Effectiveness of Friction Dampers in Seismic and Wind Response Control of Connected Adjacent Steel Buildings

Effectiveness of friction dampers (FDs) is investigated for connected dynamically similar and dissimilar steel buildings under uncorrelated seismic ground motion and wind excitations. (e steel buildings involving moment-resisting frame (MRF) and braced frame (BF) are varied from five storeys to twenty storeys, which are connected by different configurations of the FDs. (e steel buildings without and with bracing systems are modeled as plane frame structures with inertial masses lumped at each joint node. (e FDs are modeled an element having yield force equal to slip load, with force-deformation behavior as elastic-perfectly plastic material. (e dynamic responses of the unconnected and connected steel buildings are obtained in terms of top floor displacement and acceleration under the considered ground motion and wind excitations. It is concluded that the FDs help minimizing the gap between two adjacent buildings having utilized the space to connect the buildings. Moreover, the effectiveness of the FDs in terms of response reduction in dynamically dissimilar buildings is more than that in the similar buildings under the considered excitation scenarios. However, the effectiveness of the installed devices varies significantly under the multiple loading scenarios. Finally, the separation gap may be reduced by ∼30%, which would eventually minimize structural pounding as well as utilize the space for effective construction. Hence, important essential guidelines are outlined for structures installed with such passive control devices against such multiple scenario loadings.


Introduction
Structures constructed in moderate-to-high seismicity and windy regions have experienced damages due to extreme vibrational effects under severe ground shaking and gusty wind loading imparted [1][2][3][4][5][6]. To minimize these damaging effects and improve the behavior of the structures under such dynamic excitations, friction damper (FD) has been one of the potential passive response control devices developed in minimizing the large response of a structure under the extreme earthquake and wind excitations [7,8]. In a typical FD, the generated frictional force helps to dissipate the external energy and stabilize the structure under the dynamic excitation scenarios [9]. e FDs are also not prone to thermal effects and possess a stable hysteretic behavior for a considerable number of cycles under such dynamic excitations [10]. Moreover, the FDs have a reliable performance under the dynamic excitations as compared to the other conventional methods and their installation and maintenance are relatively simple. erefore, these advantages make the FDs a suitable choice for design of new structures as well as rehabilitation and strengthening of existing structures to achieve safety of the structures under the multiple catastrophic seismic and wind hazards [11,12].
With the recent increase in urbanization and globalization, the structural engineers and designers are enforced to construct buildings at a close vicinity resulting in insufficient separation gap between the buildings. Such insufficient gap leads to structural pounding under the effects of seismic ground motions and gusty winds, which may lead to catastrophic collapse of the buildings, as observed during 1985 Mexico City earthquake. e primary reason of impact between the adjacent buildings under the effects of earthquake (or wind excitations) is the difference in their dynamic properties. ese differences in structural properties lead to out-of-phase vibrations causing structural pounding, which warrants technical knowhow for constructions in high-urbanized regions across the world [13]. Hence, in order to have effective utilization of the space between two structures, coupling of the adjacent structures with suitable control mechanisms becomes an effective solution to reduce the overall responses of the building systems under the effects of earthquake and wind excitations [14]. e friction damper (FD) was initially used in steel buildings for improving the seismic performance [15,16]. e proposed device was helpful to upgrade the seismic resistance of the existing building frames.
ereafter, the FDs were adopted for braced frames, buildings with shear walls, and low-rise buildings to mitigate the large deformations caused by earthquake ground motions and winds [17][18][19]. e application of this novel structural system was further focused on construction of an 18-storey steel apartment building in India [20]. It was observed that significant seismic response reduction was achieved on application of the Pall FDs in the steel building. Research further progressed in assessing and designing the parameters of the FDs for different structural systems under ground motion excitations [10,21]. Lately, the FDs were used in mid-rise to high-rise buildings along with diagonal bracing, which reduced the seismic responses considerably [22,23]. Moreover, Montuori et al. [24] presented an innovative approach to design a seismic resistant system for the combination of moment-resisting frame (MRF) and a bracing system installed with the FDs. ereafter, multiobjective optimization procedure was applied to find the optimal placements of the FDs in building frame [25][26][27]. Research is also conducted to optimize the slip load and investigate the hysteretic behavior of structures using rotational FD [28,29]. e FD has also found its application in the infrastructure system, such as transmission tower to control the large seismic deformations [30].
Coupling of adjacent buildings has been an emerging technique to mitigate the large structural responses due to wind and seismic excitations [31,32]. e concept allows two dynamically similar and/or dissimilar structures to exert the forces upon one another for overall response reduction of the system. e available studies showed improved performance of the structural systems by connecting different passive control devices to limit the pounding actions under earthquake ground motions [14,[33][34][35][36][37][38][39]. Overall, the FDs have offered its potential in minimizing the extreme vibrations installed in a structure; however, research strategies have not been implemented to assess the response and quantify the effectiveness of the FDs for coupled adjacent buildings under both seismic and wind excitations. erefore, it becomes important to investigate the connected structures installed with the FDs to mitigate the responses of adjoining building and avoiding poundings against the multihazard scenario of earthquake and wind loadings during design life of structures.
Herein, effectiveness of the FDs is investigated for connected dynamically similar and dissimilar adjacent steel moment-resisting frame (MRF) and braced frame (BF) buildings with varying storeys under the multihazard uncorrelated scenarios of seismic and wind hazards. Sitespecific earthquake ground motions and wind excitations are assumed to describe the multihazard scenario for assessment of the unconnected and connected steel structures. In view of the abovementioned gaps, the main objectives of the current study are as follows: (i) to study the effectiveness of the FDs for the connected dynamically similar and dissimilar multistorey buildings under multihazard earthquake and wind excitations and (ii) to investigate the effects of varying number of storeys of the connected dynamically similar and dissimilar multistorey buildings under earthquake and wind excitations evaluating the response of the FDs in multihazard conditions.

Mathematical Modeling
Mathematical models for N-storey dynamically similar and dissimilar moment-resisting frames (MRFs) and braced frames (BFs) connected by the FDs are developed for different configurations, as shown in Figures 1 and 2, under the dynamic earthquake and wind loadings. ree configuration systems for the connected buildings, viz., configuration A, B, and C are considered to assess the effectiveness of the FDs. Configuration A has two friction dampers at each storey in X crossing pattern, with cross-bracing at all floor levels, as shown in Figures 1(c) and 2(c). Configuration B has one friction damper at each storey in a zigzag pattern as shown in Figures 1(d) and 2(d). Configuration C has two friction dampers at each storey in X crossing pattern up to 0.4 N of upper storey of the building from the top, as shown in Figures 1(e) and 2(e), where N is the number of storey. e assumptions made for developing the mathematical models are as follows: (i) the building members except the FDs are assumed to remain in the elastic limit, a design decision in structural control, (ii) one degree of freedom (DOF) at each floor level in the direction of earthquake ground motion and wind is considered, (iii) the inertial mass is lumped at each floor level, (d) the floors are assumed to be rigid in their own plane, and (e) strength degradation of friction dampers is presently ignored in the analysis.

Moment-Resisting Frame (MRF).
e governing differential equation of motion for the MRF, in general, is written as where [M], [C], and [K] are the mass, damping, and stiffness matrices of the primary structure, respectively. Moreover, }, and {u(t)} are the acceleration, velocity, and displacement response of the primary structure, respectively. Furthermore, F(t) is the external force exerted on the structure, either during the earthquake or wind event. Here, is the inertial force vector induced because of the earthquake ground motion applied to the 2 Shock and Vibration structure (base-excited structure), or F(t) � {F 1 , F 2 , F 3 ,. . ., F n } T is the applied wind force vector at the floor mass on each storey (mass-excited structure). Here, the earthquake ground acceleration is denoted byü g (t) and {r} is the influence coefficient vector. e wind force, F n (t) � 0.5ρC d A(V+Δv) 2 , depends on the environment and building conditions, such as, density of air, ρ; coefficient of drag, C d ; depending on shape of the building; area of wind load exposure for n th floor, A n ; mean wind speed, V; and fluctuating wind component, Δv. For the MRF, the structure is defined by its mass matrix, damping matrix, and stiffness matrix as [M], [C], and [K], respectively. Here, [M] is a diagonal matrix with the diagonal element m jj � m j , the mass lumped at the j th floor. Flexural rigidity of the columns provides lateral force resistance in the MRF; therefore, only column stiffness contributes towards the formation of [K] matrix. e mass and stiffness matrix of the N-storey MRF can be given as

Braced Frame (BF).
e governing differential equation of motion for the BF is written as where [M] and [C] matrices are constructed similar as that in case of the MRF. In the BF, stiffness of the structure is the combined effect of the stiffness imparted by the columns, i.e., [K], and the braces, i.e., [K b ]. Here, θ N is the angle of the brace with horizontal at the N th storey level and k bi � k b1 , k b2 , k b3 . . . k bN denote the axial stiffness of the braces: In the BF, the braces are assumed to carry only the axial force and the brace sections are so chosen to ensure that they do not buckle under compression and do not yield under tension.

Connected Frame Using Friction Damper (FD).
Coulomb's dry friction is used to model the nonlinear behavior of the FDs. e nonlinearity is concentrated only in the friction dampers, assuming rest of the building members (the primary structural system) is in elastic range. is is done to ensure that the energy dissipation occurs in friction dampers only and not by yielding of any other structural members. Hence, the structures with the FDs can be treated as a dual system consisting of nonlinear energy-dissipating devices exhibiting elastoplastic behavior and a primary structural system exhibiting linear behavior. Based on this assumption, the governing equation of motion can be written as where C eff � C + C d and K eff � K + K d . C is the equivalent damping of the building systems, and C d is the equivalent damping of the FD. Similarly, K is the equivalent stiffness of the building systems and K d is the equivalent stiffness of the FD, which is assumed to be zero here. F d (t) � μm N gsgn(u) is the frictional force exerted by the FD under the earthquake or wind load, and m N g or W is the slip load for the FD at each storey level, with g denoting the acceleration due to gravity. e matrices for equation (6) are discussed as follows: 4 Shock and Vibration Moreover, F d (t) � μm N gsgn(u) is the frictional force exerted by the FD under the earthquake or wind load, and m N g or W is the slip load for the FD at each storey level, with g denoting the acceleration due to gravity. Figure 3 shows the force-deformation behavior of the FD assumed for this study. Furthermore, the stiffness of the brace of the FD is neglected; however, considering realistically the force-deformation behavior of the friction damper does include initial stiffness provided by the brace. e numerical solution of the governing differential equations given above for the MRF and BF connected by the FD are obtained by using Newmark's method of nonlinear modal time history adopting linear variation of acceleration over an interval of Δt. e time interval for solving the Shock and Vibration equations of motion is taken as Δt, which also depends on the time step for the external load applied (earthquake ground motion or gusty wind loading).

Multihazard Scenario under Earthquake and Wind Excitations
e multihazard assessment strategy involves proper selection of hazard models to assess a structure under the effects of earthquake and wind loadings in a region [40]. e hazard models may be generated using empirical equations, spectra established on physical models, or adopting the already available data from the past earthquake or wind events recorded at the nearest station. For the present study, actual time history data of the earthquake from a recorded station and synthesized time history data of the wind loading from the same region are assumed to investigate the effectiveness of the FD when used to connect adjacent buildings. e time history data are chosen for two different regions, viz., California region of the United States of America (USA), and Kobe city in the southeast region of Japan. e locations are carefully chosen in such a way that the probability of occurrence of the multiple hazards is considerably higher than other regions of the world. Moreover, the considered earthquakes have caused extreme devastations to socioeconomic life as observed from the global statistics. e wind loads, with static and fluctuating components, are simulated from the NatHaz online wind simulator (NOWS): simulation of Gaussian multivariate wind fields [41]. e simulation technique involves obtaining discrete frequency function with Cholesky decomposition and fast Fourier transform (FFT) for wind speed, which is considered as the wind hazard parameter here. e time histories of the wind speeds are obtained thence by summing the static and the fluctuating components obtained from the simulation based on Bernoulli's theorem.

Numerical Study
Herein, a numerical study is conducted to evaluate the effectiveness of the FDs for the connected steel MRF and BF buildings. Modal damping of ξ � 2% is considered for the two steel buildings. e normalized slip load for the FD at each storey level considered for the study is assumed 30% of the storey weight (W), which can suitably be optimized otherwise. e other relevant parameters adopted to model the FDs for the connected steel buildings are shown in Table 1. For further study, the variation of height is considered in 5, 10, 15, and 20 storey for dynamically similar and dissimilar building frames connected by the FDs. Free vibration analysis is conducted to obtain the modal responses for the unconnected MRFs and BFs, and the results are shown in Table 2. Four historical earthquake ground motions and synthesized wind excitations are selected for the numerical study, for which the details are given in Tables 3 and 4. e response spectrum of ground motion acceleration and displacement is plotted for the selected earthquakes to demonstrate the nature of the responses obtained for the steel buildings, as shown in Figure 4. e wind hazard incorporated in the study is simulated from the NatHaz online simulator with gust speed as 30 m/s, 37 m/s, 43 m/s, and 50 m/s located in urban and suburban areas with numerous closely spaced obstructions (category-B) having cutoff frequencies obtained from the free vibration analysis of the building frames. e gust wind speeds are noted from the regions of interest where multiple hazard scenarios exist. Time history of the wind excitation for different gust speeds along with the corresponding fast Fourier transform (FFT) for the steel buildings is plotted in Figure 5.
e FFT spectrum refers to the frequency in the considered wind loads, essential in evaluating the nature of the structural         Table 5, which constitutes of the most prominent configurations of the buildings. e direction of loading, earthquake or wind, is applied in the direction of left to right of the shear frames, i.e., along the degree of freedom (DOF) considered at the lumped masses. e wind load is applied from 10 m above ground level at the center of mass of the structure, as shown in Figure 2(d). e direction of wind load has no contribution to the objective of the study, rather it is just a choice of analysis procedure. Finally, the buildings are connected by the FDs keeping 5 m separation gap distance, as recommended by most of the building bylaws across the world.

Effectiveness of FD for Dynamically Similar Connected
Buildings. Herein, the effectiveness of the FDs is investigated by comparing the responses of the unconnected (U) and connected (C) steel MRFs and BFs for different configurations of the passive FD under earthquake ground motions and wind forces. e responses are illustrated in terms of time history plots under the considered loading scenarios to demonstrate the effectiveness of the FDs. Moreover, peak responses are plotted to understand the variation in the responses for the considered connected buildings obtained under the dynamic loading scenarios.        Considering top floor displacement, the reduction in peak response for 5-5 MRF-MRF when connected using configuration A is obtained from ∼7% to 41%, whereas the reduction is, respectively, obtained from 6% to 29% and ∼3% to 11% for configurations B and C under the historical earthquakes. Furthermore, for the top floor acceleration, the response reductions for configurations A, B, and C are, respectively, obtained from ∼7% to 28%, ∼4% to 22%, and ∼1% to 7%. Similar observations are also noted for the 5-5 BF-BF. Hence, the FDs used in configuration A are able to dissipate the highest amount of induced input energy as compared to the other configuration of FDs. For the considered wind loads, 15-storey connected MRF is studied, and it is observed that the reduction in the peak top floor displacement is also the highest for configuration A (∼23% to 25%) as compared to configurations B (∼17% to 20%) and C (∼21% to 23%). However, the range of difference under the wind loads is quite small as compared to the range under the earthquakes. For the peak top floor acceleration, the highest response reduction is also obtained for configuration A (∼16% to 29%), whereas the least response reduction is observed under configuration B under both earthquake and wind loads.
Similarly, the displacement and acceleration responses for all the considered dynamically similar buildings with increased storey heights under earthquakes and winds are compared from Tables 6 and 7 as well as from Figures 8(a) and 8(b). Overall, under the earthquake excitations, the response reduction for top floor displacement and acceleration of the low-rise buildings is significantly higher as compared to high-rise buildings, which is observed to be contrary for the wind scenario that has increased response reduction for high-rise buildings. e characteristics of the obtained dynamic responses depend mainly on the modal properties of the structure and nature of the dynamic excitations. e displacement responses for the dynamically similar connected buildings under the earthquakes and winds increase with increase in building height. Moreover, the displacement responses obtained under the earthquakes increased significantly as compared to the responses obtained under the wind loadings. is implies that the energy content of the earthquake is comparably higher and has significant effect in determining the responses of the structure. On the other hand, the acceleration responses for the dynamically similar connected buildings under the earthquakes decrease with increase in building height. Conversely, the acceleration responses  obtained under the wind loadings increases with increase in building height, thus demonstrating the influence of acceleration as a design parameter for high-rise structures. erefore, installation of such passive device to minimize structural response under a particular hazard may not necessarily yield satisfactory performance under the other hazard, which becomes a possible example of a multihazard situation wherein careful selection of the design parameters for such structures is a necessity for modern constructions in the regions where such multihazard scenario prevails.

Effectiveness of FD for Dynamically Dissimilar Connected
Buildings.
e effectiveness of the FDs used to connect the adjacent steel buildings with dissimilar dynamic properties is likewise assessed from the displacement and acceleration responses obtained under the earthquake ground motion and gusty wind excitations. e dissimilarity in their dynamic properties is judged based on the difference in modal properties as well as storey heights of the adjacent steel buildings, such as 5-5 MRF-BF and 5-10 MRF-MRF. Figures 9(a) and 9(b) and Tables 8 and 9 show the peak displacement and acceleration responses of the dynamically dissimilar connected buildings with equal storey height under earthquakes and winds. e peak displacement reduction for the dynamically dissimilar connected buildings with equal storey height is again observed to be the highest for configuration A; however, the range of the difference is significantly large as compared to the dynamically similar buildings of equal storey height.

12
Shock and Vibration Considering 5-5 MRF-BF and 5-5 BF-MRF, the displacement response reduction in the first building, i.e., MRF in first case and BF in second case, is observed in the range of ∼19% to 80% and ∼8% to 40%, respectively. Similarly, for the connected 20-20 MRF-BF and 20-20 BF-MRF, the range of displacement response reduction is also observed to be more for the first MRF building, although the difference in range is relatively lesser as compared to the 5-storey case. is indicates that the BF itself dissipates the earthquake-induced energy even before transferring to the FDs. Under the wind loads, the reduction for the higher number of storey is similarly more as compared to the lower number of storey; however, the range of response reduction is rather negligible.
is indicates that the wind force has negligible impact on low-rise building in case of the MRF, and for high-rise BF, the bracings resist the dynamic wind loads, thereby transferring lesser energy to the FDs. Similar observation is made for the peak top floor acceleration responses under both earthquake and wind loadings. erefore, for the dynamically dissimilar connected buildings with equal storey height,  configuration A serves as an excellent choice for the dynamic response reduction; on the other hand, configuration C is relatively inefficient to reduce the response significantly for dynamically dissimilar connected buildings.
Similarly, the responses for the adjacent steel buildings with dissimilar dynamic properties for unequal storey heights are also quantified under the considered ground motion and gusty wind excitations. Tables 10 and 11 show the peak responses of the first building for the dissimilar connected buildings under the earthquakes and winds, respectively. Figures 10(a) and 10(b) also, respectively, illustrate the displacement and acceleration responses for the adjacent connected MRF and BF steel buildings with unequal storey height under earthquakes and winds. It is observed that the response reduction for the low-rise building (say, 5 storeys) by the FDs is significantly high under the earthquakes as compared to the winds. For the same configuration, the response reduction obtained for the high-rise building (say, 20 storeys) under the winds is substantially higher than the earthquakes as observed from the difference in the responses from the plots. From the response reductions obtained, configuration A again provides with the most effective option to mitigate the dynamic responses under the earthquakes and winds, whereas the configuration C is apparently the least effective option.        Table 12 shows the effectiveness of the FDs in terms of average response reduction for the different configurations of the connected dynamically similar and dissimilar steel buildings. Based on the effectiveness achieved, it can be stated that configuration A is best suited to minimize the desired responses under the earthquakes and winds. On the other hand, the least effectiveness is achieved for configuration B for dynamically similar connected buildings and configuration C for dynamically dissimilar connected buildings. Moreover, for limited cases, with increasing the number of storeys, the effectiveness of the dampers increases for high-rise buildings under the wind loadings, becoming almost similar to response reductions under the earthquake loadings. Although the FDs are able to reduce the responses under the earthquakes for higher storeys, the effectiveness of the passive devices is restrained when used in higher stories, demonstrating a need for the multihazard analysis and design under earthquake and wind during design life of the structures. To our belief, there are several structures influenced by the effects of earthquakes and winds, and such structures are required be assessed considering the multihazard effects during their design (service) life. Hence, it can be concluded that the passive FDs are more effective for lowrise buildings under the effect of seismic ground motions, whereas the same control devices show their effectiveness for high-rise buildings under the effect of gusty wind speeds.
As observed from the data, the maximum top floor displacement under the earthquakes for the unconnected MRFs of 5, 10, 15, and 20 storeys are, respectively, obtained as 11.49 cm to 26  unconnected situation. Now, when this 20-storey building is connected by the passive response control devices, FDs, the separation gap distance reduces to minimum ∼1.52 m considering the worst case out-of-phase movement at unconnected floors. Hence, there is an opportunity to reduce the separation gap distance by ∼30%, thereby constructing buildings at a close vicinity, which would eventually minimize, if not eliminate, structural pounding as well as utilizing the premium space for effective construction.

Conclusions
e performance of dynamically similar and dissimilar adjacent steel buildings connected with friction dampers (FDs) is assessed under a set of historical earthquake and simulated wind loadings. e displacement and acceleration responses are compared in order to establish effectiveness of the FDs under the multihazard uncorrelated scenarios of earthquakes and winds. e FDs are capable to reduce the displacement and acceleration responses substantially; however, different configurations are effective under the two hazards for varying building types. is is a concern where the FDs designed for earthquake loading consideration may not necessarily perform better under wind loading. Hence, further investigations are deemed necessary on multihazard analysis and design of the passive response control devices. Nonetheless, from the study conducted herein, the major conclusions drawn are as follows: (1) e displacement response increases with increase in building height, whereas the acceleration response under the earthquakes decreases with increase in building height for the connected buildings under the seismic ground motions. On the other hand, the dynamic response obtained under the wind loadings generally increases with increase in height of the buildings. (2) e FDs are more effective in reducing the responses of connected dynamically dissimilar adjacent buildings as compared to the dynamically similar buildings, which is evident from the extent of dynamic response reduction achieved. Moreover, the effectiveness of the FDs has decreased under the earthquakes on increasing the number of stories, whereas their effectiveness substantially increased under the wind loading scenarios. (3) For the dynamically similar and dissimilar connected buildings, configuration A, with cross-bracing at all floor levels, is most effective in minimizing the responses under seismic and wind excitations, whereas configuration B and C are least effective, respectively, for the dynamically similar and dissimilar connected buildings. (4) e structures designed to resist the seismic forces in their design (service) life might become vulnerable against the wind loadings. Such structures are required to be assessed and designed carefully to mitigate the responses against the multihazard effects of earthquakes and winds.

Data Availability
All data used to support the findings of the study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.