Statics: A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities (Cambridge Library Collection - Mathematics)

A. S. Ramsey (1867-1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on statics, published in 1934, was intended as a companion volume to his Dynamics of 1929 and like the latter was based upon his lectures to students of the mathematical tripos, but it assumes no prior knowledge of the subject, provides an introduction and offers more that 100 example problems with their solutions. Topics include vectors, forces acting at a point, moments, friction, centres of gravity, work and energy, and elasticity. 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 A textbook on statics first published in 1934, based upon lectures by the distinguished twentieth-century Cambridge mathematician, with over 100 examples for solution with their answers. Topics include vectors, forces acting at a point, moments, friction, centres of gravity, work and energy, and elasticity.