Modulus of Rigidity

The modulus of rigidity is a physical property of materials that describes their ability to resist deformation when subjected to an applied force. It is defined as the ratio of the shear stress to the shear strain in a material, and is usually denoted by the symbol G. In simpler terms, it measures a material's resistance to being twisted or sheared. The modulus of rigidity is an important factor in determining the strength and stiffness of materials used in engineering and construction applications.

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Modulus of Rigidity: Definition, Formula, Units and Examples

2023/03/09

‘Modulus of Rigidity is equal to the:
also known as Shear Modulus, Modulus of Rigidity itself defines that when any material i in its natural state, it

io of shear stress with respect to shear strain, It isthe property ofa soli,

offers some resistance against the applied forces. Iisa mensure oa materials resistance to deformation when a

force i applied perpendicular o its surface.

An this Physics article, we vil talk about module of rgiity, how to ealeulate it, and its characteristics

What is Modulus of Rigidity?

A body is said to be rigid if thas a definite shape and size The solid bodies which we see around us are not

perfectly rigid. They ean be compressed, streichei, and bent when applied with an external force.

‘When an external force is applied, the objects get deformed. Some objects tend to regain their original shapes.

‘he internal fore that is acting per unit area ofthe body to regain its original shape is known as Stress. The ratio

of the change in any dimension produced inthe body to the original dimension scaled Strain.

relationship has been established between stress and train which is known as the Modulus of Klasticity. It

is defined as the ratio of stress to the corresponding strain, within the elastic Tim.

Modulus of Elasticity, = DEEE

mesi

it of elasticity is Nay and its dimensions are [META].

There are three types of Modulus of elasticity corresponding to the three types of strain (Longitudinal,
Volumetric, and Shear)

‘Young's Modulus
Bulk Modulus

„, Shear Modulus

‘Modulus of Rigidity types are deseribod below in detail, go through the nots to understand the given concept

Formula of Modulus of Rigidity

2. ‘The formula for Modulus of Rigidit is equal to:
pueda
ann

Where,

G = Modulus of Rigidity

‘The SAL unit of Modulus of Rigidity: Pascal or N/m2
Modulus of Rigidity Dimensional formula: [A*Z-"7"-*)

Shearing Stress = F/A,

Shearing Strain

on EL
‘Which isthe formula for Modulus of Rigiity.

Learn more about the concept of Deformation of solids to relate more to the topic of Modus of Rigidity here

Examples of Modulus of Rigidity
‘The following table represents the modulus of rigidity for diferent materials
Material Value (GPa)
Modul of Rigidity of deal quid o
“Modulus of Rigidity of Wood 6
Modulus of Rigidity of Stel »
‘Modulus of Rigidity of Brass 40
Modus of Rigidity of Rubber 0.0003
Moduls of Rigidity of Tungsten 16%

Also, refer to the concept of Tensile Stress here for a further insight to the related topic,
Characteristics of Modulus of Rigidity

“the following are the characteristics of Modulus of Rigidity

wit

inthe clastic limit it isthe ratio of shear stress to shear strain,
+ Mis related to change inthe shape ofthe body or deformation ofthe body.
‘Modulus o Rigiity ia relevant property of solids

Modus of Rigidity decreases at

temperatures and with inereasing pressure.

3. (One can learn about Longitudinal strain fora further insight to the related topic.

Relation Between Modulus of Rigi

ity and Modulus of Elasticity

“the relationship between Mod

us of Rigidity and Modi

us of Elaticiy can established by the following

Modulus of Hastciy

+
Where,

6 = Modis of Rigi

And = Poissons Ratio

Hence,

Ca

Also learn shout the relationship between Young's modulus and Bulk modulus of Elasticity fora further insight to

the related opi
Relation Between Modulus of Rigidity and Bulk Modulus

‘The relationship between Modulus of Rigidity and Bulk Modulus i given by the formula,

Modulus of Elasticity E

or

K

or

= mm
Young's Modulus of Elasticity

‘Within the elastic limit, the rato of longitudinal stress tothe longi
lost

strain is called Young's Modulus of

Srain jp Young's modulus
AL — y Sms JA
PR Soin © ALIL

4. As shown in the figure, suppose a wire of length ! and cross-section area A suffers an increase in length Al under a
force acting along its length L Then Young's modulus is given by

Longitudinal sees — F/A
Y= Tongitudinal strain — #4

#and Alim then Ye F

fs Modulus of east

cross-section bya uni amount, i

equal tthe Force required to extend a wire of unt length and unit area of

the force required o double the length ofthe wire,

Check Related Articles —

Bulk Modulus of Elasticity

Within the elastic limit, the:

io of normal stress tothe volumetric strain is called the bulk modulus of elasticity.

Consider a body of surface arca A and volume V suppose a force Facts uniformly over the whole surface of the
body and it decreases the volume by AV. The bulk modulus of elasticity is given by

ye = —¡ormalsmess_ = _ Fla.
Volumetric stram ~~ AV /V
Se
ar
The St unit of the bulk modulus is N

‘Shear Modulus
ean be defined as the ratio of tangential stress to shear strain within the elastic init.

‘To understand this, considera rectangular block whose lower face is fixed and a tangential force Fis applied over
its upper free of area A. an equal and apposite force 1 comes into play on its lower fixed face, The two equal and
‘opposite fares form a couplet
block into. paralllopiped by displacing its upper face through distance AAT = Ax. Tet AB = DC = x and ZABA’=
8.

A exerts a torque. As the lower face ofthe block is fixed, the couple shears the

5. Tangential stress = £

Shear stain = 02 lan a

Modulus of rigidity is given by

ne lasers SE Eta
Sr = 6 =

Test

‘Summarized Notes On Modulus Of Rigidity

Check the summarired n

so make short nates of these to prepare q

y
forthe engineering en
à. Stress the internal force applied bythe body in response o the external fore to gain ts shape.
3, The deformation occurred because the forces known as strain
‘Modulus of clastiity establishes a relationship betwoen stress and strain

3
4, The ratio of stress to train within the elastic limits know asthe modulus of ea

So, this al about the Modulus of Rigidity. Get some practice of the same on our free Testbook App: Download
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FAQs on Modulus of Rigidity

Qu What is Modulus of Rigidity and its S.L unit?
“Ansa Modulus of Rigidity is defined as he ratio of shear stress to shear strain acting on the body. The SL. unit of
‘Modulus of Rigidity

Pascal or Newton per meter square

Qu2 What is the Formula of rigidity?

Anse G — FE isthe formula tocalevat the modus of iii

9:3 What is the modulus of of steel?
Ans.3 The modulus of rigidity of steel is 79 GPa.

Q.4 Why the modulus of rigidity is zero for aliquid?

6. Q:5 Which ms nodulus of rigidity?

Ans.5 Diamond y for modulus of rigidity

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