Short Answer:

Shear strain is the measure of deformation that occurs in a material when it is subjected to shear stress. It is defined as the angular change between two originally perpendicular lines within the material. When a force acts parallel to the surface, it causes the shape of the body to distort without changing its volume.

In simple words, shear strain represents how much a material is twisted or skewed under shear force. It is expressed as the ratio of lateral displacement to the original perpendicular distance between the layers. Shear strain is usually denoted by the Greek letter “γ” (gamma) and has no unit since it is a ratio.

Detailed Explanation :

Shear Strain

When a body is subjected to forces acting tangentially to its surface, it causes the shape of the body to change. This type of deformation is called shear deformation, and the measure of this deformation is known as shear strain. Unlike normal strain, which deals with changes in length, shear strain deals with changes in shape or angular distortion of the material.

Let us consider a rectangular block of elastic material fixed at one face and subjected to a tangential force on the opposite face. Due to this tangential force, the upper face of the block tends to move or slide over the lower face. As a result, the right angles between the sides of the block get slightly altered. This change in angle is called shear strain (γ).

Mathematically,

Here,

• x = lateral displacement of the top surface
• h = vertical distance between the surfaces

Since shear strain is a ratio of two lengths, it is dimensionless and unitless.

Explanation with Example

Imagine a small rubber cube glued to a table on its bottom surface. When a tangential force is applied on its top face, the top face moves slightly sideways while the bottom face remains fixed. This causes the cube to deform into a shape similar to a parallelogram. The amount of shift of the top face compared to its original position determines the shear strain.

If the angular distortion (change in the right angle) between two sides is small, then the shear strain (γ) is approximately equal to the tangent of the angle of deformation (θ).

For very small angles (measured in radians),

Hence, the shear strain can also be represented as the angular change in radians between the two originally perpendicular lines.

Relation between Shear Stress and Shear Strain

Shear strain is closely related to shear stress (τ) through a property of the material known as the modulus of rigidity (G) or shear modulus. The relation is given by:

Where,

• τ = shear stress
• G = modulus of rigidity
• γ = shear strain

This equation shows that the shear strain in a material is directly proportional to the applied shear stress, as long as the material behaves elastically (follows Hooke’s law).

Shear Strain in Real Life

Shear strain is important in the design and analysis of many mechanical components. For example:

• In shafts under torsion, the outer surface experiences shear strain due to twisting.
• In riveted joints or bolted connections, the materials experience shear deformation when forces act tangentially.
• In beams, shear strain develops when the load tries to slide one layer of the beam over another.
• Rubber materials and elastic couplings are designed to withstand large shear strains without failure.

Understanding shear strain helps engineers to predict how materials deform under tangential forces and to design components that can safely resist such deformations.

Factors Affecting Shear Strain

1. Material Type: Different materials have different moduli of rigidity. Soft materials like rubber experience larger shear strains, whereas hard materials like steel show smaller strains under the same load.
2. Applied Shear Stress: Higher the applied shear stress, greater will be the resulting shear strain.
3. Geometry of the Object: The shape and size of the body also influence how it deforms under shear force. Taller or thinner shapes tend to experience greater angular distortion.
4. Temperature: In some materials, especially polymers, temperature changes can significantly affect shear behavior.

Units and Measurement

Although shear strain has no units, it is commonly expressed in radians since it represents an angular change. Measuring shear strain is important in testing materials using torsion or shear tests, where instruments like strain gauges are used to measure deformation accurately.

Conclusion

In summary, shear strain is a measure of angular deformation in a material caused by tangential or shear stress. It represents how much a shape changes without any change in volume. It is expressed as the ratio of lateral displacement to original height and denoted by γ. Understanding shear strain is essential for analyzing structures and components subjected to twisting or sliding forces, ensuring safety and performance in mechanical design.