About Linear Expansion Coefficient Calculation
This calculator estimates the thermal change in length of an element from three inputs: element length, temperature difference, and the material’s linear expansion coefficient. It is used to evaluate movements and to size gaps, expansion joints, and sliding connections.
Guidelines and recommendations
Calculation algorithm
Step 1. Take the element length L.
Step 2. Take the temperature difference ΔT as the difference between two conditions. The numeric value entered by the user is used in the calculation.
Step 3. Take the material’s linear thermal expansion coefficient α given as 10⁻⁶ 1/°C.
Step 4. Calculate the magnitude of the thermal length change using the formula below.
Formula and its meaning
ΔL = α · L · ΔT / 1 000 000
Explanation. Writing α in the 10⁻⁶ format means “per million”. Therefore the division by 1 000 000 is required. Otherwise the result would be one million times too large.
How to interpret the result
Movement magnitude is the calculated change in length for the specified temperature difference.
Direction depends on how you define ΔT in your scenario. If you enter ΔT as an absolute temperature difference, the calculator returns the magnitude without assigning a direction.
Value selection for a connection. If several temperature scenarios are checked, the governing value is usually the largest change in length among the scenarios. This value is used to size a gap or to select a compensating connection.
Assumptions of the calculation
Linearity. The relationship is assumed linear, and α is taken constant within the selected temperature range.
Uniformity. Temperature is assumed uniform along the length and across the cross-section. Temperature gradients are not considered.
Free deformation. The calculator provides movement without considering restraints. If movement is restrained, thermal stresses develop. They depend on the restraint scheme and stiffness and are not determined by this calculator.
Choosing ΔT in practice
Based on installation. A common approach is the difference between the installation temperature and the extreme service temperatures. For outdoor elements, two scenarios are often checked: “heating” and “cooling”, to obtain the largest change in length.
By segments. If conditions vary along the length, divide the element into segments. Calculate the length change for each segment, then combine the movements according to the adopted connection scheme.
Related European standards
Thermal actions are treated as a separate type of action. Rules for defining thermal actions and principles for combinations are given in the documents below.
- EN 1991-1-5 (Eurocode 1). Actions on structures. Part 1-5: Thermal actions.
- EN 1990 (Eurocode). Basis of structural design.
- EN 1992-1-1 (Eurocode 2). Design of concrete structures. General rules and rules for buildings.
- EN 1993-1-1 (Eurocode 3). Design of steel structures. General rules and rules for buildings.
- EN 1995-1-1 (Eurocode 5). Design of timber structures. General rules and rules for buildings.
FAQs
Why is the division by 1 000 000 required?
Because α is given as 10⁻⁶ 1/°C, meaning “per million”. Without the division, the result would be one million times too large.
How should I choose the temperature difference for the calculation?
A common approach is the difference between the installation temperature and the service temperature. For outdoor elements, two scenarios are often checked, “heating” and “cooling”, to obtain the largest change in length.
Can I use this to size a gap in a connection?
Yes, if the connection must accommodate movement. Typically, the largest change in length among the scenarios is used, with an additional construction allowance for tolerances.
What if the element is composite or uses different materials?
Split the element into segments where the material and α are constant. Calculate the length change for each segment and combine the movements according to your adopted scheme.
Why doesn’t the calculator compute thermal stresses?
Stresses develop when movement is restrained by supports or connections and depend on the restraint scheme and stiffness. Without that information, only free movement can be calculated reliably.