# Torsion | Strength of Materials (SOM) - Mechanical Engineering PDF Download

A shaft is said to be under pure torsion when it is subjected to two equal & opposite couples in a plane perpendicular to the longitudinal axis of the shaft (i.e. twisting couples) in such a way that the magnitude of twisting moment remains constant throughout the length of the shaft.
It’s magnitude is given as the product of the force and the distance between the force.

Torque, T = p x d

Magnitude and representation of Torque

Figure shows a bar or shaft of circular section, subjected to torque T. Such a case is a case of pure torsion,

Shaft is under pure torsion

J/R is known as torsional section modulus.,& GJ is known as torsional rigidity of the bar or the shaft.
The above relation states that the intensity of shear stress at any point in the cross-section of a shaft subjected to pure torsion is proportional to its distance from the center and the variation of shear stress with respect to radial distance is linear.

Variation of Torsional Shear Stress

Polar moment of inertia

(a) For a solid shaft of circular section,
Torsional section modulus

(b) For a hollow circular shaft,

### Shear Stress Distribution in Different Sections

It is zero at the center and increases in the radially outward direction and become maximum at the outer periphery And for hollow circular shaft, it is minimum at inner radius and maximum at the outer periphery.

• Solid circular section

• Hollow circular section

Power Transmitted

Design of Shaft

While designing a shaft, we calculate the maximum torque that can be transmitted from the shaft.
The resisting couple should be equal to the applied torque. Hence

### Maximum Torque Transmitted by a Circular Shaft

1. Circular Solid ShaftThe maximum torque transmitted by a circular solid shaft is obtained from the maximum shear stress-induced at the outer surface of the solid shaft.
2. Hollow Circular ShaftsTorque transmitted by a hollow circular shaft Is obtained in the same way as for a solid shaft,

### Composite Shaft

• Series connectionIf two or more shaft of different material, diameter or basic forms are connected together in such a way that each carries the same torque, then the shafts are said to be connected in series & the composite shaft so produced is therefore termed as series connection.

for two shafts in series T1 = T2 = T
θAC = θAB + θBC

• Parallel connectionIf two shafts are loaded in such a way that angle of twist on both the shaft is the same then this type of connection is known as a parallel connection of shaft.

For parallel connection of shaft
Torque is cumulative, T = T1 + Tand θ1 = θ2
T1L1 / G1J1 = T2L2 / G2J2

Strain Energy in Torsion

Consider a solid shaft of length L, under the action of torque T.
The torsional strain energy of shaft is equal to the work done in twisting.

Torsional Stiffness (K)

Torsional stiffness is defined as the amount of torque or twisting couple required to produce a twist of unit radian. And it represented by ‘K’
θ = TL / GJ, K = GJ / L

The document Torsion | Strength of Materials (SOM) - Mechanical Engineering is a part of the Mechanical Engineering Course Strength of Materials (SOM).
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## Strength of Materials (SOM)

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## FAQs on Torsion - Strength of Materials (SOM) - Mechanical Engineering

 1. What is torsion in mechanical engineering?
Ans. Torsion in mechanical engineering refers to the twisting or rotational deformation of a structural element, usually caused by the application of torque. It occurs when a torque is applied to one end of a component while the other end is fixed or restrained, resulting in shear stresses and angular deflection within the material.
 2. How is torsion calculated in mechanical engineering?
Ans. Torsion can be calculated in mechanical engineering using the torsion formula, also known as the torsion equation. This equation relates the applied torque (T), the length of the component (L), the polar moment of inertia (J), and the angle of twist (θ). The torsion formula is given as τ = (T * L) / (J * G), where τ represents the shear stress, G is the shear modulus of the material, and θ is the angle of twist.
 3. What are some common applications of torsion in mechanical engineering?
Ans. Torsion finds numerous applications in mechanical engineering. Some common examples include the design of shafts and axles in machinery, such as engines and turbines, where torsional strength and rigidity are essential. Torsion is also important in the design of springs, such as torsion springs used in garage doors or clock mechanisms. Additionally, torsion is considered in the design of structures subjected to wind or seismic loads.
 4. How does material selection affect torsion in mechanical engineering?
Ans. Material selection plays a crucial role in determining the behavior of a component under torsional load in mechanical engineering. Different materials have varying shear moduli (G), which directly influences the resistance to torsional deformation. Stiffer materials with higher shear moduli, such as steel, exhibit lower angles of twist and are more resistant to torsion. Softer materials, on the other hand, have higher angles of twist and are less resistant to torsional deformation.
 5. What are the possible failure modes associated with torsion in mechanical engineering?
Ans. Torsion can lead to several failure modes in mechanical engineering. One common failure mode is shear failure, where excessive shear stress causes the material to fracture along planes perpendicular to the axis of the component. Another failure mode is excessive angle of twist, which can cause a component to deform beyond its allowable limits, resulting in functional failure or even structural collapse. Additionally, fatigue failure due to repeated torsional loading can occur, leading to crack initiation and propagation within the material.

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