Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 119

crl

2 d /3

L

d

2 d /3

2 d /3

crl

crl

All edges simply supported

crl

Figure 4.20 Buckled pattern of a plate in bending.

distributions which vary linearly across its width. When the maximum stress
reaches the elastic buckling value σ crl , the plate can buckle out of its original
plane as shown in Figure 4.20. The elastic buckling stress can be expressed in
the form

π 2 E
12 ( 1 − ν 2 )

k σ
( d / t ) 2

σ crl = (4.35)

wherethebucklingcoefficient k σ dependsontheaspectratio L / d oftheplateand
the number of buckles along the plate. For long plates, the value of k σ is close to
its minimum value of

k σ = 23.9 (4.36)

for which the length of each buckle is approximately 2 d /3. By using this
value of k σ , it can be shown that the elastic buckling stress for a steel for which
E = 210000 N/mm 2 and ν = 0.3 is equal to the yield stress f y when

d
t

f y
235 = 138.9.

(4.37)

The buckling coefficient k σ is not significantly greater than 23.9 except when the
buckle length is reduced below 2 d /3. For this reason, transverse stiffeners are
ineffective unless more closely spaced than 2 d /3. On the other hand, longitudinal
stiffeners may be quite effective in changing the buckled shape, and therefore the
valueof k σ .Suchastiffenerismostefficientwhenitisplacedinthecompression