A — Free expansion of a length
B — Shaft centreline growth (hot alignment target)
The Calculation, Explained
The one equation
Everything in thermal expansion is this line and the judgement of what α, L and ΔT honestly are. α for the common plant materials (×10⁻⁶/°C): carbon steel 12, stainless 304 about 17 (the reason stainless piping outgrows its carbon-steel supports), cast iron 10.5, copper 17, aluminium 23. Note what the formula does not contain: cross-section. A 12 m header and a 12 m instrument line of the same steel grow the same 20 mm at ΔT 140 — diameter decides the forces, never the movement.
When expansion is prevented, it becomes stress
Hold both ends of a carbon-steel pipe rigidly and warm it 140 °C and the metal sees 200,000 × 12×10⁻⁶ × 140 = 336 MPa — at or past yield for common pipe grades. This is why expansion loops, bends and bellows exist, why anchor loads are enormous, and why a "short, stiff, well-supported" hot line is a structural problem disguised as good housekeeping.
Assumptions and applicability
- Uniform temperature through the length and section. Real lines have gradients (stratification in steam lines during warm-up is the classic case) that bow pipe in ways a single ΔT cannot describe.
- α itself rises modestly with temperature; the tabulated values are means over the usual plant range — adequate for layout and alignment, not for high-temperature creep design.
- Centreline growth (block B) uses the pedestal/casing temperature rise, not the steam temperature: the feet stand on metal that is somewhere between ambient and process temperature. OEM hot-alignment targets, where published, supersede this estimate — they were measured on the actual machine.
- Driver and driven machine rarely grow equally; the alignment target is the difference of their growths, applied deliberately cold so the shafts run true hot.
Worked example (the defaults above)
12 m of carbon steel from 25 °C ambient to 165 °C service (ΔT 140): ΔL = 12×10⁻⁶ × 12 × 140 = 20.2 mm — the travel your supports and loop must swallow. And a machine whose shaft sits 250 mm above its feet, with the casing averaging 90 °C above ambient, grows 0.27 mm upward: the cold alignment must park the shaft 0.27 mm low (relative to its partner's own growth) or the coupling runs high all its life. Feed that number into the Alignment Calculator as your intended cold offset.
References
Standard materials data (ASM/MatWeb typical values); piping flexibility practice per ASME B31.1/B31.3.
Related calculators: Alignment Shim Calculator · Bolt Torque & Preload