Lecture Notes: Stress and Strain

Introduction

• Stress and strain describe how a body responds to external loads.
• Example: A loaded metal bar under uniaxial loading with two equal and opposite forces.

Stress

• Definition: Describes the distribution of internal forces within a body due to external loads.
• Units: Newtons per meter squared (Pascals) in SI units; pounds per square inch in US units.
• Calculation: For a bar, stress (σ) = Force (F) / Cross-sectional area (A).
• Types:
  • Normal Stress: Acts perpendicular to the surface.
    • Tensile Stress: Positive values; when forces stretch the body.
    • Compressive Stress: Negative values; when forces compress the body.
  • Shear Stress: Acts parallel to the surface. Denoted by τ.
    • Calculated as F/A, but forces are parallel to the cross-section.

Strain

• Definition: Describes deformation within a body.
• Calculation: Normal strain = Change in length (ΔL) / Original length (L).
• Types:
  • Normal Strain: Can be tensile or compressive.
  • Shear Strain: Change in angle γ.

Stress-Strain Relationship

• Stress-Strain Diagram: Varies for different materials.
• Elastic Region:
  • Linear relationship (Hooke's Law: stress is proportional to strain).
  • Deformation is reversible.
  • Young’s Modulus defines the slope of the stress-strain curve.
• Plastic Region:
  • Non-linear relationship.
  • Permanent deformation.

Shear Stress and Strain

• Shear stress arises in scenarios like bolts where forces are parallel to cross-section.
• Shear Modulus (G) is used instead of Young’s Modulus for shear stress-strain relations.
• Stress element shows both normal and shear stresses at a point.

Applications

• Predicting failure: Stress calculations predict when material stress exceeds its strength.
• Example: Mild steel bar fails if stress exceeds 250 MPa.
• Note: Stress distribution is more complex in bending beams than in uniaxial bars.

Conclusion

• Understanding stress and strain is vital for advanced topics such as torsion and beam bending.
• Further resources: Stress transformation and related videos on Young's modulus, material strength, ductility, and toughness.

Next Steps

• Learn more about normal and shear stresses.
• Watch recommended videos on stress transformations.

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