Problem 912 | Combined Axial and Bending

$\Sigma M_C = 0$

$36D_V + 18(\frac{4}{5} \times 3000) + 6(\frac{3}{5} \times 3000) = 12(\frac{3}{5} \times 9000) + 6(\frac{4}{5} \times 9000)$

$36D_V + 43,200 + 10,800 = 64,800 + 43,200$

$36DV = 54,000$

$D_V = 1500 ~ \text{lb}$
 

 

$\Sigma F_H = 0$

$D_H = \frac{4}{5}(9000) + \frac{3}{5}(3000)$

$D_H = 9000 ~ \text{lb}$
 

$M_{AB} = \Sigma M_{\text{to the right of } AB}$

$M_{AB} = 12 \times 1500 = 18,000 ~ \text{lb}\cdot\text{in}$
 

$\sigma_a = \dfrac{D_H}{A_{AB}} = \dfrac{9000}{2(6)}$

$\sigma_a = 750 ~ \text{psi}$
 

$\sigma_f = \dfrac{6M_{AB}}{bd^2} = \dfrac{6(18,000)}{2(6^2)}$

$\sigma_f = 1500 ~ \text{psi}$
 

$\sigma_A = \sigma_a + \sigma_f = 750 + 1500$

$\sigma_A = 2250 ~ \text{psi}$       answer
 

$\sigma_B = \sigma_a - \sigma_f = 750 - 1500$

$\sigma_B = -750 ~ \text{psi}$       answer