.6 80.3 53.5 26.4 196

Note: In this example, Grids A and F have both been conservatively designed for the slightly higher load on Grid A due to the atrium opening. The increase in load is calculated as follows

I II

Area ft2 25,500 841 24,700

Mass kips 2,170 71.5 2,100

y-dist ft 60.5 90.5

My k-ft 131,000 6,470 125,000

y = 125,000 kip-ft/2,100 kips = 59.5 ft (100%)(121 ft – 59.5 ft)/121 ft = 50.8%



III-61 MOMENT FRAME MODEL

Grids 1 and 8 were modeled in conventional structural analysis software as two-dimensional models. The secondorder option in the structural analysis program was not used. Rather, for illustration purposes, second-order effects are calculated separately, using the “Approximate Second-Order Analysis” method described in AISC Specification Appendix 8. The column and beam layouts for the moment frames follow. Although the frames on Grids A and F are the same, slightly heavier seismic loads accumulate on grid F after accounting for the atrium area and accidental torsion. The models are half-building models. The frame was originally modeled with W14×82 interior columns and W21×44 non-composite beams, but was revised because the beams and columns did not meet the strength requirements. The W14×82 column size was increased to a W14×90 and the W21×44 beams were upsized to W24×55 beams. Minimum composite studs are specified for the beams (corresponding to ∑ Qn = 0.25Fy As ), but the beams were modeled with a stiffness of Ieq = Is. The frame was checked for both wind and seismic story drift limits. Based on the results on the computer analysis, the frame meets the L/400 drift criterion for a 10 year wind (0.7W) indicated in Commentary Section CC.1.2 of ASCE/SEI 7. In addition, the frame meets the 0.025hsx allowable story drift limit given in ASCE/SEI 7 Table 12.12-1 for Seismic Risk Category II. All of the vertical loads on the frame were modeled as point loads on the frame. The dead load and live load are shown in the load cases that follow. The wind, seismic, and notional loads from leaning columns are modeled and distributed 1/14 to exterior columns and 1/7 to the interior columns. This approach minimizes the tendency to accumulate too much load in the lateral system nearest an externally applied load. Also shown in the models below are the remainder of the half-building model gravity loads from the interior leaning columns accumulated in a single leaning column which was connected to the frame portion of the model with pinned ended links. Because the second-order analyses that follow will use the “Approximate Second-Order Analysis (amplified first-order) approach given in the AISC Specification Appendix 8, the inclusion of the leaning column is unnecessary, but serves to summarize the leaning column loads and illustrate how these might be handled in a full second-order analysis. See Geschwindner (1994), “A Practical Approach to the ‘Leaning’ Column.” There are five lateral load cases. Two are the wind load and seismic load, per the previous discussion. In addition, notional loads of Ni = 0.002Yi were established. The model layout, nominal dead, live, and snow loads with associated notional loads, wind loads and seismic loads are shown in the figures below. The same modeling procedures were used in the braced frame analysis. If column bases are not fixed in construction, they should not be fixed in the analysis.



III-62



III-63



III-64



III-65



III-66



III-67 CALCULATION OF REQUIRED STRENGTH—THREE METHODS

Three methods for checking one of the typical interior column designs at the base of the building are presented below. All three of presented methods require a second-order analysis (either direct via computer analysis techniques or by amplifying a first-order analysis). A fourth method called the “First-Order Analysis Method” is also an option. This method does not require a second-order analysis; however, this method is not presented below. For additional guidance on applying any of these methods, see the discussion in AISC Manual Part 2 titled Required Strength, Stability, Effective Length, and Second-Order Effects. GENERAL INFORMATION FOR ALL THREE METHODS

Seismic load combinations controlled over wind load combinations in the direction of the moment frames in the example building. The frame analysis was run for all LRFD and ASD load combinations; however, only the controlling combinations have been illustrated in the following examples. A lateral load of 0.2% of gravity load was included for all gravity-only load combinations. The second-order analysis for all the examples below was carried out by doing a first-order analysis and then amplifying the results to achieve a set of second-order design forces using the approximate second-order analysis procedure from AISC Specification Appendix 8. METHOD 1. DIRECT ANALYSIS METHOD

Design for stability by the direct analysis method is found in Chapter C of the AISC Specification. This method requires that both the flexural and axial stiffness are reduced and that 0.2% notional lateral loads are applied in the analysis to account for geometric imperfections and inelasticity. Any general second-order analysis method that considers both P − δ and P − Δ effects is permitted. The amplified first-order analysis method of AISC Specification Appendix 8 is also permitted provided that the B1 and B2 factors are based on the reduced flexural and axial stiffnesses. A summary of the axial loads, moments and 1st floor drifts from first-order analysis is shown below. The floor diaphragm deflection in the east-west direction was previously determined to be very small and will thus be neglected in these calculations. Second-order member forces are determined using the amplified first-order procedure of AISC Specification Appendix 8. It was assumed, subject to verification, that B2 is less than 1.7 for each load combination; therefore, per AISC Specification Section C2.2b(4), the notional loads were applied to the gravity-only load combinations . The required seismic load combinations are given in ASCE/SEI 7, Section 12.4.2.3. LRFD

1.23D ± 1.0QE + 0.5L + 0.2S (Controls columns and beams)

ASD 1.01D + 0.75L + 0.75(0.7QE) + 0.75S (Controls columns and beams)

From a first-order analysis with notional loads where appropriate and reduced stiffnesses:

From a first-order analysis with notional loads where appropriate and reduced stiffnesses:

For Interior Column Design: Pu = 317 kips M1u = 148 kip-ft (from first-order analysis) M2u = 233 kip-ft (from first-order analysis)

For Interior Column Design: Pa = 295 kips M1a = 77.9 kip-ft M2a = 122 kip-ft

First story drift with reduced stiffnesses = 0.718 in.

First story drift with reduced stiffnesses = 0.377 in.

Note: For ASD, ordinarily the second-order analysis must be carried out under 1.6 times the ASD load combinations and the results must be divided by 1.6 to obtain the required strengths. For this example, secondorder analysis by the amplified first-order analysis method is used. The amplified first-order analysis method incorporates the 1.6 multiplier directly in the B1 and B2 amplifiers, such that no other modification is needed. The required second-order flexural strength, Mr, and axial strength, Pr, are determined as follows. For typical Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-68

interior columns, the gravity-load moments are approximately balanced, therefore, Mnt = 0.0 kip-ft Calculate the amplified forces and moments in accordance with AISC Specification Appendix 8. LRFD

Mr = B1Mnt + B2Mlt

ASD (Spec. Eq. A-8-1)

Mr = B1Mnt + B2Mlt

(Spec. Eq. A-8-1)

Determine B1

Determine B1

Pr = required second-order axial strength using LRFD or ASD load combinations, kips.

Pr = required second-order axial strength using LRFD or ASD load combinations, kips.

Note that for members subject to axial compression, B1 may be calculated based on the first-order estimate Pr = Pnt + Plt.


Therefore, Pr = 317 kips (from the first-order computer analysis)

Therefore, Pr = 295 kips (from the first-order computer analysis)

Ix = 999 in.4 (W14×90)

Ix = 999 in.4 (W14×90)

τb = 1.0

τb = 1.0

Pe1 =

π2 EI *

(Spec. Eq. A-8-5)

( K1 L ) π2 ( 0.8 )( 29, 000 ksi ) ( 999 in.4 ) = 2 ⎡⎣(1.0 )(13.5 ft )(12 in./ft ) ⎤⎦ 2

= 8,720 kips

Pe1 =

π2 EI *

(Spec. Eq. A-8-5)

( K1 L ) π2 ( 0.8 )( 29, 000 ksi ) ( 999 in.4 ) = 2 ⎡⎣(1.0 )(13.5 ft )(12 in./ft ) ⎤⎦ 2

= 8,720 kips

Cm = 0.6 – 0.4(M1 / M2) (Spec. Eq. A-8-4) = 0.6 – 0.4 (148 kip-ft / 233 kip-ft) = 0.346

Cm = 0.6 – 0.4(M1 / M2) (Spec. Eq. A-8-4) = 0.6 – 0.4 (77.9 kip-ft / 122 kip-ft) = 0.345

α = 1.0

α = 1.6

Cm ≥1 αP 1− r Pe1 0.346 = ≥1 1.0 ( 317 kips ) 1− 8, 720 kips = 0.359 ≥ 1; Use 1.0

B1 =

Determine B2 1 B2 = ≥1 αPstory 1− Pe story where α = 1.0

(Spec. Eq. A-8-3)

(Spec. Eq. A-8-6)

Pstory = 5, 440 kips (from computer output)

Cm ≥1 αP 1− r Pe1 0.345 = ≥1 1.6 ( 295 kips ) 1− 8, 720 kips = 0.365 ≥ 1; Use 1.0

B1 =

Determine B2 1 B2 = ≥1 αPstory 1− Pe story where α= 1.6

(Spec. Eq. A-8-3)

(Spec. Eq. A-8-6)

Pstory = 5,120 kips (from computer output)



III-69

LRFD

ASD

Pe story may be taken as : Pe story = RM

Pe story may be taken as :

HL ΔH

(Spec. Eq. A-8-7)

where

Pe story = RM

HL ΔH

(Spec. Eq. A-8-7)

where

Pmf (Spec. Eq. A-8-8) RM = 1 − 0.15 Pstory where Pmf = 2, 250 kips (gravity load in moment frame) RM = 1 − 0.15

2, 250 kips 5, 440 kips

RM = 1 − 0.15

Pmf Pstory

where Pmf = 2, 090 kips RM = 1 − 0.15

= 0.938

(Spec. Eq. A-8-8) (gravity load in moment frame)

2, 090 kips 5,120 kips

= 0.939

H = 0.75 ( 0.7QE )

H = 1.0QE = 1.0 (196 kips )

= 0.75 ( 0.7 )(196 kips )

(Lateral)

( Lateral )

=196 kips (previous seismic force distribution calculations)

= 103 kips (previous seismic force distribution calculations)

Δ H = 0.718 in. (from computer output)


Pe story = 0.938

(196 kips )(13.5 ft )(12 in./ft ) 0.718 in.

= 41,500 kips 1 B2 = ≥1 αPstory 1− Pe story

(Spec. Eq. A-8-6)

1 ≥1 1.0 ( 5, 440 kips ) 1− 41,500 kips = 1.15 ≥ 1

Pe story = 0.939

(103 kips )(13.5 ft )(12 in./ft ) 0.377 in.

= 41, 600 kips 1 B2 = ≥1 αPstory 1− Pe story

(Spec. Eq. A-8-6)

1 ≥1 1.6 ( 5,120 kips ) 1− 41, 600 kips = 1.25 ≥ 1

=

=

Because B2 < 1.7, it is verified that it was unnecessary to add the notional loads to the lateral loads for this load combination.

Because B2 < 1.7, it is verified that it was unnecessary to add the notional loads to the lateral loads for this load combination.

Calculate amplified moment


From AISC Specification Equation A-8-1,


M r = (1.0 )( 0.0 kip-ft ) + (1.15 )( 233 kip-ft )

M r = (1.0 )( 0.0 kip-ft ) + (1.25 )(122 kip-ft )

= 268 kip-ft

= 153 kip-ft

Calculate amplified axial load

Calculate amplified axial load

Pnt = 317 kips

Pnt = 295 kips

(from computer analysis)


For a long frame, such as this one, the change in load Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION


III-70

LRFD

For a long frame, such as this one, the change in load to the interior columns associated with lateral load is negligible. Pr = Pnt + B2Plt (Spec. Eq. A-8-2) = 317 kips + (1.15)(0.0 kips) = 317 kips The flexural and axial stiffness of all members in the moment frame were reduced using 0.8E in the computer analysis. Check that the flexural stiffness was adequately reduced for the analysis per AISC Specification Section C2.3(2). α = 1.0

ASD to the interior columns associated with lateral load is negligible. Pr = Pnt + B2Plt (Spec. Eq. A-8-2) = 295 kips + (1.25)(0.0 kips) = 295 kips The flexural and axial stiffness of all members in the moment frame were reduced using 0.8E in the computer analysis. Check that the flexural stiffness was adequately reduced for the analysis per AISC Specification Section C2.3(2). α = 1.6 Pr = 295 kips

Pr = 317 kips Py = AFy = 26.5 in. ( 50.0 ksi ) = 1,330 kips 2

(W14×90 column)

Py = AFy = 26.5 in.2 ( 50.0 ksi ) = 1,330 kips

(W14×90 column)

αPr 1.6 ( 295 kips ) = = 0.355 ≤ 0.5 1,330 kips Py

αPr 1.0 ( 317 kips ) = = 0.238 ≤ 0.5 Py 1,330 kips

Therefore, τb = 1.0

o.k.

Note: By inspection τb = 1.0 for all of the beams in the moment frame.

Therefore, τb = 1.0

o.k.

Note: By inspection τb = 1.0 for all of the beams in the moment frame. For the direct analysis method, K = 1.0.

For the direct analysis method, K = 1.0. From AISC Manual Table 4-1, Pc = 1,040 kips (W14×90 @ KL = 13.5 ft) From AISC Manual Table 3-2, Mcx = φbMpx = 574 kip-ft (W14×90 with Lb = 13.5 ft)

From AISC Manual Table 3-2, M px Mcx = = 382 kip-ft (W14×90 with Lb = 13.5 ft) Ωb Pr 295 kips = = 0.428 ≥ 0.2 Pc 690 kips

Pr 317 kips = = 0.305 ≥ 0.2 Pc 1, 040 kips Pr ≥ 0.2 , use AISC Specification Pc interaction Equation H1-1a.

Because

Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ + ⎜ ⎟⎜ + ⎟ ≤ 1.0 Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠

From AISC Manual Table 4-1, Pc = 690 kips (W14×90 @ KL = 13.5 ft)

(Spec. Eq. H1-1a)

Pr ≥ 0.2 , use AISC Specification Pc interaction Equation H1-1a.

Because

Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ + ⎜ ⎟⎜ + ⎟ ≤ 1.0 Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠


(Spec. Eq. H1-1a)


III-71

LRFD

⎛ 8 ⎞ ⎛ 268 kip-ft ⎞ 0.305 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 574 kip-ft ⎠ 0.720 ≤ 1.0

o.k.

ASD ⎛ ⎞ ⎛ 8 ⎞ 153 kip-ft 0.428 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 382 kip-ft ⎠ 0.784 ≤ 1.0

o.k.

METHOD 2. EFFECTIVE LENGTH METHOD

Required strengths of frame members must be determined from a second-order analysis. In this example the second-order analysis is performed by amplifying the axial forces and moments in members and connections from a first-order analysis using the provisions of AISC Specification Appendix 8. The available strengths of compression members are calculated using effective length factors computed from a sidesway stability analysis. A first-order frame analysis is conducted using the load combinations for LRFD or ASD. A minimum lateral load (notional load) equal to 0.2% of the gravity loads is included for any gravity-only load combination. The required load combinations are given in ASCE/SEI 7 and are summarized in Part 2 of the AISC Manual. A summary of the axial loads, moments and 1st floor drifts from the first-order computer analysis is shown below. The floor diaphragm deflection in the east-west direction was previously determined to be very small and will thus be neglected in these calculations. LRFD



For Interior Column Design: Pu = 317 kips M1u = 148 kip-ft (from first-order analysis) M2u = 233 kip-ft (from first-order analysis)

For Interior Column Design: Pa = 295 kips M1a = 77.9 kip-ft (from first-order analysis) M2a = 122 kip-ft (from first-order analysis)

First-order first story drift = 0.575 in.

First-order first story drift = 0.302 in.

The required second-order flexural strength, Mr, and axial strength, Pr, are calculated as follows: For typical interior columns, the gravity load moments are approximately balanced; therefore, Mnt = 0.0 kips. LRFD

Mr = B1Mnt + B2Mlt


Mr = B1Mnt + B2Mlt

(Spec. Eq. A-8-1)

Determine B1.

Determine B1.

Pr = required second-order axial strength using LRFD or ASD load combinations, kips

Pr = required second-order axial strength using LRFD or ASD load combinations, kips



Therefore, Pr = 317 kips (from first-order computer analysis)

Therefore, Pr = 295 kips (from first-order computer analysis)

I = 999 in.4 (W14×90)

I = 999 in.4 (W14×90)

Pe1 =

π2 EI *

( K1 L )

2

(Spec. Eq. A-8-5)

Pe1 =

π2 EI *

( K1 L )

2


(Spec. Eq. A-8-5)


III-72

LRFD

π ( 29, 000 ksi ) ( 999 in. 2

=

4

ASD

)

⎡⎣(1.0 )(13.5 ft )(12 in./ft ) ⎤⎦ = 10,900 kips

π ( 29, 000 ksi ) ( 999 in.4 ) 2

=

⎡⎣(1.0 )(13.5 ft )(12 in./ft ) ⎤⎦ = 10,900 kips

2

2

Cm = 0.6 – 0.4(M1 / M2) (Spec. Eq. A-8-4) = 0.6 – 0.4 (148 kip-ft / 233 kip-ft) = 0.346

Cm = 0.6 – 0.4(M1 / M2) (Spec. Eq. A-8-4) = 0.6 – 0.4 (77.9 kip-ft / 122 kip-ft) = 0.345

α = 1.0

α = 1.6

Cm ≥1 αP 1− r Pe1 0.346 = ≥1 1.0 ( 317 kips ) 1− 10,900 kips = 0.356 ≥ 1; Use 1.00

B1 =

(Spec. Eq. A-8-3)

Determine B2. B2 =

(Spec. Eq. A-8-3)

Determine B2.

1 ≥1 αPstory 1− Pe story

(Spec. Eq. A-8-6)

where

1 ≥1 αPstory 1− Pe story where

B2 =

(Spec. Eq. A-8-6)

α= 1.6

α = 1.0 Pstory = 5, 440 kips (from computer output)

HL ΔH

Pstory = 5,120 kips (from computer output) Pe story may be taken as

Pe story may be taken as Pe story = RM

Cm ≥1 αP 1− r Pe1 0.345 = ≥1 1.6 ( 295 kips ) 1− 10,900 kips = 0.361 ≥ 1; Use 1.00

B1 =

(Spec. Eq. A-8-7)

Pe story =RM

HL ΔH

(Spec. Eq. A-8-7)

where

where Pmf Pmf (Spec. Eq. A-8-8) (Spec. Eq. A-8-8) RM = 1 − 0.15 RM = 1 − 0.15 Pstory Pstory where where Pmf = 2, 250 kips (gravity load in moment frame) Pmf = 2, 090 kips (gravity load in moment frame) RM = 1 − 0.15

2, 250 kips 5, 440 kips

RM = 1 − 0.15

= 0.938

2, 090 kips 5,120 kips

= 0.939

H = 196 kips (Lateral) (from previous seismic force distribution calculations)

H = 103 kips (Lateral) (from previous seismic force distribution calculations)





III-73

LRFD

Pe story = 0.938

ASD

(196 kips )(13.5 ft )(12 in./ft ) 0.575 in.


(Spec. Eq. A-8-6)

1 ≥1 1.0 ( 5, 440 kips ) 1− 51,800 kips = 1.12 ≥ 1

Pe story = 0.939

(103 kips )(13.5 ft )(12 in./ft ) 0.302 in.


(Spec. Eq. A-8-6)

1 ≥1 1.6 ( 5,120 kips ) 1− 51,900 kips = 1.19 ≥ 1

=

=

Note: B2 < 1.5, therefore use of the effective length method is acceptable.

Note: B2 < 1.5, therefore use of the effective length method is acceptable.





M r = (1.00 )( 0.0 kip-ft ) + (1.12 )( 233 kip-ft )

M r = (1.00 )( 0.0 kip-ft ) + (1.19 )(122 kip-ft )

= 261 kip-ft

= 145 kip-ft

Calculate amplified axial load.

Calculate amplified axial load.

Pnt = 317 kips

Pnt = 295 kips



For a long frame, such as this one, the change in load to the interior columns associated with lateral load is negligible.

For a long frame, such as this one, the change in load to the interior columns associated with lateral load is negligible.

Therefore, Plt = 0

Therefore, Plt = 0

Pr = Pnt + B2Plt (Spec. Eq. A-8-2) = 317 kips + (1.12)(0.0 kips) = 317 kips

Pr = Pnt + B2Plt (Spec. Eq. A-8-2) = 295 kips + (1.19)(0.0 kips) = 295 kips

Determine the controlling effective length.

Determine the controlling effective length.

For out-of-plane buckling in the moment frame

For out-of-plane buckling in the moment frame

Ky = 1.0

Ky = 1.0

K y Ly = 1.0 (13.5 ft ) = 13.5 ft

K y Ly = 1.0 (13.5 ft ) = 13.5 ft

For in-plane buckling in the moment frame, use the story stiffness procedure from the AISC Specification Commentary for Appendix 7 to determine Kx with Specification Commentary Equation C-A-7-5.

For in-plane buckling in the moment frame, use the story stiffness procedure from the AISC Specification Commentary for Appendix 7 to determine Kx with Specification Commentary Equation C-A-7-5.



III-74

LRFD

ASD

⎛ π EI ⎞ ⎛ Δ H ⎞ ΣPr ≥ ( 0.85 + 0.15RL ) Pr ⎜⎝ L2 ⎟⎠ ⎜⎝ ΣHL ⎟⎠ 2

K2 =

⎛ π2 EI ⎞ ⎛ Δ H ⎞ ΣPr ≥ ⎜ 2 ⎟⎜ ( 0.85 + 0.15RL ) Pr ⎝ L ⎠ ⎝ ΣHL ⎟⎠

K2 =

π2 EI ⎛ Δ H ⎞ ⎜ ⎟ L2 ⎝ 1.7 HL ⎠

π2 EI ⎛ Δ H ⎞ ⎜ ⎟ L2 ⎝ 1.7 HL ⎠

Simplifying and substituting terms previously calculated results in: Pstory Pe story

Kx =

⎛ Pe ⎞ ⎛ ΔH ⎞ ⎜ P ⎟ ≥ Pe ⎜ 1.7 HL ⎟ ⎝ ⎠ ⎝ r⎠

=

⎛ Pe ⎞ ⎛ ΔH ⎞ ⎜ P ⎟ ≥ Pe ⎜ 1.7 HL ⎟ ⎝ ⎠ ⎝ r⎠

where π2 EI L2 π2 ( 29, 000 ksi ) ( 999in.4 )

⎡⎣12 in./ft (13.5 ft ) ⎤⎦ = 10,900 kips Kx =

Pstory Pe story

Kx =

where Pe =

Simplifying and substituting terms previously calculated results in:

Pe = =

⎡⎣12 in./ft (13.5 ft ) ⎤⎦ = 10,900 kips

2

5, 440 kips ⎛ 10,900 kips ⎞ ⎜ ⎟≥ 51,800 kips ⎝ 317 kips ⎠

0.575 in. ⎛ ⎞ ⎟ 10,900 kips ⎜ 12 in. ⎞ ⎛ ⎜⎜ 1.7 (196 kips ) ⎜ ⎟ (13.5 ft ) ⎟⎟ ⎝ ft ⎠ ⎝ ⎠ = 1.90 ≥ 0.341

Kx =

2

5,120 kips ⎛ 10,900 kips ⎞ ⎜ ⎟≥ 51,900 kips ⎝ 295 kips ⎠

0.302 in. ⎛ ⎞ ⎟ 10,900 kips ⎜ 12 in. ⎞ ⎛ ⎜⎜ 1.7 (103 kips ) ⎜ ⎟ (13.5 ft ) ⎟⎟ ⎝ ft ⎠ ⎝ ⎠ = 1.91 ≥ 0.341

Use Kx = 1.91

Use Kx = 1.90 KLx = rx / ry

π2 EI L2 π2 ( 29, 000 ksi ) ( 999in.4 )

1.90 (13.5 ft ) 1.66

KLx 1.91(13.5 ft ) = = 15.5 ft rx / ry 1.66

= 15.5 ft

K L Because x x > K y Ly , use KL = 15.5 ft rx ry

Because

K x Lx > K y Ly , use KL = 15.5 ft rx ry

From AISC Manual Table 4-1, From AISC Manual Table 4-1, Pc = 990 kips (W14×90 @ KL = 15.5 ft)

Pc = 660 kips (W14×90 @ KL = 15.5 ft) From AISC Manual Table 3-2,

From AISC Manual Table 3-2, Mcx = 574 kip-ft (W14×90 with Lb =13.5 ft) Pr 317 kips = Pc 990 kips = 0.320 ≥ 0.2

Mcx = 382 kip-ft (W14×90 with Lb = 13.5 ft) Pr 295 kips = Pc 660 kips = 0.447 ≥ 0.2



III-75

LRFD

Because

Pr ≥ 0.2 , use interaction Equation H1-1a. Pc

Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ (Spec. Eq. H1.1-a) + ⎜ ⎟⎜ + ⎟ ≤ 1.0 Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠ ⎛ 8 ⎞ ⎛ 261 kip-ft ⎞ 0.320 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 574 kip-ft ⎠ 0.724 ≤ 1.0 o.k.

ASD Pr Because ≥ 0.2 , use interaction Equation H1-1a. Pc Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ + ⎜ ⎟⎜ + ⎟ ≤ 1.0 (Spec. Eq. H1.1-a) Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠ ⎛ 8 ⎞ ⎛ 145 kip-ft ⎞ 0.447 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 382 kip-ft ⎠ 0.784 ≤ 1.0 o.k.

METHOD 3. SIMPLIFIED EFFECTIVE LENGTH METHOD

A simplification of the effective length method using a method of second-order analysis based upon drift limits and other assumptions is described in Chapter 2 of the AISC Manual. A first-order frame analysis is conducted using the load combinations for LRFD or ASD. A minimum lateral load (notional load) equal to 0.2% of the gravity loads is included for all gravity-only load combinations. The floor diaphragm deflection in the east-west direction was previously determined to be very small and will thus be neglected in these calculations. LRFD



From a first-order analysis


For interior column design: Pu = 317 kips M1u = 148 kip-ft (from first-order analysis) M2u = 233 kip-ft (from first-order analysis)

For interior column design: Pa = 295 kips M1a = 77.9 kip-ft (from first-order analysis) M2a = 122 kip-ft (from first-order analysis)

First story first-order drift = 0.575 in.


Then the following steps are executed. LRFD

ASD

Step 1:

Step 1:

Lateral load = 196 kips

Lateral load = 103 kips

Deflection due to first-order elastic analysis

Deflection due to first-order elastic analysis

Δ = 0.575 in. between first and second floor

Δ = 0.302 in. between first and second floor

Floor height = 13.5 ft

Floor height = 13.5 ft

Drift ratio = (13.5 ft)(12 in./ft) / 0.575 in. = 282

Drift ratio = (13.5 ft)(12 in./ft) / 0.302 in. = 536

Step 2:

Step 2:

Design story drift limit = H/400

Design story drift limit = H/400

Adjusted Lateral load = (282/ 400)(196 kips) = 138 kips

Adjusted Lateral load = (536 / 400)(103 kips) = 138 kips



III-76

LRFD

ASD

total story load Load ratio = (1.0 ) lateral load 5, 440 kips = (1.0 ) 138 kips = 39.4

Step 3: (for an ASD design the ratio must be multiplied by 1.6) total story load Load ratio = (1.6 ) lateral load 5,120 kips = (1.6 ) 138 kips = 59.4

From AISC Manual Table 2-1:

From AISC Manual Table 2-1:

B2 = 1.1

B2 = 1.2

Which matches the value obtained in Method 2 to the two significant figures of the table

Which matches the value obtained in Method 2 to the two significant figures of the table

Step 3:

Note: Intermediate values are not interpolated from the table because the precision of the table is two significant digits. Additionally, the design story drift limit used in Step 2 need not be the same as other strength or serviceability drift limits used during the analysis and design of the structure. Step 4. Multiply all the forces and moment from the first-order analysis by the value of B2 obtained from the table. This presumes that B1 is less than or equal to B2, which is usually the case for members without transverse loading between their ends. LRFD

Step 5. Since the selection is in the shaded area of the chart, (B2 ≤ 1.1). For LRFD design, use K = 1.0.

ASD Step 5. Since the selection is in the unshaded area of the chart (B2 > 1.1), For ASD design, the effective length factor, K, must be determined through analysis. From previous analysis, use an effective length of 15.5 ft.

Multiply both sway and non-sway moments by B2.

Multiply both sway and non-sway moments by B2

Mr = B2(Mnt + Mlt) = 1.1(0 kip-ft + 233 kip-ft) = 256 kip-ft

Mr = B2(Mnt + Mlt) = 1.2(0 kip-ft + 122 kip-ft) = 146 kip-ft

Pr = B2(Pnt + Plt) = 1.1(317 kips +0.0 kips) = 349 kips

Pr = B2(Pnt + Plt) = 1.2(295 kips +0.0 kips) = 354 kips

From AISC Manual Table 4-1, Pc = 1,040 kips (W14×90 @ KL = 13.5 ft)

From AISC Manual Table 4-1, Pc = 675 kips (W14×90 @ KL = 13.5 ft)

From AISC Manual Table 3-2, Mcx = φbMpx = 574 kip-ft (W14×90 with Lb = 13.5 ft)

From AISC Manual Table 3-2, M px Mcx = = 382 kip-ft (W14×90 with Lb = 13.5 ft) Ωb

Pr 349 kips = = 0.336 ≥ 0.2 Pc 1, 040 kips

Because

Pr ≥ 0.2, use interaction Equation H1-1a. Pc

Pr 354 kips = = 0.524 ≥ 0.2 Pc 675 kips

Because

Pr ≥ 0.2, use interaction Equation H1-1a. Pc



III-77

Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ + ⎜ ⎟⎜ + ⎟ ≤ 1.0 Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠ ⎛ 8 ⎞ ⎛ 256 kip-ft ⎞ 0.336 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 574 kip-ft ⎠ 0.732 ≤ 1.0

Pr ⎛ 8 ⎞ ⎛ M rx M ry ⎞ + ⎜ ⎟⎜ + ⎟ ≤ 1.0 Pc ⎝ 9 ⎠ ⎝ M cx M cy ⎠ ⎛ 8 ⎞ ⎛ 146 kip-ft ⎞ 0.524 + ⎜ ⎟ ⎜ ⎟ ≤ 1.0 ⎝ 9 ⎠ ⎝ 382 kip-ft ⎠ 0.864 ≤ 1.0

o.k.

o.k.

BEAM ANALYSIS IN THE MOMENT FRAME

The controlling load combinations for the beams in the moment frames are shown below and evaluated for the second floor beam. The dead load, live load and seismic moments were taken from a computer analysis. The table summarizes the calculation of B2 for the stories above and below the second floor. 1st – 2nd

RM Pe story

LRFD Combination 1.23D + 1.0QE + 0.5L + 0.2S 196 kips 13.5 ft 0.575 in. 2,250 kips 0.938 51,800 kips

ASD Combination 1 1.02D + 0.7QE 137 kips 13.5 ft 0.402 in. 1,640 kips 0.937 51,700 kips

ASD Combination 2 1.01D + 0.75L + 0.75(0.7QE) + 0.75S 103 kips 13.5 ft 0.302 in. 2,090 kips 0.939 51,900 kips

Pstory B2

5,440 kips 1.12

3,920 kips 1.14

5,120 kips 1.19

2nd – 3rd

RM Pe story

LRFD Combination 1.23D + 1.0QE + 0.5L +0.2S 170 kips 13.5 ft 0.728 in. 1,590 0.938 35,500 kips

ASD Combination 1 1.02D + 0.7QE 119 kips 13.5 ft 0.509 in. 1,160 0.937 35,500 kips

ASD Combination 2 1.01D + 0.75L + 0.75(0.7QE) + 0.75S 89.3 kips 13.5 ft 0.382 in. 1,490 0.939 35,600 kips

Pstory B2

3,840 kips 1.12

2,770 kips 1.14

3,660 kips 1.20

H L ΔH Pmf

H L ΔH Pmf

For beam members, the larger of the B2 values from the story above or below is used. From computer output at the controlling beam: Mdead = 153 kip-ft

Mlive = 80.6 kip-ft

LRFD Combination B2 M lt = 1.12 (154 kip-ft ) = 172 kip-ft

Msnow = 0.0 kip-ft

ASD Combination 1 B2 M lt = 1.14 (154 kip-ft )

Mearthquake = 154 kip-ft ASD Combination 2 B2 M lt = 1.20 (154 kip-ft )

= 176 kip-ft


= 185 kip-ft


III-78 ⎡1.02 (153 kip-ft ) ⎤ Ma = ⎢ ⎥ ⎣⎢ +0.7 (176 kip-ft ) ⎦⎥

⎡1.23 (153 kip-ft ) ⎤ ⎢ ⎥ M u = ⎢ +1.0 (172 kip-ft ) ⎥ ⎢ ⎥ ⎣ +0.5 ( 80.6 kip-ft ) ⎦ = 400 kip-ft

= 279 kip-ft

⎡1.01(153 kip-ft ) ⎤ ⎢ ⎥ M a = ⎢ +0.525 (185 kip-ft ) ⎥ ⎢ ⎥ ⎣ +0.75 ( 80.6 kip-ft ) ⎦ = 312 kip-ft

Calculate Cb for compression in the bottom flange braced at 10.0 ft o.c. LRFD Cb = 1.86 (from computer output)

ASD 1.02D + 0.7QE Cb = 1.86 (from computer output) 1.01D + 0.75(0.7QE) + 0.75L Cb = 2.01 (from computer output)

Check W24×55

Check W24×55

From AISC Manual Table 3-2, with continuous bracing

1.02D + 0.7E

φM n = 503 kip-ft

From AISC Manual Table 3-2, with continuous bracing

From AISC Manual Table 3-10, for Lb = 10.0 ft and Cb = 1.86

Mn = 334 kip-ft Ω

φM n = ( 386 kip-ft )1.86 ≤ 503 kip-ft

From AISC Manual Table 3-10, for Lb = 10.0 ft and Cb = 1.86

= 718 kip-ft ≤ 503 kip-ft

Use φM n = 503 kip-ft > 400 kip-ft

o.k.

From AISC Manual Table 3-2, a W24×55 has a design shear strength of 252 kips and an Ix of 1350 in.4

Mn = ( 256 kip-ft )1.86 ≤ 334 kip-ft Ω = 476 kip-ft ≤ 334 kip-ft

Use

Mn = 334 kip-ft > 279 kip-ft Ω

o.k.

1.01D + 0.75(0.7QE) + 0.75L With continuous bracing Mn = 334 kip-ft Ω

From AISC Manual Table 3-10, for Lb = 10 ft and Cb = 2.01 Mn = ( 256 kip-ft ) 2.01 Ω = 515 kip-ft ≤ 334 kip-ft

Use

Mn = 334 kip-ft > 312 kip-ft Ω


o.k.


III-79

LRFD

ASD From AISC Manual Table 3-2, a W24×55 has an allowable shear strength of 167 kips and an Ix of 1,350 in.4

The moments and shears on the roof beams due to the lateral loads were also checked but do not control the design. The connections of these beams can be designed by one of the techniques illustrated in the Chapter IIB of the design examples.



III-80 BRACED FRAME ANALYSIS

The braced frames at Grids 1 and 8 were analyzed for the required load combinations. The stability design requirements from Chapter C were applied to this system. The model layout, nominal dead, live, and snow loads with associated notional loads, wind loads and seismic loads are shown in the figures below:



III-81



III-82

Second-order analysis by amplified first-order analysis In the following, the approximate second-order analysis method from AISC Specification Appendix 8 is used to account for second-order effects in the braced frames by amplifying the axial forces in members and connections from a first-order analysis. A first-order frame analysis is conducted using the load combinations for LRFD and ASD. From this analysis the critical axial loads, moments and deflections are obtained. A summary of the axial loads and 1st floor drifts from the first-order computer analysis is shown below. The floor diaphragm deflection in the north-south direction was previously determined to be very small and will thus be neglected in these calculations. LRFD





For interior column design: Pnt = 236 kips Plt = 146 kips

For interior column design: Pnt = 219 kips Plt = 76.6 kips

The moments are negligible

The moments are negligible



The required second-order axial strength, Pr, is computed as follows: LRFD

Pr = Pnt + B2Plt


Determine B2. B2 =

(Spec. Eq. A-8-6)

(previously calculated)

Pe story may be calculated as: Pe story = RM

(Spec. Eq. A-8-2)

Determine B2.


Pstory = 5,440 kips

Pr = Pnt + B2Plt

HL ΔH

B2 =


Pstory = 5,120 kips

(Spec. Eq. A-8-6)

(previously calculated)

Pe story may be calculated as: (Spec. Eq. A-8-7)

where

Pe story = RM

HL ΔH

(Spec. Eq. A-8-7)

where

H = 196 kips (from previous calculations) ΔH = 0.211 in. (from computer output) RM = 1.0 for braced frames Pe story = 1.0

(196 kips )(13.5 ft )(12 in./ft )

= 150, 000 kips

0.211 in.

H = 103 kips (from previous calculations) ΔH = 0.111 in. (from computer output) RM = 1.0 for braced frames Pe story = 1.0

(103 kips )(13.5 ft )(12 in./ft )

= 150, 000 kips Design Examples V14.0 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.111 in.


III-83

B2 =


B2 =

1 ≥1 1.0 ( 5, 440 kips ) 1− 150, 000 kips = 1.04 ≥ 1


1 ≥1 1.6 ( 5,120 kips ) 1− 150, 000 kips = 1.06 ≥ 1 =

=

Pr = Pnt + B2Plt (Spec. Eq. A-8-2) = 236 kips + (1.04)(146 kips) = 388 kips

Pr = Pnt + B2Plt = 219 kips + (1.06)(76.6 kips) = 300 kips



Pc = 514 kips (W12×53 @ KL = 13.5 ft)

Pc = 342 kips (W12×53 @ KL = 13.5 ft)

From AISC Specification Equation H1-1a,

From AISC Specification Equation H1-1a,

Pr 388 kips = = 0.755 ≤ 1.0 Pc 514 kips

o.k.

(Spec. Eq. A-8-2)

Pr 300 kips = = 0.877 ≤ 1.0 Pc 342 kips

o.k.

Note: Notice that the lower sidesway displacements of the braced frame produce much lower values of B2 than those of the moment frame. Similar results could be expected for the other two methods of analysis. Although not presented here, second-order effects should be accounted for in the design of the beams and diagonal braces in the braced frames at Grids 1 and 8.



III-84 ANALYSIS OF DRAG STRUTS

The fourth floor delivers the highest diaphragm force to the braced frames at the ends of the building: E = 80.3 kips (from previous calculations). This force is transferred to the braced frame through axial loading of the W18×35 beams at the end of the building. The gravity dead loads for the edge beams are the floor loading of 75.0 psf (5.50 ft) plus the exterior wall loading of 0.503 kip/ft, giving a total dead load of 0.916 kip/ft. The gravity live load for these beams is the floor loading of 80.0 psf (5.50 ft) = 0.440 kip/ft. The resulting midspan moments are MDead = 58.0 kip-ft and MLive = 27.8 kip-ft. The controlling load combination for LRFD is 1.23D + 1.0QE + 0.50L. The controlling load combinations for ASD are 1.01D + 0.75L + 0.75(0.7QE) or 1.02D + 0.7QE LRFD

ASD

Mu = 1.23(58.0 kip-ft) + 0.50(27.8 kip-ft) = 85.2 kip-ft

Ma = 1.01(58.0 kip-ft) + 0.75(27.8 kip-ft) = 79.4 kip-ft or Ma = 1.02(58.0 kip-ft) = 59.2 kip-ft

Load from the diaphragm shear due to earthquake loading

Load from the diaphragm shear due to earthquake loading

Fp = 80.3 kips

Fp = 0.75(0.70)(80.3 kips) = 42.2 kips or Fp = 0.70(80.3 kips) = 56.2 kips

Only the two 45 ft long segments on either side of the brace can transfer load into the brace, because the stair opening is in front of the brace. Use AISC Specification Section H2 to check the combined bending and axial stresses. LRFD

ASD

80.3 kips V= = 0.892 kip/ft 2 ( 45.0 ft )

42.2 kips V= = 0.469 kip/ft 2 ( 45.0 ft ) or V=

The top flange bending stress is fb = =

Mu Sx 85.2 kip-ft (12 in. / ft )

56.2 kips = 0.624 kip/ft 2 ( 45.0 ft )

The top flange stress due to bending fb = =

Ma Sx 79.4 kip-ft (12 in. / ft )

57.6 in.3 = 16.5 ksi

57.6 in.3 = 17.8 ksi

or



III-85

fb = =

Ma Sx 59.2 kip-ft (12 in. / ft )

57.6 in.3 = 12.3 ksi

Note: It is often possible to resist the drag strut force using the slab directly. For illustration purposes, this solution will instead use the beam to resist the force independently of the slab. The full cross section can be used to resist the force if the member is designed as a column braced at one flange only (plus any other intermediate bracing present, such as from filler beams). Alternatively, a reduced cross section consisting of the top flange plus a portion of the web can be used. Arbitrarily use the top flange and 8 times an area of the web equal to its thickness times a depth equal to its thickness, as an area to carry the drag strut component. Area = 6.00 in.(0.425 in.) + 8(0.300 in.)2 = 2.55 in.2 + 0.720 in.2 = 3.27 in.2 Ignoring the small segment of the beam between Grid C and D, the axial stress due to the drag strut force is: LRFD

fa =

ASD

80.3kips

42.2 kips

fa =

2 ( 3.27 in.2 )

= 12.3 ksi

2 ( 3.27 in.2 )

= 6.45 ksi or fa =

90.0 ft ( 0.624 kip/ft ) 2 ( 3.27 in.2 )

= 8.59 ksi

Using AISC Specification Section H2, assuming the top flange is continuously braced:

From AISC Specification Section H2, assuming the top flange is continuously braced:

Fa = φc Fy

Fa = Fy Ωc

= 0.90 ( 50 ksi )

= 50 ksi 1.67 = 29.9 ksi

= 45.0 ksi Fbw = φb Fy

Fbw = Fy Ωb

= 0.90 ( 50 ksi )

= 50 ksi 1.67 = 29.9 ksi

= 45.0 ksi f a fbw + ≤ 1.0 (from Spec. Eq. H2-1) Fa Fbw 12.3ksi 17.8 ksi + = 0.669 o.k. 45.0 ksi 45.0 ksi

f a fbw + ≤ 1.0 Fa Fbw

(from Spec. Eq. H2-1)

Load Combination 1: 6.45 ksi 16.5 ksi + = 0.768 29.9 ksi 29.9 ksi

Load Combination 2:


o.k.


III-86

8.59 ksi 12.3ksi + = 0.699 29.9 ksi 29.9 ksi

o.k.

Note: Because the drag strut load is a horizontal load, the method of transfer into the strut, and the extra horizontal load which must be accommodated by the beam end connections should be indicated on the drawings.



III-87 PART III EXAMPLE REFERENCES

ASCE (2010), Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10, Reston, VA. Geschwindner, L.F. (1994), “A Practical Approach to the Leaning Column,” Engineering Journal, AISC, Vol. 31, No. 4, 4th Quarter, pp. 141-149. SDI (2004), Diaphragm Design Manual, 3rd Ed., Steel Deck Institute, Fox River Grove, IL. SJI (2005), Load Tables and Weight Tables for Steel Joists and Joist Girders, 42nd Ed., Steel Joist Institute, Forest, VA. West, M., Fisher, J. and Griffis, L.A. (2003), Serviceability Design Considerations for Steel Buildings, Design Guide 3, 2nd Ed., AISC, Chicago, IL.



III-88


III-89

Return to Table of Contents III-90


III-91


III-92


IV-1

Chapter IV Other Resources This chapter contains additional design aids that are not available in the AISC Steel Construction Manual.



IV-2

DESIGN TABLE DISCUSSION Table 4-1. W-Shapes in Axial Compression, 65 ksi steel Available strengths in axial compression are given for W-shapes with Fy = 65 ksi (ASTM A913 Grade 65). The tabulated values are given for the effective length with respect to the y-axis (KL)y. However, the effective length with respect to the x-axis (KL)x must also be investigated. To determine the available strength in axial compression, the table should be entered at the larger of (KL)y and (KL)y eq, where ( KL ) ( KL ) y eq = r x (4-1) x ry The available strength is based on the limit states of flexural buckling, torsional buckling, and flexuralKL = 99.5 with Fy = 65 ksi. torsional buckling. The limit between elastic and inelastic buckling is r The slenderness limit between a nonslender web and a slender web is λrw = 31.5 with Fy = 65 ksi. All current ASTM A6 W-shapes have nonslender flanges with Fy = 65 ksi. Values of the ratio rx/ry and other properties useful in the design of W-shape compression members are listed at the bottom of Table 4-1. Variables Pwo, Pwi, Pwb and Pfb shown in Table 4-1 can be used to determine the strength of W-shapes without stiffeners to resist concentrated forces applied normal to the face(s) of the flange(s). In these tables it is assumed that the concentrated forces act far enough away from the member ends that end effects are not considered (end effects are addressed in Chapter 9). When Pr ≤ φRn or Rn/Ω, column web stiffeners are not required. Figures 4-1, 4-2 and 4-3 illustrate the limit states and the applicable variables for each. Web Local Yielding: The variables Pwo and Pwi can be used in the calculation of the available web local yielding strength for the column as follows: LRFD φRn = Pwo + Pwi lb

(4-2a)

ASD Rn Ω = Pwo + Pwi lb

(4-2b)

where Rn = Fywtw (5k + lb ) = 5Fywtw k + Fywtwlb , kips (AISC Specification Equation J10-2) Pwo = φ5 Fywtw k for LRFD and 5Fywtw k Ω for ASD, kips Pwi = φFywtw for LRFD and Fywtw Ω for ASD, kips/in. k lb tw φ Ω

= = = = =

distance from outer face of flange to the web toe of fillet, in. length of bearing, in. thickness of web, in. 1.00 1.50

Web Compression Buckling: The variable Pwb is the available web compression buckling strength for the column as follows: LRFD φRn = Pwb

(4-3a)

where Rn =

24tw3 EFyw h

(AISC Specification Equation J10-8)


ASD Rn Ω = Pwb

(4-3b)


IV-3

Pwb = Fyw h φ Ω

= = = =

φ24tw3 EFyw

for LRFD and

24tw3 EFyw

for ASD, kips h Ωh specified minimum yield stress of the web, ksi clear distance between flanges less the fillet or corner radius for rolled shapes, in. 0.90 1.67

Fig. 4-1. Illustration of web local yielding limit state (AISC Specification Section J10.2). Flange Local Buckling: The variable Pfb is the available flange local bending strength for the column as follows: LRFD φRn = Pfb

(4-4a)

ASD Rn Ω = Pfb

where Rn = 6.25Fyf t 2f , kips (AISC Specification Equation J10-1) Pfb = φ6.25 Fyf t 2f for LRFD and 6.25 Fyf t 2f Ω for ASD, kips φ = 0.90 Ω = 1.67

Fig. 4-2. Illustration of web compression buckling limit state (AISC Specification Section J10.5).


(4-4a)


IV-4

Fig. 4-3. Illustration of flange local bending limit state (AISC Specification Section J10.1).



IV-5

Table 4-1

Available Strength in Axial Compression, kips

Fy = 65 ksi

W-Shapes Shape lb/ft

W14

Design 0 Effective length, KL (ft), with respect to least radius of gyration, ry

W14

455h 665h 605h 550h 500h 730h P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 8370 12600 7630 11500 6930 10400 6310 9480 5720 8600 5220 7840

6 7 8 9 10

8180 8120 8040 7960 7860

12300 12200 12100 12000 11800

7450 7390 7320 7240 7150

11200 11100 11000 10900 10800

6770 6710 6640 6570 6480

10200 10100 9980 9870 9750

6150 6100 6040 5970 5890

9250 9170 9070 8970 8850

5580 5530 5470 5410 5340

8390 8310 8220 8130 8020

5080 5040 4980 4920 4860

7640 7570 7490 7400 7300

11 12 13 14 15

7760 7650 7530 7410 7270

11700 11500 11300 11100 10900

7060 6960 6850 6730 6600

10600 10500 10300 10100 9930

6400 6300 6200 6090 5970

9610 9470 9310 9150 8970

5810 5720 5620 5520 5410

8730 8590 8450 8300 8130

5260 5170 5090 4990 4890

7900 7780 7640 7500 7350

4780 4710 4620 4530 4440

7190 7070 6950 6820 6680

16 17 18 19 20

7140 6990 6840 6680 6520

10700 10500 10300 10000 9810

6470 6340 6200 6050 5900

9730 9530 9310 9100 8870

5850 5720 5590 5460 5320

8790 8600 8410 8200 7990

5300 5180 5060 4930 4810

7970 7790 7610 7420 7220

4790 4680 4560 4450 4330

7190 7030 6860 6690 6510

4340 4240 4140 4030 3920

6530 6380 6220 6060 5890

22 24 26 28 30

6190 5850 5490 5140 4780

9310 8790 8260 7720 7180

5590 5270 4950 4610 4280

8410 7920 7430 6940 6440

5030 4730 4430 4130 3820

7560 7120 6660 6200 5740

4540 4260 3980 3700 3420

6820 6410 5990 5570 5140

4080 3830 3570 3310 3050

6140 5750 5370 4980 4590

3690 3460 3220 2980 2740

5550 5200 4840 4480 4120

32 34 36 38 40

4420 4080 3740 3410 3090

6650 6130 5620 5120 4640

3960 3640 3320 3020 2730

5950 5460 4990 4540 4100

P wo , kips P wi , kips/in. P wb , kips P fb , kips L p , ft L r , ft A g , in.2 I x , in.4 I y , in.4 r y , in. r x /r y P ex (KL )2/104, k-in.2 P ey (KL )2/104, k-in.2 ASD c = 1.67

3520 5290 3150 4730 2800 4210 2510 3780 3230 4850 2880 4320 2550 3840 2290 3440 2940 4420 2620 3930 2320 3480 2070 3110 2660 4000 2360 3550 2090 3130 1860 2790 2400 3610 2130 3200 1880 2830 1680 2520 Properties 3670 5500 3140 4710 2680 4020 2280 3420 1950 2920 1670 2500 133 200 123 184 113 169 103 155 94.9 142 87.5 131 50100 75300 39200 58900 30400 45700 23300 35100 18200 27300 14200 21400 5860 8810 4970 7470 4210 6330 3550 5340 2980 4480 2510 3770 14.5 14.1 13.9 13.7 13.6 14.3 212 178 164 151 138 195 215 196 178 162 147 134 14300 4720 4.69 1.74 409000 135000 LRFD c = 0.90

12400 4170 4.62 1.73 355000 119000 h

10800 3680 4.55 1.71 309000 105000

9430 3250 4.49 1.70 270000 93000

8210 2880 4.43 1.69 235000 82400

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.


7190 2560 4.38 1.67 206000 73300


IV-6

Table 4-1 (continued)

Available Strength in Axial Compression, kips W-Shapes

W14 Shape lb/ft

W14


Fy = 65 ksi

283h 398h 370h 342h 311h 426h P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 4870 7310 4550 6840 4240 6380 3930 5910 3560 5350 3240 4870

11 12 13 14 15

4460 4380 4300 4220 4130

6700 6590 6470 6340 6210

4170 4100 4020 3940 3860

6260 6160 6040 5920 5800

3870 3810 3740 3660 3580

5820 5720 5620 5500 5390

3590 3520 3460 3390 3310

5390 5290 5200 5090 4980

3240 3180 3120 3060 2990

4870 4780 4690 4590 4490

2950 2890 2840 2780 2720

4430 4350 4270 4180 4080

16 17 18 19 20

4040 3940 3840 3740 3640

6070 5930 5780 5630 5470

3770 3680 3590 3490 3390

5670 5530 5390 5250 5100

3500 3420 3330 3240 3140

5260 5130 5000 4860 4720

3230 3150 3070 2990 2900

4860 4740 4620 4490 4360

2920 2840 2770 2690 2610

4380 4270 4160 4040 3920

2650 2580 2510 2440 2370

3980 3880 3780 3670 3560

22 24 26 28 30

3420 3200 2980 2750 2530

5140 4810 4470 4140 3800

3190 2980 2770 2560 2350

4790 4480 4160 3840 3530

2950 2750 2550 2360 2160

4430 4140 3840 3540 3240

2720 2540 2350 2160 1980

4090 3810 3530 3250 2980

2440 2280 2110 1940 1770

3670 3420 3160 2910 2660

2220 2060 1900 1750 1600

3330 3100 2860 2630 2400

32 34 36 38 40

2310 2100 1900 1700 1540

3470 3160 2850 2560 2310

2140 1940 1750 1570 1420

3220 2920 2630 2360 2130

1970 1780 1600 1440 1300

2960 2680 2410 2160 1950

1800 1630 1460 1310 1180

2710 2450 2200 1970 1780

1610 1450 1300 1170 1050

2420 2180 1950 1750 1580

1450 1310 1170 1050 945

2180 1960 1750 1570 1420

42 44 46 48 50

1390 1270 1160 1070 983

2090 1910 1750 1600 1480

1290 1170 1070 985 907

1930 1760 1610 1480 1360

1180 1770 1070 1610 980 1470 900 1350 830 1250 Properties 1320 1980 1170 1760 76.7 115 71.9 108 9600 14400 7890 11900 1980 2970 1720 2590 13.2 13.4 122 114

1070 979 896 823 758

1610 1470 1350 1240 1140

954 869 795 730 673

1430 1310 1200 1100 1010

857 781 715 656 605

1290 1170 1070 986 909

1020 66.7 6320 1480

1540 100 9490 2230 13.1 106

874 61.1 4850 1240

1310 91.7 7290 1870 13.0 96.7

746 55.9 3710 1040

1120 83.9 5580 1570 12.9 88.3


1480 2220 81.5 122 11500 17200 2250 3380 13.4 130 125 6600 2360 4.34 1.67 189000 67500 LRFD c = 0.90

117 6000 2170 4.31 1.66 172000 62100 h

109 5440 1990 4.27 1.66 156000 57000

101 4900 1810 4.24 1.65 140000 51800

91.4 4330 1610 4.20 1.64 124000 46100



83.3 3840 1440 4.17 1.63 110000 41200


IV-7



Fy = 65 ksi

W-Shapes Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

0

W14

W14 257 233 211 193 176 159 P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 2940 4420 2670 4010 2410 3630 2210 3320 2020 3030 1820 2730

6 7 8 9 10

2860 2830 2800 2760 2720

4300 4250 4200 4140 4080

2590 2560 2530 2500 2460

3890 3850 3800 3750 3690

2340 2320 2290 2260 2220

3520 3480 3440 3390 3340

2150 2120 2100 2070 2030

3220 3190 3150 3110 3060

1960 1930 1910 1880 1850

2940 2910 2870 2830 2780

1760 1740 1720 1700 1670

2650 2620 2590 2550 2510

11 12 13 14 15

2670 2620 2570 2510 2460

4010 3940 3860 3780 3690

2420 2370 2320 2270 2220

3630 3560 3490 3420 3340

2180 2140 2100 2050 2000

3280 3220 3150 3080 3010

2000 1960 1920 1880 1830

3000 2950 2890 2820 2750

1820 1780 1750 1710 1670

2740 2680 2630 2570 2500

1640 1610 1570 1540 1500

2460 2420 2360 2310 2250

16 17 18 19 20

2400 2330 2270 2200 2130

3600 3510 3410 3310 3210

2160 2110 2050 1990 1930

3250 3170 3080 2990 2890

1950 1900 1850 1790 1730

2940 2860 2780 2690 2610

1790 1740 1690 1640 1580

2680 2610 2540 2460 2380

1620 1580 1530 1490 1440

2440 2370 2300 2230 2160

1460 1420 1380 1330 1290

2190 2130 2070 2010 1940

22 24 26 28 30

2000 1850 1710 1570 1430

3000 2790 2570 2360 2150

1800 1670 1540 1410 1280

2700 2510 2310 2120 1930

1620 1500 1380 1260 1150

2430 2250 2070 1900 1720

1480 1370 1260 1150 1040

2220 2050 1890 1730 1570

1340 1240 1140 1040 941

2010 1860 1710 1560 1410

1200 1110 1020 929 842

1810 1670 1530 1400 1270

32 34 36 38 40

1290 1160 1040 932 841

1940 1750 1560 1400 1260

1160 1040 927 832 751

1740 1560 1390 1250 1130

941 841 750 673 608

1410 1260 1130 1010 914

847 756 674 605 546

1270 1140 1010 909 821

757 675 602 540 487

1140 1010 905 812 733

637 51.1 2830 869

955 76.7 4250 1310 12.8 80.7

538 46.4 2110 720

807 69.6 3170 1080 12.7 73.5

1040 1560 927 1390 827 1240 742 1120 670 1010 Properties 459 688 42.5 63.7 1630 2460 592 890 12.6 67.2

393 38.6 1220 504

590 57.9 1840 758 12.5 61.8

343 36.0 992 417

515 54.0 1490 627 12.5 57.1

289 32.3 716 344

433 48.4 1080 518 12.4 52.4


75.6 3400 1290 4.13 1.62 97300 36900 LRFD

68.5 3010 1150 4.10 1.62 86200 32900

62.0 2660 1030 4.07 1.61 76100 29500

56.8 2400 931 4.05 1.60 68700 26600

51.8 2140 838 4.02 1.60 61300 24000

c = 0.90


46.7 1900 748 4.00 1.60 54400 21400


IV-8



W14 Shape lb/ft Design 0 Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 65 ksi


6 7 8 9 10

1610 1590 1570 1550 1520

2420 2390 2360 2330 2290

1460 1440 1420 1400 1370

2190 2160 2130 2100 2060

1330 1310 1290 1270 1250

1990 1970 1940 1910 1870

1200 1190 1170 1150 1130

1810 1780 1760 1730 1700

1090 1080 1060 1040 1030

1640 1620 1600 1570 1540

995 982 968 951 933

1500 1480 1450 1430 1400

11 12 13 14 15

1500 1470 1440 1400 1370

2250 2210 2160 2110 2060

1340 1310 1280 1250 1210

2020 1970 1930 1880 1830

1220 1190 1160 1130 1100

1830 1790 1750 1700 1660

1110 1080 1050 1030 998

1660 1620 1590 1540 1500

1000 982 957 932 906

1510 1480 1440 1400 1360

914 893 871 848 824

1370 1340 1310 1270 1240

16 17 18 19 20

1330 1290 1260 1220 1180

2000 1950 1890 1830 1770

1180 1140 1100 1060 1030

1770 1720 1660 1600 1540

1070 1040 1000 965 929

1610 1560 1500 1450 1400

968 937 906 873 840

1460 1410 1360 1310 1260

878 850 821 791 761

1320 1280 1230 1190 1140

799 773 746 719 691

1200 1160 1120 1080 1040

22 24 26 28 30

1090 1010 927 844 764

1640 1520 1390 1270 1150

945 865 785 707 632

1420 1300 1180 1060 950

856 782 709 638 569

1290 1180 1070 959 856

774 707 640 576 514

1160 1060 963 866 772

700 639 578 519 463

1050 960 869 781 696

636 580 525 471 419

956 872 789 708 630

32 34 36 38 40

686 611 545 489 441

1030 918 819 735 663

559 495 442 397 358

840 744 664 596 538

454 402 359 322 290

682 604 539 484 437

408 362 323 290 261

614 544 485 435 393

370 328 292 262 237

556 492 439 394 356

249 29.5 543 289

373 44.2 816 434 12.3 48.7

228 28.0 464 258

342 41.9 697 388 11.6 44.3

503 756 446 670 398 598 357 536 322 484 Properties 197 295 25.6 38.4 356 535 215 323 11.6 41.5

166 22.8 251 180

249 34.1 377 270 11.6 39.1

145 21.0 197 148

218 31.5 297 222 11.5 36.8

125 19.1 147 123

187 28.6 222 184 11.5 34.9


42.7 1710 677 3.98 1.59 48900 19400 LRFD

38.8 1530 548 3.76 1.67 43800 15700

35.3 1380 495 3.74 1.67 39500 14200

32.0 1240 447 3.73 1.67 35500 12800

29.1 1110 402 3.71 1.66 31800 11500

c = 0.90


26.5 999 362 3.70 1.66 28600 10400


IV-9



Fy = 65 ksi



0

W14

W14 82 74 68 61 53 48c 43c P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 934 1400 849 1280 778 1170 697 1050 607 913 541 813 474 712

6 7 8 9 10

862 838 810 780 748

1300 1260 1220 1170 1120

783 761 736 709 679

1180 1140 1110 1060 1020

718 697 674 648 621

1080 1050 1010 974 933

642 623 602 579 555

965 936 905 871 834

531 506 479 449 419

798 761 720 676 630

479 457 432 405 377

720 686 649 609 567

419 401 381 358 334

630 603 572 539 502

11 12 13 14 15

714 678 641 604 566

1070 1020 964 908 851

648 616 583 549 514

974 926 876 824 773

592 562 531 500 468

890 845 798 751 703

529 502 474 446 417

795 754 712 670 627

387 356 324 293 263

582 535 487 441 396

349 320 291 263 236

524 481 438 395 355

308 282 257 231 207

464 425 386 348 311

16 17 18 19 20

528 491 454 418 384

794 738 683 629 576

480 446 413 380 348

721 670 620 571 524

436 405 374 344 315

656 609 562 517 473

389 360 333 306 280

584 542 500 460 421

234 208 185 166 150

352 312 278 250 226

210 186 166 149 134

315 279 249 224 202

184 163 145 130 117

276 244 218 196 177

22 24 26 28 30

318 267 228 197 171

478 402 343 295 257

289 243 207 179 156

435 365 311 268 234

261 219 187 161 140

392 330 281 242 211

232 195 166 143 125

348 293 249 215 187

124 104 88.8 76.6 66.7

186 157 133 115 100

111 93.2 79.4 68.5 59.7

167 140 119 103 89.7

97.1 81.6 69.5 59.9 52.2

146 123 104 90.1 78.5

32 34 36 38 40

150 133 119 107 96.3

226 200 179 160 145

137 121 108 96.9 87.5

205 182 162 146 131

58.6

88.1

160 22.1 229 178

240 33.2 344 267 7.68 26.7

135 19.5 157 150

202 29.3 236 225 7.68 25.2

123 185 110 165 109 164 97.0 146 97.5 147 86.5 130 87.5 131 77.7 117 79.0 119 70.1 105 Properties 118 177 101 151 18.0 27.0 16.3 24.4 124 186 91.3 137 126 190 101 152 7.62 7.59 24.0 22.7

100 16.0 87.4 106

150 24.1 131 159 5.95 18.4

87.7 14.7 67.9 86.1

131 22.1 102 129 5.92 17.6

74.0 13.2 49.1 68.3

111 19.8 73.8 103 5.86 16.8


24.0 881 148 2.48 2.44 25200 4240 LRFD c = 0.90

21.8 795 134 2.48 2.44 22800 3840 c

20.0 722 121 2.46 2.44 20700 3460

17.9 640 107 2.45 2.44 18300 3060

15.6 541 57.7 1.92 3.07 15500 1650

14.1 484 51.4 1.91 3.06 13900 1470

Shape is slender for compression with F y = 65 ksi.

Note: Heavy line indicates KL /r y equal to or greater than 200.


12.6 428 45.2 1.89 3.08 12300 1290


IV-10




Fy = 65 ksi

W12 210 305h 279h 252h 230h 336h P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 3850 5790 3480 5240 3190 4790 2880 4330 2640 3960 2410 3620

6 7 8 9 10

3700 3640 3580 3510 3440

5550 5470 5380 5280 5160

3340 3290 3230 3170 3100

5020 4940 4860 4760 4660

3050 3010 2950 2890 2830

4590 4520 4440 4350 4250

2760 2720 2670 2610 2550

4150 4080 4010 3920 3830

2520 2480 2430 2380 2330

3790 3730 3660 3580 3500

2300 2260 2220 2170 2120

3450 3400 3330 3260 3180

11 12 13 14 15

3350 3270 3180 3080 2980

5040 4910 4770 4630 4480

3020 2940 2860 2770 2680

4540 4420 4300 4160 4020

2760 2680 2600 2520 2430

4140 4030 3910 3790 3660

2490 2420 2340 2270 2190

3740 3630 3520 3410 3290

2270 2200 2130 2060 1990

3400 3310 3210 3100 2990

2060 2000 1940 1870 1810

3100 3010 2920 2820 2720

16 17 18 19 20

2880 2770 2660 2550 2440

4320 4170 4000 3840 3670

2580 2480 2380 2280 2180

3880 3730 3580 3430 3280

2350 2250 2160 2070 1970

3530 3390 3250 3110 2970

2110 2020 1940 1850 1770

3170 3040 2910 2780 2650

1910 1840 1760 1680 1600

2880 2760 2640 2520 2400

1740 1670 1590 1520 1450

2610 2500 2390 2280 2170

22 24 26 28 30

2220 2000 1790 1580 1380

3340 3010 2680 2370 2080

1980 1780 1580 1390 1210

2970 2670 2370 2090 1820

1790 1600 1420 1250 1090

2680 2400 2130 1870 1630

1590 1420 1260 1100 959

2390 2140 1890 1650 1440

1440 1280 1130 988 860

2160 1930 1700 1480 1290

1300 1160 1020 885 771

1950 1740 1530 1330 1160

32 34 36 38 40

1210 1080 959 861 777

1820 1620 1440 1290 1170

1070 945 843 757 683

1600 1420 1270 1140 1030

954 1430 845 1270 754 1130 676 1020 610 917 Properties 1170 1750 1020 1530 70.6 106 66.3 99.5 8770 13200 7270 10900 1790 2690 1480 2230 10.6 10.5 105 96.8

843 746 666 598 539

1270 1120 1000 898 811

756 670 597 536 484

1140 1010 898 806 727

678 600 535 481 434

1020 902 805 722 652

865 60.7 5560 1230

1300 91.0 8350 1850 10.3 88.0

746 55.9 4340 1040

1120 83.9 6530 1570 10.3 80.7

639 51.1 3340 878

959 76.7 5020 1320 10.2 73.9


1370 77.1 11400 2130

2050 116 17200 3200 10.7 116

98.9 4060 1190 3.47 1.85 116000 34100 LRFD c = 0.90

89.5 3550 1050 3.42 1.84 102000 30100 h

81.9 3110 937 3.38 1.82 89000 26800

74.1 2720 828 3.34 1.81 77900 23700

67.7 2420 742 3.31 1.80 69300 21200



61.8 2140 664 3.28 1.80 61300 19000


IV-11



Fy = 65 ksi



0

W12


6 7 8 9 10

2080 2050 2010 1960 1910

3130 3070 3020 2950 2880

1860 1820 1790 1750 1710

2790 2740 2690 2630 2560

1660 1630 1600 1560 1520

2490 2450 2400 2350 2290

1480 1450 1420 1390 1350

2220 2180 2140 2090 2040

1300 1280 1250 1220 1190

1960 1920 1880 1840 1790

1150 1130 1110 1080 1050

1730 1700 1670 1630 1580

11 12 13 14 15

1860 1810 1750 1690 1630

2800 2720 2630 2540 2450

1660 1610 1560 1500 1450

2490 2420 2340 2260 2170

1480 1430 1390 1340 1290

2220 2150 2080 2010 1930

1320 1270 1230 1190 1140

1980 1920 1850 1780 1710

1160 1120 1080 1040 1000

1740 1680 1630 1570 1500

1020 990 956 920 883

1540 1490 1440 1380 1330

16 17 18 19 20

1560 1500 1430 1370 1300

2350 2250 2150 2050 1950

1390 1330 1270 1210 1150

2090 2000 1910 1820 1730

1230 1180 1130 1070 1020

1850 1770 1690 1610 1530

1090 1050 996 947 898

1640 1570 1500 1420 1350

958 915 871 827 783

1440 1380 1310 1240 1180

845 807 768 729 689

1270 1210 1150 1100 1040

22 24 26 28 30

1160 1030 908 788 686

1750 1550 1360 1180 1030

1030 910 797 690 601

1540 1370 1200 1040 904

907 802 701 606 528

1360 1210 1050 910 793

800 705 615 530 462

1200 1060 924 797 695

697 613 532 459 400

1050 921 800 690 601

612 537 466 402 350

920 808 700 604 526

32 34 36 38 40

603 534 476 428 386

906 803 716 643 580

528 468 418 375 338

794 704 628 563 508

406 360 321 288 260

610 541 482 433 391

352 311 278 249 225

528 468 417 375 338

308 272 243 218 197

462 410 365 328 296

535 45.9 2420 737

803 68.9 3640 1110 10.1 67.4

449 41.6 1800 592

674 62.4 2710 890 9.98 60.7

464 697 411 617 366 551 329 494 297 446 Properties 377 566 37.7 56.6 1330 2000 477 717 9.88 54.8

317 34.2 1000 380

475 51.4 1500 571 9.79 49.1

262 30.8 726 300

392 46.2 1090 450 9.70 44.2

210 26.4 462 238

315 39.7 694 358 9.63 39.9


56.0 1890 589 3.25 1.79 54100 16900 LRFD

50.0 1650 517 3.22 1.78 47200 14800

44.7 1430 454 3.19 1.77 40900 13000

39.9 1240 398 3.16 1.77 35500 11400

35.2 1070 345 3.13 1.76 30600 9870

c = 0.90


31.2 933 301 3.11 1.76 26700 8620


IV-12



W12 Shape lb/ft

W12 96


Fy = 65 ksi

87

79

72 65 58 P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 1100 1650 996 1500 903 1360 821 1230 743 1120 662 994

6 7 8 9 10

1040 1020 1000 977 951

1570 1540 1510 1470 1430

946 928 908 886 862

1420 1390 1360 1330 1300

856 840 822 802 779

1290 1260 1240 1200 1170

779 764 747 728 708

1170 1150 1120 1090 1060

704 691 675 658 640

1060 1040 1020 989 962

612 595 576 555 532

920 894 865 834 800

11 12 13 14 15

923 893 861 829 795

1390 1340 1290 1250 1190

836 808 780 750 719

1260 1210 1170 1130 1080

756 731 704 677 648

1140 1100 1060 1020 975

687 664 639 614 589

1030 997 961 923 885

620 599 577 554 530

932 900 867 833 797

509 484 458 432 406

765 727 689 650 610

16 17 18 19 20

760 725 690 654 619

1140 1090 1040 983 930

687 655 622 590 557

1030 984 936 887 838

620 590 561 531 501

931 887 843 798 753

562 535 508 481 454

845 805 764 723 683

506 482 457 432 408

761 724 687 650 613

379 353 327 302 277

570 531 492 454 417

22 24 26 28 30

548 481 416 358 312

824 722 625 539 469

493 432 373 321 280

742 649 560 483 421

443 387 333 287 250

666 582 501 432 376

401 350 301 260 226

603 526 453 390 340

360 313 269 232 202

540 471 404 349 304

231 194 165 143 124

347 292 249 214 187

32 34 36 38 40

274 243 217 195 176

413 365 326 293 264

246 218 194 174 157

370 327 292 262 237

199 176 157 141 127

299 265 236 212 191

178 157 140 126 114

267 236 211 189 171

109 96.7 86.3 77.4 69.9

164 145 130 116 105

179 23.8 337 197

268 35.8 507 296 9.57 37.0

157 22.3 277 160

236 33.5 416 240 9.51 34.4

220 331 195 293 174 261 156 234 141 212 Properties 135 203 20.4 30.6 211 316 131 198 9.45 32.1

118 18.6 161 109

177 28.0 243 164 9.42 30.4

101 16.9 121 89.0

152 25.4 181 134 9.36 28.8

96.7 15.6 94.7 99.6

145 23.4 142 150 7.78 24.4


28.2 833 270 3.09 1.76 23800 7730 LRFD

25.6 740 241 3.07 1.75 21200 6900

23.2 662 216 3.05 1.75 18900 6180

21.1 597 195 3.04 1.75 17100 5580

19.1 533 174 3.02 1.75 15300 4980

c = 0.90


17.0 475 107 2.51 2.10 13600 3060


IV-13



Fy = 65 ksi


58

W12 50 P n / c c P n ASD LRFD 568 854

0

P n / c ASD 662

c P n LRFD 994

P n / c ASD 607

c P n LRFD 913

6 7 8 9 10

612 595 576 555 532

920 894 865 834 800

560 544 527 507 486

842 818 791 762 731

500 477 452 426 398

11 12 13 14 15

509 484 458 432 406

765 727 689 650 610

464 441 417 393 368

697 662 627 590 553

16 17 18 19 20

379 353 327 302 277

570 531 492 454 417

343 319 295 272 249

22 24 26 28 30

231 194 165 143 124

347 292 249 214 187

207 174 148 128 111

32 34 36 38 40

109 96.7 86.3 77.4 69.9

164 145 130 116 105

97.8 86.6 77.3 69.4 62.6

96.7 15.6 94.7 99.6

145 23.4 142 150 7.78 24.4

88.2 15.0 83.6 80.4

Design


53


17.0 475 107 2.51 2.10 13600 3060 LRFD c = 0.90

W12 45

40c P n / c c P n ASD LRFD 450 676

P n / c ASD 510

c P n LRFD 766

751 717 680 640 598

448 427 405 381 356

673 642 609 573 535

400 381 361 339 317

600 573 542 510 476

369 340 311 283 255

555 511 468 425 383

330 304 278 252 227

496 456 417 378 341

293 270 246 223 201

441 405 370 336 302

516 480 444 409 375

228 203 181 162 146

343 304 272 244 220

203 180 160 144 130

305 270 241 216 195

179 159 142 127 115

270 239 213 191 173

311 261 223 192 167

121 102 86.6 74.7 65.0

182 153 130 112 97.8

107 90.3 76.9 66.3 57.8

161 136 116 100 86.8

95.0 79.8 68.0 58.6 51.1

143 120 102 88.1 76.8

147 57.2 85.9 130 116 104 94.1 Properties 132 91.4 137 22.4 16.0 24.1 126 101 151 121 99.6 150 7.68 6.07 23.2 19.5

50.8

76.3

44.9

67.5

78.4 14.5 74.8 80.4

118 21.8 112 121 6.04 18.5

65.2 12.8 51.1 64.5

97.8 19.2 76.8 97.0 6.01 17.6

15.6 425 95.8 2.48 2.11 12200 2740

14.6 391 56.3 1.96 2.64 11200 1610

13.1 348 50.0 1.95 2.64 9960 1430

c

Shape is slender for compression with F y = 65 ksi. Note: Heavy line indicates KL /r y equal to or greater than 200.


11.7 307 44.1 1.94 2.64 8790 1260


IV-14




Fy = 65 ksi


6 7 8 9 10

1200 1170 1130 1100 1060

1800 1750 1700 1650 1590

1060 1040 1010 974 938

1600 1560 1510 1460 1410

942 918 892 862 830

1420 1380 1340 1300 1250

821 800 776 750 722

1230 1200 1170 1130 1080

720 701 680 657 632

1080 1050 1020 987 949

639 622 603 582 560

961 935 907 875 842

11 12 13 14 15

1020 973 928 881 834

1530 1460 1390 1320 1250

901 861 820 778 736

1350 1290 1230 1170 1110

796 761 724 687 648

1200 1140 1090 1030 974

692 660 627 594 560

1040 992 943 893 842

605 577 549 519 489

909 868 825 780 736

536 511 485 459 432

806 768 730 690 650

16 17 18 19 20

786 738 691 644 597

1180 1110 1040 967 898

692 649 606 564 523

1040 976 912 848 786

610 571 533 495 459

916 859 801 745 689

526 492 458 425 393

791 740 689 639 591

459 429 400 371 342

690 646 601 557 515

405 379 352 326 301

609 569 529 490 452

22 24 26 28 30

509 428 365 315 274

765 644 548 473 412

444 373 318 274 239

667 560 478 412 359

388 326 278 239 209

583 490 417 360 313

331 278 237 204 178

497 418 356 307 267

288 242 206 178 155

433 364 310 267 233

252 212 181 156 136

379 318 271 234 204

32 34 36 38 40

241 213 190 171 154

362 321 286 257 232

210 186 166 149 134

315 279 249 224 202

156 139 124 111 100

235 208 186 167 150

136 121 108 96.5 87.1

205 181 162 145 131

119 106 94.2 84.5 76.3

179 159 142 127 115

286 32.7 1080 380

429 49.1 1630 571 8.30 49.6

239 29.5 786 305

358 44.2 1180 459 8.21 44.8

183 276 162 244 145 218 130 195 117 176 Properties 195 293 26.2 39.3 556 835 238 358 8.15 39.9

157 23.0 374 184

236 34.5 563 277 8.05 35.5

129 20.4 261 144

194 30.6 392 217 8.02 32.1

107 18.2 186 112

161 27.3 280 169 7.96 29.2


32.9 716 236 2.68 1.74 20500 6750 LRFD

29.3 623 207 2.65 1.74 17800 5920

26.0 534 179 2.63 1.73 15300 5120

22.7 455 154 2.60 1.73 13000 4410

19.9 394 134 2.59 1.71 11300 3840

c = 0.90


17.7 341 116 2.57 1.71 9760 3320


IV-15



Fy = 65 ksi


54

W10 45 P n / c c P n ASD LRFD 518 778

0

P n / c ASD 615

c P n LRFD 924

P n / c ASD 560

c P n LRFD 842

6 7 8 9 10

570 555 538 519 499

857 834 809 780 750

519 505 489 472 453

780 759 735 709 681

458 438 417 393 369

11 12 13 14 15

478 455 432 408 384

718 684 649 614 578

434 413 392 370 348

652 621 589 556 523

16 17 18 19 20

360 336 313 289 267

542 505 470 435 401

326 304 282 261 240

22 24 26 28 30

223 188 160 138 120

336 282 240 207 180

32 34 36 38 40

106 93.5 83.4 74.8 67.6 89.8 16.0 127 92.0

Design


49


W10 39

33

P n / c ASD 448

c P n LRFD 673

P n / c ASD 378

c P n LRFD 568

689 659 626 591 554

395 377 358 337 316

593 567 538 507 474

332 316 299 282 263

498 475 450 423 395

344 318 292 266 242

516 478 439 401 363

293 271 248 226 204

441 407 373 339 307

243 224 204 185 167

366 336 307 278 251

489 456 424 392 361

217 194 173 155 140

327 292 260 234 211

183 163 145 130 118

275 245 218 196 177

149 132 118 106 95.4

224 198 177 159 143

200 168 143 124 108

301 253 216 186 162

116 97.4 83.0 71.5 62.3

174 146 125 108 93.7

97.2 81.7 69.6 60.0 52.3

146 123 105 90.2 78.6

78.8 66.2 56.4 48.7 42.4

118 100 84.8 73.1 63.7

159 141 125 112 102

94.7 83.9 74.8 67.2 60.6

142 126 112 101 91.1

54.8

82.3

46.0

69.1

37.3

56.0

135 24.1 192 138 7.93 27.0

78.1 14.7 98.7 76.3

70.3 13.7 78.3 68.3

105 20.5 118 103 6.13 19.7

58.7 12.6 61.2 46.0

88.1 18.9 92.0 69.2 6.01 18.0

15.8 303 103 2.56 1.71 8670 2950 LRFD

Properties 117 84.9 127 22.1 15.2 22.8 148 107 161 115 93.5 141 7.87 6.23 25.6 21.6

14.4 272 93.4 2.54 1.71 7790 2670

13.3 248 53.4 2.01 2.15 7100 1530

11.5 209 45.0 1.98 2.16 5980 1290


c = 0.90


9.71 171 36.6 1.94 2.16 4890 1050


IV-16



W8 Shape lb/ft

W8 67

Design Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 65 ksi

0

58

48

40 35 31 P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n P n / c c P n ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 767 1150 666 1000 549 825 455 684 401 603 355 534

6 7 8 9 10

687 660 631 599 565

1030 993 948 901 850

595 572 546 518 488

895 859 820 778 733

490 470 448 425 400

736 706 674 638 601

405 388 369 349 328

608 583 555 524 493

356 341 324 306 288

535 512 487 460 432

315 301 287 271 254

473 453 431 407 382

11 12 13 14 15

530 495 458 422 386

797 743 689 634 581

457 426 394 362 331

687 640 592 544 498

374 348 322 295 269

562 523 483 444 405

306 284 261 239 217

460 426 393 359 327

268 248 229 209 190

403 373 344 314 285

237 219 202 184 167

356 329 303 277 251

16 17 18 19 20

352 318 285 256 231

528 478 429 385 347

301 271 243 218 197

452 408 365 328 296

244 220 197 176 159

367 331 295 265 239

196 176 157 141 127

295 264 236 212 191

171 153 137 123 111

257 230 206 184 166

151 135 120 108 97.2

226 202 180 162 146

22 24 26 28 30

191 160 137 118 103

287 241 205 177 154

163 137 116 100 87.5

244 205 175 151 131

132 111 94.2 81.2 70.7

198 166 142 122 106

105 88.2 75.2 64.8 56.5

158 133 113 97.4 84.9

91.5 76.9 65.5 56.5 49.2

138 116 98.5 84.9 74.0

80.3 67.5 57.5 49.6 43.2

121 101 86.5 74.5 64.9

32 34

90.3 79.9

136 120

76.9 68.1

116 102

62.2 55.1

93.5 82.8

49.6

74.6

43.3

65.0

38.0

57.1

164 24.7 578 213

246 37.1 868 320 6.57 36.9

133 22.1 414 160

199 33.2 622 240 6.51 32.4

74.4 15.6 145 76.3

112 23.4 218 115 6.32 23.8

59.7 13.4 92.5 59.6

89.6 20.2 139 89.6 6.29 21.7

51.2 12.4 71.9 46.0

76.8 18.5 108 69.2 6.26 20.1


19.7 272 88.6 2.12 1.75 7790 2540 LRFD

17.1 228 75.1 2.1 1.74 6530 2150

Properties 93.6 140 17.3 26.0 199 298 114 172 6.44 27.6 14.1 184 60.9 2.08 1.74 5270 1740

11.7 146 49.1 2.04 1.73 4180 1410

10.3 127 42.6 2.03 1.73 3630 1220

Note: Heavy line indicates KL/r y equal to or greater than 200.

c = 0.90


9.13 110 37.1 2.02 1.72 3150 1060


IV-17

DESIGN TABLE DISCUSSION Table 6-1. W-Shapes in Combined Flexure and Axial Force, 65 ksi Steel W-shapes with Fy = 65 ksi (ASTM A913 Grade 65) and subject to combined axial force (tension or compression) and flexure may be checked for compliance with the provisions of Section H1.1 and H1.2 of the AISC Specification using values listed in Table 6-1 and the appropriate interaction equations provided in the following sections. Values p, bx, by, ty and tr presented in Table 6-1 are defined as follows. LRFD

ASD

Axial Compression

p =

1 , (kips) −1 φc Pn

p =

Ωc , (kips) −1 Pn

Strong Axis Bending

bx =

8 , (kip-ft) −1 9φb M nx

bx =

8Ωb , (kip-ft)−1 9 M nx

Weak Axis Bending

by =

8 , (kip-ft) −1 9φb M ny

by =

8Ωb , (kip-ft) −1 9 M ny

Tension Yielding

ty =

1 , (kips) −1 φt Fy Ag

ty =

Ωt , (kips) −1 Fy Ag

Tension Rupture

tr =

1 , (kips) −1 φt Fu 0.75 Ag

tr =

Ωt , (kips) −1 Fu 0.75 Ag

(

)

(

)

Combined Flexure and Compression Equations H1-1a and H1-1b of the AISC Specification may be written as follows using the coefficients listed in Table 6-1 and defined previously. When pPr ≥ 0.2:

pPr + bx M rx + by M ry ≤ 1.0

When pPr < 0.2: 1

2

(

)

pPr + 9 8 bx M rx + by M ry ≤ 1.0

(6-1) (6-2)

The designer may check acceptability of a given shape using the appropriate interaction equation from the preceding list. See Aminmansour (2000) for more information on this method, including an alternative approach for selection of a trial shape.

Combined Flexure and Tension Equations H1-1a and H1-1b of the AISC Specification may be written as follows using the coefficients listed in Table 6-1 and defined previously. When pPr ≥ 0.2:

(t y or tr ) Pr + bx M rx + by M ry ≤ 1.0

When pPr < 0.2: 1

2

(t y or tr ) Pr + 9 8 (bx M rx + by M ry ) ≤ 1.0

The larger value of ty and tr should be used in the preceding equations.


(6-3)

(6-4)


IV-18

The designer may check acceptability of a given shape using the appropriate interaction equation from above along with variables tr, ty, bx and by. See Aminmansour (2006) for more information on this method. It is noted that the values for tr listed in Table 6-1 are based on the assumption that Ae = 0.75Ag. See Part 5 for more information on this assumption. When Ae > 0.75Ag, the tabulated values for tr are conservative. When Ae < 0.75Ag, tr must be calculated based upon the actual value of Ae.

General Considerations for Use of Values Listed in Table 6-1 The following remarks are offered for consideration in use of the values listed in Table 6-1. 1. Values of p, bx and by already account for section compactness and can be used directly. 2. Tabulated values of bx assumed Cb = 1.0. A procedure for determining bx when Cb > 1.0 follows. 3. Given that the limit state of lateral-torsional buckling does not apply to W-shapes bent about their weak axis, values of by are independent of unbraced length and Cb. 4. Values of bx equally apply to combined flexure and compression as well as combined flexure and tension. 5. Smaller values of variable p for a given KL and smaller values of bx for a given Lb indicate higher strength for the type of load in question. For example, a section with a smaller p at a certain KL is more effective in carrying axial compression than another section with a larger value of p at the same KL. Similarly, a section with a smaller bx is more effective for flexure at a given Lb than another section with a larger bx for the same Lb. This information may be used to select more efficient shapes when relatively large amounts of axial load or bending are present.

Determination of bx when Cb > 1.0

The tabulated values of bx assume that Cb = 1.0. These values may be modified in accordance with AISC Specification Sections F1 and H1.2. The following procedure may be used to account for Cb > 1.0. bx (Cb =1.0) ≥ bxmin bx (Cb >1.0) = (6-5) Cb Values of bxmin are listed in Table 6-1 at Lb = 0 ft. See Aminmansour (2009) for more information on this method. Values for p, bx, by, ty and tr presented in Table 6-1 have been multiplied by 103. Thus, when used in the appropriate interaction equation they must be multiplied by 10-3 (0.001).



IV-19

Table 6-1

Combined Flexure and Axial Force

Fy = 65 ksi

W-Shapes W44

Shape

c

b x  10

3

p  10

-1

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

(kips) ASD LRFD

-1

(kip-ft) ASD LRFD

262c,v b x  10

3

p  10

3

-1

(kips) ASD LRFD

-1

(kip-ft) ASD LRFD

3

b x  103

-1

(kip-ft)-1 ASD LRFD

p  10

(kips) ASD LRFD

0

0.276

0.184

0.169

0.113

0.333

0.221

0.194

0.129

0.378

0.251

0.216

0.144

11 12 13 14 15

0.309 0.315 0.323 0.331 0.341

0.205 0.210 0.215 0.221 0.227

0.170 0.173 0.176 0.179 0.183

0.113 0.115 0.117 0.119 0.122

0.370 0.378 0.387 0.396 0.407

0.246 0.251 0.257 0.264 0.271

0.195 0.199 0.203 0.207 0.211

0.130 0.132 0.135 0.138 0.140

0.420 0.428 0.438 0.449 0.461

0.279 0.285 0.291 0.299 0.307

0.217 0.221 0.226 0.231 0.236

0.144 0.147 0.150 0.154 0.157

16 17 18 19 20

0.352 0.363 0.376 0.391 0.409

0.234 0.242 0.250 0.260 0.272

0.187 0.190 0.194 0.198 0.203

0.124 0.127 0.129 0.132 0.135

0.419 0.433 0.447 0.464 0.482

0.279 0.288 0.298 0.309 0.321

0.215 0.220 0.225 0.230 0.235

0.143 0.146 0.150 0.153 0.156

0.474 0.489 0.506 0.524 0.544

0.316 0.325 0.336 0.349 0.362

0.241 0.246 0.252 0.258 0.264

0.160 0.164 0.168 0.172 0.176

22 24 26 28 30

0.449 0.498 0.558 0.629 0.719

0.299 0.332 0.371 0.419 0.478

0.212 0.222 0.233 0.245 0.258

0.141 0.147 0.155 0.163 0.172

0.525 0.577 0.643 0.726 0.829

0.349 0.384 0.428 0.483 0.552

0.246 0.258 0.272 0.287 0.304

0.164 0.172 0.181 0.191 0.202

0.591 0.649 0.721 0.812 0.928

0.393 0.432 0.480 0.540 0.617

0.278 0.292 0.309 0.327 0.348

0.185 0.195 0.206 0.218 0.232

32 34 36 38 40

0.818 0.923 1.03 1.15 1.28

0.544 0.614 0.689 0.767 0.850

0.273 0.296 0.323 0.350 0.377

0.182 0.197 0.215 0.233 0.251

0.943 1.06 1.19 1.33 1.47

0.628 0.708 0.794 0.885 0.980

0.328 0.361 0.395 0.429 0.464

0.218 0.240 0.263 0.286 0.309

1.06 1.19 1.34 1.49 1.65

0.702 0.793 0.889 0.990 1.10

0.384 0.424 0.465 0.507 0.549

0.256 0.282 0.310 0.337 0.365

42 44 46 48 50

1.41 1.55 1.69 1.84 2.00

0.937 1.03 1.12 1.22 1.33

0.404 0.269 1.62 1.08 0.499 0.332 0.431 0.287 1.78 1.19 0.534 0.355 0.459 0.305 1.95 1.30 0.570 0.379 0.486 0.323 2.12 1.41 0.605 0.403 0.514 0.342 2.30 1.53 0.641 0.426 Other Constants and Properties 0.773 1.34 0.889

1.82 2.00 2.18 2.37 2.58

1.21 1.33 1.45 1.58 1.71

0.592 0.635 0.679 0.722 0.766

0.394 0.423 0.452 0.481 0.510

b y  103 (kip-ft)-1

1.16

t y  103 (kips)-1

0.261

t r  10 (kips) r x /r y

0.338

r y , in.

290c

335 3

3

W44

-1

0.174

0.301

0.226

0.390

1.51

1.00

0.200

0.333

0.221

0.260

0.432

0.288

5.10

5.10

5.10

3.49

3.49

3.47

c


v

Shape does not meet the h /t w limit for shear in AISC Specification Section G2.1(a) with F y = 65 ksi; therefore, v = 0.90 and v = 1.67.



IV-20


Combined Flexure and Axial Force W-Shapes

W44-W40 W44

Shape

h

230

b x  10

-1

503h

593 3

p  10

b x  10

p  10

b x  103

-1

p  10

0

(kips) (kip-ft) (kips) ASD LRFD ASD LRFD ASD LRFD 0.148 0.0982 0.0993 0.0661 0.174 0.116

(kip-ft)-1 ASD LRFD 0.118 0.0786

11 12 13 14 15

0.492 0.502 0.513 0.526 0.540

0.327 0.334 0.342 0.350 0.359

0.251 0.256 0.262 0.268 0.273

0.167 0.171 0.174 0.178 0.182

0.166 0.169 0.173 0.178 0.183

0.110 0.113 0.115 0.118 0.122

0.0993 0.0995 0.101 0.102 0.103

0.0661 0.0662 0.0669 0.0676 0.0684

0.196 0.200 0.205 0.211 0.217

0.130 0.133 0.137 0.140 0.144

0.118 0.119 0.120 0.122 0.123

0.0786 0.0791 0.0801 0.0811 0.0821

16 17 18 19 20

0.555 0.573 0.592 0.613 0.636

0.369 0.381 0.394 0.408 0.423

0.280 0.286 0.293 0.300 0.308

0.186 0.190 0.195 0.200 0.205

0.188 0.194 0.201 0.208 0.216

0.125 0.129 0.134 0.138 0.144

0.104 0.105 0.106 0.107 0.109

0.0691 0.0699 0.0707 0.0715 0.0723

0.224 0.231 0.239 0.248 0.258

0.149 0.154 0.159 0.165 0.172

0.125 0.127 0.128 0.130 0.132

0.0832 0.0843 0.0854 0.0866 0.0878

22 24 26 28 30

0.690 0.758 0.841 0.946 1.08

0.459 0.504 0.560 0.630 0.719

0.324 0.342 0.362 0.384 0.417

0.215 0.227 0.241 0.256 0.277

0.234 0.255 0.280 0.310 0.347

0.155 0.170 0.186 0.207 0.231

0.111 0.114 0.117 0.120 0.123

0.0740 0.0758 0.0777 0.0797 0.0817

0.280 0.307 0.339 0.377 0.423

0.186 0.204 0.225 0.251 0.281

0.136 0.140 0.144 0.148 0.153

0.0903 0.0929 0.0957 0.0986 0.102

32 34 36 38 40

1.23 1.39 1.56 1.73 1.92

0.818 0.924 1.04 1.15 1.28

0.466 0.516 0.568 0.621 0.674

0.310 0.343 0.378 0.413 0.449

0.390 0.441 0.494 0.551 0.610

0.260 0.293 0.329 0.366 0.406

0.126 0.130 0.133 0.137 0.141

0.0839 0.0862 0.0887 0.0912 0.0940

0.479 0.541 0.606 0.675 0.748

0.319 0.360 0.403 0.449 0.498

0.158 0.163 0.169 0.175 0.182

0.105 0.109 0.113 0.117 0.121

42 44 46 48 50

2.12 2.33 2.54 2.77 3.00

1.41 1.55 1.69 1.84 2.00


0.825 0.906 0.990 1.08 1.17

0.549 0.603 0.659 0.717 0.778

0.189 0.197 0.208 0.219 0.229

0.126 0.131 0.138 0.145 0.153

1.75

t y  103 (kips)-1

0.379

t r  103 (kips)-1 r x /r y

0.492

-1

3

(kip-ft) ASD LRFD 0.249 0.166

b y  103 (kip-ft)-1

-1

3

3

(kips) ASD LRFD 0.443 0.295

Design


W40

c,v

3

r y , in.

Fy = 65 ksi

0.252

0.148

0.328

0.192

-1

0.696

0.463

0.0982

0.174

0.116

0.128

0.225

0.150

5.10

4.47

4.52

3.43

3.80

3.72

c


h

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /t w limit for shear in AISC Specification Section G2.1(a) with F y = 65 ksi; therefore, v = 0.90 and v = 1.67.

v



IV-21



Fy = 65 ksi

W-Shapes W40

Shape

h

b x  10

3

p  10

-1


b x  10

p  10

b x  103

-1

0


(kip-ft)-1 ASD LRFD 0.160 0.107

11 12 13 14 15

0.229 0.235 0.241 0.247 0.255

0.152 0.156 0.160 0.165 0.170

0.140 0.141 0.143 0.145 0.147

0.0930 0.0939 0.0953 0.0967 0.0981

0.249 0.255 0.261 0.269 0.277

0.166 0.170 0.174 0.179 0.184

0.152 0.154 0.156 0.159 0.161

0.101 0.102 0.104 0.105 0.107

0.281 0.294 0.309 0.325 0.345

0.187 0.196 0.205 0.217 0.229

0.169 0.172 0.176 0.179 0.183

0.112 0.115 0.117 0.119 0.122

16 17 18 19 20

0.263 0.272 0.282 0.293 0.305

0.175 0.181 0.188 0.195 0.203

0.150 0.152 0.154 0.157 0.159

0.0995 0.101 0.103 0.104 0.106

0.286 0.296 0.307 0.319 0.332

0.190 0.197 0.204 0.212 0.221

0.164 0.166 0.169 0.172 0.175

0.109 0.111 0.112 0.114 0.116

0.366 0.391 0.418 0.450 0.486

0.244 0.260 0.278 0.299 0.323

0.187 0.191 0.195 0.199 0.204

0.124 0.127 0.130 0.133 0.136

22 24 26 28 30

0.333 0.366 0.405 0.453 0.510

0.221 0.243 0.270 0.301 0.339

0.164 0.170 0.176 0.182 0.189

0.109 0.113 0.117 0.121 0.126

0.362 0.398 0.441 0.494 0.556

0.241 0.265 0.294 0.328 0.370

0.181 0.187 0.194 0.202 0.210

0.120 0.125 0.129 0.134 0.140

0.574 0.683 0.801 0.929 1.07

0.382 0.454 0.533 0.618 0.710

0.214 0.224 0.236 0.250 0.265

0.142 0.149 0.157 0.166 0.176

32 34 36 38 40

0.580 0.655 0.734 0.818 0.906

0.386 0.436 0.488 0.544 0.603

0.196 0.204 0.213 0.222 0.234

0.131 0.136 0.142 0.148 0.155

0.633 0.714 0.801 0.892 0.989

0.421 0.475 0.533 0.594 0.658

0.219 0.228 0.239 0.250 0.268

0.146 0.152 0.159 0.167 0.178

1.21 1.37 1.54 1.71 1.90

0.807 0.911 1.02 1.14 1.26

0.285 0.307 0.329 0.350 0.372

0.189 0.204 0.219 0.233 0.248

42 44 46 48 50

0.999 1.10 1.20 1.30 1.42

0.665 0.729 0.797 0.868 0.942


2.09 2.29

1.39 1.53

0.394 0.415

0.262 0.276

0.836 0.202


0.262

-1

0.135

0.220

0.175

0.285

-1

p  10


t y  103 (kips)-1

-1

3

(kip-ft) (kips) ASD LRFD ASD LRFD 0.140 0.0930 0.220 0.146

b y  103 (kip-ft)-1

-1

392h 3

3


Design

r y , in.

397h

431 3

3

W40

1.32

0.877

0.146

0.221

0.147

0.190

0.287

0.192

4.55

4.56

6.10

3.65

3.64

2.64

h

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /r y equal to or greater than 200.



IV-22



W40

W40

Shape

h

362h

372

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.192 0.128

11 12 13 14 15

0.265 0.272 0.279 0.287 0.296

0.177 0.181 0.186 0.191 0.197

0.163 0.165 0.168 0.171 0.173

0.109 0.110 0.112 0.113 0.115

0.275 0.282 0.290 0.298 0.307

0.183 0.188 0.193 0.198 0.205

0.167 0.169 0.172 0.175 0.178

0.111 0.113 0.114 0.116 0.118

0.338 0.354 0.373 0.395 0.419

0.225 0.236 0.248 0.263 0.279

0.205 0.209 0.214 0.219 0.224

0.136 0.139 0.142 0.146 0.149

16 17 18 19 20

0.306 0.317 0.329 0.342 0.356

0.204 0.211 0.219 0.228 0.237

0.176 0.179 0.182 0.186 0.189

0.117 0.119 0.121 0.123 0.126

0.318 0.329 0.341 0.355 0.370

0.211 0.219 0.227 0.236 0.246

0.181 0.184 0.187 0.191 0.194

0.120 0.122 0.125 0.127 0.129

0.447 0.479 0.515 0.556 0.602

0.297 0.318 0.342 0.370 0.401

0.230 0.236 0.242 0.249 0.256

0.153 0.157 0.161 0.165 0.170

22 24 26 28 30

0.389 0.429 0.477 0.535 0.605

0.259 0.286 0.317 0.356 0.402

0.196 0.203 0.212 0.220 0.230

0.130 0.135 0.141 0.147 0.153

0.404 0.445 0.495 0.555 0.628

0.269 0.296 0.329 0.369 0.418

0.201 0.209 0.218 0.227 0.237

0.134 0.139 0.145 0.151 0.158

0.719 0.855 1.00 1.16 1.34

0.478 0.569 0.668 0.774 0.889

0.270 0.287 0.306 0.330 0.362

0.180 0.191 0.204 0.220 0.241

32 34 36 38 40

0.688 0.777 0.871 0.970 1.08

0.458 0.517 0.579 0.646 0.715

0.241 0.252 0.265 0.284 0.304

0.160 0.168 0.176 0.189 0.202

0.714 0.806 0.904 1.01 1.12

0.475 0.536 0.601 0.670 0.742

0.249 0.261 0.274 0.295 0.316

0.165 0.174 0.182 0.196 0.210

1.52 1.72 1.92 2.14 2.38

1.01 1.14 1.28 1.43 1.58

0.393 0.425 0.456 0.488 0.519

0.262 0.283 0.304 0.324 0.345

42 44 46 48 50

1.19 1.30 1.42 1.55 1.68

0.789 0.866 0.946 1.03 1.12

0.324 0.216 1.23 0.818 0.337 0.344 0.229 1.35 0.898 0.358 0.365 0.243 1.48 0.982 0.380 0.385 0.256 1.61 1.07 0.401 0.405 0.270 1.74 1.16 0.422 Other Constants and Properties

0.224 0.238 0.253 0.267 0.281

2.62

1.74

0.550

0.366

0

-1

331h 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

0.989

0.658

1.02

0.675

1.62

1.08

t y  103 (kips)-1

0.234

0.155

0.242

0.161

0.263

0.175

t r  103 (kips)-1 r x /r y

0.303

0.202

0.314

0.210

0.341

r y , in.

0.227

4.58

4.58

6.19

3.60

3.60

2.57

h




IV-23



Fy = 65 ksi

W-Shapes W40

Shape

h

b x  10

3

p  10

-1


b x  103


(kip-ft)-1 ASD LRFD 0.206 0.137

11 12 13 14 15

0.344 0.360 0.379 0.401 0.426

0.229 0.240 0.252 0.267 0.283

0.207 0.212 0.217 0.222 0.227

0.138 0.141 0.144 0.148 0.151

0.309 0.315 0.323 0.332 0.343

0.205 0.210 0.215 0.221 0.228

0.188 0.191 0.194 0.197 0.201

0.125 0.127 0.129 0.131 0.134

0.343 0.351 0.359 0.369 0.379

0.228 0.233 0.239 0.245 0.252

0.206 0.210 0.214 0.218 0.222

0.137 0.140 0.142 0.145 0.147

16 17 18 19 20

0.454 0.485 0.522 0.563 0.610

0.302 0.323 0.347 0.374 0.406

0.233 0.239 0.245 0.252 0.259

0.155 0.159 0.163 0.168 0.172

0.354 0.367 0.381 0.396 0.413

0.236 0.244 0.254 0.264 0.275

0.204 0.208 0.212 0.216 0.220

0.136 0.138 0.141 0.144 0.147

0.391 0.404 0.419 0.437 0.456

0.260 0.268 0.279 0.290 0.303

0.226 0.230 0.235 0.240 0.245

0.150 0.153 0.156 0.159 0.163

22 24 26 28 30

0.726 0.864 1.01 1.18 1.35

0.483 0.575 0.675 0.783 0.899

0.274 0.291 0.310 0.334 0.366

0.182 0.194 0.206 0.222 0.244

0.452 0.499 0.555 0.623 0.706

0.301 0.332 0.369 0.414 0.470

0.229 0.239 0.250 0.261 0.274

0.153 0.159 0.166 0.174 0.182

0.499 0.552 0.616 0.693 0.788

0.332 0.367 0.410 0.461 0.524

0.255 0.267 0.280 0.294 0.309

0.170 0.178 0.186 0.195 0.206

32 34 36 38 40

1.54 1.73 1.95 2.17 2.40

1.02 1.15 1.29 1.44 1.60

0.398 0.430 0.462 0.494 0.526

0.265 0.286 0.307 0.329 0.350

0.803 0.907 1.02 1.13 1.25

0.534 0.603 0.676 0.754 0.835

0.288 0.303 0.329 0.355 0.382

0.192 0.202 0.219 0.236 0.254

0.897 1.01 1.13 1.26 1.40

0.597 0.674 0.755 0.841 0.932

0.326 0.352 0.383 0.414 0.446

0.217 0.234 0.255 0.276 0.297

42 44 46 48 50

2.65

1.76

0.557

0.371

1.54 1.70 1.85 2.02 2.19

1.03 1.13 1.23 1.34 1.46

0.478 0.509 0.541 0.573 0.605

0.318 0.339 0.360 0.381 0.403

1.63 0.268


0.348

-1

-1

-1


t y  103 (kips)-1

-1

p  10


b y  103 (kip-ft)-1

r y , in.

b x  10

p  10

3


0

-1

297c 3

3


Design

c

324c

327 3

3

W40

1.38 0.921 0.408 0.272 1.52 1.01 0.435 0.289 1.66 1.10 0.461 0.307 1.81 1.20 0.488 0.324 1.96 1.30 0.514 0.342 Other Constants and Properties 1.09 1.15 0.763 0.178

0.270

0.232

0.350

1.27

0.848

0.179

0.294

0.196

0.233

0.382

0.255

6.20

4.58

4.60

2.58

3.58

3.54


h




IV-24



W40

W40

Shape

c

278c

294

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.219 0.146

11 12 13 14 15

0.385 0.404 0.425 0.450 0.479

0.256 0.269 0.283 0.300 0.318

0.232 0.238 0.244 0.250 0.257

0.154 0.158 0.162 0.166 0.171

0.405 0.426 0.449 0.476 0.507

0.270 0.283 0.299 0.317 0.337

0.249 0.255 0.262 0.269 0.276

0.165 0.170 0.174 0.179 0.184

0.375 0.383 0.392 0.402 0.413

0.250 0.255 0.261 0.267 0.275

0.219 0.223 0.227 0.231 0.236

0.146 0.148 0.151 0.154 0.157

16 17 18 19 20

0.511 0.548 0.590 0.637 0.692

0.340 0.364 0.392 0.424 0.460

0.264 0.271 0.279 0.287 0.296

0.175 0.180 0.185 0.191 0.197

0.542 0.582 0.628 0.680 0.739

0.361 0.387 0.418 0.452 0.492

0.284 0.292 0.301 0.310 0.320

0.189 0.194 0.200 0.206 0.213

0.425 0.438 0.453 0.469 0.488

0.283 0.292 0.301 0.312 0.324

0.240 0.245 0.250 0.255 0.261

0.160 0.163 0.166 0.170 0.173

22 24 26 28 30

0.827 0.985 1.16 1.34 1.54

0.550 0.655 0.769 0.892 1.02

0.315 0.337 0.363 0.402 0.442

0.210 0.224 0.241 0.268 0.294

0.887 1.06 1.24 1.44 1.65

0.590 0.702 0.824 0.956 1.10

0.342 0.367 0.401 0.445 0.490

0.227 0.244 0.267 0.296 0.326

0.530 0.583 0.649 0.728 0.825

0.352 0.388 0.432 0.485 0.549

0.272 0.285 0.299 0.314 0.331

0.181 0.190 0.199 0.209 0.220

32 34 36 38 40

1.75 1.98 2.22 2.47 2.73

1.16 1.31 1.47 1.64 1.82

0.482 0.521 0.561 0.601 0.640

0.320 0.347 0.373 0.400 0.426

1.88 2.12 2.38 2.65 2.93

1.25 1.41 1.58 1.76 1.95

0.535 0.580 0.624 0.669 0.714

0.356 0.386 0.415 0.445 0.475

0.939 1.06 1.19 1.32 1.47

0.625 0.705 0.791 0.881 0.976

0.350 0.380 0.414 0.449 0.484

0.233 0.253 0.276 0.299 0.322

42 44 46 48 50

3.02

2.01

0.679

0.452

3.23

2.15

0.758

0.504

1.62 1.78 1.94 2.11 2.29

1.08 1.18 1.29 1.41 1.53

0.519 0.555 0.590 0.625 0.661

0.345 0.369 0.393 0.416 0.440

0

-1

277c 3

3


Design


Fy = 65 ksi

Other Constants and Properties b y  103 (kip-ft)-1

1.83

1.22

1.97

1.31

1.34

0.894

t y  103 (kips)-1

0.298

0.198

0.312

0.208

0.315

0.210

t r  103 (kips)-1 r x /r y

0.387

0.258

0.405

0.270

0.409

r y , in.

0.273

6.24

6.27

4.58

2.55

2.52

3.58

c




IV-25



Fy = 65 ksi

W-Shapes W40

Shape

c

b x  10

3

p  10

-1


b x  10

p  10

b x  103

-1



(kip-ft)-1 ASD LRFD 0.271 0.181

11 12 13 14 15

0.431 0.453 0.478 0.506 0.539

0.287 0.301 0.318 0.337 0.359

0.262 0.269 0.276 0.284 0.292

0.174 0.179 0.184 0.189 0.194

0.426 0.435 0.445 0.456 0.468

0.283 0.289 0.296 0.303 0.311

0.245 0.249 0.254 0.259 0.264

0.163 0.166 0.169 0.172 0.176

0.496 0.518 0.542 0.570 0.603

0.330 0.344 0.361 0.379 0.401

0.294 0.302 0.310 0.319 0.329

0.196 0.201 0.207 0.213 0.219

16 17 18 19 20

0.576 0.619 0.667 0.723 0.786

0.383 0.412 0.444 0.481 0.523

0.301 0.310 0.319 0.330 0.340

0.200 0.206 0.212 0.219 0.227

0.482 0.497 0.513 0.532 0.552

0.321 0.331 0.342 0.354 0.367

0.270 0.275 0.281 0.287 0.294

0.179 0.183 0.187 0.191 0.195

0.640 0.686 0.739 0.800 0.869

0.426 0.457 0.492 0.532 0.578

0.339 0.350 0.361 0.373 0.386

0.226 0.233 0.240 0.248 0.257

22 24 26 28 30

0.943 1.12 1.32 1.53 1.75

0.628 0.747 0.877 1.02 1.17

0.365 0.392 0.434 0.483 0.533

0.243 0.261 0.289 0.322 0.354

0.599 0.657 0.729 0.819 0.931

0.399 0.437 0.485 0.545 0.619

0.307 0.322 0.339 0.357 0.377

0.204 0.214 0.225 0.238 0.251

1.04 1.24 1.45 1.68 1.93

0.692 0.824 0.967 1.12 1.29

0.415 0.451 0.510 0.569 0.629

0.276 0.300 0.339 0.379 0.419

32 34 36 38 40

2.00 2.25 2.53 2.81 3.12

1.33 1.50 1.68 1.87 2.07

0.582 0.632 0.681 0.730 0.780

0.387 0.420 0.453 0.486 0.519

1.06 1.20 1.34 1.49 1.65

0.705 0.795 0.892 0.994 1.10

0.405 0.446 0.488 0.530 0.573

0.270 0.297 0.325 0.353 0.381

2.20 2.48 2.79 3.10 3.44

1.46 1.65 1.85 2.06 2.29

0.690 0.750 0.811 0.872 0.932

0.459 0.499 0.540 0.580 0.620

42 44 46 48 50

3.44

2.29

0.829

0.552

1.82 1.21 0.616 0.410 2.00 1.33 0.659 0.438 2.19 1.46 0.702 0.467 2.38 1.59 0.746 0.496 2.59 1.72 0.790 0.525 Other Constants and Properties 1.38 1.51 1.00

3.79

2.52

0.993

0.661

2.08

t y  103 (kips)-1

0.332


0.431

-1

0.221

0.350

0.287

0.454

-1

p  10


b y  103 (kip-ft)-1

-1

3


0

-1

235c 3

3


Design

r y , in.

249c

264 3

3

W40

2.32

1.55

0.233

0.372

0.247

0.302

0.482

0.322

6.27

4.59

6.26

2.52

3.55

2.54

c




IV-26



W40

W40

Shape

c,v

211c

215

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.315 0.210

11 12 13 14 15

0.508 0.519 0.530 0.543 0.557

0.338 0.345 0.353 0.361 0.371

0.284 0.290 0.296 0.302 0.308

0.189 0.193 0.197 0.201 0.205

0.568 0.592 0.619 0.651 0.688

0.378 0.394 0.412 0.433 0.458

0.330 0.339 0.350 0.360 0.372

0.219 0.226 0.233 0.240 0.247

0.556 0.568 0.581 0.596 0.612

0.370 0.378 0.387 0.396 0.407

0.317 0.324 0.331 0.338 0.346

0.211 0.216 0.220 0.225 0.230

16 17 18 19 20

0.573 0.590 0.609 0.630 0.654

0.381 0.393 0.405 0.419 0.435

0.315 0.322 0.329 0.336 0.344

0.209 0.214 0.219 0.224 0.229

0.731 0.781 0.838 0.906 0.987

0.486 0.519 0.558 0.603 0.656

0.384 0.397 0.411 0.426 0.442

0.255 0.264 0.273 0.283 0.294

0.630 0.649 0.671 0.696 0.723

0.419 0.432 0.447 0.463 0.481

0.353 0.362 0.370 0.379 0.389

0.235 0.241 0.246 0.252 0.259

22 24 26 28 30

0.708 0.774 0.855 0.956 1.08

0.471 0.515 0.569 0.636 0.721

0.361 0.380 0.401 0.424 0.450

0.240 0.253 0.267 0.282 0.300

1.19 1.41 1.66 1.92 2.20

0.789 0.938 1.10 1.28 1.47

0.478 0.535 0.606 0.679 0.753

0.318 0.356 0.403 0.452 0.501

0.785 0.863 0.959 1.08 1.23

0.523 0.574 0.638 0.718 0.820

0.409 0.432 0.458 0.486 0.526

0.272 0.287 0.304 0.323 0.350

32 34 36 38 40

1.23 1.39 1.56 1.74 1.93

0.820 0.926 1.04 1.16 1.28

0.497 0.549 0.603 0.657 0.712

0.331 0.365 0.401 0.437 0.474

2.51 2.83 3.17 3.54 3.92

1.67 1.88 2.11 2.35 2.61

0.827 0.902 0.978 1.05 1.13

0.550 0.600 0.650 0.701 0.751

1.40 1.58 1.77 1.98 2.19

0.933 1.05 1.18 1.32 1.46

0.588 0.651 0.716 0.782 0.849

0.391 0.433 0.476 0.520 0.565

42 44 46 48 50

2.12 2.33 2.55 2.77 3.01

1.41 1.55 1.69 1.85 2.00

0.768 0.511 0.825 0.549 0.882 0.587 0.939 0.625 0.997 0.663 Other Constants and Properties

2.41 2.65 2.90 3.15 3.42

1.61 1.76 1.93 2.10 2.28

0.918 0.987 1.06 1.13 1.20

0.610 0.657 0.703 0.750 0.797

0

-1

199c,v 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

1.76

1.17

2.61

1.74

2.00

1.33

t y  103 (kips)-1

0.405

0.269

0.414

0.275

0.437

0.291

t r  103 (kips)-1 r x /r y

0.525

0.350

0.537

0.358

0.567

r y , in.

0.378

4.58

6.29

4.64

3.54

2.51

3.45

c


v





IV-27



Fy = 65 ksi

W-Shapes W40

Shape

c,v

b x  10

3

p  10

-1

b x  10

p  10

b x  103

-1



(kip-ft)-1 ASD LRFD 0.458 0.305

11 12 13 14 15

0.685 0.713 0.746 0.783 0.826

0.456 0.475 0.496 0.521 0.550

0.389 0.401 0.413 0.427 0.441

0.259 0.267 0.275 0.284 0.293

0.758 0.791 0.829 0.874 0.925

0.504 0.526 0.552 0.581 0.616

0.440 0.454 0.470 0.486 0.504

0.293 0.302 0.312 0.323 0.335

0.886 0.927 0.976 1.03 1.10

0.590 0.617 0.649 0.687 0.731

0.520 0.538 0.558 0.579 0.602

0.346 0.358 0.371 0.385 0.401

16 17 18 19 20

0.876 0.933 1.00 1.08 1.17

0.583 0.621 0.665 0.717 0.778

0.457 0.473 0.491 0.510 0.531

0.304 0.315 0.327 0.339 0.353

0.985 1.06 1.14 1.23 1.35

0.656 0.702 0.757 0.821 0.898

0.523 0.543 0.565 0.589 0.615

0.348 0.361 0.376 0.392 0.409

1.18 1.27 1.38 1.51 1.67

0.782 0.844 0.916 1.00 1.11

0.627 0.654 0.684 0.716 0.752

0.417 0.435 0.455 0.477 0.500

22 24 26 28 30

1.40 1.67 1.96 2.27 2.61

0.934 1.11 1.30 1.51 1.74

0.577 0.669 0.763 0.859 0.957

0.384 0.445 0.507 0.571 0.636

1.63 1.94 2.28 2.65 3.04

1.09 1.29 1.52 1.76 2.02

0.693 0.804 0.919 1.04 1.16

0.461 0.535 0.611 0.690 0.771

2.02 2.40 2.82 3.27 3.75

1.34 1.60 1.88 2.18 2.50

0.882 1.03 1.18 1.33 1.49

0.587 0.683 0.783 0.887 0.993

32 34 36 38 40

2.97 3.35 3.76 4.19 4.64

1.98 2.23 2.50 2.79 3.09

1.06 1.16 1.26 1.36 1.46

0.702 0.769 0.837 0.905 0.973

3.45 3.90 4.37 4.87 5.40

2.30 2.59 2.91 3.24 3.59

1.28 1.41 1.53 1.66 1.79

0.853 0.937 1.02 1.11 1.19

4.27 4.82 5.41 6.02

2.84 3.21 3.60 4.01

1.66 1.82 1.99 2.16

1.10 1.21 1.33 1.44

3.10

t y  103 (kips)-1

0.482

t r  103 (kips)-1 r x /r y

0.625

-1

p  10


b y  103 (kip-ft)-1

-1

3


0

-1

149c,v 3

3


Design


167c,v

183 3

r y , in.

W40

Other Constants and Properties 2.06 3.61 2.40 0.321

0.521

0.417

0.676

4.41

2.94

0.347

0.587

0.390

0.451

0.761

0.507

6.31

6.38

6.55

2.49

2.40

2.29

c


v





IV-28



W36

W36

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

487h 3

3

-1

3

b x  103

-1

p  10

0

(kips) (kip-ft) (kips) ASD LRFD ASD LRFD ASD LRFD 0.134 0.0890 0.0942 0.0627 0.165 0.110


(kip-ft)-1 ASD LRFD 0.129 0.0856

11 12 13 14 15

0.148 0.150 0.154 0.157 0.161

0.0982 0.100 0.102 0.104 0.107

0.0942 0.0942 0.0944 0.0952 0.0961

0.0627 0.0627 0.0628 0.0634 0.0639

0.183 0.186 0.190 0.195 0.200

0.122 0.124 0.127 0.130 0.133

0.118 0.118 0.118 0.120 0.121

0.0783 0.0783 0.0787 0.0796 0.0804

0.200 0.204 0.208 0.213 0.219

0.133 0.136 0.139 0.142 0.145

0.129 0.129 0.130 0.131 0.133

0.0856 0.0856 0.0863 0.0873 0.0883

16 17 18 19 20

0.165 0.169 0.174 0.180 0.185

0.110 0.113 0.116 0.119 0.123

0.0969 0.0977 0.0986 0.0995 0.100

0.0645 0.0650 0.0656 0.0662 0.0668

0.205 0.211 0.217 0.224 0.232

0.136 0.140 0.145 0.149 0.154

0.122 0.124 0.125 0.126 0.128

0.0813 0.0822 0.0831 0.0841 0.0850

0.225 0.231 0.238 0.246 0.255

0.149 0.154 0.159 0.164 0.169

0.134 0.136 0.137 0.139 0.141

0.0893 0.0904 0.0915 0.0926 0.0937

22 24 26 28 30

0.198 0.214 0.232 0.253 0.278

0.132 0.142 0.154 0.169 0.185

0.102 0.104 0.106 0.108 0.110

0.0680 0.0693 0.0706 0.0720 0.0734

0.249 0.270 0.294 0.322 0.356

0.166 0.179 0.195 0.214 0.237

0.131 0.134 0.137 0.141 0.144

0.0870 0.0890 0.0912 0.0935 0.0959

0.274 0.297 0.324 0.356 0.394

0.182 0.198 0.216 0.237 0.262

0.144 0.148 0.152 0.156 0.161

0.0961 0.0986 0.101 0.104 0.107

32 34 36 38 40

0.308 0.343 0.385 0.429 0.475

0.205 0.228 0.256 0.285 0.316

0.113 0.115 0.117 0.120 0.123

0.0749 0.0765 0.0781 0.0798 0.0816

0.395 0.444 0.497 0.554 0.614

0.263 0.295 0.331 0.369 0.409

0.148 0.152 0.156 0.161 0.165

0.0984 0.101 0.104 0.107 0.110

0.439 0.494 0.554 0.617 0.684

0.292 0.329 0.368 0.410 0.455

0.165 0.170 0.175 0.181 0.187

0.110 0.113 0.117 0.120 0.124

42 44 46 48 50

0.524 0.575 0.628 0.684 0.742

0.348 0.382 0.418 0.455 0.494


0.113 0.117 0.121 0.125 0.129

0.754 0.827 0.904 0.984 1.07

0.501 0.550 0.601 0.655 0.711

0.193 0.200 0.207 0.215 0.226

0.128 0.133 0.138 0.143 0.150

Design


529h

652 3

-1

b y  103 (kip-ft)-1

0.472

0.314

0.604

0.402

0.665

0.443

t y  103 (kips)-1

0.134

0.0890

0.165

0.110

0.180

0.120

t r  103 (kips)-1 r x /r y

0.174

0.116

0.214

0.142

0.233

r y , in. h

Fy = 65 ksi

0.155

3.95

4.00

3.99

4.10

4.00

3.96

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.



IV-29



Fy = 65 ksi

W-Shapes W36

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

361h 3

3

-1

-1

3

b x  103

-1

p  10

0





(kip-ft)-1 ASD LRFD 0.177 0.118

11 12 13 14 15

0.220 0.225 0.230 0.235 0.241

0.146 0.149 0.153 0.157 0.161

0.143 0.143 0.143 0.143 0.143

0.0955 0.0955 0.0955 0.0955 0.0955

0.247 0.252 0.258 0.265 0.272

0.164 0.168 0.172 0.176 0.181

0.160 0.160 0.162 0.165 0.167

0.107 0.107 0.108 0.110 0.111

0.271 0.277 0.283 0.290 0.298

0.180 0.184 0.189 0.193 0.199

0.177 0.177 0.180 0.182 0.185

0.118 0.118 0.120 0.121 0.123

16 17 18 19 20

0.248 0.256 0.264 0.273 0.282

0.165 0.170 0.175 0.181 0.188

0.143 0.143 0.143 0.143 0.143

0.0955 0.0955 0.0955 0.0955 0.0955

0.280 0.288 0.297 0.308 0.319

0.186 0.192 0.198 0.205 0.212

0.169 0.172 0.174 0.177 0.179

0.113 0.114 0.116 0.118 0.119

0.307 0.317 0.327 0.338 0.351

0.204 0.211 0.218 0.225 0.233

0.188 0.191 0.194 0.197 0.200

0.125 0.127 0.129 0.131 0.133

22 24 26 28 30

0.304 0.330 0.361 0.397 0.441

0.202 0.220 0.240 0.264 0.293

0.143 0.143 0.143 0.143 0.143

0.0955 0.0955 0.0955 0.0955 0.0955

0.344 0.374 0.410 0.452 0.502

0.229 0.249 0.272 0.301 0.334

0.185 0.191 0.197 0.204 0.211

0.123 0.127 0.131 0.135 0.140

0.379 0.413 0.452 0.500 0.556

0.252 0.274 0.301 0.333 0.370

0.206 0.213 0.221 0.229 0.238

0.137 0.142 0.147 0.152 0.158

32 34 36 38 40

0.492 0.554 0.622 0.693 0.767

0.327 0.369 0.414 0.461 0.511

0.154 0.168 0.181 0.194 0.207

0.103 0.111 0.120 0.129 0.138

0.562 0.634 0.711 0.792 0.878

0.374 0.422 0.473 0.527 0.584

0.218 0.227 0.236 0.245 0.256

0.145 0.151 0.157 0.163 0.170

0.624 0.705 0.790 0.880 0.976

0.415 0.469 0.526 0.586 0.649

0.247 0.258 0.269 0.281 0.296

0.165 0.171 0.179 0.187 0.197

42 44 46 48 50

0.846 0.928 1.01 1.10 1.20

0.563 0.618 0.675 0.735 0.798


0.179 0.190 0.201 0.212 0.222

1.08 1.18 1.29 1.40 1.52

0.716 0.785 0.858 0.935 1.01

0.316 0.336 0.356 0.376 0.395

0.210 0.224 0.237 0.250 0.263

Design


395h

441 3

b y  103 (kip-ft)-1

0.745

0.495

0.843

0.561

0.935

0.622

t y  103 (kips)-1

0.198

0.131

0.221

0.147

0.242

0.161

t r  103 (kips)-1 r x /r y

0.256

0.171

0.287

0.192

0.314

r y , in. h

W36

0.210

4.01

4.05

4.05

3.92

3.88

3.85




IV-30



W36

W36

Shape

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.230 0.153

11 12 13 14 15

0.297 0.303 0.310 0.318 0.327

0.197 0.202 0.207 0.212 0.218

0.194 0.195 0.198 0.201 0.204

0.129 0.130 0.131 0.134 0.136

0.325 0.331 0.338 0.347 0.357

0.216 0.221 0.225 0.231 0.237

0.214 0.215 0.218 0.222 0.225

0.142 0.143 0.145 0.148 0.150

0.354 0.361 0.369 0.377 0.387

0.236 0.240 0.245 0.251 0.257

0.230 0.231 0.235 0.239 0.243

0.153 0.154 0.156 0.159 0.162

16 17 18 19 20

0.337 0.347 0.359 0.371 0.385

0.224 0.231 0.239 0.247 0.256

0.207 0.210 0.214 0.218 0.221

0.138 0.140 0.142 0.145 0.147

0.367 0.379 0.391 0.405 0.420

0.244 0.252 0.260 0.269 0.280

0.229 0.233 0.237 0.241 0.245

0.152 0.155 0.158 0.160 0.163

0.397 0.408 0.421 0.436 0.453

0.264 0.272 0.280 0.290 0.301

0.247 0.252 0.256 0.261 0.266

0.164 0.167 0.170 0.174 0.177

22 24 26 28 30

0.417 0.454 0.498 0.551 0.614

0.277 0.302 0.331 0.367 0.409

0.229 0.238 0.247 0.256 0.267

0.152 0.158 0.164 0.171 0.178

0.455 0.496 0.544 0.602 0.671

0.302 0.330 0.362 0.401 0.447

0.255 0.264 0.275 0.286 0.299

0.169 0.176 0.183 0.191 0.199

0.490 0.535 0.588 0.652 0.727

0.326 0.356 0.391 0.434 0.484

0.276 0.287 0.299 0.313 0.327

0.184 0.191 0.199 0.208 0.218

32 34 36 38 40

0.690 0.779 0.874 0.973 1.08

0.459 0.518 0.581 0.648 0.717

0.278 0.291 0.305 0.322 0.346

0.185 0.194 0.203 0.214 0.230

0.755 0.853 0.956 1.07 1.18

0.503 0.567 0.636 0.709 0.785

0.313 0.327 0.344 0.371 0.399

0.208 0.218 0.229 0.247 0.266

0.820 0.925 1.04 1.16 1.28

0.545 0.616 0.690 0.769 0.852

0.343 0.361 0.385 0.417 0.449

0.228 0.240 0.256 0.277 0.299

42 44 46 48 50

1.19 1.30 1.43 1.55 1.69

0.791 0.868 0.949 1.03 1.12


0.284 0.303 0.322 0.341 0.360

1.41 1.55 1.69 1.84 2.00

0.939 1.03 1.13 1.23 1.33

0.482 0.514 0.547 0.580 0.612

0.320 0.342 0.364 0.386 0.407

0

-1

282c 3

3


Design


302c

330 3

b y  103 (kip-ft)-1

1.03

0.688

1.14

0.757

1.23

t y  103 (kips)-1

0.265

0.176

0.289

0.192

0.310

0.206

t r  103 (kips)-1 r x /r y

0.344

0.229

0.375

0.250

0.402

0.268

r y , in. c

Fy = 65 ksi

0.818

4.05

4.03

4.05

3.83

3.82

3.80




IV-31



Fy = 65 ksi

W-Shapes W36

Shape

c

256c

262

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.266 0.177

11 12 13 14 15

0.386 0.393 0.402 0.411 0.421

0.257 0.262 0.267 0.273 0.280

0.249 0.251 0.255 0.260 0.264

0.166 0.167 0.170 0.173 0.176

0.432 0.452 0.474 0.500 0.529

0.287 0.301 0.316 0.333 0.352

0.281 0.288 0.295 0.302 0.310

0.187 0.191 0.196 0.201 0.206

0.416 0.424 0.433 0.443 0.454

0.277 0.282 0.288 0.295 0.302

0.266 0.268 0.273 0.278 0.283

0.177 0.178 0.181 0.185 0.188

16 17 18 19 20

0.433 0.445 0.459 0.474 0.491

0.288 0.296 0.305 0.315 0.327

0.269 0.274 0.279 0.285 0.291

0.179 0.182 0.186 0.190 0.193

0.562 0.599 0.642 0.690 0.744

0.374 0.399 0.427 0.459 0.495

0.319 0.327 0.337 0.347 0.357

0.212 0.218 0.224 0.231 0.238

0.466 0.479 0.494 0.511 0.528

0.310 0.319 0.329 0.340 0.352

0.288 0.294 0.300 0.306 0.312

0.192 0.195 0.199 0.203 0.208

22 24 26 28 30

0.532 0.581 0.640 0.711 0.795

0.354 0.387 0.426 0.473 0.529

0.302 0.315 0.330 0.345 0.362

0.201 0.210 0.219 0.230 0.241

0.877 1.04 1.22 1.42 1.63

0.583 0.694 0.815 0.945 1.08

0.380 0.406 0.436 0.484 0.533

0.253 0.270 0.290 0.322 0.355

0.570 0.623 0.687 0.763 0.855

0.379 0.414 0.457 0.508 0.569

0.325 0.340 0.356 0.373 0.392

0.216 0.226 0.237 0.248 0.261

32 34 36 38 40

0.899 1.01 1.14 1.27 1.40

0.598 0.675 0.757 0.843 0.934

0.381 0.402 0.438 0.475 0.513

0.253 0.267 0.291 0.316 0.341

1.86 2.09 2.35 2.62 2.90

1.23 1.39 1.56 1.74 1.93

0.582 0.632 0.681 0.730 0.779

0.387 0.420 0.453 0.486 0.519

0.967 1.09 1.22 1.36 1.51

0.644 0.727 0.815 0.908 1.01

0.414 0.444 0.485 0.528 0.570

0.275 0.295 0.323 0.351 0.379

42 44 46 48 50

1.55 1.70 1.86 2.02 2.19

1.03 1.13 1.24 1.35 1.46

0.551 0.367 3.20 2.13 0.828 0.589 0.392 3.51 2.33 0.877 0.628 0.418 0.666 0.443 0.705 0.469 Other Constants and Properties

0.551 0.584

1.67 1.83 2.00 2.18 2.36

1.11 1.22 1.33 1.45 1.57

0.613 0.657 0.700 0.744 0.788

0.408 0.437 0.466 0.495 0.524

0

-1

247c 3

3


Design


W36

b y  103 (kip-ft)-1

1.34

0.894

2.00

1.33

1.44

t y  103 (kips)-1

0.333

0.221

0.341

0.227

0.354

0.236

t r  103 (kips)-1 r x /r y

0.432

0.288

0.443

0.295

0.460

0.307

r y , in.

0.960

4.07

5.62

4.06

3.76

2.65

3.74

c




IV-32



W36

W36

Shape

c

231c

232

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.329 0.219

11 12 13 14 15

0.487 0.507 0.530 0.559 0.592

0.324 0.337 0.353 0.372 0.394

0.314 0.322 0.330 0.339 0.349

0.209 0.214 0.220 0.226 0.232

0.448 0.457 0.466 0.477 0.489

0.298 0.304 0.310 0.317 0.325

0.285 0.287 0.292 0.298 0.304

0.189 0.191 0.195 0.198 0.202

0.545 0.567 0.594 0.624 0.659

0.363 0.378 0.395 0.415 0.439

0.355 0.365 0.376 0.386 0.398

0.236 0.243 0.250 0.257 0.265

16 17 18 19 20

0.629 0.672 0.721 0.776 0.839

0.419 0.447 0.480 0.516 0.558

0.359 0.369 0.380 0.392 0.405

0.239 0.246 0.253 0.261 0.269

0.502 0.517 0.533 0.550 0.570

0.334 0.344 0.354 0.366 0.379

0.309 0.316 0.322 0.329 0.336

0.206 0.210 0.214 0.219 0.223

0.703 0.752 0.808 0.872 0.945

0.467 0.500 0.538 0.580 0.629

0.410 0.423 0.437 0.452 0.468

0.273 0.282 0.291 0.301 0.311

22 24 26 28 30

0.993 1.18 1.39 1.61 1.85

0.661 0.787 0.923 1.07 1.23

0.432 0.464 0.512 0.571 0.631

0.288 0.309 0.341 0.380 0.420

0.614 0.669 0.738 0.822 0.922

0.409 0.445 0.491 0.547 0.613

0.350 0.367 0.384 0.404 0.425

0.233 0.244 0.256 0.269 0.283

1.13 1.34 1.57 1.82 2.09

0.749 0.891 1.05 1.21 1.39

0.503 0.545 0.616 0.690 0.765

0.335 0.362 0.410 0.459 0.509

32 34 36 38 40

2.10 2.37 2.66 2.96 3.28

1.40 1.58 1.77 1.97 2.18

0.691 0.751 0.812 0.872 0.932

0.460 0.500 0.540 0.580 0.620

1.05 1.18 1.32 1.47 1.63

0.695 0.785 0.880 0.981 1.09

0.449 0.489 0.536 0.583 0.631

0.299 0.326 0.357 0.388 0.420

2.38 2.69 3.01 3.36 3.72

1.58 1.79 2.00 2.23 2.48

0.841 0.917 0.993 1.07 1.15

0.559 0.610 0.661 0.712 0.763

42 44 46 48 50

3.62

2.41

0.992

0.660

1.80 1.20 0.680 1.98 1.31 0.729 2.16 1.44 0.778 2.35 1.56 0.828 2.55 1.70 0.878 Other Constants and Properties

0.452 0.485 0.518 0.551 0.584

4.10

2.73

1.22

0.814

0

-1

210c 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

2.25

1.49

1.56

1.04

2.56

1.70

t y  103 (kips)-1

0.378

0.251

0.377

0.251

0.415

0.276

t r  103 (kips)-1 r x /r y

0.490

0.327

0.489

0.326

0.539

r y , in.

0.359

5.65

4.07

5.66

2.62

3.71

2.58

c




IV-33



Fy = 65 ksi

W-Shapes W36

Shape

c

182c

194

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.410 0.273

11 12 13 14 15

0.605 0.630 0.658 0.691 0.730

0.403 0.419 0.438 0.460 0.485

0.388 0.399 0.410 0.423 0.436

0.258 0.265 0.273 0.281 0.290

0.653 0.680 0.710 0.745 0.786

0.435 0.452 0.472 0.496 0.523

0.415 0.427 0.440 0.454 0.468

0.276 0.284 0.293 0.302 0.311

0.713 0.742 0.775 0.813 0.857

0.474 0.493 0.516 0.541 0.570

0.448 0.461 0.476 0.491 0.507

0.298 0.307 0.317 0.327 0.337

16 17 18 19 20

0.774 0.824 0.887 0.958 1.04

0.515 0.548 0.590 0.637 0.691

0.450 0.465 0.481 0.498 0.516

0.299 0.309 0.320 0.331 0.343

0.833 0.887 0.950 1.02 1.11

0.554 0.590 0.632 0.682 0.740

0.484 0.500 0.518 0.537 0.557

0.322 0.333 0.344 0.357 0.371

0.908 0.967 1.04 1.11 1.21

0.604 0.643 0.689 0.742 0.804

0.524 0.543 0.563 0.584 0.607

0.349 0.361 0.374 0.389 0.404

22 24 26 28 30

1.24 1.48 1.73 2.01 2.31

0.826 0.983 1.15 1.34 1.54

0.557 0.616 0.700 0.786 0.873

0.370 0.410 0.466 0.523 0.581

1.33 1.58 1.86 2.16 2.47

0.885 1.05 1.24 1.43 1.65

0.603 0.677 0.771 0.868 0.966

0.401 0.451 0.513 0.577 0.642

1.45 1.72 2.02 2.35 2.69

0.964 1.15 1.35 1.56 1.79

0.659 0.751 0.857 0.966 1.08

0.439 0.500 0.570 0.643 0.717

32 34 36 38 40

2.63 2.96 3.32 3.70 4.10

1.75 1.97 2.21 2.46 2.73

0.961 1.05 1.14 1.23 1.32

0.639 0.699 0.758 0.818 0.878

2.81 3.18 3.56 3.97 4.40

1.87 2.11 2.37 2.64 2.93

1.07 1.17 1.27 1.37 1.47

0.709 0.775 0.843 0.911 0.979

3.07 3.46 3.88 4.32 4.79

2.04 2.30 2.58 2.88 3.19

1.19 1.31 1.42 1.54 1.66

0.792 0.869 0.946 1.02 1.10

42

4.52

3.01

1.41

0.938

4.85

3.23

1.57

1.05

5.28

3.51

1.77

1.18

0

-1

170c,v 3

3


Design


W36

Other Constants and Properties b y  10 (kip-ft) 3

-1

2.81

1.87

3.02

2.01

3.27

t y  103 (kips)-1

0.451

0.300

0.479

0.319

0.514

0.342

t r  103 (kips)-1 r x /r y

0.585

0.390

0.622

0.415

0.667

0.444

r y , in.

2.18

5.70

5.69

5.73

2.56

2.55

2.53

c


v





IV-34



W36

W36

Shape

c,v

150c,v

160

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.538 0.358

11 12 13 14 15

0.771 0.803 0.839 0.880 0.928

0.513 0.534 0.558 0.586 0.618

0.482 0.497 0.513 0.530 0.548

0.321 0.331 0.341 0.352 0.364

0.832 0.866 0.905 0.950 1.00

0.553 0.576 0.602 0.632 0.667

0.520 0.537 0.555 0.573 0.594

0.346 0.357 0.369 0.382 0.395

0.954 0.995 1.04 1.10 1.16

0.635 0.662 0.694 0.730 0.773

0.602 0.623 0.645 0.668 0.693

0.401 0.414 0.429 0.445 0.461

16 17 18 19 20

0.984 1.05 1.12 1.21 1.31

0.655 0.698 0.748 0.806 0.874

0.567 0.588 0.610 0.634 0.660

0.377 0.391 0.406 0.422 0.439

1.06 1.13 1.22 1.31 1.43

0.707 0.754 0.809 0.873 0.949

0.615 0.639 0.664 0.691 0.720

0.409 0.425 0.442 0.460 0.479

1.24 1.32 1.43 1.55 1.70

0.823 0.881 0.950 1.03 1.13

0.721 0.750 0.782 0.817 0.854

0.479 0.499 0.520 0.543 0.569

22 24 26 28 30

1.58 1.88 2.20 2.56 2.94

1.05 1.25 1.47 1.70 1.95

0.719 0.830 0.950 1.07 1.20

0.478 0.553 0.632 0.714 0.797

1.72 2.04 2.40 2.78 3.19

1.14 1.36 1.59 1.85 2.12

0.796 0.926 1.06 1.20 1.34

0.530 0.616 0.706 0.799 0.894

2.05 2.44 2.87 3.32 3.82

1.37 1.62 1.91 2.21 2.54

0.977 1.14 1.31 1.49 1.67

0.650 0.758 0.871 0.989 1.11

32 34 36 38 40

3.34 3.77 4.23 4.71 5.22

2.22 2.51 2.81 3.13 3.47

1.33 1.46 1.59 1.72 1.86

0.883 0.969 1.06 1.15 1.23

3.63 4.10 4.59 5.12 5.67

2.42 2.73 3.06 3.41 3.77

1.49 1.64 1.79 1.94 2.10

0.991 1.09 1.19 1.29 1.40

4.34 4.90 5.49 6.12

2.89 3.26 3.66 4.07

1.85 2.05 2.24 2.44

1.23 1.36 1.49 1.62

0

-1

135c,v 3

3


Design


Fy = 65 ksi


3.55

2.36

3.87

2.57

4.59

3.05

t y  103 (kips)-1

0.547

0.364

0.580

0.386

0.644

0.428

t r  103 (kips)-1 r x /r y

0.709

0.473

0.752

0.502

0.835

r y , in.

0.557

5.76

5.79

5.88

2.50

2.47

2.38

c


v





IV-35



Fy = 65 ksi

W-Shapes W33

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.216 0.144

11 12 13 14 15

0.253 0.259 0.265 0.272 0.280

0.168 0.172 0.176 0.181 0.186

0.176 0.176 0.179 0.181 0.183

0.117 0.117 0.119 0.120 0.122

0.278 0.284 0.291 0.299 0.308

0.185 0.189 0.194 0.199 0.205

0.193 0.194 0.197 0.199 0.202

0.128 0.129 0.131 0.133 0.135

0.309 0.316 0.324 0.333 0.343

0.206 0.211 0.216 0.222 0.228

0.216 0.217 0.221 0.224 0.227

0.144 0.145 0.147 0.149 0.151

16 17 18 19 20

0.288 0.298 0.308 0.319 0.331

0.192 0.198 0.205 0.212 0.220

0.186 0.188 0.191 0.194 0.196

0.124 0.125 0.127 0.129 0.131

0.317 0.328 0.339 0.352 0.365

0.211 0.218 0.226 0.234 0.243

0.205 0.208 0.211 0.214 0.218

0.137 0.139 0.141 0.143 0.145

0.354 0.365 0.378 0.393 0.408

0.235 0.243 0.252 0.261 0.272

0.231 0.235 0.238 0.242 0.246

0.154 0.156 0.159 0.161 0.164

22 24 26 28 30

0.359 0.392 0.432 0.480 0.536

0.239 0.261 0.288 0.319 0.357

0.202 0.208 0.215 0.221 0.229

0.134 0.138 0.143 0.147 0.152

0.397 0.434 0.479 0.532 0.596

0.264 0.289 0.318 0.354 0.397

0.225 0.232 0.240 0.248 0.257

0.149 0.154 0.160 0.165 0.171

0.444 0.486 0.537 0.598 0.671

0.295 0.323 0.357 0.398 0.446

0.255 0.264 0.274 0.285 0.296

0.170 0.176 0.182 0.189 0.197

32 34 36 38 40

0.605 0.684 0.766 0.854 0.946

0.403 0.455 0.510 0.568 0.629

0.237 0.245 0.254 0.264 0.274

0.157 0.163 0.169 0.175 0.182

0.674 0.761 0.854 0.951 1.05

0.449 0.507 0.568 0.633 0.701

0.267 0.277 0.288 0.300 0.314

0.177 0.184 0.192 0.200 0.209

0.761 0.859 0.963 1.07 1.19

0.506 0.571 0.641 0.714 0.791

0.308 0.322 0.337 0.353 0.378

0.205 0.214 0.224 0.235 0.251

42 44 46 48 50

1.04 1.14 1.25 1.36 1.48

0.694 0.762 0.832 0.906 0.984


0.221 0.235 0.248 0.261 0.274

1.31 1.44 1.57 1.71 1.86

0.872 0.957 1.05 1.14 1.24

0.403 0.428 0.453 0.477 0.502

0.268 0.285 0.301 0.318 0.334

0

-1

318 3

3


Design


354h

387 3

b y  103 (kip-ft)-1

0.878

0.584

0.972

0.647

1.10

0.729

t y  103 (kips)-1

0.225

0.150

0.247

0.164

0.274

0.182

t r  103 (kips)-1 r x /r y

0.292

0.195

0.321

0.214

0.356

r y , in. h

W33

0.237

3.87

3.88

3.91

3.77

3.74

3.71




IV-36



W33

W33

Shape

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.292 0.194

11 12 13 14 15

0.339 0.347 0.356 0.366 0.377

0.226 0.231 0.237 0.243 0.251

0.236 0.238 0.242 0.246 0.250

0.157 0.159 0.161 0.164 0.167

0.378 0.386 0.395 0.406 0.418

0.252 0.257 0.262 0.270 0.278

0.264 0.267 0.271 0.276 0.281

0.175 0.177 0.180 0.183 0.187

0.417 0.426 0.436 0.447 0.459

0.277 0.283 0.290 0.297 0.305

0.292 0.296 0.301 0.306 0.312

0.194 0.197 0.200 0.204 0.208

16 17 18 19 20

0.389 0.402 0.416 0.432 0.450

0.259 0.267 0.277 0.288 0.299

0.254 0.259 0.263 0.268 0.273

0.169 0.172 0.175 0.178 0.181

0.431 0.446 0.462 0.480 0.500

0.287 0.297 0.308 0.319 0.332

0.285 0.291 0.296 0.302 0.307

0.190 0.193 0.197 0.201 0.204

0.472 0.489 0.507 0.527 0.549

0.314 0.325 0.337 0.351 0.365

0.318 0.324 0.330 0.337 0.344

0.211 0.216 0.220 0.224 0.229

22 24 26 28 30

0.490 0.537 0.594 0.663 0.745

0.326 0.357 0.395 0.441 0.496

0.283 0.294 0.306 0.319 0.333

0.188 0.196 0.203 0.212 0.221

0.544 0.598 0.662 0.740 0.833

0.362 0.398 0.441 0.492 0.554

0.319 0.333 0.347 0.363 0.380

0.213 0.221 0.231 0.241 0.253

0.599 0.660 0.732 0.820 0.925

0.399 0.439 0.487 0.545 0.616

0.358 0.374 0.391 0.410 0.431

0.238 0.249 0.260 0.273 0.287

32 34 36 38 40

0.846 0.955 1.07 1.19 1.32

0.563 0.636 0.713 0.794 0.880

0.348 0.364 0.383 0.413 0.443

0.231 0.242 0.255 0.275 0.295

0.946 1.07 1.20 1.33 1.48

0.630 0.711 0.797 0.888 0.984

0.399 0.419 0.452 0.489 0.525

0.265 0.279 0.301 0.325 0.349

1.05 1.19 1.33 1.48 1.65

0.701 0.791 0.887 0.988 1.09

0.455 0.487 0.530 0.574 0.619

0.302 0.324 0.353 0.382 0.412

42 44 46 48 50

1.46 1.60 1.75 1.90 2.07

0.970 1.06 1.16 1.27 1.37


0.374 0.398 0.422 0.447 0.471

1.81 1.99 2.18 2.37 2.57

1.21 1.32 1.45 1.58 1.71

0.663 0.708 0.753 0.797 0.842

0.441 0.471 0.501 0.530 0.560

0

-1

241c 3

3


Design


263c

291 3

b y  103 (kip-ft)-1

1.21

0.807

1.36

0.903

1.51

1.00

t y  103 (kips)-1

0.300

0.200

0.332

0.221

0.361

0.240

t r  103 (kips)-1 r x /r y

0.389

0.260

0.431

0.287

0.469

r y , in. c

Fy = 65 ksi

0.313

3.91

3.91

3.90

3.68

3.66

3.62




IV-37



Fy = 65 ksi

W-Shapes W33

Shape

c

201c

221

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.436 0.290

11 12 13 14 15

0.462 0.472 0.482 0.495 0.508

0.307 0.314 0.321 0.329 0.338

0.320 0.325 0.331 0.337 0.344

0.213 0.216 0.220 0.224 0.229

0.521 0.531 0.544 0.557 0.573

0.346 0.354 0.362 0.371 0.381

0.355 0.361 0.368 0.376 0.383

0.236 0.240 0.245 0.250 0.255

0.710 0.740 0.776 0.817 0.864

0.472 0.493 0.516 0.543 0.575

0.476 0.490 0.505 0.521 0.538

0.317 0.326 0.336 0.347 0.358

16 17 18 19 20

0.523 0.540 0.558 0.579 0.602

0.348 0.359 0.372 0.385 0.400

0.351 0.358 0.365 0.373 0.381

0.233 0.238 0.243 0.248 0.253

0.589 0.608 0.629 0.652 0.677

0.392 0.405 0.418 0.433 0.450

0.391 0.399 0.408 0.417 0.427

0.260 0.266 0.272 0.278 0.284

0.918 0.982 1.06 1.14 1.25

0.611 0.653 0.702 0.761 0.829

0.556 0.575 0.596 0.618 0.642

0.370 0.383 0.396 0.411 0.427

22 24 26 28 30

0.658 0.725 0.807 0.905 1.02

0.438 0.483 0.537 0.602 0.682

0.398 0.417 0.437 0.460 0.485

0.265 0.277 0.291 0.306 0.323

0.736 0.810 0.902 1.01 1.15

0.489 0.539 0.600 0.675 0.766

0.447 0.469 0.493 0.520 0.551

0.297 0.312 0.328 0.346 0.366

1.50 1.78 2.09 2.43 2.79

0.997 1.19 1.39 1.62 1.85

0.695 0.786 0.891 0.999 1.11

0.463 0.523 0.593 0.664 0.737

32 34 36 38 40

1.17 1.32 1.48 1.64 1.82

0.776 0.876 0.982 1.09 1.21

0.513 0.562 0.614 0.666 0.719

0.341 0.374 0.408 0.443 0.478

1.31 1.48 1.66 1.85 2.05

0.871 0.984 1.10 1.23 1.36

0.596 0.657 0.719 0.782 0.846

0.397 0.437 0.479 0.520 0.563

3.17 3.58 4.01 4.47 4.95

2.11 2.38 2.67 2.98 3.30

1.22 1.33 1.44 1.55 1.66

0.810 0.883 0.957 1.03 1.10

42 44 46 48 50

2.01 2.20 2.41 2.62 2.85

1.34 1.47 1.60 1.75 1.89


0.606 0.649 0.692 0.736 0.780

0

-1

169c 3

3


Design


W33

b y  103 (kip-ft)-1

1.67

1.11

1.86

1.24

3.25

2.16

t y  103 (kips)-1

0.393

0.262

0.435

0.289

0.519

0.345

t r  103 (kips)-1 r x /r y

0.510

0.340

0.564

0.376

0.673

r y , in.

0.449

3.93

3.93

5.48

3.59

3.56

2.50

c




IV-38



W33

W33

Shape

c

141c,v

152

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.587 0.390

11 12 13 14 15

0.798 0.832 0.872 0.918 0.971

0.531 0.554 0.580 0.611 0.646

0.540 0.557 0.574 0.593 0.614

0.359 0.370 0.382 0.395 0.408

0.881 0.920 0.964 1.02 1.08

0.586 0.612 0.642 0.676 0.716

0.591 0.610 0.630 0.652 0.675

0.393 0.406 0.419 0.434 0.449

0.974 1.02 1.07 1.13 1.19

0.648 0.677 0.710 0.749 0.793

0.656 0.678 0.702 0.727 0.754

0.436 0.451 0.467 0.484 0.502

16 17 18 19 20

1.03 1.10 1.19 1.29 1.40

0.687 0.735 0.791 0.856 0.934

0.636 0.659 0.684 0.711 0.741

0.423 0.438 0.455 0.473 0.493

1.15 1.23 1.32 1.43 1.56

0.762 0.816 0.879 0.953 1.04

0.700 0.727 0.756 0.787 0.821

0.466 0.483 0.503 0.524 0.546

1.27 1.36 1.47 1.60 1.75

0.846 0.907 0.979 1.06 1.17

0.784 0.816 0.850 0.888 0.929

0.521 0.543 0.566 0.591 0.618

22 24 26 28 30

1.69 2.01 2.36 2.74 3.15

1.13 1.34 1.57 1.82 2.09

0.810 0.936 1.07 1.20 1.33

0.539 0.623 0.709 0.798 0.888

1.89 2.25 2.64 3.07 3.52

1.26 1.50 1.76 2.04 2.34

0.918 1.06 1.21 1.37 1.53

0.611 0.708 0.808 0.911 1.02

2.12 2.52 2.96 3.43 3.94

1.41 1.68 1.97 2.28 2.62

1.06 1.23 1.41 1.60 1.78

0.707 0.821 0.939 1.06 1.19

32 34 36 38 40

3.58 4.04 4.53 5.05 5.60

2.38 2.69 3.02 3.36 3.72

1.47 1.61 1.75 1.89 2.03

0.979 1.07 1.16 1.26 1.35

4.00 4.52 5.07 5.65 6.26

2.66 3.01 3.37 3.76 4.16

1.69 1.85 2.02 2.18 2.35

1.12 1.23 1.34 1.45 1.56

4.48 5.06 5.68 6.32

2.98 3.37 3.78 4.21

1.98 2.17 2.37 2.57

1.32 1.45 1.58 1.71

0

-1

130c,v 3

3


Design


Fy = 65 ksi


3.71

2.47

4.10

2.73

4.61

3.06

t y  103 (kips)-1

0.572

0.381

0.619

0.412

0.671

0.446

t r  103 (kips)-1 r x /r y

0.742

0.495

0.803

0.535

0.870

r y , in.

0.580

5.47

5.51

5.52

2.47

2.43

2.39

c


v





IV-39



Fy = 65 ksi

W-Shapes W30

W33

Shape

c,v

h

118

b x  10

p  10

-1

357h

391 3

3

b x  10

p  10

-1

b x  103

-1

p  10




(kip-ft)-1 ASD LRFD 0.208 0.138

11 12 13 14 15

1.11 1.16 1.22 1.29 1.37

0.738 0.771 0.811 0.856 0.910

0.747 0.773 0.802 0.832 0.865

0.497 0.514 0.533 0.554 0.576

0.253 0.259 0.265 0.273 0.281

0.168 0.172 0.176 0.181 0.187

0.189 0.190 0.192 0.195 0.197

0.126 0.127 0.128 0.130 0.131

0.277 0.284 0.291 0.300 0.309

0.184 0.189 0.194 0.199 0.205

0.208 0.209 0.212 0.215 0.218

0.138 0.139 0.141 0.143 0.145

16 17 18 19 20

1.46 1.57 1.70 1.86 2.05

0.972 1.05 1.13 1.24 1.37

0.901 0.940 0.982 1.03 1.08

0.600 0.625 0.654 0.684 0.718

0.290 0.300 0.311 0.322 0.335

0.193 0.199 0.207 0.215 0.223

0.199 0.202 0.204 0.207 0.209

0.133 0.134 0.136 0.138 0.139

0.319 0.330 0.342 0.355 0.370

0.212 0.219 0.228 0.236 0.246

0.220 0.223 0.226 0.229 0.233

0.147 0.149 0.151 0.153 0.155

22 24 26 28 30

2.48 2.95 3.47 4.02 4.62

1.65 1.97 2.31 2.68 3.07

1.27 1.48 1.70 1.92 2.16

0.845 0.984 1.13 1.28 1.44

0.365 0.401 0.444 0.496 0.558

0.243 0.267 0.295 0.330 0.371

0.215 0.220 0.226 0.233 0.239

0.143 0.147 0.151 0.155 0.159

0.403 0.444 0.492 0.550 0.620

0.268 0.295 0.327 0.366 0.413

0.239 0.246 0.254 0.261 0.270

0.159 0.164 0.169 0.174 0.179

32 34 36 38 40

5.25 5.93 6.65 7.41

3.49 3.95 4.42 4.93

2.40 2.64 2.89 3.14

1.59 1.76 1.92 2.09

0.633 0.715 0.802 0.893 0.990

0.421 0.476 0.533 0.594 0.658

0.246 0.254 0.262 0.270 0.279

0.164 0.169 0.174 0.180 0.186

0.705 0.796 0.892 0.994 1.10

0.469 0.530 0.594 0.662 0.733

0.279 0.288 0.298 0.309 0.321

0.185 0.192 0.199 0.206 0.214


0.192 0.199 0.206 0.216 0.226

1.21 1.33 1.46 1.59 1.72

0.808 0.887 0.969 1.06 1.15

0.334 0.349 0.368 0.387 0.406

0.222 0.233 0.245 0.257 0.270

42 44 46 48 50

-1

3


0

-1

3

3


Design


W33-W30

b y  103 (kip-ft)-1

5.34

3.55

0.884

0.588

0.982

t y  103 (kips)-1

0.740

0.493

0.223

0.149

0.245

0.163

t r  103 (kips)-1 r x /r y

0.961

0.640

0.290

0.193

0.317

0.212

r y , in.

0.654

5.60

3.65

3.65

2.32

3.67

3.64

c


h


v




IV-40



W30

W30

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.291 0.193

11 12 13 14 15

0.304 0.312 0.320 0.330 0.340

0.203 0.208 0.213 0.219 0.226

0.230 0.233 0.236 0.239 0.242

0.153 0.155 0.157 0.159 0.161

0.340 0.348 0.358 0.368 0.380

0.226 0.232 0.238 0.245 0.253

0.259 0.262 0.266 0.270 0.274

0.172 0.174 0.177 0.179 0.182

0.381 0.391 0.402 0.414 0.427

0.254 0.260 0.267 0.275 0.284

0.291 0.296 0.300 0.305 0.311

0.194 0.197 0.200 0.203 0.207

16 17 18 19 20

0.351 0.364 0.377 0.392 0.409

0.234 0.242 0.251 0.261 0.272

0.246 0.249 0.253 0.257 0.261

0.164 0.166 0.168 0.171 0.173

0.393 0.407 0.422 0.439 0.458

0.261 0.271 0.281 0.292 0.305

0.278 0.282 0.287 0.292 0.296

0.185 0.188 0.191 0.194 0.197

0.442 0.458 0.476 0.496 0.518

0.294 0.305 0.317 0.330 0.344

0.316 0.321 0.327 0.333 0.339

0.210 0.214 0.218 0.221 0.225

22 24 26 28 30

0.447 0.492 0.547 0.613 0.694

0.297 0.328 0.364 0.408 0.462

0.269 0.277 0.286 0.296 0.306

0.179 0.184 0.190 0.197 0.204

0.501 0.553 0.615 0.690 0.782

0.333 0.368 0.409 0.459 0.520

0.306 0.317 0.329 0.341 0.355

0.204 0.211 0.219 0.227 0.236

0.568 0.628 0.701 0.789 0.899

0.378 0.418 0.466 0.525 0.598

0.352 0.365 0.380 0.397 0.414

0.234 0.243 0.253 0.264 0.276

32 34 36 38 40

0.789 0.891 0.999 1.11 1.23

0.525 0.593 0.665 0.741 0.821

0.318 0.330 0.342 0.356 0.372

0.211 0.219 0.228 0.237 0.247

0.890 1.00 1.13 1.26 1.39

0.592 0.669 0.749 0.835 0.925

0.369 0.385 0.402 0.421 0.450

0.246 0.256 0.268 0.280 0.299

1.02 1.15 1.29 1.44 1.60

0.680 0.768 0.861 0.959 1.06

0.434 0.455 0.481 0.517 0.554

0.289 0.303 0.320 0.344 0.368

42 44 46 48 50

1.36 1.49 1.63 1.78 1.93

0.905 0.993 1.09 1.18 1.28


0.318 0.337 0.356 0.375 0.394

1.76 1.93 2.11 2.30 2.50

1.17 1.29 1.41 1.53 1.66

0.590 0.626 0.662 0.698 0.734

0.392 0.416 0.440 0.464 0.488

0

-1

261 3

3


Design


292

326 3

b y  103 (kip-ft)-1

1.09

0.724

1.23

0.818

1.40

0.930

t y  103 (kips)-1

0.268

0.178

0.299

0.199

0.334

0.222

t r  103 (kips)-1 r x /r y

0.348

0.232

0.388

0.258

0.433

r y , in. h

Fy = 65 ksi

0.289

3.67

3.69

3.71

3.60

3.58

3.53




IV-41



Fy = 65 ksi

W-Shapes W30

Shape

c

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.406 0.270

11 12 13 14 15

0.424 0.435 0.447 0.461 0.476

0.282 0.289 0.298 0.307 0.317

0.324 0.330 0.335 0.341 0.347

0.216 0.219 0.223 0.227 0.231

0.475 0.487 0.499 0.514 0.531

0.316 0.324 0.332 0.342 0.353

0.366 0.373 0.380 0.387 0.394

0.244 0.248 0.253 0.257 0.262

0.539 0.551 0.565 0.581 0.599

0.359 0.367 0.376 0.387 0.398

0.408 0.416 0.424 0.433 0.441

0.272 0.277 0.282 0.288 0.294

16 17 18 19 20

0.493 0.511 0.531 0.554 0.578

0.328 0.340 0.354 0.368 0.385

0.353 0.360 0.367 0.374 0.381

0.235 0.240 0.244 0.249 0.254

0.550 0.571 0.594 0.619 0.646

0.366 0.380 0.395 0.412 0.430

0.402 0.410 0.418 0.427 0.436

0.267 0.273 0.278 0.284 0.290

0.618 0.640 0.663 0.692 0.724

0.411 0.426 0.441 0.460 0.481

0.450 0.460 0.470 0.480 0.491

0.300 0.306 0.313 0.319 0.327

22 24 26 28 30

0.635 0.703 0.786 0.886 1.01

0.422 0.468 0.523 0.589 0.672

0.397 0.413 0.432 0.452 0.474

0.264 0.275 0.287 0.301 0.315

0.710 0.788 0.882 0.995 1.14

0.473 0.524 0.587 0.662 0.756

0.455 0.476 0.499 0.524 0.552

0.303 0.317 0.332 0.349 0.368

0.796 0.885 0.992 1.12 1.28

0.530 0.589 0.660 0.747 0.854

0.514 0.540 0.568 0.599 0.634

0.342 0.359 0.378 0.398 0.422

32 34 36 38 40

1.15 1.30 1.45 1.62 1.80

0.764 0.863 0.968 1.08 1.19

0.498 0.527 0.571 0.615 0.659

0.331 0.350 0.380 0.409 0.439

1.29 1.46 1.64 1.82 2.02

0.860 0.971 1.09 1.21 1.34

0.584 0.635 0.690 0.746 0.802

0.388 0.423 0.459 0.496 0.533

1.46 1.65 1.85 2.06 2.28

0.972 1.10 1.23 1.37 1.52

0.686 0.753 0.821 0.889 0.957

0.457 0.501 0.546 0.591 0.637

42 44 46 48 50

1.98 2.17 2.37 2.59 2.81

1.32 1.45 1.58 1.72 1.87


0.571 0.608 0.645 0.683 0.720

2.52 2.76 3.02 3.29 3.57

1.67 1.84 2.01 2.19 2.37

1.03 1.10 1.16 1.23 1.30

0.683 0.729 0.775 0.821 0.867

0

-1

191c 3

3


Design


211c

235 3

b y  103 (kip-ft)-1

1.57

1.04

1.77

1.18

1.99

1.32

t y  103 (kips)-1

0.371

0.247

0.412

0.274

0.458

0.305

t r  103 (kips)-1 r x /r y

0.481

0.321

0.535

0.357

0.594

r y , in. c

W30

0.396

3.70

3.70

3.70

3.51

3.49

3.46




IV-42



W30

W30

Shape

c

148c

173

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.627 0.417

11 12 13 14 15

0.606 0.620 0.636 0.653 0.673

0.403 0.412 0.423 0.435 0.448

0.455 0.464 0.474 0.483 0.494

0.303 0.309 0.315 0.322 0.328

0.831 0.876 0.929 0.991 1.07

0.553 0.583 0.618 0.659 0.709

0.616 0.636 0.657 0.680 0.704

0.410 0.423 0.437 0.452 0.469

0.953 1.00 1.07 1.14 1.22

0.634 0.668 0.709 0.757 0.813

0.712 0.737 0.763 0.792 0.822

0.474 0.490 0.508 0.527 0.547

16 17 18 19 20

0.695 0.719 0.746 0.776 0.810

0.462 0.478 0.496 0.516 0.539

0.504 0.515 0.527 0.539 0.552

0.336 0.343 0.351 0.359 0.367

1.16 1.26 1.38 1.53 1.69

0.769 0.839 0.920 1.02 1.12

0.731 0.759 0.789 0.823 0.859

0.486 0.505 0.525 0.547 0.571

1.32 1.45 1.59 1.76 1.95

0.880 0.962 1.06 1.17 1.30

0.856 0.892 0.931 0.974 1.02

0.569 0.593 0.619 0.648 0.679

22 24 26 28 30

0.889 0.990 1.11 1.26 1.45

0.592 0.659 0.741 0.841 0.964

0.580 0.610 0.644 0.681 0.724

0.386 0.406 0.428 0.453 0.481

2.05 2.43 2.86 3.31 3.80

1.36 1.62 1.90 2.20 2.53

0.967 1.10 1.25 1.39 1.53

0.643 0.735 0.828 0.923 1.02

2.36 2.81 3.30 3.82 4.39

1.57 1.87 2.19 2.54 2.92

1.18 1.36 1.54 1.72 1.91

0.787 0.904 1.02 1.15 1.27

32 34 36 38 40

1.65 1.86 2.09 2.32 2.57

1.10 1.24 1.39 1.55 1.71

0.802 0.882 0.964 1.05 1.13

0.533 0.587 0.641 0.696 0.751

4.33 4.89 5.48

2.88 3.25 3.64

1.67 1.82 1.96

1.11 1.21 1.30

4.99 5.64 6.32

3.32 3.75 4.21

2.09 2.28 2.47

1.39 1.52 1.64

42 44 46 48 50

2.84 3.12 3.41 3.71 4.02

1.89 2.07 2.27 2.47 2.68


0

-1

132c 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

2.23

1.48

4.03

2.68

4.69

3.12

t y  103 (kips)-1

0.505

0.336

0.589

0.392

0.662

0.441

t r  103 (kips)-1 r x /r y

0.655

0.437

0.765

0.510

0.859

r y , in.

0.573

3.71

5.44

5.42

3.42

2.28

2.25

c




IV-43



Fy = 65 ksi

W-Shapes W30

Shape

c

116c,v

124

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.792 0.527

11 12 13 14 15

1.03 1.09 1.15 1.23 1.32

0.685 0.722 0.766 0.817 0.878

0.767 0.794 0.824 0.856 0.890

0.510 0.528 0.548 0.569 0.592

1.12 1.18 1.26 1.34 1.45

0.745 0.786 0.835 0.893 0.962

0.834 0.865 0.898 0.934 0.973

0.555 0.575 0.597 0.621 0.647

1.23 1.30 1.39 1.48 1.60

0.820 0.867 0.922 0.988 1.07

0.921 0.957 0.996 1.04 1.08

0.613 0.637 0.663 0.691 0.721

16 17 18 19 20

1.43 1.56 1.72 1.91 2.11

0.951 1.04 1.14 1.27 1.40

0.927 0.968 1.01 1.06 1.12

0.617 0.644 0.673 0.706 0.745

1.57 1.72 1.89 2.11 2.34

1.04 1.14 1.26 1.40 1.55

1.01 1.06 1.11 1.17 1.26

0.675 0.706 0.739 0.776 0.837

1.74 1.91 2.12 2.36 2.62

1.16 1.27 1.41 1.57 1.74

1.13 1.19 1.25 1.32 1.44

0.754 0.791 0.831 0.877 0.959

22 24 26 28 30

2.55 3.04 3.57 4.14 4.75

1.70 2.02 2.37 2.75 3.16

1.31 1.51 1.72 1.92 2.13

0.873 1.01 1.14 1.28 1.42

2.83 3.36 3.95 4.58 5.26

1.88 2.24 2.63 3.05 3.50

1.48 1.70 1.94 2.18 2.42

0.983 1.13 1.29 1.45 1.61

3.16 3.77 4.42 5.13 5.88

2.11 2.51 2.94 3.41 3.91

1.70 1.96 2.24 2.52 2.81

1.13 1.31 1.49 1.68 1.87

32 34 36

5.40 6.10 6.84

3.60 4.06 4.55

2.35 2.56 2.78

1.56 1.70 1.85

5.98 6.75 7.57

3.98 4.49 5.04

2.67 2.92 3.17

1.78 1.94 2.11

6.69 7.56

4.45 5.03

3.10 3.40

2.06 2.26

0

-1

108c,v 3

3


Design


W30


5.08

3.38

5.57

3.71

6.24

4.15

t y  103 (kips)-1

0.704

0.468

0.751

0.500

0.810

0.539

t r  103 (kips)-1 r x /r y

0.913

0.609

0.975

0.650

1.05

r y , in.

0.701

5.43

5.48

5.53

2.23

2.19

2.15

c


v





IV-44



W30-W27

W30

Shape

W27

c,v

c,f,v

b x  10

3

p  10

-1

539h

90

99 3

-1

b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0






(kip-ft)-1 ASD LRFD 0.145 0.0965

11 12 13 14 15

1.38 1.46 1.56 1.68 1.81

0.921 0.975 1.04 1.11 1.21

1.03 1.08 1.12 1.17 1.23

0.687 0.715 0.746 0.779 0.815

1.57 1.65 1.76 1.89 2.03

1.04 1.10 1.17 1.25 1.35

1.14 1.19 1.24 1.30 1.36

0.761 0.793 0.827 0.865 0.906

0.183 0.187 0.192 0.198 0.204

0.122 0.125 0.128 0.131 0.135

0.145 0.146 0.147 0.148 0.149

0.0965 0.0970 0.0977 0.0984 0.0992

16 17 18 19 20

1.98 2.18 2.43 2.70 3.00

1.32 1.45 1.61 1.80 1.99

1.29 1.35 1.42 1.55 1.69

0.855 0.899 0.947 1.03 1.13

2.21 2.43 2.70 3.01 3.34

1.47 1.62 1.80 2.00 2.22

1.43 1.51 1.59 1.75 1.92

0.951 1.00 1.06 1.17 1.28

0.210 0.217 0.225 0.234 0.244

0.140 0.145 0.150 0.156 0.162

0.150 0.151 0.152 0.154 0.155

0.0999 0.101 0.101 0.102 0.103

22 24 26 28 30

3.63 4.31 5.06 5.87 6.74

2.41 2.87 3.37 3.91 4.49

2.00 2.32 2.65 2.99 3.34

1.33 1.54 1.76 1.99 2.22

4.04 4.80 5.64 6.54 7.51

2.69 3.20 3.75 4.35 4.99

2.28 2.65 3.04 3.44 3.85

1.52 1.76 2.02 2.29 2.56

0.266 0.292 0.324 0.362 0.407

0.177 0.194 0.215 0.241 0.271

0.157 0.160 0.162 0.165 0.168

0.105 0.106 0.108 0.110 0.112

32 34 36 38 40

7.67 8.66

5.10 5.76

3.69 4.06

2.46 2.70

8.54 9.64

5.68 6.41

4.27 4.70

2.84 3.13

0.463 0.523 0.586 0.653 0.724

0.308 0.348 0.390 0.435 0.481

0.171 0.174 0.177 0.180 0.183

0.114 0.116 0.118 0.120 0.122

0.798 0.876 0.957 1.04 1.13

0.531 0.583 0.637 0.693 0.752

0.187 0.190 0.194 0.198 0.202

0.124 0.127 0.129 0.132 0.134

Design Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 65 ksi

42 44 46 48 50 Other Constants and Properties

b y  103 (kip-ft)-1

7.10

4.72

8.07

5.37

0.627

0.417

t y  103 (kips)-1

0.886

0.589

0.977

0.650

0.162

0.108

t r  103 (kips)-1 r x /r y

1.15

0.766

1.27

0.845

0.210

r y , in.

0.140

5.57

5.60

3.48

2.10

2.09

3.65

c


f

Shape does not meet compact limit for flexure with F y = 65 ksi.

h


v




IV-45



Fy = 65 ksi

W-Shapes W27

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.266 0.177

11 12 13 14 15

0.270 0.277 0.285 0.294 0.304

0.180 0.185 0.190 0.196 0.202

0.221 0.224 0.226 0.229 0.231

0.147 0.149 0.151 0.152 0.154

0.298 0.306 0.315 0.324 0.335

0.198 0.203 0.209 0.216 0.223

0.243 0.246 0.249 0.252 0.255

0.162 0.164 0.166 0.168 0.170

0.328 0.337 0.348 0.359 0.371

0.219 0.225 0.231 0.239 0.247

0.267 0.271 0.274 0.278 0.282

0.178 0.180 0.183 0.185 0.188

16 17 18 19 20

0.315 0.327 0.340 0.354 0.370

0.209 0.217 0.226 0.236 0.246

0.234 0.237 0.239 0.242 0.245

0.156 0.157 0.159 0.161 0.163

0.348 0.361 0.376 0.392 0.410

0.231 0.240 0.250 0.261 0.273

0.258 0.262 0.265 0.268 0.272

0.172 0.174 0.176 0.179 0.181

0.385 0.400 0.417 0.436 0.456

0.256 0.266 0.278 0.290 0.303

0.286 0.290 0.294 0.298 0.302

0.190 0.193 0.196 0.198 0.201

22 24 26 28 30

0.407 0.452 0.506 0.572 0.653

0.271 0.301 0.337 0.380 0.435

0.251 0.257 0.264 0.270 0.278

0.167 0.171 0.175 0.180 0.185

0.452 0.502 0.564 0.638 0.730

0.301 0.334 0.375 0.425 0.486

0.279 0.287 0.295 0.303 0.312

0.186 0.191 0.196 0.202 0.208

0.504 0.561 0.631 0.717 0.822

0.335 0.373 0.420 0.477 0.547

0.311 0.321 0.331 0.342 0.354

0.207 0.214 0.220 0.228 0.235

32 34 36 38 40

0.743 0.839 0.941 1.05 1.16

0.494 0.558 0.626 0.697 0.773

0.285 0.293 0.302 0.311 0.320

0.190 0.195 0.201 0.207 0.213

0.831 0.938 1.05 1.17 1.30

0.553 0.624 0.700 0.780 0.864

0.322 0.332 0.343 0.355 0.367

0.214 0.221 0.228 0.236 0.244

0.935 1.06 1.18 1.32 1.46

0.622 0.703 0.788 0.878 0.972

0.366 0.379 0.394 0.409 0.426

0.244 0.252 0.262 0.272 0.283

42 44 46 48 50

1.28 1.41 1.54 1.67 1.81

0.852 0.935 1.02 1.11 1.21


0.253 0.263 0.275 0.289 0.302

1.61 1.77 1.93 2.10 2.28

1.07 1.18 1.29 1.40 1.52

0.445 0.469 0.494 0.519 0.543

0.296 0.312 0.329 0.345 0.361

0

-1

307h 3

3


Design


336h

368 3

b y  103 (kip-ft)-1

0.982

0.654

1.09

0.724

1.21

0.803

t y  103 (kips)-1

0.236

0.157

0.259

0.172

0.285

0.190

t r  103 (kips)-1 r x /r y

0.306

0.204

0.336

0.224

0.370

r y , in. h

W27

0.246

3.51

3.51

3.52

3.48

3.45

3.41




IV-46



W27

W27

Shape

281

258 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.355 0.236

11 12 13 14 15

0.357 0.367 0.378 0.390 0.404

0.238 0.244 0.252 0.260 0.269

0.295 0.299 0.303 0.307 0.312

0.196 0.199 0.202 0.205 0.207

0.391 0.402 0.414 0.428 0.443

0.260 0.267 0.276 0.285 0.295

0.324 0.329 0.334 0.339 0.345

0.216 0.219 0.222 0.226 0.229

0.430 0.442 0.456 0.472 0.489

0.286 0.294 0.303 0.314 0.325

0.359 0.365 0.371 0.377 0.383

0.239 0.243 0.247 0.251 0.255

16 17 18 19 20

0.419 0.436 0.455 0.475 0.498

0.279 0.290 0.303 0.316 0.331

0.316 0.321 0.326 0.331 0.336

0.211 0.214 0.217 0.220 0.224

0.460 0.479 0.500 0.523 0.548

0.306 0.319 0.333 0.348 0.365

0.350 0.356 0.362 0.368 0.374

0.233 0.237 0.241 0.245 0.249

0.508 0.529 0.552 0.578 0.607

0.338 0.352 0.367 0.385 0.404

0.390 0.397 0.404 0.411 0.419

0.259 0.264 0.269 0.274 0.279

22 24 26 28 30

0.550 0.614 0.692 0.787 0.903

0.366 0.408 0.460 0.523 0.601

0.347 0.359 0.371 0.384 0.398

0.231 0.239 0.247 0.256 0.265

0.607 0.679 0.766 0.874 1.00

0.404 0.452 0.510 0.582 0.668

0.387 0.401 0.416 0.433 0.450

0.258 0.267 0.277 0.288 0.300

0.673 0.754 0.853 0.976 1.12

0.448 0.501 0.567 0.649 0.745

0.435 0.452 0.471 0.492 0.514

0.289 0.301 0.313 0.327 0.342

32 34 36 38 40

1.03 1.16 1.30 1.45 1.61

0.683 0.772 0.865 0.964 1.07

0.414 0.430 0.448 0.467 0.492

0.275 0.286 0.298 0.311 0.327

1.14 1.29 1.45 1.61 1.78

0.760 0.858 0.962 1.07 1.19

0.470 0.490 0.513 0.544 0.580

0.312 0.326 0.342 0.362 0.386

1.27 1.44 1.61 1.80 1.99

0.848 0.957 1.07 1.20 1.33

0.538 0.565 0.603 0.646 0.690

0.358 0.376 0.401 0.430 0.459

42 44 46 48 50

1.77 1.94 2.12 2.31 2.51

1.18 1.29 1.41 1.54 1.67


0.409 0.433 0.456 0.479 0.503

2.20 2.41 2.63 2.87 3.11

1.46 1.60 1.75 1.91 2.07

0.733 0.776 0.818 0.861 0.904

0.487 0.516 0.544 0.573 0.601

0

-1

235 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

1.33

0.885

1.47

0.975

1.63

1.09

t y  103 (kips)-1

0.309

0.206

0.338

0.225

0.370

0.246

t r  103 (kips)-1 r x /r y

0.401

0.267

0.438

0.292

0.480

r y , in.

0.320

3.54

3.54

3.54

3.39

3.36

3.33



IV-47



Fy = 65 ksi

W-Shapes W27

Shape

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.481 0.320

11 12 13 14 15

0.467 0.481 0.496 0.513 0.532

0.311 0.320 0.330 0.341 0.354

0.390 0.397 0.403 0.411 0.418

0.259 0.264 0.268 0.273 0.278

0.524 0.540 0.557 0.577 0.598

0.349 0.359 0.371 0.384 0.398

0.441 0.449 0.457 0.466 0.475

0.293 0.299 0.304 0.310 0.316

0.572 0.590 0.609 0.631 0.655

0.381 0.392 0.405 0.420 0.436

0.489 0.499 0.509 0.519 0.530

0.325 0.332 0.338 0.345 0.352

16 17 18 19 20

0.553 0.576 0.601 0.629 0.661

0.368 0.383 0.400 0.419 0.440

0.426 0.434 0.442 0.450 0.459

0.283 0.288 0.294 0.300 0.306

0.622 0.648 0.678 0.710 0.746

0.414 0.431 0.451 0.473 0.496

0.484 0.494 0.504 0.515 0.526

0.322 0.329 0.335 0.342 0.350

0.682 0.712 0.745 0.781 0.822

0.454 0.474 0.495 0.520 0.547

0.541 0.552 0.565 0.577 0.591

0.360 0.368 0.376 0.384 0.393

22 24 26 28 30

0.733 0.822 0.931 1.07 1.22

0.488 0.547 0.619 0.710 0.814

0.478 0.499 0.521 0.545 0.572

0.318 0.332 0.347 0.363 0.381

0.830 0.932 1.06 1.22 1.40

0.552 0.620 0.704 0.809 0.928

0.549 0.575 0.604 0.635 0.670

0.366 0.383 0.402 0.422 0.446

0.916 1.03 1.18 1.35 1.55

0.610 0.687 0.782 0.901 1.03

0.619 0.651 0.686 0.725 0.768

0.412 0.433 0.456 0.482 0.511

32 34 36 38 40

1.39 1.57 1.76 1.96 2.18

0.927 1.05 1.17 1.31 1.45

0.602 0.640 0.690 0.741 0.791

0.400 0.426 0.459 0.493 0.527

1.59 1.79 2.01 2.24 2.48

1.06 1.19 1.34 1.49 1.65

0.714 0.778 0.841 0.905 0.968

0.475 0.517 0.560 0.602 0.644

1.77 2.00 2.24 2.49 2.76

1.18 1.33 1.49 1.66 1.84

0.840 0.917 0.995 1.07 1.15

0.559 0.610 0.662 0.713 0.765

42 44 46 48 50

2.40 2.63 2.88 3.13 3.40

1.60 1.75 1.91 2.09 2.26


0.687 0.729 0.771 0.813 0.855

3.05 3.34 3.66 3.98 4.32

2.03 2.23 2.43 2.65 2.87

1.23 1.31 1.38 1.46 1.54

0.817 0.869 0.920 0.972 1.02

0

-1

178c 3

3


Design


194c

217 3

b y  103 (kip-ft)-1

1.78

1.18

2.02

1.34

2.25

t y  103 (kips)-1

0.402

0.268

0.450

0.299

0.489

0.326

t r  103 (kips)-1 r x /r y

0.522

0.348

0.584

0.389

0.635

0.423

r y , in. c

W27

1.49

3.55

3.56

3.57

3.32

3.29

3.25




IV-48



W27

W27

Shape

c

146c

161

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.694 0.462

11 12 13 14 15

0.641 0.658 0.678 0.700 0.725

0.426 0.438 0.451 0.466 0.482

0.543 0.554 0.566 0.578 0.590

0.361 0.369 0.376 0.384 0.393

0.720 0.740 0.762 0.787 0.814

0.479 0.492 0.507 0.523 0.542

0.604 0.617 0.631 0.645 0.66

0.402 0.411 0.420 0.429 0.439

0.966 1.02 1.09 1.18 1.28

0.643 0.681 0.726 0.783 0.850

0.788 0.814 0.842 0.873 0.905

0.524 0.542 0.560 0.581 0.602

16 17 18 19 20

0.755 0.789 0.826 0.867 0.912

0.502 0.525 0.549 0.577 0.607

0.604 0.618 0.632 0.647 0.663

0.402 0.411 0.421 0.431 0.441

0.845 0.880 0.919 0.964 1.02

0.562 0.586 0.611 0.641 0.675

0.675 0.691 0.708 0.726 0.745

0.449 0.460 0.471 0.483 0.496

1.39 1.53 1.69 1.87 2.08

0.927 1.02 1.12 1.25 1.38

0.941 0.979 1.02 1.06 1.11

0.626 0.651 0.679 0.708 0.741

22 24 26 28 30

1.02 1.15 1.31 1.51 1.74

0.678 0.765 0.872 1.01 1.16

0.698 0.736 0.778 0.826 0.895

0.464 0.489 0.518 0.550 0.596

1.14 1.28 1.47 1.70 1.95

0.756 0.855 0.977 1.13 1.30

0.786 0.831 0.882 0.939 1.04

0.523 0.553 0.587 0.625 0.695

2.51 2.99 3.51 4.07 4.67

1.67 1.99 2.33 2.71 3.11

1.28 1.46 1.64 1.82 2.00

0.850 0.969 1.09 1.21 1.33

32 34 36 38 40

1.98 2.23 2.50 2.79 3.09

1.31 1.48 1.66 1.85 2.05

0.987 1.08 1.17 1.27 1.36

0.657 0.719 0.781 0.844 0.907

2.22 2.50 2.81 3.13 3.47

1.48 1.67 1.87 2.08 2.31

1.16 1.27 1.38 1.50 1.61

0.769 0.843 0.919 0.995 1.07

5.31 6.00 6.73

3.54 3.99 4.47

2.18 2.36 2.54

1.45 1.57 1.69

42 44 46 48 50

3.40 3.73 4.08 4.44 4.82

2.26 2.48 2.72 2.96 3.21


0

-1

129c 3

3


Design


Fy = 65 ksi

1.15 1.23 1.30 1.38 1.46

b y  103 (kip-ft)-1

2.51

1.67

2.81

1.87

4.76

t y  103 (kips)-1

0.540

0.359

0.595

0.396

0.680

0.452

t r  103 (kips)-1 r x /r y

0.700

0.467

0.772

0.514

0.882

0.588

r y , in.

3.17

3.56

3.59

5.07

3.23

3.20

2.21

c




IV-49



Fy = 65 ksi

W-Shapes W27

Shape

c

102c

114

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.986 0.656

11 12 13 14 15

1.11 1.18 1.26 1.35 1.46

0.740 0.784 0.836 0.898 0.973

0.917 0.950 0.986 1.02 1.07

0.610 0.632 0.656 0.681 0.709

1.28 1.36 1.45 1.55 1.68

0.852 0.903 0.963 1.03 1.12

1.04 1.08 1.12 1.17 1.22

0.692 0.718 0.746 0.777 0.810

1.42 1.51 1.61 1.73 1.87

0.945 1.00 1.07 1.15 1.24

1.15 1.20 1.25 1.30 1.36

0.766 0.797 0.829 0.865 0.904

16 17 18 19 20

1.60 1.76 1.94 2.17 2.40

1.06 1.17 1.29 1.44 1.60

1.11 1.16 1.21 1.27 1.35

0.739 0.771 0.807 0.846 0.900

1.83 2.02 2.24 2.49 2.76

1.22 1.34 1.49 1.66 1.84

1.27 1.33 1.39 1.47 1.60

0.846 0.885 0.928 0.976 1.07

2.04 2.25 2.50 2.79 3.09

1.36 1.49 1.66 1.86 2.06

1.42 1.49 1.57 1.69 1.84

0.946 0.993 1.04 1.12 1.23

22 24 26 28 30

2.90 3.46 4.06 4.70 5.40

1.93 2.30 2.70 3.13 3.59

1.58 1.80 2.04 2.27 2.51

1.05 1.20 1.36 1.51 1.67

3.34 3.98 4.67 5.42 6.22

2.22 2.65 3.11 3.60 4.14

1.87 2.15 2.44 2.74 3.03

1.25 1.43 1.63 1.82 2.02

3.74 4.45 5.22 6.06 6.95

2.49 2.96 3.47 4.03 4.62

2.16 2.50 2.84 3.19 3.54

1.44 1.66 1.89 2.12 2.36

32 34 36

6.14 6.94 7.78

4.09 4.61 5.17

2.75 2.99 3.23

1.83 1.99 2.15

7.07 7.99

4.71 5.31

3.33 3.63

2.22 2.42

7.91 8.93

5.26 5.94

3.90 4.26

2.59 2.83

0

-1

94c,v 3

3


Design


W27


5.56

3.70

6.31

4.20

7.06

t y  103 (kips)-1

0.765

0.509

0.856

0.570

0.931

0.619

t r  103 (kips)-1 r x /r y

0.992

0.661

1.11

0.741

1.21

0.805

r y , in.

4.70

5.05

5.12

5.14

2.18

2.15

2.12

c


v





IV-50



W27-W24

W24

W27

Shape

c,v

h

b x  10

3

p  10

-1

335h

370

84 3

b x  10

p  10

-1

b x  103

-1

p  10




(kip-ft)-1 ASD LRFD 0.269 0.179

11 12 13 14 15

1.64 1.74 1.86 2.00 2.17

1.09 1.16 1.23 1.33 1.44

1.33 1.39 1.45 1.51 1.58

0.885 0.922 0.962 1.01 1.05

0.275 0.283 0.293 0.303 0.314

0.183 0.189 0.195 0.202 0.209

0.245 0.247 0.249 0.252 0.254

0.163 0.164 0.166 0.167 0.169

0.306 0.316 0.326 0.338 0.351

0.204 0.210 0.217 0.225 0.234

0.271 0.274 0.277 0.280 0.283

0.181 0.183 0.185 0.187 0.189

16 17 18 19 20

2.37 2.62 2.93 3.27 3.62

1.58 1.75 1.95 2.17 2.41

1.66 1.75 1.86 2.05 2.24

1.11 1.16 1.24 1.36 1.49

0.327 0.341 0.357 0.374 0.393

0.218 0.227 0.237 0.249 0.262

0.257 0.259 0.262 0.264 0.267

0.171 0.172 0.174 0.176 0.178

0.366 0.382 0.400 0.420 0.442

0.243 0.254 0.266 0.279 0.294

0.287 0.290 0.293 0.296 0.300

0.191 0.193 0.195 0.197 0.199

22 24 26 28 30

4.38 5.21 6.12 7.10 8.15

2.91 3.47 4.07 4.72 5.42

2.64 3.06 3.49 3.93 4.38

1.76 2.04 2.32 2.62 2.92

0.438 0.493 0.560 0.644 0.740

0.291 0.328 0.373 0.429 0.492

0.273 0.279 0.285 0.291 0.298

0.181 0.185 0.189 0.194 0.198

0.493 0.556 0.634 0.732 0.841

0.328 0.370 0.422 0.487 0.559

0.307 0.314 0.322 0.330 0.339

0.204 0.209 0.214 0.220 0.226

32 34 36 38 40

9.27 10.5

6.17 6.96

4.84 5.31

3.22 3.53

0.842 0.950 1.07 1.19 1.32

0.560 0.632 0.709 0.790 0.875

0.305 0.312 0.320 0.328 0.336

0.203 0.208 0.213 0.218 0.224

0.957 1.08 1.21 1.35 1.49

0.636 0.718 0.806 0.897 0.994

0.348 0.358 0.368 0.379 0.390

0.232 0.238 0.245 0.252 0.260


0.230 0.236 0.242 0.249 0.257

1.65 1.81 1.98 2.15 2.34

1.10 1.20 1.32 1.43 1.55

0.402 0.415 0.429 0.444 0.461

0.268 0.276 0.285 0.295 0.307

42 44 46 48 50

-1

3


0

-1

3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

8.25

5.49

1.03

0.683

1.15

t y  103 (kips)-1

1.04

0.692

0.236

0.157

0.261

0.174

t r  103 (kips)-1 r x /r y

1.35

0.900

0.306

0.204

0.339

0.226

r y , in.

0.766

5.17

3.39

3.41

2.07

3.27

3.23

c


h


v




IV-51



Fy = 65 ksi

W-Shapes W24

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.368 0.245

11 12 13 14 15

0.337 0.347 0.359 0.372 0.387

0.224 0.231 0.239 0.248 0.257

0.301 0.304 0.308 0.312 0.315

0.200 0.203 0.205 0.207 0.210

0.370 0.382 0.395 0.410 0.426

0.246 0.254 0.263 0.273 0.284

0.333 0.337 0.342 0.346 0.351

0.222 0.224 0.227 0.230 0.233

0.413 0.427 0.442 0.459 0.478

0.275 0.284 0.294 0.305 0.318

0.375 0.380 0.385 0.391 0.397

0.249 0.253 0.256 0.260 0.264

16 17 18 19 20

0.403 0.421 0.442 0.464 0.489

0.268 0.280 0.294 0.309 0.325

0.319 0.323 0.327 0.331 0.335

0.212 0.215 0.218 0.220 0.223

0.445 0.465 0.488 0.513 0.541

0.296 0.309 0.325 0.341 0.360

0.355 0.360 0.365 0.370 0.375

0.236 0.240 0.243 0.246 0.250

0.499 0.522 0.548 0.577 0.609

0.332 0.347 0.365 0.384 0.405

0.403 0.409 0.415 0.422 0.428

0.268 0.272 0.276 0.280 0.285

22 24 26 28 30

0.547 0.619 0.707 0.818 0.939

0.364 0.412 0.470 0.544 0.625

0.344 0.354 0.363 0.374 0.385

0.229 0.235 0.242 0.249 0.256

0.606 0.687 0.788 0.913 1.05

0.404 0.457 0.524 0.607 0.697

0.386 0.398 0.410 0.423 0.437

0.257 0.265 0.273 0.281 0.291

0.684 0.778 0.893 1.04 1.19

0.455 0.517 0.594 0.690 0.792

0.442 0.457 0.473 0.490 0.509

0.294 0.304 0.315 0.326 0.338

32 34 36 38 40

1.07 1.21 1.35 1.51 1.67

0.711 0.802 0.899 1.00 1.11

0.396 0.408 0.421 0.435 0.450

0.264 0.272 0.280 0.290 0.300

1.19 1.35 1.51 1.68 1.86

0.793 0.895 1.00 1.12 1.24

0.452 0.468 0.485 0.503 0.523

0.301 0.311 0.322 0.335 0.348

1.35 1.53 1.71 1.91 2.12

0.901 1.02 1.14 1.27 1.41

0.528 0.550 0.573 0.599 0.633

0.352 0.366 0.381 0.398 0.421

42 44 46 48 50

1.84 2.02 2.21 2.40 2.61

1.22 1.34 1.47 1.60 1.73


0.362 0.382 0.401 0.420 0.439

2.33 2.56 2.80 3.05 3.31

1.55 1.70 1.86 2.03 2.20

0.669 0.706 0.742 0.778 0.814

0.445 0.469 0.494 0.518 0.541

0

-1

250 3

3


Design


279h

306 3

b y  103 (kip-ft)-1

1.28

0.852

1.42

0.945

1.60

1.07

t y  103 (kips)-1

0.286

0.191

0.314

0.209

0.350

0.233

t r  103 (kips)-1 r x /r y

0.372

0.248

0.407

0.271

0.454

r y , in. h

W24

0.302

3.41

3.41

3.41

3.20

3.17

3.14




IV-52



W24

W24

Shape

229

207 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.490 0.326

11 12 13 14 15

0.454 0.469 0.486 0.505 0.526

0.302 0.312 0.323 0.336 0.350

0.414 0.421 0.427 0.434 0.441

0.276 0.280 0.284 0.289 0.293

0.504 0.521 0.540 0.562 0.586

0.335 0.347 0.359 0.374 0.390

0.463 0.471 0.479 0.487 0.496

0.308 0.313 0.319 0.324 0.330

0.542 0.561 0.581 0.604 0.630

0.361 0.373 0.387 0.402 0.419

0.503 0.512 0.521 0.531 0.541

0.335 0.341 0.347 0.353 0.360

16 17 18 19 20

0.549 0.576 0.605 0.637 0.673

0.365 0.383 0.402 0.424 0.448

0.448 0.455 0.463 0.471 0.479

0.298 0.303 0.308 0.313 0.319

0.612 0.642 0.676 0.713 0.754

0.407 0.427 0.449 0.474 0.502

0.505 0.514 0.523 0.533 0.544

0.336 0.342 0.348 0.355 0.362

0.660 0.692 0.728 0.768 0.813

0.439 0.460 0.484 0.511 0.541

0.551 0.562 0.573 0.584 0.596

0.367 0.374 0.381 0.389 0.397

22 24 26 28 30

0.758 0.864 0.996 1.16 1.33

0.505 0.575 0.663 0.769 0.883

0.497 0.515 0.535 0.557 0.580

0.330 0.343 0.356 0.370 0.386

0.851 0.972 1.12 1.30 1.50

0.566 0.647 0.748 0.868 0.996

0.565 0.589 0.615 0.643 0.674

0.376 0.392 0.409 0.428 0.448

0.918 1.05 1.22 1.41 1.62

0.611 0.698 0.809 0.938 1.08

0.622 0.650 0.681 0.715 0.752

0.414 0.433 0.453 0.475 0.500

32 34 36 38 40

1.51 1.70 1.91 2.13 2.36

1.00 1.13 1.27 1.42 1.57

0.606 0.634 0.664 0.708 0.752

0.403 0.422 0.442 0.471 0.501

1.70 1.92 2.16 2.40 2.66

1.13 1.28 1.43 1.60 1.77

0.708 0.748 0.803 0.857 0.912

0.471 0.497 0.534 0.571 0.607

1.84 2.08 2.33 2.60 2.88

1.23 1.38 1.55 1.73 1.92

0.793 0.856 0.920 0.984 1.05

0.528 0.569 0.612 0.655 0.697

42 44 46 48 50

2.60 2.85 3.12 3.40 3.68

1.73 1.90 2.08 2.26 2.45


0.643 0.679 0.715 0.751 0.787

3.17 3.48 3.81 4.15 4.50

2.11 2.32 2.53 2.76 2.99

1.11 1.17 1.24 1.30 1.36

0.740 0.782 0.824 0.866 0.908

0

-1

192 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

1.78

1.18

2.00

1.33

2.18

t y  103 (kips)-1

0.382

0.254

0.423

0.282

0.455

0.303

t r  103 (kips)-1 r x /r y

0.496

0.331

0.549

0.366

0.590

0.393

r y , in.

1.45

3.44

3.44

3.42

3.11

3.08

3.07



IV-53



Fy = 65 ksi

W-Shapes W24

Shape

176 b x  10

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.656 0.436

11 12 13 14 15

0.594 0.615 0.638 0.664 0.693

0.396 0.409 0.425 0.442 0.461

0.552 0.563 0.573 0.585 0.597

0.367 0.374 0.382 0.389 0.397

0.642 0.664 0.689 0.717 0.748

0.427 0.442 0.459 0.477 0.498

0.603 0.615 0.628 0.641 0.655

0.401 0.409 0.418 0.426 0.436

0.717 0.743 0.771 0.803 0.839

0.477 0.494 0.513 0.535 0.558

0.679 0.693 0.708 0.724 0.740

0.452 0.461 0.471 0.482 0.493

16 17 18 19 20

0.726 0.762 0.803 0.848 0.899

0.483 0.507 0.534 0.564 0.598

0.609 0.622 0.635 0.649 0.663

0.405 0.414 0.422 0.432 0.441

0.783 0.822 0.866 0.914 0.968

0.521 0.547 0.576 0.608 0.644

0.669 0.684 0.699 0.715 0.732

0.445 0.455 0.465 0.476 0.487

0.880 0.925 0.975 1.03 1.09

0.585 0.615 0.649 0.686 0.727

0.758 0.776 0.795 0.815 0.836

0.504 0.516 0.529 0.542 0.556

22 24 26 28 30

1.02 1.17 1.36 1.57 1.80

0.677 0.776 0.902 1.05 1.20

0.695 0.729 0.766 0.808 0.855

0.462 0.485 0.510 0.538 0.569

1.10 1.25 1.46 1.69 1.94

0.729 0.835 0.969 1.12 1.29

0.769 0.809 0.854 0.904 0.969

0.512 0.538 0.568 0.602 0.645

1.24 1.43 1.66 1.93 2.21

0.826 0.949 1.11 1.28 1.47

0.881 0.931 0.988 1.05 1.17

0.586 0.620 0.657 0.700 0.775

32 34 36 38 40

2.05 2.32 2.60 2.90 3.21

1.37 1.54 1.73 1.93 2.13

0.923 1.00 1.08 1.15 1.23

0.614 0.665 0.716 0.767 0.818

2.21 2.49 2.79 3.11 3.45

1.47 1.66 1.86 2.07 2.29

1.06 1.15 1.24 1.33 1.42

0.705 0.765 0.826 0.886 0.947

2.52 2.84 3.19 3.55 3.93

1.68 1.89 2.12 2.36 2.62

1.28 1.39 1.50 1.62 1.73

0.850 0.926 1.00 1.08 1.15

42 44 46 48 50

3.54 3.88 4.24 4.62 5.01

2.35 2.58 2.82 3.07 3.34


1.01 1.07 1.13 1.19 1.25

4.34 4.76 5.20 5.67 6.15

2.89 3.17 3.46 3.77 4.09

1.85 1.96 2.07 2.19 2.30

1.23 1.30 1.38 1.45 1.53

0

-1

3

3


Design


146c

162 3

3

b y  103 (kip-ft)-1

2.38

1.59

2.61

1.74

2.94

1.96

t y  103 (kips)-1

0.497

0.331

0.537

0.358

0.597

0.398

t r  103 (kips)-1 r x /r y

0.645

0.430

0.697

0.465

0.775

r y , in. c

W24

0.517

3.45

3.41

3.42

3.04

3.05

3.01




IV-54



W24

W24

Shape

c

117c

131

b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.961 0.640

11 12 13 14 15

0.809 0.835 0.865 0.902 0.944

0.538 0.556 0.576 0.600 0.628

0.770 0.788 0.806 0.826 0.846

0.513 0.524 0.537 0.549 0.563

0.928 0.958 0.992 1.03 1.07

0.618 0.638 0.660 0.686 0.715

0.875 0.897 0.919 0.942 0.967

0.582 0.597 0.611 0.627 0.643

1.06 1.10 1.14 1.18 1.23

0.708 0.731 0.757 0.786 0.819

0.995 1.02 1.05 1.07 1.10

0.662 0.679 0.696 0.715 0.735

16 17 18 19 20

0.990 1.04 1.10 1.17 1.24

0.659 0.693 0.732 0.775 0.824

0.867 0.890 0.913 0.938 0.964

0.577 0.592 0.607 0.624 0.641

1.12 1.18 1.25 1.32 1.41

0.748 0.785 0.830 0.880 0.936

0.993 1.02 1.05 1.08 1.11

0.660 0.679 0.698 0.718 0.740

1.29 1.35 1.42 1.50 1.60

0.857 0.899 0.947 1.00 1.06

1.14 1.17 1.20 1.24 1.28

0.755 0.777 0.801 0.826 0.852

22 24 26 28 30

1.41 1.63 1.90 2.21 2.53

0.938 1.08 1.27 1.47 1.68

1.02 1.09 1.16 1.28 1.42

0.679 0.722 0.770 0.849 0.942

1.61 1.86 2.18 2.53 2.90

1.07 1.24 1.45 1.68 1.93

1.18 1.26 1.36 1.54 1.71

0.787 0.840 0.908 1.02 1.14

1.83 2.12 2.49 2.89 3.32

1.22 1.41 1.66 1.92 2.21

1.37 1.47 1.64 1.85 2.06

0.910 0.976 1.09 1.23 1.37

32 34 36 38 40

2.88 3.25 3.65 4.06 4.50

1.92 2.16 2.43 2.70 3.00

1.56 1.70 1.84 1.99 2.13

1.04 1.13 1.23 1.32 1.42

3.30 3.72 4.18 4.65 5.16

2.20 2.48 2.78 3.10 3.43

1.89 2.07 2.25 2.43 2.62

1.26 1.38 1.50 1.62 1.74

3.77 4.26 4.78 5.32 5.90

2.51 2.83 3.18 3.54 3.92

2.29 2.51 2.74 2.97 3.20

1.52 1.67 1.82 1.98 2.13

42 44 46 48

4.96 5.45 5.95 6.48

3.30 3.62 3.96 4.31

2.28 2.42 2.57 2.71

1.52 1.61 1.71 1.80

5.68 6.24 6.82 7.42

3.78 4.15 4.54 4.94

2.80 2.98 3.17 3.35

1.86 1.99 2.11 2.23

6.50 7.13 7.80 8.49

4.33 4.75 5.19 5.65

3.44 3.67 3.91 4.14

2.29 2.44 2.60 2.76

0

-1

104c,f 3

3


Design


Fy = 65 ksi


3.36

2.24

3.84

2.55

4.48

2.98

t y  103 (kips)-1

0.666

0.443

0.747

0.497

0.837

0.557

t r  103 (kips)-1 r x /r y

0.864

0.576

0.969

0.646

1.09

r y , in. c

0.724

3.43

3.44

3.47

2.97

2.94

2.91


f

Shape does not meet compact limit for flexure with F y = 65 ksi. Note: Heavy line indicates KL /r y equal to or greater than 200.



IV-55



Fy = 65 ksi

W-Shapes W24

Shape

c

94c

103

b x  10

3

p  10

3

-1

-1

84c b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0






(kip-ft)-1 ASD LRFD 1.22 0.814

11 12 13 14 15

1.29 1.39 1.52 1.67 1.85

0.860 0.928 1.01 1.11 1.23

1.16 1.20 1.25 1.30 1.36

0.769 0.799 0.831 0.866 0.904

1.43 1.54 1.67 1.84 2.03

0.954 1.03 1.11 1.22 1.35

1.28 1.34 1.39 1.45 1.52

0.854 0.888 0.926 0.967 1.01

1.65 1.78 1.93 2.11 2.34

1.10 1.18 1.28 1.41 1.56

1.48 1.54 1.61 1.69 1.77

0.982 1.02 1.07 1.12 1.18

16 17 18 19 20

2.05 2.31 2.59 2.88 3.19

1.37 1.54 1.72 1.92 2.12

1.42 1.49 1.57 1.68 1.82

0.946 0.991 1.04 1.12 1.21

2.27 2.55 2.86 3.18 3.53

1.51 1.70 1.90 2.12 2.35

1.59 1.67 1.76 1.93 2.10

1.06 1.11 1.17 1.29 1.39

2.61 2.95 3.30 3.68 4.08

1.74 1.96 2.20 2.45 2.71

1.86 1.96 2.14 2.33 2.54

1.24 1.31 1.42 1.55 1.69

22 24 26 28 30

3.86 4.60 5.40 6.26 7.19

2.57 3.06 3.59 4.16 4.78

2.09 2.37 2.65 2.94 3.22

1.39 1.58 1.77 1.95 2.14

4.27 5.08 5.96 6.92 7.94

2.84 3.38 3.97 4.60 5.28

2.43 2.76 3.10 3.44 3.79

1.61 1.84 2.06 2.29 2.52

4.94 5.88 6.90 8.00 9.18

3.28 3.91 4.59 5.32 6.11

2.95 3.37 3.80 4.24 4.67

1.96 2.24 2.53 2.82 3.11

32

8.18

5.44

3.50

2.33

9.03

6.01

4.13

2.75

6.95

5.11

3.40

Design


W24

10.4


6.60

4.39

7.31

4.86

8.41

5.59

t y  103 (kips)-1

0.848

0.564

0.928

0.617

1.04

0.692

t r  103 (kips)-1 r x /r y

1.10

0.733

1.20

0.802

1.35

r y , in.

0.900

5.03

4.98

5.02

1.99

1.98

1.95

c




IV-56



W24

W24

Shape

c,v

68c,v

76

b x  10

3

p  10

3

-1

-1

b x  10

p  10

-1

62c,v 3

3

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.45 1.50 1.57 1.65 1.75

0.963 1.00 1.04 1.10 1.16

1.37 1.42 1.48 1.54 1.60

0.913 0.947 0.984 1.02 1.07

1.66 1.72 1.80 1.90 2.01

1.10 1.15 1.20 1.26 1.34

1.56 1.62 1.69 1.76 1.84

1.04 1.08 1.12 1.17 1.22

2.01 2.16 2.35 2.60 2.93

1.34 1.43 1.56 1.73 1.95

1.96 2.07 2.19 2.33 2.50

1.30 1.38 1.46 1.55 1.66

11 12 13 14 15

1.87 2.01 2.18 2.39 2.65

1.24 1.34 1.45 1.59 1.76

1.67 1.75 1.83 1.92 2.02

1.11 1.16 1.22 1.28 1.35

2.15 2.32 2.53 2.78 3.09

1.43 1.54 1.68 1.85 2.06

1.92 2.02 2.12 2.24 2.37

1.28 1.34 1.41 1.49 1.57

3.37 3.98 4.67 5.42 6.22

2.25 2.65 3.11 3.60 4.14

2.68 2.89 3.25 3.69 4.15

1.78 1.93 2.16 2.46 2.76

16 17 18 19 20

2.97 3.35 3.76 4.19 4.64

1.98 2.23 2.50 2.79 3.09

2.14 2.30 2.53 2.77 3.02

1.42 1.53 1.68 1.85 2.01

3.49 3.94 4.42 4.92 5.45

2.32 2.62 2.94 3.27 3.63

2.51 2.76 3.05 3.35 3.66

1.67 1.84 2.03 2.23 2.43

7.08 7.99 8.96 9.98 11.1

4.71 5.31 5.96 6.64 7.36

4.62 5.11 5.60 6.10 6.61

3.08 3.40 3.72 4.06 4.40

22 24 26 28 30

5.62 6.68 7.84 9.10 10.4

3.74 4.45 5.22 6.05 6.95

3.53 4.05 4.58 5.12 5.66

2.35 2.69 3.05 3.41 3.77

6.60 7.85 9.21 10.7 12.3

4.39 5.22 6.13 7.11 8.16

4.29 4.94 5.61 6.30 6.99

2.85 3.29 3.74 4.19 4.65

13.4

8.90

7.64

5.08

32

11.9

7.90

6.21

4.13

Design


Fy = 65 ksi


9.58

6.38

11.20

7.44

17.50

t y  103 (kips)-1

1.15

0.763

1.28

0.850

1.41

0.939

t r  103 (kips)-1 r x /r y

1.49

0.992

1.66

1.11

1.83

1.22

r y , in.

11.60

5.05

5.11

6.69

1.92

1.87

1.38

c


v





IV-57



Fy = 65 ksi

W-Shapes W21

W24

Shape

c,v

201

55

b x  10

3

p  10

3

b x  10

p  10

b x  103

-1

0




(kip-ft)-1 ASD LRFD 0.576 0.383

6 7 8 9 10

2.35 2.52 2.75 3.06 3.46

1.56 1.68 1.83 2.03 2.30

2.26 2.40 2.55 2.73 2.93

1.50 1.59 1.70 1.81 1.95

0.457 0.466 0.477 0.489 0.503

0.304 0.310 0.317 0.326 0.335

0.517 0.517 0.517 0.517 0.522

0.344 0.344 0.344 0.344 0.347

0.506 0.516 0.528 0.542 0.558

0.337 0.344 0.352 0.361 0.371

0.576 0.576 0.576 0.576 0.582

0.383 0.383 0.383 0.383 0.387

11 12 13 14 15

4.00 4.74 5.57 6.46 7.41

2.66 3.16 3.70 4.29 4.93

3.16 3.43 3.96 4.51 5.08

2.10 2.28 2.63 3.00 3.38

0.520 0.538 0.558 0.581 0.607

0.346 0.358 0.371 0.387 0.404

0.530 0.537 0.545 0.554 0.562

0.352 0.358 0.363 0.368 0.374

0.576 0.597 0.620 0.646 0.675

0.383 0.397 0.412 0.430 0.449

0.591 0.601 0.611 0.621 0.632

0.394 0.400 0.406 0.413 0.420

16 17 18 19 20

8.43 9.52 10.7 11.9 13.2

5.61 6.33 7.10 7.91 8.77

5.68 6.29 6.91 7.55 8.20

3.78 4.18 4.60 5.02 5.46

0.636 0.669 0.705 0.745 0.790

0.423 0.445 0.469 0.496 0.525

0.571 0.581 0.590 0.600 0.610

0.380 0.386 0.393 0.399 0.406

0.707 0.744 0.785 0.830 0.881

0.471 0.495 0.522 0.552 0.586

0.643 0.654 0.666 0.678 0.691

0.428 0.435 0.443 0.451 0.459

22 24 26 28 30

15.9

9.52

6.34

0.896 1.03 1.20 1.39 1.59

0.596 0.684 0.797 0.924 1.06

0.631 0.654 0.679 0.705 0.734

0.420 0.435 0.452 0.469 0.488

1.00 1.15 1.34 1.56 1.79

0.666 0.766 0.893 1.04 1.19

0.717 0.746 0.777 0.811 0.849

0.477 0.496 0.517 0.540 0.565


0.509 0.531 0.556 0.589 0.625

2.03 2.30 2.57 2.87 3.18

1.35 1.53 1.71 1.91 2.11

0.889 0.934 1.00 1.07 1.13

0.592 0.622 0.666 0.710 0.754

b y  103 (kip-ft)-1

2.06

1.37

2.30

1.53

t y  103 (kips)-1

1.59

1.06

0.433

0.288

0.479

0.319

t r  103 (kips)-1 r x /r y

2.06

1.37

0.562

0.375

0.622

r y , in.

20.6

13.7

-1

p  10


32 34 36 38 40

-1

3


10.6

-1

182 3

3

-1

Design


W24-W21

0.415

6.80

3.14

3.13

1.34

3.02

3.00

c


v





IV-58



W21

W21

Shape

166

147 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.823 0.548

6 7 8 9 10

0.556 0.567 0.581 0.596 0.614

0.370 0.378 0.386 0.397 0.408

0.634 0.634 0.634 0.634 0.642

0.422 0.422 0.422 0.422 0.427

0.629 0.642 0.658 0.676 0.696

0.419 0.427 0.438 0.449 0.463

0.735 0.735 0.735 0.735 0.747

0.489 0.489 0.489 0.489 0.497

0.701 0.716 0.733 0.753 0.777

0.467 0.476 0.488 0.501 0.517

0.823 0.823 0.823 0.823 0.838

0.548 0.548 0.548 0.548 0.558

11 12 13 14 15

0.634 0.656 0.682 0.711 0.743

0.422 0.437 0.454 0.473 0.494

0.653 0.665 0.677 0.689 0.702

0.435 0.442 0.450 0.458 0.467

0.719 0.746 0.776 0.809 0.847

0.479 0.496 0.516 0.539 0.564

0.761 0.776 0.792 0.808 0.825

0.506 0.516 0.527 0.537 0.549

0.803 0.833 0.867 0.905 0.948

0.534 0.554 0.577 0.602 0.631

0.856 0.874 0.892 0.912 0.933

0.569 0.581 0.594 0.607 0.621

16 17 18 19 20

0.779 0.819 0.865 0.915 0.971

0.518 0.545 0.575 0.609 0.646

0.715 0.729 0.743 0.758 0.774

0.476 0.485 0.494 0.504 0.515

0.890 0.937 0.990 1.05 1.12

0.592 0.623 0.659 0.698 0.742

0.842 0.861 0.880 0.900 0.921

0.560 0.573 0.585 0.599 0.613

0.996 1.05 1.11 1.18 1.25

0.663 0.698 0.739 0.783 0.834

0.954 0.977 1.00 1.02 1.05

0.635 0.650 0.665 0.682 0.699

22 24 26 28 30

1.10 1.27 1.48 1.72 1.98

0.735 0.846 0.988 1.15 1.31

0.806 0.842 0.882 0.925 0.972

0.537 0.560 0.587 0.615 0.647

1.27 1.47 1.72 2.00 2.29

0.847 0.979 1.15 1.33 1.53

0.966 1.02 1.07 1.13 1.21

0.643 0.676 0.712 0.753 0.803

1.43 1.66 1.94 2.25 2.59

0.953 1.10 1.29 1.50 1.72

1.11 1.17 1.24 1.32 1.45

0.737 0.778 0.825 0.877 0.962

32 34 36 38 40

2.25 2.54 2.85 3.17 3.51

1.50 1.69 1.89 2.11 2.34


0.875 0.947 1.02 1.09 1.16

2.95 3.32 3.73 4.15 4.60

1.96 2.21 2.48 2.76 3.06

1.58 1.71 1.85 1.98 2.12

1.05 1.14 1.23 1.32 1.41

0

-1

132 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

2.54

1.69

2.96

1.97

3.33

2.22

t y  103 (kips)-1

0.526

0.350

0.595

0.396

0.662

0.441

t r  103 (kips)-1 r x /r y

0.683

0.455

0.772

0.514

0.859

r y , in.

0.573

3.13

3.11

3.11

2.99

2.95

2.93



IV-59



Fy = 65 ksi

W-Shapes W21

Shape

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.758 0.774 0.793 0.815 0.840

0.504 0.515 0.528 0.542 0.559

0.893 0.893 0.893 0.893 0.911

0.594 0.594 0.594 0.594 0.606

0.846 0.862 0.881 0.903 0.927

0.563 0.574 0.586 0.601 0.617

0.982 0.982 0.982 0.983 1.00

0.654 0.654 0.654 0.654 0.668

0.944 0.962 0.983 1.01 1.03

0.628 0.640 0.654 0.670 0.689

1.08 1.08 1.08 1.08 1.11

0.721 0.721 0.721 0.722 0.738

11 12 13 14 15

0.869 0.902 0.939 0.980 1.03

0.578 0.600 0.625 0.652 0.683

0.930 0.951 0.973 0.995 1.02

0.619 0.633 0.647 0.662 0.678

0.960 0.996 1.04 1.08 1.14

0.638 0.663 0.690 0.721 0.756

1.03 1.05 1.08 1.10 1.13

0.684 0.700 0.716 0.734 0.752

1.07 1.10 1.15 1.19 1.25

0.710 0.734 0.762 0.794 0.829

1.14 1.16 1.19 1.22 1.25

0.756 0.774 0.793 0.814 0.835

16 17 18 19 20

1.08 1.14 1.20 1.28 1.36

0.718 0.757 0.801 0.850 0.905

1.04 1.07 1.10 1.13 1.16

0.694 0.712 0.730 0.749 0.769

1.20 1.26 1.34 1.42 1.51

0.795 0.839 0.888 0.944 1.01

1.16 1.19 1.22 1.26 1.29

0.772 0.792 0.813 0.836 0.860

1.31 1.38 1.47 1.56 1.66

0.873 0.921 0.976 1.04 1.10

1.29 1.32 1.36 1.40 1.44

0.857 0.881 0.906 0.933 0.961

22 24 26 28 30

1.56 1.80 2.12 2.45 2.82

1.04 1.20 1.41 1.63 1.87

1.22 1.30 1.38 1.50 1.65

0.813 0.862 0.917 0.996 1.10

1.73 2.01 2.36 2.74 3.14

1.15 1.34 1.57 1.82 2.09

1.37 1.46 1.56 1.74 1.93

0.912 0.972 1.04 1.16 1.28

1.91 2.22 2.60 3.02 3.46

1.27 1.48 1.73 2.01 2.30

1.54 1.64 1.80 2.01 2.24

1.02 1.09 1.19 1.34 1.49

32 34 36 38 40

3.20 3.62 4.06 4.52 5.01

2.13 2.41 2.70 3.01 3.33


1.41 1.53 1.66 1.79 1.91

3.94 4.45 4.99 5.56 6.16

2.62 2.96 3.32 3.70 4.10

2.46 2.69 2.92 3.14 3.37

1.64 1.79 1.94 2.09 2.24

0

-1

101c 3

3


Design


111c

122 3

b y  103 (kip-ft)-1

3.63

2.41

4.02

2.67

4.44

2.96

t y  103 (kips)-1

0.716

0.476

0.788

0.524

0.862

0.574

t r  103 (kips)-1 r x /r y

0.929

0.619

1.02

0.682

1.12

r y , in. c

W21

0.746

3.11

3.12

3.12

2.92

2.90

2.89




IV-60



W21

W21

Shape

c

83c

93

b x  10

3

p  10

3

-1

-1

73c b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.09 1.15 1.22 1.31 1.41

0.724 0.763 0.811 0.869 0.938

1.25 1.29 1.34 1.39 1.44

0.833 0.861 0.891 0.924 0.959

1.24 1.30 1.37 1.47 1.58

0.827 0.866 0.914 0.976 1.05

1.41 1.47 1.52 1.58 1.64

0.941 0.975 1.01 1.05 1.09

1.46 1.52 1.61 1.71 1.84

0.970 1.01 1.07 1.14 1.22

1.62 1.68 1.74 1.82 1.89

1.08 1.12 1.16 1.21 1.26

11 12 13 14 15

1.53 1.68 1.86 2.08 2.34

1.02 1.12 1.24 1.38 1.56

1.50 1.56 1.62 1.70 1.77

0.996 1.04 1.08 1.13 1.18

1.73 1.90 2.10 2.35 2.64

1.15 1.26 1.40 1.56 1.76

1.71 1.79 1.87 1.96 2.06

1.14 1.19 1.24 1.30 1.37

1.99 2.18 2.42 2.71 3.06

1.32 1.45 1.61 1.80 2.04

1.98 2.07 2.17 2.28 2.41

1.32 1.38 1.45 1.52 1.60

16 17 18 19 20

2.65 3.00 3.36 3.74 4.15

1.77 1.99 2.23 2.49 2.76

1.86 1.96 2.08 2.25 2.42

1.24 1.30 1.38 1.50 1.61

3.00 3.39 3.80 4.23 4.69

2.00 2.25 2.53 2.82 3.12

2.17 2.29 2.51 2.72 2.94

1.44 1.52 1.67 1.81 1.96

3.48 3.93 4.41 4.91 5.44

2.32 2.62 2.93 3.27 3.62

2.55 2.78 3.04 3.31 3.58

1.70 1.85 2.02 2.20 2.38

22 24 26 28 30

5.02 5.97 7.01 8.13 9.33

3.34 3.97 4.66 5.41 6.21

2.77 3.12 3.46 3.81 4.16

1.84 2.07 2.30 2.54 2.77

5.67 6.75 7.93 9.19 10.6

3.78 4.49 5.27 6.12 7.02

3.37 3.81 4.25 4.69 5.13

2.24 2.53 2.83 3.12 3.41

6.58 7.83 9.19 10.7 12.2

4.38 5.21 6.12 7.09 8.14

4.13 4.68 5.24 5.81 6.37

2.75 3.12 3.49 3.86 4.24

Design


Fy = 65 ksi


7.90

5.25

8.99

5.98

t y  103 (kips)-1

0.941

0.626

1.05

0.701

1.19

t r  103 (kips)-1 r x /r y

1.22

0.814

1.37

0.911

1.55

r y , in.

10.3

6.85 0.795 1.03

4.73

4.74

4.77

1.84

1.83

1.81

c




IV-61



Fy = 65 ksi

W-Shapes W21

Shape

c

62c

68

b x  10

3

p  10

3

-1

-1

b x  10

p  10

-1

57c 3

3

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.59 1.66 1.75 1.87 2.00

1.06 1.11 1.17 1.24 1.33

1.74 1.81 1.88 1.97 2.05

1.16 1.20 1.25 1.31 1.37

1.78 1.86 1.96 2.09 2.24

1.18 1.24 1.31 1.39 1.49

1.94 2.02 2.11 2.20 2.30

1.29 1.34 1.40 1.46 1.53

2.14 2.32 2.55 2.86 3.27

1.43 1.54 1.70 1.90 2.17

2.34 2.47 2.62 2.79 2.99

1.55 1.64 1.74 1.86 1.99

11 12 13 14 15

2.17 2.37 2.62 2.94 3.33

1.44 1.58 1.75 1.96 2.21

2.15 2.26 2.37 2.50 2.65

1.43 1.50 1.58 1.67 1.76

2.43 2.66 2.95 3.31 3.76

1.62 1.77 1.96 2.20 2.50

2.41 2.53 2.67 2.82 2.99

1.60 1.69 1.78 1.88 1.99

3.82 4.53 5.32 6.17 7.08

2.54 3.02 3.54 4.10 4.71

3.21 3.47 3.92 4.42 4.94

2.14 2.31 2.61 2.94 3.29

16 17 18 19 20

3.78 4.27 4.79 5.34 5.91

2.52 2.84 3.19 3.55 3.93

2.82 3.11 3.42 3.72 4.03

1.88 2.07 2.27 2.48 2.68

4.28 4.83 5.41 6.03 6.68

2.85 3.21 3.60 4.01 4.45

3.26 3.61 3.97 4.33 4.70

2.17 2.40 2.64 2.88 3.13

8.06 9.10 10.2 11.4 12.6

5.36 6.05 6.79 7.56 8.38

5.47 6.01 6.55 7.10 7.65

3.64 4.00 4.36 4.72 5.09

22 24 26 28 30

7.16 8.52 9.99 11.6 13.3

4.76 5.67 6.65 7.71 8.85

4.66 5.31 5.95 6.60 7.26

3.10 3.53 3.96 4.39 4.83

8.09 9.63 11.3 13.1

5.38 6.40 7.52 8.72

5.46 6.24 7.02 7.81

3.63 4.15 4.67 5.20

15.2

8.76

5.83

Design


W21

10.1


11.2

7.47

12.6

8.40

18.5

t y  103 (kips)-1

1.28

0.855

1.40

0.934

1.54

t r  103 (kips)-1 r x /r y

1.67

1.11

1.82

1.21

2.00

r y , in.

12.3 1.02 1.33

4.78

4.82

6.19

1.80

1.77

1.35

c




IV-62



W21

W21

Shape

c,v

50c,v

55

b x  10

3

p  10

3

-1

0



6 7 8 9 10

2.07 2.16 2.28 2.43 2.61

1.37 1.44 1.52 1.62 1.74

2.23 2.33 2.44 2.55 2.68

11 12 13 14 15

2.84 3.11 3.46 3.89 4.45

1.89 2.07 2.30 2.59 2.96

16 17 18 19 20

5.06 5.71 6.40 7.13 7.90

21 22 23 24 25 26 27 28

Design


Fy = 65 ksi

-1

48c,f,v b x  10

3

p  10

3

-1

3

b x  103

-1

p  10

-1





1.49 1.55 1.62 1.70 1.78

2.53 2.75 3.04 3.42 3.94

1.68 1.83 2.02 2.28 2.62

2.78 2.95 3.14 3.36 3.61

1.85 1.96 2.09 2.23 2.40

2.46 2.58 2.73 2.92 3.15

1.64 1.72 1.82 1.94 2.10

2.68 2.78 2.92 3.07 3.23

1.78 1.85 1.94 2.04 2.15

2.82 2.98 3.16 3.36 3.59

1.88 1.98 2.10 2.23 2.39

4.67 5.55 6.52 7.56 8.68

3.10 3.69 4.34 5.03 5.77

3.91 4.36 5.00 5.67 6.36

2.60 2.90 3.33 3.77 4.23

3.44 3.80 4.25 4.83 5.55

2.29 2.52 2.83 3.22 3.69

3.42 3.62 3.86 4.12 4.60

2.27 2.41 2.57 2.74 3.06

3.37 3.80 4.26 4.75 5.26

4.02 4.46 4.92 5.38 5.86

2.67 2.97 3.27 3.58 3.90

9.87 11.1 12.5 13.9 15.4

6.57 7.42 8.31 9.26 10.3

7.06 7.78 8.51 9.24 9.99

4.70 5.17 5.66 6.15 6.65

6.31 7.13 7.99 8.90 9.86

4.20 4.74 5.32 5.92 6.56

5.16 5.75 6.35 6.97 7.60

3.44 3.82 4.22 4.63 5.06

8.71 9.56 10.5 11.4 12.3

5.80 6.36 6.95 7.57 8.22

6.34 6.84 7.34 7.84 8.35

4.22 4.55 4.88 5.22 5.56

17.0

11.3

10.7

7.15

10.9 11.9 13.0 14.2 15.4

7.23 7.94 8.68 9.45 10.3

8.25 8.91 9.58 10.3 10.9

5.49 5.93 6.37 6.82 7.28

13.4 14.4 15.5

8.89 9.58 10.3

8.87 9.38 9.90

5.90 6.24 6.59

16.7 18.0

11.1 12.0

11.6 12.3

7.75 8.22


14.9

9.91

22.5

14.9

19.6

13.0

t y  103 (kips)-1

1.59

1.06

1.75

1.16

1.82

1.21

t r  103 (kips)-1 r x /r y

2.06

1.37

2.27

1.51

2.36

1.58

r y , in.

4.86

6.29

4.96

1.73

1.30

1.66

c


f


v





IV-63



Fy = 65 ksi

W-Shapes c,v

h

b x  10

3

p  10

283h

311

44 3

-1

b x  10

3

p  10

3

b x  103

-1

0





(kip-ft)-1 ASD LRFD 0.405 0.270

6 7 8 9 10

2.97 3.24 3.59 4.06 4.71

1.98 2.15 2.39 2.70 3.13

3.25 3.46 3.71 3.99 4.32

2.16 2.30 2.47 2.66 2.88

0.297 0.303 0.310 0.319 0.328

0.197 0.202 0.206 0.212 0.218

0.363 0.363 0.363 0.363 0.366

0.242 0.242 0.242 0.242 0.243

0.327 0.334 0.342 0.352 0.363

0.218 0.222 0.228 0.234 0.241

0.405 0.405 0.405 0.405 0.409

0.270 0.270 0.270 0.270 0.272

11 12 13 14 15

5.62 6.68 7.84 9.10 10.4

3.74 4.45 5.22 6.05 6.95

4.71 5.43 6.25 7.11 7.99

3.13 3.61 4.16 4.73 5.32

0.339 0.352 0.366 0.382 0.400

0.226 0.234 0.243 0.254 0.266

0.369 0.372 0.375 0.378 0.381

0.245 0.247 0.249 0.251 0.254

0.375 0.389 0.405 0.423 0.444

0.250 0.259 0.270 0.282 0.295

0.412 0.416 0.420 0.424 0.428

0.274 0.277 0.279 0.282 0.284

16 17 18 19 20

11.9 13.4 15.0 16.8 18.6

7.91 8.93 10.0 11.1 12.4

8.90 9.83 10.8 11.8 12.7

5.92 6.54 7.18 7.82 8.47

0.420 0.442 0.467 0.495 0.526

0.279 0.294 0.311 0.329 0.350

0.384 0.387 0.391 0.394 0.397

0.256 0.258 0.260 0.262 0.264

0.467 0.492 0.521 0.553 0.589

0.310 0.327 0.346 0.368 0.392

0.431 0.435 0.440 0.444 0.448

0.287 0.290 0.292 0.295 0.298

0.601 0.694 0.812 0.942 1.08

0.400 0.462 0.541 0.627 0.720

0.404 0.412 0.419 0.427 0.435

0.269 0.274 0.279 0.284 0.289

0.674 0.783 0.918 1.06 1.22

0.449 0.521 0.611 0.708 0.813

0.457 0.466 0.475 0.485 0.495

0.304 0.310 0.316 0.323 0.330


0.295 0.301 0.307 0.313 0.319

1.39 1.57 1.76 1.96 2.17

0.925 1.04 1.17 1.30 1.45

0.506 0.517 0.529 0.541 0.554

0.337 0.344 0.352 0.360 0.368

32 34 36 38 40

b y  103 (kip-ft)-1

26.9

t y  103 (kips)-1

1.98

t r  103 (kips)-1 r x /r y

2.56

17.9

-1

p  10


22 24 26 28 30

-1

3

-1

Design


W18

W21

Shape

r y , in.

W21-W18

1.32

0.881

1.48

0.986

1.31

0.280

0.187

0.308

0.205

1.71

0.364

0.243

0.400

0.267

6.40

2.96

2.96

1.26

2.95

2.91

c


h


v




IV-64



W18

W18

Shape

h

Design


234h

258

211

p  10

b x  10

p  10

b x  103

p  103

b x  103

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

3

3

3

0

ASD 0.338

LRFD 0.225

ASD 0.449

LRFD 0.298

ASD 0.375

LRFD 0.249

ASD 0.499

LRFD 0.332

ASD 0.412

LRFD 0.274

ASD 0.559

LRFD 0.372

6 7 8 9 10

0.359 0.367 0.376 0.386 0.399

0.239 0.244 0.250 0.257 0.265

0.449 0.449 0.449 0.449 0.453

0.298 0.298 0.298 0.299 0.302

0.398 0.407 0.417 0.429 0.443

0.265 0.271 0.278 0.286 0.295

0.499 0.499 0.499 0.500 0.505

0.332 0.332 0.332 0.333 0.336

0.439 0.449 0.460 0.474 0.490

0.292 0.299 0.306 0.315 0.326

0.559 0.559 0.559 0.561 0.568

0.372 0.372 0.372 0.373 0.378

11 12 13 14 15

0.413 0.429 0.447 0.467 0.490

0.275 0.285 0.297 0.311 0.326

0.458 0.462 0.467 0.471 0.476

0.304 0.307 0.310 0.314 0.317

0.459 0.477 0.498 0.521 0.547

0.306 0.318 0.331 0.347 0.364

0.511 0.516 0.522 0.528 0.534

0.340 0.343 0.347 0.351 0.355

0.508 0.528 0.552 0.578 0.607

0.338 0.352 0.367 0.384 0.404

0.574 0.581 0.588 0.596 0.603

0.382 0.387 0.391 0.396 0.401

16 17 18 19 20

0.516 0.545 0.577 0.613 0.654

0.343 0.362 0.384 0.408 0.435

0.481 0.486 0.491 0.496 0.501

0.320 0.323 0.327 0.330 0.334

0.577 0.610 0.647 0.688 0.735

0.384 0.406 0.430 0.458 0.489

0.540 0.546 0.552 0.558 0.565

0.359 0.363 0.367 0.372 0.376

0.641 0.678 0.720 0.768 0.821

0.426 0.451 0.479 0.511 0.546

0.611 0.618 0.626 0.635 0.643

0.406 0.411 0.417 0.422 0.428

22 24 26 28 30

0.751 0.875 1.03 1.19 1.37

0.500 0.582 0.684 0.793 0.910

0.512 0.524 0.536 0.548 0.561

0.341 0.348 0.356 0.365 0.373

0.847 0.990 1.16 1.35 1.55

0.563 0.659 0.773 0.897 1.03

0.579 0.593 0.608 0.624 0.641

0.385 0.395 0.405 0.415 0.426

0.949 1.11 1.31 1.52 1.74

0.631 0.741 0.870 1.01 1.16

0.661 0.679 0.699 0.720 0.742

0.440 0.452 0.465 0.479 0.494

32 34 36 38 40

1.56 1.76 1.97 2.19 2.43

1.04 1.17 1.31 1.46 1.62


0.438 0.451 0.464 0.478 0.492

1.98 2.24 2.51 2.79 3.09

1.32 1.49 1.67 1.86 2.06

0.766 0.791 0.817 0.846 0.877

0.509 0.526 0.544 0.563 0.583

b y  103 (kip-ft)-1

1.65

1.10

1.84

1.22

2.08

1.38

t y  103 (kips)-1

0.338

0.225

0.375

0.249

0.412

0.274

t r  103 (kips)-1 r x /r y

0.439

0.292

0.486

0.324

0.535

r y , in. h

Fy = 65 ksi

0.357

2.96

2.96

2.96

2.88

2.85

2.82




IV-65



Fy = 65 ksi

W-Shapes W18

Shape

192

175 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.770 0.512

6 7 8 9 10

0.487 0.498 0.512 0.527 0.545

0.324 0.332 0.340 0.351 0.363

0.620 0.620 0.620 0.623 0.631

0.413 0.413 0.413 0.414 0.420

0.533 0.546 0.561 0.578 0.598

0.355 0.363 0.373 0.385 0.398

0.689 0.689 0.689 0.693 0.703

0.458 0.458 0.458 0.461 0.468

0.593 0.607 0.624 0.643 0.666

0.394 0.404 0.415 0.428 0.443

0.770 0.770 0.770 0.776 0.788

0.512 0.512 0.512 0.516 0.524

11 12 13 14 15

0.566 0.589 0.615 0.645 0.679

0.376 0.392 0.409 0.429 0.452

0.639 0.648 0.656 0.665 0.675

0.425 0.431 0.437 0.443 0.449

0.621 0.647 0.677 0.711 0.749

0.413 0.431 0.451 0.473 0.498

0.713 0.723 0.734 0.745 0.757

0.474 0.481 0.488 0.496 0.503

0.692 0.722 0.755 0.793 0.836

0.460 0.480 0.502 0.528 0.556

0.801 0.814 0.827 0.841 0.855

0.533 0.541 0.550 0.560 0.569

16 17 18 19 20

0.717 0.760 0.808 0.862 0.924

0.477 0.506 0.538 0.574 0.615

0.684 0.694 0.704 0.714 0.725

0.455 0.462 0.468 0.475 0.482

0.792 0.840 0.895 0.956 1.03

0.527 0.559 0.595 0.636 0.682

0.768 0.780 0.793 0.806 0.819

0.511 0.519 0.528 0.536 0.545

0.885 0.940 1.00 1.07 1.15

0.589 0.625 0.667 0.713 0.766

0.870 0.886 0.902 0.918 0.935

0.579 0.589 0.600 0.611 0.622

22 24 26 28 30

1.07 1.26 1.48 1.72 1.97

0.712 0.839 0.985 1.14 1.31

0.747 0.771 0.796 0.823 0.852

0.497 0.513 0.530 0.548 0.567

1.19 1.41 1.65 1.92 2.20

0.794 0.938 1.10 1.28 1.47

0.847 0.877 0.910 0.945 0.982

0.564 0.584 0.605 0.628 0.653

1.34 1.59 1.86 2.16 2.48

0.892 1.06 1.24 1.44 1.65

0.971 1.01 1.05 1.10 1.15

0.646 0.672 0.701 0.731 0.765

32 34 36 38 40

2.24 2.53 2.84 3.16 3.50

1.49 1.68 1.89 2.10 2.33


0.680 0.710 0.742 0.784 0.830

2.82 3.19 3.57 3.98 4.41

1.88 2.12 2.38 2.65 2.93

1.21 1.27 1.35 1.44 1.52

0.802 0.843 0.900 0.957 1.01

0

-1

158 3

3


Design


W18

b y  103 (kip-ft)-1

2.30

1.53

2.59

1.72

2.89

1.92

t y  103 (kips)-1

0.457

0.304

0.500

0.333

0.555

0.369

t r  103 (kips)-1 r x /r y

0.593

0.395

0.649

0.432

0.720

r y , in.

0.480

2.97

2.97

2.96

2.79

2.76

2.74



IV-66



W18

W18

Shape

143

Design


Fy = 65 ksi

130

119

p  103

b x  103

p  103

b x  103

p  103

b x  103

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

0

ASD 0.612

LRFD 0.407

ASD 0.851

LRFD 0.566

ASD 0.671

LRFD 0.446

ASD 0.945

LRFD 0.629

ASD 0.732

LRFD 0.487

ASD 1.05

LRFD 0.696

6 7 8 9 10

0.654 0.670 0.689 0.711 0.736

0.435 0.446 0.458 0.473 0.490

0.851 0.851 0.851 0.859 0.874

0.566 0.566 0.566 0.572 0.582

0.718 0.735 0.756 0.781 0.809

0.478 0.489 0.503 0.520 0.539

0.945 0.945 0.945 0.956 0.974

0.629 0.629 0.629 0.636 0.648

0.784 0.803 0.826 0.853 0.884

0.521 0.534 0.550 0.568 0.588

1.05 1.05 1.05 1.06 1.08

0.696 0.696 0.696 0.705 0.719

11 12 13 14 15

0.765 0.798 0.836 0.879 0.928

0.509 0.531 0.556 0.585 0.617

0.889 0.905 0.921 0.938 0.956

0.592 0.602 0.613 0.624 0.636

0.842 0.879 0.921 0.969 1.02

0.560 0.585 0.613 0.645 0.681

0.992 1.01 1.03 1.05 1.07

0.660 0.673 0.686 0.700 0.714

0.920 0.961 1.01 1.06 1.12

0.612 0.639 0.670 0.706 0.745

1.10 1.13 1.15 1.18 1.20

0.734 0.750 0.766 0.783 0.800

16 17 18 19 20

0.982 1.04 1.11 1.19 1.28

0.654 0.695 0.741 0.794 0.853

0.974 0.993 1.01 1.03 1.05

0.648 0.661 0.674 0.688 0.702

1.08 1.15 1.23 1.32 1.42

0.722 0.768 0.820 0.879 0.946

1.10 1.12 1.14 1.17 1.20

0.729 0.745 0.761 0.778 0.796

1.19 1.26 1.35 1.45 1.56

0.790 0.841 0.899 0.964 1.04

1.23 1.26 1.29 1.32 1.36

0.819 0.838 0.858 0.880 0.902

22 24 26 28 30

1.50 1.78 2.08 2.42 2.77

0.996 1.18 1.39 1.61 1.85

1.10 1.15 1.20 1.26 1.33

0.732 0.765 0.801 0.841 0.885

1.66 1.98 2.32 2.69 3.09

1.11 1.31 1.54 1.79 2.05

1.25 1.32 1.39 1.47 1.56

0.834 0.877 0.923 0.975 1.04

1.83 2.17 2.55 2.96 3.39

1.22 1.45 1.70 1.97 2.26

1.43 1.51 1.60 1.71 1.87

0.950 1.00 1.06 1.14 1.24

32 34 36 38 40

3.16 3.56 4.00 4.45 4.93

2.10 2.37 2.66 2.96 3.28


1.13 1.21 1.30 1.38 1.47

3.86 4.36 4.89 5.45 6.04

2.57 2.90 3.25 3.62 4.02

2.03 2.18 2.34 2.50 2.65

1.35 1.45 1.56 1.66 1.77

b y  103 (kip-ft)-1

3.21

2.14

3.57

2.38

3.97

2.64

t y  103 (kips)-1

0.612

0.407

0.671

0.446

0.732

0.487

t r  103 (kips)-1 r x /r y

0.794

0.529

0.870

0.580

0.950

r y , in.

0.633

2.97

2.97

2.94

2.72

2.70

2.69



IV-67



Fy = 65 ksi

W-Shapes W18

Shape

106 b x  10

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.886 0.908 0.935 0.966 1.00

0.589 0.604 0.622 0.643 0.667

1.19 1.19 1.19 1.21 1.24

0.793 0.793 0.793 0.806 0.824

0.967 0.992 1.02 1.06 1.10

0.643 0.660 0.679 0.702 0.729

1.30 1.30 1.30 1.32 1.35

0.864 0.864 0.864 0.880 0.900

1.10 1.12 1.15 1.19 1.24

0.730 0.747 0.767 0.793 0.824

1.47 1.47 1.47 1.50 1.54

0.980 0.980 0.980 1.00 1.03

11 12 13 14 15

1.04 1.09 1.15 1.21 1.28

0.695 0.726 0.762 0.803 0.849

1.27 1.29 1.33 1.36 1.39

0.842 0.862 0.882 0.903 0.926

1.14 1.19 1.25 1.32 1.40

0.759 0.794 0.834 0.879 0.930

1.38 1.42 1.45 1.49 1.53

0.921 0.944 0.967 0.992 1.02

1.29 1.35 1.42 1.50 1.59

0.858 0.898 0.944 0.996 1.05

1.58 1.62 1.67 1.71 1.76

1.05 1.08 1.11 1.14 1.17

16 17 18 19 20

1.36 1.44 1.55 1.66 1.79

0.902 0.961 1.03 1.11 1.19

1.43 1.46 1.50 1.54 1.59

0.949 0.974 1.00 1.03 1.06

1.48 1.58 1.70 1.82 1.97

0.988 1.05 1.13 1.21 1.31

1.57 1.62 1.66 1.71 1.76

1.05 1.07 1.11 1.14 1.17

1.69 1.80 1.93 2.07 2.24

1.12 1.20 1.28 1.38 1.49

1.81 1.87 1.93 1.99 2.05

1.21 1.24 1.28 1.32 1.37

22 24 26 28 30

2.11 2.51 2.94 3.41 3.92

1.40 1.67 1.96 2.27 2.61

1.68 1.79 1.91 2.11 2.31

1.12 1.19 1.27 1.40 1.54

2.32 2.76 3.24 3.75 4.31

1.54 1.83 2.15 2.50 2.87

1.87 2.00 2.19 2.43 2.67

1.25 1.33 1.46 1.61 1.77

2.65 3.15 3.70 4.29 4.93

1.76 2.10 2.46 2.86 3.28

2.20 2.38 2.68 2.98 3.29

1.46 1.58 1.78 1.98 2.19

32 34 36 38 40

4.46 5.03 5.64 6.29 6.97

2.97 3.35 3.75 4.18 4.63


1.93 2.09 2.25 2.41 2.57

5.61 6.33 7.10 7.91 8.76

3.73 4.21 4.72 5.26 5.83

3.59 3.90 4.21 4.51 4.82

2.39 2.60 2.80 3.00 3.21

0

-1

3

3


Design


86c

97 3

3

b y  103 (kip-ft)-1

4.53

3.01

4.96

3.30

5.66

3.77

t y  103 (kips)-1

0.826

0.550

0.901

0.600

1.02

0.676

t r  103 (kips)-1 r x /r y

1.07

0.715

1.17

0.780

1.32

r y , in. c

W18

0.878

2.95

2.95

2.95

2.66

2.65

2.63




IV-68



W18

W18

Shape

c,f

Design


71c

76

65c

p  10

b x  10

p  10

b x  10

p  10

b x  103

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

3

3

3

3

3

0

ASD 1.20

LRFD 0.799

ASD 1.69

LRFD 1.12

ASD 1.24

LRFD 0.826

ASD 1.88

LRFD 1.25

ASD 1.39

LRFD 0.927

ASD 2.06

LRFD 1.37

6 7 8 9 10

1.28 1.31 1.34 1.38 1.43

0.850 0.869 0.893 0.920 0.952

1.69 1.69 1.69 1.72 1.77

1.12 1.12 1.12 1.15 1.18

1.46 1.55 1.66 1.80 1.97

0.970 1.03 1.11 1.20 1.31

1.93 2.00 2.08 2.16 2.26

1.28 1.33 1.38 1.44 1.50

1.62 1.71 1.83 1.98 2.17

1.07 1.14 1.22 1.32 1.45

2.12 2.20 2.29 2.39 2.50

1.41 1.47 1.53 1.59 1.66

11 12 13 14 15

1.49 1.55 1.62 1.71 1.81

0.989 1.03 1.08 1.14 1.20

1.82 1.87 1.92 1.98 2.04

1.21 1.24 1.28 1.32 1.36

2.18 2.43 2.74 3.11 3.57

1.45 1.62 1.82 2.07 2.37

2.36 2.47 2.59 2.72 2.87

1.57 1.64 1.72 1.81 1.91

2.40 2.68 3.02 3.44 3.95

1.60 1.78 2.01 2.29 2.63

2.61 2.74 2.88 3.04 3.21

1.74 1.82 1.92 2.02 2.14

16 17 18 19 20

1.93 2.06 2.21 2.38 2.57

1.28 1.37 1.47 1.58 1.71

2.10 2.17 2.25 2.32 2.41

1.40 1.45 1.49 1.55 1.60

4.06 4.58 5.14 5.73 6.34

2.70 3.05 3.42 3.81 4.22

3.03 3.27 3.55 3.84 4.12

2.02 2.18 2.36 2.55 2.74

4.50 5.08 5.69 6.34 7.02

2.99 3.38 3.79 4.22 4.67

3.43 3.76 4.09 4.43 4.76

2.28 2.50 2.72 2.95 3.17

22 24 26 28 30

3.05 3.63 4.26 4.94 5.68

2.03 2.42 2.84 3.29 3.78

2.60 2.90 3.28 3.67 4.06

1.73 1.93 2.18 2.44 2.70

7.68 9.14 10.7 12.4

5.11 6.08 7.13 8.27

4.69 5.25 5.82 6.38

3.12 3.50 3.87 4.25

8.50 10.1 11.9 13.8

5.66 6.73 7.90 9.16

5.44 6.11 6.79 7.46

3.62 4.07 4.51 4.96

32 34 36 38 40

6.46 7.29 8.17 9.11 10.1

4.30 4.85 5.44 6.06 6.71


b y  103 (kip-ft)-1

6.52

4.34

t y  103 (kips)-1

1.15

0.767

1.23

0.818

1.35

t r  103 (kips)-1 r x /r y

1.49

0.997

1.59

1.06

1.75

r y , in. c

Fy = 65 ksi

11.1

7.38

12.2

8.10 0.895 1.16

2.96

4.41

4.43

2.61

1.70

1.69


f




IV-69



Fy = 65 ksi

W-Shapes W18

Shape

c

55c

60

b x  10

3

p  10

3

-1

b x  10

p  10

-1

50c 3

3

b x  103

-1

p  10

0







6 7 8 9 10

1.79 1.89 2.01 2.17 2.37

1.19 1.26 1.34 1.44 1.58

2.30 2.39 2.49 2.60 2.72

1.53 1.59 1.66 1.73 1.81

1.97 2.08 2.22 2.39 2.60

1.31 1.39 1.48 1.59 1.73

2.53 2.64 2.76 2.88 3.03

1.68 1.76 1.83 1.92 2.01

2.23 2.35 2.51 2.70 2.94

1.48 1.57 1.67 1.80 1.95

2.82 2.94 3.08 3.23 3.40

1.87 1.96 2.05 2.15 2.26

11 12 13 14 15

2.63 2.93 3.31 3.78 4.34

1.75 1.95 2.20 2.52 2.89

2.85 3.00 3.16 3.34 3.54

1.90 1.99 2.10 2.22 2.35

2.87 3.22 3.64 4.16 4.77

1.91 2.14 2.42 2.77 3.17

3.18 3.36 3.55 3.76 4.04

2.12 2.23 2.36 2.50 2.69

3.23 3.61 4.09 4.69 5.39

2.15 2.40 2.72 3.12 3.58

3.59 3.79 4.03 4.29 4.70

2.39 2.52 2.68 2.85 3.13

16 17 18 19 20

4.94 5.57 6.25 6.96 7.71

3.28 3.71 4.16 4.63 5.13

3.87 4.25 4.63 5.02 5.41

2.58 2.83 3.08 3.34 3.60

5.43 6.13 6.87 7.65 8.48

3.61 4.08 4.57 5.09 5.64

4.48 4.93 5.39 5.85 6.32

2.98 3.28 3.59 3.89 4.20

6.13 6.92 7.76 8.64 9.58

4.08 4.60 5.16 5.75 6.37

5.22 5.76 6.31 6.86 7.43

3.48 3.83 4.20 4.57 4.94

22 24 26 28

9.33 11.1 13.0 15.1

6.21 7.39 8.67 10.1

6.19 6.98 7.76 8.55

4.12 4.64 5.16 5.69

6.83 8.13 9.54

7.26 8.20 9.16

4.83 5.46 6.09

7.71 9.17 10.8

8.56 9.72 10.9

5.70 6.47 7.24

10.3 12.2 14.3

-1

3

-1

Design


W18

11.6 13.8 16.2


13.3

8.85

14.8

9.86

16.5

t y  103 (kips)-1

1.46

0.971

1.59

1.06

1.75

t r  103 (kips)-1 r x /r y

1.89

1.26

2.06

1.37

2.27

r y , in.

11.0 1.16 1.51

4.45

4.44

4.47

1.68

1.67

1.65

c




IV-70



W18

W18

Shape

c

40c,v

46

Design

35c,v

p  10

b x  10

p  10

b x  10

p  10

b x  103

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

(kips)-1

(kip-ft)-1

3

3


Fy = 65 ksi

3

3

3

0

ASD 2.12

LRFD 1.41

ASD 3.02

LRFD 2.01

ASD 2.52

LRFD 1.67

ASD 3.50

LRFD 2.33

ASD 2.97

LRFD 1.98

ASD 4.12

LRFD 2.74

6 7 8 9 10

2.68 2.93 3.27 3.71 4.33

1.78 1.95 2.17 2.47 2.88

3.37 3.57 3.81 4.07 4.37

2.24 2.38 2.53 2.71 2.91

3.17 3.47 3.87 4.39 5.10

2.11 2.31 2.57 2.92 3.40

3.93 4.18 4.47 4.80 5.18

2.62 2.78 2.97 3.19 3.45

3.78 4.15 4.65 5.33 6.27

2.51 2.76 3.10 3.55 4.17

4.73 5.06 5.45 5.90 6.43

3.14 3.37 3.62 3.92 4.28

11 12 13 14 15

5.16 6.14 7.21 8.36 9.60

3.43 4.09 4.80 5.56 6.38

4.73 5.23 5.95 6.69 7.45

3.15 3.48 3.96 4.45 4.95

6.09 7.25 8.51 9.87 11.3

4.05 4.82 5.66 6.56 7.54

5.63 6.43 7.35 8.30 9.27

3.74 4.28 4.89 5.52 6.17

7.56 9.00 10.6 12.2 14.1

5.03 5.99 7.03 8.15 9.36

7.23 8.43 9.67 11.0 12.3

4.81 5.61 6.43 7.29 8.17

6.83 7.50 8.17 8.85 9.54

16.0 18.1 20.2 22.6 25.0

13.6 15.0 16.4 17.9 19.3

9.07 10.0 10.9 11.9 12.8

16 17 18 19 20

10.9 12.3 13.8 15.4 17.1

7.26 8.20 9.19 10.2 11.3

8.21 8.98 9.75 10.5 11.3

5.46 5.97 6.49 7.01 7.53

12.9 14.5 16.3 18.2 20.1

8.57 9.68 10.9 12.1 13.4

10.3 11.3 12.3 13.3 14.3

21

18.8

12.5

12.1

8.05

22.2

14.8

15.4

10.6 12.0 13.5 15.0 16.6

10.2


23.4

15.6

27.4

18.2

34.0

22.6

t y  103 (kips)-1

1.90

1.27

2.18

1.45

2.49

1.66

t r  103 (kips)-1 r x /r y

2.47

1.65

2.82

1.88

3.24

2.16

r y , in.

5.62

5.68

5.77

1.29

1.27

1.22

c


v


Note: Heavy line indicates KL /ry equal to or greater than 200.



IV-71



Fy = 65 ksi

W-Shapes W16

Shape

100

89 b x  10

3

p  10

3

-1

-1

77 b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

0.945 0.972 1.00 1.04 1.09

0.629 0.647 0.668 0.693 0.723

1.38 1.38 1.39 1.42 1.45

0.921 0.921 0.925 0.944 0.965

1.06 1.09 1.13 1.17 1.22

0.706 0.727 0.751 0.780 0.814

1.57 1.57 1.58 1.61 1.65

1.04 1.04 1.05 1.07 1.10

1.23 1.27 1.31 1.36 1.42

0.820 0.844 0.873 0.907 0.947

1.83 1.83 1.84 1.89 1.94

1.22 1.22 1.23 1.26 1.29

11 12 13 14 15

1.14 1.19 1.26 1.34 1.42

0.756 0.795 0.839 0.890 0.948

1.48 1.51 1.55 1.58 1.62

0.986 1.01 1.03 1.05 1.08

1.28 1.35 1.42 1.51 1.61

0.852 0.897 0.947 1.01 1.07

1.69 1.73 1.78 1.82 1.87

1.12 1.15 1.18 1.21 1.24

1.49 1.57 1.66 1.76 1.88

0.992 1.04 1.11 1.17 1.25

1.99 2.04 2.10 2.16 2.22

1.32 1.36 1.40 1.44 1.48

16 17 18 19 20

1.52 1.64 1.77 1.91 2.08

1.01 1.09 1.18 1.27 1.39

1.66 1.70 1.75 1.79 1.84

1.11 1.13 1.16 1.19 1.23

1.73 1.86 2.01 2.18 2.37

1.15 1.23 1.33 1.45 1.58

1.92 1.98 2.03 2.10 2.16

1.28 1.32 1.35 1.39 1.44

2.02 2.17 2.35 2.56 2.79

1.34 1.45 1.56 1.70 1.86

2.29 2.36 2.44 2.52 2.61

1.52 1.57 1.62 1.68 1.74

22 24 26 28 30

2.50 2.98 3.50 4.06 4.66

1.67 1.98 2.33 2.70 3.10

1.95 2.07 2.20 2.40 2.62

1.30 1.38 1.46 1.60 1.74

2.85 3.40 3.99 4.62 5.31

1.90 2.26 2.65 3.08 3.53

2.30 2.46 2.71 2.99 3.26

1.53 1.64 1.80 1.99 2.17

3.36 4.00 4.70 5.45 6.25

2.24 2.66 3.13 3.62 4.16

2.80 3.09 3.46 3.83 4.20

1.86 2.06 2.30 2.55 2.80

32 34 36 38 40

5.30 5.98 6.70 7.47 8.28

3.52 3.98 4.46 4.97 5.51


2.36 2.54 2.72 2.90 3.08

7.12 8.03 9.01 10.0 11.1

4.73 5.34 5.99 6.68 7.40

4.57 4.94 5.31 5.68 6.04

3.04 3.29 3.53 3.78 4.02

Design


W16

b y  103 (kip-ft)-1

4.99

3.32

5.70

3.79

6.67

4.44

t y  103 (kips)-1

0.874

0.581

0.981

0.652

1.14

0.756

t r  103 (kips)-1 r x /r y

1.13

0.756

1.27

0.848

1.47

r y , in.

0.983

2.83

2.83

2.83

2.51

2.49

2.47



IV-72



W16

W16

Shape

c

57c

67

b x  10

3

p  10

3

-1

-1

b x  10

p  10

-1

b x  103

-1

p  10

0





6 7 8 9 10

1.45 1.49 1.53 1.59 1.65

0.963 0.989 1.02 1.06 1.10

2.11 2.11 2.13 2.19 2.25

1.40 1.40 1.42 1.45 1.50

1.85 1.99 2.15 2.36 2.61

1.23 1.32 1.43 1.57 1.74

2.72 2.82 2.94 3.07 3.21

1.81 1.88 1.96 2.04 2.14

2.16 2.30 2.47 2.71 3.00

1.44 1.53 1.64 1.80 2.00

3.11 3.25 3.40 3.57 3.75

2.07 2.16 2.26 2.37 2.49

11 12 13 14 15

1.72 1.82 1.92 2.04 2.18

1.15 1.21 1.28 1.36 1.45

2.31 2.38 2.45 2.53 2.61

1.54 1.58 1.63 1.68 1.74

2.92 3.30 3.78 4.37 5.01

1.94 2.20 2.51 2.90 3.33

3.37 3.54 3.73 3.94 4.17

2.24 2.35 2.48 2.62 2.77

3.37 3.81 4.36 5.05 5.80

2.24 2.54 2.90 3.36 3.86

3.95 4.17 4.43 4.71 5.13

2.63 2.78 2.94 3.13 3.41

16 17 18 19 20

2.34 2.52 2.73 2.97 3.24

1.56 1.68 1.81 1.97 2.16

2.70 2.79 2.89 3.00 3.11

1.80 1.86 1.92 1.99 2.07

5.70 6.44 7.22 8.04 8.91

3.79 4.28 4.80 5.35 5.93

4.55 4.97 5.39 5.81 6.23

3.03 3.31 3.58 3.86 4.14

6.60 7.45 8.35 9.31 10.3

4.39 4.96 5.56 6.19 6.86

5.66 6.20 6.74 7.28 7.83

3.77 4.12 4.48 4.85 5.21

22 24 26 28 30

3.91 4.65 5.46 6.33 7.27

2.60 3.10 3.63 4.21 4.84

3.39 3.86 4.34 4.82 5.31

2.25 2.57 2.89 3.21 3.53

7.17 8.54 10.0

7.07 7.90 8.74

4.70 5.26 5.82

12.5 14.8 17.4

8.30 9.88 11.6

8.93 10.0 11.1

5.94 6.67 7.40

32 34 36 38 40

8.27 9.34 10.5 11.7 12.9

5.50 6.21 6.96 7.76 8.60


b y  103 (kip-ft)-1

7.72

5.14

t y  103 (kips)-1

1.31

0.872

1.53

1.02

1.75

t r  103 (kips)-1 r x /r y

1.70

1.13

1.98

1.32

2.27

r y , in.

3


10.8 12.8 15.1

-1

50c 3

3


Design


Fy = 65 ksi

14.5

9.65

16.8

11.2 1.16 1.51

2.83

4.20

4.20

2.46

1.60

1.59

c




IV-73



Fy = 65 ksi

W-Shapes W16

Shape

c

40c

45

b x  10

3

p  10

3

-1

0



6 7 8 9 10

2.45 2.60 2.80 3.05 3.37

1.63 1.73 1.86 2.03 2.24

3.50 3.66 3.84 4.04 4.25

11 12 13 14 15

3.78 4.30 4.94 5.73 6.58

2.52 2.86 3.29 3.81 4.37

16 17 18 19 20

7.48 8.45 9.47 10.5 11.7

4.98 5.62 6.30 7.02 7.78

21 22 23 24 25

12.9 14.1 15.5 16.8 18.3

8.57 9.41 10.3 11.2 12.2

26

19.8

13.1

Design


W16

-1

36c,f,v b x  10

3

p  10

3

-1

3

b x  103

-1

p  10

-1





2.33 2.44 2.55 2.68 2.83

2.83 3.00 3.22 3.50 3.85

1.88 2.00 2.15 2.33 2.56

3.95 4.14 4.35 4.59 4.85

2.63 2.76 2.90 3.05 3.23

3.22 3.43 3.70 4.03 4.45

2.14 2.28 2.46 2.68 2.96

4.55 4.78 5.04 5.32 5.64

3.03 3.18 3.35 3.54 3.75

4.50 4.77 5.07 5.43 6.06

2.99 3.17 3.38 3.61 4.03

4.29 4.84 5.57 6.46 7.41

2.85 3.22 3.70 4.30 4.93

5.14 5.47 5.84 6.40 7.17

3.42 3.64 3.89 4.26 4.77

4.99 5.69 6.61 7.67 8.80

3.32 3.78 4.40 5.10 5.86

6.00 6.41 6.88 7.82 8.79

3.99 4.26 4.58 5.20 5.85

6.71 7.36 8.03 8.70 9.37

4.46 4.90 5.34 5.79 6.23

8.43 9.52 10.7 11.9 13.2

5.61 6.33 7.10 7.91 8.77

7.96 8.76 9.58 10.4 11.2

5.30 5.83 6.38 6.93 7.48

10.0 11.3 12.7 14.1 15.6

6.66 7.52 8.43 9.40 10.4

9.79 10.8 11.9 12.9 14.0

6.51 7.19 7.89 8.59 9.31

10.0 10.7 11.4 12.1 12.8

6.68 7.14 7.59 8.04 8.50

14.5 15.9 17.4 19.0 20.6

9.66 10.6 11.6 12.6 13.7

12.1 12.9 13.8 14.6 15.5

8.04 8.61 9.17 9.74 10.3

17.3 18.9 20.7 22.5 24.4

11.5 12.6 13.8 15.0 16.3

15.1 16.2 17.3 18.4 19.5

13.5

8.95

22.3

14.8

16.4

10.9

10.0 10.8 11.5 12.2 13.0

Other Constants and Properties b y  10 (kip-ft) 3

t y  10 (kips) 3

-1

18.9

12.6

21.6

14.4

25.5

16.9

-1

1.93

1.29

2.18

1.45

2.42

1.61

t r  103 (kips)-1 r x /r y

2.51

1.67

2.82

1.88

3.14

2.10

r y , in.

4.24

4.22

4.28

1.57

1.57

1.52

c


f


v





IV-74



W16

W16

Shape

c,v

26c,v

31

b x  10

3

p  10

3

-1

Design


Fy = 65 ksi

b x  103

-1


p  10

-1

(kips)

3


(kips) ASD 4.05

LRFD 2.69

5.38 6.02 6.91 8.15 9.94

3.58 4.01 4.60 5.42 6.62

7.39 7.99 8.70 9.56 10.9

4.91 5.32 5.79 6.36 7.26

0

ASD 3.27

LRFD 2.17

6 7 8 9 10

4.30 4.79 5.45 6.36 7.67

2.86 3.18 3.62 4.23 5.10

5.92 6.36 6.88 7.49 8.21

3.94 4.23 4.58 4.98 5.47

11 12 13 14 15

9.28 11.0 13.0 15.0 17.2

6.17 7.34 8.62 10.0 11.5

9.55 11.1 12.6 14.2 15.8

6.35 7.35 8.39 9.45 10.5

12.0 14.3 16.8 19.5 22.4

8.01 9.53 11.2 13.0 14.9

12.9 15.0 17.2 19.5 21.9

8.60 10.0 11.5 13.0 14.6

16 17 18 19

19.6 22.2 24.8 27.7

13.1 14.7 16.5 18.4

17.5 19.2 20.9 22.6

11.6 12.8 13.9 15.0

25.5 28.7 32.2

16.9 19.1 21.4

24.3 26.7 29.2

16.2 17.8 19.4


39.0

25.9

50.0

33.3

t y  103 (kips)-1

2.81

1.87

3.35

2.23

t r  103 (kips)-1 r x /r y

3.65

2.43

4.34

2.89

r y , in.

5.48

5.59

1.17

1.12

c


v





IV-75



Fy = 65 ksi

W-Shapes W14

Shape

h

b x  10

3

p  10

-1

-1

605h b x  10

3

p  10

3

-1

-1

b x  103

p  10

3

0

(kips) (kip-ft) ASD LRFD ASD LRFD 0.119 0.0795 0.165 0.110


(kips) (kip-ft)-1 ASD LRFD ASD LRFD 0.144 0.0960 0.208 0.138

11 12 13 14 15

0.129 0.131 0.133 0.135 0.137

0.0857 0.0870 0.0883 0.0898 0.0915

0.165 0.165 0.165 0.165 0.165

0.110 0.110 0.110 0.110 0.110

0.142 0.144 0.146 0.149 0.151

0.0943 0.0957 0.0972 0.0989 0.101

0.185 0.185 0.185 0.185 0.185

0.123 0.123 0.123 0.123 0.123

0.156 0.159 0.161 0.164 0.167

0.104 0.106 0.107 0.109 0.111

0.208 0.208 0.208 0.208 0.208

0.138 0.138 0.138 0.138 0.138

16 17 18 19 20

0.140 0.143 0.146 0.150 0.153

0.0932 0.0952 0.0973 0.0995 0.102

0.166 0.166 0.166 0.167 0.167

0.110 0.110 0.111 0.111 0.111

0.154 0.158 0.161 0.165 0.169

0.103 0.105 0.107 0.110 0.113

0.186 0.186 0.187 0.187 0.188

0.124 0.124 0.124 0.125 0.125

0.171 0.175 0.179 0.183 0.188

0.114 0.116 0.119 0.122 0.125

0.209 0.209 0.210 0.210 0.211

0.139 0.139 0.140 0.140 0.140

22 24 26 28 30

0.161 0.171 0.182 0.195 0.209

0.107 0.114 0.121 0.130 0.139

0.168 0.169 0.170 0.170 0.171

0.112 0.112 0.113 0.113 0.114

0.179 0.190 0.202 0.217 0.233

0.119 0.126 0.135 0.144 0.155

0.189 0.190 0.191 0.192 0.193

0.126 0.126 0.127 0.128 0.128

0.199 0.211 0.226 0.242 0.262

0.132 0.141 0.150 0.161 0.174

0.212 0.213 0.215 0.216 0.217

0.141 0.142 0.143 0.144 0.144

32 34 36 38 40

0.226 0.245 0.268 0.293 0.324

0.150 0.163 0.178 0.195 0.216

0.172 0.173 0.174 0.175 0.176

0.115 0.115 0.116 0.116 0.117

0.253 0.275 0.301 0.331 0.366

0.168 0.183 0.200 0.220 0.244

0.194 0.195 0.196 0.197 0.198

0.129 0.130 0.130 0.131 0.132

0.284 0.310 0.340 0.375 0.416

0.189 0.206 0.226 0.250 0.277

0.218 0.220 0.221 0.222 0.223

0.145 0.146 0.147 0.148 0.149

42 44 46 48 50

0.357 0.392 0.429 0.467 0.506

0.238 0.261 0.285 0.311 0.337


0.132 0.133 0.134 0.135 0.135

0.459 0.503 0.550 0.599 0.650

0.305 0.335 0.366 0.399 0.432

0.225 0.226 0.227 0.229 0.230

0.150 0.150 0.151 0.152 0.153

Design


665h

730 3

-1

b y  103 (kip-ft)-1

0.336

0.223

0.375

0.250

0.420

0.280

t y  103 (kips)-1

0.119

0.0795

0.131

0.0872

0.144

0.0960

t r  103 (kips)-1 r x /r y

0.155

0.103

0.170

0.113

0.187

r y , in. h

W14

0.125

1.74

1.73

1.71

4.69

4.62

4.55




IV-76



W14

W14

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.293 0.195

11 12 13 14 15

0.172 0.175 0.178 0.181 0.185

0.115 0.116 0.118 0.121 0.123

0.232 0.232 0.232 0.232 0.233

0.155 0.155 0.155 0.155 0.155

0.190 0.193 0.197 0.200 0.204

0.127 0.129 0.131 0.133 0.136

0.261 0.261 0.261 0.261 0.262

0.174 0.174 0.174 0.174 0.174

0.209 0.212 0.216 0.221 0.225

0.139 0.141 0.144 0.147 0.150

0.293 0.293 0.293 0.293 0.294

0.195 0.195 0.195 0.195 0.196

16 17 18 19 20

0.189 0.193 0.198 0.203 0.208

0.126 0.128 0.131 0.135 0.138

0.234 0.234 0.235 0.236 0.237

0.155 0.156 0.156 0.157 0.157

0.209 0.214 0.219 0.225 0.231

0.139 0.142 0.146 0.150 0.154

0.263 0.264 0.265 0.266 0.266

0.175 0.176 0.176 0.177 0.177

0.230 0.236 0.242 0.248 0.255

0.153 0.157 0.161 0.165 0.170

0.295 0.296 0.297 0.298 0.299

0.196 0.197 0.198 0.199 0.199

22 24 26 28 30

0.220 0.234 0.251 0.270 0.292

0.147 0.156 0.167 0.180 0.194

0.238 0.239 0.241 0.242 0.244

0.158 0.159 0.160 0.161 0.162

0.245 0.261 0.280 0.302 0.327

0.163 0.174 0.186 0.201 0.218

0.268 0.270 0.272 0.274 0.275

0.178 0.180 0.181 0.182 0.183

0.271 0.289 0.311 0.335 0.364

0.180 0.192 0.207 0.223 0.242

0.302 0.304 0.306 0.308 0.311

0.201 0.202 0.204 0.205 0.207

32 34 36 38 40

0.318 0.348 0.382 0.424 0.469

0.211 0.231 0.254 0.282 0.312

0.246 0.247 0.249 0.250 0.252

0.163 0.164 0.165 0.166 0.168

0.357 0.391 0.432 0.480 0.531

0.238 0.260 0.287 0.319 0.354

0.277 0.279 0.281 0.283 0.285

0.185 0.186 0.187 0.188 0.190

0.398 0.437 0.483 0.538 0.596

0.265 0.291 0.322 0.358 0.397

0.313 0.315 0.318 0.320 0.323

0.208 0.210 0.211 0.213 0.215

42 44 46 48 50

0.517 0.568 0.621 0.676 0.733

0.344 0.378 0.413 0.450 0.488


0.191 0.192 0.194 0.195 0.197

0.657 0.721 0.789 0.859 0.932

0.437 0.480 0.525 0.571 0.620

0.325 0.328 0.330 0.333 0.335

0.216 0.218 0.220 0.221 0.223

0

-1

455h 3

3


Design


500h

550 3

b y  103 (kip-ft)-1

0.470

0.313

0.525

0.349

0.586

0.390

t y  103 (kips)-1

0.159

0.106

0.175

0.116

0.192

0.128

t r  103 (kips)-1 r x /r y

0.206

0.137

0.227

0.151

0.249

r y , in. h

Fy = 65 ksi

0.166

1.70

1.69

1.67

4.49

4.43

4.38




IV-77



Fy = 65 ksi

W-Shapes W14

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.372 0.248

11 12 13 14 15

0.224 0.228 0.232 0.237 0.242

0.149 0.152 0.155 0.158 0.161

0.315 0.315 0.315 0.316 0.317

0.210 0.210 0.210 0.210 0.211

0.240 0.244 0.249 0.254 0.259

0.160 0.162 0.165 0.169 0.172

0.342 0.342 0.342 0.343 0.344

0.228 0.228 0.228 0.228 0.229

0.258 0.263 0.268 0.273 0.279

0.172 0.175 0.178 0.182 0.186

0.372 0.372 0.372 0.374 0.375

0.248 0.248 0.248 0.249 0.250

16 17 18 19 20

0.248 0.254 0.260 0.267 0.275

0.165 0.169 0.173 0.178 0.183

0.318 0.320 0.321 0.322 0.323

0.212 0.213 0.213 0.214 0.215

0.265 0.272 0.279 0.287 0.295

0.176 0.181 0.185 0.191 0.196

0.346 0.347 0.348 0.350 0.351

0.230 0.231 0.232 0.233 0.234

0.286 0.293 0.301 0.309 0.318

0.190 0.195 0.200 0.206 0.212

0.377 0.378 0.380 0.382 0.383

0.251 0.252 0.253 0.254 0.255

22 24 26 28 30

0.292 0.312 0.336 0.363 0.395

0.194 0.208 0.223 0.242 0.263

0.326 0.328 0.331 0.333 0.336

0.217 0.218 0.220 0.222 0.224

0.314 0.336 0.361 0.391 0.426

0.209 0.223 0.240 0.260 0.284

0.354 0.357 0.360 0.363 0.366

0.236 0.238 0.239 0.241 0.244

0.339 0.363 0.392 0.425 0.463

0.226 0.242 0.261 0.283 0.308

0.387 0.390 0.393 0.397 0.401

0.257 0.259 0.262 0.264 0.267

32 34 36 38 40

0.433 0.476 0.527 0.588 0.651

0.288 0.317 0.351 0.391 0.433

0.339 0.341 0.344 0.347 0.350

0.225 0.227 0.229 0.231 0.233

0.467 0.515 0.571 0.637 0.705

0.311 0.342 0.380 0.423 0.469

0.369 0.372 0.375 0.379 0.382

0.246 0.248 0.250 0.252 0.254

0.508 0.561 0.625 0.696 0.771

0.338 0.374 0.416 0.463 0.513

0.404 0.408 0.412 0.416 0.419

0.269 0.271 0.274 0.276 0.279

42 44 46 48 50

0.718 0.788 0.861 0.938 1.02

0.478 0.524 0.573 0.624 0.677


0.256 0.259 0.261 0.263 0.266

0.850 0.933 1.02 1.11 1.21

0.566 0.621 0.679 0.739 0.802

0.423 0.428 0.432 0.436 0.440

0.282 0.284 0.287 0.290 0.293

0

-1

370h 3

3


Design


398h

426 3

b y  103 (kip-ft)-1

0.631

0.420

0.682

0.454

0.741

t y  103 (kips)-1

0.206

0.137

0.220

0.146

0.236

0.157

t r  103 (kips)-1 r x /r y

0.267

0.178

0.285

0.190

0.306

0.204

r y , in. h

W14

0.493

1.67

1.66

1.66

4.34

4.31

4.27




IV-78



W14

W14

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.506 0.336

11 12 13 14 15

0.279 0.284 0.289 0.295 0.302

0.186 0.189 0.192 0.196 0.201

0.408 0.408 0.408 0.409 0.411

0.271 0.271 0.271 0.272 0.274

0.309 0.314 0.320 0.327 0.335

0.205 0.209 0.213 0.218 0.223

0.454 0.454 0.454 0.457 0.459

0.302 0.302 0.302 0.304 0.305

0.339 0.345 0.352 0.360 0.368

0.226 0.230 0.234 0.239 0.245

0.506 0.506 0.506 0.509 0.511

0.336 0.336 0.337 0.338 0.340

16 17 18 19 20

0.309 0.317 0.326 0.335 0.345

0.206 0.211 0.217 0.223 0.230

0.413 0.415 0.417 0.419 0.421

0.275 0.276 0.277 0.279 0.280

0.343 0.352 0.361 0.372 0.383

0.228 0.234 0.240 0.247 0.255

0.461 0.464 0.466 0.468 0.471

0.307 0.308 0.310 0.312 0.313

0.377 0.387 0.398 0.410 0.423

0.251 0.258 0.265 0.273 0.281

0.514 0.517 0.520 0.523 0.526

0.342 0.344 0.346 0.348 0.350

22 24 26 28 30

0.368 0.394 0.426 0.462 0.505

0.245 0.262 0.283 0.307 0.336

0.425 0.429 0.433 0.437 0.441

0.283 0.285 0.288 0.291 0.294

0.409 0.440 0.475 0.516 0.565

0.272 0.292 0.316 0.344 0.376

0.476 0.481 0.486 0.491 0.496

0.316 0.320 0.323 0.327 0.330

0.451 0.485 0.525 0.572 0.626

0.300 0.323 0.349 0.380 0.417

0.532 0.538 0.544 0.551 0.557

0.354 0.358 0.362 0.366 0.371

32 34 36 38 40

0.555 0.613 0.684 0.762 0.844

0.369 0.408 0.455 0.507 0.562

0.446 0.450 0.455 0.459 0.464

0.297 0.300 0.303 0.306 0.309

0.622 0.689 0.770 0.858 0.951

0.414 0.459 0.512 0.571 0.633

0.501 0.507 0.513 0.518 0.524

0.334 0.337 0.341 0.345 0.349

0.691 0.766 0.857 0.955 1.06

0.459 0.510 0.570 0.635 0.704

0.564 0.571 0.578 0.585 0.592

0.375 0.380 0.384 0.389 0.394

42 44 46 48 50

0.931 1.02 1.12 1.22 1.32

0.619 0.680 0.743 0.809 0.878


0.353 0.357 0.361 0.365 0.370

1.17 1.28 1.40 1.52 1.65

0.776 0.852 0.931 1.01 1.10

0.600 0.608 0.616 0.624 0.632

0.399 0.404 0.410 0.415 0.421

0

-1

283h 3

3


Design


311h

342 3

b y  103 (kip-ft)-1

0.811

0.539

0.901

0.600

1.00

t y  103 (kips)-1

0.254

0.169

0.281

0.187

0.308

0.205

t r  103 (kips)-1 r x /r y

0.330

0.220

0.365

0.243

0.400

0.267

r y , in. h

Fy = 65 ksi

0.665

1.65

1.64

1.63

4.24

4.20

4.17




IV-79



Fy = 65 ksi

W-Shapes W14

Shape

257

233 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.703 0.468

11 12 13 14 15

0.374 0.381 0.389 0.398 0.407

0.249 0.254 0.259 0.265 0.271

0.563 0.563 0.563 0.567 0.570

0.374 0.374 0.375 0.377 0.379

0.414 0.422 0.430 0.440 0.450

0.275 0.281 0.286 0.293 0.300

0.629 0.629 0.630 0.634 0.638

0.418 0.418 0.419 0.422 0.425

0.458 0.467 0.476 0.487 0.499

0.305 0.311 0.317 0.324 0.332

0.703 0.703 0.705 0.710 0.715

0.468 0.468 0.469 0.472 0.476

16 17 18 19 20

0.417 0.429 0.441 0.454 0.468

0.278 0.285 0.293 0.302 0.312

0.574 0.577 0.581 0.584 0.588

0.382 0.384 0.386 0.389 0.391

0.462 0.475 0.488 0.503 0.519

0.307 0.316 0.325 0.335 0.346

0.642 0.647 0.651 0.656 0.660

0.427 0.430 0.433 0.436 0.439

0.512 0.526 0.542 0.558 0.577

0.341 0.350 0.360 0.372 0.384

0.720 0.726 0.731 0.737 0.742

0.479 0.483 0.486 0.490 0.494

22 24 26 28 30

0.501 0.540 0.585 0.638 0.700

0.333 0.359 0.389 0.424 0.466

0.595 0.603 0.611 0.619 0.627

0.396 0.401 0.406 0.412 0.417

0.556 0.600 0.650 0.710 0.781

0.370 0.399 0.433 0.472 0.519

0.669 0.679 0.688 0.699 0.709

0.445 0.452 0.458 0.465 0.472

0.618 0.667 0.724 0.792 0.872

0.411 0.444 0.482 0.527 0.580

0.754 0.766 0.778 0.790 0.803

0.501 0.509 0.517 0.526 0.535

32 34 36 38 40

0.773 0.859 0.963 1.07 1.19

0.514 0.572 0.641 0.714 0.791

0.635 0.644 0.653 0.662 0.671

0.423 0.428 0.434 0.440 0.447

0.863 0.962 1.08 1.20 1.33

0.574 0.640 0.717 0.799 0.886

0.719 0.730 0.742 0.753 0.765

0.479 0.486 0.493 0.501 0.509

0.966 1.08 1.21 1.35 1.49

0.643 0.717 0.804 0.896 0.993

0.817 0.831 0.845 0.860 0.876

0.543 0.553 0.562 0.572 0.583

42 44 46 48 50

1.31 1.44 1.57 1.71 1.86

0.872 0.957 1.05 1.14 1.24


0.517 0.526 0.535 0.544 0.553

1.65 1.81 1.97 2.15 2.33

1.09 1.20 1.31 1.43 1.55

0.892 0.908 0.925 0.943 0.962

0.593 0.604 0.616 0.628 0.640

0

-1

211 3

3


Design


W14

b y  103 (kip-ft)-1

1.11

0.741

1.24

0.825

1.38

0.921

t y  103 (kips)-1

0.340

0.226

0.375

0.250

0.414

0.276

t r  103 (kips)-1 r x /r y

0.441

0.294

0.487

0.324

0.538

r y , in.

0.358

1.62

1.62

1.61

4.13

4.10

4.07



IV-80



W14

W14

Shape

193

176 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.955 0.635

11 12 13 14 15

0.500 0.510 0.521 0.533 0.546

0.333 0.339 0.347 0.354 0.363

0.772 0.772 0.775 0.781 0.787

0.514 0.514 0.516 0.520 0.524

0.550 0.560 0.572 0.586 0.600

0.366 0.373 0.381 0.390 0.399

0.856 0.856 0.860 0.868 0.875

0.570 0.570 0.572 0.577 0.582

0.610 0.622 0.636 0.651 0.667

0.406 0.414 0.423 0.433 0.444

0.955 0.955 0.960 0.970 0.979

0.635 0.635 0.639 0.645 0.651

16 17 18 19 20

0.560 0.576 0.593 0.611 0.632

0.373 0.383 0.394 0.407 0.420

0.794 0.800 0.807 0.814 0.820

0.528 0.533 0.537 0.541 0.546

0.616 0.634 0.653 0.673 0.696

0.410 0.422 0.434 0.448 0.463

0.883 0.891 0.899 0.907 0.916

0.588 0.593 0.598 0.604 0.609

0.685 0.704 0.726 0.749 0.775

0.456 0.469 0.483 0.498 0.515

0.989 0.999 1.01 1.02 1.03

0.658 0.664 0.671 0.678 0.685

22 24 26 28 30

0.677 0.731 0.795 0.870 0.959

0.451 0.487 0.529 0.579 0.638

0.834 0.849 0.864 0.879 0.896

0.555 0.565 0.575 0.585 0.596

0.747 0.808 0.879 0.964 1.06

0.497 0.538 0.585 0.641 0.707

0.933 0.951 0.969 0.989 1.01

0.621 0.633 0.645 0.658 0.671

0.832 0.901 0.981 1.08 1.19

0.554 0.599 0.653 0.716 0.790

1.05 1.07 1.10 1.12 1.15

0.699 0.714 0.730 0.746 0.763

32 34 36 38 40

1.06 1.19 1.33 1.48 1.65

0.707 0.791 0.887 0.988 1.09

0.912 0.930 0.948 0.966 0.986

0.607 0.618 0.630 0.643 0.656

1.18 1.32 1.48 1.65 1.83

0.786 0.880 0.987 1.10 1.22

1.03 1.05 1.07 1.10 1.12

0.685 0.700 0.715 0.731 0.747

1.32 1.48 1.66 1.85 2.05

0.879 0.986 1.11 1.23 1.36

1.17 1.20 1.23 1.26 1.29

0.781 0.800 0.819 0.840 0.861

42 44 46 48 50

1.81 1.99 2.18 2.37 2.57

1.21 1.32 1.45 1.58 1.71


0.765 0.783 0.802 0.822 0.843

2.26 2.48 2.71 2.95 3.21

1.50 1.65 1.81 1.97 2.13

1.33 1.37 1.40 1.44 1.49

0.884 0.908 0.934 0.961 0.989

0

-1

159 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

1.52

1.01

1.68

1.12

1.88

t y  103 (kips)-1

0.452

0.301

0.496

0.330

0.550

0.366

t r  103 (kips)-1 r x /r y

0.587

0.391

0.644

0.429

0.714

0.476

r y , in.

1.25

1.60

1.60

1.60

4.05

4.02

4.00



IV-81



Fy = 65 ksi

W-Shapes W14

Shape

145

132 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






11 12 13 14 15

0.668 0.681 0.696 0.713 0.731

0.444 0.453 0.463 0.474 0.486

1.05 1.05 1.06 1.07 1.08

0.701 0.701 0.706 0.714 0.721

0.744 0.761 0.780 0.801 0.823

0.495 0.506 0.519 0.533 0.548

1.17 1.18 1.19 1.20 1.22

0.779 0.783 0.792 0.801 0.811

0.819 0.838 0.859 0.882 0.907

0.545 0.558 0.571 0.587 0.604

1.29 1.30 1.32 1.33 1.35

0.860 0.864 0.875 0.887 0.898

16 17 18 19 20

0.751 0.772 0.796 0.822 0.850

0.499 0.514 0.530 0.547 0.566

1.10 1.11 1.12 1.13 1.14

0.729 0.737 0.745 0.753 0.762

0.848 0.876 0.906 0.939 0.975

0.564 0.583 0.603 0.625 0.649

1.23 1.25 1.26 1.28 1.30

0.821 0.831 0.841 0.851 0.862

0.935 0.966 0.999 1.04 1.08

0.622 0.643 0.665 0.689 0.716

1.37 1.39 1.40 1.42 1.44

0.910 0.922 0.935 0.947 0.961

22 24 26 28 30

0.914 0.990 1.08 1.18 1.31

0.608 0.659 0.718 0.788 0.871

1.17 1.20 1.23 1.26 1.29

0.779 0.798 0.817 0.837 0.858

1.06 1.16 1.27 1.41 1.58

0.704 0.769 0.848 0.941 1.05

1.33 1.37 1.40 1.44 1.48

0.885 0.908 0.933 0.960 0.987

1.17 1.28 1.41 1.57 1.76

0.778 0.851 0.938 1.04 1.17

1.49 1.53 1.58 1.62 1.68

0.988 1.02 1.05 1.08 1.12

32 34 36 38 40

1.46 1.64 1.84 2.05 2.27

0.970 1.09 1.22 1.36 1.51

1.32 1.36 1.39 1.43 1.48

0.880 0.903 0.928 0.954 0.982

1.79 2.02 2.26 2.52 2.79

1.19 1.34 1.51 1.68 1.86

1.53 1.58 1.63 1.68 1.74

1.02 1.05 1.08 1.12 1.16

1.99 2.24 2.51 2.80 3.10

1.32 1.49 1.67 1.86 2.07

1.73 1.79 1.86 1.93 2.00

1.15 1.19 1.24 1.28 1.33

42 44 46 48 50

2.50 2.74 3.00 3.26 3.54

1.66 1.82 1.99 2.17 2.36


1.20 1.24 1.30 1.37 1.43

3.42 3.76 4.11 4.47 4.85

2.28 2.50 2.73 2.97 3.23

2.09 2.21 2.33 2.45 2.57

1.39 1.47 1.55 1.63 1.71

0

-1

120 3

3


Design


W14

b y  103 (kip-ft)-1

2.06

1.37

2.43

1.61

2.69

t y  103 (kips)-1

0.602

0.400

0.662

0.441

0.728

0.484

t r  103 (kips)-1 r x /r y

0.781

0.520

0.859

0.573

0.944

0.630

r y , in.

1.79

1.59

1.67

1.67

3.98

3.76

3.74



IV-82



W14

W14

Shape

f

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






11 12 13 14 15

0.904 0.925 0.948 0.974 1.00

0.602 0.615 0.631 0.648 0.667

1.45 1.45 1.45 1.47 1.50

0.962 0.962 0.968 0.981 0.995

0.996 1.02 1.04 1.07 1.10

0.663 0.678 0.695 0.714 0.735

1.64 1.64 1.64 1.64 1.67

1.09 1.09 1.09 1.09 1.11

1.09 1.12 1.15 1.18 1.21

0.728 0.745 0.764 0.785 0.808

1.86 1.86 1.86 1.86 1.86

1.24 1.24 1.24 1.24 1.24

16 17 18 19 20

1.03 1.07 1.10 1.15 1.19

0.687 0.710 0.735 0.762 0.792

1.52 1.54 1.56 1.58 1.61

1.01 1.02 1.04 1.05 1.07

1.14 1.18 1.22 1.26 1.31

0.758 0.783 0.811 0.841 0.874

1.69 1.72 1.75 1.78 1.81

1.13 1.14 1.16 1.18 1.20

1.25 1.29 1.34 1.39 1.45

0.833 0.861 0.892 0.925 0.962

1.88 1.91 1.94 1.97 2.01

1.25 1.27 1.29 1.31 1.34

22 24 26 28 30

1.29 1.41 1.56 1.74 1.95

0.860 0.941 1.04 1.16 1.29

1.66 1.71 1.77 1.83 1.90

1.10 1.14 1.18 1.22 1.26

1.43 1.57 1.73 1.93 2.16

0.951 1.04 1.15 1.28 1.44

1.87 1.93 2.00 2.08 2.16

1.24 1.29 1.33 1.38 1.44

1.57 1.72 1.91 2.12 2.38

1.05 1.15 1.27 1.41 1.59

2.08 2.16 2.25 2.34 2.45

1.39 1.44 1.50 1.56 1.63

32 34 36 38 40

2.20 2.49 2.79 3.11 3.44

1.47 1.66 1.86 2.07 2.29

1.97 2.04 2.12 2.21 2.33

1.31 1.36 1.41 1.47 1.55

2.45 2.77 3.10 3.45 3.83

1.63 1.84 2.06 2.30 2.55

2.25 2.34 2.45 2.60 2.78

1.50 1.56 1.63 1.73 1.85

2.70 3.05 3.42 3.81 4.23

1.80 2.03 2.28 2.54 2.81

2.56 2.68 2.86 3.08 3.29

1.70 1.78 1.90 2.05 2.19

42 44 46 48 50

3.80 4.17 4.55 4.96 5.38

2.53 2.77 3.03 3.30 3.58


1.97 2.08 2.20 2.32 2.43

4.66 5.11 5.59 6.08 6.60

3.10 3.40 3.72 4.05 4.39

3.51 3.72 3.94 4.15 4.36

2.33 2.48 2.62 2.76 2.90

0

-1

90f 3

3


Design


99f

109 3

b y  103 (kip-ft)-1

3.01

2.01

3.47

2.31

3.98

t y  103 (kips)-1

0.803

0.534

0.883

0.587

0.970

0.645

t r  103 (kips)-1 r x /r y

1.04

0.694

1.15

0.764

1.26

0.839

r y , in. f

Fy = 65 ksi

2.65

1.67

1.66

1.66

3.73

3.71

3.70




IV-83



Fy = 65 ksi

W-Shapes W14

Shape

82

74 b x  10

3

p  10

3

-1

-1

68 b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.16 1.19 1.23 1.28 1.34

0.772 0.794 0.821 0.853 0.890

1.97 1.97 1.98 2.03 2.07

1.31 1.31 1.32 1.35 1.38

1.28 1.31 1.36 1.41 1.47

0.850 0.874 0.904 0.939 0.980

2.18 2.18 2.19 2.24 2.29

1.45 1.45 1.46 1.49 1.52

1.39 1.44 1.48 1.54 1.61

0.927 0.955 0.988 1.03 1.07

2.38 2.38 2.40 2.46 2.52

1.59 1.59 1.60 1.64 1.68

11 12 13 14 15

1.40 1.47 1.56 1.66 1.77

0.932 0.981 1.04 1.10 1.18

2.11 2.16 2.21 2.26 2.31

1.41 1.44 1.47 1.50 1.54

1.54 1.62 1.72 1.82 1.94

1.03 1.08 1.14 1.21 1.29

2.34 2.40 2.46 2.52 2.58

1.56 1.60 1.63 1.68 1.72

1.69 1.78 1.88 2.00 2.14

1.12 1.18 1.25 1.33 1.42

2.58 2.65 2.72 2.79 2.86

1.72 1.76 1.81 1.86 1.91

16 17 18 19 20

1.89 2.04 2.20 2.39 2.61

1.26 1.36 1.46 1.59 1.73

2.37 2.42 2.48 2.55 2.62

1.57 1.61 1.65 1.70 1.74

2.08 2.24 2.42 2.63 2.87

1.39 1.49 1.61 1.75 1.91

2.65 2.72 2.80 2.88 2.96

1.76 1.81 1.86 1.91 1.97

2.29 2.47 2.67 2.91 3.17

1.53 1.64 1.78 1.93 2.11

2.95 3.03 3.12 3.22 3.32

1.96 2.02 2.08 2.14 2.21

22 24 26 28 30

3.14 3.74 4.39 5.09 5.84

2.09 2.49 2.92 3.39 3.89

2.76 2.93 3.11 3.38 3.67

1.84 1.95 2.07 2.25 2.44

3.46 4.12 4.83 5.60 6.43

2.30 2.74 3.21 3.73 4.28

3.15 3.36 3.64 4.00 4.36

2.09 2.23 2.42 2.66 2.90

3.83 4.56 5.35 6.21 7.12

2.55 3.03 3.56 4.13 4.74

3.54 3.80 4.24 4.67 5.10

2.36 2.53 2.82 3.11 3.39

32 34 36 38 40

6.65 7.50 8.41 9.37 10.4

4.42 4.99 5.60 6.24 6.91


3.14 3.38 3.61 3.85 4.08

8.11 9.15 10.3 11.4 12.7

5.39 6.09 6.83 7.60 8.43

5.53 5.96 6.38 6.81 7.23

3.68 3.96 4.25 4.53 4.81

Design


W14

b y  103 (kip-ft)-1

6.12

4.07

6.77

4.50

7.43

t y  103 (kips)-1

1.07

0.712

1.18

0.784

1.28

0.855

t r  103 (kips)-1 r x /r y

1.39

0.926

1.53

1.02

1.67

1.11

r y , in.

4.94

2.44

2.44

2.44

2.48

2.48

2.46



IV-84



W14

W14

Shape

b x  10

3

p  10

-1

48c

53

61 3

-1

b x  10

3

p  10

3

-1

-1

b x  103

-1

p  10

0






6 7 8 9 10

1.56 1.61 1.66 1.73 1.80

1.04 1.07 1.11 1.15 1.20

2.69 2.69 2.71 2.78 2.85

1.79 1.79 1.81 1.85 1.90

1.88 1.98 2.09 2.22 2.39

1.25 1.31 1.39 1.48 1.59

3.15 3.25 3.35 3.46 3.58

2.10 2.16 2.23 2.31 2.38

2.09 2.19 2.32 2.47 2.65

1.39 1.46 1.54 1.64 1.76

3.50 3.62 3.74 3.88 4.02

2.33 2.41 2.49 2.58 2.67

11 12 13 14 15

1.89 1.99 2.11 2.24 2.40

1.26 1.33 1.40 1.49 1.60

2.93 3.01 3.09 3.18 3.28

1.95 2.00 2.06 2.12 2.18

2.58 2.81 3.08 3.41 3.80

1.72 1.87 2.05 2.27 2.53

3.71 3.85 3.99 4.15 4.32

2.47 2.56 2.66 2.76 2.88

2.87 3.13 3.44 3.80 4.24

1.91 2.08 2.29 2.53 2.82

4.17 4.34 4.52 4.71 4.92

2.78 2.89 3.01 3.14 3.28

16 17 18 19 20

2.57 2.77 3.00 3.27 3.57

1.71 1.85 2.00 2.18 2.38

3.38 3.49 3.60 3.72 3.85

2.25 2.32 2.39 2.48 2.56

4.26 4.81 5.40 6.01 6.66

2.84 3.20 3.59 4.00 4.43

4.51 4.71 4.94 5.28 5.67

3.00 3.14 3.28 3.51 3.77

4.77 5.38 6.03 6.72 7.45

3.17 3.58 4.01 4.47 4.96

5.16 5.41 5.79 6.26 6.74

3.43 3.60 3.85 4.17 4.48

22 24 26 28 30

4.32 5.14 6.03 6.99 8.02

2.87 3.42 4.01 4.65 5.34

4.14 4.59 5.13 5.66 6.20

2.75 3.05 3.41 3.77 4.13

8.06 9.60 11.3 13.1 15.0

5.36 6.38 7.49 8.69 9.98

6.44 7.22 7.99 8.76 9.53

4.29 4.80 5.32 5.83 6.34

9.01 10.7 12.6 14.6 16.8

6.00 7.14 8.38 9.72 11.2

7.69 8.64 9.59 10.5 11.5

5.12 5.75 6.38 7.01 7.65

32 34 36 38 40

9.13 10.3 11.6 12.9 14.3

6.07 6.86 7.69 8.57 9.49

6.74 4.48 17.1 11.3 10.3 7.27 4.84 7.81 5.20 8.34 5.55 8.87 5.90 Other Constants and Properties

6.85

b y  103 (kip-ft)-1

8.36

5.56

t y  103 (kips)-1

1.44

0.955

1.65

1.10

1.82

t r  103 (kips)-1 r x /r y

1.86

1.24

2.14

1.42

2.36

r y , in.

3


Design


Fy = 65 ksi

12.5

8.29

14.0

9.30 1.21 1.58

2.44

3.07

3.06

2.45

1.92

1.91

c




IV-85



Fy = 65 ksi

W-Shapes W14

Shape

c

38c

43

b x  10

3

p  10

3

-1

0



6 7 8 9 10

2.38 2.49 2.63 2.79 2.99

1.59 1.66 1.75 1.86 1.99

3.96 4.10 4.25 4.41 4.58

11 12 13 14 15

3.24 3.54 3.90 4.32 4.83

2.16 2.36 2.59 2.88 3.21

16 17 18 19 20

5.45 6.15 6.90 7.68 8.51

21 22 23 24 25 26 27 28 29 30

Design


W14

b y  103 (kip-ft)-1

-1

34c b x  10

3

p  10

3





2.63 2.72 2.82 2.93 3.05

2.89 3.08 3.33 3.64 4.06

1.92 2.05 2.22 2.42 2.70

4.70 4.92 5.16 5.43 5.72

3.12 3.27 3.43 3.61 3.81

3.31 3.53 3.81 4.17 4.62

2.20 2.35 2.54 2.78 3.08

5.32 5.58 5.87 6.20 6.56

3.54 3.71 3.91 4.12 4.36

4.77 4.97 5.19 5.44 5.70

3.17 3.31 3.45 3.62 3.79

4.57 5.21 6.02 6.98 8.01

3.04 3.47 4.00 4.64 5.33

6.05 6.42 6.84 7.42 8.26

4.03 4.27 4.55 4.94 5.50

5.21 5.96 6.92 8.02 9.21

3.47 3.97 4.60 5.34 6.13

6.96 7.42 7.94 8.85 9.89

4.63 4.94 5.28 5.89 6.58

3.63 4.09 4.59 5.11 5.66

6.00 6.37 6.95 7.53 8.12

3.99 4.24 4.62 5.01 5.40

9.11 10.3 11.5 12.9 14.2

6.06 6.85 7.68 8.55 9.48

9.12 9.99 10.9 11.8 12.6

6.07 6.65 7.23 7.82 8.41

10.5 11.8 13.3 14.8 16.4

6.97 7.87 8.82 9.83 10.9

11.0 12.0 13.1 14.2 15.3

7.29 8.01 8.73 9.47 10.2

9.39 10.3 11.3 12.3 13.3

6.25 6.85 7.49 8.16 8.85

8.71 9.31 9.90 10.5 11.1

5.80 6.19 6.59 6.99 7.39

15.7 17.2 18.8 20.5 22.3

13.5 14.4 15.3 16.2 17.1

9.00 9.60 10.2 10.8 11.4

18.0 19.8 21.6 23.6 25.6

12.0 13.2 14.4 15.7 17.0

16.5 17.6 18.7 19.8 21.0

11.0 11.7 12.4 13.2 13.9

14.4 15.5 16.7 17.9 19.2

9.57 10.3 11.1 11.9 12.7


15.8

10.5

22.6

15.1

25.9

t y  103 (kips)-1

2.04

1.36

2.29

1.53

2.57

t r  103 (kips)-1 r x /r y

2.65

1.76

2.98

1.98

3.33

r y , in.

b x  103

-1

p  10

-1

10.4 11.5 12.5 13.6 14.8

-1

3

17.2 1.71 2.22

3.08

3.79

3.81

1.89

1.55

1.53

c




IV-86



W14

W14

Shape

c,f

26c,v

30

b x  10

3

p  10

3

-1

22c,v b x  10

3

p  10

3

-1

0



6 7 8 9 10

3.83 4.09 4.43 4.86 5.41

2.55 2.72 2.95 3.24 3.60

6.19 6.52 6.88 7.29 7.75

4.12 4.34 4.58 4.85 5.15

5.29 6.05 7.11 8.65 10.7

3.52 4.02 4.73 5.76 7.11

8.20 8.87 9.67 10.6 12.3

5.45 5.90 6.44 7.07 8.16

6.58 7.57 8.97 11.1 13.6

11 12 13 14 15

6.12 7.05 8.24 9.56 11.0

4.07 4.69 5.48 6.36 7.30

8.26 8.85 9.70 11.0 12.3

5.50 5.89 6.45 7.31 8.20

12.9 15.4 18.1 20.9 24.0

8.60 10.2 12.0 13.9 16.0

14.4 16.5 18.7 20.9 23.2

9.55 11.0 12.4 13.9 15.4

16.5 19.7 23.1 26.8 30.7

16 17 18 19 20

12.5 14.1 15.8 17.6 19.5

8.31 9.38 10.5 11.7 13.0

13.7 15.1 16.5 18.0 19.4

9.12 10.0 11.0 12.0 12.9

27.3 30.9 34.6

18.2 20.5 23.0

25.5 27.8 30.1

17.0 18.5 20.0

34.9 39.4

22 24

23.6 28.1

15.7 18.7

22.4 25.4

14.9 16.9


-1


3

b x  103

-1


p  10

-1

Design


Fy = 65 ksi

(kips) ASD LRFD 4.65 3.09 4.38 5.03 5.97 7.36 9.08

10.2 11.1 12.2 13.6 16.4

6.76 7.38 8.11 9.05 10.9

11.0 13.1 15.3 17.8 20.4

19.2 22.3 25.4 28.5 31.8

12.8 14.8 16.9 19.0 21.2

23.2 26.2

35.1 38.4

23.3 25.6


31.4

20.9

49.5

32.9

62.4

t y  103 (kips)-1

2.90

1.93

3.34

2.22

3.96

t r  103 (kips)-1 r x /r y

3.77

2.51

4.33

2.89

5.14

r y , in.

41.5 2.63 3.42

3.85

5.23

5.33

1.49

1.08

1.04

c


f


v





IV-87



Fy = 65 ksi

W-Shapes W12

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.570 0.379

6 7 8 9 10

0.271 0.275 0.279 0.285 0.291

0.180 0.183 0.186 0.190 0.194

0.454 0.454 0.454 0.454 0.454

0.302 0.302 0.302 0.302 0.302

0.299 0.304 0.309 0.316 0.323

0.199 0.202 0.206 0.210 0.215

0.510 0.510 0.510 0.510 0.510

0.340 0.340 0.340 0.340 0.340

0.328 0.333 0.339 0.346 0.354

0.218 0.221 0.225 0.230 0.235

0.570 0.570 0.570 0.570 0.570

0.379 0.379 0.379 0.379 0.379

11 12 13 14 15

0.298 0.306 0.315 0.325 0.335

0.198 0.204 0.209 0.216 0.223

0.455 0.457 0.459 0.461 0.463

0.303 0.304 0.305 0.307 0.308

0.331 0.340 0.350 0.361 0.374

0.220 0.226 0.233 0.240 0.249

0.511 0.514 0.516 0.518 0.521

0.340 0.342 0.343 0.345 0.347

0.363 0.373 0.384 0.397 0.411

0.241 0.248 0.256 0.264 0.273

0.571 0.574 0.577 0.580 0.583

0.380 0.382 0.384 0.386 0.388

16 17 18 19 20

0.348 0.361 0.375 0.392 0.409

0.231 0.240 0.250 0.261 0.272

0.465 0.467 0.469 0.471 0.473

0.309 0.311 0.312 0.313 0.315

0.387 0.403 0.419 0.438 0.458

0.258 0.268 0.279 0.291 0.305

0.523 0.526 0.528 0.531 0.533

0.348 0.350 0.351 0.353 0.355

0.426 0.444 0.462 0.483 0.507

0.284 0.295 0.308 0.322 0.337

0.586 0.589 0.592 0.595 0.598

0.390 0.392 0.394 0.396 0.398

22 24 26 28 30

0.450 0.500 0.560 0.633 0.724

0.300 0.333 0.373 0.421 0.482

0.477 0.481 0.485 0.490 0.494

0.317 0.320 0.323 0.326 0.329

0.506 0.563 0.633 0.719 0.824

0.337 0.375 0.421 0.478 0.548

0.538 0.544 0.549 0.555 0.560

0.358 0.362 0.365 0.369 0.373

0.560 0.626 0.705 0.803 0.922

0.373 0.416 0.469 0.534 0.613

0.604 0.611 0.617 0.624 0.631

0.402 0.406 0.411 0.415 0.420

32 34 36 38 40

0.824 0.930 1.04 1.16 1.29

0.548 0.619 0.694 0.773 0.856


0.376 0.380 0.384 0.388 0.392

1.05 1.18 1.33 1.48 1.64

0.698 0.788 0.883 0.984 1.09

0.638 0.645 0.652 0.660 0.667

0.424 0.429 0.434 0.439 0.444

0

-1

279h 3

3


Design


305h

336 3

b y  103 (kip-ft)-1

1.00

0.665

1.12

0.747

1.25

0.829

t y  103 (kips)-1

0.260

0.173

0.287

0.191

0.314

0.209

t r  103 (kips)-1 r x /r y

0.337

0.225

0.372

0.248

0.407

r y , in. h

W12

0.271

1.85

1.84

1.82

3.47

3.42

3.38




IV-88



W12

W12

Shape

h

b x  10

3

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10





(kip-ft)-1 ASD LRFD 0.788 0.524

6 7 8 9 10

0.362 0.368 0.375 0.383 0.392

0.241 0.245 0.250 0.255 0.261

0.640 0.640 0.640 0.640 0.640

0.426 0.426 0.426 0.426 0.426

0.397 0.403 0.411 0.420 0.430

0.264 0.268 0.274 0.279 0.286

0.710 0.710 0.710 0.710 0.710

0.472 0.472 0.472 0.472 0.472

0.435 0.442 0.451 0.461 0.472

0.290 0.294 0.300 0.307 0.314

0.788 0.788 0.788 0.788 0.788

0.524 0.524 0.524 0.524 0.524

11 12 13 14 15

0.402 0.414 0.427 0.441 0.457

0.268 0.275 0.284 0.293 0.304

0.643 0.646 0.650 0.653 0.657

0.428 0.430 0.432 0.435 0.437

0.441 0.454 0.469 0.485 0.503

0.294 0.302 0.312 0.323 0.334

0.713 0.717 0.722 0.726 0.730

0.474 0.477 0.480 0.483 0.486

0.485 0.499 0.515 0.533 0.554

0.323 0.332 0.343 0.355 0.368

0.792 0.797 0.802 0.807 0.813

0.527 0.530 0.534 0.537 0.541

16 17 18 19 20

0.475 0.494 0.516 0.540 0.566

0.316 0.329 0.343 0.359 0.377

0.661 0.665 0.668 0.672 0.676

0.440 0.442 0.445 0.447 0.450

0.523 0.545 0.569 0.596 0.626

0.348 0.362 0.378 0.396 0.416

0.735 0.739 0.744 0.749 0.753

0.489 0.492 0.495 0.498 0.501

0.576 0.600 0.628 0.658 0.692

0.383 0.400 0.418 0.438 0.460

0.818 0.824 0.829 0.835 0.841

0.544 0.548 0.552 0.556 0.559

22 24 26 28 30

0.628 0.703 0.795 0.909 1.04

0.418 0.468 0.529 0.605 0.694

0.684 0.692 0.700 0.709 0.717

0.455 0.460 0.466 0.471 0.477

0.695 0.779 0.883 1.01 1.16

0.462 0.519 0.588 0.674 0.773

0.763 0.773 0.783 0.793 0.804

0.508 0.514 0.521 0.528 0.535

0.770 0.865 0.982 1.13 1.30

0.512 0.576 0.654 0.752 0.863

0.853 0.865 0.877 0.890 0.903

0.567 0.575 0.584 0.592 0.601

32 34 36 38 40

1.19 1.34 1.50 1.67 1.85

0.790 0.891 0.999 1.11 1.23


0.542 0.550 0.557 0.565 0.573

1.48 1.67 1.87 2.08 2.31

0.982 1.11 1.24 1.38 1.53

0.917 0.931 0.946 0.960 0.976

0.610 0.619 0.629 0.639 0.649

0

-1

210 3

3


Design


230h

252 3

b y  103 (kip-ft)-1

1.40

0.930

1.55

1.03

1.72

1.15

t y  103 (kips)-1

0.347

0.231

0.380

0.252

0.416

0.277

t r  103 (kips)-1 r x /r y

0.450

0.300

0.492

0.328

0.539

r y , in. h

Fy = 65 ksi

0.360

1.81

1.80

1.80

3.34

3.31

3.28




IV-89



Fy = 65 ksi

W-Shapes W12

Shape

190

170 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.481 0.489 0.498 0.510 0.522

0.320 0.325 0.332 0.339 0.347

0.881 0.881 0.881 0.881 0.881

0.586 0.586 0.586 0.586 0.586

0.539 0.548 0.559 0.572 0.586

0.359 0.365 0.372 0.380 0.390

0.997 0.997 0.997 0.997 0.997

0.663 0.663 0.663 0.663 0.663

0.603 0.614 0.626 0.641 0.658

0.401 0.408 0.417 0.426 0.437

1.13 1.13 1.13 1.13 1.13

0.750 0.750 0.750 0.750 0.751

11 12 13 14 15

0.537 0.553 0.571 0.591 0.614

0.357 0.368 0.380 0.394 0.409

0.887 0.893 0.900 0.906 0.913

0.590 0.594 0.599 0.603 0.607

0.603 0.621 0.642 0.666 0.692

0.401 0.413 0.427 0.443 0.460

1.00 1.01 1.02 1.03 1.04

0.668 0.674 0.679 0.685 0.691

0.676 0.698 0.721 0.748 0.778

0.450 0.464 0.480 0.498 0.518

1.14 1.15 1.16 1.17 1.18

0.758 0.765 0.772 0.779 0.786

16 17 18 19 20

0.639 0.667 0.698 0.732 0.770

0.425 0.444 0.465 0.487 0.513

0.920 0.927 0.934 0.941 0.948

0.612 0.617 0.621 0.626 0.631

0.720 0.753 0.788 0.828 0.871

0.479 0.501 0.524 0.551 0.580

1.05 1.06 1.06 1.07 1.08

0.696 0.702 0.708 0.714 0.720

0.811 0.848 0.889 0.934 0.984

0.540 0.564 0.591 0.621 0.655

1.19 1.20 1.22 1.23 1.24

0.793 0.801 0.809 0.816 0.824

22 24 26 28 30

0.859 0.968 1.10 1.27 1.46

0.572 0.644 0.733 0.845 0.970

0.963 0.978 0.994 1.01 1.03

0.641 0.651 0.661 0.672 0.683

0.973 1.10 1.25 1.45 1.66

0.648 0.731 0.835 0.964 1.11

1.10 1.12 1.14 1.16 1.18

0.733 0.746 0.759 0.773 0.788

1.10 1.25 1.43 1.65 1.90

0.733 0.830 0.949 1.10 1.26

1.26 1.29 1.32 1.34 1.37

0.841 0.858 0.875 0.894 0.913

32 34 36 38 40

1.66 1.87 2.10 2.34 2.59

1.10 1.25 1.40 1.56 1.72


0.803 0.819 0.835 0.852 0.870

2.16 2.43 2.73 3.04 3.37

1.43 1.62 1.82 2.02 2.24

1.40 1.43 1.47 1.50 1.54

0.933 0.954 0.976 0.999 1.02

0

-1

152 3

3


Design


W12

b y  103 (kip-ft)-1

1.92

1.28

2.18

1.45

2.47

1.64

t y  103 (kips)-1

0.459

0.305

0.514

0.342

0.575

0.382

t r  103 (kips)-1 r x /r y

0.595

0.397

0.667

0.444

0.746

r y , in.

0.497

1.79

1.78

1.77

3.25

3.22

3.19



IV-90



W12

W12

Shape

136

120 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.676 0.689 0.703 0.720 0.739

0.450 0.458 0.468 0.479 0.491

1.28 1.28 1.28 1.28 1.28

0.852 0.852 0.852 0.852 0.854

0.768 0.782 0.798 0.817 0.839

0.511 0.520 0.531 0.544 0.558

1.47 1.47 1.47 1.47 1.48

0.980 0.980 0.980 0.980 0.984

0.867 0.883 0.902 0.923 0.949

0.577 0.587 0.600 0.614 0.631

1.67 1.67 1.67 1.67 1.68

1.11 1.11 1.11 1.11 1.12

11 12 13 14 15

0.760 0.784 0.812 0.842 0.877

0.506 0.522 0.540 0.560 0.583

1.30 1.31 1.32 1.34 1.35

0.862 0.871 0.880 0.889 0.899

0.864 0.893 0.924 0.960 1.00

0.575 0.594 0.615 0.639 0.665

1.50 1.51 1.53 1.55 1.57

0.995 1.01 1.02 1.03 1.04

0.977 1.01 1.05 1.09 1.13

0.650 0.672 0.696 0.723 0.753

1.70 1.72 1.75 1.77 1.79

1.13 1.15 1.16 1.18 1.19

16 17 18 19 20

0.915 0.957 1.00 1.06 1.11

0.609 0.637 0.668 0.703 0.741

1.37 1.38 1.39 1.41 1.43

0.908 0.918 0.928 0.938 0.949

1.04 1.09 1.15 1.21 1.28

0.694 0.727 0.764 0.804 0.849

1.59 1.60 1.62 1.64 1.67

1.05 1.07 1.08 1.09 1.11

1.18 1.24 1.30 1.37 1.45

0.787 0.825 0.867 0.913 0.965

1.82 1.84 1.87 1.89 1.92

1.21 1.23 1.24 1.26 1.28

22 24 26 28 30

1.25 1.42 1.63 1.89 2.16

0.832 0.944 1.08 1.25 1.44

1.46 1.49 1.53 1.56 1.60

0.970 0.993 1.02 1.04 1.07

1.44 1.63 1.88 2.18 2.50

0.955 1.09 1.25 1.45 1.66

1.71 1.75 1.80 1.85 1.91

1.14 1.17 1.20 1.23 1.27

1.63 1.86 2.15 2.49 2.86

1.09 1.24 1.43 1.66 1.90

1.98 2.04 2.10 2.17 2.25

1.32 1.36 1.40 1.45 1.50

32 34 36 38 40

2.46 2.78 3.12 3.47 3.85

1.64 1.85 2.07 2.31 2.56


1.31 1.35 1.39 1.44 1.48

3.25 3.67 4.11 4.58 5.08

2.16 2.44 2.74 3.05 3.38

2.33 2.41 2.50 2.60 2.71

1.55 1.60 1.66 1.73 1.80

0

-1

106 3

3


Design


Fy = 65 ksi

b y  103 (kip-ft)-1

2.80

1.86

3.21

2.14

3.65

2.43

t y  103 (kips)-1

0.644

0.428

0.730

0.486

0.823

0.548

t r  103 (kips)-1 r x /r y

0.835

0.557

0.947

0.631

1.07

r y , in.

0.712

1.77

1.76

1.76

3.16

3.13

3.11



IV-91



Fy = 65 ksi

W-Shapes W12

Shape

96 b x  10

p  10

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.959 0.977 0.999 1.02 1.05

0.638 0.650 0.664 0.681 0.700

1.86 1.86 1.86 1.86 1.88

1.24 1.24 1.24 1.24 1.25

1.06 1.08 1.10 1.13 1.16

0.704 0.717 0.733 0.751 0.772

2.08 2.08 2.08 2.08 2.09

1.38 1.38 1.38 1.38 1.39

1.17 1.19 1.22 1.25 1.28

0.777 0.792 0.810 0.830 0.854

2.32 2.32 2.32 2.32 2.32

1.54 1.54 1.54 1.54 1.55

11 12 13 14 15

1.08 1.12 1.16 1.21 1.26

0.721 0.745 0.772 0.803 0.837

1.90 1.93 1.96 1.98 2.01

1.27 1.28 1.30 1.32 1.34

1.20 1.24 1.28 1.33 1.39

0.796 0.823 0.853 0.888 0.926

2.12 2.16 2.19 2.23 2.26

1.41 1.44 1.46 1.48 1.51

1.32 1.37 1.42 1.48 1.54

0.880 0.911 0.945 0.983 1.03

2.36 2.40 2.44 2.49 2.53

1.57 1.60 1.63 1.66 1.69

16 17 18 19 20

1.32 1.38 1.45 1.53 1.62

0.875 0.917 0.965 1.02 1.08

2.04 2.08 2.11 2.14 2.18

1.36 1.38 1.40 1.42 1.45

1.46 1.53 1.61 1.70 1.79

0.968 1.02 1.07 1.13 1.19

2.30 2.34 2.38 2.42 2.46

1.53 1.56 1.58 1.61 1.64

1.61 1.69 1.78 1.88 1.99

1.07 1.13 1.19 1.25 1.33

2.58 2.63 2.68 2.73 2.78

1.72 1.75 1.78 1.82 1.85

22 24 26 28 30

1.82 2.08 2.41 2.79 3.20

1.21 1.38 1.60 1.86 2.13

2.25 2.32 2.41 2.49 2.59

1.50 1.55 1.60 1.66 1.72

2.03 2.32 2.68 3.11 3.57

1.35 1.54 1.79 2.07 2.38

2.56 2.65 2.76 2.88 3.00

1.70 1.77 1.84 1.91 2.00

2.26 2.58 3.00 3.48 4.00

1.50 1.72 2.00 2.32 2.66

2.90 3.02 3.16 3.31 3.47

1.93 2.01 2.10 2.20 2.31

32 34 36 38 40

3.64 4.11 4.61 5.14 5.69

2.42 2.74 3.07 3.42 3.79


2.09 2.19 2.33 2.49 2.64

4.55 5.13 5.75 6.41 7.10

3.02 3.41 3.83 4.26 4.73

3.65 3.93 4.21 4.50 4.78

2.43 2.61 2.80 2.99 3.18

0

-1

3

3


Design


79f

87 3

3

b y  103 (kip-ft)-1

4.06

2.70

4.54

3.02

5.09

3.38

t y  103 (kips)-1

0.911

0.606

1.00

0.668

1.11

0.737

t r  103 (kips)-1 r x /r y

1.18

0.788

1.30

0.868

1.44

r y , in. f

W12

0.958

1.76

1.75

1.75

3.09

3.07

3.05




IV-92



W12

W12

Shape

f

b x  10

3

p  10

-1

-1

58 b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.28 1.31 1.34 1.37 1.41

0.855 0.871 0.891 0.913 0.939

2.61 2.61 2.61 2.61 2.61

1.74 1.74 1.74 1.74 1.74

1.42 1.45 1.48 1.52 1.56

0.945 0.963 0.985 1.01 1.04

2.99 2.99 2.99 2.99 2.99

1.99 1.99 1.99 1.99 1.99

1.63 1.68 1.74 1.80 1.88

1.09 1.12 1.16 1.20 1.25

3.17 3.17 3.19 3.26 3.34

2.11 2.11 2.12 2.17 2.22

11 12 13 14 15

1.46 1.51 1.56 1.63 1.70

0.969 1.00 1.04 1.08 1.13

2.61 2.66 2.71 2.76 2.81

1.74 1.77 1.80 1.84 1.87

1.61 1.67 1.73 1.81 1.89

1.07 1.11 1.15 1.20 1.25

2.99 2.99 3.04 3.10 3.17

1.99 1.99 2.02 2.06 2.11

1.97 2.07 2.18 2.31 2.46

1.31 1.37 1.45 1.54 1.64

3.42 3.50 3.59 3.68 3.78

2.27 2.33 2.39 2.45 2.51

16 17 18 19 20

1.78 1.87 1.97 2.08 2.20

1.18 1.24 1.31 1.38 1.47

2.87 2.93 2.99 3.05 3.12

1.91 1.95 1.99 2.03 2.07

1.98 2.08 2.19 2.31 2.45

1.31 1.38 1.46 1.54 1.63

3.23 3.30 3.38 3.46 3.54

2.15 2.20 2.25 2.30 2.35

2.64 2.83 3.06 3.31 3.60

1.75 1.88 2.03 2.20 2.40

3.88 3.99 4.10 4.22 4.35

2.58 2.65 2.73 2.81 2.89

22 24 26 28 30

2.49 2.86 3.32 3.85 4.42

1.66 1.90 2.21 2.56 2.94

3.26 3.41 3.58 3.77 3.98

2.17 2.27 2.38 2.51 2.64

2.78 3.19 3.72 4.31 4.95

1.85 2.12 2.47 2.87 3.29

3.71 3.90 4.11 4.35 4.71

2.47 2.60 2.74 2.90 3.13

4.33 5.15 6.05 7.01 8.05

2.88 3.43 4.02 4.67 5.36

4.63 4.95 5.47 6.02 6.57

3.08 3.29 3.64 4.01 4.37

32 34 36 38 40

5.03 5.68 6.37 7.09 7.86

3.35 3.78 4.24 4.72 5.23


3.41 3.69 3.98 4.25 4.53

9.16 10.3 11.6 12.9 14.3

6.09 6.88 7.71 8.59 9.52

7.12 7.66 8.21 8.75 9.29

4.74 5.10 5.46 5.82 6.18

Design


65f

72 3

b y  103 (kip-ft)-1

5.80

3.86

6.74

4.48

8.43

5.61

t y  103 (kips)-1

1.22

0.810

1.35

0.895

1.51

1.01

t r  103 (kips)-1 r x /r y

1.58

1.05

1.75

1.16

1.96

r y , in. f

Fy = 65 ksi

1.31

1.75

1.75

2.10

3.04

3.02

2.51




IV-93



Fy = 65 ksi

W-Shapes W12

Shape

f

50

53

b x  10

3

p  10

3

-1

0



6 7 8 9 10

1.78 1.84 1.90 1.97 2.06

1.19 1.22 1.26 1.31 1.37

3.58 3.58 3.58 3.63 3.72

11 12 13 14 15

2.16 2.27 2.40 2.55 2.72

1.43 1.51 1.60 1.69 1.81

16 17 18 19 20

2.91 3.13 3.39 3.68 4.01

22 24 26 28 30

4.83 5.75 6.75 7.83 8.99

Design


W12

32 34 36 38 40

10.2 11.5 12.9 14.4 16.0

b x  10

p  10

-1

b x  103

-1

p  10





2.38 2.38 2.38 2.42 2.48

2.00 2.10 2.21 2.35 2.51

1.33 1.39 1.47 1.56 1.67

3.81 3.91 4.03 4.15 4.28

2.54 2.60 2.68 2.76 2.85

2.23 2.34 2.47 2.63 2.81

1.49 1.56 1.64 1.75 1.87

4.27 4.39 4.53 4.68 4.84

2.84 2.92 3.02 3.11 3.22

3.82 3.92 4.02 4.13 4.25

2.54 2.61 2.68 2.75 2.83

2.71 2.94 3.21 3.54 3.92

1.80 1.96 2.14 2.35 2.61

4.42 4.57 4.73 4.90 5.08

2.94 3.04 3.14 3.26 3.38

3.03 3.29 3.60 3.97 4.41

2.02 2.19 2.40 2.64 2.93

5.01 5.19 5.38 5.59 5.82

3.33 3.45 3.58 3.72 3.87

1.94 2.08 2.25 2.45 2.67

4.38 4.51 4.65 4.80 4.96

2.91 3.00 3.09 3.19 3.30

4.38 4.94 5.53 6.17 6.83

2.91 3.28 3.68 4.10 4.55

5.27 5.49 5.72 5.96 6.33

3.51 3.65 3.80 3.97 4.21

4.93 5.56 6.23 6.94 7.69

3.28 3.70 4.15 4.62 5.12

6.07 6.34 6.63 7.06 7.58

4.04 4.22 4.41 4.70 5.04

3.22 3.83 4.49 5.21 5.98

5.31 5.81 6.48 7.15 7.81

3.53 3.86 4.31 4.75 5.20

8.27 9.84 11.5 13.4 15.4

5.50 6.55 7.68 8.91 10.2

7.17 8.01 8.84 9.67 10.5

4.77 5.33 5.88 6.44 6.99

9.31 11.1 13.0 15.1 17.3

6.19 7.37 8.65 10.0 11.5

8.62 9.66 10.7 11.7 12.8

5.73 6.43 7.11 7.80 8.48

7.53

19.7

13.1

13.8

9.16


b y  103 (kip-ft)-1

9.68

6.44

t y  103 (kips)-1

1.65

1.10

1.76

1.17

1.96

t r  103 (kips)-1 r x /r y

2.14

1.42

2.28

1.52

2.54

r y , in.

3

-1

6.80 7.68 8.61 9.59 10.6

-1

45 3

3

12.9

8.56

14.4

9.60 1.30 1.70

2.11

2.64

2.64

2.48

1.96

1.95

f




IV-94



W12

W12

Shape

c

35c

40

b x  10

3

p  10

3

-1



6 7 8 9 10

2.50 2.62 2.77 2.95 3.16

1.67 1.75 1.84 1.96 2.10

4.81 4.96 5.13 5.31 5.50

11 12 13 14 15

3.41 3.71 4.06 4.48 4.98

2.27 2.47 2.70 2.98 3.31

16 17 18 19 20

5.57 6.29 7.05 7.85 8.70

3.71 4.18 4.69 5.23 5.79

Design 0


Fy = 65 ksi

-1

30c b x  10

3

p  10

3

b x  103

-1

p  10

-1





3.20 3.30 3.41 3.53 3.66

3.09 3.31 3.61 3.98 4.44

2.06 2.20 2.40 2.65 2.96

5.64 5.89 6.18 6.48 6.82

3.75 3.92 4.11 4.31 4.54

3.74 4.00 4.33 4.75 5.29

2.49 2.66 2.88 3.16 3.52

6.74 7.07 7.43 7.84 8.28

4.48 4.70 4.95 5.21 5.51

5.71 5.94 6.18 6.44 6.73

3.80 3.95 4.11 4.28 4.47

5.01 5.73 6.63 7.69 8.82

3.34 3.81 4.41 5.11 5.87

7.20 7.63 8.10 8.65 9.60

4.79 5.07 5.39 5.76 6.39

5.99 6.86 7.97 9.25 10.6

3.98 4.56 5.30 6.15 7.06

8.79 9.36 10.0 11.1 12.4

5.85 6.22 6.65 7.41 8.26

7.04 7.38 7.87 8.52 9.16

4.68 4.91 5.24 5.67 6.10

10.0 11.3 12.7 14.2 15.7

6.68 7.54 8.45 9.42 10.4

10.6 11.5 12.5 13.4 14.4

7.02 7.66 8.30 8.94 9.59

12.1 13.6 15.3 17.0 18.9

8.04 9.07 10.2 11.3 12.6

13.7 15.0 16.4 17.7 19.0

9.13 10.0 10.9 11.8 12.7

19.0 22.6

12.6 15.0

16.3 18.3

22.8 27.2

15.2 18.1

21.7 24.4

14.5 16.3

22 24 26 28 30

10.5 12.5 14.7 17.1 19.6

7.01 8.34 9.79 11.3 13.0

10.5 11.8 13.1 14.4 15.7

6.96 7.83 8.69 9.56 10.4

32

22.3

14.8

16.9

11.3

-1

3

10.9 12.2


16.3

10.9

23.8

15.9

28.7

t y  103 (kips)-1

2.20

1.46

2.49

1.66

2.92

t r  103 (kips)-1 r x /r y

2.85

1.90

3.24

2.16

3.79

r y , in.

19.1 1.94 2.53

2.64

3.41

3.43

1.94

1.54

1.52

c




IV-95



Fy = 65 ksi

W-Shapes W12

Shape

c,f

b x  10

3

p  10

b x  10

p  10

b x  103

0


1 2 3 4 5

3.70 3.76 3.85 3.98 4.17

2.46 2.50 2.56 2.65 2.77

7.48 7.48 7.48 7.48 7.48

4.97 4.97 4.97 4.97 4.98

4.40 4.60 4.96 5.54 6.44

2.93 3.06 3.30 3.69 4.28

9.35 9.35 9.63 10.5 11.4

6.22 6.22 6.41 6.96 7.61

5.31 5.55 6.00 6.71 7.83

3.53 3.70 3.99 4.47 5.21

11.1 11.1 11.5 12.6 13.9

6 7 8 9 10

4.40 4.71 5.09 5.57 6.19

2.93 3.13 3.39 3.71 4.12

7.85 8.25 8.71 9.21 9.78

5.22 5.49 5.79 6.13 6.50

7.87 10.1 13.2 16.7 20.6

5.23 6.70 8.75 11.1 13.7

12.6 14.1 16.3 19.6 23.0

8.40 9.38 10.8 13.0 15.3

9.59 12.5 16.3 20.6 25.5

6.38 8.30 10.8 13.7 16.9

15.5 17.5 21.2 25.7 30.4

10.3 11.7 14.1 17.1 20.2

11 12 13 14 15

6.97 7.97 9.28 10.8 12.4

4.63 5.30 6.18 7.16 8.22

10.4 11.1 12.2 13.8 15.4

6.93 7.42 8.12 9.19 10.3

24.9 29.6 34.7 40.3

16.6 19.7 23.1 26.8

26.5 30.0 33.5 37.1

17.6 20.0 22.3 24.7

30.8 36.7 43.0

20.5 24.4 28.6

35.2 40.1 45.1

23.4 26.7 30.0

16 17 18 19 20

14.1 15.9 17.8 19.8 22.0

9.36 10.6 11.8 13.2 14.6

17.1 18.8 20.6 22.3 24.1

11.4 12.5 13.7 14.9 16.0

21 22 23 24 25

24.2 26.6 29.1 31.6 34.3

16.1 17.7 19.3 21.0 22.8

25.9 17.2 27.7 18.4 29.5 19.6 31.3 20.8 33.1 22.0 Other Constants and Properties 22.8

-1

p  10


34.3

-1

3


b y  103 (kip-ft)-1

-1

19c 3

3

-1

Design


22c

26 3


74.9

49.8

-1


92.0

7.38 7.38 7.67 8.38 9.25

61.2

t y  103 (kips)-1

3.36

2.23

3.96

2.64

4.61

3.07

t r  103 (kips)-1 r x /r y

4.36

2.90

5.14

3.43

5.98

3.99

r y , in. c

W12

3.42

5.79

5.86

1.51

0.848

0.822


f




IV-96



W12

W12

Shape

c,v

14c,f,v

16

b x  10

3

p  10

3

-1

Design Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 65 ksi


0

ASD 6.43

LRFD 4.28

1 2 3 4 5

6.53 6.85 7.43 8.39 9.94

4.34 4.56 4.95 5.59 6.61

13.6 13.6 14.4 15.9 17.8

b x  103

-1


p  10

-1

(kips)

3

(kips) ASD 7.57

LRFD 5.03

9.07 9.07 9.59 10.6 11.8

7.68 8.06 8.75 9.90 11.7

5.11 5.36 5.82 6.58 7.82

16.1 16.1 16.8 18.6 20.9

10.7 10.7 11.2 12.4 13.9

6 7 8 9 10

12.5 16.7 21.8 27.6 34.0

8.30 11.1 14.5 18.3 22.6

20.1 23.4 29.5 36.1 42.9

13.4 15.5 19.6 24.0 28.5

14.8 19.9 26.0 32.9 40.6

9.86 13.2 17.3 21.9 27.0

23.8 28.7 36.4 44.6 53.3

15.8 19.1 24.2 29.7 35.5

11 12

41.2 49.0

27.4 32.6

50.0 57.2

33.3 38.1

49.1 58.5

32.7 38.9

62.4 71.8

41.5 47.8


121

80.8

149

t y  103 (kips)-1

5.45

3.63

6.18

t r  103 (kips)-1 r x /r y

7.08

4.72

8.01

r y , in.

99.3 4.11 5.34

6.04

6.14

0.773

0.753

c


f


v





IV-97



Fy = 65 ksi

W-Shapes W10

Shape

112

100 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

0.836 0.857 0.882 0.911 0.945

0.556 0.570 0.587 0.606 0.629

1.86 1.86 1.86 1.88 1.90

1.24 1.24 1.24 1.25 1.26

0.941 0.965 0.993 1.03 1.07

0.626 0.642 0.661 0.683 0.709

2.11 2.11 2.11 2.13 2.15

1.40 1.40 1.40 1.41 1.43

1.06 1.09 1.12 1.16 1.20

0.706 0.724 0.746 0.772 0.801

2.43 2.43 2.43 2.45 2.48

1.61 1.61 1.61 1.63 1.65

11 12 13 14 15

0.983 1.03 1.08 1.13 1.20

0.654 0.684 0.717 0.755 0.798

1.91 1.93 1.95 1.97 1.99

1.27 1.29 1.30 1.31 1.33

1.11 1.16 1.22 1.28 1.36

0.739 0.772 0.811 0.855 0.905

2.17 2.20 2.22 2.25 2.28

1.45 1.46 1.48 1.50 1.51

1.26 1.31 1.38 1.46 1.54

0.835 0.874 0.919 0.969 1.03

2.51 2.55 2.58 2.61 2.65

1.67 1.69 1.72 1.74 1.76

16 17 18 19 20

1.27 1.35 1.45 1.55 1.67

0.846 0.901 0.963 1.03 1.11

2.01 2.04 2.06 2.08 2.10

1.34 1.35 1.37 1.38 1.40

1.44 1.54 1.65 1.77 1.91

0.961 1.02 1.10 1.18 1.27

2.30 2.33 2.36 2.39 2.42

1.53 1.55 1.57 1.59 1.61

1.64 1.75 1.88 2.02 2.18

1.09 1.16 1.25 1.34 1.45

2.68 2.72 2.76 2.80 2.84

1.79 1.81 1.84 1.86 1.89

22 24 26 28 30

1.96 2.34 2.74 3.18 3.65

1.31 1.55 1.82 2.11 2.43

2.15 2.20 2.25 2.30 2.36

1.43 1.46 1.50 1.53 1.57

2.25 2.68 3.15 3.65 4.19

1.50 1.78 2.09 2.43 2.79

2.48 2.54 2.61 2.68 2.76

1.65 1.69 1.74 1.79 1.84

2.58 3.07 3.60 4.18 4.79

1.72 2.04 2.40 2.78 3.19

2.92 3.01 3.11 3.21 3.31

1.94 2.00 2.07 2.13 2.21

32 34 36 38 40

4.15 4.69 5.25 5.85 6.49

2.76 3.12 3.50 3.90 4.32


1.89 1.95 2.01 2.07 2.14

5.46 6.16 6.90 7.69 8.52

3.63 4.10 4.59 5.12 5.67

3.43 3.55 3.69 3.83 3.99

2.28 2.36 2.45 2.55 2.65

0

-1

88 3

3


Design


W10

b y  103 (kip-ft)-1

3.96

2.63

4.49

2.99

5.16

3.43

t y  103 (kips)-1

0.781

0.520

0.877

0.583

0.988

0.657

t r  103 (kips)-1 r x /r y

1.01

0.675

1.14

0.758

1.28

r y , in.

0.855

1.75

1.74

1.71

2.68

2.65

2.63



IV-98



W10

W10

Shape

77

68 b x  10

3

p  10

3

-1

-1

60 b x  10

3

p  10

3

-1

-1

3

b x  103

-1

p  10

0







6 7 8 9 10

1.22 1.25 1.29 1.33 1.39

0.810 0.832 0.857 0.887 0.922

2.81 2.81 2.81 2.85 2.89

1.87 1.87 1.87 1.89 1.92

1.39 1.43 1.47 1.52 1.58

0.924 0.949 0.979 1.01 1.05

3.21 3.21 3.21 3.26 3.32

2.14 2.14 2.14 2.17 2.21

1.56 1.61 1.66 1.72 1.79

1.04 1.07 1.10 1.14 1.19

3.67 3.67 3.68 3.74 3.81

2.44 2.44 2.45 2.49 2.54

11 12 13 14 15

1.45 1.51 1.59 1.68 1.78

0.962 1.01 1.06 1.12 1.19

2.93 2.97 3.02 3.06 3.11

1.95 1.98 2.01 2.04 2.07

1.65 1.73 1.82 1.93 2.04

1.10 1.15 1.21 1.28 1.36

3.37 3.43 3.49 3.55 3.61

2.24 2.28 2.32 2.36 2.40

1.87 1.96 2.06 2.18 2.31

1.24 1.30 1.37 1.45 1.54

3.88 3.96 4.03 4.11 4.19

2.58 2.63 2.68 2.74 2.79

16 17 18 19 20

1.90 2.03 2.18 2.35 2.54

1.26 1.35 1.45 1.56 1.69

3.16 3.21 3.26 3.32 3.37

2.10 2.14 2.17 2.21 2.24

2.18 2.33 2.50 2.70 2.92

1.45 1.55 1.66 1.79 1.94

3.67 3.74 3.81 3.88 3.96

2.44 2.49 2.54 2.58 2.63

2.47 2.64 2.84 3.07 3.33

1.64 1.76 1.89 2.04 2.21

4.28 4.37 4.46 4.56 4.66

2.85 2.91 2.97 3.03 3.10

22 24 26 28 30

3.02 3.60 4.22 4.89 5.62

2.01 2.39 2.81 3.26 3.74

3.49 3.61 3.75 3.89 4.05

2.32 2.40 2.49 2.59 2.70

3.47 4.13 4.85 5.63 6.46

2.31 2.75 3.23 3.74 4.30

4.12 4.29 4.48 4.69 4.91

2.74 2.86 2.98 3.12 3.27

3.97 4.72 5.54 6.42 7.38

2.64 3.14 3.69 4.27 4.91

4.88 5.12 5.38 5.68 6.07

3.25 3.41 3.58 3.78 4.04

32 34 36 38 40

6.39 7.22 8.09 9.02 9.99

4.25 4.80 5.38 6.00 6.65


3.43 3.68 3.92 4.16 4.40

8.39 9.47 10.6 11.8 13.1

5.58 6.30 7.07 7.87 8.72

6.55 7.02 7.49 7.96 8.43

4.36 4.67 4.98 5.30 5.61

Design


Fy = 65 ksi

b y  103 (kip-ft)-1

5.97

3.97

6.83

4.55

7.83

t y  103 (kips)-1

1.13

0.753

1.29

0.859

1.45

0.966

t r  103 (kips)-1 r x /r y

1.47

0.979

1.68

1.12

1.88

1.26

r y , in.

5.21

1.73

1.70

1.71

2.60

2.59

2.57



IV-99



Fy = 65 ksi

W-Shapes W10

Shape

f

49f

54

b x  10

3

p  10

3

-1

-1

45 b x  10

3

p  10

3

-1

-1

b x  103

-1

p  10

0






6 7 8 9 10

1.75 1.80 1.86 1.93 2.00

1.17 1.20 1.24 1.28 1.33

4.13 4.13 4.13 4.20 4.29

2.75 2.75 2.75 2.80 2.85

1.93 1.98 2.04 2.12 2.21

1.28 1.32 1.36 1.41 1.47

4.66 4.66 4.66 4.66 4.75

3.10 3.10 3.10 3.10 3.16

2.18 2.28 2.40 2.54 2.71

1.45 1.52 1.60 1.69 1.80

4.99 5.09 5.22 5.35 5.50

3.32 3.38 3.47 3.56 3.66

11 12 13 14 15

2.09 2.20 2.31 2.45 2.60

1.39 1.46 1.54 1.63 1.73

4.38 4.47 4.56 4.66 4.77

2.91 2.97 3.04 3.10 3.17

2.31 2.42 2.55 2.70 2.88

1.53 1.61 1.70 1.80 1.91

4.85 4.96 5.08 5.20 5.32

3.23 3.30 3.38 3.46 3.54

2.91 3.15 3.42 3.75 4.14

1.94 2.09 2.28 2.50 2.75

5.65 5.81 5.98 6.16 6.35

3.76 3.86 3.98 4.10 4.22

16 17 18 19 20

2.78 2.97 3.20 3.46 3.75

1.85 1.98 2.13 2.30 2.49

4.88 4.99 5.11 5.24 5.37

3.25 3.32 3.40 3.49 3.57

3.07 3.29 3.55 3.84 4.17

2.04 2.19 2.36 2.55 2.77

5.46 5.60 5.74 5.90 6.06

3.63 3.72 3.82 3.92 4.03

4.60 5.15 5.78 6.44 7.13

3.06 3.43 3.84 4.28 4.75

6.55 6.76 6.99 7.24 7.51

4.36 4.50 4.65 4.82 4.99

22 24 26 28 30

4.48 5.33 6.25 7.25 8.33

2.98 3.55 4.16 4.83 5.54

5.66 5.97 6.33 6.82 7.42

3.76 3.98 4.21 4.54 4.94

4.99 5.94 6.97 8.08 9.28

3.32 3.95 4.64 5.38 6.17

6.41 6.81 7.31 8.03 8.75

4.27 4.53 4.87 5.35 5.82

8.63 10.3 12.1 14.0 16.0

5.74 6.83 8.02 9.30 10.7

8.15 9.06 9.96 10.9 11.7

5.42 6.03 6.63 7.22 7.82

32 34 36 38 40

9.47 10.7 12.0 13.4 14.8

6.30 7.12 7.98 8.89 9.85


6.30 6.77 7.24 7.71 8.18

18.3

12.1

12.6

8.41

b y  103 (kip-ft)-1

8.80

5.86

t y  103 (kips)-1

1.63

1.08

1.78

1.19

1.93

t r  103 (kips)-1 r x /r y

2.11

1.41

2.31

1.54

2.51

r y , in.

3


Design


W10

10.1

6.69

13.5

8.98 1.29 1.67

1.72

1.73

2.14

2.56

2.54

2.01

f




IV-100



W10

W10

Shape

33f

39 b x  10

3

p  10

3

-1



6 7 8 9 10

2.53 2.65 2.79 2.96 3.17

1.69 1.76 1.86 1.97 2.11

5.86 6.00 6.17 6.35 6.55

11 12 13 14 15

3.41 3.69 4.03 4.43 4.90

2.27 2.46 2.68 2.95 3.26

16 17 18 19 20

5.46 6.14 6.88 7.67 8.50

3.63 4.09 4.58 5.10 5.66

Design 0


Fy = 65 ksi

-1

30 b x  10

3

p  10

3

-1

3

b x  103

-1

p  10

-1





3.90 3.99 4.11 4.23 4.36

3.02 3.16 3.34 3.55 3.81

2.01 2.10 2.22 2.36 2.53

7.29 7.29 7.52 7.78 8.05

4.85 4.85 5.01 5.18 5.36

3.78 4.15 4.63 5.25 6.03

2.51 2.76 3.08 3.49 4.01

8.09 8.47 8.89 9.36 9.88

6.75 6.97 7.21 7.46 7.73

4.49 4.64 4.79 4.96 5.14

4.11 4.47 4.89 5.40 6.00

2.73 2.97 3.26 3.59 3.99

8.34 8.66 9.00 9.36 9.76

5.55 5.76 5.99 6.23 6.49

7.02 8.31 9.76 11.3 13.0

4.67 5.53 6.49 7.53 8.64

10.5 11.1 11.8 13.0 14.3

8.01 8.33 8.66 9.03 9.47

5.33 5.54 5.76 6.01 6.30

6.71 7.58 8.49 9.46 10.5

4.47 5.04 5.65 6.30 6.98

10.2 10.7 11.2 12.1 13.0

6.78 7.10 7.44 8.04 8.63

14.8 16.7 18.7 20.8 23.1

9.83 11.1 12.4 13.9 15.4

15.6 16.8 18.1 19.4 20.7

10.4 11.2 12.1 12.9 13.8

27.9

18.6

23.2

15.4

22 24 26 28 30

10.3 12.2 14.4 16.7 19.1

6.84 8.14 9.56 11.1 12.7

10.7 11.9 13.2 14.4 15.6

7.13 7.95 8.77 9.58 10.4

12.7 15.1 17.7 20.6 23.6

8.44 10.0 11.8 13.7 15.7

14.8 16.5 18.3 20.1 21.9

9.82 11.0 12.2 13.4 14.5

32

21.8

14.5

16.8

11.2

26.8

17.9

23.6

15.7

5.38 5.63 5.92 6.23 6.57 6.96 7.39 7.88 8.65 9.50


15.9

10.6

20.5

13.7

31.0

20.6

t y  103 (kips)-1

2.23

1.49

2.65

1.76

2.91

1.93

t r  103 (kips)-1 r x /r y

2.90

1.93

3.43

2.29

3.77

2.51

r y , in.

2.17

2.16

3.20

1.98

1.94

1.37

f




IV-101



Fy = 65 ksi

W-Shapes W10

Shape

26

c

22c b x  10

3

p  10

3

-1

19c b x  10

3

p  10

3

-1

-1

b x  103

p  10

3

-1

0





1 2 3 4 5

3.46 3.53 3.65 3.82 4.06

2.30 2.35 2.43 2.54 2.70

8.76 8.76 8.76 8.76 9.08

5.83 5.83 5.83 5.83 6.04

4.14 4.22 4.37 4.58 4.87

2.75 2.81 2.90 3.04 3.24

10.5 10.5 10.5 10.5 11.0

7.01 7.01 7.01 7.01 7.34

4.80 5.03 5.43 6.09 7.16

3.20 3.34 3.61 4.05 4.76

12.7 12.7 13.0 14.0 15.2

8.44 8.44 8.62 9.30 10.1

6 7 8 9 10

4.41 4.85 5.42 6.15 7.08

2.93 3.23 3.61 4.09 4.71

9.53 10.0 10.6 11.2 11.9

6.34 6.67 7.03 7.44 7.90

5.25 5.78 6.50 7.41 8.58

3.50 3.85 4.32 4.93 5.71

11.6 12.3 13.1 14.0 15.0

7.74 8.20 8.71 9.29 9.95

8.71 11.0 14.3 18.1 22.3

5.80 7.32 9.50 12.0 14.8

16.6 18.3 20.4 24.2 28.2

11.0 12.2 13.6 16.1 18.8

11 12 13 14 15

8.27 9.80 11.5 13.3 15.3

5.50 6.52 7.65 8.88 10.2

12.7 13.5 15.0 16.7 18.4

8.42 9.01 9.96 11.1 12.2

10.1 12.0 14.1 16.4 18.8

6.72 8.00 9.38 10.9 12.5

16.1 17.7 20.1 22.5 25.0

10.7 11.8 13.4 15.0 16.6

27.0 32.1 37.7 43.7

18.0 21.4 25.1 29.1

32.3 36.4 40.5 44.6

21.5 24.2 26.9 29.7

16 17 18 19 20

17.4 19.7 22.1 24.6 27.2

11.6 13.1 14.7 16.3 18.1

20.1 21.8 23.6 25.3 27.0

13.4 14.5 15.7 16.8 18.0

21.4 24.1 27.0 30.1 33.4

14.2 16.0 18.0 20.0 22.2

27.4 29.9 32.4 34.9 37.4

18.2 19.9 21.6 23.2 24.9

21 22

30.0 32.9

20.0 21.9

28.7 30.5

19.1 20.3

36.8 40.4

24.5 26.9

39.9 42.4

26.5 28.2

Design


W10

-1


36.5

24.3

44.9

29.9

81.8

t y  103 (kips)-1

3.38

2.25

3.96

2.63

4.57

t r  103 (kips)-1 r x /r y

4.38

2.92

5.14

3.42

5.93

r y , in.

54.4 3.04 3.95

3.20

3.21

4.74

1.36

1.33

0.874

c




IV-102



W10

W10

Shape

c

15c

17

b x  10

3

p  10

3

-1

Design


Fy = 65 ksi

-1

12c,f b x  10

3

p  10

3

-1

-1

0



1 2 3 4 5

5.50 5.76 6.24 7.02 8.31

6.34 6.66 7.25 8.21 9.81

3.66 3.83 4.15 4.67 5.53

14.7 14.7 15.1 16.4 17.9

9.75 9.75 10.0 10.9 11.9

3

b x  103

-1


5.61 5.89 6.40 7.24 8.57

22.7 22.7 22.9 25.2 28.1

15.1 15.1 15.2 16.8 18.7

p  10


4.22 4.43 4.82 5.46 6.53

17.1 17.1 17.8 19.5 21.5

11.4 11.4 11.9 13.0 14.3

8.43 8.85 9.62 10.9 12.9

6 7 8 9 10

10.3 13.2 17.2 21.8 26.9

6.83 8.76 11.4 14.5 17.9

19.8 22.1 25.4 30.6 36.0

13.2 14.7 16.9 20.4 23.9

12.3 16.2 21.2 26.8 33.1

8.21 10.8 14.1 17.8 22.0

24.0 27.1 32.8 39.6 46.8

16.0 18.0 21.8 26.4 31.1

16.1 21.5 28.1 35.6 43.9

10.7 14.3 18.7 23.7 29.2

31.7 36.6 46.2 56.5 67.2

21.1 24.4 30.8 37.6 44.7

11 12 13 14

32.5 38.7 45.4 52.7

21.6 25.8 30.2 35.1

41.4 46.8 52.3 57.8

27.5 31.2 34.8 38.5

40.1 47.7 56.0

26.7 31.7 37.2

54.0 61.4 68.8

35.9 40.9 45.8

53.1 63.2 74.2

35.4 42.1 49.4

78.3 89.6 101

52.1 59.6 67.3


65.1

119

79.3

168

111

t y  103 (kips)-1

5.15

3.43

5.83

3.88

7.26

4.83

t r  103 (kips)-1 r x /r y

6.68

4.45

7.56

5.04

9.42

6.28

r y , in. c

97.9

4.79

4.88

4.97

0.845

0.810

0.785


f




IV-103



Fy = 65 ksi

W-Shapes W8

Shape

67

58 b x  10

3

p  10

3

-1

b x  10

p  10

-1

-1

3

b x  103

-1

p  10






6 7 8 9 10

1.46 1.51 1.58 1.67 1.77

0.968 1.01 1.05 1.11 1.18

3.91 3.93 3.98 4.04 4.09

2.60 2.62 2.65 2.69 2.72

1.68 1.75 1.83 1.93 2.05

1.12 1.16 1.22 1.29 1.36

4.58 4.62 4.69 4.76 4.84

3.05 3.07 3.12 3.17 3.22

2.04 2.13 2.23 2.35 2.50

1.36 1.42 1.48 1.57 1.66

5.59 5.65 5.76 5.86 5.98

3.72 3.76 3.83 3.90 3.98

11 12 13 14 15

1.89 2.02 2.18 2.37 2.59

1.25 1.35 1.45 1.58 1.72

4.15 4.21 4.27 4.33 4.39

2.76 2.80 2.84 2.88 2.92

2.19 2.35 2.54 2.76 3.02

1.46 1.56 1.69 1.84 2.01

4.92 5.00 5.08 5.17 5.26

3.27 3.32 3.38 3.44 3.50

2.67 2.87 3.11 3.39 3.71

1.78 1.91 2.07 2.25 2.47

6.10 6.22 6.35 6.48 6.62

4.06 4.14 4.22 4.31 4.40

16 17 18 19 20

2.84 3.14 3.51 3.91 4.33

1.89 2.09 2.33 2.60 2.88

4.46 4.53 4.60 4.67 4.74

2.97 3.01 3.06 3.11 3.16

3.33 3.68 4.12 4.59 5.08

2.21 2.45 2.74 3.05 3.38

5.35 5.45 5.55 5.65 5.76

3.56 3.62 3.69 3.76 3.83

4.10 4.55 5.09 5.67 6.28

2.72 3.02 3.39 3.77 4.18

6.76 6.91 7.07 7.24 7.41

4.50 4.60 4.71 4.82 4.93

22 24 26 28 30

5.24 6.23 7.31 8.48 9.74

3.48 4.15 4.87 5.64 6.48

4.90 5.06 5.24 5.43 5.64

3.26 3.37 3.49 3.61 3.75

6.15 7.32 8.59 9.96 11.4

4.09 4.87 5.71 6.63 7.61

5.98 6.23 6.50 6.79 7.11

3.98 4.14 4.32 4.52 4.73

7.60 9.05 10.6 12.3 14.1

5.06 6.02 7.06 8.19 9.40

7.78 8.20 8.66 9.20 9.92

5.18 5.45 5.76 6.12 6.60

32 34

11.1 12.5

7.37 8.32

5.86 6.10

3.90 4.06

13.0 14.7

8.66 9.77

7.45 7.93

4.96 5.28

16.1 18.2

10.7 12.1

10.6 11.3

7.08 7.55

0

-1

48 3

3


Design


W8


8.38

5.58

9.82

6.54

t y  103 (kips)-1

1.30

0.868

1.50

1.00

1.82

t r  103 (kips)-1 r x /r y

1.69

1.13

1.95

1.30

2.36

1.75

r y , in. 2.12 Note: Heavy line indicates KL /r y greater than or equal to 200.

12.0

7.96 1.21 1.58

1.74

1.74

2.10

2.08



IV-104



W8

W8

Shape

35f

40 b x  10

3

p  10

3

-1

Design


Fy = 65 ksi

b x  103

-1


p  10

-1

(kips)

3


(kips) ASD 2.49

LRFD 1.66

0

ASD 2.20

LRFD 1.46

6 7 8 9 10

2.47 2.58 2.71 2.87 3.05

1.64 1.72 1.80 1.91 2.03

6.89 6.99 7.14 7.31 7.48

4.58 4.65 4.75 4.86 4.97

2.81 2.94 3.09 3.26 3.48

1.87 1.95 2.05 2.17 2.31

7.91 8.03 8.24 8.45 8.67

5.27 5.35 5.48 5.62 5.77

11 12 13 14 15

3.27 3.53 3.83 4.18 4.60

2.18 2.35 2.55 2.78 3.06

7.66 7.84 8.04 8.25 8.46

5.09 5.22 5.35 5.49 5.63

3.73 4.02 4.37 4.78 5.27

2.48 2.68 2.91 3.18 3.50

8.91 9.15 9.42 9.70 9.99

5.93 6.09 6.27 6.45 6.65

16 17 18 19 20

5.10 5.69 6.38 7.10 7.87

3.39 3.78 4.24 4.73 5.24

8.69 8.94 9.19 9.46 9.75

5.78 5.95 6.12 6.30 6.49

5.84 6.52 7.31 8.15 9.03

3.88 4.34 4.87 5.42 6.01

10.3 10.6 11.0 11.4 11.8

6.86 7.08 7.31 7.57 7.84

22 24 26 28 30

9.52 11.3 13.3 15.4 17.7

6.34 7.54 8.85 10.3 11.8

10.4 11.1 12.2 13.3 14.4

10.9 13.0 15.3 17.7 20.3

7.27 8.65 10.2 11.8 13.5

12.8 14.2 15.6 17.0 18.4

8.50 9.45 10.4 11.3 12.3

32 34

20.1 22.7

13.4 15.1

15.4 16.5

23.1

15.4

19.8

13.2

6.91 7.42 8.14 8.85 9.57 10.3 11.0


14.8

9.86

17.1

t y  103 (kips)-1

2.20

1.46

2.49

t r  103 (kips)-1 r x /r y

2.85

1.90

3.24

r y , in.

11.4 1.66 2.16

1.73

1.73

2.04

2.03

f




IV-105



Fy = 65 ksi

W-Shapes W8

Shape

f

28

31

b x  10

3

p  10

3

-1

Design


W8


0

ASD 2.81

LRFD 1.87

6 7 8 9 10

3.18 3.32 3.49 3.69 3.94

2.11 2.21 2.32 2.46 2.62

9.32 9.32 9.45 9.72 10.0

11 12 13 14 15

4.22 4.56 4.96 5.43 5.99

2.81 3.03 3.30 3.61 3.98

16 17 18 19 20

6.64 7.43 8.33 9.28 10.3

22 24 26 28 30 32

b x  103

-1


p  10

-1

(kips)

3

(kips) ASD 3.11

LRFD 2.07

6.20 6.20 6.29 6.47 6.66

3.76 4.02 4.35 4.75 5.25

2.50 2.68 2.89 3.16 3.49

10.4 10.7 11.1 11.5 11.9

6.92 7.15 7.39 7.66 7.94

10.3 10.6 11.0 11.3 11.7

6.86 7.07 7.30 7.55 7.81

5.85 6.60 7.52 8.67 9.96

3.89 4.39 5.00 5.77 6.62

12.4 12.9 13.4 14.0 14.6

8.25 8.58 8.93 9.32 9.74

4.42 4.94 5.54 6.18 6.84

12.2 12.6 13.1 13.6 14.2

8.08 8.38 8.71 9.06 9.43

11.3 12.8 14.3 16.0 17.7

7.54 8.51 9.54 10.6 11.8

15.3 16.1 17.4 18.6 19.8

10.2 10.7 11.6 12.4 13.2

12.4 14.8 17.4 20.2 23.1

8.28 9.86 11.6 13.4 15.4

16.0 17.8 19.6 21.4 23.3

10.6 11.8 13.1 14.3 15.5

21.4 25.5 29.9

14.2 17.0 19.9

22.1 24.5 26.9

14.7 16.3 17.9

26.3

17.5

25.1

16.7


20.4

13.6

27.1

t y  103 (kips)-1

2.81

1.87

3.11

t r  103 (kips)-1 r x /r y

3.65

2.43

4.04

r y , in.

18.1 2.07 2.69

1.72

2.13

2.02

1.62

f

Shape does not meet compact limit for flexure with F y = 65 ksi. Note: Heavy line indicates KL /r y greater than or equal to 200.



IV-106



W8

W8

Shape

f

21

24

b x  10

3

p  10

3

-1

b x  10

p  10

b x  103

0 1 2 3 4 5

3.65 3.71 3.81 3.95 4.14

2.43 2.47 2.53 2.63 2.76

11.9 11.9 11.9 11.9 11.9

7.91 7.91 7.91 7.91 7.91

4.21 4.32 4.51 4.79 5.17

2.80 2.87 3.00 3.19 3.44

13.4 13.4 13.4 13.5 14.1

8.94 8.94 8.94 8.98 9.41

4.93 5.06 5.30 5.65 6.12

3.28 3.37 3.53 3.76 4.07

16.1 16.1 16.1 16.3 17.1

10.7 10.7 10.7 10.8 11.4

6 7 8 9 10

4.39 4.70 5.09 5.57 6.15

2.92 3.13 3.39 3.70 4.09

12.3 12.8 13.3 13.8 14.4

8.18 8.49 8.82 9.18 9.57

5.69 6.36 7.24 8.39 9.88

3.78 4.23 4.82 5.58 6.57

14.8 15.6 16.5 17.5 18.6

9.88 10.4 11.0 11.6 12.3

6.76 7.61 8.72 10.2 12.1

4.50 5.06 5.80 6.76 8.03

18.1 19.2 20.4 21.8 23.3

12.0 12.8 13.6 14.5 15.5

11 12 13 14 15

6.87 7.76 8.86 10.2 11.7

4.57 5.16 5.89 6.81 7.81

15.0 15.7 16.5 17.3 18.2

9.99 10.4 11.0 11.5 12.1

11.9 14.1 16.6 19.2 22.0

7.89 9.39 11.0 12.8 14.7

19.8 21.2 23.5 26.0 28.5

13.2 14.1 15.7 17.3 18.9

14.6 17.3 20.3 23.6 27.1

9.69 11.5 13.5 15.7 18.0

25.2 28.3 31.8 35.3 38.8

16.7 18.9 21.2 23.5 25.8

16 17 18 19 20

13.4 15.1 16.9 18.8 20.9

8.89 10.0 11.3 12.5 13.9

19.6 21.2 22.9 24.5 26.1

13.0 14.1 15.2 16.3 17.4

25.1 28.3 31.7 35.4 39.2

16.7 18.8 21.1 23.5 26.1

30.9 33.4 35.9 38.3 40.7

20.6 22.2 23.9 25.5 27.1

30.8 34.8 39.0 43.5 48.2

20.5 23.1 26.0 28.9 32.0

42.4 45.9 49.4 52.9 56.4

28.2 30.5 32.9 35.2 37.5

21 22 23 24 25

23.0 25.3 27.6 30.1 32.6

15.3 16.8 18.4 20.0 21.7


28.7

21.4

-1

p  10


32.1

-1

3


b y  103 (kip-ft)-1

-1

18 3

3


Design


Fy = 65 ksi

48.2

32.0

-1

58.8

39.1

t y  103 (kips)-1

3.63

2.41

4.17

2.78

4.88

3.25

t r  103 (kips)-1 r x /r y

4.71

3.14

5.41

3.61

6.34

4.22

r y , in.

2.12

2.77

2.79

1.61

1.26

1.23

f




IV-107



Fy = 65 ksi

W-Shapes W8

Shape

15 b x  10

p  10

-1

Design

10c,f

13 3

3


W8

-1

0


1 2 3 4 5

5.89 6.21 6.79 7.70 9.04

b x  10

3

p  10

3

-1

-1


3

b x  103

-1


6.30 6.61 7.15 8.03 9.39

32.4 32.4 32.4 34.9 38.4

21.6 21.6 21.6 23.2 25.6

p  10


3.92 4.13 4.52 5.12 6.01

20.2 20.2 20.6 22.1 23.9

13.4 13.4 13.7 14.7 15.9

6.82 7.23 7.96 9.11 10.8

4.54 4.81 5.29 6.06 7.20

24.0 24.0 24.8 26.8 29.3

16.0 16.0 16.5 17.9 19.5

9.47 9.93 10.8 12.1 14.1

6 7 8 9 10

11.0 13.9 18.0 22.8 28.1

7.32 9.23 12.0 15.2 18.7

26.1 28.7 31.8 36.9 42.9

17.4 19.1 21.2 24.5 28.5

13.4 17.2 22.5 28.4 35.1

8.91 11.4 14.9 18.9 23.4

32.3 35.9 41.0 49.1 57.4

21.5 23.9 27.3 32.7 38.2

17.4 22.4 29.3 37.1 45.8

11.6 14.9 19.5 24.7 30.4

42.8 48.3 58.8 71.3 84.3

28.5 32.2 39.1 47.4 56.1

11 12 13 14

34.0 40.5 47.5 55.1

22.6 26.9 31.6 36.7

48.9 54.9 60.9 66.9

32.5 36.5 40.5 44.5

42.5 50.6 59.3 68.8

28.3 33.6 39.5 45.8

65.8 74.3 82.7 91.2

43.8 49.4 55.0 60.7

55.4 65.9 77.3 89.7

36.8 43.8 51.5 59.7

97.6 111 125 139

64.9 73.9 83.0 92.2


68.3

127

84.8

t y  103 (kips)-1

5.79

3.85

6.69

4.45

t r  103 (kips)-1 r x /r y

7.51

5.00

8.68

5.79

r y , in. c

103

177

118

8.68

5.78

11.3

7.50

3.76

3.81

3.83

0.876

0.843

0.841


f

Shape does not meet compact limit for flexure with F y = 65 ksi. Note: Heavy line indicates KL /r y greater than or equal to 200.


Steel+Construction+Manual+Design+Examples,+V14.0+part+4+of+4

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