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Mechanical Engineering Principles

299 Pages · 2007 · 2.59 MB · English

  • Mechanical Engineering Principles

    Mechanical Engineering Principles This Page Intentionally Left Blank Mechanical Engineering Principles


    JOHN BIRD


    BSc, CEng, CMath, FIMA, MIEE, FCollP, FIIE


    CARL ROSS


    BSc, PhD, DSc, CEng, FRINA, MSNAME


    Newnes


    OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Newnes


    An imprint of Butterworth-Heinemann


    Linacre House, Jordan Hill, Oxford OX2 8DP


    225 WildwoodAvenue, Woburn, MA 01801-2041


    A divisionof Reed Educational and Professional PublishingLtd


    First published2002


    © John Bird and Carl Ross 2002


    Allrightsreserved.Nopartofthispublication


    maybereproducedinanymaterialform(including


    photocopyingorstoringinanymediumbyelectronic


    meansandwhetherornottransientlyorincidentally


    tosomeotheruseofthispublication)withoutthe


    writtenpermissionofthecopyrightholderexcept


    inaccordancewiththeprovisionsoftheCopyright,


    DesignsandPatentsAct1988orunderthetermsofa


    licenceissuedbytheCopyrightLicensingAgencyLtd,


    90TottenhamCourtRoad,London,EnglandW1P9HE.


    Applicationsforthecopyrightholder’swrittenpermission


    toreproduceanypartofthispublicationshouldbeaddressed


    tothepublishers


    British Library Cataloguing in Publication Data


    A catalogue record for this book is availablefrom the British Library


    Library of Congress Cataloguing in Publication Data


    A catalogue record for this book is availablefrom the Library of Congress


    ISBN 0 7506 5228 4


    For information on all Newnes publications visit our website at www.newnespress.com


    Typeset by Laserwords Pvt. Ltd., Chennai, India


    Printed and bound in Contents


    Preface ix 4.2 Workedproblemsonmechanisms


    and pin-jointed trusses 41


    Part 1 Statics and strength of materials 1 4.3 Graphical method 42


    4.4 Method of joints (a


    mathematical method) 46


    1 The effects of forces on materials 1


    4.5 The method of sections


    1.1 Introduction 1


    (a mathematical method) 52


    1.2 Tensile force 2


    1.3 Compressive force 2


    Assignment 1 55


    1.4 Shear force 2


    1.5 Stress 2


    1.6 Strain 3 5 Simply supported beams 57


    1.7 Elasticity, limit of 5.1 The moment of a force 57


    proportionality and elastic limit 6 5.2 Equilibrium and the


    1.8 Hooke’s law 7 principle of moments 58


    1.9 Ductility, brittleness 5.3 Simply supported beams


    and malleability 11 having point loads 61


    1.10 Modulus of rigidity 12 5.4 Simply supported


    1.11 Thermal strain 12 beams with couples 64


    1.12 Compound bars 13


    6 Bending moment and 69


    2 Tensile testing 18 shear force diagrams


    2.1 The tensile test 18 6.1 Introduction 69


    2.2 Worked problems 6.2 Bending moment (M) 69


    on tensile testing 19 6.3 Shearing force (F) 69


    2.3 Further worked problems 6.4 Worked problems on


    on tensile testing 21 bending moment and


    shearing force diagrams 70


    3 Forces acting at a point 25 6.5 Uniformly distributed loads 78


    3.1 Scalar and vector quantities 25


    3.2 Centreofgravityandequilibrium 25 7 First and second moment of areas 84


    3.3 Forces 26 7.1 Centroids 84


    3.4 The resultant of 7.2 The first moment of area 84


    two coplanar forces 27 7.3 Centroid of area between


    3.5 Triangle of forces method 28 a curve and the x-axis 84


    3.6 The parallelogram 7.4 Centroid of area between


    of forces method 29 a curve and the y-axis 85


    3.7 Resultant of coplanar 7.5 Worked problems on


    forces by calculation 29 centroids of simple shapes 86


    3.8 Resultant of more than 7.6 Further worked problems on


    two coplanar forces 30 centroids of simple shapes 87


    3.9 Coplanar forces in equilibrium 32 7.7 Second moments of


    3.10 Resolution of forces 34 area of regular sections 88


    3.11 Summary 37 7.8 Second moment of area


    for ‘built-up’ sections 96


    4 Forces in structures 40


    4.1 Introduction 40 Assignment 2 102 vi MECHANICALENGINEERINGPRINCIPLES


    8 Bending of beams 103 15 Friction 170


    8.1 Introduction 103 15.1 Introduction to friction 170


    σ M E 15.2 Coefficient of friction 170


    8.2 To prove that = = 103


    y I R 15.3 Applications of friction 172


    8.3 Worked problems on 15.4 Friction on an inclined plane 173


    the bending of beams 105 15.5 Motion up a plane with


    the pulling force P


    parallel to the plane 173


    9 Torque 109


    15.6 Motion down a plane


    9.1 Couple and torque 109


    with the pulling force


    9.2 Work done and power


    P parallel to the plane 174


    transmitted by a constant torque 110


    15.7 Motion up a plane due


    9.3 Kinetic energy and


    to a horizontal force P 175


    moment of inertia 112


    15.8 The efficiency of a screw jack 177


    9.4 Power transmis-


    sion and efficiency 116


    16 Motion in a circle 182


    10 Twisting of shafts 120 16.1 Introduction 182


    10.1 Introduction 120 16.2 Motion on a curvedbankedtrack 184


    τ T Gθ 16.3 Conical pendulum 185


    10.2 To prove that = = 120 16.4 Motion in a vertical circle 187


    r J L


    10.3 Worked problems on 16.5 Centrifugal clutch 189


    the twisting of shafts 122


    17 Simple harmonic motion 191


    Assignment 3 126 17.1 Introduction 191


    17.2 Simple harmonic motion (SHM) 191


    Part 2 Dynamics 127 17.3 The spring-mass system 192


    17.4 The simple pendulum 194


    11 Linear and angular motion 127 17.5 The compound pendulum 195


    11.1 The radian 127 17.6 Torsional vibrations 196


    11.2 Linear and angular velocity 127


    11.3 Linear and angular acceleration 129 18 Simple machines 198


    11.4 Further equations of motion 130 18.1 Machines 198


    11.5 Relative velocity 132 18.2 Force ratio, movement


    ratio and efficiency 198


    12 Linear momentum and impulse 136 18.3 Pulleys 200


    12.1 Linear momentum 136 18.4 The screw-jack 202


    12.2 Impulse and impulsive forces 139 18.5 Gear trains 203


    18.6 Levers 205


    13 Force, mass and acceleration 144


    Assignment 5 209


    13.1 Introduction 144


    13.2 Newton’s laws of motion 144


    13.3 Centripetal acceleration 147 Part 3 Heat transfer and fluid mechanics 211


    13.4 Rotation of a rigid


    body about a fixed axis 149 19 Heat energy and transfer 211


    13.5 Moment of inertia (I) 149 19.1 Introduction 211


    19.2 The measurement of temperature 212


    14 Work, energy and power 153 19.3 Specific heat capacity 212


    14.1 Work 153 19.4 Change of state 214


    14.2 Energy 157 19.5 Latent heats of fusion


    14.3 Power 159 and vaporisation 215


    14.4 Potential and kinetic energy 162 19.6 A simple refrigerator 217


    14.5 Kinetic energy of rotation 165 19.7 Conduction, convec-


    tion and radiation 217


    Assignment 4 169 19.8 Vacuum flask 218 CONTENTS vii


    19.9 Use of insulation 22.10 Float and tapered-tube meter 251


    in conserving fuel 218 22.11 Electromagnetic flowmeter 252


    22.12 Hot-wire anemometer 253


    20 Thermal expansion 221 22.13 Choice of flowmeter 253


    20.1 Introduction 221 22.14 Equation of continuity 253


    20.2 Practical applications 22.15 Bernoulli’s Equation 254


    of thermal expansion 221 22.16 Impact of a jet on


    20.3 Expansion and con- a stationary plate 255


    traction of water 222


    20.4 Coefficient of linear expansion 222 23 Ideal gas laws 258


    20.5 Coefficient of super- 23.1 Introduction 258


    ficial expansion 224 23.2 Boyle’s law 258


    20.6 Coefficient of cubic expansion 225 23.3 Charles’ law 259


    23.4 The pressure law 260


    Assignment 6 229


    23.5 Dalton’s law of partial pressure 260


    21 Hydrostatics 230 23.6 Characteristic gas equation 261


    21.1 Pressure 230 23.7 Worked problems on the


    21.2 Fluid pressure 231 characteristic gas equation 261


    21.3 Atmospheric pressure 232 23.8 Further worked problems on


    21.4 Archimedes’ principle 233 the characteristic gas equation 263


    21.5 Measurement of pressure 235


    21.6 Barometers 235 24 The measurement of temperature 267


    21.7 Absolute and gauge pressure 237 24.1 Introduction 267


    21.8 The manometer 237 24.2 Liquid-in-glass thermometer 267


    21.9 The Bourdon pressure gauge 238 24.3 Thermocouples 268


    21.10 Vacuum gauges 239 24.4 Resistance thermometers 270


    21.11 Hydrostatic pressure 24.5 Thermistors 272


    on submerged surfaces 240 24.6 Pyrometers 272


    21.12 Hydrostatic thrust 24.7 Temperature indicating


    on curved surfaces 241 paints and crayons 274


    21.13 Buoyancy 241 24.8 Bimetallic thermometers 274


    21.14 The stability of floating bodies 242 24.9 Mercury-in-steel thermometer 274


    24.10 Gas thermometers 275


    22 Fluid flow 247 24.11 Choice of measuring device 275


    22.1 Introduction 247


    22.2 Differential pressure flowmeters 247 Assignment 7 277


    22.3 Orifice plate 247


    A list of formulae 279


    22.4 Venturi tube 248


    22.5 Flow nozzle 249


    Greek alphabet 283


    22.6 Pitot-static tube 249


    22.7 Mechanical flowmeters 250 Answers to multiple-choice questions 284


    22.8 Deflecting vane flowmeter 250


    22.9 Turbine type meters 250 Index 287 Preface


    Mechanical Engineering Principles aims to MathematicsandScience,eachtopicconsideredin


    broaden the reader’s knowledge of the basic the text is presented in a way that assumes that


    principles that are fundamental to mechanical the reader has little previous knowledge of that


    engineering design and the operation of mechanical topic.


    systems. MechanicalEngineeringPrinciples containsover


    Modern engineering systems and products still 280 worked problems, followed by over 470 fur-


    rely upon static and dynamic principles to make ther problems (all with answers). The further


    them work. Even systems that appear to be entirely problems are contained within some 130 Exercises;


    electronichaveaphysicalpresencegovernedbythe each Exercise follows on directly from the rele-


    principles of statics. vant section of work, every few pages. In addition,


    Forclarity,thetextisdividedintothreesections, thetextcontains260multiple-choicequestions(all


    these being: with answers), and 260 short answer questions,


    the answers for which can be determined from the


    Part 1 Statics and strength of materials preceding material in that particular chapter. Where


    Part 2 Dynamics at all possible, the problems mirror practical situ-


    Part 3 Heat transfer and fluid mechanics ations found in mechanical engineering. 330 line


    diagrams enhance the understanding of the theory.


    Mechanical Engineering Principles covers the At regular intervals throughout the text are some


    following syllabuses: 7 Assignments to check understanding. For exam-


    ple, Assignment 1 covers material contained in


    Chapters 1 to 4, Assignment 2 covers the material


    (i) National Certificate/Diploma courses in


    inChapters 5to7,andsoon.Noanswersaregiven


    Mechanical Engineering


    (ii) Mechanical Engineering Principles (Ad- forthequestionsintheassignments,butalecturer’s


    guide has been produced giving full solutions and


    vanced GNVQ Unit 8)


    (iii) FurtherMechanicalEngineeringPrinciples suggestedmarkingscheme.Theguideisofferedfree


    to those staff that adopt the text for their course.


    (Advanced GNVQ Unit 12)


    At the end of the text, a list of relevant formulae


    (iv) Any introductory/access/foundation course


    is included for easy reference.


    involving Mechanical Engineering Principles


    ‘Learning by Example’ is at the heart of


    at University, and Colleges of Further and


    MechanicalEngineeringPrinciples.


    Higher education.


    Although pre-requisites for the modules covered John Bird and Carl Ross


    in this book include GCSE/GNVQ intermediate in University of Portsmouth Part 1 Statics and strength of


    materials


    1


    The effects of forces on materials


    • perform calculations using Hooke’s law


    At the end of this chapter you should be • plot a load/extension graph from given


    able to: data


    • define force and state its unit • define ductility, brittleness and malleabil-


    ity, with examples of each


    • recogniseatensileforceandstaterelevant


    • define rigidity or shear modulus


    practical examples


    • recognise a compressive force and state • understand thermal stresses and strains


    relevant practical examples • calculates stresses in compound bars


    • recognise a shear force and state relevant


    practical examples


    • define stress and state its unit


    1.1 Introduction


    F


    • calculate stress σ from σ =


    A A force exerted on a body can cause a change in


    • define strain either the shape or the motion of the body. The unit


    x of force is the newton, N.


    • calculate strain ε from ε = No solid body is perfectly rigid and when forces


    L


    areappliedtoit,changesindimensionsoccur.Such


    • defineelasticity,plasticity,limitofpropor- changes are not always perceptible to the human


    tionality and elastic limit eye since they are so small. For example, the span


    • state Hooke’s law of a bridge will sag under the weight of a vehicle


    and a spanner will bend slightly when tightening


    • define Young’s modulus of elasticity E a nut. It is important for engineers and designers to


    and stiffness appreciatetheeffectsofforcesonmaterials,together


    with their mechanical properties.


    • appreciate typical values for E


    Thethreemaintypesofmechanicalforcethatcan


    σ


    • calculate E from E = act on a body are: (i) tensile, (ii) compressive, and


    ε (iii) shear


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