Allowable Compression Stress For A Rectangular Plate Column. 1

[RARWOOD]

I have a 3/8" x 7 1/2" x 1'-2" plate subjected to compression. When I look at Chapter E & Appendix B of the 9th Edition of the Steel Manual, it seems that all the provisions apply to elements supported on at least one edge such as stems of tees and beam flanges.

What I have is a solid column. It is loaded over the 7 1/2" x 1/4" area on the two ends of the plate but there is no support parallel to its 14", length.

What do I use as an allowable stress?

 

[Lion06]

just check it as a pin-pin column with cross-sectional dimensions of 7 1/2" x 3/8" and a length of 14". That shouldn't be too hard.
I am coming up with 8.93 ksi (assuming a 36 ksi plate)

 

[csd72]

Look under K1 - web crippling.

 

[271828]

StrlEIT and csd72, I think I'm gonna have to differ, or at least ask a question.

Pin-pin is correct if the two loaded ends are free to rotate, but are restrained against displacement. Does this describe your case? For all we know from the description, it could be rotationally fixed on one end and free on the other, so K=2 and KL/r=258.

csd, not sure how web crippling or even local buckling applies. I think it's just a lateral buckling problem.

 

[JStephen]

Design as a column as S-EIT says. Adjust effective length to match actual end conditions.

 

[RARWOOD]

I think may be I am just looking at the problem wrong. Section E2 states that for axially loaded compression members whose cross section meet the provisions of Table B5.1 the allowable stress is determined by equation E2-1 or equation E2-2.

A consultant I am working with asked me how my plate complied with table B5.1. I think the answer is that it complies with table B5.1 because it has no outstanding elements that can buckle locally before the full compression strength of the section is achieved. It complies with Table B5.1 because it does not have any outstanding flanges or stems and because it is a solid shape.

271828 is correct the final design of the plate depends on the K value. However determining the K value is another topic entierly.

 

[Lion06]

Well, what are your end conditions? You made no mention of end conditions, so I assumed pin-pin. Obviously, the actual k value matters. Although, I would say you would be hard pressed to get a k value higher than 1 unless you are welding it to a fixed support at the bottom and leaving it free at the top.
Also, while it may not have any outstanding elements to buckle locally, the entire plate may still buckle. That is what equation E2-1 and E2-2 are for.
I looked pretty closely at table B5.1 and I am not sure I see anything in there that I would say this plate qualifies as. Maybe it could be classified as a "flange cover plate between lines of fasteners" and use the 7 1/2" dimension as the distance between lines of fasteners, b.
Does anyone else have a different opinion?

 

[UcfSE]

I would calculate the compressive capacity equation using the buckling capacity of a uniformly compressed plate. I don't believe the AISC provides this information. You may find information about plate buckling capacity in the Salmon and Johnson text. You may also find some information in the AISI NASPEC B2.1. To keep it simple, you can use the lowest k value of 0.425 or 0.43, or calculate the k based on your conditions, perhaps using the chart in the Salmon and Johnson text. Note that k is the plate buckling coefficient, not the effective length factor.

 

[nutte]

This isn't a local plate buckling issue. The section is a rectangle, made up of a single plate. There is no local buckling. Elastic (Euler) buckling, inelastic buckling, or yielding will control. Use the equations in Chapter E of the AISC specification. This is an extremely simple problem. There is no need to make it more complicated than it really is.

 

[UcfSE]

Chapter E2 requires the compresion member to comply with B5. Since the plate is not supported on one side or two but rather is only supported at the ends, I don't see how you can say it meets B5. Therefore you would need an alternate method.

 

[271828]

nutte is right.

Think of it as if it *was* a local buckling problem. What would the buckling mode look like? You guessed it, the entire plate buckling in a lateral buckling mode which sends you to Chapter E.

There are higher buckling modes that look more like some of the mode shapes used in Table B5.1 derivations, but these buckling loads would be much higher so are of no interest.