Gere & Goodno — Axially Loaded Members: Problem 2.4-5

2.4-5 A solid circular steel cylinder \(S\) is 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 \(\sigma_{yS} = 340\) MPa and \(\sigma_{yA} = 410\) MPa, respectively. Assume that \(A_S = 7700\) mm\(^2\), \(A_A = 3800\) mm\(^2\), \(L = 500\) mm, \(E_S = 200\) GPa, and \(E_A = 73\) GPa.