Structural Analysis of Bridges with time-variant Modulus of Elasticity under Moving Loads (original) (raw)
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The response of a simply supported Finite Element (FE) beam model is simulated under single moving load at different velocities. The beam is discretized into small elements and strain and displacement measurements are obtained at each time step. Contrary to previous work based on a constant modulus of elasticity, here the strain measurements use a time-variant (dynamic) modulus of elasticity. A time-variant modulus influences the bridge response, being more significant at highest velocities.
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On Sensitivity of Time Step for Dynamic Analysis of Bridges under Moving Loads
In the analysis of structures under dynamic loads, selection of a proper time step has a great influence to reach exact results. In this research determination of proper time step in dynamic analysis of railway bridges under high speed moving loads is considered. Dynamic responses of four simple span steel bridges with 10, 15, 20 and 25 meter length to moving trains with speed from 100 to 400 km/h and axle distances from 13 to 23 meter are calculated considering different time steps in analysis. The results indicate that by increase in moving speed of vehicle (increase in loading speed) the length of proper time step for dynamic analysis is reduced. In contrast by increase in span length (increase in bridge vibration period) longer time steps can be used in dynamic analysis. In this research by investigation of dynamic analysis results, an equation is suggested for determination of proper time step for dynamic analysis of bridges under moving loads.
Some Observations on Bridges Dynamic Behaviour
Journal of Civil Engineering and Architecture, 2020
The paper presents rather some conclusions from large investigations over dynamic behaviour of bridges under travelling loads. There, as basic tool was applied the 3D-Time Space Method (3D-TSM) in edition proposed by present author. The method uses four-dimensional space, where besides of usual 3D space, the time is the fourth dimension. The bridge with simply supported steel girder is here modelled by means of theory for thin-walled bars (TWBs). In final calculations, solutions are obtained here on numerical way applying well known and simple Finite Differences Method (FDM). In consequence the task is brought to trivial determination of unknowns from set of linear algebraic equations. There, essential part of these equations is so called dynamical stiffness matrix (DSM). The last is additionally tested by Uniform Criterion (...) for evaluation of bridges Critical States (CrS).