Mechanical Engineering Principles

Mechanical Engineering Principles
JOHN BIRD BSc, CEng, CMath, FIMA, MIEE, FCollP, FIIE
CARL ROSS BSc, PhD, DSc, CEng, FRINA, MSNAME
Contents
Preface ix
Part 1 Statics and strength of materials 1
1 The effects of forces on materials 1
1.1 Introduction 1
1.2 Tensile force 2
1.3 Compressive force 2
1.4 Shear force 2
1.5 Stress 2
1.6 Strain 3
1.7 Elasticity, limit of
proportionality and elastic limit 6
1.8 Hooke’s law 7
1.9 Ductility, brittleness
and malleability 11
1.10 Modulus of rigidity 12
1.11 Thermal strain 12
1.12 Compound bars 13
2 Tensile testing 18
2.1 The tensile test 18
2.2 Worked problems
on tensile testing 19
2.3 Further worked problems
on tensile testing 21
3 Forces acting at a point 25
3.1 Scalar and vector quantities 25
3.2 Centre of gravity and equilibrium 25
3.3 Forces 26
3.4 The resultant of
two coplanar forces 27
3.5 Triangle of forces method 28
3.6 The parallelogram
of forces method 29
3.7 Resultant of coplanar
forces by calculation 29
3.8 Resultant of more than
two coplanar forces 30
3.9 Coplanar forces in equilibrium 32
3.10 Resolution of forces 34
3.11 Summary 37
4 Forces in structures 40
4.1 Introduction 40
4.2 Worked problems on mechanisms
and pin-jointed trusses 41
4.3 Graphical method 42
4.4 Method of joints (a
mathematical method) 46
4.5 The method of sections
(a mathematical method) 52
Assignment 1 55
5 Simply supported beams 57
5.1 The moment of a force 57
5.2 Equilibrium and the
principle of moments 58
5.3 Simply supported beams
having point loads 61
5.4 Simply supported
beams with couples 64
6 Bending moment and
shear force diagrams
69
6.1 Introduction 69
6.2 Bending moment (M) 69
6.3 Shearing force (F) 69
6.4 Worked problems on
bending moment and
shearing force diagrams 70
6.5 Uniformly distributed loads 78
7 First and second moment of areas 84
7.1 Centroids 84
7.2 The first moment of area 84
7.3 Centroid of area between
a curve and the x-axis 84
7.4 Centroid of area between
a curve and the y-axis 85
7.5 Worked problems on
centroids of simple shapes 86
7.6 Further worked problems on
centroids of simple shapes 87
7.7 Second moments of
area of regular sections 88
7.8 Second moment of area
for ‘built-up’ sections 96
Assignment 2 102vi MECHANICAL ENGINEERING PRINCIPLES
8 Bending of beams 103
8.1 Introduction 103
8.2 To prove that
σ y
=
M I
=
E R
103
8.3 Worked problems on
the bending of beams 105
9 Torque 109
9.1 Couple and torque 109
9.2 Work done and power
transmitted by a constant torque 110
9.3 Kinetic energy and
moment of inertia 112
9.4 Power transmission and efficiency 116
10 Twisting of shafts 120
10.1 Introduction 120
10.2 To prove that
τ r
=
T J
=
Gθ
L
120
10.3 Worked problems on
the twisting of shafts 122
Assignment 3 126
Part 2 Dynamics 127
11 Linear and angular motion 127
11.1 The radian 127
11.2 Linear and angular velocity 127
11.3 Linear and angular acceleration 129
11.4 Further equations of motion 130
11.5 Relative velocity 132
12 Linear momentum and impulse 136
12.1 Linear momentum 136
12.2 Impulse and impulsive forces 139
13 Force, mass and acceleration 144
13.1 Introduction 144
13.2 Newton’s laws of motion 144
13.3 Centripetal acceleration 147
13.4 Rotation of a rigid
body about a fixed axis 149
13.5 Moment of inertia (I) 149
14 Work, energy and power 153
14.1 Work 153
14.2 Energy 157
14.3 Power 159
14.4 Potential and kinetic energy 162
14.5 Kinetic energy of rotation 165
Assignment 4 169
15 Friction 170
15.1 Introduction to friction 170
15.2 Coefficient of friction 170
15.3 Applications of friction 172
15.4 Friction on an inclined plane 173
15.5 Motion up a plane with
the pulling force P
parallel to the plane 173
15.6 Motion down a plane
with the pulling force
P parallel to the plane 174
15.7 Motion up a plane due
to a horizontal force P 175
15.8 The efficiency of a screw jack 177
16 Motion in a circle 182
16.1 Introduction 182
16.2 Motion on a curved banked track 184
16.3 Conical pendulum 185
16.4 Motion in a vertical circle 187
16.5 Centrifugal clutch 189
17 Simple harmonic motion 191
17.1 Introduction 191
17.2 Simple harmonic motion (SHM) 191
17.3 The spring-mass system 192
17.4 The simple pendulum 194
17.5 The compound pendulum 195
17.6 Torsional vibrations 196
18 Simple machines 198
18.1 Machines 198
18.2 Force ratio, movement
ratio and efficiency 198
18.3 Pulleys 200
18.4 The screw-jack 202
18.5 Gear trains 203
18.6 Levers 205
Assignment 5 209
Part 3 Heat transfer and fluid mechanics 211
19 Heat energy and transfer 211
19.1 Introduction 211
19.2 The measurement of temperature 212
19.3 Specific heat capacity 212
19.4 Change of state 214
19.5 Latent heats of fusion
and vaporisation 215
19.6 A simple refrigerator 217
19.7 Conduction, convection and radiation 217
19.8 Vacuum flask 218CONTENTS vii
19.9 Use of insulation
in conserving fuel 218
20 Thermal expansion 221
20.1 Introduction 221
20.2 Practical applications
of thermal expansion 221
20.3 Expansion and contraction of water 222
20.4 Coefficient of linear expansion 222
20.5 Coefficient of superficial expansion 224
20.6 Coefficient of cubic expansion 225
Assignment 6 229
21 Hydrostatics 230
21.1 Pressure 230
21.2 Fluid pressure 231
21.3 Atmospheric pressure 232
21.4 Archimedes’ principle 233
21.5 Measurement of pressure 235
21.6 Barometers 235
21.7 Absolute and gauge pressure 237
21.8 The manometer 237
21.9 The Bourdon pressure gauge 238
21.10 Vacuum gauges 239
21.11 Hydrostatic pressure
on submerged surfaces 240
21.12 Hydrostatic thrust
on curved surfaces 241
21.13 Buoyancy 241
21.14 The stability of floating bodies 242
22 Fluid flow 247
22.1 Introduction 247
22.2 Differential pressure flowmeters 247
22.3 Orifice plate 247
22.4 Venturi tube 248
22.5 Flow nozzle 249
22.6 Pitot-static tube 249
22.7 Mechanical flowmeters 250
22.8 Deflecting vane flowmeter 250
22.9 Turbine type meters 250
22.10 Float and tapered-tube meter 251
22.11 Electromagnetic flowmeter 252
22.12 Hot-wire anemometer 253
22.13 Choice of flowmeter 253
22.14 Equation of continuity 253
22.15 Bernoulli’s Equation 254
22.16 Impact of a jet on
a stationary plate 255
23 Ideal gas laws 258
23.1 Introduction 258
23.2 Boyle’s law 258
23.3 Charles’ law 259
23.4 The pressure law 260
23.5 Dalton’s law of partial pressure 260
23.6 Characteristic gas equation 261
23.7 Worked problems on the
characteristic gas equation 261
23.8 Further worked problems on
the characteristic gas equation 263
24 The measurement of temperature 267
24.1 Introduction 267
24.2 Liquid-in-glass thermometer 267
24.3 Thermocouples 268
24.4 Resistance thermometers 270
24.5 Thermistors 272
24.6 Pyrometers 272
24.7 Temperature indicating
paints and crayons 274
24.8 Bimetallic thermometers 274
24.9 Mercury-in-steel thermometer 274
24.10 Gas thermometers 275
24.11 Choice of measuring device 275
Assignment 7 277
A list of formulae 279
Greek alphabet 283
Answers to multiple-choice questions 284
Index 287
Index
Absolute pressure, 232, 237
Acceleration, centripetal, 147, 148
linear and angular, 129
Aneroid barometer, 237
Angle of repose, 173
Angular acceleration, 113
velocity, 128
Annulus, 92
Applications of friction, 172
Archimedes’ principle, 233
Atmospheric pressure, 232
Bar, 235
Barometer, 235
Beckman thermometer, 268
Belt, 116
Bending moment, 69
diagram, 70, 72
Bending of beams, 103
Bernoulli’s equation, 254
Bimetallic thermometer, 274
Bourdon pressure gauge, 238
Bow’s notation, 42
Boyle’s law, 258
Brittleness, 11
Built-up sections, 96
Buoyancy, 241
Celsius scale, 211
Centre of gravity, 25, 84
Centrifugal clutch, 189
force, 182
Centripetal acceleration, 147, 148
force, 148, 182
Centroidal axis, 105
Centroids, 84
Change of state, 214
Characteristic equation, 261
gas constant, 261
Charles’ law, 259
Clinical thermometer, 268
Clutch, 189
Coefficient of cubic expansion, 225
discharge, 254
friction, 170
linear expansion, 222
superficial expansion, 224
Compatibility, 13
Compound bars, 13
gear train, 204
pendulum, 195
Compression, 2
Compressive force, 2
Concurrent forces, 26
Conduction, 217
Conical pendulum, 185
Contraction, 221
Convection, 217
Coplanar forces, 26
in equilibrium, 32
resultant of, 27
Cosine rule, 29
Couple, 44, 109
Couples, 64
Cubic expansion, coefficient of, 225
Cup anemometers, 251
D’Alembert’s principle, 182
Dalton’s law of partial pressure, 260
Dead weight tester 239
Deflecting vane flowmeter, 250
Differential pressure flowmeters, 247
Ductility, 11
Dynamic friction, 170
coefficient of, 172
Efficiency, 116, 158
of a screw jack, 177
of a simple machine, 198
Effort, 198
Elastic collisions, 163
limit, 6, 18
Elasticity, 6
Electromagnetic flowmeter, 252
Energy, 157
kinetic, 162
potential, 162
Equation of continuity, 253
Equations of motion, 130
Equilibrium, 13, 25, 32, 58
Expansion, 221
and contraction of water, 222
First moment of area, 84, 88
Float and tapered tube meter, 251
Flowmeters, 247
electromagnetic, 252
mechanical, 250288 INDEX
Flow nozzle, 249
Flow through an orifice, 254
Fluid flow, 247
pressure, 231
Follower, 203
Force, 1, 144
centrifugal, 182
centripetal, 148, 182
gravitational, 144
ratio, 198
Forces, 26
acting at a point, 25
in structures, 40
graphical method, 42
method of joints, 46
method of sections, 52
Formulae, list of, 279
Fortin barometer, 236
Friction, 170
applications of, 172
coefficient of, 170
on an inclined plane, 173
Fulcrum, 58, 59
Gas laws, 258
thermometers, 275
Gauge pressure, 232, 237
Gear trains, 203
Gravitational force, 144
Greek alphabet, 283
Heat, 211
Hogging, 69
Hooke’s law, 7
Horizontal component, 34
Horsepower, 110
Hot-wire anemometer, 253
Hydrostatic pressure, 240
thrust on curved surface, 241
Hydrostatics, 230
Ideal gas, 260
laws, 258
Idler wheel, 203
Impact of a jet, 255
Impulse, 139
Impulsive forces, 139
Inclined plane, friction on, 173
manometer, 238
Inelastic collisions, 163
Inertia, 144
moment of, 149
Insulation, use of conserving fuel, 218
Isobaric process, 259
Isothermal change, 258
Joule, 112, 153, 157, 212
Kelvin, 211
Kinetic energy, 112, 162
of rotation, 165
Lamina, 25, 84
Latent heat, 215
of fusion, 215
of vaporisation, 215
Levers, 205
Limiting angle of repose, 173
coefficient of friction, 172
efficiency, 199
force ratio, 199
Limit of proportionality, 6, 18
Linear and angular acceleration, 129
motion, 127
velocity, 127
Linear expansion, coefficient of, 222
momentum, 136
Liquid-in-glass thermometer, 212, 267
Load, 198
Machines, 198
Malleability, 11
Manometer, 237
Maximum/minimum thermometers, 268
McLeod gauge, 239
Measurement of pressure, 235
temperature, 267
Mechanical advantage, 198
flowmeters, 250
Mechanisms, 41
Mercury-in-steel thermometer, 274
Mercury thermometers, 268
Metacentric height, 242
Method of joints, 46
sections, 52
Mid-ordinate rule, 154
Modulus of elasticity, 7
rigidity, 12, 120
Moment, 44, 57
of a force, 57
inertia, 112, 113, 149
resistance, 105
Momentum, 136
Motion down a plane, 174
in a circle, 182
in a vertical circle, 187
on a curved banked track, 184
up a plane, 173, 175
Movement ratio, 198
Neck, 19
Neutral axis, 103
layer, 103
Newton, 1, 144INDEX 289
Newton metre, 57, 105
Newton’s laws of motion, 136, 139, 144
Normal force, 170
Optical pyrometer, 273
Orifice plate, 247
Parallel axis theorem, 89, 150
Parallelogram of forces, 29
Partial pressure, 260
Pascal, 2, 230, 235
Pendulum, compound, 195
simple, 194
Permanent elongation, 19
Perpendicular axis theorem, 90
Pirani gauge, 240
Pitometer, 250
Pitot-static tube, 249
Pivot, 58
Plasticity, 6
Platinum coil, 271
Point loading, 61
Polar second moment of area, 120
Polygon of forces, 31
Potential energy, 162, 187
Power, 110, 159
transmission, 110, 116
Practical applications of thermal expansion, 221
Pressure, 230
absolute, 232, 237
atmospheric, 232
fluid, 231
gauge, 232, 237
gauges, 237
hydrostatic, 240
law, 259
measurement of, 235
partial, 260
Principle of conservation of energy, 157, 162
mass, 253
momentum, 136
Principle of moments, 58
Pulleys, 200
Pyrometers, 212, 272
Radian, 127
Radiation, 217
Radius of gyration, 89
Reaction, 145
Reactions, 61
Refrigerator, 217
Relative velocity, 132
Resistance thermometers, 212, 270
Resolution of forces, 29, 34
Resultant, 27, 70
Resultant of coplanar forces,
by calculation, 29
by vector addition, 27, 30
Rigidity modulus, 12, 120
Rotameters, 251
Rotary vane positive displacement meters, 251
Rotation of a rigid body, 149
Sagging, 69
Scalar quantity, 25, 132
Screw jack, 202
efficiency of, 177
Second moments of area, 88
for built-up sections, 96
table of, 91
Sensible heat, 215
Shear, 2
force, 2
modulus, 120
Shearing force, 69
diagram, 70, 72
Simple harmonic motion (SHM), 191
machines, 198
pendulum, 194
Simply supported beam, 57
having point loads, 61
practical applications, 61
with couples, 64
Sine rule, 29
Sliding friction, 170
coefficient of, 172
Specific heat capacity, 212
Spring-mass system, 192
Spur gears, 203
Stability of floating bodies, 242
Standard temperature and pressure (STP), 261
Statically indeterminate trusses, 41
Static friction, 170
coefficient of, 172
Stiction, 170
Stiffness, 7
Strain, 3
thermal, 12
Stress, 2
Strut, 40
Superficial expansion, coefficient of, 224
Temperature, 211
indicating paints, 274
measurement of, 212, 267
sensitive crayons, 274
Tensile force, 2
test, 18
Tension, 2
Testing to destruction, 18
Thermal expansion, 221
practical applications, 221
Thermal strain, 12
Thermistors, 272
Thermocouples, 212, 268
Thermodynamic scale, 211290 INDEX
Thermometer, 212, 267
Tie, 40
Torsional vibrations, 196
Torsion of shafts, 120
Torque, 109, 113
Total radiation pyrometer, 272
Triangle of forces, 28
Turbine flowmeter, 251
type meters, 250
Twisting of shafts, 120
Ultimate tensile strength (UTS), 19
Uniformly distributed loads (UDL), 78
Upper yield point, 19
U-tube manometer, 237
Vacuum flask, 218
gauge, 237, 239
Vector addition, 27
quantity, 25, 26, 132
Velocity, linear and angular, 127
ratio, 198
relative, 132
Venturi tube, 248
Vertical component, 34
Waist, 19
Water, expansion and contraction, 222
Watt, 159
Wheatstone bridge circuit, 271
Work, 153
done, 110, 153
Yield point, 18
stress, 18
Young’s modulus of elasticity, 7
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net