Distributed Damage Effect on Progressive Collapse of Structures and Variability Response Functions in Stochastic 2D Elasticity Problems

This dissertation investigates the distributed damage effect on Progressive Collapse of structures highlighted by applications on the nonlinear static and dynamic behavior of buildings, and contributes to the theoretical development of the Variability Response Function concept and its applicability extension in two-dimensional elasticity stochastic problems. Part I of this dissertation focuses on the recently emerging research field of Progressive Collapse of structures. The alternate load path method has so far dominated the field of progressive collapse of structures; in order to assess the resilience of structural systems, the concept of the removal of a key element is utilized as a means of damage introduction to the system. Recent studies have indicated that the complete column loss notion is unrealistic and unable to describe a real extreme loading event, e.g. a blast, that will introduce damage to more than one elements in its vicinity. This dissertation presents a new partial distributed damage method (PDDM) for steel moment frames, by utilizing powerful finite element computational tools that are able to capture loss of stability phenomena. Through the application of a damage index δj and the investigation of damage propagation, it is shown that the introduction of partial damage in the system can significantly modify the collapse mechanisms and overall affect the response of the structure. Subsequently, Part I elaborates on the distributed column damage effect on Progressive Collapse vulnerability in steel buildings exposed to an external blast event. Recent terrorist attacks on civil engineering infrastructure around the world have initiated extensive research on progressive collapse analysis of multi-story buildings subjected to blast loading. The widely accepted alternate load path method is a threat-independent method that is able to assess the response of a structure in case of extreme hazard loads, without the consideration of the actual loads occurring. Such simplification offers great advantages but at the same time fails to incorporate the role of a wider damaged area into the collapse modes of structures. To this end, the investigation of damage distribution on adjacent structural members induced by blast loads is considered critical for the evaluation of structural robustness against abnormal loads that may initiate progressive collapse. This dissertation presents detailed 3D nonlinear finite element dynamic analyses of steel frame buildings in order to examine the spatially distributed response and damage to frame members along the building exterior facing an external blast. A methodology to assess the progressive collapse vulnerability is also proposed, which includes four consecutive steps to simulate the loading event sequence. Three case studies of steel buildings with different structural systems serve as examples for the application of the proposed methodology. A high-rise (20-story) building is firstly subjected to a blast load scenario, while the complex 3D system results in the heavily impacted region are compared with individual column responses (SDOF) obtained from a simplified analytical approach consistent with current design recommendations. Parameters affecting the spatially distributed pressure and response quantities are identified, and the sensitivity of the damage results to the spatial variation of these parameters is established for the case of the 20-story building. Subsequently, two typical mid-rise (10-story) office steel buildings with identical floor plan layout but different lateral load resisting systems are examined; one including perimeter moment resisting frames (MRFs) and one including interior reinforced concrete (RC) rigid core. It is shown that MRFs offer a substantial increase in robustness against blast events, and the role of interior gravity columns identified as the `weakest links'\ of the structural framing is discussed. Part II of this dissertation focuses on the development of Variability Response Functions for apparent material properties in 2D elasticity stochastic problems. The material properties of a wide range of structural mechanics problems are often characterized by random spatial fluctuations. Calculation of apparent properties of such randomly heterogeneous materials is an important procedure, yet no general method besides Monte Carlo simulation exists for evaluating the stochastic variability of these apparent properties for structures smaller than the representative volume element (RVE). In this direction, the concept of Variability Response Function (VRF) has been proposed as a means to capture the effect of stochastic spectral characteristics of uncertain system parameters modeled by homogeneous stochastic fields on the uncertain response of structural systems, without the need for computationally expensive Monte Carlo simulations. Recent studies have formally proved the existence of VRF for apparent properties for statically determinate linear beams through elastic strain energy equivalence of the heterogeneous and equivalent homogeneous bodies, while a Monte-Carlo based methodology for the generalization of the VRF concept to statically indeterminate beams has been recently developed. In this dissertation, the VRF methodology of apparent properties is extended to two-dimensional elasticity stochastic problems discretized on a finite element domain, in order to analytically formulate a VRF that is independent of the marginal distribution and spectral density function of the underlying random heterogeneous material property field (it depends only on the boundary conditions and deterministic structural configuration). Representative examples that illustrate the approach include two-dimensional plane stress problems and underline the dependence of the VRFs on scale, shape and aspect ratio of the finite elements.