Special case in rectangular plate bending 1

[greycloud]

Greetings

I'm dealing with a case where a rectangular plate is subjected to a bending moment applied mid span of the plate along the shorter edge. I tried looking for a formula for this case but couldn't find any so hope you can help

 

[TehMightyEngineer]

Is this weak axis or strong axis bending? What's the plate size/thickness?

Maine EIT, Civil/Structural.

 

[greycloud]

here is a skech of the problem for better understanding. u can treat the plate like a thin plate.

 

[TehMightyEngineer]

Ah, so weak-axis bending. How is it supported? Cantilever? Simple span?

Are you looking for the moment strength of the plate? That's going to be the yield strength x the plastic section modulus. Equation F11-1 in section F11 of the AISC-360 specification.

Maine EIT, Civil/Structural.

 

[paddingtongreen]

Looking at the diagram, the plate will spin like crazy, there's no reaction!

If the plate is just supported at the short ends, it is as TME says, but if supported all round, it is more complex, I don't know if Roarke covers it.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[greycloud]

its clamped around all four sides actually

 

[greycloud]

im looking for the bending moment produced in the plate due to the moment described above. it is not found in roark i looked in there.

 

[rb1957]

have you looked on prex's site (xcalcs) ... see your other thread ?

Quando Omni Flunkus Moritati

 

[greycloud]

xcalcs only gives results without equations i need the equation

 

[prex]

No solution exists for your loading AFAIK in the literature.
Also I cannot visualize how you could apply such a loading in a real situation. The problem is that the distributed moment cannot produce its effect near the boundary, as rotation and moment around the short side direction are zero there.
Note BTW that also most solutions for rectangular plates have no closed form equations: these are generally infinite series solutions, where the series expansion is replaced by a calculated coefficient like β. What you get on xcalcs (for the limited number of boundary and loading conditions provided) is an approximation by a polynomial expansion: it is also an equation, complex but usable.

prex
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[greycloud]

Prex: what is the meaning of afaik?

this loading case can happen in a real situation as in a winch pulling some load while fixed to deck structure.

the effect of the moment on the edge will be a twisting moment. but all i need is equation of the moment produced in the plate.

thanks for the info about infinte series equations, those are numerical methods aren't they?

 

[paddingtongreen]

As Far As I Know.

I agree, I haven't come across one.

You haven't told us how the moment is to be applied, at the moment it appears by magic. Is it limited in width or is it full width? it it a weldment causing it or a force couple or pressure couple?

FEA is probably the best way to go.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[greycloud]

Michael: I included a diagram that shows u how the moment is applied in a previous post. it is a uniform line moment applied full width. it is due to a winch pulling a certain load causeing a couple of two line loads resulting in the moment i'm talking about. hope it is clear now.

fea is the best way but I didn't study that. and thanks for clearing what afaik means.

 

[paddingtongreen]

If your plate is clamped, and the moment is applied full width, most of it will be resisted at the edges, it will not be applied linearly across because the plate will react differently as you move away from the edges. Perhaps it would be better to say that the stiffness of the plate will be very high at the edges and much reduced towards the center. Both plates will be warped with varying out-of-plane bending across the width and therein lies the difficulty.

This is one where you can make a model from cardboard or plastic foam board and see for yourself.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[TehMightyEngineer]

I also feel finite element analysis is probably the best way to go. Such a model would be relatively simple.

Maine EIT, Civil/Structural.

 

[greycloud]

Michael: you are correct, but what i need know is an equation for this bending case.

as i said earlier fea is the best for such situation but i cant use it now.

 

[paddingtongreen]

There is no exact equation. If you think of the plate as a series of springs, the middle ones have more movement than the edge ones under a given moment. If the edges are rigidly clamped, they will have zero spring rate and all of the moment will be resisted at the sides. The question will be as to whether the winch anchor can handle all of the reaction being at the edges.

In short, you cannot apply the moment uniformly across the plate because it will not resist uniformly.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[rb1957]

"this loading case can happen in a real situation as in a winch pulling some load while fixed to deck structure." ... modelling this as a uniform distributed moment across the plate is the problem. this load would be best applied to the plate as a point moment (two points if you're getting picky).

unless, of course the winch spans the plate is is uniformly attached to the plate ... big winch or small plate ?


Quando Omni Flunkus Moritati

 

[greycloud]

sorry i didnt reply earlier but i was busy

Peddington: u can apply the moment uniformly but reactions will be nonuniform. it is not as complicated as u make it sound, there is such a case but for a circular plate which is why i cant use it.

rb: to be exact the winch is fixed over an h beam wrapped all around its sides which is in turn welded to the deck plate

 

[paddingtongreen]

@greycloud, In your case, if your diagram is correct, the frame reaches the edge of the plate which is clamped, all of the moment is attracted to those rigid points. In any case, the stiffness of your H beam frame makes a big difference.

In the circular plate case the load does not go all the way to the clamped edge and so there is warping of the plate.

Unsubscibing.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin