D5.D.5.6 Clause 6.3.3(5) – Interaction factors kyy, kyz, kzy, and kzz

The UK-NA recommends that the method in Annex A or Annex B of BS EN 1993-1-1:2005 can be used to calculate the interaction factors for Cl. 6.3.3 checks in the case of doubly symmetric sections. The proposed implementation will hence use equations in Annex B of BS EN 1993-1-1:2005 to calculate these interaction factors for doubly symmetric sections. The current implementation of EC3 BS in STAAD.pro uses the method in Annex B.

However for non-doubly symmetric sections, the UK NA gives the option of using Annex B with some modifications as given in the NA. (Cl. NA-3.2 of the UK NA). The UK NA requires additional checks to be done to check for the maximum allowable values of λ and X to be used in equations 6.61 and 6.62 of BS EN 1993-1-1:2005.

As per the UK NA, for non-doubly symmetric sections, the slenderness about the weak axis (λy in STAAD) and the corresponding reduction factor χy should be taken as the values from the highest values of slenderness (λ) among the flexural buckling slenderness (λy), torsional slenderness (λ_T) and torsional-flexural slenderness (λ_TF) as given in Clauses 6.3.1.3 and 6.3.1.4 of BS EN 1993-1-1:2005. Hence for non-doubly symmetric sections the program will calculate the critical non-dimensional slenderness as:

λ_y = the maximum of either λ from Cl. 6.3.1.3 or λ_T from Cl. 6.3.1.4

λ_{T} = \sqrt{\frac{A f_{y}}{N_{c r}}}

Where:

N_cr = min (N_CrT, N_crTF).

The UK NA or EC3 does not however specify a method to evaluate NCrT or NcrTF. Hence this implementation will use the method specified in the NCCI document SN001a-EN-EU: Critical axial load for torsional and flexural torsional buckling modes to calculate these. See section 4.9 below for details.

Note: The UK National Annex or EC3 does not deal with angle sections in specific and hence this implementation will use the method used in the current EC3 implementation to deal with slenderness of angle sections. In the current implementation this is done as per cl 4.7.10 of BS 5950. This proposed implementation will still use the same method for single and double angle sections to evaluate the slenderness.

Clause NA 3.2 of the UK NA also requires that Where the section is not an I Section or a hollow section and is a class1 or class 2 section, it will be treated as a class 3 section for the purposes of this clause. Hence for all Class 1 or Class 2 cross sections that are NOT I, H, SHS, RHS or CHS sections, the elastic properties will be used for the purposes of 6.3.3 checks.