Syllabus

Prerequisites: Undergraduate level courses on strength of materials & structural analysis.
Module I: Buckling of Beam-Column (8 hours)
Buckling Phenomenon Differential Equations for Beam-Columns Beam-Column subjected to a Concentrated Lateral Load, Uniformly Distributed Load and End Moments Use of Differential Equations to Beam-Columns Application of Trigonometric Series to Beam and Beam-Columns
Module II: Elastic Buckling of Bars and Frames (8 hours)
Determination of Critical Load from Differential Equation for Columns with Various Boundary Conditions Euler’s Column Formula Determination of Critical Load from Differential Equation for Frames.
Module III: Elastic Buckling by Energy Methods (6 hours)
Approximate calculation of Critical Load by Energy Method Rayleigh-Ritz Method Effect of Shear Force on Critical Load
Module IV: Torsional Buckling (6 hours)
Pure Torsion of Thin-Walled Bars of Open Cross Section Warping Displacements for Pure Torsion of a Channel Cross-Section Nonuniform Torsion of Thin-Walled Bars of Open Cross-Section Nonuniform Torsion Applied to a Bar of Any Open Cross-Section Evaluation of the Warping Constant for a Channel Section Doubly Symmetrical Thin-Walled Bar
Module V: Flexural-Torsional Buckling & FEM for Elastic stability (8 hours)
Lateral Buckling of Beams in Pure Bending Lateral Buckling of a Cantilever Beam and Narrow Rectangular Beam Lateral buckling of a simply supported I beam Elastic stability with FEM- Buckling of truss members & Buckling of Beam-Column members.

Students will be able to achieve fundamental understanding of the subject of stability of structures.

Students will be able to determine the critical state(s) of a structural system and use such information to enhance the analysis and design process.

Students will be able to find out solutions for complex problems involving torsional or flexural-torsional buckling in diverse fields of civil Engineering

1. Students will understand the concept and theories related to buckling of Beam-Column.
2. Students will be able to determine the critical loads for elastic buckling of bars and frames.
3. Students will be able to find out the critical loads of structures by Energy Methods.
4. Students will be able to find out solutions of Torsional Buckling problems for uniform and non-uniform cross sections.
5. Students will be able to learn applications of torsional theories for complex problems involving flexural-torsional buckling & FEM for Elastic stability.

S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw-Hill Book Company

A. Chajes, Principles of Structural Stability Theory, Prentice-Hall Inc.

A. Kumar, Stability of Structures, Allied Publishers Ltd.

T. V. Galombos, Structural members and frames, Prentice Hall Inc.