Reduction of inelastic seismic demands in a mid‐rise rocking wall structure designed using the displacement‐based design procedure

Precast post‐tensioned rocking wall structural system has been developed in the recent past as a damage‐avoidance structural system for seismic regions. For a widespread use of this structural system, suitable design procedures are required to ensure a reliable and well‐predicted performance under different levels of seismic hazard. In the current study, a mid‐rise 20‐story rocking wall structure is selected and designed using the displacement‐based design procedure. Furthermore, two different capacity design procedures are used to predict the increased force demands due to higher mode effects. The time history results against moderate and severe level of seismic hazards show the effectiveness of displacement‐based design procedure in predicting and controlling the displacement and drift demands, while the simplified procedure and the modified modal superposition procedure for the capacity design are found to be unconservative and conservative, respectively. To further investigate the seismic demands, modal decomposition of inelastic seismic responses is carried out, and the contribution of different modes in the total responses is calculated. Based on this improved understanding, a mitigation technique of dual gap opening is employed. A detailed discussion about the location and design strength of the extra gap‐opening is carried out by considering different performance parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

Identification of the mode shapes of spatial tall multi‐storey buildings due to earthquakes: the new ‘modal time‐histories’ method

In the present article, a new method is presented which attempts to identify the dynamic characteristics (eigen frequencies, eigen periods, mode shapes and modal damping ratios) of spatial asymmetric tall multi‐storey buildings through measured seismic responses (accelerations). This new method is entitled ‘method of modal time‐histories’, because its main target is to identify the modal time‐histories of accelerations that are obtained by accelerograms recorded on the points of buildings where suitable accelerometers have been installed. In the case of an earthquake, the multi‐channel local network of accelerometers records the time‐histories of the accelerations of the building. In addition, in order to have a successful outcome, the instrumentation form of the multi‐channel local network on the building can potentially play the most important role. This paper, first, presents a relevant mathematical analysis that is adapted to the instrumentation form applied to the multi‐storey buildings and, second, outlines the new method, which consists of nine steps. Finally, in order to illustrate the theory, a suitable numerical example of an instrumented asymmetric five‐storey r/c building that has been oscillated by a weak earthquake is also provided. On the one hand, the identification of the dynamic characteristics of spatial asymmetric buildings contributes to the removal of the uncertainties of building models in order to perform advanced non‐linear analyses about inherent building seismic capacity. On the other hand, this method supports the simple monitoring of a building's ‘structural integrity’. Copyright © 2010 John Wiley & Sons, Ltd.     

A new pushover procedure for two‐way asymmetric‐plan tall buildings under bidirectional earthquakes

Conventional pushover analyses despite of extensive applications are unable to estimate the general responses of asymmetric‐plan tall buildings because of ignoring the effects of higher modes and torsion. A consecutive modal pushover procedure is one of the recent nonlinear static pushover procedures that used to analyse the seismic response of one‐way asymmetric‐plan tall buildings under one‐directional seismic ground motions. In this paper, a modified consecutive modal pushover procedure (MCMP) has been proposed to estimate the seismic demands of two‐way asymmetric‐plan tall buildings under two horizontal components of earthquakes simultaneously. The accuracy of the MCMP procedure is evaluated using different buildings and comparing with the results of FEMA (Federal Emergency Management Agency) procedures, the practical modal pushover procedure and nonlinear time history analyses as an exact solution. The results show the proposed MCMP procedure is able to estimate the displacements and storey drifts accurately and introduces a great improvement in predicting the plastic hinge rotations. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling of two‐cell cores for three‐dimensional analysis of multi‐story buildings

The reliability of simplified models for single‐cell cores, and particularly for open and semi‐open U‐cross‐section cores, has been the subject of many research papers in the recent past. In contrast, on an international level, only little mention has been made of the efficiency of such models for multi‐cell cores of multi‐story R/C buildings. This paper evaluates and comments on the reliability of several simplified models for open two‐cell cores that are often used in practice. The models examined are: (a) models composed of equivalent columns in alternative configurations; (b) models composed of panel elements; and (c) finite shell element models with one element for each flange in each story. These models are compared with one another and with the solution considered accurate, which is the one obtained by using a finite element method consisting of an adequately dense mesh of finite shell elements. The conclusions obtained refer to both the simplified modal response analysis and the multi‐modal response spectrum analysis, while the specific assumptions for the numerical investigations are compatible with the provisions of modern seismic design codes. Copyright © 2000 John Wiley & Sons, Ltd.     

Considering dynamic parameters of damaged structure in MPA and YPS nonlinear static procedures for asymmetric buildings

The yield point spectra and modal pushover procedures have already been used in seismic design of new buildings and vulnerability evaluation of existing structures. This paper initially identifies the similarities and differences of the two procedures. Then, the modal characteristics of damaged structure are used to modify their methodologies. The applications of the procedures in estimating displacement, interstory drift index and plastic hinge rotation responses of asymmetric buildings are investigated for three 5‐story reinforced concrete moment‐resisting frame‐building models. The results show considerable improvement in estimating the responses of those asymmetric buildings. Copyright © 2013 John Wiley & Sons, Ltd.     

Equivalent non‐linear single‐degree‐of‐freedom system of spatial asymmetric multi‐storey buildings in pushover procedure: theory and applications

In the present paper, the issue of the approximate definition of a new equivalent non‐linear single‐degree‐of‐freedom (NLSDF) system on spatial asymmetric reinforced concrete (r/c) tall multi‐storey buildings is presented. In order to achieve this goal, three different types of r/c systems are examined: the first type refers to multi‐storey planar r/c frames; the second type refers to asymmetric single‐storey r/c building; and the third type refers to asymmetric multi‐storey r/c buildings. The definition of the NLSDF system is mathematically derived, considering suitable dynamic loadings on the masses of each r/c system using simplified assumptions. The NLSDF system is very useful in the seismic design of the r/c systems, since it is widely used in all forms of various pushover analyses that have been published in the past. The use of the equivalent NLSDF system in combination with the inelastic design spectra can give an acceptable evaluation of the maximum required seismic floor displacement for a known design earthquake. The present paper concludes the total theory of definition of the optimum equivalent NLSDF system for the above three types of buildings that possess the required normality by the contemporary seismic codes in elevation. In order to illustrate the theory, three numerical examples are presented, respectively. The final numerical required displacement results by the use of the equivalent NLSDF system are verified and checked by non‐linear response history analyses. Copyright © 2008 John Wiley & Sons, Ltd.     

Alternative approach to compute shear amplification in high‐rise reinforced concrete core wall buildings using uncoupled modal response history analysis procedure

The seismic response of the high‐rise reinforced concrete (RC) wall structures is really complicated as several vibration modes other than the fundamental mode normally contribute significantly to the response—commonly recognized as ‘higher mode effects’. Response spectrum analysis (RSA) procedure, which can account for higher mode effects, is usually employed to compute the seismic design demand for the high‐rise structures. Recent studies show that the inelastic seismic force demands obtained from the rigorous nonlinear response history analysis procedure are much larger than the seismic force design demands obtained from the code‐based RSA procedure for the high‐rise RC wall structures. Though, the nonlinear response history analysis procedure is widely accepted for its ability to provide the most accurate estimate of nonlinear seismic responses, the obtained responses are generally so complex that it is quite difficult for engineers to grasp the overall picture of the responses and gain some insight into them and use them to understand the cause of high seismic demands. Another important issue related to the nonlinear seismic response prediction of the high‐rise RC wall structures is the realistic and accurate numerical modeling of RC walls. In this study, a simplified but reasonably accurate procedure called the uncoupled modal response history analysis procedure is used to interpret the complex nonlinear behavior of high‐rise RC wall structures. Moreover, a finite element model based on modified compression field theory is employed for accurate numerical modeling of RC walls by incorporating the axial‐flexure‐shear interaction. This study, by making use of a better computer modeling approach and an in‐depth analysis by modal decomposition, aims to resolve some of the unanswered questions regarding realistic prediction of nonlinear seismic demands of high‐rise structures.     

A comparative case study on seismic design of tall RC frame‐core‐tube structures in China and USA

To evaluate the major differences between the Chinese and the United States (US) seismic design codes from a structural system viewpoint, a comparative case study is conducted on a tall frame‐core‐tube building, a typical type of reinforced concrete system widely constructed in both countries. The building, originally designed using the US seismic design code, is firstly redesigned according to the Chinese seismic design code based on the information provided by the Pacific Earthquake Engineering Research Center. Secondly, the member dimensions, the dynamic characteristics, the seismic design forces and the material consumptions of the two designs are compared in some detail. Subsequently, nonlinear finite element models of both designs are established to evaluate their seismic performances under different earthquake intensities. Results indicate that the seismic design forces determined by the Chinese response spectrum are larger than those determined by the US spectrum at the same seismic hazard level. In addition, the upper‐bound restriction for the inter‐story drift ratio is more rigorously specified by the Chinese code. These two aspects have led to a higher level of material consumption for a structure designed by the Chinese code. Despite of the above discussions, the two designs yield roughly similar structural performances under earthquakes. Copyright © 2015 John Wiley & Sons, Ltd.     

A modified response spectrum analysis procedure to determine nonlinear seismic demands of high‐rise buildings with shear walls

The standard response spectrum analysis (RSA) procedure prescribed in various design codes is commonly used by practicing engineers to determine the seismic demands for structural design purpose. In this procedure, the elastic force demands of all significant vibration modes are first combined and then reduced by a response modification factor (R) to get the inelastic design demands. Recent studies, however, have shown that the response of higher vibration modes may experience much lower level of nonlinearity, and therefore, it may not be appropriate to reduce their demand contributions by the same factor. In this study, a modified RSA procedure based on equivalent linearization concept is presented. The underlying assumptions are that the nonlinear seismic demands can be approximately obtained by summing up the individual modal responses and that the responses of each vibration mode can be approximately represented by those of an equivalent linear SDF system. Using 3 high‐rise buildings with reinforced concrete shear walls (20‐, 33‐, and 44‐story high), the accuracy of this procedure is examined. The inelastic demands computed by the nonlinear response history analysis procedure are used as benchmark. The modified RSA procedure is found to provide reasonably accurate demand estimations for all case study buildings.     

Earthquake analysis of isotropic asymmetric multistory buildings

Isotropic multistory buildings are the ones characterized by the property: all load‐resisting planar frames have proportional lateral stiffness matrices. In the present paper it is proved that the modal analysis of an N‐story isotropic asymmetric, torsionally coupled, building (a problem of order 3N) can be separated into two independent sub‐problems: (a) a sub‐problem that corresponds to a single‐story asymmetric, torsionally coupled, building (a problem of order 3); and (b) a sub‐problem that corresponds to an N‐story, torsionally uncoupled, planar frame (a problem of order N). It is also demonstrated that the orientation of peak modal seismic forces of the building is independent of the orientation of seismic excitation, which affects only their size. The separation provides a better insight into the structural behavior of asymmetric multistory buildings under earthquake ground motion. Copyright © 2006 John Wiley & Sons, Ltd.     

Modal combination method for earthquake‐resistant design of tall structures to multidimensional excitations

This paper presents a modal combination method for earthquake‐resistant design of structures to multidimensional seismic excitations. With the assumption that an earthquake is a stationary random vibration, the correlation among the input components is considered in the proposed method. The relationship coefficients between the translational component and rotational component is then derived in the frequency domain. The combination method of response spectrum for structural response to multidimensional earthquakes is proposed based on the random vibration theory. With the help of the derived modal correlation coefficients, the formulation for structural response to the two‐dimensional earthquake excitations can be obtained. Numerical examples demonstrate the effectiveness and high precision of the proposed methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic performance of torsionally stiff and flexible multi‐story concentrically steel braced buildings

It is expected that application of torsion provisions in typical seismic codes shows different levels of efficiency for torsionally stiff and flexible buildings. This paper studies difference in performances of a range of code designed torsionally stiff and flexible five‐story building models. The models are classified in eight configurations to cover common range of buildings designed with the seismic provisions of Iranian Standard 2800 as a typical seismic design code. Seismic nonlinear dynamic time history behavior of eight building models subjected to seven horizontal bi‐directional design spectra compatible ground motions is investigated. These models cover a wide band of very torsionally stiff to very flexible buildings. Response parameters are element ductility demand and building story drift ratio. These criteria are appropriate indices for structural and nonstructural damages, respectively. The results indicate that the present linear static procedure of building codes such as the Iranian Standard 2800 is not generally adequate for structures with very low torsional stiffness. Copyright © 2012 John Wiley & Sons, Ltd.     

Improved multimode pushover procedure for asymmetric in plan buildings under biaxial seismic excitation—application to tall buildings

An improved version of a recently developed multimode pushover procedure for asymmetric in plan buildings under biaxial seismic excitation is presented and evaluated. The proposed methodology is quite similar to the well‐known modal pushover analysis. However, the establishment of the equivalent single‐degree‐of‐freedom systems is based on a new concept, which takes into account multidirectional seismic effects. The proposed methodology does not require independent analysis in the two orthogonal directions, and therefore, the application of simplified directional combination rules is avoided. The improvement presented here consists in definition of correction factors to be applied to the response values at the stiff side of buildings. An extensive evaluation study comprising applications to tall buildings is presented. The response parameters obtained from the proposed methodology in most cases envelope the values resulting from nonlinear dynamic analysis (NDA). Furthermore, the mean errors with regard to the NDA results are smaller than those obtained from a multimode pushover procedure comprising independent analysis along two horizontal axes and directional combination of the results. In general, the proposed methodology provides a reasonable estimation of the seismic performance of asymmetric buildings.     

Seismic nonlinear static new method of spatial asymmetric multi‐storey reinforced concrete buildings

In order to obtain the seismic demands of spatial asymmetric multi‐storey reinforced concrete (r/c) buildings, a new seismic nonlinear static (pushover) procedure that uses inelastic response acceleration spectra is presented in this paper. The latter makes use of the optimum equivalent nonlinear single degree of freedom system, which is used to represent the general spatial asymmetric multi‐storey r/c building. For each asymmetric multi‐storey building, a total of 12 suitable nonlinear static analyses are needed according to the new proposed procedure, whereas at least 96 suitable nonlinear dynamic analyses are required in the case of nonlinear response history analysis (NLRHA), respectively. In addition, the present paper provides answers to a series of further questions with reference to the spatial action of the two horizontal seismic components in the static nonlinear (pushover) analyses, as well as to the documented calculation of the available behaviour factor of the asymmetric multi‐storey r/c building. According to the paper, this new proposed seismic nonlinear static procedure is a natural extension of the documented equivalent seismic static linear (simplified spectral) method that is recommended by the established contemporary seismic codes, with reference to torsional provisions. Finally, through a restricted parametric analysis carried out in this paper, a relevant numerical example of a two‐storey r/c building is presented for illustration purposes, where the seismic demand floor inelastic displacements are compared with the respective displacements obtained by the NLRHA. Consequently, the new proposed seismic nonlinear static procedure, which uses inelastic response acceleration spectra, can reliably evaluate the extreme values of floor inelastic displacements (on the flexible and stiff side of the building), as is shown by the above comparisons. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic characteristics and viscous dampers design for pile‐soil‐structure system

A series of large‐scale shaking table tests are conducted on tall buildings with and without energy dissipation devices on soft soils in pile group foundations, representing pile‐soil‐structure interaction (PSSI) system and the corresponding fixed‐base situations. The superstructure is a 12‐story reinforced concrete (RC) frame. The dynamic characteristics of the test models show that the frequencies decrease and the damping ratio increase in PSSI system by comparison with the fixed‐base structures. The mode shapes of PSSI system are different from that under fixed‐base condition, and the mode shapes of structure without dampers change greater than that with energy dissipation devices under various white noises. An improved method for structural dynamic characteristics, considering the impedance function of piles, is developed to address the issue of modal parameters with PSSI effect. In addition, the structural dynamic parameters of the large‐scale shaking table tests are identified using the modification method and other regulation methods, demonstrating that the improved approach is highly accurate and effective. Subsequently, a design procedure for viscous dampers of structures with PSSI effect is presented based on the dynamic characteristics of the system. Finally, the dynamic responses of the structure with viscous dampers in the practical engineering are decreased effectively, indicating the good performance of designed viscous dampers. The numerical results also show that the damping efficiency of interstory drift is larger than the acceleration and interstory shear force. Therefore, the improved modal parameters method, validated through a series large‐scale shaking table tests, is applicable for identifying dynamic characteristics of pile‐soil‐structure with energy dissipation devices system. The design procedure of viscous dampers, proved by a reinforced concrete frame structure located on a practical Shanghai soft site, can be employed to design the viscous dampers considering seismic PSSI effect.     

Behavior of coupled shear walls with buckling‐restrained steel plates in high‐rise buildings under lateral actions

Traditional coupling beams in coupled shear walls (CSWs) may be lack of required ductility or inconvenient to be fully repaired or replaceable after earthquake damage. To improve the CSW seismic performance, a type of new structural system, which is referred to as coupled shear walls with buckling‐restrained steel plates (CSW–BRSP), is proposed and thoroughly studied. In the system, a pair of individual concrete wall is coupled through buckling‐restrained steel plates instead of traditional concrete coupling beams. Based on the continuous medium method (CMM), stiffness and strength design formulas are developed for the seismic design of this system. Intensive investigations have been conducted to assess the undesirable axial forces in the buckling‐restrained steel plates induced by lateral loads. In order to facilitate the application of this system, a detailed design procedure is also explicitly stated. Finally, an example of typical high‐rise building is presented to illustrate the design procedure as well as demonstrate the excellent seismic performance of the proposed system by means of nonlinear time‐history analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrated multi‐type sensor placement and response reconstruction method for high‐rise buildings under unknown seismic loading

Structural health monitoring system has been implemented on high‐rise buildings to provide real‐time measurement of structural responses for evaluating their serviceability, safety, and sustainability. However, because of the complex structural configuration of a high‐rise building and the limited number of sensors installed in the building, the complete evaluation of structural performance of the building in terms of the information directly recorded by a structural health monitoring system is almost impossible. This is particularly true when seismic‐induced ground motion is unknown. This paper thus proposes an integrated method that enables the optimal placement of multi‐type sensors on a high‐rise building on one hand and the reconstruction of structural responses and excitations using the information from the optimally located sensors on the other hand. The structural responses measured from multi‐type sensors are fused to estimate the full state of the building in the modal coordinates using Kalman filters, from which the structural responses at unmeasured locations and the seismic‐induced ground motion can be reconstructed. The optimal multi‐type sensor placement is simultaneously achieved by minimizing the overall estimation errors of structural responses at the locations of interest to a desired target level. A numerical study using a simplified finite element model of a high‐rise building is performed to illustrate the effectiveness and accuracy of the proposed method. The numerical results show that by using 3 types of sensors (inclinometers, Global Positioning System, and accelerometers), the proposed method offers an effective way to design a multi‐type sensor system, and the multi‐type sensors at their optimal locations can produce sufficient information on the response and excitation reconstruction.     

Three‐dimensional coupled wind‐induced vibration calculation method for super high‐rise buildings based on high‐frequency force balance technology

High‐frequency force balance test is a major technical means to evaluate the wind effect of super high‐rise buildings. Most super high‐rise buildings have the characteristic that the first two‐order modal frequencies are close, and thus, considerable modal coupling effects (MCEs) may occur under wind load. For a balance model system (BMS), MCEs increase the difficulty of correcting aerodynamic distortion signals. For the wind‐induced vibration analysis of a structural system (PSS), the calculation results of the wind‐induced response and the equivalent static wind load (ESWL) may be significantly affected without considering MCE. Based on the above‐mentioned signal distortion of BMS and the modal coupling problem of PSS, this study proposes a wind‐induced vibration calculation method for the two coupled systems (BMS and PSS). The method uses the second‐order blind identification technique based on complex modal theory and the Bayesian spectral density method considering full aerodynamic characteristics to achieve effective correction of the distortion signal in BMS. In addition, it deduces the calculation method of the wind‐induced response and ESWL considering the three‐dimensional coupled vibration of a super high‐rise building. The wind effect calculation results of a 528‐m super high‐rise building confirm the necessity and effectiveness of the proposed method.     

Hysteretic energy response of steel moment‐resisting frames with vertical mass irregularities

Dynamic analyses were carried out to study the seismic response of high‐rise steel moment‐resisting frames in 16‐storey buildings. The frames are intentionally designed using three different design procedures: strength‐controlled design, strong column–weak beam controlled design, and drift‐controlled design. The seismic performances of the so‐designed frames with vertical mass irregularities were discussed in view of drift ratio, plastic hinge rotation, hysteretic energy input and stress demand. A demand curve of hysteretic energy inputs was also presented with two earthquake levels in peak ground accelerations for a future design application. Copyright © 2004 John Wiley & Sons, Ltd.     

Assessment of inelastic response of buildings using force‐ and displacement‐based approaches

In recognition of the increasing importance of accurate seismic vulnerability assessment, this paper deals with procedures and the application of inelastic acceleration and displacement spectra in the seismic assessment of buildings. An identification procedure is outlined, whereby an equivalent single degree of freedom (SDOF) system is devised to represent the building. The SDOF system characteristics (stiffness, strength, post‐peak force response and ductility) are readily evaluated from observation of the seismic response of buildings and simple mechanics. The characteristics are then tuned using measurements from instrumented buildings. Based on the earthquake scenario and structural response characteristics, appropriate inelastic acceleration and displacement spectra are selected and used to ‘predict’ the response. Comparison between the measured and predicted responses for the five buildings studied in the paper confirm the feasibility of the procedure and the realism of the results. Copyright © 2000 John Wiley & Sons, Ltd.