Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 261

L

( )

(a) Segment providing
equal end restraints

2 EI Q

zr ms

r

= 1 -

L Q

r rs

( )

3 EI Q

(b) Segment hinged
at one end

zr ms

r

= 1 -

L Q

r rs

( )

(c) Segment fixed
at one end

4 EI Q

zr ms

r

= 1

-

L Q

r rs

Figure 6.25 Stiffness approximations for restraining segments.

(10) Calculate the elastic buckling moment M cr of the critical segment 12
using L cr in equation 6.67, and from this the corresponding improved
approximation of the elastic buckling load Q cr of the beam.

It should be noted that while the calculations for the lower bound (the first five
steps) are made for all segments, those for the improved estimate are only made
for the critical segment, and so comparatively little extra effort is involved. The
development and application of this method is further described in [36]. The use
of user-friendly computer programs such as in [18] eliminates the need for these
approximate procedures.

6.9 Rigid frames
Under some conditions, the elastic buckling loads of rigid frames with only one
memberloadedcanbedeterminedfromtheavailabletabulations[12,33,35]ina
similarmannertothatdescribedinSection6.8.1forbracedandcontinuousbeams.
Forexample,considerasymmetricallyloadedbeamwhichisrigidlyconnectedto
two equal cross-beams as shown in Figure 6.26a. In this case the comparatively
large major axis bending stiffnesses of the cross-beams ensure that end twisting
of the loaded beam is effectively prevented, and it may therefore be assumed that
R 3 = 0. If the cross-beams are of open section so that their torsional stiffness is
comparativelysmall,thenitisnotundulyconservativetoassumethattheydonot
restrain the loaded beam about its major axis, and so

R 1 = 0. (6.69)