Nonlinear Structural Analysis: Theory and Applications

By Prof. Chinmoy Kolay | IIT Kanpur

Learners enrolled: 597 | Exam registration: 76

ABOUT THE COURSE:

Over the past several decades, the development and application of performance-based engineering and design approaches have resulted in a paradigm shift in the thinking, practice, and education of structural engineers. Consequently, nonlinear structural analysis is becoming increasingly important for designing new structures and evaluating the performance 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 modelling 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 engineers

PREREQUISITES: Courses on the following:

Mechanics of Solids
Structural Analysis
Design of Steel Structures
Design of Reinforced Concrete Structures

INDUSTRY SUPPORT: Structural engineering consultancy companies

Summary

Course Status :	Ongoing
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Civil Engineering Structural Analysis
Credit Points :	3
Level :	Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	02 Feb 2026
Exam Registration Ends :	20 Feb 2026
Exam Date :	24 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1:

Brief review of linear structural analysis
Direct stiffness method

Week 2:

Examples of the direct stiffness method of structural analysis
Introduction to nonlinear structural analysis
Sources of nonlinearities and levels of structural analysis

Week 3:

Levels of structural analysis (cont.)
Overview of solution strategies and examples
Elasto-plastic behaviour of materials
Stress-strain models for metals

Week 4:

Idealisation of stress-strain curves
Hardening rules
Hysteretic models (e.g., elastic perfectly plastic, bilinear plastic, Ramberg-Osgood, Giuffré-Menegotto-Pinto, Bouc-Wen, and modified Kent-Park) and their applications

Week 5:

Hysteretic models and their applications (cont.)
Flexural yielding of structural steel shapes and the concept of plastic hinge
Moment-curvature analysis of structural steel sections
P-M interaction curves for steel sections

Week 6:

P-M interaction curves for steel sections (cont.)
Flexural behaviour of reinforced concrete sections
Moment-curvature analysis of reinforced concrete cross-sections
P-M interaction curves for reinforced concrete cross-sections
Behaviour of reinforced concrete sections under cyclic loading
Review of continuum mechanics.

Week 7:

Review of continuum mechanics (cont.)
Yield criteria: von Mises (J2 plasticity) and Tresca
Flow rules, hardening rules, and loading/unloading criteria

Week 8:

Extension of plasticity theory to P-M interaction
Lumped plasticity approach for the analysis of seismic load resisting frames
Introduction to the distributed plasticity approach

Week 9:

Displacement (or stiffness)-based elements
Force (or flexibility)-based elements

Week 10:

Distributed plasticity approach (cont.)
Introduction to geometric nonlinear analysis
Geometric stiffness matrices for 2D truss and frame elements
Second-order P-Delta and large displacement analyses

Week 11:

Load-controlled analysis and examples
Displacement-controlled analysis and examples
Pushover analysis of LLRS
Constant arc length methods

Week 12:

Introduction to dynamic analysis
Direct integration algorithms: Explicit and implicit algorithms
Numerical characteristics of direct integration algorithms
Nonlinear dynamic analysis of a buildings subjected to earthquakes

Books and references

Some general reference books are given below. Specific references for each topic will be provided in the lecture notes.

McGuire, Willam, Richard H. Gallagher, and Ronal D. Ziemian. 2014. Matrix Structural Analysis. 2nd ed. Wiley

Powell, Graham H. 2010. Modeling for Structural Analysis: Behavior and Basics. Berkeley, California, USA: Computers and Structures, Inc.

Borst, René de., M. A. Crisfield, J.C. Remmers, Joris, and Clemens V. Verhoosel. 2012. Nonlinear Finite Element Analysis of Solids and Structures. 2nd ed. Wiley.

Chen, Wai-Fah, and D. J. Han. 2007. Plasticity for Structural Engineers. Reprint ed. J. Ross Pub.

Instructor bio

Prof. Chinmoy Kolay

IIT Kanpur

Dr. Chinmoy Kolay is an assistant professor in the Department of Civil Engineering at IIT Kanpur. He holds a B.E. (First Class with Honours) in Civil Engineering from Jadavpur University, an M.Tech. in Civil Engineering (Structures) from IIT Kanpur, and a Ph.D. in Structural Engineering from Lehigh University, USA. Before joining IIT Kanpur, Dr. Kolay was a research scientist at the Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center at Lehigh University.

Dr. Kolay’s research focuses on understanding the behavior of structures under multiple hazards through nonlinear structural analysis and advanced experimental simulations, and developing structural components and systems for mitigating such hazards. He has published his work in several international journals of repute and presented at many international conferences.

At IIT Kanpur, Dr. Kolay teaches courses on Mechanics of Solids, Structural Analysis, Design of Steel Structures, Structural Dynamics, Earthquake-Resistant Design of Structures, Experimental Methods, and Nonlinear Structural Analysis. He has received several letters of appreciation from the Chairperson, Academic Senate, IIT Kanpur, for his exceptionally good performance as the instructor of many of these courses.In September 2025, IIT Kanpur awarded him the Excellence in Teaching Award. Dr. Kolay is a life member of the Indian Society of Earthquake Technology and member of the American Society of Civil Engineers (ASCE), USA and Earthquake Engineering Research Institute (EERI), USA.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: April 24, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team