Plate Deflection

[engpes]

I am applying a load to the center of a plate that is stiffended by beam elements (see attached sketch). Assuming the beams are rigid, how can I calculate the deflection if the load is applied at the center of the plate.

The plate is seal welded to the rigid beams. Thanks.

 

[rb1957]

if you have Roark, 7th Ed, table 11.4.8d

if not define a/b (long side/short side).

also load and thickness

 

[weab]

I agree, Roark is the best reference. However if the sketch is as simple and isolated as you indicate, I would assume each side is simply supported which would be a different table in Roark. I would treat the top flanges as capable of rotation about the top of the webs. Deflection should increase.

I realize that this sketch may not be the whole story though.

 

[BAretired]

Ref. Plates and Shells by Timoshenko and Woinowsky-Krieger.

[ω] = [α] Pa²/D

Values of [α] are give for various b/a ratios (length/width). When b/a = 2, 3, [∞], [α] = 0.1651, 0.1690 and 0.1695 respectively.

BA

 

[DHKpeWI]

A note of caution regarding the use of Table 11.4 in Roark’s.

The introduction to chapter 11 specifies that the tables are based on several assumptions, including that the maximum deflection is not more than one half of the plate thickness. If your deflections are larger than this, you will need to consider another approach. There is a table on page 452 for large deflections of rectangular plates, but the for uniform loads, not concentrated.

 

[ishvaaag]

For this setup and more in pattern replication the plate will be elastically fixed upon the beams. Hence some acknowledgement of the fixity will be required to get accurate prediction of the deflection.