Civil Engineering Reference
In-Depth Information
1.0
Flexural-torsional
buckling
In-plane behaviour
1
1/
F
C
m
m
0.8
0.6
m
M
M
/
F
1/
m
N
N
0.4
≡
C
m
1/
F
0.2
N
N
M
M
/
F
-1.0
-0.8
-0.6
-0.4
-0
0
0.2
0.4
0.6
0.8
1.0
End moment ratio
m
Figure 7.15
Equivalent end moments for beam-columns.
It is of interest to note that the variation of the factor 1
/
√
F
for the flexural-
torsional buckling of beam-columns is very close to that of the coefficient 1
/α
m
obtained from
α
m
=
1.75
+
1.05
β
m
+
0.3
β
m
≤
2.56
(7.44)
used for the flexural-torsional buckling of beams (see Section 6.2.1.2), and close
tothatofthecoefficient
C
m
(seeequation7.22)usedforthein-planebehaviourof
beam-columns.
However, the results shown in Figure 7.16 of a more recent investigation [12]
oftheelasticflexural-torsionalbucklingofbeam-columnshaveindicatedthatthe
factor for converting unequal end moments into equivalent equal end moments
shouldvarywith
N
/
N
cr
,
z
aswellaswith
β
m
.Moreaccuratepredictionshavebeen
obtained using
M
cr
,
MN
α
bc
M
zx
2
1
−
N
cr
,
MN
N
cr
,
T
1
−
N
cr
,
MN
N
cr
,
z
=
,
(7.45)
with
1
−
β
m
2
1
+
β
m
2
3
1
α
bc
=
0.40
−
0.23
N
cr
,
MN
N
cr
,
z
+
.
(7.46)
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