Non-Linear Structures

Notation1. 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 Exercises2. Matrix Methods of Structural Analysis Introduction 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—Exercises3. 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 Exercises4. 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 Exercises5. 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 Exercises6. Non-Linearity Due to Plasticity. Elastic-Plasticanalysis of Frames Introduction 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 Exercises7. Failure Load of Frames (Approximate Methods) Introduction The Rigid-Plastic Drooping Curve Calculation of Failure Loads-Approximate Method 1 Assumptions Analysis of Columns Analysis of Frames Rankine's Formula-Approximate Method 2 Experimental Evidence Exercises8· Elastic-Plastic Design of Sway Frames Introduction 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 Conclusion9. Optimum Design of Structures using Linear Programming Introduction 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 Exercises10. Optimum Design of Structures using Non-Linear Programming Introduction 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 ExercisesAppendix IReferencesIndex