A broad-range power-law form scalar-based seismic intensity measure

This paper aims at studying the efficiency and robustness of a proposed enhanced broad-range, spectrum shape-dependent, power-law form, scalar-based seismic Intensity Measure (IM). It is intended for estimation of structural performance for probability-based seismic assessment of structures. When traditional IMs are used, such as the peak ground acceleration or the first-mode spectral acceleration, the corresponding Engineering Demand Parameters (EDP) can display large record-to-record variability, forcing the use of many records to achieve reliable results. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. The efficiency of the proposed broad-range IM in reducing the scatter in estimated peak lateral inelastic displacement and ductility demands is investigated herein through an extensive analytical program. The program considers a large database of 80 records and a broad spectrum of first mode-dominant structures encompassing a wide range of design-inherent inelastic displacement demands. Two different constitutive material models representing steel and concrete structures covering scenarios of non-degrading and degrading response are also studied. Statistical results show the versatility and efficiency of the proposed IM in satisfactorily–by minimizing the scatter of the resulting EDPs–dealing with structures designed to undergo various levels of inelastic displacement demands.     

An area‐based intensity measure for incremental dynamic analysis under two‐dimensional ground motion input

Incremental dynamic analysis (IDA) is a useful method in performance‐based earthquake engineering. IDA curves combine the intensity measure (IM) of ground motions with structural responses (as measured by engineering demand parameter) from nonlinear dynamic analysis. However, the curves display large record‐to‐record variability. And various IMs can lead to different results. Therefore, it is important to find a desirable IM to reduce the discreteness of the IDA results. So far, the studies on IM for IDA have been carried out by many scholars from scalar‐valued to vector‐valued, but few were based on 2‐dimensional ground motion input. To make the analysis more reasonable and practical as well as investigate the desirable IM under 2‐dimensional ground motion input, incremental dynamic analyses when ground motions are inputted in 2 directions should be investigated. In this paper, 2 combinational types of area‐based IM incorporating the influence of ground motion record components in secondary directions were proposed. To investigate the applicability, efficiency and desirable combinational form of the area‐based IM under 2‐dimensional ground motion input, incremental dynamic analysis were carried out using 2 reinforced concrete frames. Then the efficiency of the IMs was measured by the residual sum of squares and R². It is concluded that the area‐based IM with a combination by the square root of the sum of the squares (SRSS) method is the most efficient for IDA under 2‐dimensional ground motion input. The methods and conclusions will provide significant reference for studying IMs under 2‐dimensional ground motion input. Further research will focus on the applicability of the area‐based IM for tall buildings whose higher modes need to be considered.     

ISCS method for the performance‐based seismic design of vertically irregular reinforced concrete frame structures

The procedure to obtain the inelastic demand curves for the multi‐degree‐of‐freedom system, composed of inter‐story shear versus inter‐story displacement curve is introduced. The demand curves are established by using mode spectrum method, and the dynamical characteristic of structure under different earthquake hazard levels is taken into account. The relation of structure performance object and displacement ductility is adopted to deduce the relation of structure performance object and inter‐story demand curve. Therefore, the inter‐story demand curves take into account the inelastic behavior of structure under earthquake action adequately. Then, considering the seismic responding characteristic and the capacity curve of the frame structure, a new method named Inter‐Story Capacity Spectrum (ISCS) is put forward for the performance‐based seismic design of vertically irregular frame structures. Examples are presented to demonstrate the applicability and the utility of the proposed method. It is concluded that the new method can control the inter‐story drift, the order and position of hinges of vertically irregular structures under different earthquake hazard levels. Comparing with time‐history analysis method, it leans to safe and is superior to direct displacement‐based design method. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating the peak structural response of high‐rise structures using spectral value‐based intensity measures

With increasing trend towards performance‐based design in earthquake engineering, running nonlinear time history analysis is becoming the routing process to quantify the relationship between ground motions intensity measure (IM) and the structural responses. Because a high‐rise structure contains many higher modes, a newly proposed spectral value‐based IM is presented in this paper to quantify the structural response of high‐rise structures. The newly proposed IM uses the modal participation masses to combine higher modes. An actual high‐rise structure is taken as an example to demonstrate the efficiency of using the newly proposed IM to quantify the peak structural response of high‐rise structures. Five alternative IMs were compared in this study: (a) PGA ‐ peak ground acceleration; (b) S₁ ‐ spectra acceleration with only 1 mode; (c) S^* ‐ modified S₁ with the consideration of period elongation after structure yielded; (d) S₁₂‐ spectra acceleration with 2 modes; and (e) S₁₂₃ ‐ spectra acceleration with 3 modes. Linear regression is fitted between the peak structural response and the IM considered. The IM with the highest correlation coefficient to the engineering demand parameter is considered the most efficient IM. The results show that S₁ has better correlation to the structural response compared with PGA. S₁₂₃ has better correlation than S^* and S₁₂. It is found that the IM with higher modes can provide better correlation than IM with lower number of structural information. For engineering applications, IM with up to 3 modes (S₁₂₃) is sufficient to produce an accurate prediction to quantify the structural response of high‐rise structures.     

基于性能的钢混框架结构多元模糊地震损伤评估

考虑了基于性能设计的位移和能量等多种因素,利用整体损伤指数、最大层问位移角、滞回耗能循环次数和楼层能量集中系数定义了钢筋混凝土框架结构三水准抗震设计的地震损伤性能目标。运用模糊数学中的综合评判方法确定多因素与模糊损伤集合的关系,建立了钢筋混凝土框架结构在地震作用下的多重模糊损伤评估方法。该方法可通过结构推覆分析和能力谱方法实现,并具有准确简单实用的效果。     

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.     

Reliable fragility functions for seismic collapse assessment of reinforced concrete special moment resisting frame structures under near‐fault ground motions

A collapse fragility function shows how the probability of collapse of a structure increases with increasing ground motion intensity measure (IM). To have a more reliable fragility function, an IM should be applied that is efficient and sufficient with respect to ground motion parameters such as magnitude (M) and source‐to‐site distance (R). Typically, pulse‐like near‐fault ground motions are known by the presence of a velocity pulse, and the period of this pulse (T_p) affects the structural response. The present study investigates the application of different scalar and vector‐valued IMs to obtain reliable seismic collapse fragility functions for reinforced concrete special moment resisting frames (RC SMRFs) under near‐fault ground motions. The efficiency and sufficiency of the IMs as the desirable features of an optimal IM are investigated, and it is shown that seismic collapse assessments by using most of the IMs are biased with respect to T_p. The results show that (Sa(T₁), Sa(T₁)/DSI) has high efficiency and sufficiency with respect to M, R, T_p, and scale factor for collapse capacity prediction of RC SMRFs. Moreover, the multiobjective particle swarm optimization algorithm is applied to improve the efficiency and sufficiency of some advanced scalar IMs, and an optimal scalar IM is proposed.     

Nonlinear seismic response of reinforced‐concrete free‐standing towers with application to TV towers on flexible foundations

Reinforced‐concrete (R/C) free‐standing towers such as TV towers are often analysed using elastic analyses as fixed‐base cantilever beams, ignoring the effect of soil–structure interaction. To take the capacity of structures after yielding into account, most designers usually prefer to decrease the peak values of the elastic response spectrum for the maximum credible earthquake (MCE) anticipated at the site by a factor called the ductility capacity factor, which varies with the design earthquake level and the structural characteristics of the structure neglecting the effect of supporting soil. To investigate the effect of foundation flexibility on the response of R/C free‐standing towers deforming into their inelastic range during intense ground shaking, a linear sway‐rocking model is applied in numerical modelling of the soil–structure system. The effect of concrete cracking and reinforcement yielding on the elements used in the structure modelling is taken into account by introducing a nonlinear model for R/C frame elements using the moment–curvature (M–?) relation. A method called pseudo‐dynamic analysis is presented to quantify the inelastic seismic response spectrum of a soil–R/C free‐standing system using response spectrum analysis method and push‐over analysis technique. The earthquake responses of cracked and uncracked systems for a practical TV tower and a practical range of soil shear wave velocity are calculated and compared with the objective of understanding how soil–structure interaction influences structural responses. Copyright © 2002 John Wiley & Sons, Ltd.     

隔震结构动力弹塑性分析地震记录选择的波谱分类法研究

高层隔震结构动力弹塑性时程分析地震记录选择是隔震结构地震响应分析的关键,针对地震记录选取提出基于模糊聚类算法结合地震动强度指标进行地震波子集选取的波谱分类法。首先采用动力弹塑性时程方法对隔震结构的等效单自由度简化模型和三维空间模型进行了地震加速度峰值、地震波速度峰值、地震波位移峰值、地震波速度峰值与加速度峰值之比、加速度反应谱、等效速度反应谱6类地震动强度指标与工程需求参数相关性的比较研究,确定了适合隔震结构的有效地震动强度指标。隔震整体结构工程需求参数包含上部结构层间变形、顶层加速度和隔震层位移响应。其后采用构造的地震动指标矩阵应用于地震波样本属性的表征,并基于模糊聚类算法对地震波样本进行了分类。以某15层高层钢框架-混凝土核心筒隔震结构为例,通过将未分类的地震波集合与分类地震波子集作用下结构的地震响应离散性对比研究,确认了波谱分类法在地震动筛选应用中的有效性。     

Determination of optimal probabilistic seismic demand models for pile-supported wharves

One of the basic components of the Performance-Based Earthquake Engineering (PBEE) framework of Pacific Earthquake Engineering Research (PEER) Center is the probabilistic seismic demand model (PSDM). PSDM is based upon a representative relation between ground motion intensity measures (IMs) and engineering demand parameters (EDPs). This research aims to develop an optimal PSDM for typical pile-supported wharf structures in western US ports by using probabilistic seismic demand analysis (PSDA). In this study, 4 bins with 20 non-near-field ground motions and 7 typical pile-supported wharf structures are used to determine an optimal PSDM by PSDA. The model geometry used in this study has a hybrid configuration incorporating many common field conditions. The optimal PSDM should be practical, sufficient, effective and efficient – all tested through several IM–EDP pairs derived by PSDA. The ground motion IMs used in this study include characteristics such as spectral quantities, duration, energy-related quantities and frequency content. Different EDPs are considered for local, intermediate and global response quantities. The considered optimal PSDM comprises a spectral IM, such as spectral acceleration and one of several EDPs. The EDPs of moment curvature ductility factor, displacement ductility factor and horizontal displacement of embankment and differential settlement between deck and behind land are considered for local, intermediate and global response quantities, respectively. Optimal PSDMs are used within PEER–PBEE framework, where they are coupled with both ground motion intensity and structural element fragility models to yield probabilities of exceeding structural performance levels under certain seismic hazard.     

Estimation of inelastic displacement factor of soil‐shallow‐foundation MDOF systems incorporating higher modes effect

This study attempts to investigate the higher‐mode effects on the constant‐ductility inelastic displacement factors of multi‐degree‐of‐freedom (MDOF) systems considering soil‐structure interaction. These factors were computed for 12,600 two‐dimensional superstructure models of shear buildings and their corresponding equivalent single‐degree‐of‐freedom (ESDOF) systems under 26 ground motions recorded on alluvium and soft soil. An intensive parametric study was carried out for a wide range of non‐dimensional parameters, which completely define the problem. The underlying soil is considered as a homogeneous half‐space based on the concept of cone model. The higher‐mode effects were then investigated through defining the ratio of inelastic displacement factor of MDOF system to that of the corresponding ESDOF one. The influence of soil‐structure interaction key parameters, fundamental period, ductility ratio, the number of stories, and dispersion of the results are evaluated and discussed. Results indicate that as the base becomes very flexible, unlike to the fixed‐base systems, in which the defined ratios are greater than unity, using the inelastic displacement factors of ESDOF models for MDOF ones would result in a remarkable overestimation of maximum inter‐story displacement demand. A new expression is proposed to estimate the ratio of inelastic displacement factor of MDOF soil‐structure systems to that of SDOF counterpart.     

Considering rupture directivity effects,which structures should be named ‘long‐period buildings’?

Recorded accelerograms in the regions near active faults may have specific characteristics that inclusion of their effects on the response of structures is necessary. Of particular importance are permanent displacement, i.e. fling‐step, rupture directivity pulses and high‐frequency content. Several researchers have focused on the effects of rupture directivity pulses on response of structures. They have shown that long‐period structures are severely affected by these types of excitations. However, in near‐fault regions, the question ‘which building structures are long period?’ has not been clearly and quantitatively answered. In this paper, responses of 10‐, 20‐, 30‐ and 40‐story steel structures designed based on Uniform Building Code 1997 regulations are investigated under artificial pulses produced by directivity effects. It is shown that, considering rupture directivity effects, a long‐period structure is the one that has a first‐mode period–to–pulse period ratio greater than about 0.44. Furthermore, the effects of variations in the period of the near‐fault velocity pulses on the characteristics of inelastic response of structures are examined. Consequently, analysis of the structures experiencing actual near‐fault records indicates that the pattern of response spectrum obtained from artificial pulses presents the behavior of the structure under real near‐fault earthquakes rather accurately. Copyright © 2010 John Wiley & Sons, Ltd.     

A temporal hybrid dynamic integration algorithm strategy for inelastic time history analysis of high‐rise reinforced concrete structures under strong earthquakes

A complete earthquake time history analysis (THA) requires a stable, accurate, and efficient dynamic integration algorithm. It is not rare to encounter numerical divergence when some implicit algorithms are used to deal with severe materially or geometrically nonlinearities. For explicit algorithms, computational efficiency is always a major concern. A temporal hybrid dynamic algorithm (THDA) strategy, which is specialized in the inelastic THAs of high‐rise reinforced concrete (RC) structures experiencing severe plasticity development, is developed herein. A preliminary evaluation is carried out on three low‐rise structural models, that is, two frame structures and one wall‐frame structure, for each group of collected implicit algorithms and explicit algorithms. From the evaluation, four alternatives are generated for the subsequent detailed assessment. A general framework for the THDA is proposed and implemented on a finite element analytical platform. The four alternatives are assessed based on their performance on a high‐rise frame core‐tube RC structure. The assessment indicates that the proposed THDA strategy can give rise to a more compatible dynamic integration algorithm for the complete THAs of high‐rise building structures when they are experiencing severe damage. The concerns about the computational stability, accuracy, and efficiency of the dynamic algorithms can be well balanced by the THDA.     

Inelastic behaviour of RC wall‐frame with a rocking wall and its analysis incorporating 3‐D effect

In a reinforced concrete wall‐frame structure, rocking of the wall and the three‐dimensional (3‐D) effect are two important factors influencing the inelastic response of the system. Rocking of the wall about a point close to the compression edge at the wall base induces large elongation along the wall tension chord, resulting in increased rotation demand on beams framing into the wall. The wall vertical elongation also triggers the 3‐D effect, which acts back to play a stabilizing role on the rocking wall. A rational analysis of the above effects requires a realistic consideration of the wall‐neutral axis migration towards the compression side, which, however, is often ignored. This paper aims to extend the relevant existing studies in the following three aspects: (1) the extent to which a rocking wall can affect the system behaviour; (2) the modelling of the wall‐neutral axis migration and its significance; and (3) a quantitative assessment of the 3‐D effect, particularly in terms of its role on controlling wall rocking. Results from a Code‐compatible planar wall‐frame specimen indicate that uncontrolled wall rocking could amount to causing beam–wall connection failure, leading to accelerated deterioration of the entire system. Pushover and dynamic time‐history analyses show that by incorporating wall‐neutral axis migration more satisfactory prediction of the inelastic response of the wall‐frame is produced. A systematic improvement of the wall‐frame inelastic behaviour can be achieved by involving the 3‐D effect. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of foundation flexibility and structural strength on response reduction factor of RC frame structures

Current force‐based design procedure adopted by most seismic design codes allows the seismic design of building structures to be based on static or dynamic analyses of elastic models of the structure using elastic design spectra. The codes anticipate that structures will undergo inelastic deformations under strong seismic events; therefore, such inelastic behaviour is usually incorporated into the design by dividing the elastic spectra by a factor, R, which reduces the spectrum from its original elastic demand level to a design level. The most important factors determining response reduction factors are the structural ductility and overstrength capacity. For a structure supporting on flexible foundation, as Soil Structure Interaction (SSI) extends the elastic period and increases damping of the structure‐foundation elastic system, the structural ductility could also be affected by frequency‐dependent foundation‐soil compliances. For inelastic systems supporting on flexible foundations, the inelastic spectra ordinates are greater than for elastic systems when presented in terms of flexible‐base structure's period. This implies that the reduction factors, which are currently not affected by the SSI effect, could be altered; therefore, the objective of this research is to evaluate the significance of foundation flexibility on force reduction factors of RC frame structures. In this research, by developing some generic RC frame models supporting on flexible foundations, effects of stiffness and strength of the structure on force reduction factors are evaluated for different relative stiffnesses between the structure and the supporting soil. Using a set of artificial earthquake records, repeated linear and nonlinear analyses were performed by gradually increasing the intensity of acceleration time histories to a level, where first yielding of steel in linear analysis and a level in which collapse of the structure in nonlinear analysis are observed. The difference between inelastic and elastic resistance in terms of displacement ductility factors has been quantified. The results indicated that the foundation flexibility could significantly change the response reduction factors of the system and neglecting this phenomenon may lead to erroneous conclusions in the prediction of seismic performance of flexibly supported RC frame structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical model and evaluation of maximum crack width for unbonded PSRC frame beam under short‐term service load

Prestressed steel reinforced concrete (PSRC) beam members have the advantages of both ordinary prestressed concrete and SRC members and are usually applied to the structures with large span or heavy load. They are often designed to crack under service load. In this paper, the service‐load behavior is studied based on the experimental results of four unbonded PSRC frame beam specimens. The cracking behavior, deflection, and strains in tensile reinforcement during service‐load stage are described in detail. A computer program for a simple macroelement analysis approach, based on conventional matrix‐displacement method, is written to predict the response of unbonded PSRC frame beam members under service load. The calculation results by this method agree well with the observed experimental results. Moreover, an approach based on two enacted Chinese codes, one for ordinary concrete members (GB50010‐2010) and another for steel‐concrete composite members (JGJ138‐2001), is provided to calculate the short‐term maximum crack width of PSRC beam members. By comparing with the test results, it implies that this approach can be applied to the evaluation of short‐term maximum crack width.     

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.     

Performance‐based plastic design method for tall hybrid coupled walls

The research presented herein involves a performance‐based design method for a tall hybrid coupled wall (HCW) system. For this study, HCW structures were designed with a performance‐based plastic design (PBPD) method. This approach directly accounts for inelastic structural behavior and considers design lateral force distribution at ultimate limit state. The design concept uses a pre‐selected target drift and yield mechanism as key performance limit states. The yield mechanism consists of shear yielding in the coupling beams and flexural yielding of reinforced concrete walls at the bases. HCW structures with varying heights and coupling ratios (CRs) were designed and subjected to a series of nonlinear dynamic analyses. The results indicated that the CR strongly influences the response of the structure. The structures could also be under‐designed when the inelastic distribution of lateral forces owing to higher modes was not properly considered. Finally, a design method to account for higher mode effects within the PBPD framework was presented. The method was validated using the results from nonlinear analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Nichtlineare Analyse der zeitlichen Antwort von Stahlbeton‐, Spannbeton‐ und Verbundkonstruktionen auf die mechanische Einwirkung und Temperatureinwirkung

Nonlinear Analysis of the Time‐Dependent Response of Reinforced and Prestressed Concrete Structures to Mechanical and Temperature Loads The developed computational procedure for the nonlinear analysis of the time‐dependent response of structures to mechanical loads and to elevated temperature in fire up to failure is limited to plane frame structures. They can be carried out as reinforced or prestressed concrete structures or as steel‐concrete composite structures. The analysis takes into account all types of structural nonlinearities, resulting from the geometry of the structure and from the material properties, including rheology. The computational procedure for the analysis is based on the finite element method. A highly effective finite element P4 is used. Its curvature along the element axis is interpolated using fourth order polynomial. The stress‐strain state of the structure is analysed gradually and iteratively according to the time intervals. The nonlinear equation systems of the structure are solved numerically using the Newton‐Raphson procedure.     

Simplified multi‐degree‐of‐freedom model for estimation of seismic response of regular wall‐frame structures

A simplified multi‐degree‐of‐freedom (MDOF) model is developed for estimation of seismic response of tall wall‐frame structures. By using the continuum technique for the structure and adopting the bilinear hysteretic model for material properties, procedure for the development of the simplified MDOF model is derived. The numerical study for a 20‐storey reinforced concrete (RC) wall‐frame structure is conducted to investigate the accuracy of seismic response predicted by the proposed model. Results from the nonlinear response history analyses based on the proposed MDOF model and the detailed structural model with member‐by‐member representation are compared and show very good agreement. The proposed simplified MDOF model is shown to provide a simple, efficient and accurate method for estimation of seismic performance of tall wall‐frame structures. Copyright © 2009 John Wiley & Sons, Ltd.