Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 114

L

d

cr

Line of zero deflection

cr

Compression diagonals

Figure 4.15 Buckling pattern of a simply supported plate in shear.

increaseswiththeaspectratio L / d .Thenumericalsolutionsfortheelasticbuckling
stress τ cr can be expressed in the form

π 2 E
12 ( 1 − ν 2 )

k τ
( d / t ) 2

τ cr = (4.21)

in which the buckling coefficient k τ is approximated by

d
L

2

k τ = 5.34 + 4 (4.22)

when L ≥ d , and by

d
L

2

k τ = 5.34 + 4 (4.23)

when L ≤ d , as shown in Figure 4.16.
The shear stresses in many structural members are transmitted by unstiffened
webs, for which the aspect ratio L / d is large. In this case the buckling coefficient
k τ approaches 5.34, and the buckling stress can be closely approximated by
τ cr = 5.34 π 2 E / 12 ( 1 − ν 2 )

( d / t ) 2 . (4.24)
This elastic buckling stress is equal to the yield stress in shear τ y = f y / √ 3 (see
Section 1.3.1) of a steel for which E = 210000 N/mm 2 and ν = 0.3 when

d
t

f y
235 = 86.4.

(4.25)