Civil Engineering Reference
In-Depth Information
Plastic collapse
Warping torsion
Rotations
Member
and
loading
Uniform torsion
Uniform
tm
GI
t
/TL
Warping
wm
EI
w
/
TL
3
w
TL/M
fp
d
f
t
T
/
T
tp
Mechanism
Mechanism
T/L
1.0
0
0.5
∞
L
T/L
1.0
2.0
0.5
0.139
L
T/L
1.0
2.0
0.5
0.292
L
L
T/L
1.0
2.0
0.5
0.250
L
L
T/L
2.0
8.0
0.125
0.0130
L
T/L
2.0
11.66
0.125
0.00541
L
T/L
2.0
16.0
0.125
0.00260
L
T/L
2.0
11.66
0.125
0.00915
L
L
T/L
L
2.0
11.66
0.125
0.00860
L
T/L
2.0
16.0
0.125
0.00417
L
T/L
L
2.0
16.0
0.125
0.00397
L
L
Free to warp
Warping torsion frictionless hinge
Warping prevented
Warping torsion plastic hinge
Uniform torsion shear hinges
Top flange
Bottom flange
Figure 10.21
Plastic collapse and maximum rotation - uniformly distributed torque.
member.Thevaryingwarpingdeflectionsinducelongitudinalstrainsandstresses
σ
w
. When these warping normal stresses also vary along the member, there are
associated warping shear stresses
τ
w
distributed around the cross-section, and
these may act in conjunction with the shear stresses due to uniform torsion to
resist the torque acting at the section [1, 11]. In the following sub-sections, the
warpingdeformations,stresses,andtorquesinthin-walledopen-sectionmembers
of constant cross-section are treated. The local warping stresses induced by the
non-uniform torsion of closed sections are beyond the scope of this topic, but are
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