how to develop influence surfaces for a simply supported one way slab

[BeFEA]

Hi everyone,

I want to find the function f(x,y) that represents the values of influence surface (for, let's say, bending moments at mid-span) of a simply supported slab. The slab is supported only on two edges (one way slab). After I have f(x,y), I will be able to calculate the slab for moving loads located at any position.

I made a research in the literature and found rather complicated formulations for slabs supported on 4 edges or even 3 edges. I believe that my situation (with only two edges) is simpler to formulate, but I can not find a simple and ready to use reference.

Can you help me with that? Do you know of any book, paper etc. dealing with influence surfaces on simply supported one way slabs? I would prefer an analytic solution, as the Finite Element solution would top my purpose of solving this problem. However, suggestions for simple application of FEM would be also welcome.

Thank you in advance!

 

[ThomasH]

Hi

If I understand the problem correct, is it not basically a beam? If so, it should be fairly straightforward to find the appropriate function f(x).

But if you want to include the load distribution in the y-direction if will be more complicated.

Or is the idea to make a more general function.

Thomas

 

[BeFEA]

Hi Thomas,

yes, I would like to include the effect of load distribution in the y-direction. I think I made something using the Finite Difference Method in Excel, but I have not finished it. I am having trouble modelling the boundary conditions for the free edge, but I think I am on the right way. Does anyone have a good tutorial/paper/book on applying the finite difference method for the analysis of plates?

Best regards,
Brisid