Torsion

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Problem

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dxdBD

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max

c

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G

max

c

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dFT dAdF

A

dAc

T 2max J

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J

Tcmax

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dAJ 2

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ddA 2 dAJ

4

2cJ

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Shaft Design

allowT

J

callow

Power, P Frequency, f

allowc

J

Design/Geometric Parameter

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Problem 1

• The drive shaft AB of an automobile is made of a steel having an allowable shear stress of 8 ksi. If the outer diameter of the shaft is 2.5 in. and the engine delivers 200 hp to the shaft when it is turning at 1140 rev/min., determine the minimum required thickness of the shaft wall.

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Problem 2The engine of the helicopter is delivering 600 HP to the rotor shaft AB when the blade is rotating at 1200 rev/min. Determine to the nearest 1/8 in. the diameter of the shaft AB if the allowable shear stress is 10.5 ksi and the vibration limit the angle of twist of the shaft to 0.005 rad. The shaft is 2 ft long and made from L2 steel.

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Problem 3

The propellers of ships are connected to a solid A-36 steel shaft that is 60 m long and has an outer diameter of 340 mm and inner diameter of 260 mm. If the power output is 4.5 MW when the shaft rotates 20 rad/s, determine the maximum torsional stress in the shaft and its angle of twist.

Summary

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cJ

T

J

Tcmax

Torsional Shear Stress

Maximum at c

Increase linearly

T

T

L

c

max

c

JG

TL in radian

Angular Displacement

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The Polar Moment of Inertia

2

4cJ

For a Hollow Shaft having inner radius ai and outer radius a0

2

440 icc

J

For a circular cross section:

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Problem 4

• A 6 cm diameter, 2 long magnesium (G=17x109Pa) shaft is welded to a hollow (c0=3cm and cj=1.5cm) aluminum (G=27x109Pa) shaft 1.2 m long.

• A moment of 2000 m.N is applied at end A.

• Determine the maximum torsional stress in each material and angle of twist of end A relative to fixed end B.

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2 m

1.2 m

B Mg

Al3 m

1.5 m

T = 2000 m.N

A

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Solution

4644

10272.12

03.0

2m

aJmg

4644

10193.12

015.003.0

2m

aJ al

The polar moment of inertia

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The angle of twist

almgalmg JG

TL

JG

TL

rad

almg

2595.00745.01850.0

102710193.1

2.12000

101710272.1

220009696

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