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.     

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.     

An improved multidimensional modal pushover analysis procedure for seismic evaluation of latticed arch‐type structures under lateral and vertical earthquakes

Pushover methods for seismic assessment of buildings under multidimensional earthquakes have been studied and retrofitted. However, these current methods are not suitable when applied to widely adopted arch‐type structures characterized by strong geometrical nonlinearity and coupling effects. An improved multidimensional modal pushover procedure with two‐stage analyses is proposed for seismic evaluation of latticed arches. Taking overall multidimensional response into consideration, modal stiffness of the equivalent single‐degree‐of‐freedom system is derived, and its capacity curve is determined during the first‐stage analysis. To provide a deformation profile with algebraic signs of response retained, the second‐stage analysis is conducted using the pushover load pattern derived from modal displacement superposition. The objective of the improved procedure is to overcome the drawback of the conventional modal pushover method, which describes the capacity curve resorting to base shear and roof displacement, and that of quadratic combination rules which eliminate the sign reversals of response. To validate its serviceability, nodal displacements and element stresses, as well as the yielding members, of two typical latticed arches are calculated. Through comparative analysis, the results by the improved procedure exhibit good agreement with those by response history analysis. Additionally, this procedure demonstrates great superiority over the conventional method for its satisfying accuracy.     

An improved consecutive modal pushover procedure for estimating seismic demands of multi‐storey framed buildings

An improved consecutive modal pushover (ICMP) procedure is proposed to enhance the accuracy of conventional CMP procedure for estimating seismic demands of tall buildings. It accounts for inelastic structural properties and interaction between vibration modes. The displacement increment at the roof of buildings used in each stage of pushover analyses is modified based on the displacement contribution of each mode. The performance of the proposed ICMP procedure is verified against three high‐rise frames subjected to various ground motions. The results obtained from the ICMP procedure are compared with those from the nonlinear time history analysis, conventional pushover analysis, and CMP analysis. The comparison shows the advantages of the ICMP over the other pushover procedures. It is concluded that the ICMP procedure is more accurate than the CMP procedure.     

A consecutive modal pushover procedure for estimating the seismic demands of tall buildings

The nonlinear static procedure (NSP), based on pushover analysis, has become a favourite tool for use in practical applications for building evaluation and design verification. The NSP is, however, restricted to single-mode response. It is therefore valid for low-rise buildings where the behaviour is dominated by the fundamental vibration mode. It is well recognized that the seismic demands derived from the conventional NSP are greatly underestimated in the upper storeys of tall buildings, in which higher-mode contributions to the response are important. This paper presents a new pushover procedure which can take into account higher-mode effects. The procedure, which has been named the consecutive modal pushover (CMP) procedure, utilizes multi-stage and single-stage pushover analyses. The final structural responses are determined by enveloping the results of multi-stage and single-stage pushover analyses. The procedure is applied to four special steel moment-resisting frames with different heights. A comparison between estimates from the CMP procedure and the exact values obtained by nonlinear response history analysis (NL-RHA), as well as predictions from modal pushover analysis (MPA), has been carried out. It is demonstrated that the CMP procedure is able to effectively overcome the limitations of traditional pushover analysis, and to accurately predict the seismic demands of tall buildings.     

Collapse behavior evaluation of asymmetric buildings subjected to bi‐directional ground motion

This paper discusses the collapse behavior of low‐rise plan‐asymmetric buildings under bi‐directional horizontal ground motions and utilizing strength and stiffness degrading nonlinear models. For this purpose, three‐dimensional three‐story and six‐story reinforced concrete frame buildings with uni‐directional mass eccentricities equal to 0% (symmetrical), 10%, 20% and 30% are subjected to nonlinear static (pushover) as well as incremental dynamic analyses using a set of far‐field two‐component ground motions and their performance are assessed on the basis of the safety margin against collapse and its probability of occurrence. Comparison of the collapse margin ratios as well as the fragility curves demonstrates significant reduction of the collapse‐level ground motion intensity with increasing eccentricity in plan. Results also indicate that current seismic design parameters including the response modification (R), overstrength (Ω) and ductility (μ) factors are not appropriate for buildings with high levels of plan eccentricity. Buildings with high values of plan eccentricity do not meet the design target life safety performance level on the basis of the calculated probability of collapse and safety margin against collapse. It appears that re‐evaluation of their design parameters is necessary. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessment of modified consecutive modal pushover analysis for estimating the seismic demands of tall buildings with dual system considering steel concentrically braced frames

According to the previous researches, conventional nonlinear static procedure (NSP), which is limited to single mode response, cannot predict the seismic demands of tall buildings with reliable accuracy. To estimate the seismic demands in upper stories for tall buildings the effects of higher modes should be included. In the recent years, developing traditional pushover analysis to consider the effects of higher modes conducted researchers to propose several methods, such as N2, MPA and MMPA procedures, that have a specific approach to estimate seismic demands of structures but the accuracy of them is doubtable for estimating of hinge plastic rotations. Recently consecutive modal pushover (CMP) procedure was proposed to consider the effects of higher modes with acceptable accuracy especially in prediction of hinge plastic rotations. The CMP procedure was limited to include two or three modes, and use of higher modes might cause some inaccuracy at results of upper stories. In CMP procedure, estimation of modal participating factors is important and choosing inadequate modes may cause large errors. In this paper some changes have been applied to the CMP procedure to improve accuracy of the results and the modified method is proposed and named modified consecutive modal pushover (MCMP) procedure. In this modified method the contribution of mode is used of effective modal participating mass ratio. The comparison of MCMP procedure to exact values derived by nonlinear response history analysis (NL-RHA) demonstrated the reliable predictions and it can overcome the limitations of traditional pushover analysis.     

Combination model for conventional pushover analysis considering higher mode vibration effects

This paper aims to propose a combination model for conventional pushover analysis with invariant lateral load patterns to consider the effects of higher mode vibrations on the seismic responses of high‐rise buildings. Rectangular concrete‐filled steel tubular (RCFT) structures having two types of deformation, namely, shear type RCFT frame structures and shear‐flexural type RCFT frame‐shear wall structures, are selected and investigated. Finite element models are created using Perform‐3D. Both pushover analysis with three conventional lateral loading patterns, namely, uniformly distributed loading, first‐mode vibration loading, and concentrated loading at the vertex, and time‐history analysis with 15–21 earthquake records chosen for each RCFT structure are performed. Regression analysis is used to fit the interstory drift ratios obtained by the pushover analysis with those from the time‐history analysis. Further, the relations between the partial regression coefficients and the structural fundamental periods under certain lateral loading patterns are analyzed. On this basis, using these conventional lateral loading patterns, combination models for high‐rise buildings with two types of deformation are proposed and verified. The results demonstrate that the proposed method can estimate the seismic responses of high‐rise buildings with a high accuracy and has the advantages of ease of implementation and operation.     

Seismic fragility relationships of reinforced concrete high‐rise buildings

A complete methodology is presented for the seismic fragility assessment of reinforced concrete high‐rise buildings. The key steps of the methodology are illustrated through an example of the fragility assessment of an existing 54‐story building with a dual core wall system. The set of rigorously derived probabilistic fragilities are the first published for high‐rise reinforced concrete buildings. The inelastic nonlinear dynamic analyses for the fragility assessments are made using a simplified lumped‐parameter model that was derived from highly detailed FE models using genetic algorithms. New definitions for performance limit states were based on the results of detailed pushover analyses of a distributed inelastic nonlinear finite element model that includes shear–flexure–axial interaction effects. To develop the fragility relationships, 1800 dynamic response history analyses were conducted. This study considered uncertainty in structural material values as well as in seismic demand. Thirty strong motion records were selected for use in the analyses that would produce an appropriate range in structural response characteristics due to variation in magnitude, distance and site condition. The overall approach is generic and can be applied to developing computationally efficient and probabilistically‐based seismic fragility relationships for reinforced concrete high‐rise buildings of different configurations. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of modal pushover analysis and conventional nonlinear static procedure with load distributions of federal emergency management agency for high‐rise buildings

The nonlinear static pushover analysis technique is mostly used in the performance‐based design of structures. However, the pushover analysis with load distributions of Federal Emergency Management Agency (FEMA) loses its accuracy in estimating the seismic responses of long‐period structures where higher mode effects are important. Recently, modal pushover analysis (MPA) has been proposed to consider these effects. Hence, FEMA load patterns and MPA are evaluated in the current study and compared with inelastic response history analysis. These approximate procedures are applied to medium‐rise (10 and 15 stories) and high‐rise (20 and 30 stories) buildings; advantages and limitations of them are elaborated. It is shown that MPA procedure presents significant advantage over FEMA load distributions in predicting story drifts. MPA is able to compute hinge plastic rotations better than FEMA load distributions at upper floor levels of high‐rise buildings due to considering higher mode effects by this procedure, but both are unsuccessful in predicting hinge plastic rotations with acceptable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Assessment of current nonlinear static procedures for seismic evaluation of BRBF buildings

Nonlinear static procedures (NSPs) are now standard in engineering practice to estimate seismic demands in the design and evaluation of buildings. This paper aims to investigate comparatively the bias and accuracy of modal, improved modal pushover analysis (MPA, IMPA) and mass proportional pushover (MPP) procedures when they are applied to buckling-restrained braced frame (BRBF) buildings which have become a favorable lateral-force resisting system for earthquake resistant buildings. Three-, 6-, 10-, and 14-storey concentrically BRBF buildings were analyzed due to two sets of strong ground motions having 2% and 10% probability of being exceeded in 50 years. The assessment is based on comparing seismic displacement demands such as target roof displacements, peak floor/roof displacements and inter-storey drifts. The NSP estimates are compared to results from nonlinear response history analysis (NL-RHA). The response statistics presented show that the MPP procedure tends to inaccurately estimate seismic demands of lower stories of tall buildings considered in this study while MPA and IMPA procedures provide reasonably accurate results in estimating maximum inter-storey drift over all stories of studied BRBF systems.     

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.     

Optimal placement of metallic dampers for seismic upgrading of multistory buildings based on a cost‐effectiveness criterion using genetic algorithm

In this paper, an optimal placement methodology for metallic dampers is proposed to upgrade the seismic performance of multistory buildings. Most previous studies on optimal damper placement (ODP) problems have been focused on minimizing the seismic responses, whereas the present study aims to utilize the minimum total cost of dampers to achieve a prescribed level of seismic response. To this end, the optimization objective is constructed based on a cost‐effectiveness criterion, and the optimization constraint is defined based on a desired level of seismic response. An improved integer‐coded genetic algorithm is presented for solving the ODP problem. A 16‐story shear building is illustrated to verify the proposed optimal placement methodology. It is shown that the proposed methodology can be used to achieve the predetermined performance level while minimizing the retrofitting cost. Moreover, different algorithms, objective functions, and levels of accuracy on the optimization are also compared. Finally, a two‐step optimization approach is proposed for achieving better placement schemes with less computational efforts.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of Modal Combinations for Nonlinear Static Analysis of Building Structures

Abstract:   An essential requisite in performance-based seismic design is the estimation of inelastic deformation demands in structural members. An increasingly popular analytical method to establish these demand values is a "pushover" analysis in which a model of the building structure is subjected to an invariant distribution of lateral forces. Although such an approach takes into consideration the redistribution of forces following yielding of sections, it does not incorporate the effects of varying dynamic characteristics during the inelastic response. Simple modal combination schemes are investigated in this article to indirectly account for higher mode effects. Because the modes that contribute to deformations may be different from the modes that contribute to forces, it is necessary to identify unique modal combinations that provide reliable estimates of both force and deformation demands. The proposed procedure is applied to typical moment frame buildings to assess the effectiveness of the methodology. It is shown that the envelope of demands obtained from a series of nonlinear static analysis using the proposed modal-combination-based lateral load patterns results in better estimation of inter-story drift, a critical parameter in seismic evaluation and design.     

考虑高阶振型影响的改进的多模态推覆分析方法

将结构静力弹塑性分析与地震反应谱结合起来的Pushover方法是一种简单有效的结构抗震能力评定方法,本文简要介绍了这种方法的原理,并在多模态pushover分析方法的基础上,提出了改进的多模态pushover分析方法,用以建立钢框架结构的能力谱曲线。求解结构在性能点处的响应时,为了考虑高阶振型对结构抗震性能的影响,首次把振型质量参与系数应用到模态推覆分析结果的组合中。通过与弹塑性时程分析的比较,表明本文提出的改进的多模态推覆分析方法是可行的和准确的。     

Seismic capacity of typical high‐rise buildings in Singapore

Pushover analysis is a simplified method to determine the lateral load capacity of buildings. However, recent studies have suggested that pushover analysis could underestimate the capacity by as much as 25%. Thus, this study uses dynamic collapse analysis to determine the overstrength of a 16‐storey and a 25‐storey building, which are typical in Singapore. The results are compared with previously performed pushover analyses to justify the adequacy of pushover analysis for determining the ultimate capacity of such buildings. It is found that the buildings in Singapore, which are not designed for earthquake loads, possess overstrength varying from 4 to 12 times the design strength depending on the type of building. Furthermore, the pushover analysis could underestimate the capacity of such buildings up to 14%. It is suggested that one may choose to adopt pushover analysis to evaluate the lateral load capacity of such high‐rise buildings to err on the conservative side. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical study of the static and dynamic characteristics of reinforced concrete cassette structures for high‐rise buildings

High‐rise buildings are extensively built in China, and the structure of these buildings is composed of different types of conventional system of which framed structures are more commonly employed. A new cassette structure with advantageous performance properties is proposed. Static and dynamic numerical simulations were applied to investigate the characteristics of this new structure. First, the components and other details are presented. A comparative analysis was conducted between the cassette structure and traditional structures using eight finite models with fiber elements in three different heights. A static pushover analysis and an incremental dynamic analysis were conducted based on 18 near‐ground motion records recommended by the Federal Emergency Management Agency. The seismic characteristics, deformation curve, interstory drift, roof displacement, and fragility curve are investigated. Based on the analysis of the models with three different heights and the variety of seismic records, the economic advantage and application of cassette structures for building industrialization are also discussed.     

Prediction of nonlinear seismic demands of high‐rise rocking wall structures using a simplified modal pushover analysis procedure

This study presents a simplified analysis procedure for the convenient estimation of nonlinear seismic demands of high‐rise rocking wall structures. For this purpose, the displacement modification approach used in the nonlinear static procedure of ASCE/SEI 41‐13 is adopted. However, in the current study, this approach is extended to every significant vibration mode of the structure whereas the displacement modifying coefficients for different modes are calculated using the typical flag‐shaped hysteresis behavior of rocking walls. The parameters of this hysteresis behavior are selected to represent rocking walls with a practical range of energy dissipation capacity and postgap‐opening stiffness. The computed peak inelastic‐to‐elastic displacement ratios are presented as mean spectra, which can be used for the convenient estimation of pushover target displacement for every significant vibration mode. The accuracy of proposed procedure is examined using the seismic demands obtained from the nonlinear response history analysis of a 20‐story case study rocking wall structure. Furthermore, a modal decomposition technique is used to determine the individual modal seismic demands. The proposed procedure is found to predict both the combined and the individual modal demands with a reasonable accuracy and can serve as a convenient analysis option for the design and performance evaluation of high‐rise rocking wall systems.     

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.