Part I
Mechanics of materials
The study of the mechanics of materials is concerned with the behaviour of solid bodies under the influence of loads. The ways in which these bodies behave as a result of the loads imposed on them, the stresses they endure, their subsequent strains and deflections, together with their internal reaction to these externally imposed loads, are of the utmost importance to engineers, particularly with respect to the design and in-service endurance of engineering structures.
In Chapter 1 some fundamental concepts are covered that may or may not be familiar to the reader but which are designed to provide essential background for the topics that follow. These topics include forces, resolution of forces, coplanar force systems, simple stress and strain, and thermal stress and strain. Chapter 2 is concerned with the analysis of beams and includes topics on shear force and bending moment, engineersâ theory of bending, centroid and second moment of area, beam selection and the slope and deflection of beams. In Chapter 3 we consider the concept of torsion in shafts used as power transmitters; topics covered include engineersâ theory of torsion, polar second moments of area and the power transmitted by shafts. Chapter 4 is concerned with the forces and stresses created by and acting on pressure vessels, where both thick-walled and thin-walled pressure vessels are considered, together with an application of the theory to the stress design of pressure vessels for specific functions. In Chapter 5 concentrically loaded columns and struts are considered; topics covered include the determination of parameters such as slenderness ratio, radius of gyration and effective length, Euler theory and the Rankineâ Gordon relationship. Chapter 6 provides an introduction to strain energy, where strain energy is considered as a result of direct stress, shear stress, torsion and bending. Castiglianoâs theorem is introduced and its use for analysing deflection of beams from externally loaded components is covered. Finally, in Chapter 7, we analyse complex stress and strain, starting with the analysis of stresses on oblique planes that result from direct tensile loading. Two-dimensional stresses acting both directly and in shear are analysed, together with the use of Mohrâs circle. Complex strain is then analysed and principal strains determined. The chapter finishes with a section on strain gauging and the use of strain gauge rosettes to determine principal strains.
Chapter 1
Fundamentals
1.1 Force
In its simplest sense a force is a push or pull exerted by one object on another. In a member in a static structure, a push causes compression and a pull causes tension. Members subject to compressive and tensile forces have special names. A member of a structure that is in compression is known as a strut and a member in tension is called a tie.
Only rigid members of a structure have the capacity to act as both a strut and a tie. Flexible members, such as ropes, wires or chains, can only act as ties.
Force cannot exist without opposition, as you will know from your previous study of Newtonâs laws. An applied force is called an action and the opposing force it produces is called a reaction.
The effects of any force depend on its three characteristics: magnitude, direction and point of application.
In general, force is that which changes, or tends to change, the state of rest or uniform motion of a body.
This formula is a consequence of Newtonâs second law, which you should already be familiar with. If not, you should refer to Part II of this book, where Newtonâs laws are revised at the...