A Manual of Applied Mechanics

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Charles Griffin and Company, 1872 - 648 من الصفحات
 

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Application to Inclined Forces acting through one Point
46
Application to any system of Forces
47
Application to Parallel Forces
48
Qf Weight and Centres of Gravity 69 Specific Gravity
49
System of Symmetrical Bodies
50
Homogeneous Body of any Figure
51
Centre of Gravity found by Addi tion
53
Centre of Gravity altered by Trans position
54
Flat Plates
55
Body with similar CrossSections
56
Curved Rod
57
Approximate Computation of In tegrals
58
Centre of Gravity found by Pro jection
61
Examples of Centres of Gravity
63
CONTENTS xi
65
Heterogeneous Body
68
Classes of Stress
69
Resultant of Stress its Magni tude
70
Centre of Stress or of Pressure
71
of º Stress
73
Moment of Bending Stress
75
Moment of Twisting Stress
76
Moments of Inertia of a Surface
77
its Composition and Resolution 96 Internal Stress in general
82
Simple Stress and its Normal In tensity 98 Reduction of Simple Stress to an Oblique Plane
83
Resolution of Oblique Stressinto Nor mal and Tangential Components
84
Pair of Conjugate Stresses
85
Planes of Equal Shear or Tan gential Stress
87
Stress on three Rectangular Planes
88
CHAPTER WI ON STABLE AND UNSTABLE EQUILIBRIUM Page
90
Tetraedron of Stress
91
Transformation of Stress
92
Principal Axes of Stress
94
Stress Parallel to one Plane
95
Principal Axes of Stress Parallel to one Plane
98
Equal Principal StressesFluid ressure
99
Opposite Principal Stresses com osing Shear
101
Ellipse of Stress Problems
105
Combined Stresses in one Plane
110
Of the Internal Equilibrium of Stress and Weight and the principles of Hydrostatics 114 Varying Internal Stress
112
General Problem of Internal Equi librium
113
Equilibrium of Fluids
117
Equilibrium of a Liquid
118
Equilibrium of a Floating Body
120
Pressure on an Immersed Body
122
Apparent Weights
123
Relative Specific Gravities
124
Pressure on an Immersed Plane
125
Pressure in an Indefinite Uni formly Sloping Solid
126
On the Parallel Projection of Stress and Weight
127
Stable and Unstable Equilibrium of a Free Body
128
OF STRUCTURES CHAPTER I DEFINITIONs AND GENERAL PRINCIPLEs 129 StructuresPiecesJoints 130 SupportsFoundations 129 129 131 Co...
129
Stability Strength and Stiffness
130
Resultant Gross Load
131
Equilibrium and Stability of Frames 137 Frame 138 Tie
132
Strut 140 Treatment of the 141 Beam under Parallel Forces
133
Beam under Inclined Forces
134
Load supported by three Parallel 135 Forces 144 Load supported by three Inclined Forces
135
Weight of a Bar
136
Triangular Frame
137
Triangular Frame under Parallel Forces
138
Polygonal FrameEquilibrium
139
Polygonal FrameStability
140
Polygonal Frame under Parallel Forces
141
arallel Forces
142
Rigidity of a Truss
144
Bar common to several Frames
145
Compound Trusses
148
Resistance of Frame at a Section
150
Halflattice Girder any Load
153
Halflattice Girder Uniform Load
156
Lattice Girder any Load
160
Lattice Girder Uniform Load
161
Transformation of Frames
162
Equilibrium of a Cord
163
168 Cord under Paraliel Loads
164
Suspension Bridge with Vertical ods
168
Flexible Tie 154 155 156 157 158 159 160 161 162 163 164
169
sººn Bridge with Sloping 008
171
Extrados and Intrados
173
Cord with Horizontal Extrados
175
Catenary
177
Centre of Gravity of a Flexible Structure 18
180
Linear Arches or Ribs
182
Circular Arch for Uniform Fluid Pressure
183
Elliptical Arches for Uniform Pressures
184
general
189
Arch see also 319A
190
Distorted Elliptic Arch
196
Stereostatic Arch
198
Pointed Arches
203
Approximate Hydrºstatic and Reostatic Arches
207
Adhesion
209
Angle of Repose
210
Table of Coefficients of Friction and Angles of Repose
211
Frictional Stability of Earth
212
Mass of Earth with Plane Surface
214
Principle of Least Resistance
215
Earth Loaded with its ownWeight216
216
Pressure of Earth against a Wer tical Plane
218
Supporting Power of Earth foundations
219
Abutting Power of Earth
220
Table of Examples
221
Frictional Tenacity or Bond of Masonry and Brickwork
222
Friction of Screws Keys and Wedges
226
Stability of a series of Blocks Line of ResistanceLine of Pressures
230
Analogy of Blockwork and Framework
231
Transformation of Blockwork Structures
232
Frictional Stability of a Trans formed Structure
233
Abutments classed
235
Rectangular Buttress
238
Towers and Chimneys
240
Dams or ReservoirWalls
243
Retaining Walls in general
249
Rectangular Retaining Walls
252
Trapezoidal Walls
254
Foundation Courses of Retaining Walls
255
Arches of Masonry
256
Line of Pressure in an Arch Condition of Stability
257
Angle Jointand Point of Rupture
259
Thrust of an Arch of Masonry
260
Abutments of Arches 26
261
Groined Vaults
262
Clustered Arches
263
Tunnels
264
Domes
265
Strength of Abutments and Vaults268
268
STRENGTH AND STIFFNEss SECTION 1 Summary of General Principles 236 Theory of Elasticity
270
Liquid Elasticity
271
Strain and Fracture
272
Strength Ultimate and Proof ToughnessStiffnessSpring
273
Determination of Proof Strength
274
Divisions of Mathematical Theory of Elasticity 249 Resolution and Composition of Strains
275
Displacements
276
Potential Energy of Elasticity
277
Coefficients of Pliability
278
Isotropic Solid
279
General Problem of Internal Equilibrium of an Elastic Solid
280
Ellipse of Strain
281
Ellipsoid of Strain
283
Transverse Elasticity of an Iso tropic Substance
284
Cubic Elasticity
285
SECTION 3 On Resistance to Stretching and Tearing 265 Stiffness and Strength of a Ticbar
286
Resilience or Spring of a TieBar Modulus of Resilience
287
Explanation of Table of the Re sistance of Materials to Stretch ing and Tearingsee Appen 288 dix 269 Additional dataWelded Joint Iron Wire Rop...
288
Fastenings of Timber Ties
301
On Resistance to Direct Compression and Crushing 282 Resistance to Compression
302
Limitations
306
Uniform Moment of Flexure
312
Deflection with Úniform Moment
330
Beam Fixed at one end and Sup
338
5
375
Internal Friction
377
Components of Varied Motion 386 Velocities 888
389
Rigid Bodieshow understood 300 Body from the Motions of three
395
common to all parts of 391 390 º of Epitrochoids
401
Property of all Motions of Rigid 397 Change of the Axis of Rotation
407
General Princi Steady Motion
416
THEORY OF MECHANISM CIIAPTER I DEFINITIONS AND GENERAL PRINCIPLEs Page 425 Theoryof PureMechanism defined
421
General Problem of Mechanism stated
422
4 Motion ºf Primary Moving pieces
423
Elementary Combinations in Me chanism
424
Train of Mechanism
425
ON ELEMENTARY CoMBINATIONs AND TRAns of MECHANISM SECTIon 1 Rolling Contact 437 PitchSurfaces
426
Circular Cylindrical Wheels
427
Bevel Wheels
428
Sliding Contact 444 SkewBevel Wheels
430
Grooved Wheels or Frictional Gearing
431
Pitch and Number of Teeth
433
Hunting Cog
434
Trains of widwork
435
Principle of Sliding Contact
437
Teeth of SpurWheels and Racks General Principle
438
Arc of Contact on Pitch Lines
440
Inside Gearing
441
Sliding of Involute Teeth
443
Epicycloidal Teethleast Pinion
444
Addendum for Epicycloidal Teeth
445
Teeth of Wheel and Trundle
447
Teeth ºf Bevel wheels 4 is 468 Teeth of SkewBevel Wheels
449
Belts Cords Chains
454
Pitch Surface of a Pulley or Drum 45 5
455
Length of an Endless Belt
456
Speed Cones
457
Linkwork 484 Definitions
458
Coupling of Parallel Axes
459
Eccentric
460
Hookes Universal Joint
461
Double Hookes Joint
462
Velocity of any Ply
463
Hydraulic Connection 498 General Principle
464
Hydraulic Press
465
ON AGGREGATE CoMBINATIONS 466 466 467 503 General Principles
466
Differential Windlass 505 Compound Screws
467
Link Motion
469
Epicyclic Trains
473
First Law of Motion
476
Conditions of Uniform Motion
477
Dynamometer or Indicator
478
Principle of Virtual Velocities
479
Energy of Component Forces and Motions
480
ON THE WARIED TRANSLATION of Poists AND RIGId BoDIEs SECTION 1 Definitions 521 Mass or Inertia
482
Variations and Deviations of Mo mentum
483
Deflecting 528 Relations between Impulse Energy and Work SECTION 2 Law of Varied Translation 529 Second Law of Motion
484
Mass in terms of Weight
485
Absolute Unit of Force
486
Projectile Unresisted
487
Motion along an Inclined Path
489
Uniform Effort or Resistance
490
Deviating Force
491
Revolving Simple Pendulum
492
Rectangular Components of De viating Force
493
Straight Oscillation
494
Elliptical Oscillations or Revo lutions
495
Simple Oscillating Pendulum
496
Cycloidal Pendulum
497
Residual Forces
498
Transformation of Energy 547 Actual Energy defined WisViva
499
Energy Stored and Restored
501
Energy due to Oblique Force
502
Reciprocating Force
503
Varied Translation of a System of Bodies 558 Conservation of Momentum
505
Angular Impulse Defined
506
Conservation of Angular Momen tum
507
Conservation of Internal Energy
508
Action of Unbalanced External Forces on a System General Equations
510
Determination of Internal Forces DAlemberts Principle
511
RotATIONs of Rigid BoDIEs
513
Motion of a Rigid Body in General Section 1 On Moments of Inertia Radii of Gyration Moments of Devia tion and Centres of Percussion 571 Mome...
514
Radius of Gyration
515
513 576 Moments of Inertia round Pa rallel Axes compared
516
Combined Moments of Inertia
517
Moments of Inertia found by Division and Subtraction
519
Centre of PercussionCentre of Gyration
520
No Centre of Percussion
522
Principal Axes of Inertia
526
Resultant Moment of Deviation
528
0n Uniform Rotation 587 Momentum
529
Actual Energy of Rotation
532
Free Rotation
533
Uniform Rotation about a Fixed Axis
535
Energy and Work of Couples 5
538
Law of Waried Rotation xiii
539
Varied Rotation about a fixed Axis540
540
Analogy of Varied Rotation and Varied Translation
541
Gyration or Angular Oscillation
542
Single Force applied to a Body with a Fixed Axis
543
Deviating Force
545
Compound Oscillating Pendulum Centre of Oscillation
546
Compound Revolving Pendulum
547
607 Ballistic Pendulum
548
Motions of PLIABLE Bodies 612 Vibrations not Isochronous
552
Isochronous Vibration Condi tion of Isochronism
553
Vibrations of a Mass held by a light Spring
554
Superposition of Small Motions
555
Vibrations of an Elastic Body in General
557
Waves of Vibration
562
Division of the Subject SECTION 1 Motion of Liquids without Friction
566
General
567
Dynamic Head
568
Total Energy
569
Free Surface
570
Contracted Wein
572
Surfaces of Equal Head
573
Radiating Current
574
Free Spiral Vortex
576
Vertical Revolution
578
Motions of Gases without Friction 635 Dynamic Head in Gases
579
Equation of Continuity for a teady Stream of Gas
581
637A Maximum Flow of Gas
582
Motions of Liquids with Friction 638 General Laws of Fluid Friction
584
566 639 Internal Fluid Friction
585
Friction in an Uniform Stream Hydraulic Mean Depth
586
Varying Stream
587
Friction in a Pipe running full
588
Resistance of Mouthpieces
589
General Problem
590
Mutual Impulse of Fluids and Solids 648 Pressure of a Jet against a fixed Surface
591
Pressure of a Forced Vortex against a Wheel
595
Centrifugal Pumps and Fans
597
Pressure of a Current 508
598
Stability of Floating Bodies Metacentre of a Ship
600
Oscillations of Floating Bodies
603
Action between a Fluid and a PistonWork of AirWork of Steam
607
Nature and Division of the Subject
609
Friction of a Pivot
616
Centrifugal Forces and Couples 621 689 Fluctuations of Speed
625
Forces 82
641
622
647

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