# SERM Steel Practice Problem 3 (Page 4-54)



## Hromis1 (Mar 14, 2010)

Ladies and Gents,

Please tell me if I am missing something in this problem. The solution computes the maximum moment at the CENTER of the beam and selects a section based on the plastic moment. (The beam is Fixed-Fixed with both a uniform distrib and a concentrated load at the center, with full lateral support).

However, unless the basic beam formulae have not changed, the real maximum moment is really at the fixed ends.

Am I missing something here? The solution the talks about "from the collapse mechanism shown in part "a"". The is a diagram showing hinge locations...but in my mind this is not the critical area.

Anyone else have thoughts on this problem?


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## McEngr (Mar 14, 2010)

Hromis1 said:


> Ladies and Gents,
> Please tell me if I am missing something in this problem. The solution computes the maximum moment at the CENTER of the beam and selects a section based on the plastic moment. (The beam is Fixed-Fixed with both a uniform distrib and a concentrated load at the center, with full lateral support).
> 
> However, unless the basic beam formulae have not changed, the real maximum moment is really at the fixed ends.
> ...



Hromis1, I'm thinking that the problem is a plastic design problem. I'm at home and my SERM is in my work office, so I'm not sure. Plastic design is tougher subject, in my opinion. There are potentially multiple loading configurations to cause a failure, but there's only one that will occur first. I'm probably not explaining it well, but that's my $0.02.


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## Hromis1 (Mar 14, 2010)

McEngr,

You are correct. It is a plastic design problem. After filling my stomach, I was able to find a reasonable explanation of the formation of collapse mechanisms in the Allan William's book. It get the concept now....

It is just a "foreign" concept to a guy who designs mostly around fatigue.

Thanks for your answer. It pointed me in the correct direction.


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## kkillgore (Mar 15, 2010)

Hromis1 said:


> McEngr,
> You are correct. It is a plastic design problem. After filling my stomach, I was able to find a reasonable explanation of the formation of collapse mechanisms in the Allan William's book. It get the concept now....
> 
> It is just a "foreign" concept to a guy who designs mostly around fatigue.
> ...


I also had problems with that problem when I went through that book last month. I have a big question mark next to it and don't fully recall why. I think I had a problem with the uniform loading moment calculation. In the solution they use PL/2 for the point load moment and WL^2/2 for the uniform moment. I thought it should have been WL^2/4. I don't know why the answer is what it is and would love to hear your reasonable explanation?


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## Hromis1 (Mar 15, 2010)

kkillgore,

It is a completely different concept from the normal approach. The problem statement is not clearly written...

However my take is on this:

The traditional solution would be to look at the beam and solve for when the section begins to yeild....ie. the highest moment produced..(at the fixed ends). In this case "failure" is defined as exceeding the allowable bending moment of the beam..

However for this problem geometry yielding does not result in a total "collapse". This only occurs after a new plastic hinge is formed at the midpoint. It is this secondary hinge that then completes the failure mechanism.

More simply for this case...The ends of the beam can bend all they want...at that point the beam behaves like pinned-pinned...failure as defined by "total collapse" only really occurs after the new hinge is formed in the center.

Is this clear as mud? This is a different definition of failure...predicting the actual point of collapse. not excessive deformation

Hromis1


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