A building boom in the 1980s allowed pre-stressed hollow-core floor construction to be widely adopted in New Zealand, even though the behaviour of these prefabricated elements within buildings was still uncertain. Inspections following the Canterbury and Kaikōura earthquakes has provided evidence of web-splitting, transverse cracking and longitudinal splitting on hollow-core units, confirming the susceptibility of these floors to undesirable failure modes. Hollow-core slabs are mainly designed to resist bending and shear. However, there are many applications in which they are also subjected to torsion. In New Zealand, hollow-core units contain no transverse reinforcement in the soffit concrete below the cells and no web reinforcement. Consequently, their dependable performance in torsion is limited to actions that they can resist before torsional cracking occurs. In previous work by the present authors, a three-dimensional FE modelling approach to study the shear flexural behaviour of precast pre-stressed hollow core units was developed and validated by full-scale experiments. This paper shows how the FE analyses have been extended to investigate the response of HC units subjected to torsional actions. Constitutive models, based on nonlinear fracture mechanics, have been used to numerically predict the torsional capacity of HC units and have been compared with experimental results. The results indicate that the numerical approach is promising and should be developed further as part of future research.
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.
As part of a seismic retrofit scheme, surface bonded glass fiber-reinforced polymer (GFRP) fabric was applied to two unreinforced masonry (URM) buildings located in Christchurch, New Zealand. The unreinforced stone masonry of Christchurch Girls’ High School (GHS) and the unreinforced clay brick masonry Shirley Community Centre were retrofitted using surface bonded GFRP in 2007 and 2009, respectively. Much of the knowledge on the seismic performance of GFRP retrofitted URM was previously assimilated from laboratory-based experimental studies with controlled environments and loading schemes. The 2010/2011 Canterbury earthquake sequence provided a rare opportunity to evaluate the GFRP retrofit applied to two vintage URM buildings and to document its performance when subjected to actual design-level earthquake-induced shaking. Both GFRP retrofits were found to be successful in preserving architectural features within the buildings as well as maintaining the structural integrity of the URM walls. Successful seismic performance was based on comparisons made between the GFRP retrofitted GHS building and the adjacent nonretrofitted Boys’ High School building, as well as on a comparison between the GFRP retrofitted and nonretrofitted walls of the Shirley Community Centre building. Based on detailed postearthquake observations and investigations, the GFRP retrofitted URM walls in the subject buildings exhibited negligible to minor levels of damage without delamination, whereas significant damage was observed in comparable nonretrofitted URM walls. AM - Accepted Manuscript
Using case studies from the 2010-2011 Canterbury, New Zealand earthquake sequence, this study assesses the accuracies of paleoliquefaction back-analysis methods and explores the challenges, techniques, and uncertainties associated with their application. While liquefaction-based back-analyses have been widely used to estimate the magnitudes of paleoearthquakes, their uncertain efficacies continue to significantly affect the computed seismic hazard in regions where they are relied upon. Accordingly, their performance is evaluated herein using liquefaction data from modern earthquakes with known magnitudes. It is shown that when the earthquake source location and mechanism are known, back-analysis methods are capable of accurately deriving seismic parameters from liquefaction evidence. However, because the source location and mechanism are often unknown in paleoseismic studies, and because accurate interpretation is shown to be more difficult in such cases, new analysis techniques are proposed herein. An objective parameter is proposed to geospatially assess the likelihood of any provisional source location, enabling an analyst to more accurately estimate the magnitude of a liquefaction-inducing paleoearthquake. This study demonstrates the application of back-analysis methods, provides insight into their potential accuracies, and provides a framework for performing paleoliquefaction analyses worldwide.
This study uses 44 high quality liquefaction case histories taken from 22 locations affected by the 2010-2011 Canterbury earthquake sequence to evaluate four commonly used CPT-VS correlations (i.e., Robertson, 2009; Hegazy and Mayne, 2006; Andrus et al., 2007; McGann et al., 2015b). Co-located CPT soundings and VS profiles, developed from surface wave testing, were obtained at 22 locations and case histories were developed for the Mw 7.1, 4 September 2010 Darfield and Mw 6.2, 22 February 2011 Christchurch earthquakes. The CPT soundings are used to generate VS profiles using each of four CPT-VS correlations. These correlated VS profiles are used to estimate the factor of safety against liquefaction using the Kayen et al. (2013) VS-based simplified liquefaction evaluation procedure. An error index is used to quantify the predictive capabilities of these correlations in relation to the observations of liquefaction (or the lack thereof). Additionally, the error indices from the CPT-correlated VS profiles are compared to those obtained using: (1) the Kayen et al. (2013) procedure with surface wave-derived VS profiles, and (2) the Idriss and Boulanger (2008) CPT-based liquefaction evaluation procedure. Based on the error indices, the evaluation procedures based on direct measurements of either CPT or VS provided more accurate liquefaction triggering estimates than those obtained from any of the CPT-VS correlations. However, the performance of the CPT-VS correlations varied, with the Robertson (2009) and Hegazy and Mayne (2006) correlations performing relatively poorly for the Christchurch soils and the Andrus et al. (2007) and McGann et al. (2015b) correlations performing better. The McGann et al. (2015b) correlation had the lowest error indices of the CPT-VS correlations tested, however, none of the CPT-VS correlations provided accurate enough VS predictions to be used for the evaluation of liquefaction triggering using the VS-based liquefaction evaluation procedures.
Seismic behaviour of typical unreinforced masonry (URM) brick houses, that were common in early last century in New Zealand and still common in many developing countries, is experimentally investigated at University of Canterbury, New Zealand in this research. A one halfscale model URM house is constructed and tested under earthquake ground motions on a shaking table. The model structure with aspect ratio of 1.5:1 in plan was initially tested in the longitudinal direction for several earthquakes with peak ground acceleration (PGA) up to 0.5g. Toppling of end gables (above the eaves line) and minor to moderate cracking around window and door piers was observed in this phase. The structure was then rotated 90º and tested in the transverse (short) direction for ground motions with PGA up to 0.8g. Partial out-of-plane failure of the face loaded walls in the second storey and global rocking of the model was observed in this phase. A finite element analysis and a mechanism analysis are conducted to assess the dynamic properties and lateral strength of the model house. Seismic fragility function of URM houses is developed based on the experimental results. Damping at different phases of the response is estimated using an amplitude dependent equivalent viscous damping model. Financial risk of similar URM houses is then estimated in term of expected annual loss (EAL) following a probabilistic financial risk assessment framework. Risks posed by different levels of damage and by earthquakes of different frequencies are then examined.
The paper discusses modelling of cyclic stress-strain behaviour of soil, in particular a simple model that can produce a desired stiffness and hysteretic damping for a given strain level as observed in laboratory testing is formulated. The unloading-reloading relationship is developed for total stress seismic site response analysis with appropriate damping at large strain. The constitutive model employs a hyperbolic equation as the backbone curve, and uses a modification of the extended Masing unloading-reloading relationship leading to correct measured modulus reduction and damping curves simultaneously. A quasi-static cyclic loading of increasing amplitude is used to demonstrate the model’s performance and its capability to allow improved modelling of the magnitude of energy dissipation based on an experimental program on native sandy soils from Christchurch, New Zealand.
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Prediction of building collapse due to significant seismic motion is a principle objective of earthquake engineers, particularly after a major seismic event when the structure is damaged and decisions may need to be made rapidly concerning the safe occupation of a building or surrounding areas. Traditional model-based pushover analyses are effective, but only if the structural properties are well understood, which is not the case after an event when that information is most useful. This paper combines hysteresis loop analysis (HLA) structural health monitoring (SHM) and incremental dynamic analysis (IDA) methods to identify and then analyse collapse capacity and the probability of collapse for a specific structure, at any time, a range of earthquake excitations to ensure robustness. This nonlinear dynamic analysis enables constant updating of building performance predictions following a given and subsequent earthquake events, which can result in difficult to identify deterioration of structural components and their resulting capacity, all of which is far more difficult using static pushover analysis. The combined methods and analysis provide near real-time updating of the collapse fragility curves as events progress, thus quantifying the change of collapse probability or seismic induced losses very soon after an earthquake for decision-making. Thus, this combination of methods enables a novel, higher-resolution analysis of risk that was not previously available. The methods are not computationally expensive and there is no requirement for a validated numerical model, thus providing a relatively simpler means of assessing collapse probability immediately post-event when such speed can provide better information for critical decision-making. Finally, the results also show a clear need to extend the area of SHM toward creating improved predictive models for analysis of subsequent events, where the Christchurch series of 2010–2011 had significant post-event aftershocks.
This paper presents the probabilistic seismic performance and loss assessment of an actual bridge– foundation–soil system, the Fitzgerald Avenue twin bridges in Christchurch, New Zealand. A two-dimensional finite element model of the longitudinal direction of the system is modelled using advanced soil and structural constitutive models. Ground motions at multiple levels of intensity are selected based on the seismic hazard deaggregation at the site. Based on rigorous examination of several deterministic analyses, engineering demand parameters (EDP’s), which capture the global and local demand, and consequent damage to the bridge and foundation are determined. A probabilistic seismic loss assessment of the structure considering both direct repair and loss of functionality consequences was performed to holistically assess the seismi risk of the system. It was found that the non-horizontal stratification of the soils, liquefaction, and soil–structure interaction had pronounced effects on the seismic demand distribution of the bridge components, of which the north abutment piles and central pier were critical in the systems seismic performance. The consequences due to loss of functionality of the bridge during repair were significantly larger than the direct repair costs, with over a 2% in 50 year probability of the total loss exceeding twice the book-value of the structure.
Recent severe earthquakes, such as Christchurch earthquake series, worldwide have put emphasis on building resilience. In resilient systems, not only life is protected, but also undesirable economic effects of building repair or replacement are minimized following a severe earthquake. Friction connections are one way of providing structure resilience. These include the sliding hinge joint with asymmetric friction connections (SHJAFCs) in beam-to-column connections of the moment resisting steel frames (MRSFs), and the symmetric friction connections (SFCs) in braces of the braced frames. Experimental and numerical studies on components have been conducted internationally. However, actual building performance depends on the many interactions, occurring within a whole building system, which may be difficult to determine accurately by numerical modelling or testing of structural components alone. Dynamic inelastic testing of a full-scale multi-storey composite floor building with full range of non-structural elements (NSEs) has not yet been performed, so it is unclear if surprises are likely to occur in such a system. A 9 m tall three-storey configurable steel framed composite floor building incorporating friction-based connections is to be tested using two linked bi-directional shake tables at the International joint research Laboratory of Earthquake Engineering (ILEE) facilities, Shanghai, China. Beams and columns are designed to remain elastic during an earthquake event, with all non-linear behaviour occurring through stable sliding frictional behaviour, dissipating energy by SHJAFCs used in MRFs and SFCs in braced frames, with and without Belleville springs. Structural systems are configurable, allowing different moment and braced frame structural systems to be tested in two horizontal directions. In some cases, these systems interact with rocking frame or rocking column system in orthogonal directions subjected to unidirectional and bidirectional horizontal shaking. The structure is designed and detailed to undergo, at worst, minor damage under series of severe earthquakes. NSEs applied include precast-concrete panels, glass curtain walling, internal partitions, suspended ceilings, fire sprinkler piping as well as some other common contents. Some of the key design considerations are presented and discussed herein
Recent major earthquakes such as Northridge 1994 and Izmit Kocaeli 1999 highlighted the poor performance of existing buildings constructed prior to the early 1970’s. Low lateral seismic design coefficients and the adopted “working stress design” methodology (essentially an elastic design) lacked any inelastic design considerations, thus leading to inadequate detailing. Insufficient development lengths, lapping within potential plastic hinge regions, lack, or total absence of joint transverse reinforcement, and the use of plain round reinforcement and hooked end anchorages were common throughout the structure. The behaviour is generally dominated by brittle local failure mechanisms (e.g. joint or element shear failures) as well as possible soft-storey mechanisms at a global level. Amongst several possible retrofit interventions, a typical solution is to provide the structure with additional structural walls i.e. external buttressing or column in-fills. Extensive developments on precast, post-tensioned, dissipative systems have shown promise for the use of rocking wall systems to retrofit existing poorly detailed frame structures. In this contribution, the feasibility of such a retrofit intervention is investigated. A displacement-based retrofit procedure is developed and proposed, based on targeting pre-defined performance criteria, such as joint shear and/or column curvature deformation limits. A design example, using the proposed retrofit strategy on a prototype frame is presented. A brief overview on experimental work ongoing at the University of Canterbury investigating the dynamic response of advanced rocking walls for retrofit purposes will be provided.
Light timber framed (LTF) structures provide a cost-effective and structurally efficient solution for low-rise residential buildings. This paper studies seismic performance of single-storey LTF buildings sheathed by gypsum-plasterboards (GPBs) that are a typical lining product in New Zealand houses. Compared with wood-based structural panels, GPBs tend to be more susceptible to damage when they are used in bracing walls to resist earthquake loads. This study aims to provide insights on how the bracing wall irregularity allowed by the current New Zealand standard NZS 3604 and the in-plane rigidity of ceiling diaphragms affect the overall seismic performance of these GPB-braced LTF buildings. Nonlinear time-history analyses were conducted on a series of single-storey baseline buildings with different levels of bracing wall irregularities and ceiling diaphragm rigidity. The results showed significant torsional effect caused by the eccentric bracing wall layout with semi-rigid/rigid ceiling diaphragms. On average, bracing wall drift demand caused by the extreme bracing wall irregularities was three times of that in the regular bracing wall layout under the rigid diaphragm assumption. This finding agreed well with the house survey after the 2011 Canterbury Earthquake in which significantly more damage was observed in the houses with irregular bracing wall layouts and relatively rigid diaphragms. Therefore, it is recommended to limit the level of bracing wall eccentricity and ensure the sufficiently rigid diaphragms to avoid excessive damage in these LTF buildings in future events.
Implementing seismic risk mitigation is a major challenge in many earthquake prone regions. The objective of this research is to investigate how property investment market practices can be used to enhance building owners’ decisions to improve seismic performance of earthquake prone buildings (EPBs). A case study method adopted, revealed the impacts of the property market stakeholders’ practices on seismic retrofit decisions. The findings from this research provide significant new insights on how property market-based incentives such as such as mandatory disclosure of seismic risks in all transactions in the property market, effective awareness seismic risk program and a unified earthquake safety assessment information system, can be used to enhance EPBs owners seismic retrofit decisions. These market-based incentives offer compelling reasons for the different property market stakeholders and the public at large to retain, care, invest, and act responsibly to rehabilitate EPBs. The findings suggest need for stakeholders involved in property investment and retrofit decisions to work together to foster seismic rehabilitation of EPBs.
This report presents the simplified seismic assessment of a case study reinforced concrete (RC) building following the newly developed and refined NZSEE/MBIE guidelines on seismic assessment (NZSEE/MBIE, semi-final draft 26 October 2016). After an overview of the step-by-step ‘diagnostic’ process, including an holistic and qualitative description of the expected vulnerabilities and of the assessment strategy/methodology, focus is given, whilst not limited, to the implementation of a Detailed Seismic Assessment (DSA) (NZSEE/MBIE, 2016c). The DSA is intended to provide a more reliable and consistent outcome than what can be provided by an initial seismic assessment (ISA). In fact, while the Initial Seismic Assessment (ISA), of which the Initial Evaluation Procedure is only a part of, is the more natural and still recommended first step in the overall assessment process, it is mostly intended to be a coarse evaluation involving as few resources as reasonably possible. It is thus expected that an ISA will be followed by a Detailed Seismic Assessment (DSA) not only where the threshold of 33%NBS is not achieved but also where important decisions are intended that are reliant on the seismic status of the building. The use of %NBS (% New Building Standard) as a capacity/demand ratio to describe the result of the seismic assessment at all levels of assessment procedure (ISA through to DSA) is deliberate by the NZSEE/MBIE guidelines (Part A) (NZSEE/MBIE 2016a). The rating for the building needs only be based on the lowest level of assessment that is warranted for the particular circumstances. Discussion on how the %NBS rating is to be determined can be found in Section A3.3 (NZSEE/MBIE 2016a), and, more specifically, in Part B for the ISA (NZSEE/MBIE 2016b) and Part C for the DSA (NZSEE/MBIE 2016c). As per other international approaches, the DSA can be based on several analysis procedures to assess the structural behaviour (linear, nonlinear, static or dynamic, force or displacement-based). The significantly revamped NZSEE 2016 Seismic Assessment Guidelines strongly recommend the use of an analytical (basically ‘by hand’) method, referred to the Simple Lateral Mechanism Analysis (SLaMA) as a first phase of any other numerically-based analysis method. Significant effort has thus been dedicated to provide within the NZSEE 2016 guidelines (NZSEE/MBIE 2016c) a step-by-step description of the procedure, either in general terms (Chapter 2) or with specific reference to Reinforced Concrete Buildings (Chapter 5). More specifically, extract from the guidelines, NZSEE “recommend using the Simple Lateral Mechanism Analysis (SLaMA) procedure as a first step in any assessment. While SLaMA is essentially an analysis technique, it enables assessors to investigate (and present in a simple form) the potential contribution and interaction of a number of structural elements and their likely effect on the building’s global capacity. In some cases, the results of a SLaMA will only be indicative. However, it is expected that its use should help assessors achieve a more reliable outcome than if they only carried out a detailed analysis, especially if that analysis is limited to the elastic range For complex structural systems, a 3D dynamic analysis may be necessary to supplement the simplified nonlinear Simple Lateral Mechanism Analysis (SLaMA).” This report presents the development of a full design example for the the implementation of the SLaMA method on a case study buildings and a validation/comparison with a non-linear static (pushover) analysis. The step-by-step-procedure, summarized in Figure 1, will be herein demonstrated from a component level (beams, columns, wall elements) to a subassembly level (hierarchy of strength in a beam-column joint) and to a system level (frame, C-Wall) assuming initially a 2D behaviour of the key structural system, and then incorporating a by-hand 3D behaviour (torsional effects).
During the past two decades, the focus has been on the need to provide communities with structures that undergo minimal damage after an earthquake event while still being cost competitive. This has led to the development of high performance seismic resisting systems, and advances in design methodologies, in order respect this demand efficiently. This paper presents the experimental response of four pre-cast, post-tensioned rocking wall systems tested on the shake-table at the University of Canterbury. The wall systems were designed as a retrofit solution for an existing frame building, but are equally applicable for use in new design. Design of the wall followed a performance-based retrofit strategy in which structural limit states appropriate to both the post-tensioned wall and the existing building were considered. Dissipation for each of the four post-tensioned walls was provided via externally mounted devices, located in parallel to post-tensioned tendons for re-centring. This allowed the dissipation devices to be easily replaced or inspected following a major earthquake. Each wall was installed with viscous fluid dampers, tension-compression yielding steel dampers, a combination of both or no devices at all – thus relying on contact damping alone. The effectiveness of both velocity and displacement dependant dissipation are investigated for protection against far-field and velocity-pulse ground motion characteristics. The experimental results validate the behaviour of ‘Advanced Flag-Shape’ rocking, dissipating solutions which have been recently proposed and numerically tested. Maximum displacements and material strains were well controlled and within acceptable bounds, and residual deformations were minimal due to the re-centring contribution from the post-tensioned tendons. Damage was confined to inelastic yielding (or fluid damping) of the external dampers.
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.
In recent years, rocking isolation has become an effective approach to improve seismic performance of steel and reinforced concrete structures. These systems can mitigate structural damage through rigid body displacement and thus relatively low requirements for structural ductility, which can significantly improve seismic resilience of structures and reduce repairing costs after strong earthquakes. A number of base rocking structural systems with only a single rocking interface have been proposed. However, these systems can have significant high mode effect for high rise structures due to the single rocking interface. This RObust BUilding SysTem (ROBUST) project is a collaborative China-New Zealand project sponsored by the International Joint Research Laboratory of Earthquake Engineering (ILEE), Tongji University, and a number of agencies and universities within New Zealand including the BRANZ, Comflor, Earthquake Commission, HERA, QuakeCoRE, QuakeCentre, University of Auckland, and the University of Canterbury. A number of structural configurations will be tested [1, 2], and non-structural elements including ceilings, infilling walls, glazed curtain walls, precast concrete panels, piping system will also be tested in this project [3]. Within this study, a multiple rocking column steel structural system was proposed and investigated mainly by Tongji team with assistance of NZ members. The concept of rocking column system initiates from the structure of Chinese ancient wooden pagoda. In some of Chinese wooden pagodas, there are continuous core columns hanged only at the top of each pagoda, which is not connected to each stories. This core column can effectively avoid collapse of the whole structure under large storey drifts. Likewise, there are also central continuous columns in the newly proposed steel rocking column system, which can avoid weak story failure mechanism and make story drifts more uniform. In the proposed rocking column system, the structure can switch between an elastic rigidly connected moment resisting frame and a controlled rocking column system when subjected to strong ground motion excitations. The main seismic energy can be dissipated by asymmetric friction beam–column connections, thereby effectively reducing residual displacement of the structure under seismic loading without causing excessive damage to structural members. Re–centering of the structure is provided not only by gravity load carried by rocking columns, but also by mould coil springs. To investigate dynamic properties of the proposed system under different levels of ground excitations, a full-scale threestory steel rocking column structural system with central continuous columns is to be tested using the International joint research Laboratory of Earthquake Engineering (ILEE) facilities, Shanghai, China and an analytical model is established. A finite element model is also developed using ABAQUS to simulate the structural dynamic responses. The rocking column system proposed in this paper is shown to produce resilient design with quick repair or replacement.
Following the devastating 1931 Hawke's Bay earthquake, buildings in Napier and surrounding areas in the Hawke's Bay region were rebuilt in a comparatively homogenous structural and architectural style comprising the region's famous Art Deco stock. These interwar buildings are most often composed of reinforced concrete two-way space frames, and although they have comparatively ductile detailing for their date of construction, are often expected to be brittle, earthquake-prone buildings in preliminary seismic assessments. Furthermore, the likelihood of global collapse of an RC building during a design-level earthquake became an issue warranting particular attention following the collapse of multiple RC buildings in the February 22, 2011 Christchurch earthquake. Those who value the architectural heritage and future use of these iconic Art Deco buildings - including building owners, tenants, and city officials, among others - must consider how they can be best preserved and utilized functionally given the especially pressing implications of relevant safety, regulatory, and economic factors. This study was intended to provide information on the seismic hazard, geometric weaknesses, collapse hazards, material properties, structural detailing, empirically based vulnerability, and recommended analysis approaches particular to Art Deco buildings in Hawke's Bay as a resource for professional structural engineers tasked with seismic assessments and retrofit designs for these buildings. The observed satisfactory performance of similar low-rise, ostensibly brittle RC buildings in other earthquakes and the examination of the structural redundancy and expected column drift capacities in these buildings, led to the conclusion that the seismic capacity of these buildings is generally underrated in simple, force-based assessments.
The development of cheap, whilst effective and relatively non-invasive structural retrofit techniques for existing non-ductile reinforced concrete (RC) structures still remains the most challenging issue for a wide implementation on a macro scale. Seismic retrofit is too often being confused as purely structural strengthening. As part of a six-years national project on “Seismic retrofit solutions for NZ multi-storey building”, focus has been given at the University of Canterbury on the development of a counter-intuitive retrofit strategy for earthquake vulnerable existing rc frame, based on a “selective weakening” (SW) approach. After an overview of the SW concept, this paper presents the experimental and numerical validation of a SW retrofit strategy for earthquake vulnerable existing RC frame with particular focus on the exterior beam-column (b-c) joints. The exterior b-c joint is a critically vulnerable region in many existing pre-1970s RC frames. By selectively weakening the beam by cutting the bottom longitudinal reinforcements and/or adding external pre-stressing to the b-c joint, a more desirable inelastic mechanism can be attained, leading to improved global seismic performance. The so-called SW retrofit is implemented on four 2/3-scaled exterior RC b-c joint subassemblies, tested under quasi-static cyclic loading at the University of Canterbury. Complemented by refined 3D Finite Element (FE) models and dynamic time-history analyses results, the experimental results have shown the potential of a simple and cost-effective yet structurally efficient structural rehabilitation technique. The research also demonstrated the potential of advanced 3D fracture-mechanics-based microplane concrete modelling for refined FE analysis of non-ductile RC b-c joints.
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.
Based on the recent developments on alternative jointed ductile dry connections for concrete multistorey buildings, the paper aims to extend and propose similar innovative seismic connections for laminated veneer lumber (LVL) timber buildings. The dry connections herein proposed are characterised by a sort of rocking occurring at the section interface of the structural elements when an earthquake occurs; unbonded post-tensioned techniques and dissipative devices respectively provide self-centring and dissipation capacities. The paper illustrates some experimental investigations of an extensive campaign, still undergoing at the University of Canterbury Christchurch, NZ) are herein presented and critically discussed. In particular, results of cyclic quasi-static testing on exterior beam-column subassemblies and wall-to-foundation systems are herein presented; preliminary results of pseudo-dynamic testing on wall-to-foundation specimens are also illustrated. The research investigations confirmed the enhanced seismic performance of these systems/connections; three key aspects , as the no-damageability in the structural elements, typical “flag-shape” cyclic behaviour (with self-centring and dissipation capacity), negligible residual deformations, i.e. limited costs of repair, joined with low mass, flexibility of design and rapidity of construction LVL timber, all create the potential for an increased use in low-rise multistorey buildings.
This paper describes part of an extensive experimental programme in progress at the University of Canterbury to develop Laminated Veneer Lumber (LVL) structural systems and connections for multistorey timber buildings in earthquake-prone areas. The higher mechanical properties of LVL, when compared to sawn timber, in addition to its low mass, flexibility of design and rapidity of construction, create the potential for increased use of LVL in multi-storey buildings. The development of these innovative ductile connections in LVL, proposed here for frame systems, have been based on the successful implementation of jointed ductile connections for precast concrete systems, started in the early 1990s with the PRESSS Program at the University of California, San Diego, further developed in Italy and currently under further refinement at the University of Canterbury. This paper investigates the seismic behaviour of the so-called “hybrid” connection, characterised by the combination of unbonded post-tensioned tendons and either external or internal energy dissipaters passing through the critical contact surface between the structural elements. Experimental results on hybrid exterior beam-to-column and column-to-foundation subassemblies under cyclic quasi-static unidirectional loading are presented. The proposed innovative solutions exhibit a very satisfactory seismic performance characterised by an appreciable energy dissipation capacity (provided by the dissipaters) combined with self-centring properties (provided by the unbonded tendons) and negligible damage of the LVL structural elements.
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.
The aim of this report is to investigate the ductile performance of concrete tilt-up panels reinforced with cold-drawn mesh to improve the current seismic assessment procedure. The commercial impact of the project was also investigated. Engineering Advisory Group (EAG) guidelines state that a crack in a panel under face loading may be sufficient to fracture the mesh. The comments made by EAG regarding the performance of cold-drawn mesh may be interpreted as suggesting that assessment of such panels be conducted with a ductility of 1.0. Observations of tilt-up panel performance following the Christchurch earthquakes suggest that a ductility higher than μ=1.0 is likely to be appropriate for the response of panels to out-of-plane loading. An experimental test frame was designed to subject ten tilt-panel specimens to a cyclic quasi-static loading protocol. Rotation ductility, calculated from the force-displacement response from the test specimens, was found to range between 2.9 and 5.8. Correlation between tensile tests on 663L mesh, and data collected from instrumentation during testing confirmed that the mesh behaves as un-bonded over the pitch length of 150mm. Recommendation: Based on a moment-rotation assessment approach with an un-bonded length equal to the pitch of the mesh, a rotation ductility of μ=2.5 appears to be appropriate for the seismic assessment of panels reinforced with cold-drawn mesh.
Recent earthquakes have highlighted the vulnerability of existing structure to seismic loading. Current seismic retrofit strategies generally focus on increasing the strength/stiffness in order to upgrade the seismic performance of a structure or element. A typical drawback of this approach is that the demand on the structural and sub-structural elements can be increased. This is of particular importance when considering the foundation capacity, which may already be insufficient to allow the full capacity of the existing wall to develop (due to early codes being gravity load orientated). In this thesis a counter intuitive but rational seismic retrofit strategy, termed "selective weakening" is introduced and investigated. This is the first stage of an ongoing research project underway at the University of Canterbury which is focusing on developing selective weakening techniques for the seismic retrofit of reinforced concrete structures. In this initial stage the focus is on developing selective weakening for the seismic retrofit of structural walls. This is performed using a series of experimental, analytical and numerical investigations. A procedure for the assessment of existing structural walls is also compiled, based on the suggestions of currently available code provisions. A selective weakening intervention is performed within an overall performance-based retrofit approach with the aim of improving the inelastic behaviour by first reducing the strength/stiffness of specific members within the structural system. This will be performed with the intention of modifying a shear type behaviour towards a flexural type behaviour. As a result the demand on the structural member will be reduced. Once weakening has been implemented the designer can use the wide range of techniques and materials available (e.g. use of FRP, jacketing or shotcrete) to ensure that adequate characteristics are achieved. Whilst performing this it has to be assured that the structure meets specific performance criteria and the principles of capacity design. A target of the retrofit technique is the ability to introduce the characteristics of recently developed high performance seismic resisting systems, consisting of a self centring and dissipative behaviour (commonly referred to as a hybrid system). In this thesis, results of experimental investigations performed on benchmark and selectively weakened walls are discussed. The investigations consisted of quasi-static cyclic uni-directional tests on two benchmark and two retrofitted cantilever walls. The first benchmark wall is detailed as typical of pre-1970's construction practice. An equivalent wall is retrofitted using a selective weakening approach involving a horizontal cut at foundation level to allow for a rocking response. The second benchmark wall represents a more severe scenario where the inelastic behaviour is dominated by shear. A retrofit solution involving vertically segmenting the wall to improve the ductility and retain gravity carrying capacity by inducing a flexural response is implemented. Numerical investigations on a multi-storey wall system are performed using non linear time history analysis on SDOF and MDOF lumped plasticity models, representing an as built and retrofitted prototype structure. Calibration of the hysteretic response to experimental results is carried out (accounting for pinching and strength degradation). The sensitivity of maximum and residual drifts to p-delta and strength degradation is monitored, along with the sensitivity of the peak base shear to higher mode affects. The results of the experimental and analytical investigations confirmed the feasibility and viability of the proposed retrofit technique, towards improving the seismic performance of structural walls.
Probabilistic Structural Fire Engineering (PSFE) has been introduced to overcome the limitations of current conventional approaches used for the design of fire-exposed structures. Current structural fire design investigates worst-case fire scenarios and include multiple thermal and structural analyses. PSFE permits buildings to be designed to a level of life safety or economic loss that may occur in future fire events with the help of a probabilistic approach. This thesis presents modifications to the adoption of a Performance-Based Earthquake Engineering (PBEE) framework in Probabilistic Structural Fire Engineering (PSFE). The probabilistic approach runs through a series of interrelationships between different variables, and successive convolution integrals of these interrelationships result in probabilities of different measures. The process starts with the definition of a fire severity measure (FSM), which best relates fire hazard intensity with structural response. It is identified by satisfying efficiency and sufficiency criteria as described by the PBEE framework. The relationship between a fire hazard and corresponding structural response is established by analysis methods. One method that has been used to quantify this relationship in PSFE is Incremental Fire Analysis (IFA). The existing IFA approach produces unrealistic fire scenarios, as fire profiles may be scaled to wide ranges of fire severity levels, which may not physically represent any real fires. Two new techniques are introduced in this thesis to limit extensive scaling. In order to obtain an annual rate of exceedance of fire hazard and structural response for an office building, an occurrence model and an attenuation model for office fires are generated for both Christchurch city and New Zealand. The results show that Christchurch city is 15% less likely to experience fires that have the potential to cause structural failures in comparison to all of New Zealand. In establishing better predictive relationships between fires and structural response, cumulative incident radiation (a fire hazard property) is found to be the most appropriate fire severity measure. This research brings together existing research on various sources of uncertainty in probabilistic structural fire engineering, such as elements affecting post-flashover fire development factors (fuel load, ventilation, surface lining and compartment geometry), fire models, analysis methods and structural reliability. Epistemic uncertainty and aleatory uncertainty are investigated in the thesis by examining the uncertainty associated with modelling and the factors that influence post-flashover development of fires. A survey of 12 buildings in Christchurch in combination with recent surveys in New Zealand produced new statistical data on post-flashover development factors in office buildings in New Zealand. The effects of these parameters on temperature-time profiles are evaluated. The effects of epistemic uncertainty due to fire models in the estimation of structural response is also calculated. Parametric fires are found to have large uncertainty in the prediction of post-flashover fires, while the BFD curves have large uncertainties in prediction of structural response. These uncertainties need to be incorporated into failure probability calculations. Uncertainty in structural modelling shows that the choices that are made during modelling have a large influence on realistic predictions of structural response.
Recently developed performance-based earthquake engineering framework, such as one provided by PEER (Deierlein et al. 2003), assist in the quantification in terms of performance such as casualty, monetary losses and downtime. This opens up the opportunity to identify cost-effective retrofit/rehabilitation strategies by comparing upfront costs associated with retrofit with the repair costs that can be expected over time. This loss assessment can be strengthened by learning from recent earthquakes, such as the 2010 Canterbury and 2016 Kaikoura earthquakes. In order to investigate which types of retrofit/rehabilitation strategies may be most cost-effective, a case study building was chosen for this research. The Pacific Tower, a 22-storey EBF apartment located within the Christchurch central business district (CBD), was damaged and repaired during the 2010 Canterbury earthquake series. As such, by taking hazard levels accordingly (i.e. to correspond to the Christchurch CBD), modelling and analysing the structure, and considering the vulnerability and repair costs of its different components, it is possible to predict the expected losses of the aforementioned building. Using this information, cost-effective retrofit/rehabilitation strategy can be determined. This research found that more often than not, it would be beneficial to improve the performance of valuable non-structural components, such as partitions. Although it is true that improving such elements will increase the initial costs, over time, the benefits gained from reduced losses should be expected to overcome the initial costs. Aftershocks do increase the predicted losses of a building even in lower intensities due to the fact that non-structural components can get damaged at such low intensities. By comparing losses computed with and without consideration of aftershocks for a range of historical earthquakes, it was found that the ratio between losses due to main shock with aftershocks to the losses due to the main shock only tended to increase with increasing main shock magnitude. This may be due to the fact that larger magnitude earthquakes tend to generate larger magnitude aftershocks and as those aftershocks happen within a region around the main shock, they are more likely to cause intense shaking and additional damage. In addition to this observation, it was observed that the most significant component of loss of the case study building was the non-structural partition walls.
High-quality ground motion records are required for engineering applications including response history analysis, seismic hazard development, and validation of physics-based ground motion simulations. However, the determination of whether a ground motion record is high-quality is poorly handled by automation with mathematical functions and can become prohibitive if done manually. Machine learning applications are well-suited to this problem, and a previous feed-forward neural network was developed (Bellagamba et al. 2019) to determine high-quality records from small crustal events in the Canterbury and Wellington regions for simulation validation. This prior work was however limited by the omission of moderate-to-large magnitude events and those from other tectonic environments, as well as a lack of explicit determination of the minimum usable frequency of the ground motion. To address these shortcomings, an updated neural network was developed to predict the quality of ground motion records for all magnitudes and all tectonic sources—active shallow crustal, subduction intraslab, and subduction interface—in New Zealand. The predictive performance of the previous feed-forward neural network was matched by the neural network in the domain of small crustal records, and this level of predictive performance is now extended to all source magnitudes and types in New Zealand making the neural network applicable to global ground motion databases. Furthermore, the neural network provides quality and minimum usable frequency predictions for each of the three orthogonal components of a record which may then be mapped into a binary quality decision or otherwise applied as desired. This framework provides flexibility for the end user to predict high-quality records with various acceptability thresholds allowing for this neural network to be used in a range of applications.
Advanced seismic effective-stress analysis is used to scrutinize the liquefaction performance of 55 well-documented case-history sites from Christchurch. The performance of these sites during the 2010-2011 Canterbury earthquake sequence varied significantly, from no liquefaction manifestation at the ground surface (in any of the major events) to severe liquefaction manifestation in multiple events. For the majority of the 55 sites, the simplified liquefaction evaluation procedures, which are conventionally used in engineering practice, could not explain these dramatic differences in the manifestation. Detailed geotechnical characterization and subsequent examination of the soil profile characteristics of the 55 sites identified some similarities but also important differences between sites that manifested liquefaction in the two major events of the sequence (YY-sites) and sites that did not manifest liquefaction in either event (NN-sites). In particular, while the YY-sites and NN-sites are shown to have practically identical critical layer characteristics, they have significant differences with regard to their deposit characteristics including the thickness and vertical continuity of their critical zones and liquefiable materials. A CPT-based effective stress analysis procedure is developed and implemented for the analyses of the 55 case history sites. Key features of this procedure are that, on the one hand, it can be fully automated in a programming environment and, on the other hand, it is directly equivalent (in the definition of cyclic resistance and required input data) to the CPT-based simplified liquefaction evaluation procedures. These features facilitate significantly the application of effective-stress analysis for simple 1D free-field soil-column problems and also provide a basis for rigorous comparisons of the outcomes of effective-stress analyses and simplified procedures. Input motions for the analyses are derived using selected (reference) recordings from the two major events of the 2010-2011 Canterbury earthquake sequence. A step-by-step procedure for the selection of representative reference motions for each site and their subsequent treatment (i.e. deconvolution and scaling) is presented. The focus of the proposed procedure is to address key aspects of spatial variability of ground motion in the near-source region of an earthquake including extended-source effects, path effects, and variation in the deeper regional geology.
In major seismic events, a number of plan-asymmetric buildings which experienced element failure or structural collapse had twisted significantly about their vertical axis during the earthquake shaking. This twist, known as “building torsion”, results in greater demands on one side of a structure than on the other side. The Canterbury Earthquakes Royal Commission’s reports describe the response of a number of buildings in the February 2011 Christchurch earthquakes. As a result of the catastrophic collapse of one multi-storey building with significant torsional irregularity, and significant torsional effects also in other buildings, the Royal Commission recommended that further studies be undertaken to develop improved simple and effective guides to consider torsional effects in buildings which respond inelastically during earthquake shaking. Separately from this, as building owners, the government, and other stakeholders, are planning for possible earthquake scenarios, they need good estimates of the likely performance of both new and existing buildings. These estimates, often made using performance based earthquake engineering considerations and loss estimation techniques, inform decision making. Since all buildings may experience torsion to some extent, and torsional effects can influence demands on building structural and non-structural elements, it is crucial that demand estimates consider torsion. Building seismic response considering torsion can be evaluated with nonlinear time history analysis. However, such analysis involves significant computational effort, expertise and cost. Therefore, from an engineers’ point of view, simpler analysis methods, with reasonable accuracy, are beneficial. The consideration of torsion in simple analysis methods has been investigated by many researchers. However, many studies are theoretical without direct relevance to structural design/assessment. Some existing methods also have limited applicability, or they are difficult to use in routine design office practice. In addition, there has been no consensus about which method is best. As a result, there is a notable lack of recommendations in current building design codes for torsion of buildings that respond inelastically. There is a need for building torsion to be considered in yielding structures, and for simple guidance to be developed and adopted into building design standards. This study aims to undertaken to address this need for plan-asymmetric structures which are regular over their height. Time history analyses are first conducted to quantify the effects of building plan irregularity, that lead to torsional response, on the seismic response of building structures. Effects of some key structural and ground motion characteristics (e.g. hysteretic model, ground motion duration, etc.) are considered. Mass eccentricity is found to result in rather smaller torsional response compared to stiffness/strength eccentricity. Mass rotational inertia generally decreases the torsional response; however, the trend is not clearly defined for torsionally restrained systems (i.e. large λty). Systems with EPP and bilinear models have close displacements and systems with Takeda, SINA, and flag-shaped models yield almost the same displacements. Damping has no specific effect on the torsional response for the single-storey systems with the unidirectional eccentricity and excitation. Displacements of the single-storey systems subject to long duration ground motion records are smaller than those for short duration records. A method to consider torsional response of ductile building structures under earthquake shaking is then developed based on structural dynamics for a wide range of structural systems and configurations, including those with low and high torsional restraint. The method is then simplified for use in engineering practice. A novel method is also proposed to simply account for the effects of strength eccentricity on response of highly inelastic systems. A comparison of the accuracy of some existing methods (including code-base equivalent static method and model response spectrum analysis method), and the proposed method, is conducted for single-storey structures. It is shown that the proposed method generally provides better accuracy over a wide range of parameters. In general, the equivalent static method is not adequate in capturing the torsional effects and the elastic modal response spectrum analysis method is generally adequate for some common parameters. Record-to-record variation in maximum displacement demand on the structures with different degrees of torsional response is considered in a simple way. Bidirectional torsional response is then considered. Bidirectional eccentricity and excitation has varying effects on the torsional response; however, it generally increases the weak and strong edges displacements. The proposed method is then generalized to consider the bidirectional torsion due to bidirectional stiffness/strength eccentricity and bidirectional seismic excitation. The method is shown to predict displacements conservatively; however, the conservatism decreases slightly for cases with bidirectional excitation compared to those subject to unidirectional excitation. In is shown that the roof displacement of multi-storey structures with torsional response can be predicted by considering the first mode of vibration. The method is then further generalized to estimate torsional effects on multi-storey structure displacement demands. The proposed procedure is tested multi-storey structures and shown to predict the displacements with a good accuracy and conservatively. For buildings which twist in plan during earthquake shaking, the effect of P-Δλ action is evaluated and recommendations for design are made. P-Δλ has more significant effects on systems with small post- yield stiffness. Therefore, system stability coefficient is shown not to be the best indicator of the importance of P-Δλ and it is recommended to use post-yield stiffness of system computed with allowance for P-Δλ effects. For systems with torsional response, the global system stability coefficient and post- yield stiffness ration do not reflect the significance of P-Δλ effects properly. Therefore, for torsional systems individual seismic force resisting systems should be considered. Accuracy of MRSA is investigated and it is found that the MRSA is not always conservative for estimating the centre of mass and strong edge displacements as well as displacements of ductile systems with strength eccentricity larger than stiffness eccentricity. Some modifications are proposed to get the MRSA yields a conservative estimation of displacement demands for all cases.
