Torsion members – the slender members subjected to torsional loading, that is loaded by couple that produce twisting of the member about its axis. Examples – A torsional moment (torque) [r]
(1)STRENGTH OF MATERIALS
TRAN MINH TU -University of Civil Engineering, Giai Phong Str 55, Hai Ba Trung Dist Hanoi, Vietnam
(2)6
CHAPTER
(3)Contents 6.1 Introduction
6.2 Torsional Loads on Circular Shafts
6.3 Strength Condition and stiffness condition 6.4 Statically Indeterminate Problem
6.5 Strain Energy 6.6 Examples
Home’s works
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(6)• Torsional Loads on Circular Shafts: the torsional moment or couple
6.1 Introduction
Torsion members – the slender members subjected to torsional loading, that is loaded by couple that produce twisting of the member about its axis
Examples – A torsional moment (torque) is applied to the lug-wrench shaft, the shaft transmits the torque to the generator, the drive shaft of an automobile
x F
A
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6.1 Introduction
Internal torsional moment diagram
• Using method of section
z M >
y
z
x
• Sign convention of Mz - Positive: clockwise
- Negative: counterclockwise
0
z
M
Mz =
z
y
(8)6.2.1 Simplifying assumptions
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6.2 Torsion of Circular Shafts
• Consider the portion of the shaft shown in the figure
• CD – before deformation • CD’ – after deformation
- From the geometry DD' d dz
=> The Shear strain: d
dz d G G dz - Following Hooke’s law:
6.2.2 Compatibility
- d – the angle of twist
(10)2
z p
A A
d d
M dA G dA G I
dz dz z p M d dz GI z M
Ip – polar moment of inertia
Mz – internal torsional moment
6.2 Torsion of Circular Shafts
6.2.3 Equilibrium
6.2.3 Torsion formulas – Shearing stress