STRUCTURAL ANALYSISINTRODUCTIONCivilisation as a whole es very largely dependent on the usage of structures is many shapes and forms. Implements such as clubs or screwdrivers; machines like a wheeled vehicle or aeroplane; buildings from mud huts to skyscrapers; waterworks like aqueducts or hidroelectric dams; sophisticated apparatus such as oil drilling rigs and interplanetary satellites; and living things such astrees and plants and even animals have structural embodiments. When one looks back at some of the marvellous structures like the pyramids or the parthenom or the roman aqueducts, it is evident that design and construction of such things was a combination of a knowledge of material, basic concepts of stability, imaginative choice of from and inherited or hard won experience.Nowadays structures vary so much in shape and purpose that the subject of design and construction tends to be divided between civil, structural, mechanical, architectural building, wter and environmental services engineering. Nevertheless the general principles of structural mechanics are common througghut and are straightforward in themselves. Their application to structural elements can be readily grasped, and this leads the way to an understanding of the behaviour of more complicated assemblies of the elements.Analysis and designIn the beginning there is no doubt that structures were accidents which were observed and remembered. For examples, a tree fell across a river and formed a bridge. A delibrate copy of this was a first step in design. Later the question of how much load (that is people, animals, barrows, etc .) could be safely supported by strength of the bridge would have been a crude attempt at analysis.Analysis is the evaluation of a structure in therms of the size of its elements and the strength and elasticity of the materials from which it is made. The two most important objetives are to determine a safe loading and the flexibility of the structure. To perfomr analysis the structure must exist either in reality or as a proconceived idea.Design starts from the other end. A specified loading has to be supported to achieve. Before much calculation can be done the form of a structure, in this case a bridge, has to be chosen. Then in the easier examples the proposed structure can be chosen. Then in the easier examples the proposed structure can be pre-determined by calculation. Alternatively for more elaborate structures it may be necessary to guess the size and shape in order to carry out an analysis of the strength and flexibility.Practical experienceThe obvious question is how one can guess the size and shape of the initial structure. The answer is by having a practical knowledge of the way structure behave; by knowing the strengths and weaknesses of materials and structural elements; and by observing what has already been built. To concentrate the adquisition of such experience into as few years as possible it is usual to follow a course of study specially arranged to teach structural mechanics. An essential part of the study is afforded by hands-on experience en the laboratory rigth up to the stage of total collapse where necessary. The balance betweenpure theory and practical laboratory work that produces good engineers varies from one student to another, but many students find a bias toward the practical side is a successful way to undestanding structural analysis and design.

Understanding structural mechanics

Theory of structures is a major subject within the overall education of a student civil engineer. This must mean thah a good adeal of time has to be spent learning the basic of the subject. The object of this book is to carry on from where structuralmechanics by durka, morgan & williams finishes by delivering the additional theory while minimising dependence on the mathematics involved. Provided that students are prepared to accept the formulae derived at the end of the theory, and can see how the assumptions made influence the application of the formulae, then they can make good use of their knowledge.As with most activities, practice aids learning. This is typically offered in the form of examples and exercises accompaying the text. These are part of the study and sould be used as a test of undestanding. Inevitably memory is an essential ingredient which expands as the learning procceds, and in the long run becomes the data base of experience. Thus a clear undertanding of structural mechanics is within the reach of all who apply themselves to this interresting subject.Equilibrium Structural mechanics, or theory of structures, is concerned with the analysis an design of rigid bodies thet are in equilibrium with the forces acting upon them. Although many structures like buildings or bridges are generally seen as stationary, it is true to state that a railway carriage or an aeroplane moving at a uniform velocity can be regardedin the same way as structures the forces acting on a structure may be static, like self weight, moving like vehicles on a bridge, developed by wind pressure or the forces due to change of velocity in the case of a railway carriage coming to a halt or travelling round a curve. In alla these cirsumstances it is possible to freeze the forces and the structure and instantaneously consider the state of equilibrium. This is how the term statical equilibrium is used when dealing with structures.To analyse the parts, or elements, that make up a structure it is usual to insolate each part and study it in detail. The equilibrium of parts of a somple structure has been dealt with in the elementry book on structural mechanics by F. Durka, W. Morgan and W. T. Williams. * In applying the methods given therein to complete strucures there are different approaches. When desgning a bulding, the analysis of the parts must follow a logical progression starting with the loads on the roof slabs, see 1 in figure 1. The next step is to deal with the beams carrying the slab such as at the outer edges 2, and the inner edges 3 which carry the slab on either side of the beam. The columns such as 4,5 and 6 must now support the loads from the beams. The procedure then repeats for the next lower storey, noting that the columns will have to carry a columns above. Finally at the ground each column, for example 7, is supported by a base 8 which distributes the load over an area that can withstand it.Alternatively, for a bridge truss the loading on the deck is transfered to the lower boom at the joints and the total load is supported at

The end bearings. It is then possible to find the force in each member separately and independently.

Elastic deformationAs the subject of structural mechanics develops in this book, a stage is quickly reached where consideration of equilibrium alone are insufficient to solve for of the forces acting on or within a

Structure. To overcome this difficulty it is necessary to investigate the elastic deformations of the structure due to the loading. The simplest examples of this is the cantilever beam shown in figure 1.3(a) carrying a distributed load which causes the beam to deflect as indicated. In figure 1.3(b) a jack has been introduced at the free end to push the end upward. The force exerted by the jack is determined by the final deflection at the end.A slightly more dificult example to visualise is that in figure 1.4 where three members share in holding up a vertical load. There are three unknown forces and only two simple equations of equilibrium. The third equation has to be whitten to arrange that the end D of each member concides in space with the ends of the other two members.This is referred to as a condition of compatibility, and would apply whether the elasticity was linear or non-linear. Generally one is dealing only with linear elasticity. In this method the force in one of the memebers is regarded as the unknown.There is, however, an alternative approach to the solution of the problem in figure 1.4 in wich the displacement of the point D is taken as the unknown. For convenience the vertical an horisontal components are used, so in fact there are two unknown values of displacement for each of which a corresponding state of equilibrium involving these unknowns can be written. These new equations are in addition to the simple conditions of equilibrium involving to be analysed. This approach, if appied to the prpped cantilever in figure 1.3(b), would have used the deflection and rotation

Elements and the strength and elasticity of the materials from which it is made. The two most important objectives are to determine a safe loading and the flexibility of the structure. To perform analysis the structure must exist either in reality or as a preconceived idea.Design starts from the other end. A specifield loading has to be supported