Structural Stability
- Introduction: The basic concept of linear buckling and stability, classification of elastic systems, (conservatives and non-conservatives)
- Stability of conservative systems: Minimum potential energy, mathematical manipulation of single degree of freedom, n degree of freedom, continuous systems, orthogonal relations, some examples
- Approximate methods and their application in stability problems: The Rayleigh-Ritz method, column with one elastic support, column on elastic foundation, Galerkin method.
- Elastic and non elastic buckling of columns: Euler formula, effective length, double module and tangent theory, columns with initial imperfections, columns with various end conditions.
- Buckling of beam columns: Introduction and basic concepts, manipulation of stability equations of beam columns, Intercation curves, the effect of boundary conditions, non elastic buckling of beam columns.
- Lateral Torsional buckling of beams: Lateral torsional buckling of thin walled open section columns with general cross section( e.g. section with single or double axis of symmetry, section with no axis of symmetry), lateral torsional buckling of beams, warping effect on buckling, buckling load of beams under( end moments, lateral point load, lateral distributed loads), non elstic buckling of beams in lateral stability, the application of theory in design codes
- Buckling of elastic rectangular frames: The method of slope-deflection on buckling of frames, general analysis of static perturbation technique, examples ( continuous two span beam axial load, two bar frame, portal frame with side sway
- Buckling of flat plates: Von-Karman theory for flat plates, plates under edge compression and shear, linearization of Von-Karman theory; plate under edge compression only, shear buckling of plates, buckling of plates in-plane bending, collection of graphs for various edge and loading conditions, practical problems, multi-web beams
- Buckling of thin walled cylindrical shells
- Post buckling of elastic systems: general analysis of one degree of freedom system (equilibrium, stability, energy surfaces, snap-through, limit point, instability, asymmetric bifurcation, symmetric bifurcation), examples; shallow arch (one degree of freedom, bifurcation model
Examples on multi degree of freedom, shallow shell (2 degree of freedom)
- Post buckling of rectangular plates: Von Karman theory of large deflection, Reyleigh Ritz solution for s.s. rectangular plates in uniaxial loading, in-plane plate stiffness in post buckling region, stress distribution after buckling, effective width concept.
- Interactive buckling: simple (Vondeneut) column, reduced Euler load, effect of local plate buckling on Euler buckling, optimization of material usage, effect of imperfection, thin walled beam in bending, effective width formulae for strength calculations.