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Structures I HW4 Solutions

# Structures I HW4 Solutions - '8.4 Determine the equations...

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'8.4. Determine the equations of the elastic curve for the beam usingthe.r1 and .r2 coordinates. Specify the beam,s maximum deflection. E/ is constant. Sryporl Rtar,tbtt ond Bbtlc Cne : Ar rbryl on FBD(r). Mo;eat Ftnctlot.. Ar rbowl oo FED(b) rnd (c). Slopo utd Elatttc Crrto : E /'u T 7i: M(xl D Forff(r,) =irr , u#.-!r,, adii-*l.o u ur -- rlrrl,+C1x1 +C2 ,d#.-p{ uff.-|t.a A "r --Pyl+C1x2+C, Doandarl Condltlow : u, aQ 11 .r, nQ, From84.[2]. Ct = 0 0, rQ tr1 ;, =1. From\$.[2], o.-S*c,, cr-P# Dr o 0 rr ,, = *. Frcm Eq. (41. o.-r\$*f,r,*c, Contlnule Coadttlons: Arr, =1ndsr r!. *-+ Frora4c.[Urd[3], -'+.'#--[-T.o) c,-# FroraQ.t5l, C..-T Tht Slope : Suhrjnru6oveluoof Cs hbq,[U, *.*f",_3.1) *.0.rfi{r,-ri) ,,-ft The Elattlc Crnr ..Subsd ino Eqs. t2l rnd (aJ, rccpccri oc thc valucr of ct' ct' c1' Jrdca ', '#(-'l*r') ua o uf f,,.i. H(+.u). o.o32rpr,r ,r.\${-*l +7Ltx2-3L') Anr t'c'h Lr-o .-It u^ . ua.S tu t21 For,t/(4) . - &r, t3l rq (r) + 'f) i-l)tnce=-ix, rfi P va.r I t44).-ftoff=c a'1 lFFl t5l Ans Hcncq 226

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85. Determine the maximum deflectioo of the beam and the slope.at A. Use the method of double integration. E/ is constant. F-r ;#-., o*-o € l v ; r g r 4 q 6 ' t A l r l r Q , s t 1 9 C r . g Lh.llor rrfi.A
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