Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 132

properties of the cross-section so that equation 4.73 is satisfied. The resulting
expression that satisfies equation 4.73 is

A eff f y /γ M 0 + M y , Ed + N Ed e Ny

N Ed

W eff , y , min f y /γ M 0 ≤ 1.

(4.74)

Equation 4.74 accounts for the additional bending moment caused by a shift e Ny
inthecompressionforce N Ed fromthegeometriccentroidofthenetcross-section
to the centroid of the effective cross-section.

4.7.4 Longitudinal stiffeners

Alogicalbasisforthedesignofawebinpurebendingistolimititsproportionsso
thatitsmaximumelasticbendingstrengthcanbeused,sothatthewebisaClass3
element. When this is done, the section resistance M y , Rd of the beam is governed
by the slenderness of the flanges. Thus EC3 requires a fully effective unstiffened
web to satisfy

h w / t w ≤ 124 ε . (4.75)

Thislimitisclosetothevalueof126.9atwhichtheelasticbucklingstressisequal
to the yield stress (see equation 4.37).
Unstiffened webs whose slenderness exceeds this limit are Class 4 elements,
but the use of one or more longitudinal stiffeners can delay local buckling so that
they become Class 3 elements, and the cross-section can be designed as a Class 2
sectionasdiscussedinSection4.7.2.EC3doesnotspecifytheminimumstiffness
of longitudinal stiffeners to prevent the web plate from deflecting at the stiffener
location during local buckling, such as in equation 4.38. Rather, it allows the
plate slenderness λ p in equation 4.56 to be determined from the local buckling
coefficient k σ , p which incorporates both the area and second moment of the area
ofthestiffener.Ifthestiffenedwebplateisproportionedsuchthat λ p ≤ 0.874,the
reductionfactorinequation4.53isunityandthelongitudinalstressinthestiffened
web can reach its yield strength prior to local buckling.
The Australian standard AS4100 [18] gives a simpler method of design in
which a first longitudinal stiffener whose second moment of area is at least that
of equation 4.28 is placed one-fifth of the web depth from the compression when
the overall depth-thickness ratio of the web exceeds the limit of

h w / t w = 194 ε (4.76)

which is greater than that of equation 4.75 because it considers the effect of the
flanges on the local buckling stress of the web. An additional stiffener whose
second moment of area exceeds

I st = h w t w

(4.77)

is required at the neutral axis when h w / t w exceeds 242 ε .