How to calculate stress in slab on ground

[SilverBeam75]

Hi,

If I have a slab 6in thick on a soil with Kwinkler = 100 pci and a live load of 150 psf.

How do you evaluate the ground stress and the slab concrete stress ?

Thank you,

SilverBeam75

 

[ishvaaag]

Typically you would operate in some FEM environment. The simpler uses a modulus of subgrade reaction leading to some Winkler's spring constant for each node as pertaining to your meshing of the slab. In the second you use both the slab and ground are made of stacked solid elements. In both cases you investigate your setup for growing areas loaded by your uniform load and chart it till the charted stress in separately soil and slab reach some value that may represent the maximum for such kind of stress under such uniform load.

This way you can test the mechanical effect of application of loads at corners, edges and inwards the slab. FEM can also acommodate jointing by weaker elements or actual joints in the model.

 

[Denial]

Be a bit careful setting up an analysis exactly as you have described your problem. A slab sitting on a foundation of uniform Winkler stiffness and acted upon by a uniform pressure loading over its entirety will experience ZERO bending stresses. Bending stresses will result from non-uniform foundation stiffness, non-uniform loading, and the fact that Winkler behaviour is an even more inadequate soil-behaviour model at the edges of the slab than it is in the slab's interior.

 

[cap4000]

Try to find Westergaards formulas which uses the radius of relative stiffness. The slab stresses are radial and the pressure on the soil looks like a cone shape

 

[JAE]

Denial is correct - 150 psf uniform load on uniformly supported slab is zero stress in the concrete and 150 psf in the soil.

 

[prex]

Look in the first site below, under 'Plates' -> '(bi)Elastic foundation' -> 'Solid circular pl.' or 'Rectangular' or '(mono)Elastic foundation' -> 'Solid circular pl.'

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

http://www.levitans.com

: Air bearing pads

 

[Ron]

Well...let's add a little dead load to the soil as well, say 75 psf for a 6" slab.

 

[JoshPlumSE]

ACI released a report 336.2R-88 titled "Suggested Analysis and Design Procedures for Combined Footings and Mats."

Despite being published in 1988, it is still (surprisingly) relevant to your question. Essentially, they recommend adjusting the soil springs in your model along the corner and edge strips of the mat. This is intended to produce a dishing or cupping effect in the slab.

IMO, this is a much easier (and more practical) method of analyzing the foundation than what others have so far recommended.

 

[trainguy]

Try to get a hold of a program called "Airport" by the Canadian Portland Cement Association.

I used this in the early 90's to design slabs on grade for point loads. There may be line load capabilities as well.

A fully distributed load will not put stress into the slab, but if you can nail down point loads (such as those from a rack or other component), these usually govern the design.

tg