Research Article

INVESTIGATION OF THE PERFORMANCE OF REINFORCED CONCRETE FRAME SYSTEMS UNDER REPEATED AND SEQUENTIAL EARTHQUAKE LOADS

Author : 1Amin Iraji Orcid , 2Seyed Yahya Jalalian

1Assistant Professor, Department of Civil Engineering (Geotechnical Engineering) Urmia University of Technology, Urmia, Iran
2M.Sc. in Structural Engineering, Researcher, Ph.D. Candidate in Geotechnical Engineering, Urmia University of Technology, Urmia, Iran

KEYWORDS

Reinforced concrete frame system, Seismic loads, Repeated and sequential earthquakes

CORRESPONDING AUTHOR

Amin Iraji

https://orcid.org/0009-0004-8057- 836X

ABSTRACT

One of the fundamental challenges in structural design and evaluation is the performance of structures under seismic conditions, particularly under repeated and sequential earthquakes. Natural earthquakes do not usually occur as single events; rather, in most cases, aftershocks and sometimes other earthquakes also occur within a short time interval. Therefore, the present research aims to investigate the performance of reinforced concrete frame systems under repeated and sequential earthquake loads. In this study, structural frames were subjected to uniform loading (to examine the system response to continuous loads) and cyclic loading (to investigate the system behavior under variable and periodic loads). In this research, seven real sequential seismic records obtained from the PEER database were used to evaluate the seismic behavior of structures under sequential earthquakes. Two reinforced concrete buildings, four-story and eight-story, with medium ductility, designed based on modern performance-based design methods, were considered. The results showed that in the four-story regular and irregular concrete structures, the Park and Ang damage index, the maximum lateral displacement of the stories, and the maximum story drift ratio under sequential seismic loading, compared to main shocks and aftershocks, were significantly increased. In some seismic records, this increase reached approximately two times. Also, in comparison, the mentioned instantaneous parameters in the irregular building were higher than in the regular building. In the eight-story regular and irregular concrete structures, it was observed that the Park and Ang damage index, both locally and globally, under sequential earthquakes, compared to main shocks and aftershocks, had higher values. However, it did not exceed the critical value.

INTRODUCTION

Sequential and repeated earthquakes, as one of the seismic hazards that can have significant destructive effects on buildings and structures, are recognized. These earthquakes not only generate strong seismic forces, but may also, due to repeated occurrences, gradually impose stress on structures and cause progressive failures. Therefore, investigating the seismic performance of structures against such earthquakes is of high importance (Parvari et al., 2023). Buildings and structures designed and constructed with lateral load-resisting systems are designed in such a way as to ensure occupant safety during earthquakes. These systems are often designed so that the structure is allowed to sustain damage under seismic action, but not collapse. It is expected that such damages are repairable, although repair costs may be high. In particular, moment-resisting frame systems, as one of the lateral load-resisting systems, due to their high stiffness and ductility, are among the common options for seismic-resistant building design.

Numerical modeling has shown that various seismic characteristics of sequential earthquakes, including amplitude, duration, and frequency content, can significantly affect structural behavior and increase the probability of failure. Using these analyses, structural weaknesses can be identified, and appropriate strengthening and retrofitting methods can be proposed. The nonlinear behavior of materials under sequential earthquakes is also strongly influenced by seismic characteristics. Concrete and steel, as the two main materials in frame structures, respond differently to seismic variations. Concrete under repeated stresses may experience cracking and stiffness degradation, while steel may enter the plastic range and experience local buckling. These cumulative material changes lead to a reduction in load-bearing capacity and structural stiffness and increase the likelihood of sudden failures. Accurate analysis of nonlinear material behavior under sequential earthquakes can lead to improved modeling and appropriate strengthening methods (Maghroon, 2022).

One of the most important strengthening strategies for frame systems against sequential earthquakes is the use of energy dampers. Dampers can effectively absorb seismic energy applied to the structure and prevent its transfer to the main structural members. These dampers reduce deformations and control vibrations, thereby preventing cumulative damage. Due to their simple installation and high efficiency in energy dissipation, dampers are among the most widely used methods for strengthening frame systems. Dampers, by creating friction between different surfaces and dissipating seismic energy, can prevent the transfer of additional stresses to structural components and thus reduce the likelihood of cumulative damage and stiffness degradation over time (Amiri, 2021).

The use of dampers can help reduce vibration amplitudes and control lateral deformations of the structure, which leads to increased structural stability during sequential earthquakes. One of the important issues in analyzing the behavior of structural connections under sequential earthquakes is material fatigue. Fatigue refers to the reduction of material strength and stiffness due to repeated loading. Under sequential earthquakes, structural members, especially connections, are subjected to repeated loads, which can lead to fatigue and a reduction in load- bearing capacity. Fatigue in bolted connections usually begins as small cracks at bolt and nut locations and gradually propagates. These cracks can lead to complete failure of the connection and affect the overall performance of the frame. The use of high-strength bolts and designing connections in a way that reduces stress concentration can help mitigate fatigue effects and increase the service life of connections. The behavior of connections under sequential

earthquakes is also strongly influenced by the type of bracing systems and frame characteristics (Shahriari, 2022).

Torsional connections typically use high-strength bolts and nuts for connecting structural members, and these types of connections show good performance against tensile and shear forces. However, under sequential earthquakes, bolts and nuts may experience fatigue, and their load-bearing capacity may be reduced. This issue becomes particularly critical when seismic forces are applied to the structure sequentially and with different amplitudes, leading to changes in force distribution and increased stress concentration in specific regions of the connection (Hatami, 2017). Welded connections, as one of the common methods for connecting structural members, also exhibit specific behavior under sequential earthquakes. Welds, due to their rigid and brittle nature, may develop cracking under plastic deformations and repeated loads. The cracks formed in welded connections can gradually propagate and lead to the complete failure of the connection. These cracks may initiate at stress concentration zones or in areas with weak welds and increase under sequential earthquakes. The use of high- quality welding techniques and proper design of welded connections can help reduce the likelihood of cracking and improve connection performance under sequential earthquakes. Connections equipped with dampers have been introduced as one of the modern methods for improving the performance of braced frames (Mohammadi, 2021). These types of connections, due to their ability to absorb energy and reduce its transfer to structural members, can effectively control plastic deformations and seismic forces. Energy dampers can be installed at connection locations and, by absorbing earthquake forces, prevent the transfer of additional stresses to structural components. These connections, especially under sequential earthquakes in which alternating and cumulative forces are applied to the structure, can perform better than traditional connections and prevent cumulative failures.

In response to existing challenges in braced frame systems, numerous studies have been conducted on the development of advanced systems to improve the seismic performance of structures. One of these systems is concentrically braced frame systems with self-centering capability. These systems have been developed with the aim of increasing displacement capacity and reducing residual lateral displacements. However, the seismic responses of these systems in consecutive earthquakes can lead to the amplification of higher modes of structural vibration and impose greater stresses on structural members. Particularly in tall structures and under severe earthquakes, these amplified responses can lead to significant structural damage (Adane et al., 2024). To reduce these effects and improve the performance of braced frame systems, the development of a self-centering frame system that does not require rocking is considered necessary. Braced frame systems are one of the new approaches to addressing these challenges. Due to their significant nonlinear displacement capacity, these systems are able to absorb seismic forces and prevent residual lateral displacements after earthquakes. In this way, structures can show better performance against successive earthquakes, and the risk of structural collapse is reduced.

Kalantari et al. (2023) in a study entitled “Seismic Conditional Fragility Functions of Special Moment-Resisting Reinforced Concrete Frames with Different Heights under Sequential Seismic Events” stated that this study investigated the effect of height on the expected seismic behavior of reinforced concrete moment frames under two sequential seismic events using a probabilistic approach. The results showed that the increase in the probability of failure of frames with different heights is significantly dependent on different scenarios of the first event. Also, conditional seismic fragility function parameters for frames with different heights were

presented. Rouhi et al. (2022), in a study entitled “Evaluation of Seismic Demands of Reinforced Concrete Frames with Steel Shear Walls under Sequential Earthquakes”, stated that this research investigated the effect of seismic sequence on reinforced concrete moment frames strengthened with steel shear walls. The results showed that the predominant period of aftershocks has a significant effect on the structural response after the main earthquake. Real seismic sequences increased story drift demand on average by 2 times and ductility demand by

1.2 to 2.5 times compared to a single earthquake. In artificial sequences, the maximum story drift demand for aftershock scale factors of 1, 1.5, and 2 was, respectively, 1, 2, and 2.6 times that of a single earthquake. Also, aftershocks can change the direction and magnitude of residual displacements in seismic sequences. Finally, an equation was derived to calculate seismic sequence ductility demand.

Yaghmaei Sabegh et al. (2022), in a study entitled “Seismic Fragility Assessment of Reinforced Concrete Frames with Infill Walls under Main Shock and Aftershock”, stated that this paper aims to evaluate the seismic fragility and residual capacity of reinforced concrete frames with masonry infill walls under main shock and aftershock sequences in near and far-field regions. Based on the obtained results, it was observed that the seismic fragility of reinforced concrete frames under the main shock and aftershock is significantly reduced. Fragility curves indicate that when 100% collapse occurs in bare frames, the probability of collapse in infilled frames at the same PGA level for both near and far-field earthquakes is significantly reduced, indicating the effective role of infill walls in increasing lateral resistance. Zamani et al. (2021), in a study entitled “Probabilistic Seismic Vulnerability Assessment of Regular High-Rise Buildings with Special Reinforced Concrete Moment Frames under Long-Period Earthquakes”, stated that this paper investigated the probabilistic seismic vulnerability of high-rise buildings with special moment-resisting frames under long-period earthquakes. The results showed that high-rise buildings are more vulnerable to long-period earthquakes, and this difference becomes more significant at higher damage levels. The median seismic fragility for long-period earthquakes at the complete damage state decreased by about 60%.

Boroumandzadeh et al. (2020), in a study entitled “Retrofitting Concrete Columns of RC Frames Using Advanced Fiber Reinforced Materials under Seismic Loading”, stated that in recent years, strengthening concrete members using fiber-reinforced polymers has been widely investigated by researchers. The seismic behavior of reinforced concrete structures has also been studied in several research works, and various solutions have been proposed to increase seismic reliability. In this study, two types of reinforced concrete structures strengthened with FRP and conventional steel reinforcement were modeled as 4-story and 8-story structures with 3-meter story height, 5 spans, and 5-meter bay width in ABAQUS finite element software under pushover analysis. The structure is located in a very high seismic risk zone, and the soil type is category II. Avil et al. (2023), in a study entitled “Evaluation of Seismic Performance of Reinforced Concrete Frames with Different Bracing Systems”, stated that seismology and earthquake engineering are essential disciplines for structural engineers worldwide. The selection of appropriate lateral load-resisting systems largely influences the performance of reinforced concrete structures. The results showed that adding bracing to frames significantly increases their seismic resistance. Furthermore, bracing elements were highly effective in reducing drift, as observed by reduced inter-story drifts compared to unbraced frames. Steel bracing also contributed to a significant reduction in the global damage index (GDI).

Oyguc et al. (2018), in a study entitled Seismic Behavior of Irregular Reinforced Concrete Structures under Multiple Earthquake Excitations, stated that this study investigated the

damaged behavior of irregular reinforced concrete structures under the influence of sequences of ground motions from the Tohoku earthquake. Three-dimensional numerical models were developed for three irregular structures, and their structural characteristics were modified into a regular configuration. The capacities of the structures were evaluated using the N2 method and the extended N2 method. The results indicate that the effects of multiple earthquake excitations are significant, and irregularity effects lead to an increase in scattered damage throughout the excitation sequences. This study demonstrates the influence of structural deterioration and irregularity in the analysis of damage induced by sequential earthquakes. Shojaei et al. (2017), in a study entitled Seismic Vulnerability Assessment of Low-Rise Irregular Reinforced Concrete Structures Using the Cumulative Damage Index, stated that this study evaluated the vulnerability of vertically irregular structures under various seismic accelerations using the Park–Ang damage index. The results show that structures with soft- story irregularity experience greater damage compared to other structures. Regular structures exhibit the least damage, and different earthquakes have a relatively limited effect on regular structures. Hatzivassiliou et al. (2015), in a study entitled Effect of Earthquake Sequences on Three-Dimensional Reinforced Concrete Buildings, investigated the effect of repeated earthquakes on the inelastic response of three-dimensional reinforced concrete structures. Two three-story and two five-story reinforced concrete buildings with regular and irregular configurations were evaluated under five real strong earthquakes. The results focus on the effects of damage accumulation, maximum displacements, inter-story drifts, and ductility demands. This study shows that earthquake direction has a significant impact on structural performance. It is concluded that for reliable seismic design of structures, the effects of multiple earthquakes and their different directions must be considered.

The results of this study can contribute to the development of new designs and strengthening standards for structures. From an applied perspective, this research is particularly important in Iran, which is located in a seismic zone. Many buildings and infrastructures are vulnerable to sequential earthquakes, and this study can provide optimal strategies for strengthening and reducing risks associated with sequential seismic events (Parvari et al., 2022). The necessity of this research in Iranian society is very high due to the country’s seismicity and the high vulnerability of structures to sequential earthquakes. Many regions in Iran are exposed to severe earthquake hazards. This study, in terms of important dimensions and components such as practical applicability of results and attention to existing knowledge, theories, and literature, has strong justification for its importance and necessity. Therefore, the necessity of conducting this research is confirmed based on existing data and the findings and recommendations of previous studies.

MATERIALS AND METHODS

This research employed both library and field methods for data collection and analysis. After data collection, numerical modeling and simulation, statistical and analytical methods were used to analyze the results. Initially, to evaluate seismic performance, samples of braced frame systems were designed. This design was based on performance-based seismic design criteria, including analysis and evaluation of various structural parameters. In this stage, braced frame models were designed using data related to probable seismic loads, material properties, and design criteria required for seismic strengthening.

In these analyses, structural frames were subjected to uniform loading (to examine system response under sustained loads) and cyclic loading (to evaluate system behavior under variable and periodic loads). During these analyses, displacements imposed on rebars and braces were carefully measured. To evaluate the seismic performance of braced frame systems, nonlinear dynamic analyses were used.

In this study, seven sets of real sequential seismic records obtained from the PEER database were used to investigate the seismic behavior of structures under sequential earthquakes. It should be noted that all these records were recorded in far-field conditions, and they include mainshock and aftershock events. The specifications of these earthquakes are presented in Table 1.

Table 1: Sequential Earthquake Data

NO.	Seismic sequence	Station			Date	Magnitude	Recorded PGA(g)
1	Mammoth	54301 Mammoth			25/05/80	6.06	0.321
	Lakes	Lake H.S.			25/05/80	5.69	0.39
2	Chalfant	54428	Zack	Brothers	20/07/86	5.9	0.285
	Valley	Ranch			21/07/86	6.3	0.447
3	Coalinga	46T04 CHP			22/07/83	6.0	0.605
					25/07/83	5.3	0.73
4	Imperial	5055 Holtville P.O			15/10/79	6.6	0.221
	Valley				15/10/79	5.2	0.211
5	Whittier	24461Alhambra,			10/01/87	6.0	0.333
		Fremont Sch			10/04/87	5.3	0.174
6	Whittier	24402 Altadena –			10/01/87	6.0	0.299
		Eaton Canyon			10/04/87	5.3	0.264
7	Whittier	24401 San Marino,			10/01/87	6.0	0.128
		SW Academy			10/04/87	5.3	0.156

Two four-story and eight-story reinforced concrete building models with moderate ductility, designed based on modern performance-based design methods, were considered. For the design of these structures, FEMA 356 guidelines were used, and member limitations under force- based and displacement-based demands were applied based on ASCE 41-13 provisions. In addition, the Iranian seismic code (Standard No. 2800 of Iran) was also employed as the governing seismic design code. These structures were located in a region with very high seismic hazard, and the soil type was classified as Type III. It should be noted that the structural plans of these buildings, which are regular and irregular in elevation, are shown in Figure 1.

Figure 1: Structural grid plan

From each building model, one frame was extracted and subjected to both sequential earthquake loading and single earthquake loading. After performing static and dynamic analyses, the obtained results were examined and evaluated. The results of static analyses were used to assess the overall system behavior. In contrast, the results of dynamic analyses were used to evaluate the seismic performance of the system under sequential earthquakes. These results included displacements, forces acting on members, and statistical diagrams, which were used as tools for assessing the vulnerability of the systems.

FINDINGS

Four-Story Reinforced Concrete Building with Moderate Ductility

Among the global damage indices considered are the Park and Ang damage index, maximum horizontal story displacement, and inter-story drift ratio. The Park–Ang damage index is defined by the following relationship, which is a combination of deformation and hysteretic energy:

where in the above equation, δm is the maximum deformation of each element, δu is the ultimate deformation, β is a constant modeling parameter typically ranging between 0.05 and 0.20, used to control strength degradation, ∫dEh is the energy dissipated by the element during the earthquake, and Py is the yield strength of the element. This damage index for different damage states is presented in Table 2.

Table 2: Damage index for various damage states

Degree of damage	Degree of damage Physical appearance	Damage index	State of building
Slight	Sporadic occurrence of cracking	o0.10	No damage

Minor	Minor cracks; partial crushing of concrete in columns						0.10-0.25	Minor damage
Moderate	Extensive large cracks; spalling of concrete in weaker elements						0.25-0.40	Repairable
Severe	Extensive crashing of concrete; disclosure of buckled reinforcement						0.40-1.00	Beyond repair
Collapse	Partial building	or	total	collapse	of	the	41.00	Loss of building

In Figure (2a, b), the geometric characteristics of the four-story reinforced concrete moment- resisting frame, with cross-sections obtained from performance-based design, are illustrated. It should be noted that the nonlinear behavior of these structures was investigated using pushover analysis. In all three performance levels, CP, LS, and IO, the acceptance criteria for members were controlled in accordance with ASCE 41-13. The allowable inter-story drift ratio was also controlled according to FEMA 356 at all three performance levels. It should be noted that the analyzed frames were selected from intermediate (mid-bay) frames.

Figure 2: Geometric characteristics of the four-story reinforced concrete moment-resisting frame with sections obtained from performance-based design

Figure 3 shows the global and local damage index values for the eight-story and four-story frames under sequential and single earthquake records. It should be noted that at the local scale, the Park–Ang damage index corresponds to the lower joint of the corner columns. These indices are presented for a single earthquake record.

Figure 3: Structural damage indices of the four-story structure at global and local scales

The maximum inter-story displacement profiles for sequential and single earthquake records are shown in Figures 4 and 5.

The obtained results indicate that considering the repeated nature of the records increases displacement demand.

(a)                                                      (b)

Figure 4: Four-story structure (a) regular, (b) irregular under the Mammoth record

(a)                                                                                                                (b)

Figure 5: Four-story structure (a) regular, (b) irregular under the Whittier record

The maximum inter-story drift ratios under sequential seismic loading and single earthquake events are presented. It is observed that, first, the maximum inter-story drift ratios for sequential earthquakes are higher than those of mainshock-aftershock cases, and second, the IDR values are greater in the irregular structure compared to the regular structure.

Eight-Story Reinforced Concrete Building with Moderate Ductility

The Park–Ang damage index is expressed through the following relations, which combine deformation and hysteretic energy. In Figures (6a, b), the geometric characteristics of the four- story reinforced concrete moment-resisting frame with sections obtained from performance- based design are illustrated.

Figure 6: Geometric characteristics of the four-story reinforced concrete moment-resisting frame with sections obtained from performance-based design

Figure 7 presents the global and local damage index values for the eight-story and four-story frames under sequential and single earthquake records. It should be noted that at the local

scale, the Park–Ang damage index corresponds to the lower joint of the corner columns.

These indices are also provided for a single earthquake event.

Park–Ang damage index at global scale Park–Ang damage index at local scale Figure 7: Damage indices of the eight-story structure

The maximum inter-story displacement profiles for sequential and single earthquake records are shown in Figures 8 and 9. The results indicate that considering the repeated nature of the records increases displacement demand.

Figure 8: Eight-story structure (a) regular, (b) irregular under the Mammoth record

(a)                                                                       (b)

Figure 9: Eight-story structure (a) regular, (b) irregular under the Chalfant record

The maximum inter-story drift ratios under sequential seismic loading and single earthquake events are presented. It is observed that, first, the maximum inter-story drift ratios for sequential earthquakes are higher than those of mainshock-aftershock cases, and second, the IDR values are greater in the irregular structure compared to the regular structure.

Figure 10: Eight-story structure (a) regular, (b) irregular under the Chalfant record

Figure 11: Eight-story structure (a) regular, (b) irregular under the Whittier record

CONCLUSION

The results showed that in both the four-story regular and irregular reinforced concrete structures, the Park–Ang damage index, maximum horizontal story displacement, and maximum inter-story drift ratio under sequential seismic loading were significantly higher compared to mainshock-aftershock cases, with increases reaching approximately two times for some seismic records. Furthermore, these parameters were consistently higher in the irregular structure compared to the regular one. In the eight-story reinforced concrete structures, both global and local Park–Ang damage indices under sequential seismic loading were higher than those under mainshock-aftershock conditions. However, they did not exceed the critical value of 1. The maximum story displacement and maximum inter-story drift ratio under sequential seismic loading were also higher compared to mainshock-aftershock cases, reaching increases of up to approximately 2.5 times under some records. Additionally, seismic response parameters for the irregular structure under sequential and mainshock-aftershock earthquakes were greater than those of the regular structure.

It is recommended that future studies use a larger set of real seismic records as well as artificial ground motion records. Furthermore, it is suggested that this research be extended to non- building structures as well.

REFERENCES

1. Adane, M., Kang, H., Chun, S., & Kim, J. (2024). Seismic performance evaluation of an external steel frame retrofit system. Steel and Composite Structures, 50(5), 549-562.

2. Ahiwale, D. D., Kontoni, D. P. N., & Darekar, P. L. (2023). Seismic performance assessment of reinforced concrete frames with different bracing systems. Innovative Infrastructure Solutions, 8(3), 102.

3. Amiri, Davood. 2021. Seismic disaster-resistant building retrofitting with emphasis on lightweight construction. First International Conference on Knowledge and Technology of Law and Humanities of Iran.

4. Boroumandzadeh, Abdollah; Eftekhari, Masib. 2020. Retrofitting reinforced concrete columns in RC frames using high-performance fibers under seismic loading. Ninth National Conference on Urban Planning, Architecture, Civil Engineering, and Environment.

5. Hatami, Seyed Saeed; Peyman Hamami; Saeid Lari. 2017. Effect of sequential earthquake characteristics on the behavior of eccentrically braced structures. Second National Conference on Applied Research in Structural Engineering and Construction Management

6. Hatzivassiliou, M., & Hatzigeorgiou, G. D. (2015). Seismic sequence effects on three- dimensional reinforced concrete buildings. Soil Dynamics and Earthquake Engineering, 72, 77-88.

7. Kalantari, Afshin; Ruhbakhsh, Hamid. 2023. Conditional seismic fragility functions of special RC moment frames with different heights under sequential earthquake events. Earthquake Science and Engineering 1: 89–100.

8. Maghroon, Farzad; Mohsen Izadi Nia. 2022. Effect of earthquake characteristics on progressive collapse potential of steel moment frames equipped with Chevron bracing. Structure and Steel 36: 17–29.

9. Mohammadi, Shahrzad; Afshin Meshkoe Eddini; Ali Masoumi. 2021. Seismic performance evaluation of high-rise perimeter moment frames under sequential earthquakes. Structure and Steel 32: 4–0.

10. Oyguc, R., Toros, C., & Abdelnaby, A. E. (2018). Seismic behavior of irregular reinforced-concrete structures under multiple earthquake excitations. Soil Dynamics and Earthquake Engineering, 104, 15-32.

11. Parvari, Ali; Seyed Behnam Beheshti. 2023. Investigation of the effects of using rocking motion systems on the seismic behavior of special steel moment frames. Structural Analysis – Earthquake 1: 15–28.

12. Rouhi, Hamzeh; Gholahaki, Majid. 2022. Evaluation of seismic demands of reinforced concrete frames strengthened with steel shear walls under sequential earthquakes. AmirKabir Journal of Civil and Environmental Engineering 2: 10–20.

13. Shahriari, Behrouz; Noorollah Majidi. 2022. Control of nonlinear dynamic vibrations of irregular structures using yielding TADAS dampers under combined blast and earthquake loading. Energetic Materials 1: 41–53.

14. Shojaei, F., & Behnam, B. (2017). Seismic vulnerability assessment of low-rise irregular reinforced concrete structures using cumulative damage index. Advances in concrete construction, 5(4), 407.

15. Yaghmaei Sabegh, Saman; Sewda Nasjian. 2022. Seismic fragility assessment of reinforced concrete frames with infill walls under mainshock-aftershock sequences. AmirKabir Journal of Civil and Environmental Engineering 4: 7–0

16. Zamani, Amir Masoud; Pehlavan, Hossein; Shamkhi Amiri, Mohammad; Rafiei, Fahimeh. 2021. Probabilistic seismic vulnerability assessment of regular high-rise RC moment-resisting frame buildings under long-period earthquakes. Journal of Structural Engineering and Construction 12: 270–291.