Plate Deflection 1

[891879]

I'm trying to spec a plate for a gaging process that will be simply supported at both ends. What is the formula to calculate deflection in a plate with 0 loading? The loading is so small it is negligable (approximately .25 lbs evenly distributed) and the major source of deflection will be the weight of the material itself. Also, if the formula you supply has moment of inertia or section modulus in it please provide these formulas as well along with each variables definition.

Grateful EE

 

[MrStohler]

I assume by "0 loading" you mean that there are no external loads applied to the plate. If that is true and only the weight of the plate creates a load then:

ASSUMING, a horizontal, rectangular steel plate, supported along two parallel edges that allow free rotation of the edges;
L=distance between supports
B=width of plate along supported edge
t=thickness of plate
g=unit weight of plate material (steel=0.283lb/in^3)
E=elastic modulus of material (steel=29,000,000lb/in^2)
w=uniform load on span ( =g*t*B )
I=moment of inertia ( =(1/12)*B*t^3 )
d=maximum deflection ( = (5/384)*w*L^4/(E*I) )

 

[891879]

I plugged your formulas into a speadsheet and as the thickensss approached zero the deflection decreased (somewhat counterintuitive). I desperately need the answer to this issue. Please feel free to contact me direclty at yaw@eznet.net or gyaw@yawautomation.com

 

[MrStohler]

Check your spreadsheet. You can see that I varies with the cube of the thickness and since it is in the denominator of the deflection equation, deflection will vary inversely with thickness.

 

[cyak]

The formula that MrStohler gives is the deflection at midspan for a simply supported beam subjected to uniform load. I think that the approach is correct since a "plate" supported at two parallel edges is a beam really rather than a plate. If however the linear dimensions along the span are comparable with the width of the plate it would be more accurate if instead of using E, the Young modulus you used E/(1 - n^2), where n the Poisson's ratio.

You will see that a plate, i.e. an element with width much larger than the thickness and comparable size to the span is a bit more stiff in bending than an analogous "beam", due to transverse anticlastic curvature formation....

 

[KALC]

Mr. Stohler and Cyak have provided good and correct solutions, in my opinion. I use these formulas often.

It seemes everyone is working on plate theory these last few days.