Where:
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- ts = shell (or head) thickness
- L = characteristic length (e.g., diameter)
Conditions:
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- When ts/L≥0.002 : Appendix 1-4(d) is applicable.
- When ts/L<0.002: In addition to UG-32 requirements, the rules of Mandatory Appendix1, 1-4(f) must also be satisfied.
Report : Covers both requirements: Appendix 1-4 (d) & (f) as applicable for torispherical head

Nozzle opening calculation:
For the nozzle opening calculation UG-37 (a), the primary reference is UG-32, which further refers to Appendix 1, 1-4(f), see:
Accordingly, the reported value of (tr) in opening calculations represents the maximum of all minimum required thicknesses calculated as per UG-32 and its associated references.
In this case, minimum required thickness (tr) in nozzle opening calculation is the smallest thickness, obtained by iteration, that satisfies condition 1-4(f)(1)(-i).
Why Head minimum thickness calculation in Summary of Thicknesses is different:
This is due to the application of paragraph 1-4(f) in Operating condition.It is the smallest thickness, obtained by iteration, that satisfies condition 1-4(f)(1)(-i).The minimum head thickness is the largest of the minimum required thicknesses, calculated according to all code requirements. In the case of ASME, there are two values to calculate: one obtained by direct calculation for Appendix 1-4(d), and another by iterative calculation for Section 1-4(f).
To this must be added the value of the straight flange (not relevant here).
These 3 calculations are clearly mentioned in the report...