Title: Response Variability of Statically Determinate Beam Structures Following Non-Linear Constitutive Laws and Analytical identication of progressive collapse modes of steel frames
Description: This thesis is divided into two distinct and independent parts. Part I focuses on the extension of the concept of Variability Response Function (VRF). The focus of research community has recently shifted from the improvement of structural models and enhancement of the performance of computational tools in a deterministic framework towards the development of tools capable of quantifying the uncertainty of parameters of the structural system and their effect on the system response in a probabilistic framework. One limitation to this direction is the inadequacy of information to fully describe the probabilistic characteristics of a structural system. In effort to bypass this barrier, VRF was introduced by Shinozuka as a tool to calculate the variability of the response of a system. VRF is a deterministic function and for the case of deterministic structural beams where the uncertain system parameters are modeled as homogeneous stochastic fields, it offers an efficient way to circumvent timely computational analyses.

In this dissertation, a flexibility-based VRF for the case of statically determinate beams following an arbitrary non-linear constitutive law is proposed. A closed-form analytical expression of VRF is derived and the constrains of the mechanics approximation embedded are discussed. No series expansion is used, thus the probabilistic part is exact and not limited by any constraint on the relative magnitude of the variations of the parameters. Part II of this dissertation explores the topic of progressive collapse. The appearance of damage in structural systems (explosions, design or construction errors, aging infrastructure) is following an upward trend during the last decades, urging for measures to be taken in order to control the damage advancement within the system. There has been an organized effort to update the design codes and regulations, in order to include provisions towards the reinforcement of buildings to eliminate their susceptibility to local damage. These efforts tend to focus on improving redundancy and alternate load paths, to ensure that loss of any single component will not lead to a general structural collapse.

The analysis of a damaged system is a very complicated phenomenon due to its non-linear nature. So far the engineering community has addressed the problem of progressive collapse by employing sophisticated computational finite element methods to accurately simulate an unexpected damaging event. In this framework, damage has been introduced in the model by removing key load-bearing elements of the building and conducting elaborate analyses which almost always require inelastic and loss of stability theories to be considered. The computational complexity renders this kind of analyses almost prohibitive for practicing engineers. In the direction of eliminating sophisticated and computationally expensive analyses, simple, trustworthy tools should be generated for practitioners to easily predict the mechanism of damage propagation and determine the governing collapse mode of a structure. In this environment, this thesis introduces a simple and less labor demanding analytical tool/method which can be used to determine the governing progressive collapse mechanism of steel moment frames under the scenario of a column removal.

After performing plain elastic analyses, the method develops critical Euler-type ductility curves for each removal scenario by performing straightforward analytical calculations. The response of structural systems under column removals is examined in a 2D and 3D context. The main objective of Part II is to investigate the response of dierent structural systems to the event of damage introduction (in this thesis, in the form of column removals in several locations of the system) and to develop a simple analytical framework for the identification of the governing progressive collapse failure modes. Although failure may occur due to a number of reasons (shear beam-to-column connection failure, beam yielding-type mechanism, loss of stability of adjacent columns, global loss of stability of the structural system, etc), in this study focus is being placed in only two of them; The proposed method establishes critical limit state functions which are used to identify whether a specic structure will experience progressive collapse through a yielding-type beam-induced collapse mechanism or through a loss-of-stability-induced column failure collapse mechanism.