• 092842 - STABILITY OF STRUCTURES

The goals of this course is to provide the student with a comprehensive primer on structural stability as the natural completion of theory of structures and basis for some important topics in further technical disciplines involving these aspects (e.g. design of steel structures).
The course exploits simple systems in order to highlight the fundamentals.

The use of static, dynamic and energetic approaches at various level of approximations, and including material non linearities, is intended to put the student into confidence with the trasversal and interconnected meanings of many structural mechanics tools and formulations.

The expected learning outcomes are the following.

The student will become confident with all the contents of the course, from the fundamentals to the applications.

In particular the student will be able to solve problems involving the computation of stability limits or post-critical behavior of simple structures, either discrete or continuous. He will also be able to provide approximate solution strategies for problems of any complexity, at least in the elastic range.

The student will be capable to extend the applications of the learning to analogous problems and, depending to his capability, to generalize into more complex fields without the need of further fundamental and/or conceptual knowledge.

General introduction to the topic with the analyses of the consequences of relaxation of the classical “small displacement hypothesis”. Static and Dynamic definitions of Stability.

Conservative (vs nonconservative) force fields and internal work. Total Energy’s Conservation Law.

Stationarity and Minimum Principles for Total Potential Energy. Energetic statement of Stability. Second order theory and applications to discrete systems and compressed bent beams.

Flexural and Flexural-Torsional buckling of axially compressed beams. Stability of compressed beams under unconservative forces. Notes on lateral buckling of bent beams. The Von Karman plate theory with some applications to plate buckling.

Eulerian problems, Rayleigh quotient and discretization methods: Ritz Method and Finite Elements.

Collapse due to structural instability. Post-critical behaviour. Elastic Plastic Instability and theoretical buckling curve. Geometrical imperfections and self-stresses effects over on bearing capacity of a compressed member. Notes on collapse interaction curves of real beams under combined compression and bending. A primer on Stability of frames. Some notes on snap-trough and dynamic instability.

An oral examination starts with the analysis of the solution of previously assigned "take-home" exercises.

Both these steps of the assesment are conceived for a straight verifications of the expected learning outcomes at different grades above a minimum threshold provided by a proper understanding of the fundamentals.