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001988

Dipl.-Ing. Marco Nikoleizig

2025-10-28

Fire Resistance Design of Steel Structures: Critical Component Temperature

Reactive fire protection materials can be applied to the coating of steel surfaces. To determine the required coating thickness, it is necessary to know the critical component temperature.

Fire Design

Fire resistance design is regulated in DIN EN 1993 Part 1-2. Section 4.2 presents “Simple design methods” which form the basis of the design in RFEM 6 and RSTAB 9.
In this case, the actions are compared with the load-bearing capacities at the component level. The fire actions resulting from temperature rise are determined on the basis of temperature curves (nominal fire curves). The actions are determined under reduced partial safety factors in the accidental design situation. The resistances are taken into account by reducing the material properties based on the increased temperature.

Critical Component Temperature Θ_a,cr

In addition to the design method mentioned above, EN 1993-1-2, Section 4.2.4, describes the design method at the temperature level based on the critical component temperature. This becomes interesting when reactive fire protection materials are applied to the steel and their layer thicknesses need to be determined.
The critical component temperature represents the maximum temperature that may be reached so that the analyzed member or member set can still withstand the actions. The lowest critical component temperature by structural component is governing.
The equation for determining Θ_a,cr is:

θ_{a, c r} = 39.19 \ln [\frac{1}{0.9674 {μ_{0}}^{3.833}} - 1] + 482

KB 1988 | Critical Component Temperature According to DIN EN 1993-1-2, Section 4.2.4, Equation (4.22)

The parameter for determining the critical component temperature is the design ratio μ₀, which represents the ratio of the actions under fire exposure E_fi,d and the resistances at the start (t = 0) of the fire R_fi,d,0. The critical component temperature is therefore independent of the fire resistance design, which determines the resistance as a function of the duration of the fire or temperature curves, and so on.

μ_{0} = \frac{E_{f i, d}}{R_{f i, d, 0}}

KB 1988 | Utilization Ratio μ₀, DIN EN 1993-1-2, Section 4.2.4, Equation (4.23)

The function graph of Θ_a,cr has the following distribution:

The function graph of the critical component temperature has the following course.

KB 1988 | Function Graph of Critical Component Temperature Θa,cr

The design ratios μ₀ may be determined using elastic or plastic design methods.

Application Limits, Boundary Conditions

The following limitations apply to the calculation of the critical component temperature in RFEM 6:

Not applicable if deformation criteria are governing,
Not applicable if it is necessary to consider stability effects,
Design ratios μ₀ < 0.013 should not be used.
There are components with cross-section class 1, 2, or 3, or components subjected to tension.
The component is heated evenly across the entire cross-section.

Calculation Example

The calculation of the critical component temperature for shear and axial stress verification is shown using the example of a single-span beam:

Material	Steel S235
Span	L = 2 m
Permanent load	g = 3 kN/m
Live load	p = 5 kN/m
Design situation	EN 1990; ULS - Exceptional - ψ_2,1
Partial safety factors	ψ_2,1 = 0.3
Design format	elastic/elastic
Cross-section	HEA 140 - DIN 1025-3
Max. static moment	max. S_y = 86.77 cm³ (determined using RSECTION 1)
Moment of inertia	I_y = 1033.34 cm⁴ (determined using RSECTION 1)
Section modulus	W_y = 155.4 cm³
Web thickness	t_w = 0.55 cm

V_{fi, z, Ed} = (3 + 0.3 * 5) * 2.0 / 2 = 4.5 kN

M_{fi, y, Ed} = (3 + 0.3 * 5) * 2 . 0^{2} / 8 = 2.25 kNm

Cross-Section Checks for Shear and Axial Stress

Shear stress design:

τ_{fi, z, Ed} = \frac{V_{fi, z, Ed} * S_{y}}{I_{y} * t_{w}} = \frac{4.5 kN * 86.77 {cm}^{3}}{1033.34 {cm}^{4} * 0.55 cm} = 0.687 \frac{kN}{{cm}^{2}}

Shear Stress

μ_{0} = \frac{τ_{fi, z, Ed}}{τ_{fi, Rd, 0}} = \frac{0.687 \frac{kN}{{cm}^{2}}}{\frac{23.5 \frac{kN}{{cm}^{2}}}{1.0 * \sqrt{3}}} = 0.0506

0.013 < μ_{0} = 0.0506 < 1.0

Design Ratio

θ_{a, cr} = 39.19 * \ln (\frac{1}{0.9674 * {0.0506}^{3.833}} - 1) + 482 = 931.4 ° C

Critical Component Temperature

Axial stress design:

σ_{fi, x, Ed} = \frac{M_{fi, y, Ed}}{W_{fi, Rd, 0}} = \frac{225.0 kNcm}{155.4 {cm}^{3}} = 1.45 \frac{kN}{{cm}^{2}}

Axial Stress

μ_{0} = \frac{σ_{fi, x, Ed}}{σ_{fi, Rd, 0}} = \frac{1.45 \frac{kN}{{cm}^{2}}}{\frac{23.5 \frac{kN}{{cm}^{2}}}{1.0}} = 0.0616

0.013 < μ_{0} = 0.0616 < 1.0

Design Ratio

θ_{a, cr} = 39.19 * \ln (\frac{1}{0.9674 * {0.0616}^{3.833}} - 1) + 482 = 901.9 ° C

Critical Component Temperature

The minimum critical component temperature is governing:

\min . θ_{a, cr} = \min . \{931.4; 901.9\} = 901.9 ° C

Minimum Critical Component Temperature

Application Example in RFEM 6

In order to perform a fire resistance design in RFEM 6, it is necessary to assign an ultimate configuration to the members to be designed in the Steel Design add-on in addition to the fire resistance configuration.
The load combinations in the design situation for the fire resistance design are determined using the main design situation ψ_2.1 according to EN 1990 | 2010-04.
In the attached example model, a fire resistance configuration is assigned to members No. 1 and 2. In the main dialog box under the design parameters, the calculation of the critical component temperature is selected.

KB 1988 | RFEM 6 – Setting for Critical Component Temperature in Fire Resistance Configuration

The decision as to whether the cross-section checks in the fire resistance design are elastic or plastic is made in the ultimate configuration: "Main|Members" tab – Options – Elastic design (also for cross-sections of Class 1 and 2). If this option is selected, the design is elastic; otherwise, if possible, it is plastic.

KB 1988 | RFEM 6 – Setting for Elastic Design in Ultimate Configuration

After the steel design calculation has been performed, the design check details show the results for the fire resistance design as well as the calculation of the critical component temperature.

The image shows the results in RFEM 6 – Steel Design add-on, Design Check Details for the critical component temperature

KB 1988 | RFEM 6 – Calculation of Critical Component Temperature in Design Check Details for Fire Design

Checking Limits of Application in RFEM 6

RFEM 6 automatically checks the application limits regarding the restriction to cross-section classes 1 to 3 and the restriction to the minimum design ratio μ_0,min = 0.013. If these limits are exceeded, corresponding messages are displayed.