Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 113

1.2

Yielding

1.0

Elastic buckling

0.8

Test results

0.6

equation 4.18 ( =0.65)

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Modified plate slenderness cr

√ ( f y )

Figure 4.14 Effective widths of simply supported plates.

to buckle prematurely and reduce its ultimate strength, as shown in Figure 4.4.
Residual stresses also cause premature yielding in plates of intermediate slender-
ness,asindicatedinFigure4.4,buthaveanegligibleeffectonthestrain-hardening
buckling of stocky plates.
Some typical test results for thin supported plates with initial curvatures and
residual stresses are shown in Figure 4.14.

4.3 Plate elements in shear

4.3.1 Elastic buckling

The thin flat plate of length L , depth d , and thickness t shown in Figure 4.15
is simply supported along all four edges. The plate is loaded by shear stresses
distributed uniformly along its edges.When these stresses are equal to the elastic
buckling value τ cr , then the plate can buckle by deflecting v laterally out of its
original plane into an adjacent position. For this adjacent position to be one of
equilibrium, the differential equilibrium equation [1-4]
∂ 4 v

∂ x 4 + 2 ∂ 4 v ∂ x 2 ∂ z 2 + ∂ 4 v

∂ 2 v
∂ x ∂ z

=− 2 τ cr t
D

(4.20)

∂ z 4

mustbesatisfied(thismaybecomparedwiththecorrespondingequation4.105of
Section 4.8.1, for a plate in compression).
Closedformsolutionsofthisequationarenotavailable,butnumericalsolutions
havebeenobtained.Theseindicatethattheplatetendstobucklealongcompression
diagonals, as shown in Figure 4.15. The shape of the buckle is influenced by
the tensile forces acting along the other diagonal, while the number of buckles