Solution to Problem 246 Statically Indeterminate

$\delta_{st} = \delta_{al} = \delta$

$\left( \dfrac{\sigma \, L}{E} \right)_{st} = \left( \dfrac{\sigma \, L}{E} \right)_{al}$

$\dfrac{\sigma_{st} \, (10)}{29 \times 10^6} = \dfrac{\sigma_{al} \, (15)}{10 \times 10^6}$

$\sigma_{st} = 4.35 \, \sigma_{al}$
 

When σ_al = 10 ksi
$\sigma_{st} = 4.35(10)$

$\sigma_{st} = 43.5 \, \text{ ksi } > 18 \, \text{ ksi}$       (not okay!)
 

When σ_st = 18 ksi
$18 = 4.35 \, \sigma_{al}$

$\sigma_{al} = 4.14 \, \text{ ksi } 10 \, \text{ ksi}$       (okay!)
 

Use σ_al = 4.14 ksi and σ_st = 18 ksi
 

$\Sigma F_H = 0$

$P = R_1 + R_2$

$P = \sigma_{al} \, A_{al} + \sigma_{st} \, A_{st}$

$P = 4.14(1.25) + 18(2.0)$

$P = 41.17 \, \text{ kips}$           answer