An elastoplastic bracing system for structural vibration control

Engineering Structures 200 (2019) 109671

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An elastoplastic bracing system for structural vibration control Mohammed Ismail

⁎

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Structural Engineering Department, Zagazig University, 44519-Zagazig, Egypt Universitat Politécnica de Catalunya (UPC)–BarcelonaTECH, 08034 Barcelona, Spain SENER Ingeniería y Sistemas, 08290 Barcelona, Spain

A R T I C LE I N FO

A B S T R A C T

Keywords: Vibration damping Passive control Mathematical modeling Near-fault Bracing Elastoplastic

This paper presents and investigates a new elastoplastic bracing system for passive vibration control of structures. It consists of a deformable elastoplastic metallic core comprising four Arcs around a central Ring and, therefore, the Bracing system is called the “AR-Brace”. Each arc is firmly attached tangentially to the central ring, then to the adjacent arc and finally to a corner of a structural panel, even directly or through a rigid arm. Different design variations of the AR-Brace could be obtained, by means of controlling the construction material and dimensions/thickness of its core, to passively adapt/tune the provided working ranges of stiffness/damping to specific requirements. In this work, some AR-Brace designs were studied to evaluate their efficiency. The device was thoroughly characterized mechanically using finite elements simulations and then modeled mathematically using the Bouc-Wen hysteresis model. The ability of the AR-Brace to control structural vibration and other vibration-dependent responses was investigated via numerical case studies under real and synthetic dynamics excitations. It was found that the displacement-based AR-Brace achieves a good balance between the added lateral rigidity and the provided damping, which was reflected in a remarkable mitigation of the undesirable effects of dynamic excitations, even at moderate levels of supplementary damping by the device.

1. Introduction Structural vibrations may arise from wind forces, seismic excitations, rotating machinery or similar dynamic actions. Under strong dynamic excitations, structural damage or even collapse may take place. The higher the inherent damping in structures, the lower the likelihood the damage will be excessive. However, in case of strong vibrations, the structural inherent damping in the structure becomes not sufficient to mitigate the structural vibration. In many situations, supplemental damping may be used to control the response of these structures. In this regard, many researchers have studied, developed and tested different supplemental damping techniques. The basic supplemental damping techniques applied to structures are passive, active and semi-active devices. The common principle of these devices is that they all need power to generate motion control forces, although the power source is different in each device. For passive control devices, no external power is needed as the device generates the required power inherently from the relative motion/velocity of the attachment points to the structure. Active control devices use attached controllers to develop motion control forces based on certain feedback inputs obtained through a variety of sensors. The main drawback of the active control devices is that they need large ⁎

external power source that may not be available in accidental conditions of sever excitations. Semi-active devices are similar in many aspects to passive systems, but use battery power controllers to adjust their mechanical properties. However, they are more complex than the purely passive ones and may require careful monitoring and frequent maintenance. It was investigated by [1] the ability to separate the load carrying function of a structure from the energy absorbing function and to explore if special devices could be incorporated into the structure with the sole purpose of absorbing the kinetic energy generated in the structure by earthquake attack. Hysteresis dampers were addressed by [2] to improve the energy-absorbtion capacity of structures under earthquakes. A parametric study was presented by [3] on the influence of the mathematical modeling of viscous damping on seismic-energy dissipation of multidegree-of-freedom (MDOF) structures. Basic principles as well as practical design and implementational issues associated with the application of base isolation systems and passive and active control devices to civil engineering structures were addressed in [4]. A threedimensional modeling procedure was proposed by [5] for cable-stayed bridges with rubber, steel, and lead energy dissipation devices. A stateof-the-art review on semi-active control systems for seismic protection of structures and nonlinear damping based semi-active building

Address: Structural Engineering Department, Zagazig University, 44519-Zagazig, Egypt. E-mail address: [email protected].

https://doi.org/10.1016/j.engstruct.2019.109671 Received 12 May 2019; Received in revised form 7 September 2019; Accepted 10 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

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M. Ismail

that can improve the viscoelastic material’s effectiveness in viscoelastic dampers. Viscous fluid dampers that dissipate energy via moving of a body into a viscous fluid were studied by [30–33]. Under near-field and far-field excitations, [34] compared linear and nonlinear viscous fluid dampers to decide which is most suitable for structures. To investigate the effects of temperature on their efficiency, [35] found that the viscoelastic dampers’ efficiency at temperatures 107°F is one-half its efficiency at lower temperature of 77°F. Another study by [36] revealed that the effect of viscoelastic dampers on the optimum damping ratio depends on the period and the design ductility ratio of the system. In addition, [37] found that the systems with viscoelastic dampers gained both stiffness and damping, whereas the systems with viscous dampers gained damping under conditions of low frequency movement. A comparative study among different methodologies using viscous dampers for seismic protection of building structures was carried out by [38]. Accordingly, the velocity-dependent devices appear to more expensive than the displacement-dependent ones, besides the earlier is being influenced by many factors that do not affect the later ones. Therefore, since the displacement-dependent devices are generally less demanding than the velocity-dependent ones, in addition to their ability to provide both stiffness and damping, they could be more promising if a good balance could be obtained between the stiffness and damping that they provide in order to be a more economic choice for efficient energy dissipation under all levels of dynamic excitations. This is one of the objectives of the present paper, which introduces and investigates a new elastoplastic bracing system for passive control of structural vibration as well as vibration-dependent responses. Section 3 provides a description of the device.

isolation system are found in [6–8], while [9] investigated the application of semi-active control for seismic protection of elevated highway bridges. A performance estimates in seismically isolated bridge structures was addressed by [10]. An innovative isolation device for aseismic design was proposed by [11] and widely applied to control of structural and nonstructural elements against seismic hazards [12–15]. The results of solving the problem of finding the optimal synthesizing control function of the damping process in the vibration isolation system were given by [16]. Concerning the passive damping devices, they are usually categorized into displacement-dependent and velocity-dependent devices. The earlier type, like steel plate dampers and friction dampers, dissipate energy through yielding of the damper elements or through sliding friction. They add both stiffness and hysteretic damping to structures, therefore, they are suitable for energy dissipation under moderate to strong excitations. On the other hand, the velocity-dependent devices rely on viscoelasticity in dissipating energy, like viscous fluid dampers and viscoelastic dampers. They generally provide structural damping (in addition to stiffness in some cases), as a result, they are used to dissipate energy under all levels of excitation. Some of the main attempts to develop and investigate both types of dampers are briefly listed below. 1.1. Displacement-dependent devices Cyclic tests on X-shaped and V-shaped flexural steel plate dampers were performed by [17,18] and they found that the X-shaped dampers performed better than the V-shaped dampers regarding the energy dissipation and durability. Another type of the X-shaped dampers known as the Added Damping and Stiffness, ADAS, was introduced by [19]. A triangular plate dampers, which is a different form of the ADAS, and referred to as TADAS, was experimentally investigated by [20]. Regarding applications, they are several, for example the ADAS dampers were utilized in retrofitting a 13-story reinforced concrete building after damaged in Mexico City [21]. Further, a structural analysis for a redesign showed that a 40% reduction in interstory drifts was achieved while the base shear was unchanged. An attempt to develop unbonded steel braces was done by [22], which consisted of a conventional brace encased in a square steel pipe filled with mortar. Those unbound braces were compared to the conventional ones by [23] on the response of a 15-story structure under moderate and severe earthquakes. Recently, [24] studied the seismic performance of braced steel frames using elliptic bracing system. In similar fashion, [25] proposed a similar ring system to control structural vibration. However, both systems are connected directly to frame beams and columns by means of moment connections at their midspans and midheights, respectively. Unfortunately, this adds extra flexural stresses to those structural elements and leads to the formation of plastic hinges into them, although the concept of passive structural control is intended to avoid the formation of any plastic hinges into the framing system of the controlled structure. Seismic performance of typical reinforced concrete framed structures was addressed by [26] using diagonal buckling restrained braces that dissipate inelastically the input seismic energy to ensure elastic behavior of the braced primary structure. The same buckling restrained braces together with pre-tensioned steel ribbons were implemented into a case study of seismic retrofitting of a confined-masonry reinforced concrete academic building, [27].

2. Paper scope The manuscript deals with a new elastoplastic bracing system composed of a particular arrangement of metallic arcs and a central ring, called AR-Brace. The study starts with a qualitative explanation of the mechanical behavior of the device, and then the determination of a reasonable force-displacement law based on finite element simulation. A suitably calibrated Bouc-Wen hysteretic model is sought to be an appropriate candidate model for describing the constitutive behavior from sophisticated nonlinear finite element simulations. Then, a parametric study is carried out to investigate the influence of the main geometrical parameters of the brace, namely the thickness of the arc and ring components, under sinusoidal imposed motion of different amplitudes. Finally, the implementation of the AR-Brace into a casestudy building structure is discussed and compared to alternative structural configurations or brace systems for emphasizing the advantages of the proposed system. Two nonlinear solid finite elements have been used in this study to capture precisely the nonlinear realistic behavior of the AR-Brace. These elements are the 20-node brick element and 15-node wedge element”. Therefore, the issue of shear-locking phenomenon is nonexistent within the present paper, as it was totally avoided by means of using the aforementioned second-order solid finite elements. Those elements were found computationally expensive but they are intended to provide accurate results in pure bending. No use of any linear solid finite elements were made during the mechanical characterization of the AR-Brace as they are not accurate in this case. Accordingly, the comparison of using linear and nonlinear solid finite elements is out of scope of this paper.

1.2. Velocity-dependent devices

3. The elastoplastic bracing system “AR-Brace”

The viscoelastic dampers’ behavior is greatly influenced by several factors, such as the environmental temperature, the number of dynamic load cycles, the amount of strain and the excitation frequency. It was found by [28] that the energy dissipated by the viscoelastic material per cycle varies inversely with the temperature. Also [29] indicated that the shear strains and volume of viscoelastic material are the parameters

This section briefly describes a new displacement-dependent damping device, proposed herein, which is intended for passive control of structural vibrations. It comprises a deformable elastoplastic metallic core, which is attached to the four corners of a structural panel, even 2

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Fig. 1. The AR-Brace, 3D and elevation views.

stiffness by the device to an AR-Braced structural panel. Any deformations within such elastic phase are self-recoverable. Hence, the device works as an elastic restoring device (or linear spring) within that elastic phase. On the other hand, deformations beyond the elastic limit are only recoverable by external actions. In addition, they represent the source of the hysteresis damping provided by the device in the structure. Different designs of the AR-Brace are attainable by means of changing the core’s construction material and its dimensions/thickness to passively adapt/tune the provided working ranges of stiffness/ damping to specific requirements. In addition, the device could be scalable in overall size as needed.

directly or by means of four (diagonal) stiff corner arms. Those arms (if any) are attached to the structure through moment connections to concentrate any relative displacements within the elastoplastic core. The core consists of four Arcs around a central Ring and, thus, the Bracing device is referred to shortly as “AR-Brace”. The four arcs of the AR-Brace are attached tangentially to the central ring (one joint per arcring) and connect it to the four stiff corner arms, or directly to the panel corners, Fig. 1. Therefore, the two diagonals of the AR-Braced structural panel are the same diagonals for the device. As the AR-Braced structural panel is deformed under lateral seismic/wind excitations, the relative deformations between every two opposite corners of the panel are transmitted into the central metallic core of the AR-Brace to initiate the elastoplastic behavior, which adds both lateral stiffness and hysteretic damping to the AR-Braced structure, Fig. 2. Positively, the four ends of the device should be attached to the corners of the structural panel in such a way as to prevent any loss of relative motion. This ensures the transmission of the entire relative diagonal movement to the AR-Brace device and, consequently, the attainment of maximum efficiency. The functional principle of the AR-Brace depends on the diagonal tension of two opposite corners at the same time in one stroke and on the simultaneous tension of the other two corners in the opposite stroke. When two of the four corners are in tension, the other two might be in compression. However, the tension will be the most dominant and, therefore, it is unlikely that any off-plane buckling of the AR-Brace will occur, Fig. 2. Both the central ring and the tangential arcs are deformed due to diagonal tension, producing flexural stresses that go beyond the elastic limit of the material to form hysteresis loops under cyclic dynamic loads. The AR-Brace’s resistance to diagonal tension before reaching the material’s elastic limit represents the added elastic

4. Mechanical characterization of the “AR-Brace” To define the structural behavior of the new AR-Brace device, an extensive set of numerical simulations was performed using sophisticated Finite Element modeling to establish its intrinsic load-deformation relation. Two main phases of AR-Brace’s characterization were passed through; initial and optimization phases.Four AR-Brace designs were characterized in the initial phase, while the optimization phase includes the characterization of three other device designs. Using sinusoidal displacement inputs, the output forces are measured to establish the force-displacement relationship of each design. Then, the provided effective damping and stiffness of each design were estimated. The chosen material for all designs is mild steel of 7.85 ton/m3 density, 210 GPa elastic modulus, 235 MPa initial yield stress, 210 MPa kinematic strain hardening modulus, maximum allowable effective plastic strain of 17%, and a mean coefficient of thermal expansion 1.2e005. The chosen material behavior is bilinear elastic-plastic material. Each of the initial four designs has the same thickness for arcs as

Fig. 2. The AR-Brace, deformed and neutral positions. 3

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Fig. 3. The four AR-Brace’ cores characterized in this study.

length per finite solid element is 25 mm, which is reasonably small relative to the dimensions of the AR-Brace’s core to achieve an equilibrium between the output accuracy and the computational cost. The outermost dimensions of the elastic-plastic core of the utilized ARBraces herein are 1700 mm high by 1700 mm wide and 2400 mm diagonally. The diameter of the central ring is 1000 mm. Based on the actual behavior of the AR-Brace, there will be no relative movement within any of the joints between the tangential arcs and the central ring. Therefore, it is not necessary to capture any response quantity, which depends on those non-existent relative movements. Arc-Ring connections are only intended to firmly join the two components, as there is no rolling, sliding or gap opening-closing behaviors between the connected two elements. This eliminates the need to use any contact algorithm. For that reason, the simplest, most realistic and least costly approach to modeling these joints between arcs and rings will be through a set of nodes, which are directly shared between those components. These shared nodes are on the line of contact between the opposite curved surfaces of the two tangential components. In Fig. 4, the AR-Brace (1x /1x ) is numerically modeled and subjected to horizontal sinusoidal displacement input at the upper two corners simultaneously, while the other two lower corners are fixed against motion. This simulates the story drift of an authentic AR-Braced structural panel subjected to a lateral dynamic excitation, see Fig. 2. Four loading cycles were used with a fixed displacement amplitude of 50 mm, Fig. 4(a). The measured output force is plotted in Fig. 4(b) versus time. Combining the input and output in a displacement scale produces the force-displacement relationship of the device, which is a hysteretic relationship, Fig. 4(c). In the next Section 6, the obtained hysteretic behavior of AR-Brace is mathematically modeled.

well as the central ring, Fig. 3. The chosen thickness of the first of those designs is 25 mm and referred to x. From the second to the fourth designs, the thickness is increased by 2x , 3x and 4x , respectively. In the optimization phase, different thickness of rings and arcs were chosen within the same design. The optimization objective is reducing the added lateral effective stiffness by the AR-Brace to the structure to reduce the overall lateral structural rigidity and, therefore, reducing the input forces to such AR-Braced structure. The arc thickness of the later three ‘optimized’ designs was fixed to x, while the chosen ring thickness is 2x , 3x and 4x , respectively. Shortly, in this study, each design of the device will be denoted within two parenthesis as a ratio of the arc’s thickness to the central ring’s thickness. For example, an AR-Brace (1x /2x ) refers to an AR-Brace design of a 1x arc thickness and a 2x ring thickness. More about testing and characterization of the AR-Brace designs of the two aforementioned phases is presented in Section 7, where a parametric study on the ARBrace’s hysteresis is carried out to evaluate energy absorption capacity of AR-Brace damper for future seismic- and wind-resistant design. In this section, only the design of 1x equal thickness (Fig. 3(a)) is characterized to initially establish the resulting force-displacement relationship, which will be mathematically modeled in Section 6. The joints between the tangential arcs and the central ring are subjected to high bending and shear stresses. Therefore, the latter cannot be locked in the Finite Element (FE) model, when the joints are simultaneously subjected to bending stresses, to simulate the actual behavior of those joints. This undesired behavior is known as shear locking. Shear locking is an error that occurs in finite element analysis due to the linear nature of quadrilateral elements. The linear elements do not accurately model the curvature present in the actual material under bending, and a shear stress is introduced. The additional shear stress in the element (which does not occur in the actual joint) causes the element to reach equilibrium with smaller displacements, i.e., it makes the element appear to be stiffer than it actually is and gives bending displacements smaller than they should be. In this paper, shear locking has been avoided using refined (nonlinear) second-order solid element, which is computationally expensive, but provides accurate results in pure bending and reduces significantly the locking effect. Two nonlinear solid finite elements are used to capture precisely the nonlinear realistic behavior of the AR-Brace. These elements are the 20node brick element and 15-node wedge element. The maximum side

5. Effective stiffness and effective damping Response analysis of a structures with linear dynamic procedure requires two values: effective stiffness and effective damping. Fig. 4(c) illustrates the physical significance of elastic, plastic and effective stiffness (k eff ). The later is a function of peak force and displacement amplitudes per cycle and may be calculated as follows:

4

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Fig. 4. Force-displacement relationship of the AR-Brace with thickness = 1 x.

k eff =

+ − |Pmax | + |Pmax | + − |d max| + |d max |

derivative, n > 1 is a parameter that governs the smoothness of the transition from elastic to plastic response, Dy > 0 is the yield constant displacement, k > 0 and 0 < α < 1 represents the post to pre-yielding stiffness ratio (kb/ k e ), while A, β and γ are non-dimensional parameters that govern the shape and size of the hysteresis loop. The Bouc-Wen model can match a hysteretic behavior by properly tuning its parameters. It is a black-box model, i.e. the model parameters may not have physical meanings. For this reason, the Bouc-Wen model has to fulfill some general physical properties. It was asserted by [41] that, for n ⩾ 1, the Bouc-Wen model is bounded-input bounded-output, passive, and consistent with physical asymptotic motion if and only if

(1)

+ − + | and | are the two force amplitudes per cycle; |d max | and |Pmax where |Pmax − |d max | are the corresponding displacements per cycle. The energy dissipation capability of the hysteretic AR-Brace system is generally represented by effective damping ζ , whereas effective damping is displacement-dependent and calculated at design displacement, d max , as follows:

ζ eff =

AD 2 2·π·k eff ·d max

(2)

A > 0,

where AD is the energy dissipated per cycle, which is obtained from the numerical test and is equivalent to the area enclosed by one complete hysteresis cycle of the force-displacement relation of the AR-Brace.

β + γ > 0,

β − γ ⩾ 0.

(5)

6.2. Bouc-Wen model parameters estimation

6. Mathematical modeling of the AR-Brace’s hysteresis

Comparing the Bouc-Wen model output to the numerically-obtained (measured) data, for a given periodic input displacement signal, the model parameters are estimated to characterize the AR-Brace. A total of 7 parameters ( A, α, β, γ , D, n , and k) are forced to obey the necessary conditions in Eq. (5). A constrained trial and error method is used to obtain the 7 model parameters in Eqs. (3) and (4), based on the constraining range of each parameter given in Table 1. The estimated model parameters were determined to fit the model to the measured output data. Those

The mechanical characterization presented in Section 4 has shown that the AR-Brace exhibits a hysteretic behavior, as shown in Fig. 4. The objective of this section is to obtain an input-output mathematical model that describes in a reasonable and manageable form the obtained force-displacement relationship exhibited by the AR-Brace. The BoucWen model of smooth hysteresis is considered, where hysteresis is the dependence of the state of a system on its history. 6.1. The Bouc-Wen model

Table 1 Identified parameters of the Bouc-Wen model to characterize the AR-Brace.

The Bouc-Wen model [39,40] is extensively used to describe nonlinear hysteretic behaviors, particularly, in vibration-resistant devices. The standard form of the model is expressed as

Fb (t ) = αkx (t ) + (1 − α ) Dy kz (t ),

(3)

z ̇ = Dy−1 (Ax ̇ − β|x |̇ |z|n − 1 z − γx |̇ z|n ),

(4)

where x is the displacement, z is an auxiliary variable, Fb is the isolator restoring force, αkx is the elastic force component, ż denotes the time 5

Parameter

Range

Value (tuned)

A α β γ D n k

0⩽A<∞ 0⩽α⩽1 γ⩽β<∞ −β⩽γ⩽β 0⩽D<∞ 1⩽n<∞ 0⩽k<∞

1 0.0041 60,000 52,000 1 2.02 3.25e5

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Fig. 5. Mathematical modeling of the F-D relationship of the AR-Brace with thickness = 1 x.

damping and stiffness, defined in Section 5, which are essential for linear dynamic response analysis of a structures.

identified parameters are listed in Table 1 for the AR-Brace of uniform thickness 1x. Fig. 5 shows the measured force-displacement of the AR-Brace against the modeled one using the Bouc-Wen model. Reasonable close matching between both curves has been obtained, which confirms that the Bouc-Wen model is a good candidate to predict the hysteretic behavior of the AR-Brace with fine accuracy.

7.1. Phases of study and AR-Brace designs As explained in Section 4, the investigation passes through two phases: initial and optimized ones. The earlier phase includes four designs, each of equal arc/ring thickness, ranging from 1x /1x up to 4x /4x , where x = 25 mm, Figs. 6–8. The later phase is intended for reducing the pre-yield stiffness of the AR-Brace to reduce the, unwanted, added lateral force to an AR-Braced structure, without minimizing the provided hysteretic damping. Three other designs of the device were investigated in this later phase, under the same excitations of the initial phase, having an arc/ring thickness of 1x /2x , 1x /3x and 1x /4x , Figs. 11–13.

6.3. Validity of the identified Bouc-Wen model’s parameters To check the validity of the identified parameters, the discrepancy between the measured Fm and predicted Fb outputs (both are expressed as f within the integration) is quantified using the L1 and L∞-norms and the corresponding relative errors ε :

||f ||1 =

∫0

Te

|f (t )|dt; ||f ||∞ = max |f (t )|; ε1, ∞ = t ∈ [0, Te]

||Fm − Fb ||1, ∞ . ||Fm ||1, ∞

(6)

7.2. Input harmonic displacements

The relative error ε1 quantifies the ratio of the bounded area between the output curves to the area of the measured force along the excitation duration Te , while ε∞ measures the relative deviation of the peak force. As shown in Fig. 5 and the small relative errors ε1 and ε∞ in Table 2, the hysteretic Bouc-Wen model can be seen as a powerful representation of the AR-Brace for further studies.

To evaluate the AR-Brace’s efficiency, even at small relative horizontal deformations of a flexible structural panel, three amplitudes of 10 mm, 15 mm and 21.50 mm were chosen for the two phases of parametric study. Further, and to investigate the AR-Brace’ performance under extra bigger displacement amplitudes, the optimization phases’s devices were tested under, reasonably, greater shear displacement amplitudes of 35 mm, 50 mm and 65 mm. This represents the story drifts of highly flexible structural panels that should require strengthening using bracing systems. After each numerical investigation test, the load-deformation output is plotted along with the estimated effective stiffness and damping, Figs. 14 and 15.

7. Parametric study on the AR-Brace’s hysteresis To assess the efficiency and energy absorption capacity of the proposed AR-Brace system, a parametric examination of the device is performed taking into account various designs and harmonic excitations of different amplitudes. The main variable parameters are the thickness of tangential arcs and central rings together with different combinations of these thickness within dissimilar designs. The main objective of such examination is to monitor the changes in the forcedeformation relationships together with the pre-yield and post-yield stiffness. Further, to estimate the two main quantities of effective

7.3. Initial phase: 10 mm displacement amplitude This section examines the four designs of AR-Brace of equal arc/ring thickness (per design) with a relative horizontal input displacement of 10 mm. In Fig. 6(a,b,c,d), the obtained force-deformation diagrams are presented. The positive skeleton curves are plotted in Fig. 6(e). The estimated effective stiffness as well as the effective damping are given in Fig. 6(f,g). The used 10 mm amplitude corresponds to a floor drift, of the same value, considering an AR-Braced structural panel. The forcedeformation diagram of the AR-Brace (1x /1x ) is shown in Fig. 6(a). Due to the small thickness of the arch/ring, the device behaves linearly with a relatively low pre-yield stiffness. As a result, this design provides no hysteretic damping at that deformation amplitude, and may behave as a flexible elastic restoring device that is equivalent to a linear spring with zero energy absorbtion capacity.

Table 2 Discrepancy between measured and modeled outputs under cyclic seismic input. Discrepancy

Bouc-Wen model

Measure

AR-Brace (Thick. = 1x)

ε1 ε∞

2.83% 2.16%

6

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Fig. 6. Force-displacement relationships of the AR-Brace with different thicknesses (amplitude = 10.0 mm).

Doubling the arc/ring thickness, using the AR-Brace (2x /2x ) in Fig. 6(b), increases the elastic stiffness up to 10 times with an effective damping a bit beyond 20%. Using AR-Braces (3x /3x ) and (4x /4x ) , the effective stiffness becomes nearly three and seven times that of the

(2x /2x ) design, respectively. However, the effective damping did not increase proportionally to the effective stiffness as it slowly goes up to 27% and 30%, respectively, using AR-Braces (3x /3x ) and (4x /4x ) . The main output of this section highlights the energy absorbtion capacity of

Fig. 7. Force-displacement relationships of the AR-Brace with different thicknesses (amplitude = 15.0 mm). 7

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Fig. 8. Force-displacement relationships of the AR-Brace with different thicknesses (amplitude = 21.5 mm).

Fig. 9. Comparisons of effective stiffness and damping of the initial phase of parametric study.

the proposed AR-Brace as it can provide effective damping up to 30% at relatively small displacement amplitude of 10 mm, although at the expense of high effective stiffness, utilizing the design (4x /4x ) .

(4x /4x ) may be the proper choice to provide notable stiffness as well as high damping. 7.5. Initial phase: 21.5 mm displacement amplitude

7.4. Initial phase: 15 mm displacement amplitude This section subjects the same initial four AR-Brace designs to a bigger displacement amplitude of 21.50 mm. The equivalent outputs, to those of Sections 7.3 and 7.3, are shown in Fig. 8. It is noted that the most flexible AR-Brace design, (1x /1x ) , has developed rapidly its energy absorption capacity with increasing the input displacement amplitude, as its equivalent damping increases from 0% through 5% up to nearly 20% for amplitudes of 10 mm, 15 mm and 21.50 mm, respectively. On the other hand, the other designs provide a slightly bigger effective damping with bigger input amplitude.

Similar to Section 7.3, the same four initial designs of the AR-Brace were reinvestigated considering a slightly bigger displacement of 15 mm. Fig. 7(a) shows that the most flexible design, AR-Brace (1x /1x ) , starts to exhibit a slightly nonlinear behavior providing only a 5% effective damping. A significant steep increase of effective damping up to 30% is obtained by doubling the arc/ring thickness, (2x /2x ) , at a relatively low effective stiffness. By increasing the thickness beyond (2x /2x ) , the effective stiffness increases steeply while the effective damping gets bigger at a slow pace from 30% up to 34% and 36% for (3x /3x ) and (4x /4x ) , respectively. In a real implementation of the device, probably the AR-Brace (2x /2x ) may be suitable for a relatively stiff structural panel that may require more damping than added stiffness, while in case of relatively flexible panels, the AR-Braces (3x /3x ) or

7.6. Summary of the parametric study Apparently, the following may be the main observations on the parametric study, Fig. 9: 8

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• The AR-Brace could provide a relatively wide range of effective

•

• • • •

Figs. 11–13. The difference in height and size of each of the two corresponding loops is evident; those of optimized design are of less height and less area than those of the initial phase. The positive Skeleton curves, sub-figures (d)(11, 12, 13), demonstrate significant reductions in pre-yield stiffness, where the peak optimized elastic stiffness became almost 10% of its corresponding initial one, Fig. 13(e). In the case of effective damping, the peak corresponding values are 40% (in initial phase) to 30% (optimized phase),i.e., the ratio after optimization is 0.75, which is not as low as that of reduced stiffness (0.10), Fig. 13(f). This confirms that the optimization objective has been accomplished successfully. The goal of AR-Brace optimization is twofold. The first is to show that the proposed system could provide broad working ranges of stiffness and damping. Further, the lateral elastic stiffness added to a flexible structure attracts additional lateral forces under horizontal seismic and wind actions, which is an unfavorable side effect of the structural energy dissipation approach. Therefore, the AR-Brace needs to be “optimized” to avoid attracting those additional lateral actions to the strengthened structure. In other words, the AR-Brace should also be able to provide wide effective damping ranges that correspond to significantly low values of added elastic stiffness to the structure. This is the second objective of the optimization performed in this section, which confirmed the AR-Brace’s (additional) ability to provide high damping with a low elastic stiffness to suit certain applications that may require higher added damping along with lower added elastic stiffness. In addition, the study carried out in the Section 7 has shown that the AR-Brace can provide almost similar effective damping along with much greater elastic stiffness to suit other possible applications requiring high added damping and high added stiffness, simultaneously. This would ensure the possible versatility and adaptability of the proposed AR-Brace simply by modifying the thickness of the arc/ring to provide the needed damping and stiffness.

damping and stiffness, simply, by changing the arc/ring thickness, which may be finely tuned to obtain precisely required values of both added stiffness and damping to an AR-Braced structural panel. In this study, high effective damping range, from 30% up to 40% could have been attained using available and inexpensive metallic yield components. The effective stiffness increases steeply with the increase of arc/ring thickness, while the parallel effective damping increases at a relatively slower rate under the same input. Since the added stiffness might not be favorable in some cases, as it attracts additional lateral force into a strengthened structure, a possible optimization attempt is presented in Section 8 to lower the provided stiffness while keeping reasonable provided damping. The provided effective stiffness decreases with the increase of input displacement amplitudes, contrary to the effective damping. The decay rate of effective stiffness is higher in case of thicker arc/ring thickness than that of the relatively thinner ones. The pace of growth of effective damping, with increasing input amplitude, is almost the same for bigger arc/ring thickness ((3x /3x ) and (4x /4x ) ). Such rate of growth becomes a relatively bit higher in case of relatively smaller arc/ring thickness ((1x /1x ) and (2x /2x ) ). Similar to changing arc/ring thickness, wider (or different) ranges of provided stiffness and damping may be obtained also via changing the radii and/or material of arcs and/or central ring. However, such additional study is out of scope of the present paper. The proposed AR-Brace may be suitable for wide range of structures due the possibility of providing reasonably wide ranges of tunable stiffness and damping.

8. A possible optimization of the AR-Brace The AR-Brace is a structural system designed to improve structural resistance to lateral forces, including wind and earthquake forces. Although the added structural rigidity is necessary to control story drift and lateral deformation of the building, such added rigidity magnifies the lateral forces into the braced structure. This section attempts to investigate another three (preliminary optimized) designs of the ARBrace that are intended for providing relatively lower stiffness than those in Section 7 while maintaining a reasonable level of effective damping. To achieve this goal, the connection between every two opposite corners of an AR-Braced panel needs to be weakened. For this purpose, unequal arc/ring thicknesses are used together with the same material of mild steel utilized in earlier sections. However, in order to decide what the variable thickness should be (arc or ring), a stress analysis was carried out, using finite element, to detect the points of greatest flexural stress during deformation in both elements. It is to decide which element is responsible for providing greater damping due to metallic yielding. A diagram of stress vectors of the deformed AR-Brace is shown in Fig. 10. In Fig. 10, it is obvious that the central ring exhibits excessive flexural deformations relative to the four tangential arcs, even taking into account the moment connections at the corners of the arcs, conservatively to flex the arcs’ ends as well. The central ring has four main points that are the most highly stressed. Therefore, it is the element that suffers metallic yielding behavior, even under relatively low deformation. Consequently, in this optimization attempt, three designs are investigated, all have the same arc thickness 1x (equivalent to 25 mm), together with ring thicknesses of 2x , 3x and 4x (equivalent to 50 mm, 75 mm and 100 mm, respectively). Figs. 11–13 show the equivalent outputs to those of the initial phase, Section 7. However, and to enable direct comparison, those outputs of the initial phase in Section 7 are re-plotted, in dashed red lines, together with their corresponding outputs of this optimization phase. The hysteresis loops are shown in sub-figures (a,b,c) of

9. The AR-Brace’s performance under relatively larger input amplitudes In this section, the “optimized” AR-Brace designs are examined under additional input displacements of amplitudes up to nearly three times larger than in earlier sections. The objective is to monitor the output force-deformation relation and the possible variations in both the effective damping and the effective stiffness provided. Fig. 14 shows nine hysteretic force-deformation relations: three for each optimized design under input amplitudes of 35 mm, 50 mm and 65 amplitudes, respectively. The hysteresis loops are nearly similar except in case of the AR-Brace designs (1x /3x ) and (1x /4x ) , which exhibit notable strain hardening that gets larger with both input amplitude and bigger ring thickness. To investigate how the effective stiffness and damping of the ARBrace are affected, see Fig. 15. The trend of effective stiffness seems to increase with increasing ring stiffness. However, it becomes almost unalterable beyond the 3x thickness of the central ring, for all the input displacement amplitudes. On the other hand, the effective damping tendency of the AR-Brace seems to be different with greater input amplitudes. It tends to decrease with greater amplitudes and greater ring thickness. However, the lowest effective damping provided is 25% under 65 mm of input amplitude and ring thickness from 3x . It is worth noting that the strain hardening behavior shown in Fig. 14 (under large input displacement amplitudes) is not related to the bilinear model of elastic-plastic material, as the chosen material model cannot produce such behavior. This stress hardening is attributed solely to a diagonal tensile resistance developed by the AR-Brace under excessive input amplitudes. This resistance appears exclusively when the AR-Braced panel is laterally deformed in excess. At this position, one diagonal of the AR-Brace (connecting the farthest opposite corners of the braced panel) is extremely stretched, while the other diagonal (connecting the other nearest opposite corners) is restrained by the 9

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Fig. 10. Stress vector plot of the AR-Brace.

Element models under synthetic and recorded real dynamic excitations. The structure is a 3-bay frame structure: two edge bays of 6 m span and a central bay of 3.5 m span. The frames are spaced at 5.5 m in the outof-plan direction and have an equal story height of 3.5 m, Fig. 16. The frame is preliminary designed under 20 kN and 15 kN vertical superimposed dead load and live loads, respectively, in addition to lateral wind loads of 2 kN including suction. The small values of design vertical loads were chosen to obtain a relatively slim structure. Then, an extra structural mass was added in the lateral direction to increase the structural flexibility (up to around 40%) in order to assess the ARBrace’s efficiency under conservatively flexible conditions. Table 3 lists the modal periods of the structure before and after increasing its mass, the later structure is the one considered in this study. For comparison,

panel’s own stiffness. This generates an effect similar to an auto-stop or auto-retention behavior due to the appearance of such diagonal tension component, which dominates the horizontal shear of the AR-Braced panel during large deformations. Such behavior did not appear in any of the Figs. 5, 6, 7, 8, 11, 12, or 13 because the shear deformations of the AR-Braced panel has dominated the aforementioned diagonal tension component at relatively smaller input amplitudes. 10. A case study using the AR-Brace To investigate the ability of the AR-Brace to control lateral structural vibration, a 12-story steel frame structure was designed and studied numerically using nonlinear time history analysis and Finite

Fig. 11. 1st Optimization of the AR-Brace (amplitude = 10 mm). 10

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Fig. 12. 1st Optimization of the AR-Brace (amplitude = 15 mm).

• X-Braced:

the Frame structure is investigated considering the following four variations of its central panel, along the entire frame height, Fig. 16:

using traditional rigid metallic cross-braces providing only lateral stiffness. The X-brace’s cross section is a square hollow section SHS200x10, which provides axial stiffness below 20% of those of the structural panel’s columns.

• Unbraced: without using any braces.

Fig. 13. 1st Optimization of the AR-Brace (amplitude = 21.5 mm). 11

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Fig. 14. Larger displacements of 1st optimization of the AR-Brace (amplitudes = 35, 50, 65 mm).

Fig. 15. Corresponding effective stiffness and damping of the larger displacements of 1st optimization of the AR-Brace (amplitudes = 35, 50, 65 mm). 12

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1000 kN, Fig. 17(b). The two synthetic excitations were only applied at the topmost floor level, while the other two real ground motions were applied only as base excitations. The first real ground motion is a horizontal component of the “Friuli” earthquake (Italy, May 06th, 1976), recorded at the Tolmezzo(000) station and contains a frequency range of 0.10–30.0 Hz, Fig. 17(c). The other ground motion is a horizontal component of the “Hollister” (USA, April 09th, 1961), recorded at the USGS Station 1028, while the contained frequency range is 0.11–11.0 Hz, Fig. 17(d). The time histories of a selected four output responses, considering each of the four structural frame variations, are shown in Figs. 18–21 under the four dynamic excitations. Therefore, each figure comprises 12 sub-figures to demonstrate every output against its corresponding one of the unbraced frame variation, which represents the reference of comparison in this study. Those chosen four outputs are: 1. 2. 3. 4.

Relative displacements at the topmost floor, Fig. 18; Absolute accelerations at the topmost floor, Fig. 19; Base shear, at the foundation level, Fig. 20; Vertical tension of the outmost columns, at the foundation level, Fig. 21.

There are two common features among all the sub-figures of Figs. 18–21. The first is having only one response output plotted against the corresponding reference response, besides providing the ratio of the earlier response to the later one as a percentage in blue, above each subfigure. The second feature is always representing the reference response in dashed red line, which represents the case of unbraced frame. As a result, the remaining three cases under comparison are the X-braced frame, AR-braced frame with 10 % damping and the AR-braced frame with 15% damping. Considering the peak relative displacement at the topmost floor, Fig. 18, it seems that the X-braced frame exhibits undesired amplified responses due to the sinusoidal force and the Fruili ground motion with response ratios of 106.64% and 122.33%, respectively, relative to the unbraced case, Fig. 18(a,c). Such behavior becomes gradually better using the AR-brace via increasing effective damping from 10% to 15% to achieve a reduction of the same responses down to 57.64%, Fig. 18(e,i)(g,k). Accordingly, the ratios of the peak response attained using the AR-brace to that obtained using the traditional rigid X-brace are 47% and 60% considering Fig. 18(i,a)(k,c), respectively, which roughly means that the AR-brace behaved nearly two times more efficient than the traditional rigid X-brace in the above cases. Similarly, regarding the structural behavior under pulse force and Hollister ground motion, the rigid X-brace was able to reduce the relative peak displacements of the unbraced frame down to 89.59% and 65.69%, Fig. 18(b,d), respectively. However, those responses were reduced further using the AR-brace down to 65.87% and 48.16%, Fig. 18(j,l),

Fig. 16. The AR-Braced structures in this study.

• AR-Braced 10%: using AR-Braces providing lateral stiffness & 10% of supplemental effective damping. • AR-Braced 15%: using AR-Braces providing lateral stiffness & 15% of supplemental effective damping. The outermost dimensions of the two AR-Brace designs in this section are 2900 mm by 2900 mm. The provided damping percentages were estimated following the same approach in Sections 7–9.

The two AR-braces (providing 10% and 15% damping) were modeled to-scale into the example building structure (i.e. the actual geometry was modeled, see Fig. 16)) in a similar way to that used in Sections 7–9. The X-brace was also implemented by modeling its true geometry to-scale. In other words, all structural components were modeled exactly as they look (material and geometry), then finely meshed and, finally, a non-linear transient dynamic analysis was carried out to obtain the FE-simulated (real) behavior of each of the four structures investigated in this section. Four horizontal dynamic excitations were considered: two synthetic and two real seismic ground motions recorded at different sites. The first synthetic excitation is a sinusoidal harmonic wave of 1 Hz frequency and an amplitude of 1000 kN, Fig. 17(a), whereas the second one is a sinusoidal pulse force of 10 Hz frequency and an amplitude of Table 3 Modal vibration frequencies and periods.

12 Story structure BEFORE increasing mass

AFTER increasing mass

Ratio

Mode No.

Freq. (Hz)

Period (sec)

Mode No.

Freq. (Hz)

Period (sec)

1 2 3 4 5 6 7 8 9 10

0.585 1.797 3.180 4.581 6.083 6.524 7.202 7.717 9.346 9.977

1.711 0.557 0.315 0.218 0.164 0.153 0.139 0.130 0.107 0.100

1 2 3 4 5 6 7 8 9 10

0.414 1.273 2.248 3.231 4.275 4.552 5.154 5.397 6.489 7.520

2.415 0.786 0.445 0.309 0.234 0.220 0.194 0.185 0.154 0.133

13

1.412 1.412 1.414 1.418 1.423 1.433 1.397 1.430 1.440 1.327

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Fig. 17. Input seismic and synthetic excitations.

Fig. 18. HL relative displacement time histories at roof level considering three braced frames against the unbraced one under four different excitations.

accelerations, different acceleration responses at the topmost floor of the AR-braced frame are compared to the unbraced and traditionally Xbraced cases in Fig. 19 considering all the dynamic excitations in this study. Initial global observation of Fig. 19 shows that the maximum response ratio obtained by the rigid X-bracing relative to the unbraced case is 295.93% (Fig. 19(c)), while the lowest ratio is 72.59% (Fig. 19(b)). This means that the structural response was amplified up to three times using traditional rigid braces under Fruili earthquake. On the other hand, the AR-brace with 15% damping has always reduced the structural response of the unbraced case, with a maximum response reduction of 42.76% (Fig. 19a minimum reduction of 62.94%

respectively. As a result, the AR-brace’s is 37% more efficient than the X-brace in these two cases. Although the above efficiency of the ARbrace was attained using a maximum supplemental effective damping of 15% in this study, it is possible to provide more AR-brace’s damping to achieve further response reductions (refer to the parametric investigation of AR-Brace in Sections 7–9). It is to be emphasized that the AR-braced frame exhibited always reduced peak displacement responses relative to the unbraced case, while the traditional rigid Xbrace did not behave desirably in all cases, as it amplified the peak displacement responses in some cases. To investigate the effect of the AR-brace on absolute structural 14

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Fig. 19. HL absolute acceleration time histories at roof level considering three braced frames against the unbraced one under four different excitations.

Fig. 20. Base HL shear time histories at foundation level considering three braced frames against the unbraced one under four different excitations.

15

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Fig. 21. Base VL tension time histories under edge columns considering three braced frames against the unbraced one under four different excitations.

• The

(Fig. 19hly, this demonstrates that the AR-brace performed up to six times more efficient than traditional bracing system of frame structures (in the case of Fruili ground motion). Under Hollister ground motion, the AR-brace was around five times more efficient than the traditional X-brace, while it was two times more efficient in case of sinusoidal force, and around 30% more efficient under the pulse force. In a similar way, the influence on the structural base shear was investigated in Fig. 20 considering three braced frames against the unbraced one under four different excitations. Due to adding only lateral rigidity, the traditional X-brace has amplified the base shear under three excitations out of four with a maximum amplification percentage of 146.98%, Fig. 20(c). The second thing to consider is the AR-Brace’s ability to mitigate nearly 60% of the base shear under synthetic pulse load, Fig. 20(j), and notable mitigation in the rest of cases. The effect of the AR-Brace was found also positive on improving the lateral structural equilibrium as well as reducing the cost of foundation needed to resist vertical uplift at extreme supports due to overturning moments under lateral dynamic excitations. Fig. 21 shows the time histories of the developed vertical tensions at the outermost supports due to different dynamic excitations. The lower the developed vertical tension the more stable the structure and the less demanding the foundation will be. The traditional X-brace seems to be an improper choice in this case due to amplifying the responses in 75% of the cases with undesirable response boost beyond two times in case of Fruili ground motion relative to the unbraced case, Fig. 21(c). On the other side, the AR-Brace has reasonably reduced the vertical tension in most cases, with a maximum mitigation of such tension close to 40% in case of Hollister ground motion, Fig. 21(l). The impact of such tension reduction is almost direct on the foundation cost, either it is of deep foundation type (tension piles under outermost columns) or of shallow type with sufficient counter weight to counteract that developed vertical tension. To summarize, the main results of present case study could be highlighted in few points:

• • •

AR-Brace is an economical metallic yield system of uncomplicated design but rich in providing broad ranges of rigidity and supplementary damping to control structural vibration and the vibration-dependent responses that arise. The AR-Brace is able to reduce structural responses due to synthetic dynamic forces as well as real ground motion excitations, even at moderate provided levels of effective supplemental damping. The AR-Brace could be the appropriate substitute of the traditional rigid X-braces in order to achieve a good balance between the added rigidity and the provided supplemental damping that results in notable vibration control and mitigation of undesired effects of dynamic excitations. The AR-Brace’s design is scalable in size and of (passively) adaptable stiffness/damping outputs to suite needs.

11. Conclusions A new elastoplastic bracing system called AR-Brace is designed and introduced in this paper for passive control of structural vibration. It consists of five deformable elastoplastic components, which are four arcs in tangential contact with a central ring. The AR-Brace has been designed to be an efficient and economic replacement of traditional cross-bracing systems, besides being a good alternative to both displacement-based and velocity-based damping systems. It is characterized by a simple design that is rich in providing broad ranges of stiffness and supplementary damping to control efficiently the structural vibration and vibration-dependent responses. In this paper, the proposed system was mechanically characterized by finite element simulations and the resulting force displacement relationships were modeled using the Bouc-Wen hysteresis model. An extensive parametric study of the AR-Brace hysteresis was then carried out to evaluate the energy absorption capacity of the device taking into account several design variations and different harmonic excitations. Finally, the ability of the ARBrace to control structural vibration and other vibration-dependent 16

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responses was investigated through a series of case studies under synthetic and real dynamics excitations. The AR-Brace was found capable of reducing all the considered structural responses either caused by synthetic dynamic forces or by real ground motion excitations, even at moderate levels of effective supplementary damping, because the ARBrace achieves a good balance between the added lateral stiffness and the provided supplementary damping, which resulted in remarkable vibration control and significant mitigation of unwanted effects of the dynamic excitations. Therefore, the AR-Brace could be an efficient and economical substitute for traditional vibration-damping systems, besides being an appropriate tool where efficient mitigation and control of structural vibration are needed at low cost.

[14] Ismail M, Casas J, Rodellar J. Near-fault isolation of cable-stayed bridges using RNC isolator. Eng Struct 2013;56:327–42. [15] Ismail M. An isolation system for limited seismic gaps in near-fault zones. Earthquake Eng Struct Dynam 2014;44(7):1115–37. [16] Chernyshev V, Fominova O. Control of damping process in system of vibration isolation. ICIE 2018: proceedings of the 4th international conference on industrial engineering. 2018. p. 341–9. [17] Bergman DM, Goel SC. Evaluation of cyclic testing of steel-plate devices for added damping and stiffness. Tech. Rep.; UMCE 87-10, The University of Michigan, Ann Arbor, MI.; 1987. [18] Whittaker AS, Bertero VV, Thompson CL, Alonso LJ. Seismic testing of steel plate energy dissipation devices. Earthquake Spectra 1991;7(4):563–604. [19] Xia C, Hanson RD, Wight JK. A study of adas element parameters and their influence on earthquake response building structures. Report UMCE 90-12, The University of Michigan, Michigan; 1990. [20] Tsai KC, Chen HW, Hong CP, Su YF. Design of steel triangular plate energy absorbers for seismic-resistant construction. Earthquake Spectra 1993;9(3):505–28. [21] Martinez-Romero E. Experiences on the use of supplemental energy dissipators on building structures. Earthquake Spectra 1993;9(3):581–625. [22] Kimura K, Takeda Y, Yoshioka K, Furuya N, Takemoto Y. An experimental study on braces encased in steel tube and mortar. In: Proceedings of the annual meeting of the Architectural Institute of Japan, Japan; 1976. [23] Black CJ, Makris N, Aiken ID. Component testing, seismic evaluation and characterization of buckling-restrained braces. J Struct Eng, ASCE 2004;130(6):880–94. [24] Jouneghani H, Haghollahi A, Moghaddam H, Moghadam A. Study of the seismic performance of steel frames in the elliptic bracing. J Vibroengineering 2016;18(5):2974–85. [25] Boostani M, Rezaifar O, Gholhaki M. Seismic performance investigation of new lateral bracing system called ”ogrid-h”. SN Appl Sci 2019. https://doi.org/10.1007/ s42452-019-0369-8. [26] Di Sarno L, Manfredi G. Seismic retrofitting with buckling restrained braces: application to an existing non-ductile rc framed building. Soil Dynam Earthquake Eng 2010;30(11):1279–97. [27] De Domenico D, Impollonia N, Ricciardi G. Seismic retrofitting of confined masonry-rc buildings: the case study of the university hall of residence in messina, italy. Ingegneria Sismica 2019;36(1):54–85. [28] Mahmoodi P. Structural dampers. Tech. Rep.; Vibration control system, Construction Market, Engineering Materials 3 M Industrial Specialties Division; 1969. [29] Samali B, Kwok KSC. Use of viscoelastic dampers in reducing wind- and earthquakeinduced motion of building structures. Eng Struct 1995;17(9):639–54. [30] Schwahn KJ, Delinic K. Verification of the reduction of structural vibrations by means of viscous dampers. In: Seismic engineering, ASME, pressure vessel and piping conference, Pittsburgh, PA, vol. 144; 1988. p. 87–95. [31] Miyazaki M, Mitsusaka Y. Design of a building with 20% or greater damping. Tenth World Conf Earthquake Engineering, Madrid; 1992. [32] Constantinou MC, Symans M, Tsopelas P, Taylor DP. Fluid viscous dampers in applications of seismic energy dissipation and seismic isolation. In: Proceedings of ATC 17–1 on seismic isolation, energy dissipation and active control, vol. 2; 1993. p. 581–91. [33] Martinez-Rodrigo M, Romero M. An optimum retrofit strategy for moment resisting frames with nonlinear viscous dampers for seismic applications. Eng Struct 2003;25:913–25. [34] Oesterle MG. Use of incremental dynamic analysis approach to assess the performance of moment-resisting-frames with fluid viscous dampers. MSC thesis. Virginia Tech 2003. [35] Chang KC, Soong TT, Oh ST, Lai ML. Seismic response of 2/5 scale steel structure with added viscoelastic dampers. Tech. Rep.; NCEER-91-0012, National Center of Earthquake Engineering Research, Buffalo, NY; 1991. [36] Munshi J. Effect of viscoelastic dampers on hysteretic response of reinforced concrete elements. Eng Struct 1997;19(11):921–35. [37] Fu Y, Kasai K. Comparative study of frames using viscoelastic and viscous dampers. J Struct Eng, ASCE 1998;124(5):513–22. [38] De Domenico D, Ricciardi G, Takewaki I. Design strategies of viscous dampers for seismic protection of building structures: a review. Soil Dynam Earthquake Eng 2019. [39] Wen Y. Method for random vibration of hysteretic systems. J Eng Mech Division 1976;102(EM2):246–63. [40] Ismail M, Ikhouane F, Rodellar J. The hysteresis Bouc-Wen model, a survey. J Arch Comput Meth Eng 2009;16:161–88. [41] Ikhouane F, Mañosa V, Rodellar J. Dynamic properties of the hysteretic Bouc-Wen model. Syst Control Lett 2007;56:197–205.

12. Future study At least two future publications on the proposed new AR-Brace are to be planned to address some fundamental issues including: (1) a simplified design methodology based on a wider parametric investigations to define and formulate the main design parameters into handy mathematical expressions; (2) a profound efficiency assessment considering many real records of seismic and wind events into various case studies; (3) experimental validation of the obtained numerical results together with the validation of the (to be) deduced design methodology of the new proposal; and (4) direct comparison between the proposed new AR-Brace and similar existing devices, including displacement- and velocity-dependent devices. The comparison will address different issues related to behavior, applicability ranges, versatility, …etc. Declaration of Competing Interest The authors declared that there is no conflict of interest. References [1] Kelly J, Skinner R, Heine A. Mechanisms of energy absorption in special devices for use in earthquake resistant structures. Bull New Zealand Natl Soc Earthquake Eng 1972;5:78–89. [2] Skinner R, Kelly J, Heine A. Hysteretic dampers for earthquake resistant structures. Earthquake Eng Struct Dynam 1975;3:287–96. [3] Leger P, Dussault S. Seismic-energy dissipation in MDOF structures. J Struct Eng ASCE 1992;118(5):1251–69. [4] Soong T, Constantinou M. Passive and active structural vibration control in civil engineering. Wien: Springer; 1994. [5] Ali H, Abdel-Ghaffar A. Seismic passive control of cablestayed bridges. Shock Vib 1995;2(4):259–72. [6] Symans M, Constantinou M. Semi-active control systems for seismic protection of structures: a state-of-the-art review. Eng Struct 1999;21(6):469–87. [7] Carmen H, Yunpeng Z, Zi-Qiang L, Stephen AB, Masayuki K, Shizuka W. Nonlinear damping based semi-active building isolation system. J Sound Vib 2018;424:302–17. [8] Bozorgnia Y, Bertero V. Earthquake engineering: from engineering seismology to performance-based engineering. CRC Press LLC; 2004 Chapter 11, Seismic Isolation, Kelly J.M. [9] Erkus B, Abé M, Fujino Y. Investigation of semi-active control for seismic protection of elevated highway bridges. Eng Struct 2002;24:281–93. [10] Warn G, Whittaker A. Performance estimates in seismically isolated bridge structures. Eng Struct 2004;26(9):1261–78. [11] Ismail M, Rodellar J, Ikhouane F. An innovative isolation device for aseismic design. J Eng Struct 2010;32:1168–83. [12] Ismail M, Rodellar J, Ikhouane F. An innovative isolation bearing for motion-sensitive equipment. J Sound Vib 2009;326(3–5):503–21. [13] Ismail M, Rodellar J, Ikhouane F. Seismic protection of low- to moderate-mass buildings using rnc isolator. Struct Control Health Monitor 2012;19:22–42.

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