A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.     

Inelastic earthquake response of single‐story asymmetric buildings: an assessment of simplified shear‐beam models

The inelastic seismic torsional response of simple structures is examined by means of shear‐beam type models as well as with plastic hinge idealization of one‐story buildings. Using mean values of ductility factors, obtained for groups of ten earthquake motions, as the basic index of post‐elastic response, the following topics are examined with the shear‐beam type model: mass eccentric versus stiffness eccentric systems, effects of different types of motions and effects of double eccentricities. Subsequently, comparisons are made with results obtained using a more realistic, plastic hinge type model of single‐story reinforced concrete frame buildings designed according to a modern Code. The consequences of designing for different levels of accidental eccentricity are also examined for the aforementioned frame buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic shear forces on RC walls: review and bibliography

Effect of higher vibration modes on the seismic shear demand of reinforced concrete cantilever walls has been studied since the 1970’s. The shear amplification becomes more important with increasing fundamental period (tall buildings) and increasing ductility demand (R or q factors). Yet, studying the relevant recommendations of structural engineering researchers and provisions of various seismic codes reveals that there is no consensus regarding the extent of shear amplification and of the inter-wall distribution of shear demand in structural systems comprising walls of different lengths. The paper presents the available formulas for predicting shear amplification in ductile walls and dual systems (wall-frames). One effect that impacts the shear amplification is shear cracking mainly in the plastic hinge zone of the wall near the base leading to appreciably lower shear amplification than previously predicted. Post yield shear redistribution among interconnected unequal walls is also addressed. Finally, an extensive bibliography is provided.     

Approximate frequency analysis of shear wall frame structures

The finite strip method is used to determine the natural frequencies of shear wall frame buildings. The structure can be modelled in two different ways. In the first approach both the shear walls and the frames are idealized simply as an assemblage of finite strips of varying thicknesses with given or computed properties, while in the second approach the shear walls are still idealized as a series of finite strips, but the frames are regarded as a number of long columns which are interconnected with each other or with finite strips through the horizontal beams. Numerical results obtained from both models indicate good agreement with finite element solutions. The proposed models can be applied to a wide range of shear wall frame assemblies and are therefore more versatile than most existing models.     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.     

Softening effects of RC nonstructural flat walls on ductile concrete buildings

Nonstructural reinforced concrete flat walls architecturally designed as exterior/partition walls in concrete buildings were severely damaged by the 2011 earthquake off the Pacific coast of Tohoku. This damage was observed in the monolithic nonstructural flat walls of relatively old ductile concrete buildings. Although these flat walls might affect the overall seismic performance and behavior of a building, the nonstructural wall effects have not been clarified because of the complex interactions among the structural components. To understand these effects, this paper conducts an experimental and numerical investigation of the nonstructural wall effects, focusing on a typical residential building damaged by the 2011 earthquake. A single‐story, one‐bay moment‐resisting frame model of the building with a nonstructural flat wall was tested to clarify the fundamental behavior. The results reveal that the wall significantly contributed to the seismic performance of the overall frame until it failed in shear, subsequently losing structural effectiveness. Such experimental wall behavior could be simulated by the isoparametric element model. Moreover, the structural effects of the nonstructural flat walls on the global seismic performance and behavior of the investigated building were discussed through earthquake response analyses using ground motions recorded near the building site and pushover analyses. Consequently, the building damage could be simulated in an analytical case considering the nonstructural flat walls, showing larger inter‐story drifts in the lower stories due to softening of the walls. The analytical results also indicated that the softening of the nonstructural flat walls decreased the building ductility, as defined by ultimate inter‐story drifts. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamics of elastic–plastic shear frames with secondary structures: shake table and numerical studies

Results from experimental and numerical studies of earthquake‐excited small‐scale primary–secondary structures are presented. The primary structure considered is a plane three‐storey shear frame with a fundamental frequency of 5.5 Hz. The columns of the first floor are built with soft aluminium and they are stressed beyond its linear range of behaviour. After each test the elastic–plastic columns are replaced by a new set of undeformed virgin aluminium bars. The elastic–plastic shear frame is tested with and without an attached secondary structure. The secondary structure is modelled as an elastic SDOF oscillator, and its natural frequency is tuned to the fundamental frequency of the shear frame. Alternatively, the oscillator is mounted on the horizontal beam of the second and third floor. The base excitation of the structural model is characterized by a broad band random process with constant spectral density in a frequency range between 3 and 30 Hz. In the numerical study, the digital recorded acceleration of the base excites the mechanical model of the investigated structures. Numerical outcomes assuming fictitious unlimited elastic material behaviour of the shear frame are set in contrast to results from experiments and computational simulations where the measured non‐linear force displacement relation of the elastic–plastic floor is approximated by a piecewise linear curve. The effect of elastic–plastic materials on the dynamic interaction between primary and secondary structure is shown and the difference to unlimited elastic material behaviour is worked out in detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluation of building period formulas for seismic design

Building period formulas in seismic design code are evaluated with over 800 apparent building periods from 191 building stations and 67 earthquake events. The evaluation is carried out with the formulas in ASCE 7‐05 for steel and RC moment‐resisting frames, shear wall buildings, braced frames, and other structural types. Qualitative comparison of measured periods and periods calculated from the code formulas shows that the formula for steel moment‐resisting frames generally predicts well the lower bound of the measured periods for all building heights. But the differences between the periods from code formula and measured periods of low‐ to‐medium rise buildings are relatively high. In addition, the periods of essential buildings designed with the importance factor are about 40% shorter than the periods of non‐essential buildings. The code formula for RC moment‐resisting frames describes well the lower bound of measured periods. The formula for braced frames accurately predicts the lower bound periods of low‐to‐medium rise buildings. The formula for shear wall buildings overestimates periods for all building heights. For buildings that are classified as other structural types, the measured building periods can be much shorter than the periods calculated with the code formula. Based on these observations, it is suggested to use C_r factor of 0.015 for shear walls and other structural types. Copyright © 2010 John Wiley & Sons, Ltd.     

Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects

A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom (MDOF) system is approximated by using the modal energy-decomposition. Energy-based base shear coefficients are verified by means of both pushover analysis and nonlinear time history (NLTH) analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.     

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Influence of lateral-load-resisting system on the earthquake response of structures—a system identification study

Analysis and comparison of the dynamic responses of three well instrumented (with accelerographs) high-rise buildings shaken during the 1984 Morgan Hill earthquake are presented. The buildings examined in the present work are (i) the Town Park Towers Apartment building, a 10-storey, concrete shear wall building; (ii) the Great Western Savings and Loan building, a 10-storey building with concrete frames and shear walls; and (iii) the Santa Clara County Office building, a 13-storey, moment-resistant steel frame building. The structures are located within 2 km of each other and, as may be confirmed by visual inspection of the recorded seismograms, experienced similar ground motions. One-dimensional and three-dimensional linear structural models are fitted to the observations using the modal minimization method' for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the buildings. The time-varying character of these parameters over the duration of the response is also investigated. Comparison of the recorded earthquake response of the structures reveals that the type of lateral-load-resisting system has an important effect on the dynamic behaviour of the structures because it controls the spacing of the characteristic modes on the frequency axis. The Santa Clara County Office building has closely spaced natural frequencies and exhibits strong torsional response and modal coupling. Its dynamic behaviour is contrasted with that of the Great Western Savings and Loan building which has well separated natural frequencies and exhibits small torsional response and no modal coupling. Strong modal coupling causes a beating-type phenomenon and makes earthquake response of structures different from that envisioned by codes.     

Strengthening of moment‐resisting frame structures against near‐fault ground motion effects

Near‐fault ground motions with forward directivity are characterized by a large pulse. This pulse‐like motion may cause a highly non‐uniform distribution of story ductility demands for code‐compliant frame structures, with maximum demands that may considerably exceed the level of code expectations. Strengthening techniques for multi‐story frame structures are explored with the objective of reducing maximum drift demands. One option is to modify the code‐based SRSS distribution of story shear strength over the height by strengthening of the lower stories of the frame. The modified distribution reduces the maximum story ductility demand, particularly for weak and flexible structures. However, this strengthening technique is less effective for stiff structures, and is almost ineffective in cases in which the maximum demand occurs in the upper stories, i.e. strong and flexible structures. As an alternative, the benefits of strengthening frames with elastic and inelastic walls are evaluated. The effects of adding walls that are either fixed or hinged at the base are investigated. It is demonstrated that strengthening with hinged walls is very effective in reducing drift demands for structures with a wide range of periods and at various performance levels. Wall inelastic behavior only slightly reduces the benefits of strengthening with hinged walls.Copyright © 2004 John Wiley & Sons, Ltd.     

设置抗拔型三重摩擦摆隔震支座框架结构地震响应分析

抗拔型三重摩擦摆隔震支座是一种新型隔震支座。以框架结构为例,利用ANSYS软件建立了6层和10层普通抗震结构和带该支座的基础隔震结构模型;通过模态分析,得到了结构的自振周期;通过地震响应分析,提取了6层框架隔震层和顶层的位移、加速度和剪力时程曲线,并提取了不同层数不同结构类型的各层间位移、加速度幅值。结果表明：与抗震结构相比,基础隔震结构周期显著增大;隔震结构的变形主要集中在隔震层,隔震层以上的结构基本为整体平动,结构的地震位移反应得到了有效的减小;采用抗拔型三重摩擦摆隔震支座能降低结构地震加速度反应;设置抗拔型三重摩擦摆隔震支座的多层数隔震结构的能量衰减不如低层数的隔震结构迅速。     

Seismic safety assessment of existing masonry infill structures in Nepal

Reinforced concrete (RC) buildings in Nepal are constructed with RC frames and masonry infill panels. These structures exhibit a highly non-linear inelastic behavior resulting from the interaction between the panels and frames. This paper presents an extensive case study of existing RC buildings in Nepal. Non-linear analyses were performed on structural models of the buildings considered as a bare frame and with masonry infill, in order to evaluate the influence of infill walls on the failure mechanisms. Five three-storey buildings with different structural configurations and detailing were selected. The effect of masonry infill panels on structural response was delineated by comparing the bare-framed response with the infill response. Seismic performance is evaluated with regard to global strength, stiffness, energy dissipation, inter-storey drift, and total deflection of the structure. A parametric analysis of structures with masonry infill is also performed. For this, the influence of different material properties is studied, namely diagonal compressive stress, modulus of elasticity and tensile stress of masonry infill panels. Study results show that masonry infill increases the global strength and stiffness of the structures; it decreases the inter-storey drift and hence the total displacement of the structure. The results quantify the influence of the infill panels on structural response and, in particular, the effect of the diagonal compressive strength of the masonry wall.     

横墙对框架结构动力响应的影响分析

填充墙具有显著的刚度和承载力贡献。建筑结构震害调查发现,不开洞横墙的破坏程度远小于开洞纵墙的破坏程度,从宏观现象可判断大部分多层建筑的破坏主要由结构纵向运动造成。为研究横墙在地震作用下的性能及其对结构整体动力响应的影响,以经受2021年5月21日云南漾濞6.4级地震震害的花椒园小学教学楼为研究对象,按当地抗震计算参数进行弹塑性时程分析。采用等效斜压杆模拟横向填充墙,设置无填充墙框架结构、带黏土砖墙的框架结构、带空心砖墙的框架结构和带加气混凝土砌块填充墙的框架结构模型,选取10组地震波横向输入。研究结果表明,4种结构自振周期均处于具有统计学意义的平台段,平均加速度响应较接近,质量和刚度变化不会使结构加速度产生规律的变化;受结构自重影响,无填充墙的框架结构底部剪力小于带填充墙的框架结构,带填充墙的框架结构位移远小于无填充墙的框架结构;带有多道不开洞横墙的多层框架结构的破坏主要是由结构纵向破坏引起的。     

Simulation analyses of buildings damaged in the 1995 Kobe,Japan, earthquake considering soil–structure interaction

A series of studies was conducted on three buildings of steel reinforced concrete structures with RC shear walls damaged in the 1995 Hyogo-ken Nanbu earthquake. These buildings are located in an area where structural damage centred around. Two of these buildings suffered severe damage, while the third was not structurally damaged. Our studies deal with site inspections, including micro-tremor measurement of buildings, the evaluation of input motions, and the response analyses considering soil–structure interaction. The results of simulation analyses of the two severely damaged buildings correspond to their actual damage state. From the response analyses of the one slender building with no structural damage, it was concluded that uplifting is the main reason it did not suffer any structural damage. Through these studies, the importance of soil–structure interaction and effective input motion is fully understood. Copyright © 1999 John Wiley & Sons, Ltd.     

Tests on low‐ductility RC frames under high‐ and low‐frequency excitations

The response of low‐ductility reinforced concrete (RC) frames, designed typically for a non‐seismic region, subjected to two frequencies of base excitations is studied. Five half‐scaled, two‐bay, two‐storey, RC frames, each approximately 5 m wide by 3.3 m high, were subjected to both horizontal and/or vertical base excitations with a frequency of 40 Hz as well as a lower frequency of about 4 Hz (close to the fundamental frequency) using a shake table. The imposed acceleration amplitude ranged from 0.2 to 1.2g. The test results showed that the response characteristics of the structures differed under high‐ and low‐frequency excitations. The frames were able to sustain high‐frequency excitations without damage but were inadequate for low‐frequency excitations, even though the frames exhibited some ductility. Linear‐elastic time‐history analysis can predict reasonably well the structural response under high‐frequency excitations. As the frames were not designed for seismic loads, the reinforcement detailing may not have been adequate, based on the crack pattern observed. The effect of vertical excitation can cause significant additional forces in the columns and moment reversals in the beams. The ‘strong‐column, weak‐beam’ approach for lateral load RC frame design is supported by experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental tests on full‐scale RC unretrofitted frame and retrofitted with buckling‐restrained braces

The results of experimental tests carried out on reinforced concrete (RC) full‐scale 2‐storey 2‐bays framed buildings are presented. The unretrofitted frame was designed for gravity loads only and without seismic details; such frame was assumed as a benchmark system in this study. A similar RC frame was retrofitted with buckling‐restrained braces (BRBs). The earthquake structural performance of both prototypes was investigated experimentally using displacement‐controlled pushover static and cyclic lateral loads. Modal response properties of the prototypes were also determined before and after the occurrence of structural damage. The results of the dynamic response analyses were utilized to assess the existing design rules for the estimation of the elastic and inelastic period of vibrations. Similarly, the values of equivalent damping were compared with code‐base relationships. It was found that the existing formulations need major revisions when they are used to predict the structural response of as‐built RC framed buildings. The equivalent damping ratio ξ_eq was augmented by more than 50% when the BRBs was employed as bracing system. For the retrofitted frame, the overstrength Ω and the ductility µ are 1.6 and 4.1, respectively; the estimated R‐factor is 6.5. The use of BRBs is thus a viable means to enhance efficiently the lateral stiffness and strength, the energy absorption and dissipation capacity of the existing RC substandard frame buildings. The foundation systems and the existing members of the superstructure are generally not overstressed as the seismic demand imposed on them can be controlled by the axial stiffness and the yielding force of the BRBs. Copyright © 2011 John Wiley & Sons, Ltd.