Stability - Computational Analysis and Design of Bridge Structures - page 441

a

x

b

N x

y

Figure 14.4 Simply supported rectangular plate uniformly compressed in one direction.

Thus, the expression for the critical value of the compressive force N x,cr
can be simplified as

2

π 2

2

D 1 a

b

N = m + (14.7)

x cr ,

2 2

a m

Equation 14.7 with m = 1 can be represented in the form

π 2

D

N = k (14.8)

x cr ,

2

a

where k is a factor depending on the ratio a / b and is shown in Figure 14.5
by the curve marked m = 1. The critical value of the compressive stress σ cr
is then given by

2 2

N
h

k E h
b

π

x cr ,

σ = = (14.9)

cr

12 1 (

2

)

2

− ν

where
h is the thickness of the plate
a is the length
b is the width
m is the number of half-waves in which the plate buckles have been
determined

14.2.2 linear buckling of steel members
14.2.2.1 Buckling of steel structure members
Steel members in compression in a truss structure have to be analyzed for
buckling loads. Usually buckling becomes a governing criterion in struc-
tures like arched bridges, guyed towers, the top chord of a pony truss, or
any other unbraced compression member.