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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
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
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
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
NON-UNIFORM TORSION
n
i ipi
iin
ii IG
LT
11 )(
• CASE 1: Bar consisting of prismatic segments with constant torque throughout each segment
• CASE 2: Bar with continuously varying cross sections and constant torque
L
p
L
xGI
Tdxd
00 )(
NON-UNIFORM TORSION
• CASE 3: Bar with continuously varying cross sections and continuously varying torque
L
p
L
xGI
dxxTd
00 )(
)(
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)
MECHANICAL POWER TRANSMISSION BY SHAFT
•Equation (2C) is the angular of equation (2A)
•All 3 equations should be remembered