Class 11 Mechanical Properties Of Solids

  March 23, 2023    

Mechanical Properties of Solids

 

# Elasticity

Property of body by virtue of which, it tends to regain its original size and shape, when applied force is removed is known as Elasticity.

# Plasticity

Object have no tendency to regain their shape and got their permanent shape, such substance is called "plastic" and property is called Plasticity.

# Stress

Restoring force per unit area set up inside the body is called stress and is measured by the magnitude of force acting on unit area of the body in equilibrium.

 

Stress = Restoring Force / Area 

 

                                                                                          Unit= N/m2, pa (Pascal), Kg m-1 sec-2

 

NOTE: Pressure is always normal to area but on other side stress can be Normal, Longitudinal and Tangential. Also, Pressure is always compressive in nature and on other side stress may be compressive or tensile in nature.

# Type of stress

1)    1) Longitudinal/ Normal Stress

a)      a)Tensile Stress                                                                         

              Tensile Stress = F⊥/A                                                            

 

b)     b) Compressive Stress

               Compressive Stress = F⊥/A

 

2)   2) Shear/ Tangential stress

 

        Shear/Tangential Stress = FTang/A

 

 3) Volumetric/ Bulk/ Hydraulic Stress

             Bulk Stress= F⊥/A= △P

# Strain

Strain is defined as change in configuration divided by original configuration.

=Change in configuration/Original configuration

àIt is dimensionless or unit less.

# Type of strain

1)   1) Longitudinal strain

             =△L/L

2)   2) Shear strain

             =△x/L

3)   3) Volumetric/ Bulk/ Hydraulic strain

             =△V/V

 

# Hooke’s law

It States that, with in elastic limit, the stress developed in a body is proportional to strain produced in body due to stress.

Stress ∝ Strain

Stress= (Modulus of elasticity) (Strain)

àModulus of elasticity is a constant depends upon type of object or material.

# Type of Modulus of Elasticity

1)     1) Young’s Modulus (Y)

 


Y=Longitudinal stress/Longitudinal strain=F⊥L/A△L

Unit= Nm-2/Pa

 

NOTE: Y is independent of size, shape, only depends upon nature and material.

NOTE: Generally, as temperature increases, Y decrease.

2)    2)  Modulus of rigidity (ɳ)

 


                                     ɳ=Shearing stress/Shearing strain= (FTang)( ϕ)/A          [tanϕ=ϕ=△x/L]

àOnly define for solids, for liquid and gas it is zero.

3)    3)  Bulk modulus (K)/(β)

 


                                                              K=  -dP/dV*(V)                [  à Slope of P-V Graph]

 

# Compressibility (c)

C=1/Bulk Modulus[K]

 

# Poisson’s ratio (σ)



σ=Lateral strain/longitudinal strain= - △D(L)/△L(D)

àIt is dimensionless.

 

# Stress-Strain Curve




 Elastic Limit: It is the maximum stress on which removal, the bodies regain their original dimension.

2)     Yield Limit: At this point wire begins to flow like viscous fluid.

3)     Ultimate/Breaking Point: At this point wire is about to break or get broken. The stress at this point is called breaking/tensile strength of that wire.

NOTE: Length of graph decides the nature of object, whether it is ductile or brittle, if plastic range is relatively high it is ductile otherwise brittle.

 

# Elastic Potential Energy

 

△U=  Stress* Strain* Volume/2

 

# Depression at the Middle of Beam


                  = WL3/4Ybd3