General membrane mechanics — not code pressure design
Thin-Wall Internal-Pressure Screening Arithmetic
Calculate an ideal hoop-membrane pressure wall from a controlled inside diameter and documented effective stress limit, then apply a documented unavailable-wall allowance and negative manufacturing tolerance. No schedule, MAWP, burst pressure or code-compliance result is generated.
tn,min=(tp+c)/(1−m)
P is differential gauge pressure; Di and ri=Di/2 are the controlled internal diameter/radius at the assessed state; tp is effective wall resisting pressure; σlim is a documented permissible effective hoop-membrane stress; c is total unavailable wall; m is a decimal maximum negative manufacturing tolerance; tn,min is the arithmetic nominal wall before that tolerance. Pressure and stress must use the same units; all lengths must use the same units.
For an ideal closed-end thin cylinder, the axial pressure membrane stress at tp is σa=P·ri/(2tp)=σlim/2. The result does not include any other axial, bending, torsional, thermal, local or cyclic load.
Applicability gate
The calculator suppresses results when tp/ri>0.1. The public University of Illinois derivation treats the thin-wall approximation as sufficient at ri/t≥10 and explicitly states uniform through-wall stress and neglected radial stress. Passing this numerical screen does not establish code applicability.
Standards boundary
ASME B31.3-2024 is the current process-piping code record and covers materials, components, design, fabrication, assembly, erection, examination, inspection and testing. Its exact pressure-design equations, coefficient tables, allowable stresses and service rules are licensed content and are not reproduced here.
ISO 4200:1991 edition 4 is published and under review. It is a general table of dimensions and masses for plain-end welded/seamless steel tubes, not a pressure-design approval. Product dimensions and tolerances must come from the selected controlled product specification.
ASTM A106/A106M-26 is the current ASTM listing for seamless carbon-steel pipe for high-temperature service. The old universal 138 MPa, 12.5% and schedule claims have been removed; exact material/tolerance/product rows require the complete applicable standards.
Kilder
University of Illinois thin-walled pressure vessels; Purdue ME323 summary; ASME B31.3-2024 official record; ISO 4200:1991; ASTM current steel-standards listing; NIST conversion factors.