1. Elasticity
Yasser Assran
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2. Stress = elastic modulus X strain
Introduction
Elasticity: is the property of solid materials to return to their original shape and size after the forces deforming them have been removed.
Stress: Stress is the external force acting on an object per unit cross sectional area.
Strain: is the change in dimension per unit dimension.
Modules of elasticity: The elastic modulus is defined as the ratio of the stress to the resulting strain.
Stress = elastic modulus X strain
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3. Elastic body
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4. Plastic body
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5. THREE TYPES OF STRESS
Normal (longitudinal) stress: arises from forces that are perpendicular to across-sectional area of the material.
volume stress. If the force acts normally and uniformly from all sides.
Shear (tangential) stress: force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
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6. THREE TYPES OF STRAIN Longitudinal (linear) Strain: ΔL/L
volume strain: ΔV/V
Shear strain: tan θ
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7. Hooke’s Law F = - kx Hook’s law is best explained by the equation:
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8. Y=tensile stress/ tensile strain
Young Modulus
We define the tensile stress as the ratio of the magnitude of the external force F to the cross sectional area A.
the tensile strain in this case is defines as the ratio of the change in length ΔL to the original length Li.
Y=tensile stress/ tensile strain
Y=(F/A)/(ΔL/Li)
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9. S= shear stress/ shear strain
Shear Modulus
We define the shear stress as F/A, the ratio of the tangential to the area of A of the force being sheared.
The shear strain is defined as the ratio ΔX/L, where ΔX is the horizontal distance that the sheared force moves and H is the height of the object.
S= shear stress/ shear strain
S= (F/A)/ (ΔX/L)
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10. B= volume stress/volume strain
Bulk Modulus (B)
The quantity P=F/A is called the pressure. If the pressure on an object changes by an amount ΔP= ΔF/A the object will experience a volume change ΔV.
The volume strain is equal to the change in volume ΔV divided by the initial volume Vi
B= volume stress/volume strain
B=-(ΔF/A)/(Δ V/Vi)
B=- Δ P/(ΔV/Vi)
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11. Young’s modulus Shear modulus Bulk modulus
Under tension and compression
Under shearing
Under hydraulic stress
Strain is
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12. Poisson’s ratio Loaded Unloaded Tension  shrink laterally
Compression  bulge.
Ratio of lateral to axial strain called
Poisson's ratio σ .
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13. WORK DONE IN STRETCHING A WIRE
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14. BEHAVIOUR OF WIRE UNDER STRESS
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15. FEATURES OF STRESS STRAIN CURVE
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16. BEHAVIOUR OF RUBBER UNDER STRESS
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