D5.D.8.8 Clause 6.3.1.4 - Slenderness for torsional and torsional-flexural buckling

Equations 6.52 and 6.53 of PN EN 1993-1-1:2005 are to be used to calculate the non-dimensional slenderness λ_T, to be used for torsional and torsional-flexural buckling checks. PN EN 1993-1-1:2005 does not provide equations to calculate the elastic critical loads N_cr,TF and N_cr,T (refer 6.3.14 of PN EN 1993-1-1:2005).

The NCCI document "SN001a-EN-EU: Critical axial load for torsional and flexural torsional buckling modes" provides methods to calculate the N_cr,TF and N_cr,T factors and therefore these methods are used to evaluate the elastic critical loads for the Polish NA.

The critical axial load for torsional buckling is evaluated as:

where

$i_{o}^{2}$	=	$i_{y}^{2} + i_{z}^{2} + y_{o}^{2} + z_{o}^{2}$
i_y and i_z	=	the radius of gyration about the Y-Y (weak axis) and Z-Z (strong axis) respectively

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

N_{c r, T F} = \frac{i_{o}^{2}}{2 (i_{y}^{2} + i_{z}^{2})} [N_{c r, y} + N_{c r, T} - \sqrt{{(N_{c r, y} + N_{c r, T})}^{2} - 4 N_{c r, y} N_{c r, T} \frac{i_{y}^{2} + i_{z}^{2}}{i_{o}^{2}}}]

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