Before we learn about the significance of Young’s Modulus, let us ask ourselves, why should we learn about material properties and what is the importance of that in design and analysis?
Quick answer: Behaviour of various materials is different in different loads. For example, concrete performs well in Compression but it is very poor under tension. Material properties significantly affect their behaviour.
By knowing the material properties, one can get an idea of how a material performs when it is subjected to different types of loads.
Various properties of materials that determine its behaviour are Young’s Modulus, Shear Modulus, Poisson’s Ratio. We shall learn more about the Significance of Young’s Modulus now.
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What is Young’s Modulus
It is one of the three Elastic Constants which is used to describe how a material deforms under loading. The other two being Bulk Modulus (K) and Shear Modulus (G).
Young’s Modulus, simply called Elastic Modulus or Modulus of Elasticity, is denoted by letter “E”. It is a fundamental property of a material which can not be changed.
Young’s modulus of a material depends only on the materials’ molecular structure and chemical composition. It is completely independent of the size and shape of the element. Hence, it is also known as Independent Constant.
Generally, it is defined as the ratio of longitudinal stress to longitudinal strain. This is, more or less, a mathematical formula.
But what actually is this Young’s Modulus? For that, we need to understand two fundamental concepts of civil engineering, Stress and Strain and their relationship.
STRESS
Stress is defined as the ratio of Load to the cross-section area. This creates certain confusion among many that stress is something that we apply on a body. But it is not.
When a load is applied on a deformable body, the body simply deforms. But the material tries to resist this deformation. Hence an internal resistance is generated within the body.
This resistance is called Stress which is proportional to the applied load.
STRAIN
The strain is generally expressed as a ratio of change in a dimension to the initial dimension. This is a measure of material deformation in response to the applied load. It is generally expressed in percentage.
STRESS – STRAIN RELATIONSHIP
Only when a body deforms, stress is developed. Which implies, stress always depends on strain i.e., the strain is independent of stress. Within the elastic limit, stress is directly proportional to strain. This is called Hooke’s law.
Robert Hooke used Young’s modulus as the proportionality constant to relate stress and strain. If the strain of a body (ϵ) and its Young’s modulus (E) is known, then their product would give the stress developed (σ) in it.
$$σ = E \times ϵ$$
DETERMINATION OF YOUNGS MODULUS
Experimentally, Young’s modulus can be determined by developing a stress-strain curve.
There are different tests to get stress-strain curves like the tensile test, compression test and flexural test. The selection of the test depends on the type of material.
Isotropic materials like steel have the same property in all directions thus stress-strain plot will be the same for all tests. Whereas, anisotropic material, like wood, has a different property in a different direction.
As we know that strain is independent, it is taken on X-axis or abscissa and stress on Y-axis or Ordinate. Young’s Modulus can be determined by measuring the initial slope of this curve i.e., Slope of the curve in Elastic Region.
What does E represent
Young’s modulus describes material behaviour under any load. It tells us the material’s ability to withstand the applied load with minimum deformation.
In short, Young’s modulus represents the stiffness of the material. If the value of ‘E’ is high for material then the material is capable of generating more internal resistance. Therefore, elastic deformations are small.
Significance of Young’s Modulus
1. The common design objective is to limit the elastic deformations as small as possible. Hence, Young’s modulus is a key parameter in the selection of materials.
2. When combined with the sectional properties, Young’s modulus gives us an idea of how the element deforms under different loads. This helps us in the design of a member or structure.
3. It plays a major role in the analysis of a structure as it is used to calculate the stiffness of a member, used in Bending equation, calculating deflections and many.
Final Words
Young’s modulus is a Material-Specific and an Independent Property of a material.
It is completely independent of material’s size, shape and also the type of loading. It depends on the material composition and Temperature.
It briefs the material’s ability to withstand the applied load with minimum deformation.
If Young’s modulus of a material is known then we can relate stress and strain. In an experiment, we can measure strain. With the help of ‘E’, stress can be calculated. This is one of the important applications of Young’s modulus.