# Problem 449 - Reactions at the Supports of a Bridge

**Problem 449**

The bridge shown in Figure P-449 consists of two end sections, each weighing 20 tons with center of gravity at G, hinged to a uniform center span weighing 12 tons. Compute the reactions at A, B, E, and F.

**Solution 449**

From Member CD
$\Sigma M_D = 0$
$\Sigma M_C = 0$
$\Sigma M_B = 0$
$\Sigma M_F = 0$

$60C_V = 30(12) + 20(6)$

$C_V = 8\text{t}$

$60D_V = 30(12) + 40(6)$

$D_V = 10\text{t}$

From the Section to the Left of C

$50R_A + 20(8) = 20(20)$

$R_A = 4.8\text{t}$ *answer*

$\Sigma M_A = 0$

$50R_B = 30(20) + 70(8)$

$R_B = 23.2\text{t}$ *answer*

From the Section to the Right of D

$50R_E = 30(20) + 70(10)$

$R_E = 26\text{t}$ *answer*

$\Sigma M_E = 0$

$50R_F + 20(10) = 20(20)$

$R_F = 4\text{t}$ *answer*