Investigating the Effect of Horizontal Dampers Arrangement Pattern in the Steel Moment Frame Structure on the Progressive Collapse Potential

Investigating the Effect of Horizontal Dampers Arrangement Pattern in the Steel Moment Frame Structure on the Progressive Collapse Potential | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Investigating the Effect of Horizontal Dampers Arrangement Pattern in the Steel Moment Frame Structure on the Progressive Collapse Potential moein nosrati This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6838436/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Nov, 2025 Read the published version in Discover Civil Engineering → Version 1 posted 13 You are reading this latest preprint version Abstract Dampers are considered among the control tools used to dissipate energy and reduce structural displacement. In this study, the effect of using viscous dampers and MR (magneto-rheological) dampers separately, with a passive control approach, on a steel moment frame structure against progressive collapse was evaluated. The damper layout in the structure was arranged diagonally and around the perimeter of the topmost floor. To consider for the variable parameters of the dampers, the structure's capacity curves were analyzed by increasing stiffness and damping for the viscous damper and increasing damping force for the MR damper. The analysis results for both dampers indicate the structure's resistance to progressive collapse under various column removal scenarios. Although this effect is more evident for the structure equipped with MR dampers. In structure equipped with viscous damper, it can be observed that by increasing the damping ratio, the stiffness of structure increased and its displacement reduced; moreover, the increase in stiffness for this damper is effective on the structure's resistance and displacement only up to a certain limit, beyond which it becomes largely ineffective. Progressive Collapse Viscous Damper MR Damper Passive Control Nonlinear Dynamic Analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Introduction After the occurrence of various incidents related to progressive collapse, different codes and guidelines, including those from the American Society of Civil Engineers, the National Building Code of Canada, the General Services Administration, the U.S. Department of Defense, and others, proposed solutions to prevent such events. These methods include the alternate load- path approach, enhancing specific local resistance, and the chain transfer of loads in the structure (prescribing requirements for the forces connecting beams and columns) [ 1 , 2 ]. Progressive collapse refers to a sequence of partial and complete failures resulting from abnormal loads and localized damage in structural elements. The onset of this phenomenon was first studied following the partial collapse of the Ronan Point building in the UK, and it gained significant attention after the terrorist attacks on the World Trade Center buildings in 2001 [ 3 ]. Engineers use various methods to prevent structural collapse and ensure resistance against abnormal loads. One of these methods is the use of dampers to control displacement and reduce the energy entering the structure. Viscous dampers are among the passive control tools and are recognized as one of the best devices for dissipating the energy entering the structure. Since they do not add stiffness to the system, they do not significantly change the modal properties of the structure but effectively increase its damping capacity [ 4 ]; Additionally, Magnetorheological (MR) dampers are semi-active control devices that offer the advantages of active control systems without the need for large power sources. Their functionality becomes particularly critical when the primary energy source is disrupted due to extreme loads or seismic events. In such cases, MR dampers operate similarly to friction dampers by utilizing passive control mechanisms to enhance structural stability [ 5 ]. In this study, a passive control approach is utilized to retrofit a steel moment-resisting frame structure against progressive collapse, first by employing viscous dampers and then by using magneto-rheological (MR) dampers. Overview of Studies on Progressive Collapse and Dampers Jingko Kim and Taiwan Kim investigated the progressive collapse resistance capacity of steel moment-resisting frames. Their analysis revealed that moment frames designed for gravity and lateral loads exhibit lower vulnerability to progressive collapse compared to steel moment frames combined with shear walls. Additionally, the potential for progressive collapse decreases as the number of stories increases, with the highest susceptibility observed when a corner column is removed. Additionally, nonlinear dynamic analysis produced significantly larger structural responses than linear analysis methods. The structural response varied considerably depending on factors such as applied load, the location of the removed column, and the number of building stories [ 6 ]. Naji and ommeh-Talab examined the influence of horizontal belt braces on the top floor of a steel moment-resisting frame to enhance resistance against progressive collapse. They analyzed an 18-story steel structure, originally designed by Galal and El-Sawy, consisting of 18 stories with two short and long spans of 3 and 6 bays, each 6 meters in length. Their findings demonstrated that horizontal braces effectively improved progressive collapse resistance. However, one of the braces was deemed unsuitable for reinforcement due to the axial compressive forces it induced [ 7 ]. Kim et al. (2010) examined the effect of viscous dampers on mitigating the potential for progressive collapse in steel moment frames. They first analyzed the influence of a viscous damper in a steel beam-column assembly. Their findings revealed that, upon the sudden removal of a column, beams longer than 2.6 meters exhibited inelastic deformation. Furthermore, as the system's damping increases, vertical displacement decreases. Following this analysis, three-span steel moment frames equipped with viscous dampers were evaluated for progressive collapse resistance with span lengths of 6, 9, and 12 meters. The results indicated that in structures with dampers, when a column in the span where the damper is installed is suddenly removed, the vertical displacement is significantly reduced. Additionally, the reduction in displacement is more evident in structure with a 12-meter span, which experience the greatest deformation and plastic hinge formation [ 8 ]. Kim et al. (2011) investigated the effect of rotational friction dampers (FDD) combined with high-strength cables on enhancing the seismic resistance and progressive collapse capacity of concrete structures. Nonlinear dynamic analysis results indicated that, using the capacity spectrum method, story drifts in a three-story structure were excessively controlled, whereas in a fifteen-story structure, they remained within acceptable limits. Additionally, nonlinear static and dynamic analyses demonstrated that all FDD-reinforced structural models remained stable against progressive collapse, regardless of which column was removed. Furthermore, when a corner column was removed, the structure exhibited greater resistance to progressive collapse compared to the removal of a middle column [ 9 ]. Kim et al. (2014) evaluated steel moment frames equipped with magnetorheological (MR) dampers to prevent progressive collapse. Nonlinear dynamic analysis results indicated that, upon the sudden removal of a column, the displacement of the beam-column assembly with MR dampers decreased. Following this assessment, 15-story moment frames with various span lengths, all equipped with identical MR dampers passively installed on each floor, were analyzed for progressive collapse resistance. The results showed that as the damping force increased, the vertical displacement of the structure decreased until reaching a saturation level (approximately at a damping force equivalent to 10% for a 6-meter span). Moreover, with increasing span length, the saturation level rose while the vertical displacement further decreased [ 5 ]. javia et al. (2016) investigated the enhancement of progressive collapse resistance using viscoelastic dampers in a four-story concrete structure. Analysis results indicated that, in cases where a middle or interior column was removed, the Demand-to-Capacity Ratio (DCR) for beam deflection exceeded the allowable limit of 1, while the shear and column DCR values surpassed the permissible limit of 2. However, when viscoelastic dampers were applied, the DCR values for beams and columns significantly decreased across all floors, remaining within the acceptable range according to the GSA guidelines. Additionally, the use of appropriately damped viscoelastic dampers at the location of the removed column substantially reduced deflection by 50–70% [ 10 ]. Progressive collapse analysis methods The Alternative Load Path Method is used for progressive collapse analysis. In this approach, the structure is designed in such a way that if a load-bearing member fails, the stability of the structure can be maintained by redistributing the loads through secondary load paths. To evaluate this method, one of the external columns on the first floor is removed due to its critical position, which increases the likelihood of damage and creates structural asymmetry. This method ensures that the structure can adapt to unexpected failures and prevent total collapse [ 3 ]. In this study, progressive collapse analysis will be performed for three column removal scenarios: ELC, FELC, and ESC, using the SAP 2000 software and nonlinear dynamic analysis method, as shown in Figure (1). For progressive collapse analysis using nonlinear dynamic analysis, a load combination of 1.25DL + 0.5LL is used according to the DOD code [ 1 ]. The values of dead load (DL) and live load (LL) for all floors are 2 and 2.4 KN/m², respectively. Structural Model Specifications In this study, an 18-story steel moment-resisting frame structure with a 3x6 bays and 6-meter span length is used. The details of the column and beam sections are shown in Figure (1). The structure is modeled without damping, and all connections between the columns and foundation, as well as between the beams and columns, are assumed to be rigid. Additionally, floor loads are applied directly to the beams without modeling the slab. The design of the structure follows the Canadian Steel Code, and SAP 2000 software is used for modeling and analysis. It is worth mentioning that the structure has been analyzed and evaluated in studies conducted by Galal and El-sawy in 2010 [ 11 ], and by Naji and Omme-Talab in 2018 [ 7 ]. Additionally, in this structural model, dampers are installed on the top floor in a diagonal arrangement, such that the end of each damper connects to the beginning of another (Fig. 2). Modeling of Dampers Viscous Dampers Depending on the type of analysis, whether linear or nonlinear, two models—Kelvin and Maxwell—are used for modeling viscous dampers. In the Maxwell model, unlike the Kelvin model, the excitation frequency is considered, and the damper force becomes a function of the loading frequency. Additionally, since the Maxwell model provides more accurate predictions in nonlinear analyses, this model is used for the project [ 12 ] (Fig. 3). Figure (3) shows the Maxwell and Kelvin models for viscous damper To define a viscous damper in the software, parameters such as stiffness, damping coefficient, and damper velocity power must first be set for nonlinear analysis. Since the damper and brace are connected in series and modeled with a single link element, the stiffness value will be the sum of the axial stiffness of the brace and the damper. Due to the high rigidity of these components, the brace stiffness can be considered equivalent [ 13 ]. Additionally, the damping coefficient for various damping ratios is calculated using Eq. (1), and the damper velocity power is equal to 1, considering the linear behavior of the viscous damper. $$\:{\varvec{\xi\:}}_{\varvec{d}}=\frac{\varvec{T}\:{\varvec{\varSigma\:}}_{\varvec{i}=1}^{\varvec{N}}\:{\varvec{C}}_{\varvec{i}}{\varvec{cos}}^{2}{\varvec{\theta\:}}_{\varvec{i}}\:\:{({\varDelta\:}_{\varvec{i}}-{\varDelta\:}_{\varvec{i}-1})}^{2}\:}{4\varvec{\pi\:}\:{\varvec{\varSigma\:}}_{\varvec{i}=1}^{\varvec{N}}{\varvec{m}}_{\varvec{i}}{\varDelta\:}_{\varvec{i}}^{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$ \(\:\varvec{T}:\) Natural fundamental period of the structure \(\:{\mathbf{C}}_{\mathbf{i}\:}:\) Damping coefficient of the damper located on the i-th floor \(\:{\varvec{\theta\:}}_{\varvec{i}}:\) Slope or deflection angle of the damper \(\:{\varDelta\:}_{\varvec{i}}:\) Maximum displacement of the i-th floor in the first mode \(\:{\varvec{m}}_{\varvec{i}}:\:\) Modal mass of the i-th floor in the first mode \(\:{\:\varvec{\xi\:}}_{\varvec{d}}:\) Damping ratio of the damper The parameters of this relation are related to the first vibration mode of the structure, which is obtained using modal analysis. It is important to note that, since the dampers are installed on the topmost floors of the structure, only the modal characteristics corresponding to the 17th and 18th floors are used to calculate the damping coefficient. Damping coefficients for damping ratios of 5%, 10%, and 20% are provided in Table (1) [ 8 ]. Table (1) Damping Coefficients of Dampers for the Desired Damping Ratios Damping Ratio (%) Damping Coefficient ( \(\:\frac{Kn\:s}{Cm})\) 5% 8/9 10% 17/8 20% 35/65 MR Dampers For the mechanical modeling of MR dampers, some researchers have proposed various models. These models have been introduced to develop control algorithms and to define the inherent properties and nonlinear behavior of the damper. Some of the well-known mechanical models include the Bingham viscoplastic model, the bi-viscous model, the bi-viscous hysteretic model, and the Bouc-Wen model. The performance of each model was compared by Yang et al. in 2001, demonstrating that the differences in structural responses are not significant depending on the model used. In this study, similar to the research conducted by Kim et al., the Bingham model is employed for MR damper modeling [ 5 ]. The Bingham model consists of a Coulomb friction element arranged in parallel with a viscous damper (Fig. 4). F and \(\:{\text{C}}_{0}\) represent the variable frictional force and the damping coefficient of the MR damper, respectively. Since the behavior of an MR damper is similar to a friction damper, the Plastic Wen element with similar hysteretic behavior is used in SAP2000 to model the frictional behavior of MR damper. Verification of Analytical performance Before conducting the project analysis, the accuracy of the progressive collapse analysis and the damper performance in SAP2000 was validated using two studies conducted by Kim et al [ 5 , 8 ]. In both studies, a progressive collapse analysis was performed to obtain the maximum vertical displacement for two cases: without dampers and with dampers (viscous and MR dampers). The validation results, along with the findings from the referenced studies, are presented in the following figures for a 2D steel moment frame with a 6-meter span, comparing structures equipped with viscous and MR dampers. As observed in the results, the comparison between the results of the referenced study and the modeled structure demonstrates a high accuracy of over 90% (error less than 10%). This discrepancy may be attributed to factors such as slight inaccuracies in section dimensions or incomplete information in the referenced studies, such as detailed damper specifications. Analysis of Results Using the Capacity Curve In this part, the capacity curve (load-displacement ratio) is used to examine the structural resistance to progressive collapse for three column removal scenarios: ELC, FELC, and ESC. This curve results from a nonlinear dynamic analysis with an increasing load factor, starting from the formation of the first plastic hinge. Additionally, according to the DOD code, the analysis continues until the axial rotation of the beam above the removed column reaches a maximum of 6 degrees. It should be noted that when the load factor reaches 1, the structure remains resistant to progressive collapse [ 1 ]. Analysis of Results for the Structure Equipped with Viscous Dampers To obtain the capacity curve of the structure in each of the different column removal scenarios, the effect of 5% damping for the damper alone is first considered. Then, by simultaneously increasing both the stiffness and damping of the damper, the capacity curves are plotted. In this study, the stiffness values for the damper are assumed to be 10,000, 40,000, and 70,000 KN/m. Additionally, for increasing the damping, the damping coefficients obtained in Table (1) are used. The ELC Column Removal scenario In this scenario, it can be observed that when the load factor exceeds one (LF = 1.03), the 5% damping ratio for the viscous damper not only reduces the vertical roof displacement but also increases the structural resistance, as shown in Figure (11-a). To account for other damper-related parameters, the capacity curves of the structure are plotted with increased stiffness and damping. As observed in Figure (11-b), increasing the damper stiffness to 10,000 KN/m, along with increased damping, enhances structural resistance (LF = 1.19 for 20% damping) without affecting the structure’s ductility. However, in Figures (11-c) and (11-d), for stiffness values greater than 10,000 KN/m, the 20% damping ratio results in lower resistance compared to Figure (11-b). The FELC Column Removal scenario Similar to the previous case, the highest load factor obtained in this scenario occurs for 5% damping ratio, with a value of 1.03. For stiffness of 10,000 KN/m, despite a reduction in ductility, the increase in damping has led to a slight improvement in structural resistance (LF = 1.05 for 20% damping), as shown in Figure (12-b). Additionally, for higher stiffness values, increasing damping compared to case (b) has had little effect on enhancing structural resistance, resulting only in a limited reduction in displacement. The ESC Column Removal scenario As observed, in this scenario, considering the effect of damping alone results in a maximum load factor of 1. For a stiffness of 10,000 KN/m, although structural resistance increases (LF = 1.05 for 10% and 20% damping), the added damping primarily contributes to reducing displacement, with limited influence on enhancing overall resistance. With the load factor increasing to at least 1, the structural resistance is enhanced by the use of the viscous damper. However, in most column removal scenarios, changing damper parameters such as increasing stiffness or damping beyond a certain threshold leads to reduced ductility due to the increased stiffness and resulting brittleness of the structure. it is important to note that for stiffness values greater than 70,000 KN/m, the maximum load factor and displacement remain largely unchanged across all three scenarios ELC, FELC, and ESC. This suggests that at higher stiffness levels, damping becomes the sole effective factor influencing the structural response. To validate this observation, a very high stiffness value of K = 10⁶ KN/m is applied, and the resulting maximum load factors are presented in Table (2). Table (2) Maximum Capacity Curve Values for Stiffness of 10⁶ KN/m and Various Damping Ratios Location Damping Ratio Maximum load factor Displacement ELC 5% 1.1 60.82 10% 1.11 61.13 20% 1.13 60.90 FELC 5% 1 45.24 10% 1 41.62 20% 1 38.32 ESC 5% 1.03 55.89 10% 1.02 46.67 20% 1.02 43.97 Analysis Results of the Structure Equipped with an MR Damper In this section, the capacity curves of the structure equipped with MR dampers are plotted for three different damping force levels (10%, 20%, and 30% of Rs) under each of the column removal scenarios. In this study, the damping force is applied as a passive control mechanism, defined as a percentage of the axial force of the removed column (Rs). It is important to note that this damping force is generated by adjusting the voltage applied to the MR damper, and depending on the damper's maximum capacity, it can exceed 30% of the column’s axial force. Table (3) Axial Force Values for the Removed Column (Rs) Column Location Axial force (KN) ELC 3090 FELC 3047 ESC 3068 As observed, in the ELC scenario, minimum damping force of 0.1Rs is sufficient to make the structure resistant to progressive collapse (LF = 1). Furthermore, increasing the damping force enhances the structural resistance without significantly affecting the ductility of the structure. For both the FELC and ESC scenarios, increasing the damping force leads to an improvement in the structural resistance, despite a reduction in ductility. In the ESC case, a damping force of 0.1Rs is insufficient to prevent progressive collapse. Additionally, the greatest reduction in ductility due to increased damping force occurs in the following order: FELC, ESC, and ELC. Investigation of Plastic Hinges in the Structure To evaluate the formation of plastic hinges in the structure, the ESC column removal scenario is considered. This scenario is selected due to the large displacement values observed at a load factor of 0.9. Figure 16 presents a view of the structure without damper when the plastic hinges formation under the applied load factor of 0.9. Since in this study, stiffness and damping are defined as two variable parameters for the viscous damper, the effect of increasing damper stiffness is first evaluated at 5% damping ratio. For this purpose, the same stiffness values used for plotting the capacity curves are employed in the analysis. Following this analysis, the formation of plastic hinges will be examined under increasing damping ratios at a fixed stiffness level. It should be noted that, due to the similar structural behavior observed across various damping ratios and stiffness levels, the analysis is restricted to these two representative cases. Effect of Increasing Viscous Damper Stiffness at 5% Damping Ratio As observed, increasing the damper stiffness has only a minor effect on the distribution of plastic hinges. Specifically, increasing the stiffness from 70,000 to 10⁶ KN/m results in negligible changes in the hinge colors, indicating minimal variation in plastic hinge development. Effect of Increasing Damping Ratio for the Viscous Damper In this section, the effect of increasing the damping ratio on the formation of plastic hinges is investigated for a constant damper stiffness of 40,000 KN/m. The results show that increasing the damping ratio has a more significant impact on structural performance compared to increasing stiffness alone. Additionally, higher damping ratios contribute to increasing in the overall stiffness of the structure. Consequently, for damping ratios of 10% and 20%, more plastic hinges shift from the Life Safety (LS) performance level to the Immediate Occupancy (IO) level, indicating improved structural performance and reduced damage. Plastic Hinges in the Structure Equipped with MR Dampers By analyzing the capacity curves of the structure equipped with MR dampers, the increase in damping force is identified as an effective factor in enhancing the structural resistance. In the ESC column removal scenario, it is observed that as the damping force increases, more plastic hinges transition from the Life Safety (LS) performance level to the Immediate Occupancy (IO) level. This indicates that the vulnerable structure, previously undergoing large deformations, managed to enhance its stiffness through alternative load paths and increased damping. It is also important to note that for all column removal scenarios, this increase in stiffness is accompanied by improved resistance and a reduction in ductility. Conclusion The use of Viscous and MR dampers with a passive control approach and circumferential arrangement, to a limited extent, improved the structural resistance against progressive collapse. The results obtained from this study for the structure equipped with viscous dampers are summarized as follows: By examining the capacity curves, it was observed that in most column removal cases, increasing in the damping ratio leads to a reduction in displacement and/or ductility (due to the increase in the stiffness of the structure). Additionally, the effect of increased damping in the viscous damper on the structural resistance varies depending on the location of the removed column and the stiffness level of the damper. The stiffness of the viscous damper can only influence the structural resistance and displacement up to a certain limit; beyond this threshold, its effect becomes minimal. A simultaneous increase in stiffness and damping in the viscous damper leads to an overall increase in the structural stiffness. This is evidenced by the formation of the first plastic hinge at a higher load factor in the capacity curves. Moreover, analysis of the plastic hinges shows that increasing the damping ratio of the viscous damper has a more significant impact on structural stiffness than increasing its stiffness alone. Only in the two cases of column removal—ESC and FELC— increasing in damper stiffness up to a certain limit leads to a reduction in structural displacement (ductility), without causing any significant change in the structural resistance. In the case of column removal at the ELC location, when the stiffness of the viscous damper is 10,000 KN/m, increasing the damper's damping ratio leads to increase in structural resistance (load factor). However, for higher stiffness values up to a certain limit, the extent of resistance enhancement resulting from increased damping gradually diminishes. Overall, for the structure equipped with MR dampers, it can be concluded that increasing the damping force in all three column removal scenarios leads to improved structural resistance against progressive collapse. Moreover, the level of resistance varies depending on the location of the removed column; and as the damper's damping force increases, the stiffness of the structure also increased, leading to a reduction in it's ductility. Declarations Funding This research was conducted as part of the author's M.Sc. thesis at Sadjad University of Technology, under the academic supervision of Dr. Naji. No external financial support was received, and the supervisor had no role in the writing or submission of this manuscript. Ethics approval and consent to participate Not applicable. Consent to publish Not applicable. Competing interests The author declares no competing financial and non‑financial interests. References U.S. Department of Defense. (2019). Design of Buildings to Resist Progressive Collapse (UFC 4-023-03). Unified Facilities Criteria. Retrieved from https://www.wbdg.org/FFC/DOD/UFC/ufc_4_023_03_2016.pd Bilow, D. N., & Kamara, M. (2002). Progressive collapse design guidelines applied to concrete moment‐resisting frame buildings (pp. 1–22). U.S. General Services Administration. American Institute of Steel Construction. (2016). Specification for Structural Steel Buildings. AISC. Retrieved from www.aisc.org Makris, N., & Constantinou, M. C. (1992). Spring-Viscous Damper Systems for Combined Seismic and Vibration Isolation. Earthquake Engineering and Structural Dynamic , Vol. 21, No. 8, pp. 649-664. Copyright © 1992 John Wiley & Sons, Ltd Kim, J., Lee, S., & Min, K. W. (2014). Design of MR Dampers To Prevent Progressive Collapse of Moment Frames. Structural Engineering and Mechanics, Vol. 52, No. 2, pp. 291-306. DOI: http://dx.doi.org/10.12989/sem.2014.52.2.291 Kim, J. & Kim, T. (2009). Assessment of Progressive Collapse-Resisting Capacity of Steel Moment Frames. Journal of Constructional Steel Research, Vol. 65, No. 1, pp. 169-179. © 2008 Elsevier Ltd. DOI: https://doi.org/10.1016/j.jcsr.2008.03.020 Naji, A., Ommetalab, M.R. (2018). Horizontal Bracing to Enhance Progressive Collapse Resistance of Steel Moment Frames. Struct Design Tall Spec Build. 2019; e1563. © 2019 John Wiley & Sons, Ltd. https://doi.org/10.1002/tal.1563 Kim, J. K., Lee, S. J., & Choi, H. H. (2010). Progressive Collapse Resisting Capacity of Moment Frames with Viscous Dampers. Journal of the Computational Structural Engineering Institute of Korea, Vol. 23, No. 5, pp. 517-524. Kim, J., Choi, H., & Min, K-W. (2011). Use of Rotational Friction Dampers to Enhance Seismic and Progressive Collapse Resisting capacity of structures. The structural Design of Tall and Special Buildings, Vol. 20, No. 4, pp. 515-537. Javia, P. D., Joshi, D. D., & Patel, P. V. (2016). Enhancing Progressive collapse Resistance of RC Building Using Viscoelastic Dampers. International Journal of Research in Engineering and Technology, Vol. 5, No. 20. https://ijret.org/volumes/2016v05/i32/IJRET20160532022.pdf Galal, K., & El-Sawy, T. (2010). Effect of retrofit strategies on mitigating progressive collapse of steel frame structures. Journal of Constructional Steel Research, 66(4), 520–531. https://doi.org/10.1016/j.jcsr.2009.12.003 Dyke, S. J., & Spencer, B. F. (1997). Modeling and Control of Structures with Viscous Dampers. Journal of Engineering Mechanics, 123(11), 1181-1191. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:11(1181) Spencer, B. F., & Nagarajaiah, S. (2003). State of the art of structural control. Journal of Structural Engineering, 129(7), 845-856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 18 Nov, 2025 Read the published version in Discover Civil Engineering → Version 1 posted Editorial decision: Revision requested 01 Sep, 2025 Reviews received at journal 12 Aug, 2025 Reviewers agreed at journal 10 Aug, 2025 Reviews received at journal 17 Jul, 2025 Reviewers agreed at journal 16 Jul, 2025 Reviewers agreed at journal 11 Jul, 2025 Reviews received at journal 11 Jul, 2025 Reviewers agreed at journal 10 Jul, 2025 Reviewers agreed at journal 03 Jul, 2025 Reviewers invited by journal 03 Jul, 2025 Editor assigned by journal 27 Jun, 2025 Submission checks completed at journal 19 Jun, 2025 First submitted to journal 19 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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nosrati","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYJCCAzDG4b///suBRR4Qp4WZ4QAPG7MxWCSBOMuYGRiAWhIbQGx8WnTbmw8eLtxhY2/efv7gAQketvT5YYcfAm2xk9NtwK7F7MyxhMMzz6QlzjmTzHDAQIInd+PtNAOglmRjswM4tNzIMTjM23Y4QYIBqCXBQCJ34+wEkJYDidtwasn/ANJiL8H/mOEAUE+64ez0DwS05DCAtDDOkEhmONhwICFBXjqHgC1njoEclpY4Q+KxwWHGhgOGG6RzCoC24fHL8ebHn3nbbIAOS3z8GahFXn52+uYPHyrs5HBpwQQGYJUGxCoHAfkGUlSPglEwCkbBSAAAQ8BmeyeC9SkAAAAASUVORK5CYII=","orcid":"","institution":"Sadjad University of Technology","correspondingAuthor":true,"prefix":"","firstName":"moein","middleName":"","lastName":"nosrati","suffix":""}],"badges":[],"createdAt":"2025-06-06 16:08:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6838436/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6838436/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s44290-025-00364-z","type":"published","date":"2025-11-19T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":86245320,"identity":"8b381011-c258-4275-be18-dd71ffee7ad1","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":115845,"visible":true,"origin":"","legend":"\u003cp\u003ethe plan and elevation view of the structure, along with the beam and column sections.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/514608885543accc599fc51c.png"},{"id":86246418,"identity":"ccfabdbc-0e7e-4c78-88e0-58d6b3594af1","added_by":"auto","created_at":"2025-07-08 11:39:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":20524,"visible":true,"origin":"","legend":"\u003cp\u003ethe arrangement of the dampers on the top floor.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/015877e728839a429896d6b4.png"},{"id":86246728,"identity":"edd644f0-e53b-4e0d-a794-2fe9bd000144","added_by":"auto","created_at":"2025-07-08 11:47:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":25798,"visible":true,"origin":"","legend":"\u003cp\u003eshows the Maxwell and Kelvin models for viscous damper\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/4a77f05b92bb9cf237ebbdfe.png"},{"id":86245321,"identity":"9d7a15c1-d1e8-4c8d-9b5d-1d9fc5de2531","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":6711,"visible":true,"origin":"","legend":"\u003cp\u003eBingham Model for MR Damper\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/6e8110a3a488be09a8858c2e.png"},{"id":86246421,"identity":"f4a932c2-9efd-49f4-be5d-28e259acb42a","added_by":"auto","created_at":"2025-07-08 11:39:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":21079,"visible":true,"origin":"","legend":"\u003cp\u003eForce-Displacement Curve of the Bingham model\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/8375cb6ded11d4e49d9136aa.png"},{"id":86245331,"identity":"6dc446ab-6f52-466f-969b-cd159e444ede","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":22098,"visible":true,"origin":"","legend":"\u003cp\u003eHysteresis Diagram of the Plastic Wen Element\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/195eeba6601dd60025498a7d.png"},{"id":86245336,"identity":"352f32ff-cdb3-42d8-8c2f-a2083049fa01","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":69049,"visible":true,"origin":"","legend":"\u003cp\u003eVertical Displacement of the Modeled Structure (a) Structure without dampers (b) Structure with viscous dampers (5% damping ratio)\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/35ecfa7bc8b1720c147224be.png"},{"id":86245345,"identity":"b581448b-3b4a-4a90-8605-34d8710c4402","added_by":"auto","created_at":"2025-07-08 11:31:38","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":49320,"visible":true,"origin":"","legend":"\u003cp\u003eVertical Displacement of the Structure with and without Viscous Dampers in the Study by Kim et al\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/3d361dd17265a15b53a4c985.png"},{"id":86245328,"identity":"8db306e0-3978-4430-bada-636b37b6794a","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":72667,"visible":true,"origin":"","legend":"\u003cp\u003eVertical Displacement of the Modeled Structure (a) Structure without dampers (b) Structure with MR dampers (Damping Force = 0.1Rs)\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/684a071c0fb50216ceac5492.png"},{"id":86246428,"identity":"2165da33-947b-4685-8c4c-4266252a0570","added_by":"auto","created_at":"2025-07-08 11:39:37","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":49821,"visible":true,"origin":"","legend":"\u003cp\u003eVertical Displacement of the Structure with and without MR Dampers in the Study by Kim et al.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/9a1e7e97e2d6a44e41e52cad.png"},{"id":86246427,"identity":"c71fd7fd-7e1d-4549-a803-313d1e8024da","added_by":"auto","created_at":"2025-07-08 11:39:37","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":95037,"visible":true,"origin":"","legend":"\u003cp\u003eCapacity Curves of the Structure with Increased Damping in the Viscous Damper for the ELC Column Removal Scenario (a) without stiffness (b) K(Stiffness) = 10,000 KN/m (c) K= 40,000 KN/m (d) K = 70,000 KN/m\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/e95b29e57a2ea3738820c3c8.png"},{"id":86245344,"identity":"0a67632c-74b7-4cd7-b5ff-68e6c1a8ab7f","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":90983,"visible":true,"origin":"","legend":"\u003cp\u003eCapacity Curves of the Structure with Increased Damping in the Viscous Damper for the FELC Column Removal Scenario (a) without stiffness (b) K=10,000 KN/m (c) K= 40,000 KN/m (d) K=70,000 KN/m\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/f67fc600b51913e1776ac0c1.png"},{"id":86247430,"identity":"336a5f23-417a-4b12-9b1d-31b11454f518","added_by":"auto","created_at":"2025-07-08 11:55:38","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":100824,"visible":true,"origin":"","legend":"\u003cp\u003eCapacity Curve of the Structure with Increased Damping in the Viscous Damper for the ESC Column Removal Scenario (a) without stiffness (b) K=10,000 KN/m (c) K= 40,000 KN/m (d) K=70,000 KN/m\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/84e98a8998c8762b9b4b9184.png"},{"id":86245341,"identity":"db76844e-f30d-40eb-838f-2bcf85a79bf9","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":79399,"visible":true,"origin":"","legend":"\u003cp\u003eCapacity Curve of the Structure Equipped with MR Dampers under Increased Damping at (a) ELC (b) FELC (c) ESC Location\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/9b575752ebdd32e71b856984.png"},{"id":86245338,"identity":"087160c4-1ff5-4003-9f50-635928f437ad","added_by":"auto","created_at":"2025-07-08 11:31:37","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":34375,"visible":true,"origin":"","legend":"\u003cp\u003ePlastic Hinges in the Structure for ESC Scenario with LF = 0.9\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/703e7b60d2cfec5c2deb703b.png"},{"id":86245378,"identity":"e0ec2327-57c0-4086-a863-a4dafec56139","added_by":"auto","created_at":"2025-07-08 11:31:39","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":90356,"visible":true,"origin":"","legend":"\u003cp\u003ePlastic Hinges in the Structure Equipped with Viscous Dampers (5% Damping Ratio) for Column Removal Scenario ESC (a) K = 10,000 KN/m (b) K = 40,000 KN/m,70,000 KN/m (c) K = 10⁶ KN/m\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/6474f6405e480ee023b6e8e6.png"},{"id":86246732,"identity":"c61ea720-950a-4ff9-9261-c3b163066453","added_by":"auto","created_at":"2025-07-08 11:47:38","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":93812,"visible":true,"origin":"","legend":"\u003cp\u003ePlastic Hinges in the Structure Equipped with Viscous Dampers with a Stiffness of 40,000 KN/m under Column Removal Scenario ESC (a) Damping Ratio = 5% (b) Damping Ratio = 10% (c) Damping Ratio = 20%\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/38c7a970f2e636f78c3de8c9.png"},{"id":86246448,"identity":"fd2f7d50-7bc9-4cf4-8e8c-8b11d0874b0f","added_by":"auto","created_at":"2025-07-08 11:39:40","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":96285,"visible":true,"origin":"","legend":"\u003cp\u003ePlastic Hinges in the Structure Equipped with MR Dampers for the ESC Column Removal Scenario: (a) Damping Force = 0.1Rs (b) Damping Force = 0.2Rs (c)Damping Force=0.3Rs\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/49b661d12e9b30872e58b181.png"},{"id":96484232,"identity":"869549aa-397b-43ce-8a45-d473eccd74aa","added_by":"auto","created_at":"2025-11-21 15:41:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1703114,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6838436/v1/e29bfed7-943e-4a08-823c-9bec0f2937e8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigating the Effect of Horizontal Dampers Arrangement Pattern in the Steel Moment Frame Structure on the Progressive Collapse Potential","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAfter the occurrence of various incidents related to progressive collapse, different codes and guidelines, including those from the American Society of Civil Engineers, the National Building Code of Canada, the General Services Administration, the U.S. Department of Defense, and others, proposed solutions to prevent such events. These methods include the alternate load- path approach, enhancing specific local resistance, and the chain transfer of loads in the structure (prescribing requirements for the forces connecting beams and columns) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eProgressive collapse refers to a sequence of partial and complete failures resulting from abnormal loads and localized damage in structural elements. The onset of this phenomenon was first studied following the partial collapse of the Ronan Point building in the UK, and it gained significant attention after the terrorist attacks on the World Trade Center buildings in 2001 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eEngineers use various methods to prevent structural collapse and ensure resistance against abnormal loads. One of these methods is the use of dampers to control displacement and reduce the energy entering the structure. Viscous dampers are among the passive control tools and are recognized as one of the best devices for dissipating the energy entering the structure. Since they do not add stiffness to the system, they do not significantly change the modal properties of the structure but effectively increase its damping capacity [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]; Additionally, Magnetorheological (MR) dampers are semi-active control devices that offer the advantages of active control systems without the need for large power sources. Their functionality becomes particularly critical when the primary energy source is disrupted due to extreme loads or seismic events. In such cases, MR dampers operate similarly to friction dampers by utilizing passive control mechanisms to enhance structural stability [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In this study, a passive control approach is utilized to retrofit a steel moment-resisting frame structure against progressive collapse, first by employing viscous dampers and then by using magneto-rheological (MR) dampers.\u003c/p\u003e"},{"header":"Overview of Studies on Progressive Collapse and Dampers","content":"\u003cp\u003eJingko Kim and Taiwan Kim investigated the progressive collapse resistance capacity of steel moment-resisting frames. Their analysis revealed that moment frames designed for gravity and lateral loads exhibit lower vulnerability to progressive collapse compared to steel moment frames combined with shear walls. Additionally, the potential for progressive collapse decreases as the number of stories increases, with the highest susceptibility observed when a corner column is removed. Additionally, nonlinear dynamic analysis produced significantly larger structural responses than linear analysis methods. The structural response varied considerably depending on factors such as applied load, the location of the removed column, and the number of building stories [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNaji and ommeh-Talab examined the influence of horizontal belt braces on the top floor of a steel moment-resisting frame to enhance resistance against progressive collapse. They analyzed an 18-story steel structure, originally designed by Galal and El-Sawy, consisting of 18 stories with two short and long spans of 3 and 6 bays, each 6 meters in length. Their findings demonstrated that horizontal braces effectively improved progressive collapse resistance. However, one of the braces was deemed unsuitable for reinforcement due to the axial compressive forces it induced [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKim et al. (2010) examined the effect of viscous dampers on mitigating the potential for progressive collapse in steel moment frames. They first analyzed the influence of a viscous damper in a steel beam-column assembly. Their findings revealed that, upon the sudden removal of a column, beams longer than 2.6 meters exhibited inelastic deformation. Furthermore, as the system's damping increases, vertical displacement decreases. Following this analysis, three-span steel moment frames equipped with viscous dampers were evaluated for progressive collapse resistance with span lengths of 6, 9, and 12 meters. The results indicated that in structures with dampers, when a column in the span where the damper is installed is suddenly removed, the vertical displacement is significantly reduced. Additionally, the reduction in displacement is more evident in structure with a 12-meter span, which experience the greatest deformation and plastic hinge formation [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKim et al. (2011) investigated the effect of rotational friction dampers (FDD) combined with high-strength cables on enhancing the seismic resistance and progressive collapse capacity of concrete structures. Nonlinear dynamic analysis results indicated that, using the capacity spectrum method, story drifts in a three-story structure were excessively controlled, whereas in a fifteen-story structure, they remained within acceptable limits. Additionally, nonlinear static and dynamic analyses demonstrated that all FDD-reinforced structural models remained stable against progressive collapse, regardless of which column was removed. Furthermore, when a corner column was removed, the structure exhibited greater resistance to progressive collapse compared to the removal of a middle column [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKim et al. (2014) evaluated steel moment frames equipped with magnetorheological (MR) dampers to prevent progressive collapse. Nonlinear dynamic analysis results indicated that, upon the sudden removal of a column, the displacement of the beam-column assembly with MR dampers decreased. Following this assessment, 15-story moment frames with various span lengths, all equipped with identical MR dampers passively installed on each floor, were analyzed for progressive collapse resistance. The results showed that as the damping force increased, the vertical displacement of the structure decreased until reaching a saturation level (approximately at a damping force equivalent to 10% for a 6-meter span). Moreover, with increasing span length, the saturation level rose while the vertical displacement further decreased [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003ejavia et al. (2016) investigated the enhancement of progressive collapse resistance using viscoelastic dampers in a four-story concrete structure. Analysis results indicated that, in cases where a middle or interior column was removed, the Demand-to-Capacity Ratio (DCR) for beam deflection exceeded the allowable limit of 1, while the shear and column DCR values surpassed the permissible limit of 2. However, when viscoelastic dampers were applied, the DCR values for beams and columns significantly decreased across all floors, remaining within the acceptable range according to the GSA guidelines. Additionally, the use of appropriately damped viscoelastic dampers at the location of the removed column substantially reduced deflection by 50\u0026ndash;70% [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eProgressive collapse analysis methods\u003c/h2\u003e \u003cp\u003eThe Alternative Load Path Method is used for progressive collapse analysis. In this approach, the structure is designed in such a way that if a load-bearing member fails, the stability of the structure can be maintained by redistributing the loads through secondary load paths. To evaluate this method, one of the external columns on the first floor is removed due to its critical position, which increases the likelihood of damage and creates structural asymmetry. This method ensures that the structure can adapt to unexpected failures and prevent total collapse [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In this study, progressive collapse analysis will be performed for three column removal scenarios: ELC, FELC, and ESC, using the SAP 2000 software and nonlinear dynamic analysis method, as shown in Figure (1). For progressive collapse analysis using nonlinear dynamic analysis, a load combination of 1.25DL\u0026thinsp;+\u0026thinsp;0.5LL is used according to the DOD code [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The values of dead load (DL) and live load (LL) for all floors are 2 and 2.4 KN/m\u0026sup2;, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"Structural Model Specifications","content":"\u003cp\u003eIn this study, an 18-story steel moment-resisting frame structure with a 3x6 bays and 6-meter span length is used. The details of the column and beam sections are shown in Figure (1). The structure is modeled without damping, and all connections between the columns and foundation, as well as between the beams and columns, are assumed to be rigid. Additionally, floor loads are applied directly to the beams without modeling the slab. The design of the structure follows the Canadian Steel Code, and SAP 2000 software is used for modeling and analysis. It is worth mentioning that the structure has been analyzed and evaluated in studies conducted by Galal and El-sawy in 2010 [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e], and by Naji and Omme-Talab in 2018 [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e]. Additionally, in this structural model, dampers are installed on the top floor in a diagonal arrangement, such that the end of each damper connects to the beginning of another (Fig. 2).\u003c/p\u003e"},{"header":"Modeling of Dampers","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eViscous Dampers\u003c/h2\u003e \u003cp\u003eDepending on the type of analysis, whether linear or nonlinear, two models\u0026mdash;Kelvin and Maxwell\u0026mdash;are used for modeling viscous dampers. In the Maxwell model, unlike the Kelvin model, the excitation frequency is considered, and the damper force becomes a function of the loading frequency. Additionally, since the Maxwell model provides more accurate predictions in nonlinear analyses, this model is used for the project [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] (Fig.\u0026nbsp;3).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure (3) shows the Maxwell and Kelvin models for viscous damper\u003c/p\u003e \u003cp\u003eTo define a viscous damper in the software, parameters such as stiffness, damping coefficient, and damper velocity power must first be set for nonlinear analysis. Since the damper and brace are connected in series and modeled with a single link element, the stiffness value will be the sum of the axial stiffness of the brace and the damper. Due to the high rigidity of these components, the brace stiffness can be considered equivalent [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Additionally, the damping coefficient for various damping ratios is calculated using Eq.\u0026nbsp;(1), and the damper velocity power is equal to 1, considering the linear behavior of the viscous damper.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{\\xi\\:}}_{\\varvec{d}}=\\frac{\\varvec{T}\\:{\\varvec{\\varSigma\\:}}_{\\varvec{i}=1}^{\\varvec{N}}\\:{\\varvec{C}}_{\\varvec{i}}{\\varvec{cos}}^{2}{\\varvec{\\theta\\:}}_{\\varvec{i}}\\:\\:{({\\varDelta\\:}_{\\varvec{i}}-{\\varDelta\\:}_{\\varvec{i}-1})}^{2}\\:}{4\\varvec{\\pi\\:}\\:{\\varvec{\\varSigma\\:}}_{\\varvec{i}=1}^{\\varvec{N}}{\\varvec{m}}_{\\varvec{i}}{\\varDelta\\:}_{\\varvec{i}}^{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{T}:\\)\u003c/span\u003e \u003c/span\u003e Natural fundamental period of the structure\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathbf{C}}_{\\mathbf{i}\\:}:\\)\u003c/span\u003e \u003c/span\u003e Damping coefficient of the damper located on the i-th floor\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{\\theta\\:}}_{\\varvec{i}}:\\)\u003c/span\u003e \u003c/span\u003e Slope or deflection angle of the damper\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:}_{\\varvec{i}}:\\)\u003c/span\u003e \u003c/span\u003e Maximum displacement of the i-th floor in the first mode\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{m}}_{\\varvec{i}}:\\:\\)\u003c/span\u003e \u003c/span\u003eModal mass of the i-th floor in the first mode \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:\\varvec{\\xi\\:}}_{\\varvec{d}}:\\)\u003c/span\u003e\u003c/span\u003e Damping ratio of the damper\u003c/p\u003e \u003cp\u003eThe parameters of this relation are related to the first vibration mode of the structure, which is obtained using modal analysis. It is important to note that, since the dampers are installed on the topmost floors of the structure, only the modal characteristics corresponding to the 17th and 18th floors are used to calculate the damping coefficient. Damping coefficients for damping ratios of 5%, 10%, and 20% are provided in Table\u0026nbsp;(1) [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;(1) Damping Coefficients of Dampers for the Desired Damping Ratios\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDamping Ratio (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDamping Coefficient (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{Kn\\:s}{Cm})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8/9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17/8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35/65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"MR Dampers","content":"\u003cp\u003eFor the mechanical modeling of MR dampers, some researchers have proposed various models. These models have been introduced to develop control algorithms and to define the inherent properties and nonlinear behavior of the damper. Some of the well-known mechanical models include the Bingham viscoplastic model, the bi-viscous model, the bi-viscous hysteretic model, and the Bouc-Wen model.\u003c/p\u003e\n\u003cp\u003eThe performance of each model was compared by Yang et al. in 2001, demonstrating that the differences in structural responses are not significant depending on the model used. In this study, similar to the research conducted by Kim et al., the Bingham model is employed for MR damper modeling [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e]. The Bingham model consists of a Coulomb friction element arranged in parallel with a viscous damper (Fig. 4).\u003c/p\u003e\n\u003cp\u003eF and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{0}\\)\u003c/span\u003e\u003c/span\u003e represent the variable frictional force and the damping coefficient of the MR damper, respectively. Since the behavior of an MR damper is similar to a friction damper, the Plastic Wen element with similar hysteretic behavior is used in SAP2000 to model the frictional behavior of MR damper.\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003eVerification of Analytical performance\u003c/h2\u003e\n \u003cp\u003eBefore conducting the project analysis, the accuracy of the progressive collapse analysis and the damper performance in SAP2000 was validated using two studies conducted by Kim et al [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e]. In both studies, a progressive collapse analysis was performed to obtain the maximum vertical displacement for two cases: without dampers and with dampers (viscous and MR dampers). The validation results, along with the findings from the referenced studies, are presented in the following figures for a 2D steel moment frame with a 6-meter span, comparing structures equipped with viscous and MR dampers.\u003c/p\u003e\n \u003cp\u003eAs observed in the results, the comparison between the results of the referenced study and the modeled structure demonstrates a high accuracy of over 90% (error less than 10%). This discrepancy may be attributed to factors such as slight inaccuracies in section dimensions or incomplete information in the referenced studies, such as detailed damper specifications.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Analysis of Results Using the Capacity Curve","content":"\u003cp\u003eIn this part, the capacity curve (load-displacement ratio) is used to examine the structural resistance to progressive collapse for three column removal scenarios: ELC, FELC, and ESC. This curve results from a nonlinear dynamic analysis with an increasing load factor, starting from the formation of the first plastic hinge. Additionally, according to the DOD code, the analysis continues until the axial rotation of the beam above the removed column reaches a maximum of 6 degrees. It should be noted that when the load factor reaches 1, the structure remains resistant to progressive collapse [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e"},{"header":"Analysis of Results for the Structure Equipped with Viscous Dampers","content":"\u003cp\u003eTo obtain the capacity curve of the structure in each of the different column removal scenarios, the effect of 5% damping for the damper alone is first considered. Then, by simultaneously increasing both the stiffness and damping of the damper, the capacity curves are plotted. In this study, the stiffness values for the damper are assumed to be 10,000, 40,000, and 70,000 KN/m. Additionally, for increasing the damping, the damping coefficients obtained in Table\u0026nbsp;(1) are used.\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eThe ELC Column Removal scenario\u003c/h2\u003e\n \u003cp\u003eIn this scenario, it can be observed that when the load factor exceeds one (LF\u0026thinsp;=\u0026thinsp;1.03), the 5% damping ratio for the viscous damper not only reduces the vertical roof displacement but also increases the structural resistance, as shown in Figure (11-a). To account for other damper-related parameters, the capacity curves of the structure are plotted with increased stiffness and damping.\u003c/p\u003e\n \u003cp\u003eAs observed in Figure (11-b), increasing the damper stiffness to 10,000 KN/m, along with increased damping, enhances structural resistance (LF\u0026thinsp;=\u0026thinsp;1.19 for 20% damping) without affecting the structure\u0026rsquo;s ductility. However, in Figures (11-c) and (11-d), for stiffness values greater than 10,000 KN/m, the 20% damping ratio results in lower resistance compared to Figure (11-b).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003eThe FELC Column Removal scenario\u003c/h2\u003e\n \u003cp\u003eSimilar to the previous case, the highest load factor obtained in this scenario occurs for 5% damping ratio, with a value of 1.03. For stiffness of 10,000 KN/m, despite a reduction in ductility, the increase in damping has led to a slight improvement in structural resistance (LF\u0026thinsp;=\u0026thinsp;1.05 for 20% damping), as shown in Figure (12-b). Additionally, for higher stiffness values, increasing damping compared to case (b) has had little effect on enhancing structural resistance, resulting only in a limited reduction in displacement.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003eThe ESC Column Removal scenario\u003c/h2\u003e\n \u003cp\u003eAs observed, in this scenario, considering the effect of damping alone results in a maximum load factor of 1. For a stiffness of 10,000 KN/m, although structural resistance increases (LF\u0026thinsp;=\u0026thinsp;1.05 for 10% and 20% damping), the added damping primarily contributes to reducing displacement, with limited influence on enhancing overall resistance.\u003c/p\u003e\n \u003cp\u003eWith the load factor increasing to at least 1, the structural resistance is enhanced by the use of the viscous damper. However, in most column removal scenarios, changing damper parameters such as increasing stiffness or damping beyond a certain threshold leads to reduced ductility due to the increased stiffness and resulting brittleness of the structure. it is important to note that for stiffness values greater than 70,000 KN/m, the maximum load factor and displacement remain largely unchanged across all three scenarios ELC, FELC, and ESC. This suggests that at higher stiffness levels, damping becomes the sole effective factor influencing the structural response. To validate this observation, a very high stiffness value of K\u0026thinsp;=\u0026thinsp;10⁶ KN/m is applied, and the resulting maximum load factors are presented in Table\u0026nbsp;(2).\u003c/p\u003e\n \u003cp\u003eTable (2) Maximum Capacity Curve Values for Stiffness of 10⁶ KN/m and Various Damping Ratios\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tabb\" border=\"1\"\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLocation\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDamping Ratio\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum load factor\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDisplacement\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eELC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60.82\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e61.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60.90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eFELC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e45.24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e41.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eESC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e55.89\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e46.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e43.97\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003eAnalysis Results of the Structure Equipped with an MR Damper\u003c/h2\u003e\n \u003cp\u003eIn this section, the capacity curves of the structure equipped with MR dampers are plotted for three different damping force levels (10%, 20%, and 30% of Rs) under each of the column removal scenarios. In this study, the damping force is applied as a passive control mechanism, defined as a percentage of the axial force of the removed column (Rs). It is important to note that this damping force is generated by adjusting the voltage applied to the MR damper, and depending on the damper\u0026apos;s maximum capacity, it can exceed 30% of the column\u0026rsquo;s axial force.\u003c/p\u003e\n \u003cp\u003eTable (3) Axial Force Values for the Removed Column (Rs)\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tabc\" border=\"1\"\u003e\n \u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eColumn Location\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAxial force (KN)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eELC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3090\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFELC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3047\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eESC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3068\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAs observed, in the ELC scenario, minimum damping force of 0.1Rs is sufficient to make the structure resistant to progressive collapse (LF\u0026thinsp;=\u0026thinsp;1). Furthermore, increasing the damping force enhances the structural resistance without significantly affecting the ductility of the structure. For both the FELC and ESC scenarios, increasing the damping force leads to an improvement in the structural resistance, despite a reduction in ductility. In the ESC case, a damping force of 0.1Rs is insufficient to prevent progressive collapse. Additionally, the greatest reduction in ductility due to increased damping force occurs in the following order: FELC, ESC, and ELC.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003eInvestigation of Plastic Hinges in the Structure\u003c/h2\u003e\n \u003cp\u003eTo evaluate the formation of plastic hinges in the structure, the ESC column removal scenario is considered. This scenario is selected due to the large displacement values observed at a load factor of 0.9. Figure 16 presents a view of the structure without damper when the plastic hinges formation under the applied load factor of 0.9.\u003c/p\u003e\n \u003cp\u003eSince in this study, stiffness and damping are defined as two variable parameters for the viscous damper, the effect of increasing damper stiffness is first evaluated at 5% damping ratio. For this purpose, the same stiffness values used for plotting the capacity curves are employed in the analysis. Following this analysis, the formation of plastic hinges will be examined under increasing damping ratios at a fixed stiffness level. It should be noted that, due to the similar structural behavior observed across various damping ratios and stiffness levels, the analysis is restricted to these two representative cases.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n \u003ch2\u003eEffect of Increasing Viscous Damper Stiffness at 5% Damping Ratio\u003c/h2\u003e\n \u003cp\u003eAs observed, increasing the damper stiffness has only a minor effect on the distribution of plastic hinges. Specifically, increasing the stiffness from 70,000 to 10⁶ KN/m results in negligible changes in the hinge colors, indicating minimal variation in plastic hinge development.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n \u003ch2\u003eEffect of Increasing Damping Ratio for the Viscous Damper\u003c/h2\u003e\n \u003cp\u003eIn this section, the effect of increasing the damping ratio on the formation of plastic hinges is investigated for a constant damper stiffness of 40,000 KN/m. The results show that increasing the damping ratio has a more significant impact on structural performance compared to increasing stiffness alone. Additionally, higher damping ratios contribute to increasing in the overall stiffness of the structure. Consequently, for damping ratios of 10% and 20%, more plastic hinges shift from the Life Safety (LS) performance level to the Immediate Occupancy (IO) level, indicating improved structural performance and reduced damage.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n \u003ch2\u003ePlastic Hinges in the Structure Equipped with MR Dampers\u003c/h2\u003e\n \u003cp\u003eBy analyzing the capacity curves of the structure equipped with MR dampers, the increase in damping force is identified as an effective factor in enhancing the structural resistance. In the ESC column removal scenario, it is observed that as the damping force increases, more plastic hinges transition from the Life Safety (LS) performance level to the Immediate Occupancy (IO) level. This indicates that the vulnerable structure, previously undergoing large deformations, managed to enhance its stiffness through alternative load paths and increased damping. It is also important to note that for all column removal scenarios, this increase in stiffness is accompanied by improved resistance and a reduction in ductility.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe use of Viscous and MR dampers with a passive control approach and circumferential arrangement, to a limited extent, improved the structural resistance against progressive collapse. The results obtained from this study for the structure equipped with viscous dampers are summarized as follows:\u003c/p\u003e\n\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eBy examining the capacity curves, it was observed that in most column removal cases, increasing in the damping ratio leads to a reduction in displacement and/or ductility (due to the increase in the stiffness of the structure). Additionally, the effect of increased damping in the viscous damper on the structural resistance varies depending on the location of the removed column and the stiffness level of the damper.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eThe stiffness of the viscous damper can only influence the structural resistance and displacement up to a certain limit; beyond this threshold, its effect becomes minimal.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eA simultaneous increase in stiffness and damping in the viscous damper leads to an overall increase in the structural stiffness. This is evidenced by the formation of the first plastic hinge at a higher load factor in the capacity curves. Moreover, analysis of the plastic hinges shows that increasing the damping ratio of the viscous damper has a more significant impact on structural stiffness than increasing its stiffness alone.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eOnly in the two cases of column removal—ESC and FELC— increasing in damper stiffness up to a certain limit leads to a reduction in structural displacement (ductility), without causing any significant change in the structural resistance.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eIn the case of column removal at the ELC location, when the stiffness of the viscous damper is 10,000 KN/m, increasing the damper's damping ratio leads to increase in structural resistance (load factor). However, for higher stiffness values up to a certain limit, the extent of resistance enhancement resulting from increased damping gradually diminishes.\u0026nbsp;\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eOverall, for the structure equipped with MR dampers, it can be concluded that increasing the damping force in all three column removal scenarios leads to improved structural resistance against progressive collapse. Moreover, the level of resistance varies depending on the location of the removed column; and as the damper's damping force increases, the stiffness of the structure also increased, leading to a reduction in it's ductility.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThis research was conducted as part of the author\u0026apos;s M.Sc. thesis at Sadjad University of Technology, under the academic supervision of Dr. Naji. No external financial support was received, and the supervisor had no role in the writing or submission of this manuscript.\u003c/p\u003e\n\u003cp\u003eEthics approval and consent to participate\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003eConsent to publish\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003eCompeting interests\u003c/p\u003e\n\u003cp\u003eThe author declares no competing financial and non‑financial interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eU.S. Department of Defense. (2019). Design of Buildings to Resist Progressive Collapse (UFC 4-023-03). Unified Facilities Criteria. Retrieved from https://www.wbdg.org/FFC/DOD/UFC/ufc_4_023_03_2016.pd\u003c/li\u003e\n\u003cli\u003eBilow, D. N., \u0026amp; Kamara, M. (2002). Progressive collapse design guidelines applied to concrete moment‐resisting frame buildings (pp. 1\u0026ndash;22). U.S. General Services Administration.\u003c/li\u003e\n\u003cli\u003eAmerican Institute of Steel Construction. (2016). Specification for Structural Steel Buildings. AISC. Retrieved from www.aisc.org \u003c/li\u003e\n\u003cli\u003eMakris, N., \u0026amp; Constantinou, M. C. (1992). Spring-Viscous Damper Systems for Combined Seismic and Vibration Isolation. \u003cem\u003eEarthquake Engineering and Structural Dynamic\u003c/em\u003e, Vol. 21, No. 8, pp. 649-664. Copyright \u0026copy; 1992 John Wiley \u0026amp; Sons, Ltd\u003c/li\u003e\n\u003cli\u003eKim, J., Lee, S., \u0026amp; Min, K. W. (2014). Design of MR Dampers To Prevent Progressive Collapse of Moment Frames. Structural Engineering and Mechanics, Vol. 52, No. 2, pp. 291-306. DOI: http://dx.doi.org/10.12989/sem.2014.52.2.291\u003c/li\u003e\n\u003cli\u003eKim, J. \u0026amp; Kim, T. (2009). Assessment of Progressive Collapse-Resisting Capacity of Steel Moment Frames. Journal of Constructional Steel Research, Vol. 65, No. 1, pp. 169-179. \u0026copy; 2008 Elsevier Ltd. DOI: https://doi.org/10.1016/j.jcsr.2008.03.020\u003c/li\u003e\n\u003cli\u003eNaji, A., Ommetalab, M.R. (2018). Horizontal Bracing to Enhance Progressive Collapse Resistance of Steel Moment Frames. Struct Design Tall Spec Build. 2019; e1563. \u0026copy; 2019 John Wiley \u0026amp; Sons, Ltd. https://doi.org/10.1002/tal.1563\u003c/li\u003e\n\u003cli\u003eKim, J. K., Lee, S. J., \u0026amp; Choi, H. H. (2010). Progressive Collapse Resisting Capacity of Moment Frames with Viscous Dampers. Journal of the Computational Structural Engineering Institute of Korea, Vol. 23, No. 5, pp. 517-524. \u003c/li\u003e\n\u003cli\u003eKim, J., Choi, H., \u0026amp; Min, K-W. (2011). Use of Rotational Friction Dampers to Enhance Seismic and Progressive Collapse Resisting capacity of structures. The structural Design of Tall and Special Buildings, Vol. 20, No. 4, pp. 515-537.\u003c/li\u003e\n\u003cli\u003eJavia, P. D., Joshi, D. D., \u0026amp; Patel, P. V. (2016). Enhancing Progressive collapse Resistance of RC Building Using Viscoelastic Dampers. International Journal of Research in Engineering and Technology, Vol. 5, No. 20. https://ijret.org/volumes/2016v05/i32/IJRET20160532022.pdf\u003cspan dir=\"RTL\"\u003e \u003c/span\u003e\u003c/li\u003e\n\u003cli\u003eGalal, K., \u0026amp; El-Sawy, T. (2010). Effect of retrofit strategies on mitigating progressive collapse of steel frame structures. Journal of Constructional Steel Research, 66(4), 520\u0026ndash;531. https://doi.org/10.1016/j.jcsr.2009.12.003\u003cspan dir=\"RTL\"\u003e \u003c/span\u003e\u003c/li\u003e\n\u003cli\u003eDyke, S. J., \u0026amp; Spencer, B. F. (1997). Modeling and Control of Structures with Viscous Dampers. Journal of Engineering Mechanics, 123(11), 1181-1191. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:11(1181)\u003c/li\u003e\n\u003cli\u003eSpencer, B. F., \u0026amp; Nagarajaiah, S. (2003). State of the art of structural control. Journal of Structural Engineering, 129(7), 845-856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Civil Engineering](https://www.springer.com/journal/44290)","snPcode":"44290","submissionUrl":"https://submission.nature.com/new-submission/44290","title":"Discover Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Progressive Collapse, Viscous Damper, MR Damper, Passive Control, Nonlinear Dynamic Analysis","lastPublishedDoi":"10.21203/rs.3.rs-6838436/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6838436/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDampers are considered among the control tools used to dissipate energy and reduce structural displacement. In this study, the effect of using viscous dampers and MR (magneto-rheological) dampers separately, with a passive control approach, on a steel moment frame structure against progressive collapse was evaluated. The damper layout in the structure was arranged diagonally and around the perimeter of the topmost floor. To consider for the variable parameters of the dampers, the structure's capacity curves were analyzed by increasing stiffness and damping for the viscous damper and increasing damping force for the MR damper. The analysis results for both dampers indicate the structure's resistance to progressive collapse under various column removal scenarios. Although this effect is more evident for the structure equipped with MR dampers. In structure equipped with viscous damper, it can be observed that by increasing the damping ratio, the stiffness of structure increased and its displacement reduced; moreover, the increase in stiffness for this damper is effective on the structure's resistance and displacement only up to a certain limit, beyond which it becomes largely ineffective.\u003c/p\u003e","manuscriptTitle":"Investigating the Effect of Horizontal Dampers Arrangement Pattern in the Steel Moment Frame Structure on the Progressive Collapse Potential","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-08 11:31:32","doi":"10.21203/rs.3.rs-6838436/v1","editorialEvents":[{"type":"communityComments","content":1},{"type":"decision","content":"Revision requested","date":"2025-09-01T13:43:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-12T07:18:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"254263771715122777137125492461233930476","date":"2025-08-11T00:36:49+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-18T02:20:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"136615838437979492903906674941903855961","date":"2025-07-16T07:20:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105445063076618453970087500933722804210","date":"2025-07-12T01:21:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-11T06:43:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"49512175193436820152321709058550022746","date":"2025-07-10T12:19:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315122013265437751743634963534818214628","date":"2025-07-03T10:33:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-03T09:41:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-27T05:16:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-19T15:59:18+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Civil Engineering","date":"2025-06-19T15:56:16+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Civil Engineering](https://www.springer.com/journal/44290)","snPcode":"44290","submissionUrl":"https://submission.nature.com/new-submission/44290","title":"Discover Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3c7f7c29-ddd8-42b2-a8af-7c48d5d28628","owner":[],"postedDate":"July 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-21T15:41:14+00:00","versionOfRecord":{"articleIdentity":"rs-6838436","link":"https://doi.org/10.1007/s44290-025-00364-z","journal":{"identity":"discover-civil-engineering","isVorOnly":false,"title":"Discover Civil Engineering"},"publishedOn":"2025-11-19 00:00:00","publishedOnDateReadable":"November 19th, 2025"},"versionCreatedAt":"2025-07-08 11:31:32","video":"","vorDoi":"10.1007/s44290-025-00364-z","vorDoiUrl":"https://doi.org/10.1007/s44290-025-00364-z","workflowStages":[]},"version":"v1","identity":"rs-6838436","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6838436","identity":"rs-6838436","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}