Slab on Grade (PCA vs. Westergaard)

[DCBII]

I'm currently designing a slab on grade for heavy industrial wheel loads. I've been reviewing ACI 360 and found that it gives the Westergaard equations and also presents the PCA load tables in the design examples. Are these two methods to be used in conjunction with each other, or can I use the Westergaard equations independently of the PCA design tables? The PCA tables must be entered knowing the wheel spacing, but the Westergaard equations are independent of wheel spacing. Why would the Westergaard equations imply that the wheel spacing does not impact flexural stresses? I'm finding that in my case the Westergaard equation (for interior slab loading) leads to thinner slabs than the PCA charts do.

Is there anyone out there who does a lot of slab design that can help me reconcile these two methods?

 

[ChadV]

Hi DCBII,

I'm not an expert on the subject but I'll give you my understanding...

My understanding is that the Westergaard solutions don't consider wheel spacing because they only include the effects of a single point load. In examples I've seen, the design stress has been increased by a set percentage to account for a second wheel (see for example, the slab-on-grade spreadsheet found here:

http://www.calculatoredge.com/index.htm).

In that sheet, they say that for a 3 to 4 foot wheel spacing, the second wheel will cause a 15% to 20% increase in stress - although I don't know what the basis is for that, so I wouldn't be inclined to take it at face value without more research.

Based on this, unless you're designing for a heavily loaded unicycle (and stranger things have happened), I would go with the PCA charts. Note also that the Westergaard equations are based on wheel load, while the PCA are based on axle load.

Hopefully this helps!

 

[ChadV]

One other note. I took the first example calculation in Appendix 1 of ACI 360 (PCA method - 22.4 kips axle load - calculated thickness 7-3/4") and did a quick calculation for a single wheel load (i.e. 11.2 kips) using the Westergaard equations as given in ACI 360 (for wheel load far from the edges of the slab). Without taking into account the second wheel, I get 7-1/4", and with a 15% stress increase to account for the second wheel I get 7-3/4" - same as the PCA method.

 

[Denial]

On my website (rmniall.com) I provide a spreadsheet for the rigorous calculation of bending moments in a slab on an elastic foundation under any combination of arbitrary pressure loadings.[ ] In fact I provide two spreadsheets:[ ] one for the "interior" case and one for the "edge" case.

You could use these to investigate the effect of multiple loads at various spacings.[ ] Results thus obtained could be used to fine-tune whatever your tables and design codes are telling you.

 

[Ron]

Use elastic layer analysis....that covers overlapping loads and provides a more realistic approach to the analysis.