Mechanics andAnalysis of Beams, Columns and Cables, Second Edition: A Modern Introduction to the ClassicTheories

9R27. Mechanics and Analysis of Beams, Columns and Cables, Second Edition: A Modern Introduction to the Classic Theories. - S Krenk (Dept of Civil Eng, Tech Univ of Denmark, Bldg 118, Brovej, Lyngby, DK-2800, Denmark). Springer-Verlag, Berlin. 2001. 245 pp. ISBN 3-540-41713-3. $54.95.Reviewed by A Cardou (Dept of Mech Eng, Laval Univ, Quebec PQ, G1K 7P4, Canada).As stated on the back cover, Krenk’s 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.” Thus, it covers material presented typically in undergraduate engineering curricula, in a “Strength of Materials” course, together with dynamic aspects generally found in vibrations textbooks—and all this material in a 245-page book. In fact, the present book emphasizes basic principles without going into the many “practical” applications which are usually found in undergraduate textbooks, and its presentation of beam, column, and cable theories is not as elementary as traditionally the case. On the contrary, being based on the virtual work approach, this book will provide an excellent preparation for those students interested in numerical applications and continuing on into a finite element course. Also, by including some beam and cable elementary dynamic analysis, the author brings together notions often obscured by the fact that they are presented to students in different courses. The book consists of four chapters, one short introduction, followed by longer chapters on each of the topics mentioned in the title: beams, columns, cables. In each chapter, basic hypotheses and results are discussed in depth and summarized in half to full-page boxes. For example, Chapter 2, on beams, includes 17 such boxes. Also, each chapter concludes with a complete final summary. The four chapters are the following: Chapter 1 (Introduction) includes a review of elementary notions on force systems, internal forces, principle of virtual work, stress, strain, and beams. Chapter 2 (Beams) covers the basic notions of beam bending theory, with emphasis put on the use of the principle of virtual work, in particular for statically indeterminate cases. This principle is also used to derive a beam element stiffness matrix and shear flexibility matrices. The chapter also covers beams (infinite and finite) on elastic foundations. Finally, beam vibration equations and stiffness matrices are treated. Chapter 3 (Columns) presents the standard Euler theory, including beam-column problems and imperfect columns, concluding with a presentation of Euler’s Elastica.In Chapter 4 (Cables), the author presents the theory of the ideal flexible suspended cable, leading to the catenary equation. He then proceeds with the shallow cable theory. In this particular case, he examines the effect of cable elasticity and flexible supports. The case of a static concentrated vertical load is also considered. Finally, equations for small amplitude vibrations of shallow cables are derived. A list of 25 references is given, many of which are classical works in the field (eg, Washizu’s book on Variational Methods in Elasticity and Plasticity) or original papers from the technical literature. In Appendix A (Beam load cases), beam bending results are summarized for typical end supports and applied loads. Appendix B (Integration formulas) gives some integration results to be used in the application of the principle of virtual work to beam bending calculations. The book ends with a detailed index. Each chapter contains several solved examples and ends with a selection of problems. These problems are designed to illustrate general principles and methods and are not oriented towards purely obtaining a numerical answer, as is generally the case in engineering “Strength of Materials” textbooks. Thus, results are either non-dimensional, or parametric, eliminating the need for an explicit unit system. The overall presentation, as well as figure quality, is fine. Notations and symbols generally follow standard practices in the field. To sum up, the book succeeds very well as regards the author’s stated aim of placing emphasis on basic principles. Mechanics and Analysis of Beams, Columns and Cables is a welcome addition to the list of currently available textbooks on the mechanics of materials and structural mechanics. With its insightful explanations and very clear mathematical presentations, it should also prove useful for self-study by practicing engineers and those wishing to review the elementary mechanics of materials from a deeper viewpoint, in particular with a perspective of getting into numerical methods.

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