Slab on grade - Software analysis results

[AnnaG20]

Hello,

I want to design a slab on grade for a large uniform load and poor subgrade modulus. I modeled it and the results have me confused. I tried two different thicknesses for the slab and I get larger moment and shear values for the thicker slab than the thinner slab. Shouldn't it be the opposite?

Thanks for your help!

 

[atrizzy]

How do your deflections and bearing pressures look?

 

[r13]

The thinner slab is more flexible and, as a result, the stresses are more uniformly distributed, but I would anticipate larger deflections.

 

[DaveAtkins]

If it is a uniform load across the entire slab, there should be no moment and no shear.

DaveAtkins

 

[Settingsun]

The thicker slab spreads the load better - think of a beam with a uniform load along its length.

The thinner slab doesn't spread the load as well so the ground pressure is greater under the loaded areas than the unloaded areas. Think of a beam with a varying load that is large at the supports and small at midspan - smaller moment than for UDL.

As a guide, 150mm unreinforced slab on poor ground can take about 50 kPa. 250mm slab can take about 65 kPa.

The critical loading case is different for different slab thickness. The thicker slab will need larger loaded and unloaded areas (widths) for maximum stresses.

 

[Ron]

I would be more concerned about shear at the load perimeter than bending. I will assume you mean an isolated distributed load on the slab rather than a uniform load over the whole slab. You mention a poor subgrade modulus. Do you mean a poor modulus of subgrade reaction or a poor resilient modulus? The modulus of subgrade reaction has little effect on the slab thickness as compared to its probable value. As an example, going from a 100 pci to a 200 pci is a change from weak to competent in terms of the Modulus of Subgrade Reaction, but has very little effect on the slab thickness when using typical Westergaard or Boussinesq approaches.

 

[bones206]

It does seem counter intuitive to have higher shear and bending forces in a thicker slab. I believe this is what is happening mathematically within the software:

1) The thicker slab plate elements deflect less under load.
2) The soil springs are compressed less due to the deflection being less.
3) When the software performs a static analysis of each node, the downward load force is the same, but now the soil spring reaction force acting upward is less. So summing vertical forces at the node results in a greater difference between downward load and upward reaction, and that greater difference translates to higher internal shear and bending forces in the plate element.

In more analogical terms, as the thinner slab deflects more, it receives a greater "cradle" of support from the soil below (more deflection, but greater support and lower internal forces). On the other hand, as a thicker slab deflects less, it tends to span over the soil and get less of a helping hand from the soil springs (less deflection, less support, higher internal forces).

 

[patswfc]

DaveAtkins,

In an analysis package your statement is correct, assuming that there is a uniform spring stiffness under the slab.
Using a uniform spring stiffness does not reflect reality and isn't appropriate, due to the soil continuum beyond the edges of the slab.
This results in the slab support stiffness being higher along the edges and higher again at the corners. Eurocode 7 has a method to increase the support stiffness's in these areas to try and capture the behaviour more accurately. In reality a slab on grade with a udl will see bending and shear forces, the magnitude of which will depend to the relative stiffness of the slab and the support, along with loading, etc.
I'll dig out a link and post it when i find it, for FE analysis of soil structure interaction, thats quite useful.

Regards

 

[DaveAtkins]

patswfc,

You raise a good point. I use RISA-3D, and I believe it calculates the spring constant based on the area of slab tributary to the spring. But the soil extends beyond the edges and corners, so a higher spring constant may be warranted.

DaveAtkins

 

[patswfc]

Dave,

Please find a couple of links below that discusses soil/structure interaction. The way that most software programs apply spring supports to a ground bearing slab is known as the winkler spring method. Whilst this is simple for engineers to use, it can be highly inaccurate. For example, I've seen examples were the reported bending moments in the slab is creating tension in one face of the slab, however when carrying out a more accurate analysis for the support stiffness the tension is actually in the out face of the slab!

http://homepage.tudelft.nl/p3r3s/MSc_projects/reportBreeveld.pdf

http://home.iitk.ac.in/~peeyush/mth426/Lec4_schandra.pdf