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NPTEL

Nonlinear Structural Analysis: Theory and Applications

NPTEL via Swayam

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Overview

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ABOUT THE COURSE:Over the past several decades, the development and application of performance-based engineering and design approaches resulted in a paradigm shift in structural engineers’ thinking, practice, and education. Consequently, nonlinear structural analysis is becoming increasingly important for designing new structures and performance evaluation of deteriorating infrastructure systems. This course aims to provide a thorough background of nonlinear structural analysis and explain key concepts through practical examples using OpenSees and Google Colab. The course will emphasize modeling and static and dynamic analysis of framed structures, including material and geometric nonlinearities. Assignments will focus on solving problems using OpenSees to deepen the understanding of the course material.INTENDED AUDIENCE:Final-year undergraduate, master’s, and PhD students, postdoctoral researchers, and practicing engineersPREREQUISITES:Courses on the following:Mechanics of SolidsStructural AnalysisDesign of Steel StructuresDesign of Reinforced Concrete StructuresINDUSTRY SUPPORT:Structural engineering consultancy companies

Syllabus

Week 1:
  • Principle of virtual work
  • Derivation of the stiffness equation of structural analysis and the concept of the direct stiffness method
  • Stiffness matrices for 2D frame and truss elements in basic/deformation coordinate system
  • Element stiffness matricesin the local coordinate system.
  • Element stiffness matrices in the global coordinate system
Week 2:
  • Assembling the structure stiffness matrix and fixed end force vector
  • Solution and determination of support reactions and member forces
  • Examples in OpenSees
  • A simple nonlinear problem
  • Sources of nonlinearities and levels of structural analysis
Week 3:
  • Levels of structural analysis (cont.)
  • Overview of solution strategies
  • Examples in OpenSees
  • Elasto-plastic behavior of metals in tension and compression
  • Stress-strain models for metals
Week 4:
  • Cyclic hardening
  • Hysteretic models and their applications: Bilinear plastic and Menegotto-Pinto models
  • Hysteretic models and their applications: Bouc-Wen model
  • Hysteretic models and their applications: Kent-Park and Mander models for concrete
  • Hysteretic models and their applications: Models including strength and stiffness deterioration and pinching
Week 5:
  • Flexural yielding of structural steel shapes and the concept of plastic hinge
  • Moment-curvature analysis of structural steel sections
  • Factors affecting the moment-curvature response of steel sections
  • P-M interaction curves for rectangular and wide-flange steel sections
  • P-M interaction curves using fiber-section analysis: Wide-flange and T sections
Week 6:
  • P-M interaction curves for concrete-filled steel tubes
  • Moment-curvature analysis of reinforced concrete cross-sections
  • P-M interaction curves for reinforced concrete cross-sections
  • Review of continuum mechanics
  • Review of continuum mechanics (cont.)
Week 7:
  • Yield criteria: von Mises (J2 plasticity) and Tresca
  • Flow rules, hardening rules, and loading/unloading criterion
  • Flow rules, hardening rules, and loading/unloading criterion (cont.)
  • Examples in OpenSees
  • P-M hinge models
Week 8:
  • P-M hinge models (cont.) and examples
  • Behavior of lateral load-resisting systems (LLRS)
  • Modeling and analysis of LLRS using the lumped plasticity approach
  • Displacement (or stiffness)-based element
  • Displacement (or stiffness)-based element (cont.)
Week 9:
  • Numerical integration
  • Examples in OpenSees
  • Force (or flexibility)-based elements
  • Force (or flexibility)-based elements (cont.)
  • Examples in OpenSees
Week 10:
  • Displacement-based versus force-based elements
  • Plastic hinge integration for force-based elements
  • Introduction and geometric stiffness matrices for 2D truss and frame elements
  • Geometric stiffness matrices for 2D truss and frame elements (cont.)
  • Second-order P-Delta and large displacement analyses
Week 11:
  • Second-order P-Delta and large displacement analyses (cont.)
  • P-(big) Delta vs P-(small) delta
  • Load-controlled analysis and example
  • Displacement-controlled analysis and example
  • Pushover analysis of LLRS
Week 12:
  • Constant arc length methods
  • Time-discretized equations of motion
  • Direct integration algorithms: Explicit and implicit algorithms
  • Numerical characteristics of direct integration algorithms
  • Nonlinear dynamic analysis of a building subjected to earthquakes

Taught by

Prof. Chinmoy Kolay

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