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What is the relationship between shear modulus and Young's modulus for isotropic

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Question: What is the relationship between shear modulus and Young\'s modulus for isotropic materials?

Options:

  1. G = E/2(1 + ν)
  2. G = E(1 + ν)/2
  3. G = E/3
  4. G = 2E

Correct Answer: G = E/2(1 + ν)

Solution: 

The shear modulus (G) is related to Young\'s modulus (E) and Poisson\'s ratio (ν) by the formula G = E/2(1 + ν).

What is the relationship between shear modulus and Young's modulus for isotropic

Practice Questions

Q1
What is the relationship between shear modulus and Young's modulus for isotropic materials?
  1. G = E/2(1 + ν)
  2. G = E(1 + ν)/2
  3. G = E/3
  4. G = 2E

Questions & Step-by-Step Solutions

What is the relationship between shear modulus and Young's modulus for isotropic materials?
  • Step 1: Understand what Young's modulus (E) is. It measures how much a material stretches or compresses when a force is applied.
  • Step 2: Understand what shear modulus (G) is. It measures how much a material deforms when a force is applied parallel to its surface.
  • Step 3: Know what Poisson's ratio (ν) is. It is the ratio of the change in width to the change in length when a material is stretched.
  • Step 4: Recognize that for isotropic materials (materials that have the same properties in all directions), there is a relationship between these three properties.
  • Step 5: Use the formula G = E / (2(1 + ν)) to find the shear modulus if you know Young's modulus and Poisson's ratio.
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