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Understanding Stress-Strain Relationship for Material Properties

Explore Generalized Hooke's Law, Dilatation, and Bulk Modulus with an example of a loaded copper bar. Learn how stress affects material dimensions and apply formulas for new dimensions. Practice problem included.

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Understanding Stress-Strain Relationship for Material Properties

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  1. Lecture # 10 Material - Property Relationships Objective: To develop relationship between stress and strain for general loads.

  2. Generalized Hooke's Law

  3. Generalized Hooke's Law (contd.)

  4. Generalized Hooke's Law (contd.)

  5. Dilatation and Bulk Modolus.

  6. Bulk Modolus.

  7. Example: The copper bar as shown in figure is subjected to a uniform loading along its edges. If it has a length a = 300 mm, width b = 50 mm and thickness t = 20 mm before the load is applied, determine its new length, width and thickness after application of the load. Take Ecu = 120 GPa, vcu = 0.34.

  8. Solution: By inspection, the bar is subjected to a state of plane stress. From the loading, we have,

  9. The associated normal strains are determined from the generalized Hooke’s law, that is,

  10. The new bar length, width and thickness are therefore, a’ = 300 mm + 0.00808 (300 mm) = 302.4mm Ans…. b’ = 50 mm + (-0.00643)(50 mm) = 49.68mm Ans…. t’ = 20 mm + (-0.000850)(20mm) = 19.98 mm Ans….

  11. The enD

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