Rectangular plate; two edges simply supported, two edge free 4

[IdanPV]

Hello everyone,

I am seeking assistance in finding formulas to calculate the stress and deflection of a flat, rectangular plate. The plate is simply supported along its long edges and free on the short edges, as illustrated in the attached figure.

I have explored resources such as Roark's and Timoshenko, but unfortunately, I have not been able to locate relevant information.

I appreciate any help you can provide.

 

[electricpete]

Leider Herr Paulus. Ich glaube es hat nicht so gut gegangen.

 

[dik]

Great comments for Herr Paulus...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[rb1957]

Ja, jeder ist im Nachhinein schlau

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[electricpete]

yup, hindsight is always 2020 I guess, lol.

When my mother was alive in her older years, I used to read from a German book to try to help her keep her mind sharp (and maybe mine too, though I'm not sure if that part worked at all). The book was full of stories with a mild sense of humor. It was somehow always funnier to figure out a joke made in a foreign language than it was to hear the same joke in our own native English.

 

[rb1957]

a book of german jokes (or funny stories) ? now that's a joke !!

how does it go ... two peanuts were walking down the street, one was assaulted ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[MintJulep]

Contrary to common belief, Germans can have a sense of humor.

https://youtu.be/-Z1R5vDG2Tg

 

[LiftDivergence]

You say you looked in Timoshenko, but which one???

It's right there in Theory of Plates and Shells... Section 48 starting on Page 214, and Table 47.

The table lists various b/a ratios.

Keep em' Flying
//Fight Corrosion!

 

[LiftDivergence]

IdanPV, Your error is in your problem statement. You don't have a "plate". You have a simply supported beam of "b" length, "a" width, and thickness of 2mm.

No, that is not correct.

Discussion of "thick" vs. "thin" plate has already been brought up, please see here:

https://www.eng-tips.com/viewthread.cfm?qid=498533

. I made a pretty detailed response.

All I remember is something about "plane sections remain plane" as an assumption for Euler Bernoulli beam theory.

It is somewhat similar for plates... the "equivalent" for Timoshenko is Mindlin-Reissner plate theory. Through-thickness shear deformation creates a situation where sections normal to the mid-plane do not necessarily remain normal during deflection. There is no all-encompassing "rule of thumb"

But in this case, the average side length is 1025 mm and the thickness to length ratio is then ~ 0.002. Do not treat this as a beam. You should be using Kirchoff-Love plate theory.

The information in Timoshenko should be fine.

Keep em' Flying
//Fight Corrosion!