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MULTICOLOUR ILLUSTRATIVE EDITION A TEXTBOOK OF (SI UNITS) R.S. KHURMI S. CHAND & COMPANY LTD. (AN ISO 9001 : 2000 COMPANY) RAM NAGAR, NEW DELHI - 110 055 PREFACE TO THE TWENTIETH MULTICOLOUR EDITION I feel thoroughly satisfied in presenting the twentieth Edition of this popular book in Multicol...

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MULTICOLOUR ILLUSTRATIVE EDITION

A TEXTBOOK OF

(SI UNITS)

R.S. KHURMI

S. CHAND & COMPANY LTD. (AN ISO 9001 : 2000 COMPANY)

RAM NAGAR, NEW DELHI - 110 055

PREFACE TO THE TWENTIETH MULTICOLOUR EDITION I feel thoroughly satisfied in presenting the twentieth Edition of this popular book in Multicolour. The present edition of this book has been thoroughly revised and a lot of useful material has been added to improve its quality and use. It also contains lot of pictures and coloured diagrams for better and quick understanding as well as grasping the subject matter. I am highly obliged to my son Mr. N.P.S. Khurmi B.Tech (Hons) for his dedicated and untiring efforts to revise and bring out the book in its present form. Although every care has been taken to check mistakes and misprints, yet it is difficult to claim perfection. Any error, omission and suggestion for the improvement of this volume, brought to my notice, will be thankfully acknowledged and incorporated in the next edition. B-510, New Friends Colony, New Delhi-110065

R.S. Khurmi

PREFACE TO THE FIRST EDITION I take an opportunity to present this standard treatise entitled as A TEXTBOOK of APPLIED MECHANICS to the Students of Degree, Diploma and A.M.I.E. (I) classes. This object of this book is to present the subject matter in a most concise, compact, to-the-point and lucid manner. While writing this book, I have constantly kept in mind the requirements of all the students regarding the latest as well as the changing trends of their examination. To make it more useful, at all levels, the book has been written in an easy style. All along the approach to the subject matter, every care has been taken to arrange matter from simpler to harder, known to unknown with full details and illustrations. A large number of worked examples, mostly examination questions of Indian as well as foreign universities and professional examining bodies, have been given and graded in a systematic manner and logical sequence, to assist the students to understand the text of the subject. At the end of each chapter, a few exercises have been added, for the students, to solve them independently. Answers to these problems have been provided, but it is too much to hope that these are entirely free from errors. In short, it is expected that the book will embrace the requirements of the students, for which it has been designed. Although every care has been taken to check mistakes and misprints, yet it is difficult to claim perfection. Any error, omission and suggestion for the improvement of this volume, brought to my notice, will be thankfully acknowledged and incorporated in the next edition. Feb. 24, 1967

R.S. Khurmi

To My Revered Guru and Guide Shree B.L.Theraja A well-known author, among Engineering students, both at home and abroad, to whom I am ever indebted for inspiration and guidance

CONTENTS 1. Introduction

1–12

1.1. Science 1.2. Applied Science 1.3. Engineering Mehanics 1.4. Beginning and Development of Engineering Mechanics 1.5. Divisions of Engineering Mechanics 1.6. Statics 1.7. Dynamics 1.8. Kinetics 1.9. Kinematics 1.10. Fundamental Units 1.11. Derived Units 1.12. Systems of Units 1.13. S.I. Units (International System of Units.) 1.14. Metre 1.15. Kilogram 1.16. Second 1.17. Presentation of Units and Their Values 1.18. Rules for S.I. Units 1.19. Useful Data 1.20. Algebra 1.21. Trigonometry 1.22. Differential Calculus 1.23. Integral Calculus 1.24. Scalar Quantitie 1.25. Vector Quantities

2. Composition and Resolution of Forces

13–27

2.1. Introduction 2.2. Effects of a Force 2.3. Characteristics of a Force 2.4. Principle of Physical Independence of Forces 2.5. Principle of Transmissibility of Forces 2.6. System of Forces 2.7. Resultant Force 2.8. Composition of Forces 2.9. Methods for the Resultant Force 2.10. Analytical Method for Resultant Force 2.11. Parallelogram Law of Forces 2.12. Resolution of a Force 2.13. Principle of Resolution 2.14. Method of Resolution for the Resultant Force 2.15. Laws for the Resultant Force 2.16. Triangle Law of Forces 2.17. Polygon Law of Forces 2.18. Graphical (vector) Method for the Resultant Force

3. Moments and Their Applications

28–42

3.1. Introduction 3.2. Moment of a Force 3.3. Graphical Representation of Moment 3.4. Units of Moment 3.5. Types of Moments 3.6. Clockwise Moment 3.7. Anticlockwise Moment 3.8. Varignon’s Principle of Moments (or Law of Moments) 3.9. Applications of Moments 3.10. Position of the Resultant Force by Moments 3.11. Levers 3.12. Types of Levers 3.13. Simple Levers 3.14. Compound Levers

4. Parallel Forces and Couples

43–54

4.1. Introduction 4.2. Classification of parallel forces. 4.3. Like parallel forces 4.4. Unlike parallel forces 4.5. Methods for magnitude and position of the resultant of parallel forces 4.6. Analytical method for the resultant of parallel forces. 4.7. Graphical method for the resultant of parallel forces 4.8. Couple 4.9. Arm of a couple 4.10. Moment of a couple 4.11. Classification of couples 4.12. Clockwise couple 4.13. Anticlockwise couple 4.14. Characteristics of a couple

5. Equilibrium of Forces

55–77

5.1. Introduction 5.2. Principles of Equilibrium 5.3. Methods for the Equilibrium of coplanar forces 5.4. Analytical Method for the Equilibrium of Coplanar Forces 5.5. Lami’s Theorem 5.6. Graphical Method for the Equilibrium of Coplanar Forces 5.7. Converse of the Law of Triangle of Forces 5.8. Converse of the Law of Polygon of Forces 5.9. Conditions of Equilibrium 5.10. Types of Equilibrium.

6. Centre of Gravity

78–99

6.1. Introduction 6.2. Centroid 6.3. Methods for Centre of Gravity 6.4. Centre of Gravity by Geometrical Considerations 6.5. Centre of Gravity by Moments 6.6. Axis of Reference 6.7. Centre of Gravity of Plane Figures 6.8. Centre of Gravity of Symmetrical Sections 6.9. Centre of Gravity of Unsymmetrical Sections 6.10. Centre of Gravity of Solid Bodies 6.11. Centre of Gravity of Sections with Cut out Holes

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7. Moment of Inertia

100–123

7.1. Introduction 7.2. Moment of Inertia of a Plane Area 7.3. Units of Moment of Inertia 7.4. Methods for Moment of Inertia 7.5. Moment of Inertia by Routh’s Rule 7.6. Moment of Inertia by Integration 7.7. Moment of Inertia of a Rectangular Section 7.8. Moment of Inertia of a Hollow Rectangular Section 7.9. Theorem of Perpendicular Axis 7.10. Moment of Inertia of a Circular Section 7.11. Moment of Inertia of a Hollow Circular Section 7.12. Theorem of Parallel Axis 7.13. Moment of Inertia of a Triangular Section 7.14. Moment of Inertia of a Semicircular Section 7.15. Moment of Inertia of a Composite Section 7.16. Moment of Inertia of a Built-up Section

8. Principles of Friction

124–148

8.1. Introduction 8.2. Static Friction 8.3. Dynamic Friction 8.4. Limiting Friction 8.5. Normal Reaction 8.6. Angle of Friction 8.7. Coefficient of Friction 8.8. Laws of Friction 8.9. Laws of Static Friction 8.10. Laws of Kinetic or Dynamic Friction 8.11. Equilibrium of a Body on a Rough Horizontal Plane 8.12. Equilibrium of a Body on a Rough Inclined Plane 8.13. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting Along the Inclined Plane 8.14. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting Horizontally 8.15. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting at Some Angle with the Inclined Plane

9. Applications of Friction

149–170

9.1. Introduction. 9.2. Ladder Friction. 9.3. Wedge Friction. 9.4. Screw Friction. 9.5. Relation Between Effort and Weight Lifted by a Screw Jack. 9.6. Relation Between Effort and Weight Lowered by a Screw Jack. 9.7. Efficiency of a Screw Jack.

10. Principles of Lifting Machines

171–184

10.1. Introduction 10.2. Simple Machine 10.3. Compound Machine 10.4. Lifting Machine 10.5. Mechanical Advantage. 10.6. Input of a Machine 10.7. Output of a Machine 10.8. Efficiency of a Machine 10.9. Ideal Machine 10.10. Velocity Ratio 10.11. Relation Between Efficiency, Mechanical Advantage and Velocity Ratio of a Lifting Machine 10.12. Reversibility of a Machine 10.13. Condition for the Reversibility of a Machine 10.14. Self-locking Machine. 10.15. Friction in a Machine 10.16. Law of a Machine 10.17. Maximum Mechanical Advantage of a Lifting Machine 10.18. Maximum Efficiency of a Lifting Machine.

11. Simple Lifting Machines

185–216

11.1. Introduction 11.2. Types of Lifting Machines 11.3. Simple Wheel and Axle. 11.4. Differential Wheel and Axle. 11.5. Weston’s Differential Pulley Block. 11.6. Geared Pulley Block. 11.7. Worm and Worm Wheel 11.8. Worm Geared Pulley Block.11.9. Single Purchase Crab Winch. 11.10. Double Purchase Crab Winch. 11.11. Simple Pulley. 11.12. First System of Pulleys.11.13. Second System of Pulleys. 11.14. Third System of Pulleys. 11.15. Simple Screw Jack 11.16. Differential Screw Jack 11.17. Worm Geared Screw Jack.

12. Support Reactions

217–243

12.1. Introduction. 12.2. Types of Loading. 12.3. Concentrated or Point Load 12.4. Uniformly Distributed Load 12.5. Uniformly Varying Load 12.6. Methods for the Reactions of a Beam 12.7. Analytical Method for the Reactions of a Beam 12.8. Graphical Method for the Reactions of a Beam 12.9. Construction of Space Diagram. 12.10. Construction of Vector Diagram 12.11. Types of End Supports of Beams 12.12. Simply Supported Beams 12.13. Overhanging Beams 12.14. Roller Supported Beams 12.15. Hinged Beams 12.16. Beams Subjected to a Moment. 12.17. Reactions of a Frame or a Truss 12.18. Types of End Supports of Frames 12.19. Frames with Simply Supported Ends 12.20. Frames with One End

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Hinged (or Pin-jointed) and the Other Supported Freely on Roller 12.21. Frames with One End Hinged (or Pin-jointed) and the Other Supported on Rollers and Carrying Horizontal Loads. 12.22. Frames with One End Hinged (or Pin-jointed) and the Other Supported on Rollers and carrying Inclined Loads. 12.23. Frames with Both Ends Fixed.

13. Analysis of Perfect Frames (Analytical Method) 244–288 13.1. Introduction. 13.2. Types of Frames. 13.3. Perfect Frame. 13.4. Imperfect Frame. 13.5.Deficient Frame. 13.6. Redundant Frame. 13.7. Stress. 13.8. Tensile Stress. 13.9. Compressive Stress. 13.10. Assumptions for Forces in the Members of a Perfect Frame. 13.11. Analytical Methods for the Forces. 13.12. Method of Joints. 13.13. Method of Sections (or Method of Moments). 13.14. Force Table. 13.15. Cantilever Trusses. 13.16. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Horizontal Loads. 13.17. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Inclined Loads. 13.18. Miscellaneous Structures.

14. Analysis of Perfect Frames (Graphical Method) 289–321 14.1. Introduction. 14.2. Construction of Space Diagram. 14.3. Construction of Vector Diagram. 14.4. Force Table. 14.5. Magnitude of Force. 14.6. Nature of Force. 14.7. Cantilever Trusses. 14.8. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Horizontal Loads. 14.9. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Inclined Loads. 14.10. Frames with Both Ends Fixed. 14.11. Method of Substitution.

15. Equilibrium of Strings

322–341

15.1. Introduction. 15.2. Shape of a Loaded String. 15.3. Tension in a String. 15.4. Tension in a String Carrying Point Loads. 15.5. Tension in a String Carrying Uniformly Distributed Load. 15.6. Tension in a String when the Two Supports are at Different Levels. 15.7. Length of a String. 15.8. Length of a String when the Supports are at the Same Level. 15.9. Length of a String when the Supports are at Different Levels. 15.10. The Catenary.

16. Virtual Work

342–360

16.1. Introduction. 16.2. Concept of Virtual Work. 16.3. Principle of Virtual Work. 16.4. Sign Conventions. 16.5. Applications of the Principle of Virtual Work. 16.6. Application of Principle of Virtual Work on Beams Carrying Point Load. 16.7. Application of Principle of Virtual Work on Beams Carrying Uniformly Distributed Load. 16.8. Application of Principle of Virtual Work on Ladders. 16.9. Application of Principle of Virtual Work on Lifting Machines. 16.10. Application of Principle of Virtual Work on Framed Structures.

17. Linear Motion

361–383

17.1. Introduction. 17.2. Important Terms. 17.3. Motion Under Constant Acceleration. 17.4. Motion Under Force of Gravity. 17.5. Distance Travelled in the nth Second. 17.6. Graphical Representation of Velocity, Time and Distance Travelled by a Body.

18. Motion Under Variable Acceleration

384–399

18.1. Introduction. 18.2. Velocity and Acceleration at any Instant. 18.3. Methods for Velocity, Acceleration and Displacement from a Mathematical Equation. 18.4. Velocity and Acceleration by Differentiation. 18.5. Velocity and Displacement by Intergration. 18.6. Velocity, Acceleration and Displacement by Preparing a Table.

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19. Relative Velocity

400–416

19.1. Introduction. 19.2. Methods for Relative Velocity. 19.3. Relative velocity of Rain and Man. 19.4. Relative Velocity of Two Bodies Moving Along Inclined Directions. 19.5. Least Distance Between Two Bodies Moving Along Inclined Directions. 19.6. Time for Exchange of Signals of Two Bodies Moving Along Inclined Directions.

20. Projectiles

417–444

20.1. Introduction. 20.2. Important Terms. 20.3. Motion of a Body Thrown Horizontally into the Air. 20.4. Motion of a Projectile. 20.5. Equation of the Path of a Projectile. 20.6. Time of Flight of a Projectile on a Horizontal Plane. 20.7. Horizontal Range of a Projectile. 20.8. Maximum Height of a Projectile on a Horizontal Plane. 20.9. Velocity and Direction of Motion of a Projectile, After a Given Interval of Time from the Instant of Projection. 20.10. Velocity and Direction of Motion of a Projectile, at a Given Height Above the Point of Projection. 20.11. Time of Flight of a Projectile on an Inclined Plane. 20.12. Range of a Projectile on an Inclined Plane.

21. Motion of Rotation

445–456

21.1. Introduction. 21.2. Important Terms. 21.3. Motion of Rotation Under Constant Angular Acceleration. 21.4. Relation Between Linear Motion and Angular Motion. 21.5. Linear (or Tangential) Velocity of a Rotating Body. 21.6. Linear (or Tangential) Acceleration of a Rotating Body. 21.7. Motion of Rotation of a Body under variable Angular Acceleration.

22. Combined Motion of Rotation and Translation 457–469 22.1. Introduction. 22.2. Motion of a Rigid Link. 22.3. Instantaneous centre. 22.4. Motion of a Connecting Rod and Piston of a Reciprocating pump. 22.5. Methods for the Velocity of Piston of a Reciprocating Pump. 22.6. Graphical Method for the Velocity of Piston of a Reciprocating Pump. 22.7. Analytical Method for the Velocity of Piston of a Reciprocating Pump. 22.8. Velocity Diagram Method for the Velocity of Piston of a Reciprocating Pump. 22.9. Motion of a Rolling Wheel Without Slipping.

23. Simple Harmonic Motion

470–480

23.1. Introduction. 23.2. Important Terms. 23.3. General Conditions of Simple Harmonic Motion. 23.4. Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion. 23.5. Maximum Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion.

24. Laws of Motion

481–502

24.1. Introduction. 24.2. Important Terms. 24.3. Rigid Body. 24.4. Newton’s Laws of Motion. 24.5. Newton’s First Law of Motion. 24.6. Newton’s Second Law of Motion. 24.7. Absolute and Gravitational Units of Force. 24.8. Motion of a Lift. 24.9. D’Alembert’s Principle. 24.10. Newton’s Third Law of Motion. 24.11. Recoil of Gun. 24.12. Motion of a Boat. 24.13. Motion on an Inclined Planes.

25. Motion of Connected Bodies

503–527

25.1. Introduction. 25.2. Motion of Two Bodies Connected by a String and Passing over a Smooth Pulley. 25.3. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Smooth Horizontal Plane. 25.4. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Rough Horizontal Plane. 25.5. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Smooth Inclined Plane. 25.6. Motion of Two Bodies connected by a String, One of which is Hanging Free and the Other is Lying on a Rough Inclined Plane. 25.7. Motion of Two Bodies Connected by a String and Lying on Smooth Inclined Planes. 25.8. Motion of Two Bodies Connected by a String Lying on Rough Inclined Planes.

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26. Helical Springs and Pendulums

528–552

26.1. Introduction. 26.2. Helical Springs. 26.3. Helical Springs in Series and Parallel. 26.4. Simple Pendulum. 26.5. Laws of Simple Pendulum. 26.6. Gain or Loss in the No. of Oscillations due to Change in the Length of String or Acceleration due to Gravity of a Simple Pendulum. 26.7. Gain or Loss in the No. of Oscillations due to Change in the Position of a Simple Pendulum. 26.8. Compound Pendulum. 26.9. Centre of Oscillation (or Centre of Percussion). 26.10. Conical Pendulum.

27. Collision of Elastic Bodies

553–571

27.1. Introduction. 27.2. Phenomenon of Collision. 27.3. Law of Conservation of Momentum. 27.4. Newton’s law of Collision of Elastic Bodies. 27.5. Coefficient of Restitution. 27.6. Types of Collisions. 27.7. Direct Collision of Two Bodies. 27.8. Loss of Kinetic Energy During Collision. 27.9. Indirect Impact of Two Bodies. 27.10. Direct Impact of a Body with a Fixed Plane. 27.11. Indirect Impact of a Body with a Fixed Plane.

28. Motion Along a Circular Path

572–585

28.1. Introduction. 28.2. Centripetal Acceleration. 28.3. Centripetal Force. 28.4. Centrifugal Force. 28.5. Centrifugal Force Acting on a Body Moving Along a Circular Path. 28.6. Superelevation. 28.7. Effect of Superelevation in Roadways. 28.8. Effect of Superelevation in Railways. 28.9. Equilibrium Speed for Superelevation. 28.10. Reactions of a Vehicle Moving along a Level Circular Path. 28.11. Equilibrium of a Vehicle Moving along a Level Circular Path. 28.12. Maximum velocity to Avoid Overturning of a Vehicle Moving along a Level Circular Path. 28.13. Maximum Velocity to Avoid Skidding Away of a Vehicle Moving along a Level Circular Path.

29. Balancing of Rotating Masses

586–598

29.1. Introduction. 29.2. Methods for Balancing of Rotating Masses. 29.3. Types of Balancing of Rotating Masses. 29.4. Balancing of a Single Rotating Mass. 29.5. Balancing of a Single Rotating Mass by Another Mass in the Same Plane. 29.6. Balancing of a Single Rotating Mass by Two Masses in Different Planes. 29.7. Balancing of Several Rotating Masses. 29.8. Analytical Method for the Balancing of Several Rotating Masses in one Plane by Another Mass in the Same Plane. 29.9. Graphical Method for the Balancing of Several Rotating Masses in One Plane by Another Mass in the Same Plane. 29.10. Centrifugal governor. 29.11. Watt Governor.

30. Work, Power and Energy

599–621

30.1. Introduction. 30.2. Units of Work. 30.3. Graphical Representation of Work. 30.4. Power. 30.5. Units of Power. 30.6. Types of Engine Powers. 30.7. Indicated Power. 30.8. Brake Power. 30.9. Efficiency of an Engine. 30.10. Measurement of Brake Power. 30.11. Rope Brake Dynamometer. 30.12. Proney Brake Dynamometer. 30.13. Froude and Thorny...