Does this replace CAESAR II?

No. Guided-cantilever sizing is a layout screening method. B31.3 still requires formal flexibility analysis for complex 3D systems, rotating equipment nozzles, and severe cyclic service.

How is U-loop width defined here?

This app sets W = H / 2 (aspect H:W = 2:1) with ΔL_leg = ΔL / 2 for a midpoint loop.

What does F_anchor include?

F_anchor = F_bending + μ · W_pipe, where F_bending uses the guided-cantilever stiffness form and W_pipe is plain-end mass × g for the entered length.

Thermal Expansion & Loop Sizing for 1 Inch Schedule 40 | FieldEngineersKit

Parameter	Value
Nominal pipe size (NPS)	1"
Schedule	Sch 40
Outside diameter (OD)	33.40 mm (1.315 in)
Wall thickness (t)	3.38 mm
Inside diameter (ID)	26.64 mm

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ASME B31.3 (2022 Edition) · (Process Piping) — flexibility & support (screening use) · ASME B31.3 (2022 Edition) · Appendix C · M.W. Kellogg guided-cantilever method (loop leg screening) · ASME B36.10M / B36.19M (OD, t, I from selected schedule)

Δ L = α \cdot L \cdot Δ T

L_{leg} = \frac{3 \cdot E _{h} \cdot D \cdot Δ L _{leg}}{S _{A}}

F_{anchor,total} = F_{bending} + F_{friction}, F_{friction} = μ \cdot W_{pipe,operating}

ASME B31.3 Appendix C & guided-cantilever thermal flexibility sizing

CS α 12.1 × 10⁻⁶ /°C304SS α 17.3 × 10⁻⁶ /°CH (leg) √(3 E_h D · ΔL/2 / S_A)W H / 2

This calculator computes unrestrained growth ΔL = α · L · ΔT with app mean α values (CS 12.1, 304SS 17.3, 316SS 16.2, Cr-Mo 13.7 ×10⁻⁶ /°C). Guided-cantilever leg H uses hot modulus E_h at T2, pipe OD D, ΔL_leg = ΔL/2, and S_A. U-loop width W = H/2. Anchor force adds rack friction μ · W_pipe. Guide spacing G₁ = 4·OD, G₂ = 14·OD. Screening only — not CAESAR II / B31.3 formal analysis.

ΔL (Total Thermal Growth) — Hero output — unrestrained expansion between anchors (mm or in).
α (Mean Expansion Coefficient) — App screening α per material family (µm/m·°C).
L (Straight Run Length) — Anchor-to-anchor free length (m or ft).
ΔT (Temperature Difference) — T2 − T1 (°C or °F in the active unit system).
H (L-shape / Loop Leg) — Guided-cantilever minimum leg: √(3 E_h D · ΔL_leg / S_A).
W (U-loop Width) — Taken as H/2 in this app (2:1 aspect).
E_h (Hot Modulus) — Elastic modulus at operating T2 (interpolated screening curve).
S_A (Allowable Displacement Stress Range) — Default 138 MPa (20 ksi) screening; override for B31.3 Eq. 1a.
F_anchor (Total Anchor Force) — F_bending + μ · pipe weight on the run.

2. Allowances, Tolerances & Standards

Results are field screening. Confirm with project stress engineering before steel fabrication.

U-loop Aspect (this app)W = H / 2

Symmetrical U-loop with H = 2W. Midpoint loop absorbs ΔL/2 on each leg.

Guide SpacingG₁ = 4·OD · G₂ = 14·OD

First and second directional guides from the loop tangent to keep growth in-plane.

Friction Screeningμ ≈ 0.30 steel · 0.10 PTFE

F_friction = μ · W_pipe for the entered straight length. Does not include fittings or contents.

Cold SpringNo S_A credit

B31.3 does not credit cold spring against the displacement stress range — same rule in this screening tool.

Quick Reference Lookup Table

Carbon-steel ΔL for L = 20 m (α = 12.1×10⁻⁶ /°C) — matches this app
T1 (°C)	T2 (°C)	ΔT (°C)	ΔL (mm)
21	70	49	11.9
21	100	79	19.1
21	150	129	31.2
21	200	179	43.3
21	300	279	67.5
15	180	165	39.9

Default case 21 → 150 °C on 20 m CS gives ΔL = 31.2 mm. Scale linearly with L at the same α and ΔT. Unit toggle converts the ΔL column.

3. Material & Code Limitations

α and E_h curves are screening approximations aligned to B31.3 App. C order of magnitude — confirm project tables for formal analysis.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
Carbon Steel (A106 / A53)	α = 12.1 × 10⁻⁶ /°C	Default S_A = 138 MPa (20 ksi)	Baseline industrial piping material in the calculator.
304 / 304L Stainless	α = 17.3 × 10⁻⁶ /°C	Default S_A = 138 MPa	~43% more growth than CS → deeper loops (H ∝ √ΔL).
316 / 316L Stainless	α = 16.2 × 10⁻⁶ /°C	Default S_A = 138 MPa	Slightly lower α than 304 in this app’s table.
Cr-Mo Alloy (P11 / P22 / P91)	α = 13.7 × 10⁻⁶ /°C	Default S_A = 138 MPa	High T2 still drives large ΔL despite moderate α.

Code Applicability & Safety Boundaries

Calculator scope: ΔL, guided-cantilever H/W, G₁/G₂, and F_anchor screening. It does not satisfy B31.3 formal computer analysis requirements.
Rotating-equipment nozzles and severe cyclic service need CAESAR II / AutoPIPE (or equal).
Confirm slide-plate travel ≥ ~1.5 × ΔL so shoes do not walk off the steel.

4. Step-by-Step Worked Example

Field VerificationShow

Reproduce the app default: CS A106, T1 = 21 °C, T2 = 150 °C, L = 20 m, NPS 4 Sch 40, S_A = 138 MPa, μ = 0.30.

Material:Carbon steel · α = 12.1 × 10⁻⁶ /°CTemperatures:T1 = 21 °C · T2 = 150 °C (ΔT = 129 °C)Straight length L:20 mPipe:NPS 4 Sch 40 (OD = 114.3 mm, t = 6.02 mm)S_A / μ:138 MPa · μ = 0.30

Compute ΔL

Δ L = α L Δ T

ΔL = 12.1×10⁻⁶ × 20 m × 129 °C × 1000 = 31.22 mm.

Result:ΔL = 31.2 mm

Matches the calculator hero for the default inputs.

Split growth per leg

Δ L_{l e g} = Δ L /2

ΔL_leg = 31.22 / 2 = 15.61 mm.

Result:ΔL_leg = 15.61 mm

Midpoint U-loop / L-bend assumption.

Hot modulus E_h at 150 °C

CS screening curve: E(100 °C) = 198 GPa, E(200 °C) = 191 GPa → E_h(150 °C) = 194.5 GPa.

Result:E_h = 194,500 MPa

Same interpolation used in the engine.

Guided-cantilever leg H and width W

H = \frac{3 E _{h} D Δ L _{l e g}}{S _{A}}, W = H /2

H = √(3 × 194500 × 114.3 × 15.61 / 138) ≈ 2747 mm = 2.75 m. W = 1.37 m.

Result:H = 2.75 m · W = 1.37 m

Matches the calculator L-shape / U-loop recommendations.

Guides and anchor force

G_{1} = 4 D, G_{2} = 14 D, F_{an c h or} = F_{b e n d in g} + μ W_{p i p e}

G₁ = 4 × 114.3 = 457 mm · G₂ = 14 × 114.3 = 1600 mm. With μ = 0.30, F_anchor ≈ 11.53 kN (bending + friction).

Result:G₁ = 457 mm · G₂ = 1600 mm · F_anchor ≈ 11.53 kN

Screening anchor load for support design — confirm with stress analysis.

Conclusion: Default app case: ΔL = 31.2 mm, H = 2.75 m, W = 1.37 m, G₁/G₂ = 457 / 1600 mm, F_anchor ≈ 11.53 kN. Use for layout budgeting only.

5. Frequently Asked Questions & Technical References

Show

App α(304SS) = 17.3×10⁻⁶ /°C vs α(CS) = 12.1×10⁻⁶ /°C (~43% more ΔL). Because H ∝ √ΔL, the leg is roughly ~19% deeper for the same L, ΔT, D, and S_A.

Thermal Expansion & Loop Sizing — 1 Inch Schedule 40

1 Inch Schedule 40 specification summary

1. Core Formula & Variable Definitions

2. Allowances, Tolerances & Standards

Quick Reference Lookup Table

3. Material & Code Limitations

Code Applicability & Safety Boundaries

4. Step-by-Step Worked Example

Compute ΔL

Split growth per leg

Hot modulus E_h at 150 °C

Guided-cantilever leg H and width W

Guides and anchor force

5. Frequently Asked Questions & Technical References

Thermal Expansion & Loop Sizing — 1 Inch Schedule 40

1 Inch Schedule 40 specification summary

1. Core Formula & Variable Definitions

2. Allowances, Tolerances & Standards

Quick Reference Lookup Table

3. Material & Code Limitations

Code Applicability & Safety Boundaries

4. Step-by-Step Worked Example

Compute ΔL

Split growth per leg

Hot modulus E_h at 150 °C

Guided-cantilever leg H and width W

Guides and anchor force

5. Frequently Asked Questions & Technical References

Why does 304SS need a deeper loop than carbon steel?

Does this replace CAESAR II?

How is U-loop width defined here?

What does F_anchor include?