Elements of Matrix and Stability Analysis of Structures

Contents- Part-I, Statical Indeterminacy, Degree of freedom, Solution of equations, Sign convention, Energy method for establishing stiffness matrices, Equivalent joint loads, Computation of reactions Part-II,Basic concepts of matrix analysis of structures, Deflections of determinate structures, A) Integral Approach Using Flexibility Coefficients for finding Deflections of Beams subjected to Continuous Loading (2007) B) Work Method for Finding Maximum Deflection in Cantilever Beams (2007) C) Collateral Method of Real Work D) Matrix method for Finding ∆max and ᴓmax of Cardinal Structure E) Potential Energy Concept for Finding ∆max and ᴓmax of Cardinal Sturcture (2007) F) The CRC Method for Finding ∆max and Ømax of Cardinal Structure G) The Rayleigh Ritz Model for Finding ∆max and Ømax of Cardinal Structure (2007) H) Extentsion of Clapeyron’s Theorem For Finding ∆max and Ømax of Cardinal Structure I) Potential Energy Method for Finding ∆max and Ømax of Cardinal Structure J) External Work Equivalence for Finding ∆max and Ømax of Cardinal Structure K) Clapeyron’s Method for Finding ∆max and Ømax of Cardinal Structure L) Moments Approach for Finding ∆max and  Ømax of Cardinal Structure.  Statically indeterminate system, Stress due to lack of fit and temperature ,Displacement method of analysis, Direct stiffness method, Frames with sloping members, Grid analysis, Stiffness matrix through potential energy, Unstable elements, Conventional Rayleigh-Ritz Method (CRRM-1908),Improved Rayleigh-Ritz Method (RRM-1994),Additional information on Rayleigh-Ritz Method, Central deflection of simply supported beams, Central deflection of fixed beams, Special problems Part-III, Introduction, The Euler columns, Simple stability problems, Generation of shape functions, Double integration method, Single integration method(1997),Centre of gravity method, Method of weighted moment of inertia, Lower bound solution for non-prismatic Euler columns, Upper bound solution for Euler columns, Work method for Euler columns, Total Moment Concept (TMC) for Finding Critical Loads, SE. Best Lower and Upper Bound Solutions for Critical Loads,Triple Integration Method for Non-prismatic Euler Columns, Moment integration concept, Equivalent Moment oflnertia Concept Using Second Moment Equation, Equivalent Moment oflnertia  Method for Group-B Columns,Slope and Deflection Comparison Method, Method of successive approximation, Timoshenko's energy method,A. Energy Method,B No Derivative Method (Equivalent Column Method), C lOC. Euler's Energy Method, D. Moment Equilibrium Method for Euler Columns, Prismatic Column Approach for Non-Prismatic Columns,  The Galerkin Method,  Finite Difference Method, imperfect Approach, Empirical formulae for column Design, Effect of Shearing Force on the Critical Load, Beam-Columns, Stability Functions, Single Joint Method (SJM), Energy Method of Finding Critical Loads of Frames, Buckling of thin Plates, Post Buckling of Plates Torsional Buckling, Real Work and Principle of Virtual Displacement, Critical loads of plates using the Energy Method (1997), Improved Energy Method for Finding the Critical Load of Non sway Frames Hinged at the Bottom, Buckling of Thin Rings, Applications of Potential Energy Concepts Columns (1998), Stodola's Method. , Applications of potential energy concepts columns (1998), Stodola's method, Questions and answers in Structural engineering, Auxiliary stability functions, Distinct stability functions, Solved exercises, Intuitive Problems, Model Question Paper & Its Solution, Appendices, References.