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MAE 2312

Torsion(5.1-5.5)

Main Rotor to tail rotor drive shaft

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Bell 222B

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HC-4 Black Stallion

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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)

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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

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Sign convention

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rdx

d

r

dxrd

max

max

dx

dtwistofrate

dx

d

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twistofratedxd

L

ddx

0

Lx

0x

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rdx

dr

dxrd

max

max

dx

d

1

2max

11

22max

r

r

L

rr

Lrr

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GG

dx

d

Direction of Shear

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Longitudinal shear associated with transverse shear stress

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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

/

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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?