Problem $1$:

A wood beam with $E_w=8\mathrm{.}75$GPa,$100mm$ wide by $220mm$ deep, has an aluminum plate $E_a=70$GPa with a net section $80mm$ by $20mm$ securely fastened to its bottom face, as shown below. Dimensions are given in millimeters. The beam is subjected to a bending moment of $20kN*m$ around a horizontal axis. Calculate the maximum stresses in both materials $($a$)$ using a transformed section of wood and $($b$)$ using a transformed section of aluminum.

Problem $2$:

A T$-$section contains a flange of size $150mm50mm$ and web of size $50mm150mm.$ This section is subjected to a vertical shear foree of $100kN.$ Determine the maximum shear stress and draw the shear stress distribution diagram along web.