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Mechanical Engineering Principles Second Edition Why are competent engineers so vital? Engineering is among the most important of all professions. It is the authors’ opinions that engineers save more lives than medical doctors (physicians). For example, poor water or the lack of it, is the second largest cause of human death in the world, and if engineers are given the tools, they can solve this problem. The largest cause of human death is caused by the malarial mosquito, and even death due to malaria can be decreased by engineers - by providing helicopters for spraying areas infected by the mosquito and making and designing medical syringes and pills to protect people against catching all sorts of diseases. Most medicines are produced by engineers! How does the engineer put 1 mg of ‘medicine’ precisely and individually into millions of pills, at an affordable price? Moreover, one of the biggest contributions by humankind was the design of the agricultural tractor, which was designed and built by engineers to increase food production many-fold for a human population which more-or-less quadruples every century! It is also interesting to note that the richest countries in the world are very heavily industrialised. Engineers create wealth! Most other professions don’t! Even in blue sky projects, engineers play a major role. For example, most rocket scientists are chartered engineers or their equivalents and Americans call their Chartered Engineers (and their equivalents), scientists. Astronomers are space scientists and not rocket scientists; they could not design a rocket to conquer outer space. Even modern theoretical physicists are mainly interested in astronomy and cosmology and also nuclear science. In general a theoretical physicist cannot, without special training, design a submarine structure to dive to the bottom of the Mariana Trench, which is 11.52 km or 7.16 miles deep, or design a very long bridge, a tall city skyscraper or a rocket to conquer outer space. This book presents a solid foundation for the reader in mechanical engineering principles, on which s/he can safely build tall buildings and long bridges that may last for a thousand years or more. It is the authors’ experience that it is most unwise to attempt to build such structures on shaky foundations; they may come tumbling down - with disastrous consequences. John O. Bird is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, U.K. More recently, he has combined freelance lecturing at the University of Portsmouth, with Examiner responsibilities for Advanced Mathematics with City & Guilds, and examining for the International Baccalaureate Organisation. He is the author of some 120 textbooks on engineering and mathematical subjects with worldwide sales approaching 1 million copies. He is currently a Senior Training Provider at the Royal Naval School of Marine Engineering in the Defence College of Marine and Air Engineering at H.M.S. Sultan, Gosport, Hampshire, U.K. Carl T. F. Ross gained his ﬁ rst degree in Naval Architecture, from King’s College, Durham University; his PhD in Structural Engineering from the Victoria University of Manchester; and was awarded his DSc in Ocean Engineering from the CNAA, London. His research in the ﬁ eld of engineering led to advances in the design of submarine pressure hulls. His publications to date exceed some 270 papers and books and he is Professor of Structural Dynamics at the University of Portsmouth, U.K. See Carl Ross’s website below, which has an enormous content on science, technology and education. http://homepage.ntlworld.com/carl.ross/page3.htm Mechanical Engineering Principles Second Edition John O. Bird, BSc(Hons), CEng, CMath, CSci, FIMA, FITE, FCollT Carl T. F. Ross, BSc(Hons), PhD, DSc, CEng, FRINA, MSNAME Second edition published 2012 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2012 John O. Bird and Carl T. F. Ross The right of John O. Bird and Carl T. F. Ross to be identified as authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. This publication presents material of a broad scope and applicability. Despite stringent efforts by all concerned in the publishing process, some typographical or editorial errors may occur, and readers are encouraged to bring these to our attention where they represent errors of substance. The publisher and author disclaim any liability, in whole or in part, arising from information contained in this publication. The reader is urged to consult with an appropriate licensed professional prior to taking any action or making any interpretation that is within the realm of a licensed professional practice. First edition published by Elsevier in 2002 Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalog record for this title has been requested ISBN: 9780415517850 (pbk) ISBN: 9780203121146 (ebk) Typeset in Times by RefineCatch Limited, Bungay, Suffolk Contents Preface ix 4.3 Forces 47 4.4 The resultant of two coplanar forces 48 4.5 Triangle of forces method 48 Part One Revision of Mathematics 1 4.6 The parallelogram of forces method 50 4.7 Resultant of coplanar forces by 1 Revisionary Mathematics 3 calculation 50 1.1 Introduction 3 4.8 Resultant of more than two 1.2 Radians and degrees 3 coplanar forces 51 1.3 Measurement of angles 4 4.9 Coplanar forces in equilibrium 53 1.4 Triangle calculations 5 4.10 Resolution of forces 54 1.5 Brackets 7 4.11 Summary 58 1.6 Fractions 8 1.7 Percentages 9 5 Simply supported beams 61 1.8 Laws of indices 11 5.1 The moment of a force 61 1.9 Simultaneous equations 14 5.2 E quilibrium and the principle of moments 62 Revision Test 1 Revisionary mathematics 18 5.3 S imply supported beams having point loads 64 5.4 Simply supported beams with couples 68 Part Two Statics and Strength Revision Test 2 F orces, tensile testing of Materials 21 and beams 72 2 The effects of forces on materials 23 2.1 Introduction 23 6 Forces in structures 73 2.2 Tensile force 24 6.1 Introduction 73 2.3 Compressive force 24 6.2 W orked problems on mechanisms 2.4 Shear force 24 and pin-jointed trusses 74 2.5 Stress 24 6.3 Graphical method 75 2.6 Strain 25 6.4 Method of joints 2.7 E lasticity, limit of proportionality (a mathematical method) 79 and elastic limit 27 6.5 The method of sections 2.8 Hooke’s law 28 (a mathematical method) 84 2.9 Ductility, brittleness and malleability 32 2.10 Modulus of rigidity 32 7 Bending moment and shear force diagrams 87 2.11 Thermal strain 33 7.1 Bending moment (M) 87 2.12 Compound bars 33 7.2 Shearing force (F) 87 7.3 Worked problems on bending 3 Tensile testing 39 moment and shearing force diagrams 88 3.1 The tensile test 39 7.4 Uniformly distributed loads 97 3.2 Worked problems on tensile testing 40 3.3 Further worked problems on 8 First and second moments of areas 102 tensile testing 42 8.1 Centroids 102 3.4 Proof stress 44 8.2 The first moment of area 102 8.3 C entroid of area between a curve 4 Forces acting at a point 46 and the x-axis 103 4.1 Scalar and vector quantities 46 8.4 C entroid of area between a 4.2 Centre of gravity and equilibrium 46 curve and the y-axis 103 vi Contents 8.5 W orked problems on centroids of 14.4 Rotation of a rigid body about a fixed axis 167 simple shapes 104 14.5 Moment of inertia (I) 167 8.6 F urther worked problems on centroids of simple shapes 105 15 Work, energy and power 170 8.7 S econd moments of area of 15.1 Work 170 regular sections 106 15.2 Energy 174 8.8 S econd moment of area for 15.3 Power 175 ‘built-up’ sections 113 15.4 Potential and kinetic energy 178 15.5 Kinetic energy of rotation 181 Revision Test 3 Forces in structures, bending moment and shear Revision Test 5 L inear and angular motion, force diagrams, and second m omentum and impulse, moments of area 119 force, mass and acceleration, work, energy and power 184 9 Bending of beams 120 9.1 Introduction 120 16 Friction 185 9.2 To prove that s = M = E 121 16.1 Introduction to friction 185 y I R 16.2 Coefficient of friction 186 9.3 W orked problems on the bending 16.3 Applications of friction 187 of beams 122 16.4 Friction on an inclined plane 188 16.5 M otion up a plane with the pulling 10 Torque 126 force P parallel to the plane 188 10.1 Couple and torque 126 16.6 M otion down a plane with the 10.2 W ork done and power transmitted pulling force P parallel to the plane 189 by a constant torque 127 16.7 M otion up a plane due to a horizontal 10.3 Kinetic energy and moment of inertia 129 force P 189 10.4 Power transmission and efficiency 132 16.8 The efficiency of a screw jack 192 11 Twisting of shafts 136 17 Motion in a circle 196 t T Gθ 11.1 To prove that = = 136 17.1 Introduction 196 r J L 17.2 Motion on a curved banked track 198 11.2 Worked problems on the 17.3 Conical pendulum 199 twisting of shafts 138 17.4 Motion in a vertical circle 201 17.5 Centrifugal clutch 203 Revision Test 4 Bending of beams, torque and twisting of shafts 142 18 Simple harmonic motion 205 18.1 Introduction to simple harmonic motion (SHM) 205 Part Three Dynamics 143 18.2 The spring-mass system 206 18.3 The simple pendulum 208 12 Linear and angular motion 145 18.4 The compound pendulum 209 12.1 The radian 145 18.5 Torsional vibrations 210 12.2 Linear and angular velocity 145 12.3 Linear and angular acceleration 147 19 Simple machines 212 12.4 Further equations of motion 148 19.1 Machines 212 12.5 Relative velocity 150 19.2 F orce ratio, movement ratio and efficiency 212 19.3 Pulleys 214 13 Linear momentum and impulse 154 19.4 The screw-jack 216 13.1 Linear momentum 154 19.5 Gear trains 216 13.2 Impulse and impulsive forces 157 19.6 Levers 218 14 Force, mass and acceleration 162 Revision Test 6 Friction, motion in a circle, 14.1 Introduction 162 simple harmonic motion and 14.2 Newton’s laws of motion 163 simple machines 222 14.3 Centripetal acceleration 165 Contents vii 23.4 Flow nozzle 263 Part Four Heat Transfer and Fluid 23.5 Pitot-static tube 263 Mechanics 223 23.6 Mechanical flowmeters 264 23.7 Deflecting vane flowmeter 264 20 Heat energy and transfer 225 23.8 Turbine type meters 264 20.1 Introduction 225 23.9 Float and tapered-tube meter 265 20.2 The measurement of temperature 226 23.10 Electromagnetic flowmeter 266 20.3 Specific heat capacity 226 23.11 Hot-wire anemometer 266 20.4 Change of state 228 23.12 Choice of flowmeter 267 20.5 Latent heats of fusion and vaporisation 229 23.13 Equation of continuity 267 20.6 A simple refrigerator 231 23.14 Bernoulli’s equation 267 20.7 Conduction, convection and radiation 231 23.15 Impact of a jet on a stationary plate 269 20.8 Vacuum flask 232 20.9 Use of insulation in conserving fuel 232 24 Ideal gas laws 272 24.1 Boyle’s law 272 21 Thermal expansion 235 24.2 Charles’ law 273 21.1 Introduction 235 24.3 The pressure law 274 21.2 P ractical applications of 24.4 Dalton’s law of partial pressure 275 thermal expansion 235 24.5 Characteristic gas equation 275 21.3 Expansion and contraction of water 236 24.6 Worked problems on the 21.4 Coefficient of linear expansion 236 characteristic gas equation 275 21.5 Coefficient of superficial expansion 238 24.7 Further worked problems on the 21.6 Coefficient of cubic expansion 239 characteristic gas equation 277 25 The measurement of temperature 281 Revision Test 7 Heat energy and transfer, 25.1 Liquid-in-glass thermometer 281 and thermal expansion 243 25.2 Thermocouples 282 25.3 Resistance thermometers 284 22 Hydrostatics 244 25.4 Thermistors 286 22.1 Pressure 244 25.5 Pyrometers 286 22.2 Fluid pressure 245 25.6 T emperature indicating paints 22.3 Atmospheric pressure 247 and crayons 287 22.4 Archimedes’ principle 248 25.7 Bimetallic thermometers 288 22.5 Measurement of pressure 249 25.8 Mercury-in-steel thermometer 288 22.6 Barometers 249 25.9 Gas thermometers 288 22.7 Absolute and gauge pressure 251 25.10 Choice of measuring devices 288 22.8 The manometer 252 22.9 The Bourdon pressure gauge 253 Revision Test 8 Hydrostatics, fluid flow, 22.10 Vacuum gauges 253 gas laws and temperature 22.11 Hydrostatic pressure on measurement 290 submerged surfaces 254 22.12 Hydrostatic thrust on curved surfaces 255 A list of formulae for mechanical 22.13 Buoyancy 255 engineering principles 291 22.14 The stability of floating bodies 255 Greek alphabet 296 23 Fluid flow 261 23.1 Differential pressure flowmeters 261 Answers to multiple-choice questions 297 23.2 Orifice plate 262 23.3 Venturi tube 262 Index 299 Preface Mechanical Engineering Principles 2nd Edition aims Although pre-requisites for the modules covered to broaden the reader’s knowledge of the basic principles in this book include Foundation Certificate/ diploma, that are fundamental to mechanical engineering design or similar, in Mathematics and Science, each topic and the operation of mechanical systems. considered in the text is presented in a way that assumes that the reader has little previous Modern engineering systems and products still rely knowledge of that topic. upon static and dynamic principles to make them work. Even systems that appear to be entirely electronic have a Mechanical Engineering Principles 2nd Edition physical presence governed by the principles of statics. contains over 325 worked problems, followed by In this second edition of Mechanical Engineering over 550 further problems (all with answers). Principles, a chapter has been added on revisionary The further problems are contained within some mathematics; it is not possible to progress in engineering 140 Exercises; each Exercise follows on directly studies without a reasonable knowledge of mathematics, from the relevant section of work, every few a fact that soon becomes obvious to both students and pages. In addition, the text contains 276 multiple- teachers alike. It is therefore hoped that this chapter on choice questions (all with answers), and 260 short basic mathematics revision will be helpful and make answer questions, the answers for which can be the engineering studies more comprehensible. Minor determined from the preceding material in that particular modifications and some further worked problems have chapter. Where at all possible, the problems mirror also been added throughout the text. practical situations found in mechanical engineering. 371 line diagrams enhance the understanding of the Free Internet downloads of full solutions to the fur- theory. ther problems and a PowerPoint presentation of all the illustrations contained in the text is available – see At regular intervals throughout the text are some page x. 8 Revision Tests to check understanding. For example, Revision Test 1 covers material contained in Chapter For clarity, the text is divided into four parts, these 1, Test 2 covers the material in Chapters 2 to 5, and being: so on. No answers are given for the questions in the Part 1 Revision of Mathematics Revision Tests, but a Lecturer’s guide has been Part 2 Statics and strength of materials produced giving full solutions and suggested marking Part 3 Dynamics scheme. The guide is offered online free to lecturer’s/ Part 4 Heat transfer and fluid mechanics instructor’s – see below. Mechanical Engineering Principles 2nd Edition is At the end of the text, a list of relevant formulae is suitable for the following: included for easy reference. (i) National Certificate/Diploma courses in ‘Learning by Example’ is at the heart of Mechanical Mechanical Engineering Engineering Principles, 2nd Edition. (ii) Undergraduate courses in Mechanical, Civil, Structural, Aeronautical & Marine JOHN BIRD Engineering, together with Naval Architecture Royal Naval School of Marine Engineering, (iii) Any introductory/access/foundation course HMS Sultan, formerly involving Mechanical Engineering Principles University of Portsmouth and Highbury at University, and Colleges of Further and College, Portsmouth Higher education. CARL ROSS Professor, University of Portsmouth