Real-World Applicationshard
0:00.0

A cantilever beam of length LL is fixed at x=0x = 0 and free at x=Lx = L. It is subjected to a distributed load w(x)=w0fracx2L2w(x) = w_0 \\frac{x^2}{L^2}. The deflection y(x)y(x) satisfies the Euler-Bernoulli beam equation EIfracd4ydx4=w(x)EI \\frac{d^4y}{dx^4} = -w(x), with boundary conditions y(0)=0,y(0)=0y(0) = 0, y'(0) = 0 (clamped at x=0x=0), and y(L)=0,y(L)=0y''(L) = 0, y'''(L) = 0 (free at x=Lx=L). What is the bending moment M(x)=EIy(x)M(x) = EI y''(x) as a function of xx?