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I'm having difficulty understanding how the stiffness matrix for finite elements is obtained. I am only having a difficult time understanding how to obtain the matrix values for K from the given information, but understand how to do everything up to and after just get stuck on this.

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The Matrices

I don't understand how the 8, -8 are obtained in the K11, K12, K21, K22 positions yet 3, -3 is obtained for K22, K23, K32, K33 following by the 18 in K33, K34, K34, K44.

Every direction I look at it falls apart at another section.

Though I just figured one thing out, but I'm not sure if it's correct or only works for this situation.

For $$ K^1 = 24/12 * 4 = 8 $$ For $$ K^2 = 24/8 * 1 = 3 $$ For $$ K^3 = 24/4 * 3 = 18 $$

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  • $\begingroup$ Hi, welcome to Engineering SE. Since this looks like homework, could you update the question, with what you have managed or tried to do so far? Then the members of this community can better help you with your question. $\endgroup$
    – NMech
    Oct 26 '20 at 8:30
  • $\begingroup$ I'm asking for an understanding on a concept on how to obtain a stiffness matrix. I'm not asking about the rest of the assignment. If I was to show what I've tried so far would show the stiffness matrix I"m asking about. I'm wondering how it is actually obtained as I can't find the information from google searches. $\endgroup$ Oct 26 '20 at 15:07
  • $\begingroup$ It's just algebra. The element matrices contain fractions 4/12, 1/8, 3/4. To add them together they were put over the same denominator, 8/24, 3/24, 18/24. $\endgroup$
    – alephzero
    Oct 26 '20 at 17:18
  • $\begingroup$ Thank you @alephzero. I just wasn't seeing that for some reason. $\endgroup$ Oct 26 '20 at 19:31

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