WRC-537 is the updated precision version of WRC-107. Published in 2010, WRC-537 standardizes and mathematically formats the original 1965 WRC-107 hand-drawn charts into precise equations. Both calculate identical theoretical stresses under Bijlaard shallow shell theory, but WRC-537 eliminates human chart-interpolation errors.

WRC-107/537 is limited to diameter ratios d/D ≤ 0.33 (or non-dimensional parameter β = 0.875 ro / Rm ≤ 0.5) and vessel shell slenderness γ = Rm / T ≤ 300. For large nozzles (d/D > 0.33) or thin-wall tanks, shallow shell theory fails to capture hoop ovalization, requiring WRC-297 or full 3D Finite Element Analysis (FEA) per ASME Section VIII Div 2 Part 5.

For sustained mechanical loads (vessel internal pressure plus piping deadweight), the localized membrane plus bending stress intensity (PL + Pb) must not exceed 1.5 Sm (where Sm is the material allowable stress at design temperature). For total operating loads including thermal piping expansion (P + Q), the stress intensity limit is 3.0 Sm (the shakedown secondary stress criterion).

Points A and B lie on the longitudinal vessel centerline axis (0° and 180°), where the longitudinal bending moment ML produces maximum shell bending stress. Points C and D lie on the transverse circumferential plane (90° and 270°), where the circumferential bending moment MC generates maximum hoop bending stress.

A repad reduces local stresses at the nozzle neck by increasing the effective shell thickness (Te = T + Tpad). However, it transfers the structural stiffness discontinuity to the outer perimeter fillet weld. Engineers must verify stress intensities both at the nozzle neck junction and at the outer pad-to-shell weld toe, where stress concentration frequently controls.