Mechanics of solids-Part-I : Mechanics of solids-Part-I By R.Buvana
Mechanics of solids-Part-I : Mechanics of solids-Part-I Interatomic and intermolecular forces
Solids
Elastic behavior of solids
Stress and strain
Hook’s law
Stress Vs. Strain graph
Modulus of elasticity
Application of elasticity
Interatomic and intermolecular forces : Interatomic and intermolecular forces The force which is responsible to hold together the atoms or molecules of a matter is called interatomic or intermolecular force.
The interatomic force is equal to the negative gradient of the corresponding potential energy function
F=-dU(r)/dr
It has been found that the intermolecular force of attraction is inversely proportional to the seventh power of the distance between the molecules.
Conti… : Conti… Fa=-A/r7 where A is constant
Fr=B/r? fr is repulsive force
The net force acting on a molecule is given by F=-A/r7 +B/r?.There is definite distance ro between the molecules at which F=0 at r=ro A/r7=B/r? or ro=(B/A)½.
At this stage the molecules are in a state of stable equilibrium.
Solids : Solids The materials having a definite shape and volume are known as solids. Solids are classified into two categories namely crystalline solids and amorphous solids.
Crystalline solids-Quartz,mica,sugar etc.
Amorphous solids-glass, rubber,plastics etc.
Elastic behaviour of solids : Elastic behaviour of solids Elasticity- The property of a solid body by virtue of which it regains its original configuration when the external deforming force acting on it is removed is called elasticity.
Plasticity –The property of the material body by virtue of which it does not regain its original configuration when the external force acting on it is removed is called plasticity.
Stress : Stress The restoring force per unit area of the body is called stress.
Stress=F/A.
In SI ,the unit of stress is N/m²orNm².
The unit of stress is also a pascal.
Types of stress
1.Normal stress and 2.Tangential stress
Strain : Strain The ratio of the change in the configuration to the original configuration of the body is called strain. It has no unit.
Types if strain.
1.Longitudinal strain
2.Volume strain
3.Shear strain
Types of materials : Types of materials 1.Ductile materials-The materials for which a large amount of plastic deformation takes place between the elastic limit and the fracture point are known as ductile materials.
2.Brittle materials-The materials for which a small amount of plastic deformation takes place between the elastic limit and the fracture point are known as brittle materials. In some of the materials like rubber, the stress-strain curves are different for increasing stress and decreasing stress.
Hooke’s Law and Modulus of Elasticity : Hooke’s Law and Modulus of Elasticity According to this law, stress is directly proportional to the strain.
Stress=constant x strain
Stress/strain=constant.
This constant is called modulus of elasticity.
Unit of modulus of elasticity is N/m²
Types of Modulus of Elasticity : Types of Modulus of Elasticity 1.Young’s modulus of elasticity(Y)
2.Bulk modulus of elasticity(K)
3.Modulus of rigidity(?)
Young’s modulus of elasticity(y)-It is defined as the ratio of the tensile stress to the longitudinal strain.Y=F/A/dL/L
Bulk modulus of elasticity(K)-It is defined as the ratio of the bulk stress to the volume strain.K=F/A/dv/v.
Modulus of rigidity(?)-It is defined as the ratio of the tangential stress to the shear strain.?=F/A/?
Conti… : Conti… Tan?=dx/L.Since ? is very small, so tan?=?.?=dx/L.
?=F/A/dx/L.
Compressibility(B)-The reciprocal of bulk modulus of elasticity is called compressibility.B=1/K.
Poisson’s ratio : Poisson’s ratio The ratio of change in diameter( dD) to the original diameter (D) is called lateral strain. The ratio if change in length(dL) to the original length(L) is called longitudinal strain.
The ratio of lateral strain to the longitudinal strain is called Poisson’s ratio
s=-dD/D/dL/L
Negative sign indicates that the diameter of the bar decreases when it is stretched.
Applications of Elasticity : Applications of Elasticity 1.Bridges are declared unsafe after long use.
2.A metallic part of a machinery will get permanently deformed if subjected to a stress beyond the elastic limit.
3.A crane is used for lifting and moving heavy loads from one place to another.
4.To estimate the maximum height of a mountain.
5.A hollow shaft is stronger than the solid shaft made of same material.
Home work questions : Home work questions 1.Explain why steel is more elastic than rubber?
2.Why are the bridges and dams declared unsafe after long use?
3.Do liquids possess rigidity?
4.Why do we prefer steel to copper in the manufacture of spring?
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