Lecture Strength of Materials I: Chapter 6 - PhD. Tran Minh Tu

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]

STRENGTH OF MATERIALS

TRAN MINH TU -University of Civil Engineering, Giai Phong Str 55, Hai Ba Trung Dist Hanoi, Vietnam

CHAPTER

TORSION

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

6.1 Introduction

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6.1 Introduction

• 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 > 0

y

z x

• Sign convention of Mz

- Positive: clockwise

- Negative: counterclockwise

0

z

M 

z

y

x

6.2.1 Simplifying assumptions

6.2 Torsion of Circular Shafts

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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

dz





    

- Following Hooke’s law:

6.2.2 Compatibility

- d – the angle of twist

=> In the cross-section, only shear stress exists

A A



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

 – the rate of twist