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# Width-to-Thickness Ratios (B4.1b) (Flexure)

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## Width-to-Thickness Ratios (B4.1b) (Flexure)

(OP)
I have been working on a spreadsheet to design monorail beams with cap channels.
Which My value should I use for case 16 in Table B4.1b? (Myc or Myt)
My instinct is to use the yield moment for compression (Myc) since hc is regarding the compression flange. Agree?

Also, when considering flange local buckling of the channel for weak axis bending(global), would you consider case 18 (Flange cover plates case) of B4.1b or just consider case 10 (Flange of channel)?

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

What is the code? Your question does not match the "subject".

(OP)
AISC's A360-16

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

Maybe that's the new way of calculating stress in built-up sections. In my time, fb,c = M/Sb,t. The subscripts represent "tension, compression, bottom, top", respectively. For underhung monorail, over the support hanger, the cap channel is in tension; in the span, it is in compression. Use appropriate section modulus to check the stress.

If the connection of beam-cap is designed correctly, the channel will not subject to weak axis buckling. You shall check the built-up beam for twisting/buckling concerns.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

(OP)
My questions are directed towards the width to thickness ratios.
To clarify, I am only interested in the simple span case, compression in the top flange.
I am concerned with local buckling of the flange due to weak-axis stresses. (lateral force)

I am also concerned with case 16 of B4.1b, since this determines whether the plastic moment can be reached in major axis bending. I have seen other spreadsheets use the lower of Myt and Myc in this check, which I think is overly conservative.
I was hoping I could get a second opinion on whether using the compression yield moment is conservative for this width to thickness check.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

A. See definition for My below.

B. Case 10.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

(OP)
Yes of course.
Which extreme fiber?
That is the question.

If you use the extreme tension fiber, you will get more conservative results.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

My opinion is whichever yield first. After given further thought, I think your original assessment was correct. Since we are talking about the compression phenomenon, it seems the formula is trying to capture/compare the ratio between imminent yielding and fully plasticizing of the compression element in concern. You might read the commentary below and conclude yourself. You might read professor Yura's paper, as referred in the commentary, for further clarification, I hope so.

#### Quote (AISC CommB4)

Limiting Width-to-Thickness Ratios for Compression Elements in Members Subject to Flexure.
Flexural members containing compression elements, all with width-to-thickness ratios less than or equal to λp as provided in Table B4.1b, are designated as compact. Compact sections are capable of developing a fully plastic stress distribution and they possess a rotation capacity, Rcap, of approximately 3 (see Figure C-A-1.2) before the onset of local buckling (Yura et al., 1978). Flexural members containing any compression element with width-to-thickness ratios greater than λp, but still with all compression elements having width-to-thickness ratios less than or equal to λr, are designated as noncompact. Noncompact sections can develop partial yielding in compression elements before local buckling occurs, but will not resist inelastic local buckling at the strain levels required for a fully plastic stress distribution.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

Use the minimum of Myc and Myt. I know that's counterintuitive. I've asked this question of one of the foremost experts on this -- twice -- and that's what he said.

Case 10.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

Can anybody reach out to AISC, this will be a good question for them.

### RE: Width-to-Thickness Ratios (B4.1b) (Flexure)

(OP)
Thanks 27128.
Did this expert mention why?

Also, why only consider Case 10?
Is it because the web of the channel isn't close to the extreme fibers in weak axis bending?

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