Civil Engineering Reference
In-Depth Information
or
qL
3
2
√
(
EI
z
GI
t
)
=
27
1.4
(ε
−
0.1
)
1
+
(
1
+
1.4
2
(ε
−
0.1
)
2
)
1.3
(ε
−
0.1
)
+
10
(
K
−
2
)
1
+
(6.59)
(
1
+
1.3
2
(ε
−
0.1
)
2
)
Cantilevers which have restraints at the unsupported end which prevent lateral
deflection and twist rotation (Figure 6.13) may be treated as beams which are
supported laterally at both ends, as in Section 6.6.
Intermediaterestraintswhichpreventlateraldeflectionandtwistrotationdivide
a cantilever into segments (Figure 6.13). The elastic buckling of each segment
can be approximated by assuming that there are no interactions between adjacent
segments. The segment with the free end can then be treated as an overhanging
beam as in Section 6.7.2 following, while the interior segments may be treated as
beams supported laterally at both ends, as in Section 6.6.
6.7.2 Overhanging beams
Overhangingbeamsaresimilartocantileversinthattheyarefreetodeflect,rotate,
and warp at one end (Figure 6.13). However, lateral rotation and warping are not
completely prevented at the supported end, but are elastically restrained by the
continuityoftheoverhangingbeamwithitscontinuationbeyondthesupport.The
buckling moments of some examples are reported in [16, 37].
It is usually very difficult to predict the degrees of lateral rotation and warping
restraint, in which case they should be assumed to be zero. The elastic buck-
ling moments of such overhanging beams with either concentrated end load or
uniformly distributed load can be predicted by using [16]
QL
2
√
(
EI
z
GI
t
)
=
6
1.5
(ε
−
0.1
)
1
+
(
1
+
1.5
2
(ε
−
0.1
)
2
)
3
(ε
−
0.3
)
+
1.5
(
K
−
2
)
1
+
(6.60)
(
1
+
3
2
(ε
−
0.3
)
2
)
or
qL
3
2
√
(
EI
z
GI
t
)
=
15
1.8
(ε
−
0.3
)
1
+
(
1
+
1.8
2
(ε
−
0.3
)
2
)
2.8
(ε
−
0.4
)
+
40
(
K
−
2
)
1
+
.
(6.61)
(
1
+
2.8
2
(ε
−
0.4
)
2
)
Search WWH ::
Custom Search