Understanding Stress Development from Perpendicular External Forces

This question explores the fundamental concept of stress within materials when subjected to external forces. Specifically, it asks about the type of stress developed when a force is applied perpendicular to a body's cross-sectional area, leading to either stretching (elongation) or squeezing (compression) along the direction of the force.

What is Stress?

In mechanics, stress is a measure of the internal forces acting within a deformable body per unit area. It quantizes how forces are distributed inside a material resisting an external load. Mathematically, stress ($\sigma$ or $\tau$) is defined as:

$ \text{Stress} = \frac{\text{Force}}{\text{Area}} $

The nature of the stress depends entirely on the direction of the applied force relative to the surface or area it acts upon.

Analyzing Different Types of Stress

Let's examine the options provided to understand why one fits the question's description:

• Shear Stress: This type of stress arises when an external force is applied parallel or tangential to the cross-sectional area of a body. Imagine trying to slide one layer of the material over another. Shear stress tends to cause deformation by sliding or twisting. The formula is $\tau = \frac{F_{\parallel}}{A}$, where $F_{\parallel}$ is the force parallel to the area $A$. This doesn't match the question, which specifies a force perpendicular to the area.
• Volumetric Stress: This stress is associated with a change in the volume of a body. It typically occurs when a force acts uniformly on all surfaces of an object, like the pressure exerted by a fluid. It is related to the bulk modulus of the material. While forces are involved, the specific scenario of elongation or compression along a single axis due to a force perpendicular to the cross-section isn't the primary definition of volumetric stress.
• Torsional Stress: This stress results from a twisting effect, known as torque, applied to an object. It causes deformation where one part of the object rotates relative to another. Torsional stress is essentially a form of shear stress distribution within the object's cross-section. This is different from the direct elongation or compression caused by a force acting perpendicularly.
• Normal Stress: This stress occurs when an external force acts perpendicular (or normal) to the cross-sectional area of a body.
  • If the force tends to pull the body apart, causing elongation, it's called tensile stress (a type of normal stress).
  • If the force tends to push the body together, causing compression, it's called compressive stress (also a type of normal stress).
  The formula for normal stress is $\sigma = \frac{F_{\perp}}{A}$, where $F_{\perp}$ is the force acting perpendicular to the area $A$. This perfectly matches the description given in the question.

Conclusion: Identifying the Correct Stress Type

The question explicitly states that the external force is applied perpendicular to the cross-sectional area and causes either elongation or compression. These are the defining characteristics of normal stress.

Therefore, the stress developed within the material under these specific conditions is fundamentally categorized as normal stress.