# Problem 352 | Equilibrium of Non-Concurrent Force System

**Problem 352**

A pulley 4 ft in diameter and supporting a load 200 lb is mounted at B on a horizontal beam as shown in Fig. P-352. The beam is supported by a hinge at A and rollers at C. Neglecting the weight of the beam, determine the reactions at A and C.

**Solution 352**

**From FBD of pulley**

$T = 200 \, \text{ lb}$

$\Sigma F_V = 0$

$B_V + T \sin 30^\circ = 200$

$B_V + 200 \sin 30^\circ = 200$

$B_V = 100 \, \text{ lb}$

$\Sigma F_H = 0$

$B_H = T \cos 30^\circ$

$B_H = 200 \cos 30^\circ$

$B_H = 173.20 \, \text{ lb}$

**From FBD of beam**

$\Sigma M_A = 0$

$8R_C = 4B_V$

$8R_C = 4(100)$

$R_C = 50 \, \text{ lb}$ *answer*

$\Sigma M_C = 0$

$8A_V = 4B_V$

$8A_V = 4(100)$

$A_V = 50 \, \text{ lb}$

$\Sigma F_H = 0$

$A_H = B_H$

$A_H = 173.20 \, \text{ lb}$

$R_A = \sqrt{{A_H}^2 + {A_V}^2}$

$R_A = \sqrt{173.20^2 + 50^2}$

$R_A = 180.27 \, \text{ lb}$

$\tan \theta_{Ax} = \dfrac{A_V}{A_H}$

$\tan \theta_{Ax} = \dfrac{50}{173.20}$

$\theta_{Ax} = 16.1^\circ$

Thus, $R_A = 180.27 \, \text{ lb}$ up to the right at $16.1^\circ$ from horizontal. *answer*