## What is meant by the system of forces?

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

A body can be under the action of a single force or multiple force systems. For instance, in structures, a beam or a truss member can be under the action of a single force, called a point load, or under a multiple force system such as distributed loads.

## Various systems of forces

There are different kinds of systems of forces that act on a member. These systems of forces induce different behaviors in the members. All these forces are represented by a vector, which is a quantity that has both magnitudes and direction. A force vector has an arrow that points towards the direction of application of the force. Force has a unit of Newton, N.

The various types of force systems acting on a body are described below:

### Coplanar force system

When all the force systems acting on a body, lie on the same plane of the body, the force system is termed to be a coplanar force system. In this kind of force system, all the forces may act at the centroid of the body or may act away from the centroid of the body.

### Non-coplanar force system

When all the force systems acting on the body, lie in different planes of the body, they are termed as a non-coplanar system of forces.

### Collinear forces

When the individual forces acting on a body, lies along the same line, the system of forces are termed as collinear forces.

### Concurrent forces

In the concurrent force system, the line of action of all the individual forces intersect at a single point. If the line of action of all the individual forces does not intersect at a single point, the system of forces are termed as non-concurrent forces.

## Resultant of force system

Multiple forces acting on a body are difficult to analyze. So, to study the effects induced on the body due to the applied system of forces, the forces are represented by a single force, this force has the same direction and magnitude as the individual forces. The resultant is also known as equivalent force. The effect of the body such as deformation, deflection, and motion can be estimated by studying the resultant force. In most cases, the parallelogram law of forces is considered in calculating the direction and magnitude of the resultant force.

According to the law of the parallelogram of forces, if forces F1 and F2 represent the two sides of a parallelogram, the resultant F3 is given by the diagonal passing through the parallelogram.

If the calculated magnitude of the resultant force is equal to zero, it means the body is in equilibrium and there is no motion of the body.

The force apart from acting at a point may also act at an angle, in such cases, resolution of forces should be done. In three dimensions, a single force acting at a point is resolved into three components, one along X-axis, one along Y-axis, and the other along Z-axis.

## Effect of the resultant force on bodies

A rectangular cross-section of a beam is acted by coplanar forces. To study the effect of these forces, the resultant of the forces must be determined. When the forces are parallel, the resultant is given by a single individual force passing through the centroid of the cross-section. In such a case, the body tends to translate from its mean position or the body undergoes motion. In some cases, the resultant force does not pass through the centroid of the body, this causes the body to rotate about the centroid along with translation. This rotational effect of the body is known as torque.

## Context and Applications

The concept is extensively taught in various applied physics and engineering degree courses. This topic is primarily studied by students of first-year undergraduate curriculums such as bachelor of science. The topic can be fined in various engineering books such as the strength of materials and engineering mechanics.

The concepts of topics are utilized by engineers in the civil engineering domain in various load calculations of trusses and structural members. The concepts are well applied as an algorithm in different computer-aided engineering software like STAAD Pro and ANSYS.

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## Practice Problems

1. Which of the following is true for a collinear force?

1. All the forces act along the same line
2. All the forces lie in the same plane
3. All the forces lie in a different plane
4. None of these

Correct option- a

Explanation: Collinear forces are those forces whose line of action lies along the same line.

2. When is a body said to be under the action of concurrent forces?

1. When all the forces act at a single particle of the body
2. When all the forces act at a single point
3. When all the forces act at a single plane
4. When all the forces act at a different plane

Correct option- b

Explanation: A body can be said to be under the action of concurrent forces if the line of action of all the forces passes through a single point.

3. Which of the following is the unit of force?

1. N
2. Kg
3. n
4. None of these

Correct option- a

Explanation: The unit of force is represented by Newton, symbolically written as N.

4. Which of the following is computer-aided engineering software?

1. ANSYS
2. Master CAM
4. Both a and c

Correct option- d

Explanation: ANSYS and STAAD Pro both are computer-aided engineering software that implements the concepts of system of forces and resultants to calculate complex structural problems.

5. Which of the following is the effect caused to the body when the resultant passes through the centroid of the cross-section?

1. Rotation
2. Rotation and translation
3. Translation only
4. None of these

Correct option- c

Explanation: When the resultant of the force passes through the centroid of the body, it causes the body to undergo translation only.

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### System of forces

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