If you are working with B31.1, I would suggest that you look at the 2004 edition (para 102.4.5) because the criteria for the minimum required thickness of a bend after bending has been revised.
TEMA (Tubular Exchanger Manufaturers Assn) has something similiar. It is based on the simple geometry of the situation. That is, the wall thinning is inversely related to bend radius.
t0 = t1(1+do/4R)
t0 = original wall thk
t1 = "minimum required" wall thk
do = OD
R = centerline bend rad.
You can solve this for t1 and "predict" the final thickness based on OD, R and t0.
You may be able to use this, it depends on whether you are working to some Code or standard, or whether you need a great deal of accuracy (if so, I wouldn't!).
