Mechanical Engineering  : Engineering mechanics, THE GATE ACADEMY
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Mechanical Engineering : Engineering mechanics, THE GATE ACADEMY

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THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of......

THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.

Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions

GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions

Bangalore Head Office:
THE GATE ACADEMY
# 74, Keshava Krupa(Third floor), 30th Cross,
10th Main, Jayanagar 4th block, Bangalore- 560011
E-Mail: info@thegateacademy.com
Ph: 080-61766222

GATE 2015, GATE EXAM, GATE ONLINE CLASSES, GATE COACHING, GATE MATERIALS , GATE BOOKS, GATE PDF BOOKS, THE GATE ACADEMY, Mechanical Engineering GATE MATERIALS

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  • 1. ENGINEERING MECHANICS for Mechanical Engineering By www.thegateacademy.com
  • 2. Syllabus Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Syllabus for Engineering Mechanics Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum (linear and angular), energy methods, central force motion. Analysis of GATE Papers (Engineering Mechanics) Year Percentage of marks Overall Percentage 2013 3.00 3.18 % 2012 1.00 2011 5.00 2010 2.00 2009 3.00 2008 3.33 2007 2.00 2006 2.67 2005 6.67
  • 3. Contents Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com CC OO NN TT EE NN TT SS Chapter Page No. #1. Introduction 1 #2. Statics 2 - 65 Equivalent Force System 2 – 3 Equilibrium and Free Body Diagram 3 – 9 Friction 9 Virtual Work 9 – 10 Trusses and Frames 10 – 12 Solved Examples 13 – 47 Assignment 1 48 – 52 Assignment 2 52 – 55 Answer Keys 56 Explanations 56 – 65 #3. Dynamics 66 – 133 Kinematics of Rectilinear Motion 66 – 73 Kinematics of Curvilinear Motion 73 – 76 Acceleration Analysis in Cylindrical Coordinates 76 – 83 Kinetics of Rectilinear Motion 83 – 90 Moment of Inertia 90 – 98 Friction 98 – 100 Impulse and Momentum 101 – 104 Collision of Elastic Bodies 104 – 107 Conversion of Angular Momentum 108 – 111 Conservative / Non conservative Force 111 – 117 Assignment 1 118 – 121 Assignment 2 121 – 124 Answer Keys 125 Explanations 125 – 133 Module Test 134 – 145  Test Questions 134 – 139  Answer Keys 140  Explanations 140 – 145 Reference Books 146
  • 4. Chapter 1 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 1 CHAPTER 1 Introduction Mechanics is the science which deals with the action of forces on different types of bodies either in motion or at rest. Engineering mechanics is the application of mechanics to solve problems involving common engineering elements. Engineering Mechanics can be broadly classified as: In this course material we will study about the mechanics of particles and rigid bodies. Particle: It is a portion of matter which is indefinitely small in size. Rigid body: A rigid body may be defined as a body in which the relative positions of any two particles do not change under the action of forces. Statics deals primarily with the calculation of external forces which act on rigid body in equilibrium. Engineering Mechanics Mechanics of fluidsMechanics of solids Rigid bodies Deformable bodies Statics Dynamics Kinematics Kinetics Strength of materials, Theory of elasticity, Theory of plasticity
  • 5. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 2 CHAPTER 2 STATICS Introduction Statics deals with system of forces that keeps a body in equilibrium. In other words the resultant of force systems on the body are zero. Force: A force is completely defined only when the following three characters are specified.  Magnitude  Point of application  Line of action/Direction Scalar and Vector: A quantity is said to be scalar if it is completely defined by its magnitude alone. e.g. length, energy, work etc. A quantity is said to be vector if it is completely defined only when its magnitude and direction is specified. e.g. force, acceleration. Equivalent Force System Coplanar force system: If all the forces in the system lie in a single plane, it is called coplanar force system. Concurrent force system: If line of action of all the forces in a system passes through a single point it is called concurrent force system. Collinear force system: In a system, all the forces parallel to each other, if line of action of all forces lie along a single line then it is called a collinear force system. Force system Example Coplanar like parallel force is straight. Weight of stationary train on rail off the track Coplanar concurrent Forces on a rod resting against wall. Coplanar non- concurrent force Forces on a ladder resting against a wall when a person stands on a rung which is not at its center of gravity. Non- coplanar parallel The weight of benches in class room Non- coplanar concurrent force A tripod carrying camera Non- coplanar non-concurrent force Forces acting on moving bus
  • 6. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 3 Newton’s law of motion First Law: Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by force acting on it. Second law: The rate of change of momentum of a body is directly proportional to the applied force & it takes place in the direction in which the force acts. F (m dv dt ) Third law: For every action, there is an equal and opposite reaction. Principle of transmissibility of force: The state of rest or motion of rigid body is unaltered if a force action on a body is replaced by another force of the same magnitude and direction but acting anywhere on the body along the line of action of applied force. Parallelogram law of forces: If two forces acting simultaneously on a body at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through the point of intersection of the two sides representing the forces. Equilibrium and Free Body Diagrams Coplanar Concurrent Forces Triangle law of forces: If two forces acting simultaneously on a body are represented by the sides of triangle taken in order, their resultant is represented by the closing side of the triangle taken in the opposite order. Polygon law of forces P1 P2P3 P4 P2 P4 C P1 P3 E R B A R2 R1 D A B P P
  • 7. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 4 If a number of forces acting at a point be represented in magnitude and direction by the sides of a polygon in order, then the resultant of all these forces may be represented in magnitude and direction by the closing side of the polygon taken in opposite order Resultant (R) = √ tan ( ) = angle between two forces, = inclination of resultant with force P1 When forces acting on a body are collinear, their resultant is equal to the algebraic sum of the forces. Lami’s theorem: (only three coplanar concurrent forces) If a body is in equilibrium under the action of three forces, then each force is proportional to the sine of the angle between the other two forces. P sin P sin P sin Free body diagram: A free body diagram is a pictorial representation used to analyze the forces acting on a free body. Once we decide which body or combination of bodies to analyze, we then treat this body or combination as a single body isolated from all our surrounding bodies A free body diagram shows all contact and non-contact forces acting on the body. P1P2 P3 P2 P1 P3 a b c P2 B C DE P1 A
  • 8. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 5 Sample Free body diagrams A ladder resting on smooth wall A cantilever beam A block on a ramp In a free body diagram all the contacts/supports are replaced by reaction forces which will exert on the structure. A mechanical system comprises of different types of contacts/supports. Types of contacts/supports Following types of mechanical contacts can be found in various structures:  Flexible cable, belt, chain or rope mgm Free body diagram of just the block ̂ ̂ F3 F2 F1 V V V V F M W=m g y x SMOOTH SMOOTH P 600N G W 600N R1 P R2
  • 9. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 6 Force exerted by the cable is always a tension away from the body in the direction of the cable.  Smooth surfaces Contact force is compressive and is normal to the surface.  Rough surfaces Rough surfaces are capable of supporting a tangential component F (frictional force as well as a normal component N of the resultant R.  Roller support Roller, rocker or ball support transmits a compressive force normal to supporting surface.  Freely sliding guide N N N N F R N N θ θ Weight of cable negligible Weight of cable not negligible θ θ T T
  • 10. Chapter 2 Engineering Mechanics THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  info@thegateacademy.com © Copyright reserved. Web: www.thegateacademy.com Page 7 Collar or slider support force normal to guide only. There is no tangential force as surfaces are considered to be smooth.  Pin connection A freely hinged pin supports a force in any direction in the plane normal to the axis; usually shown as two components Rx and Ry. A pin not free to turn also supports a couple M.  Built in or fixed end A built-in or fixed end supports an axial force F, a transverse force V, and a bending moment M. Coplanar Non-Concurrent Forces Varignon’s theorem: The algebraic sum of the moments of a system of coplanar forces about a momentum center in their plane is equal to the moment of their resultant forces about the same moment center. R.d = P1.d1 +P2.d2 Effect of couple is unchanged if  Couple is rotated through any angle.  Couple is shifted to any position.  The couple is replaced by another pair of forces whose rotated effect is the same.  Couple is free vector A B R A M F V A Weld O r A R y Rx Rx Ry M