Mechanics of Solids

Unit-I

110010

Syllabus

• Introduction:• Scalar and vector quantities, Composition and

resolution of vectors, System of units, Definition of space, time, particle, rigid body, force.

Scalar and Vector Quantities

• Scalar Quantity:• A quantity which is represented by only magnitude

is called as scalar quantity. Mass, volume and length are basic scalar quantities used in statics.

• Vector Quantity: A quantity which is represented both by magnitude and direction is called vector quantity.

• A vector quantity is represented by a letter with an arrow over it. IAI

Scalar and Vector Quantities

Scalar and Vector Quantities

Composition of Vectors

Composition of Vector is the procedure to add the vectors to obtain a resultant vector.Two vector A and B of same type may be added to get a resultant vector by using concept of parallelogram.

R= A + B

Composition of Vectors

Resolution of Vectors

• The Process of Splitting up a vector into two or more components is called resolution of vectors.

Resolution of Vectors

Fundamentals of Mechanics

• Mechanics may be defined as the branch of applied science that deals with the description and prediction of the condition of rest or motion of bodies under the action of forces.

• Mechanics may be categorized into 3 parts.• Mechanics of Rigid Bodies, commonly known as

Engineering Mechanics• Mechanics of Deformable Bodies, commonly known as

Strength of Materials.• Mechanics of Fluids, commonly known as Fluid

Mechanics.

Engineering Mechanics

• Engineering Mechanics is defined as the branch of mechanics that deals with the bodies at rest or in motion. Here, it is assumed that the bodies are perfectly rigid, and do not deform or distort when subjected to forces.

Engineering Mechanics

• Engineering Mechanics is divided into two Parts.

• Statics: It is defined as the branch of engineering mechanics, that deals with bodies at rest.

• Dynamics: It is defined as the branch of engineering Mechanics, that deals with bodies in motion. Dynamics is further divided into Kinematics and Kinetics

Engineering Mechanics

Statics

Dynamics

Strength of Material

• Strength of Material is defined as the branch of mechanics that deals with the deformable bodies and the forces acting on it. In this branch the bodies are considered as deformable bodies, and studies are carried out to understand and calculate types of deformation characteristics of bodies when acted upon by forces.

Strength of Material

Fluid Mechanics

• Fluid Mechanics deals with various mechanisms involved in dealing with fluid.

System of Units

• FPS: In this system, the fundamental unit of length, mass and time are foot, pound and second.

• CGS: In this system, the fundamental units of length are centimetre, gram and second.

• MKS: In this system, the fundamental units are meter, kilogram and second.

• SI: System International de’ SI units

SI Units

• System International units came with existence in October 1960 and is officially recognized, and is adopted by all countries of the world.

• It is based upon seven basic units or principle units.

Fundamental Units

• Basic units such as• Metre• Kilogram• Second• Amphere• Kelvin• Mole• Candela

Derived Units of SI System

• Various units are derived from fundamental units to cater the needs of the fields or stream. Some of the derived unit is given below.

• Newton (N)• Joule (J)• Pascal (Pa)• Watt (W)

SI Prefixes

Fundamental Concepts

• Space: Space is a region in all directions and contain everything within.

• e.g. Sun & Stars, planets, etc. It is also defined as unlimited expanse of physical dimension.

• Time: It is a measure of duration between successive events. In other words, it is defined as a measure of successive events.

• Its unit is Second.

Fundamental Concepts

Fundamental Concepts

• Matter: any substance which occupies space is called matter.

• Body: Any matter that is bounded by a closed surface is called a body.

• The body is considered as an accumulation of large no of particles.

• Inertia: It is the property by virtue of which a body offers resistance to any change of its state of rest or motion.

• Mass: The quantity of matter possessed by a body is called mass.

Matter

Inertia

Fundamental Concepts

• Rest: A body is said to be at rest if it does not change its position with respect to a reference point at different interval of time.

• Motion: A body is said to be in motion if it changes its position with respect to a reference point at different interval of time. e.g. a car moving on road.

Idealizations in Mechanics

• Particle: It is an idealized body which may have negligible mass and whose size and shape can be disregarded or ignored without introducing any appreciable error. In the description and prediction of its state of rest or motion.

Particle

Idealizations in Mechanics

• Rigid Body: It is an idealized body composed of a large number of particles, all of which always remain at fixed distance from each other.

• Deformable Body: A body or element whose shape and size changes under application of external forces, is known as deformable body.

Idealizations in Mechanics

• Continuum: It is defined an idealized body whose matter is assumed to be totally continuous, homogeneous and non-porous.

• e.g. surface of an aircraft.

Fundamental Principles in Mechanics

• The fundamental Principles used for solving Problems of Engineering.

• Law of Parallelogram of forces.• Law of Transmissibility.• Law of Superposition• Newton’s law of Motion.• Newton’s law of Gravitation.

Law of Parallelogram of Forces.

• This laws states that ‘If two forces are acting simultaneously on a particle and are represented in terms of magnitude and direction by two adjacent sides of a parallelogram, then the diagonal passing through the points of intersection of these forces, represents the resultant of above two forces, in terms of magnitude and direction.

Law of Transmissibility of Forces

• This law states that’ the condition of equilibrium or of motion of a rigid body will remained unchanged, if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and direction, but acting at different points, provided the two forces have same line of action.

Principle of Superposition of Forces

• This principle states that ‘ 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 as that of initial force system.

Newton’s First Law

• Every body continuous in its state of rest or uniform motion, unless it is acted upon by some external agency. In other words, if a body is subjected to a balanced set of forces, it will continue to remain in the state of rest or of uniform motion.

Newton’s First Law

Newton’s Second Law

• The rate of change of momentum of a body performing motion is directly proportional to the impressed force, and takes place in the direction in which the force acts.

• Mathematically,• Force (F)= Mass (m) x Acceleration (a)

Newton’s Second Law

Newton’s Third Law

• To every action, there is equal and opposite reaction.

Newton’s Law of Gravitational Force

• This law States ‘Any two masses m1 and m2, separated by a distance ‘r’ attracts each other with a force directly proportional to their masses and inversely proportional to square of their distance.

• F ∞ m1 m2

r 2

• Or F= G m1 m

2 where G is Gravitational Constant

r 2

Newton’s Law of Gravitational Force

Newton’s Law of Gravitational Force by a Body on the Earth

Forces

• Force is an agency that changes or tends to change the state of rest or motion of a body.

• The SI unit of force is N or KN, whereas in MKS unit is kg(f)

• 1N= 1kg x 1m/s2

• 1kg(f) = 9.81 N

Types of Forces

• Gravitational Force• Action and Reaction• Friction• Hydrostatic force• Wind force• Cohesion and Adhesion• Electric and Magnetic force• Thermal forces

Types of Forces

Force System

• When a number of forces act on a body simultaneously, they are known as a force system.

• Collinear forces• Coplanar forces • Concurrent forces• Spatial forces• Non-concurrent forces• Like forces• Unlike forces

Force System• Collinear Forces: Co-means same and linear means along a line. Thus

forces acting along a line are known as collinear forces.• Coplanar Forces: Co-means same and planer means along a plane• Thus forces acting along a plane are known as coplanar forces.• Concurrent Forces: Con-means same and current means meeting thus

forces meeting at a point or emerging from a point are known as concurrent forces.

• Spatial Forces: force, acting in space are known as spatial forces or forces acting in space.

• Non-Concurrent Forces: forces: forces not meeting at a point are known as non-concurrent forces.

• Like Forces: Forces that act parallel to each other and also act in same direction.

• Unlike Forces: Forces that act parallel to each other but donot act in the same direction.

Force System

Force System

Collinear Forces

Coplanar Forces

Concurrent Forces

Spatial Forces

Force System

Non-Concurrent Forces

Like forcesUnlike forces

References

• Mechanics of Solids By:• Prof. M.N.Patel• Prof P.V.Patel• Captain C.S.Sanghvi• Prof J.S. Thakur

• Internet Websites: