Mechanics and analysis of beams, columns and cables : a modern introduction to the classic theories

The book illustrates the use of simple maths-based analytic techniques in basic structural mechanics. It focuses on the identification of the physical background of the theories and their particular mathematical properties. And on the demonstration of mathematical techniques for analysis of simple problems in structural mechanics. The author also looks at the derivation of the solutions to a number of basic problems of structural mechanics in a form suitable for later reference. The presentation concentrates on the main principles and the characteristics of the solutions. The theory also serves as a basis for the formulation of numerical models and for intelligent interpretation of their results.

1 Introduction	p. 1
1.1 F orce systems	p. 2
1.2 Equilibrium	p. 5
1.3 Supports and reactions	p. 6
1.4 Internal forces	p. 10
1.5 Principle of virtual work	p. 13
1.6 Stress, strain and elasticity	p. 17
1.7 Summary	p. 21
1.8 Exercises	p. 22
2 Beams	p. 23
2.1 The mechanics of beam bending	p. 24
2.2 Diferential equations of beam bending	p. 33
2.3 Statically determinate beams	p. 37
2.4 Virtual work and beam displacements	p. 43
2.5 Statically indeterminate beams	p. 55
2.6 The beam bending element	p. 79
2.7 Shear lexibility	p. 90
2.8 Beams on elastic foundation	p. 103
2.9 Inertial forces and beam vibrations	p. 128
2.10 Summary	p. 144
2.11 Exercises	p. 146
3 Columns	p. 153
3.1 Beam with normal force	p. 154
3.2 Ideal straight columns	p. 160
3.3 Imperfect columns	p. 167
3.4 Bending of beam-columns	p. 170
3.5 The `Elastica'	p. 181
3.6 Summary	p. 190
3.7 Exercises	p. 192
4 Cables	p. 195
4.1 The suspended cable	p. 196
4.2 Shallow cable theory	p. 206
4.3 Static load on a cable	p. 212
4.4 Shallow cable dynamics	p. 221
4.5 Summary	p. 228
4.6 Exercises	p. 229
References	p. 233
Appendix A Beam load cases	p. 235
Appendix B Integration formulas	p. 241
Index	p. 243

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