18379x

001600

Dipl.-Ing. (DH) Sandy Matula

2019-12-04

Cross-Section Design of Column Under Axial Force and Bending

In this technical article, a hinged column with a centrally acting axial force and a linear load that acts on the major axis are designed according to EN 1993-1-1 with the aid of the RF-/STEEL EC3 add-on module. The column head and column base are assumed to be lateral and torsional restraints. The column is not held against rotation between the supports. The cross-section of the column is an HEB 360 from S235.

System, Loading, and Internal Forces

System, Loading, Internal Forces

Section Properties

h = 300 mm, b = 360 mm, t_s = 12.5 mm, t_g = 22.5 mm, r = 27 mm
A = 180.60 cm², I_y = 43,190 cm⁴, W_y = 2,400 cm³

\begin{array}{l} A_{v} = A - 2 \cdot b \cdot t_{g} (t_{s} \cdot 2 \cdot r) \cdot t_{g} \\ A_{v} = 180.60 - 2 \cdot 30 \cdot 2.25 (1.25 \cdot 2 \cdot 2.70) \cdot 2.25 = 60.56 cm ² \end{array}

Section Property A_v

Girder Section HEB 360, S235

Design of Cross-Section Class

[1], Table 5.2, cross-section parts supported on two sides
Web: c = 261 mm, t = 12.5 mm

prov (\frac{c}{t}) = (\frac{261}{12.5}) = 20.88 < limit (\frac{c}{t}) = 33 \cdot ε = 33 \cdot 1 = 33

Design of Cross-Section Class – Web

The web meets the requirements for cross-section class 1.

[1], Table 5.2, cross-section parts supported on one side
Flange: c = 116.8 mm, t = 22.5 mm

prov (\frac{c}{t}) = (\frac{116.8}{22.5}) = 5.19 < limit (\frac{c}{t}) = 9 \cdot ε = 9 \cdot 1 = 9

Design of Cross-Section Class – Flange

The flange meets the requirements for cross-section class 1.

Accordingly, the entire cross-section can be classified in cross-section class 1.

Cross-Section Design of Pressure According to 6.2.4

\begin{array}{l} \frac{N_{Ed}}{N_{c, Rd}} \leq 1.0 \\ N_{c, Rd} = \frac{A \cdot f_{y}}{γ_{M 0}} = \frac{180.60 \cdot 23.5}{1.0} = 4244.10 kN \\ \frac{2000.00}{4244.10} = 0.47 \leq 1 \end{array}

Cross-Section Design Pressure According to 6.2.4

→ Design is fulfilled.

Cross-Section Design of Shear Force in Axis z According to 6.2.6

\begin{array}{l} V_{c, Rd} = V_{pl, Rd} = \frac{A_{v} \cdot \frac{f_{y}}{\sqrt{3}}}{γ_{M 0}} = \frac{60.56 \cdot \frac{23.5}{\sqrt{3}}}{1.0} = 821.66 kN \\ \frac{\max V_{z, Ed}}{V_{pl, Rd}} = \frac{48.75}{821.66} = 0.06 \leq 1 \\ \frac{h_{w}}{t_{w}} = \frac{315}{12.5} = 25.2 \leq 72 \cdot \frac{ε}{η} = 72 \cdot \frac{1.0}{1.2} = 60.00 \end{array}

Cross-Section Design Shear Force in Axis z According to 6.2.6

→ Design is fulfilled. No shear buckling design is required.

Cross-Section Design of Bending, Shear, and Axial Force According to 6.2.9.1

The axial force must be taken into account if:

\begin{array}{l} N_{Ed} \geq 0.25 \cdot N_{pl, Rd} \\ N_{Ed} = 2000 kN > 0.25 \cdot 4244.10 = 1061.03 kN \end{array}

Consideration of Axial Force for Cross-Section Design

and

\begin{array}{l} N_{Ed} \geq \frac{0.5 \cdot h_{w} \cdot t_{w} \cdot f_{y}}{γ_{M 0}} \\ N_{Ed} = 2000 kN > \frac{0.5 \cdot 31.50 \cdot 1.25 \cdot 23.5}{1.0} = 462.66 kN \end{array}

Consideration of the axial force

→ The axial force must be taken into account.

\begin{array}{l} M_{N, y, Rd} = 630.51 \cdot \frac{(1 - 0.471)}{(1 - 0.5 \cdot 0.252)} = 381.62 kNm \\ \frac{\max M_{y, Ed}}{{M_{N}}_{, y, Rd}} = \frac{79.22}{381.62} = 0.21 < 1.0 \end{array}

Cross-Section Design Bending, Shear, and Axial Force According to 6.2.9.1

→ Design is fulfilled.

Cross-Section Design Checks

Knowledge Base

KB 001600 | Cross-Section Design of Column Under Axial Force and Bending

Knowledge Base

KB 001600 | Cross-Section Design of Column Under Axial Force and Bending

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

DIN. (2010). Eurocode 3: Design of Steel Structures – Part 1‑1: General Rules and Rules for Buildings. Berlin: Beuth Verlag GmbH.
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.

Downloads

RSTAB Model File

416 KB

;