Desig of Beams (leual emes) (Pa 5 of AISC/RD) Refeeces 1. Pa 5 of e AISC RD aual. Cae ad Aedi of e AISC RD Secificaios (Pa 16 of RD aual) 3. Cae ad Aedi of e Commea of e AISC RD Secificaios (Pa 16 of RD aual) Basic Teo e aial load effecs ae egligile, i is a eam; oeise i is a eam-colum. 1
Saes a ae uil u fom lae elemes ae usuall called lae gides; e diffeece is e eig-ickess aio of e e. 5.70 > 5.70 Bedig eam lae gide = edig mome a e coss secio ude cosideaio = eedicula disace fom e eual lae o e oi of iees I = mome of ieia i esec o e eual ais S = elasic secio modulus of e coss secio o elasic aalsis, fom e elemea mecaics of maeials, e edig sess a a oi ca e foud f = I Te maimum sess c f ma = = = I I / c S Tis is valid as log as e loads ae small ad e maeial emais lieal elasic. o seel, is meas f mus o eceed ad e edig mome mus o eceed ma = S
= e maimum mome a igs e eam o e oi of ieldig o lasic aalsis, e edig sess eveee i e secio is, e lasic mome is A = a = Z = lasic mome A = oal coss-secioal aea a = disace eee e esula esio ad comessio foces o e coss-secio Z A = a = lasic secio modulus of e coss secio Sea Sea sesses ae usuall o a coollig faco i e desig of eams, ece fo e folloig cases: 1) Te eam is ve so. ) Tee ae oles i e e of e eam. 3) Te eam is sujeced o a ve eav coceaed load ea oe of e suos. 4) Te eam is coed. f v = sea sess a e oi of iees V = veical sea foce a e secio ude cosideaio Q = fis mome, aou e eual ais, of e aea of e coss secio eee e oi of iees ad e o o oom of e coss secio 3
I = mome of ieia i esec o e eual ais = id of e coss secio a e oi of iees om e elemea mecaics of maeials, e sea sess a a oi ca e foud VQ f v = I Tis equaio is accuae fo small. Cleal e e ill comleel ield log efoe e flage egis o ield. Teefoe, ield of e e eeses oe of e sea limi saes. Take e sea ield sess as 60% of e esile ield sess, fo e e a failue V f v = = 0. 60 A A = aea of e e Te omial seg coesodig o e limi sae is V = 0. 60 A Tis ill e e omial seg i sea ovided a ee is o sea ucklig of e e. Tis deeds o, e id-ickess aio of e e. Tee cases: No e isaili:.45 V = 0.60 A AISC q. (-1) 4
Ielasic e ucklig:.45 < 3.07 V.45 / = 0.60 A / AISC q. (-) lasic e ucklig: 3.07 < 60 4.5 ( ) V = A AISC q. (-3) / ailue odes Sea: A eam ca fail due o violaio of is sea desig seg. leue: Seveal ossile failue modes mus e cosideed. A eam ca fail eacig (full lasic), o i ca fail aeal osioal ucklig (TB), elasicall o ielasicall lage local ucklig (B), elasicall o ielasicall 5
We local ucklig (WB), elasicall o ielasicall e maimum edig sess is less a e ooioal limi e ucklig occus, e failue is elasic. Oeise, i is ielasic. aeal Tosioal Bucklig Te comessive flage of a eam eaves like a aiall loaded colum. Tus, i eams coveig log sas e comessio flage ma ed o uckle. Hoeve, is edec is esised e esile flage o ceai ee. Te oveall effec is a eomeo ko as laeal osioal ucklig, i ic e eam eds o is ad dislace laeall. aeal osioal ucklig ma e eveed : 1) Usig laeal suos a iemediae ois. ) Usig osioall sog secios (e.g., o secios). 3) Usig I-secios i elaivel ide flages. ocal Bucklig Te o-olled seel secios ae i-alled secios cosisig of a ume of i laes. We omal sesses due o edig ad/o diec aial foces ae lage, eac lae (fo eamle, flage o e lae) ma uckle locall i a lae eedicula o is lae. I ode o eve is udesiale eomeo, e id-o-ickess aios of e i flage ad e e laes ae limied e code. AISC classifies coss-secioal saes as comac, ocomac ad slede oes, deedig o e value of e id-ickess aios. (RD-Secificaio Tale B5.1) λ = id-ickess aio 6
λ = ue limi fo comac caego λ = ue limi fo ocomac caego Te e ee cases ae λ λ ad e flage is coiuousl coeced o e λ e, e sae is comac. λ < λ e sae is ocomac λ > λ e sae is slede Te aove codiios ae ased o e os id-ickess aio of e elemes of e coss secio. Te folloig ale summaizes e id-ickess limis fo olled I-, H- ad C- secios (fo C- secios, λ = f / f. Te e cieio is me all sadad I- ad C- secios lised i e aual. Buil-u elded I- saes (suc as lae gides ca ave ocomac o slede elemes). leme λ λ λ lage f 0.38 f 0. 83 10 We 3.76 5.70 7
Desig Requiemes 1. Desig fo fleue (RD SPC 1) uaced leg, disace eee ois aced agais laeal dislaceme of e comessio flage (i.) limiig laeall uaced leg fo full lasic edig G caaci (i.) a oe of e secio limiig laeall uaced leg fo ielasic laeal-osioal ucklig (i.) a oe of e secio modulus of elasici fo seel (9,000 ksi) sea modulus fo seel (11,00 ksi) J osioal cosa (i. 4 ) C aig cosa (i. 6 ) limiig ucklig mome (ki-i.) lasic mome, = Z 1. 5 mome coesodig o e ose of ieldig a e eeme fie fom a elasic sess disiuio = S u coollig comiaio of facoed load mome omial mome seg φ esisace faco fo eams (0.9) Te limi of 1.5 fo is o eve ecessive okig-load defomaio a is saisfied e 8
Z = Z 1. 5 o Z 1. 5 S o 1. 5 S Desig equaio Alied facoed mome mome caaci of e secio OR Requied mome seg desig seg of e secio u φ I ode o calculae e omial mome seg, fis calculae,, ad fo I-saed memes icludig id secios ad caels as 76 = 1. - a secio oe AISC q. (1-4) X1 = 1+ 1+ X - a secio oe AISC q. (1-6) = S - secio oe AISC q. (1-7) = fo oid meme, oeise i is e smalle of f o (suscis f ad mea flage ad e) comessive esidual sess i flage, 10 ksi fo olled saes; 16.5 ksi fo elded uil-u saes 9
X X 1 π GJA = AISC q. (1-8) S 4C = I S GJ S secio modulus aou e majo ais (i. 3 ) I mome of ieia aou e mio -ais (i. 4 ) adius of gaio aou e mio -ais (i. 4 ) AISC q. (1-9) Nomial Bedig Seg of Comac Saes e sae is comac ( λ λ ) ucklig) ad WB (e local ucklig). aeal osioal ucklig (TB), o TB:, o eed o ceck B (flage local = 1. 5 AISC q. (1-1) <, ielasic TB: ( ) = C AISC q. (1-) Noe a is a liea fucio of. > (slede meme), elasic TB: = AISC q. (1-1) c 10
c = C C = π S X 1 / I GJ π + X 1+ 1 ( / ) X I C AISC q. (1-13) Noe a c is a oliea fucio of C is a faco a akes io accou e ouifom edig mome disiuio ove a uaced leg A asolue value of mome a quae oi of e uaced segme B asolue value of mome a mid-oi of e uaced segme C asolue value of mome a ee-quae oi of e uaced ma segme asolue value of maimum mome i e uaced segme C = 1.5 ma.5 ma + 3 A + 4 B + 3 AISC q. (1-3) C e edig mome is uifom, all mome values ae e same givig C = 1. Tis is also ue fo a cosevaive desig. 11
Nomial Bedig Seg of Nocomac Saes e sae is ocomac ( λ λ λ ) < ecause of e flage, e e o o, e omial mome seg ill e e smalles of e folloig: aeal osioal ucklig (TB), o TB: = 1. 5 AISC q. (1-1) <, ielasic TB: ( ) = C AISC q. (1-) 1
Noe a is a liea fucio of >, elasic TB: c = AISC q. (1-1) = C c π I GJ π + I C AISC q. (1-13) Noe a c is a oliea fucio of lage local ucklig (B) λ λ, o B. λ < λ λ, e flage is ocomac: = λ λ λ λ ( ) AISC q. (A-1-3) Noe a is a liea fucio of λ We local ucklig (WB) λ λ, o WB. λ < λ λ, e e is ocomac: = λ λ λ λ ( ) AISC q. (A-1-3) Noe a is a liea fucio of λ Slede secios λ > λ : o laeall sale slede secios = c = S c c ciical (ucklig) mome ciical sess c 13
. Desig fo sea (RD SPC ) φ v esisace faco fo sea (0.9) V u V coollig comiaio of facoed sea omial sea seg ield sess of e e (ksi) A e aea, e oveall de d imes e e ickess Desig equaio fo 60: V u φ V v Te desig sea seg of usiffeed e is φ v V, ee V 0.60A.45 / = 0.60 A / 4.5 A ( / ).45 3.07.45 < < 3.07 60 Tese ae qs. (-1), (-) ad (-3) i Cae of RD Secificaios. o > 60, e siffees ae equied, ad e ovisio of Aedi mus e cosuled. Noe a sea is ael 14
a olem i olled seel eams; e usuall acice is o desig a eam fo fleual ad ceck fo sea. 3. Desig fo seviceaili Deflecio of eam sould e cecked i sevice loads. Tis is e seviceaili equieme of a sucue. (RD-Secificaio ). Desig Pocedue u Comue e facoed load mome (equied mome seg); i sould e less a o equal o e desig seg, φ. Te eig of e eam is a of e dead load u is uko a is oi. A value ma e assumed, o igoed emoail. Selec a sae a saisfies e fleual seg equieme. Tis ca e doe i oe of e folloig o as: Assume a sae, comue e desig seg ad comae i i e facoed load mome. Revise if ecessa. Use e eam desig cas i RD Pa 5. Ceck e sea seg. Ceck e deflecio (seviceaili equieme). 15