I am studying stiffness matrix of piping system and at this point I know how to manually form the stiffness matrix with the consideration of anchor as infinitely rigid.But stress programs use a certain stiffness for an anchor which is high enough to be considered as fixed anchor. I've tried to run a simple L shape piping configuration with anchor at both ends and square corner. A plane frame problem in matrix analysis. I've manually calculated it and got some discrepancy. This due to the fact that I have not considered the stiffness of anchor (translational and rotational)in my manual calculation. As of now I'm still in progress with my self study and hang up at this point on how can I incorporate the stiffness of the anchor in the stiffness matrix. Any help is highly appreciated. Many thanks in advance.

Cheers,