Response modification and DEFLECTION AMPLIFICATION FACTORs are used in the current seismic design codes to account for the inelastic behaviour of structural systems without the need for complicated nonlinear analyses. A DEFLECTION AMPLIFICATION FACTOR, cd, is used to compute the expected maximum inelastic displacement from the elastic displacement induced by the design seismic forces. The response modification FACTOR, R, expressed as either a force reduction FACTOR or a behavior FACTOR, is used to reduce the linear elastic design response spectra. It is generally expressed as the product of three FACTORs: overstrength FACTOR, ductility FACTOR, and redundancy FACTOR. This paper tries to evaluate these FACTORs for steel intermediate moment-resisting frames. For this purpose, two dimensional steel building models with different number of stories have been designed and analyzed. After obtaining pushover curves of the models, two different approaches have been adopted to calculate the effective parameters of the response modification and DEFLECTION AMPLIFICATION FACTORs from pushover curves; the first approach that is suggested by seismic code provisions, like ATC-19, FEMA-356 and Iranian Standard No. 2800, uses the idealized pushover curve to specify the effective parameters, and the other approach that is recommended by FEMA-P695 gets the parameters directly from pushover curves. The obtained results from these two approaches for the above-mentioned FACTORs have then been compared with each other and with the recommended values of these FACTORs in the Iranian Standard No. 2800. In this evaluation, ductility FACTOR of the response modification FACTOR has been calculated based on the relations proposed by Newmark and Hall, Lai and Biggs, and Nassar and Krawinkler. According to the obtained numerical results, the average response modification FACTOR resulted from the FEMAP695 approach is 5.26, while this FACTOR was obtained 3.98 based on the Iranian Standard No. 2800 approach. Considering the recommended R FACTOR of the Iranian Standard No. 2800 for the ultimate limit state design of steel intermediate moment-resisting systems equaling 5, it is obvious that the results from the FEMA-P695 approach are more compatible with the code recommendation. In addition, the average over strength FACTORs, according to the FEMA-P695 and Iranian Standard No. 2800 approaches, are 2.37 and 1.80, respectively, when the recommended value of this FACTOR in the Iranian Standard No. 2800 is 3. The average DEFLECTION AMPLIFICATION FACTOR obtained from both approaches is 3.67 that is slightly less than the recommended value of 4 for this FACTOR in the Iranian Standard No. 2800.

One of the most common irregularities in structures is the irregularity in height and lateral stiffness. Due to the commonness of the use of irregular structures and also the different seismic responses of this type of structures, in comparison with regular structures, investigating the seismic response of irregular structures has always been the subject of several research studies. The structures designed for the reduced base shear, under the design earthquake, have inelastic response. To calculate the real (inelastic) displacements of structures under the design earthquake, the displacements obtained from the reduced base shear, are amplified by the DEFLECTION AMPLIFICATION FACTOR (Cd). Seismic codes have dedicated a Cd for each structural system. But different studies have shown that the dedicated Cd by the codes cannot accurately estimate the real displacements. The main purpose of this research is to propose the Cd values for more accurately estimating the maximum inter-story drift ratio (MIDR) and maximum roof drift ratio (MRDR) in steel special moment resisting frames (SMRFs) with the soft story. The number of stories and the location of the soft story are the variables considered in this research. The results show that the use of Cd = 5.5, recommended by the 2800 standard and ASCE 7-16 for steel SMRFs, underestimates the real MIDR and also MRDR, under the design earthquake. It is shown that by increasing the number of stories, the mean Cd obtained from the analyses increases. The reason for this issue is the P-Δ effects that increase by increasing the number of stories. In addition, it is shown that a specified trend cannot be found between the location of the soft story and the mean Cd values in the stories of the structures. Thus, for more accurately estimating MIDR in the considered structures, under the design earthquake, Cd = 8.5 is proposed. Furthermore, for more accurately estimating MRDR, Cd roof = 8.0 is proposed.

Considering the importance of the DEFLECTION AMPLIFICATION FACTOR, Cd, in the structural design and the lack of consideration of the structure-soilstructure interaction effects on structural response, this paper has investigated the effects of the most important parameters affecting this FACTOR in the structure-soil-structure systems. Key parameters are period of main (T1) and adjacent (T2) structures, distance between the structures (d) and type of soil. The purpose of this study is to correct the Cd coefficient in steel moment frames under the influence of structural-soil-structure interaction effect. For this aim, 6 structures of 2 to 15 story based on two types of clay soil in a three distances of zero, 10 and 25 meters using direct method is modelled and analyzed with nonlinear time history method. According to the results, most of the story drifts is concentrated at the first story due to soft base. The minimum ratio of first story drift with respect to the fix-base, is 1. 1 and the maximum is 3. 61. Increasing T1 and T2, the value of this ratio is increased. For the main structures with T1 in the range of 0. 7 to 1. 5 times the soil period, the structural drift is intensified. Finally, using the results of this study and regression analysis, a correlation coefficient for the Cd is presented based on the spectral response of the structural drift. Based on the obtained relationship, story drifts, especially at first story, should be increased for the design of the structures.

It is well known that during strong ground motions most of structural damages and collapses are due to excessive displacement of stories, and other structural and non-structural elements. Therefore one of the most important objectives in seismic design procedure is estimating the maximum inelastic (actual) displacement and drift of structures occurring in severe ground motions. Seismic design provisions estimate the maximum inelastic story drifts and displacements occurring in major earthquakes by amplifying the drifts and displacements computed from elastic analysis at the prescribed design seismic force level using a DEFLECTION AMPLIFICATION FACTOR. This parameter is useful for estimating minimum allowable space between two adjacent buildings, controlling story drift limitations and so on. In this research, the DEFLECTION AMPLIFICATION FACTOR for both displacement and drift of four steel concentrically braced frames (CBF) and also four steel ordinary moment resisting frames (OMRF) are studied and evaluated. For each system, 2, 4, 6, and 8-story steel building are considered. These frames are subjected to 7 selected records of ground motions having different characteristic such as frequency content, peak ground acceleration (PGA), and so on. It is concluded that the DEFLECTION AMPLIFICATION FACTOR for the systems under consideration is considerably higher than that recommended by Standard No.2800 Iran code. From the results of this research, a FACTOR for both DEFLECTION and displacement AMPLIFICATION FACTOR of each system under consideration is separately suggested.

In most seismic design codes, lateral loads are reduced by applying the response modification coefficient in the linear static analyses. Hence, the lateral displacements of the structure should be increased to obtain a realistic estimation of the actual displacements. In this regard, static drifts are multiplied by a DEFLECTION AMPLIFICATION FACTOR (Cd). This FACTOR is proposed based on single earthquakes in seismic codes such as ASCE 7 and Standard No. 2800 (4th Edition) while structures in seismic regions will typically be exposed to a number of aftershocks after a major earthquake. Since, the repair of the structures will not be practically possible before exposing to aftershocks, ensuring the proper performance of structures under successive earthquakes is essential. Accordingly, in this paper, DEFLECTION AMPLIFICATION FACTOR has been evaluated for dual system of special moment-resisting frame with shear wall under critical seismic sequences. For this purpose, 3 RC building frames with the number of 3, 7 and 11 story have been subjected to linear static, linear and nonlinear dynamic analyses and the DEFLECTION AMPLIFICATION FACTOR has been calculated and extracted for each of them under two states of successive and single earthquakes. The results show that successive shocks do not significantly affect the Cd compared to a single earthquake. In addition, a supplementary study has been performed for a number of single earthquakes (near-fault earthquakes which have been introduced in FEMA P695) to provide more reliable results. This investigation reveals that the proposed values in ASCE7-16 and Standard 2800 are not sufficient for Cd coefficient.

Structures in seismic active zones are often exposed to earthquakes that occur consecutively in a short time together. Therefore, there is not enough time to repair, rebuild or evacuate the damaged structures under the first shock before the second shocks. Despite what is often assumed by seismic design codes, the designed structures based on a single design earthquake are not capable of predicted service and performance. Considering the high damage potential of successive earthquakes, the seismic performance of RC and steel moment frames under successive shocks has been evaluated by comparing the DEFLECTION AMPLIFICATION FACTOR (Cd) in the present paper. In this regard, nonlinear dynamic analysis has been performed for three steel and RC frames with 3, 7, and 11 stories under single and consecutive critical earthquakes. The results indicate that the seismic sequence phenomenon can lead to an increase in Cd for the studied frames. Average Cd for RC and steel frames under single shocks is equal to 3.5 and 3.4 and for consecutive shocks is 3.7 and 4. Also, the largest increase in Cd was about 15% for the 3-story steel frame.In the next step, for more comprehensively investigation of the seismic performance of the studied frames, an ideal artificial neural network is designed and after the sensitivity analysis of the maximum Cd FACTOR, empirical equations are presented to estimate this parameter with acceptable accuracy.

Response modification FACTORs are used to reduce the lateral loads in "force-based design" method. Naturally the calculated lateral displacement (drift) of the structures in the linear static analyses is smaller than actual values. Hence, DEFLECTION AMPLIFICATION FACTOR (Cd) is needed to consider a realistic estimation of nonlinear displacements. Most seismic design codes such as ASCE7 and standard No. 2800-4th version propose this FACTOR for different lateral bearing systems. This paper evaluates the proposed DEFLECTION AMPLIFICATION FACTOR for dual system of special reinforced concrete moment-resisting frame with/without shear wall. For this purpose, a set of 2D reinforced concrete frames with 3, 7 and 11 story are designed based on standard No. 2800 (4th version) and implemented in Opensees software in each case without considering the soil-foundation-structure interaction. In this regard, beams and columns are modeled using concentrated plasticity method with “Elastic Beam Column Element” in the middle and “Zerolength Element” at the end of elements. Moreover, “SFI-MVLEM” element is used for modeling of shear walls. Nonlinear behavior in two ends of the beams and columns is assigned by “Modified Ibarra-Medina-Krawinkler Deterioration Model with Peak-Oriented Hysteretic Response” model which has been developed by Ibarra et al. (2005). This model is defined using the proposed equations by Haselto et al. (2007). Uniaxial behavior of steel reinforcements and concrete sections are simulated by Steel02 and ConcreteCM, respectively. Studied frames are verified using Hatzigeorgiou and Liolios (2010) and Liu et al. (2020) study for special moment-resisting frame with/without shear wall, respectively. In addition to linear static analysis (LSA), linear and nonlinear dynamic analyses (LDA and NDA) are applied to 3, 7 and 11 story frames with two lateral bearing systems. In this regard, 22 far-field ground motion records which have been introduced in FEMA P695 are used as seismic scenarios. These records are scaled based on Standard No. 2800 to have identical spectral acceleration with the design spectrum for the fundamental period (T) of each studied frames. For this purpose, each record is normalized to its peak ground acceleration and records are scaled so that the average acceleration spectrum of all records was above the design spectrum in 0. 2T to 1. 5T range. In order to evaluate the DEFLECTION AMPLIFICATION FACTOR and Cd/R, maximum drift of roof and other stories is used for each frames due to concentration of structural damage in certain floors of a multi-story structures and, consequently, creating larger lateral displacements in those floors. The calculated Cd coefficients are compared to the proposed values in ASCE7 and standard No. 2800 (4th version) for all special reinforced concrete moment-resisting frames with/without shear wall. This comparison shows that the Cd coefficients which have been proposed in above-mentioned seismic design codes are not appropriate and more realistic estimate of the structural performance in earthquake has demanded larger Cd values. Moreover, Cd and Cd/R values are changed with the height of special reinforce concrete frames with/without shear wall. Finally, adequate values of DEFLECTION AMPLIFICATION FACTORs are proposed for these frames with/without shear wall in this paper.

In seismic design codes, the maximum real relative displacement due to nonlinear behavior of the structure is estimated from variation coefficient of the relative linear displacement multiplied by the coefficient of DEFLECTION AMPLIFICATION FACTOR (Cd). This coefficient is obtained by considering nonlinear displacement of the members of the structure and depends on the lateral load-resisting system. The previous studies indicate that the panel zone can have a significant effect on the behavior of a frame, and in particular, its lateral displacement. Therefore, to predict the precise behavior of the frame, the effect of the panel zone should be considered, but this FACTOR has not been included in the estimation of the Cd value so far. Therefore, the storey drifts are under-estimated. The main purpose of this study is to consider the effect of the panel zone on Cd for Intermediate Moment Resisting Steel Frames (IMRSF). In this regard, two buildings have been designed based on the Iranian seismic design codes in ETABS software. A 4-story building is designed twice, once by I-section columns, and the other by box section columns. The structure with IPE sections has an IMRSF and, a Concentric Bracing Frame (CBF) with conventional ductility in two main directions. However, the structure of the box section has an IMRSF in both directions. After designing the structures, a flexural frame was selected from both structures and was modeled in the OpenSees Software for two conditions: with and without modeling panel zones. Incremental Dynamic Analyses (IDA) has been performed for 46 ground motion records. To determine a correction FACTOR for Cd in order to consider the panel zone effects, the ratio of the nonlinear maximum drift that of the model without panel zone effects is calculated for each ground motion. The results of the analyses show that in general, considering the effect of the panel zone in the analytical model, leads to an increase in the maximum drift values and ignoring the effect of the panel zone in the structure with the I or Box sections, causes the displacement of the floors to be 28% and 16% less than actually estimated, respectively. This effect for the structure with IPE sections is greater than Box sections, for its smaller web thickness and thus lower thickness of the panel zone. Therefore, it can be concluded that the thickness of the panel zone plays a key role in the structural response. Finally, it is recommended to increase Cd coefficient of intermediate moment resisting frames as 1. 28 and 1. 16 for the structures with I-section and Box-sections in their columns, respectively.