MATRIX ANALYSIS OF . STATICALLY INDETERMINATE STRUCTURES

Abstract

This dissertation deals with the exact solution of linear algebraic equations governing the behaviour of statically indeterminate structures. Matrix Algebra has been employed as a tool for assisting the analysis, since it makes the discussion and formulation of complex structural problems a very convenient and system-atic process which can easily be mechanised. This approach) being most general in its application, also reduces the chances of committing errors and results in a consid-erable saving in time and labour required for a particular problem. These matrix techniques are especially advant. ngnnnn when we have to deal with highly complex and redu-ndant problems, which would otherwise be impossible to solve by hand methods of computation. The chief objective of this disisertation has been to represent the subject in a manner which is systematic and easily assimilable by a common civil engineer. In addition, a few easier and direct synthetic methods to assemble the matrix of a given structure have been devel-oped. The obvious merits of the matrix methods over the existing conventional methods have been discussed while describing the techniques, and also the possibilities of making rapid design calculations on an electric desk calculator, which is more easily available to a common structural engineer, have been fully discussed. The systematic representation of the subject is contained in the following seven chapters. In the first four chapters are given the matric formulation of the two complementary basic approaches to a structural problem and the explanation of various matrix operations and methods required for the analysis. Chapters 5 and 6 deal with a detailed discussion of the flexibility matrix method and the stiffness matrix method respectively. To illustrate the techniques descr-ibed in these chapters, a good number of numerical examples are given which have been solved on a 'Marchant' electric desk calculator. The last chapter deals with Electronic Digital Computers - their brief functional description and as to how more complex problems are programmed for an automatic solution on such machines. 3