OPTIMIZATION AND EFFECTIVENESS OF THE PLACEMENT OF ENERGY DISSIPATORS IN RC FRAME STRUCTURES

This document explores and analyzes the optimization of the use and placement of energy dissipators in the bays of frame structures located in seismic zones. This study may be applied to new and existing buildings. In order to do this, three RC frames of 5, 10 and 15 stories are analyzed and compared, using four brace arrangements ( Chevron braces San Andrés cross and diagonal braces (two cases)) . The behavior of these frames is analyzed in terms of modal parameters, capacity curves (Push-over) and dynamic analyses (Time-History). For the study, the Lorca record of mean magnitude was used, also in this case, hysteretic dissipators have been used as they are cheap and easy to install solutions. The efficiency of the energy dissipators is improved as the frames increase in height. In the lower height frames, the use of braced solutions without any device improves the structural behavior. The ductility of all frames increases with the placement of dissipators.


Introduction
A significant number of buildings across the world are highly vulnerable to strong earthquakes (Bonett 2003;Gueguen 2013;Clementi et al. 2016;Adhikari et al. 2019), mainly due to the lack of design requirements in previous design codes and, less intensely, to construction deficiencies and the high level of inherent uncertainty of earthquakes (Dominguez Santos et al. 2012;Fikri et al. 2019). Different constructive solutions are used to solve these problems.
Traditional techniques mainly consist of the design of stronger and more rigid structures (Foraboschi 2016). These solutions have proved effective in reducing damage after strong seismic events. However, there are important objections: (i) the cost is generally excessive, (ii) the architectural and functional impact is important, (iii) the ductility of the structure, due to the fact that in cases of strong excitations, the damage is concentrated on the main elements of the structures (walls, beams and columns) and, (iv) the high weight of the buildings that imply an increase in seismic forces. To address these limitations, two innovative approaches have been proposed: base isolator (Marano and Greco 2003;Yingli et al. 2007;Tena-Colunga et al. 2009;Liu et al. 2011;Bîtcă et al. 2015;Tena-Colunga 2015;Hadad et al. 2017) and energy dissipator (Restrepo and Rahman 2007;Segués 2014).
A base isolator consists of incorporating elements outside the structure that are highly flexible in the horizontal direction (commonly referred to as isolators) to the foundation of the building. In this way, the building becomes more flexible, significantly lengthening its fundamental period (Su et al. 1989;Marano and Greco 2003;Liu et al. 2011). This device decouples the building from the horizontal movement of the ground; therefore, the shear force on the design base is drastically reduced. On the other hand, since most of the stress is concentrated in the isolation layer, the incorporation of additional damping to the construction is highly feasible with this device, thus improving its structural performance. Base isolation has been thoroughly investigated and used in many countries of the world, particularly in Chile and Japan. Currently, there are isolated buildings with this system that have performed satisfactorily under strong earthquakes, confirming the effectiveness of this solution. However, seismic isolation still has some important limitations (Su et al. 1989;Marano and Greco 2003;Tena-Colunga and Pérez-Osornio 2006): (i) isolators must be able to withstand the weight of the building, (ii) this technology cannot be considered for high buildings, due to the weight that must be resisted and the long fundamental period of high-rise buildings, (iii) its use in soft soils, due to the effects of soil-structure interaction, (iv) the permanent displacements produced (which can be enormous in buildings near active faults), causing the design and dimensions of the isolators to be very large, and (v) the isolation is not effective against gusts of wind.
Furthermore, power sinks are another innovative strategy, which overcomes most of the limitations of base isolation. Energy dissipators (Mazza 2019;Nuzzo et al. 2019) are devices external to the main structural system, in that they do not participate in supporting the gravity load, they are only efficient against horizontal loads (wind, earthquake etc.) (Domínguez Santos et al. 2015). These devices are connected to the structure, so that they undergo significant deformations produced by movements between floors. Through these deformations, the heatsinks absorb energy, thus protecting the rest of the construction. They can be considered to be 'structural fuses' (i.e. the 'weakest links') of the building (López-Almansa and Oller 2014). Furthermore, these elements can be easily replaced after being damaged by strong earthquakes. Fig. 1 shows the location of the energy dissipators for seismic protection of the building structures, connected to the main structure of the building using additional bracing systems ( Fig. 1(a) to 1(c)). Due to the different locations of these devices in the frames using rigid steel elements connected to the main structure, this study performs a comparative analysis between the solutions mostly used in construction with and without dissipators, in order to determine the efficiency and seismic effectiveness of each proposed solution. The solutions selected for this study will depend on the type of brace used: (i) Chevron braces ('V' inverted), (ii) San Andrés cross (double diagonal), and (iii) single diagonal.

Fig. 1 Braced solutions considered, with and without power dissipators
Given the great diversity of dissipators on the market (hysteretic (Mazza 2019;Nuzzo et al. 2019), frictional, viscoelastic materials, viscous fluids, superelastic (shape memory alloys) among others), it was decided to use hysteresis devices based on yielding metal. It is a simple, easy, quick to install technological system (it only requires reinforcing elements such as the braces outside the main structure) which is economic, since it does not require excessive maintenance. Due to these characteristics, these devices could be used in a massive and feasible way in seismically active countries, due to their low construction costs. Due to the independence that these devices have from the main structure of the building, this technology is considered to be very versatile due to the ease of installation, whether in new construction or renovation. Across the world, several buildings have been equipped with this class of device, experiencing strong seismic demands and performing satisfactorily; for example, the Titanium Building (La Portada) in Santiago, Chile, behaved properly under the Maule earthquake of 8.8 degrees in 2010. In Chile, due to its great seismicity, there have been previous investigations on the use of energy dissipators (Bin 1995;Ou and Wu 2001;Tena-Colunga and Hernández-Ramírez 2020).

General considerations
In this study, three RC (Masi 2003) frames (of 5, 10 and 15 floors) were selected, in order to represent a significant number of vulnerable buildings around the world. The primary structural elements of the frames (beams and columns) analyzed in this study were designed and dimensioned following the European regulations for structural concrete, EC-2 (2004), and earthquake-resistance, EC-8 (2005), in addition to the Spanish Concrete Regulations, EHE-08 (2008), and earthquakeresistance, NCSE-02 (2002). The design of these frames was complemented by some aspects of the American regulations for structural concrete, ACI 318 (2008).
These frames were analyzed for a medium-hard soil type (soil type C), located in a moderate seismic zone, whose acceleration is ag = 0.12g, corresponding to the location of the seismic record used in the dynamic analyses.

Dimensions of columns and beams
As discussed in Section 1, the objective of this work was to compare the seismic resistance behavior of the primary structural elements (beams and columns) using hysteretic energy dissipators (based on the plasticization of metals) and using different braced arrangements in the placement of these devices. Furthermore, the results were compared with the same structural solution, but without taking into account the arrangement of dissipators. For this, a 4-bays portal frame was used, using 4 different brace arrangements at the external bays: 1. Frame structure 'braced' in the extreme bays, with inverted 'V' reinforcement or Chevron Braces (Fig. 3a). The nomenclature used for this solution is CHB. 2. Frame structure 'braced' in the extreme bays, with reinforcement of two diagonals 'San Andrés Cross' (Fig. 3b). The nomenclature used for this solution is SAB. 3. Frame structure 'braced' at the extreme bays, with a diagonal reinforcement, placed with the same arrangement (Fig.  3c). The nomenclature used for this solution is EDB. 4. Frame structure 'braced' at the extreme bays, with a diagonal reinforcement, placed with a symmetrical arrangement (Fig. 3d). The nomenclature used for this solution is SDB.
In all cases, the main elements of the structure (columns and beams) were designed using the structural dimensions detailed in Table 1, i.e. without taking into account the strength of the devices used. With this criterion, a comparative structural study was carried out for the four proposed solutions. For this, non-linear static calculations were made (Push-Over) (Elnashai 2001;Chopra and Goel 2004) and the ductility, maximum base shear and maximum displacements of the highest floor of the proposed structures were compared, establishing the structural damage of the frames. The RISK-UE method (Barbat et al. 2016) was used to determine the damage index of the structures for the different levels of structural performance: Immediate Occupation (IO), Life Safety (LS) and Collapse Prevention (CP), as established in FEMA 356 (2000). These analyses were complemented by dynamic analyses (Time-History) (Wilson et al. 1972;Vamvatsikos and Cornell 2002), using the Lorca seismic register (Martínez-Díaz et al. 2011;Oterino et al. 2012;Giner-Robles et al. 2012) (Spain) in the NS direction that occurred in 2010. The purpose of these analyses was to compare the damage produced by the maximum structural displacements in the last floors of the frames and the absolute accelerations.

Description and design of traditional frames
The RC frame analyzed was composed of 4 bays, 5 meters long, with a regular elevation and section configuration. The design of these corresponded to the design criteria of the vast majority of the seismic resistance standards: uniform and regular shapes without overhangs throughout their entire height; the first floor was 4 m high and the remaining floors 3 m high. Therefore, the total heights of the 5, 10 and 15-story structures were 16, 31 and 46 m, respectively.
Each frame comprised 5 columns joined together by high beams (bw <hw). The columns had a square section that varied between 30 cm x 30 cm and 70 cm x 70 cm, increasing their section on the lowest floors for each of the frames, as detailed in Table 1. The dimensions of all the beams were bw = 30 x hw = 40 cm, adding the effective width portion of the slab specified in article 8.4.1.8 of the ACI Standard 318 ( Fig. 2) (2008); 28 cm long (hb), 12 cm thick (hf) in the external beam of the frame (hb <4hf) and 28 cm thick on each side of the internal beams of the frame (bw + 2hb <bw + 8hf), thus favoring the 'diaphragm effect' that must occur in the structural behavior of buildings.

Fig. 2 Effective widths of the beams (ACI 318)
Regarding the braced frames, HSS (hollow square section) profiles of grade A36 steel were used in ASTM (1958). The sections were of dimensions 100 mm x 3 mm, 160 mm x 10 mm and 200 mm x 12 mm, for the 5, 10 and 15-story buildings, respectively. The brace positions are shown in Fig. 3.

Materials
Following the criteria of the European and American Regulations, the use that the analyzed frames had is residential, administrative or equivalent, corresponding to a use overhead of L = 2 kN/m 2 . The characteristic value of the compressive strength of the concrete was fc '= 30 MPa and the yield strength of the reinforcing steel was fyk = 500 MPa. Grade A36 steel was used to make the braces.

Structural modeling
The static and dynamic behavior of the prototype frames were simulated with the SeismoStruct software package (2020). The modeling of these buildings was done with finite bar elements, implementing the formulations developed by Bathe and Wilson (1976), Spacone et al. (1996) and Neuenhofer and Filippou (1997). The cross sections of each structural element (columns and beams) and the characteristics of the construction materials were specified following the models proposed by Bento et al. (2008).
Given the symmetry and regularity of the analyzed frames, their structural behavior could be represented by flat models. The columns and beams were represented by nonlinear finite element bars (Bathe and Wilson 1976;Spacone et al. 1996;Neuenhofer and Filippou 1997); the nonlinearities were concentrated in the plastic hinge joints (Inel and Ozmen 2006;Scott and Fenves 2006;Bae and Bayrak 2008) located at the ends of each bar, equivalent to 15% of the total length of each element according to previous research (Inel and Ozmen 2006;Scott and Fenves 2006;Bae and Bayrak 2008) and the joints between the columns and the beams were considered to be rigid. The hysteretic behavior of each bar was taken into account, in terms of the dimensions, the shapes of the structural sections, the existing reinforcement and the characteristics and properties of the materials. The accuracy of the structural behavior of each element depended on the number of fibers in which they were divided. For this study, the discretization used for each section was 300 fibers.
Due to cracking of the tensioned concrete, the initial stiffness of structural members was reduced, based on gross sectional parameters, but the concrete modulus of elasticity was reduced as indicated in EHE-08 (2008) and EC-8 (2005). The sectional behavior was based on the average properties of the materials, instead of the characteristic ones. In the case of concrete, the average compressive strength is fc = fc '+ 8 = 38 MPa.
The braces were calculated as elements, following the same plastic criteria taken into account for the primary elements (beams and columns). To finish, the global damping factor considered for each structure was 5%.

Fundamental Period, Weight and Seismic forces of the prototype frames
For each prototype frame, a linear modal analysis was carried out, with seismic weight corresponding to a dead load and 30% of the live load (EC-8 2005). Table 2 and Table 3 show the weight and the fundamental period of the frame, respectively. Once the weights and the fundamental periods of each analyzed frame were obtained, the seismic forces were obtained from the European seismic resistance standard, EC-8 (2005). The analysis was carried out for a soil (Type C), with a seismic acceleration of 0.12g, corresponding to the Lorca (Spain) zoning and a building of normal importance. The seismic forces for each of the floor frames analyzed are represented in Table 4 Table 4 Seismic forces of the frames analyzed using EC-8 As expected, the results in Table 4 show how the seismic forces were considerably reduced for the frames with diagonal braces. This is due to the lower mass of the frame and the longer period. On the other hand, the maximum seismic forces correspond to the most rigid buildings, those with San Andrés cross bracing.

Lorca earthquake
Despite its moderate magnitude (Mw = 5.1), the Lorca earthquake (Martínez-Díaz et al. 2011;Oterino et al. 2012;Giner-Robles et al. 2012) constitutes one of the seismic movements with the greatest destructive power recorded in Spain in the last decade. This severity seems to be due to the low hypocentral depth (about 2 km) and the almost zero distance between the epicenter and the city center of Lorca (2.9 km from the seismological station). The earthquake left 9 people dead, 167 injured (3 seriously) and 40,000 homeless, causing significant material damage. Fig. 4a and 4b represent the accelerograms of the horizontal components (N-S, E-W) of the most severe events in the Lorca registry (Dominguez Santos et al. 2014;Dominguez Santos et al. 2016).

Overall description
The proposed damping system consisted of using additional bracing systems and installing hysteretic energy dissipators between these elements and the main structure, as indicated in Fig. 1. For example, the solution using chevron braces (Fig. 6) was considered next. As shown in Fig. 6, devices were installed on all of the floors; this guaranteed an even behavior along the frame height (vertical uniformity). Noticeably, dissipators could be freely moved along the enclosure of the building without disturbing the symmetry and torsional strength.

Hysteretic dissipators
Since the final goal of this research is to promote the use of hysteretic energy dissipators (Mazza 2019;Nuzzo et al. 2019) for the seismic protection of vulnerable buildings, no specific recommendations for any specific device are given. For instance, the devices that were installed in the Titanium building might be adequate. In this case, the hysteretic behavior of any dissipator was characterized and modeled using three major parameters: yielding force, initial (elastic) stiffness and postyielding ratio. The values used in this study are shown in table 5.
To determine the necessary parameters in the modeling of the energy dissipators, the method explained in Section 4.3 and detailed in Benavent-Climent (2011) was used. The results of the parameters that determine the design of each dissipator for each floor of the frames are described below.   Table 5 Values that determine the modeling of the design dissipators

Design of the dissipative devices
The energy that can be dissipated in the whole building in a given direction cannot be obtained by merely adding the capacities of each story, it depends on the distribution of the dissipated energy and on the accidental eccentricities between their centers of mass and rigidity. To cope with this issue, a number of formulations to select the variation of the design stiffness and yielding forces of the steel members along the building height have been proposed; in this paper, the approach in Benavent-Climent (2011) is considered. This formulation aims to obtain a uniform distribution of the cumulative ductility  in each level along the building height. The yielding shear force on the i-th floor (Vyi) is normalized with respect to the weight above that floor: In equation (1), Wj is the weight of the j-th floor and N is the number of floors. This formulation considers the influence of the vertical distribution of the lateral stiffness of the main structure. The variation of i obeys an exponential equation: In equation (2), i t is the lateral stiffness of the i-th floor, TF is the fundamental period of the building in the direction under consideration and TG is the corner period of the VE design spectrum ( Fig. ); TG separates initial and horizontal branches.
With all this, the obtained values of  1 are 0.02, 0.03 and 0.05, for the frames of 5, 10 and 15 floors. In the same way, the K1 values are 5, 10 and 15 respectively.

Seismic demand
Seismic demand is given as an input and hysteretic energy (EI and EH), expressed in terms of equivalent velocities VE and VD according to E = √2 I ⁄ and D = √2 H ⁄ , where m is the mass of the building. For practical, energy-based, earthquake-resistant design, VE is obtained from the available design energy spectra and VD is estimated from  2013) proposed design energy input spectra for moderate-tohigh seismicity regions, based on Colombian and Turkish records, respectively. These VE input energy spectra depend on the soil characteristics, the seismic design acceleration, the magnitude of the expected earthquakes and the type of seismic input (relevance of velocity pulses); conversely, they do not depend on the mass or on the damping parameters. Moreover, except in the short period range, the VE spectra are also independent of the assumed hysteretic constitutive law. A number of researchers (Akiyama 1985;Kuwamura et al. 1994;Fajfar and Vidic 1994;Decanini and Mollaioli 2001;Benavent-Climent et al. 2002;Yazgan 2012; López-Almansa 2013) have derived empirical expressions of the ratio VD / VE; such expressions depend on the soil type, the structural damping, the fundamental period of the structure, and the displacement or cumulative ductility. The obtaining of inputs and hysteretic energy for the prototype buildings to be protected with energy dissipators is described next.

Input energy in terms of equivalent velocity (VE).
In this study, the seismic demand is derived after the design spectra proposed in Benavent-Climent et al. 2002, Yazgan 2012. These spectra depend on the soil characteristics (stiff / soft), the seismic design acceleration, the magnitude of the expected earthquakes (Ms  5.5 and Ms > 5.5) and the type of seismic input (pulse-like / non pulse-like). As for the soil type, rock is broadly identified as stiff soil. The studies in Benavent-Climent et al. 2002, Yazgan 2012 were carried out assuming a design acceleration of 0.4 g. Concerning the magnitude, given the high seismicity proposed in this study, it can be conservatively assumed that Ms > 5.5. With respect to the presence of velocity pulses, since velocity pulses are more common in strike-slip mechanisms, the expected accelerograms will be mainly nonpulse-like. For stiff and soft soil conditions, the VE spectra proposed in Benavent-Climent et al. 2002, Yazgan 2012 are shown in Fig. 7(a) and Fig. 7(b), respectively. For linear analyses ( = 1,  being the displacement ductility), the spectra in Fig. contain an initial, linearly growing branch in the short period range, a plateau in the mid period range and a descendant branch in the long period range. The corner periods and the spectral ordinates for the plateau are indicated in Fig. 7; the exponents of the descending branches are 1.2 and 0.65 for stiff and soft soil, respectively. Except in the short period range, the input energy is a highly stable quantity (Akiyama 1985) with respect to the hysteretic and damping parameters of the structure under consideration. Therefore, for nonlinear behavior ( > 1) the only required modification is an increase in the initial growing branch slope. This slope increase will result in a reduction of the lowest corner period; for instance, for  = 20 the ratio between both slopes is 1.41 and 1.56 for stiff and soft soil, respectively. Therefore, the corner periods become 0.18 / 1.41 = 0.12 s (stiff soil) and 0.28 / 1.56 = 0.18 s (soft soil), as shown in Fig. 7. Both the linear and nonlinear spectra are characteristic, i.e. they correspond to the 95% percentile, and refer to a 475 year return period. The values of VE for the corresponding prototype buildings are obtained, replacing the fundamental periods in the spectra of Fig.  7. Noticeably, all of the periods lie in the plateau (mid period range).

Hysteretic energy (EH).
The VD spectrum is commonly obtained by multiplying the VE spectrum by a convenient value of the VD / VE ratio; such a ratio depends mainly on the damping factor , the displacement ductility  and the building fundamental period TF. References  (Yazgan 2012;. The values of  and  were chosen to correspond to average conditions. Noticeably, a more accurate analysis would require an iterative process in terms of ductility demand, however, it should be emphasized that, for values of  higher than 5, the ratio VD / VE is rather insensitive to that parameter.

Nonlinear analysis (Push-over)
2D static analyses (Push-over) (Elnashai 2001;Chopra and Goel 2004) have been performed using the model described in Section 2, using the SeismoStruct program (2020).  (2000) and Comartin et al. (1996). With these representations, the structural state in which each of the frames is for each level of damage will be obtained, according to the displacement that each frame has on the highest floor.
Static, nonlinear (pushover) analysis was carried out using the numerical models described in Section 2.4; second-order effects are accounted for by a P-delta analysis. The variation of the pushing forces along the height of the frame is triangular. Fig. 8,  Fig. 9 and Fig. 10 show the capacity curves in terms of base shear force and displacement at the top floor for the 5, 10 and 15-story frames, respectively.  8, 9 and 10 show the regular, expected behavior, where the resistance capacity is greater for frames with higher seismic demands (CHB and SAB). These correspond to the frames braced without dissipators. However, ductility is higher on the dissipator frame. The effectiveness of energy dissipators increases with the height of the frame.
Tables 6, 7 and 8 represent the yield deformations (dy) and ultimate deformation (du) obtained from the capacity curves of Fig. 8, 9 and 10. The yielding deformation (dy) is obtained using the graphical equality method of areas, as explained in Prestandard (2000) and Comartin et al. (1996). In addition, for each frame, the ductility (μ = du/dy) is obtained, as well as the relation between the ultimate and the yield deformation. It is noteworthy that the frames increase their ductility with the use of energy dissipators in all of the cases analyzed. The ductility ratio that exists between the braced cases and those that use dissipators increases with the height of the frames, the greatest differences being in the cases braced by means of the San Andrés cross (SAB).

Dynamic analysis
Non-linear dynamic analysis 'Time history' (Wilson et al. 1972;Vamvatsikos and Cornell 2002), was performed in discrete time using the Newmark method 'b' (Newmark 1959;Wood et al. 1980). The time discretization (Δt) of the analyses was taken to be equal to the sampling period of the Lorca records in its N-S direction (0.01 s). The damping of the structure was carried out using the Rayleigh model (Léger and Dussault 1992;Hevin et al. 1998), with a factor of 5%. All calculations were carried out using the computer program (SeismoSoft 2020). The results obtained are shown in Fig. 11, 12 and 13. The results of the dynamic analysis 'Time history' using the Lorca record in the N-S direction of Fig. 11, 12 and 13, indicate that the best structural behaviors correspond to the lower height frames. As the frames increase in height, the efficiency of the dissipators increases, the best performance being achieved by the 15-story frames. It is noteworthy that the stiffness provided by the braces on the highest frames, negatively affect its seismic resistance behavior. On the other hand, none of the analyzed models collapsed, which shows the effectiveness that both solutions had during this earthquake. In general, it was observed that the use of dissipators significantly decreased the absolute accelerations of the frames, which lead to a significant reduction in seismic forces. This decrease became more evident as the frames increased in height. However, the increased ductility of the frames caused the displacements of the upper floors to increase in all of the cases analyzed. The maximum acceleration and displacement values of the dynamic analyses are shown in Table 9.   Table 10, the efficacy of the devices in the highest frames was observed, with the most effective solutions being the least rigid bracing corresponding to those with a single diagonal (EDB and SDB).
On the other hand, Tables 11, 12 and 13 represent the maximum stresses of the primary structural elements (beams and columns) and the most unfavorable braces (with M (moment), V (shear) and N (axial)), those belonging to the primary elements, MR (moment), VR (shear) and NR (axial), those belonging to the braced bar and FD (Force) and MD (Moment), those belonging to the energy dissipators.  Table 13 Unfavorable primary elements (beams and columns) and bracing for 15-story frames The results obtained are presented in Tables 11, 12 and 13, and they show that the use of dissipators is not as effective in the 5-story frames as using braces individually. The values obtained reflect that the effectiveness of the dissipators improves with the increase in the heights of the frames (15 heights), where the placement of these devices reduces the efforts in all of the cases studied, except for the more rigid solution (SAB). The effectiveness of the placement of these dissipators, improves with the less rigid braced solutions (EDB and SDB) and with the height of the frames, the best results being those belonging to the frames with dissipators located in the center of the diagonal brace.

Conclusions
The efficiency of the energy dissipators is improved as the frames increase in height. This efficacy is dependent on less rigid braced solutions (EDB and SDB).
In the lower height frames (5 floors), the use of braced solutions without any device improves the structural behavior. These improvements are more evident with the more rigid solutions (SAB and CHB).
The ductility of all frames increases with the placement of dissipators. The increase in ductility increases with the height of the frame. The highest ductility ratio between braced and device cases occurs in the most rigid cases (CHB).
The placement of dissipators drastically reduces the absolute accelerations of the frames, especially those that are higher (15 floors). This translates into a reduction in seismic forces and, therefore, in an improvement in the seismic resistance behavior of the frames. These reductions coincide with the analysis criteria of the seismic resistance regulations.
The placement of energy dissipators using too-rigid bracing, such as the San Andrés cross (CHB), is not effective.
All of the cases would have supported the Lorca earthquake. Only the stiffer frames without dissipators and of greater height (CHB and SAB) would have had some problem in the structures, but they would not have collapsed. The good structural performance of the frames with diagonals and dissipators (EDB and SDB) is worth noting, they failed to laminate and were always in an elastic state.
We conclude that the dissipation of energy towards hysteretic 'fuse' devices (devices that cause the incoming energy to be concentrated in the main elements of the frame, i.e. beams and columns), due to the incoming earthquake energy in the frames, becomes more efficient as the frame increases in height.