JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING https://doi.org/10.1080/13467581.2023.2182645 BUILDING STRUCTURES AND MATERIALS Damage indices of steel moment-resisting frames equipped with fluid viscous dampers Mohammed Samier Sebaq, Yi Xiao and Ge Song State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China ABSTRACT ARTICLE HISTORY Received 08 December 2022 Deformations, accelerations, shear forces, and energy demands are normally utilized to eval- Accepted 16 February 2023 uate the performance of steel frames equipped with fluid viscous dampers (FVDs). This study aims to quantify damage indices (DI) and their distributions along the structural height for steel KEYWORDS frames (3, 6, 9, and 20 stories) equipped with FVDs. The damage model incorporating both Fluid viscous damper; deformation and hysteretic plastic energy is adopted to quantify damage developed in damage index; supplemental structures. A set of 20 pairs of ground motions is used to perform nonlinear time history damping ratio; velocity analyses. Influences of structural property and FVD features (supplementary damping ratio � power add and velocity power α) on DI are investigated. The results show that FVDs with lower α would reduce DI. However, nonlinear FVDs lead to higher DI compared to linear ones when � >30%, add particularly for 9- and 20-story structures. Nonlinear FVDs (α< 1) are more effective than linear ones in reducing DI during low-intensity earthquakes. The results further demonstrate that the distribution of DI along the structural height is mostly determined by structural properties, FVD characteristics, ground motion intensity, and the type of damage model used. 1. Introduction represents the viscous material; and sgn is the signum function related to x. If α = 1, FVDs present linear Steel structures may be subject to a major collapse behaviours, while nonlinear responses would develop under strong earthquake events due to large drift in FVDs if α < 1. For seismic protection of structural between stories and plastic distortions in the main systems, α is designed to be in the range between 0.3 structural components (Clifton et al. 2011). The and 1.0 (Christopoulos and Filiatrault 2006; Impollonia damage cases in social and economic losses, are not and Palmeri 2018). A nonlinear FVD would have a force acceptable to new societies that aim to achieve high that is more than 35% less than a linear one (Martinez- levels of performance to resist future earthquakes Rodrigo and Romero 2003), although the strong non- (Christopoulos and Filiatrault 2006). Therefore, a new linear FVDs (smaller α) may lead to higher damper earthquake mitigation procedure has been proposed forces than linear ones (Tubaldi et al. 2015; Scozzese by introducing passive control devices to improve et al. 2021). Several studies have been carried out to energy–dissipation capacities and reduce the struc- explore the influence of FVDs on seismic demands for tural deformation of the systems. Fluid viscous dam- various building types (Akcelyan et al. 2016; Wang pers (FVDs) have been thoroughly investigated as one 2017; Kitayama and Constantinou 2018; Chalarca of the most often utilised damping system devices due et al. 2020). Pavlou et al. 2017, Kitayama et al. 2018 to its primary benefits, comprising of significant and Chalarca et al. 2020 executed dynamic analysis energy-dissipation capacities and peak forces that are investigations of buildings with linear and nonlinear out of a phase of the original systems (Constantinou FVDs and computed peak absolute accelerations. and Symans 1993; Seleemah and Constantinou 1997; Significant reduction in absolute accelerations were Soong and Dargush 1997; Christopoulos and Filiatrault found in buildings equipped with FVDs. Results 2006). FVDs are the most effective technique for redu- showed that an increase in peak accelerations at cing deformations and beam plastic rotations (Chen some floors for buildings equipped with nonlinear et al. 2010). The generated force-velocity relationship FVDs, while less inter-story drifts are found in building of FVD can be presented as follows: equipped with nonlinear FVDs (Tubaldi et al. 2015; Dall’Asta et al. 2016). In addition, the FVDs lead to f ðx _; tÞ ¼ C sgn ðx _Þ jx _j (1) a decreased probability of collapse of the structure where x _ is the differential velocity at the ends of the (Miyamoto et al. 2010; Karavasilis 2016; Dall’Asta et al. damper; C is the coefficient that characterizes the size 2017); although the FVDs with (α = 0.3 and 0.15) tend of FVD; α is the FVD power between 0.1 to 2.0 that to increase the collapse compared with linear ones CONTACT Ge Song email@example.com State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 M. S. SEBAQ ET AL. (α = 1) particularly during high-intensity levels of earth- 1.1. Structural damage index background quakes (Tubaldi et al. 2015). Damage indices can be used to evaluate the probable On the other side, some of studies have been damage caused by earthquakes, and thus can be uti- focused on determining the energy demands of lized to evaluate the seismic sensitivity of existing buildings equipped with FVDs. Constantinou and structures and the design of new earthquake- Symans 1993; Seleemah and Constantinou 1997; resistant structures (Rodriguez 2015). Damage to struc- Soong and Dargush 1997; Christopoulos and tures is determined by a variety of factors, including Filiatrault (2006) introduced an energy-based con- the relationship between the load-deformation beha- cept to supplemental damping devices, including viour of the structure, the amount of inelastic deforma- FVDs, and validated their findings against extensive tion, and the characteristics of earthquake motions, evaluations of buildings with and without dampers. etc., (Samanta et al. 2012). There is a varied scope of Their results demonstrated that a significant reduc- damage indices that have been presented, which can tion of the energy dissipated by the original struc- be assembled into three types: (Akcelyan et al. 2016) tural system in exchange for energy dissipation by maximum response (force or displacement) (Hancock the dampers. Recently studies Sorace and Terenzi and Bommer 2007; Barbosa et al. 2016); (Akiyama 2008, Domenico and Ricciardi 2019, Domenico et al. 1985) energy dissipated by structure represented by 2019, Domenico and Hajirasouliha 2021 focused on plastic energy demand E (Akiyama 1985; Powell and energy-based optimization design. While Zhou and Allahabadi 1988; McCabe and Hall 1989; Uang and Sebaq et al. 2022 provided a design-based seismic Bertero 1990); and (ASCE 2016) combination damage level evaluation of energy dissipation demands and (Akcelyan et al. 2016; Akiyama 1985) (Park and Ang their distributions for buildings with/without FVDs 1985; Mehanny and Deierlein 2000; Malaga- and found that nonlinear FVDs are more effective in Chuquitaype and Elghazouli 2012). The maximum reducing energy demands compared with linear inelastic deformation (displacement of force) alone ones. may not be a suitable indicator for computing DI for In previous studies, the primary motivation for eval- the seismic performance (Mehanny and Deierlein 2000; uating these systems was to determine seismic Barbosa et al. 2016). In the third group, the DI is demands only as deformations, accelerations, and a combination of displacement and E (Park and Ang story shears, or determine energy demands only. 1985; Kunnath et al. 1991; Reinhorn and Valles 2009). However, when incorporating innovative control sys- The most recent reviews of current damage indices for tems, present analysis and design methodologies must structural damage evaluation were conducted by be reconsidered. Damage indices as structural as (Williams and Sexsmith 1995; Ghobarah et al. 1999; a damage evaluation appear to be more effective, as Mehanny and Deierlein 2000; Bozorgnia and Bertero a result that they are the only models that incorporate 2003). deformation and hysteretic plastic energy at the same The most common models used for computing time. The damage model also accounts for damage damage indices including inelastic deformation (dis- caused by maximum inelastic excursions, as well as placement) and energy dissipation represented by E damage caused by the history of deformations. are: (Akcelyan et al. 2016) Park & Ang model ðDI Þ, P&A Nevertheless, none of previous studies have focused (Akiyama 1985) Reinhorn and Valles (DI ). The inter- R&V on the potential damages in structures equipped with story deformation or top story displacement, as well as FVDs based on damage indices. Therefore, this work the story yield shear force or base shear yield force provides an assessment of the damage potential for (3- level, are necessary for the story and overall DI , 6-, 9-, and 20-story) steel buildings with/without FVDs (Reinhorn and Valles 2009). under two intensity levels. To this aspect, the new The DI for each story is: P&A features of this study includes: (Akcelyan et al. 2016) δ E the effect of structural properties and FVD character- m P DI ¼ þ β (2) P&A istics, namely velocity power (α) and supplemental δ δ F u u y damping ratio (� ) on the overall structural damage add And the DI for each story is: R&V and distributions along the building height; (Akiyama δ δ 1985) the difference between two damage models 1 m y DI ¼ (4) R&V proposed by Park and Ang 1985 and Reinhorn and δ δ u y 4 δ δ F ð u yÞ y Valles 2009; (ASCE 2016) showing the effect of ground motion intensity on the computation of damage index; where δ and E are the maximum story deformation m P and (Barbosa, Ribeiro, and Neves 2016) determination and cumulative dissipated hysteretic plastic energy, of the type of failure based on the distribution of respectively, obtained from NTHA subjected to ground damage indices over the building height. Finally, motions; δ , δ and F are the ultimate story deforma- u y y results can provide guidance for potential retrofit solu- tion, yield story deformation, and yield story force tions towards buildings equipped with FVDs. capacity, respectively, for the original building JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 3 Table 1. Classification of damage state for structures (Park and consequences (Barroso and Winterstein 2002; Ang 1987). Occhiuzzi 2009). For evaluation of the damage indices; Damage degree Damage index, DI State DI and DI based on Eq. (2, and ASCE 2016) are P&A R&V Collapse [1, + ∞) Total collapse/failure used in this study to show the difference between Severe [0.4, 1) Beyond repair them for UNCLT and CLT buildings. NSPA is utilized Moderate [0.2, 0.4) Repairable Minor/slight [0, 0.2) No visible damage to capture structural responses of original buildings (i.e., yield displacement capacity, ultimate displace- ment capacity, and yield force capacity). NTHA is car- (without FVDs) obtained from NSPA. β is a model con- ried out at two intensity levels and structural demands stant parameter. To estimate β, test data from 402 such as peak story deformations and hysteretic plastic reinforced concrete rectangular cross-section compo- energy demands are traced to evaluate DI. PERFORM- nents and 132 steel H-shaped section samples tested 3D Platform is used to model the four buildings. in the United States and Japan were used, yielding Figure 1 shows the steps of determining story a value of β=0.05 for reinforced concrete structures damages and overall building damage indices. and β =0.025 for steel structures (Park and Ang 1987). Table 1 shows the level of damage found in the struc- tures, as well as the calibration of damage indices 2. Buildings modeling performed by Park and Ang 1987. The following are the overall DI, which are calcu- 2.1. Steel buildings frame structures lated using factors (λ ) based on the E at each story: i P The four case studies comprise a (3-, 6-, 9-, and 20- DI ¼ ðλÞ ðDIÞ (4) story) buildings, designed in acquiescence with overall i i story story Uniform Building Code 1988 (UBC). These structures have been widely utilised as reference structures in ðE Þ ðλÞ ¼ (5) story numerous structural response control investigations ðE Þ (e.g., Gupta and Krawinkler 1999; Chalarca et al. ð Þ where E is the hysteretic plastic energy in the i-th 2020; Zhou et al. 2022). Figure 2 shows the main story, including beams and columns for the i-th story dimensions and information of the steel elements, recorded from NTHA. as well as the locations and distributions of the Other investigations have found a correlation FVDs, which was taken from the study of Zhou between structural damage and characteristics related et al. 2022. A 2-Dimensional (2D) model of the to the duration of strong ground motion. For example, four buildings was generated in the PERFORM-3D Kunnath and Chai 2004, and Iervolino et al. 2001 found software using fiber sections for columns that ground motion duration had no effect on maximal (Neuenhofer and Filippou 1998), and plastic hinge inelastic deformations. Large spectrum amplitudes of models for beams based on the recommendations ground motion are more destructive than small ampli- of (PEER2010/ATC-72; Ribeiro et al. 2017; PEER tudes of ground motion (Hancock and Bommer 2007). 2020). The details of modeling these buildings in Ground motion length is well correlated with damage PERFORM-3D are described in Zhou et al. 2022. The indices based on plastic energy dissipation (Samanta frame buildings include P-delta to consider the et al. 2012; Hou and Qu 2015). Barbosa et al. 2016 and gravity load effect of interior frames using leaning Belejo et al. 2017 and found that DI is always R&V columns as shown in Figure 2. The strength and greater than DI . P&A deformation of panel zones were neglected. In con- structing the finite element computer models, the columns were assumed to be fixed at the base level. 1.2. Study objectives The FVDs in the four studied buildings are typically The goal of this research is to improve understanding simulated using Maxwell model, which it includes the of the damage assessment considering four steel- spring element and damping coefficient. For each FVD moment resisting buildings (3-, 6-, 9-, and 20-story) model, the spring element comprises some elements, without FVDs (uncontrolled-buildings, UNCLT) and such as gusset plates, clevises, brackets. In this study, those equipped with linear and nonlinear FVDs (con- the axial stiffness was taken as 150kN=mm in the four trolled-buildings, CLT) subjected to 40 records of buildings based on the recommendations by (Akcelyan ground motions. The main parametric variables are et al. 2016; Wang 2017; Chalarca 2020). The damping four-components of supplemental damping ratio � coefficient is a function of velocity power (α), and add ( ¼ 5%; 10%; 20%and30%) and four-components of supplemental damping ratio (� ). For the first mode add velocity power α ( ¼ 1; 0:7; 0:5and0:3). It is worth and not for the higher modes, Christopoulos and noting that � >30% is typically not recommended Filiatrault 2006 proposed equations for predicting the add since it may cause changes in the inherent dynamic equivalent linear and nonlinear damping coefficients aspects of the structure, with potentially negative based on equivalent lateral stiffness method as follows: 4 M. S. SEBAQ ET AL. Figure 1. Flowchart for the determination of the story damage indices and overall building damage. distribution (Christopoulos and Filiatrault 2006). Although 2� k δ add i i C ¼ (6) L;j N 2 these procedures may be carried out with little comput- ω N δ cos θ n d i ing effort and without the use of complex software, it may pffiffiffi not be optimum from an economical point of view. In the π Gammað1:5þ 0:5αÞ 1 α C ¼ C ðω x Þ (7) context of optimization control methods, the optimum NL;j L n o 2 Gammað1þ 0:5αÞ distribution of dampers in the building may be cast where, C and C are the linear and nonlinear damp- (Takewaki 1997). Recently several new energy-based dis- L; j NL; j ing coefficients at each story, respectively. k and δ is the tribution procedures have been developed to maximize i i inter-story drift and elastic lateral stiffness at the ith story, the energy dissipative capacities of the dampers, which respectively; which can be obtained by a pushover ana- provide valuable tools for future design of FVD-controlled lysis of the elastic structures, based on the fundamental structures (Domenico and Ricciardi 2019; Domenico et al. first mode. α is the velocity power of FVD; ω is the natural 2019). But their analyses applied to a simplified elastic vibration frequency which can be taken as the fundamen- system without taking into account inelastic deformation tal frequency of the building; θ is the declination angle of of the original structural system, P-Delta effect, and higher FVD at each story; N is the number of stories; and N is modes effect. As a result, it is impractical to validate this f d the total number of FVDs. x is the maximum deformation approach before applying it to an inelastic system. The of the linear FVDs obtained from the nonlinear time energy-dissipated by FVD mainly depends on the amount history analysis under maximum considered earthquake of inelastic deformation in the original structural system; (MCE) motions, because this is the requirement of ASCE and also, the type of deformation occurs in the structure 7–16. According to Section 126.96.36.199 of ASCE 7–16. For (Hwang et al. 2013). Although recently developed more information about the designing of FVDs can be approaches have evident advantages, they are not com- found in details in Christopoulos and Filiatrault 2006. monly used in engineering practice. Therefore, the Previous research on the determination of designing selected damping coefficient for linear and nonlinear and distribution of FVD over the building, can be grouped FVDs (C and C ) in this study were designed according L NL as standard techniques such as identical FVD constants at to the equivalent lateral stiffness (ELS) (Christopoulos and each story, proportional to story shear forces (Pekcan et al. Filiatrault 2006); which is commonly used in (Whittle et al. 1999), proportional to story shear strain energy (Hwang 2012; Guo and Christopoulos 2013a; Martinez-Paneda et al. 2013), proportional to story shear strain energy to and Elghazouli 2021). Martinez-Panel and Elghazouli efficient stories (Hwang et al. 2013), stiffness-proportional 2021 found that ELS is the most effective solution for JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 5 Figure 2. Dimensions, member sizes, distribution of dampers, and leaning columns for all steel frame buildings: (a) 3-story; (b) 6-story; (c) 9-story; and (d) 20-story (Zhou et al. 2022). the distribution of FVDs. In this study, the required C and shows the story drift ratios, peak shear forces, and peak C for four levels of � (=5, 10, 20, and 30%) correspond- absolute accelerations over the building height of the NL add ing to four levels of α (= 0.7, 0.5, and 0.3) for the 3-, 6-, 9-, test structure with nonlinear FVDs (α=0.38), respectively, and 20-story buildings provided in Zhou et al. 2022 were under the 100% of the JR Takatori record from the 1995 used. Kobe earthquake between experimental data (Exp) finite element model (FE). From the figure, there is practically no difference between the Exp results and 2.2. Validation of the constructed model FE numerical models. This indicates that the constructed This validation is based on a five-story full-scale experi- FE by Perform 3D can capture of seismic demands and mental building equipped with nonlinear FVD obtained use as a useful tool for the numerical modelling of steel from shake table testing at Japan’s E-Defense facility. In moment-resisting frames Equipped with FVDs. X- and Y- loading directions, the test structure consisted of three two-bay steel moment-resisting frames. There 2.3. Ground motions selection was a total of 12 FVDs placed (four in the Y-loading direction and eight in the X-loading direction). Kasai Twenty-pairs of ground-motions were selected form et al. 2010; Akcelyan et al. 2016 provided considerable PEER 2015. Figure 4 depicts the spectrum for each details on the test structure, including material charac- ground motion, as well as the mean of the 40 response teristics, element sections, and FVD parameters. Figure 3 spectra and the ASCE 2016 target spectrum at two 6 M. S. SEBAQ ET AL. Figure 3. Structural responses of experimental test equipped with FVDs: (a–c) X-loading direction; (d–f) Y-loading direction. Figure 4. Individual response spectra for 40 ground motions and their mean response spectrum: (a) design-based earthquake level (DBE); (b) maximum considered earthquake (MCE). intensity levels: (Akcelyan et al. 2016) level of design- (Akiyama 1985) nonlinear static pushover analyses based earthquake (DBE); (Akiyama 1985) level of high- NSPA; (ASCE 2016) overall building (DI); and (Barbosa, est considered earthquake (MCE). Ribeiro, and Neves 2016) distribution of DI over the building height. 3. Analysis results 3.1. Modal analysis The NSPA is performed on the four UNCLT buildings; and the NTHA is performed on the four UNCLT and CLT Elastic Eigen-analyses were conducted to determine buildings induced to 20 pairs of motions (40-records). the vibration modes of the case-study buildings (3-, This section gives details on the computation of DI 6-, 9-, and 20-story). Vibration modes are useful to P&A and DI for (3-, 6-, 9- and 20-story) UNCLT and CLT understand the dynamic behaviour of the building R&V buildings; considering two levels: (Akcelyan et al. 2016) structures and to visually check that structural mem- DBE, and (Akiyama 1985) MCE. The main variables for bers are connected. The first 4 vibration modes in the computing DI are four-components of investigation were found using the Perform 3-D Eigen- � ð¼ 5%; 10%; 20%and30%Þ and four-components analysis (Table 2). The effective mass participation for add of αð¼ 1; 0:7; 0:5and0:3Þ. This section is divided into first mode is 93.89%, 88.87%, 82.39%, and 75.88% for 3- three portions: (Akcelyan et al. 2016) modal analysis; , 6-, 9-, and 20-story buildings, respectively. Therefore, JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 7 Table 2. Modal periods and effective mass participation for the case study buildings. Natural vibration period, T (sec) Effective mass participation, % Building Mode-1 Mode-2 Mode-3 Mode-4 Mode-1 Mode-2 Mode-3 Mode-4 3-story 0.84 0.41 0.16 - 93.89 5.32 0.21 - 6-story 1.52 0.49 0.27 0.17 88.87 8.35 2.02 0.62 9-story 1.92 0.72 0.42 0.28 82.39 10.98 3.92 1.38 20-story 3.78 1.406 0.82 0.56 75.88 13.49 4.58 2.29 for 3- story building, the fundamental mode is almost different studied buildings are shown in Figure 5, as the first mode, whereas for 6-, 9- and 20-story build- discussed in details in Zhou et al. 2022. The determina- ings, it is the first and second modes. tion of yielding force, yielding deformation, and ulti- mate deformation of each building is shown in Figure 5 based on FEMA P695, Section 6.3. Figure 6 3.2. Nonlinear static pushover analyses presents the force-deformation capacity for each story in the UNCLT buildings (3-, 6-, 9- and 20-story). It is Nonlinear static pushover analyses are performed in all noted that the top stories exhibited reverse unloading buildings (3-, 6-, 9-, and 20-story), assuming that the curves under the unidirectional NSP, which is probably lateral pattern load is based on the fundamental first due to the top stories of high-rise buildings (9- and 20- mode of vibration of each respective building. The story) are generally dominated by a combination of base shear versus roof drift angle response for the Figure 5. Pushover curves of steel frame UNCLT buildings based on different heights (3-, 6-, 9- and 20-story) (Zhou et al. 2022). Figure 6. Force-deformation capacity of each story for (3-, 6-, 9- and 20-story) UNCLT buildings. 8 M. S. SEBAQ ET AL. Figure 7. Three-story building: damage indices (DI and DI ) as a function of the � and α for two intensity levels: (a) DBE P&A R&V add and (b) MCE. shear and flexural deformations while the bottom stor- Presented in Figure 11, the ratios of two damage ies are mainly controlled only by shear deformations. indices, one associated with DI and the other asso- R&V The accompanying flexural deformation is caused by ciated with DI are computed for the both intensity P&A increasing axial column deformations. levels. For DBE level, the DI almost is higher than R&V DI by 32%, 10%, 34%, 60% in average for the four P&A UNCLT buildings, respectively. For MCE level, the DI R&V 3.3. Overall building damage index level almost increases the damage index correspond- ing to DI by 60%, 58%, 51%, 31%, and 20% in This section shows the overall building damage index P&A average for � ( ¼ 0; 5%; 10%; 20%and30%), for UNCLT and CLT buildings based on DI and DI . add P&A R&V respectively for (3-, 6-, 9-story) buildings. While, for Figure (7–10) show the average DI and DI for P&A R&V the 20-story building, the corresponding increase is various � ( ¼ 0; 5%; 10%; 20%and30%) and α add almost 31%, 26%, 41%, 56% and 71% in average for ( ¼ 1; 0:7; 0:5and0:3) for the four studied buildings, � ( ¼ 0; 5%; 10%; 20%and30%), respectively. respectively, at two levels of earthquakes. For DBE add The results show that increasing � reduces level, a comparison of results shown in Figures 7a add DI and DI for the four buildings and for two and Figure 10b indicates that DI and DI have P&A R&V P&A R&V intensity levels (Figure 7a and Figure 10b. Excepting the same damage index in all four buildings except 9-, and 20-story buildings, the effect of � > 20% is UNCLT buildings, the DI is higher than DI , this is add R&V P&A less significant (Figures (Chen, Li, and Cheang 2010; attributed to larger E demand. On the other hand, for Christopoulos and Filiatrault 2006)). It is worth men- the MCE level as shown in Figure 7b and Figure 10b, tioning that the � has a significant effect on the the DI leads to higher-damage indices, thus result- add R&V computation of the DI and DI , this is due to ing in more damage than DI ; and the difference P&A R&V P&A the � leads to decrease of structural responses between them decreases with increasing � . It is add add such as inelastic deformation and E demand. noted that the difference between DI and DI P P&A R&V (Figure 7, Figure 8, Figure 9, Figure 10) show also damage indices associated with 3-, and 6-story build- the significant effect of α on both overall DI and ings are consistently larger than the ones associated P&A DI with varying � for CLT buildings (3, 6, 9, with 9-, and 20-story buildings. Furthermore, the R&V add and 20-story). Presented in Figure 12, the ratios of damage index DI is always larger than DI , indi- R&V P&A DI and DI of two systems, one with nonlinear cating that the building response is highly sensitive to P&A R&V FVD (α) and the other with linear FVD (α = 1) for (3-, E demand. This is due to Eq. 3 defined by Reinhorn 6-, 9-, 20- story) buildings and for both (DBE and and Valles considers a large amount of E to compute MCE). The impact of α is more noteworthy on the DI unlike Eq. 2 provided by Park and Ang. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 9 decrease of DI and DI . For 3-and 6-story build- Figures 12(c and d) indicates that the structures P&A R&V ing, the nonlinear FVDs are more effective in redu- integrating FVDs (α ¼ 0:7; 0:5and0:3) experience cing DI than linear ones for both intensity levels lower DI and DI than those of the structures P&A R&V (DBE and MCE) for different values of � integrating FVDs (α ¼ 1) for 9-, and 20-story build- add ( ¼ 5%; 10%; 20%and30%) Figure 12(a and b). ings. Except for lower (α≤0:5) and higher Figure 8. Six-story building: damage indices (DI and DI ) as a function of the � and α for two intensity levels: (a) DBE and P&A R&V add (b) MCE. Figure 9. Nine-story building: damage indices (DI and DI ) as a function of the � and α for two intensity levels: (a) DBE and P&A R&V add (b) MCE. 10 M. S. SEBAQ ET AL. Figure 10. Twenty-story building: damage indices (DI and DI ) as a function of the � and α for two intensity levels: (a) DBE P&A R&V add and (b) MCE. Figure 11. Ratios of DI to DI for (3-, 6-, 9-, and 20-story) buildings with various � and α for two intensity levels (DBE and R&V P&A add MCE). (� ¼ 20%and30%), the DI ratio almost is equiva- the Appendix, the hysteretic behaviour of nonlinear add lent or greater than linear FVD, especially 9-, and FVDs with lower levels of α induces damper forces 20-story buildings. It is also noted that the non- in the building over a larger range than the displa- linear FVDs are more effective in reducing damage cements of the dampers; which may collapse the indices compared with those linear FVDs especially building and increase the DI. This means that larger for DBE level and � ( ¼ 5%; 10%; and20%), FVD forces are created if the velocity demands add whereas at the MCE level, the decreasing of α is increase more than expected in the design because slightly effective in reducing damage indices for of earthquake ground motion has a large number of different levels of � ( ¼ 5%; 10%; 20%and30%). random amplitudes. In accordance with the capa- add Many nonlinear physical phenomena play a role city-design concept, this may result in a more in explaining the somewhat illogical numerical underestimating design for non-dissipative compo- results obtained for structural damage (DI). The nents. It is highlighted that the use of a higher level strong nonlinear FVD with α ≤0.5 is not effective of � >20% is not effective 9-, and 20-story build- add in reducing DI especially for (9- and 20-story) build- ings; this is due to two reasons: (Akcelyan et al. ings, and for high intensity level (MCE). As shown in 2016) the flexural deformation is as substantial as JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 11 Figure 12. Ratios of ðDIÞ to ðDIÞ for different � , intensity levels and damage indices DI and DI : (a) 3-story building, add P&A R&V ðαÞ ðα¼1Þ (b) 6-story building, (c) 9-story building, and (d) 20-story building. the building’s shear deformation because of increas- 3.4. Distribution of damage indices ing the P-delta effect, the FVD deformation and The second section purposes at exploring the influ - velocity are predominant to shear deformation ence of properties of structural system and FVD on than flexural. Therefore, the peak FVD displacement the distributions of DI and DI over the build- P&A R&V may be reduced, and hence the energy dissipated ing height. The values of DI and DI damage by FVD can be reduced; (Akiyama 1985) the P&A R&V indices distribution over the height of the building increase of participation of the high modes effect. 12 M. S. SEBAQ ET AL. is dependent on response demands such as peak � ( ¼ 0; 5%; 10%; 20%and30%) and α add story deformation and story plastic energy demand. ( ¼ 1; 0:7; 0:5and0:3) at two intensity levels (DBE Figure (13–16) show the DI and DI distribu- and MCE). Figure (13–16) show that the DI is P&A R&V R&V tion along the height of UNCLT and CLT buildings always higher than DI over the height of all P&A (3-, 6-, 9 and 20-story), respectively with varying four UNCLT and CLT buildings, this is attributed to Figure 13. Three-story building: damage indices distribution over the building height with varying � , α and intensity levels add (DBE and MCE): (a) DI damage index, and (b) DI damage index. P&A R&V JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 13 DI is more significant to E demand rather than For the 3-story building, the DI and DI pro- R&V P P&A R&V duce nearly uniform damage distribution for two DI as discussed in Section 3.1. The distribution of P&A intensity levels (DBE and MCE) with the exception of DI and DI damage indices over the height of P&A R&V CLT buildings equipped with nonlinear FVD the buildings is strongly controlled by the structure (α ¼ 0:7; 0:5and0:3). The damage concentrates in properties (building height), ground motion inten- th th the 1 story and decreased gradually for the 2 and th sity, FVD characteristics, and the type of damage 3 stories (Figure 13). In the 6-story building, and for DBE level, the DI and DI damage indices are model used. P&A R&V Figure 14. Six-story building: damage indices distribution over the building height with varying � , α and intensity levels (DBE add and MCE): (a) DI damage index, and (b) DI damage index. P&A R&V 14 M. S. SEBAQ ET AL. Figure 15. Nine-story building: damage indices distribution over the building height with varying � , α and intensity levels (DBE add and MCE): (a) DI damage index, and (b) DI damage index. P&A R&V observed to be almost uniformly distributed in all Hajirasouliha 2021)), which indicate that the P-delta floors for UNCLT and CLT buildings (Figure 14). For effects and higher modes effect to control the plastic MCE level, the DI is also uniformly distributed in deformation over the building height. P&A all floors (Figure 14a), while the DI leads to be uni- Figure (13–16) show the influence of FVD character- R&V form in the first four stories and decrease in the top istics (� and α) on the distribution of DI andDI add P&A R&V two stories (Figure 14b). For (9- and 20-story) buildings, damage indices over the building height. The results the distribution of DI and DI are nonuniformly indicate that both DI and DI decrease with P&A R&V P&A R&V distributed over the building (Figures (Dall’Asta, increasing � along the building height, except for add Tubaldi, and Ragni 2016; De Domenico and (9- and 20-story) buildings, � > 20% is less add JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 15 Figure 16. Twenty-story building: damage indices distribution over the building height with varying � , α and intensity levels add (DBE and MCE): (a) DI damage index, and (b) DI damage index. P&A R&V significant. For 3-story building, increasing � leads a substantial coupling effect of structural and FVD add to reduce the concentration DI in the first story for α<1 features. For 3-story building, the decrease of α always (Figure 13); while for 6-, 9-, and 20-story buildings, the leads to an increase of DI andDI in the first story P&A R&V effect � on the distribution of DI over the building and decrease in the top two stories, especially for MCE add height is not significant (Figures (Dall’Asta et al. 2017; level (Figure 13). For 6-story building, the decrease of α Dall’Asta, Tubaldi, and Ragni 2016; De Domenico and decreases DI andDI in the first four stories, but P&A R&V Hajirasouliha 2021)). The influence of α on the distribu- almost has no effect in the top two stories (Figure 14). tion of DI andDI damage indices vary among the For 9-story building, the decrease of α reduces P&A R&V (3-, 6-, 9-, and 20-story) structures, demonstrating DI andDI in the first six stories and is less P&A R&V 16 M. S. SEBAQ ET AL. significant in DI andDI in the top three stories (=0.5 and 0.3) and higher � (=20 and 30%), P&A R&V add (Figure 15). For 20-story building, the decrease of α they are equivalent to or greater than linear reduces DI andDI based on the amount of � FVDs, which is especially noticeable in 9- and 20- P&A R&V add (Figure 16). Finally, the distribution of DI depends on story buildings; and the number of stories (building height), story plastic (4) Nonlinear FVDs are more effective in reducing DI energy demand (E ), FVD characteristics (� and α), than linear FVDs, particularly at the DBE level and P add and type of damage index model (DI and DI ). and � ( ¼ 5%; 10%; and20%), although at the P&A R&V add From these Figures, at the DBE level, no collapse is MCE level, the decreasing of α is slightly effective in observed in UNCLT and CLT buildings (3-, 6-, 9- and 20- reducing DI at various levels of � add story) based on the DI and DI damage indices; ( ¼ 5%; 10%; 20%and30%). P&A R&V except for the UNCLT buildings (6-, 9- and 20-story) which collapse occurs at different floor levels based on The study further investigates the effects of ground DI damage index as shown in Figure 13b and Figure motion intensity, natural vibration period T , and R&V n 16b). At MCE level, the collapse is different based on FVD characteristics (� and α) on the distribution of add the DI and DI damage indices and the amount of DI and DI over the structure height: P&A R&V P&A R&V � (Figure 13, Figure 14, Figure 15, Figure 16)). For add lower floors collapse mechanisms, it experiences (1) It noticed that the structural properties, FVD higher shear deformation demands as shown in 3- characteristics, level of ground motion intensity, and 6-story buildings. For upper the floor, the collapse and the type of damage model all have mechanism could be due to two reasons: the first is a significant contribution on the distribution of related to the strong axial deformation of the columns DI along the height of the building; and the shorter frame dimensions; and the second is (2) The DI is always higher than DI over the R&V P&A owing to the considerable flexural frame deformation height of all four UNCLT and CLT buildings par- as shown in 9- and 20-story buildings. ticularly for MCE intensity level, this is probably due to DI is more significant to E demand R&V P rather than DI ; P&A 4. Conclusions (3) The 3-, and 6-story present a relatively uniform distribution of DI along the height of the build- The supplemental FVD devices improve the seismic ing, excepting CLT building (3- story) with non- performance of the case study buildings (3-, 6-, 9-, linear FVDs (α<1) and (� ¼ 5%and10%) leads and 20-story) by reducing their DI. The computation add th to concentrate damage in the 1 story. While, of DI is a function of three primary parameters: for 9-, and 20-story buildings, the distribution of (Akcelyan et al. 2016) four frame buildings (3-, 6-, 9- damage indices is almost nonuniform over the and 20 story); (Akiyama 1985) FVD characteristics (� add building height, which indicates that the contri- and α); and (ASCE 2016) level of earthquake intensity bution effects of the P-delta effects and higher (DBE and MCE). modes effect; and With overall building DI and DI , they are P&A R&V (4) For 3-story building, increasing � leads to strongly dependent on the ground motion intensity, add reduce the concentration DI in the first story natural vibration period T , and FVD characteristics for α<1; while for 6-, 9-, and 20-story buildings, (� and α). The main findings are: add the effect � on the distribution of DI over the add building height is not significant. (1) For DBE level, DI and DI damage indices P&A R&V (5) There are coupling effects among � and α values are identical in all four buildings except- add of FVDs on DI and DI along the build- ing UNCLT buildings, the DI is higher than R&V P&A R&V ing height. In most circumstances, the rise of DI . While, for MCE level, the DI tends to be P&A R&V � and the decrease in α usually reduces higher values of damage indices compared with add DI and DI damage indices, but for the DI for UNCLT and CLT buildings. This is P&A P&A R&V 9- and 20-story buildings with higher values because of the structural response is highly sen- of � , the effect of α reverses at some sitive to E ; P add stories. (2) The � plays an important role in reducing add (6) Higher values of DI in lower stories is associated damage indices (DI and DI ) for (3-, 6-, 9- P&A R&V with higher shear deformation, as shown in low- and 20-story) buildings. Excepting (9-, and 20- rise buildings (3- and 6-story). For relatively high- story) buildings, the � > 20% is less significant; add rise buildings (9- and 20-story), the distribution (3) In the CLT buildings with smaller velocity damage occurs in both the bottom and top stories, powers (i.e., α < 1), the damage indices (DI P&A which is associated with shear deformations in and DI ) tend to decrease significantly when R&V bottom stories and flexural deformations in top compared to systems equipped with linear FVDs stories. for all four studied buildings. Except for lower α JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 17 Disclosure statement Fluid Dampers.” Structural Design and Tall Buildings 2 (2): 93–132. doi:10.1002/tal.4320020203. No potential conflict of interest was reported by the author(s). Dall’Asta, A., F. Scozzese, L. Ragni, and E. 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Journal of Asian Architecture and Building Engineering
– Taylor & Francis
Published: Mar 12, 2023
Keywords: Fluid viscous damper; damage index; supplemental damping ratio; velocity power