Practice‐oriented probabilistic seismic performance assessment of infilled frames with consideration of shear failure of columns

The objective of the study presented in this paper is to investigate the effects of masonry infills on the shear demand and failure of columns for the case when reinforced concrete frames with such infills are modeled by means of simplified nonlinear models that are not capable of the direct simulation of these effects. It is shown that an approximate simulation of the shear failure of columns can be achieved through an iterative procedure that involves pushover analysis, post‐processing of the analysis results using limit‐state checks of the components, and model adaptation if shear failure of columns is detected. The fragility parameters and the mean annual frequency of limit‐state exceedance are computed on the basis of nonlinear dynamic analysis by using an equivalent SDOF model. The proposed methodology is demonstrated by means of two examples. It was shown that the strength of the four‐story and seven‐story buildings and their deformation capacity are significantly overestimated if column shear failure due to the effects of masonry infills is neglected, whereas the mean annual frequency of limit‐state exceedance for the analyzed limit states is significantly larger than that estimated for the case if the shear failure of columns is neglected. Copyright © 2012 John Wiley & Sons, Ltd.     

Fragility functions and floor spectra of RC masonry infilled frames: influence of mechanical properties of masonry infills

A wide number of experimental studies conducted in latest years pointed out the high influence of the mechanical properties of masonry units and mortar bed joints on lateral strength and stiffness of masonry panels. This feature significantly modifies the global response of infilled frames under seismic actions as well as the local interaction phenomena. Despite a wide investigation on the influence of the infills on global behaviour of reinforced concrete (RC) frames has already been provided, different features characterizing the seismic performances of buildings suggest the need of accurately evaluating local interaction phenomena as well as the influence of the panel on specific and relevant aspects, as the accelerations transferred to non-structural components. This study provides a parametrical analysis of the influence of shear strength and elastic modulus of masonry infills on the seismic behaviour of RC frames originally designed for gravity loads. Regular buildings with different height were analysed using the Incremental Dynamic Analysis in order to provide fragility curves, investigate on the collapse mechanisms and define the floor spectra depending on the properties of the infills. Results obtained pointed out the high influence of the considered parameters on the fragility of existing RC frames, often characterized by inadequate transversal reinforcement of columns, which may lead to brittle failure due to the interaction with the infills. Floor response spectra are also significantly affected by the influence of masonry infills both in terms of shape and maximum spectral accelerations. Lastly, on the basis of the observed failure mechanisms, a parameter defining the ductility of the frames depending on the properties of the infills was also provided (Capacity Design Factor). The correlation between the mechanical properties of the infills and this parameter suggests its reliability in the simplified vulnerability analysis of existing buildings as well as for the design of new buildings.     

Shake table tests on RC frame infilled by slitted masonry panels

Unreinforced masonry infill walls are widely used as non-structural partitions in RC frames. The effects of infills on the structural responses are often ignored in the design process since they are generally considered as expendable elements. However, recent studies have shown that not only shear damage can be inflicted to the columns braced by the infill walls, but also that the structural stability can be jeopardised by the fall-off of the infills. This paper presents the development of new detailing methods for the infill walls, which features slit panels, isolation gaps between the infills and columns, and anchorage of the infills. The proposed detailing methods were tested and verified experimentally using shake-table tests on five 1/3-scale infilled RC frame specimens with different combinations of the features stated above. The design and construction of the shake-table test specimens have taken into account the similitude requirements. The test results indicate that the proposed detailing method effectively reduced the undesirable interaction between column and infill walls. And the use of proper anchorage could prevent the fall off of infills from the bounding frame. Furthermore, the specimens with slit infill walls displayed better seismic performances, which could be attributed to the rocking behaviour of the sub-panels with increased aspect ratios.     

Effect of masonry infills on seismic performance of a 3‐storey R/C frame with non‐seismic detailing

The objective of this study is to investigate the effect of masonry infills on the seismic performance of low‐rise reinforced concrete (RC) frames with non‐seismic detailing. For this purpose, a 2‐bay 3‐storey masonry‐infilled RC frame was selected and a 1 : 5 scale model was constructed according to the Korean practice of non‐seismic detailing and the similitude law. Then, a series of earthquake simulation tests and a pushover test were performed on this model. When the results of these tests are compared with those in the case of the bare frame, it can be recognized that the masonry infills contribute to the large increase in the stiffness and strength of the global structure whereas they also accompany the increase of earthquake inertia forces. The failure mode of the masonry‐infilled frame was that of shear failure due to the bed‐joint sliding of the masonry infills while that of the bare frame appeared to be the soft‐storey plastic mechanism at the first storey. However, it is judged that the masonry infills can be beneficial to the seismic performance of the structure since the amount of the increase in strength appears to be greater than that in the induced earthquake inertia forces while the deformation capacity of the global structure remains almost the same regardless of the presence of the masonry infills. Copyright © 2001 John Wiley & Sons, Ltd.     

Preliminary analysis of a soft‐storey mechanism after the 2009 L'Aquila earthquake

Observation of damage caused by the recent Abruzzo earthquake on April 6th 2009 showed how local interaction between infills and RC structures can lead to soft‐storey mechanisms and brittle collapses. Results of the present case study are based on observed damage caused by the earthquake in the zone of Pettino. Analytical model based on simulated design procedure was built up and time history analyses were employed to verify the causes of the structural collapse, as highlighted by observed damage. This failure mechanism was investigated taking into consideration all components of the ground motion. Nonlinear behavior of brick masonry infills was taken into account and two parametric hypotheses for infill mechanical properties were considered, given the uncertainties that typically characterize these nonstructural elements. Nonlinear modeling of infills was made by a three‐strut macro‐model aimed at considering both local and global interaction between RC frame and infills. Seismic input was characterized by the real signal registered during the mainshock near the case‐study structure. Different shear capacity models were considered in the assessment. Analytical results seem to confirm with good approximation the likely collapse scenario that damage observation highlighted; the lack of proper detailing in the columns made the local interaction between infills and RC columns and the strong vertical component of the ground motion to be the main causes of the brittle failure. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Procedures for calibration of linear models for damage limitation in design of masonry‐infilled RC frames

Recent earthquakes have confirmed the role played by infills in the seismic response of reinforced concrete buildings. The control and limitation of damage to such nonstructural elements is a key issue in performance‐based earthquake engineering. The present work is focused on modeling and analysis of damage to infill panels, and, in particular, it is aimed towards linear analysis procedures for assessing the damage limitation limit state of infilled reinforced concrete frames. First, code provisions on infill modeling and acceptance criteria at the damage limitation limit state are reviewed. Literature contributions on damage to unreinforced masonry infill panels and corresponding displacement capacity are reported and discussed. Two procedures are then proposed aiming at a twofold goal: (i) the determination of ‘equivalent’ interstory drift ratio limits for a bare frame model and (ii) the estimation of the stiffness of equivalent struts representing infill walls in a linear model. These two quantities are determined such that a linear model ensures a reliable estimation of seismic capacity at the damage limitation limit state, providing the same intensity level as that obtained from nonlinear analyses carried out on structural models with infills. Finally, the proposed procedures are applied to four‐story and eight‐story case study‐infilled frames, designed for seismic loads according to current technical codes. The results of these application examples are presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Strength and stiffness reduction factors for infilled frames with openings

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

A capacity curve model for confined clay brick infills

Experimental studies have proven that clay brick infills, confined with carbon-fiber-reinforced polymers (CFRP) in reinforced concrete (RC) frames, have some advantages in terms of stiffness, strength, energy dissipation capability and damage intensity. Owing to these advantages, existing infill walls in RC frames may be retrofitted with CFRP strips, especially in low-rise buildings in earthquake-prone areas. There is a gap in the literature concerning their behavior model, for use in structural analysis. A piecewise linear capacity curve model called “DUVAR” is proposed here, which estimates the envelope of force-vs.-displacement hysteresis, depending on the data compiled from the literature and the completed experimental studies. A nonlinear shear spring element is utilized in the model to represent the bare and retrofitted infills. The ultimate shear strength and the corresponding displacement, the ratio of cracking stiffness to initial stiffness, the ratio of ultimate strength to cracking strength, and the ductility ratio are the five key parameters of the model. The model is validated against the experimental results of two sovereign studies. Finally, the model is employed in the performance evaluation of an existing three-story RC building to exemplify its straightforward application.     

Shaking table testing for masonry infill walls: unreinforced versus reinforced solutions

Several factors influence the behaviour of infilled frames, which have been a subject of research in the past with moderate success. The new generation of European design standards imposes the need to prevent brittle collapse of the infills and makes the structural engineer accountable for this requirement, yet it fails to provide sufficient information for masonry infills design. Therefore, the present work aims at understanding the seismic behaviour of masonry infill walls within reinforced concrete frames, using both unreinforced and reinforced solutions (bed joint reinforcement and reinforced plaster). For this purpose, three reinforced concrete buildings with different infill solutions were constructed at a scale of 1:1.5, all with the same geometry, and were tested on the shaking table of the National Laboratory for Civil Engineering, Portugal. All solutions performed adequately for the design earthquake, with no visible damage. Still, the experimental tests show that the double‐leaf‐unreinforced infill walls underperformed during a large earthquake, collapsing out of plane by rotating as rigid bodies with multiple configurations. Also the reinforced concrete buildings collapsed, because of the adverse interaction with the infill walls. The infill walls with bed joint reinforcement and reinforced plaster did not collapse out of plane, because of their connection to the concrete frame, which is an essential requirement. Copyright © 2016 John Wiley & Sons, Ltd.     

Cyclic response of masonry infilled RC frames: Experimental results and simplified modeling

The recent large interest in nonlinear seismic analysis methods, static and dynamic, has required proper strategies of modeling based on reliable, and at the same time easy to use, constitutive laws for the structural elements. Regarding the behavior of framed structures, special attention has to be devoted to infills because of the key role they play in modifying overall stiffness, strength and ductility under seismic excitation. Pointing out the attention on this topic the paper discusses a criteria for modeling the structural behavior of infills based on a macromodeling approach, that is to say on the substitution of infills with diagonal pin jointed struts. Is here shown how multilinear plastic link elements governed by a hysteretic Pivot model, available in different FEM codes, can be appropriately used to model the equivalent struts to perform linear or nonlinear analyses. In order to enlarge experimental knowledge on cyclic behavior of infilled frames structures and as reference for developing the above mentioned modeling strategy, an experimental campaign on single-storey, single-bay, fully infilled frames with different kinds of masonry and subjected to lateral cyclical loads, was carried out, and some others available in the literature are referred to. Validation of Pivot modeling approach was carried out comparing experimental results and computer simulations of the experimental tests. In the paper hysteresis parameters values calibrating Pivot law are also given for involved masonry infills typologies and some proposals for correlation between strength and stiffness of infilled frames and of masonry infills are provided as a tool for the quick calibration of the Pivot model in practical applications.     

Seismic response of masonry-infilled steel frames via multi-scale finite-element analyses

Effects of masonry infills on the seismic vulnerability of steel frames is studied through multi-scale numerical modelling. First, a micro-modelling approach is utilized to define a homogenized masonry material, calibrated on experimental tests, which is used for modelling the nonlinear response of a one-story, single span, masonry-infilled portal under horizontal loads. Based on results of the micro-model, the constitutive behavior of a diagonal strut macro-element equivalent to the infill panel is calibrated. Then, the diagonal strut is used to model infill panels in the macro-scale analysis of a multi-span multi-story infilled moment-resisting (MR) steel frame. The seismic vulnerability of the MR frame is evaluated through a nonlinear static procedure. Numerical analyses highlight that infills may radically modify the seismic response and the failure mechanism of the frame, hence the importance of the infill correct modelling.     

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

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

高轴压比下圆钢管钢渣混凝土柱抗震性能试验研究

通过2根圆钢管普通混凝土柱与5根圆钢管钢渣混凝土柱在高轴压比下的水平低周反复加载试验,研究圆钢管钢渣混凝土柱的轴压比、钢管壁厚、钢渣砂替代率和长细比对其破坏形态、滞回耗能能力、骨架曲线、延性及耗能、刚度退化的影响规律。研究结果表明:钢渣混凝土试件破坏过程和破坏形态与普通混凝土试件基本相同,主要表现为钢管底部鼓曲的压弯破坏;所有试件滞回曲线饱满,无明显“捏缩”现象;高轴压比试件存在明显承载力突降现象,合理的径厚比（钢管直径/钢管壁厚）对高轴压比试件承载力突降有明显改善作用;低轴压比试件延性系数大于4.0,高轴压比试件延性系数介于1.57～3.76之间,轴压比增大,试件延性下降;试件破坏时等效粘滞阻尼系数ξ_eq介于0.259～0.437之间;建议采用《钢管混凝土混合结构技术标准》（GB/T51446－2021）或《钢管混凝土结构技术规程》（DBJ/T13－51－2010）计算地震作用下钢管钢渣混凝土柱压弯承载力,但高轴压比钢管钢渣混凝土柱计算结果需乘以折减系数0.8。     

Evaluation of the fishbone model in simulating the seismic response of multistory reinforced concrete moment-resisting frames

The fishbone model is a simplified numerical model for moment-resisting frames that is capable of modelling the effects of column-beam strength and stiffness ratios. The applicability of the fishbone model in simulating the seismic responses of reinforced concrete moment-resisting frames of different sets of column-beam strength and stiffness ratios are evaluated through nonlinear static, dynamic and incremental dynamic analysis on six prototype buildings of 4-, 8-and 12-stories. The results show that the fishbone model is practically accurate enough for reinforced concrete frames, although the assumption of equal joint rotation does not hold in all cases. In addition to the ground motion characteristics and the number of stories in the structures, the accuracy of the model also varies with the column-beam stiffness and strength ratios. The model performs better for strong column-weak beam frames, in which the lateral drift patterns are better controlled by the continuous stiffness provided by the strong columns. When the inelastic deformation is large, the accuracy of the model may be subjected to large record-to-record variability. This is especially the case for frames of weak columns.     

Influence of the column-to-beam flexural strength ratio on the failure mode of beam-column connections in RC frames

The column-to-beam flexural strength ratio(CBFSR)has been used in many seismic codes to achieve the strong column-weak beam(SCWB)failure mode in reinforced concrete(RC)frames,in which plastic hinges appear earlier in beams than in columns.However,seismic investigations show that the required limit of CBFSR in seismic codes usually cannot achieve the SCWB failure mode under strong earthquakes.This study investigates the failure modes of RC frames with different CBFSRs.Nine typical three-story RC frame models with different CBFSRs are designed in accordance with Chinese seismic codes.The seismic responses and failure modes of the frames are investigated through time-history analyses using 100 ground motion records.The results show that the required limit of the CBFSR that guarantees the SCWB failure mode depends on the beam-column connection type and the seismic intensity,and different types of beam-column connections exhibit different failure modes even though they are designed with the same CBFSR.Recommended CBFSRs are proposed for achieving the designed SCWB failure mode for different types of connections in RC frames under different seismic intensities.These results may provide some reference for further revisions of the SCWB design criterion in Chinese seismic codes.     

EFFECT OF INFILLS ON THE GLOBAL BEHAVIOUR OF R/C FRAMES: ENERGY CONSIDERATIONS FROM PSEUDODYNAMIC TESTS

A series of pseudo-dynamic tests were conducted on a full-scale four-storey reinforced concrete building designed according to Eurocodes 2 and 8. The building was 10 m long, 10 m wide, and 12⋅5 m high. It was designed as a ductility class ‘High’ structure, for typical live loads and for a peak ground acceleration of 0⋅3 g and medium soil conditions. A first test was conducted on the bare frame. The project was carried out within the framework of the European Association of Structural Mechanics Laboratories (EASML), and was designed to assess the adequacy of the damage indicators to be used in the calibration of Eurocode 8. The pseudodynamic test was conducted by using an artificially generated earth-quake derived from a real earthquake (Friuli, 1976), with nominal acceleration 50 per cent larger than the value adopted in design. The structure performed as expected. The pattern of the measured rotations was that of a weak-beam, strong-column mechanism. The fundamental frequency of the structure after the test was found to be half of the initial value, but the damage was limited and uniformly distributed. A second experimental programme was conducted as part of the work of the Network Prenormative Research in support of Eurocode 8, to study the influence of masonry infill panels on the global behaviour of the frame. Two pseudodynamic tests were conducted, with different infill patterns. A test was performed by infilling the two external frames with hollow brick masonry in all four storeys (uniform infill distribution). The test was then repeated on the structure without infills at the first storey, to create a soft-storey effect. The input signal was the same as in the tests on the bare frame. The purpose of the tests was to study the effects of the different layouts of infills, as well as to calibrate the computer models for the infills to be used in parametric analyses. In this paper the test results are presented and the performances of the structure with different infill configurations are compared. The global behaviour of the structure is compared with the predictions which could have been made with simplified approaches. In particular, single degree of freedom energy concepts are used to verify if the differences in the global behaviour could have been predicted. The differences in the single degree of freedom energy demands with respect to the bare frame may be used as a means of accounting for the presence of irregular distributions of non-structural infills in the simplified design of the frame.     

Dispersions for the pushover‐based risk assessment of reinforced concrete frames and cantilever walls

The paper presents the results of an investigation into the dispersion values, expressed in terms of limit‐state spectral accelerations, which could be used for the pushover‐based risk assessment of low‐height to mid‐height reinforced concrete frames and cantilever walls. The results of an extensive parametric study of a portfolio of test structures indicated that the dispersion values due to record‐to‐record variability and modelling uncertainty (β_LS,RU) are within the range from 0.3 to 0.55 for the near collapse limit state, and between 0.35 and 0.60 for the collapse limit state. The dispersions β_LS,RU proposed for the code‐conforming and the majority of old (non code‐conforming) frames are in between these values. On the other hand, the dispersions proposed for the old frames with a soft storey and an invariant plastic mechanism, and for the code‐conforming cantilever walls, are at the lower and upper bounds of the presented values, respectively. The structural parameters that influence these dispersions were identified, and the influence of different ground motion sets, and of the models used for the calculation of the rotation capacities of the columns, on the calculated fragility parameters was examined and quantified. The proposed dispersion values were employed in a practice‐oriented pushover‐based method for the estimation of failure probability for eight selected examples. The pushover‐based risk assessment method, although extremely simple and economical when compared with more rigorous probabilistic methods, was able to predict seismic risk with reasonable accuracy, thus showing it to be a practical tool for engineers. Copyright © 2016 John Wiley & Sons, Ltd.     

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete(RC) frame structures are implemented by either static pushover analysis(PA) or dynamic time history analysis,with diverse settings of the plastic hinges(PHs) on such main structural components as columns,beams and walls,the complex behavior of shear failure at beam-column joints(BCJs) during major earthquakes is commonly neglected.This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures.Based on the specifications of FEMA-356,a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established,allowing a sophisticated PA to be performed.To verify the validity of this method,the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements.By considering shear failure at BCJs,the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames,including seismic capacity and the progressive failure sequence of joints,in a precise and effective manner.