Built-up steel beam with different yield strengths 4

I would think that should work however why not just specify 50 ksi plates?

Yes, I could just reinforce the beam with a 50 ksi WT or a 50 ksi plate, I know. This is more a mental exercise but I'm working on an office spreadsheet to do built-up beams and wanted to include this feature. Also, this would work the other way with a 36 ksi beam and a 50 ksi section welded on to it.

Maine EIT, Civil/Structural.

Whoops, typo in my original post. Third paragraph should read:

"For the cases of lateral torsional buckling and compression flange buckling I should just use the yield strength of the outermost section (the plates in this case), correct?"

Maine EIT, Civil/Structural.

Funny enough if I were going the other way I would probably just design it all as 36 ksi. haha

But I guess it would in theory work each way.

I likely would use 36 ksi for the lateral and buckling checks and see where I ended up first.

Oh, believe me I know I'm going against the grain here. In previous jobs I've always matched the yield strength of the beam to avoid headaches like this.

Maine EIT, Civil/Structural.

There was actually a pretty extensive discussion of this exact topic quite recently. I couldn't find it in 30s or less though.

TME said:

For the plastic (Zx) allowable moment I should be able to calculate the plastic section modulus for the beam and plates separately and multiply them by their respective yield strengths and then add the two moments together, correct?

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Yes, so long as the composite section remains symmetric. I typically use a wider plate on the bottom.

TME said:

For tension flange yielding I can use the Sx of the tension flange multiplied by the yield strength of the flange added to the Sx of the tension plate multiplied by the plate's yield strength, correct?

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I don't think this is correct. The beam section won't be yielded when the reinforcing plates yield at the extreme fibre (My). Alternately, if you don't jack the beam to relieve internal stress, the beam flange may yield before the reinforcing plate does.

TME said:

For the cases of lateral torsional buckling and compression flange buckling I should just use the yield strength of the outermost section (the plates in this case), correct

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This is the tricky part. Certainly, assuming 36 ksi would be more conservative than 50 ksi. Even that might not be conservative enough in all situations however. The underlying principle is that, at the development of the desired moment capacity, enough of the cross section must remain elastic that you can count on it for torsional stiffness (Iy & Cw). Two basic scenarios:

1) You jack to relieve all stresses before reinforcing. In this case, you can safely use the larger of a) 36 ksi and the combined section properties or b) 50 ksi and only the W-beam section torsion properties, assuming that the plates yield early in the load history.

2) You don't jack to relieve stresses before reinforcing. In this case, you don't know which part yields first unless you do some detailed calcs. You can safely use the lesser a) 36 ksi and the torsion section properties of the reinforcing plates alone and b) 50 ksi and the torsion section properties of the beam section alone.

For both scenarios, you could probably get more capacity by working out state of yielding in the combined section and proceeding accordingly. Too much work for routine design unless you've got a spreadsheet to help.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

KootK said:

There was actually a pretty extensive discussion of this exact topic quite recently. I couldn't find it in 30s or less though.

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I'll look for it but only found this from back in 2009:

KootK said:

Yes, so long as the composite section remains symmetric. I typically use a wider plate on the bottom.

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If it wasn't symmetric would it matter? As long as my calculation of the plastic neutral axis and the resulting Zx for the plates and beam were consistent with the single symmetric beam it should still work to sum the two plastic section modulus values, right?

KootK said:

I don't think this is correct. The beam section won't be yielded when the reinforcing plates yield at the extreme fibre (My). Alternately, if you don't jack the beam to relieve internal stress, the beam flange may yield before the reinforcing plate does.

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I'll probably just make the conservative assumption that the lowest yield strength controls. I would be surprised if tension yeilding controlled in most typical designs anyway.

I've read a lot and can't find any agreement on wither shoring to remove the stress needs to occur. Obviously deflection control needs shoring but as best I can find you don't have to shore if you're reinforcing for strength. Here's a PDF presentation from Larry S. Muir on Rehabilitation of Existing Structures where he states that shoring is not required for strength reinforcement of beams:

KootK said:

Too much work for routine design unless you've got a spreadsheet to help.

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Yep, making a spreadsheet is what caused this discussion.

Maine EIT, Civil/Structural.

Yeah, unless you remember just the right combination of keywords, it can be surprisingly difficult to dig up old threads.

TME said:

If it wasn't symmetric would it matter? As long as my calculation of the plastic neutral axis and the resulting Zx for the plates and beam were consistent with the single symmetric beam it should still work to sum the two plastic section modulus values, right?

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As long as the composite section plastic centroid coincides with the w-beam plastic centroid, you're good. Otherwise, not good.

TME said:

I'll probably just make the conservative assumption that the lowest yield strength controls. I would be surprised if tension yeilding controlled in most typical designs anyway.

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Regardless of what you use for Fy, your My calc will be incorrect unless you use the Sx of the composite section. You can't split it out into the W-Beam + Reinforcing plates like you can with Zx. The difference may not be all that significant however.

TME said:

I've read a lot and can't find any agreement on wither shoring to remove the stress needs to occur.

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You can do as you please so long as your analysis is consistent with your choice. I avoid jacking whenever possible. Once you factor in the tolerances of jacking it just so, you get diminishing returns anyhow. Thanks for the paper. That's a new one for me.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

A nearly identical scenario was covered in the Steel Interchange article of the October 2014 issue of Modern Steel Construction. The article is available at under the Archives tab.

Technically, yield strength doesn't affect (elastic) lateral torsional buckling at all. Once you get to the messy part of inelastic LTB, you're into empirical equations designed to fit curves, which I wouldn't be confident applying anything but 36 ksi across the whole cross section too without reading some kind paper with testing or at least FEM behind it. Since the point where you diverge from elastic LTB to inelastic LTB is defined by Mp (in S16 at least), I've always played it safe and matched yield to yield or designed with the weaker steel for the whole section.

Here's a riddle: for a beam designed to Mp, what's the effective Iy/Cw at capacity given that every fibre of the section is assumed to be stressed to yield? Particularly given that flange tips start off with residual compression stress?

My guess is that you must glean LTB stiffness from:

1) The stiffness of the unloading curve for the portion of the compression flange that gets it's compression reduced.

2) Eventual strain hardening of the portion of the compression flange that gets its compression increased.

3) Maybe some tidbits here and there from the original residual stress pattern.

How to assess that? Who the heck knows...


The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

Kootk - agreed all those have an impacr. Inelastic buckling is a quite bit more complex than the simple interaction equation in codes makes it seem. That's why I'd err on the side of conservatism with these calcs.

Yes, and that's why I submit that even the 36 ksi assumption may not be conservative unless you start with an unloaded section which is somewhat out of vogue these days.

Imagine starting with a 36 ksi section where the flange is stressed to 80% Fy. Now add some 36 ksi reinforcing plates. By the time that you yield the reinforcing plate, the original flange may be so far along the yield curve that it will posses no Iy/Cw of its own. In this case, I'd argue that Iy and Cw should be based on the reinforcing plates alone.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

KootK: Good points all around. You're right about the composite section plastic centroid must coincide with the w-beam plastic centroid, I hadn't considered that. Nice riddle, too. I'll have to through that one around the office and see what people come up with.

Hokie93: Nice! I'm usually on top of the AISC articles, thanks for the link. I was working nights at a job site the entire month of October and then took the lateral portion of the SE exam on the 25th. I kind of don't remember what happened during that time and probably missed a lot of my usual reading.

canwesteng: Great point and also backed up by Hokie's article. I forgot that the inelastic LTB isn't a straight line like the steel book assumes, great point. I'll definitely use 36 ksi for LTB.

In conclusion I think that I should conservatively assume the lower yield strength for all limit states. This makes the most sense as it avoids the extreme complication of figuring out flange compression, tension, and LTB for the two yield stresses. If I did indeed want maximum reinforcement then the plastic moment is the way to go and it does appear possible (if somewhat complicated) to find the actual plastic moment capacity. However, as KootK pointed out it becomes much more challenging to find the plastic moment capacity if the PNA is not the same between the 36 ksi and 50 ksi pieces. Add to this that some amount of capacity may be lost without shoring the beam up to remove dead load stresses.

Thanks for all the great advice, I'll modify my spreadsheet to use the lower Fy of the design plates and beams.

Maine EIT, Civil/Structural.

On KootK's last post. A friend insisted that if you reinforced a loaded beam, you only had an available range of the yield stress (or allowable stress) minus the stress already in the beam.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

paddington: That's what I thought at first until I read some articles on it, one being the above article I mentioned by Larry S. Muir on Rehabilitation of Existing Structures. In it he states that capacity is not reduced for existing load. In many ways this makes sense, you're not ignoring the existing load as you consider it when you check the capacity of the reinforced beam. However, you are right that the beam will be stressed more than the plate and Mr. Muir states that due to steels wonderful ability to redistribute stress through plastic redistribution the ultimate capacity of the beam will not care about built-in stresses. However, for deflections of beams and columns he does recommend considering build-in stresses.

I still haven't found any testing data on this though. I'm sure it's out there but haven't found it yet.

Maine EIT, Civil/Structural.

For me, that Larry Muir presentation has been a great find. Assuming that a column reinforced under load is as strong as a column reinforced unloaded is great news, and new to me. I can't wait to read those two papers that Larry references to see if I actually buy it.

I've been working off of a similar premise for columns for a few years now. I've found that most column reinforcement comes down to improving buckling resistance by increasing flexural stiffness. For that, as long as the original column doesn't exceed it's squash load, it doesn't really matter whether or not the axial load is shared between the original column and the reinforcing.

I'd be careful assuming that the loaded/unloaded thing doesn't matter for beams however. In Larry's presentation, he specifically references floor beams. Typically, such beams are simply supported and well braced enough that LTB is not a concern. I haven't done the paper reading yet, but my intuition is that locked in stress will still matter whenever buckling matters.

This whole business of steel being awesome at load redistribution has always given me pause for concern. A while back, I read Tamboli's book on steel connections for which Muir was a contributor. The fundamental theorem of steel connections is stated, at the very beginning, as something to the tune of "we never really know the loads but, as long as everything is ductile, it doesn't matter". Unfortunately, buckling is not ductile (more so for plates obviously). So, every time that you've got a Whitmore section in compression, that fundamental theory is bunk. Welds, also, are not terribly ductile. I believe that's the idea behind the 1.25 factor that we tack on from time to time.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

The main problem I have with refining your calculations so much, is that how well can your assumptions be matched in the field?

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.