A particular bridge, with a length L , consists of a horizontal slab with a weig

Question

A particular bridge, with a length L, consists of a horizontal slab with a weight of 48.0 kN, with the weight uniformly distributed. The slab is held up by one support 20% of the way across the bridge, and a second support 80% of the way across the bridge. As shown in the picture, a truck with a weight of mg = 21.0 kN is driving from left to right across the bridge.

(a) Once the truck is completely off the bridge, how much force will the left support exert on the horizontal slab? We're looking for an answer in kilonewtons (kN), which is what values are given in above.
__________kN

(b) When the truck is at the position shown, where its full weight can be taken to act at a point 40% of the way across the bridge, calculate the force that each support exerts on the horizontal slab. We’re looking for two answers – the value of each of the support forces.
The force exerted by the left support is __________kN
The force exerted by the right support is __________kN

Explanation / Answer

Please ask if you have any doubt.

a) 24 KN .Because the weight of the bridge is distributed equally on two supports.

b) when the truck is in the given position we need to use Torque and Force equations.
we take torque around center of mass of the bridge.

let FL be the force by the left support and FR be the force by the right support.

FL + FR = 21.0KN + 48.0 KN = 69.0 KN .Torque equation is

FL(.3L) = (21.0 KN)(.1L) + FR(.3L) gives FL - FR = 7 KN .

solving these two gives FL = 38.0 KN and FR = 31.0 KN.

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