Civil Engineering Reference
In-Depth Information
conditionsintoequation10.49.Asanexampleofthisprocedure,thebeamshown
in Figure 10.26 is analysed in Section 10.8.4.
ThewarpingtorsionanalysisofequalflangedI-sectionscanalsobecarriedout
by analysing the flange bending model shown in Figure 10.27. Thus the warping
Twist rotation and
warping prevented
(+)
T
0
=
0
= 0
Free to warp
L
= 0
(b) Torque
T
x
T
T
x
TL
3
3
EI
w
L
(+)
(a) Cantilever
(c) Twist rotation
Figure 10.25
Warping torsion of a statically determinate cantilever.
Twist rotation and
warping prevented
Twist rotation
prevented,
free to warp
T
0
mL
-
T
0
(+)
(-)
0
=
0
= 0
L
=
L
= 0
(b) Torque
T
x
m
/unit length
T
0
0.0054
mL
4
mL
-
T
0
(+)
x
EI
w
L
(a) Beam
(c) Twist rotation
Figure 10.26
Warping torsion of a statically indeterminate beam.
v
f
w
/
2
=
d
f
V
f
T
x
/
=
d
f
d
f
y
T
x
y
d
f
V
f
w
z
z
(a) Flange deflection
V
f
(b) Equivalent flange shears
V
f
Figure 10.27
Flange bending model of warping torsion.
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