Compression members - The Behaviour and Design of Steel Structures to EC3 - page 63

of α to them.The design buckling resistance N b , Rd is then given by

N b , Rd = χ N y /γ M 1 (3.22)

inwhich γ M 1 isthepartialfactorformemberinstability,whichhasarecommended
value of 1.0 in EC3.
The dimensionless compressive design buckling resistances N b , Rd / N y for α =
0.13, 0.21, 0.34, 0.49, and 0.76, which represent the EC3 compression member
curves(a 0 ),(a),(b),(c),and(d),respectively,areshowninFigure3.13.Members
with higher initial crookedness have lower strengths due to premature yielding,
andtheseareassociatedwithhighervaluesof α .Ontheotherhand,memberswith
lower initial crookedness are not as greatly affected by premature yielding, and
have lower values of α assigned to them.

3.5.2 Elastic buckling load

Althoughthedesignbucklingresistance N b , Rd givenbyequation3.22wasderived
byusingtheexpressionfortheelasticbucklingload N cr givenbyequation3.2fora
pin-endedcompressionmember,equation3.22isalsousedforothercompression
members by generalising equation 3.2 to

N cr = π 2 EI / L cr (3.23)

in which L cr is the effective length (referred to as the buckling length in EC3).
The elastic buckling load N cr varies with the member geometry, loading, and
restraints,butthereisnoguidancegiveninEC3fordeterminingeither N cr or L cr .
Section3.6followingsummarisesmethodsofdeterminingtheeffectsofrestraints
ontheeffectivelength L cr ,whileSection3.7discussesthedesignofcompression
members with variable sections or loading.

3.5.3 Effects of local buckling

Compression members containing thin-plate elements are likely to be affected by
local buckling of the cross-section (see Chapter 4). Local buckling reduces the
resistances of short compression members below their squash loads N y and the
resistances of longer members which fail by flexural buckling.
Local buckling of a short compression member is accounted for by using a
reducedeffectivearea A eff insteadofthegrossarea A ,asdiscussedinSection4.7.1.
Local buckling of a longer compression member is accounted for by using A eff
instead of A and by reducing the generalised slenderness to

λ = A eff f y / N cr (3.24)

but using the gross cross-sectional properties to determine N cr .