Strength of materials – simple vs. derived strains In elementary mechanics of solids, which one of the following is NOT classified as a simple (elementary) strain? Choose the most appropriate option, keeping the standard definitions used in civil and mechanical engineering.

Introduction / Context:
Strain measures deformation per unit dimension. In strength of materials, we commonly distinguish between simple (elementary) strains and derived strains. Knowing which strain type is simple helps in selecting the correct constitutive relations and in interpreting laboratory tests and field measurements.

Given Data / Assumptions:

• Small deformations and linear elastic behavior are assumed.
• Standard engineering strain definitions are used.
• Material can be considered homogeneous and isotropic for basic classification.

Concept / Approach:
Simple strains act along a single direction or plane: tensile strain (elongation per unit length), compressive strain (shortening per unit length), and shear strain (change in angle between originally orthogonal line elements). Volumetric strain is a derived measure equal to the algebraic sum of normal strains in the three orthogonal directions; it quantifies the relative change in volume and is not a single-direction elementary strain.

Step-by-Step Solution:
Identify elementary strains: tensile, compressive, shear.Recognize volumetric strain as a resultant: epsilon_v = epsilon_x + epsilon_y + epsilon_z.Therefore, among the listed options, volumetric strain is the one that is not a simple strain.

Verification / Alternative check:
In a uniaxial test, a simple strain is measured directly along the loading direction (tension or compression). Volumetric strain requires summation of three mutually perpendicular normal strains; hence it is inherently derived.

Why Other Options Are Wrong:
Tensile, Compressive, and Shear strains each refer to a single primary deformation mode; all are simple strains.

Common Pitfalls:
Confusing volumetric strain with lateral strain or Poisson's ratio. Volumetric strain concerns total volume change; Poisson's ratio relates lateral to longitudinal strain in uniaxial loading.

Final Answer:
Volumetric strain