Beer & Johnston — Stress and Strain—Axial Loading: Problem 2.56

2.56 Determine the maximum load \( P \) that can be applied to the brass bar of Prob. 2.55 if the allowable stress in the steel bars is \( 30 \text{ MPa} \) and the allowable stress in the brass bar is \( 25 \text{ MPa} \). (Reference from Prob 2.55: Two steel bars (\( E_s = 200 \text{ GPa} \) and \( \alpha_s = 11.7 \times 10^{-6}/^\circ\text{C} \)) are used to reinforce a brass bar (\( E_b = 105 \text{ GPa}, \alpha_b = 20.9 \times 10^{-6}/^\circ\text{C} \)) that is subjected to a load \( P = 25 \text{ kN} \). When the steel bars were fabricated, the distance between the centers of the holes that were to fit on the pins was made \( 0.5 \text{ mm} \) smaller than the \( 2 \text{ m} \) needed. The steel bars were then placed in an oven to increase their length so that they would just fit on the pins. Following fabrication, the temperature in the steel bars dropped back to room temperature.)