Engineering Mechanics Query - Axial stress loads/plastic collapse 3

[miketingscott]

Hi,

I am currently trying to work through some example questions and have become stuck on one word based answer. Firstly, I wasn't sure where to post this so if anyone knows of a more appropriate area please let me know and I'll move it.

I would just like to let you know the question and then the lines that I have gone along in order to answer. I am not looking to be spoonfed, more just to know whether I'm in the right area or not and if not, maybe where I could look to help.

Here is the question:

"By considering the axial stress distribution in a double-l section beam at the instant of it's plastic collapse due to bending(in the absence of any axial loads), explain why the neutral axis then no longer passes through the centroid of the section".

 

[miketingscott]

Am I right in thinking that before the plastic collapse the neutral axis will pass through the centroid of the section because there is no axial stress acting on the section. However, at the point of plastic collapse, axial stress begins to act on the section and this cause the neutral axis to change; to a new position other than that of the centroid.

Is this along the right sort of lines?

Thanks in advance,

Mike

 

[rb1957]

is the nsion stress/strain curve the same as the compression stress/strain.

elastically, yes, plastically ??

in plastic bending, the material is stressed beyond the elastic limit, but the nett axial load on the section is still zero.

 

[rb1957]

as to your 2nd post, no, i don't think so ... i think the elastic NA is valid up to yield (ie, while the material is behaving linearly). post-yield the stress/srain curves are non-linear and different between tension and compression, therefore the axis of zero stress (about which the section is balanced in load, since no nett load is applied) moves with respect to the elastic NA.

 

[MiketheEngineer]

When you are at collapse - you are also at quite deflection - so the centroid moves because the shape has changed... Not much - but somewhat!!!!

 

[GregLocock]

All of which sounds reasonable but doesn't really seem to answer the question. Silly question - what is a double I beam?

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[miketingscott]

Can't find a better picture, but this should give you an idea Greg.

Mike

 

[miketingscott]

http://www.calibamboo.com/mm5/images/projectofthemonth/poll/feb12/1a.jpg

 

[GregLocock]

I think MikeTheEngineer is probably on the track of the original question, I suppose one other answer is that the stress strain curve beyond yield may not be symmetrical for tension and compression, and then as in your other post, compression instability of the flanges will reduce their stiffness, so the centroid will move down.

So there's no easy answer i think.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[SWComposites]

"before the plastic collapse the neutral axis will pass through the centroid of the section because there is no axial stress acting on the section" > no, the neutral axis is defined as the location of zero stress, not the other way around; the location of the neutral axis depends on the yield stress in tension and compression (likely different) and the stress-strain curve after yield in tension and compression. Except in cases of idealized elastic-plastic stress-strain behavior, working out the neutral axis location can be complicated.

"at the point of plastic collapse, axial stress begins to act on the section and this cause the neutral axis to change; to a new position other than that of the centroid" > no. the neutral axis will shift as soon as some yielding starts, unless the tension and compression stress-strain curves are identical and there is a pure moment on the section and the section is symmetric. Plastic collapse does not occur until sufficient yielding of the section occurs such that additional load cannot be carried; this can be well beyond the load at which yielding of the outer fiber occurs.

do you not have a strength of materials text that explains this?

 

[miketingscott]

Thanks a lot for everyone's answers, it has given me lots to think about and some direction on how to best answer this question.

Answering your question 'SWComposites'..all the material is delivered in a very maths based way will little wording within any of my lecture material. It has been up to me to do additional reading into the topic as well as trying to answer the questions using the maths to back it up. I have been reading a textbook on the topic but it can be quite hard to narrow an answer down.

Thanks for everyone's help

Mike

 

[dhengr]

Mike:
What kind of engineer or technician are you, what engineering or technical experience have you had on these kinds of problems? This is not really intended to be a student forum. You would do well to open your Strength of Materials, Theory of Elasticity and Structural Stability text books and study these subjects a bit more. Then discuss them in class with your instructor, you are paying them for an education after all. A ‘more appropriate area’ for this discussion would be the classroom or your Prof’s. office, and you won’t be the only student with this question. You will just be the bravest for asking for a better explanation. Eng-Tips is really not the first place to come for this kind of elementary structural mechanics discussion and education. This is not the student study room or student lounge. You will be given the bum’s rush, outa here, fairly quickly.

You really do need a good understanding of basic Strength of Materials and Structures, or it is a certainty that the mathematical presentation will boggling your mind. Can you give us a proper definition of the section centroid and the neutral axis? How are these different in doubly symmetrical sections and in sections which are symmetrical about only one axis, or not really symmetrical at all? Is your question actually talking about axial stress distribution or normal stress distribution due to bending moment through the depth of the section? You said there is no axial load or stress, right? Can you cut a section through an idealized bending member and draw the normal bending stress distribution as the max. stress progresses to yield and beyond? Cut this same section on a beam which has both bending and axial loading, and again draw us the ‘combined’ normal stresses across the depth of the beam, as the stress level increases. What is a plastic hinge? Can a member go fully plastic if it is not properly braced, that’s the stability aspect? What is likely to happen if the beam or structure is not properly braced? Tell us about this. You have two similar questions on this forum at the moment and neither of them are well enough defined to elicit an intelligent discussion. It sorta seems you’ve combined a bunch of structural engineering phrases without any understanding of their interrelation.

SWComposite’s explanation is very good, but read it carefully, there is a lot said btwn. the lines, for a full understanding. I think the question in your OP is kinda poorly worded, and your Prof. should be faulted for that. At least in my world (and by Theory of Elasticity definitions), axial stress and normal stress due to bending are two different things, but they could act in the same vectorial direction on your idealized beam, parallel to the length of the beam, but may be of different signs. I think it is kind of a trick question. Look back at SWC’s explanation about neutral axis, read it carefully, for full meaning. When the beam goes fully plastic where is the N.A. (neutral axis)? Explain this to us. In the idealized beam, first course teaching world, the tension and compression material properties are the same (the stress/strain curves, etc.), the N.A. doesn’t move (with pure bending and no axial load), look back at the cross sectional stress diagrams I asked you to draw. The real world situation can be quite different and much more complex. There’s still a trick question here, and it lies in the definition of the N.A., when the section goes fully plastic. Tell me about this.