Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of residual drift demands in regular multi‐storey frames for performance‐based seismic assessment

This paper summarizes results of a comprehensive analytical study aimed at evaluating the amplitude and heightwise distribution of residual drift demands in multi‐storey moment‐resisting frames after earthquake excitation. For that purpose, a family of 12 one‐bay two‐dimensional generic frame models was subjected to an ensemble of 40 ground motions scaled to different intensities. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record‐to‐record variability in the estimation of residual drift demands. The results were statistically processed in order to evaluate the influence of ground motion intensity, number of stories, period of vibration, frame mechanism, system overstrength, and hysteretic behaviour on central tendency of residual drift demands. In addition, a special emphasis was given to evaluate the uncertainty in the estimation of residual drift demands. Results of incremental dynamic analyses indicate that the amplitude and heightwise distribution of residual drift demands strongly depends on the frame mechanism, the heightwise system structural overstrength and the component hysteretic behaviour. An important conclusion for performance‐based assessment is that the evaluation of residual drift demands involves significantly larger levels of uncertainty (i.e. record‐to‐record variability) than that of maximum drift demands, which suggests that this variability and corresponding uncertainty should be explicitly taken into account when estimating residual drift demands during performance‐based seismic assessment of frame buildings. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic drift demands in multi‐storey cross‐laminated timber buildings

This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.     

Residual drift demands in moment‐resisting steel frames subjected to narrow‐band earthquake ground motions

This paper presents the main results of the evaluation of residual inter‐story drift demands in typical moment‐resisting steel buildings designed accordingly to the Mexican design practice when subjected to narrow‐band earthquake ground motions. Analytical 2D‐framed models representative of the study‐case buildings were subjected to a set of 30 narrow‐band earthquake ground motions recorded on stations placed in soft‐soil sites of Mexico City, where most significant structural damage was found in buildings as a consequence of the 1985 Michoacan earthquake, and scaled to reach several levels of intensity to perform incremental dynamic analyses. Thus, results were statistically processed to obtain hazard curves of peak (maximum) and residual drift demands for each frame model. It is shown that the study‐case frames might exhibit maximum residual inter‐story drift demands in excess of 0.5%, which is perceptible for building's occupants and could cause human discomfort, for a mean annual rate of exceedance associated to peak inter‐story drift demands of about 3%, which is the limiting drift to avoid collapse prescribed in the 2004 Mexico City Seismic Design Provisions. The influence of a member's post‐yield stiffness ratio and material overstrength in the evaluation of maximum residual inter‐story drift demands is also discussed. Finally, this study introduces response transformation factors, T_p, that allow establishing residual drift limits compatible with the same mean annual rate of exceedance of peak inter‐story drift limits for future seismic design/evaluation criteria that take into account both drift demands for assessing a building's seismic performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Probabilistic collapse resistance and residual drift assessment of buildings with fluidic self‐centering systems

The seismic performance of three‐ and six‐story buildings with fluidic self‐centering system is probabilistically assessed. The fluidic self‐centering systems consist of devices that are based on the technology of fluid viscous dampers but built in a way that pressurization of the devices results in preload that is explored to reduce or eliminate residual drift. The design of these buildings followed a procedure that parallels the design for structures with damping systems in ASCE 7 but modified to include the preload effect. Reference conventional buildings were also designed per ASCE 7 for comparison. These buildings were then analyzed to examine and compare their seismic collapse resistance and residual drift, where the residual drift limits of 0.2, 0.5, 1.0 and 2.0% of story height were selected as important thresholds. The study further calculated the mean annual frequency of collapse and corresponding exceedance probability over 50 years, and the mean annual frequency of exceeding the threshold residual story drift limits and the corresponding exceedance probability over 50 years. Variations in the design procedures by considering increased displacement capacity or damping or preload of the devices, different types of damping, increased ultimate strength of the self‐centering device–brace systems and increased frame strength were considered. It was found that increasing either the ultimate force capacity of the self‐centering device–brace system or the frame strength results in important improvements in the collapse resistance and in minimizing residual drift, whereas the variation of other design parameters has minor effects. Copyright © 2016 John Wiley & Sons, Ltd.     

Ductility demands of tall buildings subjected to base rocking induced by Rayleigh waves

Performance-based earthquake engineering requires accurate estimation of structural response associated with different damage states because of strong ground motion. In recent work (Meza-Fajardo and Papageorgiou, 2018, EESD), we demonstrated that a significant contribution to the response of elastic soil-structure systems for high-rise buildings is attributed to base rocking associated with Rayleigh waves. The present paper presents results of a study investigating the effects of Rayleigh waves on the response of soil-structure systems with nonlinear behavior at the level of the superstructure. By introducing a rigid-elastic rotational spring at the base of the building, we take into account the stiffness reduction due to damage to the lateral load-resisting system at its root, and with it, increased displacement demands. Considering different levels of ductility and post-yield stiffness, we investigate the impact of rocking because of Rayleigh waves on maximum and residual interstory drift ratios. Our results indicate that rocking due to surface waves should be an important consideration for design and evaluation of tall buildings, as inelastic action elongates their effective natural period, and consequently, they are more prone to be damaged by resonance and excitation of extended duration because of Rayleigh waves.     

轻钢龙骨房屋足尺模型低周反复试验

对一个具有完整边界条件的轻钢龙骨体系房屋足尺模型进行了低周反复试验。试验主要考虑转角墙对轻钢龙骨体系房屋抗震性能的影响,以及龙骨壁厚对复合承载墙体破坏模式的影响,研究房屋在低周反复荷载作用下的变形过程、破坏特征和滞回性能等。试验结果表明:轻钢龙骨房屋的抗震性能与自攻螺钉连接性能密切相关。自攻螺钉的连接性能决定了轻钢龙骨房屋的耗能机制、耗能能力以及破坏形态。由于螺钉在该结构中分布广泛,使得结构的侧向变形能力和耗能能力较好,同时,试验验证了轻钢龙骨复合墙体抗剪承载力计算时关于自攻螺钉连接受力方向的假设和受力大小分析结果的正确性。     

Effectiveness of simple approaches in mitigating residual deformations in buildings

Developments in performance‐based seismic design and assessment approaches have emphasized the importance of considering residual deformations. Recent investigations have also led to a proposed direct displacement‐based design (DDBD) approach which includes an explicit consideration of the expected residual deformations as an integral part of the design process. Having estimated the expected residual deformations in a structure, engineers are faced with the problem of reducing them to meet the targeted performance levels under pre‐defined seismic hazard levels. Previous studies have identified the post‐yield stiffness as a primary factor influencing the magnitude of residual deformations in single degree of freedom and multiple degree of freedom structures. In this paper, a series of simple approaches to increase the post‐yield stiffness of traditional framed and braced systems for the purpose of reducing residual deformations are investigated. These methods do not utilize recentring post‐tensioned technology. This contribution addresses the feasibility of altering the lateral post‐yield stiffness of structural systems by: (i) using different reinforcement materials with beneficial features in their stress–strain behaviour; (ii) re‐designing the section geometry and properties of primary seismic‐resisting elements; and (iii) introducing a secondary elastic frame to act in parallel with the primary system. The efficiency of each of these techniques is investigated through monotonic and cyclic moment‐curvature and non‐linear time‐history analyses. Of these approaches the design and introduction of an elastic secondary system was found to be most effective and consistent in reducing residual deformations. A simplified design approach for achieving the desired increase of a system's post‐yield stiffness is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 John Wiley & Sons, Ltd.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

A probabilistic framework for estimating the residual drift of idealized SDOF systems of non‐degrading conventional and damped structures

This paper presents a general framework for predicting the residual drift of idealized SDOF systems that can be used to represent non‐degrading structures, including those with supplemental dampers. The framework first uses post‐peak oscillation analysis to predict the maximum ratio of residual displacement to the peak transient displacement in a random sample. Then, residual displacement ratios obtained from nonlinear time‐history analyses using both farfield and near‐fault‐pulse records were examined to identify trends, which were explained using the oscillation mechanics of SDOF systems. It is shown that large errors can result in existing probability models that do not capture the influence of key parameters on the residual displacement. Building on the observations that were made, a general probability distribution for the ratio of residual displacement to the peak transient displacement that more accurately reflects the physical bounds obtained from post‐peak oscillation analysis is proposed for capturing the probabilistic residual displacement response of these systems. The proposed distribution is shown to be more accurate when compared with previously proposed distributions in the literature due to its explicit account of dynamic and damping properties, which have a significant impact on the residual displacement. This study provides a rational basis for further development of a residual drift prediction tool for the performance‐based design and analysis of more complex multi‐degree‐of‐freedom systems.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic behavior of steel buildings with out‐of‐plumb

A structure that has a permanent offset from a true vertical line is commonly referred to as being ‘out‐of‐plumb’. Out‐of‐plumb may result from construction tolerances or post‐earthquake permanent deformations in steel buildings. This paper quantifies the displacements of buildings with out‐of‐plumb in subsequent seismic events by means of inelastic dynamic time history analysis. Structures considered have different structural heights, force design reduction factors (R), and target inter‐story drifts. It is shown that buildings with greater out of plumb and force design reduction factor have larger normalized peak inter‐story drift ratio and ratio of residual‐to‐peak drift. Also, the ratio of residual‐to‐peak drift was not strongly dependent on structural height or design drift. A design procedure and example provided, based on the results obtained, show how peak and residual inter‐story drift ratio can be estimated. Copyright © 2015 John Wiley & Sons, Ltd.     

Collapse risk and residual drift performance of steel buildings using post-tensioned MRFs and viscous dampers in near-fault regions

The potential of post-tensioned self-centering moment-resisting frames (SC-MRFs) and viscous dampers to reduce the collapse risk and improve the residual drift performance of steel buildings in near-fault regions is evaluated. For this purpose, a prototype steel building is designed using different seismic-resistant frames, i.e.: moment-resisting frames (MRFs); MRFs with viscous dampers; SC-MRFs; and SC-MRFs with viscous dampers. The frames are modeled in OpenSees where material and geometrical nonlinearities are taken into account as well as stiffness and strength deterioration. A database of 91 near-fault, pulse-like ground motions with varying pulse periods is used to conduct incremental dynamic analysis (IDA), in which each ground motion is scaled until collapse occurs. The probability of collapse and the probability of exceeding different residual story drift threshold values are calculated as a function of the ground motion intensity and the period of the velocity pulse. The results of IDA are then combined with probabilistic seismic hazard analysis models that account for near-fault directivity to assess and compare the collapse risk and the residual drift performance of the frames. The paper highlights the benefit of combining the post-tensioning and supplemental viscous damping technologies in the near-source. In particular, the SC-MRF with viscous dampers is found to achieve significant reductions in collapse risk and probability of exceedance of residual story drift threshold values compared to the MRF.     

Structure-soil-structure interaction of adjacent buildings subjected to seismic loading

The problem of the through-soil coupling of structures has puzzled the researchers in the field for a long while, especially regarding the varied performance of identical, adjacent buildings in earthquakes. The phenomenon of structure-soil-structure interaction (SSSI) that has often been overlooked is recently being recognized: The possible effects in urban regions are yet to be thoroughly quantified. In this respect, the goal of this work was to rigorously investigate the interacting effects of adjacent buildings in a two-dimensional setting. Detailed finite element models of 5-, 15-, and 30-story structures, realistically designed, were used in forming building clusters on the viscoelastic half-space. Perfectly matched layers were used to properly define the half-space boundaries. The interaction of the structure and the soil medium because of the presence of spatially varying ground motion on the boundary of excavated region was considered. The effects of the foundation material and the distance between adjacent buildings on the structural behavior of the neighboring buildings were investigated using drift ratios and base shear quantities as the engineering demand parameters of interest. The effects of SSSI, first investigated in the frequency domain, was then quantified in the time domain using suites of appropriate ground motions in accordance with the soil conditions, and the results were compared with the counterpart SSI solution of a single building. The results showed that, for identical low-rise structures, the effects of SSSI were negligible. Yet, neglecting SSSI for neighboring closely spaced high-rise structures or building clusters with a large stiffness contrast was shown to lead to a considerable underestimation of the true seismic demands even compared with solutions obtained using the rigid base assumption.     

高层钢结构基于均匀损伤设计的整体抗震能力提高方法

本文主要研究如何通过合理设计来提高高层钢结构的整体抗震能力。首先,给出了高层钢结构的非线性计算模型;其次,建立了高层钢结构在强地震动作用下的倒塌失效模式的极限状态判别准则;然后,通过模态pushover分析,研究了高层钢结构在水平地震作用下的损伤规律;最后,重点研究了高层钢结构的整体抗震能力的提高方法,提出了均匀损伤的设计方法,该方法通过消除结构的薄弱层,来达到提高高层钢结构的整体抗震能力的目的。通过对两栋20层的高层钢框架结构进行极限时程分析和极限pushover分析,验证了文中提出的均匀损伤的设计方法的可行性。本文的工作可为高层钢结构的抗地震倒塌设计提供参考依据。     

高层钢结构地震失效模式控制的失效路径修正法

本文主要研究高层钢框架结构的地震失效模式及其控制方法。首先,给出了高层钢结构的地震失效模式的分析方法;其次,提出了根据结构的失效路径来加强构件对高层钢结构的地震失效模式进行控制的方法;然后,提出了结构整体抗震能力的分析方法以及分别相应于设计能力和屈服能力的能力储备分析方法;最后,通过对一座15层的钢框架结构进行典型地震动下的极限时程分析和极限pushover分析,得到高层钢框架结构的失效模式和整体抗震能力以及相应于最弱失效模式的能力储备,并验证了本文中地震失效模式控制方法的有效性。本文的研究表明,高层钢结构的地震失效模式控制可以采用结构失效路径修正(薄弱构件加强)来实现。     

Response of tall buildings to base rocking induced by Rayleigh waves

By now, it is well known that long‐period surface waves can induce resonant response in high‐rise buildings, in particular those located in sedimentary basins. Rayleigh wave passage has been reported to induce rocking motion at the base of the buildings which can increase displacement demands significantly. However, the building behavior to base rocking has not been extensively studied because commercially available instruments do not record rotational components of ground motion, and thus, rocking time histories have not been available to the analysts. In a recent study, we proposed an effective method for estimating the rocking associated with Rayleigh waves, which takes into account their frequency‐dependent phase velocities. In the present work, we select a number of recorded seismic motions which include surface waves on sedimentary basins from recent well‐recorded earthquake events. Then, we proceed to identify and extract the recorded surface waves by using the technique mentioned above. Using realistic soil‐structure analytical models that have been proposed in the published literature for high‐rise buildings, we study their response to Rayleigh waves as they respond to both translational and rocking motions. Of particular interest is to compare the response of such structures with and without the presence of rotational motions due to surface waves. Using the roof displacement and the building interstory drift as response quantities, our results indicate that demands are controlled by rotational (rocking) motions associated with Rayleigh waves.