 # Relation between modulus of elasticity and modulus of rigidity pdf

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## Relation between modulus of elasticity (E), modulus of rigidity (G) and bulk modulus(K)

Modulus of elasticity and modulus of rigidity are two numbers that are used by materials engineers to describe how a material gets deformed. The main difference between modulus of elasticity and modulus of rigidity is that the modulus of elasticity describes how a material gets deformed when a force is applied at right angles to a surface of an object , causing the material to elongate or shorten while the modulus of rigidity describes how a material gets deformed when a force is applied parallel to a surface of an object , causing one of the surfaces to become shifted with respect to another surface of the same object.

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Wedge friction and self-locking in engineering mechanics. Concept of force system in engineering mechanics. Difference between fan and blowers. Basics of centrifugal compressor. Recent Updates. Let us assume that we have following details as mentioned here. Now we will secure here the final dimensions of the cube in order to secure the final volume of the cube and finally we will determine the bulk modulus of elasticity. Let us consider first one side of cube i.

As we have already discussed that three mutually perpendicular tensile stresses of similar intensity are acting over the cube. Let us determine here the effect of tensile stress over the dimensions of the cube. Now we will have to think slightly here to discuss the effect on length of the cube under three mutually perpendicular tensile stresses of similar intensity.

Now we will ignore the product of small quantities in order to easy understanding. Volumetric strain in the specified cube here will be determined as displayed here.

Bulk modulus of elasticity will be defined as the ratio of volumetric stress or hydro static stress to volumetric strain and therefore we will write here as mentioned here.

As we have already seen above that. Do you have any suggestions or any amendment required in this post? Please write in comment box. Metal cutting tool definition and classification Single point cutting tool nomenclature Difference between rake angle and clearance angle of cutting tool Main characteristics of cutting tool materials Lever and its types with examples Guidelines for solving friction problems in mechanics Rolling resistance or rolling friction Wedge friction and self-locking in engineering mechanics Concept of force system in engineering mechanics Difference between fan and blowers Basics of centrifugal compressor.

Strength of material, By R. Image Courtesy: Google. We will see another important topic i. Thermal stresses in composite bars , in the category of strength of material, in our next post. Negative impact of 3D printing. Corrosion failure examples. Hardness testing methods. Basics of nanotechnology. Email This BlogThis! Labels: Engineering Materials. Dominick Newer Post Older Post Home.

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We have also discussed various basic concepts of About Me. ## Main Difference – Modulus of Elasticity vs. Modulus of Rigidity

Stress and strain may be described as follows in the case of a metal bar under tension. If a metal bar of cross-sectional area A is pulled by a force F at each end, the bar stretches from its original length L 0 to a new length L n. Simultaneously the cross section decreases. Strain is dimensionless. The value for steel is about three times greater, which means that it takes three times as much force to stretch a steel bar the same amount as a similarly shaped aluminum bar. As stresses increase, the material may either flow, undergoing permanent deformation, or finally break.

An elastic modulus also known as modulus of elasticity is a quantity that measures an object or substance's resistance to being deformed elastically i. The elastic modulus of an object is defined as the slope of its stress—strain curve in the elastic deformation region:  A stiffer material will have a higher elastic modulus. An elastic modulus has the form:. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:. Homogeneous and isotropic similar in all directions materials solids have their linear elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.

It is defined as. Modulus of Rigidity can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience. between stress and strain hold good is called elastic limit of the material. (3) Elasticity of shape or shear modulus or Modulus of Rigidity, corresponding to The above equation gives the relation connecting the three elastic constants Y, K.

### Relation between modulus of elasticity (E), modulus of rigidity (G) and bulk modulus(K)

You must find out and read the following quite useful engineering articles and these are as mentioned below. Metal cutting tools i. Metal cutting tool definition and classification. Single point cutting tool nomenclature. Difference between rake angle and clearance angle of cutting tool.

Elastic constants are those factors which determine the deformations produced by a given stress system acting on a material. When a material exhibits Same elastic properties at any point in a given directions than the material is known as homogenous material. When a material exhibits Same elastic properties at any direction at a given point than the material is known as Isotropic Material.

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