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Anonymous Poster

Stiffness Matrix for a Beam

08/18/2009 2:28 PM

I have obviously misunderstood how to use this. I don't have any books on this subject, do you guys know any good ones?

Let me illustrate what I mean with a problem. Take a look at this beam:

The stiffness matrix for a beam, which only degree of freedom at the noeds is:

M(1)=EI/L(4*thetta(1)+2*thetta(2))

But at this beam, we see that there can't be any internal moment at (1). And we also see that end 2 is not free to rotate, the stiffness matrix then says that in order to have zero moment at (1) thetta(1) must be zero. But this is obviously wrong, because if we use the method of virtual work, we get a rotation there. So where am I thinking wrong?

I expect I might have used the stiffness matrix when I can't use it?, is this correct?, and why can't I use it here?

I would very much appreciate your help.

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Anonymous Poster
#1

Re: Please tell me how to use the stiffness matrix for a beam.

08/18/2009 2:31 PM

picture of the simple beam:

http://img269.imageshack.us/i/beam.png/

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Guru

Join Date: Nov 2007
Location: Sherwood Park, Alberta, Canada
Posts: 1212
Good Answers: 74
#2

Re: Stiffness Matrix for a Beam

08/19/2009 3:47 PM

There are many books on matrix methods for beams and frames. It is not an easy concept to get your mind around at first. If you want to understand it thoroughly, you will need to spend a bit of time familiarizing yourself with the theory.

Your sketch is reproduced above. The left end is hinged. The right end is fixed. It would be more realistic to place a roller at the left support, giving Node 1 two degrees of freedom (DOF), rotation and horizontal displacement. The right end, which I will call Node 3, has zero degrees of freedom. It cannot move up or down, right or left and it cannot rotate.

Let's call the point of load application Node 2. This node has three degrees of freedom. It can move up or down, right or left and it can rotate freely as there is no support at Node 2. You can consider two beam elements, B1-2 and B2-3 and write matrix equations for each of them.

I found quite a number of articles on the internet using a google search for "stiffness matrix". One of the better links (in my opinion) was this one, but I would suggest you review a few of the others as well.

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Bruce
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Anonymous Poster
#3
In reply to #2

Re: Stiffness Matrix for a Beam

06/25/2010 6:45 AM

u r forgetting the fixed end moment.

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