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001644

Dipl.-Ing. (DH) Sandy Matula

2020-07-02

Fire Resistance Design of Column Under Axial Force

In this technical article, a hinged column with a centrally acting axial force will be designed by means of the RF-/STEEL EC3 add-on module according to EN 1993-1-2. We will use the National Annex of Germany here.

Structural System and Loading

System and Loading

1 System and Loading

Girder Section HEA 240, S355

2 Girder Section HEA 240, S355

Flexural Buckling Design Around Minor Axis

\frac{N_{Ed}}{\frac{χ_{z} \cdot N_{Rk}}{γ_{M 1}}} k_{zy} \cdot \frac{M_{y, Ed}}{χ_{LT} \cdot \frac{M_{y, Rk}}{γ_{M 1}}} \leq 1

Flexural Buckling Design Around Minor Axis

The effective length of the hinged column is L_cr = 3.50 m.

According to EN 1993-1-1, 6.3.1.2:

χ = \frac{1}{ϕ \sqrt{ϕ^{2} - {\bar{λ}}^{2}}} \leq 1

ϕ = 0.5 \cdot [1 α \cdot (\bar{λ} - 0.2) {\bar{λ}}^{2}]

{\bar{λ}}_{z} = \sqrt{\frac{A \cdot f_{y}}{N_{cr, z}}}

N_{cr, z} = \frac{π^{2} \cdot E \cdot I_{z}}{l^{2}} = \frac{π^{2} \cdot 21000 kN / {cm}^{2} \cdot 9465 {cm}^{4}}{{(350 cm)}^{2}} = 16014.10 kN

{\bar{λ}}_{z} = \sqrt{\frac{178 {cm}^{2} \cdot 23.5 kN / {cm}^{2}}{16014.10 kN}} = 0.511

Calculation for Flexural Buckling Analysis

Selection of the buckling curve according to Table 6.2:

\frac{h}{b} = \frac{440 mm}{300 mm} = 1.47 > 1.2

t_{f} = 21.0 mm \leq 40 mm

Selection of Buckling Curve According to Table 6.2

Instability perpendicular to the z-axis: Buckling stress curve BSC_z: b

Table 6.1 shows the imperfection factor α = 0.34.

ϕ = 0.5 \cdot [1 \cdot 0.34 \cdot (0.511 - 0.2) \cdot 0 . 511^{2}] = 0.683

χ_{z} = \frac{1}{0.683 \sqrt{0 . 683^{2} - 0 . 511^{2}}} = 0.879 \leq 1.0

N_{Ed} = 1.35 \cdot G_{K} \cdot 1.5 \cdot Q_{K} = 1.35 \cdot 1000 1.5 \cdot 800 = 2550 kN

Calculation According to EN 1993-1-1, 6.3.1.2

For I-, H-, and rectangular hollow cross-sections that are only subjected to compression, the coefficient k_zy = 0 may be assumed.

This results in the design as follows:

\frac{N_{Ed}}{\frac{χ_{z} \cdot N_{Rk}}{γ_{M 1}}} \leq 1

N_{Rk} = A \cdot f_{y} = 178 {cm}^{2} \cdot 23.5 \frac{kN}{{cm}^{2}} = 4183 kN

\frac{2550 kN}{\frac{0.879 \cdot 4183 kN}{1.1}} = 0.76 \leq 1

Calculation of Flexural Buckling Design Around Minor Axis

→ Design is fulfilled.

Fire Resistance Design

The final temperature is defined as 500 degrees.

Determine reduction factors:
k_y,Θ = 0.78 Table 3.1
k_E,Θ = 0.60 Table 3.1

Design under fire exposure according to Clause 4.2.3.2

Imperfection factor:

α = 0.65 \cdot \sqrt{\frac{235}{f_{y}}} = 0.65 \cdot \sqrt{\frac{235}{235}} = 0.65

Imperfection Factor

Dimensionless relative slenderness:

{\bar{λ}}_{θ} = \bar{λ} \cdot {[\frac{k_{y, θ}}{k_{E, θ}}]}^{0.5} = 0.511 \cdot {[\frac{0.78}{0.60}]}^{0.5} = 0.583

Dimensionless Relative Slenderness

Auxiliary factor:

φ_{θ} = \frac{1}{2} \cdot [1 α \cdot \bar{λ_{θ}} \bar{λ_{θ}^{2}}] = \frac{1}{2} \cdot [1 0.65 \cdot 0.583 \cdot 0 . 583^{2}] = 0.859

Auxiliary Factor

Reduction factor for flexural buckling under fire exposure:

χ_{fi} = \frac{1}{φ_{θ} \sqrt{φ_{θ}^{2} - \bar{λ_{θ}^{2}}}} = \frac{1}{0.859 \sqrt{{0.859}^{2} - 0 . 583^{2}}} = 0.671

Reduction Factor for Flexural Buckling Under Fire Exposure

Buckling resistance of structural component subjected to compression:

N_{b, fi, Ed} = \frac{χ_{fi} \cdot A \cdot k_{y, θ} \cdot f_{y}}{γ_{M, fi}} = \frac{0.671 \cdot 178.0 \cdot 0.78 \cdot 23.5}{1.0} = 2189 kN

Buckling Resistance of Structural Component Subjected to Compression

Loading in case of fire:

N_{fi, Ed} = 1.0 \cdot G_{k} \cdot 0.9 \cdot Q_{k} = 1.0 \cdot 1000.0 \cdot 0.9 \cdot 800.0 = 1720.0 kN

Loading in Case of Fire

Design:

η = \frac{N_{fi, Ed}}{N_{b, fi, Rd}} = \frac{1720}{2189} = 0.79

Fire Resistance Design

→ Design is fulfilled.

KB | 001644

Knowledge Base

KB 001644 | Fire Resistance Design of Column Under Axial Force

Author

Sandy provides support in Customer Support for technical issues related to the software. She reliably familiarizes herself with new topics and helps develop clearly structured solutions.

Links

Structural Analysis Software for Steel Structures

References

Dlubal Software. (2020). Manual RF-/STEEL EC3. Tiefenbach: Dlubal Software.
Albert, A. (2018). Schneider – Bautabellen für Ingenieure mit Berechnungshinweisen und Beispielen (23rd ed.). Cologne: Bundesanzeiger.
DIN. (1993). Eurocode 3: Design of Steel Structures – Part 1-2: General Rules – Structural Fire Design, EN 1993-1-2. Berlin: Beuth Verlag GmbH.

Downloads

Model of Technical Article | RSTAB 8 File

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