Plate Analysis
Plate Analysis
(OP)
I have a 3/8" plate that is span over a 26'x6' area and is supported every 4'3". The circumference is welded. I have a uniform load for the area at 2,200 lbs/ft or a 515 lbs/ft^2 and I also have a point load that is 4,985 lbs (there are two of them at 3' apart)
How do I go about analysis a plate for moment shear and deflection?
The formulas would really help and how the K or C factors are found.
How do I go about analysis a plate for moment shear and deflection?
The formulas would really help and how the K or C factors are found.






RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
Yes I have looked into both manuals on thos pages The load being placed is a small skid steer if that helps at all.
This system has been in service for 20+ years and there are no signs of any problems.
RE: Plate Analysis
I have information for a psi loading that k*wl^4/Et^3
k is the factor from the plate edge I tried .0834 from a question but I do not know how this applies the plate edge supports
w - load
l- longest lenght
E - 29000 ksi
t - thicknes
I got a large deflcetion that was not realistic
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
If you assume zero stiffness, you can calculate allowable loads which will be much higher- think Roark has that as well, with 1-dimensional loading. It assumes the ends are fixed for tensile forces, so you have to have adequate supports at those points.
Don't figure the loader as a "point" load, figure some way to use the actual area, or an estimate of it.
RE: Plate Analysis
for the uniform load and I calculate I = bh^3.12 isn't my b 12"? or is it 6'? if the plate spans or transfers load at the 4.33" supports?
5wl^4/384 EI
RE: Plate Analysis
Assume fixed ends: (Weld on both sides of flange fixes plate)
Mmax = 1/12 * w * L^2 (L = 4'-3") (Case 15 ASD manual)
w = unit load (typically psi or psf)
Deflection = (w * L^4) / (384 * E * I) (Case 15 ASD manual)
I = (1/12) * bi * t^3
bi = effective plate width (typically 1" or 12")
t = plate thickness
If your plate does not generate fixation at the continuous supports then I would use continuous span formulas. A lot of people like to use (1/10 * w * L^2) for moment and (.0069 * w * L^4 / (E * I)) for deflection. This is the three span condition.
RE: Plate Analysis
RE: Plate Analysis
How should I handle the load from the skid steer. do I use a point load or distribute it out of the area it is touching the ground
RE: Plate Analysis
For a uniform load and small deflection plate theory, my old Mechanics of Materials textbook has the deflection at k*wb^4/Et^3, where b is the short dimension, not the long dimension. The k factor depends on your edge conditions and may be less than .0834, which is for pinned supports.
The textbook,(Seelye and Smith) says small deflection theory is OK up to several times the thickness of the plate. With fixed supports, I'm getting deflections of 1 (for uniform load)to 2 (For 5k load) times the plate thickness, so you may be OK with small deflection theory.
Also, I'm getting bending stresses over 40 ksi for the 5k load case.
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
a=72"
b=51"
p=3.58 psi
kyf=0.464 {eq6-53}
assuming A36 steel
Fb = 0.75Fy = 27 ksi
b/t = Sqrt[Fb/(kyf*p)] = 127.5 {eq6-55}
t = 51/127.5 = 0.4" reqd plate thickness
Rather than using a heavier plate throughout to handle the concentrated loads I would add a stiffener under these two loads if possible and if they don't move.
Regards,
-Mike
RE: Plate Analysis
When calculating the bending stress what formula do you use for plate?
RE: Plate Analysis
I am going to get on a soap-box
"When the deflection becomes larger than about 1/2 the thickness, as may occur in thin plates, the middle surface becomes appreciably strained and the stress cannot be ignored. This stress, called diaphragm stress, or direct stress, enables the plate to carry part of the load as a diaphram in direct tension. This tension may be balanced by radial tension at the edges if the edges are held or by circumferential compression if the edges are not horizontally restrained. In thin plates this circumferential compression may cause buckling.
When this condition of large deflection obtains, the plate is stiffer than indicated by the ordinary theory and the load deflection and load stress relations are nonlinear. Stresses for a given load are less and stresses for a given deflection are generally greater than the ordinary theory predicts."
Now not to sound harsh or rude but you have been trying to find out online how to solve this problem since last friday. You could have easily either gone to the library over the weekend or ordered a book from Amazon.com and received it next day air this morning. (I would recommend Roark's by the way) Instead you are still trying to find out online how to solve the problem. I have been a member of this forum for 2 1/2 years and never once has someone ever flat out solved a problem for someone on here. I again suggest you take the information we have gave you and get the required information from your local library or from a book-store. You don't seem to have a very good understanding of plate theory and because of that you are trying to design something you really don't understand. It's fine not to know how to do something, we all run into that all the time and that is why this forum is so popular, but you have to be able to take the time and research it. Think of it this way. Say you just go on with the design as is. Say everything is fine for 2 years, but suddenly one day the skid-steer falls through the floor and the operator dies. When you are sitting on the witness stand and the hot shot lawyer with the PH.d in structural engineering is wearing you out about your analysis I certainly wouldn't want to say, "Well I talked to some people on a forum on the internet about it and they thought it would be ok so I went on with it.". I realize thats like worst case but the point is that you take suggestions but the design in the end falls on your sholders and is for you to understand so you better have the information at your fingertips so you can make a descision about how it should be. It drives me crazy when people just "wing" it. I will now get down from my
RE: Plate Analysis
I hope you do not feel I am taking advantage of this forum because I believe there is great knowledge to be shared here
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
RE: Plate Analysis
now that we're over that; Abutler, i think the posters are pointing you in a direction. Roark is a fabulously detailed book; somewhere in it is the solution to your problem (though probably by superposition, and maybe by approximation). have a care about using the equations if you don't understand the underlying analysis; there could be assumptions that invalidate the answers (even if they came from Roark). This problem looks quite tricky, as large flat plates with out-of-plane loads tend to be (how much membrane reaction develops?)!
several posters have suggested that the stress induced is about 30 - 40ksi, which should be good for the plate (has anyone looked at the welds?), and possibly enough untill you can calc things for yourself. presumably you don't have a simple FE program on hand ? mind you, if you want to capture the membrane action, you're either in for a lot of modelling (projecting the originally flat plat onto a surface to account for deformation), or some reasonably sophisticated software (non-linear FE); or you can say "tell heck with this membrane stuff", and be conservative by considering a pinned supported plate.
you've had several suggestions about redesigning things if you want to. no-one has suggested a thicker plate, but if you're weight insensitive, maybe its a case of why not ? other suggestions (about stiffeners (integral or separate pieces) but adopting this depends upon your faciliaty (what can you do cheaply ? what do you care about in the design ?) and after several days of discussion, you let us know that the big point loads are moving, which obviously affects things.
good luck
RE: Plate Analysis
RE: Plate Analysis