Lecture Notes on Torsion and Shaft Mechanics

Introduction

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Important Upcoming Dates

• GATE and ESE Scholarship Test: 26th June at 11 am.
• New Batch Start Date: 22nd June, focusing on Strength of Materials, Structural Analysis, and RCC.
• Target Completion Date: 15th December for course material.

Class Features

• Daily Scholarship Tests: Available for practice.
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Key Questions and Solutions

Question 54: Torsion in Shafts

• Given: Ratio of revolutions (na/nb = 2) and torque (Ta/Tb = 1/2).
• Calculation:
  • Formula: Pa/Pb = Ta * ωa / (Tb * ωb)
  • Answer: Pa/Pb = 1/1, so C is correct.

Question 56: Strain Energy in Torsion

• Formula:
  • Strain energy per unit volume = T²L / (2GJ)
  • Result: q² / 4G.

Question 61: Angle of Twist in Shafts

• Formula: θ = TL / (GJ), where J = diameter^4 for solid and hollow shafts.
• Result: Ratio of angles derived from diameter.

Question 62: Coaxial Springs

• Two springs with coefficients 80 N/mm and 120 N/mm.
• Deformation: Same compression for parallel springs.
• Net Coefficient: 200 N/mm.

Question 73: Power Transmitted by Shaft

• Formula: P = T × ω
• Find maximum shear stress and twist.

Question 81: Shear Stress Calculation

• Relates power to maximum shear stress and torque.

Question 90: Shear Stress Ratio in Different Members

• Compare thin-walled tubular members.

Question 92: Hollow Shafts in Propulsion

• Advantages: Weight reduction while maintaining torsional capacity.

Conclusion

• The lecture focused on torsion, shaft mechanics, and related formulas.
• Upcoming classes will cover principal stresses.
• Reminder to continue practicing problems and prepare for upcoming exams.