Introduction. ENCE 710 Design of Steel Structures V. Lateral-Torsional Buckling of Beams. Introduction
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1 NC 710 Desig of Seel Sucues V. Laeal-Tosioal Bucklig of Beams C. C. u, P.D., P.. Civil ad viomeal gieeig Deame Uivesi of alad Ioducio olloig sujecs ae coveed: Laeal Tosioal Bucklig (LTB) lage Local Bucklig (LB) We Local Bucklig (WLB) Sea seg Laeal Bacig Desig Readig: Caes 9 of Salmo & Joso AISC LRD Secificaio Caes B (Desig Requiemes) ad (Desig of emes fo lexue) Ioducio Desig of emes fo lexue (aou ajo Axis) A eam ca fail eacig e lasic mome ad ecomig full lasic (see las secio) o fail emauel : 1. LTB, eie elasicall o ielasicall. LB, eie elasicall o ielasicall 3. WLB, eie elasicall o ielasicall If e maximum edig sess is less a e ooioal limi e ucklig occus, e failue is elasic. lse i is ielasic. o edig ( = 0.9) 3 4
2 Laeal Tosioal Bucklig (LTB) Comac emes (AISC ) ailue ode Plasic LTB (Yieldig) Ielasic LTB lasic LTB Laeal Tosioal Bucklig (co.) ailue ode A eam ca uckle i a laeal-osioal mode e e edig mome exceeds e ciical mome. ome Gadie aco C 5 6 Laeal Tosioal Bucklig (co.) Laeal Tosioal Bucklig (co.) Nomial lexual Seg lasic e L L ad ielasic e L L L ad elasic e L ad L C 1.0 lasic ielasic elasic I-Beam i a Buckled Posiio L L L 7 8
3 Laeal Tosioal Bucklig (co.) lasic LTB couled diffeeial equaios fo oaio ad laeal aslaio 3 d d (8.5.10) z GJ C 3 dz dz ee z z G J C = mome a locaio z alog meme axis = axis alog meme leg = agle of is = sea modulus = osioal cosa (AISC Tale 1-1 fo osioal o.) = modulus of elasici = aig cosa (AISC Tale 1-1 fo aig) 9 Laeal Tosioal Bucklig (co.) Plasic LTB (Yieldig) lexual Seg Z (AISC -1) ee Z= lasic secio modulus & = secio ield sess Limis Laeal acig limi L L (AISC -5) lage ad We id/ickess limi (AISC Tale B4.1) (Noe: L d i Salmo & Joso q. (9.6.) is emoved fom AISC 13 d.) 10 Laeal Tosioal Bucklig (co.) Ielasic LTB lexue Seg (saig lie ieolaio) o C L L L C 7 L L L L L L L L 0. Sx (9.6.4) (AISC -) Laeal Tosioal Bucklig (co.) lasic LTB lexue Seg L L c S x (AISC -3) (AISC -4) C Jc L c L Sxo s s (Te squae oo em ma e cosevaivel ake equal o 1.0) (c i AISC -8a, fo doul smmeic I-sae, ad cael, esecivel) Jc 0.7 S Sxo Jc x o Limi L.95s (AISC -6) 11 s I C S x (AISC -7) 1
4 Laeal Tosioal Bucklig (co.) C fo a Simle Sa Bidge ome Gadie aco C Te mome gadie faco C accous fo e vaiaio of mome alog e eam leg eee acig ois. Is value is iges, C =1, e e mome diagam is uifom eee adjace acig ois. We e mome diagam is o uifom 1.5 (9.6.3) max C (AISC 1-1).5 max 3 A 4 B 3 C ee max = asolue value of maximum mome i uaced leg A, B, C = asolue mome values a oe-quae, oe-alf, ad ee-quae ois of uaced leg Nomial ome Seg u as affeced C lage Local Bucklig (LB) Comac We ad Nocomac/Slede lages (AISC 3) ailue ode Nocomac lage Slede lage Nomial lexual seg, = i (, 3) 15 16
5 lage Local Bucklig (co.) lage Local Bucklig (co.) ailue ode Te comessio flage of a eam ca uckle locall e e edig sess i e flage exceeds e ciical sess. Nomial lexual Seg lasic e f / f ad ielasic e f / f ad elasic e f / f ad comac ocomac slede 17 λ λ f λ f 18 lage Local Bucklig (co.) lage Local Bucklig (co.) Nocomac lage (saig lie ieolaio) lexue Seg f 0.7Sx f f (AISC 3-1) Slede lage lexue Seg Limi 0.9kcS (AISC 3-) 4 kc / (kc sall o e less a 0.35 ad o geae a 0.76) (AISC Tale B4.1) x 19 0
6 We Local Bucklig (WLB) Comac o Nocomac Wes (AISC 4) ailue ode Comac We (Yieldig) Nocomac We Slede We Nomial lexual Seg, =mi (comessio flage ieldig, LTB, comessio LB, esio flage ieldig) We Local Bucklig (co.) ailue ode Te e of a eam ca also uckle locall e e edig sess i e e exceeds e ciical sess. 1 We Local Bucklig (co.) Nomial lexual Seg lasic e ad ielasic e ad elasic e ad comac ocomac slede We Local Bucklig (co.) Comessio lage Yieldig lexual Seg R c c R c S (AISC 4-1) ee R c = e lasicificaio faco (AISC 4-9a, ) & = secio ield sess xc Limis (AISC Tales B4.1) λ λ λ 3 L L
7 We Local Bucklig (co.) We Local Bucklig (co.) LTB (Ielasic) L lexue Seg L L LTB (lasic) L L lexue Seg S c xc R c c (AISC 4-3) C R c c f R S c c L xc f f (AISC 4-1) c C L 1 J L Sxo (AISC 4-5) ee L = a sess deemied AISC 4-6a, Limi (AISC Tale B4.1) J L Sxo L S J L x o (AISC 4-8) 5 6 We Local Bucklig (co.) We Local Bucklig (co.) Comessio LB (Nocomac lage) lexue Seg f Rc c Rc c LS xc f f Comessio LB (Slede lage) lexue Seg (AISC 4-1) Tesio lage Yieldig lexue Seg R R R = e lasificaio faco o e esio flage ieldig limi Sx S xc S x (AISC 4-14) 0.9kcS x (AISC 4-13) (a) c / R = / (AISC 4-15a) () c / > (AISC 4-15) k c 4 / (k c sall o e less a 0.35 ad o geae a 0.76) 7 R 1 8
8 Sea Seg ailue ode Sea-Bucklig Coefficie lasic Sea Seg Ielasic Sea Seg Plasic Sea Seg o sea v V ( v = 0.9 exce ceai olled I- eam /.4 /, v = 1.0) V =0.6 A C v (AISC G-1) Sea Seg (co.) ailue ode Te e of a eam o lae gide uckles e e e sea sess exceeds e ciical sess Sea Seg (co.) Sea Seg (co.) Nomial Sea Seg V ( v = 0.9) lasic e ad ielasic e ad elasic e ad V V 0. 8 c AISC G Nomial Sea Seg V (a) o (AISC G-3) 1.10 kv k (a) o v kv (AISC G-4) C v 1.0 kv 1.10 Cv V lasic ielasic elasic (a) o kv (AISC G-5) kv Cv λ λ λ 31 3
9 Laeal Bacig Desig Laeal Bacig Desig AISC Povisios Saili Bacig Desig fo Beams 1. o siffess β eqd, β eqd = β ideal. o omial seg, (a) = β ideal ( 0 ); () = β ideal (0.004L ) Wee β ideal = P c /L Laeal Bacig Desig (co.) AISC Povisios LRD Saili Bacig Desig fo Beams Laeal Bacig Desig (co.) AISC Povisios LRD Saili Bacig Desig fo Colums 1. Relaive acig Re quied P C 0 d 1. Relaive acig Re quied P P Φ=0.75 Re quied 1 4 Cd L0 Φ=0.75 Re quied 1 P L. Nodal acig Re quied P 0.0 C 0 d. Nodal acig Re quied P 0. 01P Re quied 1 10 Cd L0 35 Re quied 1 8P L 36
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