# D5.D.11.7 Clause 6.3.1.4 - Slenderness for torsional and torsional-flexural buckling

Equations 6.52 and 6.53 of MS-EN 1993-1-1:2005 are to be used to calculate the non-dimensional slenderness parameter, λ

_{T}, to be used for torsional and torsional-flexural buckling checks. The MS-EN 1993-1-1:2005 does not provide equations to calculate the elastic critical loads N_{cr,T,F}and N_{cr,T}(refer 6.3.14 of SS EN 1993-1-1:2005). Therefore, the NCCI document SN001a-EN-EU: Critical axial load for torsional and flexural torsional buckling modes provides methods to calculate the N_{cr,T,F}and N_{cr,T}factors and hence will to be included in this implementation of the MS NA.The program will only consider Channel Sections and Tee- sections when evaluating the critical torsional and Flexural Torsional buckling loads as per Cl 6.3.1.4.

The critical axial load for torsional buckling is evaluated as:

= | ||

_{y} and
i_{z} | = |

The critical axial load for torsional-flexural buckling is evaluated as:

${N}_{cr,TF}=\frac{{i}_{o}^{2}}{2({i}_{y}^{2}+{i}_{z}^{2})}[{N}_{cr,y}+{N}_{cr,T}-\sqrt{{({N}_{cr,y}+{N}_{cr,T})}^{2}-4{N}_{cr,y}{N}_{cr,T}\frac{{i}_{y}^{2}+{i}_{z}^{2}}{{i}_{o}^{2}}}]$

For details on these equations, refer to the NCCI document SN001a-EN-EU.