- It is the resistive force per unit area.
- Stress = (Applied Load, P)/(Cross-sectional area, A)
- Unit- Newton per Sq. meter
- It is the ratio of change in the configuration, within the elastic limit, of a body to its original configuration is called Strain.
- It is a dimensionless quantity.
- Longitudinal/ Tensile/ Linear Strain
- Shear Strain
- Volumetric Strain
- The ratio of the change in length to the original length (within elastic limit).
L. Strain- ΔL/L
Where ‘ΔL’ is the change in length
& ‘L’ is the original length
- It is a relative displacement between two layers.
Shear Strain= tanθ≈ θ
Bulk or Volumetric Strain
- The ratio of change in volume to the original volume (within elastic limit).
Where ‘ΔV’ is the change in volume
& ‘V’ is the original volume
Read More: Hydrostatics Definition and Laws
- Maximum unit stress to which a material can be subjected and is able to return to its original form after the removal of strength.
Within the elastic limit, stress is proportional to Strain.
E = (Stress)/(Strain), E is Proportionality Constant called Young’s Modulus of Elasticity.
Within the elastic limit, the extension of an elastic body is directly proportional to the force producing it.
- The Ratio of maximum load which a specimen sustains to its original area of cross-section.
- Unit stress at which deformation first increases, without any increase in the applied load; and it is always above the proportional limit.
- The highest unit stress it can sustain before rupturing.
- Ability to resist deformation under stress.
The factor of Safety (FOS)
- The ratio of failure stress to the allowable stress (of the material).
For ductile Materials
- FOS = Ratio of Syt to σ; where Syt is yield strength of a material
- For brittle Materials
- FOS = Ratio of Sut to σ; where Sut is yield strength of a material
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Elasticity and Elasticity Types
Modulus of Elasticity Definition
- The ratio of the Stress to the Strain, within the elastic limit (Hooke’s Law), is a constant, called Modulus of Elasticity or Coefficient of Elasticity.
Modulus of Elasticity Types
- Young’s Modulus of Elasticity (E)
- Shear Modulus or Modulus of Rigidity (G)
- Bulk Modulus of Elasticity (K)
Young’s Modulus of Elasticity (E)
- It is the ratio of Longitudinal Stress to the Longitudinal Strain, within the elastic limit.
E= L. Stress/L. Strain
Modulus of Rigidity (G)
- The ratio of Shear Stress to the Shear Strain, within the elastic limit.
G= Shear Stress/Shear Strain
Bulk Modulus (K)
The ratio of Volumetric Stress to Volumetric Strain, within the elastic limit.
K= Vol. Stress/Vol. Strain
Relationships between E, G, and K
- E= 2G(1+μ)
- E= 3K(1-2μ) Here ‘μ’ is Poisson’s Ratio
- E= (9KG) / (3K+G)
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