In our daily life, we see that whenever a load
is attached to a thin hanging wire, it elongates
and the load moves downwards (sometimes
through a negligible distance). The amount,by which the wire elongates, depends upon the amount of load and the nature as well as cross – sectional area of the wire material. It has been experimentally found that the cohesive force, between molecules of the hanging wire, offers resistance against the deformation, and the force of resistance increases with the deformation. It
has also been observed that the process of
deformation stops when the force of resistance is equal to the external force (i.e., the load attached).
Sometimes, the force of resistance, offered by the molecules, is less than the external force. In such a case, the deformation continues until failure
Before entering into the details of the effects, following few terms should be clearly understood at this stage.
We have already discussed that whenever a force acts on a body, it undergoes
some deformation and the molecules offer some resistance to the deformation. It will be interesting to know that when the external force is removed, the force of resistance also vanishes ; and the body
springs back to its original position. But it is only possible, if the deformation, caused by the external force, is within a certain limit. Such a limit is called elastic limit. The property of certain materials of
returning back to their original position, after removing the external force, is known as elasticity. A body is said to be perfectly elastic, if it returns back completely to its original shape and size, after the
removal of external forces. If the body does not return back completely to its original shape and size, after the removal of the external force, it is said to be partially elastic. It has been observed that if the force, acting on a body, causes its deformation beyond the elastic limit, the body loses, to some extent, its property of elasticity. If the external force, after causing
deformation beyond the elastic limit, is completely removed, the body will not return back to its original shape and size. There will be some residual deformation to the body, which will remain permanently.
Every material is elastic in nature. That is why, whenever some external system of forces acts on a body, it undergoes some deformation. As the body undergoes deformation, its molecules set up
some resistance to deformation. This resistance per unit area to deformation, is known as stress.
Mathematically stress may be defined as the force per unit area i.e., stress.
σ = P
where P = Load or force acting on the body, and
A = Cross-sectional area of the body.
In S.I. system, the unit of stress is pascal (Pa) which is equal to 1 N/m^2
. In actual practice, we use
bigger units of stress i.e., megapascal (MPa) and gigapascal (GPa), which is equal to N/mm^2or kN/mm^2 respectively.
As already mentioned, whenever a single force (or a system of forces) acts on a body, it undergoes
some deformation. This deformation per unit length is known as strain. Mathematically strain may be
defined as the deformation per unit length. i.e., strain
ε = l
or δl = ε.l
where δl = Change of length of the body, and
l = Original length of the body.
Types of Stresses
Though there are many types of stresses, yet the following two types of stresses are important from the subject point of view:
- Tensile stress
- Compressive stress
When a section is subjected to two equal and opposite pulls and the body tends to increase its length, the stress induced is called tensile stress. The corresponding strain is called tensile strain. As a result of the tensile stress, the *cross-sectional area of the body gets reduced.
When a section is subjected to two equal and opposite pushes and the body tends to shorten its length, as shown in Fig. 2.2, the stress induced is called compressive stress. The corresponding strain is called compressive strain. As a result of the compressive stress, the cross-sectional area of the body gets increased.
We have already discussed that whenever some external system of forces acts on a body, it undergoes some deformation. If the external forces, causing deformation, are removed the body springs back to its original position. It has been found that for a given section there is a limiting value of force up to and within which, the deformation entirely disappears on the removal of force. The value of intensity of stress (or simply stress) corresponding to this limiting force is called elastic limit of the material. Beyond the elastic limit, the material gets into plastic stage and in this stage the deformation does not entirely disappear, on the removal of the force. But as a result of this, there is a residual deformation even after the removal of the force.
It states, “When a material is loaded, within its elastic limit, the stress is proportional to the strain.” Mathematically,Stress
Strain = E = Constant
It may be noted that Hooke’s Law equally holds good for tension as well as compression.
Since the volume of the body remains constant, therefore an increase in the length will automatically
reduce the cross-sectional area of the body. Similarly a decrease in the length will automatically increase
the cross-sectional area of the body.
As a matter of fact, there is a relationship between the increase (or decrease) in length of the body and
decrease (or increase) in the cross-sectional area of the body. This relation will be discussed in Art. 6.6.
** Named after Robert Hooke, who first established it by experiments in 1678. While making tensile
tests on a metallic bar, he took enough precautions, to ensure that the force is applied axially and the bending of the bar is prevented. He assumed that during tension, all the longitudinal fibres of the bar have the same elongation. All the cross-sections of the bar, which were originally plane, remain so even after extension.