Question

A cantilever beam with a uniform flexural rigidity $(EI=200\times {10}^{6}N{m}^2)$ is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 $N{m}^2$. The magnitude of the slope of beam at its free end is ___ micro radian (round off to the nearest integer)

• A. 50

Answer 1

The correct option is A 50
Assume
$A=10000N-m^2$
$EI=200\times {10}^{6}N-m^2$
As per moment area first theorem.

${\theta }_B-{\theta }_A=\left(\frac{A}{EI}\right)AB$

${\theta }_B-0=\frac{10000}{200\times {10}^6}=0.5\times {10}^{-4}$ radians

${\theta }_B=50\mu$ radians