- The video explains the different meanings of the word "beam" in physics and mechanical engineering
- It focuses on the stress and strain experienced by a beam under a force
- Stress is defined as force per unit cross-sectional area and increases with an increase in force
- The SI unit of stress is Newton per meter squared (Pascal)
- Strain is defined as the change in dimensions per unit of original dimensions and can be measured in terms of length, area, or volume
- The video concludes by mentioning that the next video will cover the types of stress and strain.

What is Stress? What is Strain? 
 Watch the video to find all about stress and strain - Mechanical Properties of Solids Class 11

In this video, we will learn: 
0:00 Introduction
1:21 What is Stress?
2:23 SI unit of stress
2:51 What is Strain?
3:17 Strain example (change in length)
3:57 Strain example (change in area and volume)

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#Elasticity #Stress #Strain

There are many different meanings of this word.

It can be thought of as a sequence of photons travelling in a straight line.

In mechanical engineering, a beam is a long piece made of some material.

It can be a wooden beam, a steel beam or a concrete beam.

We are of course interested in this kind of beam.

Let's draw a rough general sketch of a rectangular beam.

Okay, say we apply a downward force F on the surface area of a beam.

Here, the force is trying to compress the beam from the top.

Due to this, the beam will experience some stress.

It is just an uncomfortable state experienced by the object, which is the beam in this case.

The atoms inside are little too close than they want to be.

This results in inter-atomic and inter-molecular forces.

And if the applied force F is within the elastic limits of the material, these forces bring back the object to its initial state when the applied force is removed.

Mathematically, stress is defined as force per unit cross-sectional area.

So it is F over A, where A is this cross-sectional area.

What if I increase the force from F Newton to say F plus 10 Newton on this area A?

Intuitively, we know that if we push it with a greater force from above, then the beam will experience more stress.

Mathematically, this new stress will be F plus 10 over A.

The numerator increased and the denominator remained the same.

It means that this ratio is greater than this 1.

So if we increase the force, the stress will also increase.

Next, what will happen if I increase the surface area from a metre squared to say a plus 10 metre squared?

Will the stress increase in this case too?

The stress will decrease in this case because the denominator increases with the numerator remaining constant.

The SI unit of force is Newton denoted by N and that of area is meter squared.

So the SI unit of stress is Newton per meter squared.

However this unit is given a name and it's called Pascal denoted by P-A.

In very simple language, 1 can define it as change in dimensions per unit of original dimensions.

When any object is under stress, it will change 1 or more of its dimensions.

The amount by which the object's dimensions will change will depend on the force applied and the materials the object is made up of.

In our example, L is the length of the beam and it's experiencing some force.

Hence it will deform and its length will change by say, delta L.

Strain is defined as change in length per unit of the original length.

Well the ratio compares the change in length that resulted due to force with the original length of the beam.

Here, strain is calculated in terms of length of the object.

But the length may not be the only quantity changing due to deformation.

We can also find the strain in terms of area and volume.

Let's take an example of a sponge ball of volume V.

When it is compressed, its volume decreases.

So the strain in terms of volume is delta V over V.

Note that Delta V is the change in volume and not the volume of the deformed sphere.

Let's take another example where a thin rubber sheet is stretched equally from the opposite sides with a force F.

And that will result in a change in the area.

So the strain experienced by the rubber sheet is Delta A over A.

Delta A is the change in area of the sheet and A is the original area of the sheet.

So in the next video, We will see the types of stress and strain.


Speaker 0: Do you know what a beam is? There are many different meanings of this word. In physics, we use this word in 2 ways. In optics, we say a beam of light. It can be thought of as a sequence of photons travelling in a straight line.

In mechanical engineering, a beam is a long piece made of some material. It can be a wooden beam, a steel beam or a concrete beam. We are of course interested in this kind of beam. Let's draw a rough general sketch of a rectangular beam. Okay, say we apply a downward force F on the surface area of a beam.

Here, the force is trying to compress the beam from the top. Due to this, the beam will experience some stress. It is just an uncomfortable state experienced by the object, which is the beam in this case. The atoms inside are little too close than they want to be. This results in inter-atomic and inter-molecular forces.

And if the applied force F is within the elastic limits of the material, these forces bring back the object to its initial state when the applied force is removed. Mathematically, stress is defined as force per unit cross-sectional area. So it is F over A, where A is this cross-sectional area. What if I increase the force from F Newton to say F plus 10 Newton on this area A? Intuitively, we know that if we push it with a greater force from above, then the beam will experience more stress.

Mathematically, this new stress will be F plus 10 over A. The numerator increased and the denominator remained the same. It means that this ratio is greater than this 1. So if we increase the force, the stress will also increase. Next, what will happen if I increase the surface area from a metre squared to say a plus 10 metre squared?

Will the stress increase in this case too? The stress will decrease in this case because the denominator increases with the numerator remaining constant. Now what is the SI unit of stress? Any guesses? Stress is force per unit area.

The SI unit of force is Newton denoted by N and that of area is meter squared. So the SI unit of stress is Newton per meter squared. However this unit is given a name and it's called Pascal denoted by P-A. Now we know the basics about stress. What is strain?

In very simple language, 1 can define it as change in dimensions per unit of original dimensions. When any object is under stress, it will change 1 or more of its dimensions. The amount by which the object's dimensions will change will depend on the force applied and the materials the object is made up of. In our example, L is the length of the beam and it's experiencing some force. Hence it will deform and its length will change by say, delta L.

Strain is defined as change in length per unit of the original length. Mathematically, it is delta L over L. So what does this ratio do? Well the ratio compares the change in length that resulted due to force with the original length of the beam. Here, strain is calculated in terms of length of the object.

But the length may not be the only quantity changing due to deformation. We can also find the strain in terms of area and volume. Let's take an example of a sponge ball of volume V. When it is compressed, its volume decreases. So the strain in terms of volume is delta V over V.

Note that Delta V is the change in volume and not the volume of the deformed sphere. Let's take another example where a thin rubber sheet is stretched equally from the opposite sides with a force F. And that will result in a change in the area. So the strain experienced by the rubber sheet is Delta A over A. Delta A is the change in area of the sheet and A is the original area of the sheet.

So in the next video, We will see the types of stress and strain. See you there!

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Stress and Strain | Mechanical Properties of Solids | Don't Memorise