This thesis presents the results of a study of the effect of variations of systemic parameters on the structural response of single degree of freedom systems subjected to Incremental Dynamic Analysis. The systemic parameters are mass, stiffness, damping, yield strength and geometric stiffness. Each of these parameters was varied one at a time while the other values were kept constant. For each variation of parameters a set of single-record IDA curves was obtained. Five to six ground motions were used for this study to generate the single-record IDA curves. These ground motions were scaled prior to their application on the structure. The scaling factor was based on the spectral acceleration at the fundamental frequency of the structure at 5% of critical damping. The scale factor is affected if the system parameters are changed. An important issue for this study was whether to persist with scaling corresponding to the median value from the range of the values of the parameter or to update the scaling according to the system. Based on some tests using both methods, the median scaling approach was found to be more suitable. The IDA curves for variation of parameters were then investigated to identify any trends that may help in qualitatively predicting the response of a system relative to another system. The response was measured by the peak displacement and the maximum base shear of the system. A clear trend was identified when the damping or the yield strength was varied. However, no definite trend was observed when the material stiffness or the geometric stiffness of the system was varied. / Master of Science

This study investigates seismic response of the Moment-Resisting-Steel Frames (MRSF) with the architectural setbacks. The main objective of the study is to understand the variation of the elastic and inelastic, static and dynamic behavior with changes in the geometric dimensions of the tower portion. A second objective of the study is to determine the adequacy of the analysis procedures of various rigors, specified in current seismic design provision, in predicting those behaviors for MRSF with various size of setback. The analytical study is conducted using a regular and 16 irregular models to capture all possible combinations of configuration of setback in five-story, five-bay MRSFs. An irregular model is developed by gradually changing the horizontal and vertical dimensions of the tower portion of the regular base 2D frame-model. All models were designed for (a) equal global displacement and uniform distribution of inter-story drift under First-Mode (FM) lateral force distribution pattern at first significant yield, and (b) equal period of vibration at the first mode, using Nonlinear Static Seismic analysis procedure. Among the conclusions derived from the research is that the variation of (a) the elastic and inelastic inter-story drift, the ductility demand for the top three stories, and (b) the elastic and inelastic global displacement exhibited a pattern similar to the variation of the FM participation factor at the roof, PF1Φr,1. The square-root-of-sum-of-square (SRSS) distribution provided accurate estimates of elastic story shear and inter-story drift demand as well as the story yield strength and drift.

Unreinforced masonry (URM) structures have shown tobe susceptible to significant damage during strong earthquakes. Vulnerability assessment of URM buildings is needed so that appropriate mitigation strategies can be implemented. The existing Canadian practice consists of rapid seismic screening of buildings to assign priorities for further and more refined assessments, followed by refined analysis of individual critical buildings. The current seismic screening procedure, from 1992, is based on qualitative observations of seismic vulnerability, enabling the assignment of seismic priority indices, quantified on the basis of expert opinion and experience. More refined tools are needed for seismic vulnerability assessment of URM buildings in Canada, based on the current Canadian seismic hazard values. The objective of the research project is to fulfill these needs by developing fragility curves that provide a probabilistic assessment of different levels of building performance under different intensities ofeastern and western seismicity. Using an inventory of over 50,000 structures, a seismic assessment of typical low-rise and mid-rise URM structures located in eastern and western Canada was carried out. The required analyses were done using applied element method software which effectively modeled the in-plane and out-of-plane behaviour of masonry walls. Using incremental dynamic analysis, fragility curves were developed to reflect the capacity of URM structures with a wide variety of selected structural and ground motion parameters. The results were verified against available fragility information in the literature. They show the significance of selected parameters, while providing effective tools for seismic vulnerability assessment of URM buildings in eastern and western Canada.

The first purpose of this research is to investigate the effect of added viscous fluid dampers on a nine story special steel moment frame designed for strength in Seattle. At the initial stages of the work, knowing the fact that moment frames are almost always controlled by drift, it was thought that two different moment frames, controlled by strength or controlled by drift (stiffness), could be designed in Seattle and the effect of additional dampers on the structural behavior of the strength controlled design could be studied. However, since ASCE 7 permits determining the elastic drifts by using the seismic design forces based on the computed fundamental period of the structure, without the upper limit (CuTa), the strength controlled design satisfied the drift limit requirements of ASCE 7. Although the strength controlled design meets the drift requirements, the stability checks of both ASCE 7 and the AISC Seismic Design Manual were not satisfied. Thus, the strength controlled frame was redesigned to meet the stability requirements, and the process is called stability controlled design. By adding supplemental dampers to the strength controlled design, it was expected that the seismic drift would be controlled and a better structural behavior would be obtained in terms of dynamic stability. Incremental Dynamic Analysis (IDA) was implemented to investigate the benefits of the dampers on the structural behavior. Using ten different earthquakes scaled up to a maximum target multiplier two, with ten increments, damage measures such as interstory drift, residual displacement, IDA dispersion, base shear, and roof displacement were studied. Using IDA dispersion, the effect of dampers on dynamic instability was also investigated in this study. As a result, it was found that as the damping of the structure increases with the help of added dampers, the structural response gets better. Maximum and residual roof displacements, interstory drifts, and IDA dispersion decreases with increasing damping. In addition, by using supplemental damping, most of the collapses that occur for the inherently damped frames are prevented. The second purpose of this research is to develop an improved "Hybrid" moment frame without added damping but by controlling the inelastic behavior. Hybrid Frames were designed as the combination of three different moment frames: Special, Intermediate and Ordinary Moment Frames (SMF, IMF, OMF). The design procedure of each bay, which corresponds to different moment frame systems, follows the rules of the related moment frame for that bay. By varying the plastic hinge capacities across the same level stories, four different Hybrid Frame designs were obtained. Nonlinear static pushover analysis was applied to these frames, and as expected, the more reduction in the plastic capacity of the Hybrid Frame, the earlier the pushover curve starts yielding and the later the negative post yield stiffness of the pushover curve was reached. It was observed that the effect of early plastic hinge forming in the frame, which caused inelastic hysteretic damping, and the relatively late formation of negative post yield stiffness resulted in a better dynamic behavior. As a result of the IDA studies, as the frames become more "hybrid", the residual displacements decrease significantly and then collapses are even prevented. This is considered as the positive effect of reaching the negative post yield stiffness late. The residual displacement was reduced for low intensity gentle earthquakes. The ductility demand IDA study proves that as the frames become more hybrid, the ductility demand increases for the special detailing frame, where plastic capacity was reduced, and decreases for the ordinary detailing frame, where the plastic capacity was increased. The Hybrid Frame system is expected to perform better than the traditional special moment frame, and to be more economical than the special moment frame because of the limited amount of special detailing. / Master of Science

This thesis presents the results of a study that uses Incremental Dynamic Analysis to assess the seismic performance of steel moment-resisting frames with fluid viscous dampers subjected to earthquake ground motions. The study systematically investigated the effects of linear and nonlinear dampers on the response of steel moment-resisting frames to earthquakes that varied in intensity and type. Both near-field and far-field motions were considered. Two different types of nonlinear dampers were investigated; one had a hardening and the other had a softening force-velocity relationship. The nonlinear dampers were calibrated to the linear dampers so that there was a basis of comparison. Maximum damper displacement is one of the parameters of the calibration, and it was varied to investigate its effect on structural response. Several nonlinear inelastic time history analyses were performed to obtain responses, such as peak base shear, peak interstory drift, or residual displacement index, which were plotted versus earthquake intensity to create individual IDA curves. Sets of related IDA curves provide a useful summary of the structural behavior for a wide range of variables. IDA curves for the tests with different damping types are presented. The results show that for both near-field and far-field ground motions the nonlinear dampers with a hardening force-velocity relationship are best suited to reduce undesirable drifts and residual displacements; however, these reductions come at the cost of high base shear forces. / Master of Science

This thesis presents the details of a study regarding both the use of linear viscous fluid dampers in controlling the interstory drift in steel moment frames, and the use of incremental dynamic analysis as a method of visualizing the behavior of these moment frames when subjected to seismic load effects. Models of three story and nine story steel moment frames were designed to meet typical strength requirements for office buildings in Seattle, Washington. These models were intentionally designed to violate seismic interstory drift restrictions to test the ability of the linear viscous fluid dampers to reduce these drifts to the point of code compliance. Dampers were included in one bay of every story in each model. These devices were used to produce total structural damping ratios of 5%, 10%, 20%, and 30% of critical. Undamped, traditional stiffness controlled models of both three stories and nine stories were also created for comparison purposes. Incremental dynamic analysis was used to subject these models to ten ground motions, each scaled to twenty incremental levels. Two new computer applications were written to facilitate this process. The results of these analyses were studied to determine if the linear viscous fluid dampers were able to cause compliance with codified drift limits. Also, incremental dynamic analysis plots were created to examine the effects of the dampers on structural behavior as damping increased from inherent to 30% of critical. It was found that including linear viscous fluid dampers in steel moment frame design can satisfactorily control interstory drift, and incremental dynamic analysis is a beneficial tool in visualizing dynamic structural behavior. / Master of Science

During the months I have been at Virginia Tech, I have experienced the most exciting time of my life. There are many persons who helped me to pursue my Master's degree. I would like to take this opportunity to express my appreciations to them. I would like to thank my advisor and committee chairman, Dr Finley A. Charney. He has supported me for the entire duration of this project with all of his efforts. Without his assistance, it would have been very difficult for me to learn so many concepts in the field of nonlinear dynamic analysis and practical earthquake engineering. I would also like to acknowledge my other committee members, Dr. Raymond Plaut and Dr. W. Samuel Easterling, for taking the time to review the thesis and providing valuable insights and feedback on this thesis. I would like to thank my father, Chan Kwok Fung, who encouraged me to pursue my Master Degree, and my mother, Yu Yuk Ping, who brought me to life. I would like to thank my sister, Doris Chan, and my girlfriend, Ka Man Chan, for supporting and encouraging me during the past two years at Virginia Tech. Finally, I would like to give thanks to the rest of my family, friends, professors, and fellow graduate students for their help and encouragement during my stay at Virginia Tech. / Master of Science

This dissertation is relevant to structural engineers focusing on seismic design of structures using reinforced masonry. Specifically the thesis focuses on the seismic performance of reinforced masonry shear walls as seismic force resisting systems. / Reinforced masonry (RM) has been gaining a wide acceptance in the low- and mid-rise construction market as an economic and durable structural system. However, challenges still exist in the area of seismic design because of the poor performance of unreinforced masonry during recent earthquake events in Iran 2003, Haiti 2010, Japan 2011, New Zealand 2011 and Nepal 2015. The dissertation investigated the seismic performance of six concrete block structural walls in an effort to evaluate their force-, displacement- and performance- based seismic design parameters. The walls fall under the ductile shear wall/special reinforced wall seismic force resisting system (SFRS) classification according to the current North American masonry design standards. More specifically, the dissertation is focused on evaluating if such walls, designed under the same prescriptive design provisions, having different cross-section configurations would possess similar seismic performance parameters. This was established through an experimental and analytical program by subjecting the walls to a displacement controlled quasi-static cyclic analysis. Different wall configurations were tested including, rectangular, flanged and slab-coupled walls. Test results confirmed that walls designed under the same SFRS classification, but with different configurations, have different seismic performance parameters that included ductility capacity; yield and post yield displacement; stiffness degradation; period elongation and equivalent viscous damping. The current North American masonry design provisions do not account for such difference in the ductility capacities between the walls. The thesis analyses were concluded by quantifying the seismic vulnerability of a RM SFRS comprised of shear walls similar to those tested, through the development of collapse fragility curves and the assignment of an adjusted collapse margin ratio, ACMR following the FEMA P-58 and P-695 guidelines. The system were deemed acceptable since the ACMR was greater than ACMR10% (2.35 > 2.31). Therefore, the selected RM SFRS which was designed to meet the prescriptive requirements of the ductile masonry walls classification of the CSA S304 (CSA 2014), shows potential capacity against collapse under high intensity earthquakes in one of the highest seismic zones in western Canada and it should be considered as a viable SFRS to be used in seismic design. The procedure described in the chapter can be adopted to investigate the collapse fragility of other SFRS in different seismic regions through careful selection and scaling of the ground motion records associated with such region's seismicity. / Dissertation / Doctor of Philosophy (PhD)

Highway bridges are considered to be one of the most susceptible constituents of transportation networks when they are subjected to severe natural hazards such as earthquakes and environmental exposures like subfreezing temperatures. To facilitate and enhance pre-hazard event mitigation and post-hazard emergency response strategies, probabilistic risk assessment methodologies have attracted increased attention, recently. Seismic fragility assessment is one of the probabilistic techniques which predicts the damage risk of the structure for a given hazard level. While fragility curves can be developed using different methods, such as expert-based, empirical, experimental, analytical, and hybrid, analytical fragility curves are perceived to be the most reliable and least biased technique. Seismic isolation systems are prevalently used in bridge structures to mitigate the damage risk of bridge components against natural hazards. However, the effectiveness of implementing recently emerged isolators such as Stable Unbonded Fiber Reinforced Elastomeric Isolators (SU-FREI) should be examined by developing analytical fragility curves of retrofitted bridges and quantifying the mitigation in the damage probability of different bridge components. In this regard, incorporating the Soil-Structure Interaction (SSI) is critical since the lateral response of bridges relies on the relative stiffness of bridge components, such as columns and isolators and the supporting soil. In addition, all bridge components are exposed to environmental stressors like subfreezing temperature that can alter the seismic response of bridges. In the first phase of this thesis, a seismic fragility assessment is carried out on an existing multi-span continuous reinforced concrete bridge. Two bridge representations are developed to simulate the as-built bridge along with its retrofitted counterpart utilizing SU-FREI. An Incremental Dynamic Analysis (IDA) is conducted using 45 synthetic ground motion records developed for eastern Canada and damage limit states are applied to generate fragility curves and determine the probability of damage to different bridge components. Bridges are analyzed in longitudinal and transverse directions, independently, and component- and system-level fragility curves are developed. In the second phase, the previously generated bridge models are expanded to incorporate the SSI effects by introducing the pile groups under piers and abutments. Several interactions including deck-abutment, abutment-embankment, pile-soil, and pile-soil-pile interactions are considered. A significant challenge in this phase is the accurate simulation of the lateral and vertical behavior of pile groups since all pile groups comprised of closely-spaced vertical and battered piles. A ground motion suite consisting of 45 ground motions has been selected, which reflects the seismicity of the bridge site. IDA is conducted to monitor the seismic performance of the bridge from the elastic linear region up to collapse. Fragility curves, which serve as an important decision-support tool have been developed to identify the potential seismic risk of the bridge. In the third phase, a multi-hazard assessment is carried out by conditioning the previously developed bridge models (i.e. monolithic fixed-base, isolated fixed-base, monolithic with SSI, and isolated with SSI) to a range of room and subfreezing temperatures and applying a seismic excitation, simultaneously. The cold temperature behavior of the constitutive materials of different bridge components, namely, concrete, reinforcing steel, rubber, and the supporting soil are studied and reflected in the bridge models. IDA is performed and damage potential of different bridge components are quantified. In summary, it is demonstrated that SU-FREI is a competing alternative for seismic isolation of bridges by offering potentially less manufacturing time and cost, lower weight, and easier installation which is an attractive feature for accelerated bridge construction applications. In all three phases, it is shown that the bridges which are isolated using SU-FREI have improved seismic performance in comparison with monolithic bridges by exhibiting lower probability of damage to the primary bridge components like columns and pile caps and transferring the damage to less important components such as abutments at which damage does not cause bridge closure. In addition, it is shown that seismic isolation using SU-FREI can effectively mitigate the seismic demand and damage potential of the constitutive components of a bridge supported by weak soil. While occurrence of seismic events along with an environmental stressor such as cold temperature can drastically jeopardize the functionality of a bridge supported by weak soil, it is demonstrated that seismic isolation using SU-FREI can significantly alleviate the probability of damage to bridge components. / Dissertation / Doctor of Philosophy (PhD)

There is a need to develop efficient multi-hazard performance based design (PBD) tools to analyze and optimize buildings at a preliminary stage of design. The first step was to develop a database and it is supported by five major contributions: 1) development of nomenclature of variables in PBD; 2) creation of mathematical model to fit data; 3) collection of data; 4) identification of gaps and methods for filling data in PBD; 5) screening of soil, foundation, structure, and envelope (SFSE) combinations.. A unified nomenclature was developed with the collaboration of a multi-disciplinary team to navigate through the PBD. A mathematical model for incremental dynamic analysis was developed to fit the existing data in the database in a manageable way. Three sets of data were collected to initialize the database: 1) responses of structures subjected to hazard; 2) fragility curves; 3) consequence functions. Fragility curves were critically analyzed to determine the source and the process of development of the curves, but structural analysis results and consequence functions were not critically analyzed due to lack of similarities between the data and background information respectively. Gaps in the data and the methods to fill them were identified to lay out the path for the completion of the database. A list of SFSE systems applicable to typical midrise office buildings was developed. Since the database did not have enough data to conduct PBD calculations, engineering judgement was used to screen SFSE combinations to identify the potential combinations for detailed analysis. Through these five contributions this thesis lays the foundation for the development of a database for multi- hazard PBD and identifies potential future work in this area. / Master of Science