Units check in mechanics of materials: What is the unit of (engineering) strain for axial loading or bending?

Introduction / Context:Dimensional consistency is critical in mechanics of materials. Strain represents deformation per unit length, used in Hooke’s law and failure criteria.

Given Data / Assumptions:

• Engineering (normal) strain ε = ΔL / L.
• Shear strain γ is an angle in radians, also dimensionless.

Concept / Approach:Because strain is a ratio of two lengths (or an angle measured in radians), it has no physical unit. It may be reported as a pure number, percentage, or microstrain for convenience, but fundamentally it is dimensionless.

Step-by-Step Solution:

Verification / Alternative check:Hooke’s law E = σ / ε shows E carries stress units (e.g., MPa) while ε is unitless, maintaining dimensional balance.

Why Other Options Are Wrong:

• N-mm, N/mm, and MPa are force-length or stress units, not applicable to a ratio of lengths.
• mm is length, not a nondimensional ratio.

Common Pitfalls:Confusing strain with elongation (which has units); writing “mm/mm” and then treating it as “mm” rather than recognizing it cancels to a pure number.

Final Answer:no unit