Does this replace WRC 107 / 537 nozzle stress analysis?

No. UG-37 is an internal-pressure area replacement screen only. Piping deadweight, thermal, and seismic moments require WRC 107/537/297 (or equivalent) local stress evaluation.

When is f_r2 less than 1.0?

When nozzle allowable stress is below shell allowable (S_noz / S_shell < 1). UG-41 then reduces credited A₂ and A₃ by f_r2.

Why can NPS 12 fail even with a thick pad?

If D_p ≤ d_out, pad width is zero and A₄₂ = 0. Increase pad outside diameter so D_p > d_out, then re-check t_p min.

Pressure Vessel Nozzle Reinforcement Pad (ASME VIII-1 UG-37) Calculator

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ASME BPVC Section VIII Division 1 UG-37 · ASME BPVC Section VIII Division 1 UG-40 · ASME BPVC Section VIII Division 1 UG-41 · ASME BPVC Section VIII Division 1 UG-27 / UG-32 · ASME BPVC Section II Part D Table 1A

A = d · t_r · F + 2 · t_n · t_r · F · (1 − f_r1) (UG-37(c))

A_avail = A₁ + A₂ + A₃ + A₄₁ + A₄₂ (UG-40)

A₄₂ = (D_p − d_out) · t_p · f_r4

A_avail ≥ A ⇒ Pass · else Repad Required

Required area UG-37(c)Available area UG-40Strength of reinforcement UG-41Radial opening F 1.0

ASME Section VIII Division 1 Paragraphs UG-37 / UG-40 / UG-41 size openings by the area replacement method. F = 1.0 for radial openings in cylindrical shells and for openings in formed heads under this screen. Stress reduction factors f_r1, f_r2, f_r4 are capped at 1.0 (S_element / S_shell). Confirm allowable stress S from the project edition of Section II Part D Table 1A.

A (Required reinforcement area) — Minimum cross-sectional area that must be replaced for the opening (mm² or in²).
A_avail (Total available reinforcement area) — Sum of A₁ + A₂ + A₃ + A₄₁ + A₄₂ within UG-40 limits of reinforcement.
d (Finished opening diameter) — Finished diameter of the circular opening in the corroded condition — taken as nozzle ID after corrosion allowance (mm or in).
t_r (Required shell / head thickness) — UG-27 (cylinder) or UG-32 (2:1 SE / spherical) minimum required thickness of the vessel wall (mm or in).
t (Corroded shell thickness) — Nominal shell thickness less corrosion allowance (mm or in).
t_n (Corroded nozzle thickness) — Nominal nozzle wall thickness less corrosion allowance (mm or in).
t_rn (Required nozzle thickness) — UG-27 required thickness of the nozzle neck under internal pressure (mm or in).
D_p (Reinforcement pad outside diameter) — Outer diameter of the added reinforcing element (mm or in).
t_p (Reinforcement pad thickness) — Thickness of the reinforcing pad / element (mm or in).
f_r1, f_r2, f_r4 (Stress reduction factors) — min(1, S_nozzle/S_shell) or min(1, S_pad/S_shell) per UG-41 — reduces credited area when the reinforcing element is weaker than the vessel wall.
F (Correction factor) — Fig. UG-37 factor for nonradial openings. This calculator uses F = 1.0 for radial openings.

2. Design Allowances & UG-37 Scope

Default screening duty is Metric cylindrical shell ID 1200 mm, P 2.0 MPa, T 150 °C, SA-516 Gr.70 shell, NPS 6 Sch 80 nozzle (SA-106 Gr.B), E₁ = 1.00, C.A. = 3.0 mm, pad D_p = 300 mm / t_p = 12 mm. Results verify internal-pressure area replacement only.

Corrosion allowance (C.A.)0–10 mm / 0–0.4 in

Deducted from shell and nozzle nominal walls before excess-area credits. Finished opening diameter uses the corroded nozzle ID.

Joint efficiency (E₁)0.85 / 1.00

Shell / head longitudinal joint efficiency used in t_r and A₁ excess terms.

Correction factor F1.0 (radial)

Radial openings in cylinders and openings in formed heads use F = 1.0 under this screen. Nonradial Fig. UG-37 cases are out of scope.

Out of scopeWRC / vacuum / Appendix-1-7

WRC 107/537/297 nozzle local stresses, external pressure (UG-28), and large-opening Appendix 1-7 rules are not included. Complete a stamped vessel calculation for fabrication.

Quick Reference Lookup Table

UG-37 required vs available area (no pad metal) at shell ID 1200 mm, P = 2.0 MPa, T = 150 °C, SA-516 Gr.70, t_shell = 16 mm, C.A. = 3.0 mm, E₁ = 1.00, SA-106 Gr.B nozzle Sch 80
NPS	d_out (mm)	A (mm²)	A_avail (mm²)	Pad?
2	60.3	485	260	Required
4	114.3	906	569	Required
6	168.3	1337	916	Required
8	219.1	1753	1243	Required
10	273.1	2185	1671	Required
12	323.9	2589	2046	Required

With the default pad D_p = 300 mm and t_p = 12 mm on NPS 6, the engine returns Pass (A ≈ 1337 mm², A_avail ≈ 2664 mm², t_p min ≈ 2.88 mm). NPS 12 at this pad OD has D_p < d_out — increase pad diameter before sizing t_p.

3. Material Specifications & Stress Reduction Limits

Allowable stresses are interpolated from ASME Section II Part D Table 1A screening curves. When nozzle or pad allowable stress is below shell allowable, UG-41 f_r factors reduce credited reinforcement area.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
SA-516 Gr.70 (Carbon Steel Plate — shell / pad)	−29 °C to 482 °C (−20 °F to 900 °F) screening	20.0 ksi (137.9 MPa) through ≈400 °F; derates above 500 °F	Default shell and assumed pad grade. Pad f_r4 = 1.0 when pad S equals shell S.
SA-106 Gr.B (Carbon Steel Pipe — nozzle)	Up to ≈538 °C (1000 °F) screening	Same CS screen as SA-516 Gr.70 in this calculator (20.0 ksi ambient band)	Typical CS nozzle neck. Matched CS shell/nozzle pairs usually keep f_r1 = f_r2 = 1.0.
SA-240 316L (Austenitic SS Plate — shell)	Cryogenic to ≈816 °C (1500 °F) stress table screen	16.7 ksi (115 MPa) near ambient; derates with temperature	Shell option for stainless vessels; pair carefully with nozzle grade for f_r.
SA-312 TP316L (Austenitic SS Pipe — nozzle)	Cryogenic to ≈816 °C (1500 °F) stress table screen	Same 316L screen as SA-240 316L in this calculator	When nozzle S < shell S (e.g. 316L nozzle on CS shell), f_r2 < 1 reduces A₂ and A₃ credits.

Code Applicability & Safety Boundaries

UG-37 area replacement applies to internal pressure openings within the code size limits. Large openings may require Appendix 1-7.
This screen does not replace WRC 107/537/297 local stress evaluation for attached piping loads.
External pressure / vacuum on shells and nozzles requires UG-28 — not covered here.

4. Step-by-Step Worked Example

Field VerificationShow

Step-by-Step Worked Example: NPS 6 Nozzle on 1200 mm Shell

Check ASME VIII-1 UG-37 area replacement for an NPS 6 Sch 80 nozzle in a 1200 mm ID cylindrical shell at 2.0 MPa / 150 °C with a 300 mm OD × 12 mm pad.

Shell type:Cylindrical shell (UG-27 / UG-37)Shell ID (D_i):1200 mmDesign pressure (P):2.0 MPaDesign temperature (T):150 °CShell material:SA-516 Gr.70 · S = 137.9 MPaShell thickness:16.0 mm (t = 13.0 mm after C.A.)Nozzle:NPS 6 · d_out = 168.3 mm · t_niz = 11.0 mmNozzle material:SA-106 Gr.B · S = 137.9 MPa · f_r = 1.0Corrosion allowance:3.0 mmPad:D_p = 300 mm · t_p = 12 mm

Required shell and nozzle thicknesses

Formula: t_r = P·R / (S·E − 0.6·P)

R = 600 mm → t_r = 2.0 × 600 / (137.9 − 1.2) ≈ 8.78 mm. Corroded nozzle ID gives t_rn ≈ 1.11 mm.

Result:t_r ≈ 8.78 mm · t_rn ≈ 1.11 mm

Required reinforcement area A

Formula: A = d · t_r · F (f_r1 = 1)

d = d_out − 2·t_n = 168.3 − 2×8.0 = 152.3 mm → A = 152.3 × 8.78 × 1.0

Result:A ≈ 1337 mm²

Available areas without relying on speculative welds

A₁ ≈ 643 mm² (shell excess), A₂ ≈ 441 mm² (nozzle excess with pad limit), A₃ = A₄₁ = 0, A₄₂ = (300 − 168.3) × 12 ≈ 1580 mm².

Result:A_avail ≈ 2664 mm²

Pass / Fail and minimum pad thickness

A_avail ≥ A → Pass. Without pad metal, A_avail ≈ 918 mm² < A, so a pad is required. Solving A_avail(t_p) ≥ A at D_p = 300 mm gives t_p min ≈ 2.88 mm.

Result:Pass · t_p min ≈ 2.88 mm (entered t_p = 12 mm)

Conclusion: The NPS 6 / 1200 mm / 2.0 MPa duty Passes with the 12 mm pad (A ≈ 1337 mm² vs A_avail ≈ 2664 mm²). Minimum pad thickness at D_p = 300 mm is ≈ 2.88 mm. Confirm WRC local stresses and UG-28 vacuum separately before fabrication.

5. How to calculate ASME VIII-1 UG-37 nozzle reinforcement

1
Enter shell duty and nozzle size
Set shell type, ID, P, T, shell thickness/material, joint efficiency, and nozzle NPS / wall / material with corrosion allowance.
2
Enter pad geometry
Provide reinforcement pad outside diameter D_p and thickness t_p (use 0 to screen without added pad metal).
3
Read Pass / Repad Required and t_p min
Hero status is Pass when A_avail ≥ A. Badge shows minimum pad thickness at the entered D_p. Review A₁–A₄₂ rows for where the metal comes from.
4
Export and open related tools
Export JSON/CSV/PDF, then carry shell ID / P / T / material into Pressure Vessel Head Thickness or Pipe Wall Thickness as needed.

6. Frequently Asked Questions & Technical References

Show

Pass means A_avail ≥ A with the entered pad thickness. If t_p min > 0, excess shell/nozzle metal alone is not enough — a reinforcing element is required, but the entered pad is adequate.