Predicting torsion‐induced lateral displacements for pushover analysis: Influence of torsional system characteristics

The increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one. This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single‐storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above‐mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. Copyright © 2010 John Wiley & Sons, Ltd.     

Understanding the inelastic seismic behaviour of asymmetric-plan buildings

Studied in this paper is the inelastic seismic behaviour of asymmetric-plan buildings using the histories of base shear and torque. The first step in understanding this behaviour is to construct the base shear and torque surface (BST) for the building, which represents all combinations of shear and torque that applied statically lead to collapse of the structure. Several factors controlling the shape of this surface, such as strength eccentricity and bidirectional ground motion, are identified. Also, their effects on the building responses are studied considering several structural configurations. The results obtained show that the BST surface, in conjunction with the base-shear and torque histories, provides a useful conceptual framework for understanding the behaviour of asymmetric systems. Furthermore, using these surfaces, relevant aspects of the behaviour and design of such buildings become apparent even before dynamic analysis of the structure.     

A macro‐element model for inelastic building analysis

A three‐dimensional model for approximate inelastic analysis of buildings is presented herein. The model is based on a single macro‐element per building storey. The inelastic properties of the model are characterized by the so‐called ultimate storey shear and torque (USST) surfaces. Different algorithms for the construction of these surfaces, as well as their applications in building modelling, are presented and discussed. Two alternative procedures are developed to integrate the force‐deformation constitutive relationship of the macro‐elements. The first one follows the exact trajectory of the load path of the structure on the USST, and the second uses linear programming without ever forming the USST surface. The accuracy of the model and integration procedure is evaluated by means of the earthquake response of single‐storey systems. The model and integration procedure developed is finally used to compute the inelastic response of a seven‐storey R/C building. The results of this investigation show that the model proposed, although approximate, can be effective in estimating the inelastic deformation demand of a building. It also enables the engineer to capture and interpret important features of the three‐dimensional inelastic response of a structure even before performing any inelastic dynamic analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Inelastic torsion of multistorey buildings under earthquake excitations

The inelastic earthquake response of eccentric, multistorey, frame‐type, reinforced concrete buildings is investigated using three‐ and five‐storey models, subjected to a set of 10, two‐component, semi‐artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC‐97 code were included in the investigation. It is found that contrary to what the simplified one‐storey, typical, shear‐beam models predict, the so‐called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic drift demands in multi‐storey cross‐laminated timber buildings

This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.     

Force reduction factor for building structures equipped with added viscous dampers

This research work focuses on the analysis of the hysteretic seismic behaviour of inelastic SDOF systems equipped with viscous dampers. In detail, it is aimed at obtaining a practical tool useful for the seismic design of building structures with added dampers, within the framework of the traditional seismic design based on ductility. The objective is to evaluate the appropriate force reduction factor for highly damped (i.e. damping ratio greater than 5 %) SDOF systems able to guarantee a prescribed level of structural safety.     

A deformation-based seismic design method for 3D R/C irregular buildings using inelastic dynamic analysis

A new deformation-based design method concerning 3D reinforced concrete (R/C) buildings is presented, which involves the use of advanced analysis tools, i.e. response-history analysis for appropriately scaled input motions, for multiple levels of earthquake action. The critical issues concerning the inelastic response-history analysis used for the design, namely the definition of the appropriate input, the set up of the analytical model that should account for post-yield behaviour of plastic hinge zones, and the direction of loading, are discussed. The proposed method is based on a partially inelastic model, while the design of structural members is carried out for different performance levels related to their inelastic behaviour. The aforementioned method builds on previous proposals by the first author and his co-workers, nevertheless a new procedure for the design of members that are expected to develop inelastic behaviour for the serviceability earthquake is proposed; its aim is the reduction of member design forces and the a-priori definition of their inelastic performance, by exploiting the deformation limits for the specific performance level, which are related to the damage level of the structural members. The proposed method was applied to irregular multistorey R/C 3D frame buildings with setbacks, and their performance for several levels of earthquake action was assessed using a fully inelastic model and additional ground motions not used at the design phase. The same buildings were designed according to the provisions of Eurocode 8. Comparison of the two methods of seismic design, revealed the advantages of the proposed design method, in particular the more economic detailing of transverse reinforcement in the members that develop very little inelastic behaviour even for very strong earthquakes.     

An efficient performance‐based seismic design method for reinforced concrete frames

In this paper, a practical method is developed for performance‐based design of RC structures subjected to seismic excitations. More efficient design is obtained by redistributing material from strong to weak parts of a structure until a state of uniform deformation or damage prevails. By applying the design algorithm on 5, 10 and 15‐storey RC frames, the efficiency of the proposed method is initially demonstrated for specific synthetic and real seismic excitations. The results indicate that, for similar structural weight, designed structures experience up to 30% less global damage compared with code‐based design frames. The method is then developed to consider multiple performance objectives and deal with seismic design of RC structures for a design spectrum. The results show that the proposed method is very efficient at controlling performance parameters and improving structural behaviour of RC frames. Copyright © 2011 John Wiley & Sons, Ltd.     

Earthquake response analysis of the olive view hospital psychiatric day clinic

The collapse of the Olive View Hospital Psychiatric Day Clinic is studied using three biaxial force-deflection models to represent the columns of the building. These models are: shear collapse, elastic and inelastic. The biaxial models for shear and inelastic behaviour are new developments and are useful for non-linear structural dynamic studies. In the present study, the shear collapse model is intended to represent the actual prototype behaviour. The inelastic model, which is based on a hardening rule of plasticity, is used to study the performance of a hypothetical structure with the same storey shear capacity as the prototype but which exhibits ductile behaviour. The prototype structure had a base storey shear capacity of 25 per cent, and actually failed by shearing of all of the first floor columns. In the present study, the shear collapse model predicted this behaviour even with the El Centro accelerogram as input. This result may have far-reaching significance because many low-rise reinforced concrete buildings which were designed according to recent codes have similar storey shear capacity coefficients and column properties. According to this study, such buildings may collapse even in a moderate earthquake. In the inelastic representation, the structure was found to have a base storey shear capacity of 80 per cent when moment hinging was assumed to occur at the top and bottom of the columns. Even with this high strength capacity, the permanent offset computed from the inelastic model corresponded to a ductility factor of 5 when the Pacoima Dam accelerogram was used as input. On the basis of damage to other structures observed on the site, it seems likely that ground motion of about the Pacoima Dam intensity occurred at Olive View. From this it is concluded that a low-rise ductile frame concrete building, even with this high shear force capacity, may not prove satisfactory for hospital use when subjected to strong ground motion.     

Inelastic seismic response of code-designed multistorey frame buildings with regular asymmetry

Based on an asymmetric multistorey frame building model, this paper investigates the influence of a building's higher vibration modes on its inelastic torsional response and evaluates the adequacy of the provisions of current seismic building codes and the modal analysis procedure in accounting for increased ductility demand in frames situated at or near the stiff edge of such buildings. It is concluded that the influence of higher vibration modes on the response of the upper-storey columns of stiff-edge frames increases significantly with the building's fundamental uncoupled lateral period and the magnitude of the stiffness eccentricity. The application of the equivalent static torsional provisions of certain building codes may lead to non-conservative estimates of the peak ductility demand, particularly for structures with large stiffness eccentricity. In these cases, the critical elements are vulnerable to excessive additional ductility demand and, hence, may be subject to significantly more severe structural damage than in corresponding symmetric buildings. It is found that regularly asymmetric buildings excited well into the inelastic range may not be conservatively designed using linear elastic modal analysis theory. Particular caution is required when applying this method to the design of stiff-edge frame elements in highly asymmetric structures.     

上海环球金融中心大厦整体结构振动台试验设计

同济大学土木工程防灾国家重点实验室对上海环球金融中心大厦进行了整体结构模型的振动台试验.该大厦101层,结构高度492m,拟建成为世界上结构主体最高的建筑物.本文详细介绍了大厦结构体系、振动台试验模型材料的选取、动力相似关系的确定以及试验方案的设计.针对超高层整体结构小比例模型施工困难的特点,提出了模型的简化方法,并利用ANSYS对简化模型进行了计算,计算结果表明模型简化对结构自振特性和地震反应影响很小,验证了简化方法的可行性.本文提供的模型和试验的设计思路对今后有关的试验工作有一定的借鉴作用.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal design of tuned mass dampers for a multi‐storey cross laminated timber building against seismic loads

In this paper, the effectiveness of different design solutions for tuned mass dampers (TMD) applied to high‐rise cross‐laminated (X‐Lam) timber buildings as a means to reduce the seismic accelerations was investigated. A seven‐storey full‐scale structure previously tested on shaking table was used as a reference. The optimal design parameters of the TMDs, i.e. damping and frequency ratios, were determined by using a genetic algorithm on a simplified model of the reference structure, composed by seven masses each representing one storey. The optimal solutions for the TMDs were then applied to a detailed finite element model of the seven‐storey building, where the timber panels were modelled with shell elements and the steel connectors with linear spring. By comparing the numerical results of the building with and without multiple TMDs, the improvement in seismic response was assessed. Dynamic time‐history analyses were carried out for a set of seven natural records, selected in accordance with Eurocode 8, on the simplified model, and for Kobe earthquake ground motion on the detailed model. Results in terms of acceleration reduction for different TMD configurations show that the behaviour of the seven‐storey timber building can be significantly improved, especially at the upper storeys. Copyright © 2016 John Wiley & Sons, Ltd.     

A method for the direct estimation of floor acceleration spectra for elastic and inelastic MDOF structures

This paper deals with floor acceleration spectra, which are used for the seismic design and assessment of acceleration‐sensitive equipment installed in buildings. In design codes and in practice, not enough attention has been paid to the seismic resistance of such equipment. An ‘accurate’ determination of floor spectra requires a complex and quite demanding dynamic response history analysis. The purpose of the study presented in this paper is the development of a direct method for the determination of floor acceleration spectra, which enables their generation directly from the design spectrum of the structure, by taking into account the structure's dynamic properties. The method is also applicable to inelastic structures, which can greatly improve the economic aspects of equipment design. A parametric study of floor acceleration spectra for elastic and inelastic single‐degree‐of‐freedom (SDOF) and multiple‐degree‐of‐freedom structures was conducted by using (non)linear response history analysis. The equipment was modelled as an elastic single‐degree‐of‐freedom system. The proposed method was validated by comparing the results obtained with the more accurate results obtained in a parametric study. Due to its simplicity, the method is an appropriate tool for practice. In the case of inelastic structural behaviour, the method should be used in combination with the N2 method, or another appropriate method for simplified nonlinear structural analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimized earthquake response of multi‐storey buildings with seismic isolation at various elevations

The response of multi‐storey structures can be controlled under earthquake actions by installing seismic isolators at various storey levels. By vertically distributing isolation devices at various elevations, the designer is provided with numerous options to appropriately adjust the seismic performance of a building. However, introducing seismic isolators at various storey levels is not a straightforward task, as it may lead to favourable or unfavourable structural behaviour depending on a large number of factors. As a consequence, a rather chaotic decision space of seismic isolation configurations arises, within which a favourable solution needs to be located. The search for favourable isolators' configurations is formulated in this work as a single‐objective optimization task. The aim of the optimization process is to minimize the maximum floor acceleration of the building under consideration, while constraints are specified to control the maximum interstorey drift, the maximum base displacement and the total seismic isolation cost. A genetic algorithm is implemented to perform this optimization task, which selectively introduces seismic isolators at various elevations, in order to identify the optimal configuration for the isolators satisfying the pre‐specified constraints. This way, optimized earthquake response of multi‐storey buildings can be obtained. The effectiveness of the proposed optimization procedure in the design of a seismically isolated structure is demonstrated in a numerical study using time‐history analyses of a typical six‐storey building. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of depth of soil stratum on performance of buildings for site-specific earthquakes

Towards formulating guidelines for performance evaluation of buildings to site-specific earthquakes, studies are reported in literature on the effect of various critical parameters. No study is, however, reported on the effect of depth of soil stratum. In this paper, a methodology is proposed and applied for performance evaluation of buildings for site-specific earthquakes including depth of soil stratum as a parameter. The methodology integrates independent procedures meant for performance evaluation of buildings and site-specific seismic analysis. Application of the proposed methodology enables to determine performance point of a building in terms of inelastic displacement and base shear. Numerical application of the methodology is demonstrated using the particulars of Delhi region. Two typical RC buildings (B1 and B2) with significantly different inelastic behaviour, assumed to be located on soil depths ranging from 10 to 200 m are chosen for the application study. Capacity spectra of the buildings are generated from nonlinear static analysis. Studies indicate that for building B1, with elasto-plastic behaviour, the depth of soil stratum strongly influences demand on inelastic displacement compared to that on inelastic base shear. For building B2, with continuously varying inelastic behaviour, the depth of soil stratum is observed to have significant influence on both the inelastic base shear as well as inelastic displacement. Responses of the buildings are compared with that obtained based on design spectrum of Indian seismic code. For both the cases, inelastic displacements as well as inelastic base shears are underestimated by Indian seismic code for certain depths of soil stratum. Proposed methodology enables the calculation of realistic values of inelastic base shear and corresponding displacement of a building for site-specific earthquakes by considering the actual characteristics of soil stratum.     

钢框架结构的地震损伤研究

基于预定损伤法对钢框架构件主要设计参数进行损伤敏感度分析,研究主要设计参数与钢框架结构梁、柱损伤的关系;揭示钢框架结构梁、柱的损伤及梁、柱线刚度比、结构高宽比、柱轴压比、锈蚀率对楼层损伤的影响规律;获得楼层的损伤与整体结构损伤的关系,最终建立钢框架结构的损伤演化模型。研究成果可为建立地震激励下钢框架结构的损伤模型提供理论基础和数据支持。     

Torsional response of nonductile structures with soft‐first‐storey

In this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.     

Earthquake response of steel-framed multistorey buildings with set-backs

A study is made of the dynamic behaviour of multistorey steel rigid-frame buildings with set-back towers. The effects of set-backs upon the building frequencies and mode shapes are examined. Then the effects of set-backs on seismic response are investigated by analysing the response of a series of set-back building frame models to the El Centro ground motion. Finally, the computed responses to the El Centro earthquake are compared with some code provisions dealing with the seismic design of set-back buildings. The conclusions derived from the study include the following:

• 1. The higher modes of vibration of a set-back building can make a very substantial contribution to its total seismic response; this contribution increases with the slenderness of the tower.
• 2. Some of the important response parameters for the tower portion of a set-back building are substantially larger than for a related uniform building.
• 3. For very slender towers, the transition region between the tower and the base may be subjected to very large storey shears.

     

Inelastic response and design criteria of plan-wise asymmetric systems

The study of the torsional response of buildings in the inelastic range of behaviour is of great interest since the ability of structures to resist strong earthquakes mainly relies on their ductility and capacity for energy dissipation. Furthermore, an examination of the performance of structures during past earthquakes demonstrates that plan-asymmetric buildings suffered greater damage due to torsional response. The paper deals with this subject by analysing a model which idealizes a one-storey building with resisting elements oriented along two perpendicular directions. In addition to the parameters of the elastic behaviour, the inelastic system response depends on full yield capacity and plan-wise strength distribution. The influence of the criterion adopted for the design of resisting elements on local ductility demand and damage has been evaluated by parametric analysis. In particular, a comparison has been carried out between systems with equal design levels for all elements and systems with design levels dependent on the element location. For a given elastic behaviour and total capacity, the strength distributions in plan have been defined which minimize ductility demand and structural damage. Finally, based on these findings, responses from models designed according to several seismic codes have been compared.