D5.D.9.6 Clause 6.3.3(5) – Interaction factors kyy, kyz, kzy, and kzz

The Singaporean NA recommends the methods in either Annex A or Annex B of SS-EN 1993-1-1 to calculate these interaction factors. The current implementation of EC3 BS in STAAD.pro uses the method in Annex B by default. The proposed implementation of the Singaporean NA will also use Annex B for Cl.6.3.3 checks.

However for non-doubly symmetric sections, the Singaporean NA gives the option of using Annex B with some modifications as given in the NA. (Cl. NA-3.2 of the Singaporean NA). The Singaporean 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 SS EN 1993-1-1:2005.

As per the Singaporean 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 (λT) and torsional-flexural slenderness (λTF) as given in Clauses 6.3.1.3 and 6.3.1.4 of SS 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

Where:

λ_{T} = \sqrt{\frac{A {\cdot f}_{y}}{N_{c r}}}

N_cr = min (N_CrT, N_crTF).

The Singaporean NA or EC3 does not, however, specify a method to evaluate N_CrT or N_crTF. Therefore, the program uses the method specified in the NCCI document SN001a-EN-EU: Critical axial load for torsional and flexural torsional buckling modes to calculate these. Refer to D5.D.9.7 Clause 6.3.1.4 - Slenderness for torsional and torsional-flexural buckling.

Note: The Singaporean 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 Singaporean 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.