Introduction. ENCE 710 Design of Steel Structures V. Lateral-Torsional Buckling of Beams. Introduction

Transcription

1 NC 710 Desig of Seel Sucues V. Laeal-Tosioal Bucklig of Beams C. C. u, Ph.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) Shea segh Laeal Bacig Desig Readig: Chaes 9 of Salmo & Johso AISC LRD Secificaio Chaes B (Desig Requiemes) ad (Desig of emes fo lexue) Ioducio Desig of emes fo lexue (aou ajo Axis) A eam ca fail eachig he lasic mome ad ecomig full lasic (see las secio) o fail emauel : 1. LTB, eihe elasicall o ielasicall. LB, eihe elasicall o ielasicall 3. WLB, eihe elasicall o ielasicall If he maximum edig sess is less ha he ooioal limi he ucklig occus, he 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 he he edig mome exceeds he ciical mome. ome Gadie aco C 5 6 Laeal Tosioal Bucklig (co.) Laeal Tosioal Bucklig (co.) Nomial lexual Segh lasic he L L ad ielasic he L L L ad elasic he 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 hee z z G J C = mome a locaio z alog meme axis = axis alog meme legh = agle of is = shea 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 Segh Z (AISC -1) hee Z= lasic secio modulus & = secio ield sess Limis Laeal acig limi L L (AISC -5) lage ad We idh/hickess limi (AISC Tale B4.1) (Noe: L d i Salmo & Johso q. (9.6.) is emoved fom AISC 13 h d.) 10 Laeal Tosioal Bucklig (co.) Ielasic LTB lexue Segh (saigh 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 Segh L L c S x (AISC -3) (AISC -4) C Jc L c L Sxho s s (The squae oo em ma e cosevaivel ake equal o 1.0) (c i AISC -8a, fo doul smmeic I-shae, ad chael, esecivel) Jc 0.7 S h Sxho 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 The mome gadie faco C accous fo he vaiaio of mome alog he eam legh eee acig ois. Is value is highes, C =1, he he mome diagam is uifom eee adjace acig ois. Whe he mome diagam is o uifom 1.5 (9.6.3) max C (AISC 1-1).5 max 3 A 4 B 3 C hee max = asolue value of maximum mome i uaced legh A, B, C = asolue mome values a oe-quae, oe-half, ad hee-quae ois of uaced legh Nomial ome Segh u as affeced C lage Local Bucklig (LB) Comac We ad Nocomac/Slede lages (AISC 3) ailue ode Nocomac lage Slede lage Nomial lexual segh, = i (, 3) 15 16

5 lage Local Bucklig (co.) lage Local Bucklig (co.) ailue ode The comessio flage of a eam ca uckle locall he he edig sess i he flage exceeds he ciical sess. Nomial lexual Segh f / lasic he f ad ielasic he f / f ad elasic he f / f ad comac ocomac slede 17 λ λ f λ f 18 lage Local Bucklig (co.) lage Local Bucklig (co.) Nocomac lage (saigh lie ieolaio) lexue Segh f 0.7Sx f f (AISC 3-1) Slede lage lexue Segh Limi 0.9kcS (AISC 3-) 4 kc h / (kc shall o e less ha 0.35 ad o geae ha 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 Segh, =mi (comessio flage ieldig, LTB, comessio LB, esio flage ieldig) We Local Bucklig (co.) ailue ode The e of a eam ca also uckle locall he he edig sess i he e exceeds he ciical sess. 1 We Local Bucklig (co.) Nomial lexual Segh lasic he ad ielasic he ad elasic he ad comac ocomac slede We Local Bucklig (co.) Comessio lage Yieldig lexual Segh R c c R c S (AISC 4-1) hee R c = e lasicificaio faco (AISC 4-9a, ) & = secio ield sess xc Limis (AISC Tales B4.1) λ λ λ h 3 L L

7 We Local Bucklig (co.) We Local Bucklig (co.) LTB (Ielasic) L lexue Segh L L LTB (lasic) L L lexue Segh 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 Sxho (AISC 4-5) hee L = a sess deemied AISC 4-6a, Limi (AISC Tale B4.1) J L Sxho L S h J L x o (AISC 4-8) 5 6 We Local Bucklig (co.) We Local Bucklig (co.) Comessio LB (Nocomac lage) lexue Segh f Rc c Rc c LS xc f f Comessio LB (Slede lage) lexue Segh (AISC 4-1) Tesio lage Yieldig lexue Segh R R R = e lasificaio faco o he esio flage ieldig limi Sx S xc S x (AISC 4-14) 0.9kcS x (AISC 4-13) (a) h c / R = / (AISC 4-15a) () h c / > (AISC 4-15) k c 4 h / (k c shall o e less ha 0.35 ad o geae ha 0.76) 7 R 1 8

8 Shea Segh ailue ode Shea-Bucklig Coefficie lasic Shea Segh Ielasic Shea Segh Plasic Shea Segh o shea v V ( v = 0.9 exce ceai olled I- eam h/.4 /, v = 1.0) V =0.6 A C v (AISC G-1) Shea Segh (co.) ailue ode The e of a eam o lae gide uckles he he e shea sess exceeds he ciical sess Shea Segh (co.) Shea Segh (co.) Nomial Shea Segh V ( v = 0.9) lasic he ad ielasic he ad elasic he ad V V 0. 8 c AISC G Nomial Shea Segh V (a) o (AISC G-3) h 1.10 kv k (a) o v h kv (AISC G-4) C v 1.0 kv 1.10 Cv h V lasic ielasic elasic (a) o kv h (AISC G-5) kv h Cv λ λ λ 31 3

9 Laeal Bacig Desig Laeal Bacig Desig Ne: Pael Ne: Poi AISC Povisios Saili Bacig Desig fo Beams 1. o siffess β eqd, β eqd = β ideal. o omial segh, (a) = β ideal ( 0 ); () = β ideal (0.004L ) Whee β ideal = P c /L Laeal Bacig Desig (co.) AISC Povisios LRD Saili Bacig Desig fo Colums 1. Pael acig (A-6-1) Φ= P Re quied (A-6-a) L Laeal Bacig Desig (co.) AISC Povisios LRD Saili Bacig Desig fo Beams 1. Laeal Bacig 1a. Pael acig 0.01 (A-6-5) Re quied Φ= Cd Lh0 (A-6-6a). Poi acig Re quied P (A-6-3) 0. 01P 1. Poi acig 0.0 (A-6-7) Re quied 1 8P L (A-6-4a) 35. Tosioal Bacig Re quied 1 10 Cd Lh0 (A-6-8a) 36