Which of the following statements about stress, strain, and Hooke’s law is correct within the elastic limit?

Introduction / Context:
Basic definitions in strength of materials underpin all later design work. Distinguishing stress from pressure, and knowing the limits of Hooke’s law, prevents fundamental errors in calculations and interpretations.

Given Data / Assumptions:

• Small-strain linear elasticity region (elastic limit not exceeded).
• Engineering definitions of stress and strain.
• Isotropic, homogeneous materials for simplicity.

Concept / Approach:
Hooke’s law states:
σ = E * εwithin the elastic limit, i.e., stress is proportional to strain, with E (Young’s modulus) as the constant of proportionality. Strain is dimensionless; stress is force per unit area (not “pressure per unit area,” although numerically both share the same units).

Step-by-Step Solution:

Verification / Alternative check:
Tensile test data show linear σ–ε relation up to a proportional limit; beyond that, plasticity begins and the relation becomes nonlinear until fracture.

Why Other Options Are Wrong:
“Stress is pressure per unit area” is a misuse of terms; stress is force per unit area; pressure is a specific isotropic normal stress.“Strain in mm” is incorrect; strain is dimensionless.“Holds up to breaking point” is false; validity ends near the proportional/elastic limit, well before fracture.“Stress equals strain” ignores the modulus E.

Common Pitfalls:
Conflating units of pressure and stress; assuming linearity beyond yield; mixing true and engineering measures at large strains.

Final Answer:

Stress is directly proportional to strain within elastic limit