Mechanical engineering principles / John Bird and Carl Ross.

Contents

Preface ix

Part Oneâ•…Revision of Mathematics 1
1 Revisionary Mathematics 3
1.1 Introduction 3
1.2 Radians and degrees 3
1.3 Measurement of angles 4
1.4 Triangle calculations 5
1.5 Brackets 7
1.6 Fractions 8
1.7 Percentages 9
1.8 Laws of indices 11
1.9 Simultaneous equations 14
Revision Test 1 Revisionary mathematics 18
Part Twoâ•…Statics and Strength
of Materials 21

2 The effects of forces on materials 23
2.1 Introduction 23
2.2 Tensile force 24
2.3 Compressive force 24
2.4 Shear force 24
2.5 Stress 24
2.6 Strain 25
2.7 Elasticity, limit of proportionality and elastic limit 27
2.8 Hooke’s law 28
2.9 Ductility, brittleness and malleability 32
2.10 Modulus of rigidity 32
2.11 Thermal strain 33
2.12 Compound bars 33

3 Tensile testing 39
3.1 The tensile test 39
3.2 Worked problems on tensile testing 40
3.3 Further worked problems on tensile testing 42
3.4 Proof stress 44

4 Forces acting at a point 46
4.1 Scalar and vector quantities 46
4.2 Centre of gravity and equilibrium 46
4.3 Forces 47
4.4 The resultant of two coplanar forces 48
4.5 Triangle of forces method 48
4.6 The parallelogram of forces method 50
4.7 Resultant of coplanar forces by calculation 50
4.8 Resultant of more than two
coplanar forces 51
4.9 Coplanar forces in equilibrium 53
4.10 Resolution of forces 54
4.11 Summary 58

5 Simply supported beams 61
5.1 The moment of a force 61
5.2 Equilibrium and the principle of moments 62
5.3 Simply supported beams
having point loads 64
5.4 Simply supported beams with couples 68
Revision Test 2â•…Forces, tensile testing and beams 72

6 Forces in structures 73
6.1 Introduction 73
6.2 Worked problems on mechanisms and pin-jointed trusses 74
6.3 Graphical method 75
6.4 Method of joints (a mathematical method) 79
6.5 The method of sections (a mathematical method) 84

7 Bending moment and shear force diagrams 87
7.1 Bending moment (M) 87
7.2 Shearing force (F) 87
7.3 Worked problems on bending moment and shearing force diagrams 88
7.4 Uniformly distributed loads 97

8 First and second moments of areas 102
8.1 Centroids 102
8.2 The first moment of area 102
8.3 Centroid of area between a curve and the x-axis 103
8.4 Centroid of area between a curve and the y-axis 103
viâ•… Contents
8.5 Worked problems on centroids of
simple shapes 104
8.6 Further worked problems on centroids
of simple shapes 105
8.7 Second moments of area of
regular sections 106
8.8 Second moment of area for‘built-up’ sections 113
Revision Test 3â•…Forces in structures,bending moment and shear force diagrams, and second moments of area 119

9 Bending of beams 120
9.1 Introduction 120
9.2 To prove that s = M = E y I R 121
9.3 Worked problems on the bending of beams 122

10 Torque 126
10.1 Couple and torque 126
10.2 Work done and power transmitted by a constant torque 127
10.3 Kinetic energy and moment of inertia 129
10.4 Power transmission and efficiency 132

11 Twisting of shafts 136
11.1 To prove that t = T = Gθr J L 136
11.2 Worked problems on the twisting of shafts 138
Revision Test 4â•…Bending of beams, torque and twisting of shafts 142
Part Three Dynamics 143

12 Linear and angular motion 145
12.1 The radian 145
12.2 Linear and angular velocity 145
12.3 Linear and angular acceleration 147
12.4 Further equations of motion 148
12.5 Relative velocity 150

13 Linear momentum and impulse 154
13.1 Linear momentum 154
13.2 Impulse and impulsive forces 157

14 Force, mass and acceleration 162
14.1 Introduction 162
14.2 Newton’s laws of motion 163
14.3 Centripetal acceleration 165
14.4 Rotation of a rigid body about a fixed axis 167
14.5 Moment of inertia (I) 167

15 Work, energy and power 170
15.1 Work 170
15.2 Energy 174
15.3 Power 175
15.4 Potential and kinetic energy 178
15.5 Kinetic energy of rotation 181
Revision Test 5â•…Linear and angular motion,momentum and impulse,
force, mass and acceleration, work, energy and power 184

16 Friction 185
16.1 Introduction to friction 185
16.2 Coefficient of friction 186
16.3 Applications of friction 187
16.4 Friction on an inclined plane 188
16.5 Motion up a plane with the pulling force P parallel to the plane 188
16.6 Motion down a plane with the pulling force P parallel to the plane 189
16.7 Motion up a plane due to a horizontal force P 189
16.8 The efficiency of a screw jack 192

17 Motion in a circle 196
17.1 Introduction 196
17.2 Motion on a curved banked track 198
17.3 Conical pendulum 199
17.4 Motion in a vertical circle 201
17.5 Centrifugal clutch 203

18 Simple harmonic motion 205
18.1 Introduction to simple
harmonic motion (SHM) 205
18.2 The spring-mass system 206
18.3 The simple pendulum 208
18.4 The compound pendulum 209
18.5 Torsional vibrations 210

19 Simple machines 212
19.1 Machines 212
19.2 Force ratio, movement ratio and efficiency 212
19.3 Pulleys 214
19.4 The screw-jack 216
19.5 Gear trains 216
19.6 Levers 218

Revision Test 6â•…Friction, motion in a circle,

simple harmonic motion and
simple machines 222
Contentsâ•… vii
Part Four Heat Transfer and Fluid
Mechanics 223

20 Heat energy and transfer 225
20.1 Introduction 225
20.2 The measurement of temperature 226
20.3 Specific heat capacity 226
20.4 Change of state 228
20.5 Latent heats of fusion and vaporisation 229
20.6 A simple refrigerator 231
20.7 Conduction, convection and radiation 231
20.8 Vacuum flask 232
20.9 Use of insulation in conserving fuel 232

21 Thermal expansion 235
21.1 Introduction 235
21.2 Practical applications of
thermal expansion 235
21.3 Expansion and contraction of water 236
21.4 Coefficient of linear expansion 236
21.5 Coefficient of superficial expansion 238
21.6 Coefficient of cubic expansion 239
Revision Test 7â•…Heat energy and transfer, and thermal expansion 243

22 Hydrostatics 244
22.1 Pressure 244
22.2 Fluid pressure 245
22.3 Atmospheric pressure 247
22.4 Archimedes’ principle 248
22.5 Measurement of pressure 249
22.6 Barometers 249
22.7 Absolute and gauge pressure 251
22.8 The manometer 252
22.9 The Bourdon pressure gauge 253
22.10 Vacuum gauges 253
22.11 Hydrostatic pressure on submerged surfaces 254
22.12 Hydrostatic thrust on curved surfaces 255
22.13 Buoyancy 255
22.14 The stability of floating bodies 255

23 Fluid flow 261
23.1 Differential pressure flowmeters 261
23.2 Orifice plate 262
23.3 Venturi tube 262
23.4 Flow nozzle 263
23.5 Pitot-static tube 263
23.6 Mechanical flowmeters 264
23.7 Deflecting vane flowmeter 264
23.8 Turbine type meters 264
23.9 Float and tapered-tube meter 265
23.10 Electromagnetic flowmeter 266
23.11 Hot-wire anemometer 266
23.12 Choice of flowmeter 267
23.13 Equation of continuity 267
23.14 Bernoulli’s equation 267
23.15 Impact of a jet on a stationary plate 269

24 Ideal gas laws 272
24.1 Boyle’s law 272
24.2 Charles’ law 273
24.3 The pressure law 274
24.4 Dalton’s law of partial pressure 275
24.5 Characteristic gas equation 275
24.6 Worked problems on the
characteristic gas equation 275
24.7 Further worked problems on the
characteristic gas equation 277

25 The measurement of temperature 281
25.1 Liquid-in-glass thermometer 281
25.2 Thermocouples 282
25.3 Resistance thermometers 284
25.4 Thermistors 286
25.5 Pyrometers 286
25.6 Temperature indicating paints
and crayons 287
25.7 Bimetallic thermometers 288
25.8 Mercury-in-steel thermometer 288
25.9 Gas thermometers 288
25.10 Choice of measuring devices 288
Revision Test 8â•…Hydrostatics, fluid flow, gas laws and temperature measurement 290

A list of formulae for mechanical engineering principles 291
Greek alphabet 296
Answers to multiple-choice questions 297
Index 299

"Mechanical Engineering Principles offers a student-friendly introduction to core engineering topics that does not assume any previous background in engineering studies, and as such can act as a core textbook for several engineering courses. Bird and Ross introduce mechanical principles and technology through examples and applications rather than theory. This approach enables students to develop a sound understanding of the engineering principles and their use in practice. Theoretical concepts are supported by over 600 problems and 400 worked answers.The new edition will match up to the latest BTEC National specifications and can also be used on mechanical engineering courses from Levels 2 to 4"-- Provided by publisher.

"In this book John Bird and Carl Ross introduce mechanical principles and technology through examples and applications - enabling students to develop a sound understanding of the principles needed by professional engineers and technicians. No previous background in engineering is assumed and theoretical concepts are supported by over 600 problems and worked examples. This completely new text is designed to match a wide range of pre-degree courses, and provide an accessible introduction for undergraduates with no previous background in engineering studies. The authors have ensured syllabus-match for the leading UK courses at this level: AVCE optional units Mechanical Engineering Principles and Further Mechanical Engineering Principles, and the new BTEC National unit: Mechanical Principles"-- Provided by publisher.