Structural Engineering -12x12 stiffness matrix analysis

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Discussion Overview

The discussion centers on the formulation of a 12x12 stiffness matrix for 3D frame structures in the context of elastic analysis using the direct stiffness method. Participants are exploring the necessary equations and resources for implementing this in MATLAB, particularly focusing on the inclusion of bending effects in their analysis.

Discussion Character

  • Technical explanation
  • Exploratory
  • Homework-related

Main Points Raised

  • One participant is seeking the equations for a 12x12 stiffness matrix for 3D frame structures, noting a lack of explicit resources in available texts.
  • Another participant suggests that the inquiry may relate to a truss element model, which does not account for bending moments, and provides a link to a presentation discussing the 3D truss stiffness matrix.
  • The original poster clarifies the need for a 12x12 matrix due to the inclusion of bending, indicating a requirement for additional degrees of freedom.
  • There is a mention of the possibility of sharing textbook pages, raising a question about forum rules regarding copyright.
  • A participant expresses willingness to assist in finding the relevant equations from their FEA textbook.
  • The original poster indicates they have found local member stiffness equations that may be useful but seeks further verification and assistance.

Areas of Agreement / Disagreement

Participants generally agree on the need for a 12x12 stiffness matrix for the analysis of 3D frame elements, but there is no consensus on the specific equations or resources available to derive this matrix. Multiple perspectives on the type of elements being analyzed (truss vs. beam) are present, indicating a lack of resolution on the best approach.

Contextual Notes

Limitations include the potential dependence on specific definitions of stiffness matrices and the unresolved nature of the equations needed for the 12x12 stiffness matrix. The discussion also reflects uncertainty regarding copyright rules for sharing textbook materials.

elbarto
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Hi,
I am trying to write a MATLAB script to do an elastic analysis of 3D frame sturctures. The method I am using is the direct stiffness method, but I cannot find the equations for the 12x12 stiffness matrix for each member in the global system.

If anyone has any information on 3D matrix analysis I would greatly appreciate the help. So far none of the texts I have found have explicitly given these formula.

I have the 6x6 matracies for 2D analysis if anyone is interested.

Thank You

Elbarto
 
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I am assuming that you are using something along the lines of a truss element, but in a 3D structure, i.e. members can carry no bending moments.

Take a look here :
http://www.google.com/url?sa=t&source=web&ct=res&cd=6&url=http%3A%2F%2Fwww.engineer.tamuk.edu%2Fdepartments%2Fieen%2Ffaculty%2FDrLPeel%2FCourses%2FMeen5330%2Fstudent_presentations%2FFEA_F06.ppt&ei=bkvrSKziMdywmQf0mcHaCg&usg=AFQjCNFyXckTs9v56tKt3qI9Yc-c1jALjQ&sig2=k9yvGnIMuqDkYuKnyPc9kg

Towards the back of the presentation it talks about the 3D truss stiffness matrix. Both of my FEA books also discuss this as well. See if you can get a hold of a copy from your library or a fellow student.
 
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Thank you for your reply. That is almost exactly what I am chasing, tho I need the 12x12 stiffness matraix equations because I am considering bending so I will have the 6 additional degree of freedom to account for due to the rotation of each node.

If I find the equations I will post them here. Are you allowed to photo copy pages from textbooks and post them here or is that against forum rules?

Thanks, Elbarto
 
Oh. So you're using some kind of beam element. I'll see if I can dig them up in my FEA book.
 
Yes I am doing a full 3D frame element so I have to consider all 12 DOF's for each member. I had a look in my library today and think I managed to find the local member stiffness equations which will probably work ok if I play around with them a bit but I would appreciate it if you could check your textbook out.

Thanks a lot
Regards Elbarto
 

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