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Mechanics Question: Simply Supported Beam with Load

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Feb9-12, 02:39 PM
P: 2
1. The problem statement, all variables and given/known data

A bridge is idealized as a simply supported beam AB of length L, as shown in Figure 2. A
four-wheeled vehicle of weightW now drives across the bridge. Sketch the shear force diagram
for the case illustrated, where the rear wheel is a distance a from the left support. Notice that
the two wheels are a distance d apart and the center of gravity of the vehicle is a distance d/3
behind the front wheel. Use your results to determine the value of a at which the maximum
bending moment reaches its greatest value, and find this value.

2. Relevant equations

Equilibrium equations, M(x)= ∫V(x), V(x) being shear force

3. The attempt at a solution

Drew a free body diagram of the car and bridge to find the reaction forces, one at each end and at the contact points of the car and the wheel. R1=W(1-(a+2d/3)/L), R2=W/3, R3=2W/3,R4= W(a+2d/3)/L from left to right. I then sketched a shear force diagram starting at
V(0) = -R1
V(a) = -R1 + R2
V(a+d) = V(a)+R3
V(L) = 0

I tried to use the areas under this curve (3 rectangles) and have them equal 0 and try to solve for a, but I couldn't get anywhere with that. any help/direction would be awesome.
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Feb9-12, 09:00 PM
P: 2
Never mind, got it. Same approach but more perseverance.

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