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Dipl.-Ing. (BA) 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
System, Loading, Internal Forces

Section Properties

  • h = 300 mm, b = 360 mm, ts = 12.5 mm, tg = 22.5 mm, r = 27 mm
  • A = 180.60 cm², Iy = 43,190 cm4, Wy = 2,400 cm³
Av = A - 2 ⋅ b ⋅ tg  (ts · 2 ⋅ r) ⋅ tgAv = 180.60 - 2 ⋅ 30 ⋅ 2.25  (1.25 · 2 ⋅ 2.70) ⋅ 2.25 = 60.56 cm²
Section Property Av
Girder Section HEB 360, S235
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 ct = 26112.5 = 20.88 < limit ct  = 33 · ε = 33 · 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 ct = 116.822.5 = 5.19 < limit ct  = 9 · ε = 9 · 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

NEdNc,Rd ≤ 1.0Nc,Rd = A · fyγM0 = 180.60 · 23.51.0 = 4244.10 kN2000.004244.10 = 0.47 ≤ 1
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

Vc,Rd = Vpl,Rd = Av · fy3γM0 = 60.56 · 23.531.0 = 821.66 kNmax Vz,EdVpl,Rd = 48.75821.66 = 0.06 ≤ 1hwtw= 31512.5 = 25.2 ≤ 72 · εη = 72 · 1.01.2 = 60.00
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:

NEd ≥ 0.25 · Npl,RdNEd = 2000 kN > 0.25 · 4244.10 = 1061.03 kN
Consideration of Axial Force for Cross-Section Design

and
NEd  ≥ 0.5 ·hw · tw · fyγM0NEd = 2000 kN > 0.5 · 31.50 · 1.25 · 23.51.0 = 462.66 kN
Consideration of the axial force

→ The axial force must be taken into account.
MN,y,Rd = 630.51 · 1 - 0.4711 - 0.5 · 0.252 = 381.62 kNmmax My,EdMN,y,Rd = 79.22381.62 = 0.21 < 1.0
Cross-Section Design Bending, Shear, and Axial Force According to 6.2.9.1

→ Design is fulfilled.

Cross-Section Design Checks
Cross-Section Design Checks
KB|001600
EN-US | Flag General
KB 001600 | Cross-Section Design of Column Under Axial Force and Bending
KB|001600
EN-US | Flag General
KB 001600 | Cross-Section Design of Column Under Axial Force and Bending
Author

Ms. Matula provides technical support for our customers.

Links
References
  1. DIN. (1993). Eurocode 3: Design of Steel Structures – Part 1‑1: General Rules and Rules for Buildings, EN 1993-1-1:2005. Berlin: Beuth Verlag GmbH.
  2. Dlubal Software. (2020). Manual RF-/STEEL EC3. Tiefenbach: Dlubal Software.
  3. Albert, A. (2018). Schneider – Bautabellen für Ingenieure mit Berechnungshinweisen und Beispielen (23rd ed.). Cologne: Bundesanzeiger.
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