Properties of carbon steel at elevated temperatures
EN 1993-1-2 (cl. 3.2.1, Table 3.1) expresses the mechanical properties of steel at temperature θa as fractions of their values at 20 °C:
- ky,θ = fy,θ / fy is the reduction factor for the effective yield strength.
- kp,θ = fp,θ / fy is the reduction factor for the proportional limit.
- kE,θ = Ea,θ / Ea is the reduction factor for the slope of the linear elastic range (modulus of elasticity).
| θa [°C] | ky,θ (yield) | kp,θ (proportional) | kE,θ (elastic) |
|---|---|---|---|
| 20 | 1.000 | 1.000 | 1.000 |
| 100 | 1.000 | 1.000 | 1.000 |
| 200 | 1.000 | 0.807 | 0.900 |
| 300 | 1.000 | 0.613 | 0.800 |
| 400 | 1.000 | 0.420 | 0.700 |
| 500 | 0.780 | 0.360 | 0.600 |
| 600 | 0.470 | 0.180 | 0.310 |
| 700 | 0.230 | 0.075 | 0.130 |
| 800 | 0.110 | 0.050 | 0.090 |
| 900 | 0.060 | 0.0375 | 0.0675 |
| 1000 | 0.040 | 0.0250 | 0.0450 |
| 1100 | 0.020 | 0.0125 | 0.0225 |
| 1200 | 0.000 | 0.0000 | 0.0000 |
Intermediate temperatures are interpolated linearly. The yield strength is fully retained up to 400 °C, then drops from 78% to 23% between 500 and 700 °C. The modulus of elasticity starts dropping from 100 °C and, above 500 °C, falls faster than the yield strength.
The buckling reduction factor in fire χfi
For compression members (cl. 4.2.3.2) and lateral-torsional buckling (cl. 4.2.3.3), EN 1993-1-2 uses a single buckling curve regardless of the section shape:
Values of χfi as a function of λ̄θ:
| λ̄θ | S235 | S275 | S355 | S460 |
|---|---|---|---|---|
| 0.2 | 0.881 | 0.889 | 0.901 | 0.912 |
| 0.4 | 0.771 | 0.784 | 0.805 | 0.824 |
| 0.6 | 0.661 | 0.677 | 0.702 | 0.726 |
| 0.8 | 0.554 | 0.569 | 0.594 | 0.619 |
| 1.0 | 0.456 | 0.469 | 0.491 | 0.512 |
| 1.2 | 0.373 | 0.383 | 0.400 | 0.417 |
| 1.4 | 0.306 | 0.314 | 0.327 | 0.340 |
| 1.6 | 0.253 | 0.259 | 0.269 | 0.279 |
| 1.8 | 0.212 | 0.216 | 0.224 | 0.231 |
| 2.0 | 0.179 | 0.183 | 0.189 | 0.194 |
Unlike the normal-temperature design, there is no plateau for low slenderness: even at λ̄θ = 0.2 the resistance drops by about 10%. The factor α depends on the steel grade, so higher-strength steels have slightly higher χfi values at the same slenderness.
Why slenderness increases in fire
The ratio ky,θ / kE,θ is greater than one between 200 and 800 °C. For example, at 600 °C it is 0.47 / 0.31 = 1.52, so the slenderness grows by √1.52 ≈ 1.23. Thus, a column with λ̄ = 0.8 at normal temperature reaches a value of λ̄θ ≈ 0.98 at 600 °C.
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.