Siddhant Kolase - FOSD Unit-1

Unit-1: Statics

Mechanics

- Mechanics is the branch of physics that deals with the motion of bodies and the forces acting on them.

Solid Mechanics

- Solid Mechanics is the branch of mechanics that deals with the behavior of solid bodies under the action of external forces, loads, and moments.

Fluid Mechanics

- Fluid Mechanics is the branch of mechanics that deals with the behavior of fluids (liquids and gases) at rest and in motion, and the forces acting on fluids and fluid systems.

Engineering Mechanics

Engineering Mechanics is the branch of mechanics that deals with the behavior of rigid bodies under the action of forces and moments, particularly their equilibrium and motion.

Statics

- Statics is the branch of Engineering Mechanics that deals with the study of rigid bodies at rest or in equilibrium under the action of forces and moments.

Dynamics

- Dynamics is the branch of Engineering Mechanics that deals with the study of rigid bodies in motion and the forces and moments associated with that motion.

Kinetics

- Kinetics is the branch of Dynamics that deals with the study of the motion of rigid bodies considering the forces and moments responsible for that motion.

Kinematics

- Kinematics is the branch of Dynamics that deals with the motion of bodies without considering the forces and moments causing the motion.

Rigid Body

- A rigid body is an idealized solid body in which the distance between any two points remains constant, even when external forces or moments act on it.

- A rigid body is a body that does not undergo deformation under the action of external forces.

Laws of Mechanics

Newton’s first law of Motion

Newton’s second law of Motion

Newton’s third law of Motion

Newton’s law of gravitation

Law of transmissibility of forces

Principle of Superposition of Forces

Parallelogram law of forces.

Newton's First Law of Motion

A body continues to be in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force

Newton's Second Law of Motion

- The rate of change of momentum of a body is directly proportional to the applied external force and takes place in the direction of that force.

Newton's Third Law of Motion

- For every action, there is an equal and opposite reaction.

Newton's Law of Gravitation

- Every two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Principle of Transmissibility of Forces

- A force can be moved anywhere along its line of action without changing the equilibrium or motion of a rigid body.

Principle of Superposition of Forces

- When several forces act simultaneously on a body, the combined effect of these forces is equal to the vector sum of the effects produced by each force acting separately.

Parallelogram Law of Forces

- If two forces acting simultaneously at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant force is represented in magnitude and direction by the diagonal of the parallelogram passing through the common point.

Numericals on Parallelogram Law of Forces

Two forces of 80 N and 120 N act at a point with an angle of 60 degrees between them. Find the magnitude and direction of the resultant using the parallelogram law of forces. (Ans: R=174.36N, α=36.590)

Two forces of 150 N and 200 N act simultaneously on a body at an angle of 45 degrees to each other. Determine the resultant force and its inclination with the 150 N force. (Ans: R=323.91 N, α=25.880)

The resultant of two forces, one of which is double the other is 260 N. If the direction of the larger force is reversed and the other remains unaltered, the resultant reduces to 180 N. Determine the magnitude of the forces and the angle between the forces. (Ans: F1 = 100 N, F2 = 200 N, θ = 63.9°)

Mass

- Mass is the quantity of matter contained in a body and is a measure of the body's inertia.
- SI Unit: kilogram (kg)
- Mass is a scalar quantity.
- Mass remains constant irrespective of the location of the body.
- Greater mass means greater inertia.

Weight

- Weight is the force with which the Earth attracts a body towards its centre.
- Weight is a vector quantity.
- SI unit of weight is Newton (N).
- Weight depends on the value of gravitational acceleration and therefore can vary with location.
- Unlike mass, weight is not constant everywhere.

Force

- Force is an external agency that can change or tend to change the state of rest or uniform motion of a body, or change its shape or size.

Force System

- A force system is a collection of two or more forces acting simultaneously on a body.

Classification of Force Systems
1. Collinear Force SystemA force system in which the lines of action of all forces lie along the same straight line.
2. Non-collinear Force SystemA force system in which the lines of action of the forces do not lie along the same straight line.
3. Concurrent Force SystemA force system in which the lines of action of all forces meet at a common point.
4. Non-concurrent Force SystemA force system in which the lines of action of the forces do not meet at a common point.
5. Parallel Force SystemA force system in which the lines of action of all forces are parallel to each other.
6. Non-parallel Force SystemA force system in which the lines of action of the forces are not parallel to each other.
7. Coplanar Force SystemA force system in which the lines of action of all forces lie in the same plane.
8. Non-coplanar Force SystemA force system in which the lines of action of the forces do not lie in the same plane.
Types of Coplanar Force Systems
1. Coplanar Collinear Force SystemA force system in which the lines of action of all forces lie along the same straight line and inthe same plane.
2. Coplanar Concurrent Force SystemA force system in which the lines of action of all forces lie in the same plane and meet at a common point.
3. Coplanar Parallel Force SystemA force system in which the lines of action of all forces are parallel to each other and lie in the same plane.
4. Coplanar Non-concurrent and Non-parallel Force SystemA force system in which the lines of action of all forces lie in the same plane but are neither concurrent nor parallel.

Moment or Moment of Force

- The moment of a force about a point is the turning effect produced by the force about that point. M = F x d

Varignon’s Theorem

- Varignon’s theorem states that summation of moment of all forces with respect to any point is equal to moment of their Resultant force about the same point

Law of Moment

- For a body in equilibrium, the algebraic sum of the moments of all forces about any point is zero.

Resolution of Forces

Resolution of forces is the process of splitting a single force into two or more component forces acting in specified directions.

Numericals on Resolution of Forces

Composition of Forces

Composition of forces is the process of combining two or more forces acting on a body into a single equivalent force, called the resultant force.

Equilibrium

- Equilibrium is the state of a body in which the resultant force and resultant moment acting on the body are both zero.

- Equilibrium means there is no unbalanced force or unbalanced turning effect acting on the body.

Principle of Equilibrium

- The principle of equilibrium states that a body is in equilibrium when the resultant force and the resultant moment acting on the body are zero.

Lami’s Theorem

- Lami’s theorem states that if a body is in equilibrium under the action of three coplanar, concurrent, and non-parallel forces, then each force is proportional to the sine of the angle between the other two forces.

Lami’s Theorem Application

- Lami’s theorem is mainly used to determine unknown forces or reactions when a body is in equilibrium under the action of three coplanar, concurrent and non-parallel forces.

Applications:

- Finding tension in cables supporting a load.
- Finding support reactions in simple structures.
- Analysis of a suspended body supported by two strings or cables.
- Finding unknown forces in three-force equilibrium problems.
- Analysis of simple mechanical systems, such as pulleys, rings, and hooks.

Numericals on Lami’s Theorem

Types of Supports

Types of Loads

Types of Beams

Numericals on Support Reactions

Questions

1. Define statics and explain the concept of a rigid body.
2. Define force and list its main characteristics with suitable examples.
3. Explain the graphical representation of a force and different force systems.
4. State and explain the law of moment and Varignon’s theorem with an example.
5. Resolve a given force into rectangular components and determine the resultant of two concurrent forces.
6. A force of 100 N acts at an angle of 30 degrees to the horizontal. Find its horizontal and vertical components.
7. State the conditions of equilibrium for a coplanar force system and explain their significance in engineering mechanics.
8. Using Lami’s theorem, determine the unknown forces acting on a particle in equilibrium under three concurrent forces.
9. Describe the different types of supports, loads, and beams used in structural mechanics with neat sketches.
10. Determine the support reactions of a simply supported beam subjected to point load and uniformly distributed load.

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