Plastic moment, why does all new codes allow us to go there (is plastic hinge formation considered)

[Bridge_Man]

Hi,

Haven't given it much thought, but say you have a two fixed end beam with a uniform load. Max moment at ends = wl2/12 m max moment at center = wl2/24

Say you designed your beam for plastic moment (compact section) for wl2/12 (am still within the code) , say I reached my plastic limit . what will happen -> plastic hinges will form at the ends, now I have a simply supported beam with max moment = wl2/8 (not designed for this moment, failure happens)

I try not to reach plastic moment in my designs but the thought of not considering what would happen if we actually reached plastic is scary (the structural analysis will be different) . Yes, I know we have load factors/resistance factors and whatnot , but still.

any thoughts, am I missing something ?

Thanks !

 

[KootK]

any thoughts, am I missing something ?

When the plastic hinges form, they don't become points of zero moment. Rather, they hold steady at the moment at which they went plastic (Zx x Fy). As such, the moment in the post-hinge beam never gets to wL^2/8.

 

[Agent666]

You're missing the fact that your beam still isn't simply supported if it hinges at the end, it still has a moment equal to the plastic moment at each end. You can continue to increase the load and the negative moment will redistribute to the positive region until you also form a hinge at the centre of the beam. At this point you finally have a mechanism and collapse occurring as your system cannot carry any further load. The max midspan moment at collapse is the plastic moment capacity of the section (assuming you have full lateral restraint and your member is not governed by lateral torsional buckling), it is not wL^2/8 as you've assumed.

For gravity design the redistribution of moment is embodied in plastic design methods. The key is you can carry some further load past the point at which you first yield the member and up to the point where your system forms a mechanism. You can do this provided you're not buckling the beam under flexure and not exceeding any relevant hinge curvature or rotation requirements.

https://engineervsheep.com

 

[JoshPlumSE]

Saying that the nominal moment capacity of a beam is the plastic moment is not quite the same thing as "plastic design". However, I understand the confusion. My thoughts on this:

1) What others have said. After the end moment reaches the plastic moment, that doesn't mean the beam has failed, only that it won't take additional load. If you stop there, this is still considered "elastic design".

2) however, if you continue to add additional load you still have resistance of the beam. It's just that the rest of the load gets distributed like a simply supported beam. If you do this type of "moment re-distribution" then this would be "plastic design".

3) You've gone past the elastic limit of the beam, all the way to the plastic moment capacity of the section (Mp). So, why isn't this considered "plastic design"?
i) Part of it is the imperfection of our terms. The beam is not necessarily behaving elastically at that point under Ultimate Strength level loading. Actually, this was still true even true back in the Allowable Stress Design / AISC 9th edition days. It was just hidden in the Safety Factor and Allowable Stress Increase Factor.

ii) Part of it is the safety factors (ASD) or the material and load factors (LRFD) that we use. The beam should STILL be elastic under SERVICE level loads. Other than seismic, of course.

 

[MIStructE_IRE]

I’ve done it plenty of times for portal frames... but when I think about what’s actually happening it still gets me nervous..

 

[dik]

The plastification of a joint/node may allow the loading to redistribute to other parts of the structure. The plastic 'failure' load may be in excess of of the elastic 'failure' load. For example a 2 equal span UDL continuous beam will have a failure load moment of 0.0858 x ql^2 which is a bit less than the elastic failure moment of 0.125 x ql^2. In addition, it is not necessary to consider alternative loading. Been my favourite steel design for 50 years... to take advantage of this, the steel sections have to be a little more robust (Class 1, in Canada). As noted, there is a difference between Plastic Moment and Plastic Design... the latter making allowance for re-distribution... With continuous construction for steel, plastic design will likely give you the least costly framing. There are some other issues... stability, bracing, and shake-down,

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

-Dik

 

[dik]

I was only nervous with my first portal... I could feel the construction traffic underneath... when things were finished and stiffened up, my concerns went away... rather than portals you should look at continuous construction... beams over columns... I still use graphics methods (I'm a bit of a dinosaur) to draw the moments for max and min q... this is used to determine the maximum splice moment. Arnold Crosier showed my this over 50 years ago...

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

-Dik

 

[Bridge_Man]

Good stuff guys, I actually had a misunderstanding of the concept of plastic moment Vs plastic Design, Thanks for clearing that up.

Today I learned something new. like every other day

Thanks all.

 

[dik]

There's a fundamental lemma by Feldberg that, barring instability issues, if you strengthen any part of a structural system that the resulting system is at least as strong as the original... it doesn't say it's stronger, only that it is not weaker...

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

-Dik

 

[IDS]

In addition to previous comments, it is a basic requirement of most codes that the structure should not collapse even if a section reaches its actual ultimate load limit, i.e. there must be an alternative stable load path.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/