Base Plate Design w/ Large HSS Member 2

[jake1ryan]

Hello all. I've been working on base plate design using the 13th Ed. for HSS square tubes and round steel pipe members with axial compression loading only. I understand the adjustments of the m and n for the cantilevered projection of the plate, but how do I check the plate stresses occurring within the HSS member?

When the member is relatively small (HSS6x6x1/2 w/ 14"x14" base PL), the cantilevered projection controls and the plate thickness is determined by
checking a 1” strip. My problem is when the member becomes larger
(HSS12x12x1/2 w/ 20"x20" base PL), the moment from the plate bending over the center span is greater than the moment on the cantilevered projection when using a 1" strip. Technically, for the correct design, I need to do a yield line analysis, but that will be difficult and very time consuming.
My questions are, what is the best way to design for this without performing a true yield line analysis? Is there an easier way or simplified equation that takes into account the plate bending over the center span?
I'm sure I can use the 1" strip design over the center span and design it with one-way bending, but it will yield fairly conservative results. Any help would be greatly appreciated.

 

[271828]

Well, you answered your own question: Yield line analysis. If you're fluent at it, that's about a half a page and 10-15 min. If you're out-of-practice, then you're right: much longer.

If I only had a handful of these, I'd just use the 1" strip method like you're proposing. It's like a little simple-span beam with cantilever on each side. If it's 1/4" or 1/2" thicker than it needs to be, then so be it.

If I had a crapload of these, I'd probably resort to a Black Box FEA solution like RISABase.

 

[271828]

This is NOT guaranteed. I solved for it quickly just so you ahve something to compare with:

treq = B*sqrt(fp/(8*phi*Fy))

where
B = HSS dimension, in.
fp = bearing pressure, ksi
phi = 0.9 for bending
Fy in ksi

For an HSS12x12 with fp=2ksi, I get 1.05" required thickness.

AGAIN, for information and comparison use only.

 

[MikeDB]

You didn't say if your base plate is supported on anchor bolts or bearing on concrete, but either way if your only loads are axial compression, won't the maximum stress always be outside the HSS?

 

[271828]

Mike, not necessarily. Imagine an HSS12x12 with 13" square base plate. The cantilever distance outside the HSS is very small.

 

[csd72]

jake1ryan,

under the HSS the plate is stiffened by the HSS walls that are perpendicular to the bending line effectively giving you two T-beams.

google'rectangular hollow section connections and you should find an australian research paper on this exact thing (with yield line or FEM resultas to back it up).

 

[271828]

csd72, keeping in mind that I just withdrew my application for a search and rescue crew, do you have the name of that paper or the authors? I googled it and some other names and didn't find it.

 

[csd72]

I will see if I can find it.

Have you looked at the AISC Hollow sections connections manual?

 

[jake1ryan]

csd72,

I also couldn't find it and I would be very interested in reading it.



As far as this topic goes, there are very few sources that address it, probably due to the rarity that the column would be large and the baseplate would be slightly larger. From what I do know about yield line theory, it would be the best solution, but as for me, I have never done a yield line analysis. I did contact the AISC Solutions Center and I just received a reply. They suggested two options. The first was to modify the 'internal check' parameter used for bases of W-shaped columns. I've looked into that, and from AISC Design Guide 1, it specifically states to ignore the lambda coefficient when dealing with HSS and pipe members. Therefore you would have the n' value to compare to the m value. If the column was large enough, the n' value could control. The other suggestion was to look at Roark solutions for formulas for flat plates. This could help if I knew where to find Roark's work on flat plates (I'm new to engineering and I don't recall discussing Roark in school). I've also looked at somehow using the equation for cap plates, but that doesn't work because it is concerned with one-way bending. I do have a copy of the Hollow Structural Sections Connection Manual and I've done some quick skimming in it, but I could not find much help on this topic. Because I only have a handful of these (5), I will most likely take your advice, 271828, and just design it with a 1" strip and if its a 1/4" thicker, so be it.

Like I said earlier, I still would like to know how to do a correct yield line analysis on it, therefore that research paper would be good to have. Thanks for the replies. If I find any other info, I'll be sure to post it.

 

[271828]

From CSD72: "Have you looked at the AISC Hollow sections connections manual?"

I just did and didn't see anything helpful. Very disappointing that nothing made it into that Manual.

From jake1ryan: "The first was to modify the 'internal check' parameter used for bases of W-shaped columns. I've looked into that, and from AISC Design Guide 1, it specifically states to ignore the lambda coefficient when dealing with HSS and pipe members. Therefore you would have the n' value to compare to the m value. If the column was large enough, the n' value could control."

WOW!!! I need to dig in and find out how the DG1 authors got that! Not saying that I think they're wrong, but the yield line patterns are TOTALLY different for the Murray-Stockwell lambda pattern stuff for W-shapes and the interior of an HSS.

I'd say go with the one-way and just let it be thicker! I'd appreciate it if you'd let me know how the treq from my YLA equation compares to what you get.

 

[jake1ryan]

271828,

For the DG1, see the last sentence in section 3.1.3.

Also, I would be interested in knowing how to do a YLA for this situation. I really don't know where to start. Any good references? Thanks.

 

[271828]

jake1ryan, I see "The lambda term is not used for HSS and pipe." Still, this means that n'=sqrt(d*bf)/4, I assume. I don't see how this makes any sense. The Murray-Stockwell pattern is totally different.

Good references? A lot of concrete books have sections on YLA. It is really very easy after you get the hang of it.

For this problem, the only realistic YL pattern looks like "X" through the middle of the HSS, with yield lines also under the HSS walls. Like a X with a square around it with every line being a plastic hinge.

If you assume a virtual displacement at the center of the plate, Delta, the external virtual work done is fp*B*B*Delta/2. The 1/2 is because average distance fp acts through is Delta/2. The four triangular panels are assumed to remain rigid and in this case are surrounded by plastic hinge. fp uses LRFD factors to match the phi I talk about in the next paragraph. ASD can be used also.

The internal virtual work is the design plastic moment, phi*mp in kip-in./in., times the length parallel to the moment's axis (in this case the HSS dimension times two because there are plastic hinges along the HSS wall AND at the other two sides of the triangular panels) times the angle that the moment acts through. The angle is Delta/(B/2) assuming small angles. Remember there are four panels.

Set the internal virtual work equal to the external virtual work and solve for treq. That's all there is to it in this case.

This stuff is really so easy that any steel guy needs to have it down cold, IMO. I worked this problem earlier in no more than 10 min. and a half a page.

The only downside to YLA in general is that there is no indication of deflection from the virtual displacement calcs. IF deflection is needed, and it sometimes is, then a FE model of the part is usually very fast to construct and use to calc deflection. FE models are, of course, extremely convenient for getting deflections, but are very difficult to interpret for strength. YLA fills in that check nicely.

 

[jake1ryan]

Greatly appreciated ... thanks for the help!

 

[csd72]

I think this is the link:

If not it is somewhere on this web address

http://www.civil.usyd.edu.au/publications/r827.pdf