Cross-Section Classification in Case of Uniaxial Bending with Axial Force

Technical Article

This article was translated by Google Translator View original text

The RF-/STEEL EC3 add‑on module performs a detailed cross‑section classification at each design before the design is carried out. Thus, the susceptibility to local buckling of all cross‑section parts is evaluated. The defined cross-section class has an effect on the resistance and rotational capacity determination.

Cross-section classes

Eurocode 3 [1] defines four cross-section classes:

Figure 01 - 1 - Cross-Section Classes

The following parameters and boundary conditions are included in the cross-section classification:

  • Support of cross-section member (held on one or two sides)
  • Length of cross-section member c
  • Thickness of cross-section part t
  • Yield strength of the steel used in the form of the factor epsilon
  • Distribution of stresses over the considered cross-section part

The class of the most unfavorably weighted cross-section part becomes governing for the entire cross-section. For I and H sections, this is usually the relatively slender web.

stress distribution

The stress distribution is determined by the parameters alpha (plastic, class 1 and 2) or psi (elastic, class 3). In this case, alpha represents the percentage length of the compressive stress in the cross-section part, psi, however, the ratio of the edge stresses.

Figure 02 - 2 - Explanation of Alpha and Psi


  • The existing stresses are always scaled up or down to the yield strength.
  • Compression stresses must always be applied positively, tensile stresses negative.

For exclusively uniaxial bending on a double-symmetric cross-section, the determination of alpha and psi is trivial. If an additional axial force acts, additional considerations have to be considered. It is interesting to know how high the axial force is applied. There are two approaches, both of which are implemented in RF-/STEEL EC3.

Figure 03 - 3 - Types of Determination of Alpha and Psi

First, the second option "Increase N Ed and M Ed Uniformly", which is preset in RF-/STEEL EC3, will be discussed first. In the case of an elastic stress distribution, the existing stresses are increased by the ratio yield strength/maximum compressive stress in the cross-section part. The parameter psi results from the relation compressive stress/tensile stress. If the stress distribution is plastic, the moment and axial force are increased until one of the interaction conditions listed in [1] and thus the plastic limit state is reached. See also the information in [2] , Page 13.

In RF-/STEEL EC3, the interaction condition according to Formula 6.2 is used because it is easy to understand and valid for all cross-section types. The following graphic shows an example of an IPE 360, S 235, with the following internal forces and plastic load capacities:
M y, Ed = 125.0 kNm N Ed = 300.0 kN
M y, Rd = 239.5 kNm N Rd = 1,709.0 kN

Figure 04 - 4 - Interaction Diagram

The extrapolation of the existing loads results in the following limit internal forces:
M N, y, Rd = 179.2 kNm N My, Rd = 430.1 kN

From the limit axial force, the size of the stress block is now determined and applied in the surface bisector of the cross-section. Together with the remaining stress blocks of the bending moment, it is now possible to determine the length of the compressive stress in the cross-section part and thus the parameter alpha.

Figure 05 - 5 - Calculation of Alpha

The first option "N Ed fixed, Increase M Ed to reach f yd " is best explained by the plastic stress distribution. The axial force is not extrapolated but applied in the applied size. Therefore, with this option, the print area and alpha are usually slightly smaller.

The determination of the c/t limit values for the individual cross-section classes will not be described further here. They can be taken from [1], Table 5.2.


[1]   Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings; EN 1993-1-1: 2005 + AC: 2009
[2]  SEMI-COMP +: Calculation guideline for the cross-section and member design according to Eurocode 3 with a focus on semi-compact cross-sections. Graz: TU Graz - Institute of Steel Structures, July 2011



Contact us

Contact to Dlubal

Do you have questions or need advice?
Contact our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.

+49 9673 9203 0

RFEM Main Program
RFEM 5.xx

Main Program

Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

Price of First License
3,540.00 USD
RSTAB Main Program
RSTAB 8.xx

Main Program

The structural engineering software for design of frame, beam and truss structures, performing linear and nonlinear calculations of internal forces, deformations, and support reactions

Price of First License
2,550.00 USD
RFEM Steel and Aluminium Structures

Add-on Module

Design of steel members according to Eurocode 3

Price of First License
1,480.00 USD
RSTAB Steel and Aluminium Structures
STEEL EC3 8.xx

Add-on Module

Design of steel members according to Eurocode 3

Price of First License
1,480.00 USD