STRENGTH OF MATERIALS FOR MECHANICAL ENGINEERS

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

8. 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

15. 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

27. BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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

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45. BIBIN.C / ASSOCIATE PROFESSOR / MECHANICAL ENGINEERING / RMK COLLEGE OF ENGINEERING AND TECHNOLOGY

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

47. 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