Effect of axial compression (push) on dimensions:\nA 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)?

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:

Verification / 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