# Principles of Statics

In this tutorial, you will study about the principles and theories in Statics. Statics is a subtopic of Engineering Mechanics. This tutorial includes the definition of Statics, terms involved in Statics, different types of parameters, their definitions, types and their characteristics.

Contents:

## Statics – Introduction & History

Statics is one of the oldest branches of science prevailing across the world since ages. It is a sub-topic of Mechanics.

Some historical references to Statics are given below:

• The fundamental principles of Statics were used by the Egyptians and Babylonians to encounter the problems occurred in building the famous Pyramids and old temples.
• Earliest articles on this chapter were found written by Archimedes. He formulated the laws of equilibrium of the forces acting on a lever and also some principles in the subject Hydrostatics which are in use today.
• However, the subject saw a debacle after Archimedes and had waited a long period of time until the works of Newton, Varignon and Stevinus to rise again. The modern subject in its present form is derived from the works of these three scientists.
• Definition:
Statics is defined as the subject that deals with the conditions of equilibrium of bodies at rest under the action of several forces.

## Rigid and Non-Rigid Bodies

Statics is most concerned about the rigid and non-rigid bodies and their equilibrium. Physical bodies that one encounters in the design of engineering machines are never absolutely rigid. Although they deform slightly, it is very less in comparison to the size of the body.

• A rigid body is defined as a definite quantity of matter, the parts of which are fixed in position relative to one another. This means that the distance between any two particles remains same with or without the application of load onto the body.
• The physical bodies are not absolutely rigid but deform slightly under the action of loads. If the deformation is minute when compared to its size, then the body is assumed to be a Rigid Body.
• Statics study the analysis of forces acting on a rigid body whereas for the analysis on liquids and gases, Fluid Mechanics is taken into account.
• One such example is the strength of a lever. Under the action of two loads at the ends, the bar bends slightly over the fulcrum. It is shown in the figure.

The figure drawn below shows how rigid and non-rigid bodies act under the action of loads.

In the above figure, the bar in green is rigid since it does not deform under the action of balls. But the red bar got deformed easily under the action of loads. Hence it is a non-rigid body.

## What is a Force?

Force is defined as an action that tends to change the state of rest or motion of a body to which it is applied. It is an external agent that produces change in the movement of a certain body.

• Force acting on a rigid body produces one or both of the following effects:
• Linear Displacement
• Angular Displacement
• There are many types of forces acting on a body at several times at several levels. In some cases, if the forces act on both ends of a body, they create either tension or compression.
• Any kind of thing that applies either a push or a pull on another object is said to be applying some kind of force.
• The unit of force is newton. It is denoted by N.

## Examples of Forces Available in Nature

There are many kinds of forces available in nature. Some of the examples are shown below.

• Gravitational Attraction between a star and a planet: All the planets revolve around their respective star due to gravitational force itself.
• Weight: Weight or self-weight of an object is the gravitational attraction of the earth on it. Weight is the product of mass of the body and acceleration due to gravity. Mass of a body is always constant.
• Hydrostatic Pressure: When a body such as dam impounds on water, the water exerts a force on the body which is distributed on the area of contact. This is called Hydrostatic Pressure.
• Gas Pressure: Any gas confined in a container exerts pressure on the walls of the container. This is called Gas Pressure.
• Wind Pressure: Bodies exposed to wind are subjected to a force distributed over their exposed area, called the wind pressure.

## Characteristics of a Force

For complete definition of a force we must know its characteristics or specifications. They are magnitude, direction and point of application.

• Magnitude: The magnitude of a force denotes the size of force. It gives the numerical value of the effect of force as an external agent on a given body. e.g. 25 N, 45 N etc.
• Direction: The direction of a force is nothing but the passage of quantity of force in away.
• Point of Application of Force: The point of application of force is very important characteristic which determines about where a force does act. It is very must in determining or solving forces into several components.
• Simply one can say that magnitude defines the size, direction denotes the path and the point of application is at which the whole force is assumed to be concentrated.

The point of application of force defines the type of load. Load is nothing but a heavy object which is to be carried or which is to be withstood. Loads are the pressure makers of the engineering objects. Let us see some types of loads.

• Point Load: If the entire magnitude of force is acting over a small area, it is called concentrated force or a point load.
• Distributed Load: If the entire magnitude of the force is distributed over a length or an area or a volume, it is called Distributed Force.
• The concept of point load is hypothetical. This is because, in practical, forces can be transmitted through a definite area only. Nevertheless, this is an idealization that helps us to solve problems more carefully and efficiently.
• The distributed forces normally follow a definite pattern of loading over the entire area/length. It cannot be expressed in terms of length and intensity as that of point load.
• In distributed forces, the magnitude is calculated by multiplying the product of its length to that of its intensity. However, in many cases it is impossible practically.
• Center of Gravity: The center of gravity of a body is an imaginary point at which all the forces on the body appear to act. Hence, by this definition one must take care that the point load acts at the center of gravity of a body or on the axis passing through center of gravity.

## Scalars and Vectors

Every physical quantity is divided into two types based upon the units. They are scalars and vectors.

• Scalar Quantity: A physical quantity which can be represented by a single element of a number field is called Scalar Quantity.
• Vector Quantity: A physical quantity which cannot be represented in a single element form is called Vector Quantity.

Some of the properties of Scalars and Vectors are shown in the below table.

Parameters Scalar Vector
Definition A scalar has only magnitude, but no direction. Vector has both magnitude and direction.
Existence Every scalar is one dimensional. Vector can be 1-D,2-D and 3-D
Resolution Scalar quantity cannot be resolved into components. Vector can be resolved in any direction using sine or cosine or other angles.
Changes Any change in scalar quantity is reflected is the reflection of change in its magnitude. Change in vector quantity means any change either in magnitude or in the direction.
Operations Mathematical operations between two scalar quantities always result in a scalar quantity. Mathematical Operations on two vector quantities may result either in vector quantity or scalar quantity.
Examples Examples are mass, length, energy etc. Examples are displacement, acceleration etc.

The above table shows the differences between a scalar quantity and a vector quantity.

## Representation of a Force

Graphically, a force may be represented as a segment of a straight line. Here, one needs to understand the term “Line of Action”. And since force is a vector, it can be represented graphically. Some of the ways to be followed to represent a force are:

• The straight line represents the line of action of the force 1kN and its length represents its magnitude.
• Line of Action: The direction in which the force tends to move a body to which it is applied is called Line of Action.
• The direction of a force is indicated by placing an arrow head on the straight line.
• Either head or tail may be used to indicate the point of application of a force. All the forces involved must be represented consistently.

The figure given below is a representation of force acting on a point.

In the above figure, we observe that a force of 1kN is acting on an object in two cases. The representation is given as such in the diagram. Magnitude, Direction and Point of Application must be represented as shown above.

## Key Points to Remember

Here are the key points that we need to remember about “Principles of Statics”.

• Statics is one of the oldest branches of science existing in the world since ages.
• A rigid body can be converted into a non-rigid body by applying huge loads but vice-versa is not possible.
• A pull or push on an object is called force. It is applied externally and hence is called eternal agent.
• Some of the practical life examples of force are tractive effort on a locomotive, force of magnetic attraction, resistance due to friction etc.
• A point load is a type of load generally concentrated around a very small area, whereas the distributed load acts over considerable areas or volumes.
• If you multiply scalar with a scalar, then the product is a scalar. If you multiply vector with a scalar, the result is a vector.
• The SI units used by engineers to measure the magnitude are newton (N). It is a derived unit from mass, length and time.

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