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When you filled in the stiffness matrix template with the elementās stiffness matrices quadrants, and get the overlap between the green and pink area; why the pink is dominating? With other words, why the member B values have been populated to the template and not the member A values?

Hey,

Iām not sure I follow completelyā¦

No single element dominates when filling in the primary stiffness matrix (PSM). The contribution from all elements are simply added to their respective locations in the PSM.

If this hasnāt helped clear things up, perhaps leave a timestamp to the time in the video that your question relates toā¦this will help me give a better answer.

Cheers,

SeĆ”n

thanks for the explanation, however it is still not clear for me. So, if I take both `K_A,G`

and `K_B,G`

from time `1:32`

in the lecture, as below:

ā¦then I would expect to fill in the template with these ones at around `5:20`

in the lecture. But in the quadrant `K_A22`

I see different values respect to the ones in the previous slides.

With other words, why the the quadrant `K_A22`

values become `[0.405, -0.096; -0.096, 0.128]`

from `[0.333,0; 0,0]`

So I still see `K_A22`

competing with `K_B11`

for the same place in the overlapping area in the stiffness matrix.

Hey,

This is because when we generate the primary stiffness matrix, some of the values will actually be the superposition of individual values from the element stiffness matrices. This is the beauty of the methodā¦we can build up the overall primary stiffness matrix by simply ā*overlaying*ā the contribution from individual members within the structure.

So to obtain the values in the overlapping area of the primary stiffness matrix we add K_A,22 and K_B,11. This makes sense as these degrees of freedom are common to both elementsā¦since they are connected together at node 2.

Let me know if you still find this confusing.

SeĆ”n

ok, got it now, overlaying means basically just an addition of the two in the overlapping area ā¦I was completely off, just looking at the `-0.096`

and never realised that `K_A22`

has zero values in the same place, so producing the same value.

Now you have it - once youāve understood this concept of ābuilding upā the stiffness matrix, it generalises to many many more analyses.

SeĆ”n

Yess, very much make sense. ā¦above all, by now, after the Truss 2 Question exercise gave a lot of understanding working alone on the problem. Due to the larger structure (6 nodes, 8 members) it gave the concept how to fill in the template stiffness matrix. And also, how to work at āscaleā with the matrices and vectors.

And the result is so satisfying

PS.: And at some point (when solving for displacement) I got an error, the famous error which we used to get in FEA solvers a `Singular matrix`

ā¦I couldnāt invert matrix `Ks`

because I forgot to include member `F`

and `G`

in my primary stiffness matrix. So `Ks.I`

couldnāt run. So my structure didnāt make sense with only bar members.

I used the below draft for myself, but you may see that those two membrs are missing. ā¦such a nice experience

Great to hear youāre enjoying the course! Yesā¦something very satisfying about coding up a solution to a structure that would be unfeasible to solve by hand.

Ah yes, the good old singular matrixā¦wonāt be the last time you hit that !

Keep it up!

SeĆ”n