Question

3. A cantilever beam of length L is embedded at its right end, and a horizontal compressive force of P pounds is applied at the free left end of the beam. When the origin is taken as its free end, the deflection of the beam can be shown to satisfy the differential equation Ely" = -Py – w(x)} Find the deflection of the cantilever beam if w(x) = Wox, 0 < x < L, and y(0) = 0, y'(L) = 0

Answer 1

Answer: Consider the ditt erential equanon E]y'' : - Py-w(7) & w(x) = wox then I y" = -py-Wo are with y(o): y'(6)=0 ET ET chica. MP & ED Y=1 Ei Yn 3 cicos s t ca sin Jest let yp a Ax'+BX+C sit + At 2A+ f (Az+BX+C) = more As we , B=0,2A + PCSO C: -2E1 () АР ETWA C- yp: chao ? + ETA g(x) = c, cos x + (as in 5 x - wos pex? + Ex wo 2p?

using y(0)=0 ΣΤωο => Cits P2 a cis-EIWO Pz P'(B) = 0 -> Ce i sin Jeon) :D = G = 0 2 EIWO uce): - Eraseros para todo tempo y(x) = - EI WO P2 x, Woo? 2 P