Solution to Problem 262 Thermal Stress

$\delta = \delta_T + \delta_{st}$

$\dfrac{\sigma \, L}{E} = \alpha \, L \, (\Delta T) + \dfrac{PL}{AE}$

$\sigma = \alpha \, E \, (\Delta T) + \dfrac{P}{A}$

$130 = (11.7 \times 10^{-6})(200\,000)(40) + \dfrac{5000}{A}$

$A = \dfrac{5000}{36.4} = 137.36 \, \text{ mm}^2$
 

$\frac{1}{4} \pi d^2 = 137.36$

$d = 13.22 \, \text{ mm}$           answer