Civil Engineering Reference
In-Depth Information
Bottom flange
Prevention of warping
ineffective in uniform torsion
Top flange
(b) Uniform torsion collapse mechanism
T
L
T
tp
T
tp
(+)
t
T
(-)
(a) Torsion member and loading
(c) Uniform torque distribution
Figure 10.19
Uniform torsion plastic collapse.
Plastic collapse
Warping torsion
Rotations
Member
and
loading
Uniform torsion
Uniform tm
tm
GI
t
/TL
Warping
wm
EI
w
/
TL
3
w
TL/M
fp
d
f
Mechanism
Mechanism
t
T
/
T
tp
T
1.0
0
1.0
∞
L
T
1.0
1.0
1.0
0.333
L
T
1.0
1.0
1.0
0.667
LL
T
1.0
1.0
1.0
0.583
LL
T
2.0
4.0
0.25
0.0208
L
T
2.0
6.0
0.25
0.00931
L
T
2.0
8.0
0.25
0.00521
L
T
LL
T
2.0
6.0
0.25
0.0150
2.0
6.0
0.25
0.0142
L
L
T
2.0
8.0
0.25
0.00751
L
L
T
2.0
8.0
0.25
0.00721
L
L
Free to warp
Warping torsion frictionless hinge
Warping prevented
Top flange
Warping torsion plastic hinge
Uniform torsion shear hinges
Bottom flange
Figure 10.20
Plastic collapse and maximum rotation - concentrated torque.
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