# Problem 448 - Beam of Three Segments Joined by Internal Hinges

**Problem 448**

A beam carrying the loads shown in Figure P-448 is composed of three segments. It is supported by four vertical reactions and joined by two frictionless hinges. Determine the values of the reactions.

**Solution 448**

From the FBD of the first and third segments
$R_1 = H_1 = 20 ~ \text{kN}$
$R_4 = H_2 = \frac{1}{2}(6 \times 10) = 30 ~ \text{kN}$
$\Sigma M_{R3} = 0$
$\Sigma M_{R2} = 0$

From the FBD of the second segment

$10R_2 + 4(30) = 14(20) + 14(20)(7)$

$R_2 = 212 ~ \text{kN}$

$10R_3 + 4(20) = 14(30) + 14(20)(3)$

$R_3 = 118 ~ \text{kN}$

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