Question

The loading diagram is shown in figure.

The value of 'a' such that the bending moment at support will be equal to the mid-span bending moment is ____m

• A. 1.767

Answer 1

The correct option is A 1.767

$\text{B.M. at support}=-\frac{W{a}^2}{2}$

$\text{B.M. at mid-span}=-\frac{W(a+2.5{)}^2}{2}+\frac{W(5+2a)}{2}\times 2.5$

Maximum hogging BM at support= Maximum sagging BM at mid-span

$-\frac{W{a}^2}{2}=\frac{W(a+2.5{)}^2}{2}-\frac{W(5+2a)}{2}\times 2.5$

$-a^2=(a+2.5{)}^2-(5+2a)\times 2.5$

$a=1.767m$