Gere & Goodno — Axially Loaded Members: Problem 2.4-15

2.4-15 The aluminum and steel pipes shown in the figure are fastened to rigid supports at ends \(A\) and \(B\) and to a rigid plate \(C\) at their junction. The aluminum pipe is twice as long as the steel pipe. Two equal and symmetrically placed loads \(P\) act on the plate at \(C\). (a) Obtain formulas for the axial stresses \(\sigma_a\) and \(\sigma_s\) in the aluminum and steel pipes, respectively. (b) Calculate the stresses for the following data: \(P = 50 \text{ kN}\), \(A_a = 6000 \text{ mm}^2\), cross-sectional area of aluminum pipe, \(A_s = 600 \text{ mm}^2\), cross-sectional area of steel pipe, \(E_a = 70 \text{ GPa}\), modulus of elasticity of aluminum, and \(E_s = 200 \text{ GPa}\), modulus of elasticity of steel.