Deflection in plate with load in middle of plate (5'x5')
Deflection in plate with load in middle of plate (5'x5')
(OP)
Hi,
I do not have the Roark's book...and I need to evaluate the thickness required for a 5'x5' steel plate A36 simply supported on all edges. My load in the middle is 33 kips. The maximum deflection permitted is 0.25 in. How can I evaluate the thickness required ?
What is the formula ?
Thank you for the help
I do not have the Roark's book...and I need to evaluate the thickness required for a 5'x5' steel plate A36 simply supported on all edges. My load in the middle is 33 kips. The maximum deflection permitted is 0.25 in. How can I evaluate the thickness required ?
What is the formula ?
Thank you for the help






RE: Deflection in plate with load in middle of plate (5'x5')
Have a look at this site:-
http://www
desertfox
RE: Deflection in plate with load in middle of plate (5'x5')
These formulas are only valid when the deflection is less than 1/2 of the plate thickness.
RE: Deflection in plate with load in middle of plate (5'x5')
Thank you very much Desertfox, I'm not sure if I understand how to use is it.
Steel plate: E = 2.9E+7 psi (29000 ksi) and the thickness is 1 inch.
My W = 22000 lb applied on a surface 12in x 12in in the center of the plate which is 60in x 60in.
My q = 22000/(12x12) = 152 psi
The b = 1.28 (from table 1c)
my Beta = 0.16 and alpha = 0.022
Therefore: Ymax = -(alpha)*q*b^4/E*t^3
Ymax = -(0.022)*152*1.28^4/(2.9E+7)*(1)^3 = -309E-9 in.
I don't think its a correct value. Do you see my error ?
Thank you for your help,
RE: Deflection in plate with load in middle of plate (5'x5')
BA
RE: Deflection in plate with load in middle of plate (5'x5')
I get about .35 inches.
RE: Deflection in plate with load in middle of plate (5'x5')
Can you provide the calc ?
RE: Deflection in plate with load in middle of plate (5'x5')
W = 22,000 lb
b = 60 inches
t = 1 inch
E = 29,000,000 psi
Deflection = -(.1267 * 22,000 * 60^2)/(29,000,000 * 1^3)
RE: Deflection in plate with load in middle of plate (5'x5')
Have a look at this file I have uploaded.
You need to transpose the formula if you want thickness to be your unknown and put all the other parameters in.
When its comes to "e" in the formula ie radius for the load I would just use 6".
desertfox
RE: Deflection in plate with load in middle of plate (5'x5')
ω = αPa2/D
ω = 0.01160 for b/a = 1 (length to width)
P = 33,000#
D = Eh3/12
a = 60"
D = αPa^2/0.25 = 0.01160*33,000*60^2/0.25 =5,512,000
from which h = 1.32" (thickness required to limit deflection to 1/4").
The four corners must be held down against uplift.
BA
RE: Deflection in plate with load in middle of plate (5'x5')
D = Eh3/12*(1-ν2)
i.e. h (thickness) = [12D(1-ν2)/E]1/3
h = 1.28"
You need a thickness of 1.28" to hold deflection to 1/4".
BA
RE: Deflection in plate with load in middle of plate (5'x5')
Thank you all for the help.
Its really appreciated.
RE: Deflection in plate with load in middle of plate (5'x5')
I have found the eBook "Theory of Plates and Shells" by Timoshenko & Woinowsky-Krieger SECOND EDITION
Where exactly is your formula coming from ?
RE: Deflection in plate with load in middle of plate (5'x5')
BA
RE: Deflection in plate with load in middle of plate (5'x5')
to ω = αPa2/D ?