Understanding Stress and Strain in Materials

When an external force acts on a body, it causes deformation. The internal restoring forces within the body resist this deformation. Stress and strain are fundamental concepts that describe the material's response to these external forces.

What is Stress?

Stress is defined as the internal restoring force per unit area of a body. It is a measure of how much force is acting on a unit area within the material. The SI unit of stress is Pascal (Pa), which is equal to N/m².

Mathematically, stress ($\sigma$) is given by:

$$\sigma = \frac{F}{A}$$

where:

• $F$ is the applied force
• $A$ is the cross-sectional area

Stress can be of different types depending on the direction of the applied force relative to the surface and the effect it produces. Common types include tensile stress, compressive stress, and shear stress.

What is Strain?

Strain is a measure of the deformation of a body relative to its original dimensions. It is a dimensionless quantity as it is a ratio of two lengths (or volumes, etc.).

Mathematically, strain ($\epsilon$) is typically given by:

$$\epsilon = \frac{\text{Change in Dimension}}{\text{Original Dimension}}$$

Like stress, strain can also be tensile strain, compressive strain, or shear strain, corresponding to the type of stress applied.

Analyzing the Scenario: Equal and Opposite Pulls

The question describes a body subjected to "two equal and opposite pulls". Pulls are forces that tend to stretch or elongate the body. This type of force system is known as a tensile force or tension.

As a result of these tensile forces, the body "tends to extend its length". An increase in length along the direction of the applied force is a characteristic deformation associated with tension.

Identifying the Type of Stress

When a body is subjected to equal and opposite pulling forces (tension) acting perpendicular to the cross-sectional area, the internal restoring forces within the material oppose this stretching. This type of stress, which tends to increase the length of the body, is called tensile stress.

Identifying the Type of Strain

The deformation caused by tensile stress is an increase in the length of the body along the direction of the applied force. The strain associated with this increase in length relative to the original length is called tensile strain.

Tensile strain ($\epsilon_t$) is calculated as:

$$\epsilon_t = \frac{\Delta L}{L_0}$$

where:

• $\Delta L$ is the change in length (extension)
• $L_0$ is the original length

Evaluating the Options

Based on our analysis, equal and opposite pulls causing extension result in tensile stress and tensile strain. Let's examine the given options:

• Tensile stress and compressive strain

  Incorrect. Tensile stress causes extension, which is tensile strain, not compressive strain (which is caused by compression).

• Compressive stress and compressive strain

  Incorrect. Compressive stress is caused by pushes that tend to shorten the body, resulting in compressive strain.

• Compressive stress and tensile strain

  Incorrect. Compressive stress causes compressive strain. Tensile strain is caused by tensile stress.

• Tensile stress and tensile strain

  Correct. Equal and opposite pulls (tension) induce tensile stress, which leads to an increase in length, causing tensile strain.

Therefore, when a body is subjected to two equal and opposite pulls, resulting in the body tending to extend its length, the stress and strain induced are tensile stress and tensile strain.

Revision Table: Stress and Strain Types

Additional Information: Hooke's Law and Elasticity

The relationship between stress and strain for many materials within their elastic limit is described by Hooke's Law. Hooke's Law states that stress is directly proportional to strain:

$$\sigma \propto \epsilon$$

The constant of proportionality is known as the modulus of elasticity, which is a material property. For tensile and compressive stress/strain, this modulus is called Young's Modulus ($E$).

$$E = \frac{\text{Tensile or Compressive Stress}}{\text{Tensile or Compressive Strain}}$$

Understanding stress and strain is crucial for analyzing the mechanical behavior of materials under load and is a core concept in elasticity and strength of materials.