고체역학 (Gere) — Axially Loaded Members: Problem 2.4-2

2.4-2 A cylindrical assembly consisting of a brass core and an aluminum collar is compressed by a load \( P \) (see figure). The length of the aluminum collar and brass core is 350 mm, the diameter of the core is 25 mm, and the outside diameter of the collar is 40 mm. Also, the moduli of elasticity of the aluminum and brass are 72 GPa and 100 GPa, respectively. (a) If the length of the assembly decreases by 0.1% when the load \( P \) is applied, what is the magnitude of the load? (b) What is the maximum permissible load \( P_{\text{max}} \) if the allowable stresses in the aluminum and brass are 80 MPa and 120 MPa, respectively?