310105i Solids 2018 TF

Objectives of Study

  • Define key terms:

    • Elasticity, stress, strain, Hooke’s Law, Young’s Modulus of Elasticity.

  • Understand relationships among:

    • Elastic limit, yield point, ultimate strength, breaking strength, safe working stress, and factor of safety.

  • Understand stress types:

    • Compressive and shear stresses.

  • Problem-solving:

    • Related to stress, force area, and strain.

Definitions of Key Concepts

Elasticity

  • Tendency of a solid to flex or deform under external loading.

Stress

  • Defined as the external loading force over a specific area.

  • Symbol: σ (sigma)

  • Measured in pascals (N/m²) or psi.

Strain

  • Represents the amount of deformation from compression or tension per unit length.

  • Unitless, symbol: ε (epsilon).

Hooke’s Law

  • States that stress is proportional to strain.

Young’s Modulus of Elasticity

  • Defined as the slope of the stress-strain curve.

Additional Definitions

Elastic Limit

  • Deformation limit where a solid recovers after removing an external force.

Yield Point (Strength)

  • The point on the stress-strain curve where a solid begins to deform plastically.

Ultimate Strength

  • The maximum stress that a solid can withstand before fracturing.

Breaking Strength

  • The exact point on the curve at which fracturing takes place.

Safe Working Stress

  • Maximum stress a solid can safely endure (allowable stress).

Factor of Safety

  • Ratio of strength to allowable stress.

Young's Modulus Formula

  • Young’s Modulus (E) defined by:

    • E = σ/ε (Stress/Strain)

Hooke’s Law

  • As load increases from zero, stress and strain rise together, maintaining proportionality for most materials.

  • Formula: σ = E * ε (Stress = Modulus of elasticity * Strain)

Understanding Stress

Stress Formula

  • σ = (Loading Force F) / (Area A)

    • Where:

      • σ = Stress in pascals

      • F = Force in newtons

      • A = Area in square meters

Example Calculation of Stress

  • Given a force of 10kN applied to a bolt with a cross-sectional area of 19.6 x 10⁻⁶ m²:

  • Calculate Stress:

    • σ = F / A = 10,000 N / (19.6 x 10⁻⁶ m²)

Definitions of Strain

Strain Formula

  • ε = ΔL / Lo

    • Where:

      • ΔL = extension (stretched length - original length)

      • Lo = original length

Example Calculation of Strain

  • Power line example: A 100m power line stretched to 100.1m.

    • Strain: ε = ΔL / Lo = (100.1m - 100m) / 100m = 1.0 x 10⁻³.

Conclusion

  • These concepts form the foundational understanding of solids and their behaviors under various stress and strain conditions.

  • Understanding these terms and their relationships is critical for solving related physics problems.