A consecutive modal pushover procedure for nonlinear static analysis of one-way unsymmetric-plan tall building structures

Seismic responses of unsymmetric-plan tall buildings are substantially influenced by the effects of higher modes and torsion. Considering these effects, in this article, the consecutive modal pushover (CMP) procedure is extended to estimate the seismic demands of one-way unsymmetric-plan tall buildings. The procedure uses multi-stage and classical single-stage pushover analyses and benefits from the elastic modal properties of the structure. Both lateral forces and torsional moments obtained from modal analysis are used in the multi-stage pushover analysis. The seismic demands are obtained by enveloping the peak inelastic responses resulting from the multi-stage and single-stage pushover analyses. To verify and appraise the procedure, it is applied to the 10, 15, and 20-storey one-way unsymmetric-plan buildings including systems with different degrees of coupling between the lateral displacements and torsional rotations, i.e. torsionally-stiff (TS), torsionally-similarly-stiff (TSS) and torsionally-flexible (TF) systems. The modal pushover analysis (MPA) procedure is implemented for the purpose of comparison as well. The results from the approximate pushover procedures are compared with the results obtained by the nonlinear response history analysis (NL-RHA). It is demonstrated that the CMP procedure is able to take into account the higher mode influences as well as amplification or de-amplification of seismic displacements at the flexible and stiff edges of unsymmetric-plan tall buildings. The extended procedure can predict to a reasonable accuracy the peak inelastic responses, such as displacements and storey drifts. The CMP procedure represents an important improvement in estimating the plastic rotations of hinges at both flexible and stiff sides of unsymmetric-plan tall buildings in comparison with the MPA procedure.     

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.     

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 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.     

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.     

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.     

竖向不规则结构非线性静力推覆分析的水平侧向力研究

非线性静力分析方法可以较为简便地预估结构的弹塑性反应,但仅取常见水平侧向力分布模型并不能满足实际工程的需要,例如高振型的影响和不规则结构的特殊性。对竖向不规则结构进行非线性时程分析,建立了水平侧向力分布与结构层刚度的关系式,从而提出了一种新的水平侧向力分布形式和方法。结合几种常见的水平侧向力形式,对5种侧向刚度不规则的情况进行了推覆分析,并与时程分析结果进行了比较,结果表明该方法不但可以找到各种侧向刚度不规则结构的薄弱层而且还具有较高的精度。     

Target roof displacement of degrading moment-resisting frames

In application of the nonlinear static procedure or static pushover analysis for estimating seismic demands of building components due to an earthquake ground motion, the peak (target) roof displacement needs to be estimated so as to quantify the global seismic demand. Most of the methods for this estimation are based on using the response of an equivalent single-degree-of-freedom (SDF) system that does not explicitly account for degradation behaviour. Hence, these methods may not be suitable for use in reinforced-concrete (RC) buildings. This study proposes that the equivalent SDF system should include the effects of degradation and its degrading properties can be determined from cyclic pushover analyses. The accuracy of the proposed method is investigated by comparing the peak roof displacements of RC moment-resisting frame buildings estimated by the proposed degrading equivalent SDF systems to the ‘reference’ value determined by nonlinear response history analysis of multi-degree-of-freedom (MDF) system building models. It was found that the use of the degrading equivalent SDF systems can predict the peak roof displacement more accurately than using non-degrading, or bilinear, equivalent SDF systems, especially in the case of non-ductile RC frames with significant degradation.     

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.     

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.     

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.     

Multi-mode pushover procedure for deformation demand estimates of steel moment-resisting frames

The main objective of the paper is the development and evaluation of a multi-mode pushover procedure for the approximate analysis of the seismic response of steel moment-resisting frames. A generalized force vector derived from modal combination simulates the instantaneous force distribution acting on the structure when the interstorey drift reaches its maximum value during dynamic response to a seismic excitation. Considering the interstorey drift for each floor, a set of generalized force vectors (each associated to maximum drift at one story) is applied separately to the structure until the corresponding target interstorey drift is attained. The maximum value of each response parameter is obtained from the envelope of results. This multi-run and multi-mode pushover procedure allows a simple implementation, reducing the computational effort compared with adaptive nonlinear static procedures and with nonlinear response history analysis. Furthermore, it does not suffer from the statistical combination of inelastic modal responses calculated separately. Both effectiveness and accuracy are verified through a comparative study involving regular steel moment resisting frames subjected to various acceleration records. The results are finally compared with those obtained from other nonlinear static procedures and with the “exact” values from nonlinear response history analysis. It is demonstrated that the proposed procedure is able to accurately predict the seismic demands of steel moment-resisting frames. In low- and middle-rise frames, the error of interstorey drift ratios of the proposed procedure is in the range 5.8-20.8% when the intensity level of the input ground motion varies in the range 0.2-0.8 g. In high-rise frames the error of interstorey drift ratios is in the range 6.38-20.9%.

     

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.     

框架——剪力墙结构的静力弹塑性分析研究

静力弹塑性方法作为一种评价结构抗震性能和计算结构弹塑性变形的简化方法,近年来得到了广泛应用。但由于传统的定侧力模式的静力弹塑性方法只考虑第一振型,无法反映高层建筑结构的高阶振型影响。为考虑高阶振型的影响,Chopra在振型分解反应谱组合法的基础上,提出了MPA方法。本文首先讨论了应用MPA方法需注意的问题,然后用一个18层钢筋混凝土框架—剪力墙结构为算例,以逐步增量弹塑性时程分析结果为基准,对传统定侧力模式静力弹塑性方法和MPA方法的分析结果进行了对比研究。结果表明,相比于定侧力模式静力弹塑性分析结果,MPA方法的分析结果更接近弹塑性时程分析结果。     

Effect of vertical structural irregularity on seismic design of tall buildings

Many tall buildings are practically irregular as an entirely regular high‐rise building rarely exists. This study is thus devoted to assessing the approach and coefficients used in the seismic design of real‐life tall buildings with different vertical irregularity features. Five 50‐story buildings are selected and designed using finite element models and international building codes to represent the most common vertical irregularities of reinforced concrete tall buildings in regions of medium seismicity. Detailed fiber‐based simulation models are developed to assess the seismic response of the five benchmark buildings under the effect of 40 earthquake records representing far‐field and near‐source seismic scenarios. The results obtained from a large number of inelastic pushover and incremental dynamic analyses provide insights into the local and global seismic response of the reference structures and confirm the inferior local response of tall buildings with severe vertical irregularities. Due to the significant impacts of the severe irregularity types on the seismic response of tall buildings, the conservative code approach and coefficients are recommended for design. It is also concluded that although the design coefficients of buildings with moderate irregularities are adequately conservative, they can be revised to arrive at more consistent safety margins and cost‐effective designs.     

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.     

考虑高阶振型影响的非自适应Pushover分析方法的研究进展

近年来,Pushover分析方法作为一种评估建筑结构抗震性能的方法得到了广泛的应用,而且已经被列入许多国家的建筑抗震设计规范之中。由于传统的Pushover分析方法存在许多不足之处,为此很多学者进行了深入的研究并提出了一系列的改进方法。本文结合模态非耦联弹塑性时程分析方法的基本理论,简述了多种考虑高阶振型影响的非自适应Pushover分析方法,并将其中一些方法的分析结果与采用非线性时程分析方法所得的结果进行比较,评价了它们的准确性,最后指出这些Pushover分析方法存在的问题和未来发展方向。     

华润大厦超限高层的抗震性能化设计

《高层建筑混凝土结构技术规程》(JGJ 3—2010)新增加了第3.11节:结构抗震性能设计,使高层的抗震设防目标有了更进一步的深化和发展。以南宁华润大厦超限高层为工程实例,采用基于性能设计的抗震分析方法,细化了各构件在各阶段的抗震性能目标。采用多种有限元分析软件,针对超限高层详细进行了小震振型反应谱分析、中震作用下的屈服判别法分析、大震作用下的弹塑性静力推覆分析、跨多层通高柱的屈曲分析,并基于分析结果提出了该工程结构的超限抗震加强措施,保证了超限结构的安全可靠,为同类工程设计提供借鉴。     

Pushover方法的准确性和适用性研究

Pushover方法作为一种建筑结构弹塑性地震响应的简化近似计算方法和抗震性能评价方法已得到广泛应用。但由于其理论基础不严密,其准确性需要给予必要确认,同时其适用性也应受到一定的限制。本文以逐步增量弹塑性时程方法的结果为基准,分别以一个普通6层RC框架结构和一个18层RC框架-剪力墙结构为例,对Pushover方法的准确性和适用性进行了分析研究。结果表明,Pushover方法仅适用于以第一振型为主的高度不大的结构,且应采用两种以上的侧力模式;对于高阶振型影响较大的结构,该方法的准确性较差,承载力预测显著偏低。