Main Body
Thermal Expansion Stress
Thermal Expansion
Learning Objectives
At the end of this section you should be able to calculate problems involving
- Unrestricted thermal expansion
- Restricted thermal expansion
All materials subject to a temperature change will expand or contract proportional with their length and temperature difference. Some materials will expand or contract more than others; the qualitative property that indicates how much will they expand is known as the Linear Thermal Expansion Coefficient (α), measured in m/(m ºC) or (in/in ºF). Also units like 1/ºC or 1/ºF can be used.
The change in length due to thermal expansion is calculated with:
where δ is the change in length, L is the original length (makes sure both are in the same units) and ΔT is the temperature difference.
For example if steel has a thermal expansion coefficient of 11.7×10-6 1/ºC it means that a 1 m long bar subject to a temperature increase of 1ºC will expand 11.7×10-6 m, or 0.0117 mm. This may seem like a negligible amount but if you consider a steam pipe of 50 m long installed at 12ºC and operating at 212ºC (2000 kPa saturation pressure), the thermal expansion would be equivalent to 11.7 cm, or an equivalent strain of 0.002. This is very important for the piping designers because they have to allow for this expansion or factor it in the stress calculations.
Volumetric thermal expansion of solids (isotropic materials) is calculated in a similar way using (3×α) as expansion coefficient. When calculating liquids volumetric expansion, the volumetric expansion coefficient is β, with typical values as listed in The Engineering Toolbox.
Typically pipelines are relatively long and may see a significant temperature increase between installation and operating temperatures. As result, high magnitude thermal expansion stresses may develop if the supports are not adequately designed. In addition to that, the expansion of the pipe increases the load on machinery and vessels nozzles.
Pipe cold springing
There is an abundance of articles and discussions on this topic in piping design groups, easily accessible through an internet search using key word strings “pipe cold springing” or “pipe cold pull“; it is also addressed in ASME B31.3.
“Pipe cold springing is defined as the process of intentional deformation (usually accomplished by cutting short or long the pipe runs between two anchors) of piping during assembly to produce a desired initial displacement and stress. It is also defined as the intentional stressing and elastic deformation of the piping system during the erection cycle to permit the system to attain more favorable reactions and stresses in the operating condition.” [1]
Operating engineers are advised to be familiar with this practice since it may be used in steam pipes. There have been circumstances when hired contractors when disassembling steam lines complained about lines not being fitted properly; the pipes would sprung back when unbolted. Avoid costly