Strength of Materials 17ME34
Module 4
TORSION OF SHAFTS
Objectives:
Explain the structural behavior of members subjected to torque, Calculate twist and stress induced
in shafts subjected to bending and torsion. & Understand the concept of stability and derive
crippling loads for columns
Learning Structure
• 4.1 Bending Moment
• 4.2 ASSUMPTIONS IN TORSION THEORY
• 4.3 Problems
• 4.4 Columns and Struts:
• 4.5 SLENDERNESS RATIO
• 4.6 EFFECTIVE LENGTH OF COLUMN
• .7 Euler’s Theorem
• Outcomes
• Further Reading
DEPARTMENT OF MECHANICAL ENGINEERING, ATMECE, MYSURU 54
, Strength of Materials 17ME34
4.1 Bending Moment
The moment applied in a vertical plane containing the longitudinal axis is resisted by
longitudinal tensile and compressive stresses of varying intensities across the depth of bea m
and are called as bending stresses. The moment applied is called Bending Moment.
4.1.1 Torsional Moment
The moment applied in a vertical plane perpendicular to the longitudinal axis i.e., in the plane of
the cross section of the member, it causes twisting of layers which will be resisted by the shear
stresses. The moment applied is called Torsion Moment or Torsional Moment. Torsion is useful
form of transmitting power and its application is seen in screws and shafts.
4.2 ASSUMPTIONS IN TORSION THEORY
1. Material is homogenous and isotropic
2. Plane section remain plane before and after twisting i.e., no warpage of planes.
3. Twist along the shaft is uniform.
4. Radii which are straight before twisting remain straight after twisting.
5. Stresses are within the proportional limit.
4.2.1 DERIVATION OF TORSIONAL EQUATION:
Torsional Rigidity
As product (CIP ) is increased deformation q reduces. This product gives the strength of the
section to resist torque and is called Torsional rigidity.
DEPARTMENT OF MECHANICAL ENGINEERING, ATMECE, MYSURU 54
Module 4
TORSION OF SHAFTS
Objectives:
Explain the structural behavior of members subjected to torque, Calculate twist and stress induced
in shafts subjected to bending and torsion. & Understand the concept of stability and derive
crippling loads for columns
Learning Structure
• 4.1 Bending Moment
• 4.2 ASSUMPTIONS IN TORSION THEORY
• 4.3 Problems
• 4.4 Columns and Struts:
• 4.5 SLENDERNESS RATIO
• 4.6 EFFECTIVE LENGTH OF COLUMN
• .7 Euler’s Theorem
• Outcomes
• Further Reading
DEPARTMENT OF MECHANICAL ENGINEERING, ATMECE, MYSURU 54
, Strength of Materials 17ME34
4.1 Bending Moment
The moment applied in a vertical plane containing the longitudinal axis is resisted by
longitudinal tensile and compressive stresses of varying intensities across the depth of bea m
and are called as bending stresses. The moment applied is called Bending Moment.
4.1.1 Torsional Moment
The moment applied in a vertical plane perpendicular to the longitudinal axis i.e., in the plane of
the cross section of the member, it causes twisting of layers which will be resisted by the shear
stresses. The moment applied is called Torsion Moment or Torsional Moment. Torsion is useful
form of transmitting power and its application is seen in screws and shafts.
4.2 ASSUMPTIONS IN TORSION THEORY
1. Material is homogenous and isotropic
2. Plane section remain plane before and after twisting i.e., no warpage of planes.
3. Twist along the shaft is uniform.
4. Radii which are straight before twisting remain straight after twisting.
5. Stresses are within the proportional limit.
4.2.1 DERIVATION OF TORSIONAL EQUATION:
Torsional Rigidity
As product (CIP ) is increased deformation q reduces. This product gives the strength of the
section to resist torque and is called Torsional rigidity.
DEPARTMENT OF MECHANICAL ENGINEERING, ATMECE, MYSURU 54
