Civil Engineering Reference
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and for fixed base portals,
R
1
=
1
/(
1
+
L
1
I
y
2
/
2
L
2
I
y
1
)
.
(6.72)
Ifthecolumnsareofopencross-section,theirtorsionalstiffnessiscomparatively
small,anditisnotundulyconservativetoassumethatthecolumnsdonotrestrain
the beam element or its flanges against minor axis flexure, and so
R
2
=
R
4
=
0.
(6.73)
Using these values of the restraint parameters, the elastic buckling load can be
determined from the tabulations in [33, 35].
When more than one member of a rigid frame is loaded, the buckling restraint
parameterscannotbeeasilydeterminedbecauseoftheinteractionsbetweenmem-
berswhichtakeplaceduringbuckling.Thetypicalmemberofsuchaframeactsas
a beam-column which is subjected to a combination of axial and transverse loads
and end moments. The buckling behaviour of beam-columns and of rigid frames
is treated in detail in Chapters 7 and 8.
6.10 Monosymmetric beams
6.10.1 Elastic buckling resistance
When a monosymmetric I-beam (see Figure 6.27) which is loaded in its plane of
symmetry twists during buckling, the longitudinal bending stresses
M
y
z
/
I
y
exert
d
h
(
t
t
)
/
2
=
-
−
f
1
2
b
t
d
+
(
h
-
t
-
t
)(
h
-
t
)
t
/
2
2
2
f
1
2
2
w
z
=
b
t
+
b
t
+
(
h
-
t
-
t
)
t
1
1
2
2
1
2
w
b
1
t
1
2
2
3
I
=
b
t
z
+
b
t
(
d
-
z
)
+
(
h
-
t
-
t
)
t
/
12
y
1
1
2
2
f
1
2
w
2
+
(
h
--
t
t
)
t
{
y
-
(
h
-
t
)
/
2
1
2
w
2
1
z
t
w
m
=
h
3
1
+
(
b
/
b
)
(
t
/
t
)
d
f
y
2
1
2
1
C
z
0
m
z
=
(
-
)
d
-
z
S
0
f
{
}
]
[
2
2
(
d
-
z
)
b
t
/
12
b
t
(
d
-
z
)
+
b
2
f
2
2
2
f
t
2
1
y
3
1
2
=
-
z
[
b
t
/
12
+
b
t
z
]
-2
z
0
1
1
1
I
y
4
4
[(
d
-
z
-
t
/
2
)
-
(
z
-
t
/
2
)
]
t
/
4
+
z
f
2
1
w
2
2
I
b
t
d
/
12
=
w
2
f
m
Figure 6.27
Properties of monosymmetric sections.
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