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How to implement pin (hinge) jointed 2D frame with beam elements using FEA

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Dear friends,

I want to implement the pin connection between beam and column for the attached frame using finite element analysis.

For this purpose I use the attached definition of element stiffness matrix:

I want that the connection between elements 1 and 2 / 3 and 4 remains rigid. And I want that on the top of the 3rd element I have a hinge.

If I correct anderstand, to do this, I have to replace in element stiffness matrix of the 3rd element the 3rd row and the 3rd column by 0. For all other elements the element stiffness matrix remains without changing. Than I do coordinates transformation, assembling all element stiffness matrices to one global stiffness matrix [K], appling the boundary conditions and solving the following equation [K]*[u]=[F].

I checked my results with results from other FEM softwares and I have a large difference (more the 11 %). I have also calculate this frame with rigid connections between elements. The results match perfect with results from other FEM software.

I compare the nodal displacements.

Maybe I have forgotten to do something?

Many thanks in advance!

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