Structural Fire Design According to DIN EN 1993-1-2 (Thermal Material Properties)

Technical Article

Using RF-/STEEL EC3, you can apply nominal temperature‑time curves in RFEM or RSTAB. For this, the standard time‑temperature curve (ETK), the external fire curve and the hydrocarbon fire curve are implemented in the program. Based on these temperature curves, the add‑on module can calculate the temperature in the steel cross‑section and thus perform the fire design using the determined temperatures. This article explains the thermal behaviour of structural steel as this is a direct impact on the calculation of component temperatures in RF‑/STEEL EC3.

The material properties of structural steel are described in EN 1993‑1‑2 [2] by using functions in order to have an accurate value for each property at each temperature.

Thermal Expansion

The thermal expansion Δl/l is a change in geometrical dimensions caused by the temperature change.

At 20 °C ≤ Θa < 750 °C:

$$\frac{\triangle\mathrm l}{\mathrm l}\;=\;1.2\;\cdot\;10^{-5}\;\cdot\;{\mathrm\Theta}_\mathrm a\;+\;0.4\;\cdot\;10^{-8}\;\cdot\;\mathrm\Theta_\mathrm a^2\;-\;2.416\;\cdot\;10^{-4}$$

At 750 °C ≤ Θa ≤ 860 °C:

$$\frac{\triangle\mathrm l}{\mathrm l}\;=\;1.1\;\cdot\;10^{-2}$$

At 860 °C < Θa ≤ 1,200 °C:

$$\frac{\triangle\mathrm l}{\mathrm l}\;=\;2\;\cdot\;10^{-5}\;\cdot\;{\mathrm\Theta}_\mathrm a\;-\;6.2\;\cdot\;10^{-3}$$

Figure 01 - Thermal Expansion of Steel

Specific Heat Capacity

The specific heat capacity ca in J/(kgK) is the heat amount required to heat one kilogram of material by one Kelvin.

At 20 °C ≤ Θa < 600 °C:

$${\mathrm c}_\mathrm a\;=\;425\;+\;7.73\;\cdot\;10^{-1}\;\cdot\;{\mathrm\Theta}_\mathrm a\;-\;1.69\;\cdot\;10^{-3}\;\cdot\;\mathrm\Theta_\mathrm a^2\;+\;2.22\;\cdot\;10^{-6}\;\cdot\;\mathrm\Theta_\mathrm a^3$$

At 600 °C ≤ Θa < 735 °C:

$${\mathrm c}_\mathrm a\;=\;666\;+\;\frac{13,002}{738\;-\;{\mathrm\Theta}_\mathrm a}$$

At 735 °C ≤ Θa < 900 °C:

$${\mathrm c}_\mathrm a\;=\;545\;+\;\frac{17,820}{{\mathrm\Theta}_\mathrm a\;-\;731}$$

At 900 °C ≤ Θa ≤ 1,200 °C:

$${\mathrm c}_\mathrm a\;=\;650$$

Figure 02 - Specific Heat Capacity of Steel

Thermal Conductivity

The thermal conductivity λa in W/(mK) describes the ability to transfer heat energy by means of heat transfer.

At 20 °C ≤ Θa < 800 °C:

$${\mathrm\lambda}_\mathrm a\;=\;54\;-\;3.3\;\cdot\;10^{-2}\;\cdot\;{\mathrm\Theta}_\mathrm a$$

At 800 °C ≤ Θa ≤ 1,200 °C:

$${\mathrm\lambda}_\mathrm a\;=\;27.3$$

Figure 03 - Thermal Conductivity of Steel

Reference

[1]   Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2005 + AC:2009
[2]   Eurocode 3: Design of steel structures - Part 1‑2: General rules - Structural fire design; EN 1993‑1‑2:2005 + AC:2009

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Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

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Design of steel members according to Eurocode 3

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STEEL EC3 8.xx

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