Poisson’s ratio under tension vs. compression: A steel bar (2 m × 20 mm × 10 mm) carries 2 kN in tension or in compression within the elastic range. How does Poisson’s ratio in tension compare with that in compression?

Introduction / Context:Poisson’s ratio ν is a material constant in linear elasticity that relates lateral strain to axial strain. For small strains within the elastic limit, ν is independent of whether the load is tensile or compressive.

Given Data / Assumptions:

• Same prismatic steel bar loaded by ±2 kN (tension or compression).
• Material behavior in the linear-elastic range without plasticity or damage.
• Isotropy and homogeneity assumed.

Concept / Approach:By definition, ν = − ε_lateral / ε_axial in the elastic regime. For isotropic materials, ν is a constant for a given material over small strains, independent of load sign. Only once plasticity, microcracking, or other nonlinear effects occur could an apparent asymmetry develop, which is outside the problem scope.

Step-by-Step Solution:

Verification / Alternative check:Standard elastic-constant relations (E, G, K, ν) and reciprocity do not depend on load sign within the elastic domain; experimental handbooks report a single ν value for a material like steel (e.g., ~0.3).

Why Other Options Are Wrong:

• “Less than/greater than” implies nonlinearity or damage not stated.
• Dependence on bar dimensions or load magnitude conflicts with ν being an intrinsic material property.

Common Pitfalls:Confusing elastic constants with geometric stiffness; assuming plastic effects at low loads; mixing up ν with lateral contraction per se.

Final Answer:equal to