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Bilinear idealization of capacity curve and calculation of R factor (Freeman, 1990)

Bilinear idealization of capacity curve and calculation of R factor (Freeman, 1990)

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Article
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In existing seismic design codes, base shear is measured using the elastic force requirement divided by the strength reduction factor. This factor is used to take account of structures’ ability to dissipate energy by inelastic deformations. The main objective of this study is to determine the response modification factor (R) for RC frames with non-...

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Nepal lies on the high seismic risk zone and prone to major earthquakes. Bridges are lifeline facilities that must remain functional even after major earthquake. The design and construction of earthquake resistant bridges are vital for protection of economic and life safety. Due to the structural simplicity, bridges are particularly vulnerable to d...

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... Furthermore, the influence of specific building configurations on the R factor has been studied. Hussein et al. [10] calculated the R factor for reinforced concrete frames with spans and heights of different sizes throughout the structure, observing that the structure showed a faster collapse mechanism and an irregular distribution of plastic hinges by increasing the widths of the span and the heights of the floors. Shen et al. [11] calculated the response modification factor for high-strength steel frames with D-eccentric brace using an improved pushover analysis method for 8, 12, and 16-story buildings. ...
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Colombia is a country with high seismic activity due to its location at the convergence of the Nazca and South American tectonic plates, making structural safety a key priority in the design, construction, and retrofit of buildings. Currently, one of the most used seismic resistance systems are moment-resisting frames, due to their easy construction and good behavior under vertical loads, however, they are susceptible to structural damage when subjected to moderate to high-intensity earthquakes, which makes the use of seismic protection systems an adequate alternative to prevent damage during seismic events. The Colombian seismic design code NSR-10 proposes a design methodology using a linear structure that represents a non-linear behavior of the building when the expected design earthquake occurs through the response modification factor R. However, the NSR-10 seismic design code does not contemplate the response modification factor for structures with seismic protection systems. Therefore, in this research, a design procedure was configured for buildings with moment-resisting frames of reinforced concrete and steel equipped with TADAS (triangular-plate added damping and stiffness) dampers. The procedure evaluated the developed response modification factor of structures located in high seismic hazard areas in Colombia and considered regular buildings with varying numbers of stories and special energy dissipation capacity. The capacity of the structures was evaluated through nonlinear static analysis using the Pushover method in SAP2000 software. Finally, the response modification factors were calculated for regular buildings with moment-resisting frames and different numbers of stories.
... A structure must be able to withstand intense seismic events without collapsing suddenly, even though it may suffer some structural and nonstructural damage. This is the core principle of earthquake -resistant design, which involves constructing a structure to withstand seismic forces by dissipating energy a nd exhibiting inelastic behavior [1][2][3]. Recent earthquakes have shown that elastic analysis is inadequate for assessing the true seismic performance of reinforced concrete buildings. Nonlinear time history analysis (NTHA), although challenging and dependen t on ground motion data, can predict the likely inelastic response of structures [4]. ...
... It decreases as the seismic zone becomes larger and increases with a longer basic TP. Hussein et al. [1] assessed how irregularities in floor heights and span lengths affect the behavior factor for common RC frames used in various structures. The outcomes showed inconsistent R values compared to structures with uniform bay length and floor height. ...
... The concept behind the response factor is to integrate nonlinearity with the overstrength, redundancy, and ductility of a structure to accurately assess the seismic force. Figure 1 illustrates the relationship between a structure's base shear (total horizontal load) and its roof displacement, as described by [1][2][3] for nonlinear static analysis. The reduction factor is typically expressed as a function of various structural system factors, including strength, ductility, damping, and redundancy. ...
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The ability of a structure to dissipate energy through inelastic behavior is reflected in the response reduction factor (R), which is influenced by redundancy, ductility, and overstrength. Accurate determination of R is crucial for seismic design. This study focuses on determining the response factor for reinforced concrete (RC) structures with various irregularities. Non-linear static pushover analysis using SAP2000 was employed for numerical simulations to assess the impact of soil-structure interaction (SSI). The analysis included elevational and in-plan irregularities, revealing that buildings with irregular vertical geometries have lower inelastic seismic capacities compared to regular buildings. Consequently, R should be reduced by 15-40% from the ECP 2020 standard before the design phase for such structures. Irregularity was found to have a significant impact on weak soil conditions (C), leading to a reduction in R of 20.3% and 13.1% for fixed and isolated supports, respectively, on loose soil. Additionally, stiffer base soils were associated with higher R values for the same structure.
... R factor could be evaluated for a designed structure, for which alternative formulations are proposed in the literature. The following equation widely used in research works, such as [58][59][60][61][62][63][64][65], is used in this study. ...
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This paper addresses the Direct Displacement-Based Design (DDBD) approach of multi-story RC frame structures consistent with changes ‎to design criteria between Turkish earthquake codes of TSC-2007 and TBEC-2018. The corresponding response modification factor (R) of structures designed based on the DDBD approach is also estimated in this research. The design base shear forces of both codes are compared considering different R factors and also with that of the DDBD approach. The results showed that the DDBD approach, as per TBEC-2018, provides RC frame structures with higher R values compared to the similar approach in accordance with TSC-2007. The Endurance Time (ET) method is a time history-based procedure for seismic assessment of ‎structures ‎under intensifying dynamic excitations aided to judge their performance at various intensity levels. Since, up to now, the ET method has not been considered to evaluate the performance of the structures designed by the DDBD approach, this paper addresses this issue. The ET ‎performance curves of RC frames show that structures designed by the DDBD approach in ‎accordance with TBEC-2018 exhibit higher Interstory Drift Ratios (IDRs) values than TSC-2007 at various hazard levels.
... A structure must be able to withstand intense seismic events without collapsing suddenly, even though it may suffer some structural and nonstructural damage. This is the core principle of earthquake -resistant design, which involves constructing a structure to withstand seismic forces by dissipating energy a nd exhibiting inelastic behavior [1][2][3]. Recent earthquakes have shown that elastic analysis is inadequate for assessing the true seismic performance of reinforced concrete buildings. Nonlinear time history analysis (NTHA), although challenging and dependen t on ground motion data, can predict the likely inelastic response of structures [4]. ...
... It decreases as the seismic zone becomes larger and increases with a longer basic TP. Hussein et al. [1] assessed how irregularities in floor heights and span lengths affect the behavior factor for common RC frames used in various structures. The outcomes showed inconsistent R values compared to structures with uniform bay length and floor height. ...
... The concept behind the response factor is to integrate nonlinearity with the overstrength, redundancy, and ductility of a structure to accurately assess the seismic force. Figure 1 illustrates the relationship between a structure's base shear (total horizontal load) and its roof displacement, as described by [1][2][3] for nonlinear static analysis. The reduction factor is typically expressed as a function of various structural system factors, including strength, ductility, damping, and redundancy. ...
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Full-text available
The ability of a structure to dissipate energy through inelastic behavior is reflected in the response reduction factor (R), which is influenced by redundancy, ductility, and overstrength. Accurate determination of R is crucial for seismic design. This study focuses on determining the response factor for reinforced concrete (RC) structures with various irregularities. Non-linear static pushover analysis using SAP2000 was employed for numerical simulations to assess the impact of soil-structure interaction (SSI). The analysis included elevational and in-plan irregularities, revealing that buildings with irregular vertical geometries have lower inelastic seismic capacities compared to regular buildings. Consequently, R should be reduced by 15-40% from the ECP 2020 standard before the design phase for such structures. Irregularity was found to have a significant impact on weak soil conditions (C), leading to a reduction in R of 20.3% and 13.1% for fixed and isolated supports, respectively, on loose soil. Additionally, stiffer base soils were associated with higher R values for the same structure.
... Con el objetivo de aprovechar las propiedades constitutivas de los materiales, y por razones económicas, la filosofía de diseño sismorresistente actual permite el incursionamiento en el rango inelástico de los sistemas estructurales ante eventos sísmicos severos [1]. Claramente estas deformaciones inelásticas deben ser controladas para evitar el colapso [2]. Esto último se logra empleando factores de modificación de respuesta que relacionan la resistencia elástica espectral respecto a la resistencia inelástica asociada a la capacidad dúctil objetivo [3]. ...
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El presente artículo muestra los resultados de la evaluación paramétrica del factor de modificación de respuesta R, a partir de un conjunto de modelos de histéresis (MH) que representen el comportamiento inelástico de sistemas dinámicos discretos de un grado de libertad (1 gdl) tipo péndulo invertido de periodos cortos. Los MH empleados fueron el elastoplástico perfecto (MEP), el bilineal (MB2 y MB10), y Clough modificado (MCM). Se utilizaron 1380 sistemas discretos de 1 gdl con periodos de vibración T entre 0.001s y 20s, sometidos a un conjunto de registros sísmicos medidos en Perú (M_w≥5.8). Especial atención se brindó a los sistemas de periodos cortos T≤0.4s, considerando valores de ductilidad objetivo por desplazamiento lateral μ=1.5,2,3,4,5,6,8,10, y la razón de amortiguamiento crítico ξ=0,2.5,5,7.5,10,20%. A partir de la combinación media geométrica de los desplazamientos laterales espectrales de cada componente del registro de aceleraciones, se observó que el factor R está fuertemente influenciado por T, μ, ξ, y el MH. El efecto del MH en el factor R, así como su variabilidad se asemejan adecuadamente a lo reportado por otros investigadores especialmente en zona de periodos cortos. Finalmente, se proponen expresiones simplificadas para la estimación del factor R.
... Non-linear time history was performed to conduct a study for medium seismicity, three-story health care facility with varied significance factor (I) values of 1.0, 1.2, 1.4, and 1.5, where the outcome demonstrates that when an important element is higher, the building sustains less damage [12]. The impact of non-uniformity in terms of span and height on the response reduction factor was examined, where the findings suggest that non-uniformity has a significant negative impact on the R value as it relates to height [13]. An investigation was conducted on how changing the building boundary condition affected the R factor [14]. ...
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The selection of an adequate response reduction factor (R) in the seismic design of a reinforced concrete building is critical to the building’s seismic response. To construct a robust structure, the R factor should be chosen based on the building’s resilience performance. Since no background was provided for the selection of R factors, the study focuses on the right selection of R factors in relation to the building’s functionality, performance level, and resilience. In this study, a high-rise building with multiple R factors (R = 3, 4, 5, and 6) is developed. Five potential recovery paths (RP-1 to RP-5) that matched the realistic scenario were used to estimate the building’s functionality. The building was subjected to uni and bi-directional loadings, and two design levels, Design Basic Earthquake (DBE) and Maximum Considered Earthquake were used to monitor the building’s response. According to the findings, a decrease in the lateral design force with the highest R results in a high ductility requirement and a substantial loss of resilience. The maximum R factor can be recommended under uni-directional loading up to 6, in which the building’s resilience is almost 50%, whereas under bi-directional loading and taking the recommended R factor decreased from 6 to 4.
... A non-linear time history analysis (NLTHA) for a three-storey medium seismicity healthcare facility was conducted by Pérez Jiménez and Morillas [12] with varying significance/importance factor (I) values of 1.0, 1.2, 1.4 and 1.5, which are different from R. The result shows that the building receives less damage when a crucial constituent is higher. Hussein et al. [13] investigated the effect of non-uniformity on R with respect to span and height, and the results indicate that non-uniformity has a considerable negative impact on the R value with respect to height. Attia and Irheem [14] looked at the impact of modifying the building boundary condition on the R factor. ...
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Several design codes consider the non-linear response of a building by using one of the most important seismic parameters, called the response reduction factor (R). The lack of a detailed description of the R factor selection creates the need for a deeper study. This paper emphasises a methodology for the selection of a proper R factor based on resilience aspects. Unsymmetrical/ir-regular buildings have become the most common in recent times due to aesthetic purposes. However , because of the complexity due to the torsional effect, the selection of the R factor is even more difficult for this type of building. Therefore, a high-rise G+10-storey L-shaped building is herein considered. The building has re-entrant corners based on the structural/plan arrangement. Different R factors were used in the building design, considering buildings subjected to both unidirectional and bidirectional seismic loading scenarios. The building response with respect to various R factors (R equal to 3, 4, 5 and 6) in terms of its performance level, functionality, damage ratio and resilience was assessed at two design levels, i.e., design basic earthquake (DBE) and maximum considered earthquake (MCE). The study concludes that, considering the above criteria along with the resilience aspect, a maximum R factor up to 4 can be recommended for unidirectional loading, whereas for bidirectional loading, the maximum recommended R factor is 3.
... Their results showed that the building experienced less damage with higher I factors. The impact of non-uniformity, in terms of span and height, on R factor was examined, and the result showed that the R value decreases with height and is greatly affected by non-uniformity (Hussein et al., 2021). The effect of change in building boundary condition on R factor was examined (Attia and Irheem, 2018). ...
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In the seismic design of a reinforced concrete building, selecting appropriate response reduction factor (R) is vital for the building’s seismic response. Indian Standard (IS) 1893-2016 provides R values of 3 and 5 for ordinary moment resisting frames and special moment resisting frames, respectively. As R factors are used to incorporate the building’s non-linearity, R factor selection should be based on the building’s performance in terms of resilience. Since IS does not provide any clause on the background for selecting R factors for the design aspects, the study emphasizes the appropriate selection of R factors with respect to a building’s functionality, performance level, and resilience. In this study, a high-rise building was designed with various R factors (R = 3, 4, 5, and 6). To estimate the building’s functionality, five different recovery paths (RP-1 to RP-5), which match the real scenario, were used. The response of the building in each case was observed at two design levels, Design Basic Earthquake (DBE) level and MCE level. Variations in ductility demand, performance level, and resilience for each building case at each design level were observed. The R factor was used to obtain lateral design force at the DBE level by reducing the actual base shear placed on the structure. The reduction in the lateral design force with maximum R yielded high ductility demand and high loss of resilience. The result shows that the considered building can be designed with a maximum R of 6 since its resilience is almost 50%; hence, recovery is possible at a high cost. The performance level of the building at R = 6 lies at CP-C for the MCE design level. Considering the building’s resilience and performance level aspects, the maximum R factor was found to be 6. This helps the stakeholder and designer in the selection of R, based on the requirements of building functionality, performance level, and resilience.