Rectangular Plate on Elastic Foundation - Analysis Application
Rectangular Plate on Elastic Foundation - Analysis Application
(OP)
Hello all. Long time viewer, first time poster here.
Has anyone successfully applied solutions for a rectangular plate on elastic foundation with free edges to analyze/design a slab on grade? My goal is to develop a MathCAD sheet to determine the maximum bending moment in a slab on grade under, for example, an HS20-44 truck loading. I have read (or tried to read) several academic papers that derive equations for deflection, slope, and bending moment at any point in a slab, given the location and magnitude of a point load - however the math seems too complex to lend itself to a practical design application. Basically, I'm looking for a reference that someone without a PhD can apply without making a year long research project out of it.
I have done some work using the solutions for a beam on an elastic foundation, including the equations in Roark's Formulas for Stress and Strain. The issue I've run into is that idealizing a 2-dimensional slab as a 1-dimensional beam is too conservative for some cases.
Note: I am not interested in using finite element analysis software (e.g., STAAD, ANSYS) for this - I have used this software many times to perform such analysis, however I am interested in using equations in MathCAD instead.
Has anyone successfully applied solutions for a rectangular plate on elastic foundation with free edges to analyze/design a slab on grade? My goal is to develop a MathCAD sheet to determine the maximum bending moment in a slab on grade under, for example, an HS20-44 truck loading. I have read (or tried to read) several academic papers that derive equations for deflection, slope, and bending moment at any point in a slab, given the location and magnitude of a point load - however the math seems too complex to lend itself to a practical design application. Basically, I'm looking for a reference that someone without a PhD can apply without making a year long research project out of it.
I have done some work using the solutions for a beam on an elastic foundation, including the equations in Roark's Formulas for Stress and Strain. The issue I've run into is that idealizing a 2-dimensional slab as a 1-dimensional beam is too conservative for some cases.
Note: I am not interested in using finite element analysis software (e.g., STAAD, ANSYS) for this - I have used this software many times to perform such analysis, however I am interested in using equations in MathCAD instead.






RE: Rectangular Plate on Elastic Foundation - Analysis Application
I was actually really proud of the work I did. Though it didn't end up being useful for the purpose it was intended for (verifying FEM results from various programs). The problem was thick vs thin plate theory, if I remember correctly.
The reference I used was AC Ugural's "Stresses in Plates and Shells". Though I don't know if this will work for your example. You might end up having to use something more like the Finite Difference Equations, which I've never done.
Another good reference is probably Roark's formulas for Stress and Strain.
RE: Rectangular Plate on Elastic Foundation - Analysis Application
--'Principles of Pavement Design' - by E.J. Yoder and M.W. Witczak (John Wiley & Sons, 1975)
--'Design of Concrete Structures' - by Winter, Urquhart, O'Rourke, and Nilson" - (McGraw-Hill, 1962)
--'Design of Slabs on Grade' - ACI 360R-92 - by American Concrete Institute (from ACI Manual of Concrete Practice, 1999)
I have ACI 360 & 'Design of Concrete Structures' (the 1972 version) myself. The latter is an excellent resource for manually figuring stresses in unreinforced slabs with a given subgrade modulus (and you could back out of that with moments) for a variety of scenarios. (I.e. single wheel load close to corner (typically critical), wheel load far from edge, and wheel load close to an edge but far from corner.)
For a pattern (wheel) loading case the book recommends the reference: 'Influence Charts for Concrete Pavements', Trans. ASCE, vol. 116, pp.49-73. 1951. By: Pickett & Ray.
RE: Rectangular Plate on Elastic Foundation - Analysis Application
RE: Rectangular Plate on Elastic Foundation - Analysis Application
http://rmniall.com
The fully-infinite spreadsheet accommodates both Winkler and fully-elastic foundations, but the semi-infinite one can handle only Winkler. Both can handle pressure loadings of any shape in any location, and both will (at your request) move the load around to find the position that maximises or minimises whatever structural response you are interested in.
However I suspect that you are looking for more complicated edge conditions and fully-finite slabs, so the "infinite" situation might not apply sufficiently accurately.
RE: Rectangular Plate on Elastic Foundation - Analysis Application
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If the OP, but only the OP, wants to contact me for the spreadsheets, my disguised e-mail address is
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RE: Rectangular Plate on Elastic Foundation - Analysis Application
RE: Rectangular Plate on Elastic Foundation - Analysis Application
RE: Rectangular Plate on Elastic Foundation - Analysis Application