Wild differences in manual and FEM calculation results (floor on grade)

[nivoo_boss]

Hello everyone!

So I'm messing around with a concrete floor. I have a point load of 60 kN acting on an area of 0,04 m². I calculated the Winkler coefficient as 9,2 MN/m³. The floor slab is 200 mm thick, C35/45 concrete.

I have a handbook for concrete floors (it's in Estonian, so no point in mentioning the title) so I tried to calculate moments in the slab using formulas from there and also modelled a slab in SCIA Engineer and applied the aforementioned properties to it.

The results are interesting: in SCIA I get a moment of around 12 kNm/m under the load in the slab and using the Westergaard formula from the handbook I get the moment as 2,8 kNm/m. That's a difference of over 4 times. In SCIA I get a bearing pressure of 5 kPa and using the handbook I get a bearing pressure of 157,3 kPa - WTF? I have double checked the units and everything seems to be correct.

Is the Westergaard model so much more different from just a FEM plate on an elastic support that I get so wildly different results or what do you think is the reason?

 

[BridgeSmith]

Sounds like your soil support under the slab is much less stiff in the SCIA model.

Have you checked to make sure the units on the deflection per force of the elastic foundation are consistent?

 

[canwesteng]

What area are you averaging the moment over to get your results?

 

[JoshPlumSE]

What area are you averaging the moment over to get your results?

That's an excellent point. One of the frustrating parts of FEM analysis of slabs is the stress risers you can get. The way we usually deal with this is that we don't design for the maximum moment shown on the plot.... But, we average out that moment over a "representative width". Kind of like the ACI "strip method" where an elevated slab is split into column strips and middle strips.

 

[TRAK.Structural]

That's an excellent point. One of the frustrating parts of FEM analysis of slabs is the stress risers you can get. The way we usually deal with this is that we don't design for the maximum moment shown on the plot.... But, we average out that moment over a "representative width". Kind of like the ACI "strip method" where an elevated slab is split into column strips and middle strips.

Agree with this.

Rules of thumb I have used in the past are to use anywhere from 2x-3x times the thickness of the slab when considering the effective width to average the stresses over.

 

[EngDM]

Agree with this.

Rules of thumb I have used in the past are to use anywhere from 2x-3x times the thickness of the slab when considering the effective width to average the stresses over.

Would you do this same 2x-3x width for a structural suspended slab modeled with strips? Typically I do my strips as 1m just to make it easy, is this not correct for cases where you have point/line loads?

 

[canwesteng]

1m is a bit arbitrary. Would you do 1ft if you were working in imperial? For suspended slabs I average over the column strips given by ACI.

 

[nivoo_boss]

In FEM I am averaging over a 1x1 m square. The given result is average. Peak was something like 17 kNm/m.

 

[JoshPlumSE]

In FEM I am averaging over a 1x1 m square. The given result is average. Peak was something like 17 kNm/m.

A 1m square for a 0.2m thick slab. Right? That seems reasonable.

And, you applying spreading out your 60 kN point load over a 0.04m² area. Right? Which mean your mesh is about 0.2m x 0.2m, right? That's also reasonable for a 0.2m thick slab....

I have to say that the best way to understand the differences is to delve more into the assumptions that the hand calc method is based on.... And, compare that to the assumptions you made in your modeling.