Stress and strain are basic ideas that explain how materials react to outside pressures. When examining the strength and behaviour of materials under load whether in a bridge, an automobile, or even our own bones these phrases are frequently used.
What is Stress?
Stress is the internal force per unit area that a material creates in response to an external load. When we stretch a rubber band while holding it, the rubber band feels “stressed.” This stress indicates the amount of force operating on a specific region within the material.
Mathematically, stress is defined as:
Stress(σ) = Force (F) / Area (A)
Here:
Force (F): The external load applied to the material.
Area (A): The cross-sectional area of the material where the force is applied.
Units of measurement for stress is newtons per square meter (N/m2) and pascals (Pa). Depending on the kind of load being applied, stress can take many various forms:
Tensile Stress: When a material is pulled apart, like stretching a rope.
Compressive Stress: When a material is squeezed, like compressing a spring.
Shear Stress: When forces act parallel but in opposite directions, like cutting paper with scissors
Longitudinal stress :– The restoring force acting per unit area along the length of body is called longitudinal stress.
What is Strain?
Strain measure how much a material deforms or changes shape as a result of applied stress. Strain is all about how much the material stretches, compresses, or twists in response, as opposed to stress, which is about force.
The ratio of the material’s changed length to its initial length is known as strain.
Strain(ϵ) = ΔL / L0
Here:
ΔL: The change in length (elongation or compression).
L₀: The original length of the material.
Strain is a dimensionless quantity because it is a ratio of two lengths. Like stress, strain can also take different forms:
Tensile Strain: When a material stretches and its length increases.
Compressive Strain: When a material is compressed and its length decreases.
Shear Strain: When a material deforms in shape without a significant change in length, like sliding layers in a deck of cards.
Longitudinal strain:– The ratio of change of length to the original length of the body is called longitudinal strain.
Volumetric strain :– The ration of change in volume per unit original volume of the body on applying the normal deforming force to surface is called the volumetric strain.
Relationship between Stress and Strain
The elastic modulus, often known as Young’s modulus, is a material parameter that describes the close relationship between stress and strain. This characteristic indicates a material’s resistance to deformation under stress. One way to describe the relationship is:
Stress = Elastic Modulus × Strain
Materials having a low elastic modulus, like rubber, are more flexible, those with a high elastic modulus, like steel, resist deformation and are regarded as rigid.
Why Are Stress and Strain Important?
For designing secure and dependable buildings its requires a caring of stress and strain. E.g, engineers apply these ideas to calculate the maximum weight that a bridge can bear before failing.
Manufacturers make sure that under load, materials like metals and plastics don’t permanently distort.
Stress and strain are key concepts in biomechanics that describe how muscles and bones react to exercise.
Everyday Examples
Elastic Bands: The force used to stretch a rubber band produces stress, and the lengthening of the band signifies strain.
Building Columns: The weight of the structure above causes compressive stress on a building’s columns, which results in strain if the columns shorten slightly.
Springs: A spring’s capacity to compress or extend before reverting to its initial shape is determined by the stress and strain it experiences throughout these operations.
Note
Strain gauges how a material reacts by deforming, whereas stress gauges the force given to a substance. These ideas work together to help us to understand and forecast how materials will respond to different forces, which makes them vital instruments in science and engineering.
Stress is the internal force per unit area that a material experiences when subjected to an external load. It measures how much force is acting on a specific area within a material and is calculated as: Stress(σ) = Force (F) / Area (A)
It is measured in units like pascals (Pa) or newtons per square meter (N/m²).
Strain is a measurement of a material’s deformation or shape change brought on by applied stress. It is described as the proportion of the material’s altered length to its initial length: Strain(ϵ) = ΔL / L0
Strain is a dimensionless quantity because it compares two lengths.
There are three main types of stress:
Tensile Stress: When a material is stretched or pulled apart.
Compressive Stress: When a material is squeezed or compressed.
Shear Stress: When forces act parallel to a surface but in opposite directions, causing sliding.
The types of strain correspond to the types of stress:
Tensile Strain: Elongation of a material due to stretching.
Compressive Strain: Reduction in length due to compression.
Shear Strain: Change in shape (distortion) due to forces acting parallel but in opposite directions.
Stress and strain are related through a material property called the elastic modulus (Young’s modulus):
Stress = Elastic Modulus × Strain
This equation describes how much a material deforms (strain) in response to applied stress.
Rubber Bands: Stretching creates tensile stress and strain.
Bridges: Weight on a bridge causes compressive stress and strain in the supporting pillars.
Springs: Compressing or stretching a spring involves stress and strain that determines its extension or compression.