The Simulation of a Train Moving Loads on a Continuous Beam With Seven Rigid Supports Located at Same Level (I)
THE SIMULATION OF A TRAIN MOVING LOADS ON A CONTINUOUS BEAM WITH SEVEN RIGID SUPPORTS LOCATED AT THE SAME LEVEL (I) Cornel MARIN Affiliation: Valahia University of Targoviste Post Adress: Bulevard Carol I, Nr. 2, Targoviste, Jud. Dambovita, 130024, Romania Email:
[email protected] Abstract. The methods used in the calculation of the static indeterminate structures as continuous beams supported by n≥3 rigid supports, are based on writing the continuity conditions of the angular deformations in the beam’s supports for all the pairs concurrent beam spans which meet in supports 2, 3, 4, .. n-1. Solving the n-2 equations, the bending efforts from the first and last support being known, one obtains the unknown bending efforts. The matricial method proposed by this work uses the MathCAD step function Φ(x-a), which allows the unitary form analytical expression of the functions: shear efforts T(x), bending efforts M(x), angular deformations ϕ(x) and displacements w(x) depending on the train moving loads (known) and on the reaction forces from the rigid supports (unknown) which is calculated in terms of displacements of supports and allows numerical simulation by changing the value of the variable distance from the beginning of the beam. Key words: continuous beams, rigid supports, MathCAD step function.
1. Introduction This paper presents an alternative way of expressing the variation of the shear force T z (x), bending moment M iy (x), transversal cross-section rotations ϕ y (x) and displacement w(x), using the MathCAD step function
Φ(x-a) [1], [2], [3], [4] having the well-known form: x
