A particular bridge, with a length L, consists of a horizontal slab with a weigh
ID: 1369658 • Letter: A
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 = 18.0 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.
(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. What is the force exerted by the left support? (write your answer in kN) What is the force exerted by the right support? (Write your answer in kN).
(c) As the truck continues to drive to the right across the bridge, what will happen to the magnitudes of the support forces? Out of the statements below select all the correct statements, assuming the truck is entirely on the bridge.
The left support force will increase.
The left support force will decrease.
The right support force will increase.
The right support force will decrease.
Both support forces will increase.
Both support forces will decrease.
Neither support force will change.
(d) At the instant the truck's weight is directly above the right support, what is the magnitude of the force the right support exerts on the horizontal slab?
Explanation / Answer
(a) Let R1 and R2 be the support forces at left and right supports respectively.
Taking the moments of the forces about the right support, we get,
R1 * (0.6L) = 48 * (0.3L)
=> R1 = 24 kN
(b) Taking moments of forces about the left support, we get,
18*(0.2L) + 48*(0.3L) - R2*(0.6L) = 0
=> R2 = 30 kN
Vertical force balance:
R1 + 30 - 18 - 48 = 0
=> R1 = 36 kN
(c) Correct statements are:
The left support force will decrease.
The right support force will increase.
(d) Taking the moments of the forces about the right support, we get,
R1 * (0.6L) - 48 * (0.3L) = 0
=> R1 = 24 kN
Vertical force balance:
24 + R2 - 18 - 48 = 0
=> R2 = 42 kN
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