Question $2(10$ marks$)$

A composite beam $225$ mm wide $300mm$ deep $4m$ long is made by bolting two $100-mm-$ wide x $300-$mm$-$deep timber planks to the sides of a $25300-mm$ structural aluminium plate. The moduli of elasticity for the timber and aluminium are $8$ GPa and $73$ GPa $,$ respectively.

Determine the maximum tensile flexural stress in each of the materials if the composite beam is simply supported and carries a concentrated load $30$ kN in the centre of the beam. Assume that the bolt merely holds the plates together $($do not transform$)$