Shear Modulus (Modulus of Rigidity)
The ratio of tangential stress to shearing strain, representing a material's resistance to shape deformation.
What is Shear Modulus (Modulus of Rigidity)?
A measure of a solid material's resistance to shearing deformation, defined as the ratio of tangential stress to shearing strain.
Key formula / rule: Shear Modulus
Key points
- Define Shear Modulus.
- Understand the relationship between tangential stress and shearing strain.
- Calculate Shear Modulus given stress and strain values.
- Differentiate Shear Modulus from Young's Modulus and Bulk Modulus.
Common exam trap
Confusing tangential stress with normal stress.
Definitions
- Term
Shear Modulus (Modulus of Rigidity)
- Meaning
A measure of a solid material's resistance to shearing deformation, defined as the ratio of tangential stress to shearing strain.
- Term
Tangential Stress
- Meaning
The stress component parallel to the surface of a material, caused by a tangential force.
- Term
Shearing Strain
- Meaning
The deformation of a material caused by tangential stress, measured as the angle of deformation (in radians) or the ratio of displacement to the perpendicular distance.
Learning objectives
Define Shear Modulus.
Understand the relationship between tangential stress and shearing strain.
Calculate Shear Modulus given stress and strain values.
Differentiate Shear Modulus from Young's Modulus and Bulk Modulus.
Formulae
- Name
Shear Modulus
- Note
Where η is Shear Modulus, σt is tangential stress, and γ is shearing strain.
- Expression
η = σt / γ
- Name
Tangential Stress
- Note
F is the tangential force applied, A is the area over which the force is applied.
- Expression
σt = F / A
- Name
Shearing Strain (for small angles)
- Note
Δx is the displacement of the surface, L is the perpendicular distance between the surfaces.
- Expression
γ ≈ Δx / L
- Name
Shearing Strain (as angle)
- Note
θ is the angle of deformation in radians.
- Expression
γ = θ (in radians)
Prerequisites
Stress and Strain (Normal Stress, Normal Strain)
Elastic Limit
Force and Area
Common mistakes
Confusing tangential stress with normal stress.
Using angular strain in degrees instead of radians.
Applying formulas for Young's Modulus or Bulk Modulus incorrectly.
Keywords
Shear Modulus
Modulus of Rigidity
Tangential Stress
Shearing Strain
Elasticity
Deformation
Rigidity
Torsion
Practice preview
If a tangential force F is applied to the top surface of a cube of side length L, and the top surface shifts by a distance x relative to the bottom surface, what is the shearing strain?…
easy
What is the SI unit of Shear Modulus (Modulus of Rigidity)?…
easy
A solid cylinder of radius R and length L is fixed at one end. A tangential force F is applied to the free end, causing a twist. The shear modulus of the material is G. What is the angle of twist (in radians) if the tang…
medium