Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 245

Onemethodoffindingafirst-trialsectionistomakeinitialguessesfor f y (usually
the nominal value) and M b , Rd / W y f y (say 0.5), to use these to calculate a target
section plastic modulus

M Ed / f y
M b , Rd /( W y f y )

W pl , y ≥ (6.32)

and then to select a suitable trial section.
After the trial section has been selected, its elastic buckling moment M cr , yield
stress f y ,anddesignmomentresistance M b , Rd canbefoundandusedtocalculatea
new value of W pl , y , and to select a new trial section.The iterative process usually
convergeswithinafewcycles,butconvergencecanbehastenedbyusingthemean
of the previous and current values of M b , Rd / W y f y in the calculation of the target
section modulus.
Worked examples of checking and designing beams against lateral buckling
are given in Sections 6.15.1-6.15.7

6.5.5 Checking beams supported at both ends

6.5.5.1 Section moment resistance

Theclassificationofaspecifiedbeamcross-sectionasClass1,2,3,or4isdescribed
inSections4.7.2and5.6.1.2,andthedeterminationofthedesignsectionmoment
resistance M c , Rd = W y f y /γ M 0 in Sections 4.7.2 and 5.6.1.3.

6.5.5.2 Elastic buckling moment

The elastic buckling moment M cr of a simply supported beam depends on
its geometry, loading, and restraints. It may be obtained by calculating M zx
(equation 6.3), N cr , z (equation 6.12), and α m (equation 6.13), and substituting
these into equation 6.11, or by using a computer program such as those referred
to in Section 6.5.2.

6.5.5.3 Design buckling moment resistance

The design buckling moment resistance M b , Rd can be obtained as described in
Section 6.5.3.

6.6 Restrained beams

6.6.1 Simple supports and rigid restraints

Intheprevioussectionsitwasassumedthatthebeamwassupportedlaterallyonly
at its ends.When a beam with equal and opposite end moments ( β m =− 1.0) has