Lecture Notes: Stress in Physics

Introduction to Stress

• Stress refers to the internal forces that neighboring particles of a continuous material exert on each other.
• When cutting a cake, the cake experiences stress.
  • Normal Stress: Force applied perpendicular to the surface.
  • Shear Stress: Force applied parallel to the surface.

Normal Stress

• Occurs when force is perpendicular to the area of contact.
• Example: Cutting a cake with force perpendicular to the top surface.

Shear Stress

• Occurs when force is parallel to the area of contact.
• Example: Knife piercing into cake.
  • Cross-sectional areas experience stress as force is parallel.
  • Results in plastic deformation as surfaces are pushed apart.

Distinction Between Normal and Shear Stress

• Normal Stress:
  • Force perpendicular to surface.
  • Associated with normal strain:
    • Formula: ( \frac{F}{A} )
    • Strain: ( \frac{\Delta L}{L} )
  • ( F ) = applied force, ( A ) = cross-sectional area, ( \Delta L ) = change in length, ( L ) = original length.
• Shear Stress:
  • Force parallel to surface.
  • Associated with shear strain:
    • Formula for Stress: ( \frac{F}{A} )
    • Strain: Defined by displacement

Shear Stress and Strain in a Beam

• Scenario: Beam fixed at its base.
  • Normal force results in normal stress and strain.
  • Force parallel to base results in shear stress.

Shear Strain

• Defined as the tangent of the angle (θ) formed due to deformation.
  • Formula for Shear Strain: ( \tan \theta = \frac{\Delta x}{L} )
  • ( \Delta x ) = maximum deformation, ( L ) = length perpendicular to deformation.
• Shear strain explains how much the beam is stretched horizontally.

By understanding these concepts, one can explain various physical deformations and stresses in materials.