Stresses

Stress being generated

Stress is the property by which a body tends to resist the changes in its dimension when an external force is applied on a body. It is usually denoted by σ(sigma). 

Reason:

Stress traces its origin from the molecular and atomic level , i . e, the microscopic level. When a force is applied under elastic limit, work is done in order to overcome the molecular forces of attraction and this work is stored in the form of elastic potential energy. This give rise to opposing forces which tries to resist the externally applied forces. When the forces are removed the distorted lattice of molecules regains its shape, depending upon the magnitude of external force and the property of material. If the force, however small it may be, exceeds the elastic limit of the body then the original shape of the body is not regained and vice versa.

Stresses are forces which are confined inside the geometry of the body and no such devices exist till date which could measure theses confined forces inside the body. So to derive its magnitude, external force is taken into account.

Expression

σ=F (Applied Force) /A (Effected Area)   Newton/units²

Types

Tensile Stress

Tensile forces resulting elongation

When the externally applied load tends to increase the distance between any two cross-sectional layers of the body, then the forces are said to be tensile in nature. In other words, when the body elongates then the forces are tensile.

Mathematically:

Let,

∆L represents change in length.

L2=Final length

L1=Original Length

∆L=L2-L1>0         …forces are tensile in nature.

Compressive Stress

Compressive forces resulting contraction

When the externally applied forces then the reduce the distance between any two cross-sectional layers of the body, then the forces are compressive in nature.

Mathematically:

Let,

∆L represents change in length.

L2=Final length

L1=Original Length

∆L=L2-L1<0          …forces are compressive in nature.

Shear Stress

Consider the following:

Movement of upper free surface due to traction

A cuboid of unit length with its plane ABGH fixed with the plane. Initially the plane ADEH and BCFG are perpendicular to the plane below them. When tractional forces are applied on the upper surface of the cube, the cube gets deformed an the plane ADEH makes an angle Φ with the surface below. Then shear stress(denoted by 𝛕) is defined by,

 𝛕=F(traction force)/ Φ