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.     

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.     

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.     

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.     

Response modification factor for steel moment-resisting frames by different pushover analysis methods

The earthquake loads imposed to the structures are generally much more than what they are designed for. This reduction of design loads by seismic codes is through the application of response modification factor (R-factor). During moderate to severe earthquakes, structures usually behave inelastically, and therefore inelastic analysis is required for design. Inelastic dynamic analysis is time consuming and interpretation of its results demands high level of expertise. Pushover analysis, recently commonly used, is however, a simple way of estimating inelastic response of structures. Despite its capabilities, conventional pushover analysis (CPA) does not account for higher mode effects and member stiffness changes. Adaptive pushover analysis (APA) method however, overcomes these drawbacks. This research deals with derivation and comparison of some seismic demand parameters such as ductility based reduction factor, R_μ, overstrength factor, Ω, and in particular, response modification factor, R, from capacity curves obtained from different methods of APA and CPA. Three steel moment-resisting frames of 3, 9 and 20 stories adopted from SAC steel project are analyzed. In pushover analyses for each frame, eight different constant as well as adaptive lateral load patterns are used. Among the main conclusions drawn is that the maximum relative difference for response modification factors was about 16% obtained by the methods of conventional and adaptive pushover analyses.     

Behaviour Factor of code-designed steel moment-resisting frames

Current seismic codes are based on force-controlled design or capacity design, using the base shear concept. The most important parameter in this approach is the response modification factor, also called behaviour factor, which is used to design the structure at the ultimate limit state by taking into account its capacity to dissipate energy by means of plastic deformations. In this paper overstrength, redundancy and ductility response modification factors of steel moment resisting frames are evaluated. In order to cover a wide range of structural characteristics, 12 steel moment-resisting frames (6 regular and 6 irregular in elevation) have been designed and analysed. Both static pushover analyses and nonlinear incremental dynamic analyses have been performed. The investigation focuses on the effects of some parameters influencing the responsemodification factor, including the regularity, the number of spans and the number of storeys. As a conclusion, a local ductility criterion has been proposed to improve the provisions given in the Italian seismic code.     

Empirical evaluation of ductility factors for the special steel moment‐resisting frames in view of soil condition

It is well known that the response modification factor (R) takes into account the ductility, over‐strength, redundancy and damping of structural systems. The ductility factor has played an important role in seismic design, as it is a key component of R. In this study, the ductility factors (R_μ,MDOF) of special steel moment‐resisting frames are calculated by multiplying the ductility factor of single degree of freedom (SDOF) systems (R_μ,SDOF) with the multi‐degree of freedom (MDOF) modification factors (R_M). The ductility factors (R_μ,SDOF) of SDOF systems are computed from non‐linear dynamic analysis undergoing different levels of displacement ductility demands and periods when subjected to a large number of recorded earthquake ground motions. To compute the R_μ,SDOF, a group of 1,860 ground motions recorded from 47 earthquakes were considered. R_M factors are proposed to account for the MDOF systems, based on previous studies. A total of 108 prototype steel frames were designed to investigate the ductility factors, considering design parameters such as the number of stories (4, 8 and 16), framing systems (perimeter frames and distributed frames), failure mechanisms (strong column‐weak beam and weak column‐strong beam), soil profiles (S_A, S_C and S_E in Uniform Building Code 1997) and seismic zone factors (Z = 0·075, 0·2, and 0·4 in UBC 1997). The effects of these design parameters on the R_μ,MDOF of special steel‐moment‐resisting frames were investigated. Copyright © 2009 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.     

不同设防烈度下RC框架结构的抗侧向倒塌能力

地震作用下建筑结构的抗侧向倒塌能力是抗震性能评价的基础。选取4个结构整体性能参数作为结构抗侧向倒塌能力评价指标,分别为结构强屈比、超强系数、延性系数和延展系数。按中国现行规范设计了12个RC框架结构,考虑侧向力分布形式和设防烈度的影响,采用Pushover方法对结构进行计算,并根据能力曲线和结构整体性能参数对结构抗侧向倒塌能力进行评价。结果表明:结构整体性能参数能从强度储备和变形能力两个方面对结构抗侧向倒塌能力进行分析;随着设防烈度和结构高度的提高,侧向力分布形式对结构抗侧向倒塌能力的影响增大;设防烈度对结构强屈比和结构延展系数的影响较小,对结构超强系数和结构延性系数的影响较大;随着设防烈度的提高,结构超强系数减小,而结构延性系数增大。     

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.     

Seismic performance evaluation of staggered wall system structures with middle corridors

In this paper, the seismic performance of reinforced concrete (RC) staggered wall structures with middle corridor was evaluated. To this end, 6‐, 12‐ and 18‐storey structural models were designed and were analyzed to investigate the seismic load‐resisting capacity. The response modification factors were computed based on the overstrength and the ductility capacities obtained from pushover curves. The effect of a few retrofit schemes on the enhancement of strength and ductility was also investigated. The pushover analysis results showed that the response modification factors ranged between about 4.0 and 6.0 with the average value around 5.0. When the bending rigidity of the link beams increased up to 100%, the overall overstrength increased by only about 25%. When the rebar ratio of the link beams was increased by 50%, the overstrength increased by about 40%. The replacement of the RC link beams with steel box beams resulted in superior performance of the structures with reduced beam depth. The displacement time histories of the model structures subjected to the earthquake ground motions scaled to the design seismic load showed that the maximum interstorey drifts were well below the limit state specified in the design code. Based on the analysis results, it was concluded that the staggered wall systems with a middle corridor had enough capacity to resist the design seismic load. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic seismic response of steel bracing members

A survey of past experimental studies on the inelastic response of diagonal steel bracing members subjected to cyclic inelastic loading was carried out to collect data for the seismic design of concentrically braced steel frames for which a ductile response is required under earthquakes. The parameters that were examined are the buckling strength of the bracing members, the brace post-buckling compressive resistance at various ductility levels, the brace maximum tensile strength including strain hardening effects, and the lateral deformations of the braces upon buckling. Equations are proposed for each of these parameters. In addition, the maximum ductility that can be achieved by rectangular hollow bracing members is examined.     

抗弯钢框架结构影响系数研究

结构影响系数主要包括延性折减系数和超强系数。给出了按我国抗震规范设计的几个典型抗弯钢框架结构,采用弹塑性时程分析方法确定了结构的整体能力曲线。考虑了结构层数、跨数等对结构延性和超强能力的影响,给出了在典型地震波作用下的各结构的结构影响系数值。建议在我国的结构抗震设计中,抗弯钢框架的结构影响系数最小值可取4。     

Behavior and design of reinforced concrete frames retrofitted with steel bracing against progressive collapse

Steel bracing is able to improve progressive collapse resistance of reinforced concrete (RC) frames, but the bracing design is typically based on seismic retrofitting or lateral stability. There is no approach for design of steel bracing against progressive collapse. To this end, a retrofitting approach with steel braces is proposed based on analysis of macro finite element (FE) models with fiber beam elements. The FE models were initially validated through the experimental results of a braced frame and then used to investigate the effects of pertinent parameters on the progressive collapse resistance of planar frames. The results suggest the braces should be placed at the top story. Thereafter, macro FE models are built to investigate the dynamic responses of the three‐dimensional prototype RC frames under different column removal scenarios (CRS) and show the necessity of retrofitting. Accordingly, the design approach of steel bracing is proposed with incremental dynamic analysis (IDA) and assuming independent contribution of braces and frames to resistance. Finally, the fragility analysis of the frames under a corner‐penultimate‐exterior CRS is conducted through IDA and Monte Carlo simulation, and the results confirm the validity of the proposed design approach for retrofitting RC frames.     

角部连接钢框架-玻璃纤维增强无机板组合墙体抗震性能试验研究

为研究角部连接钢框架 玻璃纤维增强无机板组合墙体的抗震性能,考察人字形斜撑和玻璃纤维增强无机板对钢框架 组合墙体的影响,设计2榀足尺的双层双跨钢框架和2榀足尺的双层双跨组合墙体进行拟静力试验。观察不同形式钢框架和组合墙体在低周往复荷载下的破坏过程及破坏形态,得到了各试件的滞回曲线、骨架曲线、刚度退化曲线、累积耗能、关键部位应变、延性系数等性能指标,对比分析人字形斜撑和玻璃纤维增强无机板对钢框架 组合墙体耗能性能、延性、承载力的影响。试验结果表明：组合墙体抗侧承载力高,刚度大,而变形能力与耗能能力较差;人字形斜撑能有效提高钢框架承载力、延性及耗能能力,但在组合墙体中人字形斜撑作用不明显,且圆钢管人字形斜撑易发生平面外失稳,建议设计时采用平面外刚度大于平面内刚度的H型钢;玻璃纤维增强无机板可以较大程度提高钢框架的抗侧承载力,由于玻璃纤维增强无机板过早开裂破坏,导致其延性降低,刚度退化速度加快,耗能能力变弱。基于已有的侧移刚度公式,对其进行参数修正并给出组合墙体侧移刚度简化计算式,理论值与试验初始抗侧刚度吻合较好,可为后续研究提供理论基础。     

Equivalent viscous damping in direct displacement‐based design of steel braced reinforced concrete frames

Performance‐based design method, particularly direct displacement‐based design (DDBD) method, has been widely used for seismic design of structures. Estimation of equivalent viscous damping factor used to characterize the substitute structure for different structural systems is a dominant parameter in this design methodology. In this paper, results of experimental and numerical investigations performed for estimating the equivalent viscous damping in DDBD procedure of two lateral resistance systems, moment frames and braced moment frames, are presented. For these investigations, cyclic loading tests are conducted on scaled moment resisting frames with and without bracing. The experimental results are also used to calibrate full‐scale numerical models. A numerical investigation is then conducted on a set of analytical moment resisting frames with and without bracing. The equivalent viscous damping and ductility of each analytical model are calculated from hysteretic responses. On the basis of analytical results, new equations are proposed for equivalent viscous damping as a function of ductility for reinforced concrete and steel braced reinforced concrete frames. As a result, the new equation is used in direct displacement‐based design of a steel braced reinforced concrete frame. Copyright © 2012 John Wiley & Sons, Ltd.     

Ductility reduction factor and collapse mechanism evaluation of a new steel knee braced frame

In this study, the suitability of a new structural system called the knee braced frames (KBFs) is investigated for seismic resistant steel structures. In these structural systems, ends of beams are connected to columns by hinges (simple connection) instead of rigid connections, and ends of knee braced elements are connected to columns and beams by hinges as well. In the present paper, in addition to a comparison between elastic behaviour and elastic fundamental natural period, the ductility reduction factor and the type of collapse mechanism in steel KBFs and steel moment resisting frames (MRFs) are compared. The study revealed that the stiffness of steel buildings can be increased considerably by applying knee braced elements and the effects of knee braced elements are highly dependent on knee braced configuration. By applying the pushover analysis, it was observed that the type of collapse mechanism of KBFs is very similar to the mechanism of MRFs. Furthermore in most cases, the ductility reduction factor, R_μ, obtained from steel KBFs is greater than the ductility reduction factor obtained for steel MRFs. Based on the similarity between type of collapse mechanism and the proximity of ductility reduction coefficients of the KBFs and MRFs systems, it can be concluded that the new steel knee braced frame systems can be categorised as steel MRFs with rigid connections.     

折曲撑框架在低周反复荷载下的抗震性能试验研究与设计建议

通过设置K型砼折曲撑以及其他型式支撑的两层框架和不设支撑的纯框架在低周反复荷载下的试验,着重研究了折曲撑框架的变形能力、延性系数、阻尼比等抗震耗能性能,以及其刚度和破坏机制。试验表明,折曲支撑是很好的消能抗侧力构件,且具有空间开敞。自重轻等特点。本文根据试验分析,提出了设计原则和建议。     

Overstrength and force reduction factors of multistorey reinforced‐concrete buildings

This paper addresses the issue of horizontal overstrength in modern code‐designed reinforced‐concrete (RC) buildings. The relationship between the lateral capacity, the design force reduction factor, the ductility level and the overstrength factor are investigated. The lateral capacity and the overstrength factor are estimated by means of inelastic static pushover as well as time‐history collapse analysis for 12 buildings of various characteristics representing a wide range of contemporary RC buildings. The importance of employing the elongated periods of structures to obtain the design forces is emphasized. Predicting this period from free vibration analysis by employing ‘effective’ flexural stiffnesses is investigated. A direct relationship between the force reduction factor used in design and the lateral capacity of structures is confirmed in this study. Moreover, conservative overstrength of medium and low period RC buildings designed according to Eurocode 8 is proposed. Finally, the implication of the force reduction factor on the commonly utilized overstrength definition is highlighted. Advantages of using an additional measure of response alongside the overstrength factor are emphasized. This is the ratio between the overstrength factor and the force reduction factor and is termed the inherent overstrength (Ω _i). The suggested measure provides more meaningful results of reserve strength and structural response than overstrength and force reduction factors. Copyright © 2002 John Wiley & Sons, Ltd.     

钢板带加固砖填充墙RC框架抗震性能试验研究

为研究钢板带加固砖填充墙RC框架的抗震性能,设计了缩尺单层单跨的纯RC框架1个、砖填充墙RC框架1个以及钢板带加固砖填充墙RC框架2个,考虑砂浆强度的影响,并对钢板带施加一定的预应力。基于低周往复荷载试验,对比分析了不同类型框架的破坏过程、滞回曲线、骨架曲线、刚度、延性和耗能能力。结果表明：钢板带加固砖填充墙RC框架可提高其承载力与耗能能力,但位移延性系数略有下降;钢板带加固基本不影响砖镇充墙RC框架的初始抗侧刚度,但是在层间位移角为1/100~1/50时,割线刚度可以提高24.6%~31.9%;螺栓孔对水平灰缝的削弱会影响填充墙的破坏形态;砂浆强度的提高会增加钢板带加固砖填充墙RC框架的初始抗侧刚度、峰值荷载与耗能能力。此外,提出了预应力钢板带加固砖填充墙RC框架的水平承载力计算方法,具有较好的预测精度。