Elastic Stability and Behavior of Members

Stability is a critical design limit state for structural members and systems.

This course will cover basic concepts in stability including methods to evaluate structural stability including bifurcation method and energy methods. Both small and large deformations will be assumed, and the effects of geometric imperfections will be investigated.

The differential equations governing the behavior of structural members will be discussed along with the design of steel rolled sections to torsional moment. The differential equations governing the stability behavior of structural members will be derived, and used to evaluate the buckling of columns with asymmetric, singly symmetric, and doubly symmetric cross-sections.

Students will leave this course with an in-depth knowledge of bifurcation buckling, stability, and methods of analysis. Students will also learn about governing differential equations for stability analysis and the buckling of different types of columns. This course is best suited for students with an undergraduate civil engineering background including a structural analysis course and will build on these concepts.

Students will learn from an awarded structural engineering researcher with over 20 years of experience in the field. Professor Varma focuses on teaching through exploring example problems and applications of fundamental concepts, encouraging his students to both understand the principles of structural stability and be able to apply these concepts in realistic design scenarios.

Week 1: Introduction to Stability and Bifurcation Analysis

Introduce key stability concepts including stability, instability and buckling. Discuss different buckling analysis methods and introduce bifurcation analysis.

Week 2: Energy Methods and First Order Differential Equations (DE)

Introduce energy methods for buckling analysis including the effects of large deformations and imperfects. Begin discussing first order differential equations governing buckling behavior.

Week 3: First Order Differential Equations and Stress Calculations

Continue discussing first order differential equations with special attention to torsion differential equations. Discuss calculating the stress associated with bending, shear, and torsion.

Week 4: Second Order Differential Equations

Detail second order differential equations governing structural stability including axial, flexural, and torsion.

Week 5: Elastic Buckling of Columns

Simplify differential equations previously discussed to look at elastic buckling of columns. Derive governing equations for elastic buckling of doubly symmetric, singly symmetric, and asymmetric column buckling.