Abstract

In this doctoral thesis the nonlinear stability analysis of frame structures is presented. The phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this thesis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this thesis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3) and national (JUS) standards for the steel structures. It is important to emphasize that in these standards, calculation of the critical load in the plastic domain is also based on the approximate procedure. This procedure means that the critical load in the elastic domain should be calculated first, and after that, on the basis of the buckling curves, the critical load in the plastic domain can be obtained. These curves are defined by the approximate, empirical formulas. Instead of such “mixed” procedure given in the standards, in this thesis a more accurate procedure is presented. By this procedure it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain.