How to Solve a Frame Finite Element Problem?

[gimini75]

Hello

I have a problem to solve this question in FEM which I apload it here, if you know how to solve this problem can you please help me?


Thanks

 

[nvn]

Which part of the problem is causing you trouble? Can you explain and be specific?

 

[gimini75]

Hi

Thanks for your reply, really Iam confused i don't know which equations I have to use and which stiffness matrix, the angle 25 for the force?

 

[mathmate]

Thanks for your reply, really Iam confused i don't know which equations I have to use and which stiffness matrix, the angle 25 for the force?

The force can be resolved into two components in the x- and y- directions, assuming that you will solve the problem as a plane frame or using finite elements.

As you can see, there are three unknowns, displacements in the x-, y-directions and a rotation at the free joint.

I suggest you go back to your notes and find out how you are expected to solve the problem.

This is a statically indeterminate problem involving a plane frame with three degrees of freedom at each node, namely the displacements in x and y, as well as a rotation.
If you analyze it as a plane frame, you will not require the use of finite elements. If you analyze it as two cantilevers, you do not require matrices. It all depends on how you are expected to solve the problem, hence input from you is required as to where you have a problem with the solution.

Also,

(E 200GPa, I = 1.72x106 m4 and A = I .91x10 ni2, Force 5 KN)

You may want to check if you mean the following:

(E 200GPa, I = 1.72x10⁶ m⁴ and A = 1 .91x10 m², Force 5 KN)

 

[gimini75]

Thanks

I want to solve the problem by using FEA, but I don't know what's the stiffness matrix for this problem? I don't have a clear information about this kind of situation.


Thanks for your reply

 

[mathmate]

If you have learned about FEA in school, then this plane frame problem is almost a degenerate case.
Each element has two nodes, and each node has three degrees of freedom (two translations and a rotation).
So for three nodes, you have a global matrix of 9x9, of which six are fixed (the supports), which become your boundary conditions. The only three unknowns are the two translations and rotation of the free node.
Once the displacements are determined, you back-substitute into the stiffness matrix to find the forces.

For details, google using keywords "plane frame", "structural analysis", "force method", "matrix analysis".

An excellent article with example is shown below.
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Structural%20Analysis/pdf/m2l11.pdf

 

[nvn]

gimini75: Use the frame member global stiffness matrix, a 6 by 6 matrix. It will be in your textbook. You will assemble two of these into your structure stiffness matrix, as explained in your textbook.

 

[mathmate]

This article describes the stiffness matrix for a plane frame:
http://www.duke.edu/~hpgavin/ce131/frame-mth.pdf