# Plastic Analysis



## Casey (Oct 18, 2008)

For some reason in my bachelor's program we ignored this subject and in my masters we spend maybe a week on it. So I am not that familiar with it. I have a basic idea how to use this method, but I am not sure when I am required to apply it.

Are there certain types of questions or situations that make it obvious that plastic analysis needs to be considered? Or can I avoid it all together?

When I was studying this part, the simple beams and frames were fairly straight forward, but once the structure starts getting bigger and you run into more failure combinations I start to get confused...

Anyone have any idea what we might expect on the exam? I managed to track down one textbook and one of EIT's course notes to help me out, but I am just not sure if I should be focusing too hard on this particular subject and if I should, what parts should I be focusing on?

Thanks.


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## ARLORD (Oct 18, 2008)

I agree. I feel the same about pre-stressed concrete in building design.


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## buening (Oct 18, 2008)

I don't have the book in front of me to look it up, but I am pretty sure Plastic Design can be used when Lb &lt; Lp. It has to do with the unbraced lengths. Under either Lr or Lp you can use plastic design (plastic modulus Z * Fy), but over that length and you have to use yield design (section modulus S * Fy). That is my understanding, but look in the AISC in the beam section before the beam tables. It specifies the criteria of when plastic design can be used. I agree, we didn't cover plastic design in my undergrad class.

One thing I have yet to figure out is how to calculate the plastic modulus for sections not listed in the AISC manual. My steel textbook does a horrible job of explaining it, and the only example is a generic T section. It doesn't seem to have a formula like bh^2/6 like for a section modulus of a rectangular section. I'm praying that it isn't one of the questions on the SE I exam!!!


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## ARLORD (Oct 18, 2008)

buening said:


> I don't have the book in front of me to look it up, but I am pretty sure Plastic Design can be used when Lb &lt; Lp. It has to do with the unbraced lengths. Under either Lr or Lp you can use plastic design (plastic modulus Z * Fy), but over that length and you have to use yield design (section modulus S * Fy). That is my understanding, but look in the AISC in the beam section before the beam tables. It specifies the criteria of when plastic design can be used. I agree, we didn't cover plastic design in my undergrad class.
> One thing I have yet to figure out is how to calculate the plastic modulus for sections not listed in the AISC manual. My steel textbook does a horrible job of explaining it, and the only example is a generic T section. It doesn't seem to have a formula like bh^2/6 like for a section modulus of a rectangular section. I'm praying that it isn't one of the questions on the SE I exam!!!



Z = .25bd**2 for a rectangle. Look on pg 17-36, part 17 at the end of AISC 13th. See the following link:

http://coecs.ou.edu/ENGR2153001/www/engr21...%205/sec5.7.doc


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## Casey (Oct 19, 2008)

ARLORD said:


> I agree. I feel the same about pre-stressed concrete in building design.


I have barely touched pre-stressed as well and am banking on it not being there. I will commit half a day to it though.

I am also hoping that plastic design is more of an SE I type question, as I think it will fits the multiple-choice format better. i.e. it's more of a short answer question.

I can't honestly think of a situation where plastic design is the only option to solve a problem. Can anyone else think of one?

And Buening, thanks for your input. For beam design I will just follow AISC and try to use the tables as much as possible. I'll read over the sections you suggested to make sure I am on track.

My main problem is having to go through the iterations to find your failure mechanisms with plastic hinges. A simple beam or frame (two columns, one beam) is more or less traight forward, but after I feel it starts to get messy.


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## buening (Oct 19, 2008)

I got my AISC manual out and flipped through it to make sure I was thinking correctly. It is actually in the Spec section F. When Lb&lt;Lp then you can use plastic section modulus (F2-1). When Lp &lt; Lb &lt;Lr you have to interpolate between plastic and elastic (Equation F2-2). If Lb &gt; Lr then you have to use elastic design (Eq F2-3). Keep in mind this is for doubly symmetric COMPACT members bent about the major axis. When bent about the minor axis, make sure you note that FyZy &lt; 1.6FySy (Eq F6-1). They have an upper limit on the plastic moment.

If you happen to have a steel design textbook, they typically cover Virtual Work for frames and continuous beams. This is the only way that I know to do the plastic failure mechanisms. The SERM also covers this as well, but I don't think it gets into bents with more than two columns/one beam. I'm not a building guy, but would the leaning column theory kick in after two columns/one beam?

Don't take my advice as totally correct, as I'm a bridge guy refreshing my building stuff for the SE I. Hopefully Kevo will chime in for some sage advice :beerchug:

Thanks for the info Arlord. For some reason I forgot about that section in the AISC manual. It has now been tabbed!


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## kevo_55 (Oct 19, 2008)

Casey,

Don't you have "Structural Steel Design: LRFD" by Williams?

I have the ASD version of the book and chapter 4 is about plastic design.

buening, you are for the most part right. Virtual work (or a "mechanism" method of design) is one way to find out where your plastic hinges will occur.

I prefer a "statical" method of design where someone really smart made a bunch of nice beam diagrams of common beam diagrams with loadings on where plastic hinges will occur.

No matter what, I dont think that you'll have to do any matrix analysis or virtual work calculations during the SEII. Having knowledge of plastic design and a "feeling" on where hinges will occur is a more likely question.

Keep going guys!! We're at the home stretch!!


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## buening (Oct 19, 2008)

Thanks for the confirmation Kevo! There was a few virtual work problems in the 6 minute solutions, so I wasn't sure if I should expect them on the SE I. Ok, so say we have a simply supported beam with Lb &lt; Lr, we can just use FxZx to find the allowable design moment right (times phi of course)? Plastic hinge locations really aren't a concern for the basic SE I as far as I know, unless we are asked to determine the failure mechanism or if there are continuous beams to determine the moment in the controlling span. The more I think about it the more I second guess myself


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## Casey (Oct 19, 2008)

kevo_55 said:


> Casey,
> Don't you have "Structural Steel Design: LRFD" by Williams?
> 
> I have the ASD version of the book and chapter 4 is about plastic design.
> ...


Kevo,

Yes, I have Williams' "Structural Steel Design: LRFD" and it was with that I was getting frustrated with plastic analysis. When he started using larger structures or the whole floor network it really frightened me! I do plan on going over that again. And perhaps will focus on finding where the plastic hings will form.

Which beam diagrams are you referring to? Do you have an example? I hope you are not referring to the beam diagrams found in Part 3 of the Steel Handbook; otherwise, I will feel foolish.

Edit: If they are asking questions like the ones seen in this link then I am fine. But when they start adding more to the structure it seems to me the analysis becomes more detailed.

In any case, I am not too worried about plastic design. I don't think they will throw anything too hard at us, probably won't even get such a question. I am expecting at least one wall (either in or out-of-plan) and one diaphragm question...

Good luck everyone! Almost there...


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## kevo_55 (Oct 20, 2008)

Casey,

My work has a bunch of tables taken (stolen) from some book and then bound. Of course, now I have them as well. Some of these tables are similar to the beam diagrams in part 3, but others are slightly more complex.

At any rate, I wouldn't stress too much about plastic design. Just get a feeling on where your hinges will occur on a fixed-fixed beam with a uniform loading. I think that is the best thing to take away out of plastic analysis.

Good luck!!


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## Casey (Oct 20, 2008)

^^ I can live with that.

Thanks for all the help everyone!


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## kevo_55 (Oct 20, 2008)

Rock on Casey!

:th_rockon:

Let kick ass on exams this week everyone!! :bio:


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## buening (Oct 20, 2008)

10940623: Is it exam time yet? :brickwall:


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## Bigwolf (Oct 20, 2008)

10940623: 10940623: 10940623: Good Luck everyone! Let's do this! 10940623: 10940623: 10940623:


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## Jtiger (Nov 7, 2008)

I remember taking Plastic Design of Steel structures in grad school and the professor said the first day that it's pretty useless in the real world.


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