Problem 358 | Equilibrium of Non-Concurrent Force System

$\frac{4}{5}T + R = 60$

$R = 60 - \frac{4}{5}T$
 

$\Sigma M_A = 0$

$10T + 4(4)R = 4(60) + 3(3)(40)$

$10T + 16R = 600$

$5T + 8R = 300$

$5T + 8(60 - \frac{4}{5}T) = 300$

$-\frac{7}{5}T + 480 = 300$

$\frac{7}{5}T = 180$

$T = 128.57 \, \text{ kN up to the left}$           answer
 

$R = 60 - \frac{4}{5}(128.57)$

$R = -42.86 \, \text{ kN}$

$R = 42.86 \, \text{ kN downward}$           answer
 

$\Sigma F_H = 0$

$P + \frac{3}{5}T = 40$

$P + \frac{3}{5}(128.57) = 40$

$P = -37.14 \, \text{ kN}$

$P = 37.14 \, \text{ kN to the right}$           answer