Matrix Methods of Structural Analysis

Praveen Nagarajan

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9780815381501
• eBook ISBN: 9781351210300
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

This book deals with matrix methods of structural analysis for linearly elastic framed structures. It starts with background of matrix analysis of structures followed by procedure to develop force-displacement relation for a given structure using flexibility and stiffness coefficients. The remaining text deals with the analysis of framed structures using flexibility, stiffness and direct stiffness methods. Simple programs using MATLAB for the analysis of structures are included in the appendix.

Key Features

• Explores matrix methods of structural analysis for linearly elastic framed structures
• Introduces key concepts in the development of stiffness and flexibility matrices
• Discusses concepts like action and redundant coordinates (in flexibility method) and active and restrained coordinates (in stiffness method)
• Helps reader understand the background behind the structural analysis programs
• Contains solved examples and MATLAB codes

1

Introduction

1.1 Introduction to Matrix Methods of Structural Analysis

Structural analysis deals with the determination of response (forces and displacements) of the structure subjected to loads. The rapid development of computers and the need for complex and light weight structures lead to the development of matrix methods of structural analysis. The analysis procedure can be concisely written using matrix notations and are suitable for computer programming.

The classical methods of structural analysis (also known as system approach of analysis), such as the method of consistent deformation, slope-deflection methods, etc., consider the behavior of the entire structure for developing equations necessary for analysis. Hence, these methods are suitable only for simple or small structures. For larger structures, the use of classical methods of analysis will be difficult and time-consuming. Even though the procedures using classical methods can be written in matrix format, the matrix methods of analysis discussed in this book is different from the classical approach and is known as the element approach of analysis. In this method, the response of the whole structure is determined using the behavior of the elements or members from which the structure is made of.

There exists two ways by which a structure is analyzed using matrix methods, namely the flexibility method or the force method and the stiffness method or the displacement method. The flexibility method of analysis is discussed in Chapter 3, whereas Chapters 4 and 5 deal with the stiffness method of analysis. The methods to develop the force–displacement relation of elements are covered in Chapter 2. In this chapter, the important terms and their definitions used in matrix methods of analysis are discussed.

1.2 Framed Structures

A structure is defined as an assemblage of structural elements that can withstand load. When two dimensions (cross-sectional dimensions) of the elements are very small compared to the third dimension (length of element), the elements are modeled as one-dimensional line elements. Elements having one dimension (thickness) very small compared to the other two dimensions are modeled as two-dimensional surface elements. In some cases, all the dimensions of the element are of comparable length. These elements are modeled as three-dimensional brick elements.

A structure composed of only line elements is known as a framed structure or skeletal structure. This book deals with the analysis of framed structures. In a framed structure, joints represent the point of intersection of elements, supports, and free end of elements (A, B, C, D and E in Figure 1.1a). The supports can be fixed (support A in Figure 1.1a and 1.1b), hinged (support D in Figure 1.1a), roller (support B in Figure 1.1b), or guided-fixed (support C in Figure 1.1b). Sometimes supports can be elastic (or spring). The framed structures can be grouped into six categories, namely (i) beam, (ii) plane truss, (iii) space truss, (iv) plane frame, (v) grid, and (vi) space frame. A brief description of each type of framed structure is given below:

A beam (Figure 1.2a) is a long-slender element having one or more points of support. The forces act in a plane containing an axis of symmetry of ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Dedication Page
• Preface
• Author
• 1 Introduction
• 2 Flexibility and Stiffness: Characteristics of Structures
• 3 Flexibility Method
• 4 Stiffness Method
• 5 Direct Stiffness Method
• Appendix
• Bibliography
• Index