Under direct stress, a material elongates in the loading direction and contracts laterally at right angles. What is the name of the strain developed in the directions perpendicular to the applied load?

Introduction / Context:
Axially loaded members do not deform only in the loading direction. Due to Poisson’s effect, they also undergo deformation in perpendicular directions. Correctly naming these strains is essential for volume-change estimates and multiaxial stress analysis.

Given Data / Assumptions:

• Uniaxial direct stress is applied.
• Material is isotropic and linearly elastic.
• Small strains so superposition holds.

Concept / Approach:
Linear (longitudinal) strain is the change along the loading axis. At the same time, equal and opposite type of strain occurs laterally—this is lateral strain. The ratio of lateral strain to linear strain is Poisson’s ratio ν.

Step-by-Step Solution:

Verification / Alternative check:
Volume change can be estimated using linear and lateral strains; these calculations require ν = lateral strain / linear strain.

Why Other Options Are Wrong:
Linear strain: along the load direction, not perpendicular.Volumetric strain: ratio of change in volume to original volume; a combined effect of all three directional strains.Shear strain: change in angle between material line elements; not applicable to pure uniaxial tension without shear.Plastic strain: refers to permanent deformation, not the directional description.

Common Pitfalls:
Confusing lateral strain with volumetric strain; the latter aggregates strains in three orthogonal directions.

Final Answer:

lateral strain