Mechanical Engineering Principles

Contents
Preface  ix
Part One   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 Two   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 2    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 䭋rst 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
vi  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 3    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 ef䭋ciency  132
11   Twisting of shafts  136
11.1  To prove that 
t = T = Gθ
r J L
  136
11.2   Worked problems on the  
twisting of shafts  138
Revision Test 4   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 䭋xed 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 5    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  Coef䭋cient 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 ef䭋ciency 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 ef䭋ciency  212
19.3  Pulleys  214
19.4  The screw-jack  216
19.5  Gear trains  216
19.6  Levers  218
Revision Test 6   Friction, motion in a circle,  
simple harmonic motion and 
  simple machines  222
Contents  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  Speci8c 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 lask  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  Coef8cient of linear expansion  236
21.5  Coef8cient of super8cial expansion  238
21.6  Coef8cient of cubic expansion  239
Revision Test 7    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 loating bodies  255
23   Fluid 릹ow  261
23.1  Differential pressure lowmeters  261
23.2  Ori8ce plate  262
23.3  Venturi tube  262
23.4  Flow nozzle  263
23.5  Pitot-static tube  263
23.6  Mechanical lowmeters  264
23.7  Delecting vane lowmeter  264
23.8  Turbine type meters  264
23.9  Float and tapered-tube meter  265
23.10  Electromagnetic lowmeter  266
23.11  Hot-wire anemometer  266
23.12  Choice of lowmeter  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 8   Hydrostatics, 릹uid 릹ow, 
      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