The Basics of Stress and Strain

Posted Date: 09-Sep-2012	Category: Education
Author: Gopal Ballav Mishra	Member Level: Silver	Points: 20

The article is about some of the basics of strength of materials, that is useful for students preparing for engineering entrances as well as those pursuing it. Stress,strain, Modulus of elasticity have been discussed below along with their formulas.

Stress

It can be defined as a measure of the internal resistance provided by a material when a load is applied. For compressive or tensile loading the stress is designated s and is defined as:

stress (s) = load (w)/ Area (a)

There are 3 main types of stress -
1) Tensile stress
2) Compressive stress
3) Shear stress

--Tensile stress occurs in a material, when a force applied tries to increase it's length.
--Compressive stress occurs in a material when a force applied tries to decrease it's length.

--Shear stress is a measure of the resistance provided by a material to an applied shear load.
Shear stress is defined by :

Shear stress (t) = Shear load (w) / Area resisting shear (a)

Ultimate strength of a material

The strength of a material can be measured as the stress it can withstand during work. The ultimate strength is the stress measured at the failure of a component but this is not normally used for design as we have to consider safety factors as well.

The normal way to define a safety factor is :

safety factor = ultimate stress/ permissible stress

where, ultimate stress - stress at failure

Strain

Strain is defined as the deformation produced on a component when an external load is applied. Usually the direction in which the strain occurs is perpendicular to the direction of the stress applied.
For tensile and compressive loads:

strain (e) = increase in length (x) / original length (l)

Strain is dimensionless, i.e. it has no unit.

Units of stress and strain

- The basic unit for stress is Pascal (Pa), which is equal to kg/m2.
- As we have already discussed, strain doesn't have a unit.

Modulus of Elasticity

If the strain produced in a component is "elastic" ( i.e strain is directly proportional to stress applied ; as the stress increases the strain also increases linearly) , then Hooke's law can be used to
define the process.

Young's Modulus (E) = Stress/Strain

Young's modulus also known in other words as modulus of elasticity or stiffness, is a measure of how much strain develops due to an applied stress. As strain is a dimensionless quantity , Young's modulus has the same units as that of stress.

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The Basics of Stress and Strain

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