A bridge of length 58 m and mass 90000 kg is supported at each end. A truck of mass
44300 kg is located 27 m from the left end. What is the force on the bridge at the left
point of support? The acceleration of gravity
is 9.8 m/s^2

673040.3448 N

Explanation:

Suppose the mass of the bridge is uniform distributed along its length, so the center of gravity can be treated as at the center (58 / 2 = 29 m) from the right end.

The truck is 58 - 27 = 31 m from the right end.

For the system to stay balance, the total moments must be 0. We will pick the moment point at the right end. There are 3 forces here, in order from right to left:

- The gravity of the bridge itself that is 29m from the right end would generate moment of mgd = 90000*9.8*29 = 25578000 Nm counterclockwise

- The gravity of the truck that is 31 m from the right end would generate moment of mgd = 44300 * 9.8 * 31 = 13458340 Nm counter clockwise

- The reaction force on the left end that is 58 m from the right end would generate a moment of Fd = F*58 clockwise

For the moment to stay balance, their total must be 0. In order words, clockwise moment = counterclockwise moment

58F = 25578000 + 13458340 = 39036340 Nm

F = 39036340 / 58 = 673040.3448 N