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.     

Seismic performance and probabilistic collapse resistance assessment of steel moment resisting frames with fluid viscous dampers

This paper evaluates the seismic resistance of steel moment resisting frames (MRFs) with supplemental fluid viscous dampers against collapse. A simplified design procedure is used to design four different steel MRFs with fluid viscous dampers where the strength of the steel MRF and supplemental damping are varied. The combined systems are designed to achieve performance that is similar to or higher than that of conventional steel MRFs designed according to current seismic design codes. Based on the results of nonlinear time history analyses and incremental dynamic analyses, statistics of structural and non‐structural response as well as probabilities of collapse of the steel MRFs with dampers are determined and compared with those of conventional steel MRFs. The analytical frame models used in this study are reliably capable to simulate global frame collapse by considering full geometric nonlinearities as well as the cyclic strength and stiffness deterioration in the plastic hinge regions of structural steel members. The results show that, with the aid of supplemental damping, the performance of a steel MRF with reduced design base shear can be improved and become similar to that of a conventional steel MRF with full design base shear. Incremental dynamic analyses show that supplemental damping reduces the probability of collapse of a steel MRF with a given strength. However, the paper highlights that a design base shear equal to 75% of the minimum design base shear along with supplemental damping to control story drift at 2% (i.e., design drift of a conventional steel MRF) would not guarantee a higher collapse resistance than that of a conventional MRF. At 75% design base shear, a tighter design drift (e.g., 1.5% as shown in this study) is needed to guarantee a higher collapse resistance than that of a conventional MRF. Copyright © 2014 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.     

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...     

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.     

Semi‐explicit rate‐dependent modeling of damage‐avoidance steel connections using HF2V damping devices

A rate‐dependent modeling technique is developed for moment resisting steel connections that utilize non‐linear viscous dampers. First, a model of the Maxwell‐type is developed that considers the non‐linear viscous damper and connection flexibility for translational motion. This model is compared with experimental results at several input motion frequencies to validate the results. The model is then extended to represent an exterior steel beam‐to‐column connection using damage‐avoidance design and non‐linear viscous dampers. By including terms to represent structural member and connection flexibility, using appropriate geometric transformations the model can be formulated to give the overall lateral load‐drift structural performance. Validation analysis shows good agreement between experimental observations and the model predictions. Copyright © 2010 John Wiley & Sons, Ltd.     

基于黏滞液体阻尼器的铁路钢桁梁桥减震研究

以某高墩大跨度铁路简支钢桁梁桥为实际工程背景,研究了黏滞液体阻尼器对结构纵向抗震性能的影响.采用非线性时程分析方法,对黏滞液体阻尼器的相关参数及布置位置进行了优化分析.分析结果表明:合理选择黏滞液体阻尼器的布置位置、个数及阻尼参数,高墩大跨铁路简支钢桁梁桥具有明显的减震效果.     

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。     

铰接隅撑钢框架抗震性能研究

传统抗弯钢框架的梁柱节点通常设计为刚性连接,这种刚性节点具有很大的抗弯刚度,然而节点延性不足,罕遇地震作用导致节点脆性断裂.研究学者提出了多种解决该问题的思路,例如半刚性连接节点、节点加强或削弱方法使塑性铰外移等.本文提出了一种简化的梁柱节点连接方式-铰接连接,改变梁柱节点的传力方式,在节点处设置隅撑提供框架的抗侧刚度...     

Low cyclic fatigue and hysteretic behavior of U‐shaped steel dampers for seismically isolated buildings under dynamic cyclic loadings

Energy dissipation devices are necessary for base‐isolated buildings to control the deformation in the isolation system and to dissipate the earthquake‐induced energy. U‐shaped steel dampers (also known as U‐dampers) dissipate energy through plastic deformation of specially designed U‐shaped steel elements. This type of device can be installed at several locations in the isolation system. U‐dampers have been widely used in Japan for different types of isolated structures, such as hospitals, plants and residential buildings, since the 1995 Kobe Earthquake. Previous research has used static tests to estimate the performance of U‐dampers. However, the ultimate plastic deformation capacities and hysteretic behaviors of full‐scale U‐dampers under dynamic excitations still remain unclear. In addition, it is unclear whether the initial temperature has an effect on the hysteretic behavior and plastic deformation capacity of U‐dampers. In this paper, two series of dynamic loading tests of U‐dampers were conducted to evaluate the issues described earlier. The major findings of the study are (i) the loading speed has little effect on the plastic deformation capacity of U‐dampers; (ii) method to evaluate the ultimate plastic deformation capacities of U‐shaped steel dampers of different sizes is established using a Manson–Coffin relation‐based equation that is based on the peak‐to‐peak horizontal shear angle γ_t, which is defined as the lateral deformation amplitude (peak‐to‐peak amplitude) divided by the height of the dampers; (iii) the loading rate and the initial temperature have a minimal effect on the hysteretic behavior of the U‐dampers; and (iv) a bilinear model is proposed to simulate the force‐deformation relationships of the U‐dampers. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic design and experiment of single and coupled corner gusset connections in a full‐scale two‐story buckling‐restrained braced frame

A gusset plate is subjected to forces induced from a buckling‐restrained brace (BRB) and frame action. In this study, a performance‐based design method of the gusset connections incorporating a BRB and frame actions is investigated. The force demands resulting from the BRB axial force are computed from the generalized uniform force method. The force demands induced from the frame action effects primarily result from beam shear. A conservative method, which considers the beam axial force effect and the thereafter reduced beam flexural capacity possibly developed at the gusset tips, is adopted in estimating the maximum beam shear. An improved equivalent strut model is used to represent the gusset plate subjected to the frame action effect. The total force demands of the gusset connection are combined from the BRB force and the frame actions. For design purposes, the stress distributions on the gusset interfaces are linearized. The maximum von Mises stress combining the normal and shear stresses is considered as the demand for the gusset plate design. In order to verify the effectiveness of the proposed design method, experiments on a two‐story full‐scale buckling‐restrained braced frame (BRBF) were performed. The chevron and single diagonal brace configurations were arranged in the second and the first stories, respectively. Two different corner gusset connection configurations including one single corner gusset and one coupled corner gusset connection, where two braces in adjacent stories joined at the same beam‐to‐column joint, were tested. The BRBF specimen was subjected to cyclically increasing lateral displacements with a maximum frame drift of 0.04 rad. The maximum story drifts reached 0.035 and 0.061 rad. in the first and the second stories, respectively. At the end of the tests, no fractures were observed on any of the gusset interfaces. Along the gusset interfaces, the normal and shear stress distributions computed from the proposed design procedures and the FEM analysis correlated well with the experimental results. This paper concludes with the procedure and recommendations for the performance‐based design of gusset connections. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic behavior and strength capacity of steel tube‐reinforced concrete composite columns

The steel tube‐reinforced concrete (ST‐RC) composite column is a novel type of composite column, which consists of a steel tube embedded in RC. In this paper, the seismic behavior of ST‐RC columns is examined through a series of experiments in which 10 one‐third scale column specimens were subjected to axial forces and lateral cyclic loading. The test variables include the axial force ratio applied to the columns and the amount of transverse reinforcement. All specimens failed in a flexural mode, showing stable hysteresis loops. Thanks to the steel tube and the high‐strength concrete it is filled with, the ST‐RC column specimens had approximately 30% lower axial force ratios and 22% higher maximum bending moments relative to the comparable RC columns when subjected to identical axial compressive loads. The amount of transverse reinforcement made only a small difference to the lateral load‐carrying capacity but significantly affected the deformation and energy dissipation capacity of the ST‐RC columns. The specimens that satisfied the requirements for transverse reinforcement adopted for medium ductile RC columns as specified by the Chinese Code for Seismic Design of Buildings (GB 50011‐2010) and EuroCode 8 achieved an ultimate drift ratio of around 0.03 and a displacement ductility ratio of approximately 5. The design formulas used to evaluate the strength capacity of the ST‐RC columns were developed on the basis of the superposition method. The predictions from the formulas showed good agreement with the test results, with errors no greater than 10%. Copyright © 2013 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.     

设计参数对高层装配式钢结构建筑抗倒塌能力的影响

以某高层装配式钢结构建筑为研究对象,研究设计参数对其抗倒塌能力的影响,通过ABAQUS有限元软件,对装配式混凝土平面框架的低周反复加载试验进行模拟。结果表明,增大框架柱轴压比可提高结构承载力,在荷载峰值达到后会有较快的降低,显著降低了延性。在荷载低周反复作用下,结构延性、承载力、耗能等随着梁柱线刚度比的降低,抗震指标全部呈现增加趋势。随着梁柱线刚度比的增大,层间位移角沿楼层分布均匀性变得越来越差;由于受到荷载作用低周反复后,会大大增加混凝土的强度,并降低耗能和延性指标,同时结构承载力则略微增大。增大轴压比后,如果保持相同的地震动强度,则将会大大提高结构性能极限状态的可能性,而如果结构的轴压比较大,很可能会出现对地震响应性能水平产生破坏等问题。     

Prediction of the force–drift envelope for RC columns in flexure by the CAE method

A non‐parametric empirical approach, called the conditional average estimator (CAE) method, has been applied for the prediction of the normalized lateral force–drift envelope of reinforced concrete (RC) rectangular columns, as well as their characteristic drifts (effective yield drift, capping drift and ultimate drift), and drift‐related parameters (the ratio between the effective yield drift and elastic drift, and two ductility measures). A subset of the PEER RC column database was used. Five input parameters were employed: axial load index, index related to confinement, shear span index, concrete compressive strength, and longitudinal reinforcement index. The results suggest that the relations between the input and output parameters are complex, and that it is difficult to isolate the influence of a single parameter. Nevertheless, some trends were observed. The axial load index is the most influential input parameter. All the results decrease with an increasing axial load index, whereas they increase with an increasing longitudinal reinforcement index. An increase in the index related to confinement results in increases in the ultimate drift and in ductility. The influence of the shear span index is the most complex. The influence of the concrete strength is small with the exception of two output parameters related to elastic drift, which substantially decrease with increasing strength. The dispersion of the results is relatively large. The results of the predictions can be used for mathematical modelling of moment–rotation backbone curves for plastic hinges, and for the estimation of the deformation capacity of columns in seismic performance assessments. Copyright © 2007 John Wiley & Sons, Ltd.     

考虑阻尼器极限状态的耗能减震体系 斜拉桥抗震性能分析

在大震或特大震下,黏滞阻尼器可能因某个极限状态的出现而发生破坏。现有在斜拉桥上设置黏滞阻尼器的研究多集中在阻尼器的参数优化上,很少考虑到阻尼器失效对斜拉桥抗震性能的影响。针对这一问题,以某三塔斜拉桥为背景,利用OpenSees平台建立斜拉桥有限元模型和可以考虑承载力及行程极限的黏滞阻尼器模型;分析黏滞阻尼器的阻尼系数和阻尼指数对斜拉桥地震响应的影响,确定阻尼器参数的取值;对不安装阻尼器、安装不考虑极限状态及考虑极限状态阻尼器等多种工况的斜拉桥进行非线性时程分析,对比各工况斜拉桥的地震响应。分析结果表明,在大震下,考虑极限状态阻尼器的耗能能力及减震效果将显著降低;不考虑阻尼器达到极限状态后失效的情况将高估耗能减震设计斜拉桥的抗震能力。     

Proposed methodology for building-specific earthquake loss assessment including column residual axial shortening

This paper proposes methodological developments for quantifying the impact of residual axial shortening of first-story steel columns on earthquake loss estimations in steel moment-resisting frame (MRF) buildings. A new formulation is proposed that accounts for the likelihood of having to demolish a steel MRF building due to column residual axial deformations in addition to residual story-drift ratios. The formulation is informed by means of data from a comprehensive survey conducted worldwide to assess the likelihood of steel column repairability due to residual axial shortening. A practical method for quantifying column axial-shortening in parameterized system-level numerical simulations is presented. The proposed approach is illustrated by conducting economic seismic loss estimations in two case-study steel MRF buildings designed in urban California according to the current seismic design practice. It is found that when the ground-motion duration is appreciable, the examined steel MRFs are more prone to column axial-shortening than residual story-drifts at moderate to high seismic intensities. The results suggest that economic losses due to demolition may be underestimated if column residual axial-shortening is neglected from loss estimations. Limitations as well as directions for future research are discussed.     

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。     

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.