A timber beam $)=(8\mathrm{.}75$GPa wide and $220mm$ deep, has an aluminum plate $=70$GPa $)$ of $80mm$ width and $20mm$ depth securely bonded to its bottom face. The beam is subjected to a bending moment of $20kNm$ around a horizontal axis. Determine

a$.$ The maximum stresses in both materials using a transformed section of timber $($i$.$e$.,n=\frac{E_a}{E_w}).$ Please show the calculations for the resulting moment of inertia as well.

b$.$ The stresses in the two materials at the bonded junction

c$.$ The maximum stresses in both materials using a transformed section of aluminum $($i$.$e$.,n=\frac{E_w}{E_a}).$ Please show the calculations for the resulting moment of inertia as well.