The document discusses torsion and shafts. It covers torsional stress and shear stress in shafts caused by twisting forces. It derives the torsional equation and calculates the maximum torque that can be transmitted by solid and hollow circular shafts based on their dimensions and material properties. It also provides examples of problems calculating stresses and torque capacities in solid and hollow shafts.

1. BIBIN CHIDAMBARANATHAN
TORSION OF SHAFTS
AND
SPRINGS
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

2. Learning Objectives
• At the end of this chapter you should be able to complete torsion calculations using:
• General torsion equation
• Polar moment of inertia
• Modulus of elasticity in shear
Shafts are mechanical components, usually of circular cross-section, used to transmit
power/torque through their rotational motion. In operation they are subjected to:
• torsional shear stresses within the cross-section of the shaft, with a maximum at the
outer surface of the shaft
• bending stresses (for example a transmission gear shaft supported in bearings)
• vibrations due to critical speeds
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

3. TORQUE
• Torque is the product of
the magnitude of the force
and the perpendicular
distance of the line of
action of force from the
axis of rotation.
• If the angle of rotation is
small, the length of the
shaft and its radius will
remain unchanged.
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

4. What is Torsional stress? | Torsional Shear Stress
• Torsional shear stress or Torsional stress is the shear stress
produced in the shaft due to the twisting.
• This twisting in the shaft is caused by the couple acting on it
• When a machine member is under the twisting force then it is
said to be the shaft is subjected to torsion.
• Due to this torsion in the shaft, the stresses induced in the shaft
are known as the Torsional shear stress or simply Torsional
stress.
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

5. What is the couple?
• A couple is Two equal and opposite parallel forces acting upon a
body with a different line of acting points said as a couple.
• (the Following figure represents how a twisting is produced
when tightening of a nut with a wrench)
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

6. TORSION OF CIRCULAR SHAFTS
• When a cylindrical shaft is subjected to equal and opposite
couples at the ends, either it will be in equilibrium or it will
rotate at a uniform rate.
• In either case, it is subjected to torsion and the stresses set up by
every cross-section are shear stresses.
• At any point in the cross-section of a shaft, there is a state of
simple shear, the two planes of shear, that is the planes across
which the stress is wholly tangential being the cross-section itself
and the plane through the point and the axis of the shaft.
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

7. BIBIN CHIDAMBARANATHAN
DERIVATION
OF
TORSIONAL
EQUATION
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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14. BIBIN CHIDAMBARANATHAN
MAXIMUM TORQUE
TRANSMITTED BY
CIRCULAR SOLID
SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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26. BIBIN CHIDAMBARANATHAN
POWER
TRANSMITTED BY
SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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28. BIBIN CHIDAMBARANATHAN
PROBLEMS
ON
SOLID SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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46. BIBIN CHIDAMBARANATHAN
MAXIMUM TORQUE
TRANSMITTED BY
CIRCULAR HOLLOW
SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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51. BIBIN CHIDAMBARANATHAN
PROBLEMS
ON
HOLLOW SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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66. BIBIN CHIDAMBARANATHAN
COMPARISON
OF
SOLID & HOLLOW
SHAFT
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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85. Thank You
BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY