Effect of axial compression (push) on dimensions: A rectangular bar of length l, width b, and thickness t is subjected to a compressive axial load P. Which dimensional change is correct (considering Poisson’s effect)?
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Alength, width, and thickness increase
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Blength, width, and thickness decrease
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Clength increases, width and thickness decrease
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Dlength decreases, width and thickness increase
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Elength unchanged, width and thickness increase
Answer
Correct Answer: length decreases, width and thickness increase
Explanation
Introduction / Context:Poisson’s effect couples axial and lateral strains. Under compression (push), a bar shortens axially and tends to bulge laterally, a behavior crucial for fit tolerances, buckling, and contact problems.
Given Data / Assumptions:
- Axial compressive load P along the length.
- Linear elastic material with positive Poisson’s ratio.
- Small deformations and uniform stress state.
Concept / Approach:Axial compressive strain is negative, while lateral strains are positive and proportional to ν times the axial strain (with opposite sign). Hence, length decreases; width and thickness increase.
Step-by-Step Solution:
Axial strain: epsilon_long = -σ / E < 0Lateral strain: epsilon_lat = -ν * epsilon_long > 0Therefore: Δl < 0; Δb > 0; Δt > 0Verification / Alternative check:Cylindrical compression tests and compression of rubber blocks visibly show shortening with lateral bulging, confirming the sign pattern of strains.
Why Other Options Are Wrong:
- All dimensions increasing/decreasing contradicts Poisson’s coupling.
- Length increases (option C) is opposite to compression.
- Length unchanged (option E) is unrealistic under finite compressive stress.
Common Pitfalls:Confusing tension and compression effects; ignoring small but significant lateral expansions that influence fits and clearances.
Final Answer:length decreases, width and thickness increase