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Consider a bar of length L, breadth B and thickness t subjeced to an axial pull or tension P. The resulting volumetric strain will be equal to
  • a)
    ∈ (1 -2v)
  • b)
    2∈ (1 - v )
  • c)
    ∈ (1 + 2v)
  • d)
    3 ∈ v
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider a bar of length L, breadth B and thickness t subjeced to an a...

where v is the Poisson’s ratio and ∈ is the longitudinal strain.
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Community Answer
Consider a bar of length L, breadth B and thickness t subjeced to an a...
Explanation:
The volumetric strain (ε_v) is defined as the change in volume per unit volume of the material. When a bar is subjected to axial tension, it experiences elongation in the axial direction and contraction in the lateral directions.

Formula:
ε_v = ε_x + ε_y + ε_z
Where:
ε_x = Strain in x-direction
ε_y = Strain in y-direction
ε_z = Strain in z-direction

Given:
ε_x = P/(A*E)
ε_y = -v*ε_x
ε_z = -v*ε_x
Where:
P = Applied load
A = Cross-sectional area of the bar
E = Young's modulus of the material
v = Poisson's ratio

Calculation:
ε_v = ε_x + ε_y + ε_z
ε_v = ε_x - v*ε_x - v*ε_x
ε_v = ε_x(1 - 2v)
Therefore, the resulting volumetric strain is equal to ε_x(1 - 2v), which corresponds to option 'A' - ∈ (1 - 2v).
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