Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 126

yielding does not take place until the applied load is large enough to yield a web
area defined by a dispersion of the applied stress through the flange. Even at this
load the web does not collapse catastrophically, and some further yielding and
redistribution is possible. When the web is also subjected to shear and bending,
generalyieldinginbearingcanbeapproximatedbyusingtheHencky-VonMises
yield criterion (see Section 1.3.1)

σ p + σ b − σ p σ b + 3 τ 2 = f y (4.47)

in which σ p is the bearing stress, σ b the bending stress and τ the shear stress.
Thinstiffenedwebpanelsinbearinghaveareserveofstrengthafterelasticbuck-
lingwhichisduetoaredistributionofstressfromthemoreflexiblecentralregion
tothestiffeners.Studiesofthiseffectsuggestthatthereserveofstrengthdecreases
as the bearing loads become more concentrated [15]. The collapse behaviour of
stiffened panels is described in [16, 17].

4.7 Design against local buckling

4.7.1 Compression members

The cross-sections of compression members must be designed so that the design
compression force N Ed does not exceed the design compressive resistance N c , Rd ,
whence

N Ed ≤ N c , Rd . (4.48)

This ignores overall member buckling, as discussed in Chapter 3, for which
the non-dimensional slenderness λ ≤ 0.2. The EC3 design expression for
cross-section resistance under uniform compression is

N c , Rd = A eff f y
γ M 0

(4.49)

in which A eff is the effective area of the cross-section, f y is the nominal
yield strength for the section and γ M 0 ( = 1 ) is the partial section resistance
factor.
Thecross-sectionofacompressionmembermaybucklelocallybeforeitreaches
its yield stress f y , in which case it is defined in EC3 as a Class 4 cross-section.
Cross-sections of compression members which yield prior to local buckling are
'effective', and are defined in EC3 as being either of Class 1, Class 2, or Class 3.
For these cross-sections which are unaffected by local bucking, the effective area
A eff in equation 4.49 is taken as the gross area A . A cross-section composed of
flat-plate elements has no local buckling effects when the width-thickness ratio