Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 117

Thus the resistance of a stocky web in a flanged section for which the shear
shape factor is close to unity is closely approximated by the web plastic shear
resistance

V pl = dt τ y . (4.28)

When the depth-thickness ratio d / t of a long unstiffened steel web exceeds
86.4/ √ ( f y / 235 ) , its elastic buckling shear stress τ cr is less than the shear yield
stress (see equation 4.25). The post-buckling reserve of shear strength of such an
unstiffened web is not great, and its ultimate stress τ ult can be approximated with
reasonable accuracy by the elastic buckling stress τ cr given by equation 4.24 and
shown by the dashed line in Figure 4.18.

4.3.2.2 Stiffened plates

Stockystiffenedwebsinsteelbeamsyieldinshearbeforetheybuckle,andsothe
stiffeners do not contribute to the ultimate strength. Because of this, stocky webs
are usually unstiffened.
In a slender web with transverse stiffeners which buckles elastically before it
yields, there is a significant reserve of strength after buckling. This is caused
by a redistribution of stress, in which the diagonal tension stresses in the web
panelcontinuetoincreasewiththeappliedshear,whilethediagonalcompressive
stresses remain substantially unchanged. The increased diagonal tension stresses
formatensionfield,whichcombineswiththetransversestiffenersandtheflanges
totransfertheadditionalshearinatruss-typeaction[7,9],asshowninFigure4.19.
Theultimateshearstresses τ ult ofthewebisreachedsoonafteryieldoccursinthe
tension field, and this can be approximated by

τ ult = τ cr + τ tf (4.29)

in which τ cr is the elastic buckling stress given by equations 4.21-4.23 with L
equal to the stiffener spacing a , and τ tf is the tension field contribution at yield
which can be approximated by

√

τ tf = f y
2

( 1 − 3 τ cr / f y )

1 + ( a / d ) 2 .

(4.30)

Thus the approximate ultimate strength can be obtained from
√ 3 τ ult
f y

√ 3 τ cr
f y

√ 3
2

( 1 − √ 3 τ cr / f y )

= +

1 + ( a / d ) 2 ,

(4.31)

which is shown in Figure 4.18. This equation is conservative, as it ignores any
contributionsmadebythebendingresistanceoftheflangestotheultimatestrength
of the web [9, 10].