Why does the section 3 plastifies? 5

[Logan82]

Hi!

The equation of the moment resistance of class 3 beams is Mr = ϕ * S * Fy.

Why is it considered that the class 3 section plastifies even though the equation uses the elastic modulus S?

For class 1 and 2 sections, the equation is Mr = ϕ * Z * Fy, with Z being the plastic modulus, so it is easy to see that the section plastifies.

Source:

https://www.researchgate.net/figure...section-beam-classification-of_fig1_280609517

 

[JoshPlumSE]

It's a matter of what can be relied upon. For Class 2 you can rely on Mp, for Class 3 you can rely on My, for Class 4 you can't even get to My.

Stated another way, Class 3 merely means that you will get to Fy at the extreme fiber, but not for the entire flange.... Essentially, it fails right around My.

 

[Logan82]

for Class 1 you can't even get to My.

Did you mean that for class 4 you can't even get to My?

Stated another way, Class 3 merely means that you will get to Fy at the extreme fiber, but not for the entire flange.... Essentially, it fails right around My.

So does that mean that this figure is wrong? It appears in this figure that Fy has been reached at the extreme fiber and at the entire flange.

 

[jayrod12]

I think that a class 3 section can potentially go partially plastic. But the issue there is how much capacity beyond initial yield can it go before it fails? So that's why they limit you to Fy*S.

 

[dik]

It's a matter of the section maintaining stablility through rotation.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[skeletron]

I'm pretty sure Josh meant Class 4 not reaching Fy. His descriptions of Class 2 and 3 are correct.

Dig a bit more in the commentaries. Specifically Section 11 and 13. Class is determined by a b/t ratio which relates to the elements ability to maintain plastic and redistribute through rotation (to satisfy plastic analysis). Class 3 isn't able to redistribute that out of the flange, so you're stuck with the yield strength and the elastic section modulus. Class 4 just locally buckles. Class 1 maintains plastic through sufficient rotation. Class 2 reaches plastic, but doesn't have rotational requirements.

 

[JoshPlumSE]

I'm pretty sure Josh meant Class 4 not reaching Fy. His descriptions of Class 2 and 3 are correct.

Thanks, I went back and corrected the original post.

So does that mean that this figure is wrong? It appears in this figure that Fy has been reached at the extreme fiber and at the entire flange.

I think that figure is "representative" of the concept only.... That the section reaches yield, but that yield is not able to extend very far through the cross section before failure occurs.


Note:
In many ways, we should probably think of local buckling as a STRAIN related issues as much of as a stress related issue. How much strain can the cross section take before the compression flange buckles locally?

What's the difference between a class 1 and class 2 section if they can both reach full plastic cross section? It's the amount of strain they can take. For a class 1 section you can get so much extra ductility out of the cross section before it fails... which is very helpful for seismic moment frames. But, for a class 2 section the amount of ductility (i.e. strain) is more limited.

In a similar way you could think about class 3 sections. It can reach yield, but cannot accept much strain / deformation beyond that before local buckling occurs.