Finite Element internal hinge

[moe95]

I would like to know how to implement internal hinges in a program I'm developing. A hinge is created by changing the stiffness matrix of the beam. The problem is when two interconnected beams have a hinge at the same location, so basically we have a hinged joint, in this scenario I will obtain singularity in the stiffness matrix.
I'm mainly interested in hinged joint so is there another way to do it? Thank you

 

[Denial]

I must be missing something here, but won't you avoid that singularity if you apply the modified stiffness matrix to only one of the two connected beams?