Hinge Formation in Overhang Simply Supported Beam 4

[willowman]

Taking my first steps into plastic analysis of steel beams. I have a problem whereby I have a simply supported beam with an overhanging cantilever section. I have identified that the plastic moment will be first reached at the location of the support B.

What is the interpretation of hinge formation at an existing roller support (which we model as already allowing rotation)? Is there another approach to take in this example.

 

[dik]

Josh... agreed... only when you have multiple hinges for mechanisms... but technically as soon as you use Z for plastic section, you are getting into plastic design...

Retired13... there are some excellent texts out there... my first books were by Maissonette and Save (Sp?) Volumes 1 and 2, probably the best and about 50 years old... I don't know if they are still available. The was supplemented by a couple of classics... Baker, the Steel Skeleton Vol 1&2... all since gone... there were a couple of Mexican students visiting Canada that I met at the university and they were complaining about the lack of good texts... and another classmate and myself crated up all our texts and shipped them out...

Dik

 

[r13]

Dik,

Even the books are still available, do you think I can afford on my limit retirement income? Thanks for the info, I'll google, or check with Amazon.

Search Results - No luck on Maissonette and Save. Found "the Steel Skeleton V1 & 2" by Baker, but out of print, or currently unavailable.

 

[human909]

I don't consider designing to LRFD capacities (Mp = Z*Fy) to be "plastic design".

Agreed. In the usual terminology it requires a hinge to form. But it can be considered semantics.

I think you are mistaking your internal roller to an end roller. Rotation is not allowed at internal roller. That's how the overhang acts like a cantilever because the internal roller resist moment due to continuity.

Huh? I think you are mistaking the fixity of a support vs the behaviour of the member. You absolutely can have rotation at an internal roller, in fact the moment diagram would normally be different if there wasn't rotation allowed at this support.

 

[dik]

retired13... not surprised... they go back 50 years or more... great books in their time. There are likely better ones. You can find a lot of info on the 'net for plastic design.


Dik

 

[Tomfh]

I don’t understand the question?

Hinge forming = failure in this example.

“Plastic design” generally refers to redistribution of moments in a redundant structure. There is no such redundancy here.

 

[BridgeSmith]

That's the point I can't get over it, when a section reached "yield", will it recovery to its original position upon unloading? If it can, why name the point "yield", shouldn't the point moves further down the stress-strain curve?

When the yield moment is referred to, it generally means the moment at first yield, which is the moment when the extreme fiber of the section reaches the theoretical yield stress (My=Fy*S). If the moment on the section increases, the section will start to yield, starting at the outermost tension and compression edges and moving toward the neutral axis, until most of the section has yielded. The deformation from the onset of yielding on is expected to be permanent. Theoretically, when the entire section has yielded (which is physically not possible), half in compression and half in tension, it reaches the plastic moment capacity (Mu=Fy*Z).

If a moment of that magnitude continues to be applied to the section (the loading doesn't redistribute to other parts of the structure, as in the OP's case), it will continue to bend until the outer edges reach strain hardening. It will gain a small amount of strength before it fractures and the cantilever breaks off. Typically, plastic deformation of a cantilever is unacceptable, but given the small difference between the moment at first yield and the moment that will result in collapse of the cantilever, designing a cantilever for a moment greater than the moment at first yield would be very risky practice.

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

 

[Blackstar123]

Huh? I think you are mistaking the fixity of a support vs the behaviour of the member. You absolutely can have rotation at an internal roller, in fact the moment diagram would normally be different if there wasn't rotation allowed at this support.

I think we are saying the same thing but in different words. Let's try again.
A roller at an end allows rotation because it doesn't have the mechanism to resist the rotations.
An internal roller, resist the rotation because of the continuity of the member. If I break that member at that joint and make them rest on the internal roller, it will allow the end to rotate because now there's no continuity in the member to resist the rotation.

 

[Blackstar123]

Retired,
I agree with you. Learning is an ever going process. I remember my teachers used to say that they also learn by teaching us.
I've learnt so much in the past two months that visiting this forum is kind of becoming an obsession.

 

[Blackstar123]

I see plastic analysis as the determination of the maximum load the structure can carry before it becomes unstable.

Bridgesmith have described the load history of the OP's beam beautifully.

 

[r13]

Rod,


This is the exact sentence I am looking for on this forum. Thanks, I hope many would share the same understanding.

 

[human909]

I think we are saying the same thing but in different words. Let's try again.

I don't think we are saying the same thing (though our results might come out the same) But we can try again.

A roller at an end allows rotation because it doesn't have the mechanism to resist the rotations.

Agreed. Though I'd say a pinned-roller as a you could potentially have a moment resisting roller (though these aren't a common connection type).

An internal roller, resist the rotation because of the continuity of the member.

I disagree here. The support restraints and the member continuity are two different things.

The internal pinned roller offers no resistance to rotation. If you this support did offer resistance to rotation it would change the structure, the member wouldn't be continuous and the left side moment need not equal the right side moment.

If I break that member at that joint and make them rest on the internal roller, it will allow the end to rotate because now there's no continuity in the member to resist the rotation.

Agreed.

 

[Blackstar123]

I don't think we are saying the same thing (though our results might come out the same) But we can try again.

The support restraints and the member continuity are two different things. The internal pinned roller offers no resistance to rotation.

Oh! I get it now. But I can see how my wording implies otherwise.
And, I completely agree with you. I didn't mean that interior roller "literally" resists rotation like a fixed support.
What I mean by this

That's how the overhang acts like a cantilever because the internal roller resist moment due to continuity.

is that rotations are resisted at interior roller/hinge due to continuity of frames.

Lesson learned here: Be wise about how you put your thoughts into words. People might take your meaning literally.

 

[human909]

Oh! I get it now. But I can see how my wording implies otherwise.

Yeah I figured it was a terminology difference or misunderstanding. Half of the disputes that arise here stem from that. That said, sometimes important insight can be gain even starting from the smallest question or discussion.