Question

A simply supported beam of length '10+2a' has supports 10 m apart with an overhang 'a' over each support. The beam carries uniformly distributed load. The overhang 'a' so that at the collapse state, the overhang and span between the supports collapse simultaneously, is____m.

Answer 1

For the collapse of the span AB at the stage of collapse of the overhangs.

$M_p=\frac{\omega (10+2a)}{2}\times 5-\frac{\omega (5+a{)}^2}{2}$

$\therefore \frac{\omega a^2}{2}=\frac{\omega (10+2a)}{2}\times 5-\frac{\omega (5+a{)}^2}{2}$

$a^2=50+10a-25-a^2-10a$

$2a^2=25$

$a=3.54m$