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Mod-3 (Elasticity)

# Mod-3 (Elasticity) - MODULE 3 Elasticity Elasticity It is...

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MODULE – 3: Elasticity Elasticity: It is the property by which a body offers resistance to external forces tending to change its volume or shape or both and it will regain its original form when the deforming force is removed. Perfectly Rigid body: A body is said to be perfectly rigid when it is impossible to alter its shape by the application of force. But no body is perfectly rigid. Perfectly Elastic Body: When a body is acted upon by a force or a system of forces, it undergoes changes in its shape or size. If the body recovers its original dimension completely after withdrawing of the applied force, then the body is said to be perfectly elastic but no body is perfectly elastic. Stress: When a force is applied on a body, internal forces are generated. These internal forces react in a direction opposite to the forces applied and tend to bring the body to its original state; the restoring force per unit area of the body is known as stress. Area Force Stress = If the force is inclined to the surface, then its component, perpendicular to the surface, measured per unit area, is called normal stress and the component acting along the surface, per unit area, is called tangential or shearing stress . (i) Normal Stress: Restoring force per unit area perpendicular to the surface as called normal stress. (ii) Tangential Stress: Restoring force per unit area parallel to the surface is called tangential stress. Strain: The change produced in the dimensions of a body under a system of forces or couples in equilibrium, is called strain , and is measured by the change per unit length [linear or longitudinal strain], per unit volume [volume strain], or the angular deformation [shear strain or simply shear] according to the change that takes place in length, volume or shape of the body. Therefore, we have three kinds of strain: (i) Longitudinal strain (ii) Volume strain and (iii) Shearing strain (i) Longitudinal strain: The change in length per unit length is called longitudinal strain. That is if L is the original length and l is the change in length, then L l length original length in change strain = = al Longitudin (ii) Volume strain: The change in volume per unit volume is called volume strain. That is if V is the original volume and v is the change in volume, then V v volume original volume in change strain Volume = = 1

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(iii) Shear strain: A change in shape without change in volume is known as shear strain. A shear deformation is shown in adjacent figure. The blacked outline ABCD represents an unstressed block of material. The dashed area A B C D ′ ′ shows the same block under shear stress. A surface AB is fixed and a force F is applied parallel to the surface CD, so that the body is deformed by an angle θ . The shear strain is defined as the ratio of the displacement DD x ′ = of corner D to the transverse dimension AD h = : tan x Shear strain h θ = = In real-life situations, x is nearly always much smaller than h, tan θ is very nearly equal to θ (in radians), and the strain is simply the angle θ measured in radians.
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