Critical temperature of steel (EN 1993-1-2, cl. 4.2.4)

What the critical temperature is

The strength and stiffness of steel decrease as temperature rises. A loaded member fails in fire when the steel reaches the temperature at which its remaining resistance equals the applied action. This is the critical temperature θ_a,cr.

The less a member is loaded in the fire situation, the higher its critical temperature and the longer it resists fire.

The formula in EN 1993-1-2

Clause 4.2.4 gives the critical temperature as a function of the degree of utilisation μ₀:

θ_a,cr = 39.19 · ln [ 1 / (0.9674 · μ₀^3.833) − 1 ] + 482 [°C] EN 1993-1-2, eq. (4.22); valid for μ₀ ≥ 0.013

Degree of utilisation μ₀

μ₀ is the ratio between the design effect of actions in the fire situation and the design resistance of the member at time t = 0 (at normal temperature, but with the partial factor for fire γ_M,fi):

μ₀ = E_fi,d / R_fi,d,0

For example, for a member in tension: R_fi,d,0 = A · f_y / γ_M,fi, so μ₀ = N_fi,Ed · γ_M,fi / (A · f_y). The recommended value is γ_M,fi = 1.0; check your National Annex.

Reference values

Values calculated with the formula above:

μ₀	θ_a,cr [°C]
0.2	725
0.3	664
0.4	620
0.5	585
0.6	554
0.7	526
0.8	496

When it applies

The formula is used to determine the critical temperature of members where instability effects are not relevant, such as tension members, compression members with no risk of flexural buckling and beams restrained against lateral-torsional buckling.
For columns and beams that can buckle, the critical temperature follows from the stability check in fire. See fire design of steel columns.
For Class 4 sections, unless a detailed calculation is made, the standard recommends θ_a,cr = 350 °C.

FireSolver calculates the critical temperature for every type of loading Tension, compression (buckling), bending and/or shear (including lateral-torsional buckling) and combined compression and bending, to EN 1993-1-2, §4.2.3.1-4.2.3.5, including where the formula above does not apply. Calculate now

From critical temperature to fire resistance time

The critical temperature tells you how hot the steel may get. How fast it gets there depends on the fire curve, the section factor A_m/V and any protection. The moment the steel temperature reaches θ_a,cr is the fire resistance time, which is then compared with the required class (for example R 60). More in section factor and fire protection and fire resistance classes.

Informative material summarising the provisions of EN 1993-1-2. It does not replace the text of the standard, the National Annex or verification by a qualified engineer.