Question $3($Total: $10$ marks$)$

a$)$ A simply supported beam with $6$ m span has a rectangular cross section of $200mm300mm.$ It has been subjected to a uniformly distributed load of $10k\frac{N}{m}.$ Density of the material is $2500k\frac{g}{m^3}$ and $G=20$GPa. Calculate the strain energy stored due to shearing action.

$(10$ marks$)$

Strain Energy due to shearing $u_s={\displaystyle \underset{0}{\overset{L}{}}}\frac{F^2}{2AG}dx$