Beam Section Classes and Plastic Moment Resistance 2

[Logan82]

Hi!

If you have a class 1 beam section for a laterally supported steel member, which allows the use of plastic moment resistance (Mr = φ * Z * Fy), is it still possible to use elastic moment resistance (Mr = φ * S * Fy) to design in the elastic realm?

Also, why are there Mp as well as My for beam moment resistance? Is there the equivalent concept of Mp and My for other types of resistance (shear, axial)?

 

[Yao1989]

1. Yes I suppose but I'm not sure why you'd want to do that?
2. See attached strain vs stress diagram. My understanding is that class 1 & 2 are thick enough such that you can continue to allow high strain, and allow the extreme fiber to continue to deform past yield until the entire section above/below the neutral flange has yielded, thus all loaded to at least yield strength, hence you can use plastic modulus. You don't do this for class 3 & 4 because they are too thin and will buckle locally after the extreme fibers are past yield stress. In fact for even thinner sections you'll see on cold-form-steel, local buckling may govern the section before you even reach elastic yield of extreme fiber.

Once you understand the above it you'll see that this concept only applies for bending.

 

[Logan82]

1. I was asking this because from what I understand reaching Mp can cause high deformations, which is not always suitable for every application. However, it is sometimes unavoidable to use class 1 sections for geometric reasons. By the way, how can we calculate the plastic deformations in a beam? Is it something that can be only verified in a lab or are there analytic equations?

2. Thank you Yao for your answer, appreciated!

 

[JoshPlumSE]

Logan -

What sort of deformation are you concerned about? Drift in a moment frame, or beam deflection under gravity loads?

My thoughts on the subject:
1) When you're checking ultimate loads vs capacity, you're usually doing so under an elevated load. A load that has some factor of safety built into it. Right?

2) When you're checking deflection, you're usually looking at a lower serviceability load. Which should still be in the elastic (or nearly elastic) range.

If you've got stringent deflection requirements then I think it makes more sense to impose a more stringent deflection criteria rather than revising your capacity.

 

[Logan82]

I am thinking about big plastic deflections from live loads reaching ultimate capacity that would afterward impact service, for instance a large mechanical hoist that would require a certain alignment to work, or large deflection that would raise eyebrows.

It's true that there is a factor of safety built into the live load, but it usually is present since the load can be higher than the unfactored load in some event (for instance a school bus full of bodybuilders visiting a touristic platform). In my case, if the live load reaches the ultimate capacity, I would like it to avoid permanent deformations.

I am not worried about the elastic deformations at service, but rather by the plastic (permanent) deformations that could occur at ultimate. However, I am in the unknown regarding the magnitude of these plastic deformations. Are they small? Are they visible to the eyes?

 

[BridgeSmith]

If you don't want permanent deformations under a particular loading, then the capacity must be limited to My for that loading.

If permanent deformation is allowed under a loading condition (say a design seismic event or MCE), then for that loading, the limiting capacity would be Mp, if it's a compact section (which I'm assuming is what is meant by "class 1").

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Logan82]

Thank you BridgeSmith! By the way what is MCE?

 

[BridgeSmith]

MCE = Maximum Considered Earthquake; for bridges, at least, it's typically the 2500 year event. At that magnitude, we typically allow major damage, but not collapse.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[dik]

Usually deflections are not an issue due to the continuity required for plastic design. At service loading, you are generally in the elastic region.

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

-Dik