BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Pipe run between anchors
- What it is
- Length of straight pipe between two fixed anchors, which grows or shrinks with temperature.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 10000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thermal growth is proportional to length.
What this means: Expansion coefficient
- What it is
- Mean linear expansion coefficient of the pipe material over the temperature range, from the piping code or a materials reference.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0.000001 µm/m·K to 50 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Growth and restrained stress are proportional to it.
- Get it right
- µm/m·K is the same as 10⁻⁶ per kelvin.
What this means: Temperature change
- What it is
- Change from the installation temperature to the operating temperature of the pipe.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0.000001 K to 1000 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Growth and restrained stress are proportional to it.
What this means: Pipe outside diameter
- What it is
- Outside diameter of the pipe, from the pipe size table for its nominal size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 3000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 114.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The loop leg length rises with the square root of the diameter.
- Get it right
- Outside diameter, not the nominal bore.
What this means: Wall thickness
- What it is
- Wall thickness of the pipe for its schedule or class, used for the metal area and the anchor force.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Elastic modulus
- What it is
- Elastic modulus of the pipe material at operating temperature, from the piping code or material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter GPa, not MPa.
What this means: Allowable bending stress range
- What it is
- Allowable displacement stress range from the piping code for the material and its temperatures.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The loop leg length is inversely proportional to the square root of this stress.
What this means: Absorbed by
- What it is
- How the growth is taken up: an L-bend at the end where one leg takes all of it, or a U-loop at mid-run that shares it from both sides.
- Units and format
- Choose one of 2 options from the list: An L-bend (one leg takes the whole growth); A U-loop at mid-run (growth shared from both sides).
- Example
- The form opens with “A U-loop at mid-run (growth shared from both sides)” selected as a worked example. Choose the option that matches your case.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Thermal Expansion by the Numbers
What it covers: Calculate how parts, pipes, liquids and gases change with temperature: growth, measuring at 20 °C, thermal stress, pipe loops, shrink fits, expansion vessels, gas pressure and machine design.
BIZOMAT 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.
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