Roark's Formula Plate Fixed On Three Edges 1

[SteveMort]

Does anyone have Roark's Formulas for Stress and Strain? I need equations for maximum bending moment, shear, and deflection for a flat plate fixed on three edges and free on one edge.

 

[rb1957]

try googling "moody rectangular plates" ... seriously, moody did the work (for the US Corps of Eng's) back in the day and he's roark's reference, and he has more cases than roark.

btw, how loaded ? uniform pressure ??

Quando Omni Flunkus Moritati

 

[SteveMort]

It is a uniform triangular load perpendicular to the plate with the large magnitude along the fixed edge between the other two fixed edges converging to zero along the free edge.

 

[JedClampett]

Or try this:

http://www.usbr.gov/pmts/hydraulics_lab/pubs/EM/EM27.pdf

 

[prex]

You can try this one, from the first site below.

prex
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[Splitrings]

Should have all the tables you are looking for:

http://directives.sc.egov.usda.gov/OpenNonWebContent.aspx?content=18330.wba

 

[BAretired]

I think I would prefer to use a yield line analysis with a bit of conservatism thrown in. Calculation of external work is a bit messy, but not too difficult to manage given the symmetry of the yield lines.

BA

 

[cve60069]

Dear all

Great links.

I have been 'reading-up' on the behaviour of small thin-slabs under various load conditions for over a year and I think I am slowly getting 'there'. What I found surprising, given the number of enquiries there are for moments on slabs - UDL, concentrated, etc. - there was, or is, a lack of good worked examples on the internet. I have read Roarke, played with the on-line calculators and read as many books as I am to get on the subject and I could not find one good worked-example of a concentrated-load on a concrete two-way slab, let alone the load in, say, the corner. BS8110, and I am sure other codes are similar, have an excellent design method for two-way slabs under a UDL; so why is a standard-method for a concentrated load design, or a three-side supported slab design so difficult to obtain. Of all the engineer's I know (two) neither use a consistent design method and the results are not equal. Computer analysis is no good without understanding the method.

Hopefully, there will now be a deluge of worked examples thrown this way but it is hard trying to learn a method without good examples.

Great forum.

Regards

 

[BAretired]

so why is a standard-method for a concentrated load design, or a three-side supported slab design so difficult to obtain. Of all the engineer's I know (two) neither use a consistent design method and the results are not equal.

There is no standard method because the structure is highly indeterminate and is not fully defined by the dimensions and load on the plate being analyzed. Tables often consider an edge to be fixed, simply supported or free. In real plates, fixed and simple supports are rarely if ever found.

A concrete slab or wall responds to load according to the way it is reinforced. Two engineers may come up with different solutions, but that does not mean that either is wrong. There must be considerable flexibility in the way a highly indeterminate structure is analyzed.

BA

 

[JedClampett]

I own Roark, 5th Edition. Got it when I first started work, from the McGraw Hill Book Club (do they even exist anymore?).
In my opinion, it's pretty over rated. It has a lot of chapters I never use, some blatant typos and some formulae with so many variables that they're darn near unusable. It's nice to have so much information in one reference, but by it's nature, there's a lot of important background missing.
For plates, I like the Bureau of Reclamation tables by Moody. For other cases not covered there, I bought a copy of Timoshenko, "Theory of Plates and Shells." Note that both of these references provide the "native code" for Roark in a much more complete format.

 

[cve60069]

When I was a student, I attended a lecture on three-dimensional stress analysis on a slab. The lecturer gave the proof for three equations solving the indeterminate structure. Most of the math was above me at the time but I did recognise that the equations were very similar to Macaulay-theorems. I think it was Timoshenko that derived the equations.

 

[rb1957]

i suggest, humbly, that either your prof/lecturer gave a general solution that needs a lot of specific data (not generally available) to give a specific answer, or (more likely) made a bunch of assumptions to arrive at an answer; both are likely (and somewhat reasonably) to be missed by a student receiving the information for the first time.

Quando Omni Flunkus Moritati

 

[briancpotter]

JedClampett-

For what it's worth, there is apparently a great deal of variation in the different versions of Roark's, and people evidently are quite opinionated as to which ones are good and which ones aren't. I've heard good things about the 8th (current) and the 4th edition, while the 5th edition I've seen described as "best used as a doorstop". So take that for what you will.

Brian C Potter, PE

http://simplesupports.wordpress.com