(Solved): (b) A solid circular steel cylinder S in encased in a hollow circular aluminum tube A. The cylinder ...

(b) A solid circular steel cylinder $S$ in encased in a hollow circular aluminum tube $A$. The cylinder and tube are compressed between the rigid plates of a testing machine which applies forces $P$. Calculate the allowable value of the compressive force if the yield stresses of steel and aluminum are ${?}_{\text{steel }}=345\mathrm{MPa}$ and ${?}_{\mathrm{al}}=415\mathrm{MPa}$, respectively. Assume that ${\mathrm{A}}_{\mathrm{s}}=80{\mathrm{cm}}^2,{\mathrm{A}}_{\mathrm{al}}=40$ ${\mathrm{cm}}^2.L=1\mathrm{m}.({\mathrm{E}}_{\mathrm{s}}=200,000\mathrm{MPa}$ and ${\mathrm{E}}_{\mathrm{A}}=73,000\mathrm{MPa})$