**Problem 441**

the structure shown in Figure P-441 is hinged at A and C. Find the horizontal and vertical components of the hinge force at B, C, and A.

**Solution 441**

From the FBD of member BC
$\Sigma F_V = 0$
$\Sigma M_A = 0$

$C_V = B_V = \frac{1}{2}(20)$

$C_V = B_V = 10 ~ \text{kN}$

$\Sigma F_H = 0$

$C_H = B_H$

From the FBD of Member AB

$4B_H = 3(10) + 4(10)$

$B_H = 17.5 ~ \text{kN}$

$\therefore C_H = 17.5 ~ \text{kN}$

$\Sigma F_H = 0$

$A_H = B_H$

$A_H = 17.5 ~ \text{kN}$

$\Sigma F_V = 0$

$A_V = 10 + 10$

$A_V = 20 ~ \text{kN}$