Mechanics and Analysis of Beams, Columns and Cables

The book illustrates the use of simple mathematical analysis techniques within the area of basic structural mechanics, in particular the elementary theories of beams, columns and cables. The focus is on: i) Identification of the physical background of the theories and their particular mathematical properties. ii) Demonstration of mathematical techniques for analysis of simple problems in structural mechanics, and identification of the relevant parameters and properties of the solution. iii) 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.

Concise textbook for an elementary course in structural mechanics The use of simple mathematical analysis techniques, in contrast to computational methods, is illustrated Although the scope of the text seems to be limited to a few classes of structures, the fundamental insight gained is helpful for the understanding of advanced methods Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction.- 1.1 Force systems.- 1.2 Equilibrium.- 1.3 Supports and reactions.- 1.4 In ternalforces.- 1.5 Principle of virtual work.- 1.6 Stress, strain and elasticity.- 1.7 Summary.- 1.8 Exercises.- 2 Beams.- 2.1 The mechanics of beam bending.- 2.2 Differential equations of beam bending.- 2.3 Statically determinate beams.- 2.4 Virtual work and beam displacements.- 2.5 Statically indeterminate beams.- 2.6 The beam bending element.- 2.7 Shear flexibility.- 2.8 Beams on elastic foundation.- 2.9 Inertial forces and beam vibrations.- 2.10 Summary.- 2.11 Exercises.- 3 Columns.- 3.1 Beam with normal force.- 3.2 Ideal straight columns.- 3.3 Imperfect columns.- 3.4 Bending of beam-columns.- 3.5 The 'Elastica'.- 3.6 Summary.- 3.7 Exercises.- 4 Cables.- 4.1 The suspended cable.- 4.2 Shallow cable theory.- 4.3 Static load on a cable.- 4.4 Shallow cable dynamics.- 4.5 Summary.- 4.6 Exercises.- References.- Appendix A. Beam load cases.- Appendix B. Integration formulas.