Vehicle crossing a bridge problem.

Bridge which is supported beam and car is simplified to be a moving point force moving across the bridge with velocity v , as indicated in Figure 1 (see below).

The bridge spans L = 100m between the supports, is made of material with density ρ = 8000kg/m3. The driving lanes are in total 10m wide and the thickness of the bridge section is 1m with a solid cross section. Assume the bridge is a solid steel beam with a Young’s modulus of elasticity E=200GPa.

Questions:

If a vehicle of weight 1500kg has a velocity of v = 50km/h and the bridge is at rest in equilibrium shape at t = 0, determine the deflection of the bridge as function of time when:

t = 3.6s

t = 7.2s

equivalent load Figure 1: Car moving bridge (not to scale) and corresponding equivalent syst em. across a