Statics: A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities

Cover......Page 1
Frontmatter......Page 6
PREFACE......Page 10
Contents......Page 12
1·1. Force......Page 18
1·5. Principle of Transmissibility of Force......Page 19
2·1. Vectors and Scalars......Page 21
2·2. Composition of Vectors......Page 22
2·4. Analytical Method of Composition......Page 23
2·6. Centroids or Mean Centres......Page 25
2·7. Centroid Method of Compounding Vectors......Page 26
Examples......Page 27
3·1. Parallelogram of Forces......Page 29
3·2. Triangle of Forces......Page 31
3·21. Lami\'s Theorem......Page 32
3·22. Polygon of Forces......Page 33
3·3. Composition of Forces......Page 34
3·31. Expressions for the Resultant......Page 35
3·4. Conditions of Equilibrium......Page 36
3·42. Oblique Resolution......Page 37
3·5. Worked Examples......Page 38
3·6. Systems of Particles. Internal and External Forces......Page 39
3·7. Constraints. Smooth and Rough Bodies......Page 40
Examples......Page 43
4·2. Theorem of Moments......Page 48
4·21. Moment of a Force about a Line......Page 49
4·3. Parallel Forces......Page 50
4·4. Theorem of Moments for Parallel Forces......Page 52
4·5. Centre of Parallel Forces......Page 53
4·51. Centre of Gravity......Page 54
4·53. Analytical Formulae for Centre of Parallel Forces......Page 55
4·6. Couples......Page 57
4·61--3. Equivalence of Couples......Page 58
4·64. Specification of a Couple......Page 61
4·65. Composition of Couples......Page 62
Examples......Page 67
5·1. Reduction to a Force at any Point and a Couple......Page 73
5·2. Conditions of Equilibrium......Page 74
5·3. Analytical Method......Page 75
5·32. Worked Examples......Page 77
Examples......Page 80
6·2. Constraints and Degrees of Freedom......Page 84
6·21. Three Forces...Coplanar and Concurrent or Parallel......Page 85
6·3. Problems of two or more Bodies......Page 89
6·4. Reactions at Joints......Page 92
6·42. Working Rules......Page 94
6·5. Chain of Heavy Particles......Page 98
6·52. Chain of Heavy Rods......Page 100
Examples......Page 102
7·1, 7·2. Stresses in a Beam......Page 112
7·3. Relations between Bending Moment and Shearing Force......Page 115
7·4. Worked Examples......Page 117
Examples......Page 121
8.1. Graphical Determination of Resultant......Page 124
8.2. Pole of Force Diagram......Page 126
8.3. Parallel Forces......Page 128
8.4. Graphical Representation of Bending Moment......Page 130
8.5. Reciprocal Figures......Page 133
8.6. Frameworks......Page 134
8.63. Bow\'s Notation......Page 136
8.7. Method of Sections......Page 141
8.8. Distributed Loads......Page 142
Examples......Page 145
9.1. Laws of Friction......Page 151
9.15. Angle of Friction and Cone of Friction......Page 153
9.17. Rolling Friction......Page 154
9.2. Problems......Page 155
9.22. Indeterminateness of Problems......Page 156
9.3. Initial Motion......Page 158
9.4. Friction in Unknown Directions......Page 162
9.5. Miscellaneous Problems......Page 166
Examples......Page 169
10.1. Formulae......Page 177
10.2. Rod. Parallelogram. Triangle. Quadrilateral. Tetrahedron. Pyramid. Cone......Page 178
10.31. Curves......Page 182
10.32. Areas and Surface Distributions......Page 184
10.341. Volumes of Revolution......Page 188
10.35. Zone of the Surface, of a Sphere......Page 189
10.4. Orthogonal Projection......Page 191
10.41. Quadrant of an Ellipse......Page 192
10.5. Theorems of Pappus......Page 193
10.6. Lagrange\'s Formula......Page 194
Examples......Page 198
11.1. Work done by a Force......Page 204
11.14. Conservative Field of Force......Page 205
11.2. Virtual Work for a Single Particle......Page 207
11.23. Reactions which do no Work......Page 210
11.3. Virtual Work for a System of Bodies......Page 212
11.31. The Converse Theorem......Page 214
11.33. Applications......Page 215
11.34--6. Worked Examples......Page 217
11.4. Determination of Unknown Reactions......Page 222
11.5. Deduction of Conditions of Equilibrium......Page 226
11.6. Potential Energy......Page 228
11.62. Energy Test of Stability......Page 230
11.7. Rooking Cylinders and Spheres......Page 236
11.8. Hooke\'sLaw......Page 237
Examples......Page 238
12.1. Equations of Equilibrium......Page 247
12.11--14. String on Smooth and Rough Curves......Page 248
12.2. The Common Catenary......Page 253
12.3. The Parabolic Chain and Suspension Bridge......Page 257
12.4. Chain of Variable Density or Thickness......Page 259
12.5. Catenary of Uniform Strength......Page 260
12.6. Elastic Strings......Page 261
12.62. The Elastic Catenary......Page 262
12.7. Miscellaneous Examples......Page 263
Examples......Page 266
13.2. Extension of Bars. Young\'s Modulus......Page 272
13.21. Variable Extension......Page 273
13.23. Elastic Energy of Longitudinal Strain......Page 274
13.3. Bending of Bars.......Page 275
13.4. Applications......Page 277
13.45. Theorem of Three Moments......Page 281
13.5. Combined Extension and Bending......Page 283
13.6. Elastic Energy......Page 284
13.7. General Equations for a Thin Rod bent in One Plane......Page 285
13.8. Euler\'s Strut......Page 286
13.9. Loaded Column......Page 287
Examples......Page 288
14.1. Reduction to a Force and a Couple......Page 292
14.2. Conditions of Equilibrium......Page 294
14.3. Poinsot\'s Central Axis. The Wrench......Page 295
14.33. Condition for a Single Resultant Force......Page 296
14.4. The Invariants......Page 298
14.41. Geometrical Representation of the Moment of a Force about a Line......Page 299
14.5. Wrench Equivalent to Two Forces......Page 300
14.51. Resultant of Two Wrenches......Page 301
14.6. Nul Points, Lines and Planes......Page 302
14.7. Conjugate Forces......Page 303
14.8. Equilibrium of Four Forces......Page 306
Examples......Page 308