Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 111

action is not usually fully developed, because the elements supporting the panels
of most structural members are not very stiff.
The post-buckling effect is greater in plates supported along both longitudinal
edgesthanitisinplateswhicharefreealongonelongitudinaledge.Thisisbecause
thedeflectedshapesofthelatterhavemuchlesscurvaturethantheformerandthe
redistributionsofthein-planestressesarenotaspronounced.Inaddition,itisnot
possible to develop any lateral in-plane stresses along free edges, and so it is not
uncommon to ignore any post-buckling reserves of slender flange outstands.
Theredistributionofthein-planestressesafterbucklingcontinueswithincreas-
ing load until the yield stress f y is reached at the supported edges. Yielding then
spreadsrapidlyandtheplatefailssoonafter,asindicatedinFigure4.3.Theoccur-
rence of the first yield in an initially flat plate depends on its slenderness, and a
thick plate yields before its elastic buckling stress σ cr is reached.As the slender-
nessincreasesandtheelasticbucklingstressdecreasesbelowtheyieldstress, the
ratio of the ultimate stress f ult to the elastic buckling stress increases, as shown in
Figure 4.4.
Althoughtheanalyticaldeterminationoftheultimatestrengthofathinflatplate
isdifficult,ithasbeenfoundthattheuseofaneffectivewidthconceptcanleadto
satisfactory approximations.According to this concept, the actual ultimate stress
distributioninasimplysupportedplate(seeFigure4.13)isreplacedbyasimplified
distributionforwhichthecentralportionoftheplateisignoredandtheremaining
effective width b eff carries the yield stress f y . It was proposed that this effective
width should be approximated by

σ cr
f y ,

b eff
b

= (4.16)

Actual ultimate
stress distribution

b eff /2 b eff /2

b

≈ f y

b

Average
ultimate
stress ult

eff

f y

ult

=

b f

y

≡

Central
excess width
ignored

(a) Ultimate stress distribution (b) Effective width concept

Figure 4.13 Effective width concept for simply supported plates.