Question

A beam of length $l$ is supported at one end .If $w$ is the uniform load per unit length the bending moment $M$ at a distance $x$ form the end is given by $M=\frac{1}{2}lx-\frac{1}{2}w{x}^2$ ,find the point on the beam at which the bending moment has maximum value .

Answer 1

Bending moment $M=\frac{1}{2}$ or $\frac{-1}{2}\omega x^2$

for bending moment to be maximum $M$,

$\frac{dM}{dx}=0$

$\Rightarrow \frac{dM}{dx}=\frac{1}{2}l-\frac{1}{2}\omega \left(2x\right)$

$=\frac{l}{2}-\omega x=0$

$x=\frac{l}{2\omega }$