# Mechanics Question: Simply Supported Beam with Load

by Sarang490
Tags: bending moment, bridge, engineering, mechanics, shear force
 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. http://i43.tinypic.com/11ry5us.png 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.
 P: 2 Never mind, got it. Same approach but more perseverance.

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