Question

A beam is supported at the two ends and is uniformly loaded. The bending moment M at a distance x from one end is given by

(i) M = (WL/2)x - (W/2)x2

(ii) M = (Wx/3) - (W/3)(x3/L2)

Find the point at which M is maximum in each case.

Answer 1

Condition for the maxima and minima is dM/dx = 0

And for the M to maximum (d2M/dx2) < 0

So, for x = L/√3, M will have maximum value.