Civil Engineering Reference
In-Depth Information
Compression flange
Simply supported edge of web plate
h
Simply supported or fixed edge
of web plate
FIGURE 7.9
Pure flexural buckling of the web plate causing compression flange buckling.
The critical elastic buckling stress of a rectangular plate is
2
Et
w
k
π
F
cr
=
2
)h
2
,
(7.43)
− υ
12
(
1
where
F
cr
is the critical buckling stress,
k
is the buckling coefficient depending on
loading and plate edge conditions, and
is Poisson's ratio (0.3 for steel).
k
ranges
from 23.9 for simply supported edge conditions to 39.6 for fixed edge conditions
assumed at the two edges (at the flanges) of a long plate in pure bending (Timoshenko
and Woinowsky-Kreiger, 1959). AREMA (2008) conservatively uses
k
υ
23.9 and
reduces the ratio of web height to thickness to 90% of the theoretical values to account
for web geometry imperfections. Substitution of
k
=
=
23.9 into Equation 7.43 yields
E
F
cr
,
2
E
h
t
w
≤
23.9
π
0.90
0.3
2
)(F
cr
)
≤
4.18
(7.44)
12
(
1
−
which will preclude elastic buckling due to pure bending
(
Figure 7.10).
Rearrange-
ment of Equation 7.44 provides
0.24
h
F
cr
E
t
w
≥
(7.45)
and if
F
cr
=
0.55
F
y
0.18
h
F
y
t
w
≥
E
.
(7.46)
The allowable compressive bending stress,
F
cr
, is given by Equations 7.41 and
7.42. Therefore, when the actual calculated flexural stress at the compression flange,
f
c
, is less than
F
cr
,
f
c
F
cr
0.18
h
F
y
E
t
w
≥
(7.47)
and longitudinal stiffeners are not required for web flexural buckling stability.
