Longitudinal Strain

Stress and strain are two sides of a coin. A very common example among physics enthusiasts, while they are explaining this topic, is to tell students that the stress being referred to here is not the one that students face in their exams. We will not be using this example because we fully understand that students are capable and smart enough to figure that out on their own. Stress in terms of Physics is the force acting on a unit area of a material. The strain, on the other hand, is just a basic measure that gives us an idea of how much an object has deformed or changed due to the stress applied to it. This is the main idea behind the concept of stress and strain.

Longitudinal strain is a very interesting and simple topic that is very easy to understand. This topic literally guarantees marks as students do not really have to spend a lot of time on the understanding part of it because of its simplicity. Plus questions from the topic keep appearing in class 12 School level examinations and even competitive exams like JEE and NEET. In order to secure these marks which can be obtained by simply understanding the topic, we recommend students to read this article thoroughly and throughout. Only then will they be able to understand the chapter fully and figure out what the concept is about.

Vedantu offers nothing but the best quality articles when it comes to testing preparation. This is the same goal behind this article as well and that is why we plan on giving you the best resource on the topic of longitudinal strain that can be understood with ease at the comfort of your home, school or anywhere. 

Strain is the force inclined to pull or stretch something to an extreme or damaging degree.

When an external force per unit area (stress) is applied to an object, and there is a deformity in its shape. 

The inter-atomic particles inside the body try to regain its original position. While the body exceeds the elastic limit.

Such a condition where the internal restoration force fails to bring the body back to its original shape and this condition is called the strain.

The property of strain is that the elastic strain is irreversible.

SI Unit of Strain

In Mechanics, strain is often said to be “dimensionless” regardless of what system we use as it has no units.

Strain  = Change in length / original length

Δ L/ L  =   \ \[\left [ L^{1}\right ]\]/ \[\left [ L^{1}\right ]\]=   \[\left [ L^{0}\right ]\] = 1

If we use meters/ meters. It will always come as 1.

So,

Unit of Strain

The unit of strain in non-SI units,

Other units of strain = cm/cm or cubits/ cubits will always give 1.

Generally, we identify a number as strain.

We generally use the strain after the number such as 0.012 strain.

The measurement of strain is usually given as the numeric units in (με).

Since the changes in length are usually very small and a typical strain measurement in the English system is given as microinches per inch (i.e., in the order of 10−6

Therefore, the numeric value, which is unitless, will remain the same in any system.

Longitudinal Strain Definition

The longitudinal strain is defined as the ratio of change in length of the material due to the applied force to the original length.

Longitudinal Strain

When stress (external force per unit area) is applied on the body such that this deforming force causes a change in the length alone, and the body exceeds its elastic limit. This condition or strain produced in the body is called the longitudinal strain.

As the name longitudinal strain suggests that we are talking about the length and strain is causing deformity in its shape by elongating its length.

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In Fig.1, a rod of length ‘Lo’ is stretched along the X-axis with enough external force that its length is extended to ‘Δ L’.

Now, the new length of the rod is Lf, which equals Lo + Δ L.

 Δ L is the extended length of the rod.

This has happened due to the strain in the rod.

Longitudinal strain is denoted by a Greek symbol epsilon, ε

So, the formula for the longitudinal strain is given by,

The unit of longitudinal strain is one.

The dimensional formula =\[\left [ L^{0}\right ]\]

Young’s Modulus of Elasticity (γ) 

For a given material there can be different types of modulus of elasticity depending upon the type of stress applied, and the resulting strain produced. One of them is young’s modulus of elasticity. Young’s modulus of elasticity corresponds to the ratio of longitudinal stress to the longitudinal strain within the elastic limit. 

Consider a wire PQ (in  Fig.2) of length L of the radius of cross-section, ‘r’ and uniform cross-sectional area ‘A’ is suspended from a rigid support P. When stretched by a suspended load of ‘mg’ from the other end Q.

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Therefore, a force (perpendicular force) F is applied at its free end. Such that there is an elongation in the body by Δ L.

Young’s modulus or γ = Longitudinal stress/ longitudinal strain…(1)

Where,

Longitudinal stress is the deforming force when applied to the body, the stress is produced in the body causing elongation in its length.

Its formula is the same as the stress which is equal to F/A (Force per unit area)

       Longitudinal stress = \[\frac{F}{A}\] = \[\frac{F}{\Pi r^{2}}\] …. (2)

and, longitudinal strain  =  Δ L/ L..(3)

So,  putting values of (2) and (3)  in (1) 

=  F/πr²/  Δ L/ L 

Longitudinal Strain

• Within the elastic limit, this ratio always remains constant.

• The unit of γ  in SI is N/m² or Pascal (Pa).

• In CGS system = dyne/cm²

• The dimensional formula for γ is \[\left [ M^{1} L^{-1}T^{-2}\right ]\]

Key Point

If the length increases from its natural length, the longitudinal strain is called the tensile strain and if the length decreases from its natural or original length, then it is the compression strain.

Do You Know?

• In a suspension bridge, there is a stretch in the ropes by the load because of which length of rope varies. Hence young’s modulus of elasticity is involved in real life.

Conclusion 

We hope that this article was able to solve all your doubts about the concept of longitudinal strain. The idea behind stress and strain is not all that complex but is very easy to understand and comprehend. We suggest that students go through this article again and again to get a complete idea of what the entire concept is about. Vedantu has been a leader in the world of education because we believe in the power of good and easy to understand resources for students of all ages. It is due to the same reason that we have had so many success stories of students from around the world and across the country as they score well in their exams. This article was written with the same intention. The intention was to offer nothing but the best and the easiest to understand study document that can be studied anywhere by students on any device that they own. Vedantu hopes that we were able to solve all the doubts that you had about the topic.