1920103 – Engineering Physics UNIT I - PROPERTIES OF MATTER
Elasticity – Hooke’s law-Stress-strain diagram and its uses –Poisson ratio-factors affecting
elastic modulus and tensile strength – twisting couple - torsion pendulum: theory and
experiment (regular body) - bending of beams - bending moment – cantilever: theory and
experiment – uniform and non-uniform bending: theory and experiment - I-shaped girders.
INTRODUCTION: Elasticity is the property by which a body resists change in its size or shape
when an external force is acting on it and returns to the original state after the removal of the deforming
force.
CLASSFICATION OF ELASTIC MATERIALS `
Elastic materials are classified into two types:
➢ Perfectly elastic
➢ Plastic
Materials which recover their original state after the removal of the deforming force are called
perfectly elastic materials. Materials which do not recover their original state even after the removal
of deforming force are called as plastic materials. A material which does not undergo any relative
displacement of its parts when an external force acts on it, however large it may be, is called a perfectly
rigid material.
No substance is perfectly elastic or perfectly plastic, since every substance tends to regain its
equilibrium condition at least partially. A quartz fiber which recovers most of its original state after a
large deforming force is removed can be considered as perfectly elastic body. But a perfectly plastic
body like putty can recover its original state only if the deforming force applied is very small.
STRESS: It is defined as the restoring force per unit area which brings back the body to its original
value from the deformed state.
𝐷𝑒𝑓𝑜𝑟𝑚𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒
𝑆𝑡𝑟𝑒𝑠𝑠 = Unit of Stress is N/m2 (or) Pascal.
𝐴𝑟𝑒𝑎
TYPES OF STRESS
a. Normal Stress: When the force is applied perpendicular to the surface of the body, then the stress
applied is normal Stress.
b. Tangential Stress: When the force is applied along the surface of the body, then the stress applied
is called as tangential stress. The tangential stress is also called as Shearing Stress.
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,1920103 – Engineering Physics UNIT I - PROPERTIES OF MATTER
STRAIN: Strain is defined as the change in dimension (fractional deformation) produced by the
external force of the body. It can also be defined as the ratio of the change in dimension to the original
dimension.
TYPES OF STRAIN
a) LONGITUDINAL OR TENSILE STRAIN
It is defined as the ratio between the changes in length to the original length without
any change in its shape, after the removal of the external forces. If the original length
of the body is ‘L’ and the change in length due to applied force is ‘l’, Longitudinal
𝑙
strain = 𝐿
b) SHEARING STRAIN
It is defined as the angular deformation produced on the body due to the
application of external tangential forces on it. Let ABCD be a body with its
CD fixed as shown in the figure. A tangential force is applied on the upper
surface AB of the body. Therefore, the body shears to angle and it goes to a
new position. This angle measured in radians is called Shearing Strain.
Shearing strain is defined as the ratio of the relative displacement between
the two layers in the direction of the stress, to the distance measured
perpendicular to the layers.
𝐴𝐴′ 𝑙
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑎𝑖𝑛 (𝜃) = =
𝐴𝐹 𝐿
c) VOLUMETRIC STRAIN
It is defined as the ratio between the changes in volume to the original
volume without any change in its shape. When forces are applied
normal to the surface of the body of volume ‘V’, it undergoes a change
𝑣
in volume ‘v’, Volumetric Strain = = 𝑉
HOOKE’S LAW
Robert Hooke, in 1679, proposed a relation between stress and strain. The maximum value of the
stress within which a body completely regains its original condition of shape and size when the
deforming forces are removed is known as the elastic limit.
Hooke’s law states that within the elastic limit, the ratio of the stress to the strain is constant. This
constant is called the modulus of elasticity of the material.
Stress α strain
Stress = a constant X Strain
= Constant
The constant is a proportionality constant which is known as modulus of elasticity.
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, 1920103 – Engineering Physics UNIT I - PROPERTIES OF MATTER
TYPES OF MODULI OF ELASTICITY
There are three moduli of elasticity:
• Young’ modulus (Y)
• Bulk modulus (K)
• Rigidity modulus (n)
(i) YOUNG'S MODULUS OF ELASTICITY(Y):
Within the elastic limit, the ratio of longitudinal stress to longitudinal strain is called the young's
modulus of elasticity.
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠
𝑌𝑜𝑢𝑛𝑔′ 𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 (𝑌) =
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
𝐹 ⁄𝐴
𝑌𝑜𝑢𝑛𝑔′ 𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝑌 = 𝐿 ⁄𝑙
𝐹𝑙
𝑌=
𝐿𝐴
(ii)RIGIDITY MODULUS OF ELASTICITY(n):
Within the elastic limit, the ratio of the shearing stress to shearing strain is called rigidity modulus.
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠
𝑅𝑖𝑔𝑖𝑑𝑖𝑡𝑦 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 (𝑛) = 𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑎𝑖𝑛
Consider a rectangular block fixed at its lower face EFGH.A
force F is applied tangentially on its upper face ABCD, A force
of reaction of the same magnitude F acts on the lower face EFGH
in the opposite direction. These two equal and opposite forces
constitute a couple. Due to this couple, the body gets deformed
and its shape changes. All the four vertical sides are rotated
through an angle θ. This angle θ is known as the shearing strain.
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒 𝐹
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠 = =
𝐴𝑟𝑒𝑎 𝐴
3
Elasticity – Hooke’s law-Stress-strain diagram and its uses –Poisson ratio-factors affecting
elastic modulus and tensile strength – twisting couple - torsion pendulum: theory and
experiment (regular body) - bending of beams - bending moment – cantilever: theory and
experiment – uniform and non-uniform bending: theory and experiment - I-shaped girders.
INTRODUCTION: Elasticity is the property by which a body resists change in its size or shape
when an external force is acting on it and returns to the original state after the removal of the deforming
force.
CLASSFICATION OF ELASTIC MATERIALS `
Elastic materials are classified into two types:
➢ Perfectly elastic
➢ Plastic
Materials which recover their original state after the removal of the deforming force are called
perfectly elastic materials. Materials which do not recover their original state even after the removal
of deforming force are called as plastic materials. A material which does not undergo any relative
displacement of its parts when an external force acts on it, however large it may be, is called a perfectly
rigid material.
No substance is perfectly elastic or perfectly plastic, since every substance tends to regain its
equilibrium condition at least partially. A quartz fiber which recovers most of its original state after a
large deforming force is removed can be considered as perfectly elastic body. But a perfectly plastic
body like putty can recover its original state only if the deforming force applied is very small.
STRESS: It is defined as the restoring force per unit area which brings back the body to its original
value from the deformed state.
𝐷𝑒𝑓𝑜𝑟𝑚𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒
𝑆𝑡𝑟𝑒𝑠𝑠 = Unit of Stress is N/m2 (or) Pascal.
𝐴𝑟𝑒𝑎
TYPES OF STRESS
a. Normal Stress: When the force is applied perpendicular to the surface of the body, then the stress
applied is normal Stress.
b. Tangential Stress: When the force is applied along the surface of the body, then the stress applied
is called as tangential stress. The tangential stress is also called as Shearing Stress.
1
,1920103 – Engineering Physics UNIT I - PROPERTIES OF MATTER
STRAIN: Strain is defined as the change in dimension (fractional deformation) produced by the
external force of the body. It can also be defined as the ratio of the change in dimension to the original
dimension.
TYPES OF STRAIN
a) LONGITUDINAL OR TENSILE STRAIN
It is defined as the ratio between the changes in length to the original length without
any change in its shape, after the removal of the external forces. If the original length
of the body is ‘L’ and the change in length due to applied force is ‘l’, Longitudinal
𝑙
strain = 𝐿
b) SHEARING STRAIN
It is defined as the angular deformation produced on the body due to the
application of external tangential forces on it. Let ABCD be a body with its
CD fixed as shown in the figure. A tangential force is applied on the upper
surface AB of the body. Therefore, the body shears to angle and it goes to a
new position. This angle measured in radians is called Shearing Strain.
Shearing strain is defined as the ratio of the relative displacement between
the two layers in the direction of the stress, to the distance measured
perpendicular to the layers.
𝐴𝐴′ 𝑙
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑎𝑖𝑛 (𝜃) = =
𝐴𝐹 𝐿
c) VOLUMETRIC STRAIN
It is defined as the ratio between the changes in volume to the original
volume without any change in its shape. When forces are applied
normal to the surface of the body of volume ‘V’, it undergoes a change
𝑣
in volume ‘v’, Volumetric Strain = = 𝑉
HOOKE’S LAW
Robert Hooke, in 1679, proposed a relation between stress and strain. The maximum value of the
stress within which a body completely regains its original condition of shape and size when the
deforming forces are removed is known as the elastic limit.
Hooke’s law states that within the elastic limit, the ratio of the stress to the strain is constant. This
constant is called the modulus of elasticity of the material.
Stress α strain
Stress = a constant X Strain
= Constant
The constant is a proportionality constant which is known as modulus of elasticity.
2
, 1920103 – Engineering Physics UNIT I - PROPERTIES OF MATTER
TYPES OF MODULI OF ELASTICITY
There are three moduli of elasticity:
• Young’ modulus (Y)
• Bulk modulus (K)
• Rigidity modulus (n)
(i) YOUNG'S MODULUS OF ELASTICITY(Y):
Within the elastic limit, the ratio of longitudinal stress to longitudinal strain is called the young's
modulus of elasticity.
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠
𝑌𝑜𝑢𝑛𝑔′ 𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 (𝑌) =
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
𝐹 ⁄𝐴
𝑌𝑜𝑢𝑛𝑔′ 𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝑌 = 𝐿 ⁄𝑙
𝐹𝑙
𝑌=
𝐿𝐴
(ii)RIGIDITY MODULUS OF ELASTICITY(n):
Within the elastic limit, the ratio of the shearing stress to shearing strain is called rigidity modulus.
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑒𝑠𝑠
𝑅𝑖𝑔𝑖𝑑𝑖𝑡𝑦 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 (𝑛) = 𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑆𝑡𝑟𝑎𝑖𝑛
Consider a rectangular block fixed at its lower face EFGH.A
force F is applied tangentially on its upper face ABCD, A force
of reaction of the same magnitude F acts on the lower face EFGH
in the opposite direction. These two equal and opposite forces
constitute a couple. Due to this couple, the body gets deformed
and its shape changes. All the four vertical sides are rotated
through an angle θ. This angle θ is known as the shearing strain.
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒 𝐹
𝑆ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠 = =
𝐴𝑟𝑒𝑎 𝐴
3
