By Dr. H. J. Shah, S. B. Junnarkar

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Edition ISBN Size Binding Pages

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: 19 Edition : 2015 : 9789385039065 : 170 mm × 235 mm : Paperback : 816 + 16 = 832

About the book

In this text-book, the approach is to study systematically the laws of Mechanics and their application to engineering problems. The outline of the book is: Chapters 1 and 2 discuss Introduction of Mechanics; Fundamental Concepts and Principles; Scalars, Vectors and Tensors; SI Units, Vector Algebra, etc. Chapter 3 to 10 consist the study of Mechanics of Rigid Bodies: Fundamentals of Statics, Forces and Force systems such as coplanar concurrent force systems; Moments; Parallel Forces and Couples; Spatial forces; Reactions etc. Chapter 11 deals in Properties of Lines, Areas and Solids. Chapter 12 and 13 discuss application of the connected bodies viz., trusses, frames and mechanisms. Chapter 14 gives problems of statics in Graphics Statics Chapter 15 and 16Moments of Inertia of Areas and Masses; Friction respectively. Chapters 17 to 21 include the study of Dynamics and Kinematics such as — the motion of the particles, etc. Chapters 22 to 29 deal with topics on Kinetics of Particles such as Laws of Motion; Work and Energy; Impulse and Momentum. Special Topics such as Central Force Motion and Collisions; Kinetics of Systems of Particles, Kinetics of Rigid Bodies; Motion of Vehicles are also covered. Chapters 30 to 38 deal with topics such as Balancing and Rotating Masses; Virtual Work; The Catenary; Belt and Rope Drive; Toothed Gearing; Lifting Machine; Mechanical Vibration; Hydrostatics and Impact of Jets. This book is now contains: * 904 Neatly drawn figures; * 56 Useful tables ;* 453 Solved examples; * 670 Unsolved examples at the end of chapters. It is hoped that this edition should prove extremely useful to students of Engineering reading for Degree Examinations of all the Universities of India, Diploma Examinations conducted by various Boards of Technical Education, Certificate Courses, as well as for the U.P.S.C., G.A.T.E., A.M.I.E., I.E.S. and other similar competitive and professional examinations. It should also prove of great interest and practical use to the practising engineers.

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WORKED EXAMPLES OF

APPLIED MECHANICS By

Dr. H. J. Shah 651 Solutions of the unsolved examples given at the end of all 38 chapters from the text book “APPLIED MECHANICS” with 480 neat and self-explanatory drawings.

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CONTENT 1 : INTRODUCTION 2 : VECTORS 3 : COPLANAR CONCURRENT FORCES 4 : MOMENTS 5 : PARALLEL FORCES AND COUPLES 6 : RESULTANT OF COPLANAR FORCE SYSTEMS 7 : SPATIAL FORCES 8 : EQUILIBRIUM OF COPLANAR FORCE SYSTEMS 9 : REACTIONS 10 : EQUILIBRIUM OF SPATIAL FORCE SYSTEMS 11 : PROPERTIES OF LINES, AREAS AND SOLIDS 12 : TRUSSES 13 : FRAMES AND MECHANISMS 14 : GRAPHIC STATICS 15 : MOMENTS OF INERTIA 16 : FRICTION 17 : RECTILINEAR MOTION OF A PARTICLE 18 : MOTION UNDER VARIABLE ACCELERATION 19 : RELATIVE MOTION OF A PARTICLE 20 : CURVILINEAR MOTION OF A PARTICLE 21 : KINEMATICS OF RIGID BODIES 22 : KINEMATICS OF PARTICLES LAWS OF MOTION 23 : KINETICS OF PARTICLES : WORK AND ENERGY 24 : KINETICS OF PARTICLES : IMPULSE AND MOMENTUM 25 : CENTRAL FORCE MOTION 26 : COLLISIONS 27 : KINETICS OF SYSTEMS OF PARTICLES 28 : KINETICS OF RIGID BODIES 29 : MOTION OF VEHICLES 30 : BALANCING OF ROTATING MASSES 31 : VIRTUAL WORK 32 : THE CATENARY 33 : BELT AND ROPE DRIVE 34 : TOOTHED GEARING 35 : LIFTING MACHINES 36 : MECHANICAL VIBRATIONS 37 : HYDROSTATICS 38 : IMPACT OF JETS Appendix 1 : Selected mathematics Appendix 2 : Objective questions INDEX

Edition : 1st Edition ISBN : 8185594287 Binding : Paperback Pages : 580 + 08 = 588 Size : 170 mm × 240 mm

Charotar Publishing House Pvt. Ltd. Opposite Amul Dairy, Civil Court Road, Post Box No. 65, ANAND 388 001 India Telephone: (02692) 256237, Fax: (02692) 240089, e-mail: [email protected], http://cphbooks.in

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APPLIED MECHANICS Detailed Contents Chapter 1 Introduction 1-1. Mechanics 1-2. Fundamental concepts 1-3. Scalars, vectors and tensors 1-4. Fundamental principles 1-5. System of units: SI units 1-6. Using SI units Questions I Chapter 2 vectors 2-1. Vectors 2-2. Basic operations with vectors 2-3. Components, unit vectors and position vector 2-4. Vector algebra: Dot product 2-5. Vector algebra: Cross product 2-6. Triple product of vectors Exercise II Chapter 3 coplanar concurrent forces 3-1. Forces and force systems 3-2. Principle of transmissibility 3-3. Resultant of a force system 3-4. Resultant of two coplanar concurrent forces 3-5. Resultant of several coplanar forces acting at a point: Law of polygon of forces 3-6. Resolution of a force 3-7. Resultant of a coplanar concurrent force system: Resolution method Examples III Chapter 4 Moments 4-1. Moment of a force 4-2. Principle of moments: Varignon’s theorem 4-3. Coplanar applications 4-4. Levers 4-5. A simple pulley Examples IV Chapter 5 Parallel forces and couples 5-1. Parallel force system 5-2. Couples 5-3. Equivalent couples 5-4. Addition of couples 5-5. Operations with couples 5-6. Equivalent systems of forces 5-7. Equipollent systems of vectors Examples V Chapter 6 Resultant of coplanar force systems 6-1. Introduction 6-2. Resultant of parallel force system 6-3. Centre of parallel forces 6-4. Resultant of a general coplanar force system 6-5. Concentrated and distributed loads Examples VI Chapter 7 Spatial forces 7-1. Concurrent forces in space 7-2. Moment of a force 7-3. Resultant of spatial force system 7-4. Wrench resultant Examples VII Chapter 8 equilibrium of coplanar force systems 8-1. Equilibrium 8-2. Equilibrium of a particle 8-3. Resultant and equilibrant 8-4. Principle of action and reaction 8-5. Free body and free body diagram 8-6. Tensions of strings 8-7. Equilibrium of three forces acting on a particle: Lami’s theorem 8-8. Equilibrium of a particle under three forces acting on it 8-9. External and internal forces 8-10. Tension and compression

8-11 Connected bodies 8-12. Equilibrium of a rigid body 8-13. Conditions of equilibrium for a system of coplanar forces acting on a body 8-14. Types of supports 8-15. Solution of problems Examples VIII Chapter 9 reactions 9-1. Axial and transverse forces 9-2. Structural members 9-3. Types of beams 9-4. Reactions by proportions 9-5. Reactions by equations of statics: Principle of super-position 9-6. Determinate and indeterminate beams/structures Examples IX Chapter 10 Equilibrium of SPATIAL FORCE SYSTEMS 10-1. Equilibrium of spatial force systems Examples X Chapter 11 properties of lines, areas and solids 11-1. Introductory 11-2. Centre of gravity 11-3. Centre of mass 11-4. Centroids 11-5. First moment of an element of line and area 11-6. First moment of a line segment and a finite area 11-7. Centroids of lines and areas 11-8. Centroids of symmetrical lines and areas 11-9. Centroids by integration 11-10. Summary of centroids of common figures 11-11. Centroids of composite lines and areas 11-12. Theorems of Pappus — Guldinus 11-13. Centroid of volumes Examples XI Chapter 12 Trusses 12-1. Engineering applications of connected bodies TRUSSES 12-2. Introductory 12-3. Assumptions made in the analysis of a truss 12-4. Truss notations 12-5. Common types of trusses 12-6. Analysis of a truss 12-7. Method of joints 12-8. Method of sections 12-9. Determinateness of a truss 12-10. Truss with two hinges 12-11. Space trusses Examples XII Chapter 13 Frames and mechanisms 13-1. Frames and mechanisms Examples XIII Chapter 14 Graphic statics 14-1. Introductory 14-2. Basic concepts 14-3. Conditions of equilibrium of a point 14-4. Three force equilibrium of coplanar, non-concurrent, non-parallel forces 14-5. Resultant of non-concurrent, non-parallel forces: Funicular polygon 14-6. Resultant of parallel forces 14-7. Parallel forces: Centroid problems 14-8. Graphical conditions of rigid body equilibrium 14-9. Reactions of beams and trusses 14-10. Graphical methods applied to trusses 14-11. Force diagrams for individual joints of a truss 14-12. The Maxwell diagram 14-13. Method of substitution 14-14. Truss with two hinges with inclined loads Examples XIV

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APPLIED MECHANICS Detailed Contents Chapter 15 moments of inertia 15-1. Introduction Area Moment of Inertia 15-2. Definitions 15-3. Radius of gyration 15-4. Parallel axis theorem 15-5. Moment of inertia by integration 15-6. Moment of inertia of composite areas 15-7. Graphical method for first and second moments of a plane section about an axis in its plane 15-8. Product of inertia Moment of Inertia of Masses 15-9. Definitions 15-10. Parallel axis theorem 15-11. Moment of inertia of thin plates 15-12. Moments of inertia of standard forms 15-13. Moment of inertia of composite bodies Examples XV Chapter 16 Friction 16-1. Introduction 16-2. Types of friction 16-3. Characteristics of dry friction 16-4. Angle of friction: Cone of friction 16-5. Angle of repose 16-6. Types of problems 16-7. Equilibrium on a rough inclined plane Applications of Friction 16-8. The wedge 16-9. The screw 16-10. Screw-jack 16-11. Journal bearings, axle friction 16-12. Thrust bearings: Disc friction 16-13. Thrust bearing: Uniform wear 16-14. Friction plate clutches 16-15. Rolling resistance Examples XVI Chapter 17 Rectilinear motion of a particle 17-1. Motion of a particle 17-2. Speed 17-3. Velocity Rectilinear motion 17-4. Definitions 17-5. Motion under constant acceleration 17-6. Motion under gravity Examples XVII Chapter 18 Motion under variable acceleration 18-1. Motion under variable acceleration 18-2. Vector calculus Examples XVIII Chapter 19 Relative motion of a particle 19-1. Relative motion of a particle 19-2. Motion of connected particles Examples XIX Chapter 20 Curvilinear motion of a particle 20-1. Introductory 20-2. Velocity, Acceleration and Hodograph 20-3. Rectangular components of curvilinear motion 20-4. Normal and tangential components: Intrinsic co-ordinates 20-5. Radial and transverse components: Cylindrical co-ordinates 20-6. Angular motion of a line 20-7. Circular motion of a particle 20-8. Simple Harmonic Motion 20-9. Projectiles: Motion in a vertical plane under gravity 20-10. Motion of a projectile on an inclined plane Examples XX

Chapter 21 Kinematics of rigid bodies 21-1. Introduction 21-2. Translation 21-3. Fixed axis rotation 21-4. General plane motion 21-5. Absolute motion analysis 21-6. Relative motion analysis 21-7. Instantaneous centre: Centrodes Examples XXI Chapter 22 Kinematics of particles: laws of motion 22-1. Introduction 22-2. Inertia and mass: Inertia 22-3. Newton’s laws of motion: First law 22-4. Newton’s second law 22-5. Inertial frame 22-6. Equations of motion 22-7. Constant force acting on a particle 22-8. Variable force acting on a particle 22-9. Motion of a lift 22-10. Motion on a rough inclined plane 22-11. Motion of connected bodies 22-12. D’Alembert’s principle: Dynamic equilibrium 22-13. Curvilinear motion 22-14. Circular motion 22-15. Newton’s law of gravitation Examples XXII Chapter 23 Kinetics of Particles: work and energy 23-1. Introductory Work and energy method 23-2. Work done by a force 23-3. Standard cases 23-4. Power and efficiency 23-5. Energy 23-6. Conservative forces 23-7. Principle of conservation of energy 23-8. Total mechanical energy 23-9. Extraneous forces Examples XXIII Chapter 24 Kinetics of Particles: impulse and momentum 24-1. Linear momentum 24-2. Linear impulse 24-3. Variable force with time 24-4. Impulsive forces 24-5. Angular momentum 24-6. Angular impulse Examples XXIV Chapter 25 Central force motion 25-1. Introductory 25-2. Central force motion 25-3. Trajectory of a particle under a central force 25-4. Launching of a space vehicle 25-5. Escape velocity: Particle orbits 25-6. Periodic time of an orbit 25-7 Communication satellite 25-8. Kepler’s laws of planetary motion Examples XXV Chapter 26 Collisions 26-1. Collision of two bodies: Impact 26-2. Definitions 26-3. Phenomenon of impact 26-4. The general condition 26-5. Collision of perfectly elastic bodies 26-6 Inelastic collisions 26-7. Collision of partially elastic bodies 26-8. Oblique impact on a smooth horizontal plane 26-9. Oblique impact of two smooth spheres Examples XXVI

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APPLIED MECHANICS Detailed Contents Chapter 27 Kinetics of systems of particles 27-1. Introduction 27-2. Application of law of motion for system of particles 27-3. Principle of motion of mass centre 27-4. Work-energy 27-5. Linear and angular momentum of a system of particles 27-6. Principle of impulse and momentum for a system of particles Examples XXVII Chapter 28 Kinetics of rigid bodies 28-1. Introduction 28-2. Translation Rotation 28-3. Rotational motion 28-4. Work done by a couple: Kinetic energy of rotation 28-5. Impulse and momentum Plane motion 28-6. Wheel rolling without slipping Special topics 28-7. Flywheels 28-8. Centre of Percussion Examples XXVIII Chapter 29 Motion of vehicles 29-1. Motion of vehicles 29-2. Tractive resistance 29-3. Tractive force 29-4. Driving torque 29-5. Maximum possible tractive effort 29-6. Power to drive a vehicle 29-7. A truck rolling down a rough inclined plane 29-8. Motion of a truck along level track 29-9. Motion of a truck going round a curve 29-10. Banking a curve: Super-elevation Examples XXIX Chapter 30 Balancing of rotating masses 30-1. Static and Dynamic balance 30-2. Balancing of several masses in the same plane of revolution 30-3. Dynamical loads at bearings 30-4. Balancing of a mass by two masses in different planes of revolution Examples XXX Chapter 31 Virtual work 31-1. Introductory 31-2. Principle of virtual work Examples XXXI Chapter 32 The catenary 32-1. The Catenary 32-2. The parabolic chain 32-3. The length of the cable Examples XXXII Chapter 33 belt and rope drive 33-1. Belt drive 33-2. Velocity ratio 33-3. Compound belt drive 33-4. Length of belt: Open drive 33-5. Length of belt: Crossed drive 33-6. Transmission of power 33-7. Centrifugal tension 33-8. Optimum speed for maximum power 33-9. Rope drive Examples XXXIII

Chapter 34 Toothed Gearing 34-1. Introduction 34-2. Friction wheels 34-3. Toothed wheels: Definitions 34-4. Motion transmitted by toothed gearing 34-5. Forms of wheel teeth 34-6. Trains of wheels 34-7. Design of wheel trains 34-8. Wheel train for a 12-hour clock 34-9. Screw-cutting Lathe 34-10. Lathe back-gear for speed reduction 34-11. Three-speed gear-box of a motor car 34-12. Epicyclic gearing 34-13. Epicyclic trains with bevel wheels 34-14. Humpage’s speed-reduction gear 34-15. The differential gear 34-16. Epicyclic gearing: alternate method Examples XXXIV Chapter 35 Lifting Machines 35-1. Definitions 35-2. Basic machines 35-3. Differential wheel and axle 35-4. Differential pulley-block 35-5. Differential screw 35-6. Pulley-blocks 35-7. Lifting machines with toothed gearing 35-8. Worm gearing 35-9. Worm geared screw jack 35-10. Worm geared pulley block 35-11. Linear law of machines 35-12. Reversibility of a machine 35-13. Compound efficiency Examples XXXV Chapter 36 Mechanical Vibrations 36-1. Introduction 36-2. Classification of vibrations 36-3. Vibration parameters 36-4. Free undamped vibrations of a particle: Spring-mass system 36-5. Composite springs 36-6. Simple pendulum 36-7. Conical pendulum 36-8. Compound pendulum Examples XXXVI Chapter 37 Hydrostatics 37-1. Introductory: Fluids and liquids 37-2. Liquid pressure 37-3. Relation of pressure to depth in a liquid 37-4. Total thrust on a plane vertical area immersed in a liquid: Centre of Pressure 37-5. Total thrust on an inclined plane area immersed in a liquid 37-6. Floatation and Buoyancy Conditions of Equilibrium of a Floating Body 37-7. Metacentre 37-8. Metacentric height Examples XXXVII Chapter 38 Impact of jets 38-1. Force exerted by a jet 38-2. Flat plates: Stationary as well as moving 38-3. Curved vanes 38-4. Pelton wheel: Turbines Examples XXXVIII Appendix 1 Selected mathematics Appendix 2 Objective questions Index

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