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Extra resources for Beam Dynamics Issues for 1 TeV Linear Collider
1994), along with various integration schemes; and (3) the bk04-001 December 2, 2005 9:20 Vehicle–Bridge Interaction Dynamics Introduction bk04-001 17 Fourier transformation method (Green and Cebon, 1994; Chang and Lee, 1994). One essential feature with the VBI problem is that the number of vehicles acting on the bridge is time-dependent. The more the number of vehicles simultaneously acting on the bridge, the higher is the level for the vehicles to interact with the bridge. , the contact point positions, one feasible approach is to eliminate the DOFs of the vehicles not in direct contact with the bridge on the element level by the method of dynamic condensation (Yang and Lin, 1995).
It can be conveniently applied to cases involving a series of moving loads. The impact formulas provided by most current design codes are not consistent in physical units and lack a solid theoretical basis, of which the application should not be extended to bridges traveled by vehicles at high speeds. A more rational approach is to relate the impact factor, which is nondimensional, to the speed parameter, which is also nondimensional, deﬁned as the ratio of the driving frequency of the moving vehicles to the vibration frequency of the bridge.
2. Based on the analytical solution given in Sec. 2, impact factor formulas for the midpoint deﬂection and bending moment of the simple beam will be presented in Secs. 4, respectively, followed by the impact formulas for the end shear force in Sec. 5. The solution presented in Sec. 2 will be expanded to deal with the case of a simple beam under the passage of a train in Sec. 6, by modeling a train as the composition of two subsystems of wheel loads of constant intervals, with one subsystem consisting of all the front wheel assemblies and the other the rear assemblies.