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structural analysis example download
Prior to the development of quantitative structural theories in the mid-18th century and since, builders relied on an intuitive and highly developed sense of structural behaviour. The advent of modern mathematical modelling and numerical methods has to a large extent replaced this skill with a reliance on computer generated solutions to structural problems. Professor Hardy Cross1 aptly expressed his concern regarding this in the following quote: ‘There is sometimes cause to fear that the scientific technique, the proud servant of the engineering arts, is trying to swallow its master.’ It is inevitable and unavoidable that designers will utilize continually improving computer software for analyses. However, it is essential that the use of such software should only be undertaken by those with the appropriate knowledge and understanding of the mathematical modelling, assumptions and limitations inherent in the programs they use. Students adopt a variety of strategies to develop their knowledge and understanding of structural behaviour, e.g. the use of: • computers to carry out sensitivity analyses, • physical models to demonstrate physical effects such as buckling, bending, the development of tension and compression and deformation characteristics, • the study of worked examples and carrying out analyses using ‘hand’ methods. This textbook focuses on the provision of numerous fully detailed and comprehensive worked examples for a wide variety of structural problems. In each chapter a résumé of the concepts and principles involved in the method being considered is given and illustrated by several examples. A selection of problems is then presented which students should undertake on their own prior to studying the given solutions. Students are strongly encouraged to attempt to visualise/sketch the deflected shape of a loaded structure and predict the type of force in the members prior to carrying out the analysis; i.e. (i) in the case of pin-jointed frames identify the location of the tension and compression members, (ii) in the case of beams/rigid-jointed frames, sketch the shape of the bending moment diagram and locate points of contra-flexure indicating areas of tension and compression. A knowledge of the location of tension zones is vital when placing reinforcement in reinforced concrete design and similarly with compression zones when assessing the effective buckling lengths of steel members. When developing their understanding and confirming their own answers by studying the solutions provided, students should also analyse the structures using a computer analysis, and identify any differences and the reasons for them. The methods of analysis adopted in this text represent the most commonly used ‘hand’ techniques with the exception of the direct stiffness method in Chapter 7. This matrix based method is included to develop an understanding of the concepts and procedures adopted in most computer software analysis programs. A method for inverting matrices is given in Appendix 3 and used in the solutions for this chapter—it is not necessary for students to undertake this procedure. It is included to demonstrate the process involved when solving the simultaneous equations as generated in the direct stiffness method. Whichever analysis method is adopted during design, it must always be controlled by the designer, i.e. not a computer! This can only be the case if a designer has a highly developed knowledge and understanding of the concepts and principles involved in structural behaviour. The use of worked examples is one of a number of strategies adopted by students to achieve this. 1 Cross, H. Engineers and Ivory Towers. New York: McGraw Hill, 1952 W.M.C.McKenzie To the many students who, during the last twenty five years, have made teaching a very satisfying and rewarding experience.
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