Question

A propped cantilever beam of span 'L' is loaded with uniformly distributed load of intensity w/unit length, all through the span. Bending moment at the fixed end is

• A. $\frac{W{L}^2}{8}$
• B. $\frac{W{L}^2}{2}$
• C. $\frac{W{L}^2}{12}$
• D. $\frac{W{L}^2}{24}$

Answer 1

The correct option is A $\frac{W{L}^2}{8}$


Reaction $R$ at propped end
$\frac{W{L}^4}{8EI}=\frac{R{l}^3}{3EI}$
$R=\frac{3wl}{8}$
Now, bending moment at the fixed end:
$M=\frac{w{l}^2}{2}-\frac{3wl}{8}\times l$
$M=\frac{w{l}^2}{8}$ (hogging)

Alternatively,
$\frac{\omega l^2}{12}+\frac{\omega l^2}{24}=\frac{\omega l^2}{8}$