Collapse Capacity Of Structures Research Articles

Effect of aftershock characteristics on the fragility curve of post-mainshock RC frames

Earthquakes are not isolated events but are often followed by aftershocks. While structures are typically designed to withstand the mainshock, the presence of aftershocks poses additional challenges. In some cases, a damaged structure could collapse under a strong aftershock because of the damage evolution and cumulative damage as well as strength and stiffness degradation. Thus, it is essential to understand the structural behavior for post-mainshock decision-making and seismic assessment. The current study explores the impact of aftershock characteristics on the collapse capacity of buildings in seismic zones in accordance with a probabilistic point of view. In this regard, two non-ductile reinforced concrete (RC) frames with 3 and 6 stories were investigated and analyzed using 62 real aftershock records with varying characteristics. Frames were modeled in OpenSees software using Beam With Hinges Element with appropriate plastic hinge length and fiber section to provide suitable accuracy for dynamic analysis. The incremental dynamic analysis (IDA) was used to generate collapse diagrams and fragility curves. Some important seismic parameters including the mean period (Tm), predominant period (Tp), bandwidth frequency (Ω), significant duration of aftershock (Ds) and site characteristics were considered. The results revealed that the probability of collapse would increase in aftershocks with longer periods. For example, for Sa (T1, 5 %) of 1 g and 3-story frame, the collapse probability is increased ≈25 % in Tm > 0.5s compared to Tm < 0.5s which is remarkable. Also, site characteristics could increase the probability of collapse by ~ 6 % in the 6-story frame. The same results can also be seen for aftershocks with a larger predominant period (Tp > T1), greater significant duration (Ds > 11 s) and lower bandwidth frequency (omega <0.5). The findings emphasize the significance of aftershock characteristics on structural collapse capacity, necessitating careful selection of seismic records for accurate evaluation of seismic behavior.

An efficient framework for structural seismic collapse capacity assessment based on an equivalent SDOF system

Assessing the structural collapse capacity efficiently and accurately is a key issue in earthquake engineering. Here, an efficient framework for structural seismic collapse capacity assessment based on an accurate equivalent single-degree-of-freedom (ESDOF) system is proposed. The corresponding ESDOF system is calibrated by matching the cyclic static pushover (SPO) curves of a more complex multi-degree-of-freedom (MDOF) system (e.g., high-fidelity finite element models) through a meta-heuristic optimization method. In this way, both the backbone curve and hysteretic characteristics (the stiffness and strength deterioration, and pinching behavior) of the complex MDOF system are considered in the corresponding ESDOF system. Then, incremental dynamic analysis (IDA) is carried out to assess the structural seismic collapse capacity using the ESDOF system instead of the corresponding MDOF system to improve the computational efficiency. The efficiency and accuracy of the proposed framework have been validated through three case studies, including a bare reinforced concrete (RC) frame, a steel frame, and an infilled wall RC frame. These results affirm that the proposed framework can accurately and efficiently assess the collapse capacity of low-rise bare and infilled RC frame structures, as well as steel frame structures.

The effect of the ground motion frequency content on seismic performance and fragility curve of special concentric braced frames

Several articles have investigated the effect of various seismic parameters on the response of the structure. However, there has been limited discussion on the impact of seismic frequency content on the brace failure modes and the collapse mechanism of this system. This study investigated the effect of this parameter, considering three special concentric bracing frames of 2, 4, and 6 stories. For the frame dynamic analysis, the open system for earthquake engineering simulation software (OpenSees) is used. To evaluate the effect of frequency content, 60 earthquake records with high, medium and low frequency content are selected from the pacific earthquake engineering research center ground motion database, considering the peak ground acceleration divided by the peak ground velocity ratio. Incremental dynamic analysis is conducted to draw fragility curves and examine the response of structures.The results indicated that the collapse capacity of structures decreased as the frequency content was reduced. The percentage of reduction in collapse capacity under earthquakes with high to the low frequency content in 2, 4 and 6 story structures were 68, 67 and 71, respectively. In fact, reducing the frequency content increased the probability of occurrence of low cycle fatigue mode in the brace.

Aftershock collapse capacity assessment of special steel moment frame structures

This study assessment of the collapse capacity of special steel moment frames (SSMFs) with considering earthquake shock sequences for structures height from 4 to 20 stories. The collapse capacity is expressed in terms of the Sa(T1) value at which the system reaches the collapse state. Collapse identification relies on the capability of the model to accurately simulate damage of members and the resulting behavior deterioration. The softening in the lateral response expressed in terms of maximum interstory drift (MID) when it is expressed against the Sa(T1) values is thus used to identify collapse occurrence. The mainshock-aftershock (MS-AS) effect and the uncertainties associated with it are simulated by utilizing a set of 32 natural record pairs. The level of damage induced by MS is represented by two parameters including MID and peak residual story drift (PRSD). Using these parameters, the MS is applied so as to various pre-selected damage levels are imposed. For each MS damage level, an incremental dynamic analysis (IDA) is performed using the AS record that follows MS and a free vibration phase. The AS intensity causing the collapse state is finally identified and respected for evaluating the effect of MS damage level. The correlation between the median collapse Sa’s, called aftershock median collapse capacity, and the MS damage indicated by MID and PRSD parameters is quantified. The study results indicate that larger mainshock damages are required to reduce the collapse capacity of high-rise SSMFs compared to low- to mid-rise structures. Furthermore, the structural collapse capacity may reduce significantly when the building is subjected to a high intensity MS. A comparison between the trendlines presented by the regression equations developed in terms of the MID and PRSD variables was indicated that the MID parameter was more predictable trend.The PRSD parameter was, however, said to be useful in the sense that its value could be measured just after an MS excitation.

Modelling catastrophic degradation of flexural-dominated RC columns at ultimate displacements based on fibre beam-column model

Catastrophic degradation of the mechanical strength of reinforced concrete (RC) columns at ultimate displacements is one of the critical factors for the seismic collapse of structures. Accurately predicting this degradation is critical to assess the seismic collapse capacity of structures. However, the mechanism and theory about the degradation of RC columns are insufficient at present. This study is devoted to revealing the cause of catastrophic degradation and establishing an updated fibre beam-column model for predicting the catastrophic degradation of RC columns at ultimate displacements. First, the de-confinement effect of kernel concrete at ultimate loading displacements is described based on experimental observation and the stress state analysis of the confined concrete. The kernel concrete in the confined zone is shifted from confinement state to de-confinement state during the loading cycles. Next, an updated fibre beam-column model is proposed where a uniaxial stress-strain relation considering the de-confinement effect is introduced to represent the behaviour of kernel concrete during the loading cycles. The validity of the proposed model is confirmed by comparing experimental results and model results. Compared with the classical fibre beam-column model, the detailed discussions about the load-displacement response, moment-curvature, and strain distribution during loading cycles showed that the updated model achieves reasonable prediction of catastrophic degradation of RC columns by capturing the state shift of kernel concrete. At last, the applicability of the proposed model is discussed. Existing models including Panagiotakos and Fardis model, Eurocode 8 model, and ASCE 41 model are used as comparative models to evaluate the model accuracy of predicting the ultimate drift ratio of RC columns.

Variability in corrosion damage models and its effect on seismic collapse fragility of aging reinforced concrete frames

Corrosion of embedded reinforcement is an important form of degradation of reinforced concrete (RC) structures. The corrosion damage can degrade the mechanical behaviors of the corroded reinforcement, the surrounding concrete, and the interaction between them. These deterioration mechanisms can be simulated by different corrosion damage models. Different corrosion damage models could result in difference in the structural collapse capacity under earthquake excitations. However, the variability in these corrosion damage models and its effect on seismic collapse fragility of corroded RC structures are not well examined in the past studies. This study conducts an investigation of the variability in the available corrosion damage models. To do this, a total of 29 empirical models are collected to represent the corrosion-induced deterioration mechanisms. The results show that different corrosion damage models lead to significant variability. The changing range of the prediction by different corrosion damage models for the bond strength is even beyond three times wider than the minimum prediction value. As a further step, two typical RC frame structures are designed as the study cases. Then a suite of 19 corroded frame cases are modeled with their material parameters deteriorated according to the collected corrosion damage models. Their seismic collapse fragility curves are then generated and compared. It is found that, at a high corrosion rate of 0.2, the variability in the corrosion damage models can cause a significant difference in the collapse probability as high as 8.4% and 6.54% for the case frames designed with a low and high earthquake hazard levels, respectively. However, this effect due to the variability in the corrosion damage models is limited to the collapse probability when the structure is slightly or moderately corroded. Among the considered deterioration mechanism due to corrosion damage, the maximum difference of collapse probability are caused by the variability in the corrosion damage models for the yield strength and ultimate deformation of the corroded reinforcement, which are as high as 6.18% and 5.32%, respectively. While for the other deterioration mechanisms, the variability in their corresponding damage models leads to a limited effect on the collapse probability of structures.

Predicting the seismic collapse capacity of adjacent SMRFs retrofitted with fluid viscous dampers in pounding condition

Severe damages of adjacent structures due to structural pounding during earthquakes have emphasized the need to use some seismic retrofit strategy to enhance the structural performance. The purpose of this paper is to study the influence of using linear and nonlinear Fluid Viscous Dampers (FVDs) on the seismic collapse capacities of adjacent structures prone to pounding and proposing modification factors to modify the median collapse capacity of structures considering the effects of pounding. The factors can be used to predict the collapse capacity of structures in pounding condition. A seismic retrofit strategy employs FVDs installed in 3-, 6- and 9-story Special Moment Resisting Frames (SMRFs). The SMRFs were assumed to have different values of separation distance according to the seismic code. To model pounding phenomenon, linear viscoelastic contact elements were used in the OpenSees software. Furthermore, to determine the seismic collapse capacities of each structure, the proposed algorithm was applied to remove the collapsed structure during the incremental dynamic analysis. The results of the analyses illustrate that the existence of FVDs can substantially improve the seismic behavior of structures having a significant influence on the collapse capacities of colliding structures. Moreover, considering the adjacent SMRFs in one or two sides of the main structure can significantly affect the median collapse capacity of the main structure itself. Finally, the proposed modification factors can be successfully used to estimate the effects of pounding on the collapse capacities of adjacent structures.

Probabilistic seismic performance evaluation of composite frames with concrete-filled steel tube columns and buckling-restrained braces

The concrete-filled steel tube (CFT) composite frames using blind bolts and buckling-restrained braces (BRBs) have been studied with the development of building industrialization and energy dissipation technology. However, there has been no research so far on the probabilistic seismic fragility analysis for the blind-bolted end-plate CFT composite frames with BRBs (BRB-BECFT). Therefore, a total of 6-, 9-, 12- and 20-story BRB-BECFT prototype structures were designed based on the performance-based plastic design method. The results obtained from nonlinear static and dynamic analyses indicated that the four structures achieved predefined performance objectives in terms of story drift, joint rotation, and BRB ductility demand. Subsequently, fragility curves including non-collapse and collapse states were established to evaluate the behavior of the structure for a given intensity measure using the incremental dynamic analysis approach. Meanwhile, the geometric mean of spectral acceleration over a period range (Sa,avg) was selected as the intensity measure to assess the structural collapse capacity. Results showed that the adoption of Sa,avg can result in 32–42% lower data dispersion for the determination of collapse point, and simplification of the process of calculation of the collapse margin ratio of a structure. Furthermore, based on the combination of Sa,avg, residual story drift and BRB core plate strain, a framework of probabilistic seismic damage analysis of structures for combined damage evaluation at three levels of the system, subsystem, and component was summarized and conducted by the 6- and 12-story case study. This is practically useful to assess structural damage state after an earthquake because it could present more information on the probability distribution of various damage scenarios.

Collapse Capacity of Ordinary RC Moment Frames Considering Mainshock-Aftershock Effects

ABSTRACT The effect of mainshock-aftershock (MS-AS) sequences on seismic performance of ordinary reinforced concrete (RC) moment frames (ORCFs) is studied by considering various levels of mainshock damage represented by maximum inter-story drift (MID) parameter. Incremental dynamic analysis (IDA) is performed to extract collapse capacity of structures under aftershock records after imposing the intended mainshock damage. The study results indicate that a smooth reduction in aftershock collapse capacity occurs due to increase in mainshock damage level. Regression equations are also provided to aid in predicting the aftershock collapse capacity in presence of various mainshock damage levels.

Comparing responses of special and intermediate moment frames under repeated earthquakes

Steel moment-resisting frames (MRFs) are designed to resist a design-level single seismic event. However, every earthquake may be accompanied by several foreshocks or aftershocks. The cyclic deterioration of structural elements during early earthquakes may cause the lateral-load-resisting system to collapse under the mainshock or aftershocks. The differences in the seismic performance of special and intermediate MRFs (here called SMFs and IMFs, respectively) subjected to single and multiple earthquake events were investigated. For this purpose, four perimeter steel MRFs with four and eight storeys were designed and subjected to 22 synthesised multi-record earthquake events. The non-linear modelling technique adopted accounts for the cyclic deterioration of structural elements, which is a key parameter in the evaluation of seismic performance under sequential earthquakes. The results showed that structural collapse capacity may be reduced considerably if the structure is subjected to foreshock and aftershock events in addition to the mainshock. In addition, it was found that, for the IMF models, the switch from the life safety (LS) limit state to the collapse prevention limit state was immediate. Therefore, the design of IMFs for the LS performance level may result in a substantial risk of collapse when the structure is exposed to repeated earthquakes.

The Effect of Strong Column-Weak Beam Ratio on the Collapse Behaviour of Reinforced Concrete Moment Frames Subjected to Near-Field Earthquakes

ABSTRACT Buildings are found to be more vulnerable in near-fault regions such that they should be designed with higher strength. In this study, the importance of pulse period and peak ground velocity on the efficiency of the strong column-weak beam ratio (SCWBR) is evaluated through incremental nonlinear dynamic analysis. This work involved two aspects: improving the collapse capacity of structures and mitigation of column damage. Three 4, 8, and 12 story moment frames with varying SCWBR (from 1.2 to 3.0) are subjected to two sets of 44 far-fault and 91 near-fault ground motions. Plastic rotation of elements is utilized as a damage measure for beams and columns. The results demonstrate that idealization of collapse mechanism and early yielding of base columns are controlling factors for the 4 and 12 story buildings, respectively, in particular under long-pulse periods. Moreover, the 8 story (mid-rise) building obtains the highest improvement in the collapse capacity (up to 90%) by the increase of the SCWBR. The most dispersion in the efficiency of the SCWBR among short and large pulse period is observed for the 12 story (high-rise) building. It is also observed that the height-wise distribution of the SCWBR is significantly affected by variation in the pulse period and building height

Refined Seismic Design Method for RC Frame Structures to Increase the Collapse Resistant Capacity

In current structural design codes, elastic vibration modes are used for seismic design. However, when a structure is subjected to strong earthquakes and inelastic response or even when collapse damage is observed, the damage state is always unevenly distributed along the height of the structure. Such a phenomenon implies the materials of stories with elastic response and slight damage are not fully utilized. In this paper, a new practical and effective method, which improves collapse resistant capacity by making full use of materials, is proposed for reinforcement concrete (RC) frame structures at a structural collapse state. In this method, incremental dynamic analysis (IDA) is used to evaluate the structural collapse capacity. Tangent_ratio (TR) is formulated based on the IDA curves, and the longitudinal reinforcement of columns is modified based on the TR to achieve uniform distribution of damage along the height of building. Fewer variables are optimized and constraints of the provisions in current codes are considered, which makes the proposed procedure more computationally efficient and practical. The proposed method is employed on a 5-story RC frame structure to illustrate its feasibility and practicality. Comparison work indicates that the refined seismic design method can significantly increase the collapse resistant capacity and decrease the maximum inter-story drift ratio response under strong ground motion in a few iterative steps without a cost increase.

An efficient method for incorporating modeling uncertainties into collapse fragility of steel structures

Deterioration parameters that are commonly used to simulate nonlinear behavior of steel components were mainly calibrated based on the results from experiments on steel beams. Recently, the state of knowledge for deterioration behavior of steel columns has been improved by experimental and analytical studies on the wide-flange steel columns. These deteriorating characteristics are introduced as regression relationships in which the associated uncertainties are represented by the coefficient of variation (COV). Accounting for these uncertainties in estimating collapse fragility curves through the incremental dynamic analysis (IDA) and simulation-based reliability methods is impractical due to the large amount of required computational effort. In this study, two main goals are pursued. The first goal is comprehensive evaluation of the main, interaction, and quadratic effects of the modeling random variables on the collapse capacity of steel structures. The second goal is to propose an efficient approach to create response surface (RS), which in combination with the Monte Carlo (MC) sampling method will be used to incorporate modeling uncertainties into the collapse fragility. This efficiency will be achieved by employing screening design techniques to reduce the amount of analysis required to create a quadratic RS and also endurance time (ET) analysis as an efficient alternative nonlinear dynamic analysis method with less computational time to estimate the structural responses. In order to develop a reliable probabilistic model, the Bayesian model inference approach is applied to account for the uncertainties in the created model. The proposed procedure is performed with both IDA and ET methods on a prototype 5-story steel frame. Results indicate that collapse capacity is highly influenced by the strength modeling variables of beam as well as the ultimate rotation capacity of column components. In addition, ET method by a considerable reduction in the computational costs provides comparable responses with IDA in a probabilistic framework.

Effectiveness of physics-based collapse criteria in seismic risk assessment of code-conforming low-rise RC framed structures

The evaluation of structural collapse capacity is an integral part of the estimation of collapse risk in performance based earthquake engineering. Several methods and procedures have been proposed in the past to quantify collapse capacity. However, there is no clear consensus on which method is most appropriate. Recently physics-based collapse criteria have been proposed, but their effectiveness is yet to be compared with codes of practice. In order to ensure safety and consistency, different code/standard based recommendations enforce the use of thresholds predominantly in terms of the engineering demand parameter (EDP) for the performance level of collapse prevention. These thresholds serve as limit-state criteria to evaluate the collapse capacity of a structure. This paper compares several performance measures that are derived using different criteria to understand their impact on the final collapse risk estimates. Four different criteria are studied, two of which are based on standards, and the other two are physics-based, which use energy formulations. Three different ASCE 7-16 code conforming RC buildings are designed and analysed. The effects of modelling uncertainties and of the ground motion spectral shape have been considered to impart more confidence in the results. The collapse risk estimates are interpreted in terms of different collapse performance measures. The estimates derived from all the four criteria are compared. It was found that the collapse risk is significantly affected by the choice of the criterion. For the same collapse risk, the physics-based criteria allow higher ultimate deformation at collapse. On the other hand, the code/standard based criteria tend to be conservative as they censor the deformation response of the structure using upper bound thresholds. It was also found that the physics-based criteria could underestimate the collapse risk, yet they can still be employed to produce more economical designs.

Dynamical systems approach for the evaluation of seismic structural collapse and its integration into PBEE framework

The development of collapse fragility curves is an essential requirement for the assessment of the collapse risk of structures. These fragility curves depend on the structural collapse capacity that is evaluated in terms of either the intensity measure (IM) or the damage measure (DM); such as the engineering demand parameter (EDP). In turn, collapse capacity estimates are sensitive to the method employed for their assessment. Conventionally, the IM and DM rules are employed in conjunction with incremental dynamic analyses (IDA) to quantify the collapse capacity of a structure. However, this approach has been criticised for being subjective in nature, since it depends on the structural response approaching predetermined threshold values. Therefore, it does not relate to the actual dynamic instability. Although the selection of these thresholds stems from the results of experimental investigations and equivalent numerical models and serve as an indirect check for dynamic instability, the present study seeks to provide a mathematical basis for defining collapse criteria. A dynamical system approach is used to formulate a mathematical criterion for defining P-Delta instability induced seismic collapse in single-degree-of-freedom (SDOF) structures. The non-linear SDOF structure is considered as a non-autonomous, non-smooth system, and is studied as an ensemble of different sub-systems. Collapse is defined as the point when the dominant system eigenmode of the structure changes from stable to unstable, and remains unstable as the structure collapses. This approach can be applied to first mode governed multi-degree-of-freedom (MDOF) structures when studied as an equivalent SDOF structure. It is found that the dynamical systems approach results in higher deformations at collapse when compared to the conventional IM/DM rule based approach, suggesting the conservatism involved in the latter. However, it results in lower deformations at collapse when compared to the energy criterion, which relies on the occurrence of large deformations to predict collapse. Furthermore, the derived fragility curves show that the proposed approach yields lower probabilities of collapse when compared to the conventional method. Therefore, the proposed method can be used an alternative method for the performance design of structures.

Progressive collapse vulnerability assessment of irregular voided buildings located in Seismic-Prone areas

Nowadays, many special architectural forms of voided buildings such as hotels, commercial complexes, etc. are constructed in famous cities. In this paper, the effects of opening in the volume of low- and mid-rise irregular voided structures with low to high seismic resistance on the progressive collapse vulnerability are investigated. The structures are three and nine stories high, seismically designed with a steel moment frame system based on the AISC seismic code, and are located in sites with high, moderate, and low levels of seismicity. Detailed three-dimensional nonlinear dynamic analysis is performed to investigate spatially distributed damage to frame members and the structural robustness against abnormal loads according to the GSA 2016 guidelines. The response quantities are expressed in the form of the displacement of the node above the removed column, the spatially distributed formation of plastic hinges, the stress growth in nearby columns after progressive collapse occurrence, and the connection robustness analysis. The results show moment connections that govern the robustness of the structure and they are the most critical components in the structure. In addition, larger openings and proximity of the column removal scenario to position of the opening play a significant role in reducing the progressive collapse vulnerability of voided structures. However, in the scenarios of removing the internal column away from the opening, the progressive collapse mechanism of the structures with or without opening does not differ. Therefore, in the structural robustness analysis, internal columns away from opening of the voided buildings should be considered as critical and controllable elements in the progressive collapse capacity of structures. Among the modeled buildings, only the buildings located in high seismic areas can pass progressive collapse analyses and the seismicity level of the site is the most important parameter in robustness of the structure in comparison with the height or irregularity of the structure. Increasing the height of structures also reduces the amount of stress growth in the columns adjacent to the demolished column and the taller structures are safer structures in this regard.

Seismic collapse capacity assessment of SDOF systems incorporating duration and instability effects

This paper presents a detailed investigation into the seismic response of non-deteriorating and deteriorating single degree-of-freedom systems controlled by P -Delta effects, with due account for the influence of earthquake duration. In order to isolate the effect of duration from other ground motion characteristics, 77 pairs of records with equivalent spectral shapes are considered in the study. The structural characteristics examined include the structural period, applied gravity loading, post-yield stiffness, viscous damping, material hysteretic behaviour, as well as the level of cyclic deterioration within the pinching systems. Detailed incremental dynamic analyses are carried out, considering an intensity measure corresponding to the spectral acceleration at the structural period of vibration of the system. Based on the incremental dynamic analysis results, predictive relationships are proposed for determining the structural collapse capacity, accounting for the influence of key parameters including instability and duration effects. The median and dispersion of the collapse capacity distribution embedded in the predictive models are also presented. The effect of duration is shown to increase with longer structural periods and to decrease with higher P -Delta levels. The more rapid instigation of dynamic instability in relatively stiff systems is also shown to reduce their comparative sensitivity to variations in ground motion characteristics. Overall, it is indicated that disregarding the influence of duration could lead to over-estimations of up to 50% in the collapse capacity. The paper concludes with a discussion of other sources of structural damage that instigate collapse when using records with equivalent spectral shape but without especial consideration for duration effects.

Influence of earthquake duration on structural collapse assessment using hazard-consistent ground motions for shallow crustal earthquakes

This study quantitatively investigates the duration effect on structural collapse assessment, using hazard-consistent ground motion suites selected based on the generalized-conditional-intensity-measure approach. Sixteen scenario cases with varying magnitudes, distances, and conditioning periods are considered as targets. For each target case, four hazard-consistent ground motion suites with different distributions of duration (one base-duration (actual target) suite and three longer-duration suites respectively) are selected. Collapse fragility curves are derived by conducting incremental dynamic analysis on numerical models of four steel frames. Comparative results demonstrate that the duration effect on structural collapse capacity mainly depends on the magnitude of the mean significant duration (Ds5–75) ratio of two (longer/base) groups. The duration effect is statistically insignificant for cases where the mean Ds5–75 ratio is smaller than 1.4, while it is more significant for cases with mean Ds5–75 ratios larger than 1.4, with a reduction in median collapse capacity of, on average, about 10% when using the longer-duration suites as compared to the base-duration one. It is also found that a longer duration record suite with more cumulative intensity contained has a higher possibility to cause a reduction of structural collapse capacity.

Isolating the effect of ground-motion duration on structural damage and collapse of steel frame buildings

The debate over the significance of ground-motion duration is long-standing and the literature on the influence of duration on structural response is extensive. Decoupling of the duration from other characteristics of the ground motion is crucial for accurate quantification of its effect on structural responses. This article presents a new methodology that isolates the duration from the amplitude, frequency content, and rate of energy build-up of the ground motion. This is achieved by selecting short- and long-duration record pairs that are equated on the basis of spectral shape and the slope of the Husid plot. The use of the initial rate of Arias Intensity as a control parameter is novel in the literature. The proposed approach enables the examination of the sole effect of the duration on structural responses of 2-story and 9-story steel frame buildings. We find that the maximum interstory-drift ratios are not generally sensitive to the duration differences between short- and long-duration record sets, whereas the cumulative damage parameters (i.e. dissipated hysteretic energy and Modified Park–Ang Damage Index) of the buildings considered in this study are affected by duration. Finally, we extend the study to collapse limit states and find that duration has a small effect on structural collapse capacity, after controlling three key ground-motion parameters.

Simplified Collapse Analysis Model for RC Frames with Cyclic Deterioration Behaviors

ABSTRACT Equivalent single-degree-of-freedom (ESDOF) models are widely used to evaluate the collapse capacity of multistory structures, and their rationality is very important because it greatly affects the accuracy of the evaluation results. Prior studies have indicated that obvious cyclic deterioration (CD) behaviors exist before structural collapse, and such deterioration behaviors are the primary sources of collapse for reinforced concrete (RC) frames subjected to long-duration ground motions. Although several ESDOF models have been developed to represent the global mechanical behaviors during the collapse of RC frames, such models cannot reasonably consider CD behaviors. This paper establishes an ESDOF model capable of considering CD behaviors by utilizing the Ibarra-Krawinkler (I-K) model. The ESDOF model includes a monotonic backbone curve with a negative tangent stiffness and a hysteretic rule to consider CD behaviors based on hysteretic energy dissipation. A simple method utilizing the empirical relationship between the monotonic ductility capacity and hysteretic energy dissipation capacity of RC columns to determine the hysteretic energy dissipation capacity of the ESDOF model is proposed. The CD behaviors are simulated by calculating the hysteretic energy dissipation capacity of the ESDOF model using the empirical relationship, which is obtained by the regression analysis of the existing experimental data of the RC column tests. The proposed ESDOF model is validated by pseudo-static collapse experiments and collapse fragility analyses. The results demonstrate that CD behaviors cannot be ignored when performing the collapse analyses of RC frames and that the proposed ESDOF model can adequately predict the collapse capacity of RC frames.