Non-Linear Structures

Non-Linear Structures

Matrix Methods of Analysis and Design by Computers

1st Edition - June 28, 1972

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  • Author: K. I. Majid
  • eBook ISBN: 9781483192512

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Non-Linear Structures: Matrix Methods of Analysis and Design by Computers presents the use of matrix methods of structural analysis suitable for computers. The book consists of 10 chapters. In the first chapter a brief introduction to the behavior of structures in general is given with reference to the linear elastic and simple plastic methods of structural analysis. Chapter 2 is devoted to linear matrix methods, both force and displacement. Chapter 3 examines the stability of an individual member with various end conditions. It also derives the stability functions used in Matrix force and Matrix displacement methods. Chapter 4 tackles the elastic stability of complete frames. Chapter 5 deals with the elastic instability of frames. The sixth chapter covers the elastic-plastic analysis of frames. This is followed in Chapter 7 by a number of approximate methods for the evaluation of the failure load of frames without following the sequence of hinge formation. The last three chapters are devoted to the design of structures and the non-linear aspects of design problems. A description of non-linear programming by piecewise linearization is included in Chapter 10. Structural engineers, architects, researchers, and engineering students will find the book useful.

Table of Contents

  • Notation

    1. Introduction

    Behaviour of Idealised Structures

    Variation of Generalised Deformation of Structures with the Load Parameter

    Load-Displacement Diagrams of a Portal

    The Effect of Axial Load on the Behaviour of Idealised Structures

    The Real Behaviour of Structures

    The Rigid Plastic Theory

    The Fully Plastic Hinge Moment

    The Shape Factor

    The Load Factor

    Proportional Loading

    The Use of Virtual Work Equation

    Collapse of Continuous Beams

    Selection of Mechanisms

    Design by Rigid-Plastic Theory

    Effect of Axial Load on Mp


    2. Matrix Methods of Structural Analysis


    Matrix Displacement Method

    The Assemblage of Member Stiffness Matrices

    Transformation of Displacements

    The Overall Stiffness Matrix of a Structure

    The Use of Degrees of Freedom in Structural Representation

    Worked Examples

    Matrix Force Method

    The Flexibility Matrix

    The Overall Flexibility Matrix of a Structure

    Matrix Force Method for the Statically Determinate Structures

    Matrix Force Method for Statically Indeterminate Structures

    Worked Examples

    Automatic Construction of the Load Transformation Matrix—Exercises

    3. The Stability Functions

    The Effect of Axial Load on the Stiffness of a Member

    Rotation of a Member

    Sway of a Member

    A State of General Sway of a Member with Hinges

    The Stability Functions used in the Matrix Displacement Method

    The Stability Functions used in Matrix Force Method

    Relationships Between the Stability Functions

    General Deformation of a Member with Plastic Binges

    Effect of Lateral Loading and Gusset Plates

    A Computer Routine for the Evaluation of the Stability Functions


    4. Non-Linear Elastic Frames

    Derivation of a Non-Linear Stiffness Matrix

    Using s and c Functions

    Using φ Functions

    Matrix Displacement Method for Non-Linear Analysis of Structures

    Worked Examples

    Triangulated Frames

    Initial Stresses

    A Computer Programme for the Non-Linear Analysis of Plane Frames


    5. Elastic Instability

    Elastic Instability of Members

    Member with Single Curvature

    Member in Double Curvature

    Member Pinned at One End and Fixed at the Other

    Member in Pure Sway

    Elastic Instability of Frames

    Determination of the Instability Conditions

    Extraction of the Particular Mode from the General

    Approximation of the Axial Loads

    Elastic Critical Loads of Pitched Roof Portal Frames

    Elastic Critical Load of Trusses

    A Quick Determination of Instability Condition


    6. Non-Linearity Due to Plasticity. Elastic-Plasticanalysis of Frames


    The Displacement Transformation Matrix for a Member with a Hinge

    The Overall Stiffness Matrix

    Elastic-Plastic Analysis of a Propped Cantilever

    Elasticplastic Analysis of Frames

    The Nature of the Iteration

    Iteration to Constant Mp

    Iteration to Reduced Mp

    Alterations to the Load Vector

    A Computer Programme for the Elastic-Plastic Analysis of General Frames

    Worked Examples

    Inactive Hinges

    Computational Economy


    7. Failure Load of Frames (Approximate Methods)


    The Rigid-Plastic Drooping Curve

    Calculation of Failure Loads-Approximate Method 1


    Analysis of Columns

    Analysis of Frames

    Rankine's Formula-Approximate Method 2

    Experimental Evidence


    8· Elastic-Plastic Design of Sway Frames


    Variation of Maximum Moments

    Design of Individual Members

    Design Criteria

    Design Procedure

    Economy in Computer Time

    Design of Four-Storey Frame

    Design of Irregular Frames


    9. Optimum Design of Structures using Linear Programming


    Linear Programming

    Equality Constraints

    Constraints with Surplus Variables

    Minimisation Problems

    Minimum Weight Design of Structures

    The Rigid Plastic Minimum Weight Design

    Design of a Portal by Mechanism Method

    Minimum Weight Design using Equilibrium


    10. Optimum Design of Structures using Non-Linear Programming


    Some Properties of Convex Function

    Piecewise Linearization

    Statically Determinate Structures

    Worked Example

    Statically Indeterminate Structures

    Separation of the Variables

    Piecewise Linearisation

    Design Example

    Design of Rigidly-Jointed Frames


    Appendix I



Product details

  • No. of pages: 360
  • Language: English
  • Copyright: © Butterworth-Heinemann 1972
  • Published: June 28, 1972
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9781483192512

About the Author

K. I. Majid

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