1. TORSION Introduction, Round bar torsion, Non- uniform torsion
Relationship between Young’s Modulus, E, Poisson ratio,  and modulus of rigidity
Power Transmission on round bar

2. TORSION-INTRODUCTION
Occur when any shaft is subjected to a torque
This is true whether the shaft is rotating (e.g. drives shaft on engines, motors & turbines) or stationary (bolt/screw)
This torque makes the shaft twist and or end rotates relative to other inducing shear stress on any cross section
Failure might occur due to shear alone / Shear + stretching/bending

3. ROUND BAR TORSION EQUATION
The diagram show a shaft fixed at one end and twisted at the other end due to action of a torque T

6. POLAR 2ND MOMENT OF AREA
Solid shaft
Hollow shaft

11. NON-UNIFORM TORSION
Uniform/Pure torsion – torsion of prismatic bar subjected to torques acting only at the ends
Non-uniform torsion– the bar need not be prismatic and the applied torque may act anywhere along the axis of bar
Non-uniform torsion can be analysed by
Applying formula of pure torsion to finite segments of the bar then adding the results
Applying formula to differential elements of the bar and then integrating

12. NON-UNIFORM TORSION
CASE 1: Bar consisting of prismatic segments with constant torque throughout each segment
CASE 2: Bar with continuously varying cross sections and constant torque

13. NON-UNIFORM TORSION
CASE 3: Bar with continuously varying cross sections and continuously varying torque

14. NON-UNIFORM TORSION Limitations
Analyses described valid for bar made of linearly elastic materials
Circular cross sections (Solid /hollow)
Stresses determined from the torsion formula valid in region of the bar away from stress concentrations (diameter changes abruptly/concentrated torque applied
For the case above, Angle of twist still valid
Changes in diameter is are small and gradually (angle of taper max 10o)

15. RELATION BETWEEN E,  AND G

16. MECHANICAL POWER TRANSMISSION BY SHAFT
Equation (2C) is the angular of equation (2A)
All 3 equations should be remembered