# D5.C.5.3 Members Subject to Shear

The cross section capacity of a member subject to shear is checked as per Cl. 6.2.6 of the code. The condition to be satisfied is:

$V E d V c , R d ≤ 1.0$
where
 Vc,Rd = the is the shear design resistance given by: $V c , R d = V p l , R d = A v ( f y / 3 ) γ M 0$ Av = the shear area and is worked out for the various section types as given in Cl. 6.2.6(3) of the code

## 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.

Note: Web shear buckling is checked in STAAD.Pro V8i (SELECTseries 3) (release 20.07.08) and later.

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 $h w / t > 72 × ε / η$, the section must be checked for shear buckling.

The design resistance is calculated as:

$V b , R d = V b w , R d ≤ η f y w h w t 3 γ M 1$
$V b w , R d = χ w f y w h w t 3 γ M 1$
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
$λ ¯ w < 0.83 / η$ η η
$0.83 / η ≤ λ ¯ w < 1.08$ $0.83 / λ ¯ w$ $0.83 / λ ¯ w$
$λ ¯ w ≥ 1.08$ $1.37 0.7 + λ ¯ w$ $0.83 / λ ¯ w$
$λ ¯ w$
=
$h w 86.4 × t × ε$
2. For stiffened webs, if $h w / t > 31 × E k τ / η$, 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:

$V b , R d = V b w , R d + V b f , R d ≤ η f y w h w t 3 γ M 1$

Where:

where
 Vbf,Rd = the flange resistance per Cl.5.4 for a flange not completely utilized by bending moment Vbf,Rd = $h f t f 2 f y f c γ M 1 [ 1 − ( M E d M f , R d ) 2 ]$ 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: $1 − N E d [ ( A f 1 + A f 2 ) f y f γ M 0 ]$ Af1 ,Af2 = the areas of the top and bottom flanges, respectively c = $a ( 0.25 + 1.6 b f t f 2 f y f t h w 2 f y w )$ 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:

$η 3 = V E d V b , R d ≤ 1.0$
where
 VEd = the design shear force
Note: The shear forces due to any applied torsion will not be accounted for if the TOR parameter has been specifically set to a value of 0 (i.e., ignore torsion option).

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.