Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 103

t

x

N/bt

x

t

N SS

L

L z

Simply
supported

Simply
supported

3

Ebt
12(1- 2 )

--------------- -----------

bD =

z

3

= Ebt
12

-----------

EI

b

N/bt

b

N

y

y

( )

4 2

d d 4 4 4 2

∂ ∂ ∂ ∂

EI = - N

bD + 2 + = - N 4 2

d x d x

∂

4 2 2 4 2

x ∂ x ∂ z ∂ z ∂ x

(a) Column buckling

(b) Plate buckling

Figure 4.5 Comparison of column and plate buckling.

uniformlydistributedovereachendoftheplate.Whentheappliedloadsareequal
to the elastic buckling loads, the plate can buckle by deflecting v laterally out of
its original plane into an adjacent position [1-4].
It is shown in Section 4.8.1 that this equilibrium position is given by

v = δ sin m π x
L

sin n π z
b

(4.1)

with n = 1, where δ is the undetermined magnitude of the central deflection.The
elastic buckling load N cr at which the plate buckles corresponds to the buckling
stress

σ cr = N cr / bt , (4.2)

which is given by

π 2 E
12 ( 1 − ν 2 )

k σ
( b / t ) 2 .

σ cr = (4.3)

The lowest value of the buckling coefficient k σ (see Figure 4.6) is

k σ = 4, (4.4)

whichisappropriateforthehighaspectratios L / b ofmoststructuralsteelmembers
(see Figure 4.7).