Civil Engineering Reference
In-Depth Information
3.11 Appendix - torsional buckling
Thin-walledopen-sectioncompressionmembersmaybucklebytwisting,asshown
inFigure3.24foracruciformsection,orbycombinedbendingandtwisting.When
this type of buckling takes place, the twisting of the member causes the axial
compressive stresses
N
/
A
to exert a disturbing torque which is opposed by the
torsional resistance of the section. For the typical longitudinal element of cross-
sectional area
δ
A
shown in Figure 3.27, which rotates
a
0
(d
φ
/d
x
) (where
a
0
is the
distance to the axis of twist) when the section rotates
φ
, the axial force
(
N
/
A
)
δ
A
has a component
(
N
/
A
)
δ
Aa
0
(d
φ
/d
x
) which exerts a torque
(
N
/
A
)
δ
Aa
0
(d
φ
/d
x
)
a
0
about the axis of twist (which passes through the shear centre
y
0
,
z
0
as shown in
Chapter 5).The total disturbing torque
T
P
exerted is therefore
T
P
=
N
A
d
φ
d
x
a
0
d
A
,
A
where
a
0
=
(
y
−
y
0
)
2
+
(
z
−
z
0
)
2
.
This torque can also be written as
T
P
=
Ni
0
d
φ
d
x
,
where
i
0
=
i
p
+
y
0
+
z
0
,
(3.55)
i
p
=
√
(
I
y
+
I
z
)/
A
.
(3.56)
For members of doubly symmetric cross-section
(
y
0
=
z
0
=
0
)
, a twisted
equilibrium position is possible when the disturbing torque
T
P
exactly balances
δ
x
Axis of twist
d
f
N
N
a
t
δ
s
t
δ
s
0
d
x
A
A
d
f
N
δ
t
0
s
.
a
A
d
x
Figure 3.27
Torque exerted by axial load during twisting.
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