Elastic Stability of Structures

By Prof. Sarat Kumar Panda   |   IIT Kharagpur
Learners enrolled: 431
A thorough understanding on structural stability is essential to structural engineers whose job is to design safe and economic structures. In a structure, a small change in compressive load could cause a large variation in displacement. If this change in displacement is large enough in a critical member of the structure, a local or member instability could lead to collapse of the entire structure. Instability failures is catastrophic.

This course explains how and under what loading condition, a structure passes from a stable state to unstable state. Different structural members and systems are analyzed for their stability. This also includes how theory translates into design methods implemented in design guidelines. All major international standard specifications include provisions based on stability theory. Attention is especially focused on metal structures. Compared to structures designed using other construction materials, metal structures rely to a greater extent on stability limit states.

INTENDED AUDIENCE: Civil & Structural Engineering/ Mechanical Engineering/Aerospace Engineering/ Naval Structures students

PREREQUISITES: Mechanics of Solid

INDUSTRY SUPPORT: All Structural Engineering Industries. All Construction Industries like L&T,  Indian Space Research Organisation (ISRO), Defence Research and Development Organisation(DRDO) , GE Mechanics and Design, National Aerospace Laboratory (NAL),Aeronautical Development Establishment(ADE), Aaerospace firms like Boeing, Airbus etc., Composite manufacturing industries.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Civil Engineering
  • Structural Analysis
Credit Points : 3
Level : Postgraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 29 Oct 2022 IST

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

Page Visits

Course layout

Week 1:  Fundamental principles for elastic stability, Approximate methods in elasticity, Strong and weak forms of GDE
Week 2: Variational method in elastic problems, Euler Lagrange equation for functional having different dependent variables, Principle of minimum potential energy, Rayleigh-Ritz method
Week 3: Stability of rigid body systems for one-degree-of-freedom model by using different approaches, Two-degree-of-freedom structural model for stability analysis, Snap-through model and model with imperfect geometry
Week 4: Weak form solution for column with different boundary conditions, Strong form solution for column with different boundary conditions, Elastically supported columns
Week 5: Elastically supported columns, Critical load of portal frames with different boundary conditions, Element stiffness matrix for beam-column, Stability analysis of frames by Matrix stiffness method/Finite element method
Week 6: Buckling of Euler column: Large deflection theory, Euler column with initial imperfection, Load deflection curve for beam-column: Equilibrium approach and energy approach, Elastic curve of beam-column
Week 7: Stability analysis of beam-columns, Three moment equation for continuous beam-column, Beam-column on elastic foundation
Week 8: St Venant torsion and non-uniform torsion, Torsional buckling, Torsional-flexural buckling, Rayleigh-Ritz method for torsional flexural buckling of column
Week 9: Introduction to plate buckling and small deflection theory, Critical load of plate using equilibrium and energy approach
Week 10: Buckling of plates with different end conditions: Energy approach and Galerkin's method, Buckling and post buckling behaviour of plate using F-w formulation, Shell buckling using small deflection theory
Week 11: Shell buckling: Solution of Donnell's equation, Shell buckling by using finite deflection theory, Post buckling of axially compressed cylindrical shell panel
Week 12: Buckling of rings, curved bars and arches, Inelastic stability analysis of column, Double modulus theory and tangent modulus theory

Books and references

  1. Ashwini Kumar, “Stability Theory of Structures”, Allied publishers Ltd., New Delhi, 2003.
  2. Chajes, A. “Principles of Structures Stability Theory”, Prentice Hall, 1974.
  3. Gambhir, “Stability Analysis and Design of Structures”, springer, New York, 2004.
  4. Simitser.G.J and Hodges D.H, ”Fundamentals of Structural Stability”, Elsevier Ltd., 2006.
  5. Timoshenko.S.P, and Gere.J.M, “Theory of Elastic Stability”, McGraw Hill Book Company,1963

Instructor bio

Prof. Sarat Kumar Panda

IIT Kharagpur
Professor S K Panda is currently working as an Associate Professor in the Department of Civil Engineering, IIT(ISM) Dhanbad. He has taught this “Elastic Stability of Structures” course a number of times to the PG students of IIT(ISM) Dhanbad, and on almost all occasions, he has received very good overall student feedback. He has about 12 years of teaching experience at UG and PG levels. He has also briefly worked in the industry in the applied sector. His research interests include static and dynamic instability of different structural elements, including columns, plates and shells by considering geometric nonlinearity, shear deformation theories, thickness stretching, etc. He has guided two PhDs in the same area of research and also he has done his Ph.D. in the subject ‘Static and Dynamic Instability Analysis of plates and Cylindrical panels using Third-Order theory. He has also successfully completed one research project in the same area of research supported by DST and another structural stability project (SPARC project) is presently ongoing, which is supported by MHRD.

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: 29 October 2022 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.


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

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 Kharagpur. 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

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