Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 110

Simply supported thin
plates with constant
displacement of loaded
edges

Constant displacement
along unloaded edges

Unloaded edges
free to deflect

Thin column

N cr

Small deflection theory

Central deflection

Figure 4.12 Post-buckling behaviour of thin elastic plates.

small deflection theory of elastic buckling, usually favours the less stiff portions
of the plate, and causes an increase in the efficiency of the plate.
One of the most common causes of this redistribution is associated with the
in-plane boundary conditions at the loaded edges of the plate. In long structural
members, the continuity conditions along the transverse lines dividing consecu-
tive buckled panels require that each of these boundary lines deflects a constant
amount longitudinally. However, the longitudinal shortening of the panel due to
its transverse deflections varies across the panel from a maximum at the centre
to a minimum at the supported edges.This variation must, therefore, be compen-
sated for by a corresponding variation in the longitudinal shortening due to axial
strain,fromaminimumatthecentretoamaximumattheedges.Thelongitudinal
stressdistributionmustbesimilartotheshorteningduetostrain,andsothestress
at the centre of the panel is reduced below the average stress while the stress at
the supported edges is increased above the average. This redistribution, which
is equivalent to a transfer of stress from the more flexible central region of the
paneltotheregionsnearthesupportededges,leadstoareductioninthetransverse
deflection, as indicated in Figure 4.12.
Afurther redistribution of the in-plane stresses takes places when the longitu-
dinal edges of the panel are supported by very stiff elements which ensure that
these edges deflect a constant amount laterally, in the plane of the panel. In this
case the variation along the panel of the lateral shortening due to the transverse
deflections induces a self-equilibrating set of lateral in-plane stresses which are
tensile at the centre of the panel and compressive at the loaded edges.The tensile
stresses help support the less stiff central region of the panel, and lead to further
reductionsinthetransversedeflections,asindicatedinFigure4.12.However,this