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Instanteous Center of Rotation Help

Instanteous Center of Rotation Help

Instanteous Center of Rotation Help

(OP)
I was comparing Blodgett's method for analyzing stress in a weld to determine capacity compared to the AISC tables for a weldment group.

I get a large discrepancy. This isn't for a job or anything, just something I was doing on the side when bored. Anyone else that's more familiar with this can point out what's wrong?

I made a mathcad sheet for blodgett's method and did a quick check using the AISC table at the bottom and compared the two. attached

whatever is wrong I don't see it. Is it Jw? not sure


Thanks

RE: Instanteous Center of Rotation Help

(OP)
Oh, and blodgett's example is for a double angle but it still works for a single angle (multiplied by 2 for stresses) as far as I could tell. Also, the extra torsional moment caused by the double eccentricity (Lt) doesn't increase the stress very much.

I should have set Lt=0

attached with Lt = 0

RE: Instanteous Center of Rotation Help

The instantaneous center of rotation method is a plastic method, whereas Blodgett's method is elastic. The AISC verbage in the manual states that the elastic method is simple but extremely conservative since it neglects weld ductility.

RE: Instanteous Center of Rotation Help

I almost agree with sbissteel. Both methods are instantaneous center of rotation and I believe that both are elastic. The only difference is that Blodgett's method is linearly elastic and the latest AISC method is non-linearly elastic to reflect the latest research regarding force-displacement relationships for welds.

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.

RE: Instanteous Center of Rotation Help

(OP)
So the Jw factor would be the elastic section modulus. If I calculated the plastic section modulus of the weldment and plug it into the blodgett's, I should get similar answers, no?

RE: Instanteous Center of Rotation Help

No, KootK is right; "plastic" was not the best word to use. The tables are made assuming a deformation at the highest stressed portion of the weld, and the remaining portions of the weld (they recommend 20 portions minimum) are included with their respective strengths assuming this deformation. It requires iteration to come up with the correct solution, and is pretty tough to do manually, hence the tables.

RE: Instanteous Center of Rotation Help

I believe IC method is a plastic stress distribution. The AISC manual talks specifically about taking advantage of the ductility of the welds.

RE: Instanteous Center of Rotation Help

(OP)
I see. Do any of you know where there is more information on it, like an example showing iterations or explaining the process of analysis. The commentary references Lesik and Kennedy (1990). I'll prolly buy it unless there is something else that's preferable.

RE: Instanteous Center of Rotation Help

Quote (Lion06)

I believe IC method is a plastic stress distribution. The AISC manual talks specifically about taking advantage of the ductility of the welds.

I'm at a disadvantage as my AISC manual is at home. I'll check it out tonight. There is a a subtle difference between ductility and plasticity. If our welds truly went plastic, there would be permanent set.

Quote (Lion06)

If I calculated the plastic section modulus of the weldment and plug it into the blodgett's, I should get similar answers, no?

I don't think so. It's a numerical procedure that is not based on plastification as sbisteel has alluded above. If you make a spreadsheet using the modern non-linear method, and then switch your force-deformation relationship to be linear, you'll get Blodgett's results.

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.

RE: Instanteous Center of Rotation Help

(OP)
man I really liked blodgett's method, but it's so damn conservative nosmiley. I feel as though I must have an error though in my mathcad sheet because I get 75% more capacity than blodgett's using the ductile method. Is that typical?

Also, found this article Link

I shall read.

RE: Instanteous Center of Rotation Help

That second quote was not from me.

Regarding plastic vs. ductility - ductility is by defined by a materials ability to move past linear elastic behavior. What that means to me is plastic behavior. It doesn't necessarily mean permanent deformations until you get to the ultimate strength level. It's to a beam. It's elastic under service loading, but at ultimate strength is counting on the plastic strength of the section.

RE: Instanteous Center of Rotation Help

Jerehmy - I think you'll see the conservatism increase as the eccentricity of the applied load increases.

RE: Instanteous Center of Rotation Help

@Jerehmy: yeah, pretty typical. Still, I use Blogett's method regularly.

@Lion: sorry about the misquote. iPhone copy/paste abuse. Regarding our debate:

1) plasticity = fibers yielding = some degree of permanent deformation. This is true even when only part of a section plastifies.

2) you can be non-linear -- and ductile -- without yielding any fibers. Just ask a rubber band.
 

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.

RE: Instanteous Center of Rotation Help

I don't know if a rubber band is linear or non-linear, but the deformations are elastic. I don't consider a rubber band to be ductile. I consider it quite brittle. I've never found a rubber band to undergo any permanent deformations without snapping.

RE: Instanteous Center of Rotation Help

(OP)
my boss had my steel book but I snagged it back. It hase a pretty thorough explanation and example (salmon johnson and malhas).

Something I noticed though, none of the articles I have read talk about a double eccentricity such as a single angle connection to a beam. I modified blodgett's to include it. Any thoughts to why this is?

RE: Instanteous Center of Rotation Help

A rubber band may have been a uniquely terrible example. A little googling yielded some results that surprised me: Link

It seems that a rubber band is:

1) Non-linear.
2) Ductile.
3) Elastic? I'm not really sure.



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.

RE: Instanteous Center of Rotation Help

Quote (OP)

Something I noticed though, none of the articles I have read talk about a double eccentricity such as a single angle connection to a beam. I modified blodgett's to include it. Any thoughts to why this is?

a) because it's hard.
b) for that particular example, you'd normally assume that angle flexibility eliminates eccentricity in the one direction.

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.

RE: Instanteous Center of Rotation Help

If you can stretch something to 3x its original length and it goes back to it's original length when unloaded, that's elastic.
That stress-strain curve does not look at all like a ductile material to me.
I don't really care about the elasticity/ductility of a rubber band.

I'm struggling to think of a material that doesn't undergo permanent deformation as ductile, regardless of the nonlinearity of the elastic deformations. S&J defines ductility as the amount of permanent strain (i.e. strain exceeding proportional limit) up to the point of fracture. The very nature of ductility in this context requires permanent strain (i.e. plastic deformations).

RE: Instanteous Center of Rotation Help

(OP)
For a single angle single bolt, angle welded to stair stringer(used almost exclusively for stair stringers), you can't ignore it. And how's it hard for elastic analysis? Blodgett gives the torsion, it's judt the in plane moment which is easy to distribute to the welds.

RE: Instanteous Center of Rotation Help

Quote (OP)

For a single angle single bolt, angle welded to stair stringer(used almost exclusively for stair stringers), you can't ignore it.

I agree. That's part of what makes the single bolt, single angle connection a bit sketchy and only suitable for light loads.

Quote (OP)

And how's it hard for elastic analysis?

It's not. It's hard for the modern AISC method. These kinds of situations are precisely why I still use the Blodgett method myself, as I mentioned above.

@Lion: you've made some thought provoking points. I'll need to think on it.

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.

RE: Instanteous Center of Rotation Help

I analyzed a C-shaped weld with eccentric shear just yesterday and found a decent difference between elastic analysis and the instantaneous center of rotation method (Table 8-8 in the 14th edition AISC Manual of Steel Construction). For my case, the elastic method required a 1/2" fillet weld and the instantaneous center of rotation method required a 5/16" fillet weld. This was not too surprising since the elastic method as applied to an eccentric analysis does not take into account the fact that fillet weld strength is a function of the angle between the load and the weld axis.

@Jerehmy: The Gaylord, Gaylord, and Stallmeyer textbook ("Design of Steel Structures", third edition) indicates it "usual practice" to design the outstanding leg connection (the angle leg not attached to the beam web) to fully resist the out-of-plane moment that I believe you are questioning.

RE: Instanteous Center of Rotation Help

The rubber band curve is an example of hysteresis due to visco-elasticity. At infinitely low strain rate the up and down curves will overlap.

RE: Instanteous Center of Rotation Help

Thanks for the rubber band explanation Compositepro.

I now believe that some of the statements that I made above were wrong. Having consulted my college material science textbook and some other sources, here's my current understanding of things:

1) Ductility is a subset of the plasticity phenomenon which also includes malleability. Ductility involves plastic behaviour and permanent deformation.

2) Depending on how things shake out in the IC analysis, some weld segments may indeed plastify. So a weld group can often be said to be partially plastic at design capacity.

3) In the case of a circular arc fillet weld with its focal point at the IC, the entire weld may plastify before reaching its ultimate strength.

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.

RE: Instanteous Center of Rotation Help

(OP)
in AISC 2010 equation J2-7

Mn = Σ[FnwiyAwei(xi) - FnwixAwei(yi)]

is the subtraction of the x component because the x and y stress vectors will always be opposite in sign?

RE: Instanteous Center of Rotation Help

(OP)
x and y components of the stress vector*

RE: Instanteous Center of Rotation Help

It's just consistency with the sign conventions used. A positive Fx multiplied by a positive Y produces a negative moment.

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.

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