Strength of Materials

 Strength of materials, also known as mechanics of materials, is focused on materials under load.

Stress is defined as the  internal forces that resist external forces when applied in a particular body. The mathematical expression for stress (and expressed as “sigma”) is

F=Force Acting on the Body in Newtons.
A= Area that force is acting meter²
It is expressed in terms of pascal Pa or N/m² also.
Note that 1MPa=1 N/mm²

 Strain:

When a force is applied to a body, due to its elastic property it will deform. So, Strain is defined as the ratio of deformation per unit length or area. The mathematical expression for Strain (and expressed by Greek letter “Epsilon”) is

Here, dl is the change in length when the load is applied and l is the original length of the body.

Tensile stress:

When two equal and opposite axial pulls are subjected to a body, then the body will resist those forces, such stress are called Tensile Stress.

Tensile Strain:

When two equal and opposite axial pulls are subjected on a body, then the body gets deform and results in a change in the length. Such strain is called the Tensile Strain.

After applying the load, the body is stretched or its length is increased by “dl” where “dl” is the change in length

Change in Length (dl)= Final Length - Initial Length

The ratio of Change in Length (dl) to Original Length (l) is called Longitudinal Strain and it is positive for tensile loading.

It should be noted that the dimension along the load is increased by “dl” and the dimension perpendicular to the load is decreased by “dw” in case if tensile loading.

Change in Width or Radius (dl or dr)= Final Width or Radius - Initial Width or Radius

The ratio of Change in Width/Radius (dw or dr) to Original Width/Radius (w or r) is called Lateral Strain and it is negative for tensile loading.

It must be noted that Strain has no unit or it is unitless.