Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 104

10

m=1

2

3 b

4

5

8

L

n=1

2

6

3

4

4

2

0

0 1 2 3 4 5 6

Plate aspect ratio L/b

Figure 4.6 Buckling coefficients of simply supported plates in compression.

b

cr

cr

b b b

m

L = b

Figure 4.7 Buckled pattern of a long simply supported plate in compression.

The buckling stress σ cr varies inversely as the square of the plate slenderness
or width-thickness ratio b / t , as shown in Figure 4.4, in which the dimensionless
buckling stress σ cr / f y is plotted against a modified plate slenderness ratio

σ cr = b

f y f y

E

12 ( 1 − ν 2 )
π 2 k σ

. (4.5)

t

If the material ceases to be linear elastic at the yield stress f y , the above analysis

isonlyvalidfor √ ( f y /σ cr ) ≥ 1.Thislimitisequivalenttoawidth-thicknessratio
b / t given by

b
t

f y
235 = 56.8

(4.6)