A Summary of “Mechanics of Solids-2nd Edition” by Carl T. F. Ross, John Bird & Andrew P. F. Little.
The first edition of this book was recommended by the UK’s Council of Engineering Institutions, as the primary reading source on this topic for all British Universities. For this reason all the material that was in the first edition, is repeated in this 2nd edition, together with 4 additional chapters to bring the book right into the 21st century; and to simplify the explanations of the derivations, wherever required. The main difference with the new book is that many more worked examples are given, with more details on their solutions. Furthermore, the mathematical derivations of the first book are made simpler, by adding more steps for most derivations, than in the previous book. Moreover, Chapter 1 is on revisionary mathematics and Chapter 2 is on further revisionary mathematics.
Chapter 1 covers the important mathematics that is normally taught in the High Schools; but it is explained to a mature audience in this book. In Chapter 2 an introduction to calculus is given, but it is explained by a different approach, which is easier to understand than the traditional conventional methods of teaching calculus in other books. Chapter 3 is on statics, and shows the reader how to calculate reactions on horizontal beams subjected to lateral point and distributed loads, together with couples. The chapter also deals with calculating in-plane loads, in plane pin-jointed trusses, together with analysing the structural analysis of catenaries. Chapter 4 is on stress and strain, which are initially defined and then applied to some simple structures, together with an analysis of compound bars; these latter structures appear in reinforced concrete beams; while others, such as switches, etc, appear in “electrical contacts”.
Chapter 5 is on geometrical properties of symmetrical sections. These are important when calculating the bending properties of beams, frames, etc. The chapter is also important for introducing Ross’ method for calculating the 2nd moment of area of complex planes, such as a ship’s water plane; the method has been shown to be vastly superior to the traditional Naval Architect’s method of calculating this property. Chapter 6 is on the bending of beams, and mostly covers beams subjected to lateral loads, but also considers short struts subjected to combined lateral and axial loads. An introduction to the slope-deflection method is introduced, because it leads on to computer analysis of beams and frames, covered in Chapter 18. Chapter 7 is on bending stresses, & Chapter 8 is on the torsion of circular section but also deals with some problems on simple non-circular sections. Chapter 9 is on Complex stress and strain; which involves the two dimensional analysis of in-plane plates. The two-dimensional analysis of electrical strain gauges is also covered.
Chapter 10 is on the membrane analysis of thin-walled circular cylinders and spheres. This chapter shows how these structures can be used for colonizing the Moon. The authors argue that there are large quantities of frozen water on the North & South poles of the Moon. If this water is turned into oxygen and hydrogen, then it will be possible to develop breathable atmospheres in the manmade lunar dwellings. Moreover, the oxygen and hydrogen can be used to propel fuel cells and other means of propulsion. Chapter 11 is on energy methods in structural analysis of thin curved beams, etc, together with the plastic-hinge analysis of structures. Chapter 12 is on theories of elastic failure, and shows 5 theories of elastic failure. Chapter 13 is on thick cylinders and spheres and shows how these structures can conquer the Mariana Trench, in the Pacific Ocean, which is about 11 km deep! Chapter 14 is on axially loaded struts, which can suffer catastrophic failure, when slender structural members are subjected to axial loads.
Chapter 15 is on unsymmetrical bending of beams, which appear in complex structures; which have angle bars, channel sections, etc,. Chapter 16 is on shearing stresses on beam cross-sections, and deals with shear flow and shear centre. Chapter 17 is on composites and covers the complex theory of these structures. The chapter also shows the enormous strength of these structures when made from carbon nanotubes and graphene. Chapter 18 is on computer analysis of structures, and shows how these complicated structures can be solved by laptops, pads, smartphones, etc. Chapter 19 introduces the very famous finite element method; which can be used for many problems in continuum mechanics, including structures. The book is concluded by Chapter 20, which introduces many experimental methods in stress analysis.
Carl T. F. Ross. October 20th, 2015.