Question

A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by

• A. $\frac{PL}{3}$
• B. $\frac{2PL}{3}$
• C. $\frac{PL}{9}$
• D. $\frac{2PL}{9}$

Answer 1

The correct option is D $\frac{2PL}{9}$

Taking moment about A, we have
$R_B\times L=P\times \frac{L}{3}$

$\therefore R_B=\frac{P}{3}$

$R_A=P-R_B=P-\frac{P}{3}=\frac{2P}{3}$

Bending moment at the point of application of load,
$M=\frac{2P}{3}\times \frac{L}{3}=\frac{2PL}{9}$