Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

Model‐based predicting and correcting algorithms for substructure online hybrid tests

A set of algorithms combined with a substructure technique is proposed for an online hybrid test framework, in which the substructures are encapsulated by a standard interface that implements displacements and forces at the common substructure boundaries. A coordinator equipped with the proposed algorithms is designed to achieve boundary compatibility and equilibrium, thereby endowing the substructures the ability to behave as one piece. A model‐based predictor and corrector, and a noniterative procedure, characterize the set of algorithms. The coordinator solves the dynamics of the entire structure and updates the static boundary state simultaneously by a quasi‐Newton procedure, which gradually formulates the condensed stiffness matrix associated with corresponding degrees of freedom. With the condensed stiffness matrix and dynamic information, a condensed equation of motion is derived and then solved by a typical time integration algorithm. Three strategies for updating the condensed stiffness matrix are incorporated into the proposed algorithms. Each adopts different stiffness matrix during the predicting and correcting stage. These algorithms are validated by two numerical substructure simulations and a hybrid test. The effectiveness and feasibility are fully demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Extension of direct displacement‐based design methodology for bridges to account for higher mode effects

An improvement is suggested to the direct displacement‐based design (DDBD) procedure for bridges to account for higher mode effects, the key idea being not only the proper prediction of a target‐displacement profile through the effective mode shape method (wherein all significant modes are considered), but also the proper definition of the corresponding peak structural response. The proposed methodology is then applied to an actual concrete bridge wherein the different pier heights and the unrestrained transverse displacement at the abutments result in an increased contribution of the second mode. A comparison between the extended and the ‘standard’ DDBD is conducted, while further issues such as the proper consideration of the degree of fixity at the pier's top and the effect of the deck's torsional stiffness are also investigated. The proposed methodology and resulting designs are evaluated using nonlinear response‐history analysis for a number of spectrum‐compatible motions. Unlike the ‘standard’ DDBD, the extended procedure adequately reproduced the target‐displacement profile providing at the same time a good estimate of results regarding additional design quantities such as yield displacements, displacement ductilities, etc., closely matching the results of the more rigorous nonlinear response‐history analysis. However, the need for additional iterations clearly indicates that practical application of the proposed procedure is feasible only if it is fully ‘automated’, that is, implemented in a software package. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance‐based earthquake engineering assessment of a self‐centering,post‐tensioned concrete bridge system

Highway bridges in highly seismic regions can sustain considerable residual displacements in their columns following large earthquakes. These residual displacements are an important measure of post‐earthquake functionality, and often determine whether or not a bridge remains usable following an earthquake. In this study, a self‐centering system is considered that makes use of unbonded, post‐tensioned steel tendons to provide a restoring force to bridge columns to mitigate the problem of residual displacements. To evaluate the proposed system, a code‐conforming, case‐study bridge structure is analyzed both with conventional reinforced concrete columns and with self‐centering, post‐tensioned columns using a formalized performance‐based earthquake engineering (PBEE) framework. The PBEE analysis allows for a quantitative comparison of the relative performance of the two systems in terms of engineering parameters such as peak drift ratio as well as more readily understood metrics such as expected repair costs and downtime. The self‐centering column system is found to undergo similar peak displacements to the conventional system, but sustains lower residual displacements under large earthquakes, resulting in similar expected repair costs but significantly lower expected downtimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Inelastic seismic response of stiffening systems and development of demand spectrum: Application to MSSS bridges

A stiffening system is a system that increases its stiffness as it goes under large displacements. Such behavioural characteristic can result from constitutive behaviour or at the structural level often from closure of gaps between various components (sub‐systems) of the structure. An example of the latter situation is multi‐span simply supported (MSSS) bridges under horizontal earthquake ground motion. Unlike softening systems, stiffening systems have not been studied. In addition to the need for more understanding of the seismic response of stiffening systems, there is a need to develop response spectrum that can be used in design. Several parameters including gap size and ratios of sub‐systems stiffness, strength, and mass control the behaviour of a stiffening system. In this study, a simplified stiffening model is developed and over 367 000 cases are analysed to investigate the nonlinear stiffening behaviour and pounding. Parameters considered also include ground motion characteristic. Results are evaluated and compared in terms of displacement and dissipated hysteretic energy. Parameter study results show that, on average, the displacement response is lower for stiffening systems, however, they dissipates higher hysteretic energy, due to higher yield cycles and yield excursions, and can possibly sustain more damage than a bilinear, elastic–plastic system. Using parameter study database, design response spectrum for stiffening systems is also proposed and its practical application is demonstrated through its application to an MSSS bridge. Results of this study goes beyond MSSS bridges and will have application for many structural systems where response is characterized by a stiffening behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Centralized semi‐active control of post‐tensioned steel frames

Centralized semi‐active control is a technique for controlling the whole structure using one main computer. Centralized control systems introduce better control for relatively short to medium high structures where the response of any story cannot be separated from the adjacent ones. In this paper, two centralized control approaches are proposed for controlling the seismic response of post‐tensioned (PT) steel frames. The first approach, the stiffness control approach, aims to alter the stiffness of the PT frame so that it avoids large dynamic amplifications due to earthquake excitations. The second approach, deformation regulation control approach, aims at redistributing the demand/strength ratio in order to provide a more uniform distribution of deformations over the height of the structure. The two control approaches were assessed through simulations of the earthquake response of semi‐actively and passively controlled six‐story post‐tensioned steel frames. The results showed that the stiffness control approach is efficient in reducing the frame deformations and internal forces. The deformation regulation control approach was found to be efficient in reducing the frame displacements and generating a more uniform distribution of the inter‐story drifts. These results indicate that centralized semi‐active control can be used to improve the seismic performance of post‐tensioned steel frames. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic response control of smart sliding isolated buildings using variable stiffness systems: an experimental and numerical study

Effectiveness of a new semiactive independently variable stiffness (SAIVS) device in reducing seismic response of sliding base isolated buildings is evaluated analytically and experimentally. Through analytical and experimental study of force—displacement behaviour of the SAIVS device, it is shown that the device can vary stiffness continuously and smoothly between minimum and maximum stiffness. Passive sliding base isolation systems reduce interstorey drifts and superstructure accelerations, but with increased base displacements, which is undesirable, under large velocity near fault pulse type earthquakes. It is a common practice to incorporate non‐linear passive dampers into the isolation system to reduce bearing displacements. Incorporation of passive dampers, however, may result in increased superstructure accelerations and drifts; while, properly designed passive dampers can be beneficial. A viable alternative is to use semiactive variable stiffness systems, which can vary the period of the sliding base isolated buildings in real time, to simultaneously reduce bearing displacements and superstructure responses further than the passive systems, which deserves investigation. This study investigates the performance of a 1:5 scaled smart sliding base isolated building model equipped with the SAIVS device analytically and experimentally, under near fault earthquakes, by developing a new moving average non‐linear tangential stiffness control algorithm for control of the SAIVS device. The SAIVS device reduces bearing displacements further than the passive cases, while maintaining isolation level forces and superstructure responses at the same level as the passive minimum stiffness case, indicating the significant potential of the SAIVS system. Copyright © 2005 John Wiley & Sons, Ltd.     

A simple image‐based strain measurement method for measuring the strain fields in an RC‐wall experiment

A simple image‐based method for measuring plane strain fields on the surface of specimens in earthquake engineering experiments was developed. This method integrated camera calibration, stereo triangulation, image metric rectification and image template matching techniques to develop a method that was cost‐effective, easy to apply and provided a satisfactory level of measurement accuracy. A zero‐strain test conducted using this method showed that the measurement accuracy achieved was 0.04 pixels. That is, the relative displacement accuracy achieved was 0.005 mm and the strain accuracy was 0.001. This level of accuracy was achieved using eight‐mega‐pixel digital cameras to measure a 17 cm × 28 cm measurement region. Cracks that were 0.012 mm wide were identified in the concrete by examining the displacement fields calculated through the application of this image‐based method in an RC‐wall experiment. Copyright © 2011 John Wiley & Sons, Ltd.     

Post‐earthquake damage assessment using residual displacements

This paper presents a new, improved, post‐earthquake damage assessment method that takes into account residual deformations attained by the damaged structure during the earthquake. Local and global residual deformations and visual damage indicators are considered to estimate the maximum deformations experienced by the structure. As a particular development, the method allows measured displacements and rotations to be considered jointly. Uncertainties associated with both the excitation and the damaged structure are explicitly accounted for. The resulting maximum displacement estimates allow a more accurate evaluation of the extent of structural damage when judging the usability/reparability of the investigated structure. A trial application of the method to a real structure tested on a shaking table is presented. The results confirm the capability of the method to estimate the maximum displacement and the residual stiffness of the damaged structure. Copyright © 2011 John Wiley & Sons, Ltd.     

Study of a semi‐active stiffness damper under various earthquake inputs

Semi‐active stiffness damper (SASD) is one of many semi‐active control systems with the capability to mitigate the dynamic response using only a small amount of external power. The system consists of a hydraulic damper connected to the bracing frame in a selected story unit. In this paper, study of a SASD in two building models of five‐stories under four benchmark earthquake records is reported. The purpose of this study is to evaluate the effectiveness of the control system against structure type and varying earthquake inputs. Various control laws are chosen to work with SASD, such as: resetting control, switching control, linear quadratic regulator (LQR) and modified LQR, and the results are compared with no control and passive control cases. Numerical results show that the use of a SASD is effective in reducing seismic responses. Control effectiveness is dependent on the type of structure and earthquake excitation. Passive control is less effective than other control cases as expected. Resetting control, switching control and LQR generally perform similarly in response reduction. While modified LQR is more efficient and robust compared with other control algorithms. Copyright © 2002 John Wiley & Sons, Ltd.     

Experimental multi‐level seismic performance assessment of 3D RC frame designed for damage avoidance

This paper experimentally investigates the application of damage avoidance design (DAD) philosophy to moment‐resisting frames with particular emphasis on detailing of rocking interfaces. An 80% scale three‐dimensional rocking beam–column joint sub‐assembly designed and detailed based on damage avoidance principles is constructed and tested. Incremental dynamic analysis is used for selecting ground motion records to be applied to the sub‐assembly for conducting a multi‐level seismic performance assessment (MSPA). Analyses are conducted to obtain displacement demands due to the selected near‐ and medium‐field ground motions that represent different levels of seismic hazard. Thus, predicted displacement time histories are applied to the sub‐assembly for conducting quasi‐earthquake displacement tests. The sub‐assembly performed well reaching drifts up to 4.7% with only minor spalling occurring at rocking beam interfaces and minor flexural cracks in beams. Yielding of post‐tensioning threaded bars occurred, but the sub‐assembly did not collapse. The externally attached energy dissipators provided large hysteretic dissipation during large drift cycles. The sub‐assembly satisfied all three seismic performance requirements, thereby verifying the superior performance of the DAD philosophy. Copyright © 2007 John Wiley & Sons, Ltd.     

Energy‐based hysteresis and damage models for deteriorating systems

The low‐cycle fatigue model presented in the companion paper is employed for developing hysteresis and damage models for deteriorating systems. The hysteresis model performs strength reduction at a current displacement cycle by evaluating the loss in the energy dissipation capacity along the completed displacement path. Hence it is completely memory dependent. Pinching is accounted for implicitly by a reduced energy dissipation capacity in a displacement cycle. The model predicts the experimental results obtained from variable‐amplitude tests reasonably well. Response analysis under earthquake excitations reveals that both the maximum displacements and the number of large‐amplitude displacement response cycles increase significantly with the reduction in energy dissipation capacity, resulting in higher damage. Damage is defined as the deterioration in the effective stiffness of a displacement cycle, which is in turn related to the reduction in the energy dissipation capacity. A simple damage function is developed accordingly, consisting of displacement and fatigue components. It is observed that the fatigue component of damage is more significant than the displacement component for deteriorating systems under ground motions with significant effective durations. Copyright © 2003 John Wiley & Sons, Ltd.     

Earthquake‐resistant structural design through energy demand and capacity

An energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 John Wiley & Sons, Ltd.     

Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation

In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd.     

水平地震作用下建筑顶层重力荷载能力研究

地震灾害的发生给人们的生命财产安全带来了极大的威胁,为了保障在地震发生时建筑的安全,需要时刻对试件的荷载、初始刚度、延性系数、建筑模型的竖向位移等信息进行检测,一旦重力荷载高于峰值荷载,建筑安全将不能得到保障。为分析水平地震作用下建筑的顶层重力荷载能力,首先建立用于实验的一榀三层三跨式的房屋建筑模型,检测这种模型处于重力荷载作用情况下的侧向刚度,用来了解在建筑顶层结构在处于水平地震作用情况下重力荷载对其检测刚度的影响程度。然后从模型中选取5个试件,对这些试件的材料属性、实验结果、荷载位移进行分析,再通过实验模型的重力荷载位移曲线确定建筑的峰值荷载为700 kN,即当建筑顶层的峰值荷载超过700 kN时,建筑的安全性将难以保证。     

Structural and nonstructural performance of a seismically isolated building using stable unbonded fiber‐reinforced elastomeric isolators

Stable unbonded fiber‐reinforced elastomeric isolators (SU‐FREIs) exhibit a characteristic horizontal softening and stiffening response, similar to other adaptive devices such as the triple friction pendulum and sliding systems with variable curvature. The transition between the softening and stiffening occurs at a displacement corresponding to a unique deformation known as full rollover. In this paper, the full rollover displacement of SU‐FREIs is altered by using modified support geometry (MSG), a geometric modification of the upper and lower supports applied to tailor the hysteresis loops of the isolator. Experimental results are used to calibrate a numerical model of a base‐isolated structure. The model demonstrates that the stiffening regime provides minimal restraint against displacements during events that meet or exceed the maximum considered earthquake. A parametric study revealed that the level of stiffening required to restrain displacements during large events is significant. This increase in stiffness is reflected in an increase in the response of the structure and light nonstructural components. Full rollover and MSG is considered advantageous to maintain horizontal stability and provide control over the stiffening of SU‐FREIs. Copyright © 2015 John Wiley & Sons, Ltd.     

强震下混凝土剪力墙受弯模拟及测试实验研究

为提高混凝土剪力墙受弯性能计算的准确度,开展强震下混凝土剪力墙受弯性能试验研究。选取1个混凝土剪力墙对比试件和3个测试试件作为研究对象,对试件施加垂直荷载和水平荷载,模拟强烈地震作用力。试验前期准备工作完成后,建立分离式有限元模型,通过计算混凝土在受压和受拉状态下的损伤弹塑性刚度,完成对有限元模型中混凝土塑性损伤分析,在此基础上,计算混凝土剪力墙受弯承载力。利用有限元模型对3个测试试件进行模拟试验,结果表明,强烈地震后3个试件的荷载-位移曲线均与实际位移值接近,且混凝土剪力墙受弯承载力试验结果与实际值的误差在2%以内,表明试验研究方法具有一定的可行性,数值模拟结果较为准确。     

Prediction of elastic displacement response spectra in Europe and the Middle East

Empirical equations are presented for the prediction of displacement response ordinates for damping ratios of 2, 5, 10, 20 and 30% of critical and for response periods up to 4s, using 532 accelerograms from the strong‐motion databank from Europe and the Middle East. The records were all re‐processed and only employed for regressions at periods within the usable range, defined as a fraction of the filter cut‐off and depending on the instrument type (digital or analogue), earthquake magnitude and site class. The equations can be applied to predict the geometric mean displacement and pseudo‐acceleration spectra for earthquakes with moment magnitudes ( M ) between 5 and 7.6, and for distances up to 100km. The equations also include style‐of‐faulting and site class as explanatory variables. The predictions obtained from these new equations suggest that earlier European equations for spectral displacements underestimate the ordinates at longer periods as a result of severe filtering and the use of the spectral ordinates at periods too close to the filter cut‐off. The results also confirm that the period defining the start of the constant displacement plateau in the Eurocode 8 (EC8) spectrum is excessively short at 2s. The results not only show that the scaling factor defined in EC8 for estimating the spectral ordinates at damping ratios different from 5% of critical are a good general approximation, but also that this scaling varies with magnitude and distance (reflecting the influence of duration) and also displays a mild dependence on response period. Copyright © 2007 John Wiley & Sons, Ltd.     

Reduction of structural response to near fault earthquakes by seismic isolation columns and variable friction dampers

<正>This paper focuses on the investigation of a hybrid seismic isolation system with passive variable friction dampers for protection of structures against near fault earthquakes.The seismic isolation can be implemented by replacing the conventional columns fixed to the foundations by seismic isolating ones.These columns allow horizontal displacement between the superstructure and the foundations and decouple the building from the damaging earthquake motion.As a result, the forces in the structural elements decrease and damage that may be caused to the building by the earthquake significantly decreases.However,this positive effect is achieved on account of displacements occurring in the isolating columns.These displacements become very large when the structure is subjected to a strong earthquake.In this case,impact may occur between the parts of the isolating column yielding their damage or collapse.In order to limit the displacements in the isolating columns,it is proposed to add variable friction dampers.A method for selecting the dampers' properties is proposed.It is carried out using an artificial ground motion record and optimal active control algorithm.Numerical simulation of a seven-story structure shows that the proposed method allows efficient reduction in structural response and limits the displacements at the seismic isolating columns.     

Seismic design and response evaluation of unbonded post‐tensioned hybrid coupled wall structures

This paper presents an analytical investigation on the seismic design and response of coupled wall structures that use unbonded post‐tensioned steel coupling beams. Both monolithic cast‐in‐place reinforced concrete wall piers and precast concrete wall piers are considered. Steel top and seat angles are used at the coupling beam ends for energy dissipation. The seismic design of prototype structures to achieve target displacement‐based performance objectives is evaluated based on nonlinear static and dynamic time history analyses. Additional recommendations are provided on shear design. Comparisons with ‘conventional’ structures that use embedded steel coupling beams as well as isolated walls with no coupling are provided. The results indicate that while the peak lateral displacements of unbonded post‐tensioned coupled wall structures are larger than the peak displacements of structures with embedded beams, the residual displacements are significantly reduced as a result of the restoring effect of the post‐tensioning steel. Copyright © 2008 John Wiley & Sons, Ltd.