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,

I've missed to incorporate the shear deformation factor β=12EI/GAL^2 *fs from the modified stiffness eqution considering shear deformation 12EI/L^3(1+β). My question is what value of fs (factor for non uniform shear area) does stress programs used?I assume this is 2 because when I use this factor I've got the right results and also I've read that the average shear stress Ss= 2 (F)/A.Thanks in advance for the help