**Stress Strain**

Topics Discussed:

**Stress Definition**

- It is the resistive force per unit area.
- Stress = (Applied Load, P)/(Cross-sectional area, A)
- Unit- Newton per Sq. meter

**Strain Definition**

- 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.

**Strain Types**

- Longitudinal/ Tensile/ Linear Strain
- Shear Strain
- Volumetric Strain

**Longitudinal 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

**Shear Strain**

- It is a relative displacement between two layers.

Shear Strain= tanθ≈ θ

θ= ΔL/L

**Bulk or Volumetric Strain**

- The ratio of change in volume to the original volume (within elastic limit).

ΔV/V

Where ‘ΔV’ is the change in volume

& ‘V’ is the original volume

**Read More: Hydrostatics Definition and Laws**

**Elastic Limit**

- Maximum unit stress to which a material can be subjected and is able to return to its original form after the removal of strength.

**Hooke’s Law**

Within the elastic limit, stress is proportional to Strain.

E = (Stress)/(Strain), E is Proportionality Constant called Young’s Modulus of Elasticity.

OR

Within the elastic limit, the extension of an elastic body is directly proportional to the force producing it.

**Ultimate Stress**

- The Ratio of maximum load which a specimen sustains to its original area of cross-section.

**Yield Point**

- Unit stress at which deformation first increases, without any increase in the applied load; and it is always above the proportional limit.

**Ultimate Strength**

- The highest unit stress it can sustain before rupturing.

**Stiffness**

- 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 S
_{yt }to σ; where S_{yt}is yield strength of a material - For brittle Materials
- FOS = Ratio of S
_{ut }to σ; where S_{ut}is yield strength of a material

**Read More: Fluid Mechanics: Objective Questions**

**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)

**Read More: Surface Tension & Capillary Action**

**Read More: Strength of Materials Objective Questions**

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