Problem 357 | Equilibrium of Non-Concurrent Force System

Distance AB
$AB = \sqrt{8^2 + 8^2} = 8\sqrt{2} \, \text{ m}$
 

 

$\Sigma F_H = 0$

$T = R_B \cos 45^\circ$
 

$\Sigma M_A = 0$

$2T + 6(420) = 8\sqrt{2}R_B$

$2T + 2520 = 8\sqrt{2}R_B$

$T + 1260 = 4\sqrt{2}R_B$

$R_B \cos 45^\circ + 1260 = 4\sqrt{2}R_B$

$4.9497 R_B = 1260$

$R_B = 254.56 \, \text{ lb}$           answer
 

$T = 254.56 \cos 45^\circ$

$T = 180 \, \text{ lb}$           answer
 

$\Sigma F_V = 0$

$R_A + R_B \sin 45^\circ = 420$

$R_A + 254.56 \sin 45^\circ = 420$

$R_A = 240 \, \text{ lb}$           answer