# Superposition Principle: Principle of Superposition of Forces

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The **Principle of Superposition** is one of the most important concepts in the Mechanics of Solids. The principle of superposition can be defined as “If two equal and opposite collinear forces are added to removed from the system, there will be no change in the system as well as the position of the body”.

The principle of superposition can also be defined as “If a force system is acting on a body is superimposed with another force system that itself is in equilibrium, then, the effect of both the force systems remains same as that of initial force system”. Let us state and explain the principle of superposition of forces in detail.

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## What is the Principle of Superposition of Forces?

When several charges interact, the total force on a particular charge is the vector sum of the forces exerted on it by all other charges, according to the principle of superposition of forces. Other charges have no effect on the force between two charges.

In other words, it is assumed that the resultant force of an ensemble of forces is the vectorial sum of these forces, implying that the individual forces do not interact with one another except through the entire system.

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## Law of Superposition of Forces

The law of superposition of forces states that the combined effect of a force system acting on a particle or a rigid body is the sum of the effects of individual forces. Consider one body on which three forces P_{1}, P_{2}, and P_{3} are acting simultaneously. These forces create a deformation of the triangle in that body.

Deformation in the body due to P_{1}, P_{2}, and P_{3} is Δ.

Now, apply each force P_{1}, P_{2}, and P_{3}separately and calculate the deformation in the body because of the individual force.

Deformation due to P_{1} = Δ_{1}

Deformation due to P_{2} = Δ_{2}

Deformation due to P_{3} = Δ_{3}

After applying the Principle of Superposition

**Δ = Δ _{1} + Δ_{2} + Δ_{3}**

**Δ= PL/AE**

Overall, deformation of the body is equal to the summation of deformation of the body when subjected to a single force system.

Let us understand the concept of superposition of forces with one more example.

Consider a body with two points, A and B, as shown in the figure. Apply a force of magnitude P at A.

To differ this force system and superimpose this with another force system such that the effect created by force P at location A remains the same.

The new force system will have no additional effect on the body. Therefore, whatever effect is created in the first case also remains the same in the second case.

Now, consider the distance between A and B as ‘d’.

The effect of this force system is similar to that of the first case. All three force systems create the same effect on the body.

All three force systems create the same effect on the body.

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## Application and Limitations of the Principle of Superposition

The Principle of Superposition of forces is mainly used in all types of problems but is effectively used in changing the type of force system without changing the effect of the forces on the body. This principle is widely used in the problem of non-concurrent force systems.

In Engineering Mechanics, it applies to all types of problems. In Strength of Materials, the only limitation is body should behave as an elastic body with small deformations.