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Matrix Structural Analysis

Structural Design Concept and ProcessBasic structural design criteria., Structural analysis as part ofstructural design., Design load and idealized representation ofstructures, Analysis of Statically Determinate StructuresAnalysis of Trusses,, Beams and Frames, Arches and Cables, Deflections of Beams and Frames, Differential equation for elastic curve and its solution., Moment areamethod. Conjugate beam method., Energy Methods for Computing DeflectionsWork and energy., Principle of virtual work., Unit load method.Deflections due to temperature,, lack of fit and support settlement., Maxwell-Betti law of reciprocal deflections,, Castigliano theorem, Flexibility Method for Statically Indeterminate Structures, Redundant forces and released structures., Compatibility conditions., Flexibility coefficients and matrix., Application to trusses, beamsand frames, Stiffness Method for Statically Indeterminate Structures, General stiffness method., Slope deflection method., Momentdistribution method., Influence Lines for Statically, Determinate StructuresInfluence lines for reaction,, shear and bending moment in beamsand member force in trusses., Use of influence lines to determine themaximum values under given moving load.
• INTRODUCTION AND REVIEW OF BASIC CONCEPTS, VIRTUAL WORK PRINCIPLES AND APPLICATIONS, DIRECT STIFNESS METHOD
• NONLINEAR ANALYSIS, GEOMETRIC NONLINEAR ANALYSIS, MATERIAL NONLINEAR ANALYSIS, SOLUTION OF LINEAR ALGEBRAIC EQUATIONS
• SOLUTION OF NONLINEAR EQUILIBRIUM EQUATIONS, SPECIAL ANALYSIS POCEDURES, Static and kinematic indeterminacy of structures
• Stiffness method of analysis of beams, 2D & 3D trusses and frames, Solution of simultaneous equations, Bandwidth calculation and banded solution, Analysis of beams, frames and trusses using computer programs,determinants properties,linear independent sets,quadratic forms,singular value decomposition

Structural Analysis
analysis of determinate structures, Reactions, Shear and moment diagrams, Influence lines.

Deflections
Elastic beam theory, Double integration method, Moment area theorem, Conjugate beam method.

The force method
Statically indeterminate structures, General procedure , Maxwell’s law of reciprocity , Force analysis of beams , Force analysis of frames , Force analysis of trusses , The three moment equation , Influence lines for indeterminate beams.

Slope deflection method
Displacement analysis, Slope deflection equation , Analysis of beams , Analysis of frames without sidesway , Analysis of frames with sidesway.

Moment distribution
General principles, Analysis of beams , Stiffness factors , Analysis of frames without sidesway , Analysis of frames with sidesway.

Nonprismatic members
Deflections, Application of the conjugate beam method , Use of published tables , Application of moment distribution , Application of slope deflection.

Introduction of the stiffness method
Fundamentals, Introduction to linear algebra , Displacement and force transformation matrices , Member global stiffness matrix , Truss stiffness matrix , Application.

Kinetics
• Stress at a Point, Stress Tensor and the Cauchy Formula, Transformation of Stress Components, Principal Stresses and Principal Planes, Equations of Motion, Symmetry of the Stress Tensor, Strain at a Point, Transformation of Stress Components, Compatibility Conditions, Thermodynamic Principles, The First Law of Thermodynamics: Energy Equation, The Second Law of Thermodynamics, onstitutive Equations.
• Generalized Hooke's Law, Strain Energy Density Function, Elastic Symmetry, Thermoelastic Constitutive Equations, Boundary Value Problems of Elasticity, Summary of Equations, Classification of Boundary Value Problems, Existence and Uniqueness of Solutions, Preliminary Concepts, Introduction, Work and Energy, Strain and Complementary Strain Energy, Virtual Work, Concepts of Calculus of Variations, Concept of a Functional.
• The Variational Operator, The First Variation of a Functional, Extremum of a Functional, The Euler Equations, Natural and Essential Boundary Conditions, A More General Functional, Minimization with Linear Equality Constraints, Virtual Work and Energy Principles, Principle of Virtual Displacements, Unit Dummy Displacement Method, Principle of Total Potential Energy, Principle of Virtual Forces and Complementary Potential, Energy, Unit Dummy Load Method, Energy Theorems of Structural Mechanics, Castigliano's First Theorem, Castigliano's Second Theorem.
• Betti's and Maxwell's Reciprocity Theorems, Ritz Method, Description of the Method, Matrix Form of the Ritz Equations, One Dimensional Examples, Weighted Residual Methods, Formulation of the Displacement Based Finite Element Method, General Derivation of Finite Element Equilibrium Equations, Imposition of Displacement Boundary Conditions, Generalized Coordinate Models for Specific Problems, Lumping of Structure Properties and Loads, Convergence of Analysis Results, Definition of Convergence, Properties of the Finite Element Solution.
• Rate of Convergence, Calculation of Stresses and the Assessment of Error, Isoparametric Derivation of Bar Element Stiffness Matrix, ormulation of Continuum Elements, Quadrilateral Elements, Triangular Elements, Convergence Considerations, Element Matrices in Global Coordinate System, Formulation of Structural Elements, Beam Elements and Axisymmetric Shell Elements, Plate and Shell Elements, Numerical Integration, Direct Solution of Linear System of Equations, Types of Structural Failure, Yield Stress and Ultimate Stress, Maximum Normal Stress TheoryTresca Condition, Hydraulic Stress, von Mises Criterion, Distortion Energy Interpretation, Graphical Representation of Failure Regions, Extension to Orthotropic Materials, Hill Criterion, Hoffman Criterion, Nature of Failure Criteria, Functional Forms, General Failure Analysis Procedure, Application to Pressure Tank, Fracture Mechanics, Description of Phenomena and Importance, Energy Approach to Crack Growth, Energy Consumed by Crack Growth, , Griffith's Experiment and Formula, Definition of Stress Intensity Factor, Stresses at Crack Tip, Mode I, II and III Cracks.
• Solutions of Linear Elastic Fracture Mechanics, Geometry Effects, Combined Loading; Material Selection, Fatigue and Longevity, Terminology, SN Diagrams, Goodman Diagrams, Effects of R Value, Stress Concentrations, Ground-Air-Ground Cycle, Miner's Rule, Micromechanical Effects, Paris' Law, Fatigue Life Prediction, R Effects and Forman's Law, Sequencing Effects, Approached to Design for Longevity.

Discretization matrices, sparse matrices, QR-algorithm, symmetric eigenvalue problemssingular value decomposition, pseudo-inverses, simplex method, matrix algorithms for vector computers,linear equations,inverse of matrix,determinant operation,cramer's rule,vector spaces,spanning trees,rank of matrix,inner product spaces,gram-schmidt process,orthogonal complement,kernel and range,transition matrix,eigen values,eigen vectors,symmetric matrices,diagonalisation,complex vector spaces,unitary matrices,hermitian matrices,linear transformation,linear algebra  ,singular value decompositions, least squares, linear equations, canonicalforms ,QR decmpositions, linear differential equations