Analysis Of Structures By Matrix Methods

Matrix Methods for Advanced Structural Analysis

Divided into 12 chapters, Matrix Methods for Advanced Structural Analysis begins with an introduction to the analysis of structures (fundamental concepts and basic steps of structural analysis, primary structural members and their modeling, brief historical overview of methods of static analysis, programming principles, and suggestions for the rational use of computer programs). This is followed by the principal steps of the Direct Stiffness Method including plane trusses, plane framed structures, space trusses, and space framed structures. The case of plane or space framed structure, including possible rigid elements at their beam ends (rigid joints) is discussed in detail. Other topics discussed in this reference include the procedure for analyzing beams with internal releases (partial connection of beam elements) and elastic hinges, as well as the alternative handling of internal releases by modifying the element stiffness matrix. Furthermore, the Method of Substructures is demonstrated for the solution of large-scale models in terms of the associated number of degrees of freedom. - The principal steps of the Direct Stiffness Method are presented for plane and space trusses, as well as plane and space framed structures - The handling of beams with internal releases and elastic hinges - The method of substructures for large-scale structures - A computer code (basic steps and source files) based on MATLAB® software for the analysis of beam-like structures

Analysis of Structures by Matrix Methods

The analysis of engineering structures has always been a challenge to engineers, and in the past, classical methods were used to quantify the response of a structure to the applied forces. These methods were suitable for the analysis of relatively simple structures that could be solved by hand calculations but complicated structures had to be simplified to a model that could be solved by classical methods. The results, however, were approximations depending on the modifications made to the structure as well as on the experience and judgement of the analyst. These limitations led to the derivation of the slope-deflection equations for continuous beams, and later, formulation of the moment distribution method. With the advent of electronic computers, systematic procedures for the analysis of structures have been developed. Computer programs help in obtaining required solutions to the simultaneous equations in the case of structures where the number of equations is large and hand calculations are not suitable. The detailed work with simultaneous equations can be made in a general and compact form by using matrix notation, leading to the development of the matrix methods of structural analysis. This book deals with the analysis of engineering structures made of skeletal members and covers the type of structures that are commonly used in practice. It builds up on the subject matter dealing with matrix algebra, analysis of bar elements, special forms of members, stability and vibration of structures, and pin-connected, rigid-plane, and 3D frames. It treats the important step of formulating the overall stiffness matrix of a structure in a systematic and straightforward manner and uses simple mathematical approaches wherever possible. The book is reader friendly, particularly for beginners who have no prior knowledge in this subject and can also be used as a textbook by undergraduate and postgraduate students studying for a degree in civil, structural, or mechanical engineering as well as by practicing engineers who have not studied this subject but are using software packages that deal with the analysis of engineering structures.

Problems in Structural Analysis by Matrix Methods