Problem $3(25$ pts$)$

Shown is a steel pipe bonded to a solid magnesium core that

fills the entire pipe. The assembly is initially stress free at a

temperature of $20$ C$.$ After the temperature of the assembly

is raised to $100$ C$,$ a load P $=250$ kN is applied. Determine

the average normal stress in each material caused by the

load and temperature change, and indicate if each material

is in tension or compression. The pipe has an outer diameter

of $80$ mm and an inner diameter of $60$ mm$.$