SAMPLE — Expansion Loop / Leg Sizing Calculator (Guided Cantilever)

Piping Toolset — Calculation Report

generated by calc-core · 2026-07-21

ProjectSample Project — Demonstration Only	Job No.SAMPLE-001	Client—
CalculationExpansion Loop / Leg Sizing Calculator (Guided Cantilever)	Calc byPiping Toolset (calc-core)	Checked byUNCHECKED — sample
Date2026-07-21	Rev0	BasisGuided cantilever √(3EDΔL/kS) — Kellogg / PPI forms

1 · Design inputs

2½ in (2.875 in OD) carbon-steel line, installed at 52 °F, operating at 350 °F, 100 ft anchor-to-anchor. α = 6.7×10⁻⁶ in/in·°F, E = 29×10⁶ psi, S = 15,600 psi — the published flow-sheet example.

Config / family	L bend, metallic	—
OD	2.875	in
α	6.7×10⁻⁶	in/in·°F
T0 → T1	52 → 350	°F
Run length	100	ft
E / S	29×10⁶ / 15,600	psi

2 · Method

ΔL = α · |T₁ − T₀| · L (free growth of the run)

L_gc = √( 3·E·D·ΔL / (k·S) ) (required flexible leg)

Configurations: L change-of-direction uses the full leg; Z offset takes 0.6426·L_gc (the published 4 vs 6.225 coefficient ratio, E/S-invariant); U loop proportions the developed length as W = L_gc/5, H = 2W. With E = 29×10⁶ psi and S = 15,600 psi the metallic form reproduces the published rule W(ft) = 6.225·√(ΔL·D).

3 · Calculation

Growth: ΔL = 6.7×10⁻⁶ · (350−52) · 1,200 in = 6.7×10⁻⁶·298·1,200 = 2.396 in.
Leg: L_gc = √(3·29×10⁶·2.875·2.396 / 15,600) = √598,000,000/15,600 ≈ √38,415 = 196.0 in = 16.33 ft.
Cross-check against the published coefficient rule: 6.225·√(ΔL·D) = 6.225·√(2.396·2.875) = 6.225·2.625 = 16.34 ft ✓.
Same inputs as a Z-offset: 0.6426·196.0 = 125.9 in; as a U-loop: W = 39.2 in, H = 78.4 in.

4 · Results COMPUTED

ΔL — thermal growth	2.396	in
L-bend leg	196.0 in (16.33 ft)	—
Z-offset leg	125.9	in
U-loop W × H	39.2 × 78.4	in

5 · Verification statement

The result values above are locked as fixture expansion-loop.json, case “PDF sheet L-bend: CS 2.875 OD, 52→350°F, 100 ft (E=29e6, S=15600)”, tolerance 0.005, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: M.W. Kellogg, Design of Piping Systems — guided cantilever method (public-domain engineering method). · Published coefficient rule W = 6.225·√(ΔL·D) (L/U) and 4·√(ΔL·D) (Z) — reproduced exactly by the general form at E = 29e6, S = 15,600 psi. · PPI / Corzan CPVC practice — plastic form L = √(3·E·D·ΔL/(2·S)) with working stress at max temperature.

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.