Expansion Loop Calculator

Formula overview

SI: temperatures in °C, α in 10⁻⁶/°C, lengths in m with growth in mm, D in mm, E and S in N/mm².

ASME B31.3 para 319, guided-cantilever method:

  Δ   = α · ΔT · L_run                thermal growth
  f   = 6 · N^−0.2                    clamped to 0.15 – 1.0
  S_A = f · (1.25·Sc + 0.25·Sh)       allowable displacement stress range
  L   = √( 3·E·D·Δ / S_A )            required leg length

Worked example

Carbon steel line, 20 °C install → 200 °C operating, 30 m between
anchors, D = 168.3 mm, α = 11.7×10⁻⁶/°C, E = 203 000 N/mm²,
Sc = Sh = 138 N/mm², N = 7 000 cycles

ΔT  = 180 °C
Δ   = 11.7e−6 × 180 × 30 000 = 63.2 mm
f   = 6 × 7000^−0.2 = 1.02 → clamped to 1.0
S_A = 1.0 × (1.25 × 138 + 0.25 × 138) = 207 N/mm²
L   = √(3 × 203 000 × 168.3 × 63.2 / 207) = 5 593 mm ≈ 5.6 m

Common mistakes

• Treating the guided-cantilever result as a finished analysis. It assumes ends that are guided and free to rotate, which is idealised — a real loop with nearby restraints, branches, or unequal legs behaves differently and a critical line needs a proper flexibility model.
• Using ambient as the installation temperature without thinking. What matters is the metal temperature when the line was anchored, and on a line that also runs cold, the larger of the heating and cooling excursions governs.
• Ignoring the cycle count. f drops below 1.0 once N exceeds about 7 000 equivalent full cycles, cutting S_A and demanding a larger loop — thermal cycling on a batch or start-stop service can reach that far sooner than expected.

FAQ