Nozzle Shell Deflection & Rotation Calculator

Nozzle Shell Deflection & Rotation

Unrestrained shell growth/rotation at a shell opening, for piping flexibility analysis (API 650 Appendix P.2.5–P.2.6)

◉ API 650 APPENDIX P STYLE CHECK · NOT A REGULATORY SUBMISSION TOOL

⚠ Scoped tool — this does not cover the full Appendix P procedure. Appendix P's allowable-load determination (§P.2.4, §P.2.7) is fundamentally a graphical procedure: the stiffness coefficients K_R, K_L, K_C come from twelve figures (P-2A–P-2L), and the final allowable-load check is built by hand-constructing nomograms from six more figure sets (P-3, P-4, P-5). That's not something this tool digitizes. What is closed-form — and what this tool computes, verified against Appendix P's own worked sample problem (§P.2.9) — is the unrestrained shell deflection (W) and rotation (θ) at a nozzle from product head and thermal expansion (§P.2.5), plus the resultant deflection/rotation formulas (§P.2.6) if you already have K_R/K_L/K_C from a piping engineer or specialized software. Use this for piping flexibility inputs, not for a full allowable-load sign-off.

Identification

Company

Tank ID

Nozzle / Opening ID

Record Type

Research entries stay private to you for practice/testing. Switch to Official once this is a real design your company should see.

Tank & Nozzle Geometry

Unit System

R — Nominal Tank Radius mm

t — Shell Thickness at Opening mm

a — Opening Outside Radius mm

L — Centerline Height Above Bottom mm

H — Maximum Design Liquid Level mm

G — Design Specific Gravity

ΔT — Design Minus Installation Temp °C

E — Modulus of Elasticity MPa

α — Thermal Expansion Coefficient mm/[mm-°C] ×10⁻⁶

E and α are read from Table P-1a/b by design temperature (linear interpolation permitted between the tabulated points) — enter the values directly here.

Unrestrained Shell Deflection & Rotation (§P.2.5)

Intermediate Values

β = 1.285/√(Rt)—

βL—

λ = a/√(Rt) (needed if reading K_R/K_L/K_C from Figures P-2A–P-2L)—

Result

W — unrestrained radial growth of shell—

θ — unrestrained shell rotation—

Resultant Deflection at Opening (§P.2.6) optional — requires K_R/K_L/K_C from elsewhere

These combine the shell deflection/rotation above with piping loads (F_R, M_L, M_C) and the shell stiffness coefficients (K_R, K_L, K_C). This tool can't derive K_R/K_L/K_C itself (see the note above) — leave this section blank unless you already have them from a piping flexibility analysis or Figures P-2A–P-2L.

F_R — Radial Thrust N

M_L — Longitudinal Moment N-mm

M_C — Circumferential Moment N-mm

K_R — Radial Stiffness N/mm

K_L — Longitudinal Moment Stiffness N-mm/rad

K_C — Circumferential Moment Stiffness N-mm/rad

Result

W_R — resultant radial deflection—

θ_L — resultant longitudinal rotation—

θ_C — resultant circumferential rotation—

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