KEVOS® MAKEOS · Hydraulics
Pipe Thermal Expansion, Anchor Force and Expansion Loop
How much will this pipe run grow when hot, what force would fully restrained anchors see, and how long must the loop legs be?
Thermal expansion of a straight pipe run between anchors, the force and stress if it were fully restrained (as the thermal stress tool), and the leg length of an L-bend or U-loop needed to absorb the growth within an allowable bending stress range by the guided-cantilever method.
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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 fixed anchors. |
| Expansion coefficient | µm/m·K | Linear expansion coefficient of the pipe material. |
| Temperature change | K | Change from installation to operating temperature. |
| Pipe outside diameter | mm | Outside diameter of the pipe. |
| Wall thickness | mm | Wall thickness. |
| Elastic modulus | GPa | Elastic modulus at temperature. |
| Allowable bending stress range | MPa | Allowable displacement stress range for the piping code. |
| Absorbed by | choice | L-bend at the end of the run, or a symmetric U-loop. |
Method and formulas
- Growth Δ = α L ΔT.
- Fully restrained stress σ = E α ΔT; anchor force = σ × metal area.
- Guided-cantilever leg length to absorb displacement δ: L_leg = √(3 E D δ ÷ S_a).
- L-bend: δ = Δ; U-loop at mid-run: each leg absorbs Δ ÷ 2.
- Example: 50 m of pipe heated 150 K grows 90 mm; a U-loop needs legs about 4.5359 m long.
Limitations
- Simplified guided-cantilever estimate; final layouts need a piping flexibility analysis to the code.
- Guides and supports must allow the movement.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out an expansion loop for a steam or hot-water line
- Check whether an L-bend can absorb a run’s growth
- Estimate anchor loads before choosing bellows or loops
Who it is for
- Piping engineers
- Plant engineers
- Maintenance engineers
What you get
- Thermal growth of the run
- Restrained stress and anchor force
- Loop leg length needed
Interpreting the result
- Cold springing the loop by half the growth halves the hot anchor loads but not the stress range.
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.
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