Civil Engineering Reference
In-Depth Information
F
cr
= 0.55
F
y
Euler curve
h
t
w
E
F
cr
=
4.18
FIGURE 7.10
Elastic buckling curve for rectangular plate buckling under pure bending.
However, in cases where longitudinal stiffeners are provided, the minimum web
thickness criteria to avoid flexural buckling (and thereby prevent vertical buckling
of the compression flange) of Equation 7.47 is reduced. The optimum location for
longitudinal web plate stiffeners is at 0.22
h
from the compression flange (Rockey and
Leggett, 1962). When a longitudinal stiffener is placed at
h/
5 from the inside surface
of the compression flange, as recommended by AREMA (2008), the critical elastic
buckling stress of a rectangular plate (Equation 7.43) is
2
Et
w
π
129
F
cr
=
2
)h
2
,
(7.48)
12
(
1
− υ
where the theoretical
k
=
129 (Galambos, 1988). Equation 7.48 with
F
cr
=
0.55
F
y
can be expressed as
0.08
h
F
y
t
w
≥
E
.
(7.49)
Equation 7.49 indicates that the web thickness to preclude elastic critical flexural
buckling of the web with a longitudinal stiffer can be 43% (23.9/129) of that required
without a longitudinal stiffener (Equation 7.46). AREMA (2008) recommends that
the web thickness with a longitudinal stiffener be no less than 50% of that required
without a longitudinal stiffener.
7.2.6.1.2.1.3 Torsional Buckling
Torsional buckling of the compression
flange is essentially the buckling problem of uniform compression on a plate free
at one side and partially restrained at the other (Salmon and Johnson, 1980). The
critical elastic plate buckling stress is
2
Et
f
k
π
F
cr
=
(7.50)
− υ
2
)b
2
12
(
1
