What is Thermal Expansion?
Nearly every substance, whether solid, liquid or gas, changes its dimensions as its temperature changes. Heat increases the movement of the particles the material is made of, they take up more room, and the body grows; cooling reverses the process and the body shrinks. How much it moves for a given temperature step is a property of the material itself.
Because a body has three dimensions, the effect can be looked at in three ways: as a change in length, as a change in surface area, or as a change in volume.
The Three Forms, and Their Formulas
Linear. For anything whose length dominates, such as a mullion, a transom, a coping or a panel edge, the change in length is proportional to the original length and to the temperature change:
ΔL = α × L × ΔT
ΔL is the change in length, L the original length, ΔT the temperature change, and α the coefficient of linear thermal expansion of the material, expressed in millionths per degree (×10-6/°C). This is the form the calculator on this page uses.
Areal. For a surface, both directions grow at once, so the area coefficient of an isotropic material is about twice the linear one:
ΔA = 2α × A × ΔT
Volumetric. For a body considered as a volume, all three directions grow and the volume coefficient is about three times the linear one:
ΔV = 3α × V × ΔT
The factors of two and three hold for materials that behave the same in every direction and over moderate temperature ranges. Rolled, extruded, laminated and fibrous materials do not always meet that condition, and timber is the clearest example: it moves very differently along the grain and across it.
A Worked Example
An aluminium mullion 3.0 m long, with a coefficient of 24 ×10-6/°C, exposed to a temperature swing of 60 °C:
ΔL = 24 ×10-6 × 3000 mm × 60 = 4.32 mm
Just over four millimetres on a single storey height. The same 60 degrees on a 12 m long unbroken run of coping produces more than 17 mm, which is why the run has to be broken by movement joints rather than fixed end to end.
Why it Matters on a Facade
A facade is exposed to the widest temperature range of any part of a building. The movement that follows is small in percentage terms but large compared with the tolerances of the details that have to accommodate it. If the movement is not provided for, the load has to go somewhere: sealant joints are overstrained, gaskets are pulled out of their grooves, panels bow or oil-can, fixings are loaded in shear, glass is put in contact with metal and edge stresses appear.
The length that matters is not the length of the building but the free length of the component between the points that restrain it, so the position of the fixed point and of the sliding points has to be decided before the movement can be assessed.
Choosing the Temperature Change
Two different questions are asked on site and they need different values of ΔT. For the total movement a joint has to accommodate over the life of the building, use the difference between the lowest and the highest service temperature of the component. For the movement that will actually take place from the moment a component is fixed, use the difference between the temperature at the time of installation and the service temperature; this is why the same joint is set to a different width in winter and in summer.
Surface temperature is not air temperature. A dark, solar absorbing metal surface reaches a considerably higher temperature in summer sun than the surrounding air, while a light or reflective surface stays much closer to it. Where a project standard or the local climate data gives design temperatures, those values should be used in place of assumptions.
About the Coefficients
A coefficient of thermal expansion is not a fixed constant. It is itself temperature dependent, and published figures are quoted for the temperature at which they were measured, most commonly around room temperature, 25 °C. Over the range a facade sees, that dependence is small enough to ignore for a first assessment, but it is one more reason not to treat a table value as exact.
The values offered by the material list are typical published figures for the material group and are intended for preliminary assessment. They also vary with alloy, grade, composition, moisture content and direction, and for natural stone and timber the variation is significant. For design, use the value stated in the applicable standard or in the supplier's technical data for the actual product, and enter it in the coefficient field by selecting Custom material.
Disclaimer; This calculator applies the linear thermal expansion formula for a single, unrestrained component and is a simple and informative tool. It does not assess restrained expansion, bowing, differential movement between layers, or the movement capacity of joints and fixings. It cannot be used for construction and official use; please apply to FMT for detailed and official calculations.