BIZOMAT MAKEOS · Engineering
Expansion Gap Plan (Movement over the Temperature Range, Gap at Installation, Restrained Stress)
For a rail, beam, pipe or panel run that must move with temperature, what gap should I set when installing, will it stay within the joint’s range, and what stress would build up if the gap closed?
Plan of an expansion gap for a run fixed at one end: the length change over the temperature range from the expansion coefficient, the gap to set at the installation temperature so a least gap remains at the hottest temperature, the gap at the coldest temperature, the number of gaps needed if the range is too wide for one joint, and the thermal stress and force that would build up if the run were fully restrained (as the thermal stress tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Length free to move to the gap | m | Length of the run between its fixed point and the gap. |
| Expansion coefficient | µm/(m·K) | Linear expansion coefficient of the material (steel about 12, aluminium about 23). |
| Lowest service temperature | °C | Lowest temperature the run reaches. |
| Highest service temperature | °C | Highest temperature the run reaches (sun on dark surfaces can be well above air temperature). |
| Installation temperature | °C | Temperature of the run when the gap is set. |
| Least gap at the hottest | mm | Smallest gap to leave at the hottest temperature. |
| Largest gap the joint allows | mm | Largest gap the joint, rail or cover plate can bridge. |
| If fully restrained | ||
| Elastic modulus | GPa | Elastic modulus. |
| Cross-section area | mm² | Cross-section area of the run. |
| Yield strength | MPa | Yield strength of the material. |
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: Length free to move to the gap
- What it is
- The length of the run from its fixed point, where it cannot move, to the expansion gap.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 100000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Movement rises in direct proportion to this length.
- Get it right
- Measure from the anchor or fixed point, not the full run if it is anchored in the middle.
What this means: Expansion coefficient
- What it is
- The linear thermal expansion coefficient of the run material: how much one metre grows per kelvin.
- Units and format
- Enter a number in µm/(m·K): micrometres per metre per kelvin. The form accepts 0.000001 µm/(m·K) to 100 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
- Movement and restrained stress rise in direct proportion.
- Get it right
- Enter micrometres per metre per kelvin (the same as 10⁻⁶ per K) from the material data sheet.
What this means: Lowest service temperature
- What it is
- The lowest temperature the run itself reaches in service, when the gap is widest.
- 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 -5 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the metal temperature, which can fall below air temperature on clear nights.
What this means: Highest service temperature
- What it is
- The highest temperature the run itself reaches in service, when the gap is narrowest.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the metal temperature, which can be well above air temperature in the sun.
What this means: Installation temperature
- What it is
- The temperature of the run on the day the gap is set during installation.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1500 °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
- Measure the metal temperature at installation and recalculate the gap on the day.
What this means: Least gap at the hottest
- What it is
- The smallest gap you want left at the hottest temperature, so the ends never touch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Allow for installation tolerance and any debris that may enter the gap.
What this means: Largest gap the joint allows
- What it is
- The widest gap the joint, rail joint or cover plate can bridge, compared with the gap at the coldest temperature.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the joint or cover plate design.
If fully restrained
What this means: Elastic modulus
- What it is
- The elastic modulus of the run material, used for the stress if the run were fully restrained.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 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 it in GPa, not MPa.
What this means: Cross-section area
- What it is
- The cross-section area of the run, used for the force on the anchors if it were fully restrained.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The restrained force rises in direct proportion.
- Get it right
- Take it from the section table for the member.
What this means: Yield strength
- What it is
- The yield strength of the run material, compared with the restrained stress.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the minimum yield from the material standard.
Method and formulas
- Length change = α L ΔT.
- Gap to set = least gap + α L (T_max − T_install); gap when coldest = gap to set + α L (T_install − T_min).
- Gaps needed = ⌈α L (T_max − T_min) ÷ (largest − least gap)⌉; restrained stress = E α (T_max − T_install) and force = stress × area (as the thermal stress tool).
- Example: set a 11 mm gap at 20 °C; it opens to 20 mm when coldest; restrained, the run would see 60 MPa.
Limitations
- Uniform temperature along the run and free sliding; friction at supports takes up part of the movement.
- One fixed point per run; runs fixed at both ends need the joint in between to take both movements.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set gaps for crane or conveyor rails
- Plan expansion joints in long cladding or pipe runs
- See the stress if a gap closes
Who it is for
- Site engineers
- Maintenance engineers
- Design engineers
What you get
- Movement over the range
- Gap to set and gap when coldest
- Gaps needed and restrained stress
Interpreting the result
- Setting the gap for the temperature on the day of installation is what keeps the joint inside its range in summer and winter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–376, 578. Topic reference; no source tables or recommended settings are reproduced.
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