Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 244

-1.0

m =

-0.5 0 1.0

1.0

Section resistance W y f y

0.8

m M

Elastic buckling M cr

M

0.6

m = 1.0 0.5 0 1.0 - -

0.4

Inelastic buckling approximation
for M I (equation 6.23)
EC3 moment resistance M b,Rd , mod / W y f y
(equations 6.28, 29)

0.2

0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Generalised slenderness ( W y f y /M cr )

Figure 6.14 EC3 design buckling moment resistances.

by an elastic analysis (if the beam is statically indeterminate), or by statics (if
the beam is statically determinate). The strength design loads are obtained by
summing the nominal loads multiplied by the appropriate partial load factors γ F
(see Section 1.5.6).
In both the EC3 simple general and less conservative methods of checking a
uniformequal-flangedbeam,thesectionmomentresistance W y f y /γ M 0 ischecked
first,theelasticbucklingmoment M cr isdetermined,andthemodifiedslenderness
λ LT is calculated using equation 6.25. The appropriate EC3 values of α LT , β ,
and λ LT ,0 (the values of these differ according to which of the two methods of
designisused)arethenselectedandthedesignbucklingmomentresistance M b , Rd
calculatedusingequations6.26and6.27. Inthesimplegeneralmethod, thebeam
is satisfactory when

M Ed ≤ M b , Rd ≤ W y f y /γ M 0 (6.31)

Inthelessconservativemethod, M b , Rd inequation6.31isreplacedby M b , Rd , mod
obtained using equations 6.28-6.30.
The beam must also be checked for shear, shear and bending, and bearing
as discussed in Sections 5.6.1.5-5.6.1.7, and for serviceability, as discussed in
Section 5.7.
When a beam is to be designed, the beam section is not known, and so a trial
sectionmustbechosen.Aniterativeprocessisthenused,inwhichthetrialsection
is evaluated and a new trial section chosen, until a satisfactory section is found.