Though generally considered “natural” disasters, cyclones and earthquakes are increasingly being associated with human activities, incubated through urban settlement patterns and the long-term redistribution of natural resources. As society is becoming more urbanized, the risk of human exposure to disasters is also rising. Architecture often reflects the state of society’s health: architectural damage is the first visible sign of emergency, and reconstruction is the final response in the process of recovery. An empirical assessment of architectural projects in post-disaster situations can lead to a deeper understanding of urban societies as they try to rebuild. This thesis offers an alternative perspective on urban disasters by looking at the actions and attitudes of disaster professionals through the lens of architecture, situated in recent events: the 2010 Christchurch earthquake, the 2010 Haiti earthquake, and the 2005 Hurricane Katrina. An empirical, multi-hazard, cross-sectional case study methodology was used, employing grounded theory method to build theory, and a critical constructivist strategy to inform the analysis. By taking an interdisciplinary approach to understanding disasters, this thesis positions architecture as a conduit between two divergent approaches to disaster research: the hazards approach, which studies the disaster cycles from a scientific perspective; and the sociological approach, which studies the socially constructed vulnerabilities that result from disasters, and the elements of social change that accompany such events. Few studies to date have attempted to integrate the multi-disciplinary perspectives that can advance our understanding of societal problems in urban disasters. To bridge this gap, this thesis develops what will be referred to as the “Rittelian framework”—based on the work of UC Berkeley’s architecture professor Horst Rittel (1930-1990). The Rittelian framework uses the language of design to transcend the multiple fields of human endeavor to address the “design problems” in disaster research. The processes by which societal problems are addressed following an urban disaster involve input by professionals from multiple fields—including economics, sociology, medicine, and engineering—but the contribution from architecture has been minimal to date. The main impetus for my doctoral thesis has been the assertion that most of the decisions related to reconstruction are made in the early emergency recovery stages where architects are not involved, but architects’ early contribution is vital to the long-term reconstruction of cities. This precipitated in the critical question: “How does the Rittelian framework contribute to the critical design decisions in modern urban disasters?” Comparative research was undertaken in three case studies of recent disasters in New Orleans (2005), Haiti (2010) and Christchurch (2010), by interviewing 51 individuals who were selected on the basis of employing the Rittelian framework in their humanitarian practice. Contextualizing natural disaster research within the robust methodological framework of architecture and the analytical processes of sociology is the basis for evaluating the research proposition that architectural problem solving is of value in addressing the ‘Wicked Problems’ of disasters. This thesis has found that (1) the nuances of the way disaster agents interpret the notion of “building back better” can influence the extent to which architectural professionals contribute in urban disaster recovery, (2) architectural design can be used to facilitate but also impede critical design decisions, and (3) framing disaster research in terms of design decisions can lead to innovation where least expected. This empirical research demonstrates how the Rittelian framework can inform a wider discussion about post-disaster human settlements, and improve our resilience through disaster research.
During the 2010/2011 Canterbury earthquakes, Reinforced Concrete Frame with Masonry Infill (RCFMI) buildings were subjected to significant lateral loads. A survey conducted by Christchurch City Council (CCC) and the Canterbury Earthquake Recovery Authority (CERA) documented 10,777 damaged buildings, which included building characteristics (building address, the number of storeys, the year of construction, and building use) and post-earthquake damage observations (building safety information, observed damage, level of damage, and current state of the buildings). This data was merged into the Canterbury Earthquake Building Assessment (CEBA) database and was utilised to generate empirical fragility curves using the lognormal distribution method. The proposed fragility curves were expected to provide a reliable estimation of the mean vulnerability for commercial RCFMI buildings in the region. http://www.13thcms.com/wp-content/uploads/2017/05/Symposium-Info-and-Presentation-Schedule.pdf VoR - Version of Record
The research presented in this thesis investigated the environmental impacts of structural design decisions across the life of buildings located in seismic regions. In particular, the impacts of expected earthquake damage were incorporated into a traditional life cycle assessment (LCA) using a probabilistic method, and links between sustainable and resilient design were established for a range of case-study buildings designed for different seismic performance objectives. These links were quantified using a metric herein referred to as the seismic carbon risk, which represents the expected environmental impacts and resource use indicators associated with earthquake damage during buildings’ life. The research was broken into three distinct parts: (1) a city-level evaluation of the environmental impacts of demolitions following the 2010/2011 Canterbury earthquake sequence in New Zealand, (2) the development of a probabilistic framework to incorporate earthquake damage into LCA, and (3) using case-study buildings to establish links between sustainable and resilient design. The first phase of the research focused on the environmental impacts of demolitions in Christchurch, New Zealand following the 2010/2011 Canterbury Earthquake Sequence. This large case study was used to investigate the environmental impact of the demolition of concrete buildings considering the embodied carbon and waste stream distribution. The embodied carbon was considered here as kilograms of CO2 equivalent that occurs on production, construction, and waste management stage. The results clearly demonstrated the significant environmental impacts that can result from moderate and large earthquakes in urban areas, and the importance of including environmental considerations when making post-earthquake demolition decisions. The next phase of the work introduced a framework for incorporating the impacts of expected earthquake damage based on a probabilistic approach into traditional LCA to allow for a comparison of seismic design decisions using a carbon lens. Here, in addition to initial construction impacts, the seismic carbon risk was quantified, including the impacts of seismic repair activities and total loss scenarios assuming reconstruction in case of non-reparability. A process-based LCA was performed to obtain the environmental consequence functions associated with structural and non-structural repair activities for multiple environmental indicators. In the final phase of the work, multiple case-study buildings were used to investigate the seismic consequences of different structural design decisions for buildings in seismic regions. Here, two case-study buildings were designed to multiple performance objectives, and the upfront carbon costs, and well as the seismic carbon risk across the building life were compared. The buildings were evaluated using the framework established in phase 2, and the results demonstrated that the seismic carbon risk can significantly be reduced with only minimal changes to the upfront carbon for buildings designed for a higher base shear or with seismic protective systems. This provided valuable insight into the links between resilient and sustainable design decisions. Finally, the results and observations from the work across the three phases of research described above were used to inform a discussion on important assumptions and topics that need to be considered when quantifying the environmental impacts of earthquake damage on buildings. These include: selection of a non-repairable threshold (e.g. a value beyond which a building would be demolished rather than repaired), the time value of carbon (e.g. when in the building life the carbon is released), the changing carbon intensity of structural materials over time, and the consideration of deterministic vs. probabilistic results. Each of these topics was explored in some detail to provide a clear pathway for future work in this area.
Low Damage Seismic Design (LDSD) guidance material being developed by Engineering NZ is considering a design drift limit for multi-storey buildings of 0.5% at a new damage control limit state (DCLS). The impact of this new design requirement on the expected annual loss due to repair costs is investigated for a four-storey office building with reinforced concrete walls located in Christchurch. The LDSD guidance material aims to reduce the expected annual loss of complying buildings to below 0.1% of building replacement cost. The research tested this expectation. Losses were estimated in accordance with FEMA P58, using building responses from non-linear time history analyses (performed with OpenSees using lumped plasticity models). The equivalent static method, in line with NZS 1170.5 and NZS 3101, was used to design the building to LDSD specifications, representing a future state-of-practice design. The building designed to low-damage specification returned an expected annual loss of 0.10%, and the building designed conventionally returned an expected annual loss of 0.13%. Limitations with the NZS 3101 method for determining wall stiffness were identified, and a different method acknowledging the relationship between strength and stiffness was used to redesign the building. Along with improving this design assumption, the study finds that LDSD design criteria could be an effective way of limiting damage and losses.
Base isolation is arguably the most reliable method for providing enhanced protection of buildings against earthquake-induced actions, by virtue of a physical separation between the structure and the ground through elements/devices with controlled force capacity, significant lateral deformation capacity and (often) enhanced energy dissipation. Such a design solution has shown its effectiveness in protecting both structural and non-structural components, hence preserving their functionality even in the aftermath of a major seismic event. Despite lead rubber bearings being invented in New Zealand almost forty years ago, the Christchurch Women's hospital was the only isolated building in Christchurch when the Canterbury earthquake sequence struck in 2010/11. Furthermore, a reference code for designing base-isolated buildings in New Zealand is still missing. The absence of a design standard or at least of a consensus on design guidelines is a potential source for a lack of uniformity in terms of performance criteria and compliance design approaches. It may also limit more widespread use of the technology in New Zealand. The present paper provides an overview of the major international codes (American, Japanese and European) for the design of base-isolated buildings. The design performance requirements, the analysis procedures, the design review process and approval/quality control of devices outlined in each code are discussed and their respective pros and cons are compared through a design application on a benchmark building in New Zealand. The results gathered from this comparison are intended to set the basis for the development of guidelines specific for the New Zealand environment.
Recent advances in timber design at the University of Canterbury have led to new structural systems that are appropriate for a wide range of building types, including multi-storey commercial office structures. These buildings are competitive with more traditional construction materials in terms of cost, sustainability and structural performance. This paper provides seismic design recommendations and analytical modelling approaches, appropriate for the seismic design of post-tensioned coupled timber wall systems. The models are based on existing seismic design theory for precast post-tensioned concrete, modified to more accurately account for elastic deformation of the timber wall systems and the influence of the floor system. Experimental test data from a two storey post-tensioned timber building, designed, constructed and tested at the University of Canterbury is used to validate the analytical models.
In the last century, seismic design has undergone significant advancements. Starting from the initial concept of designing structures to perform elastically during an earthquake, the modern seismic design philosophy allows structures to respond to ground excitations in an inelastic manner, thereby allowing damage in earthquakes that are significantly less intense than the largest possible ground motion at the site of the structure. Current performance-based multi-objective seismic design methods aim to ensure life-safety in large and rare earthquakes, and to limit structural damage in frequent and moderate earthquakes. As a result, not many recently built buildings have collapsed and very few people have been killed in 21st century buildings even in large earthquakes. Nevertheless, the financial losses to the community arising from damage and downtime in these earthquakes have been unacceptably high (for example; reported to be in excess of 40 billion dollars in the recent Canterbury earthquakes). In the aftermath of the huge financial losses incurred in recent earthquakes, public has unabashedly shown their dissatisfaction over the seismic performance of the built infrastructure. As the current capacity design based seismic design approach relies on inelastic response (i.e. ductility) in pre-identified plastic hinges, it encourages structures to damage (and inadvertently to incur loss in the form of repair and downtime). It has now been widely accepted that while designing ductile structural systems according to the modern seismic design concept can largely ensure life-safety during earthquakes, this also causes buildings to undergo substantial damage (and significant financial loss) in moderate earthquakes. In a quest to match the seismic design objectives with public expectations, researchers are exploring how financial loss can be brought into the decision making process of seismic design. This has facilitated conceptual development of loss optimisation seismic design (LOSD), which involves estimating likely financial losses in design level earthquakes and comparing against acceptable levels of loss to make design decisions (Dhakal 2010a). Adoption of loss based approach in seismic design standards will be a big paradigm shift in earthquake engineering, but it is still a long term dream as the quantification of the interrelationships between earthquake intensity, engineering demand parameters, damage measures, and different forms of losses for different types of buildings (and more importantly the simplification of the interrelationship into design friendly forms) will require a long time. Dissecting the cost of modern buildings suggests that the structural components constitute only a minor portion of the total building cost (Taghavi and Miranda 2003). Moreover, recent research on seismic loss assessment has shown that the damage to non-structural elements and building contents contribute dominantly to the total building loss (Bradley et. al. 2009). In an earthquake, buildings can incur losses of three different forms (damage, downtime, and death/injury commonly referred as 3Ds); but all three forms of seismic loss can be expressed in terms of dollars. It is also obvious that the latter two loss forms (i.e. downtime and death/injury) are related to the extent of damage; which, in a building, will not just be constrained to the load bearing (i.e. structural) elements. As observed in recent earthquakes, even the secondary building components (such as ceilings, partitions, facades, windows parapets, chimneys, canopies) and contents can undergo substantial damage, which can lead to all three forms of loss (Dhakal 2010b). Hence, if financial losses are to be minimised during earthquakes, not only the structural systems, but also the non-structural elements (such as partitions, ceilings, glazing, windows etc.) should be designed for earthquake resistance, and valuable contents should be protected against damage during earthquakes. Several innovative building technologies have been (and are being) developed to reduce building damage during earthquakes (Buchanan et. al. 2011). Most of these developments are aimed at reducing damage to the buildings’ structural systems without due attention to their effects on non-structural systems and building contents. For example, the PRESSS system or Damage Avoidance Design concept aims to enable a building’s structural system to meet the required displacement demand by rocking without the structural elements having to deform inelastically; thereby avoiding damage to these elements. However, as this concept does not necessarily reduce the interstory drift or floor acceleration demands, the damage to non-structural elements and contents can still be high. Similarly, the concept of externally bracing/damping building frames reduces the drift demand (and consequently reduces the structural damage and drift sensitive non-structural damage). Nevertheless, the acceleration sensitive non-structural elements and contents will still be very vulnerable to damage as the floor accelerations are not reduced (arguably increased). Therefore, these concepts may not be able to substantially reduce the total financial losses in all types of buildings. Among the emerging building technologies, base isolation looks very promising as it seems to reduce both inter-storey drifts and floor accelerations, thereby reducing the damage to the structural/non-structural components of a building and its contents. Undoubtedly, a base isolated building will incur substantially reduced loss of all three forms (dollars, downtime, death/injury), even during severe earthquakes. However, base isolating a building or applying any other beneficial technology may incur additional initial costs. In order to provide incentives for builders/owners to adopt these loss-minimising technologies, real-estate and insurance industries will have to acknowledge the reduced risk posed by (and enhanced resilience of) such buildings in setting their rental/sale prices and insurance premiums.
The effects of soil-foundation-structure interaction (SFSI) have been a topic of discussion amongst the structural and geotechnical community for many decades. The complexity of the mechanisms, as well as the need for inter-disciplinary knowledge of geotechnical and structural dynamics has plagued the advancement and the consequent inclusion of SFSI effects in design. A rigorous performance-based design methodology should not just consider the performance of the superstructure but the supporting foundation system as well. Case studies throughout history (eg. Kobe 1995, Kocaeli 1999 and Christchurch earthquakes 2010-2011) have demonstrated that a poor performance at the foundation level can result in a full demolition of the structure and, in general terms, that the extent of damage to, and repairability of, the building system as a whole, is given by the combination of the damage to the soil, foundation and superstructure. The lack of consideration of the modifying factors of SFSI and an absence of intuitive performance levels for controlling foundation and soil behaviour under seismic loads has resulted in inadequate designs for buildings sited on soft soil. For engineers to be satisfied that their designs meet the given performance levels they must first, understand how SFSI affects the overall system performance and secondly have tools available to adequately account for it in their design/assessment. This dissertation presents an integrated performance-based design procedure for buildingfoundation systems that considers all of the major mechanisms of SFSI. A new soil-foundation macro-element model was implemented into a nonlinear finite element software and validated against several experimental tests. The numerical model was used to provide insights in to the mechanisms of SFSI and statistical analysis on the results yielded simple expressions that allow the behaviour to be quantified. Particular attention was paid to the effects of shear force on the foundation response and the quantification of the rocking mode of response. The residual deformations of the superstructure and distribution of forces up the structure were also investigated. All of the major SFSI mechanisms are discussed in detail and targeted numerical studies are used to explain and demonstrate concepts. The design procedure was validated through the design and assessment of a series of concrete buildings that were designed to account for the effects of SFSI.
Timber has experienced renewed interests as a sustainable building material in recent times. Although traditionally it has been the prime choice for residential construction in New Zealand and some other parts of the world, its use can be increased significantly in the future through a wider range of applications, particularly when adopting engineered wood material, Research has been started on the development of innovative solutions for multi-storey non-residential timber buildings in recent years and this study is part of that initiative. Application of timber in commercial and office spaces posed some challenges with requirements of large column-free spaces. The current construction practice with timber is not properly suited for structures with the aforementioned required characteristics and new type of structures has to be developed for this type of applications. Any new structural system has to have adequate capacity for carry the gravity and lateral loads due to occupancy and the environmental effects. Along with wind loading, one of the major sources of lateral loads is earthquakes. New Zealand, being located in a seismically active region, has significant risk of earthquake hazard specially in the central region of the country and any structure has be designed for the seismic loading appropriate for the locality. There have been some significant developments in precast concrete in terms of solutions for earthquake resistant structures in the last decade. The “Hybrid” concept combining post-tensioning and energy dissipating elements with structural members has been introduced in the late 1990s by the precast concrete industry to achieve moment-resistant connections based on dry jointed ductile connections. Recent research at the University of Canterbury has shown that the concept can be adopted for timber for similar applications. Hybrid timber frames using post-tensioned beams and dissipaters have the potential to allow longer spans and smaller cross sections than other forms of solid timber frames. Buildings with post-tensioned frames and walls can have larger column-free spaces which is a particular advantage for non-residential applications. While other researchers are focusing on whole structural systems, this research concentrated on the analysis and design of individual members and connections between members or between member and foundation. This thesis extends existing knowledge on the seismic behaviour and response of post-tensioned single walls, columns under uni-direction loads and small scale beam-column joint connections into the response and design of post-tensioned coupled walls, columns under bi-directional loading and full-scale beam-column joints, as well as to generate further insight into practical applications of the design concept for subassemblies. Extensive experimental investigation of walls, column and beam-column joints provided valuable confirmation of the satisfactory performance of these systems. In general, they all exhibited almost complete re-centering capacity and significant energy dissipation, without resulting into structural damage. The different configurations tested also demonstrated the flexibility in design and possibilities for applications in practical structures. Based on the experimental results, numerical models were developed and refined from previous literature in precast concrete jointed ductile connections to predict the behaviour of post-tensioned timber subassemblies. The calibrated models also suggest the values of relevant parameters for applications in further analysis and design. Section analyses involving those parameters are performed to develop procedures to calculate moment capacities of the subassemblies. The typical features and geometric configurations the different types of subassemblies are similar with the only major difference in the connection interfaces. With adoption of appropriate values representing the corresponding connection interface and incorporation of the details of geometry and configurations, moment capacities of all the subassemblies can be calculated with the same scheme. That is found to be true for both post-tensioned-only and hybrid specimens and also applied for both uni-directional and bi-directional loading. The common section analysis and moment capacity calculation procedure is applied in the general design approach for subassemblies.
The nonlinear dynamic soil-foundation-structure interaction (SFSI) can signifi cantly affect the seismic response of buildings, causing additional deformation modes, damage and repair costs. Because of nonlinear foundation behaviour and interactions, the seismic demand on the superstructure may considerably change, and also permanent deformations at the foundation level may occur. Although SFSI effects may be benefi cial to the superstructure performance, any advantage would be of little structural value unless the phenomenon can be reliably controlled and exploited. Detrimental SFSI effects may also occur, including acceleration and displacement response ampli cation and differential settlements, which would be unconservative to neglect. The lack of proper understanding of the phenomenon and the limited available simpli ed tools accounting for SFSI have been major obstacles to the implementation of integrated design and assessment procedures into the everyday practice. In this study concepts, ideas and practical tools (inelastic spectra) for the seismic design and assessment of integrated foundation-superstructure systems are presented, with the aim to explicitly consider the impact of nonlinearities occurring at the soil-foundation interface on the building response within an integrated approach, where the foundation soil and superstructure are considered as part of an integrated system when evaluating the seismic response, working synergically for the achievement of a target global performance. A conceptual performance-based framework for the seismic design and assessment of integrated foundation-superstructure systems is developed. The framework is based on the use of peak and residual response parameters for both the superstructure and the foundation, which are then combined to produce the system performance matrix. Each performance matrix allows for worsening of the performance when different contributions are combined. An attempt is made to test the framework by using case histories from the 2011 Christchurch earthquake, which are previously shown to have been severely affected by nonlinear SFSI. The application highlights the framework sensitivity to the adopted performance limit states, which must be realistic for a reliable evaluation of the system performance. Constant ductility and constant strength inelastic spectra are generated for nonlinear SFSI systems (SDOF nonlinear superstructure and 3DOF foundation allowing for uplift and soil yielding), representing multistorey RC buildings with shallow rigid foundations supported by cohesive soils. Different ductilities/strengths, hysteretic rules (Bi-linear, Takeda and Flag-Shape), soil stiffness and strength and bearing capacity factors are considered. Footings and raft foundations are investigated, characterized respectively by constant (3 and 8) and typically large bearing capacity factors. It is confi rmed that when SFSI is considered, the superstructure yielding force needed to satisfy a target ductility for a new building changes, and that similarly, for an existing building, the ductility demand on a building of a given strength varies. The extent of change of seismic response with respect to xed-base (FB) conditions depends on the class of soils considered, and on the bearing capacity factor (SF). For SF equal to 3, the stiffer soils enhance the nonlinear rotational foundation behaviour and are associated with reduced settlement, while the softer ones are associated with increased settlement response but not signi ficant rotational behaviour. On average terms, for the simplifi ed models considered, SFSI is found to be bene cial to the superstructure performance in terms of acceleration and superstructure displacement demand, although exceptions are recorded due to ground motion variability. Conversely, in terms of total displacement, a signi cant response increase is observed. The larger the bearing capacity factor, the more the SFSI response approaches the FB system. For raft foundation buildings, characterized by large bearing capacity factors, the impact of foundation response is mostly elastic, and the system on average approaches FB conditions. Well de fined displacement participation factors to the peak total lateral displacement are observed for the different contributions (i.e. peak foundation rotation and translation and superstructure displacement). While the superstructure and foundation rotation show compensating trends, the foundation translation contribution varies as a function of the moment-to-shear ratio, becoming negligible in the medium-to-long periods. The longer the superstructure FB period, the less the foundation response is signifi cant. The larger the excitation level and the less ductile the superstructure, the larger the foundation contribution to the total lateral displacement, and the less the superstructure contribution. In terms of hysteretic behaviour, its impact is larger when the superstructure response is more signifi cant, i.e. for the softer/weaker soils and larger ductilities. Particularly, for the Flag Shape rule, larger superstructure displacement participation factors and smaller foundation contributions are recorded. In terms of residual displacements, the total residual-to-maximum ratios are similar in amplitudes and trends to the corresponding FB system responses, with the foundation and superstructure contributions showing complementary trends. The impact of nonlinear SFSI is especially important for the Flag Shape hysteresis rule, which would not otherwise suffer of any permanent deformations. By using the generated peak and residual inelastic spectra (i.e. inelastic acceleration/ displacement modifi cation factor spectra, and/or participation factor and residual spectra), conceptual simplifi ed procedures for the seismic design and assessment of integrated foundation-superstructure systems are presented. The residual displacements at both the superstructure and foundation levels are explicitly considered. Both the force- and displacement-based approaches are explored. The procedures are de fined to be complementary to the previously proposed integrated performance-based framework. The use of participation factor spectra allows the designer to easily visualize the response of the system components, and could assist the decision making process of both the design and assessment of SFSI systems. The presented numerical results have been obtained using simpli ed models, assuming rigid foundation behaviour and neglecting P-Delta effects. The consideration of more complex systems including asymmetry in stiffness, mass, axial load and ground conditions with a exible foundation layout would highlight detrimental SFSI effects as related to induced differential settlements, while accounting for PDelta effects would further amplify the displacement response. Also, the adopted acceleration records were selected and scaled to match conventional design spectra, thus not representing any response ampli cation in the medium-to-long period range which could as well cause detrimental SFSI effects. While these limitations should be the subject of further research, this study makes a step forward to the understanding of SFSI phenomenon and its incorporation into performance-based design/assessment considerations.
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Beam-column joints are addressed in the context of current design procedures and performance criteria for reinforced concrete ductile frames subjected to large earthquake motions. Attention is drawn to the significant differences between the pertinent requirements of concrete design codes of New Zealand and the United States for such joints. The difference between codes stimulated researchers and structural engineers of the United States, New Zealand, Japan and China to undertake an international collaborative research project. The major investigators of the project selected issues and set guidelines for co-ordinated testing of joint specimens designed according to the codes of the countries. The tests conducted at the University of Canterbury, New Zealand, are reported. Three full-scale beam-column-slab joint assemblies were designed according to existing code requirements of NZS 3101:1982, representing an interior joint of a one-way frame, an interior joint of a two-way frame, and an exterior joint of a two-way frame. Quasistatic cyclic loading simulating severe earthquake actions was applied. The overall performance of each test assembly was found to be satisfactory in terms of stiffness, strength and ductility. The joint and column remained essentially undamaged while plastic hinges formed in the beams. The weak beam-strong column behaviour sought in the design, desirable in tall ductile frames designed for earthquake resistance, was therefore achieved. Using the laws of statics and test observations, the action and flow of forces from the slabs, beams and column to the joint cores are explored. The effects of bond performance and the seismic shear resistance of the joints, based on some postulated mechanisms, are examined. Implications of the test results on code specifications are discussed and design recomendations are made.
Earthquake Engineering is facing an extraordinarily challenging era, the ultimate target being set at increasingly higher levels by the demanding expectations of our modern society. The renewed challenge is to be able to provide low-cost, thus more widely affordable, high-seismic-performance structures capable of sustaining a design level earthquake with limited or negligible damage, minimum disruption of business (downtime) or, in more general terms, controllable socio-economical losses. The Canterbury earthquakes sequence in 2010-2011 has represented a tough reality check, confirming the current mismatch between societal expectations over the reality of seismic performance of modern buildings. In general, albeit with some unfortunate exceptions, modern multi-storey buildings performed as expected from a technical point of view, in particular when considering the intensity of the shaking (higher than new code design) they were subjected to. As per capacity design principles, plastic hinges formed in discrete regions, allowing the buildings to sway and stand and people to evacuate. Nevertheless, in many cases, these buildings were deemed too expensive to be repaired and were consequently demolished. Targeting life-safety is arguably not enough for our modern society, at least when dealing with new building construction. A paradigm shift towards damage-control design philosophy and technologies is urgently required. This paper and the associated presentation will discuss motivations, issues and, more importantly, cost-effective engineering solutions to design buildings capable of sustaining low-level of damage and thus limited business interruption after a design level earthquake. Focus will be given to the extensive research and developments in jointed ductile connections based upon controlled rocking & dissipating mechanisms for either reinforced concrete and, more recently, laminated timber structures. An overview of recent on-site applications of such systems, featuring some of the latest technical solutions developed in the laboratory and including proposals for the rebuild of Christchurch, will be provided as successful examples of practical implementation of performance-based seismic design theory and technology.
Following a major earthquake event, essential public amenities such as medical facilities and transport networks need to remain functional - not only to fulfil their ongoing role in serving the community but also to cope with the added and immediate demand of a population affected by a natural disaster. Furthermore, the economic implications of wide spread damage to housing and commercial facilities should not be discounted. A shift in design approach is required that is consistent with current trends towards performance based building design. The present aim is to achieve seismic energy dissipation during the earthquake event, without the aftermath of damage to structural elements, whilst maintaining design economies. Structures permitted to rock on their foundations and provide recoverable rotations at the beam-column interfaces offer significant advantages over those using conventional ductile detailing. A jointed construction philosophy can be applied whereby structural elements are connected with unbonded prestressing tendons. Supplemental damping is provided by replaceable flexural steel components designed to deform inelastically. For this research a multi-storey test building of one quarter scale has been constructed and tested on an earthquake simulator at the University of Canterbury. A computer model has been developed and a set ofpreliminary design procedures proposed.
Currently there is a worldwide renaissance in timber building design. At the University of Canterbury, new structural systems for commercial multistorey timber buildings have been under development since 2005. These systems incorporate large timber sections connected by high strength post-tensioning tendons, and timber-concrete composite floor systems, and aim to compete with existing structural systems in terms of cost, constructability, operational and seismic performance. The development of post-tensioned timber systems has created a need for improved lateral force design approaches for timber buildings. Current code provisions for seismic design are based on the strength of the structure, and do not adequately account for its deformation. Because timber buildings are often governed by deflection, rather than strength, this can lead to the exceedence of design displacement limitations imposed by New Zealand codes. Therefore, accurate modeling approaches which define both the strength and deformation of post-tensioned timber buildings are required. Furthermore, experimental testing is required to verify the accuracy of these models. This thesis focuses on the development and experimental verification of modeling approaches for the lateral force design of post-tensioned timber frame and wall buildings. The experimentation consisted of uni-direcitonal and bi-directional quasi-static earthquake simulation on a two-thirds scale, two-storey post-tensioned timber frame and wall building with timber-concrete composite floors. The building was subjected to lateral drifts of up to 3% and demonstrated excellent seismic performance, exhibiting little damage. The building was instrumented and analyzed, providing data for the calibration of analytical and numerical models. Analytical and numerical models were developed for frame, wall and floor systems that account for significant deformation components. The models predicted the strength of the structural systems for a given design performance level. The static responses predicted by the models were compared with both experimental data and finite element models to evaluate their accuracy. The frame, wall and floor models were then incorporated into an existing lateral force design procedure known as displacement-based design and used to design several frame and wall structural systems. Predictions of key engineering demand parameters, such as displacement, drift, interstorey shear, interstorey moment and floor accelerations, were compared with the results of dynamic time-history analysis. It was concluded that the numerical and analytical models, presented in this thesis, are a sound basis for determining the lateral response of post-tensioned timber buildings. However, future research is required to further verify and improve these prediction models.
Damage to ceiling systems resulted in a substantial financial loss to building owners in the Canterbury earthquakes. In some buildings, collapse of ceilings could easily have resulted in severe injury to occupants. This paper summarizes the types of ceiling damage observed in the Canterbury earthquakes, and draws useful lessons from the observed performance of different types of ceiling systems. Existing ceiling manufacturing and installing practices/regulations in New Zealand are critically scrutinized to identify deficiencies, and measures are suggested to improve the practice so that the damage to ceilings and the resulting loss are minimized in future earthquakes.
The recent Canterbury earthquake sequence in 2010-2011 highlighted a uniquely severe level of structural damage to modern buildings, while confirming the high vulnerability and life threatening of unreinforced masonry and inadequately detailed reinforced concrete buildings. Although the level of damage of most buildings met the expected life-safety and collapse prevention criteria, the structural damage to those building was beyond economic repair. The difficulty in the post-event assessment of a concrete or steel structure and the uneconomical repairing costs are the big drivers of the adoption of low damage design. Among several low-damage technologies, post-tensioned rocking systems were developed in the 1990s with applications to precast concrete members and later extended to structural steel members. More recently the technology was extended to timber buildings (Pres-Lam system). This doctoral dissertation focuses on the experimental investigation and analytical and numerical prediction of the lateral load response of dissipative post-tensioned rocking timber wall systems. The first experimental stages of this research consisted of component testing on both external replaceable devices and internal bars. The component testing was aimed to further investigate the response of these devices and to provide significant design parameters. Post-tensioned wall subassembly testing was then carried out. Firstly, quasi-static cyclic testing of two-thirds scale post-tensioned single wall specimens with several reinforcement layouts was carried out. Then, an alternative wall configuration to limit displacement incompatibilities in the diaphragm was developed and tested. The system consisted of a Column-Wall-Column configuration, where the boundary columns can provide the support to the diaphragm with minimal uplifting and also provide dissipation through the coupling to the post-tensioned wall panel with dissipation devices. Both single wall and column-wall-column specimens were subjected to drifts up to 2% showing excellent performance, limiting the damage to the dissipating devices. One of the objectives of the experimental program was to assess the influence of construction detailing, and the dissipater connection in particular proved to have a significant influence on the wall’s response. The experimental programs on dissipaters and wall subassemblies provided exhaustive data for the validation and refinement of current analytical and numerical models. The current moment-rotation iterative procedure was refined accounting for detailed response parameters identified in the initial experimental stage. The refined analytical model proved capable of fitting the experimental result with good accuracy. A further stage in this research was the validation and refinement of numerical modelling approaches, which consisted in rotational spring and multi-spring models. Both the modelling approaches were calibrated versus the experimental results on post-tensioned walls subassemblies. In particular, the multi-spring model was further refined and implemented in OpenSEES to account for the full range of behavioural aspects of the systems. The multi-spring model was used in the final part of the dissertation to validate and refine current lateral force design procedures. Firstly, seismic performance factors in accordance to a Force-Based Design procedure were developed in accordance to the FEMA P-695 procedure through extensive numerical analyses. This procedure aims to determine the seismic reduction factor and over-strength factor accounting for the collapse probability of the building. The outcomes of this numerical analysis were also extended to other significant design codes. Alternatively, Displacement-Based Design can be used for the determination of the lateral load demand on a post-tensioned multi-storey timber building. The current DBD procedure was used for the development of a further numerical analysis which aimed to validate the procedure and identify the necessary refinements. It was concluded that the analytical and numerical models developed throughout this dissertation provided comprehensive and accurate tools for the determination of the lateral load response of post-tensioned wall systems, also allowing the provision of design parameters in accordance to the current standards and lateral force design procedures.
On Tuesday 22 February 2011, a 6.3 magnitude earthquake struck Christchurch, New Zealand’s second largest city. The ‘earthquake’ was in fact an aftershock to an earlier 7.1 magnitude earthquake that had occurred on Saturday 4 September 2010. There were a number of key differences between the two events that meant they had dramatically different results for Christchurch and its inhabitants. The 22 February 2011 event resulted in one of New Zealand’s worst natural disasters on record, with 185 fatalities occurring and hundreds more being injured. In addition, a large number of buildings either collapsed or were damaged to the point where they needed to be totally demolished. Since the initial earthquake in September 2010, a large amount of building-related research has been initiated in New Zealand to investigate the impact of the series of seismic events – the major focus of these research projects has been on seismic, structural and geotechnical engineering matters. One project, however, conducted jointly by the University of Canterbury, the Fire Protection Association of New Zealand and BRANZ, has focused on the performance of fire protection systems in the earthquakes and the effectiveness of the systems in the event of post-earthquake fires occurring. Fortunately, very few fires actually broke out following the series of earthquake events in Christchurch, but fire after earthquakes still has significant implications for the built environment in New Zealand, and the collaborative research has provided some invaluable insight into the potential threat posed by post-earthquake fires in buildings. As well as summarising the damage caused to fire protection systems, this paper discusses the flow-on effect for designing structures to withstand post-earthquake fires. One of the underlying issues that will be explored is the existing regulatory framework in New Zealand whereby structural earthquake design and structural design for fire are treated as discrete design scenarios.
To reduce seismic vulnerability and the economic impact of seismic structural damage, it is important to protect structures using supplemental energy dissipation devices. Several types of supplemental damping systems can limit loads transferred to structures and absorb significant response energy without sacrificial structural damage. Lead extrusion dampers are one type of supplemental energy dissipation devices. A smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, have been employed in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch and San Francisco. HF2V devices have previously been designed using very simple models with limited precision. They are then manufactured, and tested to ensure force capacities match design goals, potentially necessitating reassembly or redesign if there is large error. In particular, devices with a force capacity well above or below a design range can require more testing and redesign, leading to increased economic and time cost. Thus, there is a major need for a modelling methodology to accurately estimate the range of possible device force capacity values in the design phase – upper and lower bounds. Upper and lower bound force capacity estimates are developed from equations in the metal extrusion literature. These equations consider both friction and extrusion forces between the lead and the bulged shaft in HF2V devices. The equations for the lower and upper bounds are strictly functions of device design parameters ensuring easy use in the design phase. Two different sets of estimates are created, leading to estimates for the lower and upper bounds denoted FLB,1, FUB,1, FUB,2, respectively. The models are validated by comparing the bounds with experimental force capacity data from 15 experimental HF2V device tests. All lower bound estimates are below or almost equal to the experimental device forces, and all upper bound estimates are above. Per the derivation, the (FLB,1, FUB,1) pair provide narrower bounds. The (FLB,1, FUB,1) pair also had a mean lower bound gap of -34%, meaning the lower bound was 74% of device force on average, while the mean upper bound gap for FUB,1 was +23%. These are relatively tight bounds, within ~±2 SE of device manufacture, and can be used as a guide to ensure device forces are in range for the actual design use when manufactured. Therefore, they provide a useful design tool.
This thesis describes research into developing a client/server ar- chitecture for a mobile Augmented Reality (AR) application. Following the earthquakes that have rocked Christchurch the city is now changed forever. CityViewAR is an existing mobile AR application designed to show how the city used to look before the earthquakes. In CityViewAR 3D virtual building models are overlaid onto video captured by a smartphone camera. However the current version of CityViewAR only allows users to browse information stored on the mobile device. In this research the author extends the CityViewAR application to a client-server model so that anyone can upload models and annotations to a server and have this information viewable on any smartphone running the application. In this thesis we describe related work on AR browser architectures, the system we developed, a user evaluation of the prototype system and directions for future work.
Despite their good performance in terms of their design objectives, many modern code-prescriptive buildings built in Christchurch, New Zealand had to be razed after the 2010-2011 Canterbury earthquakes because repairs were deemed too costly due to widespread sacrificial damage. Clearly a more effective design paradigm is needed to create more resilient structures. Rocking, post-tensioned connections with supplemental energy dissipation can contribute to a damage avoidance designs (DAD). However, few have achieved all three key design objectives of damage-resistant rocking, inherent recentering ability, and repeatable, damage-free energy dissipation for all cycles, which together offer a response which is independent of loading history. Results of experimental tests are presented for a near full-scale rocking beam-column sub-assemblage. A matrix of test results is presented for the system under varying levels of posttensioning, with and without supplemental dampers. Importantly, this parametric study delineates each contribution to response. Practical limitations on posttensioning are identified: a minimum to ensure static structural re-centering, and a maximum to ensure deformability without threadbar yielding. Good agreement between a mechanistic model and experimental results over all parameters and inputs indicates the model is robust and accurate for design. The overall results indicate that it is possible to create a DAD connection where the non-linear force-deformation response is loading history independent and repeatable over numerous loading cycles, without damage, creating the opportunity for the design and implementation of highly resilient structures.
With the occurrence of natural disasters on the increase, major cities around the world face the potential of complete loss of infrastructure due to design guidelines that do not consider resilience in the design. With the February 22nd, 2011 earthquake in Christchurch, being the largest insured event, lessons learnt from the rebuild will be vital for the preparation of future disasters. Therefore the objective of this research is to understand the financial implications of the changes to the waste water design guidelines used throughout the five year rebuild programme of works. The research includes a study of the SCIRT alliance model selected for the delivery that is flexible enough to handle changes in the design with minimal impact on the direct cost of the rebuild works. The study further includes the analysis and compares the impact of the three different guidelines on maintenance and replacement cost over the waste water pipe asset life. The research concludes that with the varying ground conditions in Christchurch and also the wide variety of materials in use in the waste water network up to the start of the CES, the rebuild was not a ‘one size fits all’ approach.
Supplemental energy dissipation devices are increasingly used to protect structures, limit loads transferred to structural elements and absorbing significant response energy without sacrificial structural damage. Lead extrusion dampers are supplemental energy dissipation devices, where recent development of smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, has seen deployment in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch, NZ and San Francisco, USA. HF2V devices have previously been designed using limited precision models, so there is variation in force prediction capability. Further, while the overall resistive force is predicted, the knowledge of the relative contributions of the different internal reaction mechanisms to these overall resistive forces is lacking, limiting insight and predictive accuracy in device design. There is thus a major need for detailed design models to better understand force generation, and to aid precision device design. These outcomes would speed the overall design and implementation process for uptake and use, reducing the need for iterative experimental testing. Design parameters from 17 experimental HF2V device tests are used to create finite element models using ABAQUS. The analysis is run using ABAQUS Explicit, in multiple step times of 1 second with automatic increments, to balance higher accuracy and computational time. The output is obtained from the time- history output of the contact pressure forces including the normal and friction forces on the lead along the shaft. These values are used to calculate the resistive force on the shaft as it moves through the lead, and thus the device force. Results of these highly nonlinear, high strain analyses are compared to experimental device force results. Model errors compared to experimental results for all 17 devices ranged from 0% to 20% with a mean absolute error of 6.4%, indicating most errors were small. In particular, the standard error in manufacturing is SE = ±14%. In this case, 15 of 17 devices (88%) are within ±1SE (±14%) and 2 of 17 devices (12%) are within ±2SE (±28). These results show low errors and a distribution of errors compared to experimental results that are within experimental device construction variability. The overall modelling methodology is objective and repeatable, and thus generalizable. The exact same modelling approach is applied to all devices with only the device geometry changing. The results validate the overall approach with relatively low error, providing a general modelling methodology for accurate design of HF2V devices.
The performance of buildings in recent New Zealand earthquakes (Canterbury, Seddon and Kaikōura), delivered stark lessons on seismic resilience. Most of our buildings, with a few notable exceptions, performed as our Codes intended them to, that is, to safeguard people from injury. Many buildings only suffered minor structural damage but were unable to be reused and occupied for significant periods of time due to the damage and failure of non-structural elements. This resulted in substantial economic losses and major disruptions to our businesses and communities. Research has attributed the damage to poor overall design coordination, inadequate or lack of seismic restraints for non structural elements and insufficient clearances between building components to cater for the interaction of non structural elements under seismic actions. Investigations have found a clear connection between the poor performance of non-structural elements and the issues causing pain in the industry (procurement methods, risk aversion, the lack of clear understanding of design and inspection responsibility and the need for better alignment of the design codes to enable a consistent integrated design approach). The challenge to improve the seismic performance of non structural elements in New Zealand is a complex one that cuts across a diverse construction industry. Adopting the key steps as recommended in this paper is expected to have significant co-benefits to the New Zealand construction industry, with improvements in productivity alongside reductions in costs and waste, as the rework which plagues the industry decreases.
Observations of out-of-plane (OOP) instability in the 2010 Chile earthquake and in the 2011 Christchurch earthquake resulted in concerns about the current design provisions of structural walls. This mode of failure was previously observed in the experimental response of some wall specimens subjected to in-plane loading. Therefore, the postulations proposed for prediction of the limit states corresponding to OOP instability of rectangular walls are generally based on stability analysis under in-plane loading only. These approaches address stability of a cracked wall section when subjected to compression, thereby considering the level of residual strain developed in the reinforcement as the parameter that prevents timely crack closure of the wall section and induces stability failure. The New Zealand code requirements addressing the OOP instability of structural walls are based on the assumptions used in the literature and the analytical methods proposed for mathematical determination of the critical strain values. In this study, a parametric study is conducted using a numerical model capable of simulating OOP instability of rectangular walls to evaluate sensitivity of the OOP response of rectangular walls to variation of different parameters identified to be governing this failure mechanism. The effects of wall slenderness (unsupported height-to-thickness) ratio, longitudinal reinforcement ratio of the boundary regions and length on the OOP response of walls are evaluated. A clear trend was observed regarding the influence of these parameters on the initiation of OOP displacement, based on which simple equations are proposed for prediction of OOP instability in rectangular walls.
Existing New Zealand (NZ) building stock contains a significant number of structures designed prior to 1995 with non-ductile reinforced concrete (RC) columns. Recent earthquakes and research show that columns with such details perform poorly when subjected to seismic demand, losing gravity load carrying capacity at drift levels lower than the expected one. Therefore, in order to have a better understanding of existing RC columns in NZ, the history of these elements is investigated in this paper. The evolution of RC column design guidelines in NZ standards since the 1970s is scrutinized. For this purpose, a number of RC columns from Christchurch buildings built prior to 1995 are assessed using the current code of practice.
In recent work on commons and commoning, scholars have argued that we might delink the practice of commoning from property ownership, while paying attention to modes of governance that enable long-term commons to emerge and be sustained. Yet commoning can also occur as a temporary practice, in between and around other forms of use. In this article we reflect on the transitional commoning practices and projects enabled by the Christchurch post-earthquake organisation Life in Vacant Spaces, which emerged to connect and mediate between landowners of vacant inner city demolition sites and temporary creative or entrepreneurial users. While these commons are often framed as transitional or temporary, we argue they have ongoing reverberations changing how people and local government in Christchurch approach common use. Using the cases of the physical space of the Victoria Street site “The Commons” and the virtual space of the Life in Vacant Spaces website, we show how temporary commoning projects can create and sustain the conditions of possibility required for nurturing commoner subjectivities. Thus despite their impermanence, temporary commoning projects provide a useful counter to more dominant forms of urban development and planning premised on property ownership and “permanent” timeframes, in that just as the physical space of the city being opened to commoning possibilities, so too are the expectations and dispositions of the city’s inhabitants, planners, and developers.
The seismic tremor that shook Christchurch on February 22, 2011, not only shattered buildings but also the spirit of the city’s residents. Amidst the ruins, this design-focused thesis unravels two intertwining narratives, each essential to the city’s resurrection. At its core, this thesis probes the preservation of Christchurch’s memory and character, meticulously chronicling the lost heritage architecture and the subsequent urban metamorphosis. Beyond bricks and mortar, it also confronts the silent aftershocks - the pervasive mental health challenges stemming from personal losses and the disfigured cityscape. As a native of Christchurch, intimately connected to its fabric, my lens reflects not just on the architectural reconstruction but also on the emotional reconstruction. My experience as an autistic individual, a recently discovered facet of my identity, infuses this design journey with a distinct prism through which I perceive and interact with the world. The colourful sketches that drive the design process aren’t mere illustrations but manifestations of my interpretation of spaces and concepts, evoking joy and vitality—a testament to embracing diversity in design. Drawing parallels between healing my own traumas with my colourful and joyful neurodivergent worldview, I’ve woven this concept into proposals aimed at healing the city through whimsy, joy, and vibrant colours. Personal experiences during and post-earthquakes profoundly shape my design proposals. Having navigated the labyrinth of my own mental health amid the altered cityscape, I seek avenues for reconciliation, both personal and communal. The vibrant sketches and designs presented in this thesis encapsulate this vision—a fusion of vivid, unconventional interpretations and a dedication to preserving the essence of the original cityscape while still encouraging movement into the future.
The Christchurch region of New Zealand experienced a series of major earthquakes and aftershocks between September 2010 and June 2011 which caused severe damage to the city’s infrastructure. The performance of tilt-up precast concrete buildings was investigated and initial observations are presented here. In general, tilt-up buildings performed well during all three major earthquakes, with mostly only minor, repairable damage occurring. For the in-plane loading direction, both loadbearing and cladding panels behaved exceptionally well, with no significant damage or failure observed in panels and their connections. A limited number of connection failures occurred due to large out-of-plane panel inertia forces. In several buildings, the connections between the panel and the internal structural frame appeared to be the weakest link, lacking in both strength and ductility. This weakness in the out-of-plane load path should be prevented in future designs.
This thesis is concerned with the effects of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns. The contents of the chapters are summarized as follows. In Chapter one, the general problems in seismic design are discussed and earthquake design methods based on the ductile design approach are described. Japanese, New Zealand and United States design codes are compared. Finally, the scope of this research project is outlined. In Chapter two, after reviewing previous research on confined concrete, the factors which affect the effectiveness of lateral confinement are discussed. Especially the effects of the yield strength of transverse reinforcement, the compressive strength of plain concrete and the strain gradient in the column section due to bending are discussed based on tests which were conducted by the author et al at Kyoto University and Akashi Technological College, Japan. In the axial compression tests on spirally reinforced concrete cylinders (150 mm in diameter by 300 mm in height), the yield strength of transverse reinforcement and the compressive strength of plain concrete were varied from 161 MPa to 1352 MPa and from 17 MPa to 60 MPa, respectively, as experimental parameters. It is found that, when high strength spirals are used as confining reinforcement, the strength and ductility of the confined core concrete are remarkably enhanced but need to be estimated assuming several failure modes which could occur. These are based on the observations that concrete cylinders with high strength spirals suddenly failed at a concrete compressive strain of 2 to 3.5 % due to explosive crushing of the core concrete between the spiral bars or due to bearing failure of the core concrete immediately beneath the spiral bars, while the concrete cylinders with ordinary strength spirals failed in a gentle manner normally observed. In addition, eccentric loading tests were conducted on concrete columns with 200 mm square section confined by square spirals. It is found that the effectiveness of confining reinforcement is reduced by the presence of the strain gradient along the transverse section of column. In Chapter three, the effectiveness of transverse reinforcement with various types of anchorage details which simplify the fabrication of reinforcing cages are investigated. Eight reinforced concrete columns, with either 400 mm or 550 mm square cross sections, were tested subjected to axial compression loading and cyclic lateral loading which simulated a severe earthquake. The transverse reinforcement consisted of arrangements of square perimeter hoops with 135° end hooks, cross ties with 90° and 135° or 180° end hooks, and 'U' and 'J' shaped cross ties and perimeter hoops with tension splices. Conclusions are reached with regard to the effectiveness of the tested anchorage details in the plastic hinge regions of columns designed for earthquake resistance. In Chapter four, the effectiveness of interlocking spirals as transverse reinforcement is studied. Firstly, the general aspects and the related problems of interlocking spirals to provide adequate ductility in the potential plastic hinge region of columns are discussed, referring to the provisions in the New Zealand code,the CALTRANS (California Transportation Authority) code and other related codes. Secondly, based on those discussions, a design method to securely interlock the spirals is proposed. Thirdly, the effectiveness of interlocking spirals is assessed based on column tests conducted as part of this study. Three columns with interlocking spirals and, for comparison, one rectangular column with rectangular hoopsandcross ties, were tested under cyclic horizontal loading which simulated a severe earthquake. The sections of those columns were 400 mm by 600 mm. In Chapter five, analytical models to investigate the buckling behaviour of longitudinal reinforcement restrained by cross ties with 90° and 135° end hooks and by peripheral hoops are proposed. The analyzed results using the proposed models compare well with the experimental observations described in Chapter three. Using those proposed models, a method to check the effectiveness of cross ties with 90° and 135° end hooks is proposed for practical design purposes. In Chapter six, a theory for the prediction of the ultimate longitudinal compressive concrete strain at the stage of first hoop fracture referred to as the "Energy Balance Theory", which has been developed by Mander, Priestley and Park at University of Canterbury, is introduced. After discussing the problems in the "Energy Balance Theory", a modified theory for the prediction of the ultimate longitudinal compressive concrete strain at the stage of first hoop fracture is proposed. The predictions from the modified theory are found to compare well with previous experimental results.
