Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 107

5

b

4

L

Free

3

Exact
=0.425 + ( b/L ) 2

2

k

1

0.425

0

0 1 2 3 4 5

Plate aspect ratio L/b

Figure 4.9 Buckling coefficients of plate free along one edge.

varioussupportconditionshavebeendetermined,andmanyvaluesofthebuckling
coefficient k σ to be used in equation 4.3 are given in [2-6].

4.2.1.4 Plate assemblies

Many structural steel compression members are assemblies of flat-plate elements
which are rigidly connected together along their common boundaries. The local
bucklingofsuchanassemblycanbeanalysedapproximatelybyassumingthatthe
plate elements are hinged along their common boundaries, so that each plate acts
asifsimplysupportedalongitsconnectedboundaryorboundariesandfreealong
anyunconnectedboundary.Thebucklingstressofeachplateelementcanthenbe
determinedfromequation4.3with k σ = 4or0.425asappropriate,andthelowest
ofthesecanbeusedasanapproximationfordeterminingthebucklingloadofthe
member.
Thisapproximationisconservativebecausetherigidityofthejointsbetweenthe
plate elements causes all plates to buckle simultaneously at a stress intermediate
betweenthelowestandthehighestofthebucklingstressesoftheindividualplate
elements.Anumberofanalyseshavebeenmadeofthestressatwhichsimultaneous
buckling takes place [4-6].
For example, values of the elastic buckling coefficient k σ for an I-section in
uniform compression are shown in Figure 4.10, and for a box section in uniform
compressioninFigure4.11.Thebucklingstresscanbeobtainedfromthesefigures
by using equation 4.3 with the plate thickness t replaced by the flange thickness
t f .Theuseofthesestressesandotherresults[4-6]leadstoeconomicthin-walled
compression members.