Stress: Types, Definition, Unit And Dimension, Formula, FAQs

We often use the word stress in our daily conversations. Like when someone is under pressure we say that, don’t take too much stress. It is similar to what we study in physics. Here any body which is under pressure we say that it has some stress. Infact stress and pressure have the same unit and dimension. To change the shape of any object we apply stress in the desired direction. In the image below you can see the man bending the rod by applying the force. 

There are different types of stress depending on how force is being applied. We are going to learn about all of this in this article. 

Table of Contents

• Stress
• Unit and dimension
• Types of stress
• Practice problems
• FAQs

Stress

Stress is defined as the force acting per unit area of a material. Strain is the effect of stress on the body. The force that causes a change in the structure of an object is called a deforming force. When we apply deforming force on an object, it get deforemed. In order to bring the object back to the original shape and size, there will be an opposing force generated inside the object called restoring force. 

According to Newton’s third law, if there is no permanent change in the configuration of the body, the restoring force will be equal in magnitude and opposite in direction to the applied deforming force. So stress is nothing but the measure of this restoring force generated per unit area of the material.

Mathematical formula for stress is, 

We can write it as:

Where, F = Restoring force ()

A = Cross-sectional area ()

= Stress ()

Example: Consider a elastic rod of cross sectional area A on which force is applied on both ends as shown in the picture below. 

Here is the deforming force and is restoring force. So and

Unit and Dimension

• Stress is a tensor quantity. It has a direction but does not follow the laws of vector algebra.
• It is denoted by the greek letter .
• SI Unit: or
• Dimension:

Types of Stress

There are mainly three types of stress as follows:

• Longitudinal/Normal Stress ()
• Shear Stress ()
• Volumetric Stress ()

Practice Problems

Q 1. A rod has a radius of and a length of . A force is compressed along its length.Calculate the stress developed in the rod.

Solution:

Q 2. Find stress in the rod if force is applied from one end with cross sectional area ?

Solution: The rod will start accelerating in the direction of applied force.the stress will decrease along the length of the rod and at the free end the stress will be zero.

Q 3. How do deforming forces and restoring force relate to one another?

Solution: 

If the body is in the absence of plastic behavior,

If the body is having plastic behavior that means the body will not attain its original configuration after the application of deforming force. In that case

Q 4. A given rod is under stress of and the cross section area of the rod is then find the restoring force?

Solution: 

FAQs

Q 1. What is the difference between stress and pressure?
Solution: Stress can be defined as the internal resistive force to the deformation per unit area. Pressure can be defined as the amount of force applied per unit area. Due to stress, the pressure will not be developed. Due to pressure, stress will be developed..

Q 2. What is the effect of deforming force?
Solution: Effect of the deforming force is that it can change the shape, volume or size of the object.

Q 3. How restoring force is generated in the body?
Solution: On the application of deforming force it changes the configuration of the body by changing the normal positions of the molecules or the atoms of the body. As a result internal restoring force comes into play which tends to bring the body back to its original configuration. 

Q 4. Is deforming force and restoring force always equal in magnitude?
Solution: No. Deforming force and restoring force are equal in magnitude only if the body is in the absence of plastic behavior. So if there is any permanent change in the configuration of the body these two forces will not be equal.