Applied Loads and Stability of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 191

wA eff f y
g M1

N b , Rd ¼ for class 4 cross sections ð 3 : 94 Þ

where w is the reduction factor for the relevant buckling mode. In determin-
ing A and A eff , holes for fasteners at the column ends need not be taken into
account. For axial compression in members, the value of w for the appropri-
ate nondimensional slenderness l should be determined from the relevant
buckling curve according to

1
F +

w¼ p but w 1 : 0 ð 3 : 95 Þ

l 2 F 2

h i

+ l 2

51+ a l 0

where F¼ 0 : : 2 ð 3 : 96 Þ

s

Af y
N cr

and l¼ for class 1, 2, and 3 cross sections ð 3 : 97 Þ

s

A eff f y
N cr

l¼

for class 4 cross sections ð 3 : 98 Þ

where a is an imperfection factor and N cr is the elastic critical force for the
relevant buckling mode based on the gross cross-sectional properties. The
imperfection factor a corresponding to the appropriate buckling curve
should be obtained from Tables 6.1 and 6.2, given in EC3 [2.11]. The non-
dimensional slenderness l is given by

s

Af y
N cr

L cr
i

1
l 1

l¼

¼ for class 1, 2, and 3 cross sections ð 3 : 99 Þ

q

A eff
A

s

A eff f y
N cr

L cr
i

l¼

¼

for class 4 cross sections ð 3 : 100 Þ

l 1

where L cr is the buckling length in the buckling plane considered and i is the
radius of gyration about the relevant axis, determined using the properties of
the gross cross section. The nondimensional slenderness l 1 is given by

s E

f y

l 1 ¼p ¼ 93 : 9 e ð 3 : 101 Þ

s

235
f y

with and f y in MPa.