Short Answer:

Torsion is the twisting of a structural or machine member when it is subjected to a torque or twisting moment about its longitudinal axis. It causes one end of the member to rotate relative to the other, producing shear stresses and shear strains within the material.

In simple words, torsion means twisting of a shaft or rod due to the action of applied torque. This twisting effect is common in circular shafts such as drive shafts, axles, and transmission shafts used in machines and vehicles. The amount of twist depends on the material, length, and cross-sectional shape of the shaft.

Torsion

Detailed Explanation :

Torsion is a fundamental concept in mechanical engineering that describes the twisting behavior of a member (usually a shaft) under the influence of torque. It is one of the most important loading conditions encountered in engineering applications where rotational motion or power transmission is involved, such as in engines, turbines, and gear systems.

Definition of Torsion

Torsion can be defined as:

“The deformation of a structural or machine member due to an applied torque that tends to twist it about its longitudinal axis.”

When a torque acts on a circular shaft, one end of the shaft tries to rotate relative to the other, causing shear stresses and shear strains on every cross-section. The external torque produces internal resisting moments within the shaft, maintaining equilibrium.

Concept of Torsion

To understand torsion, consider a solid circular shaft fixed at one end and subjected to a torque (T) at the other end. When torque is applied, the shaft tends to twist. The cross-section of the shaft rotates about its axis by an angle known as the angle of twist (θ).

During this twisting:

The outermost fibers experience maximum shear stress.
The shear stress varies linearly from zero at the center to maximum at the surface.
Each circular cross-section remains plane and undistorted, but rotates relative to other sections.

Hence, the phenomenon of torsion is entirely governed by shear stresses and shear deformations.

Torsional Stress and Strain Relationship

The relation between applied torque (T), shear stress (τ), and the geometry of the shaft is expressed by the torsion equation:

where,

= applied torque (N·m),
= polar moment of inertia of the cross-section (m⁴),
= shear stress at a distance from the center (N/m²),
= modulus of rigidity (N/m²),
= angle of twist in radians,
= length of the shaft (m).

This equation shows that the applied torque is directly proportional to the shear stress, and the angle of twist depends on both the material property (G) and shaft geometry (J and L).

Shear Stress Distribution in Torsion

Shear stress is zero at the center of the shaft (axis).
It increases linearly with distance from the center.
The maximum shear stress occurs at the outer surface and is given by:

where is the outer radius.

The polar moment of inertia (J) for different sections is:

For a solid circular shaft:
For a hollow circular shaft:

Thus, hollow shafts are more efficient in resisting torsion, as they provide higher strength with less weight.

Angle of Twist

When a shaft is twisted by torque , one end rotates relative to the other through an angle of twist (θ), given by:

This angle represents how much the shaft deforms due to torsion. For design purposes, engineers ensure that both shear stress and angle of twist remain within safe limits to prevent material failure or excessive deformation.

Types of Torsion

Pure Torsion:
Occurs when torque is applied uniformly along the shaft and no bending or axial forces act on it. It is the simplest form used in theoretical analysis.
Combined Torsion:
Occurs when a shaft is subjected to torque along with bending moments or axial loads. It is a common situation in practical engineering applications, such as crankshafts or propeller shafts.

Applications of Torsion

Torsion is a common phenomenon in mechanical components that transmit rotational power. Some practical examples include:

Transmission shafts in automobiles and industrial machinery.
Propeller shafts in marine and aerospace systems.
Torsion springs used in mechanical watches and door mechanisms.
Drive shafts in vehicles to transmit torque from engines to wheels.
Twisting of drill bits and tools during machining operations.

In all these cases, components must be designed to safely resist torsional stresses.

Assumptions in Torsion Theory

The standard theory of torsion is based on the following assumptions:

The shaft is circular in cross-section and homogeneous.
Material obeys Hooke’s law (linear elastic behavior).
Plane cross-sections remain plane and circular after twisting.
The twist along the shaft is uniform.
Shear stress is directly proportional to the radial distance from the center.

These assumptions help in deriving the torsion equation for circular shafts accurately within elastic limits.

Importance of Torsion in Design

Helps determine shaft diameter required to safely transmit a given torque.
Ensures that the angle of twist is within permissible limits to prevent excessive deformation.
Used in analyzing and designing couplings, gears, and axles in rotating machinery.
Helps in selecting materials with adequate modulus of rigidity (G) and shear strength.
Essential in failure analysis of components subjected to combined bending and torsion.

Conclusion

In conclusion, torsion is the twisting of a structural member, like a shaft, when subjected to a torque about its longitudinal axis. It causes shear stresses and angular deformation in the material. The relationship between torque, shear stress, and angle of twist is expressed by the torsion equation . Understanding torsion is vital in mechanical engineering for designing safe and efficient power-transmitting components such as shafts, couplings, and springs.