COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIORNIA DECEMBER 2001 COMPOSITE BEAM DESIGN AISC-LRD93 Tecnical Noe Compac and Noncompac Requiemens Tis Tecnical Noe descibes o e pogam cecks e AISC-LRD93 specificaion equiemens fo compac and noncompac beams. Te basic compac and noncompac equiemens cecked ae in AISC-LRD93 specificaion Cape B, Table B5.1. Te pogam cecks e id-o-ickness aios of e beam compession flange, beam eb, and, if i exiss and is in compession, e cove plae. Wen a singl smmeic beam is designed fo noncomposie beavio, i is also cecked fo laeal osional buckling equiemens. Ovevie Te pogam classifies beam secions as eie compac, noncompac o slende. I cecks e compac and noncompac secion equiemens a eac design locaion along e beam fo eac design load combinaion sepaael. A beam secion ma be classified diffeenl fo diffeen design load combinaions. o example, a beam ma be classified as compac fo design load combinaion A and as noncompac fo design load combinaion B. To easons a a beam ma be classified diffeenl fo diffeen design load cases ae:! Te compac secion equiemens fo beam ebs depend on e axial load in e beam. Diffeen design load combinaions ma poduce diffeen axial loads in e beam. Tis is onl an issue en beam axial loads ae specified o be consideed in e composie beam analsis and design.! Te compession flange ma be diffeen fo diffeen design load combinaions. If e sizes of e op and boom flanges ae no e same, classificaion of e secion ma depend on ic flange is deemined o be e compession flange. A eac design locaion, fo eac design load combinaion, e pogam fis cecks a beam secion fo e compac secion equiemens fo e compession flange, eb, cove plae (if applicable) and laeal osional buckling (if Ovevie Page 1 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens applicable) descibed eein. If e beam secion mees all of ose equiemens, i is classified as compac fo a design load combinaion. If e beam secion does no mee all of e compac secion equiemens, i is cecked fo e noncompac equiemens fo e flanges, eb, cove plae (if applicable) and laeal osional buckling (if applicable) descibed eein. If e beam secion mees all of ose equiemens, i is classified as noncompac fo a design load combinaion. If e beam secion does no mee all of e noncompac secion equiemens, i is classified as slende fo a design load combinaion and e pogam does no conside i fo composie beam design. Limiing Wid-o-Tickness Raios fo langes Tis secion descibes e limiing id-o-ickness aios consideed b e pogam fo beam compession flanges. Te id-o-ickness aio fo flanges is denoed b/, and is equal o b f /2 f fo I-saped secions and b f / f fo cannel secions. Compac Secion Limis fo langes o compac secions, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 1. b 65, fo compac secions Eqn. 1 f ee f is e specified ield sess of e flange consideed. Equaion 1 applies o bo olled secions seleced fom e pogam's daabase and o use-defined secions. Noncompac Secion Limis fo langes I-Saped Rolled Beams and Cannels o noncompac I-saped olled beams and cannels, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 2. b 141, fo noncompac secions Eqn. 2-10 ee is e specified ield sess of e beam o cannel. Limiing Wid-o-Tickness Raios fo langes Page 2 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Use-Defined and Hbid Beams o noncompac use-defined and bid beams, e id-o-ickness aio fo e compession flange is limied o a indicaed b Equaion 3. b 162, fo noncompac secions Eqn. 3 f - 16.5 k c ee f is e ield sess of e compession flange and, k c = 4 bu no less an 0.35 k c 0.763 Eqn. 4 Limiing Wid-o-Tickness Raios fo Webs Tis secion descibes e limiing id-o-ickness aios consideed b e pogam fo beam ebs. Compac Secion Limis fo Webs Wen cecking a beam eb fo compac secion equiemens, e id-oickness aio used is /. Te equaion used fo cecking e compac secion limis in e eb depends on e magniude of e axial compession sess aio, (P u / φ b P ) in e beam. Wen calculaing e axial compession sess aio, e folloing o ules ae used:! Te pogam akes P as A s fo olled secions and b f-op f-op f-op + + b f-bo f-bo f-bo fo use-defined secions.! Te pogam uses φ b = 0.85 if a plasic sess disibuion is used fo momen and φ b = 0.9 if an elasic sess disibuion is used fo momen.! Te pogam compues e axial compession sess aio (P u / φ b P ) based on e aea of e seel beam alone no including e cove plae, even if i exiss, and no including e concee slab. Wen (P u / φ b P ) 0.125, Equaion 5a defines e compac secion limi fo ebs. Wen (P u / φ b P ) > 0.125, Equaion 5b defines e compac secion limi fo ebs. Limiing Wid-o-Tickness Raios fo Webs Page 3 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens 640 2.75P P 1 u u, en P φ b φbp 0.125 Eqn. 5a 191 P u 253 2.33, P φb Pu en > 0.125 φ P b Eqn. 5b In Equaions 5a and 5b, e value of used is e lages of e values fo e beam flanges and e eb. If ee is no axial foce, o if ee is axial ension onl (i.e., no axial compessive foce), onl Equaion 5a applies. Noncompac Secion Limis fo Webs Wen cecking a beam eb of a beam fo noncompac secion equiemens, e id-o-ickness aio cecked is /. Te noncompac secion limis depend on ee e flanges of e beam ae of equal o unequal size. Beams i Equal Sized langes Equaion 6 defines e noncompac secion limi fo ebs in beams i equal sized flanges. 970 0.74P 1 φ b P u Eqn. 6 In Equaion 6, e value of used is e lages of e values fo e beam flanges and e eb. Beams i Unequal Sized langes Equaion 7 defines e noncompac secion limi fo ebs in beams i unequal sized flanges Limiing Wid-o-Tickness Raios fo Webs Page 4 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens ee, 253 1 + 2.83 3 4 c c 0.74P 1 φ b P 3 2 u, Eqn. 7 In Equaion 7, e value of used is e lages of e values fo e beam flanges and e eb. Equaion 7 is Equaion A-B5-1 in e AISC-LRD93 specificaion. Limiing Wid-o-Tickness Raios fo Cove Plaes Te id-o-ickness cecks made fo e cove plae depend on e id of e cove plae compaed o e id of e beam boom flange. igue 1 illusaes e condiions consideed. In Case A of e figue, e id of e cove plae is less an o equal o e id of e beam boom flange. In a case, e id-o-ickness aio is aken as b 1 / cp, and i is cecked as a flange cove plae. In Case B of igue 1, e id of e cove plae is geae an e id of e beam boom flange. To condiions ae cecked in a case. Te fis condiion is e same as a son in Case A, ee e id-o-ickness aio is aken as b 1 / cp and is cecked as a flange cove plae. Te second condiion cecked in Case B akes b 2 / cp as e id-o-ickness aio and cecks i as a plae pojecing fom a beam. Tis second condiion is onl cecked fo e noncompac equiemens; i is no cecked fo compac equiemens. Compac Secion Limis fo Cove Plaes o bo cases A and B son in igue 1, e cove plae is cecked fo compac secion equiemens as son in Equaion 8. b1 190 Eqn. 8 cp cp ee b 1 is defined in igue 1. Limiing Wid-o-Tickness Raios fo Cove Plaes Page 5 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Beam Beam Cove plae b 1 cp b 2 b 1 b 2 cp Cove plae Case A Case B igue 1: Condiions Consideed Wen Cecking Wid-o-Tickness Raios of Cove Plaes Noncompac Secion Limis fo Cove Plaes Te cecks made fo noncompac secion equiemens depend on ee e id of e cove plae is less an o equal o a of e boom flange of e beam, Case A in igue 1, o geae an a of e boom flange of e beam, Case B in igue 1. Cove Plae Wid Beam Boom lange Wid Wen e cove plae id is less an o equal o e id of e beam boom flange, Equaion 9 applies fo e noncompac ceck fo e cove plae. b1 238 Eqn. 9 cp cp Te em b 1 in Equaion 9 is defined in igue 1. Limiing Wid-o-Tickness Raios fo Cove Plaes Page 6 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens Cove Plae Wid > Beam Boom lange Wid Wen e cove plae id exceeds e id of e beam boom flange, bo Equaions 9 and 10 appl fo e noncompac ceck fo e cove plae. b 2 95 Eqn. 10 cp cp Te em b 2 in Equaion 10 is defined in igue 1. Laeal Tosional Buckling Wen a singl smmeic beam is designed fo noncomposie beavio, i is cecked fo laeal osional buckling equiemens. If e singl smmeic beam is unsoed, is ceck occus fo an consucion design load case. I also occus fo beams a ave negaive bending a ae no specified o conside e composie acion povided b e slab eba. inall, e ceck occus fo an singl smmeic beam specified o be noncomposie. Wen evieing fo laeal osional buckling equiemens, e value of L b / c is cecked. L b is e laeall unbaced leng of beam; a is, e leng beeen poins a ae baced agains laeal displacemen of e compession flange. Te em c is adius of gaion of e compession flange abou e -axis. Compac Limis fo Laeal Tosional Buckling Te compac secion limi fo laeal osional buckling is given in Equaion 11. Lb 300 Eqn. 11 c f In Equaion 11 e em f is e ield sess of e compession flange. Noncompac Limis fo Laeal Tosional Buckling Te noncompac secion limi fo laeal osional buckling is given in Equaion 12. * L b L b Eqn. 12 c c Laeal Tosional Buckling Page 7 of 8
Composie Beam Design AISC-LRD93 Compac and Noncompac Requiemens * ee L b is e value of L b fo ic M c, as defined b Equaions 13a oug 13c, is equal o M, as defined b Equaions 14a and 14b. Te fomula fo M c given in Equaions 13a oug 13c is aken fom AISC- LRD93 Table A-1.1, foonoe (e). Te value of C b is aken as 1 as specified in e Table. ee, M B 1 c = ( 57000)( 1) L b I J B1 + 1 + B2 + B 2 1 Eqn. 13a I c I = 2.25 2 1 Eqn. 13b I L b J B 2 2 I c I c 25 1 I J L = Eqn. 13c b Te fomula fo M given in Equaions 14a and 14b is aken fom AISC- LRD93 Table A-1.1. M = S S Eqn. 14a L xc f x ee, L = smalle of ( ) and Eqn. 14b f In Equaion 14a, f is e ield sess of e ension flange. In Equaion 14b, f is e ield sess of e compession flange. Te oe ems ae defined in e noaion in Tecnical Noe Geneal and Noaion Composie Beam Design AISC-LRD93. Laeal Tosional Buckling Page 8 of 8