Force and Displacement measurement - generalized or independent measurements - constrained or dependent measurements - n dimensional space - principle of superposition - methods of structural analysis. Structure with single and two coordinates - flexibility and stiffness matrices in n coordinates – examples - symmetric nature - constrained measurements - stiffness and flexibility matrices of the element as well as the system - computing the influence coefficient. Strain energy in terms of stiffness and flexibility matrices - interpretation of coefficient - Betti's law - other energy theorems using matrix notation.
Flexibility and Stiffness Methods (Element Approach): Choice of redundant - ill and well condition equation - Transformation Matrices - transformation of one set redundant to other set - thermal expansion - lack of fit – application to pin-jointed plane truss - continuous beams, frames and grids. Development of stiffness method - analogy between flexibility and stiffness - analysis due to thermal expansion, lack of fit - Stiffness matrix with rigid body motion - application to pin jointed plane and space trusses - continuous beams - frames and grids - static condensation techniques. Problem solving by computer - choice of the method.
Introduction to Finite Element Method: Basic concepts - Rayleigh-Ritz Method - Finite difference method – Variational principles - MWR (theory only) - Steps in finite element method - Axial element force formulation by displacement method only - Theory of stress model -Displacement model - Hybrid models. Analysis and Design of Pin-jointed and Rigid-jointed Framed Structures using STADD pro (2D and 3D), Introduction to SAP, ETABS, ABAQUS.