$\delta_T = \alpha L \, \Delta T$
$\delta_{T(st)} = (11.7 \times 10^{-6})(1500)(30) = 0.5265 \, \text{mm}$
$\delta_{T(br)} = (18.9 \times 10^{-6})(3000)(30) = 1.701 \, \text{mm}$
$\Sigma M_A = 0$
$4P_{br} + P_{st} = 2.5(120\,000)$
$4\sigma_{br}(1300) + \sigma_{st}(320) = 2.5(120\,000)$
$16.25\sigma_{br} + \sigma_{st} = 937.5$
$\sigma_{st} = 937.5 - 16.25\sigma_{br}$ Equation (1)
$\dfrac{\delta_{T(st)} + \delta_{st}}{1} = \dfrac{\delta_{T(br)} + \delta_{br}}{4}$
$\delta_{T(st)} + \delta_{st} = \dfrac{\delta_{T(br)}}{4} + \dfrac{\delta_{br}}{4}$
$0.5265 + \left( \dfrac{\sigma L}{E} \right)_{st} = \dfrac{1.701}{4} + \left( \dfrac{\sigma L}{4E} \right)_{br}$
$0.5265 + \dfrac{\sigma_{st} (1500)}{200\,000} = 0.425\,25 + \dfrac{\sigma_{br}(3000)}{4(83\,000)}$
$0.526\,5 + 0.007\,5\sigma_{st} = 0.425\,25 + 0.009\,04\sigma_{br}$
$0.007\,5\sigma_{st} - 0.009\,04\sigma_{br} = -0.101\,25$
$0.007\,5\,(937.5 - 16.25\sigma_{br}) - 0.009\,04\sigma_{br} = -0.101\,25$
$7.031\,25 - 0.121\,875\sigma_{br} - 0.009\,04\sigma_{br} = -0.101\,25$
$7.132\,5 = 0.130\,915\sigma_{br}$
$\sigma_{br} = 54.48 ~ \text{MPa}$ answer
$\sigma_{st} = 937.5 - 16.25(54.48)$
$\sigma_{st} = 52.2 ~ \text{MPa}$ answer
