Question

A beam of length 10 m carries a UDL of 20 kN/m over its entire length and rests on two simple supports. In order that the maximum BM produced in the beam is the least possible, the supports must be placed from the ends at a distance of

• A. 5.86 m
• B. 4.14 m
• C. 2.93 m
• D. 2.07 m

Answer 1

The correct option is D 2.07 m

Given $L_1+2a=10m$
The bending moment will be least when maximum negative moment is equal to maximum positive moment.

a= 0.207 L = 2.07 m

$Minimumnegativemoment=\frac{w{a}^2}{2}$
$\frac{20\times {\left(2.07\right)}^2}{2}=42.kN-m$