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001644

Dipl.-Ing. (BA) 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

Ms. Matula provides technical support for our customers.

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.
European Committee for Standardization (2005). Eurocode 3: Design of Steel Structures – Part 1-2: General Rules – Structural Fire Design, EN 1993-1-2. Berlin: Beuth.

Downloads

Model of Technical Article | RSTAB 8 File

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