EJMA Bellows Expansion Joint Rating Calculator — Sample Report

ProjectSample Project — Demonstration Only	Job No.SAMPLE-001	Client—
CalculationEJMA Bellows Expansion Joint Rating Calculator	Calc byPiping Toolset (calc-core)	Checked byUNCHECKED — sample
Date2026-10-28	Rev0	BasisEJMA-framework bellows screening: effective area, pressure thrust, spring loads, column squirm Psc = 0.34π·Cθ·Kax/Lb (10th Ed. Eq. (4-43), unreinforced U-shaped)

1 · Design inputs

24 in mean-diameter bellows expansion joint, design pressure 150 psi, with rated movements and spring rates and squirm-screening geometry supplied by the manufacturer. This is the case the column-squirm screen exists to catch: the loads and geometry look unremarkable, and only the squirm arithmetic reveals a problem.

P	150	psi
Dm	24	in
xAxial	0.5	in
yLateral	0.25	in
thetaDeg	1.2	deg
kAxial	1500	lbf/in
kLateral	3200	lbf/in
kBending	850	in·lbf/deg
Lb	18	in
nConv	12	—

2 · Method

Bellows loads scale off the mean-diameter effective area, independent of the actual corrugation profile:

A_e = π/4 · D_m²

F_t = P · A_e (pressure thrust)

F_ax = K_ax·|x|, F_lat = K_lat·|y|, M_b = K_b·|θ| (spring loads from movement)

Total axial anchor load = F_t + F_ax

P_sc = 0.34·π·C_θ · K_ax / L_b (column-squirm screening pressure, unreinforced U-shaped bellows, C_θ = 1 default)

This is EJMA 10th Ed. Eq. (4-43), P_sc = 0.34π·C_θ·f_i/(N²·q), rewritten in terms of the whole-bellows axial spring rate K_ax (per-convolution rate f_i = K_ax·N, pitch q = L_b/N): N²·q = N·L_b, so N cancels and the screen reduces to K_ax/L_b with no convolution-count term at all — a bellows split into more, shorter convolutions at the same overall length and the same whole-bellows stiffness has the same squirm pressure, not a higher one. P_sc is compared against an operating pressure (defaults to the design pressure P when not entered separately); an operating pressure at or above P_sc flags INSTABILITY RISK. This coefficient (0.34π) applies to unreinforced U-shaped bellows only — reinforced construction uses 0.3π and toroidal construction uses 0.15π (see the rigorous PiperEXJ bellows-verify tool, which implements all three forms); apply this screen only to unreinforced U-shaped bellows. Bellows hoop/meridional stress and EJMA fatigue cycle life N_c are outside this screening — they require the manufacturer's ply count, thickness and root/crown radii.

3 · Calculation

Effective area: Ae = π/4·24² = π/4·576 = 452.38934 in².
Pressure thrust: Ft = 150·452.38934 = 67858.4 lbf.
Axial spring force: Fax = 1500·0.5 = 750 lbf.
Lateral spring force: Flat = 3200·0.25 = 800 lbf.
Bending moment: Mb = 850·1.2 = 1020 in·lbf.
Total axial anchor load: 67858.4 + 750 = 68608.4 lbf.
Squirm screening (EJMA (4-43), Cθ = 1, N cancels): Psc = 0.34·π·1500/18 = 1.068142·1500/18 = 1602.212/18 = 89.012 psi.
Operating pressure defaults to P = 150 psi; 150 psi >= 89.012 psi → INSTABILITY RISK, status FAIL.

4 · Results FAIL

Ae — effective area	452.38934	in²
Ft — pressure thrust	67858.4	lbf
Fax — axial spring force	750	lbf
Flat — lateral spring force	800	lbf
Mb — bending moment	1020	in·lbf
Total axial anchor load	68608.4	lbf
Psc — squirm screening pressure	89.012	psi
Squirm verdict	INSTABILITY RISK	—

5 · Verification statement

The result values above are locked as fixture ejma-rating.json, case “24 in mean dia bellows, P=150, corrected squirm -> instability risk (PVP Ae anchor)”, tolerance 0.001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: EJMA — Standards of the Expansion Joint Manufacturers Association, 10th Edition, Eq. (4-43): column-squirm screening pressure for a single unreinforced U-shaped bellows. · EJMA — Standards of the Expansion Joint Manufacturers Association, effective area, pressure thrust and spring-rate load definitions.

SAMPLE REPORT — auto-generated from a verification fixture to show the report format. Not a project calculation. ⚠ Engineering-aid tool. Public code equations; allowable-stress and factor data are user-supplied. Results MUST be independently verified and reviewed by a qualified/licensed engineer before any design, fabrication, or operation decision.