As there is no standard barred tee design, there is no standard way to calculate the "real" SIF or stiffness.

I could suggest:

1. Have CAESAR calculate the welding tee SIF.
2. Uncheck and recheck the SIF, and input the SIFs manually.

This should eliminate the flexibility at the joint (i.e. make it stiff).

If the stresses in a barred tee with X force applied are to be less than a standard welding tee with X force applied, then applying the welding tee SIFs should be conservative.