Choose the correct definition of engineering stress: stress is defined as force divided by the loaded area (standard SI units N/m^2 or Pa).

Introduction / Context:
Stress is a primary concept in strength of materials. Correctly identifying its definition is fundamental before applying any failure criteria or deformation formulas.

Given Data / Assumptions:

• Axial loading concept; stress symbol σ (normal) or τ (shear).
• Engineering (nominal) stress uses original cross-sectional area unless otherwise specified.

Concept / Approach:
Normal stress σ = P / A (axial force divided by area normal to the load). Shear stress τ = V / A_s (shear force divided by the relevant shear area). Units: N/m^2 (Pa) or N/mm^2 (MPa). Length or volume denominators do not represent stress.

Step-by-Step Solution:
1) Identify the loaded area resisting the applied force.2) Compute stress as σ = Force / Area.3) Recognize that other denominators (length, volume) correspond to different physical quantities, not stress.

Verification / Alternative check:
Dimensional analysis: [Force]/[Area] = N/m^2; neither N/m nor N/m^3 aligns with stress dimensions.

Why Other Options Are Wrong:

• Force per unit length: Relates to line load intensity, not stress.
• Force per unit volume: Relates to body force density (e.g., weight density), not stress.
• None of these: Incorrect, since force per unit area is correct.

Common Pitfalls:

• Mixing engineering stress with true stress (which uses instantaneous area).
• Using average area where net area is required (e.g., bolted plates with holes).

Final Answer:
force per unit area.