IMPLEMENTATION OF A FINITE ELEMENT BASED MATLAB PROGRAM FOR THE BUCKLING ANALYSIS OF THIN-WALLED BEAMS WITH APPLICATION TO HIGH-RISE BUILDING STRUCTURES

In civil, mechanical and aerospace engineering, structural stability is an important issue when concerning open, thin-walled elements; for example C, L or Z profiles. These components are commonly found in lightweight structures due to their high strength-to-weight ratio, and can be subjected to buckling phenomena regarding local, distortional and global stability. This thesis focuses on the global buckling of open thin-walled beams, with the main objective of implementing a Matlab code with an effective and versatile one-dimensional finite element formulation of literature. The Thesis combines theoretical formulations together with analytical and numerical modelling. Firstly, the general concepts of structural stability and elastic buckling are recalled, discussing different types of bifurcation. Then, Vlasov's theory for open thin-walled sections is summarized. Also, the Finite Element Method (FEM) was introduced as a general and powerful tool to model behavior of beams subjected to various loading conditions and boundary conditions. As an original contribution, a Matlab code was implemented to analyze elastic buckling of open thin-walled profiles by exploiting a finite element formulation of literature which uses exact or approximated interpolating functions. This code aims at being an open tool allowing to get quick solutions and to be easily embedded into more general Matlab codes. In the last part of the Thesis, the analysis was extended to tall buildings, providing a global view of the effects due to wind and seismic loads, also considering the correlation between the global stability and local buckling of a structural element. The results obtained by the formulation implemented were compared with others available in literature or with those obtained with a commercial finite element program. The program implemented allows for the global elastic buckling analysis of straight beams with open cross-section under different loading and boundary conditions. Tapered beams can be analyzed by connecting a discrete sequence of segments of uniform cross-section each, but with different sections from segment to segment. Possible future developments can consider a parallel-arranged system of open thin-walled beams, as well as open-section profiles having local closures at specific locations, like those of present in some tall building structures.