Question

5. (15 pts) Consider a homogeneous horizontal beam of length L. Recall that the deflection y (x) of such a beam satisfies the fourth order differential equation EI d'y - wo where wois a constant load uniformly d.24 distributed along the length of the beam. The general solution of this equation is y(x) = (1 + c2x + c3 x2 + 4x3 + 2001x4 (a) Determine the appropriate boundary conditions if the beam is free on the left and embedded on the right (b) Solve the equation subject to the boundary conditions determined in a).

Answer 1

Answeve 0 Given that Consider a Homogteneous Horizontal beam of length Recall that the deflection yu) of such a beam satisfies The fourth order differentional equartion EI d'y dau a The appropriate "Boundary Condition XL y (0) 20, y'(o)=0 (No deflection stop zero-left) Y(L) = 0, y'(L) -o (No deflection Zero bending moment-right)

Y(n) = C, + G + Cym? + Cy x3 2 ycol= cio 24 ET yl(") = (2+2 4+ -3c4x² 4 wote + 24EI y col=C₂ = 0 y"(") = 202 + 4Cynt wo RET y" (L) = 263 + wo ocyt & 9(4) = 1² + Cyl3 + 2 ET wo 4 24E2 Since (² [g + Cult २५E2 23 & 2 ylt 2 Wo 2lz + bryl 24EI wo 261 12 2 Wo 24 EI wo Yeylt 2ET yayl + entry[] wo Cy= 4[%] 467 SWOL YEL

wol² Cza 5wol² YREL + 2461 9 = 3 wol² 48ET ولا 322 49 5L x² ។ ET 24 were unable to transcribe this image y (o)=ou'o)=0 we unable to transcribe this image Y(0) =6=0. we we unable to transcribe this image. 15 times