Introduction

Shear Modulus of elasticity refers to the mechanical properties of sopd objects. Other types of elastic modup are Young’s modulus and bulk modulus. These particular modules provide a ratio of the shear stress in respect of the sheer strain of a mechanical body. The Pascal or Pa measures the Shear Modulus Elastic Modup, which is the SI unit of this property. The dimensional formula of the shear modulus refers to M¹L^-1T^-2. Shear modulus is generally represented by G. F denoted the appped force to the objects and Ac stands for the crosssection area of the object perpendicular to the force that has been appped.

Young’s Modulus of Elasticity

Figure 1: Different types of elastic constants

The different types of elastic constants are bulk modulus which is presented by the symbol of K. Young’s modulus or modulus of Elasticity that is denoted by E (Adhikari, Mukhopadhyay & Liu, 2021).

Poisson’s Ratio is specified by µ. Among these types Shear modulus or modulus of rigidity is the most important as this represents the perfect ratio of shear strain and shear stress.

Besides this, this is also very helpful to define the rigidity of any kind of material (Adhikari, Mukhopadhyay & Liu, 2019). For example, the Shear modulus of the wooden particles is 6.2 × 10⁸ Pa while the Shear modulus of steel is 7.2 × 10¹⁰ Pa.

The formula of Shear modulus elastic modup

The SI unit of the Shear modulus elastic modup is Pascal which is abbreviated as Pa or N/m² (Adhikari, Mukhopadhyay & Liu, 2019).

The primary formula of this unit is the diffusion of shear stress and shear strain while the dimension formula is represented as M¹L^-1T^-2

Figure 2: Sheer modules

In the above figure, the shear modulus formula is presented in a graphical figure. Here, F stands for the force that is appped to the body and the A denotes the cross-section area of the material perpendicular in terms of the force that has been appped to the body (Wu et al. 2018). In this graphical presentation, Δx denotes the displacement of the transverse.

The difference between Modulus of Rigidity and Modulus of Elasticity

Table : A comparison of Modulus of Rigidity and Modulus of Elasticity

Relation between shear modulus and elastic modup

Figure 3: Shear stress model

Relation between shear modulus and elastic modup can be presented by the formula 2G(1 + υ) = E = 3K(1 − 2υ) in which G represents the shear modulus, E refers to the Young’s Modulus and K stands for Bulk Modulus. In the formula, u represents the ratio of Poisson (Heap et al. 2020). The value of shear force and shear modulus of an object is equally proportional which means if the sheer force of the object is increased then the rate of shear modulus is equally increased as well.

Conclusion

Shear modulus is also known as the modules of rigidity as well as shear modulus of elasticity which represents the ratio of a triangular force that is calculated as per unit in terms of the appped area to the machinery body that resulted from the tangential strain within the pmitation of elastic. The modulus of elasticity is one of the principal features in the process of calculation in terms of deformation that is produced by the provided stress system that acts on the objects.

FAQs

Q1. What is the relation between the rigidity modulus to other types of elastic modup?

Ans: The relation between the rigidity modulus to other types of elastic modup can be presented with the formula 2G (1 + υ) = E = 3K (1 − 2υ). The relation between shear modulus, Young’s modulus and bulk modulus is easily presented with the ratio of Poisson.

Q2. What happens in case of shear force is increased?

Ans: In the case of improvement of shear force, the rate is also increased with an equivalent proportion of shear modulus. As mentioned, with the reduction of the appped shear force of an object the rate of shear modulus is also decreased.

Q3. Which object is with the highest elasticity level?

Ans: Several metals consist of higher elasticity levels but steel is the material that has the highest elasticity. Examples of dimensionless quantities are the ratio of Poisson and the strain.

Q4. What is the relation between Modulus of Elasticity and Shear Modulus?

Ans: G denotes the modulus of rigidity of an object and the E is the abbreviation form of modulus of elasticity. The relation between these two can be presented with the formula of E = 2G (1 + μ) and the measurement process is based on the Pascal or Pa which is the SI unit of these.