고체역학 (Gere) — Axially Loaded Members: Problem 2.4-23

2.4-23 A trimetallic bar is uniformly compressed by an axial force \( P = 12 \text{ kN} \) applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by brass and copper tubes. The steel core has a diameter of 10 mm, the brass tube has an outer diameter of 15 mm, and the copper tube has an outer diameter of 20 mm. The corresponding moduli of elasticity are \( E_s = 210 \text{ GPa} \), \( E_b = 100 \text{ GPa} \), and \( E_c = 120 \text{ GPa} \). Calculate the compressive stresses \( \sigma_s \), \( \sigma_b \), and \( \sigma_c \) in the steel, brass, and copper, respectively, due to the force \( P \).