Properties of Solids - Lecture Notes

Jul 30, 2024

Lecture Notes: Properties of Solids

Introduction

  • Class by Rajan Singh.
  • Focus on Chapter: Properties of Solids.
  • The lecture will cover types of materials, stress, types of stress, types of strain, and Hooke's Law.
  • Intended Revision for all major points in the chapter.

Basics of Solids

  • Solid: Defined by fixed shape, size, and volume.
  • Perfectly rigid bodies: The distance between any two particles remains constant irrespective of external forces.
  • Real-world: No perfectly rigid bodies; all exhibit some deformation.
  • Elastic bodies: The tendency to regain their original shape.

Key Terms and Concepts

Stress

  • Stress = Restoring force per unit area.
  • Types of Stress:
    • Normal Stress: Tensile (increasing length) or Compressive (decreasing length).
    • Volume metric Stress: Change in volume due to applied external pressure.
    • Shear Stress: Deformation by forces acting tangentially to the surface.

Strain

  • Strain = Change in configuration/original configuration.
  • Types of Strain:
    • Longitudinal Strain: Change in length/original length.
    • Volume metric Strain: Change in volume/original volume.
    • Shear Strain: Angular deformation.

Hooke's Law

  • Stress is directly proportional to strain within elastic limits.
  • Formula: σ = Eε (where E is modulus of elasticity).
  • Young’s Modulus, Bulk Modulus, Shear Modulus.
  • Stress vs. Strain graph: Valid up to proportionality limit.

Important Points

  • Poisson's Ratio: Ratio of lateral strain to longitudinal strain.
  • Energy Density in solids: Energy stored per unit volume.
  • Practical applications of stress-strain relations (e.g., building materials, mechanical design).

Sample Problems and Solutions

Problem 1

  • Given: Force applied, dimensions, calculate elongation.
  • Solution steps: Use Hooke’s law, calculate stress, strain, and resulting elongation.

Problem 2

  • Given: Mass hanging on wire, calculate elongation.
  • Solution: Analyze forces, apply Hooke’s law, and solve for strain.

✅ Practice questions provided for further preparations.

Conclusion

  • Revision of key concepts related to the properties of solids, types of stresses, and strains.
  • Application of Hooke's law and related calculations.