effect of rectangular plate width on buckling resistance 1

[greycloud]

Greetings everyone

I was looking for the buckling equation of rectangular plates on supports and found bryans plate buckling equation. what i find to be strange is that increasing the width decreases the buckling strength. Take as an example a plate fixed vertically with one of its shorter edges fixed to the ground with the opposite edge loaded and the other longer edges being free; it is common sence here that increasing the width of the plate will increase the amount of compressive load it can handle. Hope someone can clear this confusion.

Thanks in advance

 

[Denial]

I've never even heard of Bryan's equation before, so I had to ask Uncle Google.[ ] Found it at equation 4.1 in

http://www.ce.jhu.edu/cfs/cfslibrary/SSRC Guide 2009 Ch 4 plates Schafer version.pdf

If this is the equation you are referring to, it only makes sense if b is the plate dimension perpendicular to the load direction. This interpretation is supported by the heading of the section of the document:[ ] "Long Rectangular Plates".[ ] I take "long" to mean "infinitely long".

Happy to be contradicted by anyone with more knowledge than my off-the-cuff view of Uncle G's offering.

 

[wadavis]

Denial, you have the right of it.

The equation referenced assumes the plate is tall enough that it does not behave as a short or intermediate column. On page 6 of the referenced document you'll find the different k-values for possible edge conditions, with 0.425 or 1.277 being appropriate in your case.

For further reading on buckling I recommend "Guide to Stability Design Criteria for Metal Structures".

Ward Davis
E.I.T.

 

[greycloud]

Denial: thanks man but this equation is not restricted to infinite plates. it is used in many actual applications.

Ward, what is the ratio of a to b to say that a plate is long or medium or short or a wide plate. do such plates have different equations

 

[JStephen]

Refer to the link posted above, effect of length is discussed on the following page.
Note that both edges free is not discussed, it is just a column then.
Note that this is elastic buckling, and actual strength of such a plate may be limited by other factors.
Some of the elastic buckling solutions can be quite a ways off from reality, so try to confirm by other sources if possible.

 

[greycloud]

JStephen: by free edges here u mean those parralel to the compression direction?
can u mention a reference that supports what u said about this case being treated like a column.

 

[JStephen]

If you have a flat plate, loaded at both ends and free on the other two edges- the plate could buckle as a column, refer to column buckling derivations for that, in particular, I think you'll find there's no assumptions made that would exclude a plate loaded like that from buckling like a column. The only issue is whether there would be some other form of buckling that resulted in a lower allowable loading, and I don't see that that would be the case.

 

[greycloud]

what about this factor 1/(1-v^2) which makes a difference. as compared with beams for example it can add 10% more rigidity

 

[Denial]

The 1/(1-v^2) factor appears all the time in formulae for plate bending.[ ] Consider a thin beam that runs in the X direction, bending downwards in the XY plane (ie deflecting in the Y direction).[ ] The beam will have positive X strains in its lower face and negative X strains in its upper face.[ ] These X-direction strains induce Z-direction strains via the Poisson effect.[ ] These Z-direction strains cause the beam's cross-section to "bow" slightly in the YZ plane.[ ] If the cross-section was originally rectangular (and bending about one of its principal axes) then this effect will change the cross-section's shape to that of an isosceles trapezium.

Now, instead of bending a thin beam, bend a strip of plate.[ ] The fact that the Z dimension of the member being bent is now significantly large hinders the ability of its cross-section to take up the trapezoidal shape.[ ] This inability manifests itself as an increase in the bending stiffness.[ ] Hence the 1/(1-v^2) factor.

Your recent plate-related questions it this and other posts suggest to me that you are presently climbing a steep learning curve.[ ] Take care.

 

[JStephen]

Good point, greycloud, I assume for long slender columns, you could incorporate that factor into the derivation and get a minor increase in allowable stress as well. For shorter columns, maybe not.

Does the actual plate in question have both long edges free or not?

 

[greycloud]

Nicely said DEnial and i'll make sure i keep everyangle covered while learning.

Jstephen: this means that the usual formula for column buckling can't be just used for plates without modification. the plate in my the case i'm talking about is free on both long edges

 

[JStephen]

That simplifies things, forget Bryan's equation. The additional stiffness effect can be conservatively ignored (it should slightly increase buckling strength), and you can use AISC or other column buckling formulas.