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7/27/2019 Chapter 5- Torsion (1)
1/17
10/23/2013 1
MAE 2312
Torsion(5.1-5.5)
Main Rotor to tail rotor drive shaft
7/27/2019 Chapter 5- Torsion (1)
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7/27/2019 Chapter 5- Torsion (1)
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Bell 222B
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HC-4 Black Stallion
7/27/2019 Chapter 5- Torsion (1)
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Torsion Modeling
Circular Bars
Prismatic Bar
Identical cross section along length
Subject to pure Torsion
Constant Torque at every section
Torsion theory of circular bars Charles A. Coulomb (1736-1806)
General Theory of Torsion
Barr de Saint-Vnant (1797-1886)
7/27/2019 Chapter 5- Torsion (1)
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Torsion Modeling
Implication of circular bars subject to pure
torsion
Cross section remain plane
Straight radii
No warping
Small twist angle Same Length
Same cross section radius
7/27/2019 Chapter 5- Torsion (1)
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Sign convention
7/27/2019 Chapter 5- Torsion (1)
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rdx
d
r
dxrd
max
max
dx
dtwistofrate
dx
d
7/27/2019 Chapter 5- Torsion (1)
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twistofratedxd
L
ddx
0
Lx
0x
7/27/2019 Chapter 5- Torsion (1)
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rdx
dr
dxrd
max
max
dx
d
1
2max
11
22max
r
r
L
rr
Lrr
7/27/2019 Chapter 5- Torsion (1)
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GG
dx
d
Direction of Shear
7/27/2019 Chapter 5- Torsion (1)
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Longitudinal shear associated with transverse shear stress
7/27/2019 Chapter 5- Torsion (1)
13/1710/23/2013 13pmax
2p
p2
IrT
dAI
IGdAGdAT
maxr
GG
dx
d
pmax
I
Tr
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Summary
TL
pT
p
p
f
GIk
GI
TLL
GIT
1
pmax
I
T
r
2dddrrt
td4
tdrr
2I
2112
2241
42p
/
7/27/2019 Chapter 5- Torsion (1)
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Torsion Design
Account for all possible modes of failure
Thickness of tube governed by wrinkling
Specified max. value for
t
r2
Limitations
Circular cross sections
Noncircular will warp
Max. Shear stress not located at farthest distancesfrom midpoints
Linearly elastic material
Away from stress concentrations
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Problem
in2.1r
psi6300
in5.5b
lb900P
1
all
Determine r2
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2001 Brooks/Cole, a division of Thomson Learning, Inc. T homson Learning
is a trademark used herein under license.
Problem
2
9
2
6all
oall
m
N1075GPa75G
m
N1060MPa60
rad180
33
m8.0mm800L
For what range of the
applied Torque Tdoes the
shear stress determine the
required diameterd? Forwhat range of values does
the angle of twist
determine the diameter?