Definition of linear strain For a member of original length l that undergoes a change in length δl under axial loading, which expression correctly defines engineering (normal) strain?

Introduction / Context:Engineering strain is a fundamental measure used throughout solid mechanics and materials testing. It quantifies relative elongation or contraction and underpins stress–strain relationships, modulus determination, and design limits.

Given Data / Assumptions:

• Original (gauge) length = l.
• Change in length under load = δl (positive in tension, negative in compression).
• Small deformations where engineering strain is appropriate.

Concept / Approach:Engineering (normal) strain is defined as change in length divided by original length. It is a dimensionless quantity that captures relative deformation independent of the absolute size of the specimen.

Step-by-Step Solution:Engineering strain: epsilon = (final length − original length)/original length.Given final length = l + δl → epsilon = (l + δl − l)/l.Hence epsilon = δl / l.Units: none (ratio of length to length).

Verification / Alternative check:For a bar under uniaxial stress sigma, Hooke's law gives epsilon = sigma / E; integrating strain over length l still yields total elongation δl = epsilon * l, which rearranges to epsilon = δl / l.

Why Other Options Are Wrong:(a) inverts the ratio; (c) and (d) have dimensions of length, not strain; (e) invents a nonstandard form with incorrect dimensionality.

Common Pitfalls:Confusing engineering strain with true (logarithmic) strain, which is ln(1 + δl/l); mixing sign conventions; using instantaneous length instead of original length for engineering strain.

Final Answer:δl/l