Comparison of nonlinear behavior of steel moment frames accompanied with RC shear walls or steel bracings

In this paper, the seismic behavior of dual structural systems in forms of steel moment‐resisting frames accompanied with reinforced concrete shear walls and steel moment‐resisting frames accompanied with concentrically braced frames, have been studied. The nonlinear behavior of the mentioned structural systems has been evaluated as, in earthquakes, structures usually enter into an inelastic behavior stage and, hence, the applied energy to the structures will be dissipated. As a result, some parameters such as ductility factor of structure (μ), over‐strength factor (R_s) and response modification factor (R) for the mentioned structures have been under assessment. To achieve these objectives, 30‐story buildings containing such structural systems were used to perform the pushover analyses having different load patterns. Analytical results show that the steel moment‐resisting frames accompanied with reinforced concrete shear walls system has higher ductility and response modification factor than the other one, and so, it is observed to achieve suitable seismic performance; using the first system can have more advantages than the second one. Copyright © 2011 John Wiley & Sons, Ltd.     

New approach to evaluate the response modification factors for steel moment resisting frames

The design force levels currently specified by most seismic codes are calculated by dividing the base shear for elastic response by the response modification factor (R). This is based on the fact that the structures possess significant reserve strength, redundancy, damping and capacity to dissipate energy. This paper proposed the evaluation methodology and procedure of the response modification factors for steel moment resisting frames. The response modification factors are evaluated by multiplying ductility factor (R _μ) for SDOF systems, MDOF modification factor (R _M ) and strength factor (R _S ) together. The proposed rules were applied to existing steel moment resisting frames. The nonlinear static pushover analysis was performed to estimate the ductility (R _μ), MDOF modification (R _M ) and strength factors (R _S ). The results showed that the response modification factors (R) have different values with various design parameters such as design base shear coefficient (V/W), failure mechanism, framing system and number of stories.     

Analytical investigation of response modification (behaviour) factor,R, for reinforced concrete frames rehabilitated by steel chevron bracing

Steel bracing of reinforced concrete (RC) frames has received noticeable attention in recent years as a retrofitting measure to increase the shear capacity of the existing RC buildings. In order to evaluate the seismic behaviour of steel-braced RC frames, some key response parameters, including the ductility and the overstrength factors, should first be determined. These two parameters are incorporated in structural design through a force reduction or a response modification factor. In this paper, the ductility and the overstrength factors as well as the response modification factor (or seismic behaviour factor) for steel chevron-braced RC frames have been evaluated by performing inelastic pushover analyses of brace-frame systems of different heights and configurations. The effects of some parameters influencing the value of behaviour factor, including the height of the frame and share of bracing system from the applied lateral load have been investigated. It is found that the latter parameter has a more localised effect on the R values and its influence does not warrant generalisation at this stage. However, the height of this type of lateral load-resisting system has a profound effect on the R factor, as it directly affects the ductility capacity of the dual system. Finally, based on the findings presented in the article, tentative R values have been proposed for steel chevron-braced moment-resisting RC frame dual systems for different ductility demands and compared with different type of bracing systems.     

An experimental investigation on the seismic behavior of cold-formed steel walls sheathed by thin steel plates

The use of cold-formed steel (CFS) frames has grown extensively in recent years, particularly in the earthquake-prone regions. However, the behavior of lateral resisting systems in CFS structures under seismic loads has not been scrutinized in detail. Towards this, an experimental investigation has been conducted on cold formed steel frames sheathed by thin galvanized steel plates, the results of which are presented here. The experiments involve 24 full-scale steel plated walls tested under cyclic loading with different configurations of studs and screws. Of particular interest were the specimens׳ maximum lateral load capacity and the load-deformation behavior as well as a rational estimation of the seismic response modification factor, R. The study also evaluates the failure modes of the systems. The main factors contributing to the ductile response of these shear walls are also discussed in order to suggest improvements so that the walls respond plastically with a significant drift and without any risk of brittle failure.     

BRBF response modification factor

In this paper, overstrength, ductility and response modification factor of Buckling Restrained Braced frames were evaluated. To do so, buildings with various stories and different bracing configuration including diagonal, split X, chevron (V and Inverted V) bracings were considered. Static pushover analysis, nonlinear incremental dynamic analysis and linear dynamic analysis have been performed using Opensees software. The effects of some parameters influencing response modification factor, including the height of the building and the type of bracing system, were investigated. In this article seismic response modification factor for each of bracing systems has been determined separately and tentative values of 8.35 and 12 has been suggested for ultimate limit state and allowable stress design methods.     

Evaluating response modification factors of concentrically braced steel frames

Response modification factor is one of the seismic design parameters to consider nonlinear performance of building structures during strong earthquake. Relying on this, many seismic design codes led to reduce loads. The present paper tries to evaluate the response modification factors of conventional concentric braced frames (CBFs) as well as buckling restrained braced frames (BRBFs). Since, the response modification factor depends on ductility and overstrength, the static nonlinear analysis has been performed on building models including single and double bracing bays, multi-floors and different brace configurations (chevron V, invert V and X bracing). The CBFs and BRBFs values for factors such as ductility, overstrength, force reduction due to ductility and response modification have been assessed for all the buildings. The results showed that the response modification factors for BRBFs were higher than the CBFs one. It was found that the number of bracing bays and height of buildings have had greater effect on the response modification factors.     

Inelastic performance of cold-formed steel strap braced walls

The inelastic performance of sixteen 2.44 m×2.44 m cold-formed steel strap braced walls was evaluated experimentally. The performance was affected by the holddown detail, which in many cases did not allow the test specimens to reach or maintain a yield capacity and severely diminished the overall system ductility. “Test-based” R_d×R_o values of 3.65, 2.11 and 1.72 indicate the low ductility levels, which were not adequate to warrant the use of a seismic response modification coefficient of R=4.0 in design. Capacity design of the SFRS elements must account for the overstrength of the strap material.     

某复杂高层钢结构静力弹塑性分析及性能评价

利用ETABS对一复杂高层钢结构进行了静力弹塑性pushover分析，对四种加载模式下结构的pushOVer分析结果进行了对比研究。在此基础上，依据我国抗震规范评价了本结构的塑性发展顺序及抗震性能水准。     

An investigation on the accuracy of pushover analysis for estimating the seismic deformation of braced steel frames

This paper investigates the potentialities of the pushover analysis to estimate the seismic deformation demands of concentrically braced steel frames. Reliability of the pushover analysis has been verified by conducting nonlinear dynamic analysis on 5, 10 and 15 story frames subjected to 15 synthetic earthquake records representing a design spectrum. It is shown that pushover analysis with predetermined lateral load pattern provides questionable estimates of inter-story drift. To overcome this inadequacy, a simplified analytical model for seismic response prediction of concentrically braced frames is proposed. In this approach, a multistory frame is reduced to an equivalent shear-building model by performing a pushover analysis. A conventional shear-building model has been modified by introducing supplementary springs to account for flexural displacements in addition to shear displacements. It is shown that modified shear-building models have a better estimation of the nonlinear dynamic response of real framed structures compared to nonlinear static procedures.     

Evaluation of deflection amplification factor in steel moment‐resisting frames

Steel moment‐resisting frames (SMRFs) are the most common type of structural systems used in steel structures. The first step of structural design for SMRFs starts with the selection of the structural sections on the basis of story drift limitation. ASCE 7 (2010) requires that the inelastic story drifts be obtained by multiplying the deflections determined by elastic analysis under design earthquake forces with a deflection amplification factor (C_d). For special moment‐resisting frames, C_d is given as 5.5 in ASCE 7 (2010). Lower C_d values will increase the overall inelastic response of the structure. On the other hand, the inelastic response of the structure is expected to be less severe when designed for higher C_d values. The performance objective is that the structure should sustain the inelastic deformation demand imposed due to design earthquake ground motions. This study aims at investigating the inelastic seismic response that low‐rise, medium‐rise and high‐rise SMRFs can experience under design earthquake ground motions and maximum considered earthquake (MCE) level ground motions and evaluating the deflection amplification factors (C_d) for SMRFs in a rational way. For this purpose, nonlinear dynamic time history and pushover analyses will be carried out on SMRFs with 4, 9 and 20 stories. The results indicate that the current practice for computing the inelastic story drifts for SMRFs is rational and the frames designed complying with the current code requirements can sustain the inelastic deformations imposed during design earthquake ground motions when seismically designed and detailed. Copyright © 2013 John Wiley & Sons, Ltd.     

考虑高阶振型影响的改进的多模态推覆分析方法

将结构静力弹塑性分析与地震反应谱结合起来的Pushover方法是一种简单有效的结构抗震能力评定方法,本文简要介绍了这种方法的原理,并在多模态pushover分析方法的基础上,提出了改进的多模态pushover分析方法,用以建立钢框架结构的能力谱曲线。求解结构在性能点处的响应时,为了考虑高阶振型对结构抗震性能的影响,首次把振型质量参与系数应用到模态推覆分析结果的组合中。通过与弹塑性时程分析的比较,表明本文提出的改进的多模态推覆分析方法是可行的和准确的。     

框架——剪力墙结构的静力弹塑性分析研究

静力弹塑性方法作为一种评价结构抗震性能和计算结构弹塑性变形的简化方法,近年来得到了广泛应用。但由于传统的定侧力模式的静力弹塑性方法只考虑第一振型,无法反映高层建筑结构的高阶振型影响。为考虑高阶振型的影响,Chopra在振型分解反应谱组合法的基础上,提出了MPA方法。本文首先讨论了应用MPA方法需注意的问题,然后用一个18层钢筋混凝土框架—剪力墙结构为算例,以逐步增量弹塑性时程分析结果为基准,对传统定侧力模式静力弹塑性方法和MPA方法的分析结果进行了对比研究。结果表明,相比于定侧力模式静力弹塑性分析结果,MPA方法的分析结果更接近弹塑性时程分析结果。     

Seismic performance factors for low‐ to mid‐rise steel diagrid structural systems

Diagrids are known as an esthetically pleasing and structurally efficient system. The current design codes and provisions, however, provide no specific guidelines for their design under extreme events such as earthquakes. This paper presents a comprehensive investigation of the performance of steel diagrid structures to evaluate their key seismic performance factors. Nonlinear static, time‐history dynamic, and incremental dynamic analyses are used to assess diagrid performance and collapse mechanisms in a high seismic region. Seismic performance factors including response modification factor, ductility factor, overstrength factor, and deflection amplification factor are quantified using 4 different methodologies. Four archetype groups of diagrid buildings ranging in height from 4 to 30 stories have been investigated. An R factor in the range of 4 to 5 is recommended for steel diagrid frames in the range of 8 to 30 stories unless supplementary analyses are conducted to find the optimal diagonal angle. For low‐rise steel diagrids (under 8 stories), an R factor in the range of 3.5 to 4 is recommended. Further, an overstrength and ductility of 2.5 and 2 are recommended. This paper lays the groundwork for including steel diagrids in design provisions.     

An experimental investigation on the lateral behavior of knee-braced cold-formed steel shear walls

Experimental investigations were conducted to evaluate the lateral seismic characteristics of light-weight knee-braced cold-formed steel structures. In all, four full-scale 2.4×2.4 m² specimens with different configurations were tested under a standard cyclic loading regime. This paper focuses on the specimens' maximum lateral load capacity and deformation behavior and provides a rational estimate of the seismic response modification factor, R, of knee-braced walls. The study also looks at the failure modes of the system and investigates the main factors contributing to the ductile response of CFS walls. That is in order to suggest improvements so that the shear steel walls respond plastically with a significant drift and without any risk of brittle failure, such as connection failure or stud buckling. A discussion on the calculated response factors in comparison to those suggested in the relevant codes of practice is also presented.     

Seismic characteristics of K-braced cold-formed steel shear walls

Detailed investigation of the lateral performance of K-braced cold-formed steel structures and their response modification coefficients, R factor, are presented in this paper. A total of 12 full-scale 2.4 × 2.4 m specimens of different configurations are considered, and the responses investigated under a standard cyclic loading regime. Of particular interest are the specimens' maximum lateral load capacity and deformation behavior as well as a rational estimation of the seismic response modification factor. The study also looks at the failure modes of the system and investigates the main factors contributing to the ductile response of the CFS walls in order to suggest improvements so that the shear steel walls respond plastically with a significant drift and without any risk of brittle failure, such as connection failure or stud buckling. A discussion on the calculated response factors in comparison to those suggested in the relevant codes of practice is also presented.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic performance of tubular structures with buckling restrained braces

In this study 36‐ and 72‐story framed and braced tubular structures were designed according to the current design code and their seismic performances were evaluated by nonlinear static and dynamic analysis. According to the analysis results, the tubular structures generally showed high earthquake‐resisting capability. The framed tube structure showed lowest stiffness and strength compared with the other model structures. The braced tube structures showed larger strength but lower overall ductility compared with framed tube structures. When buckling‐restrained braces were used instead of conventional braces, strength increased significantly compared with the framed tube, and ductility was enhanced compared with braced tube structures. As the load–displacement relationship estimated by static pushover analysis formed the lower bound of the dynamic analysis results, the response modification factors obtained based on the static pushover curve may safely be used for seismic design. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi-mode pushover procedure for deformation demand estimates of steel moment-resisting frames

The main objective of the paper is the development and evaluation of a multi-mode pushover procedure for the approximate analysis of the seismic response of steel moment-resisting frames. A generalized force vector derived from modal combination simulates the instantaneous force distribution acting on the structure when the interstorey drift reaches its maximum value during dynamic response to a seismic excitation. Considering the interstorey drift for each floor, a set of generalized force vectors (each associated to maximum drift at one story) is applied separately to the structure until the corresponding target interstorey drift is attained. The maximum value of each response parameter is obtained from the envelope of results. This multi-run and multi-mode pushover procedure allows a simple implementation, reducing the computational effort compared with adaptive nonlinear static procedures and with nonlinear response history analysis. Furthermore, it does not suffer from the statistical combination of inelastic modal responses calculated separately. Both effectiveness and accuracy are verified through a comparative study involving regular steel moment resisting frames subjected to various acceleration records. The results are finally compared with those obtained from other nonlinear static procedures and with the “exact” values from nonlinear response history analysis. It is demonstrated that the proposed procedure is able to accurately predict the seismic demands of steel moment-resisting frames. In low- and middle-rise frames, the error of interstorey drift ratios of the proposed procedure is in the range 5.8-20.8% when the intensity level of the input ground motion varies in the range 0.2-0.8 g. In high-rise frames the error of interstorey drift ratios is in the range 6.38-20.9%.

     

Pushover方法的准确性和适用性研究

Pushover方法作为一种建筑结构弹塑性地震响应的简化近似计算方法和抗震性能评价方法已得到广泛应用。但由于其理论基础不严密,其准确性需要给予必要确认,同时其适用性也应受到一定的限制。本文以逐步增量弹塑性时程方法的结果为基准,分别以一个普通6层RC框架结构和一个18层RC框架-剪力墙结构为例,对Pushover方法的准确性和适用性进行了分析研究。结果表明,Pushover方法仅适用于以第一振型为主的高度不大的结构,且应采用两种以上的侧力模式;对于高阶振型影响较大的结构,该方法的准确性较差,承载力预测显著偏低。     

The effect of foundation flexibility and structural strength on response reduction factor of RC frame structures

Current force‐based design procedure adopted by most seismic design codes allows the seismic design of building structures to be based on static or dynamic analyses of elastic models of the structure using elastic design spectra. The codes anticipate that structures will undergo inelastic deformations under strong seismic events; therefore, such inelastic behaviour is usually incorporated into the design by dividing the elastic spectra by a factor, R, which reduces the spectrum from its original elastic demand level to a design level. The most important factors determining response reduction factors are the structural ductility and overstrength capacity. For a structure supporting on flexible foundation, as Soil Structure Interaction (SSI) extends the elastic period and increases damping of the structure‐foundation elastic system, the structural ductility could also be affected by frequency‐dependent foundation‐soil compliances. For inelastic systems supporting on flexible foundations, the inelastic spectra ordinates are greater than for elastic systems when presented in terms of flexible‐base structure's period. This implies that the reduction factors, which are currently not affected by the SSI effect, could be altered; therefore, the objective of this research is to evaluate the significance of foundation flexibility on force reduction factors of RC frame structures. In this research, by developing some generic RC frame models supporting on flexible foundations, effects of stiffness and strength of the structure on force reduction factors are evaluated for different relative stiffnesses between the structure and the supporting soil. Using a set of artificial earthquake records, repeated linear and nonlinear analyses were performed by gradually increasing the intensity of acceleration time histories to a level, where first yielding of steel in linear analysis and a level in which collapse of the structure in nonlinear analysis are observed. The difference between inelastic and elastic resistance in terms of displacement ductility factors has been quantified. The results indicated that the foundation flexibility could significantly change the response reduction factors of the system and neglecting this phenomenon may lead to erroneous conclusions in the prediction of seismic performance of flexibly supported RC frame structures. Copyright © 2010 John Wiley & Sons, Ltd.