# Problem 452 - Weight Supported by a Cable Which Runs Over a Frictionless Pulley

**Problem 452**

For the frame shown in Figure P-452, determine the horizontal and vertical components of the hinge force at B as it acts upon member AC.

**Solution 452**

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From the FBD of the pulley
$\Sigma F_x = 0$
$\Sigma F_y = 0$
$\Sigma M_E = 0$
$\Sigma M_C = 0$
$\Sigma F_y = 0$
$\Sigma M_C = 0$
$\Sigma M_E = 0$
$\Sigma F_y = 0$

$A_H = 60 ~ \text{kN}$

$A_V = 60 ~ \text{kN}$

From the FBD of the whole frame

$4C_V = 6(60)$

$C_V = 90 ~ \text{kN}$

$4E_V = 10(60)$

$E_V = 150 ~ \text{kN}$

From the FBD of member AC

$B_V = 60 + 90$

$B_V = 150 ~ \text{kN upward}$ *answer*

$3B_H + 8(60) = 4B_V + 6(60)$

$3B_H + 480 = 4(150) + 360$

$B_H = 160 ~ \text{kN to the left}$ *answer*

Check Through Member DE

$3B_H = 8(60)$

$B_H = 160 ~ \text{kN}$ (*okay!*)

$B_V = 150 ~ \text{kN}$ (*okay!*)