A metal expansion joint uses corrugated bellows to accommodate movement in a piping system. Explore axial motion and calculate the free thermal growth of an ideal uniform pipe from length, expansion coefficient and temperature change.
Free Pipe Thermal-Growth Worksheet
Enter pipe length, an assumed linear expansion coefficient and a uniform temperature change. The worksheet computes unconstrained axial length change only; it does not select or rate an expansion joint.
Equation Used
- Uniform pipe temperature and constant entered expansion coefficient.
- The pipe is free to expand axially; anchors, guides, friction, bends and equipment stiffness are excluded.
- No pressure, pressure thrust, bellows spring rate, squirm, fatigue, material stress or flow interaction is computed.
- Expansion-joint selection requires the exact piping system and manufacturer/EJMA-qualified design data.
The calculation gives unconstrained pipe length change. That movement can inform a piping-system analysis, but it does not establish the allowable movement or pressure capacity of a bellows.
Corrugated pressure boundary with several movement modes
EJMA describes a metal expansion joint as a thin-walled corrugated bellows with end fittings. Convolution bending provides flexibility for axial compression or extension, angular rotation or lateral offset, depending on the assembly. Torsion is a distinct damaging load and is not treated as useful movement.
The animation shows axial movement qualitatively. It does not assign equal allowable travel to every convolution.
Movement input, not component selection
The worksheet calculates free thermal length change of a uniform pipe. That movement can be one input to a piping-system analysis, but it cannot select a bellows, anchors, guides, tie rods, hinges, liners or materials.
Free linear thermal expansion
Positive DeltaT gives extension and negative DeltaT contraction under the stated sign convention. A restrained system develops forces and redistributes movement; this worksheet does not model that behavior.
Free-growth example
For 30 m, an entered alpha of 12 ppm/C and DeltaT of 170 C, unconstrained movement is +61.2 mm, or 2.04 mm per metre. That is not a 61.2 mm expansion-joint rating.
Why convolution count alone does not establish capacity
EJMA explains that bellows design also depends on convolution geometry, wall thickness, plies, material, pressure, temperature, movement combination, spring rate and column stability. NASA system studies likewise treat bellows deflection, spring rate, hydraulic imbalance and material together. Free thermal growth alone does not determine bellows capacity, utilization, service life or installation requirements.
Expansion-joint worksheet questions
Does the result size a bellows?
No. It is free pipe growth only.
Does more convolution count guarantee more allowable travel?
No. Capacity requires a complete qualified design.
Does the worksheet include pressure thrust or squirm?
No.
Industry and technical references
- Expansion Joint Manufacturers Association, Bellows: construction, movement modes, pressure stability, accessories and restraints.
- EJMA Standards: current scope and multi-variable bellows design requirements.
- NASA AI-AEC-13092, Prototype Expansion Joint Unit: system design coupling spring rate, deflection, hydraulic imbalance, stress and materials.
- NASA, Design and Development Criteria for Metal Bellows: flow excitation and liner research.
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