Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 134

in EC3 as
V bw , Rd = χ w f yw /

√

3
γ M 1 h w t w (4.82)
in which the web reduction factor on the yield strength h w t w f yw / √ 3 due to
buckling is

1

λ w < 0.83

χ w = (4.83)

0.83 /λ w λ w ≥ 0.83

where the modified web plate slenderness is

f yw / √ 3
τ cr

f yw
τ cr

λ w = ≈ 0.76 (4.84)

and τ cr is the elastic local buckling stress in shear given in equation 4.21.
equation 4.84 is of the same form as equation 4.5. For an unstiffened web,
λ w = ( h w / t w )/ 86.4 ε , and so it can be seen from equation 4.82 that the resis-
tanceofanunstiffenedwebdecreaseswithanincreaseinitsdepth-thicknessratio
h w / t w .
Theshearresistanceofaslenderwebmaybeincreasedbyprovidingtransverse
stiffeners which increase the resistance to elastic buckling (Section 4.3.1) and
also permit the development of tension field action (Section 4.3.2.2).Thus
V c , Rd = V bw , Rd + V bf , Rd ≤ η f yw / √ 3
γ M 1

h w t w (4.85)

in which V bw , Rd is the web resistance given in equation 4.81 and V bf , Rd is
the flange shear contribution provided by the understressed flanges during the
development of the tension field in the web, which further enhances the shear
resistance. In determining the web resistance reduction factor due to buckling χ w
in equation 4.82, the modified plate slenderness is given by
λ w = h w
t w

1
37.4 ε √ k τ

(4.86)

where k τ is the local buckling coefficient given in equations 4.22 or 4.23, with L
equal to the stiffener spacing a and d equal to the web depth h w . The additional
post-buckling reserve of capacity due to tension field action for web plates with
λ w > 1.08 is achieved by the use of an enhanced reduction factor of χ w = 1.37 /
( 0.7 + λ w ) insteadofthemoreconservative χ w = 0.83 /λ w .Thepresenceoftension
field action is also accounted for implicitly in the additional flange resistance

2

M Ed
M f , Rd

b f t f
c

f yf
γ M 1

V bf , Rd = 1 − (4.87)

where M Ed is the design bending moment, M f , Rd is the moment of resistance of
the cross-section consisting of the area of the effective flanges only, f yf is the