sfd older codes

Steel Frame

De sign Man ual

AISC ASD-2001, AIS ASD-1989, AISC LRFD-1999 AISC LRFD-1993,

BS 5950-2000, BS 5950-1990, CISC 1994, Eurocode 3-1992, UBC

ASD-1997 and UBC LRFD-1997

For SAP2000® and ETABS®

ISO SAP022811M7 Rev. 0 Ver sion 15Berke ley, Cal i for nia June 2011

COPYRIGHT

Copy right ã Com put ers and Struc tures, Inc., 1978-2011.

All rights re served.

The CSI Logo®, SAP2000®, ETABS® and SAFE® are reg is teredtrade marks of Com put ers and Struc tures, Inc. Watch & LearnTM is atrade mark of Com put ers and Struc tures, Inc.

The com puter pro grams SAP2000® and ETABS® and all as so ci ateddoc u men ta tion are pro pri etary and copy righted prod ucts. World widerights of own er ship rest with Com put ers and Struc tures, Inc. Unlicenseduse of these pro grams or re pro duc tion of doc u men ta tion in any form,with out prior writ ten au tho ri za tion from Com put ers and Struc tures, Inc.,is ex plic itly pro hib ited.

No part of this pub li ca tion may be re pro duced or dis trib uted in any formor by any means, or stored in a da ta base or re trieval sys tem, with out theprior ex plicit writ ten per mis sion of the pub lisher.

Fur ther in for ma tion and cop ies of this doc u men ta tion may be ob tainedfrom:

Com put ers and Struc tures, Inc.1995 Uni ver sity Av e nueBerke ley, Cal i for nia 94704 USA

Tel: (510) 649-2200Fax: (510) 649-2299

E-mail: [email protected] (for gen eral ques tions)E-mail: sup [email protected] (for tech ni cal sup ports ques tions)

Web: www.csiberkeley.com

DISCLAIMER

CON SID ER ABLE TIME, EF FORT AND EX PENSE HAVE GONEINTO THE DE VEL OP MENT AND DOC U MEN TA TION OF ETABSAND SAP2000. THE PRO GRAMS HAVE BEEN THOR OUGHLYTESTED AND USED. IN US ING THE PRO GRAMS, HOW EVER,THE USER AC CEPTS AND UN DER STANDS THAT NO WAR -RANTY IS EX PRESSED OR IM PLIED BY THE DE VEL OP ERS ORTHE DIS TRIB U TORS ON THE AC CU RACY OR THE RE LI ABIL -ITY OF THE PRO GRAMS.

ETABS AND SAP2000 ARE VERY PRAC TI CAL TOOL FOR THEDE SIGN OF RE IN FORCED CON CRETE STRUC TURES. HOW -EVER, THE USER MUST THOR OUGHLY READ THE MAN UALAND CLEARLY REC OG NIZE THE AS PECTS OF RE IN FORCEDCON CRETE DE SIGN THAT THE PRO GRAM AL GO RITHMS DONOT AD DRESS.

THE USER MUST EX PLIC ITLY UN DER STAND THE AS SUMP -TIONS OF THE PRO GRAMS AND MUST IN DE PEND ENTLY VER -IFY THE RE SULTS.

Ta ble of Con tents

CHAP TER I In tro duc tion 1

Over view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Or ga ni za tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Rec om mended Read ing . . . . . . . . . . . . . . . . . . . . . . . . . 4

CHAP TER II De sign Al go rithms 5

De sign Load Com bi na tions. . . . . . . . . . . . . . . . . . . . . . . . 6

De sign and Check Sta tions . . . . . . . . . . . . . . . . . . . . . . . . 8

P-D Ef fects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

El e ment Un sup ported Lengths . . . . . . . . . . . . . . . . . . . . . . 9

Ef fec tive Length Fac tor (K) . . . . . . . . . . . . . . . . . . . . . . . 11

Choice of In put Units . . . . . . . . . . . . . . . . . . . . . . . . . . 14

CHAP TER III Check/De sign for AISC-ASD01 15

De sign Load ing Com bi na tions . . . . . . . . . . . . . . . . . . . . . 18

Clas si fi ca tion of Sec tions . . . . . . . . . . . . . . . . . . . . . . . . 22

Spe cial Seis mic Pro vi sions of Mem ber De sign . . . . . . . . . . . . . 24

Or di nary Mo ment Frames (OMF) . . . . . . . . . . . . . . . 24In ter me di ate Mo ment Frames (IMF) . . . . . . . . . . . . . 25Spe cial Mo ment Frames (SMF) . . . . . . . . . . . . . . . . 25Or di nary Con cen tri cally Braced Frames (OCBF) . . . . . . . 28Spe cial Con cen tri cally Braced Frames (SCBF) . . . . . . . . 28Ec cen tri cally Braced Frames (EBF) . . . . . . . . . . . . . . 29

Cal cu la tion of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 32

Cal cu la tion of Al low able Stresses . . . . . . . . . . . . . . . . . . . 33

Al low able Stress in Ten sion . . . . . . . . . . . . . . . . . . . . 33Al low able Stress in Com pres sion . . . . . . . . . . . . . . . . . 34

Flex ural Buck ling . . . . . . . . . . . . . . . . . . . . . . . 34

i

Flex ural-Tor sional Buck ling. . . . . . . . . . . . . . . . . . 36Al low able Stress in Bend ing . . . . . . . . . . . . . . . . . . . . 38

I-sec tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Chan nel sec tions . . . . . . . . . . . . . . . . . . . . . . . . 42T-sec tions and Dou ble an gles . . . . . . . . . . . . . . . . . 43Box Sec tions and Rect an gu lar Tubes . . . . . . . . . . . . . 43Pipe Sec tions. . . . . . . . . . . . . . . . . . . . . . . . . . 44Round Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 45Rect an gu lar and Square Bars . . . . . . . . . . . . . . . . . 45Sin gle-An gle Sec tions. . . . . . . . . . . . . . . . . . . . . 45Gen eral Sec tions . . . . . . . . . . . . . . . . . . . . . . . . 48

Al low able Stress in Shear . . . . . . . . . . . . . . . . . . . . . 48

Cal cu la tion of Stress Ra tios . . . . . . . . . . . . . . . . . . . . . . . 49

Ax ial and Bend ing Stresses. . . . . . . . . . . . . . . . . . . . . 49Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Joint De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

De sign of Con ti nu ity Plates . . . . . . . . . . . . . . . . . . . . 52De sign of Doubler Plates . . . . . . . . . . . . . . . . . . . . . . 56Weak Beam Strong Col umn Mea sure . . . . . . . . . . . . . . . 59Eval u a tion of Beam Con nec tion Shears . . . . . . . . . . . . . . 61Eval u a tion of Brace Con nec tion Forces . . . . . . . . . . . . . . 63

CHAP TER IV Check/De sign for AISC-ASD89 65


Clas si fi ca tion of Sec tions . . . . . . . . . . . . . . . . . . . . . . . . 68

Cal cu la tion of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 72

Cal cu la tion of Al low able Stresses . . . . . . . . . . . . . . . . . . . 73

Al low able Stress in Ten sion . . . . . . . . . . . . . . . . . . . . 73Al low able Stress in Com pres sion . . . . . . . . . . . . . . . . . 73

Flex ural Buck ling . . . . . . . . . . . . . . . . . . . . . . . 73Flex ural-Tor sional Buck ling. . . . . . . . . . . . . . . . . . 75

Al low able Stress in Bend ing . . . . . . . . . . . . . . . . . . . . 80I-sec tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Chan nel sec tions . . . . . . . . . . . . . . . . . . . . . . . . 83T-sec tions and Dou ble an gles . . . . . . . . . . . . . . . . . 84Box Sec tions and Rect an gu lar Tubes . . . . . . . . . . . . . 85Pipe Sec tions. . . . . . . . . . . . . . . . . . . . . . . . . . 86Round Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 86Rect an gu lar and Square Bars . . . . . . . . . . . . . . . . . 86Sin gle-An gle Sec tions. . . . . . . . . . . . . . . . . . . . . 87Gen eral Sec tions . . . . . . . . . . . . . . . . . . . . . . . . 89

Al low able Stress in Shear . . . . . . . . . . . . . . . . . . . . . 89

Cal cu la tion of Stress Ra tios . . . . . . . . . . . . . . . . . . . . . . . 91

Ax ial and Bend ing Stresses. . . . . . . . . . . . . . . . . . . . . 91Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

ii

CSI Steel Design Manual

CHAP TER V Check/De sign for AISC-LRFD99 95


Clas si fi ca tion of Sec tions . . . . . . . . . . . . . . . . . . . . . . . 102

Cal cu la tion of Fac tored Forces . . . . . . . . . . . . . . . . . . . . 103

Spe cial Seis mic Pro vi sions of Mem ber De sign . . . . . . . . . . . . 105

Or di nary Mo ment Frames (OMF) . . . . . . . . . . . . . . 105In ter me di ate Mo ment Frames (IMF) . . . . . . . . . . . . . 108Spe cial Mo ment Frames (SMF) . . . . . . . . . . . . . . . 108Or di nary Con cen tri cally Braced Frames (OCBF) . . . . . . 109Spe cial Con cen tri cally Braced Frames (SCBF) . . . . . . . 109Ec cen tri cally Braced Frames (EBF) . . . . . . . . . . . . . 112

Cal cu la tion of Nom i nal Strengths . . . . . . . . . . . . . . . . . . . 114

Com pres sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . 115Flex ural Buck ling . . . . . . . . . . . . . . . . . . . . . . 115Flex ural-Tor sional Buck ling . . . . . . . . . . . . . . . . . 117Tor sional and Flex ural-Tor sional Buck ling . . . . . . . . . 117

Ten sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 119Nom i nal Strength in Bend ing . . . . . . . . . . . . . . . . . . . 120

Yield ing . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Lat eral-Tor sional Buck ling. . . . . . . . . . . . . . . . . . 120Dou bly Sym met ric Shapes and Chan nels . . . . . . . . . . 120T-sec tions and Dou ble An gles . . . . . . . . . . . . . . . . 122Sin gle An gles. . . . . . . . . . . . . . . . . . . . . . . . . 123Pipe and Cir cu lar sec tions . . . . . . . . . . . . . . . . . . 124Gen eral and SD Sec tions . . . . . . . . . . . . . . . . . . . 124Flange Lo cal Buck ling . . . . . . . . . . . . . . . . . . . . 124I Shapes, Chan nels, Dou ble Chan nels . . . . . . . . . . . . 126Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127T-sec tions and Dou ble An gles . . . . . . . . . . . . . . . . 127Sin gle An gles. . . . . . . . . . . . . . . . . . . . . . . . . 128Pipe Sec tions . . . . . . . . . . . . . . . . . . . . . . . . . 128Cir cu lar, Rect an gu lar, Gen eral Sec tions, and SD-Sec tions . 129Web Lo cal Buck ling . . . . . . . . . . . . . . . . . . . . . 129I Shapes, Chan nels, Dou ble-Chan nels, and Boxes . . . . . 129T-sec tions and Dou ble An gles . . . . . . . . . . . . . . . . 132Sin gle An gles. . . . . . . . . . . . . . . . . . . . . . . . . 132Pipe Sec tions . . . . . . . . . . . . . . . . . . . . . . . . . 132Cir cu lar, Rect an gu lar, Gen eral Sec tions, and SD Sec tions. . 132

Shear Ca pac i ties. . . . . . . . . . . . . . . . . . . . . . . . . . 132Ma jor Axis of Bend ing . . . . . . . . . . . . . . . . . . . . 133Mi nor Axis of Bend ing . . . . . . . . . . . . . . . . . . . . 133

Cal cu la tion of Ca pac ity Ra tios . . . . . . . . . . . . . . . . . . . . 134

Over view . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Ax ial and Bend ing Stresses . . . . . . . . . . . . . . . . . . . . 134

Ax ial, Bend ing, Shear and Tor sion Stresses . . . . . . . . . 135Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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Table of Contents

Joint De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

De sign of Con ti nu ity Plates . . . . . . . . . . . . . . . . . . . . 136De sign of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 140Weak Beam Strong Col umn Mea sure. . . . . . . . . . . . . . . 143Eval u a tion of Beam Con nec tion Shears. . . . . . . . . . . . . . 145Eval u a tion of Brace Con nec tion Forces. . . . . . . . . . . . . . 147

CHAP TER VI Check/De sign for AISC-LRFD93 149

De sign Load ing Com bi na tions. . . . . . . . . . . . . . . . . . . . . 152



Cal cu la tion of Nom i nal Strengths . . . . . . . . . . . . . . . . . . . 158

Com pres sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . 158Flex ural Buck ling . . . . . . . . . . . . . . . . . . . . . . 158Flex ural-Tor sional Buck ling . . . . . . . . . . . . . . . . . 162Tor sional and Flex ural-Tor sional Buck ling . . . . . . . . . 162

Ten sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 164Nom i nal Strength in Bend ing . . . . . . . . . . . . . . . . . . . 165

Yield ing . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Lat eral-Tor sional Buck ling. . . . . . . . . . . . . . . . . . 165Flange Lo cal Buck ling . . . . . . . . . . . . . . . . . . . . 169Web Lo cal Buck ling . . . . . . . . . . . . . . . . . . . . . 173

Shear Ca pac i ties. . . . . . . . . . . . . . . . . . . . . . . . . . 176

Cal cu la tion of Ca pac ity Ra tios . . . . . . . . . . . . . . . . . . . . 177

Ax ial and Bend ing Stresses . . . . . . . . . . . . . . . . . . . . 178Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

CHAP TER VII Check/De sign for BS 5950-2000 181




Cal cu la tion of Sec tion Ca pac i ties . . . . . . . . . . . . . . . . . . . 189

Com pres sion Re sis tance . . . . . . . . . . . . . . . . . . . . . 189Ten sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 191Mo ment Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 191

Plas tic and Com pact Sec tions . . . . . . . . . . . . . . . . 191Semi-com pact Sec tions. . . . . . . . . . . . . . . . . . . . 193

Lat eral-Tor sional Buck ling Mo ment Ca pac ity . . . . . . . . . . 193Shear Ca pac i ties. . . . . . . . . . . . . . . . . . . . . . . . . . 195

Cal cu la tion of Ca pac ity Ra tios. . . . . . . . . . . . . . . . . . . . . 197

Lo cal Ca pac ity Check . . . . . . . . . . . . . . . . . . . . . . . 197Un der Ax ial Ten sion . . . . . . . . . . . . . . . . . . . . . 197Un der Ax ial Com pres sion . . . . . . . . . . . . . . . . . . 197

Over all Buck ling Check. . . . . . . . . . . . . . . . . . . . . . 198

iv


Shear Ca pac ity Check . . . . . . . . . . . . . . . . . . . . . . . 198

CHAP TER VIII Check/De sign for BS 5950-1990 199




Cal cu la tion of Sec tion Ca pac i ties . . . . . . . . . . . . . . . . . . . 207

Com pres sion Re sis tance . . . . . . . . . . . . . . . . . . . . . 207Ten sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 209Mo ment Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 209

Plas tic and Com pact Sec tions . . . . . . . . . . . . . . . . 209Semi-com pact Sec tions. . . . . . . . . . . . . . . . . . . . 210

Lat eral-Tor sional Buck ling Mo ment Ca pac ity . . . . . . . . . . 210Shear Ca pac i ties. . . . . . . . . . . . . . . . . . . . . . . . . . 213


Lo cal Ca pac ity Check . . . . . . . . . . . . . . . . . . . . . . . 215Un der Ax ial Ten sion . . . . . . . . . . . . . . . . . . . . . 215Un der Ax ial Com pres sion . . . . . . . . . . . . . . . . . . 215

Over all Buck ling Check. . . . . . . . . . . . . . . . . . . . . . 215Shear Ca pac ity Check . . . . . . . . . . . . . . . . . . . . . . . 216

CHAP TER IX Check/De sign for CISC94 217




Cal cu la tion of Fac tored Strengths . . . . . . . . . . . . . . . . . . . 224

Com pres sion Strength. . . . . . . . . . . . . . . . . . . . . . . 224Ten sion Strength . . . . . . . . . . . . . . . . . . . . . . . . . 225Bend ing Strengths. . . . . . . . . . . . . . . . . . . . . . . . . 225

I-shapes and Boxes . . . . . . . . . . . . . . . . . . . . . . 226Rect an gu lar Bar . . . . . . . . . . . . . . . . . . . . . . . 227Pipes and Cir cu lar Rods . . . . . . . . . . . . . . . . . . . 227Chan nel Sec tions . . . . . . . . . . . . . . . . . . . . . . . 228T-shapes and dou ble an gles . . . . . . . . . . . . . . . . . 228Sin gle An gle and Gen eral Sec tions. . . . . . . . . . . . . . 229

Shear Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . 229


Ax ial and Bend ing Stresses . . . . . . . . . . . . . . . . . . . . 231Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

CHAP TER X Check/De sign for EUROCODE 3-92 235




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Cal cu la tion of Sec tion Resistances . . . . . . . . . . . . . . . . . . 244

Ten sion Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . 245Com pres sion Re sis tance . . . . . . . . . . . . . . . . . . . . . 245Shear Ca pac ity . . . . . . . . . . . . . . . . . . . . . . . . . . 247Mo ment Re sis tance . . . . . . . . . . . . . . . . . . . . . . . . 248Lat eral-tor sional Buck ling . . . . . . . . . . . . . . . . . . . . 249


Bend ing, Ax ial Com pres sion, and Low Shear . . . . . . . . . . 251Bend ing, Ax ial Com pres sion, and High Shear . . . . . . . . . . 252Bend ing, Com pres sion, and Flex ural Buck ling . . . . . . . . . . 252Bend ing, Com pres sion, and Lat eral-Tor sional Buck ling . . . . . 253Bend ing, Ax ial Ten sion, and Low Shear . . . . . . . . . . . . . 254Bend ing, Ax ial Ten sion, and High Shear . . . . . . . . . . . . . 254Bend ing, Ax ial Ten sion, and Lat eral-Tor sional Buck ling . . . . 255Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

CHAP TER XI Check/De sign for UBC-ASD97 257


Mem ber De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Clas si fi ca tion of Sec tions . . . . . . . . . . . . . . . . . . . . . 260Cal cu la tion of Stresses . . . . . . . . . . . . . . . . . . . . . . 262Cal cu la tion of Al low able Stresses . . . . . . . . . . . . . . . . 262Cal cu la tion of Stress Ra tios . . . . . . . . . . . . . . . . . . . . 263

Ax ial and Bend ing Stresses . . . . . . . . . . . . . . . . . 263Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . 265

Seis mic Re quire ments. . . . . . . . . . . . . . . . . . . . . . . 266Or di nary Mo ment Frames . . . . . . . . . . . . . . . . . . 266Spe cial Mo ment-Re sist ing Frames . . . . . . . . . . . . . . 266Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . 267Ec cen tri cally Braced Frames . . . . . . . . . . . . . . . . . 268Spe cial Con cen tri cally Braced Frames . . . . . . . . . . . . 271

Joint De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

De sign of Con ti nu ity Plates . . . . . . . . . . . . . . . . . . . . 273De sign of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 276Beam/Col umn Plas tic Mo ment Ca pac ity Ra tio . . . . . . . . . . 278Eval u a tion of Beam Con nec tion Shears. . . . . . . . . . . . . . 279Eval u a tion of Brace Con nec tion Forces. . . . . . . . . . . . . . 281

CHAP TER XII Check/De sign for UBC-LRFD97 283


Mem ber De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

Clas si fi ca tion of Sec tions . . . . . . . . . . . . . . . . . . . . . 286Cal cu la tion of Fac tored Forces . . . . . . . . . . . . . . . . . . 288Cal cu la tion of Nom i nal Strengths. . . . . . . . . . . . . . . . . 289Cal cu la tion of Ca pac ity Ra tios . . . . . . . . . . . . . . . . . . 290

vi


Ax ial and Bend ing Stresses . . . . . . . . . . . . . . . . . 290Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . 291

Seis mic Re quire ments. . . . . . . . . . . . . . . . . . . . . . . 292Or di nary Mo ment Frames . . . . . . . . . . . . . . . . . . 292Spe cial Mo ment-Re sist ing Frames . . . . . . . . . . . . . . 292Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . 293Ec cen tri cally Braced Frames . . . . . . . . . . . . . . . . . 294Spe cial Con cen tri cally Braced Frames . . . . . . . . . . . . 297

Joint De sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

De sign of Con ti nu ity Plates . . . . . . . . . . . . . . . . . . . . 299De sign of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 303Weak Beam Strong Col umn Mea sure. . . . . . . . . . . . . . . 306Eval u a tion of Beam Con nec tion Shears. . . . . . . . . . . . . . 307Eval u a tion of Brace Con nec tion Forces. . . . . . . . . . . . . . 308

CHAP TER XIII De sign Out put 311

Over view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Graph i cal Dis play of De sign Out put . . . . . . . . . . . . . . . . . 312

Tab u lar Dis play of De sign Out put . . . . . . . . . . . . . . . . . . . 313

Mem ber Spe cific In for ma tion . . . . . . . . . . . . . . . . . . . . . 314

Ref er ences 317

In dex 319

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Table of Contents

C h a p t e r I

Introduction

Overview

SAP2000 and ETABS fea ture pow er ful and com pletely in te grated mod ules for de -sign of both steel and re in forced con crete struc tures. The pro gram pro vides the user with op tions to cre ate, mod ify, ana lyze and de sign struc tural mod els, all fromwithin the same user in ter face. The pro gram is ca pa ble of per form ing ini tial mem -ber siz ing and op ti mi za tion from within the same in ter face.

The pro gram pro vides an in ter ac tive en vi ron ment in which the user can study thestress con di tions, make ap pro pri ate changes, such as re vis ing mem ber prop er ties,and re- examine the re sults with out the need to re- run the analy sis. A sin gle mouseclick on an ele ment brings up de tailed de sign in for ma tion. Mem bers can begrouped to gether for de sign pur poses. The out put in both graphi cal and tabu latedfor mats can be read ily printed.

The pro gram is struc tured to sup port a wide va ri ety of the lat est na tional and in ter -na tional de sign codes for the auto mated de sign and check of con crete and steelframe mem bers. The pro gram cur rently sup ports the fol low ing steel de sign codes:

• U.S. AISC 360-2005/IBC 2006

• U.S. AISC ASD-2001,

• U.S. AISC LRFD-1999,

Overview 1

• U.S. AISC ASD-1989,

• U.S. AISC-LRFD-1994,

• UBC ASD-1997,

• UBC LRFD-1997,

• Ca na dian CAN/CSA- S16.1-1994,

• Brit ish BS 5950-2200,

• Brit ish BS 5950-1990, and

• Eurocode 3 (ENV 1993-1-1).

The de sign is based upon a set of user- specified load ing com bi na tions. How ever,the pro gram pro vides a set of de fault load com bi na tions for each de sign code sup -ported in the program. If the de fault load com bi na tions are ac cept able, no defi ni tion of ad di tional load com bi na tion is re quired.

In the de sign pro cess the pro gram picks the least weight sec tion re quired forstrength for each ele ment to be de signed, from a set of user speci fied sec tions. Dif -fer ent sets of avail able sec tions can be speci fied for dif fer ent groups of ele ments.Also sev eral ele ments can be grouped to be de signed to have the same sec tion.

In the check pro cess the pro gram pro duces de mand/ca pac ity ra tios for ax ial loadand bi ax ial mo ment in ter ac tions and shear. The de mand/ca pac ity ra tios are basedon ele ment stress and al low able stress for al low able stress de sign, and on fac toredloads (ac tions) and fac tored ca paci ties (re sis tances) for limit state de sign.

The checks are made for each user speci fied (or pro gram de faulted) load com bi na -tion and at sev eral user con trolled sta tions along the length of the ele ment. Maxi -mum de mand/ca pac ity ra tios are then re ported and/or used for de sign op ti mi za tion.

All al low able stress val ues or de sign ca pac ity val ues for ax ial, bend ing and shearac tions are cal cu lated by the pro gram. Te di ous cal cu la tions as so ci ated with evalu -at ing ef fec tive length fac tors for col umns in mo ment frame type struc tures are auto -mated in the al go rithms.

The pres en ta tion of the out put is clear and con cise. The in for ma tion is in a form that al lows the designer to take ap pro pri ate re me dial meas ures if there is mem ber over -stress. Backup de sign in for ma tion pro duced by the pro gram is also pro vided forcon ven ient veri fi ca tion of the re sults.

When us ing 1997 UBC-ASD or UBC-LRFD de sign codes, re quire ments for con ti -nu ity plates at the beam to col umn con nec tions are eval u ated. The pro gram per -forms a joint shear anal y sis to de ter mine if doubler plates are re quired in any of the

2 Overview


joint panel zones. Max i mum beam shears re quired for the beam shear con nec tionde sign are re ported. Also max i mum ax ial ten sion or com pres sion val ues that aregen er ated in the mem ber are re ported.

Spe cial 1997 UBC-ASD and UBC-LRFD seis mic de sign pro vi sions are im ple -mented in the cur rent ver sion of the pro gram. The ra tio of the beam flex ural ca pac i -ties with re spect to the col umn re duced flex ural ca pac i ties (re duced for ax ial forceef fect) as so ci ated with the weak beam-strong col umn as pect of any beam/col umnin ter sec tion, are re ported for spe cial mo ment re sist ing frames. Ca pac ity re quire -ments as so ci ated with seis mic fram ing sys tems that re quire duc til ity are checked.

Spe cial re quire ments for seis mic de sign are not im ple mented in the cur rent ver sionof SAP2000.

Eng lish as well as SI and MKS met ric units can be used to de fine the model ge ome -try and to spec ify de sign pa rame ters.

Organization

This man ual is or gan ized in the fol low ing way:

Chap ter II out lines vari ous as pects of the steel de sign pro ce dures of the pro gram.This chap ter de scribes the com mon ter mi nol ogy of steel de sign as im ple mented inthe program.

Each of eleven sub se quent chap ters gives a de tailed de scrip tion of a spe cific codeof prac tice as in ter preted by and im ple mented in the program. Each chap ter de -scribes the de sign load ing com bi na tions to be con sid ered; al low able stress or ca -pac ity cal cu la tions for ten sion, com pres sion, bend ing, and shear; cal cu la tions ofde mand/ca pac ity ra tios; and other spe cial con sid era tions re quired by the code.

• Chap ter III gives a de tailed de scrip tion of the AISC ASD code (AISC 2001) asim ple mented in the pro gram.

• Chap ter IV gives a de tailed de scrip tion of the AISC ASD steel code (AISC1989) as im ple mented in the pro gram.

• Chap ter V gives a de tailed de scrip tion of the AISC LRFD code (AISC 1999)as im ple mented in the pro gram.

• Chap ter VI gives a de tailed de scrip tion of the AISC LRFD steel code (AISC1993) as im ple mented in the pro gram.

• Chap ter VII gives a de tailed de scrip tion of the Brit ish code BS 5950 (BSI2000) as im ple mented in the pro gram.

Organization 3

Chapter I Introduction

• Chap ter IIIV gives a de tailed de scrip tion of the Brit ish code BS 5950 (BSI1990) as im ple mented in the pro gram.

• Chap ter IX gives a de tailed de scrip tion of the Ca na dian code (CISC 1994) asim ple mented in the pro gram.

• Chap ter X gives a de tailed de scrip tion of the Eurocode 3 (CEN 1992) as im ple -mented in the pro gram.

• Chap ter XI gives a de tailed de scrip tion of the UBC ASD (UBC 1997) as im ple -mented in the pro gram.

• Chap ter XII gives a de tailed de scrip tion of the UBC (UBC 1997) as im ple -mented in the pro gram.

Chap ter XIII out lines vari ous as pects of the tabu lar and graphi cal out put from theprogram re lated to steel de sign.

Recommended Reading

It is rec om mended that the user read Chap ter II “De sign Al go rithms” and one ofeleven sub se quent chap ters cor re spond ing to the code of in ter est to the user. Fi nally the user should read “De sign Out put” in Chap ter XIII for un der stand ing and in ter -pret ing the program out put re lated to steel de sign.

4 Recommended Reading


C h a p t e r II

Design Algorithms

This chap ter out lines vari ous as pects of the steel check and de sign pro ce dures thatare used by the pro gram. The steel de sign and check may be per formed ac cord ingto one of the fol low ing codes of prac tice.

• Ameri can In sti tute of Steel Con struc tion’s “Al low able Stress De sign and Plas -tic De sign Speci fi ca tion for Struc tural Steel Build ings”, AISC- ASD (AISC2001).

• Amer i can In sti tute of Steel Con struc tion’s “Al low able Stress De sign and Plas -tic De sign Spec i fi ca tion for Struc tural Steel Build ings”, AISC-ASD (AISC1989).

• Amer i can In sti tute of Steel Con struc tion’s “Load and Re sis tance Fac tor De -sign Spec i fi ca tion for Struc tural Steel Build ings”, AISC-LRFD (AISC 1999)

• Ameri can In sti tute of Steel Con struc tion’s “Load and Re sis tance Fac tor De -sign Speci fi ca tion for Struc tural Steel Build ings”, AISC- LRFD (AISC 1994).

• Brit ish Stan dards In sti tu tion’s “Struc tural Use of Steel work in Build ing”, BS5950 (BSI 2000).

• Brit ish Stan dards In sti tu tion’s “Struc tural Use of Steel work in Build ing”, BS5950 (BSI 1990).

5

• Ca na dian In sti tute of Steel Con struc tion’s “Limit States De sign of Steel Struc -tures”, CAN/CSA- S16.1-94 (CISC 1995).

• Euro pean Com mit tee for Stan dardi za tion’s “Eurocode 3: De sign of Steel

Struc tures C Part 1.1: Gen eral Rules and Rules for Build ings”, ENV 1993- 1-1(CEN 1992).

• In ter na tional Con fer ence of Build ing Of fi cials’ “1997 Uni form Build ingCode: Vol ume 2: Struc tural En gi neer ing De sign Pro vi sions” Chap ter 22 Di vi -

sion III “De sign Stan dard for Spec i fi ca tion for Struc tural Steel Build ings ¾Al low able Stress De sign and Plas tic De sign”, UBC-ASD (ICBO 1997).

• In ter na tional Con fer ence of Build ing Of fi cials’ “1997 Uni form Build ingCode: Vol ume 2: Struc tural En gi neer ing De sign Pro vi sions” Chap ter 22 Di vi -sion II “De sign Stan dard for Load and Re sis tance fac tor De sign Spec i fi ca tionfor Struc tural Steel Build ings”, UBC-LRFD (ICBO 1997).

De tails of the al go rithms as so ci ated with each of these codes as im ple mented andin ter preted in the pro gram are de scribed in sub se quent chap ters. How ever, thischap ter pro vides a back ground which is com mon to all the de sign codes.

It is as sumed that the user has an en gi neer ing back ground in the gen eral area ofstruc tural steel de sign and fa mili ar ity with at least one of the above men tioned de -sign codes.

For re fer ring to per ti nent sec tions of the cor re spond ing code, a unique pre fix is as -signed for each code. For ex am ple, all ref er ences to the AISC-LRFD code carry thepre fix of “LRFD”. Sim i larly,

– Ref er ences to the AISC-ASD code carry the pre fix of “ASD”

– Ref er ences to the Ca na dian code carry the pre fix of “CISC”

– Ref er ences to the Brit ish code carry the pre fix of “BS”

– Ref er ences to the Eurocode carry the pre fix of “EC3”

– Ref er ences to the UBC-ASD code carry the pre fix of “UBC

Design Load Combinations

The de sign load com bi na tions are used for de ter min ing the vari ous com bi na tions of the load cases for which the struc ture needs to be de signed/checked. The load com -bi na tion fac tors to be used vary with the se lected de sign code. The load com bi na -tion fac tors are ap plied to the forces and mo ments ob tained from the as so ci ated

6 Design Load Combinations


load cases and the re sults are then summed to ob tain the fac tored de sign forces andmo ments for the load com bi na tion.

For multi- valued load com bi na tions in volv ing re sponse spec trum, time his tory,mov ing loads and multi- valued com bi na tions (of type en vel op ing, square- root ofthe sum of the squares or ab so lute) where any cor re spon dence be tween in ter act ingquan ti ties is lost, the pro gram auto mati cally pro duces mul ti ple sub com bi na tionsus ing maxima/min ima per mu ta tions of in ter act ing quan ti ties. Sepa rate com bi na -tions with nega tive fac tors for re sponse spec trum cases are not re quired be cause the pro gram auto mati cally takes the min ima to be the nega tive of the maxima for re -sponse spec trum cases and the above de scribed per mu ta tions gen er ate the re quiredsub com bi na tions.

When a de sign com bi na tion in volves only a sin gle multi- valued case of time his -tory or mov ing load, fur ther op tions are avail able. The pro gram has an op tion to re -quest that time his tory com bi na tions pro duce sub com bi na tions for each time stepof the time his tory. Also an op tion is avail able to re quest that mov ing load com bi -na tions pro duce sub com bi na tions us ing maxima and min ima of each de sign quan -tity but with cor re spond ing val ues of in ter act ing quan ti ties.

For nor mal load ing con di tions in volv ing static dead load, live load, wind load, andearth quake load, and/or dy namic re sponse spec trum earth quake load, the pro gramhas built- in de fault load ing com bi na tions for each de sign code. These are based onthe code rec om men da tions and are docu mented for each code in the cor re spond ingchap ters.

For other load ing con di tions in volv ing mov ing load, time his tory, pat tern liveloads, sepa rate con sid era tion of roof live load, snow load, etc., the user must de finede sign load ing com bi na tions ei ther in lieu of or in ad di tion to the de fault de signload ing com bi na tions.

The de fault load com bi na tions as sume all static load cases de clared as dead load tobe ad di tive. Simi larly, all cases de clared as live load are as sumed ad di tive. How -ever, each static load case de clared as wind or earth quake, or re sponse spec trumcases, is as sumed to be non ad di tive with each other and pro duces mul ti ple lat eralload com bi na tions. Also wind and static earth quake cases pro duce sepa rate load ing com bi na tions with the sense (posi tive or nega tive) re versed. If these con di tions arenot cor rect, the user must pro vide the ap pro pri ate de sign com bi na tions.

The de fault load com bi na tions are in cluded in de sign if the user re quests them to bein cluded or if no other user de fined com bi na tion is avail able for con crete de sign. Ifany de fault com bi na tion is in cluded in de sign, then all de fault com bi na tions will

Design Load Combinations 7

Chapter II Design Algorithms

auto mati cally be up dated by the pro gram any time the user changes to a dif fer entde sign code or if static or re sponse spec trum load cases are modi fied.

Live load re duc tion fac tors can be ap plied to the mem ber forces of the live load case on an element- by- element ba sis to re duce the con tri bu tion of the live load to thefac tored load ing.

The user is cau tioned that if mov ing load or time his tory re sults are not re quested to be re cov ered in the analy sis for some or all the frame mem bers, then the ef fects ofthese loads will be as sumed to be zero in any com bi na tion that in cludes them.

Design and Check Stations

For each load com bi na tion, each el e ment is de signed or checked at a num ber of lo -ca tions along the length of the el e ment. The lo ca tions are based on equally spacedseg ments along the clear length of the el e ment. The num ber of seg ments in an el e -ment is re quested by the user be fore the anal y sis is made. The user can re fine thede sign along the length of an el e ment by re quest ing more seg ments.

The ax ial-flexure interaction ra tios as well as shear stress ra tios are cal cu lated foreach sta tion along the length of the mem ber for each load com bi na tion. The ac tualmem ber stress com po nents and cor re spond ing al low able stresses are cal cu lated.Then, the stress ra tios are evalu ated ac cord ing to the code. The con trol ling com -pres sion and/or ten sion stress ra tio is then ob tained, along with the cor re spond ingiden ti fi ca tion of the sta tion, load com bi na tion, and code- equation. A stress ra tiogreater than 1.0 in di cates an over stress or ex ceed ing a limit state.

P-D Effects

The program de sign al go rithms re quire that the analy sis re sults in clude the P-D ef -fects. The P-D ef fects are con sid ered dif fer ently for “braced” or “non sway” and“un braced” or “sway” com po nents of mo ments in frames. For the braced mo mentsin frames, the ef fect of P-D is lim ited to “in di vid ual mem ber sta bil ity”. For un -braced com po nents, “lat eral drift ef fects” should be con sid ered in ad di tion to in di -vid ual mem ber sta bil ity ef fect. In the program, it is as sumed that “braced” or “non -sway” mo ments are con trib uted from the “dead” or “live” loads. Whereas, “un -braced” or “sway” mo ments are con trib uted from all other types of loads.

For the in di vid ual mem ber sta bil ity ef fects, the mo ments are mag ni fied with mo -ment mag ni fi ca tion fac tors as in the AISC-LRFD code is con sid ered di rectly in thede sign equa tions as in the Ca na dian, Brit ish, and Eu ro pean codes. No mo mentmag ni fi ca tion is ap plied to the AISC-ASD code.

8 Design and Check Stations


For lat eral drift ef fects of un braced or sway frames, the program as sumes that theam pli fi ca tion is al ready in cluded in the re sults be cause P-D ef fects are con sid eredfor all but AISC- ASD code.

The us ers of the pro gram should be aware that the de fault anal y sis op tion in theprogram is turned OFF for P-D ef fect. The de fault number of it era tions for P-Danaly sis is 1. The user should turn the P-D analy sis ON and set the maxi mumnumber of it era tions for the analy sis. No P-D analy sis is re quired for the AISC- ASD code. For fur ther ref er ence, the user is re ferred to CSI Analy sis Ref er enceMan ual (CSI 2005).

Element Unsupported Lengths

To ac count for col umn slen der ness ef fects, the col umn un sup ported lengths are re -quired. The two un sup ported lengths are l33 and l22 . See Figure II-1. These are thelengths be tween sup port points of the ele ment in the cor re spond ing di rec tions. Thelength l33 cor re sponds to in sta bil ity about the 3-3 axis (ma jor axis), and l22 cor re -sponds to in sta bil ity about the 2-2 axis (mi nor axis). The length l22 is also used forlateral- torsional buck ling caused by ma jor di rec tion bend ing (i.e., about the 3-3axis). See Figure II-2 for cor re spon dence be tween the program axes and the axes inthe de sign codes.

Normally, the un sup ported el e ment length is equal to the length of the el e ment, i.e., the dis tance be tween END-I and END-J of the el e ment. See Figure II-1. The pro -gram, how ever, al lows us ers to as sign sev eral el e ments to be treated as a sin glemem ber for de sign. This can be done dif fer ently for ma jor and mi nor bend ing. There fore, ex tra ne ous joints, as shown in Figure II-3, that af fect the un sup portedlength of an el e ment are au to mat i cally taken into con sid er ation.

Element Unsupported Lengths 9


In de ter min ing the val ues for l22 and l33 of the el e ments, the pro gram rec og nizesvar i ous as pects of the struc ture that have an ef fect on these lengths, such as mem ber con nec tiv ity, di a phragm con straints and sup port points. The pro gram au to mat i -cally lo cates the el e ment sup port points and eval u ates the cor re spond ing un sup -ported el e ment length.

There fore, the un sup ported length of a col umn may ac tu ally be eval u ated as be inggreater than the cor re spond ing el e ment length. If the beam frames into only one di -rec tion of the col umn, the beam is as sumed to give lat eral sup port only in that di rec -tion. The user has op tions to spec ify the un sup ported lengths of the el e ments on anel e ment-by-el e ment ba sis.

10 Element Unsupported Lengths


l33

l22

Axis 1

Axis 3

Axis 2

End I

End j

Figure II-1Major and Minor Axes of Bending

Effective Length Factor (K)

The col umn K-fa ctor al go rithm has been de vel oped for building- type struc tures,where the col umns are ver ti cal and the beams are hori zon tal, and the be hav ior is ba -si cally that of a moment- resisting na ture for which the K-fa ctor cal cu la tion is rela -tively com plex. For the pur pose of cal cu lat ing K-fa ctors, the ele ments are iden ti -fied as col umns, beams and braces. All ele ments par al lel to the Z- axis are clas si fiedas col umns. All ele ments par al lel to the X-Y plane are clas si fied as beams. The restare braces.

Effective Length Factor (K) 11


2

33

2

SAP2000

EUROCODE 3

z

z

y y

ASD89, LRFD95 & AASHTO

y

y

x x

CISC95

y

y

x x

y

y

x x

BS5950

Figure II-2Correspondence between the program Axes and Code Axes

The beams and braces are as signed K-fac tors of unity. In the cal cu la tion of theK-fac tors for a col umn el e ment, the pro gram first makes the fol low ing four stiff -ness sum ma tions for each joint in the struc tural model:

S = E I

Lcx

c c

c x

æ

èçç

ö

ø÷÷å S =

E I

Lbx

b b

b x

æ

èçç

ö

ø÷÷å

S = E I

Lcy

c c

c y

æ

èçç

ö

ø÷÷å S =

E I

Lby

b b

b y

æ

èçç

ö

ø÷÷å

where the x and y sub scripts cor re spond to the global X and Y di rec tions and the cand b sub scripts re fer to col umn and beam. The lo cal 2-2 and 3-3 terms EI l22 22

and EI l33 33 are ro tated to give com po nents along the global X and Y di rec tions toform the ( / )EI l x and ( / )EI l y val ues. Then for each col umn, the joint sum ma tionsat END-I and the END-J of the mem ber are trans formed back to the col umn lo cal1-2-3 co or di nate sys tem and the G-val ues for END-I and the END-J of the mem berare cal cu lated about the 2-2 and 3-3 di rec tions as fol lows:

12 Effective Length Factor (K)


Figure II-3Unsupported Lengths are Affected by Intermediate Nodal Points

G = S

S

II

c

Ib

2222

22

G = S

S

JJ

c

Jb

2222

22

G = S

S

II

c

Ib

3333

33

G = S

S

JJ

c

Jb

3333

33

If a ro ta tional re lease ex ists at a par tic u lar end (and di rec tion) of an el e ment, thecor re spond ing value is set to 10.0. If all de grees of free dom for a par tic u lar joint arede leted, the G-val ues for all mem bers con nect ing to that joint will be set to 1.0 forthe end of the mem ber con nect ing to that joint. Finally, if G I and G J are known fora par tic u lar di rec tion, the col umn K-fac tor for the cor re spond ing di rec tion is cal cu -

lated by solv ing the fol low ing re la tion ship for a:

a a

a

2 I J

I J

36

6( + )=

tan

G G

G G

-

from which K = p / a. This re la tion ship is the mathe mati cal formulation for theevalua tion of K fac tors for moment- resisting frames as sum ing sidesway to be un in -hibi ted. For other struc tures, such as braced frame struc tures, trusses, space frames,trans mis sion tow ers, etc., the K-fa ctors for all mem bers are usu ally unity andshould be set so by the user. The fol low ing are some im por tant as pects as so ci atedwith the col umn K-fa ctor al go rithm:

• An ele ment that has a pin at the joint un der con sid era tion will not en ter the stiff -ness sum ma tions cal cu lated above. An ele ment that has a pin at the far endfrom the joint un der con sid era tion will con trib ute only 50% of the cal cu latedEI value. Also, beam ele ments that have no col umn mem ber at the far end fromthe joint un der con sid era tion, such as can ti le vers, will not en ter the stiff nesssum ma tion.

• If there are no beams fram ing into a par ticu lar di rec tion of a col umn ele ment,the as so ci ated G-value will be in fin ity. If the G-value at any one end of a col -umn for a par ticu lar di rec tion is in fin ity, the K-fa ctor cor re spond ing to that di -rec tion is set equal to unity.

• If ro ta tional re leases ex ist at both ends of an ele ment for a par ticu lar di rec tion,the cor re spond ing K-fa ctor is set to unity.

• The auto mated K-fa ctor cal cu la tion pro ce dure can oc ca sion ally gen er ate ar ti fi -cially high K-fa ctors, spe cifi cally un der cir cum stances in volv ing skewedbeams, fixed sup port con di tions, and un der other con di tions where the pro -gram may have dif fi culty rec og niz ing that the mem bers are lat er ally sup portedand K-fa ctors of unity are to be used.

Effective Length Factor (K) 13


• All K-fa ctors pro duced by the pro gram can be over writ ten by the user. Theseval ues should be re viewed and any un ac cept able val ues should be re placed.

Choice of Input Units

Eng lish as well as SI and MKS met ric units can be used for in put. But the codes arebased on a spe cific sys tem of units. All equa tions and de scrip tions pre sented in thesub se quent chap ters cor re spond to that spe cific sys tem of units un less oth er wisenoted. For ex am ple, AISC- ASD code is pub lished in kip-inch- second units. By de -fault, all equa tions and de scrip tions pre sented in the chap ter “Check/De sign forAIS C-ASD89” cor re spond to kip- inch- second units. How ever, any sys tem of unitscan be used to de fine and de sign the struc ture in the program.

14 Choice of Input Units


C h a p t e r III

Check/Design for AISC-ASD01

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the program when the user se lects the AISC-ASD01 de -sign code (AISC 2001). Var i ous no ta tions used in this chap ter are de scribed inTable IV-1.

For re fer ring to per ti nent sec tions and equa tions of the origi nal ASD code, a uniquepre fix “ASD” is as signed. However, all ref er ences to the “Speci fi ca tions for Al -low able Stress De sign of Single- Angle Mem bers” carry the pre fix of “ASD SAM”.

The de sign is based on user- specified load ing com bi na tions. But the pro gram pro -vides a set of de fault load com bi na tions that should sat isfy re quire ments for the de -sign of most build ing type struc tures.

In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this chapter. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di catesover stress. Simi larly, a shear ca pac ity ra tio is also cal cu lated sepa rately.

15

16


A = Cross- sectional area, in2

Ae = Effective cross- sectional area for slen der sections, in2

A f = Area of flange , in2

Ag = Gross cross- sectional area, in2

A Av v2 3, = Ma jor and mi nor shear ar eas, in2

Aw = Web shear area, dt w , in2

Cb = Bend ing Co ef fi cient

Cm = Mo ment Co ef fi cient

Cw = Warp ing con stant, in6

D = Out side di ame ter of pipes, in

E = Modu lus of elas tic ity, ksi

Fa = Al low able ax ial stress, ksi

Fb = Al low able bending stress, ksi

F Fb b33 22, = Al low able ma jor and mi nor bend ing stresses, ksi

Fcr = Criti cal com pres sive stress, ksi

Fe33¢ =

( )12

23

2

33 33 33

2

E

K l r

p

Fe22¢ =

( )12

23

2

22 22 22

2

E

K l r

p

Fv = Al low able shear stress, ksi

Fy = Yield stress of ma te rial, ksi

K = Ef fec tive length fac tor

K K33 22, = Ef fec tive length K- factors in the ma jor and mi nor directions

M M33 22, = Major and mi nor bend ing mo ments in mem ber, kip- in

M ob = Lateral- torsional mo ment for an gle sections, kip- in

P = Axial force in mem ber, kips

Pe = Euler buck ling load, kips

Q = Re duc tion fac tor for slen der sec tion, = Q Qa s

Qa = Re duc tion fac tor for stiff ened slen der elements

Qs = Re duc tion fac tor for unstiff ened slen der elements

S = Sec tion modu lus, in3

S S33 22, = Ma jor and mi nor sec tion moduli, in3

Table III-1AISC-ASD Notations

17

Chapter III Check/Design for AISC-ASD01

S Seff eff, ,,33 22 = Ef fec tive major and mi nor sec tion moduli for slen der sections, in3

S c = Sec tion modu lus for com pres sion in an an gle section, in3

V V2 3, = Shear forces in major and mi nor directions, kips

b = Nomi nal di men sion of plate in a sec tion, inlonger leg of an gle sections,b tf w- 2 for welded and b tf w-3 for rolled box sec tions, etc.

be = Ef fec tive width of flange, in

bf = Flange width, in

d = Over all depth of mem ber, in

f a = Axial stress ei ther in com pres sion or in tension, ksi

f b = Nor mal stress in bend ing, ksi

f fb b33 22, = Nor mal stress in ma jor and minor di rec tion bending, ksi

f v = Shear stress, ksi

f fv v2 3, = Shear stress in ma jor and minor di rec tion bending, ksi

h = Clear dis tance be tween flanges for I shaped sec tions ( )d t f- 2 , in

he = Ef fec tive dis tance be tween flanges less fil lets, in

k = Dis tance from outer face of flange to web toe of fil let , in

k c = Pa rame ter used for clas si fi ca tion of sec tions,

[ ]4.05

0.46h t w

if h t w > 70 ,

1 if h t w £ 70 .

l l33 22, = Ma jor and mi nor di rec tion un braced mem ber lengths, in

lc = Criti cal length, in

r = Ra dius of gy ra tion, in

r r33 22, = Ra dii of gy ra tion in the ma jor and mi nor di rec tions, in

rz = Mini mum Ra dius of gy ra tion for an gles, in

t = Thick ness of a plate in I, box, chan nel, an gle, and T sections, in

t f = Flange thick ness, in

t w = Web thick ness, in

bw = Spe cial sec tion prop erty for an gles, in

Table III-1AISC-ASD Notations (cont.)

Eng lish as well as SI and MKS met ric units can be used for in put. But the code isbased on Kip- Inch- Second units. For sim plic ity, all equa tions and de scrip tions pre -sented in this chap ter cor re spond to Kip- Inch- Second units un less oth er wisenoted.

Design Loading Combinations

The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. For the AISC-ASD01 code, if a struc tureis sub jected to dead load (DL), live load (LL), wind load (WL), and earth quake in -duced load (EL), and con sid er ing that wind and earth quake forces are re versi ble,then the fol low ing load com bi na tions may have to be de fined (ASD A4). The DLmultiplier and r fac tors are spec i fied in ASCE 7-02:

1.0 DL (ASCE 2.4.1-1)1.0 DL + 1.0 LL (ASCE 2.4.1-2)

1.0 DL ± 1.0 WL (ASCE 2.4.1-5)0.6 DL ± 1.0 WL (ASCE 2.4.1-7)1.0 DL + 0.75 (1.0 LL ± 1.0 WL) (ASCE 2.4.1-6)

1.0 DL (0.6 - 0.7 DLmultiplier ) ± 0.7 r EL (ASCE 2.4.1-8)

1.0 DL (1 + 0.7 DLmultiplier ) ± 1.0 r EL (ASCE 2.4.1-5)

1.0 DL + 0.75 (0.7 DLmultiplier + 1.0 LL ± 0.7 r EL) (ASCE 2.4.1-6)

It is noted here that when ever spe cial seis mic load ing com bi na tions are re quiredby the code for spe cial cir cum stances, the pro gram au to mat i cally gen er ates thoseload com bi na tions in ter nally. The fol low ing ad di tional seis mic load com bi na tionsare fre quently checked for spe cific types of mem bers and spe cial cir cum stances.

(0.9-0.2SDS) DL ± W 0 EL (ASCE 9.5.2.7.1, 2.3, LRFD SEIS MIC 4.1)

(1.2 + 0.2SSDS) DL + 1.0 LL ± W 0 EL

where, W 0 is the seis mic force am pli fi ca tion fac tor which is re quired to ac count forstruc tural overstrength. The de fault value of W 0 is taken as 3.0 in the pro gram. Ifthe user de fines one or more auto-seis mic loads, then the value of W 0 de fined foreach auto-seis mic load cases. Also if spe cial seis mic data is de fined by the user, the user spec i fies an W 0 value, and the user re quests the pro gram to in clude the spe cialseis mic de sign data, then the user spec i fied W 0 takes pre ce dence over the de fault

18 Design Loading Combinations


Design Loading Combinations 19


Figure III-1AISC-ASD Definition of Geometric Properties



Section Description

Ratio Checked

CompactSection

NoncompactSection

SlenderSection

I-SHAPE

b tf f2

( rolled)£ F

y65 £ F y95 No limit

b tf f2

(welded)£ F

y65 £ 95 F ky c/ No limit

d t w

For f F a y £ 0.16

£ -640

1F

f

Fy

a

y

( )3.74 ,

For f Fa y/ > 0.16

£ 257 / Fy .

No limit No limit

h t w No limit

If compression only,

£ F y253

otherwise

£ F b760

( )£

+

£

14000

16.5

260

F Fy y

BOX

b t f £ F


d t w As for I-shapes No limit No limit

h t w No limit As for I-shapes As for I-shapes

Other t tw f³ 2 , d bw f£ 6 None None

CHANNEL

b t f As for I-shapes As for I-shapes No limit



Other No limit No limit

If welded b df w £ 0.25, t tf w £ 3.0

If rolled b df w £ 0.5, t tf w £ 2.0

Table III-2Limiting Width-Thickness Ratios for

Classification of Sections Based on AISC-ASD

val ues and those de fined for the auto-seis mic load cases. More over, W 0 can beover writ ten for each in di vid ual mem ber. The over writ ten W 0 gets the high est pre -ce dence. The guide lines for se lect ing a rea son able value for W 0 can be found inANSI/AISC 341 SEIS MIC sec tion 4.1 and Ta ble I-4-1.

These are also the de fault de sign load com bi na tions in the program when ever theAISC-ASD01 code is used. The user should use other ap pro pri ate load ing com bi -



Section Description

Ratio Checked

CompactSection

NoncompactSection

SlenderSection

T-SHAPE

b tf f2 £ F


d t w Not applicable £ F

y127 No limit


If welded b df w ³ 0.5, t tf w ³ 1.25

If rolled b df w ³ 0.5, t tf w ³ 1.10

DOUBLEANGLES

b t Not applicable £ F

y76 No limit

ANGLE b t Not applicable £ F

y76 No limit

PIPE D t £ F

y3 300, £ F y3 300,

£ F y13,000

(Compression only)No limit for flexure

ROUND BAR ¾ Assumed Compact

RECTANGLE ¾ Assumed Noncompact

GENERAL ¾ Assumed Noncompact


Classification of Sections Based on AISC-ASD (Cont.)

na tions if roof live load is sepa rately treated, if other types of loads are pres ent, or if pat tern live loads are to be con sid ered.

When de sign ing for com bi na tions in volv ing earth quake and Wind loads, al low able stresses are NOT in creased by the 4/3 fac tor per the ASD Sup ple ment No. 1 whichref er ences ASCE7. For seis mic com bi na tions, the al low able stresses are in creasedby 1.7 fac tor in ac cor dance with ANSI/AISC 341 Seis mic Sec tion 4.2.


Classification of Sections

The al low able stresses for ax ial com pres sion and flex ure are de pend ent upon theclas si fi ca tion of sec tions as ei ther Com pact, Non compact, Slen der, or Too Slen der.The program clas si fies the in di vid ual mem bers ac cord ing to the lim it ingwidth/thick ness ra tios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). Thedefi ni tion of the sec tion prop er ties re quired in this ta ble is given in Figure III-1 andTable III-1.

If the sec tion di men sions sat isfy the lim its shown in the ta ble, the sec tion is clas si -fied as ei ther Com pact, Non com pact, or Slen der. If the sec tion sat is fies the cri te riafor Com pact sec tions, then the sec tion is clas si fied as Com pact sec tion. If the sec -tion does not sat is fy the cri te ria for Com pact sec tions but sat is fies the cri te ria forNon com pact sec tions, the sec tion is clas si fied as Noncom pact sec tion. If the sec -tion does not satisfy the cri te ria for Com pact and Non com pact sec tions but sat is fiesthe cri te ria for Slen der sec tions, the sec tion is clas si fied as Slender sec tion. If thelim its for Slen der sec tions are not met, the sec tion is clas si fied as Too Slen der.Stress check of Too Slen der sec tions is be yond the scope of the program.

In gen eral the de sign sec tions need not nec es sar ily be Com pact to sat isfyANSI/AISC 341-02 codes. How ever, for cer tain spe cial seis mic cases they have tobe Com pact and have to sat isfy spe cial slen der ness re quire ments. See sub sec tion“Seis mic Re quire ments” later in this man ual. The sec tions which do sat isfy thesead di tional re quire ments are clas si fied and re ported as “SEIS MIC” in the pro gram.These spe cial re quire ments for clas si fy ing the sec tions as “SEIS MIC” in the pro -gram are given in Table III-3 (ANSI/AISC 341SEISMIC 8.2, Ta ble I-8-1). If thesecri te ria are not sat is fied, when the code re quires them to be sat is fied, the user mustmod ify the sec tion prop erty. In this case the pro gram gives an er ror mes sage in theout put file.

22 Classification of Sections


Classification of Sections 23


Descriptionof Section

Width-Thickness

Ratio

(l)

COMPACT(SEISMIC ZONE)

(l ps)

NONCOMPACT(Uniform

Compression)(M M22 33 0» » )

(l r )

I-SHAPE

b tf f2

(rolled)£

E

Fy

0 3. £ E F y056.

b tf f2

(welded)£

E

Fy

0 3. £ E F y056.

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷314 1.E

F -

P

Py

u

b y

1.54j

For P P u b yj > 0.125

£æ

è

çç

ö

ø

÷÷ ³ìíï

îï

üýï

þï112 1 49. .

E

F -

P

P

E

Fy

u

b y y

2.33j

£ E F y1 49.

BOXb t

f

h tc w

0 64.E

Fy

Not applicable

£ E F y0 64.

£ E F y1 49.

CHANNEL,DOUBLE CHANNEL

b tf f

h tc w

As for I-shapesAs for I-shapes


T-SHAPEb tf

f2

d t w

Not applicableNot applicable

As for I-shapes

£ E F y075.

ANGLE b t

0 3.E

Fy

£ E F y0 45.

DOUBLE-ANGLE(Separated)

b t

0 3.E

Fy

£ E F y0 45.


Classification of Sections (Special Cases) based on AISC-LRFD

In clas si fy ing web slen der ness of I-shapes, Box, and Chan nel sec tions, it is as -sumed that there are no in ter me di ate stiff en ers (ASD F5, G1). Dou ble an gles arecon ser va tively as sumed to be sepa rated.

Special Seismic Provisions of Member Design

When us ing the AISC-ASD01 op tion, the fol low ing Fram ing Sys tems are rec og -nized (ANSI/AISC 341 SEIS MIC 9, 10, 11, 12, 13, 14, 15):

• Or di nary Mo ment Frame (OMF)

• In ter me di ate Mo ment Frame (IMF)

• Spe cial Mo ment Frame (SMF)

• Or di nary Con cen tri cally Braced Frame (OCBF)

• Spe cial Con cen tri cally Braced Frame (SCBF)

• Ec cen tri cally Braced Frame (EBF)

• Spe cial Truss Mo ment Frame (STMF)

By de fault the frame type is taken as Spe cial Mo ment-Re sist ing Frame (SMRF) inthe pro gram. How ever, the frame type can be over writ ten in the Pref er ence form tochange the de fault and in the Overwrites form on a mem ber by mem ber ba sis. If any mem ber is as signed with a frame type, the change of the frame type in the Pref er -ence will not mod ify the frame type of the in di vid ual mem ber for which it is as -signed. Cur rently the pro gram does not ap ply any spe cial re quire ment for STMF.

The spe cial seis mic re quire ments checked by the pro gram for mem ber de sign arede pend ent on the type of fram ing used and are de scribed be low for each type offram ing. Thus spe cial pro vi sions for build ings are only ap plied if the build ingframe is clas si fied as seis mic de sign cat e gory (SDC) D or E. (ANSI/AISC 341SEIS MIC 1). No spe cial re quire ment is checked for frames with seis mic de signcat e gory A, B, or C.

Or di nary Mo ment Frames (OMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported (ANSI/AISC 341 SEIS MIC 11):

• When P

Pu

njin col umns due to pre scribed load ing com bi na tions with out con sid -

er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear for

24 Special Seismic Provisions of Member Design


the fol low ing Spe cial Seis mic Load Com bi na tions (ANSI/AISC 341 SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3).

( )0 9 0 2 0. .- ±S DL ELDS W

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W

Intermediate Mo ment Frames (IMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported (ANSI/AISC 341 SEIS MIC 10):

• When P

Pu

nj in col umns due to pre scribed load ing com bi na tions with out con sid -

er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear forthe fol low ing Spe cial Seis mic Load Com bi na tions (ANSI/AISC 341 SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2).

( )0 9 0 2 0. .- ±SDS DL ELW

( )12 0 2 10 0. . .+ + ±SDS DL LL ELW

Spe cial Moment Frames (SMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported (ANSI/AISC 341 SEIS MIC 9):

• When P

Pu


er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear forthe fol low ing Spe cial Seis mic Load Com bi na tions (AISC SEIS MIC 8.3, 4.1,ASCE 9.5.2.7.1, 2.3.2).

( )0 9 0 2 0. .- ±S DL ELDS W

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W


25




SectionType

Re duc tion Fac tor for Un stiff ened Slen der Ele ments(Qs)

EquationReference

I-SHAPE [ ]Q

if b t F k

b t F k if Fs

f f y c

f f y c y=

£

-

1.0 95

1.293 0.00309 95

2

2

,

[ ]{ }k b t F k

k b t F if b t F k

c f f y c

c f f y f f y c

< <

³

ì

2

2 22

195

26,200 195

,

.

íïï

îïï

ASD A-B5-3,ASD A-B5-4

BOX Qs =1 ASD A-B5.2c

CHANNEL As for I-shapes with b tf f2 replaced by b tf f .ASD A-B5-3,ASD A-B5-4

T-SHAPE

For flanges, as for flanges in I-shapes. For web see below.

[ ]Q

if d t F

d t F if F d ts

w y

w y y w£

£

- <

1.0 , 127

1.908 0.00715 127

,

,

[ ]{ }<

³

ì

íïï

îïï

176

20,000 176

F

d t F if d t F

y

w y w y

,

, .2

ASD A-B5-3,ASD A-B5-4,ASD A-B5-5,ASD A-B5-6

DOUBLE-ANGLE

[ ]Q

if b t F

b t F if F b ts

y

y y=

£

- < <

1.0 , 76

1.340 0.00447 76 155

,

,

[ ]{ }F

b t F if b t F

y

y y

,

, .15,500 1552

³

ì

íïï

îïï

ASD A-B5-1,ASD A-B5-2,

SAM 4-3

ANGLE [ ]Q

if b t F

b t F if F b ts

y

y y=

£

- < <

1.0 , 76

1.340 0.00447 76 155

,

,

[ ]{ }F

b t F if b t F

y

y y

,

, .15,500 1552

³

ì

íïï

îïï


SAM 4-3

PIPE Qs =1 ASD A-B5.2c

ROUNDBAR

Qs =1 ASD A-B5.2c

RECTAN-GULAR

Qs =1 ASD A-B5.2c

GENERAL Qs =1 ASD A-B5.2c

Table III-4Re duc tion Fac tor for Un stiff ened Slen der Ele ments, Q s


27


SectionType

Effective Width for Stiffened Sections EquationReference

I-SHAPE h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï

(compression only, fP

A g

= ) ASD A-B5-8

BOX

h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï


A g

= )

b

b ifb

t f

t

f h t fif

b

t

e

f

f

f

=

£

-é

ëêê

ù

ûúú

, ,

( ),

183.74

253 50.31 >

ì

í

ïï

î

ïï

183.74

f.

(compr., flexure, f Fy= 0.6 )

ASD A-B5-8

ASD A-B5-7

CHANNEL h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï


A g

= ) ASD A-B5-8

T-SHAPE b be = ASD A-B5.2c

DOUBLE-ANGLE

b be = ASD A-B5.2c

ANGLE b be = ASD A-B5.2c

PIPE Qa = 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9

ROUNDBAR

Not applicable ¾

RECTAN-GULAR

b be = ASD A-B5.2c

GENERAL Not applicable ¾

Table III-5Effective Width for Stiffened Sections

• The I-, Chan nel-, and Dou ble-Chan nel Shaped beams and col umns are ad di -tion ally checked for com pact ness cri te ria as de scribed in Ta ble VI-1 (AISCSEIS MIC 9.4, 8.2, Ta ble I-8-1). If this cri te ria is sat is fied the sec tion is re -ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca tions. If this cri -te ria is not sat is fied the, the pro gram is sues an er ror mes sage.

• The pro gram checks the lat er ally un sup ported length of beams to be less than

( )0 08. E Fy yr . If this cri te ria is not sat is fied, the pro gram is sues an er ror mes -

sage.(ANSI/AISC 341 SEIS MIC 9.8)

• The pro gram checks the slen der ness ra tio, L®, for col umns to be less than 60(ANSI/AISC 341 SEIS MIC 9.7.b(2)). If the cri te ria is not sat is fied, the pro -gram is sues an er ror mes sage.

Ordinary Concentrically Braced Frames (OCBF)


• The col umns and beams (NOT braces) are de signed for the fol low ing spe cialam pli fied seis mic load com bi na tions (AISC/ANSI 341 SEIS MIC 14.2, ASCI9.5.2.7.1, 2.3.2.1, 2.3.2).

( )0 9 0 2 0. .- ±S DL ELDS W

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W

• The max i mum Kl

r ra tio of the braces for V or in verted-V con fig u ra tions is

checked not to ex ceed 4 23.E

Fy

(ANSI/AISC 341 SEIS MIC 14.2). If this cri te -

ria is not met, an er ror mes sage is re ported in the out put.

Spe cial Con cen tri cally Braced Frames (SCBF)


• When P

Pu


er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear for



the fol low ing Spe cial Seis mic Load Com bi na tions (ANSI/AISC 341 SEIS MIC 8.34.1, ASCE 9.5.2.7.1, 2.3.2).

( )0 9 0 2 0. .- ±S DL ELDS W

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W

• All beam, col umns and brace mem bers are checked to be Com pact ac cord ing to Table V-2(ANSI/AISC 341 SEIS MIC 13.5, 13.2d, 8.2, Ta ble I-8-1). If this cri -te ria is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear lier un dersec tion clas si fi ca tions. If this cri te ria is not sat is fied the pro gram is sues an er ror mes sage.

This spe cial cri te ria is only checked for I, Chan nel, Dou ble-Chan nel, An gle,Dou ble-An gle, Box and Pipe sec tions.

• The com pres sive strength for braces is taken as j c nP .

P Pu c n£ j (ANSI/AISC 341 SEIS MIC 13.26)

• The max i mum K l r ra tio of the braces is checked not to ex ceed 5.87F

E

y. If

this check is not met, the pro gram is sues an er ror mes sage.

Note: Beams in ter sected by Chev ron (V or in verted-V) braces are NOT cur -rently checked to have a strength to sup port loads for the fol low ing two con di -tions (ANSI/AISC 341 SEIS MIC 13.4a):

a A beam that is in ter sected by braces shall be de signed to sup port the ef fects ofall trib u tary dead and live loads form load com bi na tions stip u lated by the code,as sum ing the brac ings are not pres ent, and

b A beam that is in ter sected by braces shall be de signed to re sist the ef fects ofload com bi na tions stip u lated by the code, ex cept that a load q b shall be sub sti -tuted for the term E. q b is given by the dif fer ence of R F Ay y for the ten sionbrace and 0 3. j c nP for the com pres sion brace.

Us ers need to check for this re quire ment in de pend ently.

Ec cen tri cally Braced Frames (EBF)

For this fram ing sys tem, the pro gram looks for and rec og nizes the ec cen tri callybraced frame con fig u ra tions shown in Fig ure VI-II. The fol low ing ad di tional re -


29


quire ments are checked or re ported for the beams, col umns and braces as so ci atedwith these con fig u ra tions (ANSI/AISC 341 SEIS MIC 15).

• When P

Pu


er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear forthe fol low ing Spe cial Seis mic Load Com bi na tions (ANSI/AISC 341 SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2).

( )0 9 0 2 0. .- ±S DL ELDS W

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W

• The I-shaped, Chan nel-shaped, and Dou ble-Chan nel Shaped beams are ad di -tion ally checked for com pact ness cri te ria as de scribed in Ta ble VI-III (ANSI/AISC 341 SEIS MIC 15.2, 8.2, Ta ble I-8-1). If this cri te ria is sat is fiedthe sec tion is re ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi -ca tions. If this cri te ria is not sat is fied the user must mod ify the pro gram is suesan er ror mes sage.

• The link beam yield strength, Fy , is checked not to ex ceed the fol low ing (AISC SEIS MIC 15.2):

Fy £ 50 ksi (ANSI/AISC 341 SEIS MIC 15.2)

If the check is not sat is fied, the pro gram is sue an er ror mes sage.

• The shear strength for link beams is taken as fol lows (AISC SEIS MIC 15.2):

V Vu v n£ j , (ANSI/AISC 341 SEIS MIC 15.2)

where,

( )j j jV V M en pa pa= min , 2 , (ANSI/AISC 341 SEIS MIC 15.2)

V VP

Ppa p

u

y

= -æ

è

çç

ö

ø

÷÷1

2

, (ANSI/AISC 341 SEIS MIC 15.1)

M MP

Ppa p

u

y

= -é

ëê

ù

ûú1.18 1 , (ANSI/AISC 341 SEIS MIC 15.2)



V F d t tp y f w= -0.6 ( )2 , (ANSI/AISC 341 SEIS MIC 15.2)

M Z Fp y= , (ANSI/AISC 341 SEIS MIC 15.2)

j j= v (de fault is 0.9) , (ANSI/AISC 341 SEIS MIC 15.2)

P A Fy g y= . (ANSI/AISC 341 SEIS MIC 15.2)

• If P A Fu g y> 0.15 , the link beam length, e, is checked not to ex ceed the fol low -ing (ANSI/AISC 341 SEIS MIC 15.2):

e

A

A

M

Vif

A

Aw

g

p

p

w

g£

- ¢é

ëê

ù

ûú

é

ëê

ù

ûú ¢ ³1.15 0.5 1.6 0.3 ,

1

r r

.6 0.3 ,M

Vif

A

A

p

p

w

g

é

ëê

ù

ûú ¢ <

ì

í

ïï

î

ïï

r

(ANSI/AISC 341 SEIS MIC 15.2)

where,

A d t tw f w= -( )2 , and (ANSI/AISC 341 SEIS MIC 15.2)

¢ =r P Vu u . (ANSI/AISC 341 SEIS MIC 15.2)

If the check is not sat is fied, the pro gram re ports an er ror mes sage.

• The link beam ro ta tion, q, of the in di vid ual bay rel a tive to the rest of the beamis cal cu lated as the story drift D M times bay length di vided by the to tal lengthsof link beams in the bay. The link beam ro ta tion, q, is checked as fol lows(ANSI/AISC 341 SEIS MIC 15.2).

q £ 0.08 ra dian , where link beam clear length, e M Vs s£ 1.6 ,

q £ 0.03 ra dian , where link beam clear length, e M Vs s³ 2.6 , and

q £ value in ter po lated be tween 0.08 and 0.02 as the link beam clear length var ies from 1.6 M Vs s to 2.6 M Vs s .

• The beam strength out side the link is checked to be at least 1.1 times the beamforces cor re spond ing to the con trol ling link beam shear strength (ANSI/AISC341 SEIS MIC 15.6). The con trol ling link beam nom i nal shear strength is taken as fol lows:

( )min ,V M epa pa2 , (ANSI/AISC 341 SEIS MIC 15.6, 15.2)


31


The val ues of Vpa and M pa are cal cu lated fol low ing the pro ce dure de scribedabove (ANSI/AISC 341SEISMIC 15.2). The cor re spon dence be tween braceforce and link beam force is ob tained from the as so ci ated load cases, which ever has the high est link beam force of in ter est.

All braces are checked to be at least com pact per reg u lar ANSI/AISC 341code(ANSI/AISC 341 SEIS MIC 15.6). If this cri te ria is not sat is fied, the pro gramis sues an er ror mes sage.

The brace strength is checked for 1.25Ry times the brace forces cor re spond ingto the con trol ling link beam nom i nal shear strength (ANSI/AISC 341 SEIS -MIC 15.6). The con trol ling link beam nom i nal shear strength and the cor re -spond ing forces are ob tained by the pro cess de scribed ear lier.

The I-, Chan nel-, and Dou ble-Chan nel- shaped col umn sec tions are checked tobe at least com pact per reg u lar ANSI/AISC 341 code (ANSI/AISC 341 SEIS -MIC 8.2, Ta ble I-8-1, LRFD B.5.1). If this cri te rion is not sat is fied, the pro -gram is sues an er ror mes sage.

• The col umn strength is checked for 1.1Ry times the col umn forces cor re spond -ing to the con trol ling link beam nom i nal shear strength (ANSI/AISC 341SEIS MIC 15.8). The con trol ling link beam nom i nal shear strength and the cor -re spond ing forces are ob tained by the pro cess de scribed above.

Note: Ax ial forces in the beams are in cluded in check ing the beams. The user is re -minded that us ing a rigid di a phragm model will re sult in zero ax ial forces in thebeams. The user must dis con nect some of the col umn lines from the di a phragm toal low beams to carry ax ial loads. It is rec om mended that only one col umn line perec cen tri cally braced frame be con nected to the rigid di a phragm or a flex i ble di a -phragm model be used.

Calculation of Stresses

The stresses are cal cu lated at each of the pre vi ously de fined sta tions. The mem berstresses for nonslender sec tions that are cal cu lated for each load com bi na tion are,in gen eral, based on the gross cross- sectional prop er ties.:

f = P/Aa

f = M /Sb33 33 33

f = M /Sb22 22 22

f = V /Av v2 2 2

f = V /Av v3 3 3

32 Calculation of Stresses


If the sec tion is slen der with slen der stiff ened ele ments, like slen der web in I, Chan -nel, and Box sec tions or slen der flanges in Box, ef fec tive sec tion moduli based onre duced web and re duced flange di men sions are used in cal cu lat ing stresses.

f = P/Aa (ASD A-B5.2d)f = M /Sb eff33 33 33, (ASD A-B5.2d)f = M /Sb eff22 22 22, (ASD A-B5.2d)f = V /Av v2 2 2 (ASD A-B5.2d)f = V /Av v3 3 3 (ASD A-B5.2d)

The flexural stresses are cal cu lated based on the prop er ties about the principal axes. For I, Box, Chan nel, T, Dou ble-an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, theprin ci pal axes co in cide with the geo met ric axes. For Single- angle sec tions, the de -sign con sid ers the prin ci pal properties. For gen eral sec tions it is as sumed that allsec tion prop er ties are given in terms of the prin ci pal di rec tions.

For Single- angle sec tions, the shear stresses are cal cu lated for di rec tions along thegeo met ric axes. For all other sec tions the shear stresses are cal cu lated along thegeo met ric and prin ci ple axes.

Calculation of Allowable Stresses

The al low able stresses in com pres sion, ten sion, bend ing, and shear are com putedfor Com pact, Non com pact, and Slen der sec tions ac cord ing to the fol low ing sub -sec tions. The al low able flexural stresses for all shapes of sec tions are cal cu latedbased on their prin ci pal axes of bend ing. For the I, Box, Chan nel, Cir cu lar, Pipe, T,Dou ble-an gle and Rec tan gu lar sec tions, the prin ci pal axes co in cide with their geo -met ric axes. For the An gle sec tions, the prin ci pal axes are de ter mined and all com -pu ta tions re lated to flex ural stresses are based on that.

If the user speci fies nonz ero al low able stresses for one or more ele ments in the de -sign over write form, these val ues will over ride the above men tioned cal cu latedval ues for those ele ments as de fined in the fol low ing sub sec tions. The speci fied al -low able stresses should be based on the prin ci pal axes of bend ing.

Allowable Stress in Tension

The al low able ax ial ten sile stress value Fa is as sumed to be 0.60 Fy .

F = Fa y0.6 (ASD D1, ASD SAM 2)

Calculation of Allowable Stresses 33


It should be noted that net sec tion checks are not made. For mem bers in ten sion, if l r is greater than 300, a mes sage to that ef fect is printed (ASD B7, ASD SAM 2).For sin gle an gles, the mini mum radius of gy ra tion, rz , is used in stead of r22 and r33

in com put ing l r .

Allowable Stress in Compression

The al low able ax ial com pres sive stress is the minimum value ob tained from flex -ural buck ling and flexural- torsional buck ling. The al low able com pres sive stressesare de ter mined ac cord ing to the fol low ing sub sec tions.

For mem bers in com pres sion, if Kl r is greater than 200, a warn ing mes sage isprinted (ASD B7, ASD SAM 4). For sin gle an gles, the mini mum radius of gy ra -tion, rz , is used in stead of r22 and r33 in com put ing Kl r .

Flex ural Buck ling

The al low able ax ial com pres sive stress value, Fa , de pends on the slen der ness ra tio Kl r based on gross sec tion prop er ties and a cor re spond ing criti cal value, C c , where

Kl

r

K l

r

K l

r= ì

íî

üýþ

max ,33 33

33

22 22

22

, and

C c =2 2p E

Fy

. (ASD E2, ASD SAM 4)

For sin gle an gles, the mini mum radius of gy ra tion, rz , is used in stead of r22 and r33

in com put ing Kl r .

For Com pact or Non com pact sec tions Fa is evalu ated as fol lows:

( )F =

Kl/r

CF

+ Kl/r

C

Ka

c

y

c

1.0 -ìíî

üýþ

-

( ) 2

22

5

3

3

8

( )l/r

C

c

3

38

, if Kl

r C c£ , (ASD E2-1, SAM 4-1)

F = E

Kl ra

12

23

2

2

p

( ) , if

Kl

r C c> . (ASD E2-2, SAM 4-2)

34 Calculation of Allowable Stresses


If Kl r is greater than 200, then the cal cu lated value of Fa is taken not to ex ceed thevalue of Fa cal cu lated by us ing the equa tion ASD E2-2 for Com pact and Non com -pact sec tions (ASD E1, B7).

For Slender sec tions, ex cept slen der Pipe sec tions, Fa is evalu ated as fol lows:

( )F = Q

Kl/r

CF

+ Kl/r

C

ac

y1.0 -ìíï

îï

üýï

þï¢

( ) 2

22

5

3

3

8

( )c

c

Kl/r

C¢ ¢

-

3

38

, if Kl

r C c£ ¢ , (ASD A-B5-11, SAM 4-1)

F = E

Kl ra

12

23

2

2

p

( ) , if

Kl

r C c> ¢ . (ASD A-B5-12, SAM 4-2)

where,

CE

Q Fc

y

¢ =2 2p

. (ASD A-B5.2c, ASD SAM 4)

For slen der sec tions, if Kl r is greater than 200, then the cal cu lated value of Fa istaken not to ex ceed its value cal cu lated by us ing the equa tion ASD A-B5-12 (ASD B7, E1).

For slen der Pipe sec tions Fa is evalu ated as fol lows:

F = D t

Fa y

6620.40+ (ASD A- B5-9)

The re duc tion fac tor, Q, for all com pact and non com pact sec tions is taken as 1. Forslen der sec tions, Q is com puted as fol lows:

Q Q Qs a= , where (ASD A-B5.2.c, SAM 4)

Q s = re duc tion fac tor for un stiff ened slen der ele ments, and (ASD A-B5.2.a)

Q a = re duc tion fac tor for stiff ened slen der ele ments. (ASD A-B5.2.c)

The Q s fac tors for slen der sec tions are cal cu lated as de scribed in Table III-4 (ASDA-B5.2a, ASD SAM 4). The Q a fac tors for slen der sec tions are cal cu lated as thera tio of ef fec tive cross- sectional area and the gross cross- sectional area.



QA

Aa

e

g

= (ASD A- B5-10)

The ef fec tive cross- sectional area is com puted based on ef fec tive width as fol lows:

( )A A b b te g e= - -å

be for un stiff ened el e ments is taken equal to b, and be for stiff ened el e ments istaken equal to or less than b as given in Table III-5 (ASD A-B5.2b). For webs in I,box, and Chan nel sec tions, he is used as be and h is used as b in the above equa tion.

Flex ural-Torsional Buck ling

The al low able ax ial com pres sive stress value, Fa , de ter mined by the limit states oftor sional and flexural- torsional buck ling is de ter mined as fol lows (ASD E3, C-E3):

( )

( )F = Q

Kl/r

CF

+ Kl/r

C

a

e

c

y

e

1.0 -ì

íï

îï

ü

ýï

þï¢

2

22

5

3

3

8

( )c

e

c

Kl/r

C¢ ¢

-

3

38

, if ( )Kl/r Ce c£ ¢ , (E2-1, A- B5- 11)

( )F =

E

Kl/ra

e

12

23

2

2

p , if ( )Kl/r C

e c> ¢ . (E2-2, A- B5- 12)

where,

CE

Q Fc

y

¢ =2 2p

, and (ASD E2, A-B5.2c, SAM 4)

( )Kl/rE

Fee

=p 2

. (ASD C- E2-2, SAM 4-4)

ASD Com men tary (ASD C-E3) re fers to the 1986 ver sion of the AISC-LRFD codefor the cal cu la tion of Fe . The 1993 ver sion of the AISC-LRFD code is the same asthe 1986 ver sion in this respect. Fe is cal cu lated in the pro gram as fol lows:

• For Rec tan gu lar, I, Box, and Pipe sec tions:



( )F

EC

K lGJ

I Ie

w

z z

= +é

ë

êê

ù

û

úú +

p 2

222 33

1 (LRFD A- E3-5)

• For T-sections and Dou ble-angles:

F = F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù

ûúú (LRFD A- E3-6)

• For Channels:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Sin gle-angle sec tions with equal legs:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù

ûúú (ASD SAM C- C4-1)

• For Single- angle sec tions with une qual legs, Fe is cal cu lated as the mini mumreal root of the fol low ing cu bic equa tion (ASD SAM C- C4-2, LRFD A- E3-7):

( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e- - - - - -33 22

222

02

02

2 F Fy

re e- =33

02

02

0) ,

where,

x y0 0, are the co or di nates of the shear cen ter with re spect to the cen troid, x 0 0= for doubleangle and T- shaped mem bers (y-axis of sym me -

try),

r x yI I

Ag

0 02

02 22 33= + + +

= po lar ra dius of gy ra tion about the shear center,

Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

, (LRFD A- E3-9)

( )F

E

K l re33

2

33 33 33

2= p

, (LRFD A- E3-10)



( )F

E

K l re22

2

22 22 22

2= p

, (LRFD A- E3-11)

( )F

EC

K lGJ

Arez

w

z z

= +é

ë

êê

ù

û

úú

p 2

202

1 , (LRFD A- E3-12)

K K22 33, are ef fec tive length fac tors in mi nor and ma jor di rec tions,

K z is the ef fec tive length fac tor for tor sional buck ling, and it is taken equal to K 22 in the pro gram,

l l22 33, are ef fec tive lengths in the mi nor and ma jor di rec tions,

lz is the ef fec tive length for tor sional buck ling, and it is taken equal to l22 .

For an gle sec tions, the prin ci pal mo ment of in er tia and ra dii of gy ra tion are used for com put ing Fe (ASD SAM 4). Also, the maxi mum value of Kl, i .e, max( , )K l K l22 22 33 33 , is used in place of K l22 22 or K l33 33 in cal cu lat ing Fe22 and Fe33

in this case.

Allowable Stress in Bending

The al low able bend ing stress de pends on the fol low ing cri te ria: the geo met ricshape of the cross- section, the axis of bend ing, the com pact ness of the sec tion, anda length pa rame ter.

I-sections

For I- sections the length pa rame ter is taken as the lat er ally un braced length, l22 , which is com pared to a criti cal length, lc . The criti cal length is de fined as

lb

F

A

d Fc

f

y

f

y

=ìíï

îï

üýï

þïmin ,

,76 20 000 , where (ASD F1-2)

A f is the area of com pres sion flange,



Major Axis of Bending

If l22 is less than lc , the ma jor al low able bend ing stress for Com pact andNoncom pact sec tions is taken de pend ing on whether the sec tion is welded orrolled and whether fy is greater than 65 ksi or not.

For Com pact sec tions:

F = Fb y33 0.66 if fy £ 65 ksi , (ASD F1-1)

F = Fb y33 0.60 if fy > 65 ksi , (ASD F1-5)

For Non com pact sec tions:

F = b

tF Fb

f

f

y y332

0.79 0.002-æ

è

çç

ö

ø

÷÷ , if rolled and fy £ 65 ksi, (ASD F1-3)

F = b

t

F

k Fb

f

f

y

c

y332

0.79 0.002-æ

è

çç

ö

ø

÷÷

, if welded and fy £ 65 ksi, (ASDF1-4)

F = Fb y33 0.60 if fy > 65 ksi.. (ASD F1-5)

If the un braced length l22 is greater than lc , then for both Com pact and Non -com pact I- sections the al low able bend ing stress de pends on the l rT22 ra tio.

For l

r

C

FT

b

y

22 102 000£

, ,

F Fb y33 = 0.60 , (ASD F1-6)

for 102 000 510 00022, ,C

F

l

r

C

Fb

y T

b

y

< £ ,

FF l r

CF Fb

y T

b

y y33

222

2

3 1530 000= -

é

ëêê

ù

ûúú

£( / )

,0.60 , and (ASD F1-6)

for l

r

C

FT

b

y

22 510 000> , ,



FC

l rFb

b

T

y33

222

170 0000=

é

ëê

ù

ûú £

,

( / )0.6 , (ASD F1-7)

and Fb33 is taken not to be less than that given by the fol low ing for mula:

( )F

C

l d AFb

b

f

y33

22

12 000= 0.6

,

/£ (ASD F1-8)

where,

rT is the ra dius of gy ra tion of a sec tion com pris ing the com pres sion flange and 1 3 the com pres sion web taken about an axis in the plane of the web,

C = + M

M +

M

Mb

a

b

a

b

1.75 1.05 0.3æ

èçç

ö

ø÷÷

æ

èçç

ö

ø÷÷ £

2

2.3, where (ASD F1.3)

M Ma band are the end mo ments of any un braced seg ment of the mem ber and M a is nu meri cally less than M b ; M Ma b be ing posi tive for dou ble cur va turebend ing and nega tive for sin gle cur va ture bend ing. Also, if any mo ment withinthe seg ment is greater than M b , Cb is taken as 1.0. Also, Cb is taken as 1.0 forcan ti le vers and frames braced against joint trans la tion (ASD F1.3). Theprogram de faults Cb to 1.0 if the un braced length, l22 , of the mem ber is re de -fined by the user (i.e. it is not equal to the length of the mem ber). The user canover write the value of Cb for any mem ber by speci fy ing it.

The al low able bend ing stress for Slen der sec tions bent about their ma jor axis isde ter mined in the same way as for a Non com pact sec tion. Then the fol low ingad di tional con sid era tions are taken into ac count.

If the web is slen der, then the pre vi ously com puted al low able bend ing stress isre duced as fol lows:

F R R Fb PG e b33 33¢ = , where (ASD G2-1)

RA

A

h

t FPG

w

f b

= - -é

ëêê

ù

ûúú

£1.0 0.0005 1.0760

33

, (ASD G2)

( )R

A

A

A

A

e

w

f

w

f

=+ -

+£

12

12 2

1.0

3 3a a

, (hy brid gird ers) (ASD G2)



Re =1.0 , (non- hybrid gird ers) (ASD G2)

Aw = Area of web, in 2 ,

A f = Area of com pres sion flange, in 2 ,

a = £0.6

1.0F

F

y

b33

(ASD G2)

Fb33 = Al low able bend ing stress as sum ing the sec tion is noncompact, and

Fb33¢ = Al low able bend ing stress af ter con sid er ing web slenderness.

In the above ex pres sions, Re is taken as 1, be cause cur rently the pro gram dealswith only non-hy brid gird ers.

If the flange is slen der, then the pre vi ously com puted al low able bend ing stressis taken to be lim ited as follows.

( )F Q Fb s y33¢ £ 0.6 , where (ASD A-B5.2a, A-B5.2d)

Q s is de fined ear lier.

Minor Axis of Bending

The mi nor di rec tion al low able bend ing stress Fb22 is taken as fol lows:




For Non com pact and Slen der sec tions:

F = b

tF Fb

f

f

y y222

1.075 0.005-æ

è

çç

ö

ø

÷÷ , if fy £ 65 ksi, (ASD F2-3)





F R R Fb e PG b33 33¢ = (ASD G2-1)

If the flange is slen der, the pre vi ously com puted al low able bend ing stress istaken to be lim ited as follows:

( )F Q Fb s y33¢ £ 0.6 (ASD A-B5.2a, A-B5.2d)

The defi ni tion for rT , Cb , A f , Aw , Re , RPG , Q s , Fb33 , and Fb33¢ are given ear lier.



F = Fb y22 0.60 (ASD F2-2)

T-sections and Double angles

For T sec tions and Dou ble an gles, the al low able bend ing stress for both ma jorand mi nor axes bending is taken as,

F = Fb y0.60 .

Box Sections and Rectangular Tubes

For all Box sec tions and Rec tan gu lar tubes, the length pa rame ter is taken as thelat er ally un braced length, l22 , meas ured com pared to a criti cal length, lc . Thecriti cal length is de fined as

l M /Mb

F,

b

Fc a b

y y

= +ìíî

üýþ

max ( )1950 12001200

(ASD F3-2)

where M a and M b have the same defi ni tion as noted ear lier in the for mula for

Cb . If l22 is speci fied by the user, lc is taken as 1200 b

Fy

in the pro gram.


If l22 is less than lc , the al low able bend ing stress in the ma jor di rec tion ofbend ing is taken as:



F = Fb y33 0.66 (for Com pact sec tions) (ASD F3-1)

F = Fb y33 0.60 (for Non com pact sec tions) (ASD F3-3)

If l22 ex ceeds lc , the al low able bend ing stress in the ma jor di rec tion of bend -ing for both Com pact and Non com pact sec tions is taken as:

F = Fb y33 0.60 (ASD F3-3)

The ma jor di rec tion al low able bend ing stress for Slen der sec tions is de ter -mined in the same way as for a Non com pact sec tion. Then the fol low ing ad di -tional con sid era tion is taken into ac count. If the web is slen der, then the pre vi -ously com puted al low able bend ing stress is re duced as fol lows:

F R R Fb e PG b33 33¢ = (ASD G2-1)

The defi ni tion for Re , RPG , Fb33 , and Fb33¢ are given ear lier.

If the flange is slen der, no ad di tional con sid er ation is needed in com put ing al -low able bend ing stress. How ever, ef fec tive sec tion di men sions are cal cu latedand the sec tion modu lus is modi fied ac cord ing to its slen der ness.


If l22 is less than lc , the al low able bend ing stress in the minor di rec tion of bend -ing is taken as:


F = Fb y22 0.60 (for Non com pact and Slender sec tions) (ASD F3-3)

If l22 ex ceeds lc , the al low able bend ing stress in the minor di rec tion of bend -ing is taken, ir re spec tive of com pact ness, as:

F = Fb y22 0.60 (ASD F3-3)

Pipe Sections

For Pipe sec tions, the al low able bend ing stress for both ma jor and mi nor axesof bend ing is taken as

F = Fb y0.66 (for Com pact sec tions), and (ASD F3-1)

F = Fb y0.60 (for Non com pact and Slen der sec tions). (ASD F3-3)



Round Bars

The al low able stress for both the ma jor and mi nor axis of bend ing of round bars is taken as,

F = Fb y0.75 . (ASD F2-1)

Rectangular and Square Bars

The al low able stress for both the ma jor and mi nor axis of bend ing of solidsquare bars is taken as,

F = Fb y0.75 . (ASD F2-1)

For solid rec tan gu lar bars bent about their ma jor axes, the al low able stress isgiven by

F = Fb y0.60 , And

the al low able stress for mi nor axis bend ing of rec tan gu lar bars is taken as,

F = Fb y0.75 . (ASD F2-1)

Single-Angle Sections

The al low able flex ural stresses for Single- angles are cal cu lated based on their prin -ci pal axes of bend ing (ASD SAM 5.3).


The al low able stress for ma jor axis bend ing is the mini mum con sid er ing the limitstate of lateral- torsional buck ling and lo cal buck ling (ASD SAM 5.1).

The al low able ma jor bend ing stress for Single- angles for the limit state of lateral- torsional buck ling is given as fol lows (ASD SAM 5.1.3):

F = F

FFb major

ob

y

ob, 0.55 0.10-é

ëê

ù

ûú , if F Fob y£ (ASD SAM 5-3a)

F = F

FF Fb major

y

ob

y y, 0.95 0.50 0.66-é

ë

êê

ù

û

úú

£ , if F Fob y> (ASD SAM 5-3b)

where, Fob is the elas tic lateral- torsional buck ling stress as cal cu lated be low.



The elas tic lateral- torsional buck ling stress, Fob , for equal- leg an gles is taken as

F Cl t

ob b= 28,250 , (ASD SAM 5-5)

and for unequal- leg an gles Fob is cal cu lated as

F CI

S llt rob b

major

w w= + +éë

ùû

143,100 0.052minmin2

2 2b b( ) , (ASD SAM 5-6)

where,

( )t t tw f= min , ,

( )l l l= max ,22 33 ,

Imin = mi nor prin ci pal mo ment of in er tia,

Imax = major prin ci pal mo ment of in er tia,

Smajor = ma jor sec tion modu lus for com pres sion at the tip of one leg,

rmin = ra dius of gy ra tion for mi nor prin ci pal axis,

bwAI

z w z dA z= +é

ëê

ù

ûú -ò

122 2

0

max

( ) , (ASD SAM 5.3.2)

z = co or di nate along the ma jor prin ci pal axis,

w = co or di nate along the mi nor prin ci pal axis, and

z0 = co or di nate of the shear cen ter along the ma jor prin ci pal axis with re spect to the cen troid.

bw is a spe cial sec tion prop erty for an gles. It is posi tive for short leg in com pres -sion, nega tive for long leg in com pres sion, and zero for equal- leg an gles (ASDSAM 5.3.2). How ever, for con ser va tive de sign in the pro gram, it is al ways taken asnega tive for unequal- leg an gles.

In the above ex pres sions Cb is cal cu lated in the same way as is done for I sec tionswith the ex cep tion that the up per limit of Cb is taken here as 1.5 in stead of 2.3.

C = + M

M +

M

Mb

a

b

a

b

1.75 1.05 0.3æ

èçç

ö

ø÷÷

æ

èçç

ö

ø÷÷ £

2

1.5 (ASD F1.3, SAM 5.2.2)



The al low able ma jor bend ing stress for Single- angles for the limit state of lo calbuck ling is given as fol lows (ASD SAM 5.1.1):

F = Fb major y, 0.66 , if b

t Fy

£65

, (ASD SAM 5-1a)

F = Fb major y, 0.60 , if 65 76

F

b

t Fy y

< £ , (ASD SAM 5-1b)

( )F = Q Fb major y, 0.60 , if b

t Fy

> 76 , (ASD SAM 5-1c)

where,

t = thick ness of the leg un der consideration,

b = length of the leg un der con sid era tion, and

Q = slen der ness re duc tion fac tor for lo cal buck ling. (ASD A- B5-2, SAM 4)

In cal cu lat ing the al low able bend ing stress for Single- angles for the limit state oflo cal buck ling, the al low able stresses are cal cu lated con sid er ing the fact that ei therof the two tips can be un der com pres sion. The mini mum al low able stress is con sid -ered.


The al low able minor bend ing stress for Single- angles is given as fol lows (ASDSAM 5.1.1, 5.3.1b, 5.3.2b):

F = Fyb,minor 0.66 , if b

t Fy

£65

, (ASD SAM 5-1a)

F = Fyb,minor 0.60 , if 65 76

F

b

t Fy y

< £ , (ASD SAM 5-1b)

( )F = Q Fyb,minor 0.60 , if b

t Fy

> 76 , (ASD SAM 5-1c)

In cal cu lat ing the al low able bend ing stress for Single- angles it is as sumed that thesign of the mo ment is such that both the tips are un der com pres sion. The mini mumal low able stress is con sid ered.



General Sections

For Gen eral sec tions the al low able bend ing stress for both ma jor and mi noraxes bending is taken as,

F = Fb y0.60 .

Allowable Stress in Shear

The shear stress is cal cu lated along the geo met ric axes for all sec tions. For I, Box,Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci palaxes co in cide with their geo met ric axes. For Single- angle sec tions, prin ci pal axesdo not co in cide with the geometric axes.


The al low able shear stress for all sec tions ex cept I, Box and Chan nel sec tions istaken in the pro gram as:

F Fv y= 0.40 (ASD F4-1, SAM 3-1)

The al low able shear stress for ma jor di rec tion shears in I- shapes, boxes and chan -nels is evalu ated as fol lows:

F Fv y= 0.40 , if h

t

Fw y

£380

, and (ASD F4-1)

FC

F Fvv

y y= £2.89

0.40 , if 380

260F

h

t

y w

< £ . (ASD F4-2)

where,

( )C

k

F h tif

h

t

k

F

h t

k

Fif

h

t

v

v

y ww

v

y

w

v

y

=

³45 000

2

,, ,

,

56,250

190

w

v

y

k

F<

ì

í

ïï

î

ïï

56,250 ,

(ASD F4)



( )

( )

ka h

ifa

h

a hif

a

h

v =

+ £

+ >

ì

í

ïï

î

ïï

4.005.34

5.344.00

2

2

1

1

, ,

, ,

(ASD F4)

t w = Thick ness of the web,

a = Clear dis tance be tween trans verse stiff en ers, in. Cur rently it is taken con ser va tively as the length, l22 , of the mem ber in the pro -

gram,

h = Clear dis tance be tween flanges at the sec tion, in.


The al low able shear stress for mi nor di rec tion shears is taken as:

F Fv y= 0.40 (ASD F4-1, SAM 3-1)

Calculation of Stress Ratios

In the calculation of the ax ial and bend ing stress ca pac ity ra tios, first, for each sta -tion along the length of the mem ber, the ac tual stresses are cal cu lated for each loadcom bi na tion. Then the cor re spond ing al low able stresses are calculated. Then, theca pac ity ra tios are calculated at each sta tion for each mem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol ling ca pac ity ra tio is then ob -tained, along with the as so ci ated sta tion and load com bi na tion. A ca pac ity ra tiogreater than 1.0 in di cates an overstress.

Dur ing the de sign, the ef fect of the pres ence of bolts or welds is not con sid ered.Also, the joints are not de signed.

Ax ial and Bend ing Stresses

With the com puted al low able ax ial and bend ing stress val ues and the fac tored ax ialand bend ing mem ber stresses at each sta tion, an in ter ac tion stress ra tio is pro ducedfor each of the load com bi na tions as fol lows (ASD H1, H2, SAM 6):

• If fa is com pres sive and f Fa a > 0.15, the com bined stress ra tio is given bythe larger of

Calculation of Stress Ratios 49


f

F+

C f

f

F' F

+ C fa

a

m b

a

e

b

m b33 33

33

33

22 22

1 1-æ

èçç

ö

ø÷÷

f

F' Fa

e

b-æ

èçç

ö

ø÷÷

22

22

, and (ASD H1-1, SAM 6.1)

( )

f

F

f

F

f

Fa

y

b

b

b

bQ 0.60+ +33

33

22

22

, where (ASD H1-2, SAM 6.1)

fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are de fined ear lier in this chapter,

Cm33 and Cm22 are co ef fi cients rep re sent ing dis tri bu tion of mo ment along themem ber length.

Cm =

1.00 , if length is overwritten,

1.00 , if tension member,

0.85 , if sway frame,

0.6 0.4 if -M

aM

b

, nonsway, no transverse loading,

0.85 , if nonsway, trans. load, end restrained,

1.00 , if nonsway, trans. load, end unrestrained.

ì

í

ïïïï

î

ïïïï

(ASD H1)

For sway frame Cm = 0.85 , for nonsway frame with out trans verse load C M Mm a b= -0.6 0.4 , for nonsway frame with trans verse load and end re -strained com pres sion mem ber Cm = 0.85 , and for nonsway frame with trans -verse load and end un re strained com pres sion mem ber Cm =1.00 (ASD H1), where M Ma b is the ra tio of the smaller to the larger mo ment at the ends of themem ber, M Ma b be ing pos i tive for dou ble cur va ture bend ing and neg a tive forsin gle cur va ture bend ing. When M b is zero, Cm is taken as 1.0. The pro gramde faults Cm to 1.0 if the un braced length fac tor, l, of the mem ber is re de finedby ei ther the user or the pro gram, i.e., if the un braced length is not equal to thelength of the mem ber. The user can over write the value of Cm for any mem ber. Cm as sumes two val ues, Cm22 and Cm33 , as so ci ated with the ma jor and mi nor di -rec tions.

Fe¢ is given by

FE

Kl re¢ = 12

23

2

2

p

( / ) . (ASD H1)

• If fa is com pres sive and f Fa a £ 0.15 , a rel a tively sim pli fied for mula is used for the com bined stress ra tio.

50 Calculation of Stress Ratios


f

F +

f

F +

f

Fa

a

b

b

b

b

33

33

22

22

(ASD H1-3, SAM 6.1)

• If fa is ten sile or zero, the com bined stress ra tio is given by the larger of

f

F

f

F

f

Fa

a

b

b

b

b

+ +33

33

22

22


f

F

f

Fb

b

b

b

33

33

22

22

+ , where

fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are de fined ear lier in this chap ter. How ever, ei -ther Fb33 or Fb22 need not be less than 0.6Fy in the first equa tion (ASD H2-1). The sec ond equa tion con sid ers flex ural buck ling with out any be nefi cial ef fectfrom ax ial com pres sion.

For cir cu lar and pipe sec tions, an SRSS com bi na tion is first made of the two bend -ing com po nents be fore add ing the ax ial load com po nent, in stead of the sim ple ad -di tion im plied by the above for mu lae.

For Single- angle sec tions, the com bined stress ra tio is cal cu lated based on the prop -er ties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Chan nel, T, Dou -ble-an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci pal axes co in cide withtheir geo met ric axes. For Single- angle sec tions, prin ci pal axes are de ter mined inthe pro gram. For gen eral sec tions no ef fort is made to de ter mine the prin ci pal di rec -tions.

Shear Stresses

From the al low able shear stress val ues and the fac tored shear stress val ues at eachsta tion, shear stress ra tios for ma jor and minor di rec tions are computed for each ofthe load com bi na tions as fol lows:

f

Fv

v

2 , and

f

Fv

v

3 .

For Sin gle-an gle sec tions, the shear stress ra tio is cal cu lated for di rec tions alongthe geo met ric axis. For all other sec tions the shear stress is cal cu lated along theprin ci ple axes which co in cide with the geo met ric axes.



Joint Design

When us ing AISC-ASD01 de sign code, the struc tural joints are checked and/or de -signed for the fol low ing:

• Check for the re quire ment of con ti nu ity plate and de ter mi na tion of its area

• Check for the re quire ment of doubler plate and de ter mi na tion of its thick ness

• Check for the ra tio of beam flex ural strength to col umn flex ural strength

• Re port ing the beam con nec tion shear

• Re port ing the brace con nec tion force

De sign of Con ti nu ity Plates

In a plan view of a beam/col umn con nec tion, a steel beam can frame into a col umnin the fol low ing ways:

• The steel beam frames in a di rec tion par al lel to the col umn ma jor di rec tion, i.e.the beam frames into the col umn flange.

• The steel beam frames in a di rec tion par al lel to the col umn mi nor di rec tion, i.e.the beam frames into the col umn web.

• The steel beam frames in a di rec tion that is at an an gle to both of the prin ci palaxes of the col umn, i.e. the beam frames par tially into the col umn web and par -tially into the col umn flange.

To achieve a proper beam/col umn mo ment con nec tion strength, con ti nu ity platessuch as shown in are usu ally placed on the col umn, in line with the top and bot tomflanges of the beam, to trans fer the com pres sion and ten sion flange forces of thebeam into the col umn.

For con nec tion con di tions de scribed in the last two steps above, the thick ness ofsuch plates is usu ally set equal to the flange thick ness of the cor re spond ing beam.How ever, for the con nec tion con di tion de scribed by the first step above, where thebeam frames into the flange of the col umn, such con ti nu ity plates are not al waysneeded. The re quire ment de pends upon the mag ni tude of the beam-flange forceand the prop er ties of the col umn. This is the con di tion that the pro gram in ves ti -gates. Col umns of I-sec tions only are in ves ti gated. The pro gram eval u ates the con -ti nu ity plate re quire ments for each of the beams that frame into the col umn flange(i.e. par al lel to the col umn ma jor di rec tion) and re ports the max i mum con ti nu ityplate area that is needed for each beam flange. The con ti nu ity plate re quire ments

52 Joint Design

SAP2000 Steel Design Manual

are eval u ated for mo ment frames (OMF, IMF, SMF) only. No check is made forbraced frames (OCBC, SCBF, EBF).

The pro gram first eval u ates the need for con ti nu ity plates. Con ti nu ity plates will be re quired if any of the fol low ing four con di tions are not sat is fied:

• The col umn flange de sign strength in bend ing must be larger than the beamflange force, i.e.,

jR = t F Pn fc yc bf(0.9)6.25 2 ³ if not at top story (LRFD K1-1)

jR t F Pn fc yc bc= ³( . )( . ) .0 5 0 9 6 25 2 if at top story (LRFD K1-2)

• The de sign strength of the col umn web against lo cal yield ing at the toe of thefil let must be larger than the beam flange force, i.e.,

jR k +t F t Pn c fb yc wc bf= (1.0) (5.0 ) ³ , if not at top story (LRFD K1-2)

jR k t F t Pn c fb yc wc bf= + ³( . )( . )10 2 5 , if at top story (LRFD K1-3)

• The de sign strength of the col umn web against crip pling must be larger than the beam flange force, i.e.,

jR t + t

d

t

tn wc

fb

c

wc

fc

= (0.75) 0.80 2 1 3æ

èçç

ö

ø÷÷æ

è

çç

ö

ø

÷÷

é

ë

êê

ù

û

úú

³

1.5

EFt

t Pyc

fc

wc

bf ,

if not at top story (LRFD K1-4)

jR t + t

d

t

tn wc

fb

c

wc

fc

=æ

èçç

ö

ø÷÷æ

è

çç

ö

ø( . )( . )0 75 0 40 1 32 ÷

÷

é

ë

êê

ù

û

úú

³

1.5

EFt

t Pyc

fc

wc

bf ,

it at top story (LRFD K1-5a)

• The de sign com pres sive strength of the col umn web against buck ling must belarger than the beam flange force, i.e.,

jR t EF

d Pn

wc yc

c

bf= (0.9)24 3

³ , if not at top story (LRFD K1-8)

jR t EF

d Pn

wc yc

c

bf= (0.9)12 3

³ , if at top story (LRFD K1.9, E2)

Joint Design 53


If any of the con di tions above are not met the pro gram cal cu lates the re quired con ti -nu ity plate area as,

A = P

F tcp

bf

yc

wc(0.85)(0.9 )

- 25 2 , if not at top story (LRFD K1.9, E2)

A = P

F tcp

bf

yc

wc(0.85)(0.9 )

- 12 2 , if at top story (LRFD K1.9, E2)

If A cp £ 0, no con ti nu ity plates are re quired.

The for mula above as sumes the con ti nu ity plate plus a width of web equal to 12 t wc

or 25t wc act as a com pres sion mem ber to re sist the ap plied load (LRFD K1.9). Thefor mula also as sumes j = 0.85 and F Fcr yc= 0.9 . This cor re sponds to an as sump tionof l c = 0.5 in the col umn for mu las (LRFD E2-2). The user should choose the con -ti nu ity plate cross-sec tion such that this is sat is fied. As an ex am ple when us ing Fyc = 50 ksi and as sum ing the ef fec tive length of the stiff ener as a col umn to be 0.75h (LRFD K1.9) the re quired min i mum ra dius of gy ra tion of the stiff enercross-sec tion would be r h= 0.02 to ob tain l c = 0.5 (LRFD E2-4).

If con ti nu ity plates are re quired, they must sat isfy a min i mum area spec i fi ca tion de -fined as fol lows:

• The min i mum thick ness of the stiff en ers is taken in th pro gram as fol lows:

t = t bcpmin

fb fb 0.5max , .179F

E

ycìíï

îï

üýï

þï(LRFD K1.9.2)

• The min i mum width of the con ti nu ity plate on each side plus ½ the thick ness of the col umn web shall not be less than 1/3 of the beam flange width, or

b = 2 b

3

t

2cpmin fp wc-

æ

èçç

ö

ø÷÷ (LRFD K1.9.1)

• So that the min i mum area is given by:

A = t bcpmin

cpmin

cpmin (LRFD K1.9.1)

There fore, the con ti nu ity plate area pro vided by the pro gram is ei ther zero or thegreater of Acp and Acp

min .

In the equa tions above,

54 Joint Design


Acp = Re quired con ti nu ity plate area Fyc = Yield stress of the col umn and con ti nu ity plate ma te riald b = Beam depthd c = Col umn depthh = Clear dis tance be tween flanges of col umn

less fil lets for rolled shapesk c = Dis tance be tween outer face of the

col umn flange and web toe of its fil let. M u = Fac tored beam mo mentPbf = Beam flange force, as sumed as ( )M d tu b fb-

Rn = Nom i nal strengtht fb = Beam flange thick ness t fc = Col umn flange thick nesst wc = Col umn web thick ness j = Re sis tance fac tor

The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and the Seis mic De sign Cat e gory. If the struc ture isiden ti fied as Seis mic De sign Cat e gory D or E, the spe cial seis mic re quire ments aresat is fied (ANSI/AISC 341 SEIS MIC 1). No spe cial check is made if the Seis micDe sign Cat e gory is A, B, or C.

Con ti nu ity plate re quire ments for seis mic de sign are eval u ated for mo ment frames(OMF, IMF, SMF) only. No checks are done for braced frames (LCBF, SCBF, andEBF).

• For OMF the con ti nu ity plates are checked and de signed for a beam flangeforce, ( )P M d tbf pb b fb= - .

( )P M d tbf pb b fb= - (ANSI/AISC 341 SEIS MIC 11.5)

• For SMF and IMF, the con ti nu ity plates are checked and de signed for a beamflange force, P R F b tbf y y fb fb= .

P R F b tbf y y fb fb=

Note that the code in sists on de sign ing con ti nu ity pate to match with testedcon nec tion (ANSI/AISC 341 SEUISMIC 9.5, 10.5)

Joint Design 55


De sign of Dou bler Plates

One as pect of the de sign of a steel fram ing sys tem is an eval u a tion of the shearforces that ex ist in the re gion of the beam col umn in ter sec tion known as the panelzone.

Shear stresses sel dom con trol the de sign of a beam or col umn mem ber. How ever,in a Mo ment-Re sist ing frame, the shear stress in the beam-col umn joint can be crit i -cal, es pe cially in fram ing sys tems when the col umn is sub jected to ma jor di rec tionbend ing and the joint shear forces are re sisted by the web of the col umn. In mi nordi rec tion bend ing, the joint shear is car ried by the col umn flanges, in which case the shear stresses are sel dom crit i cal, and this con di tion is there fore not in ves ti gated bythe pro gram.

Shear stresses in the panel zone, due to ma jor di rec tion bend ing in the col umn, mayre quire ad di tional plates to be welded onto the col umn web, de pend ing upon theload ing and the ge om e try of the steel beams that frame into the col umn, ei theralong the col umn ma jor di rec tion, or at an an gle so that the beams have com po nents along the col umn ma jor di rec tion. See Fig ure . The pro gram in ves ti gates such sit u -a tions and re ports the thick ness of any re quired doubler plates. Only col umns withI-shapes are in ves ti gated for doubler plate re quire ments. Also doubler plate re -quire ments are eval u ated for mo ment frames (OMF, IMF, SMF) only. No check ismade for braced frames(OCBF, SCBF, EBF).

The pro gram cal cu lates the re quired thick ness of doubler plates us ing the fol low ing al go rithms. The shear force in the panel zone, is given by

V = M

d - t Vp

n =

nbn n

n fn

c

b

1å -

cos q

The nom i nal panel shear strength is given by

R = F d t P Pv y c r u y0.6 for 0.4, £ or if Pu is ten sile, and (LRFD K1-9)

R = F d t P

PP > v y c r

u

y

u0.6 1.4 , for 0.-é

ëê

ù

ûú 4Py . (LRFD K1-10)

By us ing V Rp v= j , with j = 0.9 (by de fault), the re quired col umn web thick ness t r can be found.

The ex tra thick ness, or thick ness of the doubler plate is given by

t = t tdp r w- , (LRFD F2-1)

56 Joint Design


where,

Fy = Col umn and doubler plate yield stresst r = Re quired col umn web thick ness t fn = Flange thick ness of n-th beam con nect ing to the col umn t dp = Re quired doubler plate thick ness t fc = Col umn Flange thick ness

t w = Col umn web thick ness h = d tc fc- 2 if welded, d kc c- 2 if rolledVp = Panel zone shearVc = Col umn shear in col umn aboveFy = Beam flange forcesnb = Num ber of beams con nect ing to col umn d n = Depth of n-th beam con nect ing to col umn q n = An gle be tween n-th beam and col umn ma jor di rec tion d c = Depth of col umn clear of fil lets, equals d k- 2M bn = Cal cu lated fac tored beam mo ment from

the cor re spond ing load ing com bi na tionRv = Nom i nal shear strength of panelPu = Col umn fac tored ax ial loadPy = Col umn ax ial yield strength, F Ay

The larg est cal cu lated value of t dp cal cu lated for any of the load com bi na tionsbased upon the fac tored beam mo ments and fac tored col umn ax ial loads is re -ported.

The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and the Seis mic De sign Cat e gory. If the struc ture isiden ti fied as Seis mic De sign Cat e gory D or E, the spe cial seis mic re quire ments aresat is fied (ANSI/AISC 341 SEIS MIC 1). No spe cial check is made if the Seis micDe sign Cat e gory is A, B, or C.

Doubler plate re quire ments for seis mic de sign are eval u ated for SMF only. No fur -ther check/de sign is done for other types of frames.

• For Spe cial Mo ment-Re sist ing Frames, the panel zone doubler plate re quire -ments that are re ported will de velop at least the beam mo ments equal to of theplas tic mo ment ca pac ity of the beam or beam mo ments due to spec i fied loadcom bi na tions in volv ing seis mic load (ANSI/AISC 341 SEIS MIC 9.3a).

• For seis mic de sign, Vp is cal cu lated us ing the same equa tion as given above, ex -cept that M pb is taken as R F Zy y 33 .

Joint Design 57


The ca pac ity of the panel zone in re sist ing this shear is taken as (ANSI/AISC341 SEIS MIC 9-5):

j jv n v y c p

cf cf

b c p

V = F d t + b t

d d t 0.60 1

3 2æ

è

çç

ö

ø

÷÷

for P Pu y£ 0 75. (ANSI/AISC 341 SEIS MIC 9-5)

j jv n v y c p

cf cf

b c p

uV F d tb t

d d t

P

P= +

æ

è

çç

ö

ø

÷÷ -0 6 1

319 12

2

. . .y

æ

è

çç

ö

ø

÷÷

for P Pu y> 0 75. (ANSI/AISC 341 SEIS MIC 9.3a, LRFD K1-12)

giv ing the re quired panel zone thick ness as

tV

F d

b t

d dp

p

v y c

cf cf

b c

= -0.6 j

3 2

, if P Pu y£ 0 75.

tV

F dP

P

b tp

p

v y cu

y

cf cf=

-æ

è

çç

ö

ø

÷÷

æ

è

çç

ö

ø

÷÷

-

0 6 19 12

3 2

. . .jd db c

, if P Pu y> 0 75. (by de fault),

(ANSI/AISC 341 SEIS MIC 9.3a)

and the re quired doubler plate thick ness as

t = t - tdp p wc

where,

j v = 0.90 by de fault,bcf = width of col umn flange,t cf = thick ness of col umn flange,t p = re quired col umn web thick ness, h = d tc fc- 2 if welded, d kc c- 2 if rolled, andd b = depth of deep est beam fram ing into the ma jor di rec tion of

the col umn.

Py = F Ay

Pu = Ax ial force in col umn

58 Joint Design


• For Spe cial Mo ment-Re sist ing Frames, the panel zone col umn web thick nessre quire ment the pro gram checks the fol low ing:

td t d tc fc b fb

³- + -( ) ( )2 2

90(ANSI/AISC 341 SEIS MIC 9.36)

Here, t is taken as t wc + t dp when the dou ble plate is plug welded to pre vent lo calbuck ling. In such case t dp is in creased if nec es sary to meet this cri te ria. If thedoubler plate is not plug welded to the web, then t is taken as t wc and also as t dp

for check ing both the plates. If t wc can not sat isfy the cri te ria, then a fail ure con -di tion is de clared. If t dp does not sat isfy this cri te ria, then its value is in creasedto meet this cri te ria.

If the check is not sat is fied, it is noted in the out put.

Weak Beam Strong Column Measure

Only for Spe cial Mo ment Frames with Seis mic De sign Cat e gory D and E, the codere quires that the sum of col umn flex ure strengths at a joint should be more than thesum of beam flex ure strengths (ANSI/AISC 341 SEIS MIC 1, 9.6). The col umnflex ure strength should re flect the pres ence of ax ial force pres ent in the col umn.The beam flex ural strength should re flect po ten tial in crease in ca pac ity for strainhard en ing to fa cil i tate the re view of the strong col umn weak beam cri te rion, thepro gram will re port a beam/col umn plas tic mo ment ca pac ity ra tio for ev ery joint inthe struc ture.

For the ma jor di rec tion of any col umn (top end) the beam to col umn strength ra tiois ob tained as

R =

M

M + Mmaj

n =

n

n

pcax pcby

b

pbn

1å *

* *

cos q

(ANSI/AISC 341 SEIS MIC 9.6)

For the mi nor di rec tion of any col umn the beam to col umn strength ra tio is ob tained as

R =

M

M + M

n =

n

pbn n

pcay pcby

b

min1

å sin q

, (ANSI/AISC 341 SEIS MIC 9.6)

where,

Joint Design 59


Rmaj min, = Plas tic mo ment ca pac ity ra tios, in the ma jor andmi nor di rec tions of the col umn, re spec tively

Mpbn

* = Plas tic mo ment ca pac ity of n-th beam con nect ing

to col umnq n = An gle be tween the n-th beam and the col umn

ma jor di rec tionM

pcax y,

* = Ma jor and mi nor plas tic mo ment ca pac i ties, re duced for

ax ial force ef fects, of col umn above story levelM

pcbx y,


ax ial force ef fects, of col umn be low story levelnb = Num ber of beams con nect ing to the col umn

The plas tic mo ment ca pac i ties of the col umns are re duced for ax ial force ef fectsand are taken as

( )M = Z F - P Apc c yc uc g* , (ANSI/AISC 341 SEIS MIC 9.6)

The plas tic mo ment ca pac i ties of the beams are am pli fied for po ten tial in -crease in ca pac ity for strain hard en ing as,

M R F Z fpb y yb b mv* .= 11 ,

where,

Z b = Plas tic modulus of beam,

Z c = Plas tic modulus of col umn,

Fyb = Yield stress of beam ma te rial,

Fyc = Yield stress of col umn ma te rial,

Puc = Ax ial com pres sion force in col umn for the load com bi na tion un dercon sid er ation,Agc = Gross area of col umn,

fmv = The mo ment am pli fi ca tion fac tor. It is taken as the ra tio of beammo ment at the cen ter line of col umn to the mo ment the col umn face. Thisfac tor takes care of the M v of the code (ANSI/AISC 341 SEIS MIC 9.6). Fmv is taken as fol lows:

1+ d

Lc

b

,

60 Joint Design


d c = Depth of col umn sec tion, and

Lb = Clear span length of the beam.

For the above cal cu la tions the sec tion of the col umn above is taken to be the sameas the sec tion of the col umn be low as sum ing that the col umn splice will be lo catedsome dis tance above the story level.

Evalua tion of Beam Con nec tion Shears

For each steel beam in the struc ture the pro gram will re port the max i mum ma jorshears at each end of the beam for the de sign of the beam shear con nec tions. Thebeam con nec tion shears re ported are the max ima of the fac tored shears ob tainedfrom the load ing com bi na tions.

For spe cial seis mic de sign, the beam con nec tion shears are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The spe cial seis mic re -quire ments ad di tion ally checked by the pro gram are de pend ent on the type of fram -ing used and the Seis mic De sign Cat e gory. If the struc ture is iden ti fied as Seis micDe sign Cat e gory D or E, the spe cial seis mic re quire ments are sat is fied(ANSI/AISC 341 SEIS MIC 1). No spe cial check is made if the Seis mic De signCat e gory is A, B, or C.

• For spe cial mo ment frames, the beam con nec tion shear is taken as the max i -mum of those from reg u lar load com bi na tions and those re quired for the de vel -op ment of full plas tic mo ment ca pac ity of the beams. The con nec tion shear forthe de vel op ment of the full plas tic mo ment ca pac ity of beam is as fol lows:

V = C M

L + V Vu

pb

DL LL1.2 0.5+ (ANSI/AISC 341 SEIS MIC 9.2.a(3))

where

V = Shear force cor re spond ing to END I or END J of beam,C = 0 if beam ends are pinned, or for can ti le ver beam,

= 1 if one end of the beam is pinned,= 2 if no ends of the beam are pinned,

M pb = Plas tic mo ment ca pac ity of the beam, Z Fy ,L = Clear length of the beam,VDL = Ab so lute max i mum of the cal cu lated fac tored beam

shears at the cor re spond ing beam ends from the dead load only, and

VLL = Ab so lute max i mum of the cal cu lated fac tored beam

Joint Design 61


shears at the cor re spond ing beam ends from the live load only.

• For In ter me di ate Mo ment Frames and Or di nary Mo ment Frames, the beamcon nec tion shear is taken as the max i mum of those from reg u lar load com bi na -tions and those from spe cial seis mic con sid er ation. the beam con nec tion shearfrom spe cial seis mic con sid er ation is taken as the min i mum of those re quiredfor the de vel op ment of full plas tic mo ment ca pac ity of the beam and those re -quired for am pli fied seis mic load and those re quired (ANSI/AISC 341 SEIS -MIC 10.2, 11.2). The con nec tion shear for the de vel op ment of the full plas ticmo ment ca pac ity of beam is as fol lows:

VCM

LV Vu

pb

DL LL= + +1 2 0 5. . (ANSI/AISC 341 SEIS MIC 10.2, 11.2)

All pa ram e ters in the above equa tion have been de scribed ear lier.

The load com bi na tions for am pli fied seis mic loads are (ANSI/AISC 341SEIS MIC 8.3, 4.1, ASCI 9.5.2.7.1, 2.3.2):

( )0 9 0 2 0. .+ ±S DL ELDS W

( )12 0 2 10 0. . ) .+ + ±S DL LL ELDS W

• For OCBF, the beam con nec tion shear is taken as the max i mum of those fromreg u lar load com bi na tions and those from am pli fied seis mic load com bi na tions (ANSI/AISC 341 SEIS MIC 14.2).

• For SCBF, the beam con nec tion shear is taken as the max i mum of those fromreg u lar load com bi na tions and those from am pli fied seis mic load com bi na tion(ANSI/AISC 341 SEIS MIC 13.4a(2)).

Note: Beams in ter sected by Chev ron (V or in verted-V) braces are NOT cur -rently checked to have a strength to sup port loads for the fol low ing two con di -tions (ANSI/AISC 341 SEIS MIC 13.4a):


b A beam that is in ter sected by braces shall be de signed to re sist the ef fects ofload com bi na tions stip u lated by the code, ex cept that a load q b shall be sub sti -tuted for the term E. q b is given by the dif fer ence of R F Ay y for the ten sionbrace and 0 3. f c nP for the com pres sion brace.

62 Joint Design



• For EBF, the beam con nec tion shear is taken as the beam con nec tion shear istaken as the max i mum of those from reg u lar load com bi na tions and those fromspe cial seis mic con sid er ations. The beam con nec tion shear from spe cial seis -mic con sid er ation is taken as the min i mum of those re quired for yield ing oflink beam and those re quired for am pli fied seis mic load (ANSI/AISC 341SEIS MIC 15.1, 15.4, 15.6). The load fac tor for the seis mic com po nent of loads in the com bi na tion is cal cu lated to achieve forces re lated to yield ing of linkbeam. For con nec tion shear de ter mi na tion the forces are fur ther am pli fied by 11. Ry (ANSI/AISC 341 SEIS MIC 15.6(2)). The load com bi na tions for Am pli -fied Seis mic Loads are given ear lier.

Evalua tion of Brace Con nec tion Forces

For each steel brace in the struc ture the pro gram re ports the max i mum ax ial force at each end of the brace for the de sign of the brace to beam con nec tions. The bracecon nec tion forces re ported are the max ima of the fac tored brace ax ial forces ob -tained from the load ing com bi na tions.

For spe cial seis mic de sign, the brace con nec tion forces are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The spe cial seis mic re quire -ments ad di tion ally checked by the pro gram are de pend ent on the type of fram ingused and the Seis mic De sign Cat e gory. If the struc ture is iden ti fied as Seis mic De -sign Cat e gory D or E, the spe cial seis mic re quire ments are sat is fied (ANSI/AISC341 SEIS MIC 1). No spe cial check is made if the Seis mic De sign Cat e gory is A, B, or C.

Brace ax ial forces for seis mic de sign are eval u ated for braced frames (OCBF,SCBF, EBF) only. No spe cial checks are done for mo ment frames (OMF, IMF,SMF).

• For OBF, the brac ing con nec tion force is re ported at least the ex pected ten silestrength of the brace (R F Ay y g ) (ANSI/AISC 341 SEIS MIC 14.2):

• For SCBF, the brac ing con nec tion force is re ported at least as the ex pected theten sile strength of the brace (R F Ay y g ) (ANSI/AISC 341 SEIS MIC 13.3a).

For EBF, the brace con nec tion force is taken as the max i mum of those from reg u larload com bi na tions and those from spe cial seis mic con sid er ation. The brace con -nec tion force from spe cial seis mic con sid er ation is taken as the min i mum of thosere quired for yield ing of link beam and those re quired for Am pli fied Seis mic Load(ANSI/AISC 341 SEIS MIC 15.1, 15.4, 15.6). The load fac tor for the seis mic com -

Joint Design 63


po nent of loads in the com bi na tion is cal cu lated to achieve forces re lated to yield -ing of Link beam. for con nec tion force de ter mi na tion, the forces are fur ther am pli -fied by 125. Ry (ANSI/AISC 341 SEIS MIC 15.6). The load com bi na tions for Am -pli fied Seis mic Load are given ear lier in this doc u ment.

64 Joint Design


C h a p t e r IV

Check/Design for AISC-ASD89

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the AISC- ASD89 de -sign code (AISC 1989). Vari ous no ta tions used in this chap ter are de scribed inTable III-1.

For re fer ring to per ti nent sec tions and equa tions of the origi nal ASD code, a uniquepre fix “ASD” is as signed. However, all ref er ences to the “Speci fi ca tions for Al -low able Stress De sign of Single- Angle Mem bers” carry the pre fix of “ASD SAM”.


In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this chapter. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di catesover stress. Simi larly, a shear ca pac ity ra tio is also cal cu lated sepa rately.

65

66




A f = Area of flange , in2



Aw = Web shear area, dt w , in2

Cb = Bend ing Co ef fi cient

Cm = Mo ment Co ef fi cient




Fa = Al low able ax ial stress, ksi

Fb = Al low able bending stress, ksi

F Fb b33 22, = Al low able ma jor and mi nor bend ing stresses, ksi


Fe33¢ =

( )12

23

2

33 33 33

2

E

K l r

p

Fe22¢ =

( )12

23

2

22 22 22

2

E

K l r

p

Fv = Al low able shear stress, ksi



K K33 22, = Ef fec tive length K- factors in the ma jor and mi nor directions

M M33 22, = Major and mi nor bend ing mo ments in mem ber, kip- in

M ob = Lateral- torsional mo ment for an gle sections, kip- in

P = Axial force in mem ber, kips







Table IV-1AISC-ASD Notations

67

Chapter IV Check/Design for AISC-ASD89



V V2 3, = Shear forces in major and mi nor directions, kips





f a = Axial stress ei ther in com pres sion or in tension, ksi

f b = Nor mal stress in bend ing, ksi

f fb b33 22, = Nor mal stress in ma jor and minor di rec tion bending, ksi

f v = Shear stress, ksi

f fv v2 3, = Shear stress in ma jor and minor di rec tion bending, ksi

h = Clear dis tance be tween flanges for I shaped sec tions ( )d t f- 2 , in

he = Ef fec tive dis tance be tween flanges less fil lets, in

k = Dis tance from outer face of flange to web toe of fil let , in

k c = Pa rame ter used for clas si fi ca tion of sec tions,

[ ]4.05

0.46h t w

if h t w > 70 ,

1 if h t w £ 70 .


lc = Criti cal length, in



rz = Mini mum Ra dius of gy ra tion for an gles, in

t = Thick ness of a plate in I, box, chan nel, an gle, and T sections, in


t w = Web thick ness, in


Table IV-1AISC-ASD Notations (cont.)



The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. For the AISC- ASD89 code, if a struc tureis sub jected to dead load (DL), live load (LL), wind load (WL), and earth quake in -duced load (EL), and con sid er ing that wind and earth quake forces are re versi ble,then the fol low ing load com bi na tions may have to be de fined (ASD A4):

DL (ASD A4.1)DL + LL (ASD A4.1)

DL ± WL (ASD A4.1)DL + LL ± WL (ASD A4.1)

DL ± EL (ASD A4.1)DL + LL ± EL (ASD A4.1)

These are also the de fault de sign load com bi na tions in the pro gram when ever theAISC-ASD89 code is used. The user should use other ap pro pri ate load ing com bi -na tions if roof live load is sepa rately treated, if other types of loads are pres ent, or if pat tern live loads are to be con sid ered.

When de sign ing for com bi na tions in volv ing earth quake and wind loads, al low ablestresses are in creased by a fac tor of 4/3 of the regu lar al low able value (ASD A5.2).



The al low able stresses for ax ial com pres sion and flex ure are de pend ent upon theclas si fi ca tion of sec tions as ei ther Com pact, Non compact, Slen der, or Too Slen der.The pro gram clas si fies the in di vid ual mem bers ac cord ing to the lim it ingwidth/thick ness ra tios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). Thedefi ni tion of the sec tion prop er ties re quired in this ta ble is given in Figure III-1 andTable III-1.





Figure IV-1AISC-ASD Definition of Geometric Properties



Section Description

Ratio Checked

CompactSection

NoncompactSection

SlenderSection

I-SHAPE

b tf f2

( rolled)£ F


b tf f2

(welded)£ F

y65 £ 95 F ky c/ No limit

d t w

For f F a y £ 0.16

£ -640

1F

f

Fy

a

y

( )3.74 ,

For f Fa y/ > 0.16

£ 257 / Fy .

No limit No limit

h t w No limit

If compression only,

£ F y253

otherwise

£ F b760

( )£

+

£

14000

16.5

260

F Fy y

BOX

b t f £ F




Other t tw f³ 2 , d bw f£ 6 None None

CHANNEL

b t f As for I-shapes As for I-shapes No limit




If welded b df w £ 0.25, t tf w £ 3.0

If rolled b df w £ 0.5, t tf w £ 2.0

Table IV-2Limiting Width-Thickness Ratios for

Classification of Sections Based on AISC-ASD

If the sec tion di men sions sat isfy the lim its shown in the ta ble, the sec tion is clas si -fied as ei ther Com pact, Non com pact, or Slen der. If the sec tion sat is fies the cri te riafor Com pact sec tions, then the sec tion is clas si fied as Com pact sec tion. If the sec -tion does not sat is fy the cri te ria for Com pact sec tions but sat is fies the cri te ria forNon com pact sec tions, the sec tion is clas si fied as Noncom pact sec tion. If the sec -tion does not satisfy the cri te ria for Com pact and Non com pact sec tions but sat is fies



Section Description

Ratio Checked

CompactSection

NoncompactSection

SlenderSection

T-SHAPE

b tf f2 £ F


d t w Not applicable £ F

y127 No limit


If welded b df w ³ 0.5, t tf w ³ 1.25

If rolled b df w ³ 0.5, t tf w ³ 1.10

DOUBLEANGLES


y76 No limit


y76 No limit

PIPE D t £ F

y3 300, £ F y3 300,

£ F y13,000



RECTANGLE ¾ Assumed Noncompact


Table IV-2Limiting Width-Thickness Ratios for

Classification of Sections Based on AISC-ASD (Cont.)

the cri te ria for Slen der sec tions, the sec tion is clas si fied as Slender sec tion. If thelim its for Slen der sec tions are not met, the sec tion is clas si fied as Too Slen der.Stress check of Too Slen der sec tions is be yond the scope of SAP2000.

In clas si fy ing web slen der ness of I-shapes, Box, and Chan nel sec tions, it is as -sumed that there are no in ter me di ate stiff en ers (ASD F5, G1). Dou ble an gles arecon ser va tively as sumed to be sepa rated.


The stresses are cal cu lated at each of the pre vi ously de fined sta tions. The mem berstresses for nonslender sec tions that are cal cu lated for each load com bi na tion are,in gen eral, based on the gross cross- sectional prop er ties.:

f = P/Aa

f = M /Sb33 33 33

f = M /Sb22 22 22

f = V /Av v2 2 2

f = V /Av v3 3 3

If the sec tion is slen der with slen der stiff ened ele ments, like slen der web in I, Chan -nel, and Box sec tions or slen der flanges in Box, ef fec tive sec tion moduli based onre duced web and re duced flange di men sions are used in cal cu lat ing stresses.

f = P/Aa (ASD A-B5.2d)f = M /Sb eff33 33 33, (ASD A-B5.2d)f = M /Sb eff22 22 22, (ASD A-B5.2d)f = V /Av v2 2 2 (ASD A-B5.2d)f = V /Av v3 3 3 (ASD A-B5.2d)

The flexural stresses are cal cu lated based on the prop er ties about the principal axes. For I, Box, Chan nel, T, Dou ble-an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, theprin ci pal axes co in cide with the geo met ric axes. For Single- angle sec tions, the de -sign con sid ers the prin ci pal properties. For gen eral sec tions it is as sumed that allsec tion prop er ties are given in terms of the prin ci pal di rec tions.

For Single- angle sec tions, the shear stresses are cal cu lated for di rec tions along thegeo met ric axes. For all other sec tions the shear stresses are cal cu lated along thegeo met ric and prin ci ple axes.

72 Calculation of Stresses



The al low able stresses in com pres sion, ten sion, bend ing, and shear are com putedfor Com pact, Non com pact, and Slen der sec tions ac cord ing to the fol low ing sub -sec tions. The al low able flexural stresses for all shapes of sec tions are cal cu latedbased on their prin ci pal axes of bend ing. For the I, Box, Chan nel, Cir cu lar, Pipe, T,Dou ble-an gle and Rec tan gu lar sec tions, the prin ci pal axes co in cide with their geo -met ric axes. For the An gle sec tions, the prin ci pal axes are de ter mined and all com -pu ta tions re lated to flex ural stresses are based on that.

If the user speci fies nonz ero al low able stresses for one or more ele ments in the pro -gram “Overwrites Ele ment De sign Data” form, these val ues will over ride theabove men tioned cal cu lated val ues for those ele ments as de fined in the fol low ingsub sec tions. The speci fied al low able stresses should be based on the prin ci pal axes of bend ing.

Allowable Stress in Tension

The al low able ax ial ten sile stress value Fa is as sumed to be 0.60 Fy .

F = Fa y0.6 (ASD D1, ASD SAM 2)

It should be noted that net sec tion checks are not made. For mem bers in ten sion, if l r is greater than 300, a mes sage to that ef fect is printed (ASD B7, ASD SAM 2).For sin gle an gles, the mini mum radius of gy ra tion, rz , is used in stead of r22 and r33

in com put ing l r .

Allowable Stress in Compression

The al low able ax ial com pres sive stress is the minimum value ob tained from flex -ural buck ling and flexural- torsional buck ling. The al low able com pres sive stressesare de ter mined ac cord ing to the fol low ing sub sec tions.

For mem bers in com pres sion, if Kl r is greater than 200, a warn ing mes sage isprinted (ASD B7, ASD SAM 4). For sin gle an gles, the mini mum radius of gy ra -tion, rz , is used in stead of r22 and r33 in com put ing Kl r .

Flex ural Buck ling

The al low able ax ial com pres sive stress value, Fa , de pends on the slen der ness ra tio Kl r based on gross sec tion prop er ties and a cor re spond ing criti cal value, C c , where



Kl

r

K l

r

K l

r= ì

íî

üýþ

max ,33 33

33

22 22

22

, and

C c =2 2p E

Fy

. (ASD E2, ASD SAM 4)



For Com pact or Non com pact sec tions Fa is evalu ated as fol lows:

( )F =

Kl/r

CF

+ Kl/r

C

Ka

c

y

c

1.0 -ìíî

üýþ

-

( ) 2

22

5

3

3

8

( )l/r

C

c

3

38

, if Kl

r C c£ , (ASD E2-1, SAM 4-1)

F = E

Kl ra

12

23

2

2

p

( ) , if

Kl

r C c> . (ASD E2-2, SAM 4-2)

If Kl r is greater than 200, then the cal cu lated value of Fa is taken not to ex ceed thevalue of Fa cal cu lated by us ing the equa tion ASD E2-2 for Com pact and Non com -pact sec tions (ASD E1, B7).

For Slender sec tions, ex cept slen der Pipe sec tions, Fa is evalu ated as fol lows:

( )F = Q

Kl/r

CF

+ Kl/r

C

ac

y1.0 -ìíï

îï

üýï

þï¢

( ) 2

22

5

3

3

8

( )c

c

Kl/r

C¢ ¢

-

3

38

, if Kl

r C c£ ¢ , (ASD A-B5-11, SAM 4-1)

F = E

Kl ra

12

23

2

2

p

( ) , if

Kl

r C c> ¢ . (ASD A-B5-12, SAM 4-2)

where,

CE

Q Fc

y

¢ =2 2p

. (ASD A-B5.2c, ASD SAM 4)



For slen der sec tions, if Kl r is greater than 200, then the cal cu lated value of Fa istaken not to ex ceed its value cal cu lated by us ing the equa tion ASD A-B5-12 (ASD B7, E1).

For slen der Pipe sec tions Fa is evalu ated as fol lows:

F = D t

Fa y

6620.40+ (ASD A- B5-9)


Q Q Qs a= , where (ASD A-B5.2.c, SAM 4)

Q s = re duc tion fac tor for un stiff ened slen der ele ments, and (ASD A-B5.2.a)

Q a = re duc tion fac tor for stiff ened slen der ele ments. (ASD A-B5.2.c)

The Q s fac tors for slen der sec tions are cal cu lated as de scribed in Table III-4 (ASDA-B5.2a, ASD SAM 4). The Q a fac tors for slen der sec tions are cal cu lated as thera tio of ef fec tive cross- sectional area and the gross cross- sectional area.

QA

Aa

e

g

= (ASD A- B5-10)


( )A A b b te g e= - -å

be for un stiff ened el e ments is taken equal to b, and be for stiff ened el e ments istaken equal to or less than b as given in Table III-5 (ASD A-B5.2b). For webs in I,box, and Chan nel sec tions, he is used as be and h is used as b in the above equa tion.


The al low able ax ial com pres sive stress value, Fa , de ter mined by the limit states oftor sional and flexural- torsional buck ling is de ter mined as fol lows (ASD E3, C-E3):

( )

( )F = Q

Kl/r

CF

+ Kl/r

C

a

e

c

y

e

1.0 -ì

íï

îï

ü

ýï

þï¢

2

22

5

3

3

8

( )c

e

c

Kl/r

C¢ ¢

-

3

38

, if ( )Kl/r Ce c£ ¢ , (E2-1, A- B5- 11)





SectionType


EquationReference

I-SHAPE [ ]Q

if b t F k

b t F k if Fs

f f y c

f f y c y=

£

-

1.0 95

1.293 0.00309 95

2

2

,

[ ]{ }k b t F k

k b t F if b t F k

c f f y c

c f f y f f y c

< <

³

ì

2

2 22

195

26,200 195

,

.

íïï

îïï

ASD A-B5-3,ASD A-B5-4

BOX Qs =1 ASD A-B5.2c

CHANNEL As for I-shapes with b tf f2 replaced by b tf f .ASD A-B5-3,ASD A-B5-4

T-SHAPE


[ ]Q

if d t F

d t F if F d ts

w y

w y y w£

£

- <

1.0 , 127

1.908 0.00715 127

,

,

[ ]{ }<

³

ì

íïï

îïï

176

20,000 176

F

d t F if d t F

y

w y w y

,

, .2

ASD A-B5-3,ASD A-B5-4,ASD A-B5-5,ASD A-B5-6

DOUBLE-ANGLE

[ ]Q

if b t F

b t F if F b ts

y

y y=

£

- < <

1.0 , 76

1.340 0.00447 76 155

,

,

[ ]{ }F

b t F if b t F

y

y y

,

, .15,500 1552

³

ì

íïï

îïï


SAM 4-3

ANGLE [ ]Q

if b t F

b t F if F b ts

y

y y=

£

- < <

1.0 , 76

1.340 0.00447 76 155

,

,

[ ]{ }F

b t F if b t F

y

y y

,

, .15,500 1552

³

ì

íïï

îïï


SAM 4-3

PIPE Qs =1 ASD A-B5.2c

ROUNDBAR

Qs =1 ASD A-B5.2c

RECTAN-GULAR

Qs =1 ASD A-B5.2c

GENERAL Qs =1 ASD A-B5.2c

Table IV-3Re duc tion Fac tor for Un stiff ened Slen der Ele ments, Q s



SectionType


I-SHAPE h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï


A g

= ) ASD A-B5-8

BOX

h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï


A g

= )

b

b ifb

t f

t

f h t fif

b

t

e

f

f

f

=

£

-é

ëêê

ù

ûúú

, ,

( ),

183.74

253 50.31 >

ì

í

ïï

î

ïï

183.74

f.

(compr., flexure, f Fy= 0.6 )

ASD A-B5-8

ASD A-B5-7

CHANNEL h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

195.74

253 44.31

195.74

f.

ì

í

ïï

î

ïï


A g

= ) ASD A-B5-8

T-SHAPE b be = ASD A-B5.2c

DOUBLE-ANGLE

b be = ASD A-B5.2c

ANGLE b be = ASD A-B5.2c

PIPE Qa = 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9

ROUNDBAR

Not applicable ¾

RECTAN-GULAR

b be = ASD A-B5.2c


Table IV-4Effective Width for Stiffened Sections

( )F =

E

Kl/ra

e

12

23

2

2

p , if ( )Kl/r C

e c> ¢ . (E2-2, A- B5- 12)

where,

CE

Q Fc

y

¢ =2 2p

, and (ASD E2, A-B5.2c, SAM 4)

( )Kl/rE

Fee

=p 2

. (ASD C- E2-2, SAM 4-4)

ASD Com men tary (ASD C-E3) re fers to the 1986 ver sion of the AISC-LRFD codefor the cal cu la tion of Fe . The 1993 ver sion of the AISC-LRFD code is the same asthe 1986 ver sion in this respect. Fe is cal cu lated in the pro gram as fol lows:


( )F

EC

K lGJ

I Ie

w

z z

= +é

ë

êê

ù

û

úú +

p 2

222 33

1 (LRFD A- E3-5)


F = F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Channels:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Sin gle-angle sec tions with equal legs:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù

ûúú (ASD SAM C- C4-1)

• For Single- angle sec tions with une qual legs, Fe is cal cu lated as the mini mumreal root of the fol low ing cu bic equa tion (ASD SAM C- C4-2, LRFD A- E3-7):



( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e- - - - - -33 22

222

02

02

2 F Fy

re e- =33

02

02

0) ,

where,


try),

r x yI I

Ag

0 02

02 22 33= + + +


Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

, (LRFD A- E3-9)

( )F

E

K l re33

2

33 33 33

2= p

, (LRFD A- E3-10)

( )F

E

K l re22

2

22 22 22

2= p

, (LRFD A- E3-11)

( )F

EC

K lGJ

Arez

w

z z

= +é

ë

êê

ù

û

úú

p 2

202

1 , (LRFD A- E3-12)





For an gle sec tions, the prin ci pal mo ment of in er tia and ra dii of gy ra tion are used for com put ing Fe (ASD SAM 4). Also, the maxi mum value of Kl, i .e, max( , )K l K l22 22 33 33 , is used in place of K l22 22 or K l33 33 in cal cu lat ing Fe22 and Fe33

in this case.



Allowable Stress in Bending

The al low able bend ing stress de pends on the fol low ing cri te ria: the geo met ricshape of the cross- section, the axis of bend ing, the com pact ness of the sec tion, anda length pa rame ter.

I-sections

For I- sections the length pa rame ter is taken as the lat er ally un braced length, l22 , which is com pared to a criti cal length, lc . The criti cal length is de fined as

lb

F

A

d Fc

f

y

f

y

=ìíï

îï

üýï

þïmin ,

,76 20 000 , where (ASD F1-2)








F = b

tF Fb

f

f

y y332

0.79 0.002-æ

è

çç

ö

ø


F = b

t

F

k Fb

f

f

y

c

y332

0.79 0.002-æ

è

çç

ö

ø

÷÷

, if welded and fy £ 65 ksi, (ASDF1-4)


If the un braced length l22 is greater than lc , then for both Com pact and Non -com pact I- sections the al low able bend ing stress de pends on the l rT22 ra tio.



For l

r

C

FT

b

y

22 102 000£

, ,

F Fb y33 = 0.60 , (ASD F1-6)

for 102 000 510 00022, ,C

F

l

r

C

Fb

y T

b

y

< £ ,

FF l r

CF Fb

y T

b

y y33

222

2

3 1530 000= -

é

ëêê

ù

ûúú

£( / )

,0.60 , and (ASD F1-6)

for l

r

C

FT

b

y

22 510 000> , ,

FC

l rFb

b

T

y33

222

170 0000=

é

ëê

ù

ûú £

,

( / )0.6 , (ASD F1-7)

and Fb33 is taken not to be less than that given by the fol low ing for mula:

( )F

C

l d AFb

b

f

y33

22

12 000= 0.6

,

/£ (ASD F1-8)

where,

rT is the ra dius of gy ra tion of a sec tion com pris ing the com pres sion flange and 1 3 the com pres sion web taken about an axis in the plane of the web,

C = + M

M +

M

Mb

a

b

a

b

1.75 1.05 0.3æ

èçç

ö

ø÷÷

æ

èçç

ö

ø÷÷ £

2

2.3, where (ASD F1.3)

M Ma band are the end mo ments of any un braced seg ment of the mem ber and M a is nu mer i cally less than M b ; M Ma b be ing pos i tive for dou ble cur va turebend ing and neg a tive for sin gle cur va ture bend ing. Also, if any mo ment withinthe seg ment is greater than M b , Cb is taken as 1.0. Also, Cb is taken as 1.0 forcan ti le vers and frames braced against joint trans la tion (ASD F1.3). The pro -gram de faults Cb to 1.0 if the un braced length, l22 , of the mem ber is re de finedby the user (i.e. it is not equal to the length of the mem ber). The user can over -write the value of Cb for any mem ber by spec i fy ing it.





F R R Fb PG e b33 33¢ = , where (ASD G2-1)

RA

A

h

t FPG

w

f b

= - -é

ëêê

ù

ûúú

£1.0 0.0005 1.0760

33

, (ASD G2)

( )R

A

A

A

A

e

w

f

w

f

=+ -

+£

12

12 2

1.0

3 3a a

, (hy brid gird ers) (ASD G2)

Re =1.0 , (non- hybrid gird ers) (ASD G2)

Aw = Area of web, in 2 ,

A f = Area of com pres sion flange, in 2 ,

a = £0.6

1.0F

F

y

b33

(ASD G2)

Fb33 = Al low able bend ing stress as sum ing the sec tion is noncompact, and

Fb33¢ = Al low able bend ing stress af ter con sid er ing web slenderness.


If the flange is slen der, then the pre vi ously com puted al low able bend ing stressis taken to be lim ited as follows.

( )F Q Fb s y33¢ £ 0.6 , where (ASD A-B5.2a, A-B5.2d)

Q s is de fined ear lier.








For Non com pact and Slen der sec tions:

F = b

tF Fb

f

f

y y222

1.075 0.005-æ

è

çç

ö

ø

÷÷ , if fy £ 65 ksi, (ASD F2-3)


Channel sections

For Chan nel sec tions the length pa rame ter is taken as the lat er ally un bracedlength, l22 , which is com pared to a criti cal length, lc . The criti cal length is de -fined as

lb

F

A

d Fc

f

y

f

y

=ìíï

îï

üýï

þïmin ,

,76 20 000 , where (ASD F1-2)








F = b

tF Fb

f

f

y y33 0.79 0.002-æ

è

çç

ö

ø




F = b

t

F

k Fb

f

f

y

c

y33 0.79 0.002-æ

è

çç

ö

ø

÷÷

, if welded and fy £ 65 ksi, (ASD F1-4)


If the un braced length l22 is greater than lc , then for both Com pact andNoncom pact Chan nel sections the al low able bend ing stress is taken as follows:

( )F

C

l d AFb

b

f

y33

22

12 000= 0.6

,

/£ (ASD F1-8)



F R R Fb e PG b33 33¢ = (ASD G2-1)

If the flange is slen der, the pre vi ously com puted al low able bend ing stress istaken to be lim ited as follows:

( )F Q Fb s y33¢ £ 0.6 (ASD A-B5.2a, A-B5.2d)

The defi ni tion for rT , Cb , A f , Aw , Re , RPG , Q s , Fb33 , and Fb33¢ are given ear lier.



F = Fb y22 0.60 (ASD F2-2)

T-sections and Double angles

For T sec tions and Dou ble an gles, the al low able bend ing stress for both ma jorand mi nor axes bending is taken as,

F = Q Fb s y0.60 .



Box Sections and Rectangular Tubes

For all Box sec tions and Rec tan gu lar tubes, the length pa rame ter is taken as thelat er ally un braced length, l22 , meas ured com pared to a criti cal length, lc . Thecriti cal length is de fined as

l M /Mb

F,

b

Fc a b

y y

= +ìíî

üýþ

max ( )1950 12001200

(ASD F3-2)

where M a and M b have the same defi ni tion as noted ear lier in the for mula for

Cb . If l22 is speci fied by the user, lc is taken as 1200 b

Fy

in the pro gram.


If l22 is less than lc , the al low able bend ing stress in the ma jor di rec tion ofbend ing is taken as:


F = Fb y33 0.60 (for Non com pact sec tions) (ASD F3-3)

If l22 ex ceeds lc , the al low able bend ing stress in the ma jor di rec tion of bend -ing for both Com pact and Non com pact sec tions is taken as:

F = Fb y33 0.60 (ASD F3-3)

The ma jor di rec tion al low able bend ing stress for Slen der sec tions is de ter -mined in the same way as for a Non com pact sec tion. Then the fol low ing ad di -tional con sid era tion is taken into ac count. If the web is slen der, then the pre vi -ously com puted al low able bend ing stress is re duced as fol lows:

F R R Fb e PG b33 33¢ = (ASD G2-1)

The defi ni tion for Re , RPG , Fb33 , and Fb33¢ are given ear lier.

If the flange is slen der, no ad di tional con sid er ation is needed in com put ing al -low able bend ing stress. How ever, ef fec tive sec tion di men sions are cal cu latedand the sec tion modu lus is modi fied ac cord ing to its slen der ness.


If l22 is less than lc , the al low able bend ing stress in the minor di rec tion of bend -ing is taken as:




F = Fb y22 0.60 (for Non com pact and Slender sec tions) (ASD F3-3)

If l22 ex ceeds lc , the al low able bend ing stress in the minor di rec tion of bend -ing is taken, ir re spec tive of com pact ness, as:

F = Fb y22 0.60 (ASD F3-3)

Pipe Sections

For Pipe sec tions, the al low able bend ing stress for both ma jor and mi nor axesof bend ing is taken as

F = Fb y0.66 (for Com pact sec tions), and (ASD F3-1)

F = Fb y0.60 (for Non com pact and Slen der sec tions). (ASD F3-3)

Round Bars

The al low able stress for both the ma jor and mi nor axis of bend ing of round bars is taken as,

F = Fb y0.75 . (ASD F2-1)

Rectangular and Square Bars

The al low able stress for both the ma jor and mi nor axis of bend ing of solidsquare bars is taken as,

F = Fb y0.75 . (ASD F2-1)

For solid rec tan gu lar bars bent about their ma jor axes, the al low able stress isgiven by

F = Fb y0.60 , And

the al low able stress for mi nor axis bend ing of rec tan gu lar bars is taken as,

F = Fb y0.75 . (ASD F2-1)



Single-Angle Sections

The al low able flex ural stresses for Single- angles are cal cu lated based on their prin -ci pal axes of bend ing (ASD SAM 5.3).


The al low able stress for ma jor axis bend ing is the mini mum con sid er ing the limitstate of lateral- torsional buck ling and lo cal buck ling (ASD SAM 5.1).

The al low able ma jor bend ing stress for Single- angles for the limit state of lateral- torsional buck ling is given as fol lows (ASD SAM 5.1.3):

F = F

FFb major

ob

y

ob, 0.55 0.10-é

ëê

ù

ûú , if F Fob y£ (ASD SAM 5-3a)

F = F

FF Fb major

y

ob

y y, 0.95 0.50 0.66-é

ë

êê

ù

û

úú

£ , if F Fob y> (ASD SAM 5-3b)

where, Fob is the elas tic lateral- torsional buck ling stress as cal cu lated be low.

The elas tic lateral- torsional buck ling stress, Fob , for equal- leg an gles is taken as

F Cl t

ob b= 28,250 , (ASD SAM 5-5)

and for unequal- leg an gles Fob is cal cu lated as

F CI

S llt rob b

major

w w= + +éë

ùû

143,100 0.052minmin2

2 2b b( ) , (ASD SAM 5-6)

where,


( )l l l= max ,22 33 ,

Imin = mi nor prin ci pal mo ment of in er tia,

Imax = major prin ci pal mo ment of in er tia,

Smajor = ma jor sec tion modu lus for com pres sion at the tip of one leg,




bwAI

z w z dA z= +é

ëê

ù

ûú -ò

122 2

0

max

( ) , (ASD SAM 5.3.2)




bw is a spe cial sec tion prop erty for an gles. It is posi tive for short leg in com pres -sion, nega tive for long leg in com pres sion, and zero for equal- leg an gles (ASDSAM 5.3.2). How ever, for con ser va tive de sign in the pro gram, it is al ways taken asnega tive for unequal- leg an gles.

In the above ex pres sions Cb is cal cu lated in the same way as is done for I sec tionswith the ex cep tion that the up per limit of Cb is taken here as 1.5 in stead of 2.3.

C = + M

M +

M

Mb

a

b

a

b

1.75 1.05 0.3æ

èçç

ö

ø÷÷

æ

èçç

ö

ø÷÷ £

2

1.5 (ASD F1.3, SAM 5.2.2)

The al low able ma jor bend ing stress for Single- angles for the limit state of lo calbuck ling is given as fol lows (ASD SAM 5.1.1):

F = Fb major y, 0.66 , if b

t Fy

£65

, (ASD SAM 5-1a)

F = Fb major y, 0.60 , if 65 76

F

b

t Fy y

< £ , (ASD SAM 5-1b)

( )F = Q Fb major y, 0.60 , if b

t Fy

> 76 , (ASD SAM 5-1c)

where,



Q = slen der ness re duc tion fac tor for lo cal buck ling. (ASD A- B5-2, SAM 4)



In cal cu lat ing the al low able bend ing stress for Single- angles for the limit state oflo cal buck ling, the al low able stresses are cal cu lated con sid er ing the fact that ei therof the two tips can be un der com pres sion. The mini mum al low able stress is con sid -ered.


The al low able minor bend ing stress for Single- angles is given as fol lows (ASDSAM 5.1.1, 5.3.1b, 5.3.2b):

F = Fyb,minor 0.66 , if b

t Fy

£65

, (ASD SAM 5-1a)

F = Fyb,minor 0.60 , if 65 76

F

b

t Fy y

< £ , (ASD SAM 5-1b)

( )F = Q Fyb,minor 0.60 , if b

t Fy

> 76 , (ASD SAM 5-1c)

In cal cu lat ing the al low able bend ing stress for Single- angles it is as sumed that thesign of the mo ment is such that both the tips are un der com pres sion. The mini mumal low able stress is con sid ered.

General Sections

For Gen eral sec tions the al low able bend ing stress for both ma jor and mi noraxes bending is taken as,

F = Fb y0.60 .

Allowable Stress in Shear

The shear stress is cal cu lated along the geo met ric axes for all sec tions. For I, Box,Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci palaxes co in cide with their geo met ric axes. For Single- angle sec tions, prin ci pal axesdo not co in cide with the geometric axes.


The al low able shear stress for all sec tions ex cept I, Box and Chan nel sec tions istaken in the pro gram as:



F Fv y= 0.40 (ASD F4-1, SAM 3-1)

The al low able shear stress for ma jor di rec tion shears in I- shapes, boxes and chan -nels is evalu ated as fol lows:

F Fv y= 0.40 , if h

t

Fw y

£380

, and (ASD F4-1)

FC

F Fvv

y y= £2.89

0.40 , if 380

260F

h

t

y w

< £ . (ASD F4-2)

where,

( )C

k

F h tif

h

t

k

F

h t

k

Fif

h

t

v

v

y ww

v

y

w

v

y

=

³45 000

2

,, ,

,

56,250

190

w

v

y

k

F<

ì

í

ïï

î

ïï

56,250 ,

(ASD F4)

( )

( )

ka h

ifa

h

a hif

a

h

v =

+ £

+ >

ì

í

ïï

î

ïï

4.005.34

5.344.00

2

2

1

1

, ,

, ,

(ASD F4)

t w = Thick ness of the web,

a = Clear dis tance be tween trans verse stiff en ers, in. Cur rently it is taken con ser va tively as the length, l22 , of the mem ber in the pro -

gram,

h = Clear dis tance be tween flanges at the sec tion, in.


The al low able shear stress for mi nor di rec tion shears is taken as:

F Fv y= 0.40 (ASD F4-1, SAM 3-1)




In the calculation of the ax ial and bend ing stress ca pac ity ra tios, first, for each sta -tion along the length of the mem ber, the ac tual stresses are cal cu lated for each loadcom bi na tion. Then the cor re spond ing al low able stresses are calculated. Then, theca pac ity ra tios are calculated at each sta tion for each mem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol ling ca pac ity ra tio is then ob -tained, along with the as so ci ated sta tion and load com bi na tion. A ca pac ity ra tiogreater than 1.0 in di cates an overstress.





f

F+

C f

f

F' F

+ C fa

a

m b

a

e

b

m b33 33

33

33

22 22

1 1-æ

èçç

ö

ø÷÷

f

F' Fa

e

b-æ

èçç

ö

ø÷÷

22

22


( )

f

F

f

F

f

Fa

y

b

b

b

bQ 0.60+ +33

33

22

22


fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are de fined ear lier in this chapter,




Cm =



0.85 , if sway frame,

0.6 0.4 if -M

aM

b

, nonsway, no transverse loading,

0.85 , if nonsway, trans. load, end restrained,

1.00 , if nonsway, trans. load, end unrestrained.

ì

í

ïïïï

î

ïïïï

(ASD H1)

For sway frame Cm = 0.85 , for nonsway frame with out trans verse load C M Mm a b= -0.6 0.4 , for nonsway frame with trans verse load and end re -strained com pres sion mem ber Cm = 0.85 , and for nonsway frame with trans -verse load and end un re strained com pres sion mem ber Cm =1.00 (ASD H1), where M Ma b is the ra tio of the smaller to the larger mo ment at the ends of themem ber, M Ma b be ing pos i tive for dou ble cur va ture bend ing and neg a tive forsin gle cur va ture bend ing. When M b is zero, Cm is taken as 1.0. The pro gramde faults Cm to 1.0 if the un braced length fac tor, l, of the mem ber is re de finedby ei ther the user or the pro gram, i.e., if the un braced length is not equal to thelength of the mem ber. The user can over write the value of Cm for any mem ber. Cm as sumes two val ues, Cm22 and Cm33 , as so ci ated with the ma jor and mi nor di -rec tions.

Fe¢ is given by

FE

Kl re¢ = 12

23

2

2

p

( / ) . (ASD H1)

A fac tor of 4/3 is ap plied on Fe¢ and 0.6Fy if the load com bi na tion in cludes any

wind load or seis mic load (ASD H1, ASD A5.2).

• If fa is com pres sive and f Fa a £ 0.15 , a rela tively sim pli fied for mula is used for the com bined stress ra tio.

f

F +

f

F +

f

Fa

a

b

b

b

b

33

33

22

22

(ASD H1-3, SAM 6.1)


f

F

f

F

f

Fa

a

b

b

b

b

+ +33

33

22

22


92 Calculation of Stress Ratios


f

F

f

Fb

b

b

b

33

33

22

22

+ , where

fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are de fined ear lier in this chap ter. How ever, ei -ther Fb33 or Fb22 need not be less than 0.6Fy in the first equa tion (ASD H2-1). The sec ond equa tion con sid ers flex ural buck ling with out any be nefi cial ef fectfrom ax ial com pres sion.


For Single- angle sec tions, the com bined stress ra tio is cal cu lated based on the prop -er ties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Chan nel, T, Dou -ble-an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci pal axes co in cide withtheir geo met ric axes. For Single- angle sec tions, prin ci pal axes are de ter mined inthe pro gram. For gen eral sec tions no ef fort is made to de ter mine the prin ci pal di rec -tions.

When de sign ing for com bi na tions in volv ing earth quake and wind loads, al low ablestresses are in creased by a fac tor of 4/3 of the regu lar al low able value (ASD A5.2).

Shear Stresses

From the al low able shear stress val ues and the fac tored shear stress val ues at eachsta tion, shear stress ra tios for ma jor and minor di rec tions are computed for each ofthe load com bi na tions as fol lows:

f

Fv

v

2 , and

f

Fv

v

3 .


When de sign ing for com bi na tions in volv ing earth quake and wind loads, al low ableshear stresses are in creased by a fac tor of 4/3 of the regular al low able value (ASDA5.2).



C h a p t e r V

Check/Design for AISC-LRFD99

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the AISC- LRFD99 de -sign code (AISC 1999). Vari ous no ta tions used in this chap ter are de scribed inTable V-1.

This code cov ers the 1999 edi tion of AISC-LRFD code with all re vi sions throughJan u ary 2003. This also cov ers the 2000 LRFD code for Sin gle An gle Mem bers,2000 LRFD code for Hol low Struc tural Sec tions, and 2002 LRFD seis mic pro vi -sions (AISC 2001, AISC 2000a, AISC 2000b, AISC 2002).

For re fer ring to per ti nent sec tions and equa tions of the orig i nal LRFD code, aunique pre fix “LRFD” is as signed. How ever, all ref er ences to the “Load and Re sis -tance Fac tor De sign spec i fi ca tion for Sin gle-An gle Mem bers” (AISC 2000) carrythe pre fix of “LRFD SAM”. All ref er ences to the “Load and Re sis tance Fac tor De -sign spec i fi ca tion for Hol low Struc tural Mem bers” (AISC 2000) carry the pre fix of“LRFD BOX”. All ref er ences to the “Seis mic Pro vi sions for Struc tural Steel Build -ings” (AISC 2002) carry the pre fix of “LRFD SEISMIC”.


95

96






Aw = Shear area, equal dt w per web, in2

B1 = Mo ment mag ni fi ca tion fac tor for mo ments not caus ing sidesway

B2 = Mo ment mag ni fi ca tion fac tor for mo ments caus ing sidesway

Cb = Bend ing co ef fi cient

Cm = Mo ment co ef fi cient





Fr = Com pres sive re sid ual stress in flange as sumed 10.0 for rolled sec tions and 16.5 for welded sec tions, ksi


G = Shear modu lus, ksi

I 22 = Mi nor mo ment of in er tia, in4

I 33 = Major mo ment of in er tia, in4

J = Tor sional con stant for the sec tion, in4


K K33 22, = Ef fec tive length K- factors in the ma jor and mi nor di rec tions

Lb = Lat er ally un braced length of mem ber, in

L p = Lim it ing lat er ally un braced length for full plas tic ca pac ity, in

Lr = Lim it ing lat er ally un braced length for ine las tic lateral- torsional buck ling, in

M cr = Elas tic buck ling mo ment, kip- in

M lt = Fac tored mo ments caus ing sidesway, kip- in

M nt = Fac tored mo ments not caus ing sidesway, kip- in

M Mn n33 22, = Nomi nal bend ing strength in ma jor and mi nor di rec tions, kip- in

M ob = Elas tic lateral- torsional buck ling mo ment for an gle sections, kip- in

M Mr r33 22, = Ma jor and mi nor lim it ing buck ling mo ments, kip- in

M u = Fac tored mo ment in mem ber, kip- in

M Mu u33 22, = Fac tored ma jor and mi nor mo ments in mem ber, kip- in


Pn = Nomi nal ax ial load strength, kip

Pu = Fac tored ax ial force in mem ber, kips

Py = A Fg y , kips


Table V-1AISC-LRFD Notations

97

Chapter V Check/Design for AISC-LRFD99







V Vn n2 3, = Nomi nal ma jor and mi nor shear strengths, kips

V Vu u2 3, = Fac tored ma jor and mi nor shear loads, kips

Z = Plas tic modu lus, in3

Z Z33 22, = Ma jor and mi nor plas tic moduli, in3





d e = Ef fec tive depth of web, in

hc = Clear dis tance be tween flanges less fil lets, in as sumed d k- 2 for rolled sec tions, and d t f- 2 for welded sec tions

k = Dis tance from outer face of flange to web toe of fil let, in

k c = Pa rame ter used for sec tion clas si fi ca tion, 4 h t

w , 0.35 0.763£ £k c




t = Thick ness, in


t w = Thick ness of web, in


l = Slen der ness pa rame ter

l lc e, = Col umn slen der ness pa rame ters

l p = Lim it ing slen der ness pa rame ter for com pact ele ment

lr = Lim it ing slen der ness pa rame ter for noncompact ele ment

ls = Lim it ing slen der ness pa rame ter for seismic ele ment

lslender = Lim it ing slen der ness pa rame ter for slender ele ment

jb = Re sis tance fac tor for bend ing, 0.9

jc = Re sis tance fac tor for com pres sion, 0.85

j ty = Re sis tance fac tor for ten sion yielding, 0.9

jv = Re sis tance fac tor for shear, 0.9

Table V-1AISC-LRFD Notations (cont.)

In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this chapter. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than stress ra tiolimit in di cates ex ceed ing a limit state. The de fault stress ra tio limit is 0.95 whichcan be changed us ing the de sign pref er ences in Op tions menu. Sim i larly, a shearca pac ity ra tio is also cal cu lated sepa rately.



The de sign load com bi na tions are the var i ous com bi na tions of the load cases forwhich the struc ture needs to be checked. For the AISC-LRFD99 code, if a struc ture is sub jected to dead load (DL), live load (LL), wind load (WL), and earth quake in -duced load (EL), and con sid er ing that wind and earth quake forces are re vers ible,then the fol low ing load com bi na tions may have to be de fined (LRFD A4, ASCE

7-02 2.3.2). The DLmultiplier and r fac tors are spec i fied in ASCE 7-02:

1.4 DL (ASCE 2.3.2-1)1.2 DL + 1.6 LL (ASCE 2.3.2-2)

0.9 DL ± 1.6 WL (ASCE 2.3.2-6)1.2 DL ± 0.8 WL (ASCE 2.3.2-3)1.2 DL + 1.0 LL ± 1.6 WL (ASCE 2.3.2-4)

0.9(1-DLmultiplier ) ± 1.0 r EL (ASCE 2.3.2-7)

1.2(1+DLmultiplier ) ± 1.0 r EL (ASCE 2.3.2-5)

1.2(1+DLmultiplier ) + 1.0 LL ± 1.0 r EL (ASCE 2.3.2-5)

These are also the de fault de sign load com bi na tions in the pro gram when ever theAISC-LRFD99 code is used. The user should use other ap pro pri ate load ing com bi -na tions if roof live load is sepa rately treated, if other types of loads are pres ent, or if pat tern live loads are to be con sid ered.





tw

tw tw

tw tw

t f t f

t f

t

t f

t f

d

t = t = tw f

t t

z

2, y

2, y

3, x 3, x

AISC-LRFD93 : Axes Conventions

2-2 is the cross-section axis parallel to the webs,the longer dimension of tubes,the longer leg of single angles, orthe side by side legs of double-angles.This is the same as the y-y axis.

3-3 is orthogonal to 2-2. This is the same as the x-x axis.

b f

b f b fb f

b f

b f

b b

dh d

b

b

b b = b - 3tff

D

hc hchc

k

b b

K

Figure V-1AISC-LRFD Definition of Geometric Properties




Check

(l)COMPACT

(l p )NONCOMPACT

(l r )SLENDER

(l slender )

I-SHAPE

b tf f2

(rolled)£

E

Fy

038.£ E F -

y083 10. / ( )No limit

b tf f2

(welded)£

E

Fy

038. £ EK

F -

c

y

0 95.( 16.5)

No limit

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷376 1.E

F -

P

Py

u

b y

2.75

j


£

æ

è

çç

ö

ø

÷÷

³

ì

íï

îï

ü

ýï

þï

112

1 49

.

. /

E

F -

P

P

E F

y

u

b y

y

2.33j

£é

ëê

ù

ûú

E

F

P

Py

u

b y

57. 1- 0.74j

( )£ +

£

ì

íï

îï

ü

ýï

þï

0.48E

16.5

260

F Fy y

BOXb t

f

h tc w

£ E Fy112. /

As for I-shapes

£ E Fy1 40. /

As for I-shapes

No limit

£ 970 Fy

CHANNELb tf

f

h tc w

As for I-shapes As for I-shapes


No limitAs for I-shapes

T-SHAPEb tf

f2

d t w

As for I-Shapes

03. /E Fy

As for I-Shapes

£ E Fy075. /No limitNo limit

ANGLE b t 03. /E Fy £ E Fy0 45. / No limit

DOUBLE-ANGLE

(Separated)

b t 03. /E Fy £ E Fy0 45. / No limit

PIPE D t £ E F

y0.0714 £ E F y0309. £ E F

y0 448.

ROUND BAR ¾ Assumed Noncompact

RECTAN-GULAR

b/h or h/b 2.5 No limit No limit

GENERAL/

SD Section¾ Assumed Noncompact

Table V-2Limiting Width-Thickness Ratios for

Classification of Sections in Flexure based on AISC-LRFD




Width-Thickness

Ratio

(l)


(l ps)

NONCOMPACT(Uniform

Compression)(M M22 33 0» » )

(l r )

I-SHAPE

b tf f2

(rolled)£

E

Fy

0 3. £ E F y056.

b tf f2

(welded)£

E

Fy

0 3. £ E F y056.

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷314 1.E

F -

P

Py

u

b y

1.54j


£æ

è

çç

ö

ø

÷÷ ³ìíï

îï

üýï

þï112 1 49. .

E

F -

P

P

E

Fy

u

b y y

2.33j

£ E F y1 49.

BOXb t

f

h tc w

0 64.E

Fy

Not applicable

£ E F y0 64.

£ E F y1 49.

CHANNEL,DOUBLE CHANNEL

b tf f

h tc w



T-SHAPEb tf

f2

d t w


As for I-shapes

£ E F y075.

ANGLE b t

0 3.E

Fy

£ E F y0 45.


b t

0 3.E

Fy

£ E F y0 45.

PIPE D t

0 044.E

Fy

£ E F y0114.

Table V-3Limiting Width-Thickness Ratios for



(0.9-0.2SDS) DL ± W 0 EL (ASCE 9.5.2.7.1, 2.3, LRFD SEIS MIC 4.1)

(1.2 + 0.2SSDS) DL + 1.0 LL ± W 0 EL

(ASCE 9.5.2.7.1, 2.3.2, LRFD SEIS MIC 4.1)

where, W 0 is the seis mic force am pli fi ca tion fac tor which is re quired to ac count forstruc tural overstrength. The de fault value of W 0 is taken as 3.0 in the pro gram. Ifthe user de fines one or more auto-seis mic loads, then the value of W 0 de fined foreach auto-seis mic load cases. Also if spe cial seis mic data is de fined by the user, the user spec i fies an W 0 value, and the user re quests the pro gram to in clude the spe cialseis mic de sign data, then the user spec i fied W 0 takes pre ce dence over the de faultval ues and those de fined for the auto-seis mic load cases. More over, W 0 can beover writ ten for each in di vid ual mem ber. The over writ ten W 0 gets the high est pre -ce dence. The guide lines for se lect ing a rea son able value for W 0 can be found inLRFD SEIS MIC sec tion 4.1 and Ta ble I-4-1.

These above com bi na tions are in ter nal to the pro gram. The user does NOT need tocre ate ad di tional load com bi na tions for these load com bi na tions. The spe cial cir -cum stances for which these load com bi na tions are ad di tion ally checked are de -scribed later in this chap ter as ap pro pri ate. The spe cial load ing com bi na tion fac torsare ap plied di rectly to the pro gram load cases. It is as sumed that any re quired scal -ing (such as may be re quired to scale re sponse spec tra re sults) has al ready been ap -plied to the pro gram load cases.


When us ing the AISC-LRFD99 code, the pro gram design as sumes that a P-Danaly sis has been per formed so that mo ment mag ni fi ca tion fac tors for mo mentscaus ing sidesway can be taken as unity. It is recommended that the P-D analy sis bedone at the fac tored load level of 1.2 DL plus 1.0 LL (White and Hajjar 1991).


The nom i nal strengths for ax ial com pres sion and flex ure are de pend ent on the clas -si fi ca tion of the sec tion as Seis mi cally com pact, Com pact, Noncompact, Slen der or



Too Slen der. Pro gram clas si fies in di vid ual mem bers ac cord ing to the lim it ingwidth/thick ness ra tios given in Table V-2, and Table III-3 (LRFD B5.1, A-G1, Ta -ble A-F1.1, LRFD SEIS MIC Ta ble I-8-1, HSS Ta ble 2.2-1). The def i ni tion of thesec tion prop er ties re quired in these ta bles is given in Figure V-1 and Table V-1.More over, spe cial con sid er ations are re quired re gard ing the lim its of width-thick -ness ra tios for Com pact sec tions in Seis mic zones and Noncompact sec tions withcom pres sive force as given in Table III-3. If the lim its for Slen der sec tions are notmet, the sec tion is clas si fied as Too Slen der. Stress check of Too Slen der sec tionsis be yond the scope of the pro gram.

In gen eral the de sign sec tions need not nec es sar ily be Com pact to sat isfyAISC-LRFD99 codes. How ever, for cer tain spe cial seis mic cases they have to beCom pact and have to sat isfy spe cial slen der ness re quire ments. See sub sec tion“Seis mic Re quire ments” later in this man ual. The sec tions which do sat isfy thesead di tional re quire ments are clas si fied and re ported as “SEIS MIC” in the pro gram.These spe cial re quire ments for clas si fy ing the sec tions as “SEIS MIC” in the pro -gram are given in Table III-3 (AISC SEIS MIC 8.2, Ta ble I-8-1). If these cri te ria are not sat is fied, when the code re quires them to be sat is fied, the user must mod ify thesec tion prop erty. In this case the pro gram gives an er ror mes sage in the out put file.

In clas si fy ing web slen der ness of I-shapes, Box, and Chan nel sec tions, it is as -sumed that there are no in ter me di ate stiff en ers. Dou ble an gles are con ser va tivelyas sumed to be sep a rated.

Calculation of Factored Forces

The fac tored mem ber loads that are cal cu lated for each load com bi na tion are Pu , M u33 , M u22 , Vu2 and Vu3 cor re spond ing to fac tored val ues of the ax ial load, the ma -jor mo ment, the mi nor mo ment, the ma jor di rec tion shear force and the mi nor di -rec tion shear force, re spec tively. These fac tored loads are cal cu lated at each of thepre vi ously de fined sta tions.

For load ing com bi na tions that cause com pres sion in the mem ber, the fac tored mo -ment M u (M u33 and M u22 in the cor re spond ing di rec tions) is mag ni fied to con sidersec ond or der ef fects. The mag ni fied mo ment in a par ticu lar di rec tion is given by:

M = B M + B Mu nt lt1 2 , where (LRFD C1-1, SAM 6)

B1 = Mo ment mag ni fi ca tion fac tor for non- sidesway mo ments,B2 = Mo ment mag ni fi ca tion fac tor for sidesway mo ments,M nt = Fac tored mo ments not caus ing sidesway, andM lt = Fac tored mo ments caus ing sidesway.

Calculation of Factored Forces 103


The mo ment mag ni fi ca tion fac tors are as so ci ated with cor re spond ing di rec tions.The mo ment mag ni fi ca tion fac tor B1 for mo ments not caus ing sidesway is given by

( )B =

C

P P m

u e

1

11 -³ 1.0 , where (LRFD C1-2, SAM 6-2)

Pe1 is the Eu ler buck ling load (PEI

kLe1

2

2= p

( ) ), (LRFD C1-2)


Cm =

1.00 , if unbraced length is overwritten,


1.00 , if end unrestrained,

0.6 0.4 i-M

Ma

b

, f no transverse loading,

0.85 , if trans. load, end restrained, and

1.00 , if trans. load, end unrestrained.

ì

í

ïïïï

î

ïïïï

(LRFD C1-3)

M Ma b is the ra tio of the smaller to the larger mo ment at the ends of the mem -ber, M Ma b be ing pos i tive for dou ble cur va ture bend ing and neg a tive for sin -gle cur va ture bend ing. For sin gle an gle, the fac tored mo ments about the geo -met ric axes are trans formed to get the fac tored mo ments about the prin ci palaxes for com put ing M Ma b . The pro gram de faults Cm to 1.0 if the un bracedlength fac tor, l, of the mem ber is re de fined by ei ther the user or the pro gram,i.e., if the un braced length is not equal to the length of the mem ber. The usercan over write the value of Cm for any mem ber. Cm as sumes two val ues, Cm22

and Cm33 , as so ci ated with the ma jor and mi nor di rec tions.

The mag ni fi ca tion fac tor B1 , must be a pos i tive num ber. There fore Pu must be lessthan Pe1 . If Pu is found to be greater than or equal to Pe1 , a fail ure con di tion is de -clared.

The pro gram design as sumes the analy sis in cludes P-D ef fects, there fore B2 istaken as unity for bend ing in both di rec tions. It is suggested that the P-D analy sis bedone at the fac tored load level of 1.2 DL plus 1.05 LL (LRFD C2.2). See also White and Hajjar (1991).

For sin gle an gles, where the prin ci pal axes of bend ing are not co in ci dent with thegeo met ric axes (2-2 and 3-3), the pro gram con ser va tively uses the max i mum of

104 Calculation of Factored Forces


K l22 22 and K l33 33 for de ter min ing the ma jor and mi nor di rec tion Eu ler buck ling ca -pac ity, Pe1 . The re sult ing Pe1 is used for ei ther di rec tion of bend ing.

If the pro gram as sump tions are not satisfactory for a par ticu lar struc tural model ormem ber, the user has a choice of ex plic itly speci fy ing the val ues of B1 and B2 forany mem ber.


When us ing the AISC-LRFD99 op tion, the fol low ing Fram ing Sys tems are rec og -nized (AISC SEIS MIC 9, 10, 11, 12, 13, 14, 15):


• In ter me di ate Mo ment Frame (IMF)

• Spe cial Mo ment Frame (SMF)

• Or di nary Con cen tri cally Braced Frame (OCBF)

• Spe cial Con cen tri cally Braced Frame (SCBF)

• Ec cen tri cally Braced Frame (EBF)

• Spe cial Truss Mo ment Frame (STMF)

By de fault the frame type is taken as Spe cial Mo ment-Re sist ing Frame (SMRF) inthe pro gram. How ever, the frame type can be over writ ten in the Pref er ence form tochange the de fault and in the Overwrites form on a mem ber by mem ber ba sis. If any mem ber is as signed with a frame type, the change of the frame type in the Pref er -ence will not mod ify the frame type of the in di vid ual mem ber for which it is as -signed. Cur rently the pro gram does not ap ply any spe cial re quire ment for STMF.

The spe cial seis mic re quire ments checked by the pro gram for mem ber de sign arede pend ent on the type of fram ing used and are de scribed be low for each type offram ing. Thus spe cial pro vi sions for build ings are only ap plied if the build ingframe is clas si fied as seis mic de sign cat e gory (SDC) D or E. (AISC SEIS MIC 1). No spe cial re quire ment is checked for frames with seis mic de sign cat e gory A, B, orC.

Or di nary Mo ment Frames (OMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported (AISC SEIS MIC 11):


105



107


SectionType


I-SHAPE h

h ifh

tE f

tE

f h t

E

fi

e

w

w

w

=

£

-é

ëê

ù

ûú

, . / ,

..

( / ),

149

191 10 381

fh

tE f

w

>

ì

í

ïï

î

ïï

1 49. / .


A g

= )LRFD A-B5-12

BOX

h

h ifh

tE f

tE

f h t

E

fi

e

w

w

w

=

£

-é

ëê

ù

ûú

, . / ,

..

( / ),

1 40

1 91 10 381

fh

tE f

w

>

ì

í

ïï

î

ïï

1 40. / .


A g

= )

b

b ifb

tE f

tE

f b t

E

fi

e

f

f

f

=

£

-é

ëê

ù

ûú

, . / ,

..

( / ),

1 40

1 91 10 381

fb

tE f

f

>

ì

í

ïï

î

ïï

1 40. / .

(compr. or flexure, f Fy= )

LRFD A-B5-12

LRFD A-B5-11

CHANNEL h

h ifh

tE f

tE

f h t

E

fif

e

w

w

w

=

£

-é

ëê

ù

ûú

, . / ,

..

( / ),

149

191 10 34 h

tE f

w

>

ì

í

ïï

î

ïï

149. / .


A g

= ) LRFD A-B5-12

T-SHAPE b be = LRFD A-B5.3b

DOUBLE-ANGLE

(Separated)

b be = LRFD A-B5.3b

ANGLE b be = LRFD A-B5.3b

PIPE

( )Q

ifD

t F

D t

E

Fif

D

t

E

F

ay

y y

=£

+ >

ì1

0114

, ,

,.

.

0.114 E

0.0379 2

3

íïï

îïï

(compression only)LRFD A-B5-13

HSS 4.2-5

ROUNDBAR

Not applicable ¾

RECTAN-GULAR

b be = LRFD A-B5.3b

Table V-5Effective Width for Stiffened Sections

• When P

Pu

njin col umns due to pre scribed load ing com bi na tions with out con sid -

er ation of am pli fied seis mic load is greater than 0.4, the ax ial com pres sive andten sile strengths are checked in ab sence of any ap plied mo ment and shear forthe fol low ing Spe cial Seis mic Load Com bi na tions (AISC SEIS MIC 8.3).

( )0 9 0 2 0. .- ±S DL ELDS W (AISC SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2)

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W

(AISC SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2)

Intermediate Mo ment Frames (IMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported (AISC SEIS MIC 10):

• When P

Pu



( )0 9 0 2 0. .- ±SDS DL ELW (AISC SEIS MIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2)

( )12 0 2 10 0. . .+ + ±SDS DL LL ELW


Spe cial Moment Frames (SMF)

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported (AISC SEIS MIC 9):

• When P

Pu






( )12 0 2 10 0. . .+ + ±S DL LL ELDS W


• The I-, Chan nel-, and Dou ble-Chan nel Shaped beams and col umns are ad di -tion ally checked for com pact ness cri te ria as de scribed in Ta ble VI-1 (AISCSEIS MIC 9.4, 8.2, Ta ble I-8-1). If this cri te ria is sat is fied the sec tion is re -ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca tions. If this cri -te ria is not sat is fied the, the pro gram is sues an er ror mes sage.

• The pro gram checks the lat er ally un sup ported length of beams to be less than

( )0 08. E Fy yr . If this cri te ria is not sat is fied, the pro gram is sues an er ror mes -

sage.(AISC SEIS MIC 9.8)

• The pro gram checks the slen der ness ra tio, L®, for col umns to be less than 60(AISC SEIS MIC 9.7.b(2)). If the cri te ria is not sat is fied, the pro gram is sues aner ror mes sage.

Ordinary Concentrically Braced Frames (OCBF)


• The col umns and beams (NOT braces) are de signed for the fol low ing spe cialam pli fied seis mic load com bi na tions (AISC SEIS MIC 14.2).

( )0 9 0 2 0. .- ±S DL ELDS W (AISC SEIS MIC 14.2, ASCI 9.5.2.7.1, 2.3.2.1,

2.3.2)

( )12 0 2 10 0. . .+ + ±S DL LL ELDS W (AISC SEIS MIC 14.2, ASCI 9.5.2.7.1,

2.3.2)

• The max i mum Kl

r ra tio of the braces for V or in verted-V con fig u ra tions is

checked not to ex ceed 4 23.E

Fy

(AISC SEIS MIC 14.2). If this cri te ria is not

met, an er ror mes sage is re ported in the out put.

Spe cial Con cen tri cally Braced Frames (SCBF)



109


• When P

Pu




( )12 0 2 10 0. . .+ + ±S DL LL ELDS W


• All beam, col umns and brace mem bers are checked to be Com pact ac cord ing to Table V-2(AISC SEIS MIC 13.5, 13.2d, 8.2, Ta ble I-8-1). If this cri te ria is sat -is fied the sec tion is re ported as SEIS MIC as de scribed ear lier un der sec tionclas si fi ca tions. If this cri te ria is not sat is fied the pro gram is sues an er ror mes -sage.

This spe cial cri te ria is only checked for I, Chan nel, Dou ble-Chan nel, An gle,Dou ble-An gle, Box and Pipe sec tions.

• The com pres sive strength for braces is taken as j c nP .

P Pu c n£ j (AISC SEIS MIC 13.26)

• The max i mum K l r ra tio of the braces is checked not to ex ceed 5.87F

E

y. If

this check is not met, the pro gram is sues an er ror mes sage.

Note: Beams in ter sected by Chev ron (V or in verted-V) braces are NOT cur -rently checked to have a strength to sup port loads for the fol low ing two con di -tions (AISC SEIS MIC 13.4a):


b A beam that is in ter sected by braces shall be de signed to re sist the ef fects ofload com bi na tions stip u lated by the code, ex cept that a load q b shall be sub sti -tuted for the term E. q b is given by the dif fer ence of R F Ay y for the ten sionbrace and 0 3. j c nP for the com pres sion brace.





111


Figure V-2Ec cen tri cally Braced Frame Con figu ra tions

Ec cen tri cally Braced Frames (EBF)

For this fram ing sys tem, the pro gram looks for and rec og nizes the ec cen tri callybraced frame con fig u ra tions shown in Fig ure VI-II. The fol low ing ad di tional re -quire ments are checked or re ported for the beams, col umns and braces as so ci atedwith these con fig u ra tions (AISC SEIS MIC 15).

• When P

Pu




( )12 0 2 10 0. . .+ + ±S DL LL ELDS W


• The I-shaped, Chan nel-shaped, and Dou ble-Chan nel Shaped beams are ad di -tion ally checked for com pact ness cri te ria as de scribed in Ta ble VI-III (AISCSEIS MIC 15.2, 8.2, Ta ble I-8-1). If this cri te ria is sat is fied the sec tion is re -ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca tions. If this cri -te ria is not sat is fied the user must mod ify the pro gram is sues an er ror mes sage.

• The link beam yield strength, Fy , is checked not to ex ceed the fol low ing (AISC SEIS MIC 15.2):

Fy £ 50 ksi (AISC SEIS MIC 15.2)

If the check is not sat is fied, the pro gram is sue an er ror mes sage.

• The shear strength for link beams is taken as fol lows (AISC SEIS MIC 15.2):

V Vu v n£ j , (AISC SEIS MIC 15.2)

where,

( )j j jV V M en pa pa= min , 2 , (AISC SEIS MIC 15.2)

V VP

Ppa p

u

y

= -æ

è

çç

ö

ø

÷÷1

2

, (AISC SEIS MIC 15.1)



M MP

Ppa p

u

y

= -é

ëê

ù

ûú1.18 1 , (AISC SEIS MIC 15.2)

V F d t tp y f w= -0.6 ( )2 , (AISC SEIS MIC 15.2)

M Z Fp y= , (AISC SEIS MIC 15.2)

j j= v (de fault is 0.9) , (AISC SEIS MIC 15.2)

P A Fy g y= . (AISC SEIS MIC 15.2)

• If P A Fu g y> 0.15 , the link beam length, e, is checked not to ex ceed the fol low -ing (AISC SEIS MIC 15.2):

e

A

A

M

Vif

A

Aw

g

p

p

w

g£

- ¢é

ëê

ù

ûú

é

ëê

ù

ûú ¢ ³1.15 0.5 1.6 0.3 ,

1

r r

.6 0.3 ,M

Vif

A

A

p

p

w

g

é

ëê

ù

ûú ¢ <

ì

í

ïï

î

ïï

r

(AISC SEIS MIC 15.2)

where,

A d t tw f w= -( )2 , and (AISC SEIS MIC 15.2)

¢ =r P Vu u . (AISC SEIS MIC 15.2)

If the check is not sat is fied, the pro gram re ports an er ror mes sage.

• The link beam ro ta tion, q, of the in di vid ual bay rel a tive to the rest of the beamis cal cu lated as the story drift D M times bay length di vided by the to tal lengthsof link beams in the bay. The link beam ro ta tion, q, is checked as fol lows(AISC SEIS MIC 15.2).

q £ 0.08 ra dian , where link beam clear length, e M Vs s£ 1.6 ,

q £ 0.03 ra dian , where link beam clear length, e M Vs s³ 2.6 , and


• The beam strength out side the link is checked to be at least 1.1 times the beamforces cor re spond ing to the con trol ling link beam shear strength (AISC SEIS -


113


MIC 15.6). The con trol ling link beam nom i nal shear strength is taken as fol -lows:

( )min ,V M epa pa2 , (AISC SEIS MIC 15.6, 15.2)

The val ues of Vpa and M pa are cal cu lated fol low ing the pro ce dure de scribedabove (AISC SEIS MIC 15.2). The cor re spon dence be tween brace force andlink beam force is ob tained from the as so ci ated load cases, which ever has thehigh est link beam force of in ter est.

All braces are checked to be at least com pact per reg u lar LRFD code (LRFDSEIS MIC 15.6). If this cri te ria is not sat is fied, the pro gram is sues an er ror mes -sage.

The brace strength is checked for 1.25Ry times the brace forces cor re spond ingto the con trol ling link beam nom i nal shear strength (AISC SEIS MIC 15.6). The con trol ling link beam nom i nal shear strength and the cor re spond ing forces are ob tained by the pro cess de scribed ear lier.

The I-, Chan nel-, and Dou ble-Chan nel- shaped col umn sec tions are checked tobe at least com pact per reg u lar LRFD code (LRFD SEIS MIC 8.2, Ta ble I-8-1,LRFD B.5.1). If this cri te rion is not sat is fied, the pro gram is sues an er ror mes -sage.

• The col umn strength is checked for 1.1Ry times the col umn forces cor re spond -ing to the con trol ling link beam nom i nal shear strength (AISC SEIS MIC 15.8).The con trol ling link beam nom i nal shear strength and the cor re spond ing forces are ob tained by the pro cess de scribed above.

Note: Ax ial forces in the beams are in cluded in check ing the beams. The user is re -minded that us ing a rigid di a phragm model will re sult in zero ax ial forces in thebeams. The user must dis con nect some of the col umn lines from the di a phragm toal low beams to carry ax ial loads. It is rec om mended that only one col umn line perec cen tri cally braced frame be con nected to the rigid di a phragm or a flex i ble di a -phragm model be used.

Calculation of Nominal Strengths

The nomi nal strengths in com pres sion, ten sion, bend ing, and shear are com putedfor Com pact, Non com pact, and Slen der sec tions ac cord ing to the fol low ing sec -tions. The nomi nal flex ural strengths for all shapes of sec tions are cal cu lated basedon their prin ci pal axes of bend ing. For the Rec tan gu lar, I, Box, Chan nel, Cir cu lar,Pipe, T, and Double- angle sec tions, the prin ci pal axes co in cide with their geo met -

114 Calculation of Nominal Strengths


ric axes. For the An gle sec tions, the prin ci pal axes are de ter mined and all com pu ta -tions ex cept shear are based on that.

For all sec tions, the nom i nal shear strengths are cal cu lated for di rec tions along their geo met ric axes which co in cide with the prin ci pal axes for most of the sec tion de -sign in the pro gram ex cept the an gle sec tion.

The strength re duc tion fac tor, j , is taken as fol lows (LRFD A5.3):

j ty = Re sis tance fac tor for ten sion yield ing, 0.9 (LRFD D1, H1, SAM 2, 6)j tf = Re sis tance fac tor for ten sion frac ture, 0.75 (LRFD D1, H1, SAM 2, 6)

j c = Re sis tance fac tor for com pres sion, 0.85 (LRFD E2, E3, H1)j c = Re sis tance fac tor for com pres sion in an gles, 0.90 (LRFD SAM 4, 6)j b = Re sis tance fac tor for bend ing, 0.9 (LRFD F1, H1, A-F1, A-G2, SAM 5)j v = Re sis tance fac tor for shear, 0.9 (LRFD F2, A-F2, A-G3, SAM 3)

j T = Re sis tance fac tor for ten sion, 0.7 (LRFD HSS 6.1 HSS 7.2)

The val ues shown with the j fac tors are the de fault val ues and they are code spec i -fied. How ever, user has the op tion to mod ify the fac tors in the Pref er ences menu.The spec i fied nom i nal strengths should be based on the prin ci pal axes of bend ing.

Compression Capacity

The nomi nal compression strength is the minimum value ob tained from flex uralbuck ling, tor sional buckling and flexural- torsional buck ling. The strengths are de -ter mined ac cord ing to the fol low ing sub sec tions.

For mem bers in com pres sion, if Kl r is greater than 200, a mes sage to that ef fect isprinted (LRFD B7, SAM 4, HSS 2.3). For sin gle an gles, the mini mum radius of gy -ra tion, rz , is used in stead of r22 and r33 in com put ing Kl r .

Flex ural Buck ling

The nomi nal ax ial com pres sive strength, Pn , de pends on the slen der ness ra tio, Kl r, and its associated value, l c , where

Kl

r

K l

r

K l

r= ì

íî

üýþ

max ,33 33

33

22 22

22

, and

lp

c =Kl

r

F

E

y . (LRFD E2-4, SAM 4, HSS 4.2-4)

Calculation of Nominal Strengths 115




Pn for Com pact or Non com pact sec tions is evalu ated for flex ural buck ling as fol -lows:

P = A Fn g cr , where (LRFD E2-1, SAM 4)

( )F = Fcr yc0.658l2

, for l c 1.5£ , and (LRFD E2-2)

F = Fcr y

0.877

c2l

é

ëê

ù

ûú , for l c > 1.5. (LRFD E2-3)

Pn for Slender sec tions is evalu ated for flex ural buck ling as fol lows:

P = A Fn g cr , where (LRFD A-B3d, SAM 4, HSS 4.2-1)

( )F = Q Fcr yc0.658Ql2

, for l c 1.5Q £ , and(LRFD A-B5-15, SAM 4-1,)

F = Fcr y

0.877

c2l

é

ëê

ù

ûú , for l c > 1.5Q . (LRFD A-B5-16, SAM 4-2)

The re duc tion fac tor, Q, for all com pact and non com pact sec tions is au to mat i callybe comes equal to1. For slen der sec tions, Q is com puted as fol lows:

Q Q Qs a= , where (LRFD A- B5-17, SAM 4)

Q s = re duc tion fac tor for un stiff ened slen der ele ments, and (LRFD A-B5.3a)

Q a = re duc tion fac tor for stiff ened slen der ele ments. (LRFD A-B5.3c)

The Q s fac tors for slen der sec tions are cal cu lated as de scribed in Table V-4 (LRFDA-B5.3a). The Q a fac tors for slen der sec tions are cal cu lated as the ra tio of ef fec tive cross- sectional area and the gross cross- sectional area (LRFD A-B5.3c).

QA

Aa

e

g

= (LRFD A-B5-14, HSS 4.2-6)


( )A A b b te g e= - -å

be for un stiff ened el e ments is taken equal to b, and be for stiff ened el e ments istaken equal to or less than b as given in Table V-5 (LRFD A-B5.3b). For webs in I,



box, and Chan nel sec tions, he is used as be and h is used as b in the above equa tion.For pipe sec tions, the Q a is cal cu lated di rectly from ta ble VI-5.


Pn for flexural- torsional buck ling of Double- angle and T- shaped com pres sionmem bers whose ele ments have width- thickness ra tios less than l r is given by

P = A Fn g crft , where (LRFD E3-1)

F = F F

H

F F H

F Fcrft

cr crz cr crz

cr

2 2

22

1 14+æ

èçç

ö

ø÷÷ - -

+( crz )2

é

ëêê

ù

ûúú , where (LRFD E3-1)

FGJ

Arcrz =

02 ,

Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

,

r0 = Po lar ra dius of gy ra tion about the shear cen ter, (LRFD A-E 3-8)

x y0 0, are the coor di nates of the shear cen ter with re spect to the cen troid, x 0 0= for doubleangle and T- shaped mem bers (y-axis of sym me -

try),

Fcr2 is de ter mined ac cord ing to the equa tion LRFD E2 for flex ural

buck ling about the mi nor axis of sym me try for lp c

yKl

r

F

E= 22

22

.

Torsional and Flex ural-Torsional Buck ling

The strength of a I, Channel, Dou ble-Chan nel, Tee, An gle and Dou ble-An gleshaped com pres sion mem ber, Pn , for the limit states of tor sional and flexural- torsional buck ling is de ter mined as fol lows:

P = A Fn g cr , where (LRFD A- E3-1)

( )F = Q Fcr ye0.658Ql2

, for l e 1.5Q £ , and (LRFD A-E3-2)

F = Fcr y

0.877

e2l

é

ëê

ù

ûú , for l e > 1.5Q . (LRFD A-E3-3)

In the above equa tions, the slen der ness pa rame ter l e is cal cu lated as



l e =F

F

y

e

, (LRFD A-E3-4)

where Fe is cal cu lated as fol lows:

• For I sec tions:

( )F

EC

K lGJ

I Ie

w

z z

= +é

ë

êê

ù

û

úú +

p 2

222 33

1 (LRFD A- E3-5)


F = F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Channels:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Sin gle-angles sec tions with equal legs:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Single- angle sec tions with une qual legs, Fe is cal cu lated as the mini mumreal root of the fol low ing cu bic equa tion (LRFD A- E3-7):

( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e- - - - - -33 22

222

02

02

2 F Fy

re e- =33

02

02

0) ,

where,


try),

r x yI I

Ag

0 02

02 22 33= + + +




Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

, (LRFD A- E3-9)

( )F

E

K l re33

2

33 33 33

2= p

, (LRFD A- E3-10)

( )F

E

K l re22

2

22 22 22

2= p

, (LRFD A- E3-11)

( )F

EC

K lGJ

Arez

w

z z

= +é

ë

êê

ù

û

úú

p 2

202

1 , (LRFD A- E3-12)


K z is the ef fec tive length fac tor for tor sional buck ling, and it is taken equal to K 22 in pro gram,



For an gle sec tions, the prin ci pal mo ment of in er tia and ra dius of gy ra tion are usedfor com put ing Fe . Also, the maxi mum value of Kl, i.e, max( , )K l K l22 22 33 33 , is used in place of K l22 22 or K l33 33 in cal cu lat ing Fe22 and Fe33 in this case.

The limit state of tor sional and flex ural-tor sional buck ling is ig nored for closed sec -tions, such as cir cu lar, rect an gu lar, Gen eral, and Sec tion De signer sec tions.

Tension Capacity

The nomi nal ax ial ten sile strength value Pn is based on the gross cross- sectionalarea and the yield stress.

P A Fn g y= (LRFD D1-1, SAM 2, HSS 3.1-1)

Also, the frac ture based on net sec tion is checked as fol lows:

P A Fn e u= (LRFD D1-2, SAM 2, HSS 3.1-2)



where Ae is the ef fec tive net area. By de fault is taken as Ag . User has op tion to mod -ify the net area to to tal area i.e., A Ae g/ in the over write. For Pn based on net area

frac ture limit state, the as so ci ated j fac tor is dif fer ent from yield ing.

It should be noted that no net sec tion checks are made. For mem bers in ten sion,if l r is greater than 300, a mes sage to that ef fect is printed (LRFD B7, SAM 2, HSS 2.3). For sin gle an gles, the min i mum ra dius of gy ra tion, rz , is used in stead of r22 and r33 in com put ing Kl r .

Nominal Strength in Bending

The nominal bend ing strength de pends on the fol low ing cri te ria: the geo met ricshape of the cross- section, the axis of bend ing, the com pact ness of the sec tion, anda slen der ness pa rame ter for lateral- torsional buck ling. The nomi nal strengths for all shapes of sec tions are cal cu lated based on their prin ci pal axes of bend ing. For theRec tan gu lar, I, Box, Chan nel, Cir cu lar, Pipe, T, and Double- angle sec tions, theprin ci pal axes co in cide with their geo met ric axes. For the Sin gle An gle sec tions,the prin ci pal axes are de ter mined and all com pu ta tions re lated to flex ural strengthsare based on that. The nomi nal bend ing strength is the minimum value ob tained ac -cord ing to the limit states of yield ing, lateral- torsional buck ling, flange lo cal buck -ling, and web lo cal buck ling, as fol lows (LRFD F1, A-F1, Ta ble A-F1.1):

Yielding

The flex ural de sign strength of beams, de ter mined by the limit state of yield ing is:

M Z F S Fp y y= £ 1.5 (LRFD F1-1, SAM 5.1.3, HSS 5.1)

Lateral-Torsional Buckling

Doubly Symmetric Shapes and Channels

For I, Chan nel, Dou ble chan nel, Box, and Rec tan gu lar shaped members bent aboutthe ma jor axis, the mo ment ca pac ity is given by the fol low ing equa tion (LRFD F1):



M =

M if L L

C M - M - ML - L

L -n

p b p

b p p r

b p

r

33

33

33 33 33

, ,£

( ) L

M if L L L

M M if L

p

p p b r

cr p

æ

è

çç

ö

ø

÷÷

é

ëêê

ù

ûúú

£ < £

£

33

33 33

, ,

, b r L>

ì

í

ïïï

î

ïïï .

(LRFD F1-1, F1-2, F1- 12)

where,

M n33 = Nom i nal ma jor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 , (LRFD F1.1)M r33 = Ma jor lim it ing buck ling mo ment,

( )F F Sy r- 33 for I-shapes, dou ble chan nel and chan nels, (LRFD F1-7)

and F Sy eff , 33 for rect an gu lar bars and boxes, (LRFD F1-11)M cr33 = Crit i cal elas tic mo ment,

C

LEI GJ +

E

LI Cb

b b

w

p p22

2

22

æ

èçç

ö

ø÷÷

for I-shapes, chan nels, and dou ble-chan nels (LRFD F1-13)

2

22

E C JA

L rb

b

for boxes and rec tan gu lar bars, (LRFD F1-14, TableA-F1.1)

Lb = Lat er ally un braced length, l22 ,

L p = Lim it ing lat er ally un braced length for full plas tic ca pac ity,

176 22. rE

Fy

for I-shapes, chan nels, and dou ble chan nels, (LRFD F1-4)0 13 22

33

. r E

MJA

p

for boxes and rect an gu lar bars, (LRFD F1-5)

Lr = Lim it ing lat er ally un braced length forin elas tic lat eral-tor sional buck ling,



[ ]r X

F F + X F - F

y r

y r22 1

21-

ìíî

üýþ

1+ ( )21

2

12

for I-shapes and chan nels, and (LRFD F1-6)

2 22

33

r E JA

M r

for boxes and rect an gu lar bars, (LRFD F1-10)

X1 =p

S

EGJA

33 2 , (LRFD F1-8)

X 2 = 422

33

2C

I

S

GJw æ

èç

ö

ø÷ , (LRFD F1-9)

Cb =12.5

2.5

M

M + M + M + MA B C

max

max 3 4 3 , and (LRFD F1-3)

M max , M M MA B C, ,and are ab so lute val ues of max i mum mo ment, ¼ point, cen terof span and ¾ point ma jor mo ments re spec tively, of the un braced segment of themem ber. In the ab sence of phys i cal model of lat eral brac ing points in the pro gram,the braced length is as sumed to be lo cated in the mid dle of the mem ber. Cb shouldbe taken as 1.0 for can ti le vers. How ever, the pro gram is un able to de tect whetherthe mem ber is a can ti le ver. The user should over write Cb for can ti le vers. The

pro gram also de faults Cb to 1.0 if the mi nor un braced length, l22 , of the mem ber isover written by the user (i.e. it is not equal to the length of the mem ber). The usercan over write the value of Cb for any mem ber.

For I, Chan nel, Dou ble Chan nel, Box, and Rec tan gu lar shaped members bent about the minor axis, the mo ment ca pac ity is given by the fol low ing equa tion:

M = M = Z F S Fn p y y22 22 22 22£ 1.5 (LRFD F1)

For pipes and cir cu lar bars bent about any axis,

M = M = Z F S Fn p y y£ 1.5 . (LRFD F1)

T-sections and Double Angles

For T- shapes and Dou ble-an gles the nomi nal ma jor bend ing strength is given as,

M = EI GJ

LB + + Bn

b

3322 21

p éë

ùû , where (LRFD F1- 15)

M F Sn y33 33£ 1.5 , for posi tive mo ment, stem in tension (LRFD F1.2c)



M F Sn y33 33£ , for negative mo ment, stem in com pres sion (LRFD F1.2c)

Bd

L

I

Jb

= ± 2.3 22 . (LRFD F1- 16)

The pos i tive sign for B ap plies for ten sion in the stem of T-sec tions or the out -stand ing legs of dou ble an gles (pos i tive mo ments) and the neg a tive sign ap plies forcom pres sion in stem or legs (neg a tive mo ments).

For T- shapes and dou ble an gles the nomi nal mi nor bend ing strength is as sumed as,

M = S Fn y22 22 .

Single Angles

The nomi nal strengths for Single- angles are cal cu lated based on their prin ci palaxes of bend ing. The nomi nal ma jor bend ing strength for Single- angles for thelimit state of lat eral-tor sional buck ling is given as fol lows (LRFD SAM 5.1.3):

M = M

MM Mn major

ob

y major

ob y m,

,

,0.92 0.17 1.5-é

ëê

ù

ûú £ ajor ob y major if M M, ,,£

M = M

MMn major

y major

ob

y major,

,

,.1.92 1 1.5-é

ë

êê

ù

û

úú

£17 M if M My major ob y major, ,, ,>

where,

M y major, = yield mo ment about the ma jor prin ci pal axis of bend ing, con sid er ing the pos si bil ity of yield ing at the heel and both of the leg tips,

M ob = elas tic l ateral-tor sional buck ling mo ment as cal cu lated be low.

The elas tic lat eral-tor sional buck ling mo ment, M ob , for equal- leg an gles is taken as

M CE b t

lob b= 0.46 2 2

, (LRFD SAM 5-5)

and for unequal- leg an gles the M ob is cal cu lated as

M ECI

llt rob b w w= + +é

ëùû

4.9 0.052minmin2

2 2b b( ) , (LRFD SAM 5-6)

where,




( )l l l= max ,22 33 ,

Imin = mi nor prin ci pal axis mo ment of in er tia,

Imax = major prin ci pal axis mo ment of in er tia,


bwAI

z w z dA z= +é

ëê

ù

ûú -ò

122 2

0

max

( ) , (LRFD SAM 5.3.2)




bw is a spe cial sec tion prop erty for an gles. It is posi tive for short leg in com pres -sion, nega tive for long leg in com pres sion, and zero for equal- leg an gles (LRFDSAM 5.3.2). How ever, for con ser va tive de sign in the program, it is al ways taken asnega tive for unequal- leg an gles.

Pipe and Circular sections

For pipe and cir cu lar sec tions, lat eral-tor sional buck ling is not con sid ered in thepro gram as it is not im por tant.

General and SD Sections

For General and SD sec tions the nomi nal ma jor and mi nor di rec tion bend ingstrengths are as sumed as,

M = S Fn y .

Note: S is used for the Gen eral shape be cause LTB and other buck ling cri te ria is un -known.

Flange Local Buckling

The flex ural de sign strength, M n , of Non com pact and Slender beams for the limitstate of Flange Lo cal Buck ling is cal cu lated as fol lows (LRFD A-F1):



For major di rec tion bend ing,

M =

M if

M M Mn

p p

p p r

p

r p

33

33

33 33 33

, ,l l

l l

l l

£

- --

-

æ

è( ) ç

ç

ö

ø

÷÷ < £

£ >

ì

í

ïïï

î

ïï

, ,

, .

if

M M if

p r

cr p r

l l l

l l33 33ï

(LRFD A-F1)

and for mi nor di rec tion bend ing,

M =

M if

M M Mn

p p

p p r

p

r p

22

22

22 22 22

, ,l l

l l

l l

£

- --

-

æ

è( ) ç

ç

ö

ø

÷÷ < £

£ >

ì

í

ïïï

î

ïï

, ,

, .

if

M M if

p r

cr p r

l l l

l l22 22ï

(LRFD A-F1)

where,

M n33 = Nomi nal ma jor bend ing strength,M n22 = Nomi nal mi nor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 ,M p22 = Mi nor plas tic mo ment, Z F S Fy y22 22£ 1.5 ,M r33 = Ma jor lim it ing buck ling mo ment,M r22 = Mi nor lim it ing buck ling mo ment, M cr33 = Ma jor buck ling mo ment,M cr22 = Mi nor buck ling mo ment, l = Con trol ling slen der ness pa rame ter, l p = Larg est value of l for which M Mn p= , andl r = Larg est value of l for which buck ling is ine las tic.

The pa rame ters l, l p , l r , M r33 , M r22 , M cr33 , and M cr22 for flange lo cal buck ling fordif fer ent types of shapes are given be low:



I Shapes, Channels, Double Channels

l =b

t

f

f2 , (for I sec tions) (LRFD B5.1, Ta ble A-F1.1)

l =b

t

f

f

, (for Chan nel sec tions) (LRFD B5.1, Ta ble A-F1.1)

l =-b s

t

f

f2 , (for Dou ble Chan nel sec tions) (LRFD B5.1, Ta ble A-F1.1)

l p

y

E

F= 0 38. , (LRFD B5.1, Ta ble A-F1.1)

l rL

L c

E

F

E

F k

=0 83

0 95

. ,

./

,

For rolled shape,

For welded shape,

ì

í

ïï

î

ïï

(LRFD Ta ble A-F1.1)

M F Sr L33 33= , (LRFD Ta ble A-F1.1)

M F Sr y22 22= , (LRFD Ta ble A-F1.1)

MS

E kS

crc

33

2 33

2 33

9=

0.69EFor rolled shape,

0 F

l

l

,

., or welded shape,

ì

íï

îï


MS

E kS

crc

22

2 22

2 22

9=

0.69EFor rolled shape,

0 F

l

l

,

., or welded shape,

ì

íï

îï


Fr = 10 ksi, For rolled shpae,

16.5 ksi, For welded shape.

ìíî

(LRFD A-F1)



Boxes

l 33 =

-

-

b t

t

b t

t

f w

f

f w

f

3

2

,

,

For rolled shape,

For welded shape,

ì

í

ïï

î

ïï

(LRFD B5.1, Ta ble A-F1.1,HSS 2.2)

l 22 =

-

-

( ),

( ),

h t

th t

t

f

w

f

w

3

2

For rolled shape,

For welded shape,

ì

í

ïï

î

ïï

(LRFD B5.1, Ta ble A-F1.1,HSS 2.2)

l p

y

E

F= 112. , (LRFD B5.1, Ta ble A-F1.1,HSS Ta ble 2.2-1)

l r

y

E

F= 140. , (LRFD B5.1, Ta ble A-F1.1, HSS Ta ble 2.2-1)

M F Sr y eff33 33= , , (LRFD Ta ble A-F1.1, HSS 5.1)

M F Sr y eff22 22= , , (LRFD Ta ble A-F1.1, HSS 5.1)

M F Scr y eff33 33= , , (LRFD Ta ble A-F1.1, HSS 5.1-6)

M F Scr y eff22 22= , , (LRFD Ta ble A-F1.1, HSS 5.1-6)


16.5 ksi, For welded shape,

ìíî

(LRFD A-F1)

Seff , 33 = ef fec tive ma jor sec tion modulus con sid er ing slen der ness, and

Seff , 22 = ef fec tive mi nor sec tion modulus con sid er ing slen der ness.


No lo cal buck ling is con sid ered for T sec tions and Dou ble an gles in the program. Ifspe cial con sid er ation is re quired, the user is ex pected to an a lyze this sep a rately.



Single Angles

The nom i nal strengths for Sin gle-an gles are cal cu lated based on their prin ci palaxes of bend ing. The nom i nal ma jor and mi nor bend ing strengths for Sin gle-an glesfor the limit state of flange lo cal buck ling are given as fol lows (LRFD SAM 5.1.1):

M =

F S ifb

t F

F S

F

n

y c

y

y c

y

1.5 0.54E

1.5 .93b t

0.54E

, ,£

- -

æ

0 1

è

ççççç

ö

ø

÷÷÷÷÷

é

ë

êêêêê

ù

û

úúúúú

< £, ,ifF

b

t Fy y

0.54E

0.91E

1.34Q 0.91E

F S ifb

t Fy c

y

, ,>

ì

í

ïïïïï

î

ïïïïï

where,

Sc = sec tion modulus for com pres sion at the tip of one leg,

t = thick ness of the leg un der con sid er ation,

b = length of the leg un der con sid er ation, and

Q = strength re duc tion fac tor due to lo cal buck ling.

In cal cu lat ing the bend ing strengths for Sin gle-an gles for the limit state of flangelo cal buck ling, the ca pac i ties are cal cu lated for both the prin ci pal axes con sid er ingthe fact that ei ther of the two tips can be un der com pres sion. The min i mum ca pac i -ties are con sid ered.

Pipe Sections

l = D

t , (LRFD Ta ble A-F1.1, HSS Ta ble 2.2-1)

l p

yF= 0 0714.

E , (LRFD Ta ble A-F1.1, HSS Ta ble 2.2-1)



l r

yF= 0 309.

E (LRFD Ta ble A-F1.1, HSS Ta ble 2.2-1)

M = M = D t

+ F Sr r

y33 22 0 0207 1.E / Fyæ

èçç

ö

ø÷÷ , (LRFD Ta ble A-F1.1, HSS 5.1-2)

M = M = D t

F Scr cr

y33 22 0 330.

E

Fy

æ

è

çççç

ö

ø

÷÷÷÷

, (LRFD Ta ble A-F1.1, HSS 5.1-3)

Circular, Rectangular, General Sections, and SD-Sections

No con sid er ation of lo cal buck ling is re quired for solid cir cu lar shapes, rect an gu lar plates (LRFD Ta ble A-F1.1). No lo cal buck ling is con sid ered in the pro gram forcir cu lar, rect an gu lar, gen eral shapes and SD-Sec tions. If spe cial con sid er ation isre quired, the user is ex pected to an a lyze this sep a rately.

Web Local Buckling

The flex ural de sign strengths for the limit state of Web Lo cal Buck ling are con sid -ered in the program only for the ma jor axis bend ing (LRFD Ta ble A-F1.1).

I Shapes, Channels, Double-Channels, and Boxes

The flex ural de sign strength for the ma jor axis bend ing, M n , of beams withNoncompact and Slen der webs for the limit state of Web Lo cal Buck ling is cal cu -lated as fol lows (LRFD A-F1-1, A-F1-3, A-G2-2):

M =

M if

M M Mn

p p

p p r

p

r p

33

33

33 33 33

, ,l l

l l

l l

£

- --

-

æ

è

çç

( )ö

ø

÷÷ < £

>

ì

í

ïïï

î

ïïï

, ,

, ,

if

R R S F if

p r

PG e cr r

l l l

l l33

(A-F1,A-G2)

where,

M n33 = Nom i nal ma jor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 , (LRFD F1.1)



M r33 = Ma jor lim it ing buck ling mo ment,R S Fe y33 ,(LRFD TableA-F1.1)l = Web slen der ness pa ram e ter, l p = Larg est value of l for which M Mn p= , l r = Larg est value of l for which buck ling is in elas tic,RPG = Plate girder bend ing strength re duc tion fac tor,Re = Hy brid girder fac tor, andFcr = Crit i cal com pres sion flange stress, ksi.

The web slen der ness pa ram e ters are com puted as fol lows, where the value of Pu istaken as pos i tive for com pres sion and zero for ten sion:

l = h

tc

w

,\

lj j

p

y

u

b y

u

b y

E

F -

P

P

P

P

=

æ

è

çç

ö

ø

÷÷ £376 1. ,2.75 for 0.125, (LRFD B5.1)

2.33112 1. .E

F -

P

Py

u

b yj

æ

è

çç

ö

ø

÷÷³ 49

E

F

P

P

y

u

b y

, for 0.125, andj

>

ì

í

ïï

î

ïï

lj

r

y

u

b y

E

F -

P

P=

æ

è

çç

ö

ø

÷÷570 1. 0.74 (LRFD Ta ble B5.1)

The pa ram e ters RPG , Re , and Fcr for slen der web sec tions are cal cu lated in the pro -gram as fol lows:

Ra

a

h

t

E

FPG

r

r

c

w cr

= -+

-æ

è

çç

ö

ø

÷÷£11,200 300

1.0570. , (LRFD A-G2-3)

( )R

a m m

ae

r

r

=+ -

+£

12 2

12 21.0

3

(for hy brid sec tions), (LRFD A-G2)

Re =1.0 , (for non-hy brid sec tion), where (LRFD A-G2)

( )a andrweb area

compression flange area= £ 10, (LRFD A-G2)

mF

F F

y

cr y

=min( , )

, taken as 1.0. (LRFD A-G2)



In the above ex pres sions, Re is taken as 1, be cause cur rently the program dealswith only non-hy brid gird ers.

The crit i cal com pres sion flange stress, Fcr , for slen der web sec tions is cal cu latedfor limit states of lat eral-tor sional buck ling and flange lo cal buck ling for the cor re -spond ing slen der ness pa ram e ter h in the pro gram as fol lows:

F =

F if

C F F ifcr

y p

b y

p

r p

y p

, ,

,

h h

h h

h hh h

£

--

-

é

ëê

ù

ûú £ <1

1

2

Cif

r

PGr

£

>

ì

í

ïïïï

î

ïïïï

h

hh h

,

, ,2

(LRFD A-G2-4, 5, 6)

The pa ram e ters h, hp , hr , and CPG for lat eral-tor sional buck ling for slen der web I,Chan nel, Dou ble Chan nel and Box sec tions are given be low:

h = L

rb

T

, (LRFD A-G2-7)

hp

y

E

F= 176. , (LRFD A-G2-8)

hr

y

E

F= 4 44. , (LRFD A-G2-9)

C CPG b= 286,000 , and (LRFD A-G2-10)

rT = ra dius of gy ra tion of the com pres sion flange plus one-third of the com pres sion por tion of the web.

Cb = a fac tor which de pends on span mo ment. It is cal cu lated us ing the equa tion given in page 122.

The pa ram e ters h, hp , hr , and CPG for flange lo cal buck ling for slen der web I,Chan nel, Dou ble Chan nel and Box sec tions are given be low:

h = b

t , (LRFD A-G2-11)

hp

y

E

F= 0 38. , (LRFD A-G2-12)



hr

y

c

E

F

k

=æ

èçç

ö

ø÷÷

135. , (LRFD A-G2-13)

C kPG c= 26,200 , and (LRFD A-G2-14)

Cb = 1 . (LRFD A-G2-15)


No lo cal buck ling is con sid ered for T-sec tions and Dou ble-an gles in the pro gram.If spe cial con sid er ation is re quired, the user is ex pected to an a lyze this sep a rately.

Single Angles

The nom i nal ma jor and mi nor bend ing strengths for Sin gle-an gles for the limit state of web lo cal buck ling are the same as those given for flange lo cal buck ling (LRFDSAM 5.1.1). No ad di tional check is con sid ered in the program.

Pipe Sections

The nom i nal ma jor and mi nor bend ing strengths for Pipe sec tions for the limit stateof web lo cal buck ling are the same as those given for flange lo cal buck ling (LRFDTa ble A-F1.1, HSS 5.1). No ad di tional check is con sid ered in the program.

Circular, Rectangular, General Sections, and SD Sections

No web lo cal buck ling is re quired for solid cir cu lar shapes and rect an gu lar plates(LRFD Ta ble A-F1.1). No web lo cal buck ling is con sid ered in the program for cir -cu lar, rect an gu lar, and gen eral shapes and SD Sec tions. If spe cial con sid er ation isre quired, the user is ex pected to an a lyze them sep a rately.

Shear Capacities

The nom i nal shear strengths are cal cu lated for shears along the geo met ric axes forall sec tions. For I, Box, Chan nel, Dou ble Chan nel, T, Dou ble an gle, Pipe, Cir cu larand Rect an gu lar sec tions, the prin ci pal axes co in cide with their geo met ric axes. For Sin gle-an gle sec tions, prin ci pal axes do not co in cide with their geo met ric axes.




The nom i nal shear strength, Vn2 , for ma jor di rec tion shears in I-shapes, boxes andchan nels, and dou ble-chan nels is eval u ated as fol lows:

For h

t

E

Fw y

£ 2 45. ,

V = F An y w2 0.6 , (LRFD F2-1, A-F2-1, HSS 5.2-5)

for 2 45 3 07. .E

F <

h

t

E

Fy w y

£ ,

V = F A

EF

ht

n y w

y

w

2 2 450.6 .

æ

è

çççç

ö

ø

÷÷÷÷

, and (LRFD F2-2, A-F2-2, HSS 5.2-6)

for 3 07.E

F <

h

ty w

£ 260 ,

[ ]V =

E

h tA n

w

w2 24 52. . (LRFD F2-3, A-F2-3, HSS 5.2-7)

The nom i nal shear strength, Vn, for both pipe sec tion in any di rec tion is taken asfol lows:

V FA

n cr

g=2

(LRFD HSS 5.2-1)

where, FE

D

t

Fcr y=æ

èç

ö

ø÷

£0 78

0 63

2

.. (LRFD HSS 5.2-2)


The nom i nal shear strength for mi nor di rec tion shears is as sumed as:

V = F An y v3 30.6



Calculation of Capacity Ratios

This sec tion de scribes the cal cu la tion of ca pac ity ra tios when the user se lects theAISC-LRFD 99 code.

Overview

In the cal cu la tion of the ax ial force/bi axial mo ment ca pac ity ra tios, first, for eachsta tion along the length of the mem ber, the ac tual mem ber force/mo ment com po -nents are cal cu lated for each load com bi na tion. Then the cor re spond ing ca pac i tiesare cal cu lated. Then, the ca pac ity ra tios are cal cu lated at each sta tion for eachmem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol -ling com pres sion and/or ten sion ca pac ity ra tio is then ob tained, along with the as -so ci ated sta tion and load com bi na tion. A ca pac ity ra tio greater than the Uti li za tionFac tor Limit (whose de fault value is 1.0) in di cates ex ceed ing a limit state.



The ca pac ity ra tio is de ter mined based on the ra tio P

Pu

nj .

For P

P u

nj³ 0.2 , the ca pac ity ra tio is given as

P

P +

M

M +

M

Mu

n

u

b n

u

b nj j j

8

933

33

22

22

æ

èçç

ö

ø÷÷ . (LRFD H1-1a, SAM 6-1a, HSS 7.1-1)

For P

P < u

nf0.2 , the ca pac ity ra tio is given as

P

P +

M

M +

M

Mu

n

u

b n

u

b n233

33

22

22j j j

æ

èçç

ö

ø÷÷ . (LRFD H1-1b, SAM 6-1a, HSS 7.1-2)

If Pu is ten sile, Pn is the nom i nal ax ial ten sile strength and j j= = 0.9t ; and if Pu is com pres sive, Pn is the nom i nal ax ial com pres sive strength and j j= = 0.85c , ex cept for an gle sec tions j j= = 0.90c (LRFD SAM 6). In ad -di tion, the re sis tance fac tor for bend ing, j b = 0.9.

134 Calculation of Capacity Ratios


For cir cu lar sec tions an SRSS (Square Root of Sum of Squares) com bi na tion isfirst made of the two bend ing com po nents be fore add ing the ax ial load com po nentin stead of the sim ple al ge braic ad di tion im plied by the above for mu las(LRFD HSS7.1-3.

For Sin gle-an gle sec tions, the ca pac ity ra tio is cal cu lated based on the prop er tiesabout the prin ci pal axis (LRFD SAM 5.3, 6). For I, Box, Chan nel, Dou ble Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rect an gu lar sec tions, the prin ci pal axes co in -cide with their geo met ric axes. For Sin gle-an gle sec tions, prin ci pal axes are de ter -mined in the pro gram. For gen eral sec tions and Sec tion De signer sec tions, it is as -sumed that the sec tion prop er ties are given in terms of the prin ci pal di rec tions.

Ax ial, Bend ing, Shear and Tor sion Stresses

The in ter ac tion of ax ial, bend ing, shear and tor sion are only con sid ered for pipe and box sec tions. For box sec tions, the in ter ac tion ra tio is taken as,

P

P

M

M

M

M

V

V

V

V

Tu

n

u

n

u

n

u

v n

u

v n

u

Tf f f f f f+ + + + +33

33

22

22

3

3

2

2' ' Tn

æ

èçç

ö

ø÷÷

2

(LRFD HSS 7.2-1)

and for pipe sec tions, the in ter ac tion is taken as

P

P

M

M

V V

v

T

Tu

n

u

b n

u u

v n

u

T nf f f f+ +

++

æ

è

çç

ö

ø

÷÷

332

33

32

22

3

2

'(LRFD HSS 7.2-1)

For both pipe and box sec tions,

P

P

M M

M

V V

V

T

Tu

n

u u

b n

u u

v n

u

T nf f f f+

++

++

æ

è

çç

332

222

33

32

22

3'

ö

ø

÷÷

2

(LRFD HSS 7.2-1)

For both pipe and box sec tions,

M M F Sn n y33 33 33' min( , )= (LRFD HSS 7.2)

For box sec tions,

M M F Sn n y22 22 22' min( , )= (LRFD HSS 7.2)

Calculation of Capacity Ratios 135


Shear Stresses

Sim i larly to the nor mal stresses, from the fac tored shear force val ues and the nom i -nal shear strength val ues at each sta tion for each of the load com bi na tions, shear ca -pac ity ra tios for ma jor and mi nor di rec tions are cal cu lated as fol lows:

V

Vu

v n

2

2j , and

V

Vu

v n

3

3j ,

where j v = 0.9 .

For Sin gle-an gle sec tions, the shear stress ra tio is cal cu lated for di rec tions alongthe geo met ric axis. For all other sec tions the shear stress is cal cu lated along theprin ci ple axes which co in cide with the geo met ric axes. For pipe and cir cu lar sec -tions, an SRSS (Square Root of Sum of Squares) com bi na tion of the two shearcom po nents, are first made be fore cal cu lat ing the shear ra tios.

Joint Design

When us ing AISC-LRFD99 de sign code, the struc tural joints are checked and/orde signed for the fol low ing:




• Re port ing the beam con nec tion shear

• Re port ing the brace con nec tion force





136 Joint Design



To achieve a proper beam/col umn mo ment con nec tion strength, con ti nu ity platessuch as shown in are usu ally placed on the col umn, in line with the top and bot tomflanges of the beam, to trans fer the com pres sion and ten sion flange forces of thebeam into the col umn.

For con nec tion con di tions de scribed in the last two steps above, the thick ness ofsuch plates is usu ally set equal to the flange thick ness of the cor re spond ing beam.How ever, for the con nec tion con di tion de scribed by the first step above, where thebeam frames into the flange of the col umn, such con ti nu ity plates are not al waysneeded. The re quire ment de pends upon the mag ni tude of the beam-flange forceand the prop er ties of the col umn. This is the con di tion that the pro gram in ves ti -gates. Col umns of I-sec tions only are in ves ti gated. The pro gram eval u ates the con -ti nu ity plate re quire ments for each of the beams that frame into the col umn flange(i.e. par al lel to the col umn ma jor di rec tion) and re ports the max i mum con ti nu ityplate area that is needed for each beam flange. The con ti nu ity plate re quire mentsare eval u ated for mo ment frames (OMF, IMF, SMF) only. No check is made forbraced frames (OCBC, SCBF, EBF).



jR = t F Pn fc yc bf(0.9)6.25 2 ³ if not at top story (LRFD K1-1)

jR t F Pn fc yc bc= ³( . )( . ) .0 5 0 9 6 25 2 if at top story (LRFD K1-2)


jR k +t F t Pn c fb yc wc bf= (1.0) (5.0 ) ³ , if not at top story (LRFD K1-2)

jR k t F t Pn c fb yc wc bf= + ³( . )( . )10 2 5 , if at top story (LRFD K1-3)


Joint Design 137


jR t + t

d

t

tn wc

fb

c

wc

fc

= (0.75) 0.80 2 1 3æ

èçç

ö

ø÷÷æ

è

çç

ö

ø

÷÷

é

ë

êê

ù

û

úú

³

1.5

EFt

t Pyc

fc

wc

bf ,

if not at top story (LRFD K1-4)

jR t + t

d

t

tn wc

fb

c

wc

fc

=æ

èçç

ö

ø÷÷æ

è

çç

ö

ø( . )( . )0 75 0 40 1 32 ÷

÷

é

ë

êê

ù

û

úú

³

1.5

EFt

t Pyc

fc

wc

bf ,

it at top story (LRFD K1-5a)


jR t EF

d Pn

wc yc

c

bf= (0.9)24 3

³ , if not at top story (LRFD K1-8)

jR t EF

d Pn

wc yc

c

bf= (0.9)12 3

³ , if at top story (LRFD K1.9, E2)


A = P

F tcp

bf

yc

wc(0.85)(0.9 )

- 25 2 , if not at top story (LRFD K1.9, E2)

A = P

F tcp

bf

yc

wc(0.85)(0.9 )

- 12 2 , if at top story (LRFD K1.9, E2)



or 25t wc act as a com pres sion mem ber to re sist the ap plied load (LRFD K1.9). Thefor mula also as sumes j = 0.85 and F Fcr yc= 0.9 . This cor re sponds to an as sump tionof l c = 0.5 in the col umn for mu las (LRFD E2-2). The user should choose the con -ti nu ity plate cross-sec tion such that this is sat is fied. As an ex am ple when us ing Fyc = 50 ksi and as sum ing the ef fec tive length of the stiff ener as a col umn to be 0.75h (LRFD K1.9) the re quired min i mum ra dius of gy ra tion of the stiff enercross-sec tion would be r h= 0.02 to ob tain l c = 0.5 (LRFD E2-4).

138 Joint Design



• The min i mum thick ness of the stiff en ers is taken in th program as fol lows:

t = t bcpmin

fb fb 0.5max , .179F

E

ycìíï

îï

üýï

þï(LRFD K1.9.2)


b = 2 b

3

t

2cpmin fp wc-

æ

èçç

ö

ø÷÷ (LRFD K1.9.1)


A = t bcpmin

cpmin

cpmin (LRFD K1.9.1)


min .






The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and the Seis mic De sign Cat e gory. If the struc ture isiden ti fied as Seis mic De sign Cat e gory D or E, the spe cial seis mic re quire ments are

Joint Design 139


sat is fied (AISC SEIS MIC 1). No spe cial check is made if the Seis mic De sign Cat e -gory is A, B, or C.

Con ti nu ity plate re quire ments for seis mic de sign are eval u ated for mo ment frames(OMF, IMF, SMF) only. No checks are done for braced frames (LCBF, SCBF, andEBF).

• For OMF the con ti nu ity plates are checked and de signed for a beam flangeforce, ( )P M d tbf pb b fb= - .

( )P M d tbf pb b fb= - (AISC SEIS MIC 11.5)

• For SMF and IMF, the con ti nu ity plates are checked and de signed for a beamflange force, P R F b tbf y y fb fb= .

P R F b tbf y y fb fb=

Note that the code in sists on de sign ing con ti nu ity pate to match with testedcon nec tion (AISC SEUISMIC 9.5, 10.5)



Shear stresses sel dom con trol the de sign of a beam or col umn mem ber. How ever,in a Mo ment-Re sist ing frame, the shear stress in the beam-col umn joint can be crit i -cal, es pe cially in fram ing sys tems when the col umn is sub jected to ma jor di rec tionbend ing and the joint shear forces are re sisted by the web of the col umn. In mi nordi rec tion bend ing, the joint shear is car ried by the col umn flanges, in which case the shear stresses are sel dom crit i cal, and this con di tion is there fore not in ves ti gated bythe pro gram.

Shear stresses in the panel zone, due to ma jor di rec tion bend ing in the col umn, mayre quire ad di tional plates to be welded onto the col umn web, de pend ing upon theload ing and the ge om e try of the steel beams that frame into the col umn, ei theralong the col umn ma jor di rec tion, or at an an gle so that the beams have com po nents along the col umn ma jor di rec tion. See Figure . The pro gram in ves ti gates such sit u -a tions and re ports the thick ness of any re quired doubler plates. Only col umns withI-shapes are in ves ti gated for doubler plate re quire ments. Also doubler plate re -quire ments are eval u ated for mo ment frames (OMF, IMF, SMF) only. No check ismade for braced frames(OCBF, SCBF, EBF).

140 Joint Design


The pro gram cal cu lates the re quired thick ness of doubler plates us ing the fol low ing al go rithms. The shear force in the panel zone, is given by

V = M

d - t Vp

n =

nbn n

n fn

c

b

1å -

cos q



R = F d t P

PP > v y c r

u

y

u0.6 1.4 , for 0.-é

ëê

ù


By us ing V Rp v= j , with j = 0.9 (by de fault), the re quired col umn web thick ness t r can be found.


t = t tdp r w- , (LRFD F2-1)

where,

Fy = Col umn and doubler plate yield stresst r = Re quired col umn web thick ness t fn = Flange thick ness of n-th beam con nect ing to the col umn t dp = Re quired doubler plate thick ness t fc = Col umn Flange thick ness

t w = Col umn web thick ness h = d tc fc- 2 if welded, d kc c- 2 if rolledVp = Panel zone shearVc = Col umn shear in col umn aboveFy = Beam flange forcesnb = Num ber of beams con nect ing to col umn d n = Depth of n-th beam con nect ing to col umn q n = An gle be tween n-th beam and col umn ma jor di rec tion d c = Depth of col umn clear of fil lets, equals d k- 2M bn = Cal cu lated fac tored beam mo ment from


Joint Design 141



The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and the Seis mic De sign Cat e gory. If the struc ture isiden ti fied as Seis mic De sign Cat e gory D or E, the spe cial seis mic re quire ments aresat is fied (AISC SEIS MIC 1). No spe cial check is made if the Seis mic De sign Cat e -gory is A, B, or C.

Dou bler plate re quire ments for seis mic de sign are eval u ated for SMF only. No fur -ther check/de sign is done for other types of frames.

• For Spe cial Mo ment-Re sist ing Frames, the panel zone doubler plate re quire -ments that are re ported will de velop at least the beam mo ments equal to of theplas tic mo ment ca pac ity of the beam or beam mo ments due to spec i fied loadcom bi na tions in volv ing seis mic load (AISC SEIS MIC 9.3a).

• For seis mic de sign, Vp is cal cu lated us ing the same equa tion as given above, ex -cept that M pb is taken as R F Zy y 33 .

The ca pac ity of the panel zone in re sist ing this shear is taken as (AISC SEIS -MIC 9-5):

j jv n v y c p

cf cf

b c p

V = F d t + b t

d d t 0.60 1

3 2æ

è

çç

ö

ø

÷÷

for P Pu y£ 0 75. (AISC SEIS MIC 9-5)

j jv n v y c p

cf cf

b c p

uV F d tb t

d d t

P

P= +

æ

è

çç

ö

ø

÷÷ -0 6 1

319 12

2

. . .y

æ

è

çç

ö

ø

÷÷

for P Pu y> 0 75. (AISC SEIS MIC 9.3a, LRFD K1-12)


tV

F d

b t

d dp

p

v y c

cf cf

b c

= -0.6 j

3 2

, if P Pu y£ 0 75.

142 Joint Design


tV

F dP

P

b tp

p

v y cu

y

cf cf=

-æ

è

çç

ö

ø

÷÷

æ

è

çç

ö

ø

÷÷

-

0 6 19 12

3 2

. . .jd db c

, if P Pu y> 0 75. (by de fault),

(AISC SEIS MIC 9.3a)


t = t - tdp p wc

where,

j v = 0.90 by default,bcf = width of col umn flange,t cf = thick ness of col umn flange,t p = re quired col umn web thick ness, h = d tc fc- 2 if welded, d kc c- 2 if rolled, andd b = depth of deep est beam fram ing into the ma jor di rec tion of

the col umn.

Py = F Ay

Pu = Ax ial force in column

• For Spe cial Mo ment-Re sist ing Frames, the panel zone col umn web thick nessre quire ment the pro gram checks the fol low ing:

td t d tc fc b fb

³- + -( ) ( )2 2

90(AISC SEIS MIC 9.36)

Here, t is taken as t wc + t dp when the dou ble plate is plug welded to pre vent lo calbuck ling. In such case t dp is in creased if nec es sary to meet this cri te ria. If thedoubler plate is not plug welded to the web, then t is taken as t wc and also as t dp

for check ing both the plates. If t wc can not sat isfy the cri te ria, then a fail ure con -di tion is de clared. If t dp does not sat isfy this cri te ria, then its value is in creasedto meet this cri te ria.



Only for Spe cial Mo ment Frames with Seis mic De sign Cat e gory D and E, the codere quires that the sum of col umn flex ure strengths at a joint should be more than thesum of beam flex ure strengths (AISC SEIS MIC 1, 9.6). The col umn flex ure

Joint Design 143


strength should re flect the pres ence of ax ial force pres ent in the col umn. The beamflex ural strength should re flect po ten tial in crease in ca pac ity for strain hard en ing to fa cil i tate the re view of the strong col umn weak beam cri te rion, the pro gram will re -port a beam/col umn plas tic mo ment ca pac ity ra tio for ev ery joint in the struc ture.


R =

M

M + Mmaj

n =

n

n

pcax pcby

b

pbn

1å *

* *

cos q

(AISC SEIS MIC 9.6)


R =

M

M + M

n =

n

pbn n

pcay pcby

b

min1

å sin q

, (AISC SEIS MIC 9.6)

where,


Mpbn

* = Plas tic mo ment ca pac ity of n-th beam con nect ing

to col umnq n = An gle be tween the n-th beam and the col umn

ma jor di rec tionM

pcax y,


ax ial force ef fects, of col umn above story levelM

pcbx y,


ax ial force ef fects, of col umn be low story levelnb = Num ber of beams con nect ing to the col umn


( )M = Z F - P Apc c yc uc g* , (AISC SEIS MIC 9.6)

The plas tic mo ment ca pac i ties of the beams are am pli fied for po ten tial in -crease in ca pac ity for strain hard en ing as,

144 Joint Design


M R F Z fpb y yb b mv* .= 11 ,

where,

Z b = Plas tic modulus of beam,

Z c = Plas tic modulus of col umn,

Fyb = Yield stress of beam ma te rial,

Fyc = Yield stress of col umn ma te rial,

Puc = Ax ial com pres sion force in col umn for the load com bi na tion un dercon sid er ation,Agc = Gross area of col umn,

fmv = The mo ment am pli fi ca tion fac tor. It is taken as the ra tio of beammo ment at the cen ter line of col umn to the mo ment the col umn face. Thisfac tor takes care of the M v of the code (AISC SEIS MIC 9.6). Fmv is taken asfol lows:

1+ d

Lc

b

,

d c = Depth of col umn sec tion, and

Lb = Clear span length of the beam.




For spe cial seis mic de sign, the beam con nec tion shears are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The spe cial seis mic re -quire ments ad di tion ally checked by the pro gram are de pend ent on the type of fram -ing used and the Seis mic De sign Cat e gory. If the struc ture is iden ti fied as Seis micDe sign Cat e gory D or E, the spe cial seis mic re quire ments are sat is fied (AISC

Joint Design 145


SEIS MIC 1). No spe cial check is made if the Seis mic De sign Cat e gory is A, B, orC.

• For spe cial mo ment frames, the beam con nec tion shear is taken as the max i -mum of those from reg u lar load com bi na tions and those re quired for the de vel -op ment of full plas tic mo ment ca pac ity of the beams. The con nec tion shear forthe de vel op ment of the full plas tic mo ment ca pac ity of beam is as fol lows:

V = C M

L + V Vu

pb

DL LL1.2 0.5+ (AISC SEIS MIC 9.2.a(3))

where





VLL = Ab so lute max i mum of the cal cu lated fac tored beamshears at the cor re spond ing beam ends from the live load only.

• For In ter me di ate Mo ment Frames and Or di nary Mo ment Frames, the beamcon nec tion shear is taken as the max i mum of those from reg u lar load com bi na -tions and those from spe cial seis mic con sid er ation. the beam con nec tion shearfrom spe cial seis mic con sid er ation is taken as the min i mum of those re quiredfor the de vel op ment of full plas tic mo ment ca pac ity of the beam and those re -quired for am pli fied seis mic load and those re quired (AISC SEIS MIC 10.2,11.2). The con nec tion shear for the de vel op ment of the full plas tic mo ment ca -pac ity of beam is as fol lows:

VCM

LV Vu

pb

DL LL= + +1 2 0 5. . (AISC SEIS MIC 10.2, 11.2)

All pa ram e ters in the above equa tion have been de scribed ear lier.

The load com bi na tions for am pli fied seis mic loads are:

( )0 9 0 2 0. .+ ±S DL ELDS W (AISC SEIS MIC 8.3, 4.1, ASCI 9.5.2.7.1, 2.3.2)

146 Joint Design


( )12 0 2 10 0. . ) .+ + ±S DL LL ELDS W

(AISC SEIS MIC 8.3, 4.1, ASCI 9.5.2.7.1, 2.3.2)

• For OCBF, the beam con nec tion shear is taken as the max i mum of those fromreg u lar load com bi na tions and those from am pli fied seis mic load com bi na tions (AISC SEIS MIC 14.2).

• For SCBF, the beam con nec tion shear is taken as the max i mum of those fromreg u lar load com bi na tions and those from am pli fied seis mic load com bi na tion(AISC SEIS MIC 13.4a(2)).

Note: Beams in ter sected by Chev ron (V or in verted-V) braces are NOT cur -rently checked to have a strength to sup port loads for the fol low ing two con di -tions (AISC SEIS MIC 13.4a):


b A beam that is in ter sected by braces shall be de signed to re sist the ef fects ofload com bi na tions stip u lated by the code, ex cept that a load q b shall be sub sti -tuted for the term E. q b is given by the dif fer ence of R F Ay y for the ten sionbrace and 0 3. f c nP for the com pres sion brace.


• For EBF, the beam con nec tion shear is taken as the beam con nec tion shear istaken as the max i mum of those from reg u lar load com bi na tions and those fromspe cial seis mic con sid er ations. The beam con nec tion shear from spe cial seis -mic con sid er ation is taken as the min i mum of those re quired for yield ing oflink beam and those re quired for am pli fied seis mic load (AISC SEIS MIC 15.1,15.4, 15.6). The load fac tor for the seis mic com po nent of loads in the com bi na -tion is cal cu lated to achieve forces re lated to yield ing of link beam. For con -nec tion shear de ter mi na tion the forces are fur ther am pli fied by 11. Ry (AISCSEIS MIC 15.6(2)). The load com bi na tions for Am pli fied Seis mic Loads aregiven ear lier.



Joint Design 147


For spe cial seis mic de sign, the brace con nec tion forces are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The spe cial seis mic re quire -ments ad di tion ally checked by the pro gram are de pend ent on the type of fram ingused and the Seis mic De sign Cat e gory. If the struc ture is iden ti fied as Seis mic De -sign Cat e gory D or E, the spe cial seis mic re quire ments are sat is fied (AISC SEIS -MIC 1). No spe cial check is made if the Seis mic De sign Cat e gory is A, B, or C.

Brace ax ial forces for seis mic de sign are eval u ated for braced frames (OCBF,SCBF, EBF) only. No spe cial checks are done for mo ment frames (OMF, IMF,SMF).

• For OBF, the brac ing con nec tion force is re ported at least the ex pected ten silestrength of the brace (R F Ay y g ) (AISC SEIS MIC 14.2):

• For SCBF, the brac ing con nec tion force is re ported at least as the expected theten sile strength of the brace (R F Ay y g ) (AISC SEIS MIC 13.3a).

For EBF, the brace con nec tion force is taken as the max i mum of those from reg u larload com bi na tions and those from spe cial seis mic con sid er ation. The brace con -nec tion force from spe cial seis mic con sid er ation is taken as the min i mum of thosere quired for yield ing of link beam and those re quired for Am pli fied Seis mic Load(AISC SEIS MIC 15.1, 15.4, 15.6). The load fac tor for the seis mic com po nent ofloads in the com bi na tion is cal cu lated to achieve forces re lated to yield ing of Linkbeam. for con nec tion force de ter mi na tion, the forces are fur ther am pli fied by 125. Ry (AISC SEIS MIC 15.6). The load com bi na tions for Am pli fied Seis mic Loadare given ear lier in this doc u ment.

148 Joint Design


C h a p t e r VI

Check/Design for AISC-LRFD93

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the AISC- LRFD93 de -sign code (AISC 1994). Vari ous no ta tions used in this chap ter are de scribed inTable V-1.

For re fer ring to per ti nent sec tions and equa tions of the origi nal LRFD code, aunique pre fix “LRFD” is as signed. However, all ref er ences to the “Speci fi ca tionsfor Load and Resistance Fac tored De sign of Single- Angle Mem bers” carry the pre -fix of “LRFD SAM”.


In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this chapter. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di catesex ceed ing a limit state. Simi larly, a shear ca pac ity ra tio is also cal cu lated sepa -rately.

149

150






Aw = Shear area, equal dt w per web, in2

B1 = Mo ment mag ni fi ca tion fac tor for mo ments not caus ing sidesway

B2 = Mo ment mag ni fi ca tion fac tor for mo ments caus ing sidesway

Cb = Bend ing co ef fi cient

Cm = Mo ment co ef fi cient





Fr = Com pres sive re sid ual stress in flange as sumed 10.0 for rolled sec tions and 16.5 for welded sec tions, ksi


G = Shear modu lus, ksi

I 22 = Mi nor mo ment of in er tia, in4

I 33 = Major mo ment of in er tia, in4

J = Tor sional con stant for the sec tion, in4


K K33 22, = Ef fec tive length K- factors in the ma jor and mi nor di rec tions

Lb = Lat er ally un braced length of mem ber, in

L p = Lim it ing lat er ally un braced length for full plas tic ca pac ity, in

Lr = Lim it ing lat er ally un braced length for ine las tic lateral- torsional buck ling, in

M cr = Elas tic buck ling mo ment, kip- in

M lt = Fac tored mo ments caus ing sidesway, kip- in

M nt = Fac tored mo ments not caus ing sidesway, kip- in

M Mn n33 22, = Nomi nal bend ing strength in ma jor and mi nor di rec tions, kip- in

M ob = Elas tic lateral- torsional buck ling mo ment for an gle sections, kip- in

M Mr r33 22, = Ma jor and mi nor lim it ing buck ling mo ments, kip- in

M u = Fac tored mo ment in mem ber, kip- in

M Mu u33 22, = Fac tored ma jor and mi nor mo ments in mem ber, kip- in


Pn = Nomi nal ax ial load strength, kip

Pu = Fac tored ax ial force in mem ber, kips

Py = A Fg y , kips


Table VI-1AISC-LRFD Notations

151

Chapter VI Check/Design for AISC-LRFD93







V Vn n2 3, = Nomi nal ma jor and mi nor shear strengths, kips

V Vu u2 3, = Fac tored ma jor and mi nor shear loads, kips

Z = Plas tic modu lus, in3

Z Z33 22, = Ma jor and mi nor plas tic moduli, in3





d e = Ef fec tive depth of web, in

hc = Clear dis tance be tween flanges less fil lets, in as sumed d k- 2 for rolled sec tions, and d t f- 2 for welded sec tions

k = Dis tance from outer face of flange to web toe of fil let, in

k c = Pa rame ter used for sec tion clas si fi ca tion, 4 h t

w , 0.35 0.763£ £k c




t = Thick ness, in


t w = Thick ness of web, in



l lc e, = Col umn slen der ness pa rame ters

l p = Lim it ing slen der ness pa rame ter for com pact ele ment

lr = Lim it ing slen der ness pa rame ter for noncompact ele ment

ls = Lim it ing slen der ness pa rame ter for seismic ele ment

lslender = Lim it ing slen der ness pa rame ter for slender ele ment

jb = Re sis tance fac tor for bend ing, 0.9

jc = Re sis tance fac tor for com pres sion, 0.85

j t = Re sis tance fac tor for ten sion, 0.9

jv = Re sis tance fac tor for shear, 0.9

Table VI-1AISC-LRFD Notations (cont.)



The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. For the AISC- LRFD93 code, if a struc ture is sub jected to dead load (DL), live load (LL), wind load (WL), and earth quake in -duced load (EL), and con sid er ing that wind and earth quake forces are re versi ble,then the fol low ing load com bi na tions may have to be de fined (LRFD A4.1):

1.4 DL (LRFD A4-1)1.2 DL + 1.6 LL (LRFD A4-2)

0.9 DL ± 1.3 WL (LRFD A4-6)1.2 DL ± 1.3 WL (LRFD A4-4)1.2 DL + 0.5 LL ± 1.3 WL (LRFD A4-4)

0.9 DL ± 1.0 EL (LRFD A4-6)1.2 DL ± 1.0 EL (LRFD A4-4)1.2 DL + 0.5 LL ± 1.0 EL (LRFD A4-4)

These are also the de fault de sign load com bi na tions in the pro gram when ever theAISC- LRFD93 code is used. The user should use other ap pro pri ate load ing com bi -na tions if roof live load is sepa rately treated, if other types of loads are pres ent, or if pat tern live loads are to be con sid ered.


When us ing the AISC- LRFD93 code, the pro gram design as sumes that a P-Danaly sis has been per formed so that mo ment mag ni fi ca tion fac tors for mo mentscaus ing sidesway can be taken as unity. It is recommended that the P-D analy sis bedone at the fac tored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).


The nom i nal strengths for ax ial com pres sion and flex ure are de pend ent on the clas -si fi ca tion of the sec tion as Com pact, Noncompact, Slen der or Too Slen der. The





tw

tw tw

tw tw

t f t f

t f

t

t f

t f

d

t = t = tw f

t t

z

2, y

2, y

3, x 3, x

AISC-LRFD93 : Axes Conventions



b f

b f b fb f

b f

b f

b b

dh d

b

b

b b = b - 3tff

D

hc hchc

k

b b

K

Figure VI-1AISC-LRFD Definition of Geometric Properties




Check

(l)COMPACT

(l p )NONCOMPACT

(l r )SLENDER

(l slender )

I-SHAPE

b tf f2

(rolled)£ F

y65 £ F - . y141 10 0 No limit

b tf f2

(welded)£ F

y65 £ F -

k

y

c

16216.5

No limit

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷640

1F

- P

Py

u

b y

2.75

j


£

æ

è

çç

ö

ø

÷÷

³

ì

í

ïï

î

ïï

ü

ý

ïï

þ

ïï

191

253

F -

P

P

F

y

u

b y

y

2.33j

£é

ëê

ù

ûú

F

P

Py

u

b y

9701- 0.74

j

( )£ +

£

ì

íï

îï

ü

ýï

þï

14000

16.5

260

F Fy y

BOXb t

f

h tc w

£ F y190

As for I-shapes

£ F y238

As for I-shapes

No limit

£ 970 Fy

CHANNELb tf

f

h tc w



No limitAs for I-shapes

T-SHAPEb tf

f2

d t w

As for I-ShapesNot applicable

As for I-Shapes

£ F y127

No limitNo limit


y76 No limit

DOUBLE-ANGLE

(Separated)


y76 No limit

PIPE D t £ F

y2070 £ F y8970

£ F y13000



RECTAN-GULAR

¾ Assumed Noncompact


Table VI-2Limiting Width-Thickness Ratios for

Classification of Sections in Flexure based on AISC-LRFD




Width-Thickness

Ratio

(l)


(l s)

NONCOMPACT(Uniform Compression)

(M M22 33 0» » )(l r )

I-SHAPE

b tf f2

(rolled)£ F

y52 £ F y95

b tf f2

(welded)£ F

y52 £ F y95

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷520

1F

- P

Py

u

b y

1.54j


£æ

è

çç

ö

ø

÷÷ ³ìíï

îï

üýï

þï

191 253

F -

P

P Fy

u

b y y

2.33j

£ Fy253

BOXb t

f

h tc w


£ F y238

£ F y253

CHANNELb tf

f

h tc w



T-SHAPEb tf

f2

d t w


As for I-shapes

£ F y127


y76



y76

PIPE D t Not applicable £ F

y3300


RECTANGULAR ¾ Assumed Noncompact


Table VI-3Limiting Width-Thickness Ratios for


pro gram clas si fies in di vid ual mem bers ac cord ing to the lim it ing width/thick nessra tios given in Table V-2 and Table III-3 (LRFD B5.1, A-G1, Ta ble A-F1.1). Thedef i ni tion of the sec tion prop er ties re quired in these ta bles is given in Figure V-1and Table V-1. More over, spe cial con sid er ations are re quired re gard ing the lim itsof width-thick ness ra tios for Com pact sec tions in Seis mic zones and Noncompactsec tions with com pres sive force as given in Table III-3. If the lim its for Slen dersec tions are not met, the sec tion is clas si fied as Too Slen der. Stress check of TooSlen der sec tions is be yond the scope of SAP2000.

In clas si fy ing web slen der ness of I-shapes, Box, and Chan nel sec tions, it is as -sumed that there are no in ter me di ate stiff en ers. Dou ble an gles are con ser va tivelyas sumed to be sep a rated.


The fac tored mem ber loads that are cal cu lated for each load com bi na tion are Pu , M u33 , M u22 , Vu2 and Vu3 cor re spond ing to fac tored val ues of the ax ial load, the ma -jor mo ment, the mi nor mo ment, the ma jor di rec tion shear force and the mi nor di -rec tion shear force, re spec tively. These fac tored loads are cal cu lated at each of thepre vi ously de fined sta tions.

For load ing com bi na tions that cause com pres sion in the mem ber, the fac tored mo -ment M u (M u33 and M u22 in the cor re spond ing di rec tions) is mag ni fied to con sidersec ond or der ef fects. The mag ni fied mo ment in a par ticu lar di rec tion is given by:

M = B M + B Mu nt lt1 2 , where (LRFD C1-1, SAM 6)

B1 = Mo ment mag ni fi ca tion fac tor for non- sidesway mo ments,B2 = Mo ment mag ni fi ca tion fac tor for sidesway mo ments,M nt = Fac tored mo ments not caus ing sidesway, andM lt = Fac tored mo ments caus ing sidesway.

The mo ment mag ni fi ca tion fac tors are as so ci ated with cor re spond ing di rec tions.The mo ment mag ni fi ca tion fac tor B1 for mo ments not caus ing sidesway is given by

( )B =

C

P P m

u e

11 -

³ 1.0 , where (LRFD C1-2, SAM 6-2)

Pe is the Eu ler buck ling load (PA F Kl

r

F

Ee

g y y= =l

lp2

, with ), and




Cm =



1.00 , if end unrestrained,

0.6 0.4 if no trans-M

Ma

b

, verse loading,

0.85 , if trans. load, end restrained,

1.00 , if trans. load, end unrestrained,

ì

í

ïïïï

î

ïïïï

(LRFD C1-3)

M Ma b is the ra tio of the smaller to the larger mo ment at the ends of the mem -ber, M Ma b be ing posi tive for dou ble cur va ture bend ing and nega tive for sin -gle cur va ture bend ing. For tension mem bers Cm is as sumed as 1.0. For com -pres sion mem bers with trans verse load on the mem ber, Cm is as sumed as 1.0for mem bers with any un re strained end and as 0.85 for mem bers with two un re -strained ends. When M b is zero, Cm is taken as 1.0. The pro gram de faults Cm to 1.0 if the un braced length factor, l, of the mem ber is re de fined by ei ther theuser or the pro gram, i.e., if the un braced length is not equal to the length of themem ber. The user can over write the value of Cm for any mem ber. Cm assumestwo val ues, Cm22 and Cm33 , as so ci ated with the ma jor and mi nor di rec tions.

The mag ni fi ca tion fac tor B1 , must be a posi tive number. There fore Pu must be lessthan Pe . If Pu is found to be greater than or equal to Pe , a fail ure con di tion is de -clared.

The pro gram de sign as sumes the anal y sis in cludes P-D ef fects, there fore B2 istaken as unity for bend ing in both di rec tions. It is sug gested that the P-D anal y sis bedone at the fac tored load level of 1.2 DL plus 0.5 LL (LRFD C2.2). See also Whiteand Hajjar (1991).

For sin gle an gles, where the prin ci pal axes of bend ing are not co in ci dent with thegeo met ric axes (2-2 and 3-3), the pro gram con ser va tively uses the maxi mum of K l22 22 and K l33 33 for de ter min ing the ma jor and mi nor di rec tion Euler buck ling ca -pac ity.

If the pro gram as sump tions are not satisfactory for a par ticu lar struc tural model ormem ber, the user has a choice of ex plic itly speci fy ing the val ues of B1 and B2 forany mem ber.




The nomi nal strengths in com pres sion, ten sion, bend ing, and shear are com putedfor Com pact, Non com pact, and Slen der sec tions ac cord ing to the fol low ing sub -sec tions. The nomi nal flex ural strengths for all shapes of sec tions are cal cu latedbased on their prin ci pal axes of bend ing. For the Rec tan gu lar, I, Box, Chan nel, Cir -cu lar, Pipe, T, and Double- angle sec tions, the prin ci pal axes co in cide with theirgeo met ric axes. For the An gle sec tions, the prin ci pal axes are de ter mined and allcom pu ta tions ex cept shear are based on that.

For Single- angle sec tions, the shear stresses are cal cu lated for di rec tions along thegeo met ric axes. For all other sec tions the shear stresses are cal cu lated along theirgeo met ric and prin ci ple axes.


j t = Re sis tance fac tor for ten sion, 0.9 (LRFD D1, H1, SAM 2, 6)j c = Re sis tance fac tor for com pres sion, 0.85 (LRFD E2, E3, H1)j c = Re sis tance fac tor for com pres sion in angles, 0.90 (LRFD SAM 4, 6)j b = Re sis tance fac tor for bend ing, 0.9 (LRFD F1, H1, A-F1, A-G2, SAM 5)j v = Re sis tance fac tor for shear, 0.9 (LRFD F2, A-F2, A-G3, SAM 3)

If the user speci fies nomi nal strengths for one or more ele ments in the“Overwrites” form, these val ues will over ride the above men tioned cal cu latedval ues for those ele ments as de fined in the fol low ing sub sec tions. The speci fiednomi nal strengths should be based on the prin ci pal axes of bending.

Compression Capacity

The nomi nal compression strength is the minimum value ob tained from flex uralbuck ling, tor sional buckling and flexural- torsional buck ling. The strengths are de -ter mined ac cord ing to the fol low ing sub sec tions.

For mem bers in com pres sion, if Kl r is greater than 200, a mes sage to that ef fect isprinted (LRFD B7, SAM 4). For sin gle an gles, the mini mum radius of gy ra tion, rz , is used in stead of r22 and r33 in com put ing Kl r .

Flex ural Buck ling

The nomi nal ax ial com pres sive strength, Pn , de pends on the slen der ness ra tio, Kl r, and its criti cal value, l c , where



Kl

r

K l

r

K l

r= ì

íî

üýþ

max ,33 33

33

22 22

22

, and

lp

c =Kl

r

F

E

y . (LRFD E2-4, SAM 4)



Pn for Com pact or Non com pact sec tions is evalu ated for flex ural buck ling as fol -lows:

P = A Fn g cr , where (LRFD E2-1)

( )F = Fcr yc0.658l2

, for l c 1.5£ , and (LRFD E2-2)

F = Fcr y

0.877

c2l

é

ëê

ù

ûú , for l c > 1.5. (LRFD E2-3)

Pn for Slender sec tions is evalu ated for flex ural buck ling as fol lows:

P = A Fn g cr , where (LRFD A-B3d, SAM 4)

( )F = Q Fcr yc0.658Ql2

, for l c 1.5Q £ , and (LRFD A-B5-15, SAM 4-1)

F = Fcr y

0.877

c2l

é

ëê

ù

ûú , for l c > 1.5Q . (LRFD A-B5-16, SAM 4-2)


Q Q Qs a= , where (LRFD A- B5-17, SAM 4)

Q s = re duc tion fac tor for un stiff ened slen der ele ments, and (LRFD A-B5.3a)

Q a = re duc tion fac tor for stiff ened slen der ele ments. (LRFD A-B5.3c)

The Q s fac tors for slen der sec tions are cal cu lated as de scribed in Table V-4 (LRFDA-B5.3a). The Q a fac tors for slen der sec tions are cal cu lated as the ra tio of ef fec tive cross- sectional area and the gross cross- sectional area (LRFD A-B5.3c).

QA

Aa

e

g

= (LRFD A- B5- 14)





SectionType


EquationReference

I-SHAPE

[ ]Q

if b t F

b t F if Fs

f f y

f f y y=

£

- <

1.0 , 95

1.415 0.00437 95

2

2

,

,

[ ]{ }b t F

b t F if b t F

f f y

f f y f f y

2

2 22

<

³

ì

íïï

îïï

176

20,000 176

,

, .

(rolled)

LRFD A-B5-5,LRFD A-B5-6

[ ]Q

if b t F k

b t F k if Fs

f f y c

f f y c=

£

-

1.0 109

1.415 0.00381 109

2

2

,

[ ]{ }y c f f y c

c f f y f f y c

k b t F k

k b t F if b t F k

< <

³

2

2 22

200

26,200 200

,

.

ì

íïï

îïï

(welded)


BOX Qs =1 LRFD A-B5.3d

CHANNEL As for I-shapes with b tf f2 replaced by b tf f .

LRFD A-B5-5,LRFD A-B5-6,LRFD A-B5-7,LRFD A-B5-8

T-SHAPE


[ ]Q

if d t F

d t F if F d ts

w y

w y y w£

£

- <

1.0 , 127

1.908 0.00715 127

,

,

[ ]{ }<

³

ì

íïï

îïï

176

20,000 176

F

d t F if d t F

y

w y w y

,

, .2

LRFD A-B5-5,LRFD A-B5-6,LRFD A-B5-7,LRFD A-B5-8,LRFD A-B5-9,LRFDA-B5-10

DOUBLE-ANGLE

(Separated)

[ ]Q

if b t F

b t F if F b ts

y

y y=

£

- < <

1.0 , 76

1.340 0.00447 76 155

,

,

[ ]{ }F

b t F if b t F

y

y y

,

, .15,500 1552

³

ì

íïï

îïï


ANGLE [ ]Q

if b t F E

b t F E if F E bs

y

y y=

£

- <

1.0 , 0.446

1.34 0.761 0.446

,

,

[ ] [ ]{ }t F E

b t F E if b t F E

y

y y

<

³

ì

íïï

îïï

0.910

0.534 0.910

,

, .2

LRFD SAM4-3

PIPE Qs =1 LRFD A-B5.3d

ROUNDBAR

Qs =1 LRFD A-B5.3d

RECTAN-GULAR

Qs =1 LRFD A-B5.3d

GENERAL Qs =1 LRFD A-B5.3d

Table VI-4Re duc tion Fac tor for Un stiff ened Slen der Ele ments, Q s



SectionType


I-SHAPE h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

253

326 57.2 2531

f.

ì

í

ïï

î

ïï


A g

= ) LRFD A-B5-12

BOX

h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

253

326 57.2 2531

f.

ì

í

ïï

î

ïï


A g

= )

b

b ifb

t f

t

f b t fif

b

t

e

f

f

f f

=

£

-é

ëêê

ù

ûúú

>

, ,

( ),

238

326 64.9 21

38

f.

ì

í

ïï

î

ïï

(compr. or flexure, f Fy= )

LRFD A-B5-12

LRFD A-B5-11

CHANNEL h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

=

£

-é

ëê

ù

ûú >

, ,

( ),

253

326 57.2 2531

f.

ì

í

ïï

î

ïï


A g

= ) LRFD A-B5-12

T-SHAPE b be = LRFD A-B5.3b

DOUBLE-ANGLE

(Separated)

b be = LRFD A-B5.3b

ANGLE b be = LRFD A-B5.3b

PIPE

( )Q

ifD

t F

D t Fif

D

t F

ay

y y

=£

+ >

ì

íïï

îï

1, ,

, .

3,300

1,100 2

3

3,300

ï

(compression only) LRFD A-B5-13

ROUNDBAR

Not applicable ¾

RECTAN-GULAR

b be = LRFD A-B5.3b


Table VI-5Effective Width for Stiffened Sections


( )A A b b te g e= - -å

be for un stiff ened el e ments is taken equal to b, and be for stiff ened el e ments istaken equal to or less than b as given in Table V-5 (LRFD A-B5.3b). For webs in I,box, and Chan nel sec tions, he is used as be and h is used as b in the above equa tion.


Pn for flexural- torsional buck ling of Double- angle and T- shaped com pres sionmem bers whose ele ments have width- thickness ra tios less than l r is given by

P = A Fn g crft , where (LRFD E3-1)

F = F F

H

F F H

F Fcrft

cr crz cr crz

cr

2 2

22

1 14+æ

èçç

ö

ø÷÷ - -

+( crz )2

é

ëêê

ù

ûúú , where (LRFD E3-1)

FGJ

Arcrz =

02 ,

Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

,

r0 = Po lar ra dius of gy ra tion about the shear cen ter,

x y0 0, are the coor di nates of the shear cen ter with re spect to the cen troid, x 0 0= for doubleangle and T- shaped mem bers (y-axis of sym me -

try),

Fcr2 is de ter mined ac cord ing to the equa tion LRFD E2-1 for flex ural

buck ling about the mi nor axis of sym me try for lp c

yKl

r

F

E=

22

.

Torsional and Flex ural-Torsional Buck ling

The strength of a com pres sion mem ber, Pn , de ter mined by the limit states of tor -sional and flexural- torsional buck ling is de ter mined as fol lows:

P = A Fn g cr , where (LRFD A- E3-1)



( )F = Q Fcr ye0.658Ql2

, for l e 1.5Q £ , and (LRFD A-E3-2)

F = Fcr y

0.877

e2l

é

ëê

ù

ûú , for l e > 1.5Q . (LRFD A-E3-3)

In the above equa tions, the slen der ness pa rame ter l e is cal cu lated as

l e =F

F

y

e

, (LRFD A-E3-4)

where Fe is cal cu lated as fol lows:


( )F

EC

K lGJ

I Ie

w

z z

= +é

ë

êê

ù

û

úú +

p 2

222 33

1 (LRFD A- E3-5)


F = F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Channels:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Sin gle-angles sec tions with equal legs:

F = F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14+æ

èçç

ö

ø÷÷ - -

+

é

( )ëêê

ù


• For Single- angle sec tions with une qual legs, Fe is cal cu lated as the mini mumreal root of the fol low ing cu bic equa tion (LRFD A- E3-7):

( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e- - - - - -33 22

222

02

02

2 F Fy

re e- =33

02

02

0) ,

where,




try),

r x yI I

Ag

0 02

02 22 33= + + +


Hx y

r= -

+æ

èçç

ö

ø÷÷1 0

202

02

, (LRFD A- E3-9)

( )F

E

K l re33

2

33 33 33

2= p

, (LRFD A- E3-10)

( )F

E

K l re22

2

22 22 22

2= p

, (LRFD A- E3-11)

( )F

EC

K lGJ

Arez

w

z z

= +é

ë

êê

ù

û

úú

p 2

202

1 , (LRFD A- E3-12)





For an gle sec tions, the prin ci pal mo ment of in er tia and ra dii of gy ra tion are used for com put ing Fe . Also, the maxi mum value of Kl, i.e, max( , )K l K l22 22 33 33 , is used inplace of K l22 22 or K l33 33 in cal cu lat ing Fe22 and Fe33 in this case.

Tension Capacity

The nomi nal ax ial ten sile strength value Pn is based on the gross cross- sectionalarea and the yield stress.

P A Fn g y= (LRFD D1-1)



It should be noted that no net sec tion checks are made. For mem bers in ten sion,if l r is greater than 300, a mes sage to that ef fect is printed (LRFD B7, SAM 2). Forsin gle an gles, the min i mum ra dius of gy ra tion, rz , is used in stead of r22 and r33 incom put ing Kl r .

Nominal Strength in Bending

The nominal bend ing strength de pends on the fol low ing cri te ria: the geo met ricshape of the cross- section, the axis of bend ing, the com pact ness of the sec tion, anda slen der ness pa rame ter for lateral- torsional buck ling. The nomi nal strengths for all shapes of sec tions are cal cu lated based on their prin ci pal axes of bend ing. For theRec tan gu lar, I, Box, Chan nel, Cir cu lar, Pipe, T, and Double- angle sec tions, theprin ci pal axes co in cide with their geo met ric axes. For the Sin gle An gle sec tions,the prin ci pal axes are de ter mined and all com pu ta tions re lated to flex ural strengthsare based on that. The nomi nal bend ing strength is the minimum value ob tained ac -cord ing to the limit states of yield ing, lateral- torsional buck ling, flange lo cal buck -ling, and web lo cal buck ling, as fol lows:

Yielding

The flex ural de sign strength of beams, de ter mined by the limit state of yield ing is:

M Z F S Fp y y= £ 1.5 (LRFD F1-1)

Lateral-Torsional Buckling

Doubly Symmetric Shapes and Channels

For I, Chan nel, Box, and Rec tan gu lar shaped members bent about the ma jor axis,the mo ment ca pac ity is given by the fol low ing equa tion (LRFD F1):

M =

M if L L

C M - M - ML - L

L -n

p b p

b p p r

b p

r

33

33

33 33 33

, ,£

( ) L

M if L L L

M M if L

p

p p b r

cr p

æ

è

çç

ö

ø

÷÷

é

ëêê

ù

ûúú

£ < £

£

33

33 33

, ,

, b r L>

ì

í

ïïï

î

ïïï .

(LRFD F1-1, F1-2, F1- 12)

where,



M n33 = Nomi nal ma jor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 , (LRFD F1.1)M r33 = Ma jor lim it ing buck ling mo ment,

( )F F Sy r- 33 for I- shapes and chan nels, (LRFD F1-7)and F Sy eff , 33 for rec tan gu lar bars and boxes, (LRFD F1- 11)

M cr33 = Criti cal elas tic mo ment,

C

LEI GJ +

E

LI Cb

b b

w

p p22

2

22

æ

èçç

ö

ø÷÷

for I- shapes and chan nels, and (LRFD F1- 13)

57 000

22

C JA

L rb

b

for boxes and rec tan gu lar bars, (LRFD F1- 14)

Lb = Lat er ally un braced length, l22 ,

L p = Lim it ing lat er ally un braced length for full plas tic ca pac ity,300 22r

Fy

for I- shapes and chan nels, and (LRFD F1-4)

3750 22

33

r

MJA

p

for boxes and rec tan gu lar bars, (LRFD F1-5)

Lr = Lim it ing lat er ally un braced length forine las tic lateral- torsional buck ling,

[ ]r X

F F + X F - F

y r

y r22 1

21-

ìíî

üýþ

1+ ( )21

2

12

for I- shapes and chan nels, and (LRFD F1-6)

57 000 22

33

r JA

M r

for boxes and rec tan gu lar bars, (LRFD F1- 10)

X1 =p

S

EGJA

33 2 , (LRFD F1-8)

X 2 = 422

33

2C

I

S

GJw æ

èç

ö

ø÷ , (LRFD F1-9)

Cb =12.5

2.5

M

M + M + M + MA B C

max

max 3 4 3 , and (LRFD F1-3)

M max , M M MA B C, ,and are ab so lute val ues of max i mum mo ment, ¼ point, cen terof span and ¾ point ma jor mo ments re spec tively, in the mem ber. Cb should betaken as 1.0 for can ti le vers. How ever, the pro gram is un able to de tect whether the



mem ber is a can ti le ver. The user should over write Cb for can ti le vers. The pro -

gram also de faults Cb to 1.0 if the mi nor un braced length, l22 , of the mem ber is re -de fined by the user (i.e. it is not equal to the length of the mem ber). The user canover write the value of Cb for any mem ber.

For I, Chan nel, Box, and Rec tan gu lar shaped members bent about the minor axis,the mo ment ca pac ity is given by the fol low ing equa tion:

M = M = Z F S Fn p y y22 22 22 22£ 1.5 (LRFD F1)

For pipes and cir cu lar bars bent about any axis,

M = M = Z F S Fn p y y£ 1.5 . (LRFD F1)


For T- shapes and Dou ble-an gles the nomi nal ma jor bend ing strength is given as,

M = EI GJ

LB + + Bn

b

3322 21

p éë

ùû , where (LRFD F1- 15)

M F Sn y33 33£ 1.5 , for posi tive mo ment, stem in tension (LRFD F1.2c)

M F Sn y33 33£ , for negative mo ment, stem in com pres sion (LRFD F1.2c)

Bd

L

I

Jb

= ± 2.3 22 . (LRFD F1- 16)


For T- shapes and dou ble an gles the nomi nal mi nor bend ing strength is as sumed as,

M = S Fn y22 22 .

Single Angles

The nomi nal strengths for Single- angles are cal cu lated based on their prin ci palaxes of bend ing. The nomi nal ma jor bend ing strength for Single- angles for thelimit state of lat eral-tor sional buck ling is given as fol lows (LRFD SAM 5.1.3):



M = M

MM Mn major

ob

y major

ob y,

,

,0.92 0.17 1.25-é

ëê

ù

ûú £ major ob y major if M M, ,,£

M = M

MMn major

y major

ob

y major,

,

,1.58 0.83 1.2-é

ë

êê

ù

û

úú

£ 5M if M My major ob y major, ,, ,>

where,

M y major, = yield mo ment about the ma jor prin ci pal axis of bend ing, con sid er ing the pos si bil ity of yield ing at the heel and both of the leg tips,

M ob = elas tic l ateral-tor sional buck ling mo ment as cal cu lated be low.

The elas tic lat eral-tor sional buck ling mo ment, M ob , for equal- leg an gles is taken as

M CE b t

lob b= 0.46 2 2

, (LRFD SAM 5-5)

and for unequal- leg an gles the M ob is cal cu lated as

M ECI

llt rob b w w= + +é

ëùû

4.9 0.052minmin2

2 2b b( ) , (LRFD SAM 5-6)

where,


( )l l l= max ,22 33 ,

Imin = mi nor prin ci pal axis mo ment of in er tia,

Imax = major prin ci pal axis mo ment of in er tia,


bwAI

z w z dA z= +é

ëê

ù

ûú -ò

122 2

0

max

( ) , (LRFD SAM 5.3.2)






bw is a spe cial sec tion prop erty for an gles. It is posi tive for short leg in com pres -sion, nega tive for long leg in com pres sion, and zero for equal- leg an gles (LRFDSAM 5.3.2). How ever, for con ser va tive de sign in the pro gram, it is al ways taken asnega tive for unequal- leg an gles.

General Sections

For General sec tions the nomi nal ma jor and mi nor di rec tion bend ing strengths areas sumed as,

M = S Fn y .

Flange Local Buckling

The flex ural de sign strength, M n , of Non com pact and Slender beams for the limitstate of Flange Lo cal Buck ling is cal cu lated as fol lows (LRFD A-F1):

For major di rec tion bend ing,

M =

M if

M M Mn

p p

p p r

p

r p

33

33

33 33 33

, ,l l

l l

l l

£

- --

-

æ

è( ) ç

ç

ö

ø

÷÷ < £

£ >

ì

í

ïïï

î

ïï

, ,

, .

if

M M if

p r

cr p r

l l l

l l33 33ï

(A-F1-3)

and for mi nor di rec tion bend ing,

M =

M if

M M Mn

p p

p p r

p

r p

22

22

22 22 22

, ,l l

l l

l l

£

- --

-

æ

è( ) ç

ç

ö

ø

÷÷ < £

£ >

ì

í

ïïï

î

ïï

, ,

, .

if

M M if

p r

cr p r

l l l

l l22 22ï

(A-F1-3)

where,



M n33 = Nomi nal ma jor bend ing strength,M n22 = Nomi nal mi nor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 ,M p22 = Mi nor plas tic mo ment, Z F S Fy y22 22£ 1.5 ,M r33 = Ma jor lim it ing buck ling mo ment,M r22 = Mi nor lim it ing buck ling mo ment, M cr33 = Ma jor buck ling mo ment,M cr22 = Mi nor buck ling mo ment, l = Con trol ling slen der ness pa rame ter, l p = Larg est value of l for which M Mn p= , andl r = Larg est value of l for which buck ling is ine las tic.

The pa rame ters l, l p , l r , M r33 , M r22 , M cr33 , and M cr22 for flange lo cal buck ling fordif fer ent types of shapes are given be low:

I Shapes, Channels

l =b

t

f

f2 , (for I sec tions) (LRFD B5.1, Ta ble A-F1.1)

l =b

t

f

f

, (for Chan nel sec tions) (LRFD B5.1, Ta ble A-F1.1)

l p

yF= 65

, (LRFD B5.1, Ta ble A-F1.1)

( )l r

y r

y r c

F F

F F k

=-

-

141For rolled shape,

162 For wel

,

, ded shape,

ì

í

ïï

î

ïï


M F F Sr y r33 33= -( ) , (LRFD Ta ble A-F1.1)

M F Sr y22 22= , (LRFD Ta ble A-F1.1)

MS

kS

crc

33

2 33

2 33

=

20,000For rolled shape,

26,200

l

l

,

, For welded shape,

ì

íï

îï




MS

kS

crc

22

2 22

2 22

=

20,000For rolled shape,

26,200

l

l

,

, For welded shape,

ì

íï

îï



16.5 ksi, For welded shape.

ìíî

(LRFD A-F1)

Boxes

l =

-

-

b t

t

b t

t

f w

f

f w

f

3

2

,

,

For rolled shape,

For welded shape,

ì

í

ïï

î

ïï

(LRFD B5.1, Ta ble A-F1.1)

l p

yF= 190


l r

yF= 238


M F F Sr y r eff33 33= -( ) , , (LRFD Ta ble A-F1.1)

M F F Sr y r eff22 22= -( ) , , (LRFD Ta ble A-F1.1)

( )M F S S Scr y eff eff33 33 33 33= , , , (LRFD Ta ble A-F1.1)

M F Scr y eff22 22= , , (LRFD Ta ble A-F1.1)


16.5 ksi, For welded shape,

ìíî

(LRFD A-F1)

Seff , 33 = ef fec tive ma jor sec tion modu lus con sid er ing slen der ness, and

Seff , 22 = ef fec tive minor sec tion modu lus con sid er ing slen der ness.


No lo cal buck ling is con sid ered for T sec tions and Dou ble an gles in the pro gram. Ifspe cial con sid era tion is re quired, the user is ex pected to ana lyze this sepa rately.



Single Angles

The nomi nal strengths for Single- angles are cal cu lated based on their prin ci palaxes of bend ing. The nomi nal ma jor and mi nor bend ing strengths for Single- anglesfor the limit state of flange lo cal buck ling are given as fol lows (LRFD SAM 5.1.1):

M =

F S ifb

t F

F S

F

n

y c

y

y c

1.25 0.382E

1.25 1.49b t

0.382E

, ,£

-

y

y

ifF

b

t-

æ

è

ççççç

ö

ø

÷÷÷÷÷

é

ë

êêêêê

ù

û

úúúúú

< £1 , 0.382E

0.446E

Q 0.446E

F

F S ifb

t F

y

y c

y

,

, ,>

ì

í

ïïïïï

î

ïïïïï

where,

Sc = sec tion modu lus for com pres sion at the tip of one leg,



Q = strength re duc tion fac tor due to lo cal buck ling.

In cal cu lat ing the bend ing strengths for Single- angles for the limit state of flangelo cal buck ling, the ca paci ties are cal cu lated for both the prin ci pal axes con sid er ingthe fact that ei ther of the two tips can be un der com pres sion. The mini mum ca paci -ties are con sid ered.

Pipe Sections

l = D

t , (LRFD Ta ble A-F1.1)

l p

yF= 2,070

, (LRFD Ta ble A-F1.1)



l r

yF= 8,970


M = M = D t

+ F Sr r

y33 22

600æ

èçç

ö

ø÷÷ , (LRFD Ta ble A-F1.1)

M = M = D t

Scr cr

33 22

9,570æ

èçç

ö

ø÷÷ , (LRFD Ta ble A-F1.1)

Circular, Rectangular, and General Sections

No con sid er ation of lo cal buck ling is re quired for solid cir cu lar shapes, rec tan gu lar plates (LRFD Ta ble A-F1.1). No lo cal buck ling is con sid ered in the pro gram forcir cu lar, rec tan gu lar, and gen eral shapes. If spe cial con sid era tion is re quired, theuser is ex pected to ana lyze this sepa rately.

Web Local Buckling

The flex ural de sign strengths are considered in the pro gram for only the ma jor axisbend ing (LRFD Ta ble A-F1.1).

I Shapes, Channels, and Boxes

The flex ural de sign strength for the ma jor axis bending, M n , of Non com pact andSlender beams for the limit state of Web Lo cal Buck ling is cal cu lated as fol lows(LRFD A- F1-1, A- F1-3, A-G2-2):

M =

M if

M M Mn

p p

p p r

p

r p

33

33

33 33 33

, ,l l

l l

l l

£

- --

-

æ

è

çç

( )ö

ø

÷÷ < £

>

ì

í

ïïï

î

ïïï

, ,

, ,

if

S R R F if

p r

PG e cr r

l l l

l l33

(A-F1,A-G1)

where,

M n33 = Nomi nal ma jor bend ing strength,M p33 = Ma jor plas tic mo ment, Z F S Fy y33 33£ 1.5 , (LRFD F1.1)M r33 = Ma jor lim it ing buck ling mo ment,R S Fe y33 ,(LRFD TableA- F1.1)l = Web slen der ness pa rame ter, l p = Larg est value of l for which M Mn p= ,



l r = Larg est value of l for which buck ling is ine las tic,RPG = Plate girder bend ing strength re duc tion factor,Re = Hy brid girder fac tor, andFcr = Criti cal com pres sion flange stress, ksi.

The web slen der ness pa rame ters are com puted as fol lows, where the value of Pu istaken as posi tive for com pres sion and zero for tension:

l = h

tc

w

,

lj j

p

y

u

b y

u

b yF -

P

P

P

P

=

æ

è

çç

ö

ø

÷÷ £

6402.75 for 0.11 , 25,

1912.33 for

F -

P

P F

P

P

y

u

b y y

u

b yj j

æ

è

çç

ö

ø

÷÷³

253, >

ì

í

ïï

î

ïï

0.125, and

lj

r

y

u

b yF -

P

P=

æ

è

çç

ö

ø

÷÷

9700.741 .

The pa rame ters RPG , Re , and Fcr for slen der web sec tions are cal cu lated in the pro -gram as fol lows:

Ra

a

h

t FPG

r

r

c

w cr

= -+

-æ

è

çç

ö

ø

÷÷

£11,200 300

9701.0 , (LRFD A- G2-3)

( )R

a m m

ae

r

r

=+ -

+£

12 2

12 21.0

3

(for hy brid sec tions), (LRFD A- G2)

Re =1.0 , (for non-hy brid sec tion), where (LRFD A- G2)

a r = £web area

compression flange area1.0 , and (LRFD A- G2)

mF

F F

y

cr y

=min( , )

, taken as 1.0. (LRFD A- G2)




The criti cal com pres sion flange stress, Fcr , for slen der web sec tions is cal cu latedfor limit states of lateral- torsional buck ling and flange lo cal buck ling for the cor re -spond ing slen der ness pa rame ter h in the pro gram as fol lows:

F =

F if

C F F ifcr

y p

b y

p

r p

y p

, ,

,

h h

h h

h hh h

£

--

-

é

ëê

ù

ûú £ <1

1

2

Cif

r

PGr

£

>

ì

í

ïïïï

î

ïïïï

h

hh h

,

, ,2

(LRFD A- G2-4, 5, 6)

The pa rame ters h, hp , hr , and CPG for lateral-torsional buck ling for slen der web I,Chan nel and Box sec tions are given be low:

h = L

rb

T

, (LRFD A- G2-7)

hp

yF= 300

, (LRFD A- G2-8)

hr

yF= 756

, (LRFD A- G2-9)

C CPG b= 286,000 , and (LRFD A- G2-10)

rT = ra dius of gy ra tion of the com pres sion flange plus one- third of the

com pres sion por tion of the web, and it is taken as bf 12 in the pro -

gram.

Cb = a fac tor which de pends on span mo ment. It is cal cu lated us ing the equa tion given in page 122.

The pa rame ters h, hp , hr , and CPG for flange local buck ling for slen der web I,Chan nel and Box sec tions are given be low:

h = b

t , (LRFD A- G2- 11)

hp

yF= 65

, (LRFD A- G2- 12)



hr

y cF k= 230

, (LRFD A- G2- 13)

C kPG c= 26,200 , and (LRFD A- G2-14)

Cb = 1 . (LRFD A- G2- 15)


No lo cal buck ling is con sid ered for T- sections and Dou ble-an gles in the pro gram.If spe cial con sid era tion is re quired, the user is ex pected to ana lyze this sepa rately.

Single Angles

The nomi nal ma jor and mi nor bend ing strengths for Single- angles for the limit state of web lo cal buck ling are the same as those given for flange lo cal buckling (LRFDSAM 5.1.1). No ad di tional check is con sid ered in the pro gram.

Pipe Sections

The nomi nal ma jor and mi nor bend ing strengths for Pipe sections for the limit stateof web lo cal buck ling are the same as those given for flange lo cal buck ling (LRFDTa ble A-F1.1). No ad di tional check is con sid ered in the pro gram.

Circular, Rectangular, and General Sections

No web lo cal buck ling is re quired for solid cir cu lar shapes and rec tan gu lar plates(LRFD Ta ble A-F1.1). No web lo cal buck ling is con sid ered in the pro gram for cir -cu lar, rec tan gu lar, and gen eral shapes. If spe cial con sid era tion is re quired, the useris ex pected to ana lyze them sepa rately.

Shear Capacities

The nomi nal shear strengths are cal cu lated for shears along the geo met ric axes forall sec tions. For I, Box, Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rec tan gu larsec tions, the prin ci pal axes co in cide with their geo met ric axes. For Single- anglesec tions, prin ci pal axes do not co in cide with their geo met ric axes.


The nomi nal shear strength, Vn2 , for ma jor di rec tion shears in I- shapes, boxes andchan nels is evalu ated as fol lows:



For h

t

Fw y

£418

,

V = F An y w2 0.6 , (LRFD F2-1)

for 418 523

F <

h

t

Fy w y

£ ,

V = F AF

h

tn y w

y w

2 0.6418

, and (LRFD F2-2)

for 523

260F

< h

ty w

£ ,

[ ]V =

A

h t n

w

w

2 2132000 . (LRFD F2-3 and A- F2-3)

The nomi nal shear strength for all other sec tions is taken as:

V = F An y v2 20.6 .


The nomi nal shear strength for mi nor di rec tion shears is as sumed as:

V = F An y v3 30.6


In the calculation of the ax ial force/bi ax ial mo ment ca pac ity ra tios, first, for eachsta tion along the length of the mem ber, the ac tual mem ber force/mo ment com po -nents are cal cu lated for each load com bi na tion. Then the cor re spond ing ca paci tiesare calculated. Then, the ca pac ity ra tios are calculated at each sta tion for eachmem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol -ling com pres sion and/or ten sion ca pac ity ra tio is then ob tained, along with the as -so ci ated sta tion and load com bi na tion. A ca pac ity ra tio greater than 1.0 in di catesex ceed ing a limit state.





The in ter ac tion ra tio is de ter mined based on the ra tio P

Pu

nj . If Pu is ten sile, Pn is the

nomi nal ax ial ten sile strength and j j= = 0.9t ; and if Pu is com pres sive, Pn isthe nomi nal ax ial com pres sive strength and j j= = 0.85c , ex cept for an gle sec -tions j j= = 0.90c (LRFD SAM 6). In ad di tion, the re sis tance fac tor for bend -ing, j b = 0.9.

For P

P u


P

P +

M

M +

M

Mu

n

u

b n

u

b nj j j

8

933

33

22

22

æ

èçç

ö

ø÷÷ . (LRFD H1- 1a, SAM 6-1a)

For P

P < u


P

P +

M

M +

M

Mu

n

u

b n

u

b n233

33

22

22j j j

æ

èçç

ö

ø÷÷ . (LRFD H1- 1b, SAM 6-1a)

For cir cu lar sec tions an SRSS (Square Root of Sum of Squares) com bi na tion isfirst made of the two bend ing com po nents be fore add ing the ax ial load com po nentin stead of the sim ple al ge braic ad di tion im plied by the above for mu las.

For Single- angle sec tions, the com bined stress ra tio is cal cu lated based on the prop -er ties about the principal axis (LRFD SAM 5.3, 6). For I, Box, Chan nel, T, Dou blean gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci pal axes co in cide withtheir geo met ric axes. For Single- angle sec tions, prin ci pal axes are de ter mined inthe pro gram. For gen eral sec tions it is as sumed that the sec tion prop er ties are givenin terms of the prin ci pal di rec tions.

Shear Stresses

Simi larly to the nor mal stresses, from the fac tored shear force val ues and the nomi -nal shear strength val ues at each sta tion for each of the load com bi na tions, shear ca -pac ity ra tios for ma jor and minor di rec tions are calculated as fol lows:

V

Vu

v n

2

2j , and



V

Vu

v n

3

3j ,

where j v = 0.9 .




C h a p t e r VII

Check/Design for BS 5950-2000

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the BS 5950-00 de signcode (BSI 2000). Vari ous no ta tions used in this chap ter are de scribed in TableVII-1.


In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this sec tion. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di catesex ceed ing a limit state. Simi larly, a shear ca pac ity ra tio is also cal cu lated sepa -rately.

Eng lish as well as SI and MKS met ric units can be used for in put. But the code isbased on Newton- Millimeter- Second units. For sim plic ity, all equa tions and de -scrip tions pre sented in this chap ter cor re spond to Newton- Millimeter- Secondunits un less oth er wise noted.

181

182


A = Cross- sectional area, mm2

Ag = Gross cross- sectional area, mm2

A Av v2 3, = Ma jor and mi nor shear ar eas, mm2

B = Breadth, mm

D = Depth of sec tion, mm or out side di ame ter of pipes, mm

E = Modu lus of elas tic ity, MPa

Fc = Ax ial com pres sion, N

Ft = Ax ial ten sion, N

F Fv v2 3, = Ma jor and mi nor shear loads, N

G = Shear modu lus, MPa

H = Warp ing con stant, mm6

I 33 = Ma jor mo ment of in er tia, mm4

I 22 = Mi nor mo ment of in er tia, mm4

J = Tor sional con stant for the sec tion, mm4


K K33 22, = Ma jor and mi nor ef fec tive length fac tors

M = Ap plied mo ment, N-mm

M 33 = Ap plied mo ment about ma jor axis, N-mm

M 22 = Ap plied mo ment about mi nor axis, N-mm

M a33 = Ma jor maxi mum bend ing mo ment, N-mm

M a22 = Mi nor maxi mum bend ing mo ment, N-mm

M b = Buck ling re sis tance mo ment, N-mm

M c = Mo ment ca pac ity, N-mm

M c33 = Ma jor mo ment ca pac ity, N-mm

M c22 = Mi nor mo ment ca pac ity, N-mm

M E = Elas tic criti cal mo ment, N-mm

Pc = Com pres sion re sis tance, N

P Pc c33 22, = Ma jor and mi nor com pres sion re sis tance, N

Pt = Ten sion ca pac ity, N

P Pv v2 3, = Ma jor and mi nor shear ca paci ties, N

S S33 22, = Ma jor and mi nor plas tic sec tion moduli, mm3

T = Thick ness of flange or leg, mm

Ys = Speci fied yield strength, MPa

Z Z33 22, = Ma jor and mi nor elas tic sec tion moduli, mm3

Table VII-1BS 5950-2000 Notations

183

Chapter VII Check/Design for BS 5950-2000

a = Rob ert son con stant

b = Out stand width, mm

d = Depth of web, mm

h = Story height, mm

k = Dis tance from outer face of flange to web toe of fil let , mm

l = Un braced length of mem ber, mm

l l33 22, = Ma jor and mi nor di rec tion un braced mem ber lengths, mm

l le e33 22, = Ma jor and mi nor ef fec tive lengths, mm ( , )K l K l33 33 22 22

m = Equiva lent uni form mo ment fac tor

n = Slen der ness correction fac tor

qe = Elas tic criti cal shear strength of web panel, MPa

qcr = Criti cal shear strength of web panel, MPa

r r33 22, = Ma jor and mi nor ra dii of gy ra tion, mm

rz = Mini mum ra dius of gy ra tion for an gles, mm

t = Thick ness, mm

t f = Flange thick ness, mm

t w = Thick ness of web, mm

u = Buck ling pa rame ter

v = Slen der ness fac tor

b = Ra tio of smaller to larger end mo ments

e = Con stant 275

12

r y

æ

è

çç

ö

ø

÷÷


lo = Lim it ing slen der ness

lLT = Equiva lent slen der ness

lLo = Lim it ing equiva lent slen der ness

h = Perry fac tor

hLT = Perry co ef fi cient

r c = Com pres sive strength, MPa

r E = Euler strength, MPa

r y = Yield strength, MPa

y = Mono sym me try in dex

Table VII-1BS 5950-2000 Notations (cont.)


The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. Ac cord ing to the BS 5950-00 code, if astruc ture is sub jected to dead load (DL), live load (LL), wind load (WL), and earth -quake load (EL), and con sid er ing that wind and earth quake forces are re versi ble,then the fol low ing load com bi na tions may have to be con sid ered (BS 2.4):

1.4 DL1.4 DL + 1.6 LL (BS 2.4.1.1)

1.0 DL ± 1.4 WL 1.4 DL ± 1.4 WL 1.2 DL + 1.2 LL ± 1.2 WL (BS 2.4.1.1)

1.0 DL ± 1.4 EL 1.4 DL ± 1.4 EL 1.2 DL + 1.2 LL ± 1.2 EL

These are also the de fault de sign load com bi na tions when ever BS 5950-00 Code isused. The user should use other ap pro pri ate load ing com bi na tions if roof live loadis sepa rately treated, other types of loads are pres ent, or if pat tern live loads are tobe con sid ered.


In ad di tion to the above load com bi na tions, the code re quires that all build ingsshould be ca pa ble of re sist ing a no tional de sign hori zon tal load ap plied at eachfloor or roof level. The no tional load should be equal to the maxi mum of 0.01 timesthe fac tored dead load and 0.005 times the fac tored dead plus live loads (BS 2.4.2.3and 2.3.2.4). The no tional forces should be as sumed to act in any one di rec tion at atime and should be taken as act ing si mul ta ne ously with the fac tored dead plus ver ti -cal im posed live loads. They should not be com bined with any other hori zon tal load cases (BS 5.1.2.4). It is rec om mended that the user should de fine ad di tional loadcases for con sid er ing the no tional load in the pro gram and de fine the ap pro pri atede sign com bi na tions.

When us ing the BS 5950-00 code, the pro gram de sign as sumes that a P-D analy sishas al ready been per formed, so that mo ment mag ni fi ca tion fac tors for the mo mentscausing sidesway can be taken as unity. It is suggested that the P-D analy sis be



done at the fac tored load level cor re sponding to 1.2 dead load plus 1.2 live load.See also White and Hajjar (1991).


The nom i nal strengths for ax ial com pres sion and flex ure are de pend ent on the clas -si fi ca tion of the sec tion as Plas tic, Com pact, Semi-com pact, or Slen der. Pro gramchecks the sec tions ac cord ing to Table VII-2 (BS 3.5.2). The pa ram e ters r r1 2, and ealong with the slen der ness ra tios are the ma jor fac tors in clas si fi ca tion of sec tion.

• r1 and r2 is the ra tio of mean lon gi tu di nal stress in the web to r y in a sec tion.This im plies that for a sec tion in pure bend ing r1 and r2 are zero. In cal cu lat ing r1 and r2 , com pres sion is taken as pos i tive and ten sion is taken as neg a tive. ForI, H, RHS and welded box sec tions with equal flanges, r1 and r2 are cal cu latedas fol lows:

rP

dtwhere r

rP

A

y

g y

1 1

2

1 1= - < £

=

r

r

• e is de fined as fol lows:

er

=æ

è

çç

ö

ø

÷÷

2751 2

y

/

The sec tion is clas si fied as ei ther Class 1 (Plas tic), Class 2 (Com pact), or Class 3(Semi- compact) as ap pli ca ble. If a sec tion fails to sat isfy the lim its for Class 3(Semi- compact) sec tions, the sec tion is clas si fied as Class 4 (Slen der). Cur -rently program does not check stresses for Slen der sections.


The fac tored mem ber loads that are cal cu lated for each load com bi na tion are Ft or Fc , M 33 , M 22 , Fv 2 , and Fv 3 cor re spond ing to fac tored val ues of the ten sile or com -pres sive ax ial load, the ma jor mo ment, the mi nor mo ment, the ma jor di rec tionshear load, and the mi nor di rec tion shear load, re spec tively. These fac tored loadsare cal cu lated at each of the pre vi ously de fined sta tions.





Description ofSection

RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3(Semi-compact)

I-SHAPE

b T (Rolled) £ 9 e £ 10 e £ 15 e

b T (welded) £ 8 e £ 9 e £ 13 e

b T (Compression

due to bending)£ 28 e £ 32 e £ 40 e

b T (Axial

compression)Not Applicable Not applicable £ 40 e

d t

(Neutral axis atmid-depth)

£ 80 e £ 100 e £ 120 e

d t

(r1 is negative)

£+

80

1 1

e

r

³ 40e

£+

100 e

1 1r

³ 40e

£120

1 +

e

2 2r

³ 40e

d t

(r2 is positive)

£+

80

1 1

e

r

³ 40e

£+100 e

1 15 1. r

³ 40e

£120

1 +

e

2 2r

³ 40e

d t

(Axial compression)Not applicable Not applicable

£120

1 +

e

2 2r

³ 40e

BOX

b T (Flange

compression due tobending)

£ 28e ³ -80e d t/

£ 32e³ -80e d t/

£ 40e

b T

(Flange axialcompression)

Not applicable Not applicable £ 40e

d t

(Web neutral axis atmid-depth)

£ 64e £ 80e £120e

Table VII-2Limiting Width-Thickness Ratios for

Classification of Sections based on BS 5950-2000



Description of Section

RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3 (Semi-compact

)

BOX

d t

(Generally)

£+64

1 0 6 1

e

. r

³ 40e

£+80e

1 1r

³ 40e

£+120e

1 2 2r

³ 40e

d t

(web axialcompression)

Not applicable Not applicable £ 40e

CHANNEL d t £ 40e £ 40e £ 40e

T-SHAPE d t £ 8e £ 9e £ 18e

ANGLE, DOUBLEANGLE

(separated)

(Ax ial compression)

d t

d t

( )b + d t

Not applicable Not applicable£15e£15e£ 24e

ANGLE

(com pres sion due tobend ing)

b t

d t

£ 9e

£ 9e

£ 10e

£ 10e

£ 15 e

£ 15 e

PIPE

(compression due tobending)

(Ax ial com pres sion)

D t

D t

£ 40 2e

Not ap pli ca ble

£ 50 2e

Not ap pli ca ble

£ 140 2e

£ 80 2e

SOLIDCIRCLE

¾ Assumed Compact

SOLIDRECTANGLE

¾ Assumed Compact

Table VII-2 (cont.)Limiting Width-Thickness Ratios for




b

b

b

bb

b

t

d

d

d

r

d

d = D - 3t

t t

T

T

T

T T

t

t

t

t

tD

D

b b b

td

b = B - 3t

B

Dd d

z

2, y

2, yBS 5950 : Axes Conventions



3, x 3, x

Figure VII-1BS 5950-2000 Definition of Geometric Properties

The mo ment mag ni fi ca tion for non-sidesway mo ments is in cluded in the over allbuck ling in ter ac tion equa tions.

M = M +

Mg s

1

1 200-

ìíî

üýþj s,max

, where (BS 5.6.6, Ap pen dix E)

j s,max = Maxi mum story- drift di vided by the story- height, M g = Fac tored mo ments not caus ing trans la tion, andM s = Fac tored mo ments caus ing side sway.

The mo ment mag ni fi ca tion fac tor for mo ments caus ing sidesway can be taken asunity if a P-D anal y sis is car ried out. the pro gram de sign as sumes a P-D anal y sis hasbeen done and, there fore, j s max, for both ma jor and mi nor di rec tion bend ing istaken as 0. It is sug gested that the P-D anal y sis be done at the fac tored load level of1.2 DL plus 1.2 LL. See also White and Hajjar (1991).

Calculation of Section Capacities

The nomi nal strengths in com pres sion, ten sion, bend ing, and shear are com putedfor Class 1, 2, and 3 sec tions ac cord ing to the fol low ing sub sec tions. By de fault,program takes the de sign strength, r y , to be 1.0 times the mini mum yield strengthof steel, Ys , as speci fied by the user. In in put ting val ues of the yield strength, theuser should en sure that the thick ness and the ul ti mate strength limi ta tions given inthe code are sat is fied (BS 3.1.1).

r y sY= 1.0 (BS 3.1.1)

For Class 4 (Slen der) sec tions and any sin gly symmetric and un sym met ric sec tionsre quir ing spe cial treat ment, such as the con sid era tion of lo cal buck ling, flexural- torsional and tor sional buck ling, or web buck ling, re duced sec tion ca paci ties maybe ap pli ca ble. The user must sepa rately in ves ti gate this re duc tion if such ele mentsare used.

If the user speci fies nominal strengths for one or more ele ments in the“Overwrites”, these val ues will over ride all above the men tioned cal cu lated val -ues for those ele ments as de fined in the fol low ing sub sec tions.

Compression Resistance

The com pres sion re sis tance for plas tic, com pact, or semi- compact sec tions isevalu ated as fol lows:

Calculation of Section Capacities 189


P = Ac g cr , (BS 4.7.4)

where r c is the com pres sive strength given by

rr r

j j r rc

E y

E y

=+( )2 -

12

, where (BS C.1)

jr h r

=+( +1)

2

y E , (BS C.1)

190 Calculation of Section Capacities



Thickness (mm)

Axis of Bending

Major Minor

I-SHAPE (rolled)

£ 40> 40

2.03.5

3.55.5

H-SHAPE (rolled)

£ 40> 40

3.55.5

5.58.0

I or H-SHAPE(welded)

£ 40> 40

3.53.5

5.58.0

BOX or Pipe(Rolled)

any 2.0 2.0

BOX(welded)

£ 40> 40

3.55.5

3.55.5

CHANNEL,T-SHAPE, ANGLE

any 5.5 5.5

RECTANGULARor CIRCLE

£ 40> 40

3.55.5

3.55.5

GENERAL any 5.5 5.5

Table VII-3Robertson Constant in BS 5950-2000

r E = Eu ler strength, p l2 2E ,

h = Perry fac tor, 0.001 ( - 0 a l l ) ³ 0 , (BS C.2)a = Rob ert son con stant from Table VII-3, (BS C2, BS Ta ble 25)

l 0 = Lim it ing slen der ness, 0.22

12

p

r

E

y

æ

è

çç

ö

ø

÷÷ , and (BS C.2)

l = the slen der ness ra tio in ei ther the ma jor, l 33 = /l re33 33 , or in the mi nor, l 22 = /l re22 22 di rec tion (BS 4.7.2). The larger of the two val ues is used in the above equa tions to cal cu late Pc .

For sin gle an gles rz is used in stead of r33 and r22 . For mem bers in com pres sion,if l is greater than 180, a mes sage to that ef fect is printed al though there is nosuch lim i ta tion ex ists in BS 5950-2000 code.

Tension Capacity

The ten sion ca pac ity of a mem ber is given by

P = At g r y . (BS 4.6.1)

It should be noted that no net sec tion checks are made. If l is greater than 250, ames sage is dis played al though there is no such lim i ta tion ex ists in BS 5950-2000code.

The user may have to sepa rately in ves ti gate the mem bers which are con nected ec -cen tri cally to the axis of the mem ber, for ex am ple an gle sections.

Moment Capacity

The mo ment ca paci ties in the ma jor and mi nor di rec tions, M Mc c33 22and are basedon the de sign strength and the sec tion modu lus, the co -ex is tent shear and the pos si -bil ity of lo cal buck ling of the cross- section. Lo cal buck ling is avoided by ap ply inga limi ta tion to the width/thick ness ra tios of ele ments of the cross- section. The mo -ment ca paci ties are cal cu lated as fol lows:

Plastic and Compact Sections

For plas tic and com pact sec tions, the mo ment ca paci ties about the ma jor and themi nor axes of bend ing de pend on the shear force, Fv , and the shear ca pac ity, Pv .



For I, Box, Chan nel, and Dou ble-Chan nel sec tions bend ing about the 3-3 axis themo ment ca pac i ties con sid er ing the ef fects of shear force are com puted as

M = S Z , F Pc y y v vr r£ £1.5 for 0.6 , (BS 4.2.5.2)

M = S S Z , F Pc y v y v vr r r( )- £ >1.5 for 0.6 , (BS 4.2.5.3)

ex cept for sim ply sup ported and can ti le ver beams, the bend ing about the 3-3axis the mo ment ca pac i ties con sid er ing the ef fects of shear force are com -puted as

M = S Z , F Pc y y v vr r£ £1.2 for 0.6 , (BS 4.2.5.2)

M = S S Z , F Pc y v y v vr r r( )- £ >1.2 for 0.6 , (BS 4.2.5.3)

where

S = Plas tic modu lus of the gross sec tion about the relev ant axis,

Z = Elastic modu lus of the gross sec tion about the relev ant axis,

Sv = Plas tic modu lus of the gross sec tion about the rel e vant axis less the plas tic modu lus of that part of the sec tion re main ing af ter de duc tion of shear area i.e. plas tic modu lus of shear area. For ex am ple, for rolled I-shapes Sv 2 is taken to be tD 2 4 and

for welded I-shapes it is taken as td 2 4 ,

Pv = The shear ca pac ity de scribed later in this chap ter,

r =2

1F

P v

v

-é

ëê

ù

ûú

2

.

The com bined ef fect of shear and ax ial forces is not be ing con sid ered be cause prac -ti cal situa tions do not war rant this. In rare cases, how ever, the user may have to in -ves ti gate this in de pend ently, and if nec es sary, over write val ues of the sec tionmoduli.

For all other cases, the re duc tion of mo ment ca pac i ties for the pres ence of shearforce is not con sid ered. The user should in ves ti gate the re duced mo ment ca pac itysep a rately. The mo ment ca pac ity for these cases is com puted in program as

M = S Zc y yr r£ 12. . , for sim ply sup ported/cantilevered beam (BS 4.2.5.2)

M = S Zc y yr r£ 15. . , for sim ply sup ported/can ti le vered beam (BS 4.2.5.2)



Semi-compact Sections

For semi-com pact sec tions, the mo ment ca pac i ties about the ma jor and the mi noraxes of bend ing de pend on the shear force, Fv , and the shear ca pac ity, Pv .

For I, Box, Chan nel, and Dou ble-Chan nel sec tions bend ing about the 3-3 axis themo ment ca pac i ties con sid er ing the ef fects of shear force are com puted as:

M = Z , F Pc y v vr for 0.6£ , (BS 4.2.5.2)

M = Z S , F Pc y v v vr r( / . )- >15 for 0.6 , (BS 4.2.5.3)

Lateral-Torsional Buckling Moment Capacity

The lat eral tor sional buck ling strength, r b , of a mem ber is cal cu lated from the fol -low ing equa tions. The pro gram as sumes the mem bers to be uni form (of con stantprop er ties) through out their lengths. Fur ther more mem bers are as sumed to be sym -met ri cal about at least one axis.

For I, Box, T, Chan nel, and Dou ble-Chan nel sec tions M b is ob tained from

rr r

j j r rT T

b

E y

L L E y

= +( -

2) /1 2

, where (BS B2.1)

jr h r

TL

y LT E=

+( +1)

2 ,

r E = The elas tic crit i cal stress, p

l

2 E

LT

2 , and (BS B2.3)

hLT = The Perry co ef fi cient.

The Perry co ef fi cient, hLT , for rolled and welded sec tions is taken as fol lows:

For rolled sec tions

{ }h a l lTLT LT LL= 0- ³0 , and (BS B2.3)

for welded sec tions

h a lLT LT L= 02 0 ³ ,

with a l l h a l lTLT LT L LT L LT L( ) ( )- £ £ -0 02 . (BS B2.2)



In the above defi ni tion of hLT , l L 0 and l LT are the lim it ing equiva lent slen der ness and the equiva lent slen der ness, re spec tively, and a b is a con stant. a LT is taken as0.007 (BS 2.3). For flanged mem bers sym met ri cal about at least one axis and uni -form throughout their length, l L 0 is de fined as fol lows:

lp

rL

y

E0

2

= 0.4 , (BS B2.29b)

For I, Chan nel, Dou ble-Chan nel, and T sections l LT is de fined as

l lbwLT b= 2 25. F , (BS B2.3)

and for Box sec tions l LT is de fined as

( )l f lLT bn= 2.251 2

, where (BS B2.6)

• l is the slen der ness and is equiv a lent to l re22 22 . (BS B4.3.6.7)

• The ra tio bw should be taken as follows.

for class 1 plas tic or class 2 com pact cross-sec tion:

bw = 1.0

for class 3 semi-com pact cross-sec tion:

if M Zb b x= r then bwx

x

Z

S= , and

if M Sb b x ef= r then bw

x eff

x

S

S=

• u is the buck ling pa ram e ter. It is con ser va tively taken as 0.9 for rolled I-shapes and chan nels. For any other sec tion, u is taken as 1.0 (BS 4.3.7.5). For I, Chan -nel, and Dou ble-Chan nel sec tions,

uS

A D T=

4 332

2 2

1 4

g

( )-

æ

èçç

ö

ø÷÷ , for I, Chan nel, and Dou ble-Chan nel, (BS B2.5b)

uS

A D T=

4

2

332

2 2

1 4

g

( / )-

æ

èçç

ö

ø÷÷ , for T sec tion, where (BS B2.5b)



g = -æ

èçç

ö

ø÷÷1 22

33

I

I . (BS B2.5b)

• v is the slen der ness fac tor. For I, Chan nel, Dou ble-Chan nel, and T sec tions, itis given by the fol low ing for mula.

v

N N + x

=1

12

4 11

20

2

2( )-é

ëê

ù

ûú +

ìíï

îï

üýï

þï+

é

ë

êê

ù

û

úly y

ú

12

, where (BS B2.4)

N =0.5 , for I, Channel, Double - Channel sections,

1.0 , for T sections with flange in compression,

0.0 , for T sections with flange in tension, and

ì

íï

îï

(BS B2.4)

y =0.0 , for I, Channel, Double - Channel sections,

0.8 , for T sections with flange in compression, and

-1.0 , for T sections with flange in tension.

ì

íï

îï

(BS B2.4)

• f b is the buck ling in dex for box section fac tor. It is given by the fol low ing for -mula. (BS B2.6.1).

fg

b

S

AJ= 33

21 2

¢æ

èçç

ö

ø÷÷ , where (BS B2.6.1)

g¢ = -æ

èçç

ö

ø÷÷ -

æ

èçç

ö

ø÷÷1 122

33 33

I

I

J

I2.6 . (BS B2.6.1)

For all other sections, lat eral tor sional buck ling is not considered. The user shouldin ves ti gate mo ment ca pac ity con sid er ing lateral- torsional buck ling sepa rately.

Shear Capacities

The shear ca paci ties for both the ma jor and mi nor di rec tion shears in I- shapes,boxes or chan nels are evalu ated as fol lows:

P = Av y v2 20.6 r , and (BS 4.2.3)

P = Av y v3 30.6 r . (BS 4.2.3)






Condition

Axis of Bending

Major Minor

I-SHAPE RolledWelded

tDtd

( )0.9 4bT

( )0.9 4bT

CHANNELRolledWelded

tDtd

( )0.9 2bT

( )0.9 2bT

DOUBLE CHANNELRolledWelded

2.0 tD2.0 td

( )2.0 0.9* 2bT

( )2.0 0.9* 2bT

BOX ¾D

D BA

+B

D BA

+

T-SHAPERolledWelded

td

( )t d T-( )0.9 2bT

( )0.9 2bT

DOUBLE ANGLE ¾ 2td 2bt

ANGLE ¾ td bt

RECTANGULAR ¾ 0.9 A 0.9 A

CIRCLE ¾ 0.9 A 0.9 A

PIPE ¾ 0.6 A 0.6 A

GENERAL ¾ 0.9 A 0.9 A

Table VII-4Shear Area in BS 5950-2000

The shear ar eas Av 3 and Av 2 are given in Ta ble VII-4.

More over, the shear ca pac ity com puted above is valid only if d t £ 70 e for rolledsec tion and d t £ 62 e for welded sec tion. For d t £ 70 e for rolled sec tion and d t £ 62 e for welded sec tion, the shear buck ling of the thin mem bers should bechecked in de pend ently by the user in ac cor dance with the code (BS 4.4.5).


In the calculation of the ax ial force/bi ax ial mo ment ca pac ity ra tios, first, for eachsta tion along the length of the mem ber, for each load com bi na tion, the ac tual mem -ber force/mo ment com po nents are cal cu lated. Then the cor re spond ing ca paci tiesare calculated. Then, the ca pac ity ra tios are calculated at each sta tion for eachmem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol -ling com pres sion and/or ten sion ca pac ity ra tio is then ob tained, along with the as -so ci ated sta tion and load com bi na tion. A ca pac ity ra tio greater than 1.0 in di catesex ceed ing a limit state.


Local Capacity Check

For mem bers un der ax ial load and mo ments, lo cal ca pac ity ra tios are cal cu lated asfol lows:

Under Axial Tension

A sim pli fied ap proach al lowed by the code is used to check the lo cal ca pac ity forplas tic and com pact sec tions.

F

A +

M

M +

M

Mt

g y c cr33

33

22

22

(BS 4.8.2)

Under Axial Compression

Simi larly, the same sim pli fied ap proach is used for ax ial com pres sion.

F

A +

M

M +

M

Mc

g y c cr33

33

22

22

(BS 4.8.3.2)



Overall Buckling Check

In ad di tion to lo cal ca pac ity checks, which are car ried out at sec tion level, a com -pres sion mem ber with bend ing mo ments is also checked for over all buck ling in ac -cor dance with the fol low ing in ter ac tion ra tio:

F

A

m M

M +

m M

Zc

g c b yr r+ 33 33 22 22

22

(BS 4.8.3.3.1)

The equiva lent uni form mo ment fac tor, m, for mem bers of uni form sec tion andwith flanges, not loaded be tween ad ja cent lat eral re straints, is de fined as

m = + M M M

M M0.2

0.8M240 1 0 6 0 12 3 4. . .

max max

+ +³ . (BS Ta ble 26)

For other mem bers, the value of m is taken as 1.0. The pro gram de faults m to 1.0 if the un braced length, l, of the mem ber is over writ ten by the user (i.e. if it is not equalto the length of the mem ber). The user can over write the value of m for any mem -ber by spec i fy ing it. The mo ment M 2 and M 4 are the val ues at the quar ter points and the mo ment M 3 is the value at mid-length. If M 2 , M 3 and M 4 all lie on the same side of the axis, their val ues are taken as pos i tive. If they lie both sides of the axis, theside lead ing to the larger value is taken as the pos i tive side. The val ues M max and M 24 are al ways taken as pos i tive. M max is the mo ment in the seg ment and the M 24 isthe max i mum mo ment in the cen tral half of the seg ment.

Shear Capacity Check

From the fac tored shear force val ues and the shear ca pac ity val ues at each sta tion,shear ca pac ity ra tios for ma jor and minor di rec tions are pro duced for each of theload com bi na tions as fol lows:

F

Pv

v

2

2

, and

F

Pv

v

3

3

.



C h a p t e r VIII

Check/Design for BS 5950-1990

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the BS 5950-90 de signcode (BSI 1990). Vari ous no ta tions used in this chap ter are de scribed in Ta bleIX-1.




199

200





B = Breadth, mm

D = Depth of sec tion, mm or out side di ame ter of pipes, mm


Fc = Ax ial com pres sion, N

Ft = Ax ial ten sion, N

F Fv v2 3, = Ma jor and mi nor shear loads, N


H = Warp ing con stant, mm6






M = Ap plied mo ment, N-mm

M 33 = Ap plied mo ment about ma jor axis, N-mm

M 22 = Ap plied mo ment about mi nor axis, N-mm

M a33 = Ma jor maxi mum bend ing mo ment, N-mm

M a22 = Mi nor maxi mum bend ing mo ment, N-mm

M b = Buck ling re sis tance mo ment, N-mm

M c = Mo ment ca pac ity, N-mm

M c33 = Ma jor mo ment ca pac ity, N-mm

M c22 = Mi nor mo ment ca pac ity, N-mm

M E = Elas tic criti cal mo ment, N-mm

Pc = Com pres sion re sis tance, N

P Pc c33 22, = Ma jor and mi nor com pres sion re sis tance, N

Pt = Ten sion ca pac ity, N

P Pv v2 3, = Ma jor and mi nor shear ca paci ties, N

S S33 22, = Ma jor and mi nor plas tic sec tion moduli, mm3

T = Thick ness of flange or leg, mm

Ys = Speci fied yield strength, MPa

Z Z33 22, = Ma jor and mi nor elas tic sec tion moduli, mm3

Table VIII-1BS 5950-1990 Notations

201

Chapter VIII Check/Design for BS 5950-1990

a = Rob ert son con stant

b = Out stand width, mm


h = Story height, mm




l le e33 22, = Ma jor and mi nor ef fec tive lengths, mm ( , )K l K l33 33 22 22

m = Equiva lent uni form mo ment fac tor

n = Slen der ness correction fac tor

qe = Elas tic criti cal shear strength of web panel, MPa

qcr = Criti cal shear strength of web panel, MPa

r r33 22, = Ma jor and mi nor ra dii of gy ra tion, mm

rz = Mini mum ra dius of gy ra tion for an gles, mm

t = Thick ness, mm


t w = Thick ness of web, mm

u = Buck ling pa rame ter

v = Slen der ness fac tor

b = Ra tio of smaller to larger end mo ments

e = Con stant 275

12

r y

æ

è

çç

ö

ø

÷÷


lo = Lim it ing slen der ness

lLT = Equiva lent slen der ness

lLo = Lim it ing equiva lent slen der ness

h = Perry fac tor

hLT = Perry co ef fi cient

r c = Com pres sive strength, MPa

r E = Euler strength, MPa

r y = Yield strength, MPa

y = Mono sym me try in dex

Table VIII-1BS 5950-1990 Notations (cont.)


The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. Ac cord ing to the BS 5950 code, if a struc -ture is sub jected to dead load (DL), live load (LL), wind load (WL), and earth quakeload (EL), and con sid er ing that wind and earth quake forces are re versi ble, then thefol low ing load com bi na tions may have to be con sid ered (BS 2.4):

1.4 DL1.4 DL + 1.6 LL (BS 2.4.1.1)

1.0 DL ± 1.4 WL 1.4 DL ± 1.4 WL 1.2 DL + 1.2 LL ± 1.2 WL (BS 2.4.1.1)

1.0 DL ± 1.4 EL 1.4 DL ± 1.4 EL 1.2 DL + 1.2 LL ± 1.2 EL

These are also the de fault de sign load com bi na tions when ever BS 5950 Code isused. The user should use other ap pro pri ate load ing com bi na tions if roof live loadis sepa rately treated, other types of loads are pres ent, or if pat tern live loads are tobe con sid ered.


In ad di tion to the above load com bi na tions, the code re quires that all build ingsshould be ca pa ble of re sist ing a no tional de sign hori zon tal load ap plied at eachfloor or roof level. The no tional load should be equal to the maxi mum of 0.01 timesthe fac tored dead load and 0.005 times the fac tored dead plus live loads (BS2.4.2.3). The no tional forces should be as sumed to act in any one di rec tion at a timeand should be taken as act ing si mul ta ne ously with the fac tored dead plus ver ti calim posed live loads. They should not be com bined with any other hori zon tal loadcases (BS 5.1.2.3). It is rec om mended that the user should de fine ad di tional loadcases for con sid er ing the no tional load in the pro gram and de fine the ap pro pri atede sign com bi na tions.

When us ing the BS 5950 code, the pro gram de sign as sumes that a P-D analy sis hasal ready been per formed, so that mo ment mag ni fi ca tion fac tors for the mo mentscausing sidesway can be taken as unity. It is suggested that the P-D analy sis be



done at the fac tored load level cor re sponding to 1.2 dead load plus 1.2 live load.See also White and Hajjar (1991).


The nom i nal strengths for ax ial com pres sion and flex ure are de pend ent on the clas -si fi ca tion of the sec tion as Plas tic, Com pact, Semi-com pact, or Slen der. The pro -gram checks the sec tions ac cord ing to Table VII-2 (BS 3.5.2). The pa ram e ters R, g c and e along with the slen der ness ra tios are the ma jor fac tors in clas si fi ca tion ofsec tion.

• R is the ra tio of mean lon gi tu di nal stress in the web to r y in a sec tion. This im -plies that for a sec tion in pure bend ing R is zero. In cal cu lat ing R, com pres sionis taken as pos i tive and ten sion is taken as neg a tive. R is cal cu lated as fol lows:

RP

Ag y

=r

• a is given as 2 cg d, where g c is the dis tance from the plas tic neu tral axis to the edge of the web con nected to the com pres sion flange. For a >2 , the sec tion istreated as hav ing com pres sion through out.

ag= c

d 2

gr

cy

DT

P

t=

-æ

èç

ö

ø÷-

2 2, for I and Channel section

for Box and Double Channel sD

TP

ty2 4-

æ

èç

ö

ø÷-

r, ection

ì

í

ïï

î

ïï

In cal cu lat ing g c , com pres sion is taken as neg a tive and ten sion is taken as pos i -tive.

• e is de fined as fol lows:

er

=æ

è

çç

ö

ø

÷÷

2751 2

y

/

The sec tion is clas si fied as ei ther Class 1 (Plas tic), Class 2 (Com pact), or Class 3(Semi- compact) as ap pli ca ble. If a sec tion fails to sat isfy the lim its for Class 3






RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3(Semi-compact)

I-SHAPE

b T (Rolled) £ 8.5 e £ 9.5 e £ 15 e

b T (welded) £ 7.5 e £ 8.5 e £ 13 e

d t

webs (a < 2)

£79

0.4 + 0.6

e

a£

98 e

a

For R > 0 :

£120

1 + 1.5

e

R and £

æ

èç

ö

ø÷

41

R- 13 e (welded)

£120

1.5

e

1 + R and £

æ

èç

ö

ø÷

41

R- 2 e (rolled)

For R = 0 : £ 120 e , and

For R < 0 : £120

( )2

e

1 + R and £ 250 e .

d t

webs (a ³ 2)(rolled)

£ 39 e £ 39 e £ 39 e

d t

webs (a ³ 2)(welded)

£ 28 e £ 28 e £ 28 e

BOX

b T (Rolled) £ 26 e £ 32 e £ 39 e

b T (welded) £ 23 e £ 25 e £ 28 e

d t

As for I-shapes

As for I-shapes

As for I-shapes

CHANNELb T

d t

As forI-shapes

As for I-shapes

As for I-shapes

T-SHAPEb T

d t

£ 8.5 e£ 8.5 e

£ 9.5 e£ 9.5 e

£ 19 e£ 19 e

DOUBLEANGLE

(separated)

d t

£ 8.5 e £ 9.5 e £ 15 e

( )b + d t £ 23 e £ 23 e £ 23 e

Table VIII-2Limiting Width-Thickness Ratios for


(Semi- compact) sec tions, the sec tion is clas si fied as Class 4 (Slen der). Cur -rently the pro gram does not check stresses for Slen der sections.


The fac tored mem ber loads that are cal cu lated for each load com bi na tion are Ft or Fc , M 33 , M 22 , Fv 2 , and Fv 3 cor re spond ing to fac tored val ues of the ten sile or com -pres sive ax ial load, the ma jor mo ment, the mi nor mo ment, the ma jor di rec tionshear load, and the mi nor di rec tion shear load, re spec tively. These fac tored loadsare cal cu lated at each of the pre vi ously de fined sta tions.

The mo ment mag ni fi ca tion for non- sidesway mo ments is in cluded in the over allbuck ling in ter ac tion equa tions.

M = M +

Mg s

1

1 200-

ìíî

üýþj s,max

, where (BS 5.6.3)

j s,max = Maxi mum story- drift di vided by the story- height, M g = Fac tored mo ments not caus ing trans la tion, andM s = Fac tored mo ments caus ing side sway.



Description of Section

RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3 (Semi-compact)

ANGLE

b t

( )b + d t

£ 8.5 e

£ 23 e

£ 9.5 e

£ 23 e

£ 15 e

£ 23 e

PIPE D t £ 40 2e £ 57 2e £ 80 2e

SOLIDCIRCLE

¾ Assumed Compact

SOLIDRECTANGLE

¾ Assumed Compact

GENERAL ¾ Assumed Semi-compact

Table VIII-2 (cont.)Limiting Width-Thickness Ratios for




b

b

b

bb

b

t

d

d

d

r

d

d = D - 3t

t t

T

T

T

T T

t

t

t

t

tD

D

b b b

td

b = B - 3t

B

Dd d

z

2, y

2, yBS 5950 : Axes Conventions



3, x 3, x

Figure VIII-1BS 5950-1990 Definition of Geometric Properties

The mo ment mag ni fi ca tion fac tor for mo ments caus ing sidesway can be taken asunity if a P-D anal y sis is car ried out. The pro gram de sign as sumes a P-D anal y sishas been done and, there fore, j s max, for both ma jor and mi nor di rec tion bend ing istaken as 0. It is sug gested that the P-D anal y sis be done at the fac tored load level of1.2 DL plus 1.2 LL. See also White and Hajjar (1991).

Calculation of Section Capacities

The nomi nal strengths in com pres sion, ten sion, bend ing, and shear are com putedfor Class 1, 2, and 3 sec tions ac cord ing to the fol low ing sub sec tions. By de fault, the pro gram takes the de sign strength, r y , to be 1.0 times the mini mum yield strengthof steel, Ys , as speci fied by the user. In in put ting val ues of the yield strength, theuser should en sure that the thick ness and the ul ti mate strength limi ta tions given inthe code are sat is fied (BS 3.1.1).

r y sY= 1.0 (BS 3.1.1)


If the user speci fies nominal strengths for one or more ele ments in the“Overwrites”, these val ues will over ride all above the men tioned cal cu lated val -ues for those ele ments as de fined in the fol low ing sub sec tions.


The com pres sion re sis tance for plas tic, com pact, or semi- compact sec tions isevalu ated as fol lows:

P = Ac g cr , (BS 4.7.4)

where r c is the com pres sive strength given by

rr r

j j r rc

E y

E y

=+( )2 -

12

, where (BS C.1)

jr h r

=+( +1)

2

y E , (BS C.1)



r E = Euler strength, p l2 2E ,

h = Perry fac tor, 0.001 ( - 0 a l l ) ³ 0 , (BS C.2)a = Rob ert son con stant from Table VII-3, (BS C2, BS Ta ble25)

l 0 = Lim it ing slen der ness, 0.22

12

p

r

E

y

æ

è

çç

ö

ø

÷÷ , and (BS C.2)

l = the slen der ness ra tio in ei ther the ma jor, l 33 = /l re33 33 , or in the mi nor, l 22 = /l re22 22 di rec tion (BS 4.7.3.1). The larger of the two val ues is used in the above equa tions to cal cu late Pc .




Thickness (mm)

Axis of Bending

Major Minor

I-SHAPE (rolled)

any 2.0 3.5

H-SHAPE (rolled)

£ 40> 40

3.55.5

5.58.0

I-SHAPE(welded)

£ 40> 40

3.53.5

5.58.0

BOX or Pipe(Rolled)

any 2.0 2.0

BOX(welded)

£ 40> 40

3.55.5

3.55.5

CHANNEL,T-SHAPE, ANGLE

any 5.5 5.5

RECTANGULARor CIRCLE

£ 40> 40

3.55.5

3.55.5

GENERAL any 5.5 5.5

Table VIII-3Robertson Constant in BS 5950

For sin gle an gles rz is used in stead of r33 and r22 . For mem bers in com pres sion,if l is greater than 180, a mes sage to that ef fect is printed (BS 4.7.3.2).

Tension Capacity

The ten sion ca pac ity of a mem ber is given by

P = At g r y . (BS 4.6.1)

It should be noted that no net sec tion checks are made. For main mem bers in ten -sion, the slen der ness, l, should not be greater than 250 (BS 4.7.3.2). If l is greaterthan 250, a mes sage is dis played accordingly.

The user may have to sepa rately in ves ti gate the mem bers which are con nected ec -cen tri cally to the axis of the mem ber, for ex am ple an gle sections.

Moment Capacity

The mo ment ca paci ties in the ma jor and mi nor di rec tions, M Mc c33 22and are basedon the de sign strength and the sec tion modu lus, the co -ex is tent shear and the pos si -bil ity of lo cal buck ling of the cross- section. Lo cal buck ling is avoided by ap ply inga limi ta tion to the width/thick ness ra tios of ele ments of the cross- section. The mo -ment ca paci ties are cal cu lated as fol lows:

Plastic and Compact Sections

For plas tic and com pact sec tions, the mo ment ca paci ties about the ma jor and themi nor axes of bend ing de pend on the shear force, Fv , and the shear ca pac ity, Pv .

For I, Box, Chan nel, and Dou ble-Chan nel sec tions bend ing about the 3-3 axis themo ment ca pac i ties con sid er ing the ef fects of shear force are com puted as

M = S Z , F Pc y y v vr r£ £1.2 for 0.6 , (BS 4.2.5)

M = S S Z , F Pc y v y v vr r r( )- £ >1 1.2 for 0.6 , (BS 4.2.6)

where

S = Plas tic modu lus of the gross sec tion about the relev ant axis,

Z = Elastic modu lus of the gross sec tion about the relev ant axis,



Sv = Plas tic modu lus of the gross sec tion about the rel e vant axis less the plas tic modu lus of that part of the sec tion re main ing af ter de duc tion of shear area i.e. plas tic modu lus of shear area. For ex am ple, for rolled I-shapes Sv 2 is taken to be tD 2 4 and

for welded I-shapes it is taken as td 2 4 ,

Pv = The shear ca pac ity de scribed later in this chap ter,

r1 =2.5

1.5F

P v

v

- .

The com bined ef fect of shear and ax ial forces is not be ing con sid ered be cause prac -ti cal situa tions do not war rant this. In rare cases, how ever, the user may have to in -ves ti gate this in de pend ently, and if nec es sary, over write val ues of the sec tionmoduli.

For all other cases, the re duc tion of mo ment ca pac i ties for the pres ence of shearforce is not con sid ered. The user should in ves ti gate the re duced mo ment ca pac itysep a rately. The mo ment ca pac ity for these cases is com puted in the pro gram as

M = S Zc y yr r£ 1.2 . (BS 4.2.5)

Semi-compact Sections

Re duc tion of mo ment ca pac ity due to co ex is tent shear does not ap ply for semi- compact sec tions.

M Zc y= r (BS 4.2.5)

Lateral-Torsional Buckling Moment Capacity

The lat eral tor sional buck ling re sis tance mo ment, M b , of a mem ber is cal cu latedfrom the fol low ing equa tions. The pro gram as sumes the mem bers to be uni form (of con stant prop er ties) through out their lengths. Fur ther more mem bers are as sumedto be sym met ri cal about at least one axis.

For I, Box, T, Chan nel, and Dou ble-Chan nel sec tions M b is ob tained from

M = S M

S Mb

y E

B B y E

r

j j r

33

331 2+( -

2) /

, where (BS B2.1)



jr h

B

y LT ES M=

+( +1)

2

33 ,

M E = The elas tic criti cal mo ment, S E

LT

33

2

p

l

2

, and (BS B2.3)

hLT = The Perry co ef fi cient.

The Perry co ef fi cient, hLT , for rolled and welded sec tions is taken as fol lows:

For rolled sec tions

{ }h a l lLT b LT L= 0- ³0 , and (BS B2.3)

for welded sec tions

h a lLT b L= 02 0 ³ , with a l l h a l lb LT L LT b LT L( ) ( )- £ £ -0 02 .(BS B2.2)

In the above defi ni tion of hLT , l L 0 and l LT are the lim it ing equiva lent slen der ness and the equiva lent slen der ness, re spec tively, and a b is a con stant. a b is taken as0.007 (BS 2.3). For flanged mem bers sym met ri cal about at least one axis and uni -form throughout their length, l L 0 is de fined as fol lows:

lp

rL

y

E0

2

= 0.4 , (BS B2.4)

For I, Chan nel, Dou ble-Chan nel, and T sections l LT is de fined as

l lLT nu v= , (BS B2.5)

and for Box sec tions l LT is de fined as

( )l f lLT bn= 2.251 2

, where (BS B2.5)

• l is the slen der ness and is equiva lent to l re22 22 .

• n is the slen der ness cor rec tion fac tor. For flanged mem bers in gen eral, notloaded be tween ad ja cent lat eral re straints, and for can ti le vers with out in ter me -di ate lat eral re straints, n is taken as 1.0. For mem bers with equal flanges loadedbe tween ad ja cent lat eral re straints, the value of n is con ser va tively taken asgiven by the fol low ing for mula. This, how ever, can be over writ ten by the userfor any mem ber by speci fy ing it (BS Ta ble 13).



nCb

= £1

1.0 , where

Cb = 12.5

2.5

M

M + M + M + MA B C

max

max 3 4 3 , and

M max , M M MA B C, , and are ab so lute val ues of maxi mum mo ment, ¼point, cen ter of span and ¾ point ma jor mo ments re spec tively, in the mem -ber. The pro gram also de faults Cb to 1.0 if the un braced length, l, of themem ber is re de fined by the user (i.e. it is not equal to the length of themem ber). Cb should be taken as 1.0 for can ti le vers. How ever, the pro gramis un able to de tect whether the mem ber is a can ti le ver. The user can over -write the value of Cb for any mem ber.

• u is the buck ling pa ram e ter. It is con ser va tively taken as 0.9 for rolledI-shapes and chan nels. For any other sec tion, u is taken as 1.0 (BS 4.3.7.5). ForI, Chan nel, and Dou ble-Chan nel sec tions,

uS

A D T=

4 332

2 2

1 4

g

( )-

æ

èçç

ö

ø÷÷ , for I, Chan nel, and Dou ble-Chan nel, (BS B2.5b)

uI S

A H= 22 33

2

2

1 4

gæ

èçç

ö

ø÷÷ , for T sec tion, where (BS B2.5b)

g = -æ

èçç

ö

ø÷÷1 22

33

I

I . (BS B2.5b)

• v is the slen der ness fac tor. For I, Chan nel, Dou ble-Chan nel, and T sec tions, itis given by the fol low ing for mula.

v

N N + x

=1

12

4 11

20

2

2( )-é

ëê

ù

ûú +

ìíï

îï

üýï

þï+

é

ë

êê

ù

û

úly y

ú

12

, where (BS B2.5d)

N =0.5 , for I, Channel, Double - Channel sections,

1.0 , for T sections with flange in compression,

0.0 , for T sections with flange in tension, and

ì

íï

îï

(BS B2.5d)



y =0.0 , for I, Channel, Double - Channel sections,

0.8 , for T sections with flange in compression, and

-1.0 , for T sections with flange in tension.

ì

íï

îï

(BS B2.5d)

• f b is the buck ling in dex for box section fac tor. It is given by the fol low ing for -mula. (BS B2.6.1).

fg

b

S

A J= 33

2

2

1 2

¢æ

èçç

ö

ø÷÷ , where (BS B2.6.1)

g¢ = -æ

èçç

ö

ø÷÷ -

æ

èçç

ö

ø÷÷1 122

33 33

I

I

J

I2.6 . (BS B2.6.1)

For all other sections, lat eral tor sional buck ling is not considered. The user shouldin ves ti gate mo ment ca pac ity con sid er ing lateral- torsional buck ling sepa rately.

Shear Capacities

The shear ca paci ties for both the ma jor and mi nor di rec tion shears in I- shapes,boxes or chan nels are evalu ated as fol lows:

P = Av y v2 20.6 r , and (BS 4.2.3)

P = Av y v3 30.6 r . (BS 4.2.3)

The shear ar eas Av 3 and Av 2 are given in Ta ble VII-4.

Moreo ver, the shear ca pac ity com puted above is valid only if d t £ 63e, strictlyspeak ing. For d t > 63e, the shear buck ling of the thin mem bers should be checkedin de pend ently by the user in ac cor dance with the code (BS 4.4.5).








Condition

Axis of Bending

Major Minor

I-SHAPE RolledWelded

tDtd

( )0.9 4bT

( )0.9 4bT

CHANNELRolledWelded

tDtd

( )0.9 2bT

( )0.9 2bT

DOUBLE CHANNELRolledWelded

2.0 tD2.0 td

( )2.0 0.9* 2bT

( )2.0 0.9* 2bT

BOX ¾D

D BA

+B

D BA

+

T-SHAPERolledWelded

td

( )t d T-( )0.9 2bT

( )0.9 2bT

DOUBLE ANGLE ¾ 2td 2bt

ANGLE ¾ td bt

RECTANGULAR ¾ 0.9 A 0.9 A

CIRCLE ¾ 0.9 A 0.9 A

PIPE ¾ 0.6 A 0.6 A

GENERAL ¾ 0.9 A 0.9 A

Table VIII-4Shear Area in BS 5950-1990


Local Capacity Check

For mem bers un der ax ial load and mo ments, lo cal ca pac ity ra tios are cal cu lated asfol lows:

Under Axial Tension

A sim pli fied ap proach al lowed by the code is used to check the lo cal ca pac ity forplas tic and com pact sec tions.

F

A +

M

M +

M

Mt

g y c cr33

33

22

22

(BS 4.8.2)

Under Axial Compression

Simi larly, the same sim pli fied ap proach is used for ax ial com pres sion.

F

A +

M

M +

M

Mc

g y c cr33

33

22

22

(BS 4.8.3.2)

Overall Buckling Check

In ad di tion to lo cal ca pac ity checks, which are car ried out at sec tion level, a com -pres sion mem ber with bend ing mo ments is also checked for over all buck ling in ac -cor dance with the fol low ing in ter ac tion ra tio:

F

A

m M

M +

m M

Zc

g c b yr r+ 33 33 22 22

22

(BS 4.8.3.3.1)

The equiva lent uni form mo ment fac tor, m, for mem bers of uni form sec tion andwith flanges, not loaded be tween ad ja cent lat eral re straints, is de fined as

m = + 0.57 0.33 +0.10 0.432b b ³ . (BS Ta ble 18)

For other members, the value of m is taken as 1.0. The pro gram de faults m to 1.0 if the un braced length, l, of the mem ber is over writ ten by the user (i.e. if it is not equalto the length of the mem ber). The user can over write the value of m for any mem -ber by speci fy ing it. b is the ra tio of the smaller end mo ment to the larger end mo -



ment on a span equal to the un re strained length, be ing posi tive for sin gle cur va turebend ing and nega tive for dou ble cur va ture bend ing.

Shear Capacity Check

From the fac tored shear force val ues and the shear ca pac ity val ues at each sta tion,shear ca pac ity ra tios for ma jor and minor di rec tions are pro duced for each of theload com bi na tions as fol lows:

F

Pv

v

2

2

, and

F

Pv

v

3

3

.



C h a p t e r IX

Check/Design for CISC94

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the CAN/CSA- S16.1-94 de sign code (CISC 1995). Vari ous no ta tions used in this chap ter are de -scribed in Table IX-1.




217

218





Aw = Shear area, mm2

C e = Euler buck ling strength, N

C f = Fac tored com pres sive ax ial load, N

Cr = Fac tored com pres sive ax ial strength, N

Cw = Warp ing con stant, mm6

C y = Com pres sive ax ial load at yield stress, A Fg y , N

D = Out side di ame ter of pipes, mm


Fy = Speci fied mini mum yield stress, MPa


I 33 , I 22 = Ma jor and mi nor mo ment of in er tia, mm4



K K33 22, = Ef fec tive length K-fac tors in the ma jor and mi nor di rec tions (as sumed as 1.0 un less over writ ten by user)

L = Lat er ally un braced length of mem ber, mm

M Mf f33 22, = Fac tored ma jor and mi nor bend ing loads, N-mm

M Mp p33 22, = Ma jor and mi nor plas tic mo ments, N-mm

M Mr r33 22, = Fac tored ma jor and mi nor bend ing strengths, N-mm

M u = Criti cal elas tic mo ment, N-mm

M My y33 22, = Ma jor and mi nor yield mo ments, N-mm

S S33 22, = Ma jor and mi nor sec tion moduli, mm3

Tf = Fac tored ten sile ax ial load, N

Tr = Fac tored ten sile ax ial strength, N

U1 = Mo ment mag ni fi ca tion fac tor to ac count for de for ma tion of mem ber be tween ends

U 2 = Mo ment mag ni fi ca tion fac tor ( on sidesway mo ments) to ac count for P-D

V Vf f2 3, = Fac tored ma jor and mi nor shear loads, N

V Vr r2 3, = Fac tored ma jor and mi nor shear strengths, N

Z Z33 22, = Ma jor and mi nor plas tic moduli, mm3

Table IX-1CISC 94 Notations

219

Chapter IX Check/Design for CISC94

b = Nomi nal di men sion of longer leg of an gles

( )b tf w- 2 for welded

( )b tf f-3 for rolled box sec tions, mm

bf = Flange width, mm

d = Over all depth of mem ber, mm

h = Clear dis tance be tween flanges , taken as ( )d t f- 2 , mm

k = Web plate buck ling co ef fi cient, as sumed as 5.34 (no stiff en ers)




r = Ra dius of gy ra tion, mm

r r33 22, = Ra dii of gy ra tion in the ma jor and mi nor di rec tions, mm

rz = Mini mum Ra dius of gy ra tion for an gles, mm

t = Thick ness, mm


t w = Web thick ness, mm


j = Re sis tance fac tor, taken as 0.9

w1 = Mo ment Co ef fi cient

w w13 12, = Ma jor and mi nor di rec tion mo ment co ef fi cients

w2 = Bend ing co ef fi cient

Table IX-1CISC 94 Notations (cont.)


The de sign load com bi na tions are the vari ous com bi na tions of the load cases forwhich the struc ture needs to be checked. For the CAN/CSA- S16.1-94 code, if astruc ture is sub jected to dead load (DL), live load (LL), wind load (WL), and earth -quake in duced load (EL), and con sid er ing that wind and earth quake forces are re -versi ble, then the fol low ing load com bi na tions may have to be de fined (CISC 7.2):

1.25 DL1.25 DL + 1.50 LL (CISC 7.2.2)

1.25 DL ± 1.50 WL 0.85 DL ± 1.50 WL 1.25 DL + 0.7 (1.50 LL ± 1.50 WL) (CISC 7.2.2)

1.00 DL ± 1.00 EL 1.00 DL + 0.50 LL ± 1.00 EL (CISC 7.2.6)

These are also the de fault de sign load com bi na tions when ever the CISC Code isused. In gen er at ing the above de fault load ing com bi na tions, the im por tance fac toris taken as 1.

The user should use other ap pro pri ate load ing com bi na tions if roof live load issepa rately treated, other types of loads are pres ent, or if pat tern live loads are to becon sid ered.


When us ing the CISC code, the pro gram de sign as sumes that a P-D analy sis hasbeen per formed so that mo ment mag ni fi ca tion fac tors for mo ments caus ingsidesway can be taken as unity. It is suggested that the P-D analy sis be done at thefac tored load level of 1.25 DL plus 1.05 LL. See also White and Hajjar (1991).

For the grav ity load case only, the code (CISC 8.6.2) re quires that notional lat eralloads be ap plied at each story, equal to 0.005 times the fac tored grav ity loads act ing at each story. If ex tra load cases are used for such analy sis, they should be in cludedin the load ing com bi na tions with due con sid era tion to the fact that the no tionallateral forces can be posi tive or nega tive.




For the de ter mi na tion of the nomi nal strengths for ax ial com pres sion and flex ure,the sec tions are clas si fied as ei ther Class 1 (Plas tic), Class 2 (Com pact), Class 3(Noncompact), or Class 4 (Slender). The pro gram clas sifies the in di vid ual sec tionsac cord ing to Table IX-2 (CISC 11.2). Ac cord ing to this ta ble, a sec tion is clas si fied as ei ther Class 1, Class 2, or Class 3 as ap pli ca ble.

If a sec tion fails to sat isfy the lim its for Class 3 sections, the sec tion is clas si fied asClass 4. Cur rently the pro gram does not check stresses for Class 4 sections.


The fac tored mem ber forces for each load com bi na tion are cal cu lated at each of thepre vi ously de fined sta tions. These mem ber forces are Tf or C f , M f 33 , M f 22 , Vf 2

and Vf 3 cor re spond ing to fac tored val ues of the ten sile or com pres sive ax ial load,the ma jor mo ment, the mi nor mo ment, the ma jor di rec tion shear, and the mi nor di -rec tion shear, re spec tively.

Be cause the pro gram de sign as sumes that the analy sis in cludes P-D ef fects, anymag ni fi ca tion of sidesway mo ments due to the sec ond or der ef fects are al ready in -cluded, there fore U 2 for both di rec tions of bend ing is taken as unity. It is suggestedthat the P-D analy sis be done at the fac tored load level of 1.25 DL plus 1.05 LL. Seealso White and Hajjar (1991).

How ever, the user can over write the val ues of U 2 for both ma jor and mi nor di rec -tion bend ing. In this case M f in a par ticu lar di rec tion is taken as:

M M U Mf fg ft= + 2 , where (CISC 8.6.1)

U 2 = Mo ment mag ni fi ca tion fac tor for sidesway mo ments,M fg = Fac tored mo ments not caus ing trans la tion, andM ft = Fac tored mo ments caus ing sidesway.






RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3 (Noncompact)

I-SHAPE

b tf f2 £145

yF £170 yF £ 200

yF

h t w

£æ

è

çç

ö

ø

÷÷1100

1 039F

- .C

Cy

f

y

£æ

è

çç

ö

ø

÷÷1700

1 0 61F

- .C

Cy

f

y

£æ

è

çç

ö

ø

÷÷1900

1 0 65F

- .C

Cy

f

y

BOX

b t f

£ 420 yF (rolled)

£ 525 yF (welded)

£ 525 yF £ 670

yF

h t w As for I-shapes As for I-shapes As for I-shapes

CHANNELb tf

f

h t w



£ 200 yF

As for I-shapes

T-SHAPEb tf

f2

d t w



£ 200 yF

£ 340 yF

DOUBLEANGLE

b t Not applicable Not applicable £ 200

yF

ANGLE b t Not applicable Not applicable £ 200

yF

PIPE(Flexure)

D t £13000

yF £18000 yF £ 66000

yF

PIPE (Axial) D t ¾ ¾ £ 23000

yF

ROUND BAR ¾ Assumed Class 2

RECTAN-GULAR

¾ Assumed Class 2

GENERAL ¾ Assumed Class 3

Table IX-2Limiting Width-Thickness Ratios for

Classification of Sections based on CISC 94



tw

tw tw

tw tw

t f t f

t f

t

t f

t f

d d

t = t = tw f

t t

z

2, y

2, y

3, x 3, x

CISC95: AxesC onventions

2-2i s thec ross-sectiona xis parallel tot hew ebs,thel onger dimensiono f tubes,thel onger lego f singlea ngles, orthes ideb y sidel egs of double-angles.This is thes amea s they -y axis.

3-3i s orthogonal to2 -2. This is thes amea s thex -x axis.

b f

b fb f

b

b f

b

h hh

b

dh d

bb

b

b = b - 3tff

Db b

Figure IX-1CISC 94 Definition of Geometric Properties

Calculation of Factored Strengths

The factored strengths in com pres sion, ten sion, bend ing, and shear are com puted

for Class 1, 2, and 3 sec tions in the pro gram. The strength re duc tion fac tor, j , istaken as 0.9 (CISC 13.1).

For Class 4 (Slen der) sec tions and any sin gly sym met ric and un sym met ric sec tionsre quir ing con sid era tion of lo cal buck ling, flexural- torsional and tor sional buck -ling, or web buck ling, re duced nomi nal strengths may be ap pli ca ble. The user mustsepa rately in ves ti gate this re duc tion if such ele ments are used.

If the user speci fies nomi nal strengths for one or more ele ments in the“Overwrites", these val ues will over ride all the above men tioned cal cu lated val -ues for those ele ments as de fined in the fol low ing sub sec tions.

Compression Strength

The fac tored ax ial com pres sive strength value, C r , for Class 1, 2, or 3 sec tions de -pends on a fac tor, l, which even tu ally de pends on the slen der ness ra tio, Kl r,which is the larger of ( )K l r33 33 33 and ( )K l r22 22 22 , and is de fined as

lp

= Kl

r

F

E

y .

For sin gle an gles rZ is used in place of r r33 22and . For mem bers in com pres sion, if Kl r is greater than 200, a mes sage is printed (CISC 10.2.1).

Then the fac tored ax ial strength is eval u ated as fol lows (CISC 13.3.1):

( )C AFr yn n= +

-

j l1 21

, where (CISC 13.3.1)

n is an ex po nent and it takes three pos si ble val ues to match the strengths re lated to three SSRC curves. The de fault n is 1.34 which is as signed to W-shapesrolled in Can ada, fab ri cated boxes and I shapes, and cold-formed non-stress re -lieved (Class C) hol low struc tural sec tions (HSS) (CISC 13.3.1, CISC C13.3,Man ual Page 4-12, Man ual Ta ble 6-2). The WWF sec tions pro duced in Can ada from plate with flame-cut edges and hot-formed or cold-re lieved (Class H)HSS are as signed to a fa vor able value of n = 2.24 (CISC 13.3.1, CISC C13.3,Man ual Page 4-12). For heavy sec tions, a smaller value of n (n = 0.98) is con -sid ered ap pro pri ate (CISC C13.3). The pro gram as sumes the value of n as fol -lows:

224 Calculation of Factored Strengths


n =

2.24 , for WWF, HS (Class H) and HSS (Class H) sections,

1.34 , for W, L, and 2L sections and normal HS and HSS sections,

1.34 , for other sections with thickness less than 25.4 mm,

0.98 , for other sections with thickness larger than or equal to 25.4 mm.

ì

í

ïï

î

ïï

The HSS sec tions in the cur rent Ca na dian Sec tion Da ta base of the pro gram arepre fixed as HS in stead of HSS. Also, to con sider any HSS sec tion as Class H, itis ex pected that the user would put a suffix to the HS or HSS sec tion names.

Tension Strength

The fac tored ax ial ten sile strength value, Tr , is taken as j A Fg y (CISC 13.2.(a).(I)). For mem bers in ten sion, if l r is greater than 300, a mes sage is printed ac cord ingly(CISC 10.2.2).

T A Fr g y= j (CISC 13.2)

Bending Strengths

The fac tored bend ing strength in the ma jor and mi nor di rec tions is based on thegeo met ric shape of the sec tion, the sec tion clas si fi ca tion for com pact ness, and theun braced length of the mem ber. The bend ing strengths are evalu ated ac cord ing toCISC as fol lows (CISC 13.5 and 13.6):

For lat er ally sup ported mem bers, the mo ment ca paci ties are con sid ered to be as fol -lows:

For Class 1 and 2, M ZFr y= j , and (CISC 13.5)

For Class 3, M SFr y= j . (CISC 13.5)

Spe cial con sid era tions are re quired for lat er ally un sup ported mem bers. The pro ce -dure for the de ter mi na tion of mo ment ca paci ties for lat er ally un sup ported mem bers (CISC 13.6) is de scribed in the fol low ing sub sec tions.

If the ca pac i ties (M r22 and M r33 ) are over writ ten by the user, they are used in the in -ter ac tion ra tio cal cu la tion when strengths are re quired for ac tual un braced lengths. None of these over writ ten ca pac i ties are used for strengths in lat er ally sup portedcase.

Calculation of Factored Strengths 225


I-shapes and Boxes


For Class 1 and 2 sec tions of I- shapes and boxes bent about the ma jor axis,

when M > Mu p0.67 33 ,

M = M - M

M Mr p

p

u

p3 33

33

3311.15 0.28j jæ

èçç

ö

ø÷÷ £ , and (CISC 13.6)

when M Mu p£ 0.67 33 ,

M r33 = j M u , where (CISC 13.6)

M r33 = Fac tored ma jor bend ing strength,M p33 = Ma jor plas tic mo ment, Z Fy33 ,M u = Criti cal elas tic mo ment,

w p p2

LEI GJ +

E

LI Cw22

2

22

æ

èç

ö

ø÷ , (CISC 13.6)

L = Lat er ally un braced length, l22 ,Cw = Warp ing con stant as sumed as 0.0 for boxes, pipes,

rec tan gu lar and cir cu lar bars, and

w2 = 1.75 1.05 0.30 + M

M +

M

M a

b

a

b

æ

èçç

ö

ø÷÷

æ

èçç

ö

ø÷÷ £

2

2.5 . (CISC 13.6)

M a and M b are end mo ments of the un braced seg ment and M a is less than M b , M

Ma

b

æ

èçç

ö

ø÷÷ be ing posi tive for dou ble cur va ture bend ing and nega tive for sin gle

cur va ture bend ing. If any mo ment within the seg ment is greater than M b , w2 istaken as 1.0. The pro gram de faults w2 to 1.0 if the un braced length, l of themem ber is over writ ten by the user (i.e. it is not equal to the length of the mem -ber). w2 should be taken as 1.0 for can ti le vers. How ever, the pro gram is un ableto de tect whether the mem ber is a can ti le ver. The user can over write the value

of w2 for any mem ber by speci fy ing it.

For Class 3 sec tions of I- shapes, chan nels, boxes bent about the ma jor axis,

when M Mu y> 0.67 33 ,



M = M M

MMr y

y

u

y33 33

33

3311.15 0.28j j-æ

èçç

ö

ø÷÷£ , and (CISC 13.6)

when M Mu y£ 0.67 33 ,

M Mr u33 = j , where (CISC 13.6)

M r33 and M u are as de fined ear lier for Class 1 and 2 sec tions andM y 33 is the ma jor yield mo ment, S Fy33 .


For Class 1 and 2 sec tions of I- shapes and boxes bent about their mi nor axis,

M = M = Z Fr p y22 22 22j j .

For Class 3 sec tions of I- shapes and boxes bent about their mi nor axis,

M = M = S Fr y y22 22 22 .

Rectangular Bar


For Class 2 rec tan gu lar bars bent about their ma jor axis,

when M > Mu p0.67 33 ,

M = M - M

MMr p

p

u

p33 33

33

3311.15 0.28jæ

èçç

ö

ø÷÷£ f , and (CISC 13.6)

when M Mu p£ 0.67 33 ,

M = Mr u33 j . (CISC 13.6)


For Class 2 sec tions of rec tan gu lar bars bent about their mi nor axis,

M = M = Z Fr p y22 22 22j j .

Pipes and Circular Rods

For pipes and cir cu lar rods bent about any axis



When M > Mu p0.67 33 ,

M = M - M

M Mr p

p

u

p33 33

33

3311.15 0.28j jæ

èçç

ö

ø÷÷ £ , and (CISC 13.6)

when M Mu p£ 0.67 33 ,

M = Mr u33 j . (CISC 13.6)

Channel Sections


For Class 3 chan nel sec tions bent about their ma jor axis,

when M Mu y> 0.67 33 ,

M = M M

M Mr y

y

u

y33 33

33

3311.15 0.28 j j-æ

èçç

ö

ø÷÷ £ , and (CISC 13.6)

when M Mu y£ 0.67 33 ,

M = Mr u33 j .


For Class 3 chan nel sec tions bent about their mi nor axis,

M = M = S Fr y y22 22 22 .

T-shapes and double angles


For Class 3 sec tions of T- shapes and dou ble an gles the fac tored ma jor bend ingstrength is as sumed to be (CISC 13.6d),

M = EI GJ

LB + + B F Sr y33

22 2331j

w p2 éë

ùû

£ f , where

B = d L I J ± 2.3( ) 22 .





For Class 3 sec tions of T- shapes and dou ble an gles the fac tored mi nor bend ingstrength is as sumed as,

M = F Sr y22 22j .

Single Angle and General Sections

For Class 3 sin gle an gles and for General sec tions, the fac tored ma jor and mi nor di -rec tion bend ing strengths are as sumed as,

M = F Sr y33 33j , and

M = F Sr y22 22j .

Shear Strengths

The fac tored shear strength, Vr2 , for ma jor di rec tion shears in I- shapes, boxes andchan nels is evalu ated as fol lows (CISC 13.4.1.1):

• For h

t

k

Fw

v

y

£ 439 ,

{ }V = A Fr w y2 j 0.66 . (CISC 13.4.1.1)

• For 439k

F <

h

t

k

Fv

y w

v

y

£ 502 ,

V = A k F

h tr w

v y

w

2 290jìíï

îï

üýï

þï . (CISC 13.4.1.1)

• For 502 621k

F <

h

t

k

Fv

y w

v

y

£ ,

{ }V = A F Fr w cri t2 j + , where (CISC 13.4.1.1)



F = k F

h tcri

v y

w

290 , and

( )F = F F a/h

t y cri0.5 0.866( )

-+

ìíï

îï

üýï

þï

1

1 2 .

As sum ing no stiff ener is used, the value of Ft is taken as zero.

• For h

t>

k

Fw

v

y

621 ,

{ }V = A F Fr w cre t2 j + , where (CISC 13.4.1.1)

F = k

h/tcre

v

w

180 0002( )

.

In the above equa tions, k v is the shear buck ling co ef fi cient, and it is de fined as:

ka h

v = +42

5.34

( / ) , a h/ < 1

ka h

v = +5.344

2( / ) , a h/ ³ 1

and the as pect ra tio a h is the ra tio of the dis tance be tween the stiff en ers to webdepth. As sum ing no stiff ener is used, the value of k v is taken as 5.34.

The fac tored shear strength for mi nor di rec tion shears in I- shapes, boxes and chan -nels is as sumed as

V F Ar y v2 3 = 0.66 j . (CISC 13.4.2)

The fac tored shear strength for ma jor and mi nor di rec tion shears for all other sec -tions is as sumed as (CISC 13.4.2):

V F Ar y v2 2 = 0.66 j , and (CISC 13.4.2)

V F Ar y v3 3 = 0.66 j . (CISC 13.4.2)





If the ax ial, flex ural, and shear strengths of a sec tion are over writ ten by the user, the over writ ten val ues are used in cal cu lat ing the stress ra tios. How ever, cer tainstrengths can not be over writ ten. If the ax ial and bend ing ca pac i ties are over writ ten by the user, they are used in the in ter ac tion ra tio cal cu la tion when strengths are re -quired for ac tual un braced lengths. None of these over writ ten ca pac i ties are usedfor strengths in lat er ally sup ported case. More spe cific in for ma tion is given in thefol low ing sub sec tions as needed.


Axial and Bending Stresses

From the fac tored ax ial loads and bend ing mo ments at each sta tion and the fac toredstrengths for ax ial ten sion and com pres sion and ma jor and mi nor bend ing, an in ter -ac tion ca pac ity ra tio is pro duced for each of the load com bi na tions as fol lows:

Compressive Axial Load

If the ax ial load is com pres sive, the ca pac ity ra tio is given by:

C

C +

U M

M +

U M

M

f

r

f

r

f

r

13 33

33

12 22

22

, for all but Class 1 I-shaped sec tions (13.8.1)

C

C +

U M

M +

U M

M

f

r

f

r

f

r

0.85 0.613 33

33

12 22

22

, for Class 1 I-shaped sec tions (13.8.2)

The above ra tios are cal cu lated for each of the fol low ing con di tions and the largestra tio is re ported:



• Cross-sec tional Strength:

– The ax ial com pres sion ca pac ity is based on l = 0 .

C A Fr y= j (CISC 13.3.1)

– The M Mr r33 22and are cal cu lated as sum ing that the mem ber is lat er allyfully sup ported ( l22 0= and l33 0= ) ir re spec tive of its ac tual lat eral brac -ing length (CISC 13.5), and

– U12 and U13 are taken as 1.

U U13 12= =1.0 . (CISC 13.8.1, 13.8.2)

If the ca pac i ties (C r , M r22 and M r33 ) are over writ ten by the user, they are as -sumed not to ap ply to this case and are ignored.

• Over all Mem ber Strength:

– The ax ial com pres sion ca pac ity is based on both ma jor and mi nor di rec tion

buck ling us ing both K l

r22 22

22

and K l

r33 33

33

as de scribed in an ear lier sec tion

(CISC 13.3.1) .

– M Mr r33 22and are cal cu lated as sum ing that the mem ber is lat er ally fully sup ported ( l22 0= and l33 0= ) ir re spec tive of its ac tual lat eral brac inglength (CISC 13.5), and

– U12 and U13 are cal cu lated us ing the ex pres sion given be low for U1 . In thisequa tion spe cific val ues for ma jor and mi nor di rec tions are to be used tocal cu late val ues of U12 and U13 (CISC 13.8.3).

If the ca pac i ties (C r , M r22 , and M r33 ) are over writ ten by the user, the onlyover writ ten ca pac ity used in this case is C r .

• Lat eral-Tor sional Buckling Strength:

– The ax ial com pres sion ca pac ity is based on weak-axis buck ling only based

on K l

r22 22

22

(CISC 13.3.1),

– M Mr r33 22and are cal cu lated based on ac tual un braced length (CISC 13.6), and



– U12 and U13 are cal cu lated us ing the ex pres sion given be low for U1 . In thisequa tion spe cific val ues for ma jor and mi nor di rec tions are to be used tocal cu late val ues of U12 and U13 (CISC 13.8.3). More over,

U13 1³ is en forced. (CISC 13.3.1, 13.8.2)

If the ca pac i ties (C r , M r22 , and M r33 ) are over writ ten by the user, all three over -writ ten ca pac i ties are used in this case.

In ad di tion, For Class 1 I-shapes, the fol low ing ra tio is also checked:

M

M

M

M

f

r

f

r

33

33

22

22

+ . (CISC 13.8.2)

If the ca pac i ties (M r22 and M r33 ) are over writ ten by the user, all these over writ -ten ca pac i ties are used in this case.

In the above ex pres sions,

U =

- C /Cf e

11

1

w , (CISC 13.8.3)

C E I

Le = p 2

2 ,

w1 = 0.6 0.4 - M M .a b ³ 0 4 , and

M Ma b is the ra tio of the smaller to the larger mo ment at the ends of the mem ber, M Ma b be ing posi tive for dou ble cur va ture bend ing and nega tive for sin gle cur va -ture bend ing. w1 is as sumed as 1.0 for beams with trans verse load and when M b iszero.

The pro gram de faults w1 to 1.0 if the un braced length, l, of the mem ber is redefined by the user (i.e. it is not equal to the length of the mem ber). The user can over writethe value of w1 for any mem ber by speci fy ing it. The fac tor U1 must be a posi tivenumber. There fore C f must be less than C e . If this is not true, a fail ure con di tion isde clared.

Tensile Axial Load

If the ax ial load is ten sile the ca pac ity ra tio is given by the larger of two ra tios. Inthe first case, the ra tio is cal cu lated as



T

T +

M

M +

M

M

f

r

f

r

f

r

é

ëê

ù

ûú

é

ëê

ù

ûú

33

33

22

22

, (CISC 13.9)

as sum ing M Mr r33 22and are cal cu lated based on fully sup ported mem ber ( l22 0=and l33 0= ). If the ca pac i ties (Tr , M r22 and M r33 ) are over writ ten by the user, theonly over writ ten ca pac ity used in this case is Tr . M r22 and M r33 overwrites are as -sumed not to ap ply to this case and are ig nored.

In the sec ond case the ra tio is cal cu lated as

M

M +

M

M

T Z

M A

f

r

f

r

f

r

33

33

22

22

33

33

é

ëê

ù

ûú -

é

ëê

ù

ûú (for Class 1 and 2), or (CISC 13.9)

M

M +

M

M

T S

M A

f

r

f

r

f

r

33

33

22

22

33

33

é

ëê

ù

ûú -

é

ëê

ù

ûú (for Class 3). (CISC 13.9)

If the ca pac i ties (M r22 and M r33 ) are over writ ten by the user, both of these over writ -ten ca pac i ties are used in this case.

For cir cu lar sec tions an SRSS com bi na tion is first made of the two bend ing com po -nents be fore add ing the ax ial load com po nent in stead of the sim ple al ge braic ad di -tion im plied by the above in ter ac tion for mu las.

Shear Stresses

From the fac tored shear force val ues and the fac tored shear strength val ues at eachsta tion, for each of the load com bi na tions, shear ca pac ity ra tios for ma jor and minor di rec tions are pro duced as fol lows:

V

V

f

r

2

2

and

V

V

f

r

3

3

.



C h a p t e r X

Check/Design for EUROCODE 3-92

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the Eurocode 3 de signcode (CEN 1992). The pro gram in ves ti gates the lim it ing states of strength and sta -bil ity but does not ad dress the serv ice abil ity limit states. Vari ous no ta tions used inthis chap ter are de scribed in Table X-1.


In the evalua tion of the ax ial force/bi ax ial mo ment ca pac ity ra tios at a sta tion alongthe length of the mem ber, first the ac tual mem ber force/mo ment com po nents andthe cor re spond ing ca paci ties are cal cu lated for each load com bi na tion. Then the ca -pac ity ra tios are evalu ated at each sta tion un der the in flu ence of all load com bi na -tions us ing the cor re spond ing equa tions that are de fined in this sec tion. The con -trol ling ca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di catesex ceed ing a limit state. Simi larly, a shear ca pac ity ra tio is cal cu lated sepa rately.


235

236


A = Gross cross- sectional area, mm2

A Av v2 3, = Ar eas for shear in the 2- and 3-d ire ctions, mm2

C1 = Bend ing coefficient



I t = Tor sion con stant, mm4

I w = Warp ing con stant, mm6




L = Length, span, mm


M b Rd. = De sign buck ling re sis tance mo ment, N-mm

M cr = Elas tic criti cal mo ment for lateral- torsional buck ling, N-mm

M g Sd. = De sign mo ments not caus ing sidesway , N-mm

M s Sd. = De sign mo ments caus ing sidesway, N-mm

MV Sd. = De sign mo ment re sis tance af ter con sid er ing shear, N-mm

M Sd33. = De sign value of mo ment about the ma jor axis, N-mm

M Sd22. = De sign value of mo ment about the mi nor axis, N-mm

M Rd33. = De sign mo ment re sis tance about the ma jor axis, N-mm

M Rd22. = De sign mo ment re sis tance about the mi nor axis, N-mm

Nb Rd. = De sign buck ling re sis tance of a com pres sion mem ber, N

Nb Rd33. = De sign buck ling re sis tance of a com pres sion mem ber about the ma jor axis, N

Nb Rd22. = De sign buck ling re sis tance of a com pres sion mem ber about the mi nor axis, N

N c Sd. = De sign value of com pres sive force, N

N c Rd. = De sign com pres sion re sis tance, N

N t Sd. = De sign value of ten sile force, N

N t Rd. = De sign ten sion re sis tance, N

N pl Rd. = De sign plas tic shear re sis tance, N

V Sd2. = De sign value of shear force in the major di rec tion, N

V Sd3. = De sign value of shear force in the minor di rec tion, N

V Rd2. = De sign shear re sis tance in the major di rec tion, N

Table X-1Eurocode 3 Notations

237

Chapter X Check/Design for EUROCODE 3-92

V Rd3. = De sign shear re sis tance in the minor di rec tion, N

W Wel el. .,33 22 = Ma jor and mi nor elas tic sec tion moduli, mm3

W Wpl pl. .,33 22 = Ma jor and mi nor plastic sec tion moduli, mm3

b = Width, mm

c = Dis tance, mm


f y = Nomi nal yield strength of steel, MPa

h = Over all depth, mm


i i33 22, = Ma jor and mi nor ra dii of gy ra tion, mm

iz = Mini mum ra dius of gy ra tion for an gles, mm

k k33 22, = Fac tors ap plied to the ma jor and mi nor de sign mo ments in the in ter ac tion equa tions

kLT = Fac tor ap plied to the ma jor de sign mo ments in the in ter ac tion equa tion check ing for fail ure due to lateral- torsional buck ling

t = Thick ness, mm


t w = Web thick ness, mm

a = Ra tio used in clas si fi ca tion of sec tions

g M 0 , g M1 = Ma te rial par tial safety fac tors

e = f

y

2351

2é

ëêê

ù

ûúú

(f y in MPa)

r = Re duc tion fac tor

tba = Post- critical shear strength, MPa

c c33 22, = Re duc tion fac tors for buck ling about the 3-3 and 2-2 axes

c LT = Re duc tion fac tor for lat eral-tor sional buck ling

y = Ratio of smaller to larger end mo ment of un braced seg ment

y s = Am pli fi ca tion fac tor for sway mo ments

Table X-1Eurocode 3 Notations (cont.)


The de sign load ing com bi na tions de fine the vari ous fac tored com bi na tions of theload cases for which the struc ture is to be checked. The de sign load ing com bi na -tions are ob tained by mul ti ply ing the char ac ter is tic loads with ap pro pri ate par tialfac tors of safety. If a struc ture is sub jected to dead load (DL) and live load (LL)only, the de sign will need only one load ing com bi na tion, namely 1.35 DL + 1.5 LL.

How ever, in ad di tion to the dead load and live load, if the struc ture is sub jected towind (WL) or earth quake in duced forces (EL), and con sid er ing that wind andearth quake forces are sub ject to re ver sals, the fol low ing load com bi na tions mayhave to be con sid ered (EC3 2.3.3):

1.35 DL1.35 DL + 1.50 LL (EC3 2.3.3)

1.35 DL ± 1.50 WL 1.00 DL ± 1.50 WL 1.35 DL + 1.35 LL ± 1.35 WL (EC3 2.3.3)

1.00 DL ± 1.00 EL 1.00 DL + 1.5*0.3 LL ± 1.0 EL (EC3 2.3.3)

In fact, these are the de fault load com bi na tions which can be used or over writ ten bythe user to pro duce other criti cal de sign con di tions. These de fault load ing com bi na -tions are pro duced for per sis tent and tran sient de sign situa tions (EC3 2.3.2.2) bycom bin ing forces due to dead, live, wind, and earth quake loads for ul ti mate limitstates. See also sec tion 9.4 of Eurocode 1 (CEN 1994) and Ta ble 1, 3, and 4 and sec -tion 4 of United King dom Na tional Ap pli ca tion Docu ment (NAD).

The de fault load com bi na tions will usu ally suf fice for most build ing de sign. Theuser should use other ap pro pri ate load ing com bi na tions if roof live load is sepa -rately treated, other types of loads are pres ent, or if pat tern live loads are to be con -sid ered.


In ad di tion to the loads de scribed ear lier, equiva lent lat eral load cases for geo met -ric im per fec tion should be con sid ered by the user. This equiva lent load is simi lar tothe no tional load of the Brit ish code, and de pends on the number of sto ries andnumber of col umns in any floor (EC3 5.2.4.3). Ad di tional load com bi na tions arealso needed for these load cases.



When us ing Eurocode 3, the pro gram de sign as sumes that a P-D analy sis has beenper formed so that mo ment mag ni fi ca tion fac tors for mo ments caus ing sideswaycan be taken as unity. It is sug gested that the P-D analy sis should be done at the fac -tored load level corresponding to 1.35 dead load plus 1.35 live load. See also Whiteand Hajjar (1991).


The de sign strength of a cross- section sub ject to com pres sion due to mo mentand/or ax ial load de pends on its clas si fi ca tion as Class 1 (Plas tic), Class 2 (Com -pact), Class 3 (Semi- compact), or Class 4 (Slen der). Ac cord ing to Eurocode 3, theclas si fi ca tion of sec tions de pends on the clas si fi ca tion of flange and web ele ments.The clas si fi ca tion also de pends on whether the com pres sion ele ments are in purecom pres sion, pure bend ing, or un der the in flu ence of com bined ax ial force andbend ing (EC3 5.3.2).

The pro gram con ser va tively clas si fies the com pres sion el e ments ac cord ing toTable X-2 and Table X-3. Table X-2 is used when the sec tion is un der the in flu enceof ax ial com pres sion force only or com bined ax ial com pres sion force and bend ing.Table X-3 is used when the sec tion is in pure bend ing or un der the in flu ence ofcom bined ax ial ten sile force and bend ing. The sec tion di men sions used in the ta -bles are given in Figure X-1. If the sec tion di men sions sat isfy the lim its shown inthe ta bles, the sec tion is clas si fied as Class 1, Class 2, or Class 3 as ap pli ca ble. Across-sec tion is clas si fied by re port ing the high est (least fa vor able) class of its com -pres sion el e ments.

If a sec tion fails to sat isfy the lim its for Class 3 sec tions, the sec tion is clas si fiedas Class 4. Cur rently the pro gram does not check stresses for Class 4 sections.

One of the ma jor fac tors in de ter min ing the lim it ing width- thickness ra tio is e. This pa rame ter is used to re flect the in flu ence of yield stress on the sec tion clas si fi ca tion.

e = 235

fy

(EC3 5.3.2)

In clas si fy ing I, Box, Chan nel, Dou ble-Chan nel, and T sec tions, two other fac tors

( )a y, are de fined as fol lows:





Section Element Ratio Checked Class 1 Class 2 Class 3

I-SHAPE

web d t w

If a > 0.5 ,

( )396

13 1

e

a - ,

else if a ³ 0.5, 36 e

a .

If a > 0.5,

( )456

13 1

e

a - ,

else if a ³ 0.5, 41.5 e

a .

If y > -1 , 42 e

y0.67 0.33+ ,

else if y ³ -1,

( )62 1e y

y

-

-

flange

c t f (rolled) 10 e 11 e 15 e

c t f (welded) 9 e 10 e 14 e

BOX

web d t w

Same asI-Shape

Same asI-Shape

Same asI-Shape

flange

( )b t tf f-3(rolled)

42 e 42 e 42 e

b t f (welded) 42 e 42 e 42 e

CHANNEL

web d t w

Same asI-Shape

Same asI-Shape

Same asI-Shape

flange b t f 10 e 11 e 15 e

T-SHAPE

web d t w 33 e 38 e 42 e

flange

b t f2 (rolled) 10 e 11 e 15 e

b t f2 (welded) 9 e 10 e 14 e

DOUBLEANGLES

¾h t

[ ]( ) max( , )b h t b+ 2 Not applicable Not applicable15e

11.5e

ANGLE ¾h t

[ ]( ) max( , )b h t b+ 2 Not applicable Not applicable15e

11.5e

PIPE ¾ d t 50e2 70e2 90e2

ROUND BAR ¾ None Assumed Class 1

Table X-2Limiting Width-Thickness Ratios for

Classification of Sections based on Eurocode 3 (Compression and Bending)



Section Element Ratio Checked Class 1 Class 2 Class 3

I-SHAPE

web d t w 72 e 83 e 124 e

flange

c t f (rolled) 10 e 11 e 15 e

c t f (welded) 9 e 10 e 14 e

BOX

web d t w 72 e 83 e 124 e

flange

( )b t tf f-3 (rolled) 33 e 38 e 42 e

b t f (welded) 33 e 38 e 42 e

CHANNEL

web

d t w (Major axis) 72 e 83 e 124 e

d t w (Minor axis) 33 e 38 e 42 e

flange b t f 10 e 11 e 15 e

T-SHAPE

web d t w 33 e 38 e 42 e

flange

b t f2 (rolled) 10 e 11 e 15 e

b t f2 (welded) 9 e 10 e 14 e

DOUBLEANGLES

¾

h t

( )[ ]( ) max ,b h t b+ 2 Notapplicable

Not applicable

15.0 e

11.5 e

ANGLE ¾

h t

( )[ ]( ) max ,b h t b+ 2 Notapplicable

Notapplicable

15.0e

11.5e

PIPE ¾ d t 50e2 70e2 90e2

ROUND BAR ¾ None Assumed Class 1

RECTANGLE ¾ None Assumed Class 2

Table X-3Limiting Width-Thickness Ratios for

Classification of Sections based on Eurocode 3 (Bending Only)



Figure X-1Eurocode 3 Definition of Geometric Properties

a =-

1

2

1

2

N

ht f

c Sd

w f

, , for I, Channel, and T sections,

for Box and D1

2

1

2 2-

N

ht f

c Sd

w f

, , ouble - Channel sections, and

ì

í

ïï

î

ïï

y = - +æ

è

çç

ö

ø

÷÷1 2

N

Af

c Sd

y

, ,

0< £a 1.0 ,

-3.0 1.0< £y .

In the above ex pres sion, N c Sd, is taken as pos i tive for ten sion and neg a tive for com -pres sion. a equals 0.0 for full ten sion, 0.5 for pure bend ing and 1.0 for full com -pres sion. y equals -3.0 for full ten sion, -1.0 for pure bend ing and 1.0 for full com -pres sion.


The in ter nal de sign loads which are cal cu lated for each load com bi na tion are N t Sd.

or N c Sd. , M Sd33. , M Sd22. , V Sd2. and V Sd3. cor re spond ing to de sign val ues of the ten sile or com pres sive ax ial load, the ma jor mo ment, the mi nor mo ment, the ma jor di rec -tion shear and the mi nor di rec tion shear re spec tively. These de sign loads are cal cu -lated at each of the pre vi ously de fined sta tions of each frame ele ment.

The de sign mo ments and forces need to be cor rected for sec ond or der ef fects. Thiscor rec tion is dif fer ent for the so called “sway” and “non sway” com po nents of themo ments. The code re quires that the ad di tional sway mo ments in tro duced by thehori zon tal de flec tion of the top of a story rela tive to the bot tom must be taken intoac count in the elas tic analy sis of the frame in one of the fol low ing ways (EC35.2.6.2):

• Di rectly ¾ by car ry ing out the global frame anal y sis us ing P-D anal y sis. Mem -ber de sign can be car ried out us ing in-plane buck ling lengths for nonswaymode.

• In di rectly ¾ by mod i fy ing the re sults of a lin ear elas tic anal y sis us ing an ap -prox i mate method which makes al low ance for the sec ond or der ef fects. There

are two al ter na tive ways to do this ¾ “am pli fied sway mo ment method” or“sway mode in-plane buck ling method”.



The ad van tage of the di rect sec ond or der elas tic analy sis is that this method avoidsun cer tainty in ap proxi mat ing the buck ling length and also avoids split ting up mo -ments into their “sway” and “non sway” com po nents.

The pro gram de sign as sumes that P-D ef fects are in cluded in the anal y sis.There fore any mag ni fi ca tion of sidesway mo ments due to sec ond or der ef fectsis al ready ac counted for, I. e. y s in the fol low ing equa tion is taken as 1.0. It is

sug gested that the P-D anal y sis be done at the fac tored load level of 1.35 DL plus1.35 LL. See also White and Hajjar (1991). How ever, the user can over write theval ues of y s for both ma jor and mi nor di rec tion bend ing in which case M Sd in apar tic u lar di rec tion is taken as:

M = M + MSd g.Sd s s.Sdy , where (EC3 5.2.6.2)

M g Sd. = De sign mo ments not caus ing trans la tion, andM s Sd. = De sign mo ments caus ing sidesway.

Mo ment mag ni fi ca tion for non- sidesway mo ments is in cluded in the over all buck -ling in ter ac tion equa tions.

Sway mo ments are pro duced in a frame by the ac tion of any load which re sults insway dis place ments. The hori zon tal loads can be ex pected al ways to pro duce swaymo ments. How ever, they are also pro duced by ver ti cal loads if ei ther the load or the frame are un sym met ri cal. In the case of a sym met ri cal frame with sym met ri cal ver -ti cal loads, the sway mo ments are sim ply the in ter nal mo ments in the frames due tothe hori zon tal loads (EC3 5.2.6.2).

Calculation of Section Resistances

The nomi nal strengths in com pres sion, ten sion, bend ing, and shear are com putedfor Class 1, 2, and 3 sec tions ac cord ing to the fol low ing sub sec tions. The ma te rialpar tial safety fac tors used by the pro gram are:

g M 0 = 1.1 , and (EC3 5.1.1)g M 1 = 1.1 . (EC3 5.1.1)


244 Calculation of Section Resistances


If the user speci fies nomi nal capabilities for one or more ele ments in the“Overwrites”, these val ues are will over ride all the above men tioned cal cu latedval ues for those ele ments as de fined in the fol low ing sub sec tions.

Tension Capacity

The de sign ten sion re sis tance for all classes of sec tions is evalu ated in the pro gramas fol lows:

N = A ft.Rd y Mg 0 (EC3 5.4.3)

It should be noted that the de sign ul ti mate re sis tance of the net cross- section at theholes for fas ten ers is not com puted and checked. The user is ex pected to in ves ti gate this in de pend ently.


The de sign com pres sive re sis tance of the cross- section is taken as the smaller of the de sign plas tic re sis tance of the gross cross- section (N pl Rd. ) and the de sign lo calbuck ling re sis tance of the gross cross- section (N b Rd. ).

N N Nc Rd pl Rd b Rd. . , .min ( )= (EC3 5.4.4)

The plas tic re sis tance of Class 1, Class 2, and Class 3 sec tions is given by

N = A fpl.Rd y g M0 . (EC3 5.4.4)

The de sign buck ling re sis tance of a com pres sion mem ber is taken as

N = A fb.Rd y Mc b gmin A 1 , where (EC3 5.5.1)

bA = 1 , for Class 1, 2 or 3 cross- sections.

c is the re duc tion fac tor for the rele vant buck ling mode. This fac tor is cal cu -lated be low based on the as sump tion that all mem bers are of uni form cross- section.

cj j l

=1

+[ - ]1

2 2 12

£ , in which (EC3 5.5.1.2)

j a l l= 0.5[1+ ( 0.2 ) + ]2- ,

Calculation of Section Resistances 245




Section Limitsa

(major axis)a

(minor axis)

I-SHAPE (rolled)h b > 1 2.

t f £ 40 mm 0.21 0.34

t f > 40 mm 0.34 0.49

I-SHAPE (rolled)h b £ 1.2

t f £100 mm 0.34 0.49

t f >100 mm 0.76 0.76

I-SHAPE (welded)

t f £ 40 mm 0.34 0.49

t f > 40 mm 0.49 0.76

BOXRolled 0.21 0.21

welded 0.34 0.34

CHANNEL any 0.49 0.49

T-SHAPE any 0.49 0.49

DOUBLEANGLES

any 0.49 0.49

ANGLE any 0.49 0.49

PIPE any 0.21 0.21

ROUND BAR any 0.49 0.49

RECTANGLE any 0.49 0.49

GENERAL any 0.49 0.49

Table X-4The a factor for different sections and different axes of buckling

ll

lb= [ ]

1

0.5ìíî

üýþ

A ,

l = orK l

i

K l

i33 33

33

22 22

22

. The two val ues of l give c 3 and c 2 . c min is

the lesser of the two.

Kl

L= £ 1 . K is con ser va tively taken as 1 in the pro gram de sign (EC3

5.5.1.5). The user can, how ever, over ride this de fault op tion if it is deemednec es sary. An ac cu rate es ti mate of K can be ob tained from the An nex E ofthe code. See also EC3 5.2.6.2(2).

l is the buck ling length,

L is the length of the col umn,

i is the ra dius of gy ra tion about the neu tral axis, and is de ter mined us ing the prop er ties of the gross cross- section,

l p1 =

12

E

fy

é

ëê

ù

ûú , and

a is an im per fec tion fac tor and is ob tained from Table X-4. Val ues of thisfac tor for dif fer ent types of sec tions, axes of buck ling, and thick ness of ma -te ri als are ob tained from Ta bles 5.5.1 and 5.5.3 of the code.

An gle, Chan nel, and T-sec tions in com pres sion are sub jected to an ad di tional mo -ment due to the shift of the centroidal axis of the ef fec tive cross-sec tion (EC35.4.4). the pro gram does not cur rently con sid ers this ec cen tric ity. The user is ex -pected to in ves ti gate this is sue sep a rately.

Shear Capacity

The de sign shear re sis tance of a sec tion is the mini mum of the plas tic shear ca pac ity and the buck ling shear ca pac ity. For all types of sec tions, the plas tic shear re sis -tance is com puted as

V = V = A f

Rd pl.Rd

v y

M

30g , (EC3 5.4.6)



where Av is the ef fec tive shear area for the sec tion and the ap pro pri ate axis of bend -ing.

The buck ling shear ca paci ties are only com puted for the I, Box, and Chan nel sec -tions if the width- thickness ra tio is large (d t w > 69e). The ca paci ties are com puted as

V = V = d tRd ba.Rd w ba Mt g 1 , (for d

t w

> 69 e) (EC3 5.6.3)

where, t ba is the sim ple post- critical shear strength which is de ter mined as fol lows:

t ba

ywf=

3, for lw £ 0.8 , (EC3 5.6.3)

[ ]t lba w

ywf= 1 0.625( - 0.8 )-

3 , for 0.8 < < 1.2lw , and (EC3 5.6.3)

[ ]t lba w

ywf= 0.9

3 , for lw ³ 1.2 . (EC3 5.6.3)

in which lw is the web slen der ness ra tio,

le t

w

wd t

k=

37.4 , and (EC3 5.6.3)

kt is the buck ling fac tor for shear. For webs with trans verse stiff en ers at the sup -ports but no in ter me di ate trans verse stiff en ers,

kt = 5.34 . (EC3 5.6.3)

Moment Resistance

The mo ment re sis tance in the ma jor and mi nor di rec tions is based on the sec tionclas si fi ca tion. Mo ment ca pac ity is also in flu enced by the pres ence of shear forceand ax ial force at the cross sec tion. If the shear force is less than half of the shear ca -pac ity, the mo ment ca pac ity is al most un af fected by the pres ence of shear force. Ifthe shear force is greater than half of the shear ca pac ity, ad di tional fac tors need tobe con sid ered.

If V VSd pl.Rd£ 0.5

• For Class 1 and Class 2 Sec tions



M M = W fc Rd pl Rd pl y . .= g M0 . (EC3 5.4.5.2)

• For Class 3 Sec tions

M = M = W fc Rd el Rd el y. . g M0 . (EC3 5.4.5.2)

If V > VSd pl.Rd0.5

• For I, Box, and Chan nel sec tions bend ing about the 3-3 axis the moment ca -paci ties con sid er ing the ef fects of shear force are com puted as

M = W - A

t

f MV Rd pl

v

w

y

M

c Rd. .

r

g

2

04

é

ëê

ù

ûú £ , where (EC3 5.4.7)

r =

2

21

V

V - Sd

pl.Rd

é

ëê

ù

ûú .

• For all other cases, the re duc tion of mo ment ca paci ties for the pres ence of shear force is not con sid ered. The user should in ves ti gate the re duced mo ment ca pac -ity sepa rately.

Lateral-torsional Buckling

For the de ter mi na tion of lat eral-tor sional buck ling re sis tance, it is as sumed that thesec tion is uni form, dou bly sym met ric, and loaded through its shear cen ter. The lat -eral-tor sional buck ling re sis tance of I, Box, and Dou ble Chan nel sec tions is eval u -ated as,

M = W fb.Rd LT w pl. y Mc b g33 1 , where (EC3 5.5.2)

bw = 1 , for Class 1 and Class 2 sec tions,

bwel.

pl.

= W

W33

33

, for Class 3 sec tions,

cj j l

LT

LT LT LT

=1

+[ - ]1

122 2

£ , in which

[ ]j a l lLT LT LT LT = 0.5 1+ ( 0.2 ) +- 2 , where

a LT = 0.21 , for rolled sec tions,



a LT = 0.49 , for welded sec tions, and

lb

LT

w pl. y

cr

. W f

M=

33

0 5

é

ëê

ù

ûú , where

M = C E I

L

I

I +

L G I

E Icr

w t

.

1

222

222

2

222

0

p

p

é

ëê

ù

ûú

5

, (EC3 F1.1)

I t = The tor sion con stant,

Iw = The warp ing con stant,

L = Laterally un braced length for buck ling about the mi nor axis. It istaken as l22 ,

C = - 1 1.88 1.40 +0.52 2.72y y £ , and

y = The ra tio of smaller to larger end mo ment of un braced seg ment, M

Ma

b

. y

var ies be tween -1 and 1 (- £ £1 1y ). A nega tive value im plies dou ble cur va -ture. M a and M b are end mo ments of the un braced seg ment and M a is less than

M b , M

Ma

b

æ

èçç

ö

ø÷÷ be ing nega tive for dou ble cur va ture bend ing and posi tive for sin -

gle cur va ture bend ing. If any mo ment within the seg ment is greater than M b , C1 is taken as 1.0. The pro gram de faults C1 to 1.0 if the un braced length, l22 ofthe mem ber is over writ ten by the user (i.e. it is not equal to the length of themem ber). C1 should be taken as 1.0 for can ti le vers. How ever, the pro gram isun able to de tect whether the mem ber is a can ti le ver. The user can over write thevalue of C1 for any mem ber by speci fy ing it.

If lLT £ 0.4 , no spe cial consideration for lat eral tor sional buck ling is made inthe de sign.

The lat eral-tor sional buck ling re sis tance of a Chan nel, T, An gle, Dou ble-An gle and General sec tions is eval u ated as,

M = W fb.Rd el y M, 33 1g ,

and the lat eral-tor sional buck ling re sis tance of Rect an gle, Cir cle and Pipe sec tionsis eval u ated as,

M = W fb.Rd pl y M, 33 1g .



Cur rently the pro gram does not consider other spe cial con sid er ations forcom put ing buck ling re sis tance of Rect an gle, Cir cle, Pipe, Chan nel, T, An gle,Dou ble An gle and Gen eral sec tions.




Bending, Axial Compression, and Low Shear

When the de sign value of the co ex ist ing shear, VSd , is less than half of the cor re -spond ing ca paci ties for plas tic re sis tance, Vpl Rd. and buck ling re sis tance, Vba Rd. , i.e.

V VSd pl Rd£ 0.5 . , and (EC3 5.4.9)

V VSd ba Rd£ 0.5 . , (EC3 5.4.9)

the ca pac ity ra tios are com puted for dif fer ent types of sec tions as fol lows:

For Class 1 and Class 2 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

N +

M

M +

M

Mc.Sd

pl.Rd

.Sd

pl. Rd

.Sd

pl. Rd

33

33

22

22. .

. (EC3 5.4.8.1)

For Class 3 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

Af +

M

W f +

M

W fc.Sd

yd

.Sd

el. yd

.Sd

el. yd

33

33

22

22

, where (EC3 5.4.8.1)

ff

yd

y

M

=g 0

.



Bending, Axial Compression, and High Shear

When the de sign value of the co ex ist ing shear, VSd , is more than half the cor re -spond ing ca paci ties for plas tic re sis tance, Vpl Rd. or buck ling re sis tance, Vba Rd. , theshear is con sid ered to be high, i.e. the shear is high if

V VSd pl Rd> 0.5 . , or (EC3 5.4.9)

V VSd ba Rd> 0.5 . . (EC3 5.4.9)

Un der these con di tions, the ca pac ity ra tios are com puted for dif fer ent types of sec -tions as fol lows (EC3 5.4.9):

For Class 1, 2, and 3 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

N +

M

M +

M

Mc.Sd

pl.Rd

.Sd

V. .Rd

.Sd

V. .Rd

33

33

22

22

, where (EC3 5.4.8.1)

MV. .Rd33 and MV. .Rd22 are the de sign mo ment resistances about the ma jor and themi nor axes, re spec tively, con sid er ing the ef fect of high shear (see page 248).

Bending, Compression, and Flexural Buckling

For all mem bers of Class 1, 2, and 3 sec tions sub ject to ax ial com pres sion, N Sd ,ma jor axis bend ing, M Sd33. , and mi nor axis bend ing, M Sd22. , the ca pac ity ra tio isgiven by

N

N +

k M

M +

k Mc.Sd .Sd

c. .Rd

.Sd

b.min.Rd

33 33

33

22 22

h hM c. .Rd22

, where (EC3 5.5.4)

{ }N N Nb min Rd b Rd b Rd. . . . . .min ,= 33 22 ,

hg

g= M

M

0

1

,

k = - N

A f c.Sd

y

3333

33

1m

c£ 1.5 ,

k = - N

A f c.Sd

y

2222

22

1m

c£ 1.5 ,



m l b33 33= ( )2 433

33 33

33

M.

pl. el.

el.

- + W - W

W

é

ëê

ù

ûú £ 0.9 , (Class 1 and Class 2),

m l b22 22 22

22 22

22

2 4= - + W - W

W M.

pl. el.

el.

( )é

ëê

ù

ûú £ 0.9 , (Class 1 and Class 2),

m l b33 33 33 4= ( 2 0.9M. - ) £ , (for Class 3 sec tions),

m l b22 22 22 4 - M.= ( 2 0.9) £ , (for Class 3 sec tions),

bM.33 = Equiva lent uni form mo ment fac tor for flex ural buck ling about the 3-3 (ma jor) axis be tween points braced in 2-2 di rec tion, and

bM.22 = Equiva lent uni form mo ment fac tor for flex ural buck ling about the 2-2 (mi nor) axis be tween points braced in 3-3 di rec tion.

The equiva lent uni form mo ment fac tors, bM.33 and bM.22 , are de ter mined from

b y yMQ= +

M

M (1.8 0.7 ) ( 0.7 0.5 )- -

D , and

MQ = Ab so lute maxi mum mo ment due to lat eral load only as sum ing sim ple sup port at the ends,

y = Ab so lute value of the ra tio of smaller to larger end mo ment. y var ies between -1 and 1 (- £ £1 1y ). A nega tive value im plies dou ble cur va ture.

DM = Ab so lute maxi mum value of mo ment for mo ment dia gram with out change of sign, and

DM = Sum of ab so lute maxi mum and ab so lute mini mum value of mo ments for mo ment dia gram with change of sign.

Bending, Compression, and Lateral-Torsional Buckling

For all mem bers of Class 1, 2, and 3 sec tions sub ject to ax ial com pres sion, N Sd , ma -jor axis bend ing, M Sd33. , and mi nor axis bend ing, M Sd22. , the ca pac ity ra tio is givenby

N

N +

k M

M +

k M

Mc.Sd

b. Rd

LT .Sd

b Rd

.Sd

c.22

33 22 22

22. . h .Rd

, where (EC3 5.5.4)



k 22 and h are as de fined in the pre vi ous sub sec tion “Bend ing, Com pres sion,and Flex ural Buck ling”,

k = - N

A f LT

LT c.Sd

y

1 122

m

c£ , where

m l bLT M.LT = - 0.15 0.15 0.922 £ , and

bM.LT = Equiva lent uni form mo ment fac tor for lateral- torsional buck ling. It is de ter mined for bend ing about the y-y axis and be tween two points braced in the y-y di rec tion.

Bending, Axial Tension, and Low Shear

When the de sign value of the co ex ist ing shear, VSd , is less than half of the cor re -spond ing ca paci ties for plas tic re sis tance, Vpl Rd. and buck ling re sis tance, Vba Rd. , i.e.

V VSd pl Rd£ 0.5 . , and (EC3 5.4.9)

V VSd ba Rd£ 0.5 . , (EC3 5.4.9)

the ca pac ity ra tios are com puted for dif fer ent types of sec tions as fol lows:

For Class 1 and Class 2 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

N +

M

M +

M

Mt.Sd

t.Rd

.Sd

pl. Rd

.Sd

pl. Rd

33

33

22

22. .

. (EC3 5.4.8.1)

For Class 3 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

Af +

M

W f +

M

W ft.Sd

yd

.Sd

el. yd

.Sd

el. yd

33

33

22

22

. (EC3 5.4.8.1)

Bending, Axial Tension, and High Shear

When the de sign val ues of the co ex ist ing shear, VSd , is more than half the cor re -spond ing ca paci ties for plas tic re sis tance, Vpl Rd. or buck ling re sis tance, Vba Rd. , theshear is con sid ered to be high, i.e. the shear is high if

V VSd pl Rd> 0.5 . , or (EC3 5.4.9)

V VSd ba Rd> 0.5 . . (EC3 5.4.9)



Un der these con di tions, the ca pac ity ra tios are com puted for dif fer ent types of sec -tions as fol lows (EC3 5.4.9):

For Class 1, 2, and 3 sec tions, the ca pac ity ra tio is con ser va tively taken as

N

N +

M

M +

M

Mt.Sd

t.Rd

.Sd

V. .Rd

.Sd

V. .Rd

33

33

22

22

. (EC3 5.4.8.1)

Bending, Axial Tension, and Lateral-Torsional Buckling

The ax ial ten sile force has a bene fi cial ef fect for lateral- torsional buck ling. In or derto check whether the mem ber fails un der lateral- torsional buck ling, the ef fec tive in -ter nal mo ment about the 3-3 axis is cal cu lated as fol lows:

M MN W

Aeff Sd Sd vec

t Sd com. . .

. .33 33

33= - y , where (EC3 5.5.3)

y vec = 0.8 (ac cord ing to the EC3 box value), and

Wcom. 33 is the elastic sec tion modu lus for the ex treme com pres sion fi ber.

For all mem bers of Class 1, 2, and 3 sec tions sub ject to ax ial tension, N t Sd. , ma joraxis bend ing, M Sd33. , and mi nor axis bend ing, M Sd22. , the ca pac ity ra tio is taken as

N

N +

k M

M +

k M

Mt.Sd

t.Rd

LT .Sd

b.Rd

.Sd

c. .Rd

33 22 22

22h- y vec LT

t Sd com

b Rd

kN W

A M. .

.

33 , (EC3 5.5.4)

where k LT , k 22 and h are as de fined in the pre vi ous sub sec tions.

Shear

From the de sign val ues of shear force at each sta tion, for each of the load com bi na -tions and the shear re sis tance val ues, shear ca pac ity ra tios for ma jor and minor di -rec tions are pro duced as fol lows:

V

V.Sd

.Rd

2

2

and V

V.Sd

.Rd

3

3

.



C h a p t e r XI

Check/Design for UBC-ASD97

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the UBC-ASD97 de -sign code. The UBC-ASD97 de sign code in the pro gram im ple ments the In ter na -tional Con fer ence of Build ing Of fi cials’ 1997 Uni form Build ing Code: Vol ume 2:Struc tural En gi neering De sign Pro vi sions, Chap ter 22, Di vi sion III, “De sign Stan -

dard for Spec i fi ca tion for Struc tural Steel Build ings ¾ Al low able Stress De signand Plas tic De sign” (ICBO 1997).

Chap ter 22, Di vi sion III, of UBC adopted the Amer i can In sti tute of Steel Con struc -tion’s Spec i fi ca tion for Struc tural Steel Build ings: Al low able Stress De sign andPlas tic De sign, June 1, 1989 with Commentary (AISC 1989a), which has been im -ple mented in the AISC-ASD89 code in the pro gram. The pro gram im ple men ta tionof AISC-ASD89 is de scribed in Chap ter “De sign/Check for AISC-ASD89” of thisman ual. The cur rent chap ter fre quently re fers to Chap ter . It is sug gested that theuser read Chap ter be fore con tin u ing to read this chap ter.

For re fer ring to per ti nent sec tions and equa tions of the UBC code, a unique pre fix“UBC” is as signed. For re fer ring to per ti nent sec tions and equa tions of theAISC-ASD code, a unique pre fix “ASD” is as signed. How ever, all ref er ences to the “Spec i fi ca tions for Al low able Stress De sign of Sin gle-An gle Mem bers” (AISC1989b) carry the pre fix of “ASD SAM”.

257

Var i ous no ta tions used in this chap ter are de scribed in Table III-1.

When us ing the UBC-ASD97 op tion, the fol low ing Framing Sys tems are rec og -nized (UBC 1627, 2213):


• Spe cial Mo ment-Resisting Frame (SMRF)

• Con cen trically Braced Frame (CBF)

• Ec cen trically Braced Frame (EBF)

• Spe cial Con cen trically Braced Frame (SCBF)

By de fault the frame type is taken as Spe cial Mo ment-Re sisting Frame (SMRF) inthe pro gram. How ever, the frame type can be over writ ten in the Pref er ence form tochange the de fault and in the Over writes form on a mem ber by mem ber ba sis. If any mem ber is as signed with a frame type, the change of the frame type in the Pref er -ence will not mod ify the frame type of the in di vid ual mem ber for which it is as -signed.

When us ing the UBC-ASD97 op tion, a frame is as signed to one of the fol low ingfive Seis mic Zones (UBC 2213, 2214):

• Zone 0

• Zone 1

• Zone 2

• Zone 3

• Zone 4

By de fault the Seis mic Zone is taken as Zone 4 in the pro gram. How ever, the frame type can be over writ ten in the Pref er ence form to change the de fault.

The de sign is based on user-spec i fied load ing com bi na tions. But the pro gram pro -vides a set of de fault load com bi na tions that should sat isfy re quire ments for the de -sign of most build ing type struc tures.

Eng lish as well as SI and MKS met ric units can be used for in put. But the code isbased on Kip-Inch-Sec ond units. For sim plic ity, all equa tions and de scrip tions pre -sented in this chap ter cor re spond to Kip-Inch-Sec ond units un less oth er wisenoted.


258


The de sign load com bi na tions are the var i ous com bi na tions of the load cases forwhich the struc tural mem bers and joints needs to be de signed or checked. For theUBC-ASD97 code, if a struc ture is sub jected to dead load (DL), live load (LL),wind load (WL), and earth quake in duced load (EL), and con sid er ing that wind andearth quake forces are re vers ible, then the fol low ing load com bi na tions may have to be de fined (UBC 1612.3):

DL (UBC 1612.3.1 12-7)DL + LL (UBC 1612.3.1 12-8)

DL ± WL (UBC 1612.3.1 12-9)DL + 0.75 LL ± 0.75 WL (UBC 1612.3.1 12-11)

DL ± EL/1.4 (UBC 1612.3.1 12-9)0.9 DL ± EL/1.4 (UBC 1612.3.1 12-10)DL + 0.75 LL ± 0.75 EL/1.4 (UBC 1612.3.1 12-11)

These are also the de fault de sign load com bi na tions in the pro gram when ever theUBC-ASD89 code is used. The user should use other ap pro pri ate load ing com bi na -tions if roof live load is sep a rately treated, if other types of loads are pres ent, or ifpat tern live loads are to be con sid ered.

When de sign ing for com bi na tions in volv ing earth quake and wind loads, al low ablestresses are NOT in creased by a fac tor of 4/3 of the reg u lar al low able value (UBC1612.3.1, 2209.3).

Live load re duc tion fac tors can be ap plied to the mem ber forces of the live load case on an el e ment-by-el e ment ba sis to re duce the con tri bu tion of the live load to thefac tored load ing.


1.0 DL + 0.7 LL ± W 0 EL (UBC 2213.5.1.1)0.85 DL ± W 0 EL (UBC 2213.5.1.2)

where, W 0 is the seis mic force am pli fi ca tion fac tor which is re quired to ac count forstruc tural overstrength. The de fault value of W 0 is taken as 2.8 in the pro gram.How ever, W 0 can be over writ ten in the Pref er ence form to change the de fault andin the Over writes form on a mem ber by mem ber ba sis. If any mem ber is as signed a


Chapter XI Check/Design for UBC-ASD97

value for W 0 , the change of W 0 in the Pref er ence form will not mod ify the W 0 ofthe in di vid ual mem ber for which W 0 is as signed. The guide line for se lect ing a rea -son able value can be found in UBC 1630.3.1 and UBC Ta ble 16-N. There are othersim i lar spe cial load ing com bi na tions which are de scribed lat ter in this chap ter.

These above spe cial seis mic loading com bi na tions are in ter nal to the pro gram. Theuser does NOT need to cre ate ad di tional load com bi na tions for these load com bi na -tions. The spe cial cir cum stances for which these load com bi na tions are ad di tion -ally checked are de scribed later in this chap ter as ap pro pri ate. The spe cial load ingcom bi na tion fac tors are ap plied di rectly to the ETABS load cases. It is as sumedthat any re quired scal ing (such as may be re quired to scale re sponse spec tra re sults)has al ready been ap plied to the ETABS load cases.

Member Design

A mem ber is rec og nized in the pro gram as ei ther a beam, col umn, or brace. In thecal cu la tion of the ax ial and bend ing stress ra tios, first, for each sta tion along thelength of the mem ber, the ac tual stresses are cal cu lated for each load com bi na tion.Then the cor re spond ing al low able stresses are cal cu lated. Then, the stress ra tios are cal cu lated at each sta tion for each mem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol ling stress ra tio is then ob tained, along with the as -so ci ated sta tion and load com bi na tion. A stress ra tio greater than 1.0 in di cates anover stress. Sim i larly, a shear ca pac ity ra tio is also cal cu lated sep a rately. IN ad di -tion, if re quired for seis mic de sign, mem bers are checked for spe cial load ing com -bi na tions, l r ra tio, sec tion slen der ness ra tio, etc.


The al low able stresses for ax ial com pres sion and flex ure de pend upon the clas si fi -ca tion of sec tions. The sec tions are clas si fied in UBC-ASD97 as ei ther Com pact,Noncompact, Slen der or Too Slen der in the same way as de scribed in sec tion“Clas si fi ca tion of Sec tions” of Chap ter with some ex cep tions as de scribed in thenext paragraph. the pro gram clas si fies the in di vid ual sections ac cord ing to the lim -it ing width/thick ness ra tios given in Table III-2 (UBC 2208, 2212, 2213, ASDB5.1, F3.1, F5, G1, A-B5-2). The def i ni tion of the sec tion prop er ties re quired inthis ta ble is given in Figure III-1 and Table III-1 of Chap ter .

In gen eral the de sign sec tions need not nec es sar ily be Com pact to sat isfyUBC-ASD97 codes (UBC 2213.4.2). How ever, for cer tain spe cial seis mic casesthey have to be Com pact and have to sat isfy spe cial slen der ness re quire ments. Seesub sec tion “Seis mic Re quire ments” later in this chapter. The sec tions which do sat -

260 Member Design


Member Design 261



Width-Thickness

Ratio

(l)

SEISMIC(Special requirements in

seismic design )(l p )

Section References

I-SHAPE

b tf f2

(beam)£ F

y52 UBC 2213.7.3 (SMRF)UBC 2213.10.2 (EBF)

b tf f2

(column)

8.5 for Fy £ 368.0 for 36 42£ £Fy

7.4 for 42 45£ £Fy

7.0 for 45 50£ £Fy

6.6 for 50 55£ £Fy

6.3 for 55 60£ £Fy

6.0 for Fy > 60

UBC 2213.7.3 (SMRF)UBC 2213.9.5 (SCBF)

ASD N7

BOX

b t f

andh tc

w

(column)

£ F y110 UBC 2213.7.3 (SMRF),

UBC 2213.9.5 (SCBF)

b t f

andh tc

w

(brace)

£ F y110 UBC 2213.8.2.5 (BF),

UBC 2213.9.2.4 (SCBF)

ANGLEb t

(brace)£ F

y52 UBC 2213.8.2.5 (BF)UBC 2213.9.2.4 (SCBF)

DOUBLE-ANGLEb t

(brace)£ F

y52 UBC 2213.8.2.5 (BF)UBC 2213.9.2.4 (SCBF)

PIPED t

(brace)£ F

y1300 UBC 2213.8.2.5 (BF)UBC 2213.9.2.4 (SCBF)

CHANNELb tf

f

h tc w

No special requirementNo special requirement

T-SHAPEb tf

f2

d t w


ROUND BAR ¾ No special requirement

RECTANGULAR ¾ No special requirement

GENERAL ¾ No special requirement

Table XI-1Limiting Width-Thickness Ratios for Classification of Sections when Special Seismic

Conditions Apply as per UBC-ASD

isfy these ad di tional re quire ments are clas si fied and re ported as “SEIS MIC” inETABS. These spe cial re quire ments for clas si fy ing the sec tions as “SEIS MIC” inETABS ( “Com pact” in UBC) are given in Table XI-1 (UBC 2213.7.3, 2213.8.2.5,2213.9.2.4, 2213.9.5, 2213.10.2). If these cri te ria are not sat is fied, when the codere quires them to be sat is fied, the user must mod ify the sec tion prop erty. In this caseETABS gives a warn ing mes sage in the out put file.


The ax ial, flex ural, and shear stresses at each of the pre vi ously de fined sta tions foreach load com bi na tion in UBC-ASD97 are cal cu lated in the same way as de scribed in sec tion “Cal cu la tion of Stresses” of Chap ter with out any ex cep tion (UBC 2208,ASD A-B5.2d). For nonslender sec tions, the stresses are based on the grosscross-sec tional ar eas (ASD A-B5.2c), for slen der sec tions the stresses are based onef fec tive sec tion prop er ties (ASD A-B5.2c), and for Sin gle-an gle sec tions thestresses are based on the prin ci pal prop er ties of the sec tions (ASD SAM 6.1.5).

The flex ural stresses are cal cu lated based on the prop er ties about the prin ci pal axes. For I, Box, Chan nel, T, Dou ble-an gle, Pipe, Cir cu lar and Rect an gu lar sec tions, theprin ci pal axes co in cide with the geo met ric axes. For Sin gle-an gle sec tions, the de -sign con sid ers the prin ci pal prop er ties. For gen eral sec tions it is as sumed that allsec tion prop er ties are given in terms of the prin ci pal di rec tions.

The shear stresses for Sin gle-an gle sec tions are cal cu lated for di rec tions along thegeo met ric axes. For all other sec tions the shear stresses are cal cu lated along thegeo met ric/prin ci ple axes.


The al low able stresses in com pres sion, ten sion, bend ing, and shear for Com pact,Noncompact, and Slen der sec tions ac cord ing to the UBC-ASD97 are cal cu lated inthe same way as de scribed in sec tion “Cal cu la tion of Al low able Stresses” of Chap -ter with out any ex cep tion (UBC 2208, ASD A-B5.2d). The al low able stresses forSeis mic sec tions are cal cu lated in the same way as for Com pact sec tions.

The al low able flex ural stresses for all shapes of sec tions are cal cu lated based ontheir prin ci pal axes of bend ing. For the I, Box, Chan nel, Cir cu lar, Pipe, T, Dou -ble-an gle and Rect an gu lar sec tions, the prin ci pal axes co in cide with their geo met -ric axes. For the An gle sec tions, the prin ci pal axes are de ter mined and all com pu ta -tions re lated to flex ural stresses are based on that.


262 Member Design

The al low able shear stress is cal cu lated along the geo met ric axes for all sec tions.For I, Box, Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rect an gu lar sec tions, theprin ci pal axes co in cide with their geo met ric axes. For Sin gle-an gle sec tions, prin -ci pal axes do not co in cide with the geo met ric axes.

All lim i ta tions and warn ings re lated to al low able stress cal cu la tion inAISC-ASD89 also apply in this code.

If the user spec i fies non zero al low able stresses for one or more el e ments in theprogram “Al low able Stress Overwrites” form, these val ues will over ride the above men tioned cal cu lated val ues for those el e ments . The spec i fied al low able stressesshould be based on the prin ci pal axes of bend ing.


The stress ra tios in UBC-ASD97 are cal cu lated in the same way as de scribed insec tion “Cal cu la tion of Stress Ra tios” of Chap ter with some mod i fi ca tions as de -scribed be low.

In the cal cu la tion of the ax ial and bend ing stress ra tios, first, for each sta tion alongthe length of the mem ber, the ac tual stresses are cal cu lated for each load com bi na -tion. Then the cor re spond ing al low able stresses are cal cu lated. Then, the stress ra -tios are cal cu lated at each sta tion for each mem ber un der the in flu ence of each ofthe de sign load com bi na tions. The con trol ling stress ra tio is then ob tained, alongwith the as so ci ated sta tion and load com bi na tion. A stress ra tio greater than 1.0 in -di cates an over stress. Sim i larly, a shear ca pac ity ra tio is also cal cu lated sep a rately.

Dur ing the de sign, the ef fect of the pres ence of bolts or welds is not con sid ered.




f

F+

C f

f

F' F

+ C fa

a

m b

a

e

b

m b33 33

33

33

22 22

1 1-æ

èçç

ö

ø÷÷

f

F' Fa

e

b-æ

èçç

ö

ø÷÷

22

22


Member Design 263


( )

f

F

f

F

f

Fa

y

b

b

b

bQ 0.60+ +33

33

22

22


fa , fb33 , fb22 , Fa , Fb33 , Fb22 , and Fe¢ are de fined ear lier in Chap ter . A fac tor of

4/3 is NOT ap plied on Fe¢ and 0.6Fy if the load com bi na tion in cludes any wind

load or seis mic load (UBC 1612.3.1).

Cm33 and Cm22 are co ef fi cients rep re sent ing dis tri bu tion of mo ment along themem ber length. They are cal cu lated in the same way as in Chap ter .

When the stress ra tio is cal cu lated for Spe cial Seis mic Load Com bi na tions, thecol umn ax ial al low able stress in com pres sion is taken to be 1.7 Fa in stead of Fa

(UBC 2213.4.2).

• If fa is com pres sive and f Fa a £ 0.15 , a rel a tively sim pli fied for mula is used for the com bined stress ra tio.

f

F +

f

F +

f

Fa

a

b

b

b

b

33

33

22

22

(ASD H1-3, SAM 6.1)


f

F

f

F

f

Fa

a

b

b

b

b

+ +33

33

22

22


f

F

f

Fb

b

b

b

33

33

22

22

+ , where

fa , fb33 , fb22 , Fa , Fb33 , and Fb22 are de fined ear lier in Chap ter . How ever, ei ther Fb33 or Fb22 need not be less than 0.6Fy in the first equa tion (ASD H2-1). Thesec ond equa tion con sid ers flex ural buck ling with out any ben e fi cial ef fect fromax ial com pres sion.

When the stress ra tio is cal cu lated for Spe cial Seis mic Load Com bi na tions, thecol umn ax ial al low able stress in ten sion is taken to be Fy in stead of Fa (UBC2213.4.2)


For Sin gle-an gle sec tions, the com bined stress ra tio is cal cu lated based on the prop -er ties about the prin ci pal axes (ASD SAM 5.3, 6.1.5). For I, Box, Chan nel, T, Dou -ble-an gle, Pipe, Cir cu lar and Rect an gu lar sec tions, the prin ci pal axes co in cide with

264 Member Design


their geo met ric axes. For Sin gle-an gle sec tions, prin ci pal axes are de ter mined inthe pro gram. For gen eral sec tions it is as sumed that all sec tion prop er ties are givenin terms of the prin ci pal di rec tions and con se quently no ef fort is made to de ter minethe prin ci pal di rec tions.

In con trast to the AISC-ASD code, when de sign ing for com bi na tions in volv ingearth quake and wind loads, al low able stresses are NOT in creased by a fac tor of 4/3of the reg u lar al low able value (UBC 1612.3.1, 2209.3).

Shear Stresses

From the al low able shear stress val ues and the fac tored shear stress val ues at eachsta tion, shear stress ra tios for ma jor and mi nor di rec tions are com puted for each ofthe load com bi na tions as fol lows:

f

Fv

v

2 , and

f

Fv

v

3 .


In con trast to AISC-ASD code, when de sign ing for com bi na tions in volv ing earth -quake and wind loads, al low able shear stresses are NOT in creased by a fac tor of 4/3 of the reg u lar al low able value (UBC 1612.3.1, 2209.3).

Member Design 265


Seis mic Re quire ments

The spe cial seis mic re quire ments checked by the pro gram for mem ber de sign arede pend ent on the type of fram ing used and are de scribed be low for each type offram ing. The re quire ments checked are based on UBC Sec tion 2213 for frames inSeis mic Zones 3 and 4 and on UBC Sec tion 2214 for frames in Seis mic Zones 1 and 2 (UBC 2204.2, 2205.2, 2205.3, 2208, 2212, 2213, 2214). No spe cial re quire mentis checked for frames in Seis mic Zone 0.

Or di nary Mo ment Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported:

• In Seis mic Zones 3 and 4, whenever the ax ial stress, fa , in col umns due to thepre scribed load ing com bi na tions ex ceeds 0.3Fy , the Spe cial Seis mic LoadCom bi na tions as de scribed be low are checked with re spect to the col umn ax ialload ca pac ity only (UBC 2213.5.1).


In this case col umn forces are replaced by the col umn forces for the Spe cialSeis mic Load Com bi na tions, whereas the other forces are taken as ze ros. Forthis case the col umn ax ial al low able stress in com pres sion is taken to be 1.7 Fa

in stead of Fa and the col umn ax ial al low able stress in ten sion is taken to be Fy

in stead of Fa (UBC 2213.5.1, 2213.4.2).

Spe cial Moment-Resisting Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported:



In this case col umn forces are re placed by the col umn forces for the Spe cialSeis mic Load Com bi na tions, whereas the other forces are taken as ze ros. For


266 Member Design

this case the col umn ax ial al low able stress in com pres sion is taken to be 1.7 Fa


in stead of Fa (UBC 2213.5.1, 2213.4.2).

• In Seis mic Zones 3 and 4, the I-shaped beams, I-shaped col umns, and Boxshaped col umns are ad di tion ally checked for com pact ness cri te ria as de scribedin Table XI-1 (UBC 2213.7.3). Com pact I-shaped beam sec tions are ad di tion -

ally checked for b tf f2 to be less than 52 Fy . Com pact I-shaped col umn

sec tions are ad di tion ally checked for b tf f2 to be less than the num bers givenfor plas tic sec tions in Table XI-1. Com pact box shaped col umn sec tions are ad -

di tion ally checked for b t f and d t w to be less than 110 Fy . If this cri te ria

is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear lier un der sec -tion clas si fi ca tions. If this cri te ria is not sat is fied the user must mod ify the sec -tion prop erty.

• In Seis mic Zones 3 and 4, the pro gram checks the lat er ally un sup ported lengthof beams to be less than 96 ry . If the check is not sat is fied, it is noted in the out -put (UBC 2213.7.8).

Braced Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported:



In this case col umn forces are re placed by the col umn forces for the Spe cialSeis mic Load Com bi na tions, whereas the other forces are taken as ze ros. Forthis case the col umn ax ial al low able stress in com pres sion is taken to be 1.7 Fa


in stead of Fa (UBC 2213.5.1, 2213.4.2).

• In Seis mic Zones 3 and 4, the pro gram checks the lat er ally un sup ported lengthof beams to be less than 96 ry . If the check is not sat is fied, it is noted in the out -put (UBC 2213.8.1, 2213.7.8).

Member Design 267


• In Seis mic Zones 3 and 4, the max i mum l r ra tio of the braces is checked not to

ex ceed 720 Fy . If this check is not met, it is noted in the out put (UBC

2213.8.2.1).

• In Seis mic Zones 3 and 4, the An gle, Dou ble-an gle, Box, and Pipe shapedbraces are ad di tion ally checked for com pact ness cri te ria as de scribed in TableXI-1 (UBC 2213.8.2.5). For an gles and dou ble-angles b t is lim ited to

52 Fy , for box sec tions b t f and d t w is lim ited to 110 Fy , for pipe

sec tions D t is lim ited to 1300 Fy . If this cri te ria is sat is fied the sec tion isre ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca tions. If thiscri te ria is not sat is fied the user must mod ify the sec tion prop erty.

• In Seis mic Zones 3 and 4, the al low able com pres sive stress for braces is re -duced by a fac tor, B, where

BKl r

C c

=+

1

12

(UBC 2213.8.2.2)

In Seis mic Zones 1 and 2, the al low able com pres sive stress for braces is re -duced by the same fac tor, B, where

B ³ 0.8 (UBC 2214.6.2.1)

• In Seis mic Zones 3 and 4, Chevron braces are de signed for 1.5 times the spec i -fied load ing com bi na tions (UBC 2213.8.4.1).

Ec cen tri cally Braced Frames

For this fram ing sys tem, the pro gram looks for and rec og nizes the ec cen tri callybraced frame con figu ra tions shown in Figure XI-1. The fol low ing ad di tional re -quire ments are checked or re ported for the beams, col umns and braces as so ci atedwith these con figu ra tions. Spe cial seis mic de sign of ec cen tri cally braced frames inSeis mic Zones 1 and 2 is the same as those in Seis mic Zones 3 and 4 (UBC 2214.8).

• In all Seis mic Zones ex cept Zone 0, the I-shaped beam sec tions are ad di tion ally checked for com pact ness cri te ria as de scribed in Table XI-1. Com pact I-shaped

beam sec tions are ad di tion ally checked for b tf f2 to be less than 52 Fy .

If this cri te ria is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear -lier un der sec tion clas si fi ca tions. If this cri te ria is not sat is fied the user mustmod ify the sec tion prop erty (UBC 2213.10.2). Other sec tions meet ing this cri -te ria are also re ported as SEIS MIC.


268 Member Design

• In all Seis mic Zones ex cept Zone 0, the link beam strength in shear V F dts y w= 0.55 and mo ment M Z Fs y= are cal cu lated. If V M es s£ 2.0 , thelink beam strength is as sumed to be gov erned by shear and is so re ported. If the above con di tion is not sat is fied, the link beam strength is as sumed to be gov -erned by flex ure and is so re ported. When link beam strength is gov erned byshear, the ax ial and flex ural prop er ties (area, A and sec tion modu lus, S) for usein the in ter ac tion equa tions are cal cu lated based on the beam flanges only(UBC 2213.10.3).

• In all Seis mic Zones ex cept Zone 0, if the link beam is con nected to the column, the link beam length, e, is checked not to ex ceed the fol low ing (UBC2213.10.12):

eM

V

p

p

£ 1.6 (UBC 2213.10.12)


• In all Seis mic Zones ex cept Zone 0, the link beam ro ta tion, q, of the in di vid ualbay rel a tive to the rest of the beam is cal cu lated as the story drift D M times baylength di vided by the to tal lengths of link beams in the bay di vided by height ofthe story. The link beam ro ta tion, q, is checked to be less than the fol low ingval ues (UBC 2213.10.4).

q £ 0.090 , where link beam clear length, e M Vs s£ 1.6 ,

q £ 0.030 , where link beam clear length, e M Vs s³ 3.0 , and


• In all Seis mic Zones ex cept Zone 0, the link beam shear un der the spec i fiedload ing com bi na tions is checked not to ex ceed 0.8Vs (UBC 2213.10.5).

• In all Seis mic Zones ex cept Zone 0, the brace strength is checked to be at least1.5 times the ax ial force cor re spond ing to the con trol ling link beam strength(UBC 2213.10.13). The con trol ling link beam strength is ei ther the shearstrength, Vs as V F dts y w= 0.55 , or the re duced flex ural strength, M rs , which -ever pro duces the lower brace force. The value of M rs is taken as M Z F frs y a= -( ) (UBC 2213.10.3), where fa is the lower of the ax ial stress in the link beam cor re spond ing to yield ing of the link beam web in shear or thelink beam flanges in flex ure. The cor re spon dence be tween brace force and linkbeam force is ob tained from the as so ci ated load cases, which ever has the high -est link beam force of in ter est.

Member Design 269


• In all Seis mic Zones ex cept Zone 0, the col umn is checked not to be come in -elas tic for grav ity loads plus 1.25 times the col umn forces cor re spond ing to thecon trol ling link beam strength (UBC 2213.10.14). The con trol ling link beamstrength and the cor re spond ing forces are as ob tained by the pro cess de scribedabove. If this con di tion gov erns, the col umn ax ial al low able stress in com pres -sion is taken to be 1.7 Fa in stead of Fa and the col umn ax ial al low able stress inten sion is taken to be Fy in stead of Fa .


270 Member Design

Figure XI-1Ec cen tri cally Braced Frame Con figu ra tions

• In all Seis mic Zones ex cept Zone 0, ax ial forces in the beams are in cluded incheck ing of the beams (UBC 2211.10.17). The user is re minded that us ing arigid di a phragm model will re sult in zero ax ial forces in the beams. The usermust dis con nect some of the col umn lines from the di a phragm to al low beamsto carry ax ial loads. It is rec om mended that only one col umn line per ec cen tri -cally braced frame be con nected to the rigid di a phragm or a flex i ble di a phragmmodel be used.

• In all Seis mic Zones ex cept Zone 0, the beam lat er ally un sup ported length is

checked to be less than 76 b Ff y . If not sat is fied it is so noted as a warn ing

in the out put file (UBC 2213.10.18).

Note: The beam strength in flex ure, of the beam out side the link, is NOT cur rentlychecked to be at least 1.5 times the mo ment cor re spond ing to the con trol ling linkbeam strength (UBC 2213.10.13). Users need to check for this re quire ment.

Spe cial Con cen tri cally Braced Frames

Spe cial seis mic de sign of spe cial con cen tri cally braced frames in Seis mic Zones 1and 2 is the same as those in Seis mic Zones 3 and 4 (UBC 2214.7). For this fram ingsys tem, the fol low ing ad di tional re quire ments are checked or re ported:

• In all Seis mic Zones ex cept Zone 0, when ever the ax ial stress, fa , in col umnsdue to the pre scribed load ing com bi na tions ex ceeds 0.3Fy , the Spe cial Seis mic Load Com bi na tions as de scribed be low are checked with re spect to the col umnax ial load ca pac ity only (UBC 2213.9.5, 2213.5.1).


In this case col umn forces are re placed by the col umn forces for the Spe cialSeis mic Load Com bi na tions, whereas the other forces are taken as ze ros. Forthis case the col umn ax ial al low able stress in com pres sion is taken to be 1.7 Fa


in stead of Fa (UBC 2213.5.1, 2213.4.2).

• In all Seis mic Zones ex cept Zone 0, the I-shaped and Box shaped col umns aread di tion ally checked for com pact ness cri te ria as de scribed in Table XI-1. Com pact I-shaped col umn sec tions are ad di tion ally checked for b tf f2 to beless than the num bers given for plas tic sec tions in Table XI-1. Com pact boxshaped col umn sec tions are ad di tion ally checked for b t f and d t w to be less

than 110 Fy . If this cri te ria is sat is fied the sec tion is re ported as SEIS -

Member Design 271


MIC as de scribed ear lier un der sec tion clas si fi ca tions. If this cri te ria is not sat -is fied the user must mod ify the sec tion prop erty (UBC 2213.9.5, 2213.7.3).

• In all Seis mic Zones ex cept Zone 0, brac ing mem bers are checked to be com -pact and are so re ported. The An gle, Box, and Pipe sec tions used as braces aread di tion ally checked for com pact ness cri te ria as de scribed in Table XI-1. For

an gles b t is lim ited to 52 Fy , for box sec tions b t f and d t w is lim ited

to 110 Fy , for pipe sec tions D t is lim ited to 1300 Fy . If this cri te ria is

sat is fied the sec tion is re ported as SEIS MIC. If this cri te ria is not sat is fied theuser must mod ify the sec tion prop erty (UBC 2213.9.2.4).

• In all Seis mic Zones ex cept Zone 0, the max i mum Kl r ra tio of the braces is

checked not to ex ceed 1000 Fy . If this check is not met, it is noted in the

out put (UBC 2213.9.2.1).

Note: Beams in ter sected by Chev ron braces are NOT cur rently checked tohave a strength to sup port loads rep re sented by the fol low ing load ing com bi na -tions (UBC 2213.9.4.1):

1.2DL + 0.5LL Pb± (UBC 2213.9.4.1)

0.9DL Pb± (UBC 2213.9.4.1)

where Pb is given by the dif fer ence of F Ay for the ten sion brace and 0.3 times 1.7 F Aa for the com pres sion brace. Users need to check for this re quire ment(UBC 2213.9.4.1, 2213.4.2).

Joint Design

When us ing UBC-ASD97 de sign code, the struc tural joints are checked and/ordesigned for the following:


• Check for the re quire ment of doubler plate and de ter mi na tion of its thickness


• Re porting the beam con nec tion shear

• Re porting the brace con nec tion force


272 Joint Design






To achieve a beam/col umn mo ment con nec tion, con ti nu ity plates such as shown in are usu ally placed on the col umn, in line with the top and bot tom flanges of thebeam, to trans fer the com pres sion and ten sion flange forces of the beam into thecol umn.

For con nec tion con di tions de scribed in the last two steps above, the thick ness ofsuch plates is usu ally set equal to the flange thick ness of the cor re spond ing beam.How ever, for the con nec tion con di tion de scribed by the first step above, where thebeam frames into the flange of the col umn, such con ti nu ity plates are not al waysneeded. The re quire ment de pends upon the mag ni tude of the beam-flange forceand the prop er ties of the col umn. This is the con di tion that the pro gram in ves ti -gates. Col umns of I-sec tions only are in ves ti gated. The pro gram eval u ates the con -ti nu ity plate re quire ments for each of the beams that frame into the col umn flange(i.e. par al lel to the col umn ma jor di rec tion) and re ports the max i mum con ti nu ityplate area that is needed for each beam flange. The con ti nu ity plate re quire mentsare eval u ated for mo ment frames only. No check is made for braced frames.

The con ti nu ity plate area re quired for a par tic u lar beam fram ing into a col umn isgiven by:

A = P

F t t + 5kcp

bf

yc

wc fb c- ( ) (ASD K1-9)

If A cp £ 0, no con ti nu ity plates are re quired pro vided the fol low ing two con di tionsare also sat is fied:

• The depth of the col umn clear of the fil lets, i.e. d kc c- 2 , is less than or equalto:

Joint Design 273


4100 t F

P

wc3

yc

bf

(ASD K1-8)

• The thick ness of the col umn flange, t fc , is greater than or equal to:

0.4P

F

bf

yc

, where (ASD K1-1)

P f Abf b bf= .

fb is the bend ing stress cal cu lated from the larger of 5/3 of load ing com bi na tions

with grav ity loads only ( ) ( )[ ]5 3 M d t Af fb- and 4/3 of the load ing com bi na -

tions with lat eral loads ( ) ( )[ ]4 3 M d t Af fb- (ASD K1.2). For spe cial seis mic

de sign, fb is spec i fied to be beam flange strength.


• The thick ness of the stiff en ers is at least 0.5t fb , or

t = tcpmin

fb 0.5 (ASD K1.8.2)

• The width of the con ti nu ity plate on each side plus ½ the thick ness of the col -umn web shall not be less than 1/3 of the beam flange width, or

b = 2 b

3

t

2cpmin fb wc-

æ

èçç

ö

ø÷÷ (ASD K1.8.1)


A = t bcpmin

cpmin

cpmin


min .

Where

Abf = Area of beam flangeAcp = Re quired con ti nu ity plate area Fyb = Yield stress of beam ma te rialFyc = Yield stress of the col umn and con ti nu ity plate ma te rial


274 Joint Design

t fb = Beam flange thick ness t wc = Col umn web thick ness k c = Dis tance be tween outer face of the col umn flange and

web toe of its fil letd c = Col umn depthd b = Beam depthfb = Beam flange width t cp = Con ti nu ity plate thick nessbcp = Con ti nu ity plate widthfb = Bending stress cal cu lated from the larger of 5/3 of load ing

com bi na tions with grav ity loads only ( ) ( )[ ]5 3 M d t Af fb-

and 4/3 of the load ing com bi na tions with lat eral loads

( ) ( )[ ]4 3 M d t Af fb- (ASD K1.2).

The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and are de scribed be low for each type of fram ing.The re quire ments checked are based on UBC Sec tion 2213 for frames in Seis micZones 3 and 4 and on UBC Sec tion 2214 for frames in Seis mic Zones 1 and 2 (UBC2204.2, 2205.2, 2213, 2214). No spe cial re quire ment is checked for frames in Seis -mic Zone 0.

• In all Seis mic Zones ex cept Zone 0, for Or di nary Mo ment Frames the con ti nu -ity plates are checked and de signed for a beam flange force, Pbf .

P f Abf yb bf= (UBC 2213.6.1, 2213.7.1.1, 2214.4.1, 2214.5.1.1)

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, for de ter min -ing the need for con ti nu ity plates at joints due to ten sion trans fer from the beamflanges, the force Pbf is taken as 1.8 f Ayb bf (UBC 2213.7.4). For de sign of thecon ti nu ity plate the beam flange force is taken as f Ayb bf (UBC 2213.7.1.1).

In Seis mic Zones 1 and 2, for Spe cial Mo ment-Re sisting Frames, for de ter min -ing the need for con ti nu ity plates at joints due to ten sion trans fer from the beamflanges, the force Pbf is taken as f Ayb bf . For de sign of the con ti nu ity plate thebeam flange force is taken as f Ayb bf (UBC 2214.5.1.1).

• In all Seis mic Zones ex cept Zone 0, for Ec cen trically Braced Frames, the con ti -nu ity plates are checked and de signed for a beam flange force, Pbf .

P f Abf yb bf= (UBC 2213.10.12, 2213.10.19)

Joint Design 275




Shear stresses sel dom con trol the de sign of a beam or col umn mem ber. How ever,in a Mo ment-Re sisting frame, the shear stress in the beam-col umn joint can be crit i -cal, es pe cially in fram ing sys tems when the col umn is sub jected to ma jor di rec tionbend ing and the joint shear forces are re sisted by the web of the col umn. In mi nordi rec tion bend ing, the joint shear is car ried by the col umn flanges, in which case the shear stresses are sel dom crit i cal, and this con di tion is there fore not in ves ti gated bythe pro gram.

Shear stresses in the panel zone, due to ma jor di rec tion bend ing in the col umn, mayre quire ad di tional plates to be welded onto the col umn web, de pend ing upon theload ing and the ge om e try of the steel beams that frame into the col umn, ei theralong the col umn ma jor di rec tion, or at an an gle so that the beams have com po nents along the col umn ma jor di rec tion. See . The pro gram in ves ti gates such sit u a tionsand re ports the thick ness of any re quired doubler plates. Only col umns withI-shapes are in ves ti gated for doubler plate re quire ments. Also doubler plate re -quire ments are eval u ated for mo ment frames only. No check is made for bracedframes.

The shear force in the panel zone, is given by

V = P - Vp c , or

V = M

d – t - Vp

n =

nbn n

n f

c

b

n1

åcosq

The re quired web thick ness to re sist the shear force, Vp , is given by

t = V

F d

h

Fr

p

v c yc

³380

(ASD F4)


t = t - tdp r wc , where,

Fv = 0.40 Fyc (ASD F4)Fyc = Yield stress of the col umn and doubler plate ma te rialt r = Re quired col umn web thick ness


276 Joint Design

t dp = Re quired doubler plate thick ness t fn = Thick ness of flange of the n-th beam con nect ing to col umnt wc = Col umn web thick ness Vp = Panel zone shear Vc = Col umn shear in col umn aboveP = Beam flange forces nb = Num ber of beams con nect ing to col umn d n = Depth of n-th beam con nect ing to col umnh = d tc fc- 2 if welded, d kc c- 2 if rolled,q n = An gle be tween n-th beam and col umn ma jor di rec tion d c = Depth of col umnM bn = Cal cu lated fac tored beam mo ment from the cor re spond ing

load ing com bi na tion

The larg est cal cu lated value of Vp cal cu lated for any of the load com bi na tionsbased upon the fac tored beam mo ments is used to cal cu late doubler plate areas.

The spe cial seis mic re quire ments checked by the pro gram for cal cu lat ing doublerplate ar eas are de pend ent on the type of fram ing used and are de scribed be low foreach type of fram ing. The re quire ments checked are based on UBC Sec tion 2213for frames in Seis mic Zones 3 and 4 and on UBC Sec tion 2214 for frames in Seis -mic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213, 2214). No spe cial re quire ment ischecked for frames in Seis mic Zones 0, 1 and 2.

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the panelzone doubler plate re quire ments that are re ported will de velop the lesser ofbeam mo ments equal to 0.8 of the plas tic mo ment ca pac ity of the beam

( )0.8 M pbå , or beam mo ments due to grav ity loads plus 1.85 times the seis -

mic load (UBC 2213.7.2.1).

The ca pac ity of the panel zone in re sist ing this shear is taken as (UBC2213.7.2.1):

V = F d t + b t

d d t p yc c r

c cf

b c r

0.55 13 2æ

è

çç

ö

ø

÷÷ (UBC 2213.7.2.1)


t = V

F d

b t

d d

h

Fr

p

yc c

c cf

b c yc0.55

- ³3

380

2

(UBC 2213.7.2.1, ASD F4)


Joint Design 277


t = t - tdp r wc

where

bc = width of col umn flange,h = d tc fc- 2 if welded, d kc c- 2 if rolled,t cf = thick ness of col umn flange, andd b = depth of deep est beam fram ing into the ma jor di rec tion of

the col umn.

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the panelzone col umn web thick ness re quire ment the pro gram checks the fol low ing:

td t d t

wc

c fc b fb³

- + -( ) ( )2 2

90(UBC 2213.7.2.2)


• In Seis mic Zones 3 and 4, for Ec cen trically Braced Frames, the doubler platere quire ments are checked sim i lar to the doubler plate checks for spe cial Mo -ment-Re sisting frames as dis cussed ear lier (UBC 2213.10.19).

Beam/Column Plastic Moment Capacity Ratio

In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the code re quiresthat the sum of beam flex ure strengths at a joint should be less than the sum of col -umn flex ure strengths (UBC 2213.7.5). The col umn flex ure strength should re flectthe pres ence of ax ial force pres ent in the col umn. To fa cil i tate the re view of thestrong col umn weak beam cri te rion, the pro gram will re port a beam/col umn plas ticmo ment ca pac ity ra tio for ev ery joint in the struc ture.


R =

M

M + Mmaj

n =

n

pbn n

pcax pcbx

b

1å cos q

(UBC 2213.7.5)

For the mi nor di rec tion of any col umn the beam to col umn strength ratio is ob tained as


278 Joint Design

R =

M

M + M

n =

n

pbn n

pcay pcby

b

min1

å sin q

, (UBC 2213.7.5)

where,

Rmaj min, = Plas tic mo ment ca pac ity ra tios, in the ma jor andmi nor di rec tions of the col umn, re spec tively,

M pbn = Plas tic mo ment ca pac ity of n-th beam con nect ingto col umn,

q n = An gle be tween the n-th beam and the col umnma jor di rec tion,

M pcax y, = Ma jor and mi nor plas tic mo ment ca pac i ties, re duced forax ial force ef fects, of col umn above story level. Cur rently, it is be ing taken equal to M pcbx y, if there is a col umn above the joint as sum ing that the col umn splice is done far away from the joint. If there is no col umn above the joint, M pcax y, is taken as zero,

M pcbx y, = Ma jor and mi nor plas tic mo ment ca pac i ties, re duced forax ial force ef fects, of col umn be low story level, and

nb = Num ber of beams con nect ing to the col umn.


M = Z F - fpc c yc a( ) , (UBC 2213.7.5)

where,

Z c = Plas tic modu lus of col umn,Fyc = Yield stress of col umn ma te rial, andfa = Max i mum ax ial stress in the col umn.



For each steel beam in the struc ture the pro gram will re port the max i mum ma jorshears at each end of the beam for the de sign of the beam shear con nec tions. The

Joint Design 279


beam con nec tion shears re ported are the max ima of the fac tored shears ob tainedfrom the load ing com bi na tions.

For spe cial seis mic de sign, the beam con nec tion shears are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The re quire ments checkedare based on UBC Sec tion 2213 for frames in Seis mic Zones 3 and 4 and on UBCSec tion 2214 for frames in Seis mic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213,2214). No spe cial re quire ment is checked for frames in Seis mic Zones 0.

• In all Seis mic Zones ex cept Zone 0, for Or di nary Mo ment Frames, the beamcon nec tion shears re ported are the max i mum of the spec i fied load ing com bi na -tions and the fol low ing ad di tional load ing com bi na tion (UBC 2213.6.2,2214.4.2):

1.0 DL + 1.0 LL ± W 0 EL (UBC 2213.6.2, 2214.4.2)

• In all Seis mic Zones ex cept Zone 0, for Spe cial Mo ment-Re sisting Frames, thebeam con nec tion shears that are re ported al low for the de vel op ment of the fullplas tic mo ment ca pac ity of the beam (UBC 2213.7.1, 2214.5.1.1). Thus:

V = C M

L + V

pb

DL LL+ (UBC 2213.7.1.1, 2214.5.1.1)

where,



M pb = Plas tic mo ment ca pac ity of the beam, Z Fy ,L = Clear length of the beam, andVDL LL+ = Ab so lute max i mum of the cal cu lated fac tored beam

shears at the cor re spond ing beam ends from the dead load and live load com bi na tions only.

• In all Seis mic Zones ex cept Zone 0, for Ec cen trically Braced Frames, the beamcon nec tion shears re ported are the max i mum of the spec i fied load ing com bi na -tions and the fol low ing ad di tional load ing com bi na tion:

1.0 DL + 1.0 LL ± W 0 EL

280 Joint Design




For spe cial seis mic de sign, the brace con nec tion forces are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The re quire ments checkedare based on UBC Sec tion 2213 for frames in Seis mic Zones 3 and 4 and on UBCSec tion 2214 for frames in Seis mic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213,2214). No spe cial re quire ment is checked for frames in Seis mic Zones 0.

• In all Seis mic Zones ex cept Zone 0, for or di nary Braced Frames, the brac ingcon nec tion force is re ported at least as the smaller of the ten sile strength of thebrace (F Ay ) and the fol low ing spe cial load ing com bi na tion (UBC 2213.8.3.1,2214.6.3.1):

1.0 DL + 1.0 LL ± W 0 EL (UBC 2213.8.3.1, 2214.6.3.1)

• In all Seis mic Zones ex cept Zone 0, for Spe cial Con cen trically Braced Frames,the brac ing con nec tion force is re ported at least as the smaller of the ten silestrength of the brace (F Ay ) and the fol low ing spe cial load ing com bi na tion(UBC 2213.9.3.1, 2214.7):

1.0 DL + 1.0 LL ± W 0 EL (UBC 2213.9.3.1, 2214.7)

• In all Seis mic Zones ex cept Zone 0, for Ec cen trically Braced Frames, the brac -ing con nec tion force is re ported as at least the brace strength in com pres sionwhich is com puted as 1.7 F Aa (UBC 2213.10.6, 2214.8). 1.7 F Aa is lim ited not to ex ceed F Ay .

Joint Design 281


C h a p t e r XII

Check/Design for UBC-LRFD97

This chap ter de scribes the de tails of the struc tural steel de sign and stress check al -go rithms that are used by the pro gram when the user se lects the UBC-LRFD97 de -sign code. The UBC-LRFD97 de sign code in the pro gram im ple ments the In ter na -tional Con fer ence of Build ing Of fi cials’ 1997 Uni form Build ing Code: Vol ume 2:Struc tural En gi neering De sign Pro vi sions, Chap ter 22, Di vi sion II, “De sign Stan -dard for Load and Re sis tance Fac tor De sign Spec i fi ca tion for Struc tural SteelBuild ings” (ICBO 1997).

Chap ter 22, Di vi sion III, of UBC adopted the Amer i can In sti tute of Steel Con struc -tion’s Load and Re sis tance Fac tor De sign Spec i fi ca tion for Struc tural Steel Build -ings (AISC 1993), which has been im ple mented in the AISC-LRFD93 code in thepro gram. The pro gram im ple men ta tion of UBC-LRFD97 is de scribed in Chap ter “Check/De sign for AISC-LRFD93” of this man ual. The cur rent chap ter fre quentlyre fers to Chap ter . It is sug gested that the user read Chap ter be fore con tin u ing toread this chap ter.

For re fer ring to per ti nent sec tions and equa tions of the UBC code, a unique pre fix“UBC” is as signed. For re fer ring to per ti nent sec tions and equa tions of theUBC-LRFD code, a unique pre fix “LRFD” is as signed. How ever, all ref er ences tothe “Spec i fi ca tions for Load and Re sis tance Fac tored De sign of Sin gle-An gleMem bers” (AISC 1994) carry the pre fix of “LRFD SAM”. More over, all sec tions of the “Seis mic Pro vi sions for Struc tural Steel Build ings June 15, 1992” (AISC

283

1994) are re ferred to as Sec tion 2211.4 of the UBC code. In this man ual, all sec tions and sub sec tions ref er enced by “UBC 2211.4” or “UBC 2211.4.x” re fer to theLRFD Seis mic Pro vi sions af ter UBC amend ments through UBC Sec tion 2210.Var i ous no ta tions used in this chap ter are de scribed in Table V-1.

When us ing the UBC-LRFD97 op tion, the fol low ing Framing Sys tems are rec og -nized (UBC 1627, 2210):


• Spe cial Mo ment-Re sisting Frame (SMRF)

• Con cen trically Braced Frame (CBF)

• Ec cen trically Braced Frame (EBF)

• Spe cial Con cen trically Braced Frame (SCBF)

By de fault the frame type is taken as Spe cial Mo ment-Re sisting Frame (SMRF) inthe pro gram. How ever, the frame type can be over writ ten in the Pref er ence form tochange the de fault and in the Over writes form on a mem ber by mem ber ba sis. If any mem ber is as signed with a frame type, the change of the frame type in the Pref er -ence will not mod ify the frame type of the in di vid ual mem ber for which it is as -signed.

When us ing the UBC-LRFD97 op tion, a frame is as signed to one of the fol low ingfive Seis mic Zones (UBC 2210):

• Zone 0

• Zone 1

• Zone 2

• Zone 3

• Zone 4

By de fault the Seis mic Zone is taken as Zone 4 in the pro gram. How ever, the frame type can be over writ ten in the Pref er ence form to change the de fault.

The de sign is based on user-spec i fied load ing com bi na tions. But the pro gram pro -vides a set of de fault load com bi na tions that should sat isfy re quire ments for the de -sign of most build ing type struc tures.

Eng lish as well as SI and MKS met ric units can be used for in put. But the code isbased on Kip-Inch-Sec ond units. For sim plic ity, all equa tions and de scrip tions pre -sented in this chap ter cor re spond to Kip-Inch-Sec ond units un less oth er wisenoted.

284



The de sign load com bi na tions are the var i ous com bi na tions of the load cases forwhich the struc tural mem bers and joints needs to be de signed or checked. For theUBC-LRFD97 code, if a struc ture is sub jected to dead load (DL), live load (LL),wind load (WL), and earth quake in duced load (EL), and con sid er ing that wind andearth quake forces are re vers ible, then the fol low ing load com bi na tions may have to be de fined (UBC 2204.1, 2206, 2207.3, 2210.3, 1612.2.1):

1.4 DL (UBC 1612.2.1 12-1)1.2 DL + 1.6 LL (UBC 1612.2.1 12-2)

1.2 DL ± 0.8 WL (UBC 1612.2.1 12-3)0.9 DL ± 1.3 WL (UBC 1612.2.1 12-6)1.2 DL + 0.5 LL ± 1.3 WL (UBC 1612.2.1 12-4)

1.2 DL ± 1.0 EL (UBC 1612.2.1 12-5)0.9 DL ± 1.0 EL (UBC 1612.2.1 12-6)1.2 DL + 0.5 LL ± 1.0 EL (UBC 1612.2.1 12-5)

These are also the de fault de sign load com bi na tions in the pro gram when ever theUBC-LRFD97 code is used. The user should use other ap pro pri ate load ing com bi -na tions if roof live load is sep a rately treated, if other types of loads are pres ent, or if pat tern live loads are to be con sid ered.

Live load re duc tion fac tors can be ap plied to the mem ber forces of the live load case on an el e ment-by-el e ment ba sis to re duce the con tri bu tion of the live load to thefac tored load ing.

When us ing the UBC-LRFD97 code, the pro gram de sign as sumes that a P-D anal y -sis has been per formed so that mo ment mag ni fi ca tion fac tors for mo ments caus ingsidesway can be taken as unity. It is rec om mended that the P-D anal y sis be done atthe fac tored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).


0.9 DL ± W 0 EL (UBC 2210.3, 2211.4.3.1)1.2 DL + 0.5 LL ± W 0 EL (UBC 2210.3, 2211.4.3.1)

where, W 0 is the seis mic force am pli fi ca tion fac tor which is re quired to ac count forstruc tural overstrength. The de fault value of W 0 is taken as 2.8 in the pro gram.


Chapter XII Check/Design for UBC-LRFD97

How ever, W 0 can be over writ ten in the Pref er ence form to change the de fault andin the Over writes form on a mem ber by mem ber ba sis. If any mem ber is as signed avalue for W 0 , the change of W 0 in the Pref er ence form will not mod ify the W 0 ofthe in di vid ual mem ber for which W 0 is as signed. The guide line for se lect ing a rea -son able value can be found in UBC 1630.3.1 and UBC Ta ble 16-N. There are othersim i lar spe cial load ing com bi na tions which are de scribed lat ter in this chap ter.

These above com bi na tions are in ter nal to the pro gram. The user does NOT need tocre ate ad di tional load com bi na tions for these load com bi na tions. The spe cial cir -cum stances for which these load com bi na tions are ad di tion ally checked are de -scribed later in this chap ter as ap pro pri ate. The spe cial load ing com bi na tion fac torsare ap plied di rectly to The pro gram load cases. It is as sumed that any re quired scal -ing (such as may be re quired to scale re sponse spec tra re sults) has al ready been ap -plied to The pro gram load cases.

Member Design

A mem ber is rec og nized in the pro gram as ei ther a beam, col umn, or brace. In theeval u a tion of the ax ial force/bi axial mo ment ca pac ity ra tios at a sta tion along thelength of the mem ber, first the ac tual mem ber force/mo ment com po nents and thecor re spond ing ca pac i ties are cal cu lated for each load com bi na tion. Then the ca pac -ity ra tios are eval u ated at each sta tion un der the in flu ence of all load com bi na tionsus ing the cor re spond ing equa tions that are de fined in this chap ter. The con trol lingca pac ity ra tio is then ob tained. A ca pac ity ra tio greater than 1.0 in di cates over -stress. Sim i larly, a shear ca pac ity ra tio is also cal cu lated sep a rately.


The nom i nal strengths for ax ial com pres sion and flex ure are de pend ent on the clas -si fi ca tion of the sec tion as Com pact, Noncompact, Slen der or Too Slen der. Thesec tions are clas si fied in UBC-LRFD97 as ei ther Com pact, Noncompact, Slen deror Too Slen der in the same way as de scribed in sec tion “Clas si fi ca tion of Sec tions”of Chap ter with some ex cep tions as de scribed in the next para graph. the pro gramclas si fies in di vid ual mem bers ac cord ing to the lim it ing width/thick ness ra tiosgiven in Table V-2 and Table III-3 (UBC 2204.1, 2205, 2206, and 2210; LRFDB5.1, A-G1, and Ta ble A-F1.1). The def i ni tion of the sec tion prop er ties re quired in these ta bles is given in Figure V-1 and Table V-1 of Chap ter . The same lim i ta tionsap ply.

In gen eral the de sign sec tions need not nec es sar ily be Com pact to sat isfyUBC-LRFD97 codes (UBC 2213.2). How ever, for cer tain spe cial seis mic cases

286 Member Design


Member Design 287



Width-Thickness

Ratio

(l)

SEISMIC(Special requirements

in seismic design )(l p )

Section References

I-SHAPE

b tf f2 £ F

y52 UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

h tc w

For P P u b yj £ 0.125,

£æ

è

çç

ö

ø

÷÷520

1F

- P

Py

u

b y

1.54j


£æ

è

çç

ö

ø

÷÷ ³ìíï

îï

üýï

þï

191 253

F -

P

P Fy

u

b y y

2.33j

UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

BOX

b t f or

h tc w

£ F y110 (Beam and

column in SMRF, column inSCBF, Braces in BF)

UBC 2210.8 (SMRF)UBC 2210.10.g (SCBF)UBC 2211.4.9.2.d (BF)

b t f or

h tc w

£ F y100

(Braces in SCBF)UBC 2210.10.c (SCBF)

CHANNELb tf

f

h tc w

Same as I-ShapesSame as I-Shapes

UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

ANGLE b t

£ F y52

(Braces in SCBF)

UBC 2210.10.c (SCBF)UBC 2211.4.9.2.d (SCBF)

DOUBLE-ANGLE b t

£ F y52

(Braces in SCBF)

UBC 2210.10.c (SCBF)UBC 2211.4.9.2.d (SCBF)

PIPE D t £ F

y1300 UBC 2210.10.c (Braces in SCBF)UBC 2211.4.9.2.d (Braces in BF)

T-SHAPEb tf

f2

d t w


ROUND BAR ¾ No special requirement

RECTANGULAR ¾ No special requirement

GENERAL ¾ No special requirement

Table XII-1Limiting Width-Thickness Ratios for Classification of Sections when Special Seismic

Conditions Apply as per UBC-LRFD

they have to be Com pact and have to sat isfy spe cial slen der ness re quire ments. Seesub sec tion “Seis mic Re quire ments” later in this sec tion. The sec tions which do sat -isfy these ad di tional re quire ments are clas si fied and re ported as “SEIS MIC” in thepro gram. These spe cial re quire ments for clas si fy ing the sec tions as “SEIS MIC” inthe pro gram (“Com pact” in UBC) are given in Table XII-1 (UBC 2210.8,2210.10c, 2211.4.8.4.b, 2211.9.2.d, 2210.10g, 2211.4.10.6.e). If these cri te ria arenot sat is fied, when the code re quires them to be sat is fied, the user must mod ify thesec tion prop erty. In this case the pro gram gives a warn ing mes sage in the out putfile.


The fac tored mem ber loads that are cal cu lated for each load com bi na tion are Pu , M u33 , M u22 , Vu2 and Vu3 cor re spond ing to fac tored val ues of the ax ial load, the ma -jor mo ment, the mi nor mo ment, the ma jor di rec tion shear force and the mi nor di -rec tion shear force, re spec tively. These fac tored loads are cal cu lated at each of thepre vi ously de fined sta tions for each load com bi na tion. They are cal cu lated in thesame way as de scribed in sec tion “Cal cu la tion of Fac tored Forces” of Chap ter with out any ex cep tion (UBC 2204.1 2205.2, 2205.3, 2206, 2210).

The bend ing mo ments are ob tained along the prin ci pal di rec tions. For I, Box,Chan nel, T, Dou ble-an gle, Pipe, Cir cu lar and Rect an gu lar sec tions, the prin ci palaxes co in cide with the geo met ric axes. For the An gle sec tions, the prin ci pal axesare de ter mined and all com pu ta tions re lated to bend ing moment are based on that.For gen eral sec tions it is as sumed that all sec tion prop er ties are given in terms of the prin ci pal di rec tions and con se quently no ef fort is made to de ter mine the prin ci paldi rec tions.

The shear forces for Sin gle-an gle sec tions are obtained for di rec tions along the geo -met ric axes. For all other sec tions the shear stresses are cal cu lated along the geo -met ric/prin ci ple axes.

For load ing com bi na tions that cause com pres sion in the mem ber, the fac tored mo -ment M u (M u33 and M u22 in the cor re spond ing di rec tions) is mag ni fied to con sidersec ond or der ef fects. The mag ni fied mo ment in a par tic u lar di rec tion is given by:

M = B M + B Mu nt lt1 2 , (LRFD C1-1, SAM 6)

where M nt , M lt , B1 and B2 are de fined in Chap ter . B1 and B2 are mo ment mag ni fi -ca tion fac tors. B1 is cal cu lated in the same way as in Chap ter . Sim i larly toAISC-LRFD93, the pro gram de sign as sumes the anal y sis in cludes P-D ef fects inthis code too, there fore B2 is taken as unity for bend ing in both di rec tions. If thepro gram as sump tions are not sat is fac tory for a par tic u lar struc tural model or mem -

288 Member Design


ber, the user has a choice of ex plic itly spec i fy ing the val ues of B1 and B2 for anymem ber.

When us ing the UBC-LRFD97 code, the pro gram de sign as sumes that a P-D anal y -sis has been per formed so that mo ment mag ni fi ca tion fac tors for mo ments caus ingsidesway can be taken as unity. It is rec om mended that the P-D anal y sis be done atthe fac tored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).

The same con di tions and lim i ta tions as AISC-LRFD93 ap ply.


The nom i nal strengths in com pres sion, ten sion, bend ing, and shear for Seis mic,Com pact, Noncompact, and Slen der sec tions ac cord ing to the UBC-LRFD97 arecal cu lated in the same way as de scribed in sec tion “Cal cu la tion of Nom i nalStrengths” of Chap ter with out any ex cep tion (UBC 2204.1 2205.2, 2205.3, 2206,2210.2, 2210.3). The nom i nal strengths for Seis mic sec tions are cal cu lated in thesame way as for Com pact sec tions.

The nom i nal flex ural strengths for all shapes of sec tions in clud ing Sin gle-an glesec tions are cal cu lated based on their prin ci pal axes of bend ing. For the I, Box,Chan nel, Cir cu lar, Pipe, T, Dou ble-an gle and Rect an gu lar sec tions, the prin ci palaxes co in cide with their geo met ric axes. For the An gle sec tions, the prin ci pal axesare de ter mined and all com pu ta tions re lated to flex ural strengths are based on that.

The nom i nal shear strengths are cal cu lated along the geo met ric axes for all sec -tions. For I, Box, Chan nel, T, Dou ble an gle, Pipe, Cir cu lar and Rect an gu lar sec -tions, the prin ci pal axes co in cide with their geo met ric axes. For Sin gle-an gle sec -tions, prin ci pal axes do not co in cide with the geo met ric axes.

If the user spec i fies non zero fac tored strengths for one or more el e ments in the“Ca pac ity Over writes” form, these val ues will over ride the above men tioned cal -cu lated val ues for those el e ments. The spec i fied fac tored strengths should bebased on the prin ci pal axes of bend ing.


j t = Re sis tance fac tor for ten sion, 0.9 (LRFD D1, H1, SAM 2, 6)j c = Re sis tance fac tor for com pres sion, 0.85 (LRFD E2, E3, H1)j c = Re sis tance fac tor for com pres sion in an gles, 0.90 (LRFD SAM 4, 6)j b = Re sis tance fac tor for bend ing, 0.9 (LRFD F1, H1, A-F1, A-G2, SAM 5)j v = Re sis tance fac tor for shear, 0.9 (LRFD F2, A-F2, A-G3, SAM 3)

Member Design 289


All lim i ta tions and warn ings re lated to nom i nal strengths cal cu la tion inAISC-LRFD93 also apply in this code.


The ca pac ity ra tios in UBC-LRFD97 are cal cu lated in the same way as de scribedin sec tion “Cal cu la tion of Ca pac ity Ra tios” of Chap ter with some mod i fi ca tions as de scribed be low.

In the cal cu la tion of the ax ial force/bi axial mo ment ca pac ity ra tios, first, for eachsta tion along the length of the mem ber, the ac tual mem ber force/mo ment com po -nents are cal cu lated for each load com bi na tion. Then the cor re spond ing ca pac i tiesare cal cu lated. Then, the ca pac ity ra tios are cal cu lated at each sta tion for eachmem ber un der the in flu ence of each of the de sign load com bi na tions. The con trol -ling ca pac ity ra tio is then ob tained, along with the as so ci ated sta tion and load com -bi na tion. A ca pac ity ra tio greater than 1.0 in di cates ex ceed ing a limit state.

Dur ing the de sign, the ef fect of the pres ence of bolts or welds is not con sid ered.


The in ter ac tion ra tio is de ter mined based on the ra tio P

Pu

nj . If Pu is ten sile, Pn is the

nom i nal ax ial ten sile strength and j j= = 0.9t ; and if Pu is com pres sive, Pn isthe nom i nal ax ial com pres sive strength and j j= = 0.85c , ex cept for an gle sec -tions j j= = 0.90c (LRFD SAM 6). In ad di tion, the re sis tance fac tor for bend -ing, j b = 0.9.

For P

P u


P

P +

M

M +

M

Mu

n

u

b n

u

b nj j j

8

933

33

22

22

æ

èçç

ö

ø÷÷ . (LRFD H1-1a, SAM 6-1a)

For P

P < u


P

P +

M

M +

M

Mu

n

u

b n

u

b n233

33

22

22j j j

æ

èçç

ö

ø÷÷ . (LRFD H1-1b, SAM 6-1a)

290 Member Design


For cir cu lar sec tions an SRSS (Square Root of Sum of Squares) com bi na tion isfirst made of the two bend ing com po nents be fore add ing the ax ial load com po nentin stead of the sim ple al ge braic ad di tion im plied by the above for mu las.

For Sin gle-an gle sec tions, the com bined stress ra tio is cal cu lated based on the prop -er ties about the prin ci pal axes (LRFD SAM 5.3, 6). For I, Box, Chan nel, T, Dou blean gle, Pipe, Cir cu lar and Rect an gu lar sec tions, the prin ci pal axes co in cide withtheir geo met ric axes. For Sin gle-an gle sec tions, prin ci pal axes are de ter mined inthe pro gram. For gen eral sec tions it is as sumed that all sec tion prop er ties are givenin terms of the prin ci pal di rec tions and con se quently no ef fort is made to de ter minethe prin ci pal di rec tions.

Shear Stresses

Sim i larly to the nor mal stresses, from the fac tored shear force val ues and the nom i -nal shear strength val ues at each sta tion for each of the load com bi na tions, shear ca -pac ity ra tios for ma jor and mi nor di rec tions are cal cu lated as fol lows:

V

Vu

v n

2

2j , and

V

Vu

v n

3

3j ,

where j v = 0.9 .


Member Design 291


Seismic Requirements

The spe cial seis mic re quire ments checked by the pro gram for mem ber de sign arede pend ent on the type of fram ing used and are de scribed be low for each type offram ing (UBC 2204.1, 2205.2, 2205.3). The re quire ments checked are based onUBC Sec tion 2211.4.2.1 for frames in Seis mic Zones 0 and 1 and Zone 2 with Im -por tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec tion2211.4.2.2 for frames in Seis mic Zone 2 with Im por tance fac tor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Sec tion 2211.4.2.3 for frames inSeis mic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No spe cial re quire ment ischecked for frames in Seis mic Zones 0 and 1 and in Seis mic Zone 2 with Im por -tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

Or di nary Mo ment Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked and re -ported (UBC 2210.2, 2211.4.2.2.c, 2211.4.2.3.c):

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, when ever P Pu nj > 0.5 in col umns due to the pre scribed load ing com -bi na tions, the Spe cial Seis mic Load Com bi na tions as de scribed be low arechecked (UBC 2210.2, 2211.4.2.2.b, 2211.4.2.3.b, 2210.5, 2211.4.6.1).


Spe cial Moment-Resisting Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported (UBC 2210.2, 2211.4.2.2.d, 2211.4.2.3.d):

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, when ever P Pu nj > 0.5 in col umns due to the pre scribed load ing com -bi na tions, the Spe cial Seis mic Load Com bi na tions as de scribed be low arechecked (UBC 2210.2, 2211.4.2.2.d, 2211.4.2.3.d, 2210.5, 2211.4.6.1).


• In Seis mic Zones 3 and 4, the I-shaped beams or col umns, Chan nel-shapedbeams or col umns, and Box shaped col umns are ad di tion ally checked for com -pact ness cri te ria as de scribed in Table XII-1 (UBC 2210.8, 2211.4.8.4.b, Ta ble 2211.4.8-1). Com pact I-shaped beam and col umn sec tions are ad di tion ally


292 Member Design

checked for b tf f2 to be less than 52 Fy . Com pact Chan nel-shaped

beam and col umn sec tions are ad di tion ally checked for b tf f to be less than

52 Fy . Com pact I-shaped and Chan nel-shaped col umn sec tions are ad di -

tion ally checked for web-slen der ness h t w to be less than the num bers given inTable XII-1. Com pact box shaped col umn sec tions are ad di tion ally checked

for b t f and d t w to be less than 110 Fy . If this cri te ria is sat is fied the

sec tion is re ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca -tions. If this cri te ria is not sat is fied the user must mod ify the sec tion prop erty.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the pro gram checks the lat er ally un sup ported length of beams to be lessthan ( )2500 F ry y . If the check is not sat is fied, it is noted in the out put (UBC

2211.4.8.8).

Braced Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e):

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, when ever P Pu nj > 0.5 in col umns due to the pre scribed load ing com -bi na tions, the Spe cial Seis mic Load Com bi na tions as de scribed be low arechecked (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e, 2210.5, 2211.4.6.1).


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the max i mum l r ra tio of the braces is checked not to ex ceed

720 Fy . If this check is not met, it is noted in the out put (UBC

2211.4.9.2.a).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the com pres sive strength for braces is re duced as 0.8j c nP (UBC2211.4.9.2.b).

P Pu c n£ 0.8j (UBC 2211.4.9.2.b)

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, all braces are checked to be ei ther Com pact or Noncompact ac cord ingto Table V-2 (UBC 2211.4.9.2.d). The Box and Pipe shaped braces are ad di -tion ally checked for com pact ness cri te ria as de scribed in Table XII-1 (UBC

Member Design 293


2211.4.9.2.d). For box sec tions b t f and d t w is lim ited to 110 Fy , for

pipe sec tions D t is lim ited to 1300 Fy . If this cri te ria is sat is fied the sec -tion is re ported as SEIS MIC as de scribed ear lier un der sec tion clas si fi ca tions.If this cri te ria is not sat is fied the user must mod ify the sec tion prop erty.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, Chev ron braces are de signed for 1.5 times the spec i fied load ing com bi -na tions (UBC 2211.4.9.4.a.1).

Ec cen tri cally Braced Frames

For this fram ing sys tem, the pro gram looks for and rec og nizes the ec cen tri callybraced frame con fig u ra tions shown in Figure V-2. The fol low ing ad di tional re -quire ments are checked or re ported for the beams, col umns and braces as so ci atedwith these con fig u ra tions (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, when ever P Pu nj > 0.5 in col umns due to the pre scribed load ing com -bi na tions, the Spe cial Seis mic Load Com bi na tions as de scribed be low arechecked (UBC 2210.2, 2211.4.2.2.b, 2211.4.2.3.b, 2210.5, 2211.4.6.1).


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the I-shaped and Chan nel-shaped beams are ad di tion ally checked forcom pact ness cri te ria as de scribed in Table XII-1 (UBC 2211.4.10.2.a, 2210.8,2211.4.8.4.b, Ta ble 2211.4.8-1). Com pact I-shaped and Chan nel-shaped beam

sec tions are ad di tion ally checked for b tf f2 to be less than 52 Fy . If this

cri te ria is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear lier un -der sec tion clas si fi ca tions. If this cri te ria is not sat is fied the user must mod ifythe sec tion prop erty.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the link beam yield strength, Fy , is checked not to ex ceed the fol low ing(UBC 2211.4.10.2.b):

Fy £ 50 ksi (UBC 2211.4.10.2.b)


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the shear strength for link beams is taken as fol lows (UBC 2210.10.b,2211.4.12.2.d):


294 Member Design

V Vu v n£ j , (UBC 2211.4.10.2.d)

where,

( )j j jV V M en pa pa= min , 2 , (UBC 2211.4.10.2.d)

V VP

Ppa p

u

y

= -æ

è

çç

ö

ø

÷÷1

2

, (UBC 2211.4.10.2.f)

M MP

Ppa p

u

y

= -é

ëê

ù

ûú1.18 1 , (UBC 2211.4.10.2.f)

V F d t tp y f w= -0.6 ( )2 , (UBC 2211.4.10.2.d)

M Z Fp y= , (UBC 2211.4.10.2.d)

j j= v (de fault is 0.9) , (UBC 2211.4.10.2.d, 2211.4.10.2.f)

P A Fy g y= . (UBC 2211.4.10.2.e)

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, if P A Fu g y> 0.15 , the link beam length, e, is checked not to ex ceed thefol low ing (UBC2211.4.10.2.f):

e

A

A

M

Vif

A

Aw

g

p

p

w

g£

-é

ëê

ù

ûú

é

ëê

ù

ûú ³1.15 0.5 1.6 0.3 ,

1.6

r r

M

Vif

A

A

p

p

w

g

é

ëê

ù

ûú <

ì

í

ïï

î

ïï

r 0.3 ,

(UBC 2211.4.10.2.f)

where,

A d t tw f w= -( )2 , and (UBC 2211.4.10.2.f)

r = P Vu u . (UBC 2211.4.10.2.f)


• The link beam ro ta tion, q, of the in di vid ual bay rel a tive to the rest of the beamis cal cu lated as the story drift D M times bay length di vided by the to tal lengthsof link beams in the bay. In Seis mic Zones 3 and 4 and in Seis mic Zone 2 withIm por tance fac tor greater than 1, the link beam ro ta tion, q, is checked asfollows (UBC 2211.4.10.2.g).

Member Design 295


q £ 0.090 , where link beam clear length, e M Vs s£ 1.6 ,

q £ 0.030 , where link beam clear length, e M Vs s³ 2.6 , and


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the brace strength is checked to be at least 1.25 times the ax ial force cor -re spond ing to the con trol ling link beam strength (UBC 2211.4.10.6.a). Thecon trol ling link beam nom i nal strength is taken as fol lows:

( )min ,V M epa pa2 , (UBC 2211.4.10.2.d)

The val ues of Vpa and M pa are cal cu lated fol low ing the pro ce dure de scribedabove. The cor re spon dence be tween brace force and link beam force is ob -tained from the as so ci ated load cases, which ever has the high est link beamforce of in ter est.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the col umn strength is checked for 1.25 times the col umn forces cor re -spond ing to the con trol ling link beam nom i nal strength (UBC 2211.4.10.8).The con trol ling link beam strength and the cor re spond ing forces are as ob -tained by the pro cess de scribed above.

• Ax ial forces in the beams are in cluded in check ing the beams. The user is re -minded that us ing a rigid di a phragm model will re sult in zero ax ial forces in the beams. The user must dis con nect some of the col umn lines from the di a phragmto al low beams to carry ax ial loads. It is rec om mended that only one col umnline per ec cen tri cally braced frame be con nected to the rigid di a phragm or aflex i ble di a phragm model be used.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the beam lat er ally un sup ported length is checked to be less than

76 b Ff y . If not sat is fied it is so noted as a warn ing in the out put file (UBC

2210.11, 2211.4.10.5).

Note: The beam strength in flex ure of the beam out side the link, is NOT cur rentlychecked to be at least 1.25 times the mo ment cor re spond ing to the con trol ling linkbeam strength (UBC 2211.4.10.6.b). Users need to check for this re quire ment.

296 Member Design


Spe cial Con cen tri cally Braced Frames

For this fram ing sys tem, the fol low ing ad di tional re quire ments are checked or re -ported (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e):

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, when ever P Pu nj > 0.5 in col umns due to the pre scribed load ing com -bi na tions, the Spe cial Seis mic Load Com bi na tions as de scribed be low arechecked (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e, 2210.5, 2211.4.6.1).

Member Design 297


Figure XII-1Ec cen tri cally Braced Frame Con figu ra tions


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, all col umns are checked to be Com pact ac cord ing to Table V-2. Com -pact box shaped col umn sec tions are ad di tion ally checked for b t f and d t w to

be less than 110 Fy as de scribed in Table XII-1 (UBC 2211.4.12.5.a). If

this cri te ria is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear lierun der sec tion clas si fi ca tions. If this cri te ria is not sat is fied the user must mod -ify the sec tion prop erty (UBC 2210.10.g, 2211.4.12.5.a).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, all braces are checked to be Com pact ac cord ing to Table V-2 (UBC2210.10.c, 2211.4.12.2.d). The An gle, Dou ble-an gle, Box and Pipe shapedbraces are ad di tion ally checked for com pact ness cri te ria as de scribed in TableXII-1 (UBC 2210.10.c, 2211.4.12.2.d). For box sec tions b t f and d t w is

lim ited to 100 Fy , for pipe sec tions D t is lim ited to 1300 Fy . If this

cri te ria is sat is fied the sec tion is re ported as SEIS MIC as de scribed ear lier un -der sec tion clas si fi ca tions. If this cri te ria is not sat is fied the user must mod ifythe sec tion prop erty.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the com pres sive strength for braces is taken as j c nP (UBC 2210.10.b,2211.4.12.2.b). Un like Braced Frames, no re duc tion is re quired.

P Pu c n£ j (UBC 2211.4.12.2.b)

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, the max i mum l r ra tio of the braces is checked not to ex ceed

1,000 Fy . If this check is not met, it is noted in the out put (UBC 2210.10.a,

2211.4.12.2.a).

Note: Beams in ter sected by Chev ron braces are NOT cur rently checked tohave a strength to sup port loads rep re sented by the fol low ing load ing com bi na -tions (UBC 2213.9.4.1):

1.0DL + 0.7 LL Pb± (UBC 2210.10.e, 2211.4.12.4.a.3)0.9DL Pb± (UBC 2210.10.e, 2211.4.12.4.a.3)

where Pb is given by the dif fer ence of F Ay for the ten sion brace and 0.3j c nPfor the com pres sion brace. Users need to check for this re quire ment.


298 Member Design

Joint Design

When us ing UBC-LRFD97 de sign code, the struc tural joints are checked and/orde signed for the fol low ing:




• Re porting the beam con nec tion shear

• Re porting the brace con nec tion force






To achieve a beam/col umn mo ment con nec tion, con ti nu ity plates such as shown in are usu ally placed on the col umn, in line with the top and bot tom flanges of thebeam, to trans fer the com pres sion and ten sion flange forces of the beam into thecol umn.

For con nec tion con di tions de scribed in the last two steps above, the thick ness ofsuch plates is usu ally set equal to the flange thick ness of the cor re spond ing beam.How ever, for the con nec tion con di tion de scribed by the first step above, where thebeam frames into the flange of the col umn, such con ti nu ity plates are not al waysneeded. The re quire ment de pends upon the mag ni tude of the beam-flange forceand the prop er ties of the col umn. This is the con di tion that the pro gram in ves ti -gates. Col umns of I-sec tions only are in ves ti gated. The pro gram eval u ates the con -ti nu ity plate re quire ments for each of the beams that frame into the col umn flange(i.e. par al lel to the col umn ma jor di rec tion) and re ports the max i mum con ti nu ityplate area that is needed for each beam flange. The con ti nu ity plate re quire mentsare eval u ated for mo ment frames only. No check is made for braced frames.

Joint Design 299




jR = t F Pn fc yc bf(0.9)6.25 2 ³ (LRFD K1-1)


jR k +t F t Pn c fb yc wc bf= (1.0) (5.0 ) ³ (LRFD K1-2)


jR t + t

d

t

tn wc

fb

c

wc

fc

= (0.75) 68 2 1 3æ

èçç

ö

ø÷÷æ

è

çç

ö

ø

÷÷

1.5é

ë

êê

ù

û

úú

³ Ft

t Pyc

fc

wc

bf (LRFD K1-5a)


jR t F

d Pn

wc yc

c

bf= (0.9)4100 3

³ (LRFD K1-8)


A = P

F tcp

bf

yc

wc(0.85)(0.9 )

12- 2 (LRFD K1.9, E2)



act as a com pres sion mem ber to re sist the ap plied load (LRFD K1.9). The for mulaalso as sumes j = 0.85 and F Fcr yc= 0.9 . This cor re sponds to an as sump tion of l = 0.5 in the col umn for mu las (LRFD E2-2). The user should choose the con ti nu -ity plate cross-sec tion such that this is sat is fied. As an ex am ple when us ing Fyc = 50ksi and as sum ing the ef fec tive length of the stiff ener as a col umn to be 0.75h(LRFD K1.9) the re quired min i mum ra dius of gy ra tion of the stiff ener cross-sec -tion would be r h= 0.02 to ob tain l = 0.5 (LRFD E2-4).

300 Joint Design



• The min i mum thick ness of the stiff en ers is taken in the pro gram as fol lows:

t = t bcpmin

fb fb 0.5max ,Fy

95

ìíï

îï

üýï

þï(LRFD K1.9.2)


b = 2 b

3

t

2cpmin fp wc-

æ

èçç

ö

ø÷÷ (LRFD K1.9.1)


A = t bcpmin

cpmin

cpmin (LRFD K1.9.1)


min .






The spe cial seis mic re quire ments ad di tion ally checked by the pro gram are de pend -ent on the type of fram ing used and are de scribed be low for each type of fram ing.

Joint Design 301


The re quire ments checked are based on UBC Sec tion 2211.4.2.1 for frames in Seis -mic Zones 0 and 1 and Zone 2 with Im por tance fac tor equal to 1 (UBC 2210.2,UBC 2211.4.2.1), on UBC Sec tion 2211.4.2.2 for frames in Seis mic Zone 2 withIm por tance fac tor greater than 1 (UBC 2210.2, UBC 2211.4.2.2), and on UBC Sec -tion 2211.4.2.3 for frames in Seis mic Zones 3 and 4 (UBC 2210.2, UBC2211.4.2.3). No spe cial re quire ment is checked for frames in Seis mic Zones 0 and 1 and in Seis mic Zone 2 with Im por tance fac tor equal to 1 (UBC 2210.2, UBC2211.4.2.1).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Or di nary Mo ment Frames the con ti nu ity plates are checked and de -signed for a beam flange force, ( )P M d tbf pb b fb= - (UBC 2211.4.7.2.a,

2211.4.8.2.a.1).

( )P M d tbf pb b fb= - (UBC 2211.4.7.2.a, 2211.4.8.2.a.1)

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, for de ter min -ing the need for con ti nu ity plates at joints due to ten sion trans fer from the beamflanges, the force Pbf is taken as f Ayb bf for all four checks de scribed above(LRFD K1-1, K1-2, K1-5a, K1-8), ex cept for check ing col umn flange de signstrength in bend ing Pbf is taken as 1.8 f Ayb bf (UBC 2211.4.8.5, LRFD K1-1).In Seis mic Zone 2 with Im por tance fac tor greater than 1, for Spe cial Mo -ment-Re sisting Frames, for de ter min ing the need for con ti nu ity plates at jointsdue to ten sion trans fer from the beam flanges, the force Pbf is taken as f Ayb bf

(UBC 2211.4.8.2.a.1).

P f Abf yb bf=1.8 (Zone 3 and 4) (UBC 2211.4.8.5)

P f Abf yb bf= (Zone 2 with I >1) (UBC 2211.4.8.2.a.1)

For de sign of the con ti nu ity plate the beam flange force is taken as

( )P M d tbf pb b fb= - (UBC 2211.4.8.2.a.1).

( )P M d tbf pb b fb= - (UBC 2211.4.8.2.a.1)

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Ec cen trically Braced Frames, the con ti nu ity plate re quire ments arechecked and de signed for a beam flange force of P f Abf yb bf= .

302 Joint Design




Shear stresses sel dom con trol the de sign of a beam or col umn mem ber. How ever,in a Mo ment-Re sisting frame, the shear stress in the beam-col umn joint can be crit i -cal, es pe cially in fram ing sys tems when the col umn is sub jected to ma jor di rec tionbend ing and the joint shear forces are re sisted by the web of the col umn. In mi nordi rec tion bend ing, the joint shear is car ried by the col umn flanges, in which case the shear stresses are sel dom crit i cal, and this con di tion is there fore not in ves ti gated bythe pro gram.

Shear stresses in the panel zone, due to ma jor di rec tion bend ing in the col umn, mayre quire ad di tional plates to be welded onto the col umn web, de pend ing upon theload ing and the ge om e try of the steel beams that frame into the col umn, ei theralong the col umn ma jor di rec tion, or at an an gle so that the beams have com po nents along the col umn ma jor di rec tion. See . The pro gram in ves ti gates such sit u a tionsand re ports the thick ness of any re quired doubler plates. Only col umns withI-shapes are in ves ti gated for doubler plate re quire ments. Also doubler plate re -quire ments are eval u ated for mo ment frames only. No check is made for bracedframes.

The pro gram cal cu lates the re quired thick ness of doubler plates (see ) forAISC-LRFD93 sim i lar to the pro ce dure de scribed in Sec tion “De sign of DoublerPlates” in Chap ter ex cept that the fol low ing al go rithms are used. The shear force in the panel zone, is given by

V = M

d - t Vp

n =

nbn n

n fn

c

b

1å -

cos q



R = F d t P

PP > v y c r

u

y

u0.6 1.4 , for 0.-é

ëê

ù


By us ing V Rp v= j , with j = 0.9, the re quired col umn web thick ness t r can befound.


Joint Design 303


t = t th

Fdp r w

y

- ³418

, (LRFD F2-1)

where,

Fy = Col umn and doubler plate yield stresst r = Re quired col umn web thick ness t dp = Re quired doubler plate thick ness t w = Col umn web thick ness h = d tc fc- 2 if welded, d kc c- 2 if rolled,Vp = Panel zone shearVc = Col umn shear in col umn aboveFy = Beam flange forcesnb = Num ber of beams con nect ing to col umn d n = Depth of n-th beam con nect ing to col umn q n = An gle be tween n-th beam and col umn ma jor di rec tion d c = Depth of col umn clear of fil lets, equals d k- 2M bn = Cal cu lated fac tored beam mo ment from



The spe cial seis mic re quire ments checked by the pro gram for cal cu lat ing doublerplate ar eas are de pend ent on the type of fram ing used and are de scribed be low foreach type of fram ing. The re quire ments checked are based on UBC Sec tion2211.4.2.1 for frames in Seis mic Zones 0 and 1 and Zone 2 with Im por tance fac torequal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec tion 2211.4.2.2 for framesin Seis mic Zone 2 with Im por tance fac tor greater than 1 (UBC 2210.2, UBC2211.4.2.2), and on UBC Sec tion 2211.4.2.3 for frames in Seis mic Zones 3 and 4(UBC 2210.2, UBC 2211.4.2.3). No spe cial re quire ment is checked for frames inSeis mic Zones 0 and 1 and in Seis mic Zone 2 with Im por tance fac tor equal to 1(UBC 2210.2, UBC 2211.4.2.1).

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the panelzone doubler plate re quire ments that are re ported will de velop the lesser ofbeam mo ments equal to 0.9 of the plas tic mo ment ca pac ity of the beam

304 Joint Design


( )0.9 j b pbMå , or beam mo ments due to spec i fied load com bi na tions

involving seis mic load (UBC 2211.4.8.3.a).

The ca pac ity of the panel zone in re sist ing this shear is taken as (UBC2211.8.3.a):

j jv n v y c p

cf cf

b c p

V = F d t + b t

d d t 0.60 1

3 2æ

è

çç

ö

ø

÷÷ (UBC 2211.4.8.3.a)


tV

F d

b t

d d

h

Fp

p

v y c

cf cf

b c y

= - ³0.6 j

3

418

2

, (UBC 2211.4.8.3, LRFD F2-1)


t = t - tdp p wc

where,

j v = 0.75,bcf = width of col umn flange,t cf = thick ness of col umn flange,t p = re quired col umn web thick ness, h = d tc fc- 2 if welded, d kc c- 2 if rolled, andd b = depth of deep est beam fram ing into the ma jor di rec tion of

the col umn.

• In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the panelzone col umn web thick ness re quire ment the pro gram checks the fol low ing:

td t d t

wc

c fc b fb³

- + -( ) ( )2 2

90(UBC 2211.4.8.3.b)


• In Seis mic Zones 3 and 4, for Ec cen trically Braced Frames, the doubler platere quire ments are checked sim i lar to the doubler plate checks for spe cial Mo -ment-Re sisting frames as dis cussed above (UBC 2211.4.10.7).

Joint Design 305



In Seis mic Zones 3 and 4, for Spe cial Mo ment-Re sisting Frames, the code re quiresthat the sum of beam flex ure strengths at a joint should be less than the sum of col -umn flex ure strengths (UBC 2211.4.8.6). The col umn flex ure strength should re -flect the pres ence of ax ial force pres ent in the col umn. To fa cil i tate the re view ofthe strong col umn weak beam cri te rion, the pro gram will re port a beam/col umnplas tic mo ment ca pac ity ra tio for ev ery joint in the struc ture.


R =

M

M + Mmaj

n =

n

pbn n

pcax pcbx

b

1å cos q

(UBC 2211.4.8.6 8-3)


R =

M

M + M

n =

n

pbn n

pcay pcby

b

min1

å sin q

, (UBC 2211.4.8.6 8-3)

where,


M pbn = Plas tic mo ment ca pac ity of n-th beam con nect ingto col umn

q n = An gle be tween the n-th beam and the col umnma jor di rec tion

M pcax y, = Ma jor and mi nor plas tic mo ment ca pac i ties, re duced forax ial force ef fects, of col umn above story level

M pcbx y, = Ma jor and mi nor plas tic mo ment ca pac i ties, re duced forax ial force ef fects, of col umn be low story level

nb = Num ber of beams con nect ing to the col umn


( )M = Z F - P Apc c yc uc gc , (UBC 2211.4.8.6 8-3)

306 Joint Design


where,

Z c = Plas tic modu lus of col umn,Fyc = Yield stress of col umn ma te rial, Puc = Max i mum ax ial strength in the col umn in compression, Puc ³ 0 , andAgc = Gross area of col umn.




For spe cial seis mic de sign, the beam con nec tion shears are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The re quire ments checkedare based on UBC Sec tion 2211.4.2.1 for frames in Seis mic Zones 0 and 1 and Zone 2 with Im por tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec -tion 2211.4.2.2 for frames in Seis mic Zone 2 with Im por tance fac tor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Sec tion 2211.4.2.3 for frames inSeis mic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No spe cial re quire ment ischecked for frames in Seis mic Zones 0 and 1 and in Seis mic Zone 2 with Im por -tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Or di nary Mo ment Frames, the beam con nec tion shears re ported arethe max i mum of the spec i fied load ing com bi na tions and the fol low ing ad di -tional load ing com bi na tions (UBC 2211.4.7.2.a, 2211.4.8.2.b):


• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Spe cial Mo ment-Re sisting Frames, the beam con nec tion shears thatare re ported al low for the de vel op ment of the full plas tic mo ment ca pac ity ofthe beam. Thus:

V = C M

L + V Vu

pb

DL LL1.2 0.5+ (UBC 2211.4.8.2.b)

Joint Design 307


where





VLL = Ab so lute max i mum of the cal cu lated fac tored beamshears at the cor re spond ing beam ends from the live load only.

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Ec cen trically Braced Frames, the link beam con nec tion shear is re -ported as equal to the link beam web shear ca pac ity (UBC 2211.4.10.7).



For spe cial seis mic de sign, the brace con nec tion forces are not taken less than thefol low ing spe cial val ues for dif fer ent types of fram ing. The re quire ments checkedare based on UBC Sec tion 2211.4.2.1 for frames in Seis mic Zones 0 and 1 and Zone 2 with Im por tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec -tion 2211.4.2.2 for frames in Seis mic Zone 2 with Im por tance fac tor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Sec tion 2211.4.2.3 for frames inSeis mic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No spe cial re quire ment ischecked for frames in Seis mic Zones 0 and 1 and in Seis mic Zone 2 with Im por -tance fac tor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for or di nary Braced Frames, the brac ing con nec tion force is re ported atleast as the smaller of the ten sile strength of the brace (F Ay ) (UBC2211.4.9.3.a.1) and the fol low ing spe cial load ing com bi na tions (UBC2211.4.9.3.a.2):

308 Joint Design



• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Ec cen trically Braced Frames, the brac ing con nec tion force is re -ported as at least the nom i nal strength of the brace (UBC 2211.4.10.6.d).

• In Seis mic Zones 3 and 4 and in Seis mic Zone 2 with Im por tance fac tor greaterthan 1, for Spe cial Con cen trically Braced Frames, the brac ing con nec tion force is re ported at least as the smaller of the ten sile strength of the brace (F Ay ) (UBC 2210.10, 2211.4.12.3.a.1) and the fol low ing spe cial load ing com bi na tions(UBC 2211.10, 2211.4.12.3.a.2):


Joint Design 309


C h a p t e r XIII

Design Output

Overview

The pro gram cre ates de sign out put in three dif fer ent ma jor for mats: graph i cal dis -play, tab u lar out put, and mem ber spe cific de tailed de sign in for ma tion.

The graphi cal dis play of steel de sign out put in cludes in put and out put de sign in for -ma tion. In put de sign in for ma tion in cludes de sign sec tion la bels, K-fa ctors, liveload re duc tion fac tors, and other de sign pa rame ters. The out put de sign in for ma tionin cludes ax ial and bend ing in ter ac tion ra tios and shear stress ra tios. All graphi calout put can be printed.

The tabu lar out put can be saved in a file or printed. The tabu lar out put in cludesmost of the in for ma tion which can be dis played. This is gen er ated for added con -ven ience to the de signer.

The mem ber-spe cific de tailed de sign in for ma tion shows de tails of the cal cu la tionfrom the de sign er’s point of view. It shows the de sign sec tion di men sions, ma te rialprop er ties, de sign and al low able stresses or fac tored and nomi nal strengths, andsome in ter me di ate re sults for all the load com bi na tions at all the de sign sec tions ofa spe cific frame mem ber.

Overview 311

In the fol low ing sec tions, some of the typi cal graphi cal dis play, tabu lar out put, andmem ber-spe cific de tailed de sign in for ma tion are de scribed. Some of the de sign in -for ma tion is spe cific to the cho sen steel de sign codes which are avail able in the pro -gram and is only de scribed where re quired. The AISC- ASD89 de sign code is de -scribed in the lat ter part of this chap ter. For all other codes, the de sign out puts aresimi lar.

Graphical Display of Design Output

The graphi cal out put can be pro duced ei ther as color screen dis play or in gray- scaled printed form. Moreo ver, the ac tive screen dis play can be sent di rectly to theprinter. The graphi cal dis play of de sign out put in cludes in put and out put de sign in -for ma tion.

In put de sign in for ma tion, for the AISC-ASD89 code, in cludes

• De sign sec tion labels,

• K-fa ctors for ma jor and mi nor di rec tion of buck ling,

• Unbraced Length Ra tios,

• Cm -fa ctors,

• Cb -fa ctors,

• Live Load Re duc tion Fac tors,

• d s -fa ctors,

• d b -fa ctors,

• de sign type,

• al low able stresses in ax ial, bend ing, and shear.

The out put de sign in for ma tion which can be dis played is

• Color coded P-M in ter ac tion ra tios with or with out val ues, and

• Color coded shear stress ra tios.

The graphi cal dis plays can be ac cessed from the De sign menu. For ex am ple, thecolor coded P-M in ter ac tion ra tios with values can be dis played by se lect ing theDis play De sign Info... from the De sign menu. This will pop up a dia log box calledDis play De sign Re sults. Then the user should switch on the De sign Out put option but ton (de fault) and se lect P-M Ra tios Col ors & Val ues in the drop-down box.Then click ing the OK but ton will show the in ter ac tion ra tios in the ac tive win dow.

312 Graphical Display of Design Output


The graph ics can be dis played in ei ther 3D or 2D mode. The pro gram stan dard view trans for ma tions are avail able for all steel de sign in put and out put dis plays. Forswitch ing be tween 3D or 2D view of graphi cal dis plays, there are sev eral but tonson the main tool bar. Al ter na tively, the view can be set by choos ing Set 3D View...from the View menu.

The graphi cal dis play in an ac tive win dow can be printed in gray scaled black andwhite from the pro gram pro gram. To send the graphi cal out put di rectly to theprinter, click on the Print Graph ics but ton in the File menu. A screen cap ture ofthe ac tive win dow can also be made by fol low ing the stan dard pro ce dure pro videdby the Win dows op er at ing sys tem.

Tabular Display of Design Output

The tabu lar de sign out put can be sent di rectly ei ther to a printer or to a file. Theprinted form of tabu lar out put is the same as that pro duced for the file out put withthe ex cep tion that for the printed out put font size is ad justed.

The tabu lar de sign out put in cludes in put and out put de sign in for ma tion which de -pends on the de sign code of choice. For the AISC- ASD89 code, the tabu lar out putin cludes the fol low ing. All ta bles have for mal head ings and are self- explanatory, so fur ther de scrip tion of these ta bles is not given.

In put de sign in for ma tion in cludes the fol low ing:

• Load Com bi na tion Mul ti pli ers

– Com bi na tion name,

– Load types, and

– Load fac tors.

• Steel Stress Check Ele ment In for ma tion (code de pend ent)

– Frame ID,

– De sign Sec tion ID,

– K-fa ctors for ma jor and mi nor di rec tion of buck ling,

– Unbraced Length Ra tios,

– Cm -fa ctors,

– Cb -fa ctors, and

– Live Load Re duc tion Fac tors.

Tabular Display of Design Output 313

Chapter XIII Design Output

• Steel Mo ment Mag ni fi ca tion Fac tors (code de pend ent)

– Frame ID,

– Sec tion ID,

– Fram ing Type,

– d b -fa ctors, and

– d s -fa ctors.

The out put de sign in for ma tion in cludes the fol low ing:

• Steel Stress Check Out put (code de pend ent)

– Frame ID,

– Sec tion location,

– Con trol ling load com bi na tion ID for P-M in ter ac tion,

– Ten sion or com pres sion in di ca tion,

– Ax ial and bend ing in ter ac tion ra tio,

– Con trol ling load com bi na tion ID for ma jor and mi nor shear forces, and

– Shear stress ra tios.

The tab u lar out put can be ac cessed by se lect ing Print De sign Ta bles... from theFile menu. This will pop up a di a log box. Then the user can spec ify the de signquan ti ties for which the re sults are to be tab u lated. By de fault, the out put will besent to the printer. If the user wants the out put stream to be re di rected to a file,he/she can check the Print to File box. This will pro vide a de fault file name. Thede fault file name can be ed ited. Al ter na tively, a file list can be ob tained by click ingthe File Name but ton to chose a file from. Then click ing the OK but ton will di rect

the tab u lar out put to the re quested stream ¾ the file or the printer.

Member Specific Information

The mem ber spe cific de sign in for ma tion shows the de tails of the cal cu la tion fromthe de sign er’s point of view. It pro vides an ac cess to the ge ome try and ma te rialdata, other in put data, de sign sec tion di men sions, de sign and al low able stresses, re -in force ment de tails, and some of the in ter me di ate re sults for a mem ber. The de signde tail in for ma tion can be dis played for a spe cific load com bi na tion and for a spe -cific sta tion of a frame mem ber.

314 Member Specific Information


The de tailed de sign in for ma tion can be ac cessed by right click ing on the de siredframe mem ber. This will pop up a dia log box called Steel Stress Check In for ma -tion which in cludes the fol low ing tabu lated in for ma tion for the spe cific mem ber.

– Frame ID,

– Sec tion ID,

– Load com bi na tion ID,

– Sta tion location,

– Ax ial and bend ing in ter ac tion ra tio, and

– Shear stress ra tio along two axes.

Ad di tional in for ma tion can be ac cessed by click ing on the Re Des ign and De tailsbut tons in the dia log box. Ad di tional in for ma tion that is avail able by click ing onthe Re Des ign but ton is as fol lows:

• De sign Fac tors (code de pend ent)

– Ef fec tive length fac tors, K , for ma jor and mi nor di rec tion of buck ling,

– Unbraced Length Ra tios,

– Cm -fa ctors,

– Cb -fa ctors,

– Live Load Re duc tion Fac tors,

– d s -fa ctors, and

– d b -fa ctors.

• Ele ment Sec tion ID

• Ele ment Fram ing Type

• Over writ ing al low able stresses

Ad di tional in for ma tion that is avail able by click ing on the De tails but ton is givenbe low.

• Frame, Sec tion, Sta tion, and Load Com bi na tion IDs,

• Sec tion geo met ric in for ma tion and graphi cal rep re sen ta tion,

• Ma te rial prop er ties of steel,

• Mo ment fac tors,

• De sign and al low able stresses for ax ial force and bi ax ial mo ments, and

• De sign and al low able stresses for shear.

Member Specific Information 315

Chapter XIII Design Output

References

AISC, 1989

Man ual of Steel Con struc tion, Al low able Stress De sign, 9th Edi tion, Ameri canIn sti tute of Steel Con struc tion, Chi cago, Ill, 1989.

AISC, 1994

Man ual of Steel Con struc tion, Load & Re sis tance Fac tor De sign, 2nd Edi tion,Ameri can In sti tute of Steel Con struc tion, Chi cago, Ill, 1994.

AISC, 1999

Man ual of Steel Con struc tion, Load & Re sis tance Fac tor De sign, 3rd Edi tion,Amer i can In sti tute of Steel Con struc tion, Chi cago, Ill, 1999.

BSI, 1990

Struc tural Use of Steel work in Build ing, Part 1, Code of Prac tice for De sign inSim ple and Con tinu ous Con struc tion: Hot Rolled Sec tions, BS 5950 : Part 1 :1990, Brit ish Stan dards In sti tu tion, Lon don, UK, 1990.

BSI, 2000

Struc tural Use of Steel work in Build ing, Part 1, Code of Prac tice for De sign inSim ple and Con tin u ous Con struc tion: Hot Rolled Sec tions, BS 5950 : Part 1 :2000, Brit ish Stan dards In sti tu tion, Lon don, UK, 2000.

CEN, 1992

317

De sign of Steel Struc tures, Part 1.1 : Gen eral Rules and Rules for Build ings,ENV 1993- 1-1 : 1992, Euro pean Com mit tee for Stan dardi za tion, Brus sels,Bel gium, 1992.

CISC, 1995

Hand book of Steel Con struc tion, CAN/CSA- S16.1-94, 6th Edi tion, Ca na dianIn sti tute of Steel Con struc tion, Willowdale, On tario, Can ada, 1995.

CSI, 2005a

SAP2000 Get ting Started, Com put ers and Struc tures, Inc., Berke ley, Cal i for -nia, 2005.

CSI, 2005b

Wel come to ETABS,, Com put ers and Struc tures, Inc., Berke ley, Cal i for nia,2005.

CSI, 2005c

CSI Anal y sis Ref er ence Man ual, Com put ers and Struc tures, Inc., Berke ley,Cal i for nia, 2005.

ICBO, 1997

Uni form Build ing Code, 1997, In ter na tional Con fer ence of Build ing Of fi cials,Whit tier, Cali for nia, 1997.

D. W. White and J. F. Hajjar, 1991

“Ap pli ca tion of Second- Order Elas tic Analy sis in LRFD: Re search to Prac -tice,” En gi neer ing Jour nal, Ameri can In sti tute of Steel Con struc tion, Inc., Vol. 28, No. 4, 1991.

318


Index

Beam Con nec tion ShearUBC-ASD, 279UBC-LRFD, 61, 145, 307

Beam-col umn ca pac ity ra tiosUBC-ASD, 278UBC-LRFD, 306

Bend ing strengthASD (al low able), 38, 80BS, 191, 209CISC, 225Eurocode, 248LRFD, 120, 165

Brace Con nec tion ForceUBC-ASD, 281UBC-LRFD, 63, 147, 308

Braced frames, 8BS, 189, 207CISC, 221Eurocode, 243LRFD, 103, 156UBC-ASD, 267UBC-LRFD, 28, 109, 293

Ca pac ity ra tio, 2, 8ASD, 15, 49, 65, 91BS, 181, 197, 199, 213

CISC, 217, 231Eurocode, 235, 251LRFD, 98, 134, 149, 177UBC-ASD, 258, 263UBC-LRFD, 24, 105, 284, 290

Check sta tions, 8

Clas si fi ca tion of sec tionsASD, 22, 68BS, 185, 203CISC, 221Eurocode, 239LRFD, 102, 152UBC-ASD, 260UBC-LRFD, 286

Com pact sec tionSee Clas si fi ca tion of sec tions

Com pres sive strengthASD, 34, 73ASD (al low able), 34, 73BS, 189, 207CISC, 224Eurocode, 245LRFD, 115, 158

Con ti nu ity PlatesUBC-ASD, 273

319

UBC-LRFD, 52, 136, 299

De sign codes, 1See Also "Sup ported de sign codes"

De sign load com bi na tions, 6

De sign out put, 311graph i cal, 312mem ber spe cific, 314tab u lar, 313

De sign sta tions, 8

Doubler PlatesUBC-ASD, 276UBC-LRFD, 56, 140, 303

EBFUBC-ASD, 268UBC-LRFD, 29, 112, 294

Ef fec tive length fac tor, 11

Eu ler buck ling loadASD, 35, 74BS, 189, 207CISC, 224Eurocode, 245LRFD, 104, 156UBC-LRFD, 288

Fac tored forces and mo mentsBS, 185, 205CISC, 221Eurocode, 243LRFD, 103, 156UBC-LRFD, 288

Flex ural buck lingASD, 34, 73BS, 189, 207CISC, 224Eurocode, 245LRFD, 34, 73, 115, 158

Graph i cal out put, 312

In ter ac tion equa tionsSee Ca pac ity ra tio

In ter ac tive en vi ron ment, 1

Lat eral drift ef fect, 9See Also P-Delta anal y sis

Lat eral-tor sional buck lingASD, 38, 80BS, 193, 210CISC, 225Eurocode, 249LRFD, 120, 126, 129, 165, 170, 173

Link Beam Ro ta tionUBC-ASD, 269UBC-LRFD, 31, 113, 295

Live load re duc tion fac tor, 8, 18, 22, 68,102, 152, 184, 202, 220, 238, 259,285

Load ing com bi na tions, 2ASD, 18, 68BS, 184, 202CISC, 220Eurocode, 238LRFD, 98, 152UBC-ASD, 259UBC-LRFD, 285

Mem ber spe cific out put, 314

Mem ber sta bil ity ef fect, 8See Also P-Delta anal y sis

Mo ment mag ni fi ca tionBS, 185, 205CISC, 221Eurocode, 244LRFD, 104, 156UBC-LRFD, 288

Noncompact sec tionSee Clas si fi ca tion of sec tions

320


Nonsway, 8BS, 189, 207CISC, 221Eurocode, 243LRFD, 103, 156

No tional loadBS, 184, 202CISC, 220Eurocode, 238

OMFUBC-ASD, 266UBC-LRFD, 24 - 25, 105, 108, 292

Out put, 2 - 3de tails, 315graph i cal, 311tab u lar, 311

P-Delta anal y sis, 8BS, 184, 189, 202, 207CISC, 220 - 221Eurocode, 239, 244LRFD, 102, 104, 152, 157, 288UBC-LRFD, 285, 289

P-Delta ef fects, 8

Perry fac tor, 189, 207

Plas tic sec tionSee Clas si fi ca tion of sec tions

Re de sign, 315

Rob ert son con stant, 189, 207

SCBFUBC-ASD, 271UBC-LRFD, 28, 109, 297

Sec ond or der ef fectsSee P-Delta ef fects

Shear strengthASD (al low able), 48, 89BS, 195, 213CISC, 229

Eurocode, 247LRFD, 133, 176

Slen der sec tionSee Clas si fi ca tion of sec tions

SMRFUBC-ASD, 266, 275UBC-LRFD, 25, 55, 108, 140, 292,302

Strength re duc tion fac torsBS (par tial fac tors), 189, 207CISC, 224Euro (par tial fac tors), 244LRFD, 114, 158UBC-LRFD, 289

Sup ported de sign codes, 1ASD, 15, 65BS, 6, 181, 199CISC, 6, 217Eurocode, 6, 235LRFD, 5, 95, 149UBC-ASD, 257UBC-LRFD, 283

Sway, 8BS, 189, 207CISC, 221Eurocode, 243LRFD, 103, 156

Tab u lar out put, 313

Ten sile strengthASD (al low able), 33, 73BS, 191, 209CISC, 225Eurocode, 245LRFD, 119, 164

Un braced frames, 8BS, 189, 207CISC, 221Eurocode, 243

321

Index

LRFD, 103, 156

Units, 3, 14ASD, 18, 68BS, 181, 199CISC, 217Eurocode, 235LRFD, 98, 152UBC-ASD, 258UBC-LRFD, 24, 105, 284

Un sup ported length, 9

322


sfd older codes

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