Mechanical properties: the units of Young’s modulus of elasticity are identical to the units of which other quantity?

Introduction / Context:
Young’s modulus E relates stress to strain in linear elastic materials. Recognizing its dimensional form helps interpret test data, validate formulas, and ensure unit consistency in calculations involving deflection, vibration, and pressure‐boundary design.

Given Data / Assumptions:

• Linear elastic behavior: σ = E * ε.
• Stress σ carries units of force per area; strain ε is dimensionless.
• Standard SI or engineering unit systems are acceptable.

Concept / Approach:
From σ = E * ε, and ε being dimensionless, E must have the same units as σ. Thus, E is expressed in Pascals (N/m^2), MPa, GPa, or in psi/ksi in US customary units. This identity ensures dimensional consistency in beam bending, pressure vessel theory, and finite-element formulations.

Step-by-Step Solution:
Write the linear Hooke’s law: σ = E * ε.Since ε is unitless, E must have units identical to σ.Therefore, E shares the same units as stress: force per unit area.

Verification / Alternative check:
Check common values: steel E ≈ 200 GPa, which is indeed a pressure unit; typical working stresses are also stated in MPa—consistent units.

Why Other Options Are Wrong:
Strain and Poisson’s ratio are dimensionless; modular ratio is a ratio of moduli and dimensionless; therefore only stress shares the units with E.

Common Pitfalls:
Confusing engineering stress with true stress; mixing units (psi vs. MPa) without proper conversion; misreading GPa as a force or energy unit rather than pressure.

Final Answer:
Stress