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Re: Question about Modified Westergaard's formulae

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Look for , "Stresses in Concrete Pavements Computed by Theoretical Analysis" 
by H.M Westergaard, printed in "Public Roads" published by U.S. Department of 
Agriculture, Bureau of Public Roads, Vol. 7, No. 2, 1926.   

I don't have a copy, but it is referenced in Roark's "Formulas for Stress and 
Strain".  Roark adapts Westergaard's formulas in the section on flat plates.  
The 6th edition was published in 1989 by McGraw-Hill, the author of the 6th 
edition is Warren C. Young.

Roark's use of Westergaard's method seems to be for structural flat plates.  
My interpretation of your request is that you are looking for an analysis 
method for a plate on an elastic foundation, as an extension of Terzaghi's 
beam on an elastic foundation analysis.  Someone else may know of a good 
foundation analysis text that covers that.   

Nels Roselund
Structural Engineer