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Difference and relationship between stress and strain

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Stress

It is defined as the force applied on unit area to produce change in the shape,volume or length of a body.Mathematically it is expressed as:

stress formula

The SI unit of stress (σ) is newton per square meter (Nm-2),which is given the name pascal  (pa).

Stress may cause a change in length,volume and shape.

Tensile stresstensile stress

When a stress  changes the length,it is called tensile stress.

Compressional stress

When a stress changes its volume, it is called compressional stress.

Shear stress

When stress changes the shape, it is called shear stress.

Strain

Strain is a measure of the deformation of a solid when stress is applied to it.In the case of deformation in one dimensional strain is defined as the frictional change in length.If Δl is the change in length and l is the original length,then strain is given by:

strain formula

Since strain is ratio of lengths,it is dimensionless,and therefore,has no units.

Tensile strain

If strain is ε is due to tensile stress σ,it is called tensile strain.

tensile strain formula

Compressive strain:

If strain is produced as a result of compressive stress,it is called compressive strain.

Volumetric strain

When the applied stress changes the volume,the change in volume per unit volume is known as volumetric strain.

volumetric strain formula

Shear strain

When the opposite faces of a rigid cube are subjected to shear stress.

shear strain formula

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