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The experience of previous earthquakes shows that the inelastic response of structure relates to the intensity and content of ground motion. In this case, the evaluation of nonlinear response of structure demonstrates the reduction in the base shear force. This reduction leads to inelastic base shear is defined by Behavior Factor (strength reduction factor) in seismic codes. One of the important parts in R factor is ductility reduction factor Rμ or. While Rμ is related to type of earthquake, it seems that for near fault motions there would be a different value in comparison to ordinary earthquakes. Fir the near fault earthquakes, due to direction of fault rupture from the site, the directivity effect becomes an important parameter. Previous researches show that for forward directivity effect, there would be two components for earthquakes. One is strike normal and the other is strike parallel. In this paper these components are named as the SN and SP. Also, in concept of performance -based design, to calculate target displacement, the ratio between inelastic and elastic response of structure is an important index. In this paper, this ratio is named as CR. It is good to mention that CR factor is defined as a C1 coefficient in FEMA440. In the previous research, the evaluation of CR for near and far fault motions has less considered.
To evaluate Rμ and CR, the extended number of SDOF systems (from 0.2 to 4 Sec.) for four levels of target ductility (2, 3, 4 and 5) have been considered. Then, Rμ and CR calculated for near field (normal and parallel component) and far fault earthquakes. At the end, for the strike normal component, a sensitivity analysis was carried out due to strain hardening ratio and inherent damping. To perform the analysis in Opensees, the nonlinear time history analysis was selected. During the assessment of Rμ and CR, the strain hardening slope and damping have been selected 3% and 5% respectively. The steel material was defined as bilinear. To set the demand ductility with prescribed target ductility, during trial and error procedure, the yield strength of SDOF was changed since the target ductility achieved. To evaluate sensitivity of Rμ and CR to the effect of strain hardening slope, this factor was selected as 0, 3, 5 and 10%. In the case of damping sensitivity, inherent damping were selected as 2, 5. 10 and 20%. To solve the inelastic equation of motion, the Newmark-Beta method was selected. The inelasticity in Opensees was modeled with distributed plasticity using the fiber element. Finally to calculate Rμ and CR for near and far field motions, approximately 84000 nonlinear time history analysis have been carried out. Also, to study sensitivity of Rμ and CR to damping and strain hardening ratio for the strike normal earthquake, approximately 22400 nonlinear time history analysis have been carried out.
The results show that for all three sets of the earthquake, the Rμ increases and then constant while the fundamental period (T) increases. For small value of ductility (μ), increasing T may lead that Rμ converges to target ductility. In the near field, while T and μ increase, Rμ is almost greater than μ. Also, for small value of T, Rμ is not depend on demand μ. The study shows using far field value of Rμ for near field motions may lead to Non-conservative value. Furthermore, while T increases, the CR value converges to the unit. In the short period, CR depends on μ and T severely. Using CR of far field against SN component leads to Non-conservative result. For a constant value of μ and T, increasing damping increases CR. Using C1 for near field motions is Non-conservative for near field motions. Also, for short periods and high ductility demand, CR, corresponding to SN component is 40% greater than C1. Evaluation of ratio between displacement modification factor and behavior factor shows (Cd/R) for T greater than 1 Sec. this ratio converges to the unit. For small period value, this ratio is dependent to period significantly. Also, using Cd/R of far field for near field motions may lead to inaccurate results.

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Earthquake loads induce significant damages and cause widespread failures into buildings. Having appropriate system against seismic loads is a minimum necessary requirement for a structure. Moment Resisting Frame Systems (MRFS) are one of the common seismic resisting systems against lateral seismic loads. Ductility is the most important properties of these kinds of systems; but increase in ductility leads to decrease stiffness and increase lateral deflections and hence induces damages to nonstructural components. Although stiffness can be magnified through increasing section sizes of members, but it would not be economical. To compensate this deficiency, the combination of these systems with reinforced concrete (RC) shear walls may be useful. Although in general, this combination (RC shear walls and MRFS) decreases the section size and increase stiffness; but in low rise structures using this combined system cause decrease in ductility and dissipation of energy under moderate/strong earthquakes.This deficiency can be improved by using vertical slits in RC shear walls of low to moderate height. These slits invert shear behavior of RC shear wall into flexural behavior of several columns and are able to increase ductility. So, for the first time in this paper, a study was conducted on introducing behavior factor (R) for Steel Moment Frame (SMF) with reinforced concrete slit shear wall system at two levels of demand and supply.
In view of existing concerns about precise of behavior factors in seismic design codes, due to developing these factors based on engineering judgment from observing seismic performance of structures subjected to past earthquakes besides the lake of these information in current seismic design codes causes the seismic design of RC slit shear wall system needs more research works. The behavior factors are used to reduce the linear elastic design spectrum to account for the energy dissipation capacity, over-strength and redundancy of the structure. The most distinctive feature of this study respecting to similar studies is multi-level definition of behavior factors and their extraction with respect to seismic intensity, and accepted damage level as expected performance levels in designing RC slit shear wall structural system. Hence, the demand/supply behavior factors are determined with a more accurate attitude involving the effective parameters such as ductility, over-strength, redundancy, seismic hazard level, performance levels, etc.
In this study, to determine the appropriate behavior factor, static pushover analysis along with Incremental Dynamic Analysis (IDA), are used. The behavior factors in two levels of demand and supply are obtained with two procedures: At the first, the pushover analysis was applied on case study structures and then relationship for SDOF system of Newmark and Hall, Nassar and Krawinkler, and Miranda to evaluate behavior factor for MDOF structures were used. At the second stage both pushover and incremental dynamic analysis were used to achieve directly the behavior factor for MDOF structures.
In this paper, two 5 and 10-story steel moment resisting frame with RC slit and ordinary shear wall systems were designed by ETABS software. These structures were designed in which their behavior factors were the same values. Then the pushover and IDA were conducted on sample structures using nonlinear analysis software PERFORM. Results show that, although initial elastic stiffness has not been considerably changed in slit RC shear wall systems, but they show higher behavior factor relative to regular RC shear wall systems. Converting the shear behavior of RC ordinary shear wall to ductile flexural behavior of a series of wall pieces as columns by providing slits in shear wall may be considered as the reason for achieving more ductility and dissipating high seismic energy in this innovative systems.

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Nowadays, with rapid grows of population and need of space for living, work or other activities in one hand and the limitation of natural resources in the other hand, make researchers and engineers introduce high rise building as a solution to respond for human needs. High rise building become a concept for future cities. At first the structural performance of tall building was very important, but the dimension and the size of these buildings have spirit and vision effects on humans, so the facade aspect of these buildings become more important than past. In recent decades, because of rising the attention to the facade of the tall building addition of structural performance, systems with both structural performance and façade were introduced and diagrid structural system is the most recent kind of these systems. Diagrid structure system is containing of an interior core that usually carries gravity loads and has no need to have shear rigidity and exterior diagrid configuration that carries gravity and lateral loads with diagonal members. This system brings good structural performance, flexible architectural design in form and plan, decrees in material consumption, and etc. because of these benefits, diagrid structures become more useful for tall building instead of common tubular structures. In studying structures seismic performance, one of the important factors for relate linear to nonlinear analysis and show structure energy absorption ability is Response factor. In this paper, five 3d diagrid structure model that are studied, contain of one 36 story model with 50.2-degree diagrid member’s angel, one 36 story model with 67.4-degree diagrid member’s angel and one 36 story model with 74.5-degree diagrid member’s angel for comparing the member’s angle change on diagrid system Response, one 50 story with 67.4-degree diagrid member’s angel and one 60 story with 67.4-degree diagrid member’s angel, to compare with 36 model story with 67.4-degree diagrid member’s angle to see the height or number of stories effect on the diagrid system Response. 67.4-degree diagrid members was selected for the optimum angle according to the articles about this issue that introduced 65 to 75 degree for the optimum angle range. First, linear analysis and designed carried out for the models by using Iran building codes to select the member’s sections, then by using FEMA-356, nonlinear static analysis (Pushover) was done for all models. At last at the final target displacement, under critical load pattern, the pushover curve was obtained. From the pushover curve the over strength factor, ductility factor and Response factor were calculated. In addition to estimating Response factor of diagrid structures, effects of changing diagrid members angle and number of stories on Response factor of this kind of structure are also studied. From the result, the suggested over strength factor is 1.5, ductility factor is 2.15 and Response factor is 3.22 for the optimum diagrid members angle (67.4 degree) of diagrid structures up to 50 story of 180-meter height and conclude that the Response factor increases with increasing of story numbers as well as with increasing of diagrid member’s angel increases.

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Today, most seismic design codes reduce the lateral elastic force by the behavior factor to design structures, so that by designing a structure based on elastic analysis, the effects of non-elastic behavior of the structure are applied. To obtain a behavior factor of structures, a nonlinear analysis is necessary. Research has shown that the nonlinear behavior of RC members depends on factors such as the effect of varying axial load, the effect of shear failure of the members and the effect of the buckling of the longitudinal bars. It is now generally accepted that axial load plays a dominant role in evaluating the seismic behavior of reinforced concrete columns. However columns, especially the exterior ones, can be subjected to varying axial loads depending on the lateral loads. Also the effects of shear on beams and columns are usually neglected in nonlinear analysis, which is carried out based on the flexural behavior of each element. In this research, the behavior factor of 2, 4, and 8 story reinforced concrete frames with intermediate and special ductility based on the proposed nonlinear analysis is considered. Initially, for verification, the proposed nonlinear analysis model was compared with existing experimental models. The verification results show that the proposed model has a very high accuracy. Designing and detailing of the 2, 4 and 8 story reinforced concrete structures are on the basis of the regulation of the Standard 2800 and the National building regulation chapter 9. In order to obtain the behavior of the 2, 4, and 8 story reinforced concrete frames, the effect of varying axial load, shear failure of the members and the buckling of the longitudinal bars are considered in nonlinear analysis. The behavior factor is mostly effected by ductility factor and over strength factor. The ductility factor has dependence with ductility of the reinforced concrete frames. To obtain ductility of reinforced concrete frames, ultimate deformation is needed. To calculate the frames' behavior factor, various criteria are used to calculate the ultimate deformation of frames. One of the criteria is the deformation correspond to the 0.75 percent of ultimate rotation in critical structure member. The other criteria is the deformation correspond to ultimate rotation of critical structure member. The results of the study and comparison of the obtained behavior factor with the proposed behavior factor of the reinforced concrete structures of Standard 2800 with intermediate and special ductility have shown that the calculated behavior factor for 2, 4 and 8 story reinforced concrete frames is bigger than the behavior factor in Standard 2800. Also the results indicate that the calculated behavior factor with the ultimate deformation correspond to the 75 percent of ultimate rotation in critical structure member is close to the proposed value of Standard 2800. In intermediate reinforced concrete frames, the amount of ductility factor and over strength factor decreased when the height of the reinforced concrete frames raised, which is not seen in concrete frames with special ductility.

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Based on the seismic design, energy absorption by plastic deformation is necessary to prevent structures from collapsing during a severe earthquake. Therefore, estimating the behavior of structures to understand their response to earthquakes is particularly important. Seismic loads applied to structures are more significant than forces applied during design. This reduction in design applied loads is accomplished using a behavior factor. It is necessary to employ a behavior factor when evaluating the behavior of structures using linear analysis.
The behavior coefficient depends on ductility coefficient, structural damping coefficient, soil characteristics, earthquake characteristics, over strength coefficient, and design reliability coefficient. While in seismic code, this coefficient is entirely dependent on the type of lateral strength system used. At the same time, the behavior coefficient depends on the structural geometric properties which are investigated in this paper. Since nonlinear analysis is required to determine the effect of earthquake forces during design and nonlinear dynamic analysis is time-consuming, designers typically use nonlinear static analysis. Nonlinear static analysis is one of the nonlinear analysis methods that use the lateral load to represent the earthquake load on the structure statically and increasingly.
Estimating the behavior factor before starting the design process is a vital aid to designers. In this paper, we have examined the behavior factor of the reinforced concrete (RC) frame using gene expression programming. Gene expression programming is highly effective in this instance. Its effectiveness largely determines the success of the method. Gene expression programming is a class of genetic algorithms that utilizes a population of individuals, selects them based on their fit, and introduces genetic changes via one or more genetic operators.
Numerous inputs are required for this purpose, including the number of stories, the span length, the seismicity of the construction site, and the ratio of the compressive strength of concrete to the yield stress of longitudinal reinforcements. Afterward, 168 RC frames were designed via SAP2000 software, and the behavior factor value was obtained using nonlinear static analysis for each frame and subsequently transferred to the GeneXpro Tools software. The sixth and ninth national building regulations, Iran's seismic code, with the American Concrete Institute Code (ACI318-14), were used to analyze and design the structures examined. In the designed frames, the number of stories is 2, 4, 6, 8, 10, 12, and 15, and the ratio of span length to story height is 1, 15, 2, and 2.5, respectively.
The design base accelerations were 0.35, 0.3, and 0.25 in this study, and the longitudinal reinforcements' yield stress was initially set to 340 MPa and then increased to 400 MPa. The obtained results demonstrate that employing the gene expression programming method makes it possible to estimate the reinforced concrete frame's behavior factor with an acceptable degree of accuracy before initiating the design process.  Finally, the results show that the variations of the span length and the number of the stories significantly affect behavior factor. Furthermore, as the number of stories increases, the behavior factor decreases initially and then increases. Moreover, the impact of parameters, such as design base acceleration and yield stress of longitudinal reinforcements, is negligible in calculating the behavior coefficient.

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Surrounding the central core of a concrete component by means of an internal or external factor such as transverse reinforcements, carbon and polymer fibers and steel sheets causes confinement for the concrete. Confining generally improves the strength and ductility of concrete components. As a result of boosting the local performance of elements, the overall performance of structure is made progress. Recently, tending to build irregular structures has been increasing. The presence of irregularity in the structure has always been one of the challenges faced by engineers.  In this investigation, the influence of confinement phenomenon on the seismic performance (damage level and behavior factor) of the moment resisting reinforced concrete frames with vertical irregularity is assessed. To do so, 31 moment resisting frames with vertical irregularity are categorized in four classes including 3-, 6-, 9- and 12-story and the roof displacement-base shear curves of them are acquired using pushover analysis. The capacity curve of each frame is achieved in two states including neglecting the confinement effect and considering it. The outcomes indicate that not only can confining improve the seismic performance of structures but also it can decrease the imposed damage of structures. In other words, comparing the capacity curves of each frame with/without confining effect shows that taking the confinement effect leads to improving the secant stiffness and strength of the frame. Furthermore, due to confinement effect, lateral load carrying capacities of the frames are boosted and the considered damage levels are achieved in higher base shear and roof displacements in comparison with the state that confinement is not considered. The observed values of damage levels indicate that the influence of confinement for higher frames is more significant and the maximum base shears for the frames with the confining action is around 3-19% higher than those of the frames without confinement effect. For 3-story frames, considering confinement effect leads to improving 3.9, 3.6 and 2.9% in damage levels of DL, SD, and NC. For 6-story frames these values are 6.9, 9.5, and 6.8% respectively. Taking confinement effect results in improving 18.25, 11.8, and 14.6% in damage levels of DL, SD, and NC and 14.3, 14.2, and 13.3% improvement for 12-story frames. Comparing the behavior factors in the two states demonstrates that considering confining effect improves the mean values of behavior factors around 10.4%. In addition, the observed values of behavior factors show that the differences between the amounts of behavior factors (with/without confinement effect) for the frames with more stories are higher. It is manifested that type of irregularity plays significant role on the seismic behavior of the moment-resisting reinforced concrete frames. Comparing the analytical behavior factor obtained in the current study with the prescribed value of behavior factor in Iranian seismic code shows that although the proposed value of Iranian seismic code is conservative for low-rise frames, this value is not met for high-rise frames.