Overview
Shear modulus is the ratio of shear stress to shear strain. It measures resistance to a change in shape caused by tangential force.
Learning Outcomes
- Shear force acts tangentially to a surface.
- Shear strain is ΔXY and is approximately the shear angle θ in radians.
- S = FAΔXY = FY/(AΔX).
- For small angles, S = FAθ.
- Its SI unit is Pa.
Shear Geometry
A tangential force F acts across area A and displaces the upper face by ΔX relative to a fixed face separated by height Y.
Angle of Shear
For a very small angle measured in radians, tan θ ≈ θ.
1Given- F = 400 N
- A = 0.020 m²
- strain = 2.0 × 10⁻⁴
2WorkingShear stress = FA = 2.0 × 10⁴ Pa
4Step 3S = 2.0 × 10⁴2.0 × 10⁻⁴
Final answer: S = 1.0 × 10⁸ Pa
Textbook Material Values
| Material | S (10¹⁰ Pa) |
|---|
| Steel | 8.0 |
| Aluminium | 2.5 |
| Copper | 4.0 |
| Iron | 5.0 |
| Brass | 3.6 |
Common Mistakes
- Use the stress and strain of the same deformation type.
- Convert all data to SI units.
- Modulus has the same unit as stress because strain is dimensionless.
- A larger modulus means greater stiffness, not greater strain.
Short-Question Preparation
Q. Define shear modulus.
A. The ratio of shear stress to shear strain.
Q. Define shear strain.
A. The lateral displacement ΔX divided by the perpendicular height Y.
Q. What is angle of shear?
A. For small deformation, θ ≈ ΔXY in radians.
Q. State the SI unit.
A. Pascal, Pa.
Sticky Notes
- Shear force acts tangentially to a surface.
- Shear strain is ΔXY and is approximately the shear angle θ in radians.
- S = FAΔXY = FY/(AΔX).
- For small angles, S = FAθ.
- Its SI unit is Pa.
60-Second Revision
Shear modulus is the ratio of shear stress to shear strain. It measures resistance to a change in shape caused by tangential force.
Summary
Shear modulus is the ratio of shear stress to shear strain. It measures resistance to a change in shape caused by tangential force.
Ask-the-Tutor Modes
- Explain the modulus simply.
- Derive its formula.
- Solve a numerical problem.
- Compare the elastic moduli.
- Test me with an MCQ.
