Solution to Problem 242 Statically Indeterminate

$\Sigma M_O = 0$

$0.75P_{st} = 1.5P_{al}$

$P_{st} = 2P_{al}$

$\sigma_{st} \, A_{st} = 2(\sigma_{al} A_{al})$

$\sigma_{st} = \dfrac{2 \sigma_{al} \, A_{al}}{A_{st}}$

$\sigma_{st} = \dfrac{2 \, [ \, \sigma_{al} (3000 \, ]}{250}$

$\sigma_{st} = 2.4 \sigma_{al}$

$\delta_{al} = \delta_{B}$
 

By ratio and proportion:
$\dfrac{\delta_A}{0.75} = \dfrac{\delta_B}{1.5}$

$\delta_A = 0.5 \delta_B$

$\delta_A = 0.5 \delta_{al}$
 

$\Delta = \delta_{st} + \delta_A$

$5 = \delta_{st} + 0.5 \delta_{al}$

$5 = \dfrac{\sigma_{st} (2\,000 - 5)}{200\,000} + 0.5 \left[ \dfrac{\sigma_{al} (2000)}{70\,000} \right]$

$5 = (9.975 \times 10^{-3}) \, \sigma_{st} + (14.28 \times 10^{-3}) \, \sigma_{al}$

$\sigma_{al} = 350 - 0.69825 \, \sigma_{st}$

$\sigma_{al} = 350 - 0.69825(2.4 \, \sigma_{al})$

$2.6758 \sigma_{al} = 350$

$\sigma_{al} = 130.8 \, \text{ MPa}$           answer