What is Eurocode 1 Part 1-5 (EN 1991-1-5)?

EN 1991-1-5 is the part of Eurocode 1 that specifies thermal actions on structures, including uniform temperature changes, temperature differences through the depth of members and temperature gradients for bridges and buildings.

What is a uniform temperature component in Eurocode 1?

The uniform temperature component is a constant temperature change applied to the whole cross-section of a member. It causes overall expansion or contraction without curvature and is used to check global restraint forces and movements.

What is a temperature difference component?

The temperature difference component is a linear or non-linear variation of temperature through the depth of a member, such as top surface hotter than bottom. It produces curvature and internal stresses even if the member is free to expand.

How do I combine thermal actions with other Eurocode load cases?

Thermal actions from EN 1991-1-5 are combined with other actions using the load combination rules in EN 1990. Thermal actions are usually treated as variable actions with appropriate partial factors and combination factors specified in the National Annex.

Can I use this calculator instead of the Eurocode standard?

No. This calculator is an educational and pre-design aid. For final design you must always refer to the official text of EN 1991-1-5 and the relevant National Annex, and apply professional engineering judgement.

Eurocode 1 Thermal Actions Calculator (EN 1991-1-5)

Compute uniform and linear temperature components according to Eurocode 1 Part 1-5 for buildings and bridges. Get characteristic and design temperature differences, curvature and equivalent strains in one place.

Thermal Actions on Building Elements

Element type

Material

Thickness h Member depth in m Coefficient of thermal expansion α Default from material (1/°C) Restraint factor k_r 0 = free, 1 = fully restrained

Temperature components (EN 1991-1-5)

Uniform temperature range ΔT_u Characteristic, °C (top/bottom same) Temperature difference ΔT_d Top minus bottom, °C (positive = top hotter)

Results (Characteristic):

Uniform strain ε_u: –

Linear gradient θ (°C/m): –

Curvature κ (1/m): –

Top fibre ΔT_top, bottom fibre ΔT_bot (°C): –

Note: For design values, ΔT and resulting strains are multiplied by γ_Q (default 1.5). Adjust according to your National Annex.

Thermal Actions on Bridges / Decks

Bridge type

Exposure

Deck depth h m α (1/°C) Default from material Restraint factor k_r 0–1

Temperature components (EN 1991-1-5 bridges)

Uniform component ΔT_u (°C) Characteristic Vertical gradient ΔT_d (°C) Top minus bottom

Results (Characteristic):

Uniform strain ε_u: –

Gradient θ (°C/m): –

Curvature κ (1/m): –

Top / bottom temperatures (°C): –

Exposure and bridge type presets are indicative only. Always check the exact values in EN 1991-1-5 and the National Annex for your country.

How this Eurocode 1 thermal actions calculator works

This tool implements the basic concepts of EN 1991-1-5 (Eurocode 1: Actions on structures – Part 1‑5: Thermal actions) for everyday design checks. It separates the thermal action into:

Uniform temperature component ΔT_u – same temperature change across the whole cross-section.
Temperature difference component ΔT_d – linear variation between top and bottom fibres.

1. Uniform temperature component

A uniform temperature change causes free expansion (or contraction) if the member is unrestrained. The free thermal strain is:

\( \varepsilon_u = \alpha \, \Delta T_u \) where:

\( \alpha \) = coefficient of thermal expansion (1/°C)
\( \Delta T_u \) = uniform temperature change (°C)

If the member is partially or fully restrained, the effective strain is reduced by a restraint factor \( k_r \) (0–1). This calculator reports the free strain; you can multiply by \( k_r \) to estimate restrained strain.

2. Temperature difference and curvature

For a linear temperature profile through the depth \( h \) (top hotter than bottom):

Temperature gradient:

\( \theta = \dfrac{\Delta T_d}{h} \quad [^\circ\text{C/m}] \)

Equivalent curvature (assuming linear strain distribution):

\( \kappa = \alpha \, \theta = \alpha \, \dfrac{\Delta T_d}{h} \quad [1/\text{m}] \)

The calculator assumes a linear profile and reports:

Top fibre temperature change: \( \Delta T_{\text{top}} = \Delta T_u + \tfrac{1}{2}\Delta T_d \)
Bottom fibre temperature change: \( \Delta T_{\text{bot}} = \Delta T_u - \tfrac{1}{2}\Delta T_d \)

3. Characteristic vs design values

EN 1991‑1‑5 provides characteristic temperature ranges. For design, they are combined with partial factors and combination factors from EN 1990 and the National Annex.

This calculator offers a simple option:

Characteristic: uses the input ΔT values directly.
Design: multiplies ΔT by a default partial factor \( \gamma_Q = 1.5 \) (you can adapt this in your own workflow).

Typical values and assumptions

Typical coefficients of thermal expansion used here:

Concrete: \( \alpha \approx 10 \times 10^{-6} \, 1/^\circ\text{C} \)
Steel: \( \alpha \approx 12 \times 10^{-6} \, 1/^\circ\text{C} \)
Composite steel–concrete: \( \alpha \approx 11 \times 10^{-6} \, 1/^\circ\text{C} \)

The actual values and temperature ranges must always be taken from EN 1991‑1‑5 and the relevant National Annex for your country and climate.

Worked example (building slab)

Consider a concrete roof slab:

Thickness \( h = 0.25 \,\text{m} \)
Concrete \( \alpha = 10 \times 10^{-6} \, 1/^\circ\text{C} \)
Uniform temperature change \( \Delta T_u = 30^\circ\text{C} \)
Temperature difference \( \Delta T_d = 15^\circ\text{C} \) (top hotter)

Uniform strain:

\( \varepsilon_u = \alpha \Delta T_u = 10 \times 10^{-6} \times 30 = 3.0 \times 10^{-4} \)

Gradient and curvature:

\( \theta = \dfrac{15}{0.25} = 60^\circ\text{C/m} \) \( \kappa = \alpha \theta = 10 \times 10^{-6} \times 60 = 6.0 \times 10^{-4} \, 1/\text{m} \)

Top and bottom fibre temperatures:

\( \Delta T_{\text{top}} = 30 + \tfrac{1}{2} \cdot 15 = 37.5^\circ\text{C} \) \( \Delta T_{\text{bot}} = 30 - \tfrac{1}{2} \cdot 15 = 22.5^\circ\text{C} \)

Limitations and good practice

This tool assumes linear temperature variation through depth.
It does not generate full load combinations; use EN 1990 and your National Annex.
For complex bridge decks, box girders or non-uniform exposure, a more detailed thermal model may be required.
Always document the chosen temperature ranges and references to EN 1991‑1‑5 clauses in your design notes.

FAQ

Do I need to consider both uniform and gradient components?

Yes. EN 1991‑1‑5 generally requires checking both the uniform component (for global expansion and restraint forces) and the temperature difference component (for curvature and internal stresses).

How do I choose ΔT values?

Use the tables and figures in EN 1991‑1‑5 for your structural type (building or bridge), location (climate), and exposure (roof, wall, shaded, etc.), then adjust according to the National Annex.

Can I use this for steel, concrete and composite members?

Yes. The calculator lets you select the material and uses a suitable default coefficient of thermal expansion, which you can override if needed.