Civil Engineering Reference
In-Depth Information
F
cr
=
F
y
Elastic curve
Critical
stress
Transition curve to
F
y
Width to thickness
ratio,
b
/2
t
f
kE
0.95
kE
0.67
F
y
F
y
FIGURE 7.11
Plate buckling curve for uniform compression.
and the limiting width-to-thickness ratio
∗
at
F
cr
=
F
y
is
0.95
kE
F
y
2
E
b
2
t
f
≤
k
π
0.3
2
)F
y
=
.
(7.51)
12
(
1
−
However, this is an elastic buckling curve and at
F
cr
=
F
y
the plate axial strength is
overestimated (above the transition curve as shown in Figure 7.11). To mitigate this,
it is customary to use a limiting width-to-thickness ratio of
0.67
kE
F
y
b
2
t
f
≤
,
(7.52)
which is the approximate value corresponding to the transition curve at
F
cr
=
F
y
.
For plates with a free edge, the buckling coefficient,
k
, is 0.425 with the other edge
considered as simply supported and 1.277 with the other edge considered as fixed
(Bleich, 1952). Tests have indicated that the lowest value of buckling coefficient,
k
,
for partially restrained elements is about 0.70 (typical of a girder flange) (Tall, 1974).
Therefore, substitution of
k
=
0.7 into Equation 7.52 yields
0.56
E
F
y
b
2
t
f
≤
.
(7.53)
AREMA (2008) recommends that this width to thickness ratio for local flange
buckling be decreased further based on practical experience with local com-
pression forces from ties,
†
fabrication tolerances, and other unaccounted effects.
∗
Based on yield strength of the plate.
†
Particularly, if poorly framed.
