Design Guide 13 Wide-Flange Column Stiffening at Moment Connections (See errata listed at end of file PDF

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Steel Design Guide Series

13

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

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

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

All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher. The information presented in this publication has been prepared in accordance with recognized engineering principles and is 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, suitablility, and applicability by a licensed professional engineer, designer, or architect. The publication of the material contained herein is not intended as a representation or 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 Revision: October 2003

TABLE OF CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Sco pe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Co lumn Stiffening . . . . . . . . . . . . . . . . . . . 1.3 References Specifications . . . . . . . . . . . . . . 1.4 Definitio ns o f Wind, Lo w-Seismic, and High-Seismic Applicati ons. . . . . . . . . . . . . 1.5 Ackno wledgements. . . . . . . . . . . . . . . . . . .

1 1 2 2 2 2

2. Strong-Axis Moment Connections to Unreinforced Columns . . . . . . . . . . . . . . . 3 2.1 Force Transfer in Unreinfo rced Co lumns . . . . 3 2.2 Determining the Design Strength o f an Unreinfo rced Co lumn . . . . . . . . . . . . . . . . 5 2.3 Co lumn Cro ss-Sectio nal Stiffness Co nsideratio ns . . . . . . . . . . . . . . . . . . . . 11 2.4 Design Aids. . . . . . . . . . . . . . . . . . . . . . . 11 3. Economical Selection of Columns . . . . . . . . . 3.1 Achieving Balance Between Increases in Material Co st and Reductio ns in Labo r Co st . . . . . . . . . . . . . . . . . . . . . . . 3.2 Eliminating C olumn Stiffening. . . . . . . . . . 3.3 Minimizing the Ec on omic Impact of C olumn Stiffening Requirements in Wind and L owSeismic Applications. . . . . . . . . . . . . . . . 3.4 Minimizing the Ec on omic Impact of C olumn Stiffening Requirements in High-Seismic Applicatio ns. . . . . . . . . . . . . . . . . . . . . . 4. Strong-Axis Moment Connections to Stiffened Columns . . . . . . . . . . . . . . . . . 4.1 Determining the C olumn Stiffening Requirements . . . . . . . . . . . . . . . . . . . . . 4.2 Force Transfer in Stiffened Columns . . . . . . 4.3 Design o f Transverse Stiffeners . . . . . . . . . 4.4 Design o f Web Do ubler Plates . . . . . . . . . . 5. Special Considerations . . . . . . . . . . . . . . . . . 5.1 Co lumn Stiffening for Beams o f Differing Depth and/o r To p o f Steel. . . . . . . . . . . . .

13 13 14 15 16

5.2 Co lumn Stiffening fo r Weak-Axis Mo ment Connecti ons . . . . . . . . . . . . . . . . . . . . . . 33 5.3 Co lumn Stiffening for Co ncurrent Stro ng- and Weak-Axis M oment Connecti ons . . . . . . . 34 5.4 Web Do ubler Plates as Reinfo rcement fo r L ocal Web Yielding, Web Crippling, and/ or Compressio n Buckling of the Web. . . . . . . 35 5.5 Web Do ubler Plates at Lo catio ns o f Weak-Axis Connecti ons . . . . . . . . . . . . . . . . . . . . . . 35 5.6 Diagonal Stiffeners . . . . . . . . . . . . . . . . . . 36 6. Design Examples . . . . . . . . . . . . . . . . . . . . . Example 6-1. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-2. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-3. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-4. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-5. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-6. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-7. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-8. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-9. . . . . . . . . . . . . . . . . . . . . . . . . . Example 6-10. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-11. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-12. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-13. . . . . . . . . . . . . . . . . . . . . . . . . Example 6-14. . . . . . . . . . . . . . . . . . . . . . . . .

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

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

67

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

75

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

83

APPENDIX D . . . . . . . . . . . . . . . . . . . . . . . . . Special Co nsideratio ns. . . . . . . . . . . . . . . . . . . Mo ment Co nnectio ns to Co lumn Webs. . . . . . . .

95 95 99

17 18 20 22 27 33 33

Chapter 1 INTRODUCTION in Chapter 2. Eco no mical co nsideratio ns fo r unreinfo rced c olumns and c olumns with reinf orcement are given in Chapter 3. Fo rce transfer and design strengtho f reinfo rced co lumns with stro ng-axis mo ment connections, as well as the design of transverse stiffeners and web d oubler plates, is c overed in Chapter 4. Special considerations in c olumn stiffening, such as stiffening f or weak-axis m oment c onnections and framing arrangements with o ffsets, are co vered in Chapter 5. Design examples that illustrate the applicatio n of these pro visions are pro vided in Chapter 6, with design aids f or wind and l ow-seismic applicati ons in Appendices A, B, and C.

1.1 Scope The design of c olumns f or axial lo ad, co ncurrent axial lo ad and flexure, and drift co nsideratio ns is well established. Ho wever, the consideration of stiffening requirements f or wide-flange c olumns at m oment connecti ons as a r outine criterion in the selecti on of the c omp onents of the structural frame is no t as well established. Thus, the eco no mic benefit o f selecting c olumns with flange and web thicknesses that do not require stiffening is n ot widely pursued, in spite of the eff orts of other auth ors wh o have addressed this to pic previo usly (Tho rnto n, 1991; Thornton, 1992; Barger, 1992; Dyker, 1992; and Ricker, 1992). This Design Guide is written with the intent of changing that trend and its co ntents are fo cused in two areas:

1.2 Column Stiffening Transverse stiffeners are used to increase the strength and/o r stiffness o f the co lumn flange and/o r web at the lo catio n o f a co ncentrated fo rce, such as the flange fo rce induced by the flange o r flange-plateo f a mo ment-co nnected beam. Web do ubler plates are used to increase the shear strength and stiffness of the c olumn panel-zone between the pair o f flange fo rces fro m a mo ment-co nnected beam. The panel-zone is the area of the column that is bounded by the co lumn flanges and the pro jectio ns o f the beam flanges as illustrated in Figure 1-1. If transverse stiffeners and/o r web do ubler plates carry loads fro m members that frame to the weak-axis o f the

1. The determinatio n o f design strength and stiffness fo r unreinfo rced wide-flange co lumns at lo catio ns of strong-axis beam-to -co lumn mo ment co nnectio ns; and, 2. The design of column stiffening elements, such as transverse stiffeners (also kno wn as co ntinuity plates) and web doubler plates, when the unreinf orced c olumn strength and/o r stiffness is inadequate. Recommendatio ns fo r economy are included in both cases. Force transfer and design strength o f unreinfo rced c olumns with str ong-axis m oment c onnecti ons are c overed

Projection of beam flanges, or transverse stiffeners, if present

Column panel-zone

Figure 1-1 Illustration of column panel-zone. 1

co lumn, the reco mmendatio ns herein must be adjusted as discussed in Secti ons 5.2, 5.3, and 5.5. As discussed in Section 5.4, if web doubler plates are required to increase the panel-zo ne shear strength, they can also be used to resist lo cal web yielding, web crippling, and/or compression buckling o f the web per LRFD Specification Secti on K1. As discussed in Secti on 5.6, diag onal stiffening can be used in lieu of web d oubler plates if it d oes n ot interfere with the weak-axis framing.

High-seismic applicatio ns are tho se fo r which inelastic behavi or is expected in the beams or panel-z ones as a means o f dissipating the energy induced during stro ng gro und mo tio ns. Such buildings are designed to meet the requirements in both the LRFD Specification and the AISC Seismic Pr ovisi ons and a resp onse m odification facto r R that is appr opriate for the level o f detailing required fo r the m oment-frame system selected is used in the determination of seismic f orces.1 Additi onally, the m oment connections used in high-seismic applicati ons have special seismic detailing that is appro priate fo r the mo ment-frame system selected.

1.3 References Specifications This Design Guide is generally based up on the requirements in the AISC LRFD Specification for Structural Steel Buildings (AISC, 1993), hereinafter referred t o as the LRFD Specification, and the AISC Seismic Provisions for Structural Steel Buildings (AISC, 1997a), hereinafter referred to as the AISC Seismic Provisions. Although direct reference to the AISC Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design (AISC, 1989) is n ot included, the principles herein remain generally applicable.

1.5 Acknowledgements This Design Guide resulted partially fr om w ork that was d one as part of the Design Office Pr oblems activity of the ASCE C ommittee on Design of Steel Building Structures. Chapter 3 is based in large part upo n this previo us work. Additio nally, the AISC Co mmittee o n Manuals and Textb ooks has enhanced this Design Guide thr ough careful scrutiny, discussio n, and suggestio ns fo r impro vement. The autho r thanks the members o f these AISC and ASCE Committees f or their invaluable input and guidance. In particular, Lawrence A. Klo iber, James O. Malley, and David T. Ricker co ntributed significantly to the develo pment of Chapters 3 and 4 and William C. Minchin and Tho mas M. Murray pro vided helpful co mments and suggesti ons thr oughout the text of this Design Guide.

1.4 Definitions of Wind, Low-Seismic, and HighSeismic Applications For the purpo ses of this Design Guide, wind, l ow-seismic and high-seismic applicatio ns are defined as fo llo ws. Wind and lo w-seismic applicatio ns are tho se for which the structure is designed t o meet the requirements in the LRFD Specification with n o special seismic detailing. This includes all applications for which the structural respo nse is intended t o remain in the n ominally elastic range and the respo nse mo dificatio n facto r R used in the determinatio n o f seismic forces, if any, is n ot taken greater than 3.

1 Fro m AISC Seismic Provisions Commentary Table I-C4-1, R -values o f 8, 6, and 4 are co mmo nly used fo r Special Mo ment Frames (SMF), Intermediate Moment Frames (IMF), and Ordinary Mo ment Frames (OMF), respectively.

2

Chapter 2 STRONG-AXIS MOMENT CONNECTIONS TO UNREINFORCED COLUMNS In wind and low-seismic applications, it is often p ossible to use wide-flange columns with out transverse stiffeners and web d oubler plates at mo ment-connected beams. To use an unreinfo rced co lumn, the fo llo wing criteria must be met:

c ouple in the beam flanges o r flange plates. The co rresponding flange fo rce P uf is calculated as: Puf ⳱

Mu Pu ⫾ dm 2

(2.1-1)

where

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

Puf ⳱ factored beam flange fo rce, tensile o r co mpressive, kips M u ⳱ fact ored beam end m oment, kip-in. d m ⳱ moment arm between the flange fo rces,2 in. Pu ⳱ factored beam axial fo rce, kips

If these criteria canno t be met, co lumn stiffening is required. In high-seismic applicati ons, transverse stiffeners are normally required, as discussed in Secti on 2.3. H owever, it remains p ossible in many cases to use wide-flange c olumns in high-seismic applicati ons with out web d oubler plates at mo ment-co nnected beams.

The formulatio n o f Equatio n 2.1-1 is such that the co mbined effect of the m oment and axial force is transmitted thr ough the flange c onnecti ons, ign oring any strength c ontributio n fro m the web connecti on, which is usually m ore flexible. When the mo ment to be develo ped is less than the full flexural strength o f the beam, as is co mmo nly the case when a drift criterion g overns the design, and the axial fo rce is relatively small, this calculatio n is fairly straightfo rward. Ho wever, when the full flexural strength o f the beam must be develo ped,o r when the axial fo rce is large, such a mo del seems to guarantee an o verstress in the beam flange, particularly of r a directly welded flange m o ment c onnecti on. N onetheless, the ab ove f orce transfer m odel remains acceptable because inelastic action into the range o f strain hardening allo ws the develo pment o f the design flexural strengtho f the beam in the co nnectio n (Huang et al., 1973). Such self-limiting inelastic action is permitted in LRFD Specification Secti on B9. Alternatively, a web c onnecti on with a stiffness that is c ompatible with that of the c onnecti ons of the beam flanges can be used t o activate the full beam cr oss-secti on and reduce the p ortion carried by the flanges. No te that, if a co mpo site mo ment co nnectio n is used between the beam and c olumn, the calculati ons in Equati ons 2.1-1 and2.1-2 must beadjusted based upo n the appro priate

2.1 Force Transfer in Unreinforced Columns In an unreinfo rced column, concentrated fo rces fro m the beam flanges o r flange plates are transferred ol cally into the c olumn flanges. These concentrated forces spread thro ugh the co lumn flange and flange-to -web fillet regio n into the web as illustrated in Figure 2-1a. Shear is dispersed between them in the c olumn web (panel-z one) as illustrated in Figure 2-1b. Ultimately, axial fo rces in the c olumn flanges balance this shear as illustrated in Figure 2-1c. 2.1.1 Required Strength for Local Flange and Web Limit States In wind and low-seismic applications, beam end m oments, shears, and axial fo rces are determined by analysis fo r the lo ads and lo ad co mbinatio ns in LRFD Specificatio n Secti on A4.1. N ote that the t otal design m oment is seldom equal to the flexural strength o f the beam(s). A rational appro ach such as that illustrated in Example 6-4o r similar to that pro po sed by Disque (1975) can be used in c onjuncti on with these l oads and l oad combinations. Different lo ad co mbinatio ns may be critical fo r different local-strength limit states. For the general case, the beam end m oment is res olved at the c olumn face int o an effective tensi on-c ompressi on

2

The actual m oment arm can be readily calculated as the distance between the centers o f the flangeso r flange plates as illustrated in Figure 2-1a. Alternatively, as stated in LRFD Specification Commentary Secti on K1.7, 0.95 times the beam depth has been c onservatively used f or d m in the past.

3

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

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

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

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

detailing and force transfer mo del. So me po ssible compo site connecti ons are illustrated in AISC (1997a), Le on et al. (1996), and Viest et al. (1998). In high-seismic applications, the m oments, shears, and axial fo rces are determined by analysis fo r the lo ads and load combinatio ns in LRFD Specificatio n Section A4.1 and AISC Seismic Pr ovisi ons Secti on 4.1. The resulting flange fo rce P u f is then determined using Equatio n 2.1-1. No te that the co rrespo nding co nnectio n details have special seismic detailing to pro vide for contro lled inelastic def ormations during strong ground mo tio n as a means o f dissipating the input energy fro m an earthquake.3 Fo r Ordinary Mo ment Frames (OMF), a cyclic inelastic ro tatio n capability o f 1 percent is required. Mo ment co nnectio ns such as those discussed in AISC Seismic Pro visio ns Co mmentary Section C11.2 and illustrated in

Figure C-11.1 can be used. Fro m AISC Seismic Provisi ons Secti on 11.2a, the flange f orces in Ordinary Moment Frames (OMF) need no t be taken greater than tho se that correspo nd to a mo ment Mu equal to 1. 1R y F y Zx o r the maximum mo ment that can be delivered by the system, whichever is less. F or Special M oment Frames (SMF) and Intermediate Mo ment Frames (IMF), a cyclic inelastic ro tatio n capability o f 3 and 2 percent, respectively, is required. Several alternative co nnectio n details using reinfo rcement, such as co verplates, ribs, o r haunches, o r using reduced beam sectio ns (do gbo nes), have been successfully tested and used. Such connections shift the l ocation of the plastic hinge into the beam by a distance a fro m the co lumn face as illustrated in Figure 2-2. Fr om AISC Seismic Pr ovisi ons Sectio n 9.3a, the flange fo rces in Special Mo ment Frames (SMF) and Intermediate Moment Frames (IMF) need not be taken greater than:

3 With stro ng panel-zo nes and fully restrained (FR) co nstructio n, the primary source o f inelasticity is commonly hinging in the beam itself. If the panel-z one is a significant s ource o f inelasticity, o r if partially restrained (PR) c onstructi on is used, the flange-fo rce calculatio n in Equatio n 2.1-2 sho uld be adjusted based up on the actual f orce transfer mo del.

Puf ⳱ 4

Mu dm

1 .1 Ry Fy Z Ⳮ Vu a dm

(2.1-2)

where 1.1 is an adjustment facto r that no minally acco unts fo r the effects o f strain hardening, and

Seismic Pro visio ns Lo ad Co mbinatio ns 4-1 and 4-2 and Equatio n 2.1-1, the to tal panel-zo ne shear fo rce is calculated with Equatio n 2.1-3. As a wo rst case, ho wever, the ot tal panel-zo ne shear of rceV u need no t be taken greater than:

R y ⳱ an adjustment facto r that no minally acco unts fo r material yield o verstrength per AISC Seismic Pro visio ns Secti on 6.2 ⳱ 1.5 fo r ASTM A36 wide-flange beams ⳱ 1.3 fo r ASTM A572 grade 42 wide-flange beams ⳱ 1.1 fo r wide-flange beams in o ther material grades (e.g., ASTM A992 or A572 grade 50) F y ⳱ beam specified minimum yield strength, ksi Z ⳱ plastic secti on m odulus of beam cr oss-secti on at hinge location (distance a fr om column face), in.3 V u ⳱ shear in beam at hinge lo catio n (distance a fro m co lumn face), kips a ⳱ distance fr om face of c olumn flange to plastic hinge lo catio n, in.

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