Probabilistic economic seismic loss estimation in steel buildings using post‐tensioned moment‐resisting frames and viscous dampers

The potential of post‐tensioned self‐centering moment‐resisting frames (SC‐MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic‐resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC‐MRFs; or (iv) SC‐MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P‐58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post‐tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post‐tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post‐tensioning and supplemental viscous damping by showing that the SC‐MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF. Copyright © 2016 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.     

Seismic design and evaluation of steel moment‐resisting frames with compressed elastomer dampers

This paper evaluates the hysteretic behavior of an innovative compressed elastomer structural damper and its applicability to seismic‐resistant design of steel moment‐resisting frames (MRFs). The damper is constructed by precompressing a high‐damping elastomeric material into steel tubes. This innovative construction results in viscous‐like damping under small strains and friction‐like damping under large strains. A rate‐dependent hysteretic model for the compressed elastomer damper, formed from a parallel combination of a modified Bouc–Wen model and a non‐linear dashpot is presented. The model is calibrated using test data obtained under sinusoidal loading at different amplitudes and frequencies. This model is incorporated in the OpenSees [17] computer program for use in seismic response analyses of steel MRF buildings with compressed elastomer dampers. A simplified design procedure was used to design seven different systems of steel MRFs combined with compressed elastomer dampers in which the properties of the MRFs and dampers were varied. The combined systems are designed to achieve performance, which is similar to or better than the performance of conventional steel MRFs designed according to current seismic codes. Based on the results of nonlinear seismic response analyses, under both the design basis earthquake and the maximum considered earthquake, target properties for a new generation of compressed elastomer dampers are defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Modified capacity design rule for columns in tall steel MRFs with linear viscous dampers within the framework of Eurocode 8

Seismic design codes enforce a set of capacity design rules for steel moment-resisting frames (MRFs) to promote a ductile sway plastic mechanism that involves plastic hinges in beams and column bases. Previous research showed that these capacity design rules may not be effective for tall steel MRFs with viscous dampers under strong earthquakes due to high axial forces in columns. To address this issue, steel MRFs with linear viscous dampers of different stories are designed according to Eurocode 8 along with using a slightly modified conservative capacity design rule. According to this rule, the axial force for the capacity design of a column in the force path of viscous dampers is calculated as the envelope of the axial force from the peak drift state, and, the axial force from the peak velocity state times a scale factor. This envelope axial force value along with the bending moment and shear force from the peak drift state are used to carry out the capacity design of the column by using the formulae of Eurocode 8, i.e. in the same way with a column of a steel MRF without dampers. Incremental dynamic analyses for 44 earthquake ground motions show that the modified conservative capacity design rule results in steel MRFs with viscous dampers that have plastic mechanisms similar to those of steel MRFs without dampers. Moreover, the proposed capacity design rule becomes stricter for buildings with more than 10 stories to address that available analysis methods for structures with dampers underestimate the peak damper forces in the lower stories of yielding tall steel MRFs. More work is needed to extend the findings of this work to the case of steel MRFs with nonlinear viscous dampers.     

Optimal seismic design of moment‐resisting steel frames with hysteretic passive devices

The effectiveness of hysteretic passive devices to protect and mitigate the response of a structure under seismic loading is well established by both analytical and experimental research. Nevertheless, a systematic and well‐established methodology for the topological distribution and size of these devices in order to achieve a desired structural response performance does not exist. In this paper, a computational framework is proposed for the optimal distribution and design of yielding metallic buckling restrained braces (BRB) and/or friction dampers within steel moment‐resisting frames (MRF) for a given seismic environment. A Genetic Algorithm (GA) is used to solve the resulting discrete optimization problem. Specific examples involving two three‐story, four‐bay steel MRFs and a six‐story, three‐bay steel MRF retrofitted with yielding and/or friction braces are considered. The seismic environment consists of four synthetic ground motions representative of the west coast of the United States with 5% probability of exceedance in 50 years. Non‐linear time‐history analyses are employed to evaluate the potential designs. As a result of the evolutionary process, the optimal placement, strength and size of the dampers are obtained throughout the height of the steel MRF. Furthermore, the developed computational approach for seismic design based upon GAs provides an attractive procedure for design of MRFs with hysteretic passive dampers. Copyright © 2009 John Wiley & Sons, Ltd.     

设置黏滞阻尼器的钢结构实用减震设计方法

黏滞阻尼器作为一种有效的消能减震装置,已在钢结构建筑中得到了大量应用.然而由于钢结构的延性和阻尼特征,实用的钢结构附加黏滞阻尼器设计方法仍需深度探讨.文中提出一种基于黏滞阻尼器延性需求的减震设计方法.首先,根据钢结构需求量化层间位移角性能目标及目标附加阻尼比,计算黏滞阻尼器延性需求,并确定黏滞阻尼器布置数量、进行控制效...     

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.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Design formulations for supplemental viscous dampers to highway bridges

Design formulas for supplemental viscous dampers to building structures are readily available in FEMA provisions and MCEER research reports. However, for the design of supplemental viscous dampers corresponding to a desired system damping ratio of highway bridges, there exist, if any, few design guidelines. This is particularly true if the bridge components such as elastomeric bearings, piers and abutment possess different damping ratios, stiffnesses, and lumped masses. In this paper, the design formulas for supplemental viscous dampers to highway bridges have been derived based on the concept of ‘composite damping ratio’. The design formulas can be used to determine the damping coefficients of the dampers corresponding to a desired system damping ratio of the bridge in which different component damping ratios may be assumed for the elastomeric bearings, piers and abutments. The proposed design formulas are numerically validated by comparing the seismic responses of a three‐span bridge equipped with viscous dampers with those of the same bridge without viscous dampers but with an assigned inherent system damping ratio equal to the target system damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Tests and model calibration of high‐strength steel tubular beam‐to‐column and column‐base composite joints for moment‐resisting structures

Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.     

The role of damping in seismic isolation

In the current code requirements for the design of base isolation systems for buildings located at near-fault sites, the design engineer is faced with very large design displacements for the isolators. To reduce these displacements, supplementary dampers are often prescribed. These dampers reduce displacements, but at the expense of significant increases in interstorey drifts and floor accelerations in the superstructure. An elementary analysis based on a simple model of an isolated structure is used to demonstrate this dilemma. The model is linear and is based on modal analysis, but includes the modal coupling terms caused by high levels of damping in the isolation system. The equations are solved by a method that avoids complex modal analysis. Estimates of the important response quantities are obtained by the response spectrum method. It is shown that as the damping in the isolation system increases, the contribution of the modal coupling terms due to isolator damping in response to the superstructure becomes the dominant term. The isolator displacement and structural base shear may be reduced, but the floor accelerations and interstorey drift are increased. The results show that the use of supplemental dampers in seismic isolation is a misplaced effort and alternative strategies to solve the problem are suggested. Copyright © 1999 John Wiley & Sons, Ltd.     

A two‐step direct method for estimating the seismic response of nonlinear structures equipped with nonlinear viscous dampers

The insertion of fluid viscous dampers in building structures is an innovative technology that can improve significantly the seismic response. These devices could be very useful also in the retrofit of existing buildings. The effect of this typology of damping system is usually identified with an equivalent supplemental damping ratio, which depends on the maximum displacement of the structure, so that iterative procedures are required. In this paper, a simplified direct assessment method for nonlinear structures equipped with nonlinear fluid viscous dampers is proposed. The method proposed in this study is composed by two steps. The first one yields the direct estimate of the supplemental damping ratio provided by nonlinear viscous dampers in presence of a linear elastic structural response. The second step extends the procedure to structures with nonlinear behavior. Both graphical and analytical approaches have been developed. The proposed method has then been verified through several applications and comparisons with nonlinear dynamic analyses. Moreover, an investigation has been performed with regard to the influence of the relations that define the damping reduction factor and the hysteretic damping. Copyright © 2014 John Wiley & Sons, Ltd.     

An alternative practical design method for structures with viscoelastic dampers

Viscoelastic dampers (VEDs) are one of the most common passive control devices used in new and retrofit building projects which reduce the structure responses and dissipate seismic energy during an earthquake. Various methods to design this kind of dampers have been proposed based on the desired level of additional damping, eigenvalue assignment, modal strain energy, linear quadratic regulator control theories, and other approaches. In the current engineering practice, the popular method is the one based on the modal strain energy that uses the inter-story lateral stiffness as one of the main variables for damper design. However, depending on the configuration of the structure, in some cases the resulting interstory lateral stiffness can be very large. Consequently, the dampers size would also be large producing much more damping than that effectively necessary, resulting in an increase of the overall cost of the supplemental damping system and causing excessive stress on the structural elements connected to the dampers. In this paper an alternative practical design method for structures with VEDs is proposed. This method uses the inter-story shear forces as one of the main variables to accomplish the damper design compared to what was done in previous studies. Nonlinear time-history analyses were conducted on a 7-story reinforced concrete (RC) structure to check the reliability and effectiveness of the proposed method. Comparisons on the seismic performance between the structure without dampers and that equipped with VEDs were carried out. It is concluded that the proposed method results in a very suitable size of dampers, which are able to improve the performance of the structure at all levels of earthquake ground motions and satisfying the drift requirement prescribed in the codes.     

Seismic performance evaluation of typical dampers designed by Chinese building code

Adding dampers is a commonly adopted seismic risk mitigation strategy for modern buildings, and the corresponding design procedure of dampers has been well established by the Chinese Building Code. Even though all types of dampers are designed by the same procedure, actual seismic performance of the building may differ from one to the others. In this study, a nine-story benchmark steel building is established, and three different and typical types of dampers are designed according to the Chinese Building Code to realize structural vibration control under strong earthquake excitation. The seismic response of the prototype building equipped with a viscoelastic damper, viscous damper and buckling-restrained brace(BRB) subjected to 10 earthquake records are calculated, and Incremental Dynamic Analysis(IDA) is performed to describe progressive damage of the structure under increasing earthquake intensity. In the perspective of fragility, it shows that the viscoelastic damper has the highest collapse margin ratio(CMR), and the viscous damper provides the best drift control. Both the BRB and viscoelastic dampers can effectively reduce the floor acceleration responses in the mid-rise building.     

Damping identification of a full‐scale passively controlled five‐story steel building structure

A series of large‐scale dynamic tests was conducted on a passively controlled five‐story steel building on the E‐Defense shaking table facility in Japan to accumulate knowledge of realistic seismic behavior of passively controlled structures. The specimen was tested by repeatedly inserting and replacing each of four damper types, that is, the buckling restrained braces, viscous dampers, oil dampers, and viscoelastic dampers. Finally, the bare steel moment frame was tested after removing all dampers. A variety of excitations was applied to the specimen, including white noise, various levels of seismic motion, and shaker excitation. System identification was implemented to extract dynamic properties of the specimen from the recorded floor acceleration data. Damping characteristics of the specimen were identified. In addition, simplified estimations of the supplemental damping ratios provided by added dampers were presented to provide insight into understanding the damping characteristics of the specimen. It is shown that damping ratios for the specimen equipped with velocity‐dependent dampers decreased obviously with the increasing order of modes, exhibiting frequency dependency. Damping ratios for the specimen equipped with oil and viscoelastic dampers remained constant regardless of vibration amplitudes, whereas those for the specimen equipped with viscous dampers increased obviously with an increase in vibration amplitudes because of the viscosity nonlinearity of the dampers. In very small‐amplitude vibrations, viscous and oil dampers provided much lower supplemental damping than the standard, whereas viscoelastic dampers could be very efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response of steel frame structures with hybrid passive control systems

The concept of the hybrid passive control system is studied analytically by investigating the seismic response of steel frame structures. Hybrid control systems consist of two different passive elements combined into a single device or system. The hybrid systems investigated in this research consist of a rate‐dependent damping device paired with a rate‐independent energy dissipation element. The innovative configurations exploit individual element strengths and offset their weaknesses through multiphased behavior. A nine‐story, five‐bay steel moment‐frame was used for the analysis. Six different seismic resisting systems were analyzed and compared. The conventional systems included a special moment‐resisting frame (SMRF) and a dual SMRF–buckling‐restrained brace (BRB) system. The final four configurations are hybrid passive systems. The different hybrid configurations utilize a BRB and either a high‐damping rubber damper or viscous fluid damper. The analyses were run in the form of an incremental dynamic analysis. Several damage measures were calculated, including maximum roof drift, base shear, and total roof acceleration. The results demonstrate the capability of hybrid passive control systems to improve structural response compared with conventional lateral systems and to be effective for performance‐based seismic design. Each hybrid configuration improved some aspect of structural response with some providing benefits for multiple damage measures. The multiphased nature provides improved response for frequent and severe seismic events. Copyright © 2011 John Wiley & Sons, Ltd.     

非线性黏滞阻尼减震结构基于位移的设计方法

结合我国抗震设计规范,提出非线性黏滞阻尼减震结构基于位移的设计方法.根据减震结构的特点,将其性能划分为使用良好、人身安全和防止倒塌3个水平,并用层间位移角限值予以量化;以简化的方法计算非线性黏滞阻尼器的等效阻尼比.在此基础上将结构转化为等效单自由度体系,利用基于位移的设计方法对非线性黏滞阻尼减震结构进行设计,通过算例,介绍用该方法对框架结构进行非线性黏滞阻尼减震设计的设计过程.实例分析表明,提出的非线性黏滞阻尼减震结构基于位移的设计方法是可行的,并且与时程分析得出的平均结果吻合较好,而且该方法简单实用,便于操作,能够控制减震结构在不同强度水准地震作用下的性能.     

Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers

This paper presents a direct displacement-based design procedure for seismic retrofit of existing buildings using nonlinear viscous dampers according to equivalent linear systems. Unlike conventional methods, the equivalent linear viscous damping provided by the nonlinear viscous dampers is derived based on the assumption that the average energy dissipated between the linear and the nonlinear viscous dampers is equal. Also, the equivalent period and viscous damping for the equivalent linear systems which are used for representing the behavior of bare frames (the buildings without dampers) are derived from the concept of average storage energy and average dissipated energy, respectively. It is shown from nonlinear time-history analyses that the nonlinear action of the retrofitted structures can be reasonably captured by the presented direct displacement-based procedure.     

台湾某钢框架大楼采用阻尼器补强结构减震效果评析

阻尼器是一种效果良好的减震装置,将阻尼器安装于结构中能够适时为结构体系提供阻尼力,从而减小地震作用对结构的破坏。黏滞阻尼器对振动的反应比较敏感,在结构受到较小振动时就可以发挥其减震效果,其阻尼力会随着振动周期和使用状态温度的不同而变化。当地震发生时,安装在结构中的阻尼器会消减地震作用,降低传导到主结构体系的地震能量,减小结构相对位移。本文介绍了黏滞阻尼器的工作原理和安装有黏滞阻尼器的结构体系的阻尼比的计算方法,对减震结构的减震效果的评析方法做出探讨,并以一安装有黏滞阻尼器的台湾某既有钢框架结构为例,分析了(1)该结构在遭受地震作用时的地震反应;(2)该结构体系在不同地震作用水平时的阻尼比,包括主体结构阻尼比和黏滞阻尼器阻尼比;(3)结构安装黏滞阻尼器后的减震效果。实例对本文的减震评析方法和减震效果进行了说明和分析,计算及分析结果表明利用黏滞阻尼器加固既有结构能够取得较好的减震效果,本文所提减震效果评析方法是一种实用有效的评析方法,对类似工程的减震评析具有一定的参考价值。