Maximum slenderness ratio of the individual plate of a W shape Column?

[X4vier]

Hello,

I know the KL/r<200 for the full member. But what are the slenderness ratio limits for the individual plates (flanges and web) of a W shape or built-up Shape?

I know beyond the Table 4.1 limits they become slender, but is there a top limit for that plate slenderness ratio (b/t, h/tw)?

 

[WesternJeb]

These compaction limits are covered AISC 360 chapter B. In the 2016 version, it is table B4.1a&b.

If parts of your member are slender then different failure mechanisms will apply, and this will be covered in each part of the specification.

 

[X4vier]

Yes, that is clear. But is there a Top limit to the slenderness ratio of the individual plates? web and flanges?
For example b/t<300 h/tw<300?

 

[KootK]

But is there a Top limit to the slenderness ratio of the individual plates? web and flanges?

Not that I'm aware of. Once you exceed the limits that WesternJeb correctly alluded to, you start having to do things like:

1) Downgrading your usable stresses to account for the extreme slenderness or;

2) Relying on only upon the portions of the plates that do fall within the slenderness limits.

In this sense, the portions of the plates that extend beyond the slenderness limits simply become structurally useless / ineffective.

As with kL/r<300 for tension members, one aspect of the slenderness limits on plate elements is surely their "survivability" in terms handling. At some point, your plates would just become unreasonably floppy. I just don't know what that limit would be. A good analog might be to take a look at the proportions that are typically utilized in cold formed members.

 

[JStephen]

The KL/R=200 is for columns. For the flange or web of a beam, they are supported to some extent by being connected to each other, so the KL/R doesn't apply for axial loading.
If you're cutting the beam to separate the web from the flanges, then yes, that could be a consideration for each of the individual elements.
Otherwise, you just get into the slenderness issues above.
If you're looking at forces normal to the axis of the beam (ie, crushing the web between the two flanges), that's handled by web-cripping provisions/ web yielding forces for localized loading. If you had uniform loads along the center of both flanges crushing the web, that would involve treating the web itself as a column.
I don't recall if there are similar provisions for localized loading on flange tips in the plane of the flange.

 

[X4vier]

So the web and flanges of a W shape or built-up can be unlimitedness slender plates and the equation will continue to estimate adequately their capacity?

 

[KootK]

So the web and flanges of a W shape or built-up can be unlimitedness slender plates and the equation will continue to estimate adequately their capacity?

No. Firstly, you have to satisfy one of #1 or #2 that I described above.

Secondly, if you made a web infinitely slender, it would cease to rotationally brace the flange. And that would be bad.

A better approach here might be to tell what you want to do, proportionally, such that we might then be able to comment on how reasonable that is or, possibly, suggest applicable limits based on the scale of the proportions that you are proposing.

I feel that it much goes without saying that pretty much anything will be a problem at "infinite slenderness".

 

[271828]

The AISC Spec. Section F13 has some h/tw limits for plate girders. That seems like a good place to start.

The AISI Cold-Formed Steel spec has some upper limits. See Table B4.1-1.

The issue for very large ratios is distortion of the section. The flanges might not remain parallel to each other. Like KootK was describing.

 

[lexpatrie]

There are slenderness limits for the web and flanges and for a "compact" section they don't control the design, when you have a non-compact section (say a W14x99), there are some reductions that apply that are covered in the specification. If you want to familiarize yourself with the effects, work through the calcs for a non-compact or slender section (look at the footnotes in the tables in the Steel Construction Manual), and I think the AISC design examples also contain a non-compact column. Most W shapes are compact at 50 ksi and almost all at 36 ksi. Provided you aren't talking about W6 columns and the like.

The "higher" the yield stress for elements, the more likely a local buckling limit may affect things (the equations involve the square root of (E / Fy), so with larger Fy, the lambda values get lower. If you look at older manuals they have 36 ksi yield stress tables (if they are now deleted from the Steel Construction Manual), and there are different sections involved. As we switched to 50 ksi steel, a few more sections become non-compact or slender.

Steel Interchange, and for that matter, the Ask AISC folks, can be really helpful as well.

https://www.aisc.org/modernsteel/sections/steel-interchange/

https://www.aisc.org/globalassets/aisc/manual/v15.1-companion/v15.1_vol-1_design-examples.pdf

https://www.bgstructuralengineering.com/BGSCM13/BGSCM006/BGSCM00603.htm

https://www.aisc.org/globalassets/modern-steel/steel-interchange/2008/092008_si_web.pdf

https://www.aisc.org/globalassets/modern-steel/steel-interchange/2004/2004v03_si_web.pdf

https://www.aisc.org/globalassets/modern-steel/steel-interchange/2008/062008_2008v06_si_web.pdf

https://www.aisc.org/globalassets/modern-steel/steel-interchange/2004/2004v12_si_web.pdf

https://www.aisc.org/globalassets/modern-steel/archives/2016/02/si.pdf

Regards,
Brian

 

[X4vier]

The AISC Spec. Section F13

Thank you.
I think F13 defines the TOP limits I was searching.

Thank you all for your comments.

 

[271828]

I think you'd be fine if you satisfy the F13 limits, which will probably put you at something like 232 or 260 depending what you're doing. Those are not extremely high b/t ratios. For example, the AISI limit for a stiffened element in compression is 500. I would probably start getting nervous and looking for detailed info on distortional buckling if I exceeded the F13 limits. In such cases, I'd start with the AISI commentary to B4.2 "Members Falling Outside the Application Limits."