The connections between walls of unreinforced masonry (URM) buildings and flexible timber diaphragms are critical building components that must perform adequately before desirable earthquake response of URM buildings may be achieved. Field observations made during the initial reconnaissance and the subsequent damage surveys of clay brick URM buildings following the 2010/2011 Canterbury, New Zealand, earthquakes revealed numerous cases where anchor connections joining masonry walls or parapets with roof or floor diaphragms appeared to have failed prematurely. These observations were more frequent for adhesive anchor connections than for through-bolt connections (i.e., anchorages having plates on the exterior facade of the masonry walls). Subsequently, an in-field test program was undertaken in an attempt to evaluate the performance of adhesive anchor connections between unreinforced clay brick URM walls and roof or floor diaphragm. The study consisted of a total of almost 400 anchor tests conducted in eleven existing URM buildings located in Christchurch, Whanganui and Auckland. Specific objectives of the study included the identification of failure modes of adhesive anchors in existing URM walls and the influence of the following variables on anchor load-displacement response: adhesive type, strength of the masonry materials (brick and mortar), anchor embedment depth, anchor rod diameter, overburden level, anchor rod type, quality of installation, and the use of metal mesh sleeves. In addition, the comparative performance of bent anchors (installed at an angle of minimum 22.5° to the perpendicular projection from the wall surface) and anchors positioned horizontally was investigated. Observations on the performance of wall-to-diaphragm connections in the 2010/2011 Canterbury earthquakes, a summary of the performed experimental program and test results, and a proposed pull-out capacity relationship for adhesive anchors installed into multi-leaf clay brick masonry are presented herein. AM - Accepted Manuscript
The connections between walls of unreinforced masonry (URM) buildings and flexible timber diaphragms are critical building components that must perform adequately before desirable earthquake response of URM buildings may be achieved. Field observations made during the initial reconnaissance and the subsequent damage surveys of clay brick URM buildings following the 2010/2011 Canterbury, New Zealand earthquakes revealed numerous cases where anchor connections joining masonry walls or parapets with roof or floor diaphragms appeared to have failed prematurely. These observations were more frequent for adhesive anchor connections than for through-bolt connections (i.e. anchorages having plates on the exterior façade of the masonry walls). Subsequently, an in-field test program was undertaken in an attempt to evaluate the performance of adhesive anchor connections between unreinforced clay brick URM walls and roof or floor diaphragms. The study consisted of a total of almost 400 anchor tests conducted in eleven existing URM buildings located in Christchurch, Whanganui and Auckland. Specific objectives of the study included the identification of failure modes of adhesive anchors in existing URM walls and the influence of the following variables on anchor load-displacement response: adhesive type, strength of the masonry materials (brick and mortar), anchor embedment depth, anchor rod diameter, overburden level, anchor rod type, quality of installation and the use of metal mesh sleeve. In addition, the comparative performance of bent anchors (installed at an angle of minimum 22.5o to the perpendicular projection from the wall surface) and anchors positioned horizontally was investigated. Observations on the performance of wall-to-diaphragm connections in the 2010/2011 Canterbury earthquakes, a snapshot of the performed experimental program and the test results and a preliminary proposed pull-out capacity of adhesive anchors are presented herein.
The connections between walls of unreinforced masonry (URM) buildings and flexible timber diaphragms are critical building components that must perform adequately before desirable earthquake response of URM buildings may be achieved. Field observations made during the initial reconnaissance and the subsequent damage surveys of clay brick URM buildings following the 2010/2011 Canterbury, New Zealand earthquakes revealed numerous cases where anchor connections joining masonry walls or parapets with roof or floor diaphragms appeared to have failed prematurely. These observations were more frequent for adhesive anchor connections than for through-bolt connections (i.e. anchorages having plates on the exterior façade of the masonry walls). Subsequently, an in-field test program was undertaken in an attempt to evaluate the performance of adhesive anchor connections between unreinforced clay brick URM walls and roof or floor diaphragm. The study consisted of a total of almost 400 anchor tests conducted in eleven existing URM buildings located in Christchurch, Whanganui and Auckland. Specific objectives of the study included the identification of failure modes of adhesive anchors in existing URM walls and the influence of the following variables on anchor load-displacement response: adhesive type, strength of the masonry materials (brick and mortar), anchor embedment depth, anchor rod diameter, overburden level, anchor rod type, quality of installation and the use of metal mesh sleeve. In addition, the comparative performance of bent anchors (installed at an angle of minimum 22.5o to the perpendicular projection from the wall surface) and anchors positioned horizontally was investigated. Observations on the performance of wall-to-diaphragm connections in the 2010/2011 Canterbury earthquakes, a snapshot of the performed experimental program and the test results and a preliminary proposed pull-out capacity of adhesive anchors are presented herein. http://www.confer.co.nz/nzsee/ VoR - Version of Record
The connections between walls of unreinforced masonry (URM) buildings and flexible timber diaphragms are critical building components that must perform adequately before desirable earthquake response of URM buildings may be achieved. Field observations made during the initial reconnaissance and the subsequent damage surveys of clay brick URM buildings following the 2010/2011 Canterbury, New Zealand earthquakes revealed numerous cases where anchor connections joining masonry walls or parapets with roof or floor diaphragms appeared to have failed prematurely. These observations were more frequent for the case of adhesive anchor connections than for the case of through-bolt connections (i.e. anchorages having plates on the exterior façade of the masonry walls). Subsequently, an in-field test program was undertaken in an attempt to evaluate the performance of adhesive anchor connections between unreinforced clay brick URM walls and roof or floor diaphragm. The study consisted of a total of almost 400 anchor tests conducted in eleven existing URM buildings located in Christchurch, Whanganui and Auckland. Specific objectives of the study included the identification of failure modes of adhesive anchors in existing URM walls and the influence of the following variables on anchor load-displacement response: adhesive type, strength of the masonry materials (brick and mortar), anchor embedment depth, anchor rod diameter, overburden level, anchor rod type, quality of installation and the use of metal foil sleeve. In addition, the comparative performance of bent anchors (installed at an angle of minimum 22.5o to the perpendicular projection from the wall surface) and anchors positioned horizontally was investigated. Observations on the performance of wall-to-diaphragm connections in the 2010/2011 Canterbury earthquakes and a snapshot of the performed experimental program and the test results are presented herein. http://hdl.handle.net/2292/21050
Between September 4, 2010 and December 23, 2011, a series of earthquakes struck the South Island of New Zealand including the city of Christchurch producing heavy damage. During the strongest shaking, the unreinforced masonry (URM) building stock in Christchurch was subjected to seismic loading equal to approximately 150-200% of code values. Post-earthquake reconnaissance suggested numerous failures of adhesive anchors used for retrofit connection of roof and floor diaphragms to masonry walls. A team of researchers from the Universities of Auckland (NZ) and Minnesota (USA) conducted a field investigation on the performance of new adhesive anchors installed in existing masonry walls. Variables included adhesive type, anchor diameter, embedment length, anchor inclination, and masonry quality. Buildings were selected that had been slated for demolition but which featured exterior walls that had not been damaged. A summary of the deformation response measured during the field tests are presented. AM - Accepted Manuscript
The majority of Christchurch’s stormwater has historically been discharged untreated directly into urban surface waterways. These receiving waterways have become adversely affected by the contaminants carried in the stormwater, particularly sediment and heavy metals. An event-based contaminant load model was developed to identify the distribution and magnitude of contaminant loads entering the waterway, as well as to assess the reduction in TSS and heavy metal loads that can be achieved by various stormwater management options. The GIS-Excel based model estimates contaminant loads from an individual storm event based on different contributing impervious surfaces and key rainfall characteristics (rainfall intensity, duration, pH and antecedent dry days). It then calculates contaminant reduction loads that could be achieved through source reduction (e.g. green roofs, repainting) as well as from treatment (e.g. raingardens, wet ponds) applied to different surfaces within the catchment. This model differs from other annual load models as it is event-based and accounts for storm characteristics in its calculation of contaminant loads. Christchurch is a valuable case setting due the unique opportunity for retrofitting improved stormwater management in the post-earthquake rebuild. It is anticipated that this modelling approach could later be adapted for use in other urban settings outside of Christchurch.
The ultimate goal of this study is to develop a model representing the in-plane behaviour of plasterboard ceiling diaphragms, as part of the efforts towards performance-based seismic engineering of low-rise light timber-framed (LTF) residential buildings in New Zealand (NZ). LTF residential buildings in NZ are constructed according to a prescriptive standard – NZS 3604 Timberframed buildings [1]. With regards to seismic resisting systems, LTF buildings constructed to NZS3604 often have irregular bracing arrangements within a floor plane. A damage survey of LTF buildings after the Canterbury earthquake revealed that structural irregularity (irregular bracing arrangement within a plane) significantly exacerbated the earthquake damage to LTF buildings. When a building has irregular bracing arrangements, the building will have not only translational deflections but also a torsional response in earthquakes. How effectively the induced torsion can be resolved depends on the stiffness of the floors/roof diaphragms. Ceiling and floor diaphragms in LTF buildings in NZ have different construction details from the rest of the world and there appears to be no information available on timber diaphragms typical of NZ practice. This paper presents experimental studies undertaken on plasterboard ceiling diaphragms as typical of NZ residential practice. Based on the test results, a mathematical model simulating the in-plane stiffness of plasterboard ceiling diaphragms was developed, and the developed model has a similar format to that of plasterboard bracing wall elements presented in an accompany paper by Liu [2]. With these two models, three-dimensional non-linear push-over studies of LTF buildings can be undertaken to calculate seismic performance of irregular LTF buildings.
Structures of the Lowry Peaks Range - Waikari Valley district are complex. The majority comprise three members of a predominantly WSW -ENE striking major northwards-directed, leading edge imbricate thrust system, with associated angular, asymmetric fault-propagation folds. This system forms anomalously within a large NESW trending belt of structures characterising the entire east coast of north Canterbury, both onshore and offshore and terminates westwards against N-S striking, east facing fold-fault zone. The objectives of this study address the origin, geometry and kinematics of the interaction between these diversely trending systems. Stratigraphy and small-scale structures denote three periods of deformation, namely: i) Middle Cretaceous deformation of the basement rocks, ii) weak Middle Oligocene deformation associated with the inception of the plate boundary through the South Island, and iii) major Pliocene - Recent deformation that formed the majority of the above-mentioned structures. Stress tensor analyses within competent basement and limestone cover rocks suggest two sets of sub-horizontal compression, NE-SW and NW-SE, the former likely to relate to a localised earlier period of deformation, now overprinted by the latter. NW-SE oriented sub-horizontal compression correlates well with results from other parts of north Canterbury. The result of NW-SE compression on the W-E to WSW-ENE striking structures is a large component of oblique motion, which is manifest in four ways: i) movement on two, differently oriented splays rather than a single fault strand, ii) the development of a sinuous trace for a number of the major folds, whereby the ends are oriented normal to the compression direction, the centres parallel to the strike of the faults, iii) the development of a number of cross-folds, striking NNE-SSW and iv) the apparently recent development of a strike-slip component on at least one of the major thrust faults. The origin of the W-E, or WSW-ENE striking structures may be reactivation of Late Cretaceous faults, stratigraphic evidence for the existence of a "structural high" (the Hurunui High) over the majority of the area in the Late Cretaceous to Early Eocene times suggests the formation of a W-E trending horst structure, with a corresponding asymmetric graben to the south. The junction of WSW-ENE trending structures with N-S trending structures to the west centres on an alluvial-filled depression, Waikari Flat, into which the structures of the WSW-ENE trending imbricate thrust system plunge, locally curling to the SW at their ends to link with N-S trending structures to the south. Roof thrusting on two orientations, W-E and N-S, towards to SE is currently occurring above these structures. Currently the area is not highly seismically active, although a magnitude ~6.4 Ms earthquake in historic times has been recorded. The effects of tectonics on the drainage of the area does suggest that the majority of the systems, are still potentially active, albeit moving at a comparatively slow rate. The majority of the recent motion appears to be concentrated on the roof-thrusting occurring in Waikari Flat, and uplift along the Lowry Peaks Fault System. Increasing amounts of secondary movement on back-thrusts and cross fractures is also implied for western ends of the major imbricate thrust system. In contrast, the southern-most fault system appears to be largely sustaining dextral strike-slip motion, with some local folding in central portions.
Christchurch Ōtautahi, New Zealand, is a city of myriad waterways and springs. Māori, the indigenous people of New Zealand, have water quality at the core of their cultural values. The city’s rivers include the Avon/Ōtākaro, central to the city centre’s aesthetic appeal since early settlement, and the Heathcote/Ōpāwaho. Both have been degraded with increasing urbanisation. The destructive earthquake sequence that occurred during 2010/11 presented an opportunity to rebuild significant areas of the city. Public consultation identified enthusiasm to rebuild a sustainable city. A sustainable water sensitive city is one where development is constructed with the water environment in mind. Water sensitive urban design applies at all scales and is a holistic concept. In Christchurch larger-scale multi-value stormwater management solutions were incorporated into rapidly developed greenfield sites on the city’s outskirts and in satellite towns, as they had been pre-earthquake. Individual properties on greenfield sites and within the city, however, continued to be constructed without water sensitive features such as rainwater tanks or living roofs. This research uses semi-structured interviews, policy analysis, and findings from local and international studies to investigate the benefits of building-scale WSUD and the barriers that have resulted in their absence. Although several inter-related barriers became apparent, cost, commonly cited as a barrier to sustainable development in general, was strongly represented. However, it is argued that the issue is one of mindset rather than cost. Solutions are proposed, based on international and national experience, that will demonstrate the benefits of adopting water sensitive urban design principles including at the building scale, and thereby build public and political support. The research is timely - there is still much development to occur, and increasing pressures from urban densification, population growth and climate change to mitigate.
To this extent, modern buildings generally demonstrated good resistance to collapse during the recent earthquakes in New Zealand. However, damage to non-structural elements (NSE) has been persistent during these events. NSEs include secondary systems or components attached to the floors, roofs, and walls of a building or industrial facility that are not explicitly designed to participate in the main vertical or lateral load-bearing mechanism of the structure. They play a major role in the operational and functional aspects of buildings and contribute a major portion of the building’s overall cost. Therefore, they are expected to accommodate the effects of seismic actions such as drifts and accelerations. Typical examples of NSEs include internal non-loadbearing partitions, suspended ceilings, sprinkler piping systems, architectural claddings, building contents, mechanical/electrical equipment, and furnishings. The main focus of this thesis is the drift sensitive NSEs: precast concrete cladding panels and internal partition walls. Even though most precast concrete cladding panels performed well from a life-safety point of view during recent earthquakes in NZ, some collapsed panels posed a significant threat to life safety. It is, therefore, important that the design and detailing of the panel-to-structure connections ensure that their strength and displacement capacity are adequate to meet the corresponding seismic demands, at least during design level earthquakes. In contrast, the partition wall is likely to get damaged and lose serviceability at a low inter-story drift unless designed to accommodate the relative deformations between them and the structure. Partition walls suffered wide-ranging damage such as screw failures, diagonal cracking, detachments to the gypsum linings, and anchorage failures during the 2011 Canterbury Earthquake Sequence in NZ. Therefore, the thesis is divided into two parts. Part I of the thesis focuses on developing novel low-damage precast concrete cladding panel connections, i.e. “rocking” connection details comprising vertically slotted steel embeds and weld plates. The low-damage seismic performance of novel “rocking” connection details is verified through experimental tests comprising uni-directional, bi-directional, and multi-storey scaled quasi-static cyclic tests. Comparison with the seismic performance of traditional panel connections reported in the literature demonstrated the system’s significantly improved seismic resilience. Furthermore, the finite element models of panel connections and sealants are developed in ABAQUS. The force-drift responses of the “rocking” panel system modelled in SAP2000 is compared with the experimental results to evaluate their accuracy and validity. Part II of the thesis focuses on a) understanding the seismic performance of traditional rigid timber-framed partition wall, b) development and verification of low-damage connections (i.e. “rocking” connection details comprising of dual-slot tracks), and c) seismic evaluation of partition walls with a novel “bracketed and slotted” connections (comprising of innovative fastener and plastic bracket named Flexibracket) under uni-directional and bidirectional quasi-static cyclic loadings. Moreover, parametric investigation of the partition walls was conducted through several experimental tests to understand better the pros and cons of the rocking connection details. The experimental results have confirmed that the implementation of the proposed low damage solutions of precast cladding panels and internal partition walls can significantly reduce their damage in a building.
Land cover change information in urban areas supports decision makers in dealing with public policy planning and resource management. Remote sensing has been demonstrated as an efficient and accurate way to monitor land cover change over large extents. The Canterbury Earthquake Sequence (CES) caused massive damage in Christchurch, New Zealand and resulted in significant land cover change over a short time period. This study combined two types of remote sensing data, aerial imagery (RGB) and LiDAR, as the basis for quantifying land cover change in Christchurch between 2011 – 2015, a period corresponding to the five years immediately following the 22 February 2011 earthquake, which was part of the CES. An object based image analysis (OBIA) approach was adopted to classify the aerial imagery and LiDAR data into seven land cover types (bare land, building, grass, shadow, tree and water). The OBIA approach consisted of two steps, image segmentation and object classification. For the first step, this study used multi-level segmentation to better segment objects. For the second step, the random forest (RF) classifier was used to assign a land cover type to each object defined by the segmentation. Overall classification accuracies for 2011 and 2015 were 94.0% and 94.32%, respectively. Based on the classification result, land cover changes between 2011 and 2015 were then analysed. Significant increases were found in road and tree cover, while the land cover types that decreased were bare land, grass, roof, water. To better understand the reasons for those changes, land cover transitions were calculated. Canopy growth, seasonal differences and forest plantation establishment were the main reasons for tree cover increase. Redevelopment after the earthquake was the main reason for road area growth. By comparing the spatial distribution of these transitions, this study also identified Halswell and Wigram as the fastest developing suburbs in Christchurch. These results provided quantitative information for the effects of CES, with respect to land cover change. They allow for a better understanding for the current land cover status of Christchurch. Among those land cover changes, the significant increase in tree cover aroused particularly interest as urban forests benefit citizens via ecosystem services, including health, social, economic, and environmental benefits. Therefore, this study firstly calculated the percentages of tree cover in Christchurch’s fifteen wards in order to provide a general idea of tree cover change in the city extent. Following this, an automatic individual tree detection and crown delineation (ITCD) was undertaken to determine the feasibility of automated tree counting. The accuracies of the proposed approach ranged between 56.47% and 92.11% in thirty different sample plots, with an overall accuracy of 75.60%. Such varied accuracies were later found to be caused by the fixed tree detection window size and misclassifications from the land cover classification that affected the boundary of the CHM. Due to the large variability in accuracy, tree counting was not undertaken city-wide for both time periods. However, directions for further study for ITCD in Christchurch could be exploring ITCD approaches with variable window size or optimizing the classification approach to focus more on producing highly accurate CHMs.
The Canterbury Earthquakes of 2010-2011, in particular the 4th September 2010 Darfield earthquake and the 22nd February 2011 Christchurch earthquake, produced severe and widespread liquefaction in Christchurch and surrounding areas. The scale of the liquefaction was unprecedented, and caused extensive damage to a variety of man-made structures, including residential houses. Around 20,000 residential houses suffered serious damage as a direct result of the effects of liquefaction, and this resulted in approximately 7000 houses in the worst-hit areas being abandoned. Despite the good performance of light timber-framed houses under the inertial loads of the earthquake, these structures could not withstand the large loads and deformations associated with liquefaction, resulting in significant damage. The key structural component of houses subjected to liquefaction effects was found to be their foundations, as these are in direct contact with the ground. The performance of house foundations directly influenced the performance of the structure as a whole. Because of this, and due to the lack of research in this area, it was decided to investigate the performance of houses and in particular their foundations when subjected to the effects of liquefaction. The data from the inspections of approximately 500 houses conducted by a University of Canterbury summer research team following the 4th September 2010 earthquake in the worst-hit areas of Christchurch were analysed to determine the general performance of residential houses when subjected to high liquefaction loads. This was followed by the detailed inspection of around 170 houses with four different foundation types common to Christchurch and New Zealand: Concrete perimeter with short piers constructed to NZS3604, concrete slab-on-grade also to NZS3604, RibRaft slabs designed by Firth Industries and driven pile foundations. With a focus on foundations, floor levels and slopes were measured, and the damage to all areas of the house and property were recorded. Seven invasive inspections were also conducted on houses being demolished, to examine in more detail the deformation modes and the causes of damage in severely affected houses. The simplified modelling of concrete perimeter sections subjected to a variety of liquefaction-related scenarios was also performed, to examine the comparative performance of foundations built in different periods, and the loads generated under various bearing loss and lateral spreading cases. It was found that the level of foundation damage is directly related to the level of liquefaction experienced, and that foundation damage and liquefaction severity in turn influence the performance of the superstructure. Concrete perimeter foundations were found to have performed most poorly, suffering high local floor slopes and being likely to require foundation repairs even when liquefaction was low enough that no surface ejecta was seen. This was due to their weak, flexible foundation structure, which cannot withstand liquefaction loads without deforming. The vulnerability of concrete perimeter foundations was confirmed through modelling. Slab-on-grade foundations performed better, and were unlikely to require repairs at low levels of liquefaction. Ribraft and piled foundations performed the best, with repairs unlikely up to moderate levels of liquefaction. However, all foundation types were susceptible to significant damage at higher levels of liquefaction, with maximum differential settlements of 474mm, 202mm, 182mm and 250mm found for concrete perimeter, slab-on-grade, ribraft and piled foundations respectively when subjected to significant lateral spreading, the most severe loading scenario caused by liquefaction. It was found through the analysis of the data that the type of exterior wall cladding, either heavy or light, and the number of storeys, did not affect the performance of foundations. This was also shown through modelling for concrete perimeter foundations, and is due to the increased foundation strengths provided for heavily cladded and two-storey houses. Heavy roof claddings were found to increase the demands on foundations, worsening their performance. Pre-1930 concrete perimeter foundations were also found to be very vulnerable to damage under liquefaction loads, due to their weak and brittle construction.
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.
