Classification for Cross-section design and Member buckling design

Cross-section design (section classification):

For each intermediary section, the classification for cross-section design is determined and the proper section check is performed. The classification can change for each intermediary point.

Member buckling design (stability classification):

In case of the classification for member buckling design there are 2 approaches to choose from in the steel setup, namely:

• Maximum class along the member

• Utilisation factor η (eta)

The alternative regulations given in EN 1993-1-1 art. 5.5.2(9) - (12) are not supported.

Maximum class along the member

For each load case/combination, the classification for member buckling design is determined as the maximum class along the member. This class is used to perform the stability check since stability effects are related to the whole member and not to a single cross-section.

To determine this critical classification, all sections in the Ly and Lz system lengths of the buckling system are checked and the worst classification is used as the critical. Note that only sections on the actual member are used so in case the system length spans multiple members, only the sections of the actual member are used to determine the critical classification.

For non-prismatic sections, the stability section classification is determined for each intermediary section.

Utilisation factor η (Eta)

The utilisation factor η is in essence a value that reflects how much the section is utilized. The stability classification is taken as the section classification at the section with the maximum utilisation factor η. This is also called as the equivalent section class for member buckling design.

This approach leads to a more economic design of steel structures as the stability classification is based on the section with the highest utilisation in contrary to the previous approach which conservatively takes the worst classification along the member.

This implementation has been verified with benchmarks based on all the worked examples provided by Ref.[5] on p. 141-193. With one minor remark in which worked example 7 of Ref.[5] contains wrong values for η due to mixing up steel grades (S355 & S235) between the classification and individual checks.

Utilisation factor calculation via direct formulas:

The utilisation factor η can be derived via direct formulas in certain use cases.

• Only single section checks are used:
  Basically if the only section checks are single section checks such as single bending and/or compression, meaning no combined section checks are present. In such cases the utilisation factor η can be determined as follows depending which single section check has the highest unity check:

  • Maximum section check is coming from the compression check:
    

  • Maximum section check is coming from the bending M_y check:
    

  • Maximum section check is coming from the bending M_z check:
    

• Certain linear combined section checks are used:

  • linear summation (eq. 6.2 of EN1993-1-1):
    

  • maximum longitudinal stress in case of Class 3 (eq. 6.42 of EN1993-1-1):
    

  • maximum longitudinal stress in case of Class 4 (eq. 6.43 of EN1993-1-1):
    

  • linear effective summation in case of Class 4 (eq. 6.44 of EN1993-1-1):

    
    

Utilisation factor calculation via an iterative approach:

An iterative approach is used for more complicated combined section checks in which a direct formula cannot be derived.
The iterative approach increases a set of internal forces (N, M_yEd, M_zEd) simultaneously in small steps until the point is reached where one of the section checks reaches a unity check of 1. The increase of internal forces happens by means of dividing the set of internal forces (N, M_yEd, M_zEd) with the same utilisation factor η.