Matrix Methods for Advanced Structural Analysis

Manolis Papadrakakis, Evangelos Sapountzakis

• Publisher: Butterworth-Heinemann
• Year: 2017
• ISBN:
  9780128118825
• Topic: Tecnologia e ingegneria
• Subtopic: Ingegneria civile

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

Chapter One

Introduction to Matrix Methods of Structural Analysis

Abstract

In Chapter 1, an introduction to the analysis of structures is presented (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).

Keywords

Structural analysis; Matrix methods; Design procedure; Direct stiffness method; Computational model

1.1 Overview of Matrix Structural Analysis and Design

Structures can be viewed as mechanical systems comprising of structural elements of different types, connected together with connection-joints, and other nonstructural elements. The main purpose of a structure is to withstand the applied actions (loads) arising from its own weight, its use (live loads) and environmental effects (e.g., temperature loads and seismic excitations), and transfer them with safety to its supports. Structures are analyzed, designed, and constructed following specific financial, safety, and functionality requirements due to human needs. These human needs constitute the motive for the development and progress of static and dynamic analysis of structures, which are part of the mechanics of structures, with the main objective of analysis, design, and dimensioning of structural elements.

The analysis of structures, under static or dynamic loads, is the computation procedure for the evaluation of internal stress and strain components of the structural elements arising from external actions. Based on this computation, the designer has to ensure that the developed internal stress and strain components do not exceed specific allowable limits. It is worth noting here that during computation, safety coefficients are employed for considering any uncertainty due to loading, material properties, foundation ground characteristics, and any approximation resulting from the assumptions in modeling and analysis of the structure.

As mentioned previously, every structure is designed to satisfy at the same time specific constraints of safety and efficiency requirements, without neglecting construction and operational costs, completion time, technical difficulties during the construction phase, and any environmental effect. Therefore, the best possible design of a structure results from the examination and comparison of various alternative solutions based on rational and technical criteria.

1.2 Matrix Structural Analysis and Design Procedure

For the analysis of structures, the corresponding models should be developed representing structural elements, foundation, and external actions. More specifically, during the modeling of a structure, assumptions regarding the response of individual structural elements and their connections, their mechanical properties, the intensity of external actions and their combination, as well as the soil properties of the foundation should be made.

In Fig. 1.1, the steps for modeling the structure, soil-foundation, and actions of a structural system are presented. Following the modeling, the analysis of the structural system is performed, where various simplifications and assumptions regarding the numerical simulation are made. Finally, the analysis is followed by the evaluation of the stress resultants and deformations, and possibly by a reanalysis of the structure with a repetition of the aforementioned steps.

Fig. 1.1 Modeling of structure, soil-foundation, and external actions.

The matrix structural analysis procedure is repeated until the basic requirements of the structure are satisfied. It is worth noting that the associated uncertainties and “inaccuracies” at different stages of the simulation are u...