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Rectangular Plate on Elastic Foundation - Analysis Application

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.

RE: Rectangular Plate on Elastic Foundation - Analysis Application

I did something similar some years ago. Simply supported rectangular plate on an elastic foundation using Navier's solution (infinite series) in MathCAD.

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

I typically do a FEA solution.......but as a alternative: I have a spreadsheet that does that (IIRC, it was written by Alex Tomanovich (who is pretty much a spreadsheet legend in these parts)). If you look at the sources within it....they include:

--'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

Assume two crossed perpendicular beams (beam width can be proportional to the slab width) and the load applies on the cross point. Based on "beams of finite length on elastic foundation", you can derive the deflection and bending moment in the beams. You can correlate the relationship between "assumed beam width and slab thickness" considering other factors.

RE: Rectangular Plate on Elastic Foundation - Analysis Application

I have developed a pair of spreadsheets for this situation:  one for where the slab extends infinitely in all directions, and the other for a slab with a single (straight) edge.  These can be downloaded from my website
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

Since making my above post three hours ago I have been advised by my web site hosting service that my account has been suspended for security reasons.  The full text of the message they sent me is

We have detected a network attack from your domain which was completely injected/compromised, a computer connected to it is probably infected and being part of a botnet.  At this point, we can suggest you that reinstall your WordPress completely.  Meanwhile, we're suspending your account to prevent the server from attack.

I do not believe in coincidences, and my site does not normally get many visits in a day.  So I strongly suspect that this attack results, completely inadvertently, from an Eng-Tips user accessing the site in the last three hours.  This person must have a compromised computer, and should attend to it.

Meanwhile, I will endeavour to attend to my web site.  However for personal reasons this might take some time.  My apologies for any inconvenience this might cause.

If the OP, but only the OP, wants to contact me for the spreadsheets, my disguised e-mail address is
\r/m\n/i\a/l\l/4\8/*\g/m\a/i\l/.\c/o\m/
which can be made more useful by changing * to @ then removing all slashes.  (Note that the "l" character is a lower-case "L", not an upper-case "i" or a digit.)

The time is now 23:25 UTC/GMT.


RE: Rectangular Plate on Elastic Foundation - Analysis Application

Just to eliminate one suspect: it wasn't me Denial. I did go to your site for that Dynamic Buckling spreadsheet (that you were kind enough to provide) back in August......but haven't been since. (I run scans on my computer all the time anyway......famous last words. smile)

RE: Rectangular Plate on Elastic Foundation - Analysis Application

Thanks for the reassurance, WARose.  I have just been informed that the infection on the web site has been lurking for at least two months, so everyone is eliminated.  As a result all the hosting site's backups are dirty, so it looks like I have no option but to re-install things from scratch.  It will be some time before I can turn my attentions to that task.

RE: Rectangular Plate on Elastic Foundation - Analysis Application

I believe that my website is now restored to how it was a week or so ago (but hopefully without the infection).

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