Nonlinear Time History Analysis for the Different Column Orientations under Seismic Wave Synthetic Approach

The significant impact of earthquakes on human lives and the built environment underscores the extensive human and economic losses caused by structural collapses. Over the years, researchers have focused on improving seismic design to mitigate earthquake-induced damages and enhance structural performance. In this study, a specific reinforced concrete (RC) frame structure at Kyungpook National University, designed for educational purposes, is analyzed as a representative case. Utilizing SAP 2000, the research conducts a nonlinear time history analysis to assess the structural performance under seismic conditions. The primary objective is to evaluate the influence of different column section designs, while maintaining identical column section areas, on structural behavior. The study employs two distinct seismic waves from Abeno (ABN) and Takatori (TKT) for the analysis, comparing the structural performance under varying seismic conditions. Key aspects examined include displacement, base shear force, base moment, joint radians, and layer displacement angle. This research is anticipated to serve as a valuable reference for seismic restraint reinforcement work on RC buildings, enriching the methods used for evaluating structures through nonlinear time history analysis based on the synthetic seismic wave approach.

Seismic performance evaluation of an infilled rocking wall frame structure through quasi-static cyclic testing

Earthquake investigations have illustrated that even code-compliant reinforced concrete frames may suffer from soft-story mechanism.This damage mode results in poor ductility and limited energy dissipation.Continuous components offer alternatives that may avoid such failures.A novel infilled rocking wall frame system is proposed that takes advantage of continuous component and rocking characteristics.Previous studies have investigated similar systems that combine a reinforced concrete frame and a wall with rocking behavior used.However,a large-scale experimental study of a reinforced concrete frame combined with a rocking wall has not been reported.In this study,a seismic performance evaluation of the newly proposed infilled rocking wall frame structure was conducted through quasi-static cyclic testing.Critical joints were designed and verified.Numerical models were established and calibrated to estimate frame shear forces.The results evaluation demonstrate that an infilled rocking wall frame can effectively avoid soft-story mechanisms.Capacity and initial stiffness are greatly improved and self-centering behavior is achieved with the help of the infilled rocking wall.Drift distribution becomes more uniform with height.Concrete cracks and damage occurs in desired areas.The infilled rocking wall frame offers a promising approach to achieving seismic resilience.

Experimental study on the seismic response of braced reinforced concrete frame with irregular columns

A 15-storey K-braced reinforced concrete model frame with irregular columns, i.e., T-shaped, L-shaped, as well as ＋-shaped columns, was constructed and tested on the six-degree-of-freedom shaking table at the State Key Laboratory for Disaster Reduction in Civil Engineering in Tongji, China. Two types of earthquake records, El-Centro wave （south-north direction） and Shanghai artificial wave （SHAW） with various peak accelerations and principal-secondary sequences, were input and experimentally studied. Based on the shaking table tests and theoretical analysis, several observations can be made. The failure sequence of the model structure is brace→beam→column→joints, so that the design philosophy for several lines of defense has been achieved. Earthquake waves with different spectrums not only influence the magnitude and distribution of the earthquake force and the storey shear force, but also obviously affect the magnitude of the displacement response. The aftershock seismic response of previously damaged reinforced concrete braced frames with irregular columns possesses the equivalent elastic performance characteristic. Generally speaking, from the aspects of failure features and drift ratio, this type of reinforced concrete structure provides adequate earthquake resistance and can be promoted for use in China.

Seismic performance analysis and design suggestion for frame buildings with cast-in-place staircases

Many staircases in reinforced concrete （RC） frame structures suffered severe damage during the Wenchuan earthquake. Elastic analyses for 18 RC structure models with and without staircases are conducted and compared to study the influence of the staircase on the stiffness, displacements and internal forces of the structures. To capture the yielding development and damage mechanism of frame structures, elasto-plastic analysis is carried out for one of the 18 models. Based on the features observed in the analyses, a new type of staircase design i.e., isolating them from the master structure to eliminate the effect of K-type struts, is proposed and discussed. It is concluded that the proposed method of staircase isolation is effective and feasible for engineering design, and does not significantly increase the construction cost.

Effectiveness of two conventional methods for seismic retrofit of steel and RC moment resisting frames based on damage control criteria

This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation methods, concentric chevron bracing（CCB） and cylindrical friction damper（CFD） were selected. The performance assessment procedure of the frames is divided into two distinct phases. First, the limit state probabilities of the structures before and after rehabilitation are investigated. In the second phase, the seismic risk of structures in terms of life safety and financial losses（decision variables） using the recently published FEMA P58 methodology is evaluated. The results show that the proposed retrofitting methods improve the serviceability and life safety performance levels of steel and RC structures at different rates when subjected to earthquake loads. Moreover, these procedures reveal that financial losses are greatly decreased, and were more tangible by the application of CFD rather than using CCB. Although using both retrofitting methods reduced damage state probabilities, incorporation of a site-specific seismic hazard curve to evaluate mean annual occurrence frequency at the collapse prevention limit state caused unexpected results to be obtained. Contrary to CFD, the collapse probability of the structures retrofitted with CCB increased when compared with the primary structures.

Study of the seismic response of a recycled aggregate concrete frame structure

Based on six-degree-of-freedom three-dimensional shaking table tests, the seismic response of a recycled aggregate concrete （RAC） frame was obtained. The analysis results indicate that the maximum story shear force and overturning moment reduce proportionally along the height of the model under the same earthquake wave. The story shear force, base shear coefficient and overturning moment of the structure increase progressively as the acceleration amplitude increases. The base shear coefficient is primarily controlled by the peak ground acceleration （PGA）. The relationships between the PGA and the shear coefficient as well as between the PGA and the dynamic amplification factor are obtained by mathematical fitting. The dynamic amplification factor decreases rapidly at the elastic-plastic stage, but decreases slowly with the development of the elastic-plasticity stage. The results show that the RAC frame structure has reasonable deformability when compared with natural aggregate concrete frame structures. The maximum inter-story drift ratios of the RAC frame model under frequent and rare intensity 8 test phases are 1/266 and 1/29, respectively, which are larger than the allowable value of 1/500 and 1/50 according to Chinese seismic design requirements. Nevertheless, the RAC frame structure does not collapse under base excitations with PGAs from 0.066 g up to 1.170 g.

Optimal seismic retrofit model for steel moment resisting frames with brittle connections

Based on performance-based seismic engineering, this paper proposes an optimal seismic retrofit model for steel moment resisting frames（SMRFs） to generate a retrofit scheme at minimal cost. To satisfy the acceptance criteria for the Basic Safety Objective（BSO） specified in FEMA 356, the minimum number of upgraded connections and their locations in an SMRF with brittle connections are determined by evolutionary computation. The performance of the proposed optimal retrofitting model is evaluated on the basis of the energy dissipation capacities, peak roof drift ratios, and maximum interstory drift ratios of structures before and after retrofitting. In addition, a retrofit efficiency index, which is defined as the ratio of the increment in seismic performance to the required retrofitting cost, is proposed to examine the efficiencies of the retrofit schemes derived from the model. The optimal seismic retrofit model is applied to the SAC benchmark examples for threestory and nine-story SMRFs with brittle connections. Using the retrofit efficiency index proposed in this study, the optimal retrofit schemes obtained from the model are found to be efficient for both examples in terms of energy dissipation capacity, roof drift ratio, and maximum inter-story drift ratio.

Seismic retrofitting of reinforced concrete frame structures using GFRP-tube-confined-concrete composite braces

This paper presents a new type of structural bracing intended for seismic retrofitting use in framed structures. This special composite brace, termed glass-fiber-reinforced-polymer （GFRP）-tube-confined-concrete composite brace, is comprised of concrete confined by a GFRP tube and an inner steel core for energy dissipation. Together with a contribution from the GFRP-tube confined concrete, the composite brace shows a substantially increased stiffness to control story drift, which is often a preferred feature in seismic retrofitting. An analysis model is established and implemented in a general finite element analysis program - OpenSees, for simulating the load-displacement behavior of the composite brace. Using this model, a parametric study of the hysteretic behavior （energy dissipation, stiffness, ductility and strength） of the composite brace was conducted under static cyclic loading and it was found that the area ratio of steel core to concrete has the greatest influence among all the parameters considered. To demonstrate the application of the composite brace in seismic retrofitting, a three-story nonductile reinforced concrete （RC） frame structure was retrofitted with the composite braces. Pushover analysis and nonlinear time-history analyses of the retrofitted RC frame structure was performed by employing a suite of 20 strong ground motion earthquake records. The analysis results show that the composite braces can effectively reduce the peak seismic responses of the RC frame structure without significantly increasing the base shear demand.

Self-centering seismic retrofit scheme for reinforced concrete frame structures:SDOF system study

This paper presents the results of a parametric study of self-centering seismic retrofit schemes for reinforced concrete (RC) frame buildings. The self-centering retrofit system features flag-shaped hysteresis and minimal residual deformation. For comparison purpose,an alternate seismic retrofit scheme that uses a bilinear-hysteresis retrofit system such as buckling-restrained braces (BRB) is also considered in this paper. The parametric study was carried out in a single-degree-of-freedom (SDOF) system framework since a multi-story building structure may be idealized as an equivalent SDOF system and investigation of the performance of this equivalent SDOF system can provide insight into the seismic response of the multi-story building. A peak-oriented hysteresis model which can consider the strength and stiffness degradation is used to describe the hysteretic behavior of RC structures. The parametric study involves two key parameters -the strength ratio and elastic stiffness ratio between the seismic retrofit system and the original RC frame. An ensemble of 172 earthquake ground motion records scaled to the design basis earthquake in California with a probability of exceedance of 10% in 50 years was constructed for the simulation-based parametric study. The effectiveness of the two seismic retrofit schemes considered in this study is evaluated in terms of peak displacement ratio,peak acceleration ratio,energy dissipation demand ratio and residual displacement ratio between the SDOF systems with and without retrofit. It is found from this parametric study that RC structures retrofitted with the self-centering retrofit scheme (SCRS) can achieve a seismic performance level comparable to the bilinear-hysteresis retrofit scheme (BHRS) in terms of peak displacement and energy dissipation demand ratio while having negligible residual displacement after earthquake.

Behavior of ductile steel X-braced RC frames in seismic zones

A satisfactory ductile performance of moment-resisting reinforced concrete concentric braced frame structures (RC-MRCBFs) is not warranted by only following the provisions proposed in Mexico’s Federal District Code (MFDC-04). The nonlinear behavior of low to medium rise ductile RC-MRCBFs using steel X-bracing susceptible to buckling is evaluated in this study. The height of the studied structures ranges from 4 to 20 stories and they were located for design in the lakebed zone of Mexico City. The design of RC-MRCBFs was carried out considering variable contribution of the two main lines of defense of the dual system (RC columns and steel braces). In order to observe the principal elements responsible for dissipating the earthquake input energy, yielding mappings for diff erent load-steps were obtained using both nonlinear static and dynamic analyses. Some design parameters currently proposed in MFDC-04 as global ductility capacities, overstrength reduction factors and story drifts corresponding to diff erent limit states were assessed as a function of both the considered shear strength and slenderness ratios for the studied RC-MRCBFs using pushover analyses. Additionally, envelopes of response maxima of dynamic parameters were obtained from the story and global hysteresis curves. Finally, a brief discussion regarding residual drifts, residual drift ratios, mappings of residual deformations in steel braces and residual rotations in RC beams and columns is presented. From the analysis of the obtained results, it is concluded that when a suitable design criterion is considered, good structural behavior of RC-MRCBFs with steel-X bracing can be obtained. It is also observed that the shear strength balance has an impact in the height-wise distribution of residual drifts, and an important “shake-down” eff ect is obtained for all cases. There is a need to improve design parameters currently proposed in MFDC to promote an adequate seismic performance of RC-MRCBFs.

Evaluation of collapse resistance of RC frame structures for Chinese schools in seismic design categories B and C

According to the Code for Seismic Design of Buildings （GB50011-2001）, ten typical reinforced concrete （RC） frame structures, used as school classroom buildings, are designed with different seismic fortification intensities （SFIs） （SFI=6 to 8.5） and different seismic design categories （SDCs） （SDC=B and C）. The collapse resistance of the frames with SDC=B and C in terms of collapse fragility curves are quantitatively evaluated and compared via incremental dynamic analysis （IDA）. The results show that the collapse resistance of structures should be evaluated based on both the absolute seismic resistance and the corresponding design seismic intensity. For the frames with SFI from 6 to 7.5, because they have relatively low absolute seismic resistance, their collapse resistance is insufficient even when their corresponding SDCs are upgraded from B to C. Thus, further measures are needed to enhance these structures, and some suggestions are proposed.

Performance of Rigid Steel Frames under Adequate Soil Conditions Using Seismic Code Provisions

This study is focused on?nonlinear analysis and design of?spatial and perimeter moment resisting frames for a 9-storeys?office building?having?9.15?m span.?Seismic?design criteria of Eurocode 8?Ductility Class High (DCH)?with behavior factor (q) of 6.5 and AISC/ASCE code,?Special Moment resisting Frame (SMF) with response modification factor (R) of 8 were employed.?The design outcomes?are?expressed in terms of frame performance?(non-linear analysis), section profiles?(code recommendations), strength-demand to capacity ratios, drift-demand to capacity?ratios and structural weight. The consequences of the research compare?two codes in term of weights and design performances.?This will aid professional engineers and researchers to select effective design criteria and capacity design rules?efficiently.

Topographic effects on seismic response of long-span rigid-frame bridge under SV seismic wave

Seismic ground motions of two neighboring mountains and the free surface between them are calculated under the SV seismic waves with three different incident angles. The results are then taken as the inputs of multi-point seismic excitations for the foundation of a long-span bridge built over the valley in the analysis considering the integrated influence of traveling wave and topography. On the basis of a dynamic analytical method, a finite element model is created for the seismic responses of a four-span rigid-frame bridge of 440 m. The pier-top displacement and the pier-bottom internal force of the bridge are calculated. Then the results are compared with those considering traveling-wave effect only. The conclusions can serve as a seismic design reference for the structures located on the complex mountain topography.

Effect of URM infills on seismic vulnerability of Indian code designed RC frame buildings

Unreinforced Masonry (URM) is the most common partitioning material in framed buildings in India and many other countries. Although it is well-known that under lateral loading the behavior and modes of failure of the frame buildings change significantly due to infill-frame interaction, the general design practice is to treat infills as nonstructural elements and their stiffness, strength and interaction with the frame is often ignored, primarily because of difficulties in simulation and lack of modeling guidelines in design codes. The Indian Standard, like many other national codes, does not provide explicit insight into the anticipated performance and associated vulnerability of infilled frames. This paper presents an analytical study on the seismic performance and fragility analysis of Indian code-designed RC frame buildings with and without URM infills. Infills are modeled as diagonal struts as per ASCE 41 guidelines and various modes of failure are considered. HAZUS methodology along with nonlinear static analysis is used to compare the seismic vulnerability of bare and infilled frames. The comparative study suggests that URM infills result in a significant increase in the seismic vulnerability of RC frames and their effect needs to be properly incorporated in design codes.

Seismic design factors for RC special moment resisting frames in Dubai,UAE

This study investigates the seismic design factors for three reinforced concrete （RC） framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code （IBC＇09）. Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years （10/50 and 2/50, respectively） are used. The nonlinear dynamic resPonses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor （R）, deflection amplification factor （Cd）, system overstrength factor （Ωo）, and response modification factor for ductility （Rd） in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion （10/50 versus 2/50）. Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the D~ factor, which shows a mere 30% increase. Based on the observed trends, perioddependent R and Cd factors are recommended if consistent collapse probability （or collapse prevention performance） in moment frames with varying heights is to be expected.

A new methodology for energy-based seismic design of steel moment frames

A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom （SDOF） systems are applied to multi-degree-of-freedom （MDOF） steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault- normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design （EBSD） procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.

Peak displacement patterns for the performance-based seismic design of steel eccentrically braced frames

Performance-based seismic design(PBSD) aims to assess structures at different damage states. Since damage can be directly associated to displacements, seismic design with consideration of displacement seems to be logical. In this study, simple formulae to estimate the peak floor displacement patterns of eccentrically braced frames(EBFs) at different performance levels subjected to earthquake ground motions are proposed. These formulae are applicable in a PBSD and especially in direct displacement-based design(DDBD). Parametric study is conducted on a group of 30 EBFs under a set of 15 far field and near field accelerograms which they scaled to different amplitudes to adapt various performance levels. The results of thousands of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis in order to recognize the major parameters that influence the peak displacement pattern of these frames. Results show that suggested displacement patterns have relatively good agreement with those acquired by an exact nonlinear dynamic analysis.

Seismic Evaluation of Steel Moment Resisting Frames (MRFs)—Supported by Loose Granular Soil

Soil underneath a structure might affect the behavior and the overall response of the structure in seismic events. The role of loose soil conditions and the inclusion of soil-structure interaction (SSI) in the analysis are important issues that need to be addressed. Since steel structures are light, two configurations designed as spatial and perimeter are considered to study the effect of soil on the steel structural frames for the same building. The paper provides a parametric analysis on the influence of SSI on the overall performance of MRFs (Moment Resisting Frames) according to the provisions of Saudi Building Code (SBC) [1]. A case study has been developed in which spatial and perimeter moment resisting frames of 12, 6 and 3 stories residential buildings are designed using Saudi Building Code (SBC) prescriptions. A modal response spectrum analysis has been carried out to see the influence of SSI on the fundamental period of vibration, top story displacement and inter-story drift limitations. Moreover, a static non-linear analysis has been performed to investigate the performance of frames, thus allowing to identify the influence of SSI on the structural design of steel MRFs.

Seismic response of high-rise steel framed buildings with Chevron-braced designed according to Venezuelan codes

The object of this study is to determine the seismic response of regular high-rise steel buildings with chevron-braced frames. Mechanics models of three buildings of 14, 18 and 20 stories are studied, all of them with similar geometric characteristics in plant and elevation. These models are realized using prescriptions and parameters from venezuelan design codes. The seismic action is carry on through varius synthetic design spectrum compatible accelerograms defined by the seismic codes in this study, with three levels of intensity corresponding to three specific Limit States. Dynamic analysis is used to compute parameters of ductility, over strength and maximum displacements. From these results it can be concluded that chevron-braced frames presented a good overall performance and non V-braced frames show greater damage due to dynamic actions, validating non linear dynamic analysis as a very powerful tool to seismic-resistance design and chevron-braced frames as a very useful choice in improving the response of tall steel structures. since this lateral bracing system is absent from Venezuelan seismic codes.

考虑台地效应的泸定6.8级地震某框架结构震害调查与分析

2022年9月5日四川省泸定县发生6.8级地震,在磨西台地上某框架结构的震害调查中,发现其东区和西区的框架结构出现不同程度的震害,且差异明显。其中,东、西区框架的首层柱上端均发生了“强梁弱柱”型破坏,西区框架中等及以上破坏等级的比例达到81%,而东区框架仅为13%,呈现出与台地边缘的强关联性。为分析东、西区框架结构震害差异的原因,采用FK-SEM方法分析了磨西台地的地震放大效应。计算结果表明,距离台地边缘越近,地震放大系数越大。其中,水平和竖向的地震放大系数在西区建筑场地分别为2.30和2.25,而在东区建筑场地则分别为2.01和1.99。在此基础上,采用磨西台站的地震动记录,对东、西区框架结构进行了震害模拟,分析了其破坏原因。研究结果表明:磨西台地边缘的地震影响系数的实际放大系数超过了《抗规》规定,存在不利地段影响和近场地震效应叠加的情况,仅按《抗规》不利地段进行考虑,多层框架结构难以实现“大震不倒”的设防目标;竖向地震作用是框架柱下端破坏的直接原因,主要破坏形态为偏拉、偏压破坏,水平地震作用导致其二次破坏;“仿雀替”构造对结构整体变形能力不利,是框架结构“强梁弱柱”型破坏的主要原因。根据震害调查和分析结果,建议在9度近断层设防地区,靠近台地边缘的多层框架结构,设计前宜对建筑场地进行分析,并考虑竖向地震的影响;在有民族特色的建筑设计中,应将“仿雀替”等装饰物与框架脱离,设计为非结构构件,以减少其对框架结构抗震性能的不利影响。