A text book on Engineering Mechanics.pdf

Dr. U.C. JindalM.Tech, Ph.D.

Former Professor & Head of the Department

Department of Mechanical Engineering

Delhi College of Engineering, Delhi

by

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Engineering Mechanics : Dr. U.C. JindalCopyright 2013, by MADE EASY Publications.All rights are reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photo-copying, recording or otherwise), without the prior written permission of the above mentioned publisher of this book.

First Edition: 2013ISBN: 978-93-81069-12-7

Published by: MADE EASY Publications, New Delhi-110016

MADE EASY

Dedicated to

My Students

PREFACE

At the outset I must thank Mr. B. Singh (Chairman and Managing Director of MADE EASY

Group) who has very kindly given me an opportunity to serve the student community

through the publication of this book on Engineering Mechanics.

The present book has been designed as a self study book taking into account the severe

shortage of technical teachers in engineering colleges and technical institutions.

The text in the book is well explained through examples supplemented by self

explanatory illustrations, exercises supplemented by hints, key points to remember,

thought provoking multiple choice questions, special problems so that a student can

learn this basic subject in the shortest possible time.

The book covers all the syllabi in Engineering Mechanics of all the universities, IITs,

NITs, deemed universities. Students appearing in competitive examinations of UPSC,

GATE, PSUs will find the book as an asset to them. The book also serves the purpose

of AMIE students.

The book will greatly help the students who could not grasp the subject in the class

room.

Any suggestion for the improvement in the text of the book will be thankfully

acknowledged.

March, 2013 Dr. U. C. Jindal

Author

1. Vector Quantities in Mechanics ........................................................11.1 Introduction .................................................................................................................. 11.2 Position Vector ............................................................................................................. 11.3 Displacement Vector .................................................................................................... 21.4 Force Vector ................................................................................................................. 31.5 Moment of a Force about a Point ................................................................................. 41.6 Varignons Theorem ..................................................................................................... 61.7 Moment of a Force about an Axis ................................................................................ 71.8 Couple and its Moment ................................................................................................ 91.9 Component of a Couple about a Line ........................................................................ 11

Problems ..................................................................................................................... 13Key points to Remember ............................................................................................ 16Practice Problems ....................................................................................................... 17Special Problems ........................................................................................................ 19Multiple Choice Questions ......................................................................................... 20

2. eQuiValent coplanar Force systeMs ...........................................222.1 Introduction ................................................................................................................ 222.2 Resultant of a Force by an Equivalent Couple and a Force at any Other Point ......... 242.3 Resultant of a Coplanar Force System ....................................................................... 252.4 Resultant of a Parallel Forces Systems ...................................................................... 262.5 System of Distributed Forces ..................................................................................... 28

Problems ..................................................................................................................... 30Key Points to Remember ........................................................................................... 32Practice Problems ....................................................................................................... 33Special Problems ........................................................................................................ 34Multiple Choice Questions ......................................................................................... 35

3. eQuilibriuM oF rigid bodies ...............................................................383.1 Introduction ................................................................................................................ 383.2 Support Reactions ...................................................................................................... 383.3 Free body Diagrams ................................................................................................... 403.4 Conditions of Equilibrium.......................................................................................... 423.5 System of Concurrent Coplanar Forces ..................................................................... 443.6 Coplanar Force Systems ............................................................................................. 453.7 Equilibrium of a Two Force Body .............................................................................. 473.8 Equilibrium of a Three Force Body ........................................................................... 48

CONTENTS

3.9 Lamis Theorem ......................................................................................................... 503.10 Two Parallel Forces .................................................................................................... 513.11 Several Parallel Forces in a Plane .............................................................................. 53


4. plane trusses .........................................................................................674.1 Introduction ................................................................................................................ 674.2 Types of Plane Trusses ............................................................................................... 674.3 Determination of Support Reactions .......................................................................... 684.4 Determination of Forces in Members of the Truss..................................................... 704.5 Method of Joints ......................................................................................................... 714.6 Graphical Method....................................................................................................... 724.7 Method of Sections .................................................................................................... 754.8 Wind Loads on a Truss ............................................................................................... 78

Practice Problems ....................................................................................................... 85Special Problems ........................................................................................................ 87Multiple Choice Questions ......................................................................................... 88

5. centroid and center oF graVity .....................................................965.1 Introduction ................................................................................................................ 965.2 Location of Centroid .................................................................................................. 965.3 Centroid of Simple Sections....................................................................................... 995.4 Centroid of Area Covered under a Curve ................................................................. 1035.5 Centroid of Composite Section ................................................................................ 1075.6 Centre of Gravity of 3 Dimensional Bodies ............................................................. 1095.7 Centre of Gravity of Composite Bodies ................................................................... 1115.8 Theorems of Pappus-Guldinus ................................................................................. 112

Problems ................................................................................................................... 113Key Points to Remember ......................................................................................... 117Practice Problems ..................................................................................................... 118Special Problems ...................................................................................................... 119Multiple Choice Questions ....................................................................................... 121

6. beaMs ........................................................................................................1246.1 Introduction .............................................................................................................. 1246.2 Shear Force in a Beam Section ................................................................................ 1246.3 Bending Moment on a Beam Section....................................................................... 126

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3.9 Lamis Theorem ......................................................................................................... 503.10 Two Parallel Forces .................................................................................................... 513.11 Several Parallel Forces in a Plane .............................................................................. 53


4. plane trusses .........................................................................................674.1 Introduction ................................................................................................................ 674.2 Types of Plane Trusses ............................................................................................... 674.3 Determination of Support Reactions .......................................................................... 684.4 Determination of Forces in Members of the Truss..................................................... 704.5 Method of Joints ......................................................................................................... 714.6 Graphical Method....................................................................................................... 724.7 Method of Sections .................................................................................................... 754.8 Wind Loads on a Truss ............................................................................................... 78

Practice Problems ....................................................................................................... 85Special Problems ........................................................................................................ 87Multiple Choice Questions ......................................................................................... 88

5. centroid and center oF graVity .....................................................965.1 Introduction ................................................................................................................ 965.2 Location of Centroid .................................................................................................. 965.3 Centroid of Simple Sections....................................................................................... 995.4 Centroid of Area Covered under a Curve ................................................................. 1035.5 Centroid of Composite Section ................................................................................ 1075.6 Centre of Gravity of 3 Dimensional Bodies ............................................................. 1095.7 Centre of Gravity of Composite Bodies ................................................................... 1115.8 Theorems of Pappus-Guldinus ................................................................................. 112


6. beaMs ........................................................................................................1246.1 Introduction .............................................................................................................. 1246.2 Shear Force in a Beam Section ................................................................................ 1246.3 Bending Moment on a Beam Section....................................................................... 126

6.4 Uniformly distributed Load on a Beam ................................................................... 1286.5 Variable Load on Beam ............................................................................................ 1306.6 Turning Moment Applied on a Beam ....................................................................... 131

Problems ................................................................................................................... 132Key Points to Remember ......................................................................................... 134Practice Problems ..................................................................................................... 134Multiple choice questions ........................................................................................ 135

7. spatial Forces ......................................................................................1387.1 Introduction .............................................................................................................. 1387.2 Rectangular Components of a Force in Space ......................................................... 1387.3 A Force Passing Through Two Points ...................................................................... 1407.4 Resultant of Forces in Space .................................................................................... 1417.5 General Case of Three Dimensional Forces ............................................................. 143

Problems ................................................................................................................... 144Key Points to Remember ......................................................................................... 145Practice Problems ..................................................................................................... 146Special Problems ...................................................................................................... 147Multiple choice Questions........................................................................................ 148

8. Friction ....................................................................................................1508.1 Introduction .............................................................................................................. 1508.2 Laws of Dry Friction or Coulombs Friction ........................................................... 1518.3 Angle of Friction ...................................................................................................... 1528.4 Block on a Horizontal Plane .................................................................................... 1548.5 Two Mating Blocks .................................................................................................. 1558.6 Cylinder Resting on a Floor and Against a Vertical Wall ......................................... 1568.7 Angle of Repose ....................................................................................................... 1588.8 A Force Applied on a Body Lying on an Inclined Plane .......................................... 1588.9 Bodies on Inclined Plane Connected Through a Link ............................................. 1608.10 Ladder ...................................................................................................................... 1628.11 Wedge ....................................................................................................................... 1648.12 Friction in Wheels .................................................................................................... 165


9. application oF Friction in Machines ............................................1789.1 Introduction .............................................................................................................. 178

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9.2 Screw Threads .......................................................................................................... 1789.3 Flat Belt Drive .......................................................................................................... 1829.4 Types of Flat Belt Drives ......................................................................................... 1869.5 V-Belt and Rope Drive ............................................................................................. 1879.6 Rolling Resistance .................................................................................................... 188


10. second MoMent oF area (MoMent oF inertia) ..........................19710.1 Introduction .............................................................................................................. 19710.2 Rectangular Section ................................................................................................. 19710.3 Triangular Section .................................................................................................... 19810.4 Circular Section ........................................................................................................ 19910.5 Polar Moment of Inertia ........................................................................................... 20010.6 Parallel Axes Theorem ............................................................................................. 20210.7 Moment of Inertia of a Section Enclosed by a Curve .............................................. 20410.8 Principal Axes and Product of Inertia ...................................................................... 20610.9 Parallel Axes Theorem for Product of Inertia .......................................................... 208


11. Virtual Work .........................................................................................21611.1 Introduction .............................................................................................................. 21611.2 Virtual Work ............................................................................................................. 21611.3 Work Done by a Couple ........................................................................................... 21711.4 Principle of Virtual Work Applied to Beams ............................................................ 21811.5 Potential Energy and Stability .................................................................................. 22111.5 Multiple Degrees of Freedom .................................................................................. 225


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12. rectilinear Motion .............................................................................23512.1 Introduction .............................................................................................................. 23512.2 Rectilinear Motion with Constant Acceleration ....................................................... 23612.3 Motion Under Gravity .............................................................................................. 23712.4 Acceleration as a Function of Time ......................................................................... 23912.5 Acceleration as a Function of Velocity .................................................................... 24112.6 Acceleration as a Function of Displacement ............................................................ 242 Problems ................................................................................................................... 244

Key Points to Remember ......................................................................................... 247Practice Problems ..................................................................................................... 248Special Problems ...................................................................................................... 248Multiple Choice Questions ....................................................................................... 249

13. curVilinear Motion .............................................................................25213.3 Hodograph ................................................................................................................ 25313.4 Rectangular Co-ordinates ......................................................................................... 25413.5 Tangential and Normal Co-ordinates ....................................................................... 25613.1 Introduction .............................................................................................................. 25213.2 Plane Curvilinear Motion ......................................................................................... 252


14. projectiles ............................................................................................26914.1 Introduction .............................................................................................................. 26914.2 Flight of a Projectile ................................................................................................. 26914.2 Trajectory of a Projectile .......................................................................................... 27114.3 Motion of a Body Thrown Horizontally .................................................................. 27314.4 Range of a Projectile along an Inclined Plane ......................................................... 274


15. relatiVe Velocity ................................................................................28415.1 Introduction .............................................................................................................. 28415.2 Motion Relative to a Frame in Translation .............................................................. 284

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15.3 Absolute and Relative Velocity in Plane Motion ..................................................... 287Problems ................................................................................................................... 289Key Points to Remember ......................................................................................... 294Practice Problems ..................................................................................................... 295Special Problems ...................................................................................................... 296Multiple Choice Questions ....................................................................................... 297

16. Motion oF rotation .............................................................................30116.1 Introduction .............................................................................................................. 30116.2 Rotation about a Fixed Axis ..................................................................................... 30216.3 Various Types of Motion of Rotation ....................................................................... 30416.4 Instantaneous Centre of Rotation ............................................................................. 308


17. kinetics oF a particle ........................................................................31817.1 Introduction .............................................................................................................. 31817.2 Newtons Second Law of Motion ............................................................................ 31817.3 Types of Problems .................................................................................................... 31917.4 Motion of Two Bodies in Contact ............................................................................ 32217.5 Tangential and Normal Forces in Curvilinear Motion ............................................. 32717.6 Constrained Motion .................................................................................................. 32817.7 Motion of a Bicycle Rider Along a Circular Track ................................................. 32917.8 Motion of a Vehicle on a Level Circular Road......................................................... 330

Problems ................................................................................................................... 332Key points to Remember .......................................................................................... 336Practice Problems ..................................................................................................... 336Special Problems ...................................................................................................... 337Multiple Choice Questions ....................................................................................... 338

18. dynaMics oF rigid bodies in translation ...................................34118.1 Introduction .............................................................................................................. 34118.2 D Alemberts Principle ............................................................................................ 342


xii

19. Motion oF connected bodies ..........................................................35519.1 Introduction .............................................................................................................. 355

Key Points to Remember ......................................................................................... 361Special Problems ...................................................................................................... 361Multiple Choice Questions ....................................................................................... 362

20. Mass MoMent oF inertia ....................................................................36420.1 Introduction .............................................................................................................. 36420.2 Moment of Inertia with Respect to a Co-ordinate Axis ........................................... 36520.3 Parallel-Axes Theorem ............................................................................................. 36720.4 Moment of Inertia of Thin Plates ............................................................................. 370

Problems ................................................................................................................... 371Key Points to Remember ......................................................................................... 374Practice Problems ..................................................................................................... 374Multiple Choice Questions ....................................................................................... 376

21. dynaMics oF rigid bodies in plane Motion .................................37821.1 Introduction .............................................................................................................. 378 Problems ................................................................................................................... 383

Key Points to Remember ......................................................................................... 388Practice Problems ..................................................................................................... 388Multiple Choice Questions ....................................................................................... 390

22. rotation about Fixed axis ................................................................39422.1 Introduction .............................................................................................................. 39422.2 Rotation about Centroidal Axis ................................................................................ 39622.3 Inertia Force Method ................................................................................................ 39722.4 Centre of Percussion ................................................................................................ 399


23. Work and energy .................................................................................41023.1 Introduction .............................................................................................................. 41023.2 Work done by a Force during Sliding Motion.......................................................... 41423.3 Work done by a Moment during Motion of Rotation............................................... 41523.4 Change of Potential Energy in a Spring ................................................................... 41723.5 Rolling Motion under Gravity .................................................................................. 418

Problems ................................................................................................................... 419

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Practice Problems ..................................................................................................... 424Special Problems ...................................................................................................... 425Multiple Choice Questions ....................................................................................... 426

24. iMpulse and MoMentuM .....................................................................43024.1 Introduction .............................................................................................................. 43024.2 Angular Impulse and Angular Momentum Principle ............................................... 43224.3 Pulse of Water Jet on a Vane .................................................................................... 43324.4 Pile and Pile Hammer............................................................................................... 436


25. iMpact: collision oF elastic bodies .............................................44825.1 Introduction .............................................................................................................. 44825.2 CoefficientofRestitution ......................................................................................... 44925.3 Oblique Central Impact ............................................................................................ 45125.4 Impact of a Body on another Stationery Body ......................................................... 45225.5 Loss of Kinetic Energy during Collision ................................................................. 453


index .........................................................................................................468

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A text book on Engineering Mechanics.pdf