Question

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

Answer 1

Answer:

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

Answer 2

The force on the bridge at the left point of support 673040.3448 N

What is force?

Force is an external agent applied on any object to displace it from its position. Force is a vector quantity, so with magnitude it also requires direction. Direction is necessary to examine the effect of the force and to find the equilibrium of the force.

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

$mgd = 90000\times 9.8\times 29 = 25578000$ Nm counterclockwise

The gravity of the truck that is 31 m from the right end would generate moment of

$mgd = 44300 \times 9.8 \times 31 = 13458340$Nm counter clockwise

The reaction force on the left end that is 58 m from the right end would generate a moment of

$Fd = F\times 58$ clockwise

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

$58F = 25578000 + 13458340 = 39036340 \ Nm$

$F = \dfrac{39036340} { 58} = 673040.3448 N$

Hence the force on the bridge at the left point of support 673040.3448 N

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