# Problem 444 - Analysis of an A-Frame by Method of Members

**Problem 444**

The frame shown in Figure P-444 is supported by a hinge at A and a roller at E. Compute the horizontal and vertical components of the hinge forces at B and C as they act upon member AC.

**Solution 444**

From the FBD of the whole system
$\Sigma M_A = 0$
$\Sigma F_V = 0$
$B_H = 4 ~ \text{kN to the right}$

$5R_E = 5.5(24)$

$R_E = 26.4 ~ \text{kN}$

$\Sigma M_E = 0$

$5A_V = 0.5(24)$

$A_V = 2.4 ~ \text{kN}$

$\Sigma F_H = 0$

$A_H = 0$

From the FBD of the horizontal member

$\Sigma M_D = 0$

$3B_V = 1.5(24)$

$B_V = 12 ~ \text{kN}$

From the FBD of member BC

$C_V + 2.4 = 12$

$C_V = 9.6 ~ \text{kN}$

$\Sigma M_B = 0$

$3C_H + 1(2.4) = 1.5C_V$

$3C_H + 2.4 = 1.5(9.6)$

$C_H = 4 ~ \text{kN}$

$\Sigma F_H = 0$

$B_H = C_H$

$B_H = 4 ~ \text{kN}$

Answer:

$B_V = 12 ~ \text{kN upward}$

$C_H = 4 ~ \text{kN to the left}$

$C_V = 9.6 ~ \text{kN downward}$

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