# Stress Strain Lecture Notes

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Contents

## Definitions

### Stress

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

## Strain and Strain Types

• 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 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

Read More: Fluid Mechanics: Objective Questions

## Elasticity and Elasticity Types

### Modulus of Elasticity

• 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