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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.
List of contents
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.
Summary
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.
Additional text
From the reviews of the second edition:
"As the title truly predicts, the book is restricted to elementary theory of beams, columns, and cables within their elastic regimes. … The whole book is written in a simple and clear style, appropriate for lecture notes. It can be recommended to undergraduate students." (A. Bertram, Technische Mechanik, Vol. 23 (1), 2003)
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From the reviews of the second edition:
"As the title truly predicts, the book is restricted to elementary theory of beams, columns, and cables within their elastic regimes. ... The whole book is written in a simple and clear style, appropriate for lecture notes. It can be recommended to undergraduate students." (A. Bertram, Technische Mechanik, Vol. 23 (1), 2003)
