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

Lecture Strength of Materials I - Chapter 6: Torsion. The following will be discussed in this chapter: Introduction, torsional loads on circular shafts, strength condition and stiffness condition, statically indeterminate problem, strain energy, examples. | Lecture Strength of Materials I: Chapter 6 - PhD. Tran Minh Tu STRENGTH OF MATERIALS 1/10/2013 TRAN MINH TU - University of Civil Engineering, 1 Giai Phong Str. 55, Hai Ba Trung Dist. Hanoi, Vietnam CHAPTER 6 TORSION 1/10/2013 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 1/10/2013 3 6.1. Introduction 1/10/2013 4 6.1. Introduction 1/10/2013 5 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. • Torsional Loads on Circular Shafts: the torsional moment or couple A F x Q2 B C Q1 t z 2 T t T 1 1 2 y 1/10/2013 6 6.1. Introduction Internal torsional moment diagram • Using method of section • Sign convention of Mz - Positive: clockwise - Negative: counterclockwise Mz > 0 M z 0 Mz = y y z z x x 1/10/2013 7 6.2. Torsion of Circular Shafts 6.2.1. Simplifying assumptions 1/10/2013 8 6.2. Torsion of Circular Shafts => In the cross-section, only shear stress exists 6.2.2. Compatibility • Consider the portion of the shaft shown in the figure • CD – before deformation • CD’ – after deformation - From the geometry DD ' d dz d => The Shear strain: dz - d – the angle of twist - Following Hooke’s law: d G G 1/10/2013 dz 9 6.2. Torsion of Circular Shafts 6.2.3. Equilibrium d 2 d M z dA G dA G Ip A dz A dz d M z – the rate of twist dz GI p 6.2.3. Torsion formulas – Shearing stress Mz – internal torsional moment Mz Ip – polar moment of inertia