Residual stresses

[Lion06]

AISC says to use 0.8EI when using the DAM, in part, to account for residual stresses and the section seeing plastic stresses/deformations before analysis tells us that it wants to.

My understanding is that the 0.8 is geared toward WF sections (since that is what is used in typical building construction). AISC doesn't give any guidance on a stiffness reduction for HSS sections. I know it would be conservative to use 0.8, but I'm up against a wall and I believe that 0.8 is unnecessarily conservative as an HSS is uniform thickness (except for the corners) and will cool much more evenly. Additionally, if you do consider the residual stresses, the tension stresses occur where it helps the section (at the corners), unlike a WF section.

Does anyone have any literature that might address this? I don't expect to find anything related specifically to the DAM, but if I could at least find something generically relating the residual stresses in HSS's to those in WF's it would be helpful.

 

[271828]

You have a very good point. However, I thought taub was for dealing with residual stresses and the 0.8 has a bit more mysterious origin. For long, skinny columns, the 0.8 plays a similar role as the 0.877 factor for column buckling. I honestly don't know exactly why it's there for stockier columns, but I've assumed it was a fudge factor to account for out-of-straightness and whatever else hasn't been explicitly accounted for.

I have never seen a residual stress plot for an HSS. I would've thought that the situation would be entirely different from that of a W-shape, though. For a W-shape, residual stresses exist because the flange tips and web mid-depth cool faster than the web-flange junction. Threfore, there is compression at the tips and web mid-depth and tension at the junction. For an HSS, it would seem that the residual stresses would be due to welding at the seam. I don't see why there would be residual stresses at teh corners other than those from the process of making the corner. These plastic stresses are transverse, though. I don't know enough about plasticity to know what longitudinal stresses should result from these. I admit to never digging into this subject or running across a paper or reference, though. If anybody has one, I'd be interested in seeing it.

For now, I think I would stick with the DAM as is even for HSS. My reasoning is that we have to deal with Ch. E inelastic buckling and elastic buckling with exactly the same equations for W-shapes and HSS columns. If there was some more favorable condition known for HSS, then it seems like there would be different Ch. E equations for those.

If anybody would know about this, it would be someone like Fred Palmer at the Steel Tube Institute. You might try to contact him.

 

[WillisV]

The 0.8 is to deal with residual stresses for general softening, the tau just added extra softening for the increased stresses in highly loaded compression members.

The 0.877 factor in the Fcr equation accounts for member out of straightness. Out of plumbness is handled in part by the K factor in the ELM and notional loading or direct geometrical modeling in the DAM.

The 0.8 is a pretty rough number, so I do not believe its revision for HSS would be warranted - I'd try to eek it out somewhere else.

 

[271828]

WillisV, I do not read the Commentary that way, but I admit that the info seems a bit sketchy to me at the moment. I need to dig up the papers and read them.

Check out the last sentence on Page 436, continuing onto Page 437. It talks about how for elasic buckling systems, 0.8 is approx equal to phi*0.877 so we end up with a strength equal to 0.8 times the "elastic stability limit." Why 0.8 is our magic number, I do not know. My guess is that it's simply to be consistent with Ch. E, which is good enough for me.

Below that, it talks about why we have 0.8*taub for stockier members.

taub is described as "similar to the inelastic stiffness reduction factor implied in the column curve..." I interpret that as meaning that we have a tangent modulus situation because we can't count the portions of the flange tips that have yielded (residual stress + P/A exceeds Fy for some part of the flanges). We need a smaller EI for larger P/A because we've lost more of the flange tips. Finally, as P approaches Fy*As, we have taub = 0.0. If we have P/A < 0.5Fy, we have no yielding at the flange tips, so taub = 1.0

0.8 "accounts for additional softening under combined axial compression and bending." This doesn't say anything about residual stresses. I think this is because EI is effectively smaller if the member is in axial compression, completely independent of whether or not we have residual stresses or yielding. For instance, the natural frequency of a column goes down if the column is in compression even using a completely elastic, theoretical solution. This 0.8 should also be a function of the axial load, but they just made it 0.8 so that it matches what they wanted for the elastic buckling "stability limit" mentioned at the top of Page 437.

I'm interested to know if you agree with this.

 

[WillisV]

My comments weren't based on the commentary, they were based on seminar notes from Don White and Larry Griffis (both on the committee that developed the provisions).

 

[271828]

I don't have any seminar notes, but the draft Stability Design Guide was written by White and Griffis. At the bottom of Page 29, they start a section on column inelasticity.

In the first paragraph, they state "The effect of these residual stresses is to induce premature yielding across the scross section, which in turn reduces the effective moment of inertia, I of hte cross section. A simple but convenient [LOL] way to account for this effect is to modify the moment of inertia I from I to tau*I where tau is a stiffness reduction factor."

They then give a couple of different tau factors, one of which is taub at the bottom of Page 30. On Page 31, they state "This equation is the original CRC parabola equation for the column tangent modulus. It may be considered approximately to include the effects of residual stresses but not include the effects of column geometric imperfections."

Two paragraphs later, they state "It is appropriate to use taub when modifying member properties for use in the DAM of a frame...and frame out-of-straightness or out-of-plumbness is considered explicitly."

From this, I am sure that taub is for modeling hte tangent stiffness.

I couldn't find an explanation of 0.8. I think it's for initial OOS (as suggested above) and/or the fact that EI is effectively lowered if an axial load is present in a purely elastic analysis.

 

[Lion06]

271828-
Any idea when that design guide might be out?

 

[271828]

No clue. Last I heard, it was out of the authors' hands and in AISC's, but that's second-hand info. Third-hand now, LOL.

 

[strucguy]

AISC is planning to release it sometime this summer. Atleast, this is what I heard from one of my friends who works there.

-strucguy

 

[271828]

LOL, ask him what 0.8 is for!

 

[dik]

It's my understanding that the residual stresses are of a 10ksi to 15ksi range and the 0.8 is a rough measure of these. Residual stresses for very slender columns have little effect.

Dik

 

[271828]

How is 0.8 a rough measure of 10 ksi to 15 ksi? Where did you get this idea? (not saying it's wrong--just curious if you have a reference I can find and read)

 

[Lion06]

I guess he's saying 10ksi out of 50ksi is a 20% reduction, hence the value of the reduced EI=0.8EI actual.

 

[271828]

I do not believe that's right and I won't until someone comes up with a stronger reference than merely noticing that 10 is 20% of 50, LOL!

I think I'm going to contact the AISC Solutions Center about the 0.8 factor because I'm convinced so far that nobody here really knows what it's for.

 

[strucguy]

I did attend a seminar on AISC DAM that was offered by Bentley couple of months back, and happened to talk to the gentleman responsible for the development of RAM Frame module. His explanation to this stiffness reduction was to account for both "residual stresses and geometric imperfections" in a member. In the case of stocky columns it is the residual stresses that account for major part of stiffness reduction. Where as, in slender columns it is the geometic imperfections that account for the major portion of stiffness reduced. But, in any case the reduced stiffness equations proposed in AISC account for both residual stresses and geometric imperfections. Again, this is not my explanation. But, you are more than welcome to comment on this. Thanks.

-strucguy

 

[271828]

strucguy,

Thank you for your answer. What I still don't understand is where the 0.8 comes from for stockier columns. According to Griffis and White's Stability Design GUide draft, taub is all that is needed for reducing EI for residual stresses, so 0.8 is still a mystery.

It is not for the reason that I speculated earlier, however--the idea that EI is effectively smaller, even for a purely elastic analysis, when the member is in compression. I realized this morning that this effect will be captured in the second-order analysis that considers P-little delta effects.

I asked four big-name AISC guys this question so far this morning and none of them knows what 0.8 is for except for the obvious case of slender columns. I also tracked down everything I could find by Nair, who developed this stuff, and haven't found anything helpful yet.

I'll get to the bottom of this!!
100000e

 

[WillisV]

For frames with slender members, the 0.8 is roughly equivalent to 0.9*0.877Pe = 0.79Pe.

For frames with stockier members, tau is like the inelastic stiffness reduction factor implied in the column curve to account for lost of stiffness under high compression loads - the 0.8 factor then accounts for additional softening under combined axial compression and bending.

It is just nice that the factor for both slender and stocky columns are close enough to use the same one.

 

[271828]

WillisV,

I've read in the COmmentary what's in your second paragraph. My question is: What is additional softening under combined axial compression and bending? I know the Comm. words it this way, but there must be an underlying physical behavior. What is it? It is not what I said before, or at least shouldn't be, because that's already in teh second-order analysis.

I agree with your last sentence. I'm starting to think 0.8 is needed for the slender column cases and has no purpose for the stockier ones...but they decided to just make it easy and keep the factor for all cases.

I have a question to the Steel Solutions Center, so hopefully they'll know what's up. If they don't, I'll try Don White.

 

[haynewp]

There is also general softening since the DAM has to be carried out under ultimate loads. This plus residual stresses are the reasons I remember the 0.8 is used. But I am not 100% sure nor am I sure why exactly 0.8 was chosen for this.

 

[271828]

haynewp,

Please help me understand your first sentence. I don't see why softening (whatever that is, exactly--presumably reduction in EI and EA) is a function of the type of load. What is the idea behind this?

Residual stresses are fully taken care of in taub--that much I am sure of, so I don't understand the second sentence either.

I'm with you on the third sentence, though, LOL.

All: I'm not trying to be difficult or abrasive here. I just really want to know where 0.8 comes from and no explanation I've heard so far makes sense.

I only know three reasons that EI can be reduced, and I don't believe 0.8 is for one or more of these.

1. Residual stresses--the elastic core is all that can be counted toward EI when the flange tips are yielded. This is *completely* taken care of by taub because it's the old CRC parabolic tangent modulus equation.

2. Reduction of EI, in a purely elastic analysis sense, due to the presence of axial compression (geometric stiffness). This is *completely* taken care of in the second-order analysis.

3. Local buckling. Presumably that's not the intention here...or is it?