Chapter 2.3, Problem 56P

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 MPa and the allowable stress in the brass bar is 25 MPa.

2.55 Two steel bars (E_s = 200 GPa and α_s = 11.7 × 10^-6/°C) are used to reinforce a brass bar (E_b = 105 GPa, α_b = 20.9 × 10^-6/°C) that is subjected to a load P = 25 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 mm smaller than the 2 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. Determine (a) the increase in temperature that was required to fit the steel bars on the pins, (b) the stress in the brass bar after the load is applied to it.

Fig. P2.55