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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.

With all the improvement in wave and hydrodynamics numerical models, the question rises in our mind that how the accuracy of the forcing functions and their input can affect the results. In this paper, a commonly used numerical third generation wave model, SWAN is applied to predict waves in Lake Michigan. Wind data were analyzed to determine wind variation frequency over Lake Michigan. Wave predictions uncertainty due to wind local effects were compared during a period where wind had a fairly constant speed and direction over the northern and southern basins. The study shows that despite model calibration in Lake Michigan area, the model deficiency arises from ignoring wind effects in small scales. Wave prediction also emphasizes that small scale turbulence in meteorological forces can increase error in predictions up to 35%. Wave frequency and coherence analysis showed that both models are able to reveal the time scale of the wave variation with same accuracy. Insufficient number of meteorological stations can result in neglecting local wind effects and discrepancies in current predictions. The uncertainty of wave numerical models due to input uncertainties and model principals should be taken into account for design risk factors., Comment: This paper has been withdrawn by the author due to a crucial sign error in equation 1