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Plane stress at a point in a body is defined by principal stresses 3σ and σ. The ratio of the normal stress to the maximum shear stresses on the plane of maximum shear stress is:
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?
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Plane stress at a point in a body is defined by principal stresses 3&#...
Given data:
Principal stresses, σ1 = 3 and σ2 = σ3 = 0

To find: Ratio of normal stress to maximum shear stress on the plane of maximum shear stress

Solution:
Let us consider a plane AB passing through the point of interest on which the maximum shear stress acts.

On this plane, normal stress is given by:
σn = (σ1 + σ3)/2 = (3 + 0)/2 = 1.5

And maximum shear stress is given by:
τmax = (σ1 - σ3)/2 = (3 - 0)/2 = 1.5

Therefore, ratio of normal stress to maximum shear stress on this plane is:
σn/τmax = 1.5/1.5 = 1

Hence, the correct option is (B) 1.
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Plane stress at a point in a body is defined by principal stresses 3&#...
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