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Definition of Strain

Definition of Strain. Define variables the cause deformation of a material and the response of the material. System Response – Linear Deformation:. Suppose that a wire of length L is stretched by a force F then:. Linear Strain =. System Response – Volume Deformation:.

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Definition of Strain

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  1. Definition of Strain Define variables the cause deformation of a material and the response of the material. • System Response – Linear Deformation: Suppose that a wire of length L is stretched by a force F then: Linear Strain = • System Response – Volume Deformation: Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Volume Strain = PHY 2053

  2. Definition of Stress Define variables the cause deformation of a material and the response of the material. • Linear Deformation: Suppose that a wire of length L is stretched by a force F then: Area A Linear Stress = • Volume Deformation: Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Volume Stress = PHY 2053

  3. Hooke’s Law Spring • Linear Restoring Force: Ideal Spring Spring Constant k Spring Force Stress = C × Strain Generalized Hooke’s Law! Constant PHY 2053

  4. Stress Proportional to Strain • Linear Deformation: Suppose that a wire of length L is stretched by a force F then: Stress = Y × Strain Area A Young’s Modulus Units = Pa • Volume Deformation: Consider an object immersed in a fluid. The fluid will exert a pressure P from all sides causing a volume deformation. Stress = -B × Strain Bulk Modulus Units = Pa PHY 2053

  5. Example Problem: Young’s Modulus • Linear Deformation: A wrecking ball with mass M is to be lifted by a crane with a steel cable that has a diameter of 1.5 cm and an unstretched length of 30 m. The Young’s modulus of steel is 2.0 × 1011 Pa. Ignoring the weight of the cable itself, when the ball is lifted and held at rest the cable stretches by 1.66 cm, what is the mass M of the wrecking ball? PHY 2053

  6. Example Problem: Bulk Modulus • Volume Deformation: The atmospheric pressure at the surface of a clear lake is 101 kPA. By what percentage does the density of lake water increase at a depth of 1.0 km below the surface of the lake? The bulk modulus for water is 2.2×109 Pa? 0.445% PHY 2053

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