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## Structures Book: Preface

Prior to the era of computers as the means of digital computation, laws of mechanics were the only practical means of structural analysis. The analytical methods developed then required the simplification of structures by introducing some assumptions to reduce the computation work. Whilst, most of those classical and approximate structural analysis methods are still sufficient to analyse many structures where computer facilities are still a remote however, the concept of finite elements and the development of matrix methods of structural analysis using high speed computers have revolutionized the approach to structural analysis. Analysis of tall buildings, bridges and other important structures subjected to both static and dynamic loads which had hitherto been regarded either as very complex or insoluble has become simple without introducing many assumptions.

From the analytical point of view there are only two categories of structures:

1. Framed structures, and
2. Continuum or surface structures

A framed structure is an assemblage of individual members inter-connected at the joints either by mechanical fasteners or joined monolithically. The cross-sectional dimensions of a member are generally much smaller than its length, which may either be straight or curved. Whereas a continuum or a surface structure cannot be distinguished as being comprised of individual members, it can be further categorized into two or three-dimensional forms. Two-dimensional surface structures include plates, shell roofs, membranes and domes because the thickness of such structures is much smaller than their primary dimension. Three dimensional surface structures depend on their third dimension for their resistance to applied loads. A typical example of a three dimensional surface structure is a gravity dam.

Structural Analysis is a pre-requisite to the design and proportioning of the members of a structure and it is a tool to establish the stability of the structure. Whilst analysing, we have to distinguish between two types of structures depending upon their configuration like whether a structure is statically determinate or indeterminate. Statically determinate structures can be analysed by using the equations of static equilibrium. Nature has liking for determinate structures. Internal forces at any section of a member can be determined using the equations of equilibrium. The first or an introductory course in structural analysis covers statically determinate structures.

The other type of structures are known as statically indeterminate structures in which all the forces, internal and external, in various members cannot be determined simply by using the equations of static equilibrium. These are manmade complex structures and require special techniques or methods of analysis. However, it should be realised that indeterminate structures are more economical and are generally preferred. The methods presented in this book are mainly confined to indeterminate skeletal structures.

So many textbooks are already available on this subject that one may question the justification of yet another book. Each author has his own way of presenting the subject, which, according to him, is more illustrative and comprehensive. I believe that with the use of computer methods, based on commercially available software, the basic concepts of structural analysis are generally being ignored. I taught structural analysis courses for several years at the Indian Institute of Technology, Delhi and at The University of Tripoli, Libya as a visiting Professor both at undergraduate and postgraduate levels. According to my experience, whilst matrix methods of structural analysis have become the main tool of analysis using computers these days it is realised that during the switch over from classical to matrix methods the connecting link of fundamental concepts of deformations of structures is being overlooked by students. They are getting rather used to robot like application of matrix methods using a number of standard programs like STRAD to analyse the structures. The insight to the basic concept of structural analysis is getting somewhat diluted, if not missing. Whilst the majority of the contents of this book are essentially the same as in other textbooks on this subject, the approach and presentation is much more atone to students and practicing engineers. The chapters have been arranged so as to maintain the continuity of the various techniques of analysis. A chapter on dynamic analysis of structures has also been added to introduce students to the response of structures to time varying loads like those due to earthquakes, winds and blast effects which is not included in other text books.

The first chapter of this book contains different methods to determine the degree of indeterminacy of structures. Both static and kinematic degrees of indeterminacy are discussed. The knowledge of these two degrees of indeterminacy will help students and engineers to choose a suitable method of analysis such as flexibility or stiffness from the consideration of computation time.

The second chapter deals with the Principle of Virtual Work which can be conveniently used to find displacements or forces in any type of structure with either elastic or inelastic characteristics. This knowledge of displacements is essential for the analysis of statically indeterminate structures using the flexibility method – in which all the forces whether external and/or internal cannot be found simply by using the equations of static equilibrium.

Chapter three describes the Flexibility method of structural analysis. The forces are present as the unknown quantities in the formulation of this method and as such are also called the Force method. The use of column analogy technique is derived as an application of the flexibility method.

Chapter four describes the stiffness method to analyse beams and frames. This chapter is a transitional chapter that serves as a bridge between the classical slope deflection method and the basic matrix formulation. An introduction to Finite Element method for skeletal structures is also included. Chapter five presents the Moment distribution method of analysis of beams and frames as an application of the stiffness method in which the force displacement equations are solved by iteration technique, generally known as a desk method. Chapter six describes various methods of analysing Multi-storey building frames subjected to lateral loads which may either be due to wind blast or earthquakes. Of course analysis of multi-storey and multi-bay frames is conveniently performed by stiffness method using matrix formulation on computers but the methods presented in this chapter are a shortcut for making preliminary design of multi-storey buildings since analysing a structure is a pre-requisite to the design and proportioning the members.

The method of drawing Influence lines for indeterminate structures using the Müller-Breslau principle is given in chapter seven – a subject which must be included in any structural analysis course for civil engineering students. Plastic analysis of beams and frames is presented in chapter eight. Chapter nine presents an introduction to dynamic analysis of structures. A procedure for determining the lateral forces in multi-storey buildings due to earthquakes using the Indian standard code of earthquake resisting structures is also described.

Each chapter of the book contains a number of solved illustrative examples to create confidence amongst students. Since a large number of solved examples are already included within each chapter, no exercises are provided at the end of any chapter which is also different from other text books. In this book, it is left to the individual tutors themselves to devise exercises based on their own experience and following the solved examples given in this book. However it is intended that every tutor should introduce practical projects as tutorials where each student can visualize the real structures subjected to actual applied loads according to the local code of practice. In this way each tutor should be able to make his own contribution to the course and use his experience to motivate the pupils to gain a better understanding of real structures. This project approach will not only create interest amongst students in structural engineering but will also make them confident in tackling actual design projects later on in their profession.

The contents of this book are essential for any advance or major course in structural analysis at undergraduate level and a regular course for the postgraduate students of structural and architectural engineering.

```D.V. Mallick
Niklausstrasse 34
CH-Regensdorf,Switzerland
March, 2011
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