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- ENGINEERING MECHANICS - EM
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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 (vii)

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