Defaults come from the pipe and material databases. Override only if you have project-specific values.
Formulas & Engineering Reference
| Symbol | Variable | Unit (SI) |
|---|---|---|
| ΔL | Thermal growth of the straight run | mm |
| α | Mean coefficient of thermal expansion | 1/°C |
| L | Anchored straight length | mm |
| ΔT | Operating − installation temperature | °C |
| E | Modulus of elasticity | MPa |
| D | Pipe outside diameter | mm |
| S | Allowable (displacement) stress | MPa |
| Ew | Weld joint efficiency | – |
| Lleg | Required loop leg length | mm |
| Rmin | Minimum bend radius = 5·D | mm |
These are simplified screening relations based on the guided-cantilever method used in ASME B31.3 flexibility checks. They give a defensible first-pass loop size; the final design must be confirmed with a formal pipe-stress (flexibility) analysis that accounts for real boundary conditions, branch connections, and code stress-intensification factors.
NPS 4 SCH 40 carbon-steel line (OD 114.3 mm), 30 m anchored run, 20 → 200°C.
ΔT = 180°C, α ≈ 11.7×10⁻⁶/°C. ΔL = 11.7e-6 × 30000 × 180 = 63.2 mm.
With E = 200 GPa, S = 117 MPa, Ew = 1: Lleg = √(3 × 200000 × 114.3 × 63.2 / (5 × 117 × 1)) = √(7.41e6) ≈ 2.72 m (recommend ≈ 3.0 m). The simplified thermal stress lands well below allowable, so a U loop with ~2.7 m legs is a sound starting point.
What This Means
Every metre of hot pipe wants to grow. Pin both ends with anchors and that growth has nowhere to go — it turns into force and stress that punishes elbows, anchors, and equipment nozzles. The loop is the give in the system: a deliberate offset that flexes so the pipe can breathe. The leg length is simply how long those flexing arms need to be to keep the stress comfortable.
Why It Matters
Get it wrong on the short side and you overload a pump or vessel nozzle — that is how flanges leak and rotating equipment goes out of alignment. Get it wildly oversized and you have wasted pipe, supports, insulation, and plot space, and added more dead legs to drain and inspect. The stress ratio and bend-radius check are your two quick guards against the dangerous side of that trade.
Common Mistakes
The classic error is forgetting that ΔT is measured from the installation temperature, not from zero or from ambient design — a line installed on a cold morning and run hot sees more growth than people expect. Others: ignoring the cold spring, putting the loop next to an anchor instead of mid-span, tightening the bend radius below 5·D to save space, and treating this screening number as a final stress report.
Practical Field Notes
Loops live at the top of pipe racks for a reason — they need guides on the approach legs so the movement is directed into the loop and not sideways. Leave the loop free to move; do not let an insulation contractor jam it against a steel member. On long racks, share one big loop between several lines where the routing allows. And always confirm the final geometry in a proper flexibility model (CAESAR II or equivalent) before it goes on a drawing.
A deliberate U, L, or Z offset in a pipe run that flexes to absorb the thermal growth of the straight pipe between two anchors, keeping stress and anchor loads within limits instead of forcing the growth into equipment.
It is a screening tool using the guided-cantilever approximation. It gets you a defensible first-pass loop size and a feel for the stress margin, but final loops must be confirmed with a formal flexibility analysis that models real anchors, guides, and stress-intensification factors.
A larger pipe is stiffer in bending, so it needs a longer flexing arm to absorb the same movement without overstress. That is why the leg length scales with √D — big lines need noticeably bigger loops.
Prefer a loop where space allows — it is passive and maintenance-free. Use a bellows expansion joint where there is no room, where movements are very large, or at tight equipment connections, accepting the added leak path and inspection burden.
Expansion Loop Design Guide
3 topics • Pipe flexibility & thermal stressThermal flexibility is one of those quiet disciplines that nobody notices until a flange weeps or a pump trips on high vibration. Hot pipe grows, and if the run is anchored at both ends, that growth has to be absorbed somewhere. An expansion loop is the cleanest way to do it: a passive shape change in the pipe that flexes through thousands of thermal cycles without complaint.
The engineering is a balance. The loop has to be big enough to keep the bending stress and the anchor loads within code, but no bigger — every extra metre is pipe, supports, insulation, and plot space you pay for. This guide covers how thermal growth builds, how the loop absorbs it, and where the simplified numbers hand off to a full flexibility analysis.