AISC check for width-to-thickness ratio for channels 1

[NNC20]

I am sizing some C-channels and checking that shapes are compact. However, the AISC Manual seems clear to me regarding W-sections. With channels, I am trying to determine what h should be. T makes sense, but for a C10x30, T is 8 and k is 1 1/16". d-2K does not equal T and does not seem accurate enough. Using d-2(t_f) makes sense, but I believe h would be a bit smaller because t_f is an average.

I think this shape is clearly compact, but I am curious as to what is normally done.

 

[r13]

See the linked blog. Link

AISC manual used to indicate a section is compact or not. If it still does, suggest to always select a compact section.

 

[JoshPlumSE]

h is defined as "the clear distance between the flanges, less the fillet at each flange". This should be the T distance in the tables.

The h/tw is not explicitly given in the manual anymore. But, if you look at the AISC Shape database (available on-line), you'll see in there.

A C9x20, for example, has a h/t of 16.8 with a T of 7.0 inches and a tw of 0.448. That should give a h/t of 15.6 instead of 16.8. Why the difference? I honestly don't know. It's a little frustrating to me, to be honest. I suppose there must be some difference between the values in the manual for T and tw and the ones used to calculate h/tw.


Note: These values aren't 100% accurate. Each manufacturer may have some slight variation. Each value represents an "average value" for the table that should be used by engineers. You can see thing when AISC give different values for design vs detailing. I suspect something similar is happening here. There is a difference in flange thickness or slope that results in them using a more conservative h/tw for the channels than we would manually calculate based on their numbers.

 

[r13]

The note was from 13th ed., it should be still on current code. However, compactness should still be checked for element subjects to compression.

Note: All current ASTM W, S, M, C, & MC shapes have compact flanges except W21x48, W14x99, W14x90, W12x65, W10x12, W8x31, W8x10, W6x15, W6x9, W6x8.5, & M4x6 (for Fy = 50 ksi). All current ASTM W, S, M, HP, C, & MC shapes have compact webs for Fy ≤ 65 ksi.

[ADD] I recall read somewhere that said, due to variation in fillet sizes, the h (AISC) used in h/t_w calculation is less than the channel width minus flange thickness, but larger than T, so that's probably why JoshPlum's example does not check out.

 

[NNC20]

Since there is variability, wouldn't it be more conservative to take the d-2(t_f) because it would make for a "longer" web, especially since we do not know if the manufacturer will be closer to T or closer to the average flange thickness?

 

[r13]

Exactly. For tapered flange, I think you may use flange thickness at the root.

 

[JoshPlumSE]

ncortes -

What's so frustrating is that no combination of what I do seems to come up with the AISC number. For that C9x20, if I use h = d-2*tf = 9 -2*0.413 = 8.17, then I get h/tw = 18.24.

Too large to match the 16.8 that AISC gives. Yes, it's more conservative. Though it doesn't truly match the letter of the code (based on the definition of h and tw).

It's almost amusing that the AISC value is essentially the average of these two values. There is likely some logic to it, but I'm not sure that we can divine it from what AISC's given us.

Thought at this point, it's kind of moot since, as retired13 points out, all of these sections are compact.

 

[NNC20]

It does seem to be somewhat important though because h/t_w is used in 360-16 Chapter G a lot to determine which equations to use.

 

[r13]

In my opinion, AISC (the committee) does not want to promote the use of channel for compression, as it is innately unstable. If necessary, use code given ratio if there is one, otherwise, be conservative. Note AISC statement quoted on my previous response holds true for sections subject to flexural bending, thus there should be no need for checking.