Compact vs Slender and Non-Slender 1

[Rocks1]

Can an axial compression member be slender and the same member be compact in flexure? Or once it is slender is it automatically non-compact or considered a slender element?

 

[271828]

Sure.

In the AISC Specification Table B4.1a, compare b/t to lambda_r to determine if the element is nonslender or slender for axial compression. This will determine what part of Chapter E is used to compute the axial strength.

Then go over to Table B4.1b and compare b/t to lambda_p and lambda_r to determine if the element is compact, noncompact, or slender for flexure. This will determine what part of Chapter F is used to compute the flexural strength.

An example of a section that is slender for axial but compact for flexure is a Gr. 50 W16x26 (among many others). In Table 1-1, there's a "c" footnote on W16x26 indicating it is slender for compression. h/tw > lambda_r from Table B4.1a. However, there's no "f" footnote. It's compact for flexure per Table B4.1b.

 

[JoshPlumSE]

Yes, there are different code sections to determine the element of a cross sections slenderness depending on whether it is stressed from axial compression or flexure.

Therefore, when I'm calculating the flexural strength, I base it on the slenderness classification of elements in flexural compression. Similarly, when I look at compressive strength, I base those calculations on the classification of elements in axial compression.

It's a little weird to think about. But, that's the way it is.

 

[ProgrammingPE]

The flange and web will have separate limits so you need to check them both.

I'll show you the check for a W12x14 with 50ksi steel, which has a web that is Slender for compression and Compact for flexure.
_________________________________________________________________________
FLANGE CHECK:
Per Table B4.1a:
lambda_r = 0.56√E/Fy = 13.5 (Compression Slenderness Limit - I-Shape Flange)

Per Table B4.1b:
lambda_p = 0.38√E/Fy = 9.2 (Flexural Slenderness Limit for Compact - I-Shape Flange)
lambda_r = 1.0 √E/Fy = 24.1 (Flexural Slenderness Limit for NonCompact - I-Shape Flange)

bf/(2*tf) = 8.82, so flange is Nonslender for compression and Compact for flexure

__________________________________________________________________________
WEB CHECK:
Per Table B4.1a:
lambda_r = 1.49√E/Fy = 35.9 (Compression Slenderness Limit - I-Shape Web)

Per Table B4.1b:
lambda_p = 3.76√E/Fy = 90.6 (Flexural Slenderness Limit for Compact - I-Shape Web)
lambda_r = 5.70√E/Fy = 137 (Flexural Slenderness Limit for NonCompact - I-Shape Web)

h/tw = 54.3, so web is Slender for compression and Compact for flexure


Structural Central

http://www.structuralcentral.com

http://www.youtube.com/channel/UCOj2mXXf3ZbZtgxTc6BtkGg

 

[KootK]

We had a very interesting, recent discussion about this here: Link. That thread was in the context of the Canadian steel code but all of the important bits should be germane to this thread.