CE 223 STRUCTURAL STABILITY
Instructor: C S Manohar
Term: January-April
Credits: 3:0
Syllabus
Analysis of beam columns. Stability functions. Behavior of ideal columns. Bifurcation buckling
and limit point instability. Mechanical models of stability. Static and dynamic formulations.
Energy methods. Finite element formulation. Buckling of frames. Imperfection sensitivity and
post critical behavior. Buckling of beams on elastic foundations, arches and plates. Inelastic
buckling. Dynamic analysis of stability. Parametric instabilities and stability under
nonconservative forces. Divergence and flutter.
List of recommended books.
General theory and sources of exercise problems
1.
2.
3.
4.
5.
S P Timoshenko and J M Gere, 1963, Theory of elastic stability, McGraw Hill, London.
A Chajes, 1974, Principles of elastic stability, Prentice Hall, NJ.
G J Simitses, 1976, An introduction to the elastic stability of structures, Prentice Hall, NJ.
Z P Bazant and L Cedolin, 1990, Stability of structures, Oxford University Press, Oxford.
N G R Iyengar, 1986, Structural stability of columns and plates, Affiliated East-West Press,
New Delhi.
6. D O Brush and B O Almoroth, 1975, Buckling of bars, plates and shells, McGraw Hill, NY.
Design issues
7. T V Galambos, 1998, Guide to stability design criteria for metal structures, Wiley, NY
Finite element method for stability analysis
8. I H Shames and C L Dym, 1991, Energy and finite element methods in structural mechanics,
Wiley Eastern Limited, New Delhi.
9. R D Cook, D S Malkus and M E Plesha, 1989, Concepts and applications of finite element
analysis, Wiley, NY.
10. M F Rubinstein, 1970, Structural systems- statics, dynamics and stability, Prentice-Hall, NJ
11. F W Beaufait, W H Rowan, P G Hoadley and R M Hackett, 1970, Computer methods of
structural analysis, Prenitce Hall, NJ.
12. W McGuire, R H Gallagher and R D Zieman, 2000, Matrix structural analysis, John Wiley,
NY.
Advanced level treatment
13. J M T Thompson and G W Hunt, 1973, A general theory of elastic stability, John Wiley,
London.
14. H H E Leipholz, 1978, Stability of elastic structures, Springer Verlag, Wien.
15. H Ziegler, 1968, Principles of structural stability, Blaisdel Publishing Company, Waltham.
16. H H E Leipholz, 1975, Six lectures on stability of elastic systems, University of Waterloo
Press, Ontario.
17. M S El Naschie, 1990, Stress, stability and chaos, McGraw Hill, London.
Problems of dynamics stability
18. V V Bolotin, 1962, Nonconservative theory of the theory of elastic stability,
Pergamon Press, Oxford.
19. V V Bolotin, 1964, Dynamic stability of elastic systems, Holden-Day, San Fransisco.
20. A H Nayfeh and D T Mook, 1979, Nonlinear oscillations, John Wiley, NY.
21. Y G Panovko, 1965, Stability and oscillations of elastic systems, Consultants Bureau,
NY.
Evaluation scheme
3 Tests [Open book] (30 points)
4 Assignments (20 points)
1 Final examination [Open book] (50 points)
Schedule for tests: 14th February, 14th March and 14th April.
Course objectives:
1. To study, through analytical means, class of static problems amenable for exact solutions.
Learn, through this study, the basic notion of elastic stability.
2. Formulate problems of elastic stability using energy principles.
3. Develop an understanding of how finite element method can be used to investigate elastic
stability of static systems.
4. To study, through analytical means, class of dynamic stability problems amenable for
acceptable approximate solutions. Learn through this study, the basic notions of dynamic
stability, divergence and flutter.
Details of lectures
1. Analysis of beam columns. Stability functions. Breakdown of traditional linear
superposition principle. Modified version of principle of superpositioning. Single span
and multi-span beam columns. Modified three moment equations. Eccentrically applied
axial loads. Effect of initial imperfections. Effect of support flexibility. Southwell plot.
Secant formula and Perry-Robertson formula.
2. Behavior of ideal columns. Concept of equilibrium states in the proximity. Buckling
loads as eigenvalues of governing differential equation. Buckling mode shapes and their
orthogonality. Tilt buckling. Beams with rigid segments. Concept of critical spring
stiffness. Buckling under self-weight.
3. Mechanical models of stability. Static and dynamic formulations. Linear and nonlinear
formulations. Lyapunov stability. Stability matrix. Singular points and their
classification. Models for limit load buckling: snap through instability. Elements of
Koiter’s theory.
4. Energy methods. Hamilton’s principle and Lagrange’s equation. Axioms for determining
equilibrium and stability for static systems. Rayleigh-Ritz and Galerkin formulations. FE
formulation of elastic stability problem.
5. Buckling of frames: exact solutions. FE solutions. Demonstrations on NISA/ANSYS
softwares.
6. Topics in static stability: Lateral buckling of beams; Beams on elastic foundation.
Buckling of perfect Arches. Von Mise’s truss. Snap through. Inelastic buckling. Double
modulus theory.
7. Topics in dynamic stability: Introduction to parametric instability. Strutt’s diagram.
Floquet’s coefficients. Nonconservative loads. Divergence and flutter. Concept of
follower forces and discussion of conflicting views on its existence.