Bend Angle Effect on B₂ and C₂ Stress Indices for Piping Elbows

$B2$ and $C2$ stress indices are used for calculation of stress terms corresponding to moment loading in evaluation of nuclear piping components. The formulas given in the ASME Boiler & Pressure Vessel Code for calculating these indices for elbows and curved pipes are independent of the bend angle. The objective of this investigation was to study the effect of the bend angle on the values of $B2$ and $C2.$ For this purpose, elbows with sizes ranging from 2.5 to 20 in. have been studied. The values of $B2$ and $C2$ have been calculated by detailed analysis using finite element models. Each elbow size has been analyzed for various bend angles (e.g., 15, 30,…90 deg and above). The results of this study show that the values of $B2$ and $C2$ based on the ASME Code formulas are conservative and more so if the bend angle is less than 90 deg. The values of $B2$ and $C2$ decrease as the bend angle is decreased. The reduction in the values is very significant for smaller bend angles. Simple relations have been established to express the dependence of $B2$ and $C2$ on the bend angle. Based on these results, a modified form of ASME Code formulas is proposed to account for the bend angle effect.