310105i Solids 2018 TF

Page 1: Objectives

  • Define the following concepts related to solids:

    • Elasticity

    • Stress

    • Strain

    • Hooke’s Law

    • Young’s Modulus of Elasticity

  • Explain the relationship between:

    • Elastic limit

    • Yield point

    • Ultimate strength

    • Breaking strength

    • Safe working stress

    • Factor of safety

  • Define compressive and shear stresses.

  • Solve problems involving stress, force, area, and strain.

Page 2: Key Definitions

  • Elasticity: The tendency of a solid to flex or deform under external force loading.

  • Stress (σ): The external loading force divided by a specific area, measured in Pascals (N/m²) or psi.

  • Strain (ε): The deformation from compression or tension per unit length, dimensionless.

  • Hooke’s Law: States that stress is proportional to strain.

  • Young’s Modulus of Elasticity: The slope of the stress-strain curve, indicating the stiffness of a material.

Page 3: Material Properties Definitions

  • Elastic Limit: The maximum deformation a solid can undergo and still return to its original shape after the external force is removed.

  • Yield Point (Strength): The point on the stress-strain curve where a solid begins to deform plastically (permanently).

  • Ultimate Strength: The highest stress at which a solid can resist before breaking.

  • Breaking Strength: The precise point on the curve where fracture occurs.

  • Safe Working Stress: The maximum allowable stress a solid can safely withstand.

  • Factor of Safety: The ratio of a material's strength to the allowable stress; used in engineering design to provide a safety margin.

Page 4: Young’s Modulus Equation

  • Young’s Modulus Equation:

    • E = σ/ε

    • Where:

      • E = Young’s Modulus

      • σ = Stress

      • ε = Strain

Page 5: Hooke’s Law Explanation

  • As loading force increases from zero, both stress and strain increase in proportion.

  • Stress is generally proportional to strain for most materials:

    • E (Young's Modulus) * ε (Strain) = σ (Stress)

Page 6: Stress Formula

  • Stress Formula: σ = F/A

    • Where:

      • σ = Stress (in Pascals)

      • F = Loading Force (in Newtons)

      • A = Area (in square meters)

  • Stress is defined as the force per unit area in solid materials affected by tension or compression forces.

Page 7: Stress Calculation Example

  • Example Problem: Calculate the stress when a force of 10 kN is applied to a bolt with a cross-sectional area of 19.6 x 10⁻⁶ m²:

    • Formula: σ = F/A

    • Substituting values: σ = 10,000 N / (19.6 x 10⁻⁶ m²)

Page 8: Strain Definition

  • Strain Definition: Strain (ε) is the extension (ΔL) per unit length (L₀):

    • ε = ΔL / L₀

    • Where:

      • L₀ = Original Length

      • L = Stretched Length

      • ΔL = Extension (L - L₀)

Page 9: Strain Calculation Example

  • Example Problem: Calculate the strain when a 100 m power line is stretched to 100.1 m:

    • ΔL = 100.1 m - 100 m = 0.1 m

    • Strain (ε) = ΔL / L₀ = 0.1 m / 100 m = 1.0 x 10⁻³

Page 10: Conclusion

  • End of the material.

  • Complete the self-test ILM 3101051 to review understanding and applications of these concepts.