The primary seismic response mode of freestanding slender building contents is rocking. Rocking is one of the most damaging response modes due to large accelerations at impact and the possibility of toppling. This study investigates the rocking response of contents within fixed-base and base-isolated buildings so that better-informed decisions can be made, either at the design stage for new structures or during the performance evaluation for existing structures, to mitigate the effects of the destructive rocking behaviour and consequently minimize injury, economic loss, and downtime. A 3D model of a hospital building was created in OpenSees and analyzed to obtain floor accelerations for a suite of 20 broadband ground motions. These motions were then used as input to compute the rocking responses of many building contents. The rocking responses were compared and contrasted to determine the effect of the block’s size, slenderness, floor level, and placement within a level. The rocking response of contents in buildings isolated with lead plug and triple friction pendulum bearings were compared to the fixed-base building to determine the effectiveness of isolation as a means to control rocking. Fragility curves were also created for the fixed-base and isolated buildings. The vertical component of the floor accelerations had little effect on the rocking response of contents. The significance of this is that the location of an object on a given story does not affect its rocking response. However, higher vertical accelerations did increase the likelihood of the object lifting off the floor. The rocking response of stocky contents increased from one story to the next, but as the slenderness increased this transition became less evident. Base isolation was found to be effective at reducing both the likelihood to uplift and overturn. The longer period systems provided superior protection despite the long period pulse like motion while the damping of the systems had little effect on the rocking response. / Thesis / Master of Applied Science (MASc) / During an earthquake slender building contents respond by rocking about their edges. Rocking causes damage to sensitive and brittle objects as well as safety hazards if it results in the overturning of heavy objects. One goal of this study was to define the rocking response of rigid contents in a conventional braced frame hospital. In general, larger and stockier objects were less likely to overturn. Also, overturning was more prevalent higher up in the building while the location of an object within a given story had little effect. Another objective was to determine the effectiveness of base isolation, a technique that decouples the motion of the building from the ground using flexible bearings, as a strategy to protect contents that are vulnerable to rocking during an earthquake. This was found to be quite effective at reducing both the occurrence of uplift (the initiation of rocking) as well as toppling.

Controlled Rocking Steel Braced Frames (CRSBFs) have been developed as a high-performance structural solution to resist seismic forces, due to their ability to minimize structural damage and self-centre the structure back to its original position after an earthquake. A CRSBF is intentionally allowed to uplift and rock on its foundation, which acts as the nonlinear mechanism for the system rather than member yielding and buckling. While the CRSBF is in the rocking phase, the response of the system is controlled by prestressing which anchors the frame to the foundation and energy dissipation devices which are engaged by uplift. Although CRSBFs have shown promising structural performance, an assessment of the overall effectiveness of this system must also consider the performance of nonstructural components which have a significant impact on the safety and economic performance of the system. The purpose of this thesis is to compare the performance of nonstructural components in buildings with CRSBFs to their performance in a conventional codified system such as a buckling restrained braced frame (BRBF), while also investigating which design parameters influence nonstructural component demands in CRSBFs. The responses of various types of nonstructural components, including anchored components, stocky unanchored components that slide, and slender unanchored components that rock, are determined using a cascading analysis approach where absolute floor accelerations generated from nonlinear time-history analyses of each structural system are used as input for computing the responses of nonstructural components. The results show that the trade-off of maintaining elastic behaviour of the CRSBF members is, in general, larger demands on nonstructural components compared to the BRBF system. The results also show that the stiffness of the frame and vibration of the frame in its elastic higher modes are the main influencers for nonstructural component demands in buildings with CRSBFs, while energy dissipation has a minimal impact. / Thesis / Master of Applied Science (MASc) / Controlled Rocking Steel Braced Frames (CRSBFs) have been proposed as a high-performance structural system that resists earthquake forces on buildings. This system has the ability to minimize damage to structural members and self-centre the building back to its original position after an earthquake, two characteristics that are typically not achieved by current conventional systems. However, an assessment of the CRSBF’s overall effectiveness cannot be limited to the consideration of only the structural skeleton, as the performance of nonstructural components (e.g. architectural elements, mechanical and electrical equipment, furnishings, and building contents) that are not part of the structural skeleton can have a significant impact on the safety and economic performance of earthquake resisting systems. This thesis compares the demands on nonstructural components in buildings with CRSBFs to their demands in a more conventional system during earthquake motions. The results show that the trade-off for avoiding damage to structural members in the CRSBFs is often higher demands on the nonstructural components.

Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.

Immediate occupancy and functionality of critical facilities including hospitals, emergency operations centers, communications centers, and police and fire stations is of utmost importance immediately after a damaging earthquake, as they must continue to provide fundamental health, emergency, and security services in the aftermath of an extreme event. Although recent earthquakes have proven the acceptable performance of the structural system in such buildings, when designed according to recent seismic design codes, in many cases damage to the nonstructural components and systems was the main cause of disruption in their functionality. Seismic isolation is proven to be an effective technique to protect building structures from damaging earthquakes. It has been the method of choice for critical facilities, including hospitals in Japan and the United States in recent years. Seismic isolation appears to be an ideal solution for protecting the nonstructural components as well. While this claim was made three decades ago, the supporting research for freestanding (unanchored) equipment and contents (EC) is fairly new. With the focus on freestanding EC, this study investigates the seismic performance of sliding and wheel/caster-supported EC in fixed-base and base-isolated buildings. The study adopts a comparative approach to provide a better understanding of the advantages and disadvantages of using each structural system. The seismic response of sliding EC is investigated analytically in the first part of the thesis, while the response of EC supported on wheels/casters is examined through shake table experiments on two pieces of hospital equipment. The study finds base isolation to be generally effective in reducing seismic demands on freestanding EC, but it also exposes certain situations where isolation in fact increases demands on EC. Increasing the frictional resistance for sliding EC or locking the wheel/casters in the case of wheel/caster-supported EC is highly recommended for EC in base-isolated buildings to prevent excessive displacement demands. Furthermore, the study suggests several design probability functions that can be used by practicing engineers to estimate the peak seismic demands on sliding and wheel/caster-supported EC in fixed-base and base-isolated buildings. / Dissertation / Doctor of Philosophy (PhD)