3.31. The structure in Fig. P3.31 is subjected to an increase in temperature, \(\Delta T = 80^\circ C\). Determine the displacements, stresses, and support reactions. Solve this problem by hand calculation, using the elimination method for handling boundary conditions.
\(P_1 = 60\text{ kN}\)
\(P_2 = 75\text{ kN}\)
\(\Delta T = 80^\circ C\)
800 mm
600 mm
400 mm
Bronze
Aluminum
Steel
\(A = 2400\text{ mm}^2\)
\(1200\text{ mm}^2\)
\(600\text{ mm}^2\)
\(E = 83\text{ GPa}\)
\(70\text{ GPa}\)
\(200\text{ GPa}\)
\(\alpha = 18.9 \times 10^{-6}/^\circ C\)
\(23 \times 10^{-6}/^\circ C\)
\(11.7 \times 10^{-6}/^\circ C\)
\((1\text{ GPa} = 10^9 \text{N/}m^2)\)
FIGURE P3.31
