Modulus of Elasticity and Types

Definition

Elastic modulus is the ratio of stress, below the proportional limit, to the equivalent stress. It is the measure of rigidity or stiffness of a substance (material).

In regards to the stress-strain curve, the modulus of elasticity is the slope of the stress-strain curve in the series of linear symmetry of stress to strain.

Elastic modulus is additionally known as modulus of elasticity and is in some cases referred to as Young’s modulus.

According to Hook’s law:

Stress is directly proportional to strain, within elastic limit.

Stress ∝Strain

Stress = constant (Strain)

Or it can be

Constant = stress/strain

So, within the elastic limit, the ratio of stress to strain remains constant. This constant is called elastic constant or modulus of elasticity.

Unit: The unit of elastic modulus is N / m2 or Pascal.

Types of Elastic Modulus

Elastic Moduli can be of three kinds. These are Young’s modulus, Shear modulus, and Bulk modulus.

Young’s Modulus

The ratio of the tensile stress to the tensile strain is referred to as Young’s modulus.

Young's-Modulus-1

Let us take into consideration a wire of size ‘L’ with an area of cross-section ‘A’. Allow one end of the wire is fixed with and also the other end is loaded or stretched. Let ‘I’ be the change in size due to the activity of the force, after that

Young's-Modulus-2

Shear Modulus

Also known as the modulus of rigidity, the ratio of the shear stress to the shear strain is called the shear modulus. Shear Modulus is normally signified with the letter C.

Shear-Modulus

Bulk Modulus

The ratio of the stress applied to the body on the body’s fractional reduction in volume is called the bulk modulus.

Or simply, the ratio of volumetric stress to volumetric strain is called bulk modulus.

Therefore, when a body is subjected to three mutually perpendicular stresses of the same strength, the ratio of the same intensity to the corresponding volumetric stress is what we call the Bulk Modulus. Bulk Modulus is generally signified with the letter K.

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Shear-Modulus-2

Let us take into consideration a body of volume ‘V’ with an area of cross-section ‘A’. Allow three equal forces to act upon the body in equally perpendicular directions Let ‘V’ be the change in volume, because of the action of forces, after that

Bulk-Modulus

 

MCQs

  • 1. What is the modulus of elasticity?
    • A) Measure of strength
    • B) Ratio of stress to strain
    • C) Unit of force
    • D) Rate of deformation

    Answer: B) Ratio of stress to strain

  • 2. Which law states that stress is directly proportional to strain within the elastic limit?
    • A) Newton’s Law
    • B) Pascal’s Law
    • C) Boyle’s Law
    • D) Hook’s Law

    Answer: D) Hook’s Law

  • 3. What is the unit of elastic modulus?
    • A) Newton per meter
    • B) Joule per meter
    • C) Pascal
    • D) Newton per second

    Answer: C) Pascal

  • 4. Which type of elastic modulus measures the ratio of tensile stress to tensile strain?
    • A) Shear modulus
    • B) Bulk modulus
    • C) Young’s modulus
    • D) Modulus of rigidity

    Answer: C) Young’s modulus

  • 5. What is another name for the shear modulus?
    • A) Modulus of elasticity
    • B) Bulk modulus
    • C) Modulus of rigidity
    • D) Poisson’s ratio

    Answer: C) Modulus of rigidity

  • 6. What does the bulk modulus measure?
    • A) Ratio of shear stress to shear strain
    • B) Ratio of volumetric stress to volumetric strain
    • C) Ratio of tensile stress to tensile strain
    • D) Ratio of longitudinal stress to longitudinal strain

    Answer: B) Ratio of volumetric stress to volumetric strain

  • 7. Which letter typically represents the shear modulus?
    • A) S
    • B) Y
    • C) C
    • D) K

    Answer: C) C

  • 8. What is the ratio measured by the bulk modulus when a body is subjected to three mutually perpendicular stresses of the same strength?
    • A) Ratio of shear stress to shear strain
    • B) Ratio of volumetric stress to volumetric strain
    • C) Ratio of tensile stress to tensile strain
    • D) Ratio of longitudinal stress to longitudinal strain

    Answer: B) Ratio of volumetric stress to volumetric strain

  • 9. What is Young’s modulus also known as?
    • A) Modulus of elasticity
    • B) Shear modulus
    • C) Bulk modulus
    • D) Poisson’s ratio

    Answer: A) Modulus of elasticity

  • 10. Which law defines the constant ratio of stress to strain within the elastic limit?
    • A) Pascal’s Law
    • B) Hooke’s Law
    • C) Newton’s Law
    • D) Boyle’s Law

    Answer: B) Hooke’s Law

  • 11. What does the shear modulus measure?
    • A) Tensile stress
    • B) Shear stress
    • C) Volumetric stress
    • D) Longitudinal stress

    Answer: B) Shear stress

  • 12. Which modulus measures the body’s resistance to compression or expansion under different pressures?
    • A) Shear modulus
    • B) Young’s modulus
    • C) Bulk modulus
    • D) Modulus of rigidity

    Answer: C) Bulk modulus

  • 13. What is the unit of stress?
    • A) Newton per meter
    • B) Pascal
    • C) Newton
    • D) Meter per second

    Answer: B) Pascal

  • 14. Which modulus measures the resistance of a material to shearing forces?
    • A) Young’s modulus
    • B) Shear modulus
    • C) Bulk modulus
    • D) Modulus of rigidity

    Answer: B) Shear modulus

  • 15. What is the ratio of stress to strain called within the elastic limit?
    • A) Elastic constant
    • B) Elastic limit
    • C) Young’s constant
    • D) Young’s modulus

    Answer: D) Young’s modulus

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Summary:

The modulus of elasticity, often referred to as elastic modulus or Young’s modulus, measures the rigidity or stiffness of a material. It represents the ratio of stress to strain within the proportional limit. According to Hooke’s law, stress is directly proportional to strain within this limit.

There are three main types of elastic modulus: Young’s modulus, shear modulus, and bulk modulus. Young’s modulus measures the ratio of tensile stress to tensile strain, indicating a material’s response to stretching or compression. Shear modulus, also known as the modulus of rigidity, quantifies a material’s resistance to shearing forces. Bulk modulus measures a material’s resistance to compression or expansion under different pressures.

Understanding these elastic moduli is essential in various fields of engineering and material science, providing insights into material behavior under different types of stress.