Strength and stiffness reduction factors for infilled frames with openings

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence of infill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.     

Equating incremental dynamic analysis with static nonlinear analysis at near-field excitation

In an incremental dynamic analysis(IDA) using a set of ground motion records,nonlinear time history analysis needs to be performed on structures.It is well recognized that IDA calls for high computational efforts and the results are highly sensitive to selected ground motions.As a result,alternative static methods are needed.This study aims to introduce a new double-stage(N1- N2) static method to estimate capacity curves of MR frames.The technique is regulated to resemble IDA results with specific emphasis on near-field ground motions.Using an ensemble of 56 near-field earthquake records,required ID As have been carried out for SAC-Los Angeles 3-,9- and 20-story buildings and an additional 15-story building.The results of the proposed static method are compared with those from IDA,displacement-based adaptive procedure(DAP),and multimodal procedure(MMP).The results indicate that in addition to enhanced accuracy,very little time is required in the case of N1-N2 method.Thus,for the 3-story structure,the time required is less than 1 minute.The proposed N1-N2 method shows the best accuracy in terms of lateral mechanisms for the 15-story frame while for the other cases,the first mode load pattern leads to the best accuracy.     

On the stability of colonnade structural systems under static and dynamic loading conditions

The structural behavior of colonnade structural systems subjected to static and dynamic loading is investigated to identify the main factors affecting the stability and to improve our understanding of their behaviour. In particular, the discrete element method of analysis is utilised to study the static and dynamic behaviour of a typical section of the two storey colonnade of the Forum in Pompeii. Static analysis indicated that the failure of colonnade structures occur at higher friction angles as the weight above the structure decreases and so a sudden collapse can occur when parts of the monument are disassembled. For the dynamic analysis, the mechanical behavior of the colonnade was investigated for both harmonic and real seismic excitations. For excitations with relatively low dominant frequencies, the primary response is rocking; as the excitation frequency increases, the response becomes more complicated demonstrating both sliding and rocking movements. It was also shown that the construction methods used in ancient times, such as multi-block segmented trabeations and solid block beam, have quite significant impact on the mechanical response of the structures under static and dynamic loading.     

A higher order continuum model for the dynamic shear behaviour of multi-storey frames

A continuum model is developed to predict the response of multi-storey frames to dynamic excitations. The equations of the proposed theory are derived in a systematic manner using smoothing operations. The order of the theory is kept arbitrary. To appraise the validity of the theory natural frequencies and vibration shapes predicted by discrete and continuum models are compared. This comparison provides valuable information about goodness of the proposed model because natural frequencies and vibration shapes represent spectral structure of the theory. The most crucial finding obtained from the analysis is that, as an implication of the smoothing operations used in the derivation of the theory, one should define an effective height which is equal to the height of the frame plus half of the height of the top storey. The numerical results indicated that the use of effective height in the analysis improves the prediction of the theory considerably. It is found also that the number of modes the continuum model can describe correctly increases with the number of storeys and that the lowest number of storeys for which the theory can be used is three. Further, it is observed that an increase in the order of the theory improves greatly its prediction and that in the presence of non-uniform distributions of frame properties, such as, of mass, stiffness, etc., the theory still remains valid.     

Load distribution in large pile groups under static and dynamic loading

Research on the action of pile groups in resisting lateral loading is usually based on analysis, field and centrifuge tests of small pile groups. The interaction between piles in these groups is modelled by modifying the lateral resistance p–y curves developed for a single pile using row dependent reduction factors or a group factor for the entire group to simulate the effect of soil–pile–soil interaction. The modifying factors for the p–y curves and the appropriate group factors for pile groups are based entirely on static tests and there is no direct verification that these factors are appropriate to handle the dynamic loading of earthquake induced ground motions. In this paper we investigate the interaction effects between piles under static and seismic loading using the computer program VERSAT-P3D, which uses an equivalent linear constitutive model for the soil. The analytical procedure is calibrated using data from a static field load test on a single pile. Several pile groups, 2 × 2, 3 × 3, 4 × 4, 5 × 5, 8 × 8, 10 × 10, 10 × 2 and 15 × 2 were analysed for the study. Each group was subjected to static pushover and earthquake loading and the distribution of static and dynamic shear forces at various lateral displacements were evaluated. The study shows that the distribution of load within a pile group under dynamic loading varies significantly from the distribution under static loading and is strongly load intensity dependent. Current practice assumes that the distributions are similar.     

A study on the seismic behavior of a retrofitted building based on nonlinear static and dynamic analyses

This study describes the seismic performance of an existing five storey reinforced concrete building which represents the typical properties of low-rise non-ductile buildings in Turkey. The effectiveness of shear walls and the steel bracings in retrofitting the building was examined through nonlinear static and dynamic analyses. By using the nonlinear static analysis, retrofitted buildings seismic performances under lateral seismic load were compared with each other. Moreover, the performance points and response levels of the existing and retrofitting cases were determined by way of the capacity-spectrum method described in ATC-40 (1996). For the nonlinear dynamic analysis the records were selected torepresent wide ranges of duration and frequency content. Considering the change in the stiffness and the energy dissipation capacities, the performance of the existing and retrofitted buildings were evaluated in terms of story drifts and damage states. It was found that each earthquake record exhibited its own peculiarities, dictated by frequency content, duration, sequence of peaks and their amplitude. The seismic performance of retrofitted buildings resulted in lower displacements and higher energy dissipation capacity depending mainly on the properties of the ground motions and the retrofitting strategies. Moreover, severe structural damage (irreparable or collapse) was observed for the existing building. However, buildings with retrofit alternatives exhibited lower damage levels changing from no damage to irreparable damage states.     

Numerically based proposals for the stiffness and strength of masonry infills with openings in reinforced concrete frames

Aimed at investigating the effect of openings on the in‐plane behaviour of masonry infills in reinforced concrete frames, a parametric study is presented based on model calibration via experimental tests. Two types of openings are investigated: central window openings and different combinations of door and window openings based on the typologies of southern European countries. First, a finite element model of the structure is made using the DIANA software program. Then, after calibration with experimental results, a parametric analysis is carried out to investigate the effect of the presence and location of the different types of openings on the in‐plane behaviour of the infilled frame. Finally, different equations for predicting the initial stiffness and lateral strength of infilled frames with any types of openings were obtained. An α factor related to the geometry of the piers between openings is proposed to take into account the location of the openings in the developed equations. Subsequently, the masonry infill panel is replaced by a diagonal strut. An empirical equation is also proposed for the width of an equivalent strut to replace a masonry infill panel with openings in such a way that they possess the same initial stiffness. Copyright © 2015 John Wiley & Sons, Ltd.     

Lateral stiffness estimation in frames and its implementation to continuum models for linear and nonlinear static analysis

Continuum model is a useful tool for approximate analysis of tall structures including moment-resisting frames and shear wall-frame systems. In continuum model, discrete buildings are simplified such that their overall behavior is described through the contributions of flexural and shear stiffnesses at the story levels. Therefore, accurate determination of these lateral stiffness components constitutes one of the major issues in establishing reliable continuum models even if the proposed solution is an approximation to actual structural behavior. This study first examines the previous literature on the calculation of lateral stiffness components (i.e. flexural and shear stiffnesses) through comparisons with exact results obtained from discrete models. A new methodology for adapting the heightwise variation of lateral stiffness to continuum model is presented based on these comparisons. The proposed methodology is then extended for estimating the nonlinear global capacity of moment resisting frames. The verifications that compare the nonlinear behavior of real systems with those estimated from the proposed procedure suggest its effective use for the performance assessment of large building stocks that exhibit similar structural features. This conclusion is further justified by comparing nonlinear response history analyses of single-degree-of-freedom (sdof) systems that are obtained from the global capacity curves of actual systems and their approximations computed by the proposed procedure.     

A new modelling strategy for the behaviour of shear walls under dynamic loading

A new simplified modelling strategy to simulate the non‐linear behaviour of reinforced concrete shear walls under dynamic loading is presented. The equivalent reinforced concrete (ERC) model is derived from the framework method and uses lattice meshes for concrete and reinforcement bars and uniaxial constitutive laws based on continuum damage mechanics and plasticity. Results show the capacity of the model to analyse structures having different slenderness and boundary conditions. For low reinforcement ratios however, results are sensitive to the angle formed by the diagonals of the concrete lattice and the horizontal bars. The method is compared with the shear multi‐layered beam model that uses Timoshenko multi‐layered 2D beam elements and biaxial constitutive laws. Comparisons for both models with experimental results of two research programs (one organized by NUPEC and the other by COGEMA and EDF) are provided. ERC is a simplified method that intends to save computer time and allows parametrical studies. Copyright © 2002 John Wiley & Sons, Ltd.     

Soil behaviour under dynamic loading conditions: experimental procedures and statistical trends

Soil behaviour under dynamic conditions is a crucial component of several studies concerned with the environmental effects of earthquakes, risk assessment and geological hazards. This work presents experimental procedures for studying soil behaviour under repeated loading and examines the role of uncertain parameters in the expected soil performance. Laboratory techniques are used to obtain stress controlled cyclic triaxial soil measurements, and a series of test programs are performed in order to study general statistical trends in the response of soils under simulated earthquake conditions, to investigate the processes causing soil failure, and to examine factors that may influence the results obtained in the laboratory.This work has been supported by grants from the National Institute of Environmental Health Sciences (Grant no. P42-ES05948 and P30-ES10126) and the Army Research Office (DAAG55-98-1-0289).     

Implementation and verification of a masonry panel model for nonlinear dynamic analysis of infilled RC frames

The effect of infill panels on the response of RC frames subjected to seismic action is widely recognised and has been subject of numerous experimental investigations, while several attempts to model it analytically have been reported. In this work, the implementation, within a fibre-based Finite Elements program, of a double-strut nonlinear cyclic model for unreinforced masonry panels is carried out. The adequacy of the model in predicting the cyclic/seismic response of multi-storey infilled reinforced concrete frames is then verified through comparisons against experimental results.     

Assessing the seismic behavior of steel moment frames equipped by elliptical brace through incremental dynamic analysis (IDA)

Incremental dynamic analysis and nonlinear static pushover analysis are carried out on a performance-based design to determine the seismic demands and capacities of an elliptic braced moment resisting frame (ELBRF). The objective is to assess ductility, overstrength and response modification factors in a modern steel-braced structural system based on incremental dynamic analysis. This integrated system is connected to a beam and column with an appropriate length while providing enough architectural space to allow for an opening without having the common problems associated with architectural spaces in braced systems. Several different classes of buildings are considered on soil type II. Linear dynamic analysis, nonlinear static pushover analysis and incremental nonlinear dynamic analysis related to 12 records from past earthquakes are carried out using OpenSees software. The factors of ductility, overstrength and response modification are calculated for this system. The values of 9.5 and 6.5 are found and suggested only for the response modification factor for ELBRF systems in allowable stress and ultimate limit state methods, respectively. The fragility curves are plotted for the first time for this type of bracing, which contributes to the assessment of building seismic damage.     

Comparative assessment of nonlinear static and dynamic methods for analysing building response under sequential earthquake and tsunami

This paper presents a comprehensive comparison of different dynamic and static approaches for assessing building performance under sequential earthquakes and tsunami. A 10-storey reinforced concrete seismically designed Japanese vertical evacuation structure is adopted as a case study for the investigation. The case study building is first assessed under sequential earthquake and tsunami nonlinear response history analyses: the first time this is done in the literature. The resulting engineering demand parameters are then compared with those obtained when the analysis procedure is systematically simplified by substituting different static approaches for the nonlinear response history analyses in both the earthquake and tsunami loading phases. Different unloading approaches are also tested for the cases when an earthquake pushover is adopted. The results show that an earthquake nonlinear response history analysis, followed by a transient free vibration and a tsunami variable depth pushover, provides the best alternative to full dynamic analyses in terms of accuracy and computational efficiency. This structural analysis combination is recommended and has the advantage that it does not require the tsunami inundation time history to be known in advance. The proposed double pushover approach is instead deemed only suitable for the collapse assessment of regular low to mid-rise buildings and for the development of collapse fragility functions. An important observation made is that sustained earthquake damage seems not to affect the tsunami resistance of the case study building when the fully dynamic analysis is carried out for the sequential loading. This observation will be the subject of future work.     

非线性隔震立式浮顶储罐双向地震作用分析

研究浮顶振动对立式储罐地震响应的影响时,假定浮顶运动为均质刚性圆板振动,其波高沿半径方向线性变化,建立了含有波高参量的运动方程、基底剪力和倾覆力矩表达式.同时,在Park恢复力模型的基础上,给出了铅芯橡胶支座的双向耦合恢复力计算模型,并用该模型模拟了铅芯橡胶支座的力-变形非线性行为.采用时程分析方法对双向地震作用下的浮顶储罐地震响应进行分析,并与未考虑浮顶作用以及单向地震作用的储罐地震响应进行对比.数值结果表明,考虑浮顶作用具有降低地震响应的效果;特定工况下,地震响应峰值可能出现在非主震方向.     

基于变轴力柱恢复力模型的钢框筒地震反应分析

建立了考虑轴力变化影响的钢结构杆件的恢复力模型,介绍了模型构成和经试验比较得到的模型的适用性,采用这一模型,对钢框筒结构进行了多维地震作用下的非线性分析,对这类结构的弹塑性特征进行了考察。     

模型化方法对钢筋混凝土框架地震反应的影响分析

结构非线性动力分析平台OpenSees具备丰富的材料、单元、模型化方法等分析选项和强大的求解功能。在OpenSees平台,对按我国规范设计的八度区二级和九度区一级典型钢筋混凝土框架结构进行了一系列罕遇烈度地震作用下的非线性动力反应分析。通过对分析结果的对比、判断,并结合各种模型化方法对结构地震反应的影响方式进行解释,从顶点侧移、层间侧移角、基底剪力、框架塑性铰分布等方面揭示了不同单元力学模型以及箍筋、板筋对结构整体、局部地震反应的影响规律。     

Enhanced nonlinear static analysis with the drift pushover procedure for tall buildings

In this study a new method for nonlinear static analysis based on the relative displacements of stories is proposed that is able to be implemented in a single stage analysis and considers the effects of an arbitrary number of higher modes. The method is called the extended drift pushover analysis procedure (EDPA). To define the lateral load pattern, values of the relative displacements of stories are calculated using the elastic modal analysis and the modal combination factors introduced. For determining the combination factors, six different approaches are examined. Buildings evaluated in this study consist of four special steel moment-resisting frames with 10–30 stories. Responses including relative displacements of stories, story shear forces and rotation of plastic hinges in each story are calculated using the proposed approaches in addition to modal pushover analysis and nonlinear dynamic time history analyses. The nonlinear dynamic analysis is implemented using ten consistent earthquake records that have been scaled with regard to ASCE7-10. Distribution of response errors of story shears and plastic hinge rotations show that a major part of error corresponds to the second half of the buildings studied. Thus, the mentioned responses are corrected systematically. The final results of this study show that implementing the EDPA procedure using the third approach of this research is able to effectively overcome the limitations of both the traditional and the modal pushover analyses methods and predict the seismic demands of tall buildings with good accuracy.     

Influence of the nonlinear behavior of viscous dampers on the seismic demand hazard of building frames

This paper analyzes the influence of damper properties on the probabilistic seismic performance of building frames equipped with viscous dampers. In particular, a probabilistic methodology is employed to evaluate the influence of the damper nonlinearity, measured by the damper exponent, on the performance of structural and nonstructural components of building frames, as described by the response hazard curves of the relevant engineering demand parameters. The performance variations due to changes in the damper nonlinearity level are evaluated and highlighted by considering two realistic design scenarios and by comparing the results of a set of cases involving dampers with different exponents designed to provide the same deterministic performance. By this way, it is possible to evaluate the influence of the nonlinear response and of its dispersion on the demand hazard. It is shown that the damper nonlinearity level strongly affects the seismic performance and different trends are observed for the demand parameters of interest. A comparison with code provisions shows that further investigation is necessary to provide more reliable design formulas accounting for the damping nonlinearity level. Copyright © 2015 John Wiley & Sons, Ltd.