## Stability of Structures

Major Structural Engineering , Faculty of Structural Engineering Structural Mechanics Assoc. Prof. Dr. Eng. Sonia Parvanova-Yoncheva

Year of education: IV, Semester: 7, WINTER
Assessment: exam
Method of teaching: lectures and seminars
Total hours: 30 lectures and 30 seminars (Academic Hours)
ECTS credits 4

Goals and objectives of the subject:
Materials with high strength characteristics give the opportunity for the wide spread of building structures constructed of light and slender elements. In such structures, strength checks only are not sufficient, but problems of their general and local stability and the more accurate examination of their strained and deformed states, taking into account the geometrical and physical non-linearity, are of primary importance.
In the course are being studied methods to determine the critical loads of individual structural elements, such as straight rods, arches, thin-walled bars and beams, thin plates and shells, as well as complex structures built up by them are being studied. Explained are also procedures for the calculation of strains and stresses by using the deformed scheme of structures made of linear elastic, non-linear elastic and elastic-plastic materials. For this purpose, along with classical analytical methods, modern numerical methods (finite element method) are applied.
In short, the objectives are as follows:
1) Introduction to conservative systems, modes of stability and bifurcation theory;
2) Introduction to buckling analysis and nonlinear stability problems;
3) Introducing the theories behind the nonlinear structural analysis and their mathematical models;
4) Stability analysis of structural elements and structures: beams, arcs, frames, plates.
5) Reducing the risk of loss of stability by local strengthening of the structures.
Characteristics of the subject:
Structural stability is essential for the proper analysis and safety design of the structures. The determination of the critical loading of a structure ensures more safe and economically justified design. The subjects of the course are: 1) determination of the critical load of discrete systems with elastic constraints; 2) buckling (eigenvalue) analysis of elastic frame structures and plates; 3) stability analysis with nonlinear iterative solution in the case of geometric nonlinearity with small displacements (P-Δ effect); 3) buckling analysis of thin elastic plates.
Acquired knowledge:
The aim of the course is to give to the students basic and solid understanding about the buckling analysis, nonlinear stability analysis with geometric and material nonlinearity and the influence of the initial imperfections.
Acquired skills:
At the end of the course the student acquire the following skills:
1) Buckling analysis of frame structures and plates;
2) Nonlinear stability analysis (P-Δ effect, or large displacements) of frame
structures;
3) Ability to work with specialized FEM software for structural analysis
Preliminary requirements:

• Mathematics: mathematical analysis and linear algebra
• Strength of materials: stresses, strains and reduced forces, Euler buckling
• Statics: structural analysis of statically determinate and indeterminate structures
• Elasticity theory: main principles and formulation, theory of thin elastic plates
• FEM: main principles and formulation, ability to work with specialized software for structural analysis