Mechanical Engineering Principles

299 Pages·2007·2.59 MB·English

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
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First published2002
© John Bird and Carl Ross 2002
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ISBN 0 7506 5228 4
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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