Equation Needed
Equation Needed
(OP)
I am trying to find an equation that will give me the deflection of a plate that is held at its Center of Gravity (CG). The plate 1"x8'x12' is hung from a cable and what I am trying to figure out is the deflection. Given that the ends are free and the only weight is its own what equation can I use or manipulate others to get the oveall deflection. Needs some help. Violator






RE: Equation Needed
Curmudgeon
RE: Equation Needed
RE: Equation Needed
The closest results to your problem I have found are for a square plate, so I hope this will be sufficient for you to guess what you want.
Now for a square plate of sides a with 4 supported corners and a distributed load P=qa2 the center deflection and the deflection at mid sides are respectively:
fc=0.025Pa2/D
fs=0.017Pa2/D
where as usual D=Et3/12(1-ni2)
If the load is concentrated at the center the above deflections become:
fc=0.039Pa2/D
fs=0.022Pa2/D
The original reference for the above results is a german book published by Springer in 1924. The author is H. Marcus.
Now, by superposition, you'll find that the deflection at the corners and at mid sides (both with respect to center) are (of course the corners are now unsupported, as the same total load is used in the superposition):
fc=0.014Pa2/D
fs=0.009Pa2/D
I guess that to find the full solution to your problem with Fourier series shouldn't be too difficult, but a non negligible effort would be required.
prex
motori@xcalcsREMOVE.com
http://www.xcalcs.com
Online tools for structural design
RE: Equation Needed
Deflection = wL^4 / 8EI
which would occur at the free end.
RE: Equation Needed
RE: Equation Needed
I suggest that you look into what PREX has noted or work out a solution from plate theory.
RE: Equation Needed
f=Pa2/128D(1-D2)=0.0086Pa2/D.
So Curmudgeon, pylko and Conex can see that the beam theory underestimates deflections quite a bit (as Qshake intended to say, of course).
As always, it all depends on what Violator is looking for: a rule of thumb? Beam theory is OK. A check for measured values (different at corners and at mid sides)? Then plate theory is a must.
prex
motori@xcalcsREMOVE.com
http://www.xcalcs.com
Online tools for structural design
RE: Equation Needed
RE: Equation Needed
Ok, now I'm really curious. What are you planning on doing? Could you describe your project?
Imagineer
RE: Equation Needed
RE: Equation Needed
It should be quite easy to get it modelled by someone with finite element analysis software. The model is simple to create, and the modelled support node must be located just above the plate for stability.