Shear Buckling

For sections that are susceptible to shear buckling, the program will perform the shear buckling checks as given in Section 5 of EN 1993-1-5. The shear buckling checks will be done only for I –Sections and Channel sections. Shear stresses induced from torsional loads are taken into account while performing torsion checks.

The susceptibility of a section to shear buckling will be based on the criteria given in Cl 5.1(2) of EN 1993-1-5 as is as given as follows:

1. For unstiffened webs, if $h_w/t>72\times \epsilon /\eta$, the section must be checked for shear buckling.

   The design resistance is calculated as:

   $V_{b,Rd}=V_{bw,Rd}\le \frac{\eta f_{yw}{h}_{w}t}{\sqrt{3}{\gamma }_{M1}}$
   $V_{bw,Rd}=\frac{{\chi }_w{f}_{yw}{h}_{w}t}{\sqrt{3}{\gamma }_{M1}}$
   where

   hw	=	distance between flanges of an I Section (i.e., depth - 2x flange thickness)
   t	=	thickness of the web
   ε	=	√(235/fy), where fy is the yield stress
   η	=	1.2 for steel grades up to and including S 460 and = 1.0 for other steel grades
   kτ	=	as defined in sections below
   χw	=	the web contribution factor obtained from Table 5.1 of the EC3 code and is evaluated per the following table: Table 1. Evaluate of χw Slenderness Parameter Rigid End Post Non-rigid End Post ${\overline{\lambda }}_w<0.83/\eta$ η η $0.83/\eta \le {\overline{\lambda }}_w<1.08$ $0.83/{\overline{\lambda }}_w$ $0.83/{\overline{\lambda }}_w$ ${\overline{\lambda }}_w\ge 1.08$ $\frac{1.37}{0.7+{\overline{\lambda }}_w}$ $0.83/{\overline{\lambda }}_w$
   ${\overline{\lambda }}_w$	=	$\frac{h_w}{86.4\times t\times \epsilon }$

2. For stiffened webs, if $h_w/t>31\times E\sqrt{k_{\tau }/\eta }$, the section must be checked for shear buckling.

   The design resistances considers tension field action of the web and flanges acting as struts in a truss model. This is calculated as:

   $V_{b,Rd}=V_{bw,Rd}+V_{bf,Rd}\le \frac{\eta f_{yw}{h}_{w}t}{\sqrt{3}{\gamma }_{M1}}$

   Where:

   where

   Vbf,Rd	=	the flange resistance per Cl.5.4 for a flange not completely utilized by bending moment
   Vbf,Rd	=	$\frac{h_f{t}_f^2{f}_{yf}}{c{\gamma }_{M1}}[1-{\left(\frac{M_{Ed}}{M_{f,Rd}}\right)}^2]$
   bf	=	the width of the flange which provides the least axial resistance, not to be taken greater than 15εtf on each side of the web
   tf	=	the thickness of the flange which provides the least axial resistance
   Mf,Rd	=	Mf,k/γM0 , the moment of resistance of the cross section consisting of the effective area of the flanges only. For a typical I Section or PFD, this is evaluated as b·tf·hw . When an axial load, NEd, is present, the value of Mf,Rd is reduced by multiplying by the following factor: $1-\frac{N_{Ed}}{\left[\frac{(A_{f1}+A_{f2})f_{yf}}{{\gamma }_{M0}}\right]}$
   Af1 ,Af2	=	the areas of the top and bottom flanges, respectively
   c	=	$a(0.25+\frac{1.6b_f{t}_f^2{f}_{yf}}{t{h}_w^2{f}_{yw}})$
   a	=	transverse stiffener spacing. The equation of c is likewise used to solve for a sufficient stiffener spacing in the case of demand from loads exceeding the calculated capacity for a specified stiffener spacing

The following equation must be satisfied for the web shear buckling check to pass:

If the stiffener spacing has not been provided (using the STIFF parameter), then the program assumes that the member end forms a non-rigid post (case c) and proceeds to evaluate the minimum stiffener spacing required.