Expansion Loop Sizing

Guided-cantilever loop leg to absorb thermal growth per ASME B31.3 para 319

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Engineering Tips

Sizes the perpendicular loop leg (offset) needed to absorb the thermal growth of an anchored run within the allowable displacement stress range, using the guided-cantilever method.

Guided cantilever:

• Δ = α·ΔT·L_run — growth to absorb

• S_A = f·(1.25·Sc + 0.25·Sh)

• L = √(3·E·D·Δ / S_A) — required leg

• σ = 3·E·D·Δ / L² — leg stress

Recommended values

Modulus E: Use the hot Young’s modulus for the displacement stress. 203,000 N/mm² carbon steel.
Sc / Sh: Basic allowable stress at cold (install) and hot (operating) temperature from Table A-1.
Cycles N: ≤ 7000 → f = 1.0. Higher cycle counts reduce S_A and lengthen the loop.

Limitations

Screening: Assumes a symmetric square-cornered loop; ignores pressure, weight and SIF effects. Not a formal flexibility analysis.
Critical lines: Confirm with a beam/FEA pipe-stress model for large-bore, high-temperature or cyclic-critical services.

About the standards

ASME B31.3 para 319: flexibility and displacement stress range.
ASME B31.3 para 302.3.5: S_A and the cyclic stress-range factor f.

Expansion Loop Sizing

Input Parameters

Thermal Growth

Pipe & Material

Allowable Stress Range