The Design of Modern Steel Bridges - TEDI

Figure 5.3 Beam cross-section.
In the case of axially loaded struts, the most critical parameter for its strength is
the slenderness ratio Le/r. The critical, i.e. the Euler, load is given by
and (Le/r) can be expressed as
where
sy ¼ yield stress
A ¼ area
Py ¼ squash load ¼ syA.
PE ¼ p2 EA
ðLe=rÞ 2
Le
r ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p2 s
E
Similarly, for lateral buckling of beams there is a slenderness parameter l LT
such that
and
Rolled Beam and Plate Girder Design 99
sy
Py
PE
Mcr ¼ p2 EZp
ðlLTÞ 2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p
lLT ¼
2 s
E Mp
sy
Mcr
where Mp is the plastic moment of resistance ¼ Zpsy.
Putting equation (5.4) in equation (5.7b), one obtains
lLT ¼ kv Le
ry
ð5:7aÞ
ð5:7bÞ
ð5:8Þ