Statics

Contents......Page 6
Preface......Page 4
1-1. Force......Page 11
1-5. Principle of Transmissibility of Force......Page 12
2-1. Vectors and Scalars......Page 14
2-2. Composition of Vectors......Page 15
2-4. Analytical Method of Composition......Page 16
2-6. Centroids or Mean Centres......Page 18
Examples......Page 20
3-1. Parallelogram of Forces......Page 22
3-2. Triangle of Forces......Page 24
3-21. Lami's Theorem......Page 25
3-22. Polygon of Forces......Page 26
3-3. Composition of Forces......Page 27
3-31. Expressions for the Resultant......Page 28
3-4. Conditions of Equilibrium......Page 29
3-42. Oblique Resolution......Page 30
3-5. Worked Examples......Page 31
3-6. Systems of Particles. Internal and External Forces......Page 32
3-7. Constraints. Smooth and Rough Bodies......Page 33
Examples......Page 36
4-2. Theorem of Moments......Page 41
4-21. Moment of a Force about a Line......Page 42
4-3. Parallel Forces......Page 43
4-4. Theorem of Moments for Parallel Forces......Page 45
4-5. Centre of Parallel Forces......Page 46
4-51. Centre of Gravity......Page 47
4-53. Analytical Formulae for Centre of Parallel Forces......Page 48
4-6. Couples......Page 50
4-61-3. Equivalence of Couples......Page 51
4-64. Specification of a Couple......Page 54
4-65. Composition of Couples......Page 55
Examples......Page 60
5-1. Reduction to a Force at any Point and a Couple......Page 66
5-2. Conditions of Equilibrium......Page 67
5-3. Analytical Method......Page 68
5-32. Worked Examples......Page 70
Examples......Page 73
6-2. Constraints and Degrees of Freedom......Page 77
6-21. Three Forces. Coplanar and Concurrent or Parallel......Page 78
6-3. Problems of two or more Bodies......Page 82
6-4. Reactions at Joints......Page 85
6-42. Working Rules......Page 87
6-5. Chain of Heavy Particles......Page 91
6-52. Chain of Heavy Rods......Page 93
Examples......Page 95
7-1, 7-2. Stresses in a Beam......Page 105
7-3. Relations between Bending Moment and Shearing Force......Page 108
7-4. Worked Examples......Page 110
Examples......Page 114
8-1. Graphical Determination of Resultant......Page 117
8-2. Pole of Force Diagram......Page 119
8-3. Parallel Forces......Page 121
8-4. Graphical Representation of Bonding Moment......Page 123
8-5. Reciprocal Figures......Page 126
8-6. Frameworks......Page 127
8-63. Bow's Notation......Page 129
8-7. Method of Sections......Page 134
8-8. Distributed Loads......Page 135
Examples......Page 138
9-1. Laws of Friction......Page 144
9-15. Angle of Friction and Cone of Friction......Page 146
9-17. Rolling Friction......Page 147
9-2. Problems......Page 148
9-22. Indeterminateness of Problems......Page 149
9-3. Initial Motion......Page 151
9-4. Friction in Unknown Directions......Page 155
9-5. Miscellaneous Problems......Page 159
Examples......Page 162
10-1. Formulae......Page 170
10-2. Rod. Parallelogram. Triangle. Quadrilateral. Tetrahedron. Pyramid. Cone......Page 171
10-31. Curves......Page 175
10-32. Areas and Surface Distributions......Page 177
10-341. Volumes of Revolution......Page 181
10-35. Zone of the Surface of a Sphere......Page 182
10-4. Orthogonal Projection......Page 184
10-41. Quadrant of an Ellipse......Page 185
10-5. Theorems of Pappus......Page 186
10-6. Lagrange's Formula......Page 187
Examples......Page 191
11-1. Work done by a Force......Page 197
11-14. Conservative Field of Force......Page 198
11-2. Virtual Work for a Single Particle......Page 200
11-23. Reactions which do no Work......Page 203
11-3. Virtual Work for it System of Bodies......Page 205
11-31. The Converse Theorem......Page 207
11-33. Applications......Page 208
11-34-6. Worked Examples......Page 210
11-4. Determination of Unknown Reactions......Page 215
11-5. Deduction of Conditions of Equilibrium......Page 219
11-6. Potential Energy......Page 221
11-62. Energy Test of Stability......Page 223
11-7. Rocking Cylinders and Spheres......Page 229
11-8. Hooke's Law......Page 230
Examples......Page 231
12-1. Equations of Equilibrium......Page 240
12-11-14. String on Smooth and Rough Curves......Page 241
12-2. The Common Catenary......Page 246
12-3. The Parabolic Chain and Suspension Bridge......Page 250
12-4. Chain of Variable Density or Thickness......Page 252
12-5. Catenary of Uniform Strength......Page 253
12-6. Elastic Strings.......Page 254
12-62. The Elastic Catenary......Page 255
12-7. Miscellaneous Examples......Page 256
Examples......Page 259
13-2. Extension of Bars. Young's Modulus......Page 265
13-21. Variable Extension......Page 266
13-23. Elastic Energy of Longitudinal Strain......Page 267
13-3. Bending of Bars......Page 268
13-4. Applications......Page 270
13-45. Theorem of Three Moments......Page 274
13-5. Combined Extension and Bending......Page 276
13-6. Elastic Energy......Page 277
13-7. General Equations for a Thin Rod bent in One Plane......Page 278
13-8. Euler's Strut......Page 279
13-9. Loaded Column......Page 280
Examples......Page 281
14-1. Reduction to a Force and a Couple......Page 285
14-2. Conditions of Equilibrium......Page 287
14-3. Poinsot's Central Axis. The Wrench......Page 288
14-33. Condition for a Single Resultant Force......Page 289
14-4. The Invariants......Page 291
14-41. Geometrical Representation of the Moment of a Force about a Line......Page 292
14-5. Wrench Equivalent to Two Forces......Page 293
14-51. Resultant of Two Wrenches......Page 294
14-6. Nul Points, Lines and Planes......Page 295
14-7. Conjugate Forces......Page 296
14-8. Equilibrium of Four Forces......Page 299
Examples......Page 301