Enhanced nonlinear static analysis with the drift pushover procedure for tall buildings

In this study a new method for nonlinear static analysis based on the relative displacements of stories is proposed that is able to be implemented in a single stage analysis and considers the effects of an arbitrary number of higher modes. The method is called the extended drift pushover analysis procedure (EDPA). To define the lateral load pattern, values of the relative displacements of stories are calculated using the elastic modal analysis and the modal combination factors introduced. For determining the combination factors, six different approaches are examined. Buildings evaluated in this study consist of four special steel moment-resisting frames with 10–30 stories. Responses including relative displacements of stories, story shear forces and rotation of plastic hinges in each story are calculated using the proposed approaches in addition to modal pushover analysis and nonlinear dynamic time history analyses. The nonlinear dynamic analysis is implemented using ten consistent earthquake records that have been scaled with regard to ASCE7-10. Distribution of response errors of story shears and plastic hinge rotations show that a major part of error corresponds to the second half of the buildings studied. Thus, the mentioned responses are corrected systematically. The final results of this study show that implementing the EDPA procedure using the third approach of this research is able to effectively overcome the limitations of both the traditional and the modal pushover analyses methods and predict the seismic demands of tall buildings with good accuracy.     

Approximate analysis methods for asymmetric plan base‐isolated buildings

An approximate method for linear analysis of asymmetric‐plan, multistorey buildings is specialized for a single‐storey, base‐isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh–Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single‐storey systems, each with vibration properties and eccentricities (labelled ‘effective eccentricities’) similar to corresponding properties of the isolation system or the fixed‐base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single‐storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh–Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparative assessment of nonlinear static and dynamic methods for analysing building response under sequential earthquake and tsunami

This paper presents a comprehensive comparison of different dynamic and static approaches for assessing building performance under sequential earthquakes and tsunami. A 10-storey reinforced concrete seismically designed Japanese vertical evacuation structure is adopted as a case study for the investigation. The case study building is first assessed under sequential earthquake and tsunami nonlinear response history analyses: the first time this is done in the literature. The resulting engineering demand parameters are then compared with those obtained when the analysis procedure is systematically simplified by substituting different static approaches for the nonlinear response history analyses in both the earthquake and tsunami loading phases. Different unloading approaches are also tested for the cases when an earthquake pushover is adopted. The results show that an earthquake nonlinear response history analysis, followed by a transient free vibration and a tsunami variable depth pushover, provides the best alternative to full dynamic analyses in terms of accuracy and computational efficiency. This structural analysis combination is recommended and has the advantage that it does not require the tsunami inundation time history to be known in advance. The proposed double pushover approach is instead deemed only suitable for the collapse assessment of regular low to mid-rise buildings and for the development of collapse fragility functions. An important observation made is that sustained earthquake damage seems not to affect the tsunami resistance of the case study building when the fully dynamic analysis is carried out for the sequential loading. This observation will be the subject of future work.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

平面不规则混凝土框架结构非线性静力分析侧向力计算方法的研究

针对平面不规则混凝土框架结构，考虑地震作用对其产生的附加扭转振动效应，提出了两种计算侧向力分布的方法。通过对一平面不规则框架结构进行推覆分析，得到各楼层侧移、层间问侧移角和塑性铰分布情况，并与时程分析结果进行了比较分析。结果表明，两种方法推覆分析得到的塑性铰分布情况与时程分析得到的情况相符合，楼层侧移和层间位移角与时程分析结果吻合也较好，并且从结果精度上看，分层法的误差要小一些。     

Response spectrum techniques for asymmetric buildings

A scheme is proposed to calculate the effect of torsion on each lateral load resisting element of asymmetrical buildings in the context of the response spectrum technique. The scheme consists of: (i) Obtain the modal shear and torque on the building by the response spectrum technique, (ii) Compute the total modal shear forces on each frame by resolving the modal shear and torque on the building according to principles of structural mechanics. The shears on each frame due to the lateral load effect and torsional effect are combined algebraically, (iii) Obtain the total shear force on each frame by combining the total modal shears on that frame in a root sum square manner. Since the proper phase relationship between the lateral load effect and torsional effect is accounted for on a modal basis, it is believed that the proposed scheme provides a more realistic load estimate on the frames than the conventional approach. An example of a simplified mono-symmetrical frame structure is chosen to illustrate the accuracy of the proposed scheme, using dynamic time-history analysis as a standard for comparison.     

On the evaluation of seismic response of structures by nonlinear static methods

In the most recent seismic codes, the assessment of the seismic response of structures may be carried out by comparing the displacement capacity, provided by nonlinear static analysis, with the displacement demand. In many cases the code approach is based on the N2 method proposed by Fajfar, which evaluates the displacement demand by defining, as an intermediate step, a single degree‐of‐freedom (SDOF) system equivalent to the examined structure. Other codes suggest simpler approaches, which do not require equivalent SDOF systems, but they give slightly different estimation of the seismic displacement demand. The paper points out the differences between the methods and suggests an operative approach that provides the same accuracy as the N2 method without requiring the evaluation of an equivalent SDOF system. A wide parametric investigation allows an accurate comparison of the different methods and demonstrates the effectiveness of the proposed operative approach. Copyright © 2009 John Wiley & Sons, Ltd.     

钢筋混凝土高层建筑抗震时程分析选波方法比较研究

针对钢筋混凝土高层建筑抗震时程分析输入地震波选择问题,以《建筑抗震设计规范》（GB 50011-2016）设计谱为目标谱,将满足谱匹配原则的加权调幅选波方法与国内学者建议的其它输入地震波选择方法进行了对比研究。以3栋钢筋混凝土高层建筑（15层、30层和44层）为实例,针对8度罕遇地震作用和Ⅱ类场地条件,将上述方法建议的各7条地震波输入结构进行弹塑性时程分析。以结构最大层间位移角均值沿楼层分布为比较参数。结果表明:加权调幅法可用于钢筋混凝土高层建筑抗震时程分析,可以较好地降低结构地震反应均值的离散性。在8度罕遇地震作用条件下,以不同学者建议选择的地震波为输入,高层建筑时程分析结果仍呈现出较大的不同。     

Code‐based record selection methods for seismic performance assessment of buildings

The recent concerns regarding the seismic safety of the existing building stock have highlighted the need for an improvement of current seismic assessment procedures. Alongside with the development of more advanced commercial software tools and computational capacities, nonlinear dynamic analysis is progressively becoming a common and preferable procedure in the seismic assessment of buildings. Besides the complexity associated with the formulation of the mathematical model, major issues arise related with the definition of the seismic action, which can lead to different levels of uncertainty in terms of local and global building response. Aiming to address this issue, a comparative study of different code‐based record selection methods proposed by Eurocode 8, ASCE41‐13 and NZS1170.5:2004 is presented herein. The various methods are employed in the seismic assessment of four steel buildings, designed according to different criteria, and the obtained results are compared and discussed. Special attention is devoted to the influence of the number of real ground motion records selected on the estimation of the mean seismic response and, importantly, to the efficiency that is achieved when an additional selection criteria, based on the control of the spectral mismatch of each individual record with respect to the reference response spectrum, is adopted. The sufficiency of the methods with respect to the pairs of M–R of the selected group of records and the robustness of the scaling procedure are also examined. The paper closes with a study which demonstrates the suitability of a simplified probability‐based approach recently proposed for estimating mean seismic demands. Copyright © 2015 John Wiley & Sons, Ltd.     

Prediction of the largest peak nonlinear seismic response of asymmetric buildings under bi-directional excitation using pushover analyses

A simplified procedure is proposed to predict the largest peak seismic response of an asymmetric building to horizontal bi-directional ground motion, acting at an arbitrary angle of incidence. The main characteristics of the proposed procedure is as follows. (1) The properties of two independent equivalent single-degree-of-freedom models are determined according to the principal direction of the first modal response in each nonlinear stage, rather than according to the fixed axis based on the mode shape in the elastic stage; the principal direction of the first modal response in each nonlinear stage is determined based on pushover analysis results. (2) The bi-directional horizontal seismic input is simulated as identical spectra of the two horizontal components, and the contribution of each modal response is directly estimated based on the unidirectional response in the principal direction of each. (3) The drift demand at each frame is determined based on four pushover analyses considering the combination of bi-directional excitations. In the numerical example, nonlinear time-history analyses of six four-story torsionally stiff (TS) asymmetric buildings are carried out considering various directions of seismic inputs, and these results are compared with the predicted results. The results show that the proposed procedure satisfactorily predicts the largest peak response displacement at the flexible-side frame of a TS asymmetric building.     

高层建筑结构静力弹塑性分析的Pushover-QR法

将QR法与Pushovcer分忻方法相结合,提出了高层建筑结构静力弹塑性分析的Pushover-QR（PO-QR）法。该方法沿用了常规Pushover方法进行抗震结构静力弹塑性分析的实施思路,用QR法代替Pushover分析方法中的有限元部分,充分利用这两种方法的优点,使得抗震结构静力弹塑性分析的计算得到较大的简化。PO-QR法程序的工程算例表明,该法是一种经济、有效、可行的分析方法。     

Lateral force distributions for the linear static analysis of base-isolated buildings

This paper presents a new approach for the evaluation of accurate lateral force distributions for the Linear Static Analysis (LSA) of Base Isolated (BI-) buildings. In essence, the proposed lateral force distributions depend on a factor measuring the degree of non- linearity of the Isolation System (IS) and on the ratio between the effective period of the BI-structure (T_is) and the fundamental period of the Fixed Based (FB-) structure (T_fb). The proposed approach is fully compatible with the Direct Displacement-Based Design (DDBD) method, recently developed by Priestley and co-workers. The proposed lateral force distributions have been derived from the results of a large number of Nonlinear Time-History Analyses (NTHA), carried out on six numerical models of multi-storey buildings, differing in storey number (3, 5 and 8, respectively) and fundamental period of vibration (from 0.25 to 0.8 s) in the fixed-base configuration. A great variety of Isolation Systems (ISs), characterised by either Elasto-Plastic with Hardening (EPH) or Flag-Shaped (FS) force-displacement behaviour, have been considered in the NTHA. The numerical parameters of the IS models have been varied in such a way as to reproduce the actual mechanical behaviour of the main currently used ISs, including: (i) Lead Rubber Bearings (LRB), (ii) High-Damping Rubber Bearings (HDRB), (iii) Friction Pendulum Bearings (FPB), (iv) combinations of flat Sliding Bearings (SB) and Low-Damping Rubber Bearings (LDRB) and (v) Combinations of flat SB and re-centring devices based on Shape Memory Alloys (SMA). Comparisons between the storey shear forces derived with the proposed method and those obtained from NTHA clearly show the great improvements in the accuracy of LSA predictions, when using the proposed lateral force distributions.     

Corrective eccentricities for assessment by the nonlinear static method of 3D structures subjected to bidirectional ground motions

Nonlinear static methods are reliable in the evaluation of the seismic response of planar structural schemes, but they are not very effective in the assessment of three-dimensional building structures. The authors of this paper have recently proposed a nonlinear static approach for asymmetric structures, which is an improvement on that stipulated by seismic codes. This method is based on the observation that the distribution of the maximum dynamic displacements of the deck can be enveloped by two pushover analyses performed by applying the lateral force with two eccentricities with respect to the center of mass of the deck. These eccentricities, named “corrective eccentricities”, are defined so that the two corresponding pushover analyses provide displacements that are equal to those evaluated by nonlinear dynamic analysis at the two sides of the deck. In this paper, the corrective eccentricities are determined for a wide set of single-story systems. The equations for their analytical evaluation are determined and their reliability is demonstrated. Finally, the analysis of a multi-story structure is conducted to show how the method can be applied to real buildings. Copyright © 2012 John Wiley & Sons, Ltd.     

Benchmarking the software packages to model and assess the seismic response of unreinforced masonry existing buildings through nonlinear static analyses

Bulletin of Earthquake Engineering - Seismic modelling of unreinforced masonry (URM) buildings is addressed worldwide according to different approaches, not only at research level, but also in the...     

Free vibration of asymmetric shear wall-frame buildings

The Galerkin method of weighted residuals is used to determine the frequencies and associated mode shapes of asymmetric shear wall-frame structures. The governing equations are formulated using the continuum approach by idealizing the structure as a shear-flexure beam. Varying properties along the height of the building are considered. The effect of translational, rocking and torsional flexibilities of the foundation on the natural frequencies is also investigated. The method presented herein utilizes polynomial and transcendental displacement functions, and is found to be simple, versatile and efficient.     

Seismic code analysis of multi-storey asymmetric buildings

Static torsional provisions in most seismic codes require that the lateral force at each floor level be applied at some distance from the reference centre at that floor. However, codes do not specify how to determine the locations of these centres. As a result, several different definitions of the reference centres are being used to implement the code analysis. This investigation examined how the results using various reference centres differ and which of these centres would lead to results that are in agreement with those of dynamic analysis. For this purpose three different buildings ranging form torsionally stiff to torsionally flexible were analysed. It was shown that for the class of buildings studied in this investigation that although the locations of the reference centres were quite different, the results were very similar and nearly independent of the reference centre. Comparison of results calculated from static code equivalent lateral force procedures and results from dynamic response spectrum analyses showed that the static code procedures led to design forces very close (flexible wall) or slightly conservative (stiff wall) when compared to the dynamic analysis for the torsionally stiff building. However, the static code procedures significantly underestimated the design forces of the stiff walls and significantly overestimated the design forces of the flexible walls for the torsionally flexible buildings. © 1998 John Wiley & Sons, Ltd.     

A nonlinear macroelement model for the seismic analysis of masonry buildings

The macroelement technique for modelling the nonlinear response of masonry panels is particularly efficient and suitable for the analysis of the seismic behaviour of complex walls and buildings. The paper presents a macroelement model specifically developed for simulating the cyclic in‐plane response of masonry walls, with possible applications in nonlinear static and dynamic analysis of masonry structures. The model, starting from a previously developed macroelement model, has been refined in the representation of flexural–rocking and shear damage modes, and it is capable of fairly simulating the experimental response of cyclic tests performed on masonry piers. By means of two internal degrees of freedom, the two‐node macroelement permits to represent the coupling of axial and flexural response as well as the interaction of shear and flexural damage. Copyright © 2013 John Wiley & Sons, Ltd.     

An analytical method for the evaluation of the in-plan irregularity of non-regularly asymmetric buildings

This paper describes a new method for the evaluation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ of uncoupled torsional to lateral frequencies in real multi-storey buildings. The above-mentioned parameters greatly affect the lateral-to-torsional coupling of the response of asymmetric systems and thus are of paramount importance in the assessment of the in-plan irregularity of buildings. The proposed method, which is a generalization of that suggested by Calderoni et al. (Earthq Spectra 18(2):219–231, 2002), allows the calculation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ from the structural response to arbitrary distributions of forces and torsional couples. The effectiveness of the method is validated on some regularly and non-regularly asymmetric buildings characterised by different in-plan irregularity. The analyses demonstrate that the results of the method are rigorous in the case of regularly asymmetric systems and only slightly depend upon the heightwise distribution of the forces in the case of non-regularly asymmetric systems. Finally, the values of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ resulting from the proposed method are compared to those obtained by means of the procedure suggested by Makarios and Anastassiadis in (Struct Des Tall Spec Build 7(1):33–55, 1998a; Struct Des Tall Spec Build 7(1):57–71, 1998b) .     

A modified static procedure for the design of torsionally unbalanced multistorey frame buildings

Seismic building codes include design provisions to account for the torsional effects arising in torsionally unbalanced (asymmetric) buildings. These provisions are based on two alternative analytical procedures for determining the design load for the individual resisting structural elements. A previous study has shown that the linear elastic modal analysis procedure may not lead to conservative designs, even for multistorey buildings with regular asymmetry, when such structures are excited well into the inelastic range of response. The equivalent static force procedure as recommended by codes may also be deficient in accounting for additional ductility demand in the critical stiff-edge elements. This paper addresses the non-conservatism of existing static torsional provisions and examines aspects of element strength distribution and its influence on inelastic torsional effects. A recommendation is made for improving the effectiveness of the code-type static force procedure for torsionally unbalanced multistorey frame buildings with regular asymmetry, leading to a design approach which estimates conservatively the peak ductility demand of edge elements on both sides of the building. The modified approach also retains the simplicity of existing code provisions and results in acceptable levels of additional lateral design strength. It has recently been adopted by the new Australian earthquake code, which is due to be implemented early in 1993.     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.