# Problem 446 - Compound Truss Formed Into Three-Hinged Arch

**Problem 446**

A three-hinged arch is composed of two trusses hinged together at D in Figure P-446. Compute the components of the reaction at A and find the forces acting in bars AB and AC.

**Solution 446**

From the FBD of the Whole Section
$\Sigma F_V = 0$

$\Sigma M_G = 0$

$24A_V = 18(36) + 6(60)$

$A_V = 42 ~ \text{kN}$ *answer*

From the FBD to the section to the left of D

$\Sigma M_D = 0$

$9A_H + 6(36) =12(42)$

$A_H = 32 ~ \text{kN}$ *answer*

From the FBD of joint A

$F_{AB}(\frac{3}{5}) = 42$

$F_{AB} = 70 ~ \text{kN}$ *answer*

$\Sigma F_H = 0$

$F_{AC} + 32 = \frac{4}{5}F_{AB}$

$F_{AC} + 32 = \frac{4}{5}(70)$

$F_{AC} = 24 ~ \text{kN}$ *answer*

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