Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 136

w 0 = h w / 300, usingsecond-orderelasticanalysis, forwhichthemaximumstress
is limited by

σ z , Rd = f y /γ M 1 . (4.91)

The effective stiffener cross-section for this design check consists of the cross-
sectionofthestiffeneritselfplusawidthoftheweb15 ε t w eachsideofthestiffener,
and the force to be resisted by the effective stiffener cross-section is

f yw / √ 3
γ M 1

N z , Ed = V Ed − h w t w
λ w

(4.92)

where λ w is given by equation 4.85. Using equation 3.8 for the bending of an
initially crooked compression member, this procedure implies that the maximum
stress in the effective stiffener cross-section is
σ z , Rd = N z , Ed
A st

h w A st
300 W x , st , min

N z , Ed / N cr
1 − N z , Ed / N cr

1 + (4.93)

where

N cr = π 2 EI st / h w (4.94)

is the elastic flexural buckling load of the effective stiffener area and A st and I st
aretheareaandsecondmomentofareaoftheeffectivestiffenerarea,and W x , st , min
is its minimum elastic section modulus.
A worked example of checking a pair of transverse stiffeners is given in
Section 4.9.8.

4.7.5.4 End panels

At the end of a plate girder, there is no adjacent panel to absorb the horizontal
component of the tension field in the last panel, and so this load may have to be
resistedbytheendstiffener.Arigidendpostisrequirediftensionfieldactionisto
be utilised in design. Special treatment of this end stiffener may be avoided if the
length of the last (anchor) panel is reduced so that the tension field contribution
τ tf to the ultimate stress τ ult is not required (see equation 4.29). This is achieved
by designing the anchor panel so that its shear buckling resistance V bw , Rd given
byequation4.82isnotlessthanthedesignshearforce V Ed .Aworkedexampleof
checking an end panel is given in Section 4.9.7.
Alternatively, a rigid end post consisting of two double-sided load-bearing
transverse stiffeners (see Section 4.7.6.2) may be used to anchor the tension field
at the end of a plate girder. The end post region consisting of the web and twin
pairsofstiffenerscanbethoughtofasashortbeamoflength h w ,andEC3requires
this beam to be designed to resist the in-plane stresses in the web resulting from
the shear V Ed .