downward force?

Question

As a truck moves across a bridge, the downward force due to its weight
(a)acts against both supporting piers
(b)is parallel to the upward forces exerted by the piers
(c)remains equally divided between the two piers
(d)is parallel to the weight of the bridge itself
please explain how u got the answer.

the answer doesnt have to be a,b,c, or d it can be a and b or a, b , and d menaing the answer is each letter that forms a correct statement.

Answer 1

a) This is the answer and can be modeled using torque
b) Is not the answer unless the bridge is exactly horizontal
c) is proportional to the distance it is from each pier
d) not exactly correct since the weight of the bridge and the truck will be pointing to the center of the Earth. Since the bridge is distributed, it can be approximated as a single force vector at its center of mass. When the truck is directly over the center of mass the vectors will be parallel.

j

Answer 2

You can consider this to be a series of separate Statics questions. Every ME just loves CE stuff, heh. Anyhow, consider the truck to be two point loads (or even one) and then determine how they interact with the bridge at different points. What you need to keep in mind is that both the Shear and Moment forces must balance. In other words, if the truck is very near one support, it will support almost the entirety of the trucks weight. When the the truck is in the middle, and only then, will the supports share the weight equally. The force exerted by the piers/supports may be assumed, under ideal conditions, to act opposite the downward force of the truck due to gravity (which would be parallel). Because the weight of the bridge and the weight of the truck both depend on gravity, they may be assumed to act in the same direction (parallel) as well. I recommend you draw a the appropriate Shear and Moment diagrams to familiarize yourself with this concept.

Edit: I guess I was short on explanation. OK, it's like this. When you consider the moment/torque on the supports you see that they cannot share the load of the truck equally at all times. Check it out: Say the truck exerts a force of 2 Newtons down, we will neglect the bridge's weight for now. If the supports both exert and upward force of 1 N, what do we have? Well, when the truck is at the left most support (I am using left and right to keep it easy) you have a net force of -1 N acting there, but it does not create any toque because the torque arm is 0m. The other support, while it balances the vertical forces, creates torque because (say it is a 100m bridge) you now have a 1 N force acting with a 100 m torque arm. The bridge would then rotate. . . which, obviously, it doesn't. So, if the truck is directly over one support, that support will receive all of the trucks weight and exert and equal and opposite force in this idealized instance. If the truck is in the middle, both supports are equal and the resulting moments balance. Supposing the truck is 3/4 of the way across you need to pick a point to balance the forces and moments and then have a look. I choose the near side. So, you have the support force exerting a moment CCW and the truck exerting a moment CW. The truck is 2 N * 75m and the support is R * 100m. Because the moments must be equal and opposite in this instance, you may set them equal to one another and calculate the reaction force at the far support (R = 2N * .75 = 1.5 N) and thus the result at the near support based on the fact that the two supports and the truck must sum to zero in the vertical direction (the near support, therefore, is .5 N). Does that make sense at all? I apologize for the spelling and grammar, I am a bit tired.