Cap plate design for round HSS or pipes

[MacGruber22]

Regarding cap plate design for round HSS or pipes per AISC equations K1-11 & K1-12:

Although the 2.5 to 1 load angle model is permitted, I see no guidance in the steel manual or in design guide 24 for effectively using equation K1-12 (wall crippling) with round tube members. Firstly, it seems eq. K1-12 doesn't care whether the member has slender or non-compact walls - that confuses me (especially with respect to square or rect HSS). I guess the good thing is that there are not many standard AISC tubular shapes that are slender.

Does it make sense to unitize the resisting force over the effective arc length (based on chord length = 5tp + N) to check the crippling? I feel like this is quite conservative for non-slender walls. The values I am getting for local crippling "feel" good, but maybe someone can spot a problem if you dare to look at my excel file. Link

Otherwise, general comment is good too.

"It is imperative Cunth doesn't get his hands on those codes."

 

[KootK]

Although the 2.5 to 1 load angle model is permitted, I see no guidance in the steel manual or in design guide 24 for effectively using equation K1-12 (wall crippling) with round tube members.

I think that using this procedure for round HSS would be appropriate and conservative. For relatively large diameter HSS, the walls will present as pretty near straight and therefore analogous. For tighter diameters, the curvature of the walls will stiffen them and make the procedure quite conservative I'd think.

Firstly, it seems eq. K1-12 doesn't care whether the member has slender or non-compact walls - that confuses me (especially with respect to square or rect HSS)

With the slenderness ratios, we are considering a uniformly-ish compressed plate and a buckling mode where the buckling ripples would be on a longitudinal axis. For localized crippling, we're considering transverse ripples. I think that's why the usual slenderness parameter doesn't come into play. Apples and oranges.

Does it make sense to unitize the resisting force over the effective arc length (based on chord length = 5tp + N)Does it make sense to unitize the resisting force over the effective arc length (based on chord length = 5tp + N)

I'm sure that's sufficiently accurate. I'd probably be inclined to use the chord length 5tb + N straight up for convenience. Then, if I felt compelled to milk it for more, I'd compute the arc length associated with N and add 5tp to that as I feel that would be the most accurate representation.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[MacGruber22]

With the slenderness ratios, we are considering a uniformly-ish compressed plate and a buckling mode where the buckling ripples would be on a longitudinal axis. For localized crippling, we're considering transverse ripples. I think that's why the usual slenderness parameter doesn't come into play. Apples and oranges.

Envisioning the different controlling orientation of "local" buckling is easy enough, but understanding why they occur differently still feels fuzzy. If the cap is welded to the HSS (as it always is), how does this not restrain the local crippling? Or maybe it just forces the cripple wave some distance down the HSS length? Man...the importance of sticking with the codified terminology is critical.



"It is imperative Cunth doesn't get his hands on those codes."

 

[KootK]

If the cap is welded to the HSS (as it always is), how does this not restrain the local crippling? Or maybe it just forces the cripple wave some distance down the HSS length?

Exactly this. In fact, I'm pretty sure that the crippling provisions assume that the loaded edge is braced.

Envisioning the different controlling orientation of "local" buckling is easy enough, but understanding why they occur differently still feels fuzzy.

The trouble with all things buckling is that the math is so damn complicated that it's impractical to develop rigorous solutions except for the simplest of cases. As you know, regular Euler column buckling is itself the product of fourth order differential equations. And that's fairly simple in the grand scheme of things.

So the reality is that we are often conservatively (hopefullly) using stability results for situations much simpler than the case at hand. With that in mind:

1) Regular wall slenderness limits assume that we're looking at a nicely behaved "Bernoulli" location where the compression stresses are already distributed out nice and smooth about the section. They also assume a member of infinite length where where the two transverse edges of the plate being studied are effectively "free". Lastly, the assumption is also made that the compression stress isn't changing along the length of the member. In this case, the longitudinal ripple buckling mode will always be a lower energy condition than a transverse ripple buckling mode.

2) Crippling is sort of a local "disturbed region" check to deal with locations where the stresses haven't yet spread out. Your classic crippling check assumes that the loaded edge is braced and that the two edges parallel to the load extend off into infinity in either direction without being laterally braced. In the case that we're discussing here, matters are surely improved by the bracing provided to the plate being examined by the side walls of the HSS. In the interest of keeping things simple/tractable, we choose to ignore that.

I'm probably just telling you things that you already know here but it's the best that I can do with respect to providing an explanation or sorts.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.