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Generalized Hooke's Law

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Derivation of Multi-axial Loading Formulas

In the derivation of the following formulas, we apply the concept of superposition, that is, adding the individual effects of deformations caused by loads acting on specific directions. We utilize here Poisson's Ratio $ \nu =-\dfrac{\varepsilon_{\text{lateral}}}{\varepsilon_{\text{longitudinal}}}$ where longitudinal strain is developed along the direction of the applied stress.

Concept Concept Concept

Shear Strain and Deformation

Concept

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 1: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 2: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 3: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 4: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 5: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 6: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 7: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram

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Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram Generalized Hooke's Law: Multiaxial Strain | Mechanics of Deformable Bodies – Problem 8: – Diagram
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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q557

PSAD - Mechanics of Deformable Bodies / Generalized Hooke's Law / Engr. Deguma

A steel has a modulus of elasticity of 200GPa and a Poisson's Ratio of 0.2. Compute the shear modulus of steel.

Answer:

  1. 83.33GPa
  2. 79.11GPa
  3. 103.33GPa
  4. 86.67GPa

Solution pending in psadquestions/q557.json.