Solution to Problem 245 Statically Indeterminate

$\Sigma F_H = 0$

$R_1 + R_2 = 50\,000$

$R_1 = 50\,000 - R_2$
 

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

$\left( \dfrac{PL}{AE} \right)_{al} = \left( \dfrac{PL}{AE} \right)_{st}$

$\dfrac{R_1 \, (15)}{1.25(10 \times 10^6)} = \dfrac{R_2 \, (10)}{2.0(29 \times 10^6)}$

$R_2 = 6.96R_1$

$R_2 = 6.96(50\,000 - R_2)$

$7.96R_2 = 348\,000$

$R_2 = 43\,718.59 \, \text{lb}$
 

$\sigma_{st} = \dfrac{R_2}{A_{st}} = \dfrac{43\,718.59}{2.0}$

$\sigma_{st} = 21\,859.30 \, \text{ psi}$           answer
 

$R_1 = 50\,000 - 43\,718.59$

$R_1 = 6281.41 \, \text{lb}$
 

$\sigma_{al} = \dfrac{R_1}{A_{al}} = \dfrac{6281.41}{1.25}$

$\sigma_{al} = 5025.12 \, \text{ psi}$           answer