KEVOS® MAKEOS · Hydraulics
Pipe Run Thermal Expansion Check (Growth, Loop Leg, Anchor Force)
How much will this hot pipe run grow, is the expansion loop or bend leg I have room for long enough, and what force will it put on the anchors?
Check of a straight pipe run between anchors that heats up: thermal growth, the stress and anchor force if the run were fully restrained (as the thermal stress tool), the displacement the bend or loop leg must take and the leg length needed for the allowable bending stress range (as the pipe expansion loop tool), and for the leg length you have, the bending stress and the anchor force from a guided cantilever, checked against the allowable stress and the anchor load limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pipe run between anchors | m | Length of straight pipe between the fixed anchors. |
| Expansion coefficient | µm/m·K | Mean coefficient of thermal expansion over the temperature range. |
| Installation temperature | °C | Temperature when the pipe is installed. |
| Operating temperature | °C | Highest operating temperature. |
| Pipe outside diameter | mm | Outside diameter of the pipe. |
| Wall thickness | mm | Wall thickness of the pipe. |
| Elastic modulus | GPa | Elastic modulus of the pipe material. |
| Absorbed by | choice | How the growth is taken up. |
| What you have and your limits | ||
| Leg length available | mm | Length of the leg perpendicular to the run that you have room for. |
| Allowable bending stress range | MPa | Allowable bending stress range from your piping code. |
| Allowable anchor force | kN | Largest force the anchors and structure may take. |
Method and formulas
- Growth = α L ΔT; restrained stress = E α ΔT and force = stress × area (as the thermal stress tool).
- Each leg takes δ = growth (L-bend) or growth ÷ 2 (U-loop); leg needed = √(3 E D δ ÷ S_a) (as the pipe expansion loop tool).
- With leg ℓ: bending stress = 3 E D δ ÷ ℓ²; anchor force = 12 E I δ ÷ ℓ³ (guided cantilever).
- Example: the run grows 90 mm; the leg needs 4,535.9 mm, and with 5000 mm the stress is 123.44 MPa and the anchor force 2.6011 kN.
Limitations
- Guided-cantilever estimate; elbow flexibility makes real stresses lower and real forces different.
- Friction at guides and supports adds to anchor loads.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an expansion loop or L-bend on a steam or hot water line
- Estimate anchor loads for the structure
- Decide whether bellows are needed
Who it is for
- Piping designers
- Plant engineers
- Maintenance engineers
What you get
- Growth and fully restrained stress and force
- Leg length needed
- Stress and anchor force with the leg you have
Interpreting the result
- A longer leg cuts both the stress (with ℓ²) and the anchor force (with ℓ³).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–378, 3401–3402. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Pipe Run Thermal Expansion Check (Growth, Loop Leg, Anchor Force) calculator
