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NPTEL

Advanced Structural Analysis

NPTEL via Swayam

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Overview

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ABOUT THE COURSE:The course ‘Advanced Structural Analysis’ will cover the application of matrix methods in analysis of skeletal structures. The stiffness and flexibility matrix approach will be developed based on the basic understanding of the displacement and force methods. The course will also introduce the computer implementation of the stiffness approach so that users can get familiar with the working of the standard structural analysis software packages. The course will further give brief introduction to geometrical and material nonlinear analysis procedure in the context of standard truss and beam members.INTENDED AUDIENCE: M.Tech Structural Engineering and B.Tech final year students of civil engineeringPREREQUISITES: Structural analysisINDUSTRY SUPPORT: Structural engineering consultancies- Atkins global, Spectrum Engineering, TCE, Tata steel, KEC, Arup etc.Aerospace firms and institutes- ISRO, DRDO, Boeing, Airbus, General electricals etc.

Syllabus

Week 1: Review of basic concepts
  • Structural elements, actions and deformations,
  • Equilibrium and compatibility
  • Static and kinematic indeterminacy
  • Loading & equivalent joint loads
  • Introduction to energy concept and virtual work
Week 2:Indeterminate structures- Force method
  • Slope and deflections using energy approach,
  • Force method for indeterminate structures
  • Choice of redundant and compatibility condition
  • Force method with deformable supports
  • Inclusion of thermal loads and pre-strains
Week 3:Indeterminate structures- Displacement method
  • Kinematically indeterminate structures,
  • Introduction to displacement methods
  • Slope-deflection approach
  • Equilibrium equations and deformable supports
  • Temperature change and pre-strains
Week 4:Introduction to matrix methods- Flexibility approach
  • Introduction to flexibility matrix,
  • Element based flexibility approach
  • Action & reaction transformation matrices
  • Assembled flexibility matrix
  • Numerical problem solving
Week 5:Introduction to matrix methods- Stiffness approach
  • Introduction to stiffness matrix,
  • Member stiffness matrix
  • Displacement transformation matrix
  • Assembled stiffness matrix
  • Numerical problem solving
Week 6:Direct stiffness approach- Computer implementation
  • Generalized element stiffness,
  • Direct stiffness assembly
  • Nodal connectivity and assembly
  • Member loading data input
  • Continuous beam member- Computer implementation
Week 7:Stiffness matrix- axial force members
  • Stiffness matrix for axial elements
  • Transformation for 2D-truss stiffness
  • Formulation and assembly for space truss
  • Reduced stiffness formulation
  • Computer implementation for space truss
Week 8:Stiffness matrix- Beam and grid members
  • Stiffness matrix for flexural elements
  • Joint load vectors assembly
  • Inclusion of shear and torsional deformations
  • Formulation for grid members
  • Reduced stiffness formulation
Week 9:Stiffness matrix- Frame structures
  • Generalized stiffness matrix for frame members
  • Member axis and global coordinates
  • Assembly of stiffness matrix and load vector
  • Space frame stiffness formulation
  • Reduced stiffness formulation
Week 10:Geometrical nonlinear analysis- Truss members
  • Geometrical nonlinearity- Introduction
  • Large axial deformations- stiffness formulation
  • Geometric stiffness due to axial loads
  • Tangent stiffness matrix for truss members
  • Solution scheme- Newton Raphson method
Week 11:Geometrical nonlinear analysis- Beam & frames
  • Large deformations in flexural members
  • Formulation of geometric stiffness
  • Assembly of tangent stiffness matrix
  • Elastic buckling analysis
  • P-D effects and nonlinear frame analysis
Week 12:Material nonlinear analysis and further study
  • Basics of plasticity
  • Distributed and lumped plasticity
  • Incremental nonlinear analysis
  • Computer implementation for nonlinear analysis
  • Finite element methods and way forward in software-based analysis

Taught by

Prof. Devesh Punera

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