Dimensions of Stress

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Dimensional Formula for Stress

The dimensional formula of Stress is represented as:

[M1 L-1 T-2]

Where,

  • M denotes the mass

  • L denotes the length

  • T denotes the time


What is Stress?

Stress is the external restoring force that acts on per unit area and it is denoted by σ. It is denoted as N/m². It is used to find stress which is applied on any given body when force and area on which it is exerted is given in a problem. 

Therefore, σ = F/A 

σ  is the amount of stress on the object

F is the force that is acting on the object.

A is the cross-sectional area

Or it can also be said that stress is the force applied on an object making it completely to deform. In Physics terminology, we found how the derivation of the stress formula is done. It is known that larger objects can withstand a large amount of forces. By using stress as an alternative to force we are able to use the same yield stress for the same material, it doesn’t matter how large the object is. 

Also, stress and strain are directly related with each other and if one increases, the other automatically increases. And, the more is the stress of the object, the more deformation it experiences.


Derivation of Dimension of Stress   

Stress = Force × [Area]⁻¹ . . . . . (i)

The dimensional formula of area = [M0 L² T0] . . . . (ii)

Since we know, 

Force = M × a = [M] × [M0 L¹ T⁻²]

Therefore, the dimensional formula of force = [M¹ L¹ T⁻²] . . . . (iii)

On substituting equation (ii) and (iii) in equation (i) we get,

Stress = Force × [Area]⁻¹

Or, Stress = [M¹ L¹ T⁻²]  × [M0 L ² T0]⁻¹ = [M¹ L⁻¹ T⁻²]

Therefore, dimensional formula of stress is represented as [M¹ L⁻¹ T⁻²].


Example of a Solved Problem

Question: If an elastic spring is given a force of 1000 N over an area of 0.2 m2. Calculate the amount of stress?

Answer: As we know from the above problem,

F (Force) = 1000 N,

A (Area) = 0.2 m ²

σ = \[\frac{F}{A}\]

= \[\frac{1000N}{0.2}\]

σ =  \[\frac{5000N}{m^2}\]


Types of Stress

1. Normal Stress

When an object is loaded by an axial force, it is called normal stress. Normal stress is represented when axial force is divided by the cross-sectional area. It will occur when an object is placed in compression.

2. Longitudinal Stress

When the length of the body changes its length by the applied normal stress, it is called longitudinal stress.

Longitudinal stress is represented by the division of the deforming force by the area of cross section.

3. Bulk Stress or Volume Stress 

It is the stress in which the body volume changes due to the stress. Normal stress on an object changes its length or volume and the tangential stress leads to change in the shape of the body which is called volume stress. 

Shearing Stress is the force applied tangentially over the plane’s surface area. When the forces being applied to the surface is parallel to it and the stress acting on the surface plots a tangent, it is known as shearing stress.

4. Tensile Stress 

It is the force per unit area and the stress when applied and increases the length of the body because of the force, it is called tensile stress. It is observed when a rod is stretched under motion’s third law. A common example of tensile stress is rubber and stretching is its quantity associated with it.

5. Compression Stress 

It occurs when we apply a tangential force on the body and the shape plus volume of the object change. Compression stress results in a decrease of the length of the object. It is opposite to the tensile stress. 


Importance of Stress

Stress analysis is an important part of applied Physics and it helps in classification of the internal distribution of internal forces in solid objects.

An important part of engineering, stress helps in studying and designing of structures such as structural frames, dams, runners and mechanical parts. It is also important in other regimentation, for instance, in Geology, studying theory like plate tectonics, volcanism and avalanches, and in Biology, it is important to understand the anatomy of living beings.