D5.C.5.4.1 Basic stress check

This method is used when the TORSION parameter is specified as one (1).

This method is intended to be a simplified stress check for torsional effects per Cl. 6.2.7(5). Any warping stresses that may develop due to the end conditions will be ignored for this option. The program will consider the forces (including torsion) at various sections along the length of the member and for each section, will calculate the resultant stress (Von Mieses) at various points on the cross section. The location and number of points checked for a cross section will depend on the cross section type and will be as described below.

The stress check will be performed using equation 6.1 of EN 1993-1-1:2005 as given below:

{(\frac{σ_{x, E d}}{f_{y} / γ_{M 0}})}^{2} + {(\frac{σ_{z, E d}}{f_{y} / γ_{M 0}})}^{2} - (\frac{σ_{x, E d}}{f_{y} / γ_{M 0}}) (\frac{σ_{z, E d}}{f_{y} / γ_{M 0}}) + 3 {(\frac{τ_{E d}}{f_{y} / γ_{M 0}})}^{2} \leq 1

where

σ_x,Ed	=	the longitudinal stress
σ_z,Ed	=	the transverse stress and
τ_Ed	=	the resultant shear stress.

Note: Since transverse stresses are very small under normal loading conditions (excluding hydrostatic forces), the term will be negligible and hence is taken as zero.

σ_x,Ed = σ_x + σ_bz + σ_by = F_x/A_x + M_z/Z_z + M_y/Z_y

τ_Ed = T/J · t + V_y·Q/(I_z·t) + V_z·Q/(I_y*t)

where

T	=	the torsion at the particular section along the length of the member
J	=	the torsion constant
t	=	the thickness of the web/flange
V	=	the shear force
Q	=	the statical moment about the relevant axis
I	=	the second moment of area about the relevant axis

The stress check as per equation 6.1 is performed at various stress points of a cross section as shown in figures below:

Shape	Section Sketch
Doubly symmetric wide flange profile
Pipe profiles α = tan^-1(M^z/M_y)
Tube profiles
Channel profiles

The resultant ratio will be reported under Cl. 6.2.7(5) in the detailed design output.