Introduction

One of the effective solutions to reduce earthquake consequences is to modify and improve the regulations for seismic design and seismic retrofit of structures. To evaluate the seismic response of structures, most regulations allow different dynamic analyses to be used. Structures' seismic response is highly dependent on selecting and scaling earthquake records procedures. This issue highlights the importance of studying different methods of selecting and scaling earthquake records for the seismic design of structures.

Due to limited earthquake databases, it is usually impossible to find earthquakes for seismic design at all sites. For this purpose, the regulations suggested accelerograms related to several earthquakes should be scaled with standards' spectral acceleration. Scaling earthquakes is used to estimate the scale factor for each earthquake. This procedure aims to prevent the dispersion of seismic responses. However, the response of structures to earthquakes that were selected and scaled according to regulations has a significant dispersion, and this is a fundamental problem in seismic design. One of the main goals of this research is to investigate the reasons for the dispersion of the seismic response of structures under the effect of earthquakes selected and scaled according to seismic codes, and provide some recommendations for solving this problem.

In recent decades, engineers have increasingly used the performance-based seismic design method. In this method, different damage levels are considered for structures, but there are no different levels for scaling earthquakes. In the method of selecting earthquakes, despite the defined levels of earthquake intensity based on magnitude, it is necessary to evaluate the adequacy of this method. Therefore, analyzing the adequacy of methods for selecting and scaling earthquakes is of particular importance in calculating structures' seismic responses.

In recent years, different aspects of research have been carried out on earthquake selection and scaling methods. These include Shahrozi and Sazjini (2012), Boore (2016), Li et al. (2022) and Li et al. (2023). In addition, Nassar and Krawinkler (1991) examined the relationship between the dominant period, behavior coefficients, and ductility coefficients and recorded scaled to PGA and showed that there was a large dispersion in the results obtained. Miranda (1993) showed that PGA scaling ground motions created large response dispersion. Shome et al. (1998) and Shome and Cornell (1998) demonstrated that when scaling methods were based on maximum features of ground motions, the dispersion of the results was significant. Ay and Akkar (2012) developed a method for selecting and scaling earthquake records in order to study the nonlinear seismic response of structural systems. For a given target hazard level, the methodology modified each strong ground motion record based on basic seismological features. The scaled ground motions and estimated target dispersion provided robust estimates of target building response. Boore (2015) evaluated the simulations of the point-source stochastic method of earthquake ground motions. Kaiser et al. (2017) and Van Houtte et al. (2017) presented international strong-motion databases such as the GeoNet database of New Zealand. Mansouri (2020) showed that considering the vertical earthquake component in the seismic design of bridges is crucial. Eren et al. (2021) examined an inter-story drift-based scaling procedure using earthquake records. According to the results, this method accurately calculates linear elastic inter-story drifts because the bias is insignificant. Furthermore, it is significantly more effective than conventional seismic code procedures. A flowchart was presented by Mansouri (2021) for selecting near-fault earthquakes for the design of structures. Hu et al. (2021) examined site-specific response spectra and presented guidelines for engineering practice. Kaveh et al., (2015, 2019, 2021) investigated procedures for the selection of earthquake records, such as (1) reduced record method (2015), (2) multi-objective optimization algorithms (2019), and optimization-based approach (2021). Kaveh et al. (2013), Kaveh and Nasrollahi (2014), Kaveh (2017) and Kaveh et al., (2022a, 2022b) applied soft computing techniques to reinforced concrete and steel structures. Mansouri et al. (2022) demonstrated that considering the duration and intensity of earthquakes in the seismic retrofit of bridges is significant. Hu et al. (2022) investigated the selection and scaling of earthquake ground motions for stable areas. The application of a scaling procedure to the central Anatolian fault was evaluated by Gumus et al. (2022). According to current design response spectra, earthquake ground motion records along the Central Anatolian Fault Zone (CAFZ) were scaled for SDOF systems. Scaling records successfully requires selecting records with certain features. These records are in accordance with the seismic code's spectral acceleration. A perspective on future destructive earthquakes in the CAFZ was provided by this study. Tang et al. (2022) presented a prediction equation of ground motion for seismicity areas. A set of far-fault earthquake records was presented by Hassani Sokhtesaraei et al. (2022) to conduct a time history analysis of Tehran City and compare the results with FEMA-P695 records. Hu et al. (2023) investigated site-specific spectral acceleration and accelerograms on the surface of soil and bedrock. Kontoni and Farghaly (2018, 2019a, 2019b, 2020, 2023), Farghaly and Kontoni (2022), Kontoni et al. (2023) and Hosseini Lavassani et al. (2023) investigated double pounding, soil-structure interaction, and the effectiveness of various vibration control systems in mitigating seismic responses in buildings and bridges. Rouhi and Kontoni (2023) investigated the spectral correction factor for the design of reinforced concrete frames equipped with steel plate shear walls under near-field earthquakes.

Despite the extensive research about the present study, some of which were mentioned, until now, a detailed study on the adequacy of the method presented in the Iranian Standard No. 2800 for selecting, scaling accelerograms, and comparing it with the ASCE regulation has not been conducted. This research attempts to fill this huge research gap. In this paper, "Methodology" provides the research methodology. Selecting and scaling approaches to Iranian Standard No. 2800 are examined in "Evaluation of the procedures for selecting and scaling earthquake records according to the seismic code Standard No. 2800". Part 4 is related to seismic input definition. In "The studied structures", the studied structures are described. Nonlinear time history analysis results are presented in "Nonlinear time history analysis (NTHA)". The conclusions of this research are evaluated in part 7.

Methodology

Initially, the method of selecting and scaling earthquake records according to Iranian seismic code Standard No. 2800 is described. Second, in two case studies, earthquakes are selected and scaled according to this standard, and scale factors are estimated. Then, the seismic response of a seven-story building and a reinforced concrete bridge under the influence of the discussed earthquakes is evaluated and the reasons for the dispersion of their responses are explained. Then, recommendations are given to improve this method, and finally, research conclusions are presented.

Evaluation of the procedures for selecting and scaling earthquake records according to the seismic code Standard No. 2800

The proposed method

Accelerograms are chosen to estimate the seismic response of structures that should represent strong ground motions at the target site. For this purpose, it is necessary to select accelerograms belonging to earthquake horizontal components that provide design-based earthquake conditions. The magnitude, the distance from the fault, and the seismic source mechanism should also be considered when selecting earthquakes. Also, their sites in terms of geological, tectonic, and seismological characteristics and especially the characteristics of the soil layers should be similar to the target site.

In the period range of 0.2–1.5 T, the average spectral acceleration with the Iranian Standard No. 2800’s response spectrum (2015) is compared. According to the Iranian seismic code, scale factors should be determined to have the following two conditions in this period:

  • The average spectral acceleration should not be higher than 1.3 times the Iranian standard spectral acceleration.

  • The maximum value that the average spectral acceleration can be lower than 1.3 times the Iranian standard spectral acceleration is 10%.

Ambiguities

  • In the Iranian seismic code Standard No. 2800, magnitude is considered for selecting earthquakes and does not pay attention to the maximum amount of strong ground motion in selecting earthquakes, including peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD). Usually, PGV and PGD are the maximum parameters of ground motions that are significant only for structures in the near region of the fault. This is because they decrease with the distance from the fault. However, PGA may be a vital factor in selecting far-fault earthquakes to prevent seismic response dispersion of structures. In this research, structures' seismic response is investigated under far-fault earthquakes. For this purpose, only the effects of PGA value are examined in selecting earthquakes.

  • According to the Iranian Standard No. 2800 for scaling accelerograms, the average spectral acceleration of earthquakes can be only higher than the spectral acceleration of Iranian Standard No. 2800 in the period range of 0.2–1.5 T, but no classification is presented. However, the average spectral acceleration can be lower than Iranian Standard No. 2800's spectral acceleration in the aforementioned period and is limited to a 10% difference. It should be noted that in the ASCE regulation, the upper and lower allowed limits for the difference between the average spectral acceleration and the standard spectral acceleration are 10%. In this research, the allowed difference between the average spectral acceleration of earthquakes and the spectral acceleration of Iranian Standard No. 2800 will be reviewed.

  • The discussed regulations are only limited to considering the accelerograms of the horizontal components to obtain the average spectral acceleration. In scaling, the earthquake's vertical component is not considered. This issue will also be discussed.

Definition of seismic inputs

In selecting earthquakes, the effects of magnitude, distance from the fault, and seismic source mechanism are considered. The selected earthquakes have a distance of 20–60 km from the fault. They do not have near-fault earthquake characteristics such as directivity, fling-step, etc. Additionally, all the studied earthquakes have a magnitude ranging from 6.5 to 7.5 Richter, and their soil is type II. It should be noted that the minimum items provided in Standard No. 2800 on the duration of ground motion are applied to selected earthquakes. Earthquake records are downloaded from the PEER (Pacific Earthquake Engineering Research Center) website (2022) and edited using SeismoSignal (2022).

First study

In the first case study, selected accelerograms are related to the Tabas, Landers, Loma Prieta, Northridge, San Fernando, Chi-Chi, and Park Field earthquakes. The horizontal spectrums of each earthquake are combined using the SRSS method. This is so that there is only one spectrum for each earthquake. Then the average graph of seven earthquakes and the response spectrum of Iranian Standard No. 2800 were obtained and compared to each other. According to Standard No. 2800, if the average spectral acceleration of seven earthquakes is higher than the response spectrum of Iranian Standard No. 2800, all earthquake scale factors are equal to 1 g. In Fig. 1 the spectral acceleration of earthquakes and in Fig. 2 the spectral acceleration of Iranian Standard No. 2800 and the average spectral acceleration of the mentioned earthquakes are presented. According to Fig. 2, the scale factor values will be considered equal to 1 g.

Fig. 1
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A view of the spectral acceleration of seven earthquakes

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Fig. 2
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A view of the average spectral acceleration and the spectral acceleration of Iranian Standard No. 2800

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The second study

In the second case study, selected accelerograms are related to the Landers, Loma Prieta, Manjil, Tabas, New Zealand, Northridge, and Park Field earthquakes. Both horizontal spectrums of each earthquake are combined by the SRSS method and a response spectrum is obtained for each earthquake. Then, the average graph of seven earthquakes is compared to the response spectrum of Iranian Standard No. 2800. Scale factors should be estimated in accordance with the limits of Standard No. 2800. The scale factors of each earthquake are presented in Table 1.

Table 1 Scale factors of the studied earthquakes
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The studied structures

Materials are classified according to AASHTO recommendations (2011). The study of Mander et al. (1988) is used as a reference for modeling confined concrete in this study. In Table 2, the properties of steel and reinforced concrete materials are described. A steel rebar's yield strength is 4200 MPa. Table 3 shows the nonlinear properties of confined and unconfined concrete. Figure 3 illustrates stress–strain curves of concrete and steel.

Table 2 Materials properties
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Table 3 Nonlinear properties of confined concrete
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Fig. 3
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Graphs of stress–strain for a steel and b concrete materials (in compression)

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First study: a 7-story reinforced concrete building

In this case study, the seismic response of a 7-story reinforced concrete building (7RCB) with special moment frames is evaluated. The building's length and width are 28 m. In each longitudinal and transverse direction, 8 columns have been used at an equal distance of 4 m. The dimensions of the studied structure components can be seen in Table 4 and a view of its model in Fig. 4. The building is modeled and designed in ETABS software (2015) according to the National Building Regulations of Iran, 6th Chapter by H.a.U.D. Committee (2015) and 9th Chapter by H.a.U.D. Committee (2020), and the Iranian Standard No. 2800 (2015), and its interpretation by Mansouri (2017).

Table 4 The dimensions of 7-story building elements
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Fig. 4
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A view of the 7-story reinforced concrete building (7RCB) model

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Second study: a RC bridge

In this case study, an isolated bridge with six spans is used. Each middle span is 18.5 m long and each lateral span is 12.6 m long. The deck width is 17 m, and the bridge deck is I-girder. The thickness of its slab is 30 cm, and its transverse diaphragms are also 30 cm. Cap beams and abutments have 1.8 m width and 1.2 m depth. In this bridge, four columns with a circular cross-section with a diameter of 1.5 m are used in every cap beam. Elastomeric bearings (EB) are used between the deck with the abutments and cap beams. Figure 5 shows views of the plan, the cross-sections and model of the studied bridge (Mansouri et al., 2022). The bridge is modeled and designed in CSI Bridge software according to Iranian code No. 139 (2000), Iranian code No. 463 (2008), and Iranian code No. 523 (2010). The ED can be modeled in CSI Bridge software using the following specifications:

$$K_{H} = k_{eff} = \frac{{G_{eff} A}}{{H_{r} }} = \frac{680 \times 0.1575}{{0.061}} = 1755{\text{ kN/m}}$$
$$K_{V} = \frac{{E_{C} A}}{H} = \frac{617263 \times 0.1575}{{0.085}} = 1143752{\text{ kN/m}}$$
$$K_{\theta } = \frac{E I}{{H_{r} }} = \frac{617263 \times 0.0016}{{0.061}} = 16270{\text{ kN/m}}$$
Fig. 5
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The plan view, the cross-sections and the model of the studied RC bridge

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Nonlinear time history analysis (NTHA)

In this research, using nonlinear time history analysis (NTHA), the seismic response of the studied structures is evaluated against different earthquakes with different scale factors, such as the Tabas earthquake (TE), the Loma Prieta earthquake (LPE), and the Landers earthquake (LE).

Figure 6 shows a view of base shear forces for the studied building against different earthquakes and with different scale factors. The studied building has the highest base shear force when it is under the effect of LE and the lowest value under the effect of TE (the magnitude of both TE and LE is 7.3 Richter). The results obtained from NTHA are according to Fig. 6 showing that there is a significant difference between the response of each of the studied structures under earthquakes with the same magnitude and scale factors. The maximum base shear force in X direction for the studied building under the effect of TE and LE (with 1 g scale factor) is equal to 1269 tons and 5593 tons, respectively, which shows that the response of the structure in this case under the effect of LE is more than four times the response of the structure under the effect of TE. Figures 7 and 8 show the maximum lateral displacement values of different floors in the studied building under the effect of different earthquakes in X and Y directions, respectively.

Fig. 6
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A view of base shear force in X and Y-direction and axial force for the studied building for the Tabas earthquake, the Landers earthquake, and the Loma Prieta earthquake (with different scale factors)

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Fig. 7
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A view of lateral displacement of different stories for the studied building in X-direction for the Tabas earthquake, the Loma Prieta earthquake, and the Landers earthquake (with different scale factors)

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Fig. 8
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A view of lateral displacement of different stories for the studied building in Y-direction for the Tabas earthquake, the Loma Prieta earthquake, and the Landers earthquake (with different scale factors)

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Figures 9 and 10 show stories drift and Figs. 11 and 12 show stories shear for the studied building under the effect of different earthquakes in X and Y directions, respectively.

Fig. 9
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A view of stories drift for the studied building in X-direction for the Tabas earthquake, the Landers earthquake, and the Loma Prieta earthquake (with different scale factors)

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Fig. 10
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A view of stories drift for the studied building in Y-direction for the Tabas earthquake, the Landers earthquake, and the Loma Prieta earthquake (with different scale factors)

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Fig. 11
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A view of stories shear for the studied building in X-direction for the Tabas earthquake, the Loma Prieta earthquake, and the Landers earthquake (with different scale factors)  

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Fig. 12
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A view of stories shear for the studied building in Y-direction for the Tabas earthquake, the Loma Prieta earthquake, and the Landers earthquake  (with different scale factors)

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Figure 13 shows the base shear force and axial force of the studied bridge under different earthquakes. Figure 14 shows a view of the deck's maximum lateral displacement.

Fig. 13
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A view of base shear force in X and Y-direction and axial force for the studied bridge for the Tabas earthquake, the Landers earthquake, and the Loma Prieta earthquake (with different scale factors) 

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Fig. 14
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A view of lateral displacement of the studied bridge in X and Y-direction for the Tabas earthquake, the Landers earthquake, and the Loma Prieta earthquake (with different scale factors)

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The results show that in this study, the maximum base shear force, lateral displacement, shear and axial forces, and drift in the studied bridge and building occurred when the structures are affected by the LE and their minimum occurs when structures are affected by the TE.

The results of the studies are shown in Figs. 6, 7, 8, 9, 10, 11, 12, 13 and 14, it is apparent that in both studies, when the scale factor is equal to 1 g for all earthquakes and when the scale factor is equal to 1.3 g for the LPE, 1.5 g for the LE and 1.7 g for the TE, there is a significant difference in the response of each of the investigated structures under the effect of the mentioned earthquakes. By examining the results obtained from the lateral displacement of the middle point of the deck in the studied bridge and the lateral displacement and drift of the floors in the studied building, it is clear that the response obtained from the structures under the effect of different earthquakes has a significant difference. It is clear by comparing the obtained results, with the increase of the scale factors, the forces applied to the structures and the lateral displacement of the examined points increase. By comparing the results of base shear force in two horizontal orthogonal directions and vertical axial force estimated in the examined structures under the effect of the TE and the LE, which have the same magnitude, it is evident that there is a significant difference in the seismic response of the studied structures in both cases.

By studying the response of the studied building under the effect of the TE and the LPE, it is clear that the selection of earthquake based on magnitude is not a suitable criterion in the estimation of the response of structures, and there is no clear relationship between the earthquake magnitude and the seismic response of the structure. In this case study, the response of the structure against the LPE with a magnitude of 6.9 is much higher than the response of the structure against the TE with a magnitude of 7.3.

According to Figs. 15, 16, 17, 18, 19, 20, 21, 22, 23 and 24, the reason for the significant difference in the structure's response to TE and the LPE with the same scale factor can be seen in their acceleration-time records and spectral acceleration. The PGA value of the horizontal orthogonal components for the TE earthquake is equal to 0.328 g and 0.406 g and for the LPE it is equal to 0.512 g and 0.322 g (Fig. 15). The PGA value of the vertical component for the TE is equal to 0.183 g and for the LPE is equal to 0.389 g (Fig. 16). The duration of strong ground motions in the components of the LPE is much higher than the similar value in the TE earthquake (Figs. 17, 18, 19). Due to the significant difference in the values of PGA and the duration of strong ground motions of the LPE compared to the TE earthquake, the response of the structure against the LPE is much higher than the response of the structure against the TE. This is despite the fact that the magnitude of TE is bigger than the LPE. The magnitude of LE and TE is equal to 7.3 Richter. But the seismic response of structures under the effect of LE is much larger than the response of the structure under the effect of TE. The duration of LE is much larger than TE and LPE, and for this reason, the structures under the effect of LE have a much larger response than TE and LPE. Figure 15 shows the PGA values for the horizontal components and Fig. 16 shows the PGA values for the vertical components of TE, LPE, and LE. Figures 17, 18 and 19 show the comparison of horizontal and vertical component records of the TE, the LPE, and the LE.

Fig. 15
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The PGA of horizontal components of the TE, the LPE, and the LE

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Fig. 16
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The PGA of vertical components of the TE, the LPE, and the LE

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Fig. 17
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Comparison of horizontal components records of the TE, the LPE, and the LE

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Fig. 18
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Comparison of other horizontal components records of the TE, the LPE, and the LE

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Fig. 19
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Comparison of vertical components records of the TE, the LPE, and the LE

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Fig. 20
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The spectral acceleration of the TE in horizontal and vertical directions

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Fig. 21
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The spectral acceleration of the LE in horizontal and vertical directions

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Fig. 22
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The spectral acceleration of the LPE in horizontal and vertical directions

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Fig. 23
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Comparison of the spectral acceleration of the horizontal components of the TE, the LPE, and the LE

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Fig. 24
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Comparison of the spectral acceleration of the vertical components of the TE, the LPE, and the LE

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One of the main discussions is how to apply the vertical component of an earthquake to scaling accelerograms. By examining the characteristics of different earthquakes, it is clear that the vertical component of an earthquake can have different values compared to its horizontal components, so that in some earthquakes their vertical component is equal to the horizontal component, and in others, it can be much less or much larger. Figures 20, 21 and 22 show the spectral acceleration of the horizontal and vertical components of the TE, LE, and LPE, respectively. In Fig. 20, it is clear that the horizontal components of the TE are much stronger than its vertical component, but in Fig. 21, it is evident that the vertical component of the LE is much stronger than its horizontal components. Therefore, it is suggested that the horizontal components be scaled together, and the vertical components be scaled separately. According to Figs. 23 and 24, it is clear that the spectral acceleration of the horizontal and vertical components of the LE is much stronger than TE and LPE.

Conclusions

The Iranian standard No. 2800 and the ASCE code use only magnitude criteria to select earthquake records. According to the results of the present study, the main factors affecting the seismic response of structures in far areas of the fault include PGA, magnitude, intensity, and duration of strong ground motion. Considering earthquake magnitude as the only criterion for selecting earthquake records cannot be used to accurately estimate structures' seismic response.

In this research, using nonlinear time history analysis (NTHA), the seismic response of the studied RC structures is evaluated against different earthquakes with different scale factors, such as the Tabas earthquake (TE), the Loma Prieta earthquake (LPE), and the Landers earthquake (LE).

Iranian standard No. 2800 says the duration of strong ground motion should be at least equal to the maximum of two values. First, 10 s. Second, three times the structure's first (dominant) period. This item is the lowest allowed value. There is no maximum value or limit stated. In the selection of earthquakes recorded in the present study, this section of the regulation has been applied. However, the dispersion of the seismic response of structures is significant. Because of this, the studies indicate that specific classifications should be considered to determine the duration and intensity of strong ground motion. The duration of strong ground motion in the LPE is many times greater than that in the TE. That is why, the seismic response of structures under the LPE is much larger than the seismic response of structures under the TE. However, its magnitude is lower than the TE. Therefore, the items mentioned in Standard No. 2800 are appropriate as a minimum, but determining the classified ranges for the duration and intensity of strong ground motion depending on the importance, usage, and performance levels of the structure is of particular importance and can reduce the dispersion of the seismic response of the structures.

Not considering the maximum for the average spectral acceleration to be higher than Iranian Standard No. 2800's spectral acceleration in most studies causes different decisions by designers. Because of this, there is usually a significant difference between seismic responses under different earthquakes. For example, the response of the studied structures to the LE with a scale factor of 1 g is several times larger than the response of the same structures to the TE with a scale factor of 1 g, while both have 7.3 Richter magnitude.

As a result, if the vertical component of an earthquake is necessary to estimate the seismic response of structures based on seismic codes, it is necessary to use the vertical component of the earthquake in scaling earthquakes. If all three components of the earthquake have an almost equal amount, they can be added together, and if there is a significant difference between the horizontal orthogonal components and the vertical component of the earthquake, scaling accelerograms in addition to horizontal components, also should be conducted separately for the vertical component. According to the realistic features of the structure and site, Iranian Standard No. 2800's spectral acceleration for horizontal and vertical components can be different.

By examining the obtained results and accuracy in the selecting and scaling methods, it was found that two major factors cause significant seismic response dispersion:

  • Firstly, it is related to the conditions of selecting earthquake records, which consider magnitude as the only criterion for selecting an earthquake record. This problem will be solved to some extent by simultaneously considering the magnitude, PGA and classifying the intensity and duration of strong ground motions.

  • Secondly, it is related to the ratio of the average spectral acceleration to the Iranian Standard No. 2800's spectral acceleration. Considering the maximum value for the difference between the average spectral acceleration and the Iranian Standard No. 2800's spectral acceleration (10% according to ASCE regulation) has advantages such as optimal design and preventing designers' different decisions. However, the adequacy of 10% for the seismic design of all structures (with different performance levels) cannot be considered adequate. Depending on the importance and usage of different structures, classification levels should be considered.