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` from the end is given by `M=1/2l x-1/2W x^2dot` Find the point on the beam at which the bending moment has the maximum value.

Explanation

`M=frac{1}{2}` or `frac{-1}{2} omega {x}^{2}`

For M to Maximum `{M}`,

`frac{{dM}}{{dx}}=0 `

`Rightarrow frac{{dM}}{{dx}}=frac{1}{2} 1-frac{1}{2} omega(2 {x}) `

`=frac{1}{2}-omega {x}=0 `

`x=frac{1}{2 omega}`