BIZOMAT 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. |
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
- The length of straight pipe between the two fixed anchors, the run whose growth the loop or bend must take up.
- 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 the run length.
What this means: Expansion coefficient
- What it is
- The average amount the pipe material grows per metre for each degree of temperature change over the range from installation to operation, from material data.
- 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, restrained stress and leg length all rise with it.
- Get it right
- Type micrometres per metre per kelvin; data in 1/K must be multiplied by one million.
What this means: Installation temperature
- What it is
- The temperature of the pipe when it is installed and anchored, the starting point for the thermal growth.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the coldest temperature the pipe sees if it can drop below the installation temperature.
What this means: Operating temperature
- What it is
- The highest temperature the pipe reaches in service, including any start-up, steam-out or cleaning conditions.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 170 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Growth is proportional to the difference between the operating and installation temperatures.
What this means: Pipe outside diameter
- What it is
- The outside diameter of the pipe, from the pipe standard 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 leg length needed rises with the square root of the diameter.
- Get it right
- Use the outside diameter, not the nominal size or bore.
What this means: Wall thickness
- What it is
- The wall thickness of the pipe, from the pipe schedule or class. It sets the cross-section and the bending stiffness.
- 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
- The elastic modulus of the pipe material at the operating temperature, from the material data or piping code tables.
- 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
- Type gigapascals; 1 GPa = 1000 MPa.
What this means: Absorbed by
- What it is
- How the growth is taken up: a U-loop at mid-run, where each side takes half the growth, or an L-bend, where one leg takes all of it.
- Units and format
- Choose one of 2 options from the list: A U-loop at mid-run (growth shared from both sides); An L-bend (one leg takes the whole growth).
- 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.
- Get it right
- The choice halves or doubles the movement each leg takes, so check it matches the layout.
What you have and your limits
What this means: Leg length available
- What it is
- The length of the pipe leg at right angles to the run that you have room for. It bends like a guided cantilever to absorb the growth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress falls with the square of the leg length; anchor force falls with its cube.
- Get it right
- Type millimetres, not metres.
What this means: Allowable bending stress range
- What it is
- The allowable bending stress range for the pipe, from the piping code you design to.
- 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
- A higher allowable reduces the leg length needed.
- Get it right
- Take it from your piping code for the material and temperature.
What this means: Allowable anchor force
- What it is
- The largest force the anchors and the structure they are fixed to may take from the pipe, from the anchor design or structural engineer.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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.
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
Pipe strain
In Shaft Alignment by the Numbers
What it covers: How connected pipes pull a pump out of alignment, how to support pipe weight and absorb thermal growth so the pump carries neither, and how to measure pipe strain at the coupling.
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Open the Pipe Run Thermal Expansion Check (Growth, Loop Leg, Anchor Force) calculator