Overview
This lecture introduces the fundamental concepts of stress and strain, explaining how materials respond to external forces, with emphasis on uniaxial loading and the differences between normal and shear stress.
Basics of Stress
- Stress describes how internal forces are distributed within a body under external loads.
- In uniaxial loading, forces act along the same axis, stretching or compressing the object.
- Stress is measured as force per unit area (Newtons/m² or Pascals in SI units).
- Normal stress (σ) acts perpendicular to a surface and is calculated as σ = F/A.
Types and Calculation of Normal Stress
- Normal stress can be tensile (stretching, positive) or compressive (shortening, negative).
- Material failure occurs when stress exceeds material strength (e.g., mild steel fails above 250 MPa).
- For a bar with known diameter, failure load can be determined by stress = strength × area.
Strain and Stress-Strain Relationship
- Strain (ε) measures deformation, calculated as change in length/original length (ΔL/L).
- Strain is dimensionless and often shown as a percentage.
- The stress-strain diagram shows the material's response under loading.
- In the elastic region (small strains), stress and strain are linearly related (Hooke's Law).
- Young’s modulus (E) is the ratio of stress to strain in the elastic region.
- Plastic deformation occurs at larger strains, where deformations are permanent.
Shear Stress and Strain
- Shear stress (Ï„) arises when forces are parallel to a surface, as in bolts loaded sideways.
- Average shear stress is Ï„ = F/A, but actual distribution may vary.
- Shear stress on an element requires equilibrium in both force and torque.
- Shear strain (γ) is the change in angle caused by shear, with γ denoted as gamma.
- Hooke's law applies for shear: the ratio of shear stress to shear strain is the shear modulus (G).
Combined Stress States
- A point within a material can experience both normal and shear stresses.
- The specific values depend on the orientation of the plane considered.
- Stress elements are used to represent stresses at a point in 2D or 3D.
Key Terms & Definitions
- Stress (σ) — Internal force per unit area (N/m² or Pa).
- Strain (ε) — Ratio of change in length to original length, measures deformation.
- Normal Stress — Stress perpendicular to a surface (tensile or compressive).
- Shear Stress (τ) — Stress parallel to a surface.
- Young’s Modulus (E) — Ratio of normal stress to strain in the elastic region.
- Shear Modulus (G) — Ratio of shear stress to shear strain.
- Elastic Deformation — Temporary, reversible change in shape.
- Plastic Deformation — Permanent, non-reversible change in shape.
Action Items / Next Steps
- Review the related video on stress transformation for more on normal and shear stresses.
- Prepare to study advanced topics like torsion and beam bending in future lectures.