(ii). Engineering Mechanics stantes Dynamics. Statics. Dynamics. Kinematics units: The basic quantities or fundamental quantities of mechanics are those. Basic principles: Equivalent force system; Equations of equilibrium; Free R. C. Hibbler, Engineering Mechanics: Principles of Statics and Dynamics, Pearson. PDF Drive is your search engine for PDF files. As of today we have 78,, eBooks for you to download for free. No annoying ads, no download limits, enjoy .
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𝗣𝗗𝗙 | Introduction to Engineering Mechanics | ResearchGate, the The following are the terms basic to study mechanics, which should be. BASIC ENGINEERING. MECHANICS. j.H. HUGHES. goudzwaard.info Department of Mechanical Engineering and Engineering Production, UWIST. M. Download Engineering Mechanics Pdf 1st year Notes Pdf. We have provided Engineering Mechanics 1st Year Study Materials and Lecture Notes for CSE, ECE.
Center of Gravity and Moment 5 of Inertia: First and second moment of area; Radius of gyration; 7 Parallel axis theorem; Product of inertia, Rotation of axes and principal Assignment moment of inertia; Moment of inertia of simple and composite bodies.
Mass moment of inertia. Beer and E. Meriam and L. T1 L1 Dr. Karuna Kalita T2 L2 Dr. Satyajit Panda T3 L3 Dr. Deepak Sharma T4 L4 Dr. M Ravi Sankar T Dr. Ganesh Natrajan T6 1G1 Dr. Swarup Bag T Prof.
Sudip Talukdar T Dr. Arbind Singh T Prof. Anjan Dutta T Dr. Kaustubh Dasgupta T Dr. Bishnupada Mandal T13 4G3 Prof. Moholkar T14 4G4 Dr. Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies subjected to the action of forces. Rigid-body Mechanics ME Statics Dynamics Deformable-Body Mechanics, and Fluid Mechanics 9 Engineering Mechanics Rigid-body Mechanics a basic requirement for the study of the mechanics of deformable bodies and the mechanics of fluids advanced courses.
A rigid body does not deform under load! Force acting on a body is related to the mass of the body and the variation of its velocity with time.
Force can also occur between bodies that are physically separated Ex: gravitational, electrical, and magnetic forces 14 Mechanics: Fundamental Concepts Remember: Mass is a property of matter that does not change from one location to another. Weight refers to the gravitational attraction of the earth on a body or quantity of mass.
Its magnitude depends upon the elevation at which the mass is located Weight of a body is the gravitational force acting on it. Earth can be modeled as a particle when studying its orbital motion 16 Mechanics: Idealizations Rigid Body: A combination of large number of particles in which all particles remain at a fixed distance practically from one another before and after applying a load. Material properties of a rigid body are not required to be considered when analyzing the forces acting on the body.
In most cases, actual deformations occurring in structures, machines, mechanisms, etc. Provided the area over which the load is applied is very small compared to the overall size of the body. Ex: Contact Force between a wheel and ground. First Law: A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force.
First law contains the principle of the equilibrium of forces main topic of concern in Statics 19 Mechanics: Newton s Three Laws of Motion Second Law: A particle of mass m acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force. Third law is basic to our understanding of Force Forces always occur in pairs of equal and opposite forces. This law governs the gravitational attraction between any two particles.
Ex: time, volume, density, speed, energy, mass Vectors: possess direction as well as magnitude, and must obey the parallelogram law of addition and the triangle law. Sliding Vector: has a unique line of action in space but not a unique point of application Ex: External force on a rigid body Principle of Transmissibility Imp in Rigid Body Mechanics Fixed Vector: for which a unique point of application is specified Ex: Action of a force on deformable body 28 Vector Addition: Procedure for Analysis Parallelogram Law Graphical Resultant Force diagonal Components sides of parallelogram Algebraic Solution Using the coordinate system Trigonometry Geometry Resultant Force and Components from Law of Cosines and Law of Sines 29 Force Systems Force: Magnitude P , direction arrow and point of application point A is important Change in any of the three specifications will alter the effect on the bracket.
Force is a Fixed Vector In case of rigid bodies, line of action of force is important not its point of application if we are interested in only the resultant external effects of the force , we will treat most forces as External effect: Forces applied applied force ; Forces exerted by bracket, bolts, Foundation reactive force Cable Tension P Internal effect: Deformation, strain pattern permanent strain; depends on material properties of bracket, bolts, etc.
F 1 and F 2 are components of R. Determine their resultant. Graphical solution -construct a parallelogram with sides in the same direction as P and Q and lengths in proportion.
Graphically evaluate the resultant which is equivalent in direction and proportional in magnitude to the diagonal. A metre is defined as length of the standard bar of platinum-iridium kept at the International Bureau of Weights and Measures.
To overcome difficulties of accessibility and reproduction, now meter is defined as Referring to Fig.
Velocity B The rate of change of displacement with respect to time is defined as velocity. Acceleration Fig. It is a well known fact that each particle can be subdivided into molecules, atoms and electrons. It is not possible to solve any engineering problem by treating a body as a conglomeration of such discrete particles.
The body is assumed to consist of a continuous distribution of matter.
In other words, the body is treated as continuum. Rigid Body A body is said to be rigid, if the relative positions of any two particles in it do not change under the action of the forces. In Fig. Particle A particle may be defined as an object which has only mass and no size. Such a body cannot exist theoretically. However in dealing with problems involving distances considerably larger compared to the size of the body, the body may be treated as particle, without sacrificing accuracy.
Examples of such situations are — A bomber aeroplane is a particle for a gunner operating from the ground. This leads to the definition of force as the external agency which changes or tends to change the state of rest or uniform linear motion of the body.
Consider the two bodies in contact with each other. Let one body applies a force F on another. According to this law the second body develops a reactive force R which is equal in magnitude to force F and acts in the line same as F but in the opposite direction.
The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them. According to this law the force of attraction between the bodies of mass m1 and mass m2 at a distance d as shown in Fig. Let F be the force acting on a rigid body at point A as shown in Fig. According to the law of transmissibility of force, this force has the same effect on the state of body as the force F ap- plied at point B.
In using law of transmissibility of forces it F should be carefully noted that it is applicable only A if the body can be treated as rigid. In this text, the F B engineering mechanics is restricted to study of state of rigid bodies and hence this law is frequently used. The law of transmissibility of forces can be proved using the law of superposition, which can be stated as the action of a given system of forces on a rigid body is not changed by adding or subtracting another system of forces in equilibrium.
It is subjected to a force F at A. B is another point on the line of action of the force. From the law of superposition it is obvious that if two equal and opposite forces of magnitude F are applied at B along the line of action of given force F, [Ref. Force F at A and opposite force F at B form a system of forces in equilibrium.
If these two forces are subtracted from the system, the resulting system is as shown in Fig. Looking at the system of forces in Figs. This law was formulated based on experimental results.
Though Stevinces employed it in , the credit of presenting it as a law goes to Varignon and Newton This law states that if two forces acting simultaneously on a body at a point are presented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant is represented in magni- tude and direction by the diagonal of the parallelogram which passes through the point of intersection of the two sides representing the forces.
Then according to this law, the diagonal AD represents the resultant in the direction and magnitude. Then AD should represent the resultant of F1 and F2. Then we have derived triangle law of forces from fundamental law parallelogram law of forces.
The Triangle Law of Forces may be stated as If two forces acting on a body are represented one after another by the sides of a triangle, their resultant is represented by the closing side of the triangle taken from first point to the last point. If more than two concurrent forces are acting on a body, two forces at a time can be combined by triangle law of forces and finally resultant of all the forces acting on the body may be obtained.
A system of 4 concurrent forces acting on a body are shown in Fig. Let it be called as R2. The units of all other quantities may be expressed in terms of these basic units. The units of length, mass and time used in the system are used to name the systems.
Using these basic units, the units for other quantities can be found. From eqn. Hence the constant of proportionality k becomes units. Unit of force can be derived from eqn.
Gravitational acceleration is 9. In all the problems encountered in engineering mechanics the variation in gravitational acceleration is negligible and may be taken as 9.
Hence the constant of proportionality in eqn. Unit of Constant of Gravitation From eqn.
Thus if two bodies one of mass 10 kg and the other of 5 kg are at a distance of 1 m, they exert a force 6. Now let us find the force acting between 1 kg-mass near earth surface and the earth. Hence the force between the two bodies is 6. Thus weight of 1 kg mass on earth surface is 9. Compared to this force the force exerted by two bodies near earth sur- face is negligible as may be seen from the example of 10 kg and 5 kg mass bodies.
Denoting the weight of the body by W, from eqn. Any body falling freely near earth surface experiences this acceleration. The value of g is 9. The prefixes used in SI system when quantities are too big or too small are shown in Table 1. Table 1. At point C, a person weighing N is standing. The force applied by N B the person on the ladder has the following characters: — magnitude is N C — the point of application is at C which is 2 m from A along the ladder.
Note that the magnitude of the force is written near the arrow. The line of the arrow shows the line of application and the arrow head represents the point of application and the A direction of the force.
If all the forces in a system do not lie in a single plane they constitute the system of forces in space. If all the forces in a system lie in a single plane, it is called a coplanar force system.
If the line of action of all the forces in a system pass through a single point, it is called a concurrent force system. In a system of parallel forces all the forces are parallel to each other. If the line of action of all the forces lie along a single line then it is called a collinear force system. Various system of forces, their characteristics and examples are given in Table 1.
Coplanar parallel forces All forces are parallel to each other System of forces acting on a beam and lie in a single plane. Coplanar like parallel All forces are parallel to each other, Weight of a stationary train on a forces lie in a single plane and are acting rail when the track is straight.
Coplanar concurrent forces Line of action of all forces pass Forces on a rod resting against a through a single point and forces wall. Coplanar non-concurrent All forces do not meet at a point, Forces on a ladder resting against forces but lie in a single plane. Non-coplanar parallel All the forces are parallel to each The weight of benches in a class- forces other, but not in same plane.
Non-coplanar concurrent All forces do not lie in the same A tripod carrying a camera. Non-coplanar All forces do not lie in the same Forces acting on a moving bus. A quantity is said to be scalar if it is completely defined by its magnitude alone. Examples of scalars are length, area, time and mass.
A quantity is said to be vector if it is completely defined only when its magnitude as well as direction are specified. Hence force is a vector. The other examples of vector are velocity, acceleration, momentum etc. We come across several relations among the physical quantities. Some of the terms may be having dimensions and some others may be dimensionless. However in any equation dimensions of the terms on both sides must be the same. This is called dimensional homogenity.
The branch of mathematics dealing with dimensions of quantities is called dimensional analysis. There are two systems of dimensional analysis viz. In absolute system the basic quantities selected are Mass, Length and Time.
Hence it is known as MLT-system.