A composite bar is constructed from two materials: an internal rod crafted from

steel and an external tube fabricated from aluminum. The steel rod measures $1$ meter

in length with a diameter of $20mm,$ while the aluminum tube possesses an inner

diameter of $30mm$ and an outer diameter of $40mm.$ The compound bar is initially at

a temperature of $25C.$ When uniformly heated to $100C,$ analyze the thermal stresses

that develop in both the steel rod and the aluminum tube. Assume coefficients of linear

expansion for steel and aluminum as $12{10}^{{?}^{{?}^{?}}}(-6)$ per $C$ and $23{10}^{{?}^{{?}^{?}}}(-6)$ per $C,$

respectively. Provide the necessary steps and formulas in your solution.