Roark's (7th Ed.) Table 11.4, Case 2 1

[doct9960]

Roark's Table 11.4, Case 2 is for a rectangular plate with three edges simply supported and one edge free. The sketch shows the "free edge" is along the dimension "b".

For the formulas and aspect ratio (a/b) on the 3rd column to be correct, shouldn't the sketch show the "free edge" along the dimension "a"? (just like the skecthes on Case 7 and Case 10)

I would like to hear from those who are familiar with the plate theory or those who have older versions of the Roark's book where Roark is the still the original author (not Young or Budynas).

 

[Denial]

I have 5th edition, by Roark & Young. In this edition, your case is Case 2 in Table 26 (Chapter 10). I do not understand your reference to a "third column", but the table for "beta" for a uniform pressure load is
[tt]
a/b 0.5 ... 1.0 ... 2.0
Beta 0.36 ... 0.67 ... 0.79
[/tt]
These values, and their trend, look to me to be reasonable and to reflect that the single free edge is along the "b" dimension.

(Beta is defined by MaxStress = beta*q*b^2/t^2)

 

[gr2vessels]

doct9960,
Have you seen the

http://www.roarksformulas.com

? Check it out!
cheers,
gr2vessels

 

[BarryEng]

Have a look at this site (provided by bridgebuster in another thread).

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

This will give you heaps of tables on various rectangular slabs, various support types, various loading conditions etc etc. It gives moments in each direction & support reactions (all in proportions of the span or support length).

These tables were originally developed (in the 1970's I think) using the method of finite differences. I believe the values have been verified by modern analysis methods with very good (& close) values.

Do a search on rectangular slabs (top of this page in this web site) for many types of queries on slabs, supports etc for info on previous threads.

 

[doct9960]

So what can you guys say about the formulas, plate aspect ratio, and coefficients on this Efunda plate calculator...

http://www.efunda.com/formulae/solid_mechanics/plates/calculators/FSSS_PUniform.cfm

Are they valid or not?

 

[prex]

It's OK: you can compare it with the results from the first site below, under Plates -> Simple bending -> Rectangular -> 3 supp.,1 free -> Unif.load

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[40818]

The table in Roarks 4th gives the same data as in the 7th edition, though the 7th edition has more aspect ratio's.

The data seems reasonable to me, i had a quick look through Timoshenko's plates and shells, and he (not surprisingly) covers the topic well. If you dont have the book, then if you let me know an email address (Rot13 etc) then i will copy and send the couple of pages that cover the derivations.