in-plane vs. out-plain bend flexibility

I have an elbow in my test model to which I have applied equal F1 and F2 in vertical and horizontal directions respectively.
I figured the displacements due to 'force-only' cases are not the same even though the in-plain and out-plain flexibilities of the elbow are equal.

I wonder if there is a sensible explanation for this case.

many thanks in advance

Hello Pooria,

You can try this manually by generating the stiffness matrix of the pipe and the elbow and see the results. Normally the flexibility matrix of elbow is given and need to invert it to get the stiffness matrix.

You can simplify the model, by including only the vertical rigid pipe and elbow only. This would reduce the stiffness matrix to 12 x 12 matrix.

Any other opinion is highly appreciated.

Cheers!!

Or you can make it more simple by fixing one end of the elbow and applying the force on the other end of the elbow. This would reduce your matrix to 6x6. I think, Caesar has an article for this flexibility matrix of elbow.

Warm Regards,

Explanation is that the vertical force will bend first elbow element on X and the second on Y while the lateral force will bend only on Z. You can try to see on simple pipe elements without using bend.
Regards,

Dan's explanation make sense. You can try pipe element stiffness matrix and see the result. The stiffness matrix of a bend took me a while to make a manual calculation out of the given flexibility matrix.

Cheers!!