Notes on Stress and Strain

Introduction

• Stress and strain are key concepts in understanding how materials respond to external loads.
• Example used: A solid metal bar under uniaxial loading (equal and opposite forces causing it to stretch).

Stress

• Definition: Describes the distribution of internal forces within a body.
• Units:
  • SI: Newtons per meter squared (Pascals).
  • US: Pounds per square inch.
• Calculation: Stress = Internal force / Cross-sectional area.
• Normal Stress:
  • Acts perpendicular to a surface.
  • Calculated as: ( \sigma = \frac{F}{A} ) (Force/Area).
  • Can be tensile (positive) or compressive (negative).
• Importance: Helps predict failure when stress exceeds material strength (e.g., mild steel strength = 250 MPa).
• Uniform Stress Assumption: Simple scenarios like our bar assume uniform stress distribution.

Strain

• Definition: Describes deformation within a body.
• Calculation: Strain = Change in length / Original length (( \varepsilon = \frac{\Delta L}{L} )).
• Units: Non-dimensional, often expressed as a percentage.
• Relationship with Stress: Illustrated using stress-strain diagrams.
  • Deformations in the elastic region are reversible.
  • Beyond elastic limit: Plastic deformations occur.
  • Hooke's Law: Linear relationship in the elastic region, ( \sigma = E \varepsilon ), where ( E ) is Young's modulus.

Stress-Strain Diagram

• Tensile Test: Used to obtain stress-strain diagrams.
• Ductile Materials: Exhibit linear relationship (elastic) at low strains.
• Young's Modulus: Defines the ratio of stress to strain in the elastic region.

Shear Stress

• Definition: Acts parallel to a surface.
• Example: Shear loading in bolts.
• Calculation: ( \tau = \frac{F}{A} ) (similar to normal stress, but is an average).
• Equilibrium: Shear stress on one face must be balanced by opposite shear stress and additional stresses for rotational equilibrium.
• Shear Strain: Change in angle (denoted by ( \gamma )).
  • Ratio described by shear modulus ( G ).

Combined Stress States

• Stress State at a Point: Has both normal and shear components.
• Stress Element Representation: Shows 2D and 3D stress components.
• Example: Inclined plane in uniaxial loading shows both normal and shear stresses.

Conclusion

• Understanding stress and strain is crucial for advanced topics like torsion and beam bending.
• Further exploration recommended in stress transformation videos.

Recommendations

• Further learning: Watch videos on Young's modulus, material strength, ductility, and toughness.
• Future topics: Torsion and beam bending.