Modulus of Rigidity Experiment – For Schools, Teachers, and Students
Definition
The modulus of rigidity, also known as the shear modulus, measures a material’s resistance to shear deformation. It describes how much a material resists changes in shape when a shear force is applied. The modulus of rigidity is measured in Newton per square meter or Pascal.
This concept is demonstrated in Dencity – Online Science Lab and Simulations to enhance interactive learning.
Theory
1. Shear Stress
Shear stress is the force per unit area applied parallel to the surface of a material:
Shear Stress = Force divided by Area
where:
- Shear Stress is measured in Newton per square meter.
- Force is measured in Newton.
- Area is measured in square meters.
2. Shear Strain
Shear strain is the relative deformation of the material due to applied shear stress:
Shear Strain = Lateral Displacement divided by Original Length
where:
- Shear Strain is a ratio and has no units.
- Lateral Displacement is the shift in position due to force.
- Original Length is the material’s length before deformation.
For small deformations, shear strain is approximately equal to the shear angle in radians.
3. Modulus of Rigidity or Shear Modulus
The modulus of rigidity relates shear stress to shear strain:
Modulus of Rigidity = Shear Stress divided by Shear Strain
where:
- Modulus of Rigidity is measured in Newton per square meter.
- Shear Stress is measured in Newton per square meter.
- Shear Strain is a ratio with no units.
This formula is valid only within the elastic limit of the material.
4. Relation to Other Elastic Constants
The modulus of rigidity is related to Young’s modulus and Poisson’s ratio:
Modulus of Rigidity = Young’s Modulus divided by two times one plus Poisson’s Ratio
where:
- Young’s Modulus measures resistance to stretching.
- Poisson’s Ratio describes how materials shrink or expand under stress.
This relation helps in understanding material elasticity and predicting deformation.
Applications of Modulus of Rigidity
- Structural Engineering → Used in designing beams, shafts, and load-bearing structures.
- Mechanical Systems → Helps in calculating deformation under shear forces.
- Material Science → Used for determining material elasticity in research and testing.
Real-World Uses of Modulus of Rigidity
- Building Bridges and Skyscrapers → Ensures materials resist shear forces without bending excessively.
- Automotive Industry → Used in designing strong and durable car frames.
- Aerospace Engineering → Helps in selecting materials for aircraft and spacecraft structures.
- Manufacturing Industry → Used in machines and mechanical parts that experience shear forces.
Observations
- Materials with a high modulus of rigidity are more resistant to shear deformation.
- Shear strain increases with increasing shear stress for materials with a lower modulus of rigidity.
- Beyond the elastic limit, shear deformation becomes permanent.
