On the Seismic Response of Composite Structures Equipped with Wall Dampers Under Multiple Earthquakes

Abstract

This study investigates the seismic performance of two-, four-, and six-story composite buildings equipped with viscous wall dampers, focusing on structures with concrete-filled steel tubular (CFST) columns and steel beams. Through nonlinear time history analyses using sequential ground motions, the research evaluates the effectiveness of viscous wall dampers in mitigating seismic demands. Results demonstrate significant reductions in both interstory drift ratios and peak floor accelerations across all building heights when dampers are installed. The study particularly highlights the dampers’ effectiveness in controlling drift demands in lower and middle floors while managing acceleration amplification at upper levels. The findings validate the integration of viscous wall dampers into mid-rise composite structures and underscore the importance of considering sequential ground motions in seismic performance evaluations.

1. Introduction

The considerable risk that seismic events pose to global building infrastructure has prompted engineers and researchers to pursue innovative methods for strengthening structural resilience. Over the past several decades, the field of earthquake engineering has made remarkable progress in understanding and mitigating the effects of seismic forces on different structures. A significant breakthrough in this field is the utilization of supplementary damping devices, which have demonstrated a substantial improvement in the seismic performance of both new and existing buildings [1,2,3].

Supplementary damping is fundamentally related to the dissipation of energy. In the context of seismic activity, ground motions transfer kinetic energy to structures, which must be absorbed or dissipated to lessen damage and prevent structural collapse [4,5,6,7]. Historically, seismic design practices have focused on the inherent damping properties of building materials and the ductile characteristics of structural elements to address this energy. However, these traditional strategies often lead to considerable structural damage during severe seismic events, causing significant financial losses and risking human lives [8,9].

The integration of additional damping devices serves as a viable method for enhancing energy dissipation mechanisms in structures. This group of devices, which includes viscous dampers, viscoelastic dampers, friction dampers, and tuned mass dampers, is essential for alleviating the seismic forces that act on primary structural elements. By efficiently absorbing and dissipating seismic energy, these systems contribute to the reduction of structural deformations, the mitigation of internal forces, and the overall enhancement of structural performance during earthquakes [10,11,12].

In their research, Cho and Kwon [13] developed a wall-type friction damper to enhance the resilience of reinforced concrete (RC) framed structures against earthquake forces. Historically, dampers have been primarily designed as brace-type members, which have been found to create complications in RC frame structures, particularly in the connection zones where concrete is prone to damage during seismic events. The wall-type damper they propose presents a significant advantage for the retrofitting of RC structures.

Hejazi et al. [14] have developed an analytical model for a viscous wall damper (VWD) device using a finite element approach, presenting it as a viable alternative to existing earthquake energy dissipation systems. This model is designed to lessen the effects of earthquakes on structures and to enhance the seismic performance of multistory buildings exposed to ground motion. The proposed analytical model for VWD was validated against experimental test data, confirming that this energy dissipation system effectively reduces and dissipates the seismic responses experienced by structures.

Each viscous wall damper is composed of a slender steel tank that is affixed to the lower floor and filled with a non-toxic, odorless, and transparent fluid (Figure 1). Inside this tank, an inner steel plate, referred to as a vane, is connected to the upper floor. When seismic activity occurs or during strong winds, the relative movement of the floors causes the vane to traverse the viscous fluid. The damping force generated by the shearing action of the fluid is influenced by both the displacement and the velocity of the relative motion. Additionally, viscous wall dampers can be designed with two vanes, which effectively doubles the damping force while only slightly increasing the overall plan dimensions [15].

Additionally, the seismic design and analysis of steel–concrete composite structures face numerous significant challenges that demand extensive investigation. While these structures are frequently employed, there are considerable uncertainties regarding the complex interactions between steel and concrete elements when subjected to severe seismic forces. Existing design codes often do not sufficiently address the nonlinear behavior of composite systems, particularly at the junctions of the materials [16,17]. Furthermore, the variety of composite configurations complicates the formulation of standardized design methodologies, and the lack of extensive long-term performance data adds further uncertainty to durability assessments [18,19]. Conventional analytical models may overly simplify the dynamic response characteristics of composite structures, which could lead to designs that are either excessively conservative or inadequately robust [20]. In addition, the construction industry struggles with evaluating the cost-effectiveness of innovative composite solutions in relation to traditional building methods, especially when considering life-cycle performance during seismic events [21]. As urban areas continue to grow and face increasing seismic risks, understanding the behavior of these composite systems under earthquake loading is vital for ensuring structural safety and resilience [22,23,24,25].

Many current design codes focus solely on a singular earthquake scenario defined by the response spectrum outlined in local regulations. This approach fails to account for the repetitive nature of earthquakes, resulting in an insufficient estimation of design earthquake forces. Consequently, the research presented in [26] aims to introduce a probabilistic model that systematically addresses the frequency of earthquake sequences relevant to a specific location. The findings underscore the cumulative damage in terms of response parameters, highlighting the importance of incorporating repeated earthquake sequences into seismic analysis [27,28,29]. Hatzigeorgiou et al. [30,31,32,33] investigated the ductility demands and behavioral factors of single-degree-of-freedom (SDOF) systems subjected to seismic sequences, including both near-fault and far-fault earthquakes. Hatzigeorgiou and Liolios [34] conducted a comprehensive parametric study on the inelastic response of eight reinforced concrete (RC) planar frames exposed to forty-five sequential ground motions. Their results indicate that the sequences of ground motions significantly influence the response and, consequently, the design of reinforced concrete frames. Additionally, it was determined that the ductility demands of sequential ground motions can be effectively estimated through suitable combinations of the corresponding demands from individual ground motions. Chorafa et al. [35] analyzed the seismic performance of moment-resistant composite frames with concrete-filled steel tube (CFT) columns and composite steel beams subjected to multiple earthquake events, while also considering the implications of soil–structure interaction (SSI). Their findings demonstrate that successive ground motions generally increase displacement demands and residual deformations compared to single-event scenarios. These results challenge traditional assumptions in seismic engineering and emphasize the necessity of accounting for multiple earthquake scenarios, building-specific characteristics, and SSI effects.

The aim of this work is to explore the seismic resilience of composite buildings with two, four, and six stories that are fitted with viscous wall dampers. It concentrates on structures that incorporate concrete-filled steel tubular (CFST) columns alongside steel beams. Through nonlinear time history analyses that utilize sequential ground motions, the research assesses the effectiveness of viscous wall dampers in reducing seismic demands. The findings indicate notable reductions in interstory drift ratios and peak floor accelerations for all building heights when dampers are employed. The study particularly underscores the dampers’ efficiency in managing drift demands on the lower and middle floors while also addressing acceleration amplification on the upper levels. These results validate the integration of viscous wall dampers in mid-rise composite buildings and stress the importance of considering sequential ground motions in seismic performance evaluations.

2. Description of the Composite Structures Equipped with the Wall Damper

The present study focuses on 2-, 4-, and 6-story buildings. The structures consist of circular concrete-filled steel tube (CFST) columns, represented in Figure 2, and steel beams that are connected to concrete floor slabs.

Table 1. Material properties.

Material	Elastic Modulus (GPa)	Yield Strength (MPa)
Concrete (C30/37)	32	~30 (compressive)
Steel (S275)	210	275

depicts the material properties and

Table 2. Cross-section properties.

Structure	Shape of Columns	Dimensions	Steel Beams
2-story	Circular CFST	D = 0.406 m, t = 0.0063 m	IPE 330
4-story	Circular CFST	D = 0.559 m, t = 0.01 m	IPE400
6-story	Circular CFST	D = 0.610 m, t = 0.0142 m	IPE500

provides the sectional dimensions of the analyzed structures.

The floor height was established at 3.0 m. The structures were organized into three bays in both horizontal and vertical directions, with each bay measuring 6 m in span. The structural frames analyzed in this research adhered to the standards set forth by Eurocode-3 [36], Eurocode-4 [37], and Eurocode-8 [38], utilizing SAP2000 software [39]. Two distinct load combinations were evaluated: one addressing seismic conditions and the other focusing on gravity, as outlined by Eurocode 8 [38]. The seismic load combination is represented as G + 0.3Q + E, where G denotes the dead load, Q signifies the live load, and E represents the earthquake load. The gravity load combination is formulated as 1.35G + 1.5Q.

As shown in Figure 3, viscous wall dampers were strategically placed in the central bay of the perimeter frames along the x-direction on each level. The decision to position the wall dampers around the perimeter of the composite structures, as illustrated in Figure 3, is deliberate to mitigate any potential torsional effects arising from the distribution of stiffness and mass, beyond those considered due to accidental eccentricity.

For every level within the structure, the dead loads were quantified at 5 kN/m², and the live loads were established at 2 kN/m². The design incorporated a ground acceleration of 0.24 g and utilized a behavior factor (q) of 4.0, which meets the criteria for medium structural ductility and Spectrum Type 1. The behavior factor, q, was in accordance with the requirements set forth in §5.2.2.2 of EC8 [38].

3. Modeling of the Composite Structures and of the Wall Damper

To evaluate the inelastic behavior of structures, one must consider the potential emergence of plastic hinges at the ends of each structural member, which can be illustrated via a bi-linear hysteresis model. The P-M2-M3 hinge property signifies the interplay between axial load and biaxial bending moments in the tower section, while the M3 hinge property represents the bending moment response of the beams. The behavior of composite sections is described by the following equations [40]:

The strength ratio is given by

$$\xi ={\displaystyle \frac{\left[D^2-{\left(D-2t\right)}^2\right]f_s}{\left[{\left(D-2t\right)}^2\right]f_c}}$$

(1)

The bending moment of the P-M curve is [40]

$${\displaystyle \frac{M}{M_{pred}}}={\displaystyle \frac{m_1+m_2\mathit{ln}\left(\xi \right)+m_3\left(\frac{P}{P_{pred}}\right)}{1+m_4\mathit{ln}\left(\xi \right)+m_5{\mathit{ln}}^2\left(\xi \right)+m_6\left(\frac{P}{P_{pred}}\right)+m_7{\left(\frac{P}{P_{pred}}\right)}^2}}$$

(2)

and the m₁–m₇ parameters are presented in

Table 3. Parameters for P-M curve.

m1	m2	m3	m4	m5	m6	m7
0.954363	0.006437	−0.946844	0.050883	−0.024529	−1.591625	0.880543

.

$$P_{pred}=\left[\left(a_1+a_2\left({\displaystyle \frac{D}{t}}\right)+a_3\left({\displaystyle \frac{f_y}{f_c}}\right)\right)P_c+\left(b_1+b_2\left({\displaystyle \frac{D}{t}}\right)+b_3\left({\displaystyle \frac{f_y}{f_c}}\right)\right)P_s\right]\left(1-c_1{\left({\displaystyle \frac{D}{L}}\right)}^{c_2}\right)$$

(3)

where $c_1$ and $c_2$ are parameters that are presented in

Table 4. Parameters for axial load.

a1	a2	a3	b1	b2	b3	c1	c2
0.935594	0.000474	25.19892	20.0523	−6.29828	−0.00406	1.07973	2.378821

and D/t is the diameter-to-thickness ratio of circular sections.

In the modeling of a viscous wall damper, the beams were segmented into three distinct elements, with the central element’s length being specified. This central element was further divided into two equal parts. The beam elements that fall within the width of the viscous wall damper (VWD) can be represented as highly rigid. At the mid-height of each bay and story that incorporates a VWD, a pair of nodes was established at a minimal distance from each other. This node pair is to be positioned centrally within the width of the VWD. The center of the beam located beneath one of these nodes was linked to a stiff frame element, while the center of the beam above was connected to the other node. Additionally, a horizontal link element was established between the two nodes at the mid-height of the story and bay that contained the VWD. The wall damper featured nonlinear viscous dampers with damping exponent a = 0.5 and damping coefficient of 1600 kNs/m. The values were provided by the manufacturer [15].

The superstructure’s damping matrix was constructed based on the Rayleigh damping model, which factors in the current stiffness of the structure at each time increment, thereby yielding a tangent damping matrix. The inherent viscous damping ratio for the superstructure was defined as ξ = 4% for both the first and second modes of the system.

4. Ground Motions

The present analysis incorporates the seismic sequences documented by PEER [41], as shown in

Table 5. Data for multiple earthquakes under consideration.

No.	Earthquakes	Component	Station	Date/Time	Magnitude	PGA (g)
1	Mammoth Lakes	54099 Convict Creek	N-S	25 May 1980 (16:34)	6.1	0.442
				25 May 1980 (16:49)	6.0	0.178
				25 May 1980 (19:44)	6.1	0.208
				25 May 1980 (20:35)	5.7	0.432
				27 May 1980 (14:51)	6.2	0.316
2	Imperial Valley	5055 Holtville P.O.	HPV315	15 October 1979 (23:16)	6.6	0.221
				15 October 1979 (23:19)	5.2	0.211
3	Coalinga	46T04 CHP	N-S	22 July 1983 (02:39)	6.0	0.605
				25 July 1983 (22:31)	5.3	0.733
4	Chalfant Valley	54428 Zack Brothers Ranch	E-W	20 July 1986 (14:29)	5.9	0.285
				21 July 1986 (14:42)	6.3	0.447
5	Whittier Narrows	24401 San Marino	N-S	1 October 1987 (14:42)	5.9	0.204
				4 October 1987 (10:59)	5.3	0.212

. The seismic events under consideration are the Mammoth Lakes, Imperial Valley, Coalinga, Chalfant Valley, and Whittier Narrows earthquakes. To prevent structural vibrations resulting from damping, a 100 s gap was implemented between each ground motion. Figure 4 provides a visual representation of these sequences. Furthermore, the structures also experienced the ground motions detailed in

Table 6. Data for near-fault earthquakes.

No.	Date	Earthquake	Station Name	Comp.	PGA (g)
1	4 October 1987	Whittier Narrows	24399 Mt Wilson—CIT Station	NS	0.158
2	4 October 1987	Whittier Narrows	24399 Mt Wilson—CIT Station	EW	0.142
3	20 September1999	Chi-Chi, Taiwan	HWA056	056-N	0.107
4	20 September 1999	Chi-Chi, Taiwan	HWA056	056-N	0.107
5	1 October 1987	Whittier Narrows	24399 Mt Wilson—CIT Station	NS	0.186
6	1 October 1987	Whittier Narrows	24399 Mt Wilson—CIT Station	EW	0.123
7	9 February1971	San Fernando	127 Lake Hughes #9	N069	0.157
8	9 February1971	San Fernando	127 Lake Hughes #9	N159	0.134
9	17 January1994	Northridge	90019 San Gabriel—E. Gr. Ave.	NS	0.256
10	17 January1994	Northridge	90019 San Gabriel—E. Gr. Ave.	EW	0.141
11	20 September 1999	Chi-Chi, Taiwan	TAP103	NS	0.177
12	20 September 1999	Chi-Chi, Taiwan	TAP103	EW	0.122
13	17 January1994	Northridge	90017 LA—Wonderland Ave	N005	0.172
14	17 January1994	Northridge	90017 LA—Wonderland Ave	N175	0.112
15	7 June 1975	Northern Calif	1249 Cape Mendocino, Petrolia	N060	0.115
16	7 June 1975	Northern Calif	1249 Cape Mendocino, Petrolia	N150	0.179
17	8 July 1986	N. Palm Springs	12206 Silent Valley	NS	0.139
18	18 October1989	Loma Prieta	58539 San Francisco	N205	0.105
19	18 October 1989	Loma Prieta	47379 Gilroy Array #1	NS	0.473
20	18 October 1989	Loma Prieta	47379 Gilroy Array #1	EW	0.411

.

5. Results

This investigation employs nonlinear time history analysis to evaluate the structural behavior when subjected to consecutive seismic excitations. Critical performance indicators examined in this research encompass maximum floor acceleration values, permanent deformations after the events, and the relative lateral displacements between adjacent stories. These parameters serve as key metrics for assessing the dynamic response of the system.

5.1. Natural Vibration Periods

A comparative assessment of the primary vibrational characteristics is presented in

Table 7. Fundamental periods of the structures under study.

Wall Damper	Structure	T1 (s)
No	2-story	0.34
Yes	2-story	0.30
No	4-story	0.84
Yes	4-story	0.79
No	6-story	1.30
Yes	6-story	1.16

, highlighting the dynamic response of the investigated composite systems. The analysis contrasts the fundamental periods between configurations incorporating viscous wall dampers and their conventional counterparts without supplemental damping devices.

5.2. Two-Story Configuration

Figure 5 illustrates the lateral deformation behavior of a two-story structure without supplemental damping mechanisms, expressed through interstory drift ratio (IDR) measurements. The comparative analysis reveals distinct response patterns: under isolated seismic excitation, the structure exhibits a maximum IDR of 0.37%, whereas exposure to consecutive ground motions elevates this value to 0.47%. This differential response highlights the amplified structural demands imposed by multiple sequential earthquakes.

The dynamic response characteristics of the damper-equipped two-story system are depicted in Figure 6, where IDR measurements are evaluated under both isolated and sequential earthquake scenarios. The analysis reveals peak lateral deformations of 0.36% during single seismic events, with a modest increase to 0.39% when subjected to consecutive ground motions. As evidenced in Figure 7, the integration of viscous wall dampers yields notable performance improvements, manifested through significant attenuation of interstory drift magnitudes. This enhanced structural behavior demonstrates the effectiveness of the implemented damping mechanism in controlling lateral deformations.

Figure 7 illustrates the distribution of peak floor acceleration (PFA) responses throughout the two-story structure without supplemental damping devices. Under consecutive seismic excitations, the acceleration demands intensify significantly, reaching magnitudes of 0.35 g and 0.36 g at the lower and upper levels, respectively. When subjected to single ground motion, the structure exhibits more moderate acceleration responses, with recorded values of 0.28 g at the first story and 0.33 g at the second story, demonstrating the amplification effect of floor acceleration along the building height.

As depicted in Figure 8, the implementation of viscous wall dampers in the two-story configuration yields favorable acceleration control characteristics. The damper-equipped system demonstrates attenuated peak floor acceleration (PFA) responses, maintaining levels below 0.35 g during isolated seismic events and exhibiting consistent values of approximately 0.36 g across both stories when subjected to consecutive ground motions. This enhanced dynamic behavior, achieved through supplemental damping mechanisms, manifests in diminished acceleration demands compared to the conventional structure. Such performance characteristics suggest improved protection for acceleration-sensitive non-structural elements and building contents throughout the vertical profile of the structure.

5.3. Four-Story Structure

Figure 9 illustrates the distribution of interstory drift ratios (IDR) in the four-story structure without supplemental damping mechanisms. The analysis reveals a distinctive pattern of deformation demands, with maximum lateral displacements concentrated at the base level. Under consecutive seismic events, the ground story experiences peak drift values of 0.69%, exceeding the 0.65% recorded during isolated excitations. A gradual attenuation of drift magnitudes is observed along the building height, with the second level exhibiting values of 0.65% and 0.55% for sequential and individual seismic scenarios, respectively. This diminishing trend continues through the third level (0.52% sequential, 0.49% isolated) and culminates at the uppermost story, where minimal deformations of 0.5% and 0.45% are recorded under respective loading conditions.

With the implementation of viscous wall dampers, the maximum IDR in the first story decreased to 0.62% for sequential motions and 0.6% for single motions. The second story exhibited IDRs of 0.59% and 0.57%, while the third story showed values of 0.4% and 0.39% for sequential and single motions, respectively. The fourth story maintained the lowest drifts at 0.33% (sequential) and 0.31% (single) (Figure 10).

Figure 11 demonstrates the amplification of floor acceleration demands along the vertical profile of the structure. The analysis reveals a progressive intensification of peak floor acceleration (PFA) responses, initiating from 0.17 g (consecutive events) and 0.15 g (isolated excitation) at the ground level. This acceleration pattern evolves through the intermediate stories, with recorded values of 0.17 g and 0.14 g at the second level, followed by a notable increase to 0.24 g and 0.22 g at the third story under sequential and individual seismic scenarios, respectively. The acceleration demands reach their maximum magnitude at the building’s uppermost level, where values of 0.47 g and 0.42 g are observed under consecutive and isolated ground motions, illustrating the characteristic acceleration amplification toward higher elevations.

The implementation of supplemental damping devices demonstrates notable effectiveness in mitigating acceleration responses throughout the structure, as illustrated in Figure 12. The damper-equipped configuration exhibits moderated peak floor acceleration (PFA) characteristics, with ground level responses of 0.17 g and 0.16 g under consecutive and isolated seismic events, respectively. The acceleration profile develops moderately through the intermediate levels, registering 0.18 g and 0.14 g at the second story, followed by values of 0.26 g and 0.22 g at the third level for the respective loading scenarios. The control effectiveness of the damping system is particularly evident at the uppermost story, where peak accelerations are constrained to 0.43 g and 0.39 g under sequential and single ground motions, representing a significant attenuation compared to the conventional system.

5.4. Six-Story Structure

A comparative analysis of lateral deformation behavior in the six-story configuration without supplemental damping is presented in Figure 13. The evaluation of interstory drift ratios (IDR) reveals distinct response patterns under different loading scenarios. Maximum lateral deformations concentrate at the ground level, where drift magnitudes reach 0.67% during isolated seismic events, with a slight amplification to 0.68% under consecutive ground motions. The structural response characteristics of the upper levels (stories two through six) exhibit notable sensitivity to loading sequence effects. While isolated seismic excitations induce moderate drift demands ranging between 0.3% and 0.4%, exposure to sequential events results in substantially elevated deformations, with IDR values escalating to the range of 0.5–0.55%. This differential response pattern underscores the amplified structural demands imposed by multiple seismic sequences.

The installation of viscous wall dampers in the six-story structure resulted in a marked improvement in drift control. Under individual seismic events, the structure’s first floor exhibited a maximum interstory drift ratio (IDR) of roughly 0.65%. When subjected to consecutive earthquake loadings, the highest IDR reached approximately 0.66%, which represents an improvement compared to the 0.68% recorded in the conventional structure. The performance of the damping system was particularly evident in the higher levels, where IDRs remained under 0.6% even during sequential seismic events, highlighting the system’s ability to minimize effectively lateral displacements, as illustrated in Figure 14.

The six-story structure with viscous wall dampers demonstrated regulated acceleration responses, exhibiting ground-level peak floor acceleration (PFA) measurements of approximately 0.1 g during individual seismic events. The structure showed effective control of acceleration amplification, with the uppermost level recording PFA values of about 0.42 g during single earthquakes and 0.44 g during successive seismic events. Intermediate floors (spanning from the second to fifth levels) registered moderate PFA measurements ranging between 0.1 g and 0.4 g, as depicted in Figure 15.

The six-story structure without dampers demonstrated notably increased acceleration demands, recording ground-level peak floor acceleration (PFA) starting at 0.4 g with considerable amplification at higher elevations. The structure’s highest level recorded acceleration peaks of roughly 0.44 g during individual seismic events, which intensified to approximately 0.48 g when subjected to consecutive earthquakes. The intermediate floor levels experienced PFA measurements varying between 0.1 g and 0.4 g, as shown in Figure 16.

The sequential evolution of lateral displacements, measured at a connection point on the structure’s top level, is illustrated in Figure 17. The results demonstrate that earthquake excitations significantly influence the dynamic nonlinear behavior of composite structural systems, particularly in terms of residual displacement patterns.

6. Comparison Between Composite Structures with and Without the Viscous Wall Dampers

The investigation carried out in this study on composite structures that incorporate concrete-filled steel tube (CFT) columns and composite steel beams has yielded several significant insights concerning their structural performance, both with and without the inclusion of viscous wall dampers. A review of Figure 18, Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23 allows for a direct comparison of the structural performance of buildings equipped with viscous wall dampers against those without, across various heights, taking into account interstory drift ratios (IDR) and peak floor accelerations (PFA).

The evaluation of the two-story building, depicted in Figure 18 and Figure 19, clearly illustrates the effectiveness of the dampers. As shown in Figure 18, the presence of dampers consistently reduces drift ratios, with the most substantial reductions occurring at the first floor, where drift demands are typically highest. Correspondingly, the acceleration data in Figure 19 indicate a similar improvement, with PFA values decreasing across both floors. These notable reductions are especially significant given the relatively simple configuration of the two-story building, suggesting that viscous wall dampers can greatly enhance seismic performance even in structures of lower height.

The configuration of the four-story structure (see Figure 20 and Figure 21) showcases the performance of the damping system in medium-height edifices. Figure 20 demonstrates that the incorporation of dampers results in a reduction of drift ratios, with the most significant effects noted on the second and third floors, where drift demands are typically at their peak. In Figure 21, the acceleration analysis reveals a steady reduction in PFA values throughout the building’s height, highlighting the damping system’s effectiveness in mitigating the acceleration amplification that often occurs on the upper levels. The more even distribution of drift and acceleration demands suggests that the dampers play a crucial role in enhancing the overall dynamic response of the structure.

For the six-story structure (refer to Figure 22 and Figure 23), the effectiveness of the damping system is particularly clear in its management of drift and acceleration demands in taller buildings. As depicted in Figure 22, the presence of dampers results in a drift ratio reduction with the most significant enhancements observed in the middle floors (third to fifth levels), where drift demands are usually at their highest. Furthermore, Figure 23 illustrates that the acceleration comparisons indicate consistent reductions in peak floor acceleration (PFA) throughout the height of the building, with the damping system showing remarkable efficacy in the upper floors, where acceleration amplification effects are most pronounced. The evidence suggests that viscous wall dampers effectively control both drift and acceleration demands, even in taller structures.

The analysis of building heights reveals that the comparative metrics consistently affirm the effectiveness of viscous wall dampers in enhancing seismic performance. This system is particularly advantageous in regulating peak responses in critical sections of each building type: lower floors for drift in shorter buildings, middle floors for drift in taller buildings, and upper floors for acceleration across all heights. This broad enhancement in performance suggests that viscous wall dampers are a feasible option for increasing the seismic resilience of composite structures of varying heights.

7. Limitations and Financial and Practical Implications of the VWD

The limitations of this study are as follows: despite the advantages of numerical analysis, it is unable to fully capture the intricate interactions and unpredictable behaviors that can arise during an actual seismic event. Factors such as material degradation, connection slip, localized stress concentrations, and unexpected structural interactions pose significant challenges that are difficult to accurately simulate in computational models.

The implementation of viscous wall dampers carries substantial financial implications within the field of structural engineering. The associated expenditures comprise: (i) costs for the raw materials necessary for the dampers, (ii) specialized manufacturing processes for custom damper units, (iii) increased design and engineering time for proper integration, and (iv) possible improvements in foundation and structural support requirements.

The integration of viscous wall dampers carries several practical implications that must be considered: (i) the need for accurate installation procedures, (ii) the use of specialized welding and connection techniques, (iii) the importance of meticulous alignment to achieve optimal functionality, (iv) the potential for increased complexity in architectural and structural coordination, and (v) the requirement for skilled labor with specific technical knowledge in the installation of dampers.

Another important consideration pertains to the long-term maintenance of viscous wall dampers. These devices are not intended for a “set and forget” methodology. Their upkeep requires: (i) regular monitoring of fluid levels within the damper, (ii) assessment for any signs of seal degradation, (iii) examination of mechanical parts for signs of wear, (iv) potential replacement of internal damping components, and (v) routine performance testing to confirm their ongoing effectiveness.

The research findings are relevant to regions with diverse seismic hazard considerations, necessitating unique strategies for various seismic zones. In high-seismicity areas like California, Japan, and Chile, it is vital to adopt critical modifications, such as specifying stronger dampers, enhancing damper capacity, refining connection detailing, and instituting more regular inspection protocols. On the other hand, moderate-seismicity regions allow for more cost-effective approaches, prioritizing the optimization of damper sizing, minimizing over-design, and achieving a balance between performance and economic factors.

The research findings also reveal that vital adjustments for scenarios characterized by multiple seismic incidents require the development of design guidelines that focus on: (i) cumulative structural damage, (ii) constraints on residual drift, (iii) procedures for swift post-event evaluations, and (iv) the creation of performance metrics pertaining to repeated seismic loading, structural resilience, and the ability to recover quickly.

8. Conclusions

This research of composite structures incorporating viscous wall dampers leads to several important conclusions:

• Viscous wall dampers effectively decrease interstory drift ratios for buildings of varying heights.
• Peak floor accelerations are reduced with notable effectiveness observed at the upper levels.
• Sequential seismic activities generate greater demands compared to isolated ground motions.
• The dampers effectively alleviate the cumulative impacts of these sequential ground motions.
• The system sustains its performance across multiple seismic occurrences.
• The system effectively controls acceleration amplification at the upper floors and it enhances the management of drift concentrations at critical levels within the structure.

These insights affirm that viscous wall dampers are a practical and effective means of improving the seismic performance of composite structures. Their consistent efficacy across different building heights and loading scenarios indicates their wide applicability in seismic design and retrofitting efforts.