Civil Engineering Reference
In-Depth Information
7.2.6.1.3.1.1 Elastic Buckling under Pure Bending
Flexural buckling of the
web plate is precluded by limiting the ratio of web height,
h
, to thickness,
t
w
,orby
including a longitudinal stiffener. The elastic buckling of the web plate under bending
was considered above in conjunction with the investigation of vertical buckling of the
compression flange.
Web plate design without longitudinal stiffeners considering Equation 7.47, pre-
sented again as Equation 7.56, requires a minimum web plate thickness to preclude
elastic flexural buckling of
f
c
F
cr
≥
0.24
h
f
c
0.18
h
F
y
E
t
w
≥
E
.
(7.56)
Rearrangement of Equation 7.56 and substitution of
F
cr
=
0.55
F
y
(preclude elastic
buckling per
Figure 7.10)
yield the criteria that
E
f
c
.
h
t
w
≤
4.18
(7.57)
Otherwise, longitudinal stiffeners are required for web flexural buckling stability.
Web plate design with a longitudinal stiffener at 0.20
h
from the compression flange
consideringEquation7.49,presentedagainasEquation7.58,requiresaminimumweb
plate thickness to preclude elastic flexural buckling of
f
c
F
cr
≥
0.08
h
F
y
E
0.10
h
f
c
t
w
≥
E
.
(7.58)
7.2.6.1.3.1.2 Elastic Buckling under Pure Shear
The critical elastic plate
buckling shear stress is
2
Et
w
k
π
τ
cr
=
2
)h
2
,
(7.59)
12
(
1
− υ
where
k
5.35 for infinitely long simply supported plate under pure shear
(Timoshenko and Gere, 1961).
Shear yield stress,
=
τ
y
, is related to tensile yield stress,
F
y
, as (see Chapter 2)
F
y
√
3
.
τ
cr
= τ
y
=
(7.60)
Therefore, from Equation 7.59,
E
F
y
.
h
t
w
≤
2.89
(7.61)
