Typical Poisson’s ratio range for steel\n\nSelect the most commonly accepted range of Poisson’s ratio (ν) for structural steels under small strains.

Introduction / Context:
Poisson’s ratio relates lateral contraction to axial extension and is used in 3D stress-strain relations and in determining other elastic constants such as shear modulus and bulk modulus.

Given Data / Assumptions:

• Isotropic, homogeneous steel in the elastic range.
• Room temperature behavior without significant anisotropy.

Concept / Approach:
Most common steels exhibit Poisson’s ratio around 0.3. Typical handbook ranges place ν for steel approximately between 0.27 and 0.30 in design calculations.

Step-by-Step Solution:
Use ν ≈ 0.3 for quick estimates.Engineering references often list 0.28–0.30; a broader tolerance may be 0.27–0.30.Hence, among the options, 0.27 to 0.30 best matches standard practice.

Verification / Alternative check:
Cross-check via relationships: E = 2G(1 + ν) and K = E / [3(1 − 2ν)]. With typical E and G values for steel, ν backs out near 0.3.

Why Other Options Are Wrong:
0.23–0.27 is low for typical steels; 0.31–0.34 and 0.32–0.42 are high for most structural steels; 0.10–0.20 is characteristic of some foams or ceramics, not steel.

Common Pitfalls:
Using ν beyond elastic range; assuming stainless or specialty steels always share the same ν (they may differ slightly, but still near 0.3).

Final Answer:
0.27 to 0.30