Stress Strain Relation

Stress and Strain

How does a force applied on a body generates stress and know the stress-strain relationship with the help of stress-strain curve!

Stress

In mechanics, stress is defined as force applied per unit area. It is given by

\(\sigma = \frac{F}{A}\)

where,

\(\sigma\) is the stress applied
F is the force applied
A is the area of force application

Stress is expressed as \(N/m^{2}\)

tensile stress

Tensile stress due to force applied

Stress applied to a material can be of two types. They are:

Tensile: It is the force applied per unit area which results in the increase in length (or area) of a body. Objects under tensile stress become thinner and longer.
Compressive: It is the force applied per unit area which results in the decrease in length (or area) of a body. The object under compressive stress becomes thicker and shorter.

Strain

The strain is the amount of deformation experienced by the body in the direction of force applied, divided by initial dimensions of the body. The relation for deformation in terms of length of a solid is given below.

\(\epsilon = \frac{\delta l}{L}\)

where,

\(\epsilon\) is the strain due to stress applied
\(\delta l\) is the change in length
L is the original length of the material.

The strain is a dimensionless quantity as it just defines the relative change in shape.

Depending on stress application, strain experienced in a body can be of two types. They are:

Tensile Strain: It is the change in length (or area) of a body due to the application of tensile stress.
Compressive Strain: It is the change in length (or area) of a body due to application of compressive strain

When we study solids and their mechanical properties, information regarding their elastic properties is most important. These can be obtained by studying the stress – strain relationships, under different loads, in these materials.

Stress-Strain Curve

The stress-strain relationship for a material is given by that material’s stress-strain curve. Under different loads, the stress and corresponding strain values are plotted. An example of a stress-strain curve is given below.
stress strain curve

Stress-Strain Curve

Also explore the terms related to stress-strain – Poisson’s ratio, Hooke’s Law, Young’s Modulus.

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Practise This Question

A bar is subjected to equal and opposite forces as shown in the figure. PQRS is a plane making angle θ with the cross-section of the bar. If the area of cross-section be ‘A’, then what is the tensile stress on PQRS