# Dynamic analysis (time step)

Hi everyone

I’m analyzing the dynamic response of my bridge under a load train.

My question is that how we can define the proper time step value for a time integration analysis ?

Because in my model, I tried different time steps, and each time I found different values for my acceleration. (my acceleration was doubled when I changed my time step from 0.13s to 0.013 s)

Here is my code

Best resgards

Please have a look inside our Rolling Stock tutorial. There is a recommendation written about the time step.
https://www.sofistik.de/documentation/2022/en/tutorials/dynamics/rolling-stock/rolling-stock.html

Thanks a lot
It was really helpful, but about the time step, it is recommended :

it means that we have to divide the lowest periode of our bridge by 20 , am I right ?
(but in the example the lowest periode is not 0.1 !!, because the biggest frequency is 45Hz and I dont know how it has obtained 0.1 !!?)

and in addition, do you know where does this formula come from?
As is said the choice of step time really change my results (even doubled acceleration) and I want to be sure about it.

BEst regards,

Servus, Tofighan

in the train passage analysis, you can define the step in this way if you dont take the oscillation after passage of the train into consideration

STEP divider + total passage time

dynamic analysis is like sampling, the sampling rate is usually 20 times smaller than the lowerest eigenfrequency, in order to satisfy the stability (convergent or not especially by central differential method) and the accurancy by the numerical calculation. I suggest using uncondittional convergent methods, like Newmark’s method, and the sampling rate as 10 times smaller thab the lowerst mode, considering the cost of the calculation.

As reference ,you can also find this theory in the dynamic analysis part of the book written by Bathe Klaus “finite element method”

Best wishes
Yuan
24.04.2022

Great thank to you,
I found this expression in some other sources,

as a result the expression is reliable,

Best regards,