A high four-tower structure is interconnected with a long sky corridor bridge on the top floor. To reduce the earthquake responses and member forces of the towers and sky corridor bridge, a passive control strategy with a friction pendulum tuned mass damper (FPTMD) was adopted. The sky corridor bridge was as the mass of FPTMD. The connection between the towers and the sky corridor bridge was designed as flexible links, where friction pendulum bearings (FPBs) and viscous dampers were installed. Elastoplastic time-history analysis was conducted by using Perform-3D model to look into its seismic behavior under intensive seismic excitation. The optimal design of the FPTMD with varying friction coefficients and radius of friction pendulum bearing (FPB) under seismic excitations was carried out, and the seismic behavior of the structure was also investigated at the same time.Results show that, for this four-tower connected structure, the friction pendulum tuned mass damper (FPTMD) has very well effect on seismic reduction. The structure can meet the seismic resistance design requirements.
Nowadays, when building a high-rise building, height is not the only pursuit. More unique forms are used to show the rich connotation and vitality of buildings. Connected structures conform to these requirements, and many connected structures in varied forms have been or are being built in recent years. Most of them are urban landmark buildings and the symbol of economic and social development. In the early days, most connected tower structures were symmetrical. Recently, however, more and more asymmetric connection towers have emerged. The types of the connection between corridor and building can be classified as rigid connection and flexible or weak connection. With rigid connection, corridors are totally constrained by towers. In order to coordinate the displacement between different towers, corridors are, normally, connected to core tube or shear wall of the primary structure. Rigid connection was used in most of the connected structures, such as La Defense Arch (110 m high), Pairs; Bocom Financial Towers (235 m high), Shanghai; CCTV main building (234 m high), Beijing; and Marina Bay Sands, Singapore (198 m high). When the flexible connection is adopted, the corridors are allowed to move relative to the primary structure. Furthermore, some damping devices may be set between the corridors and the primary towers to reduce vibration, such as Petronas Twin Towers (452 m high), Kuala Lumpur, and Museum of Modern Art, Beijing. The irregularity and complexity of structures are inevitable for these special buildings. It is very important to set reasonable seismic performance goals and carry out structural analysis in detail. Lu et al. [
In order to reduce the seismic response or the interaction in different parts of the connected structure, seismic energy dissipation technology was applied in this type of structure gradually. Bhaskararao and Jangid [
While it has a long history for TMD used in wind vibration control for high-rise building, TMD has also been applied to structural earthquake resistance. Huber [
Friction pendulum bearings are sliding devices that utilize a spherical surface to provide a restoring force and friction to dissipate energy. It has been used for base isolation of buildings and seismic protection of bridges. Mosqueda et al. [
When the tuned mass damper (TMD) frequency is tuned to the fundamental frequency near the primary structure, the energy of the structure vibration will be transferred to TMD. The damper of the TMD can also dissipate the transferred energy from the structure excited by earthquake. In this paper, in order to reduce the earthquake responses of a high four-tower structure connected with a long sky corridor bridge on the top floor, a passive control strategy with a friction pendulum tuned mass damper (FPTMD) was adopted. The mass of sky corridor bridge and the load on it was taken as the mass of TMD. Friction pendulum bearings (FPBs) were used as springs and dampers of TMD. The mass of the sky corridor bridge and the load on it, which belonged to the primary structure originally, were turned to be the mass of the TMD. With the control strategy, not only the mass was reduced from the primary structure but also the additional mass for TMD could be omitted. Consequently, structural safety under earthquake can be improved. The finite element analysis models of this building were developed by using NosaCAD, which was used to form nonlinear finite element analysis models for Perform-3D. The two pieces of nonlinear structural analysis software have been widely used in structural analysis [
Chongqing Raffles City (Figure
Perspective view of the buildings.
The layout of the towers.
In South Towers, the connected building (Figure
Structure elevation.
Structural plan layout of the towers and the sky corridor bridge.
Plan layout of the FPB and viscous damper on the top of towers.
According to the Chinese Code for Seismic Design of Building (CSDB, GB50011-2010) [ The height of these towers is beyond the specified maximum height of 220 m for SRC frame and RC core tube system. And the height-width ratio of these towers both exceeds the limitation ruled in the TSCSTB of 7. The ratios of the maximum horizontal displacement to the average horizontal displacement in T2, T4S, and T5 towers are 1.38, and the ratio in T3S tower is 1.30. According to the TSCSTB, if the ratio exceeds 1.2, the structure belongs to torsion irregular structure. A few floors of the towers draw back more than 4 meters, so the towers belong to vertical irregular structure according to the TSCSTB.
In elastoplastic analysis, characteristic values were adopted for the strength of materials. Concrete C30 was adopted for plates and beams, and C60 was adopted for the core tube wall and the frame tube column. The normal rebar was employed with HPB235, HPB335, and HRB400, and profile steel was employed with Q345B.
The bilinear and trilinear moment-curvature hysteretic models were adopted for the elastoplastic segments of steel beams, concrete beams, and steel-reinforced concrete beams, respectively, and the fiber model was employed to describe the nonlinear behavior for the frame columns and braces. The frame member consisted of three components, one in middle was linear elastic and the others at two ends were elastoplastic.
Macrolayered element was adopted to simulate the shear wall component. One-dimensional fiber element is used for simulating the compression-bending effect, while using nonlinear or linear shear model for the shear effect in plane and elastic model for the bending, shear, and torsion effect out of plane.
The intent of the Perform-3D action-deformation relationship, with points Y, U, L, and R, is to catch the main characters of the material behavior, namely, the initial stiffness, strain hardening, ultimate strength, and strength loss [
Main aspects of inelastic behavior in Perform-3D [
Steel constitutive model with bulking or nonbulking is available in Perform-3D. Nonbulking steel model was applied for reinforcement. Concrete constitutive model with Mander stress-strain relationship should be transferred in the action-deformation relationship of Perform-3D, which can be determined by 5 parameters, and strength loss was taken into account. The moment-curvature hysteretic relationship for the frame element section was also defined by the action-deformation relationship of Perform-3D, which can be determined by 3 parameters or 5 parameters.
As known that energy can be dissipated by the nonlinear component under cyclic loading, and the amount of the dissipated energy can be represented by the area of hysteretic loop. In Perform-3D, parameters of energy degradation are determined by the maximum deformation and can be specified optionally (Figure
Hysteretic loop of energy degradation.
Degradation coefficients of concrete.
The friction-pendulum isolator element is shown in Figure
Friction pendulum element.
Behavior of friction-pendulum element.
The sliding stiffness or hardening stiffness is equal to the current bearing axial force divided by the radius of the slip surface. The restoring shear force can be
Maxwell model was adopted for viscous bar element. The viscous bar element consists of two components, which are linear elastic bar and fluid damper, respectively. The fluid damper component has no elastic stiffness. Its relationship between axial force and axial deformation rate can be
The structural model was established by NosaCAD (Figure
NosaCAD model.
Perform-3D model.
In general, when the structure encounters the earthquake, static load such as gravity and service load has already acted on the structure. Therefore, prior to the nonlinear dynamic time-history analysis, a nonlinear static analysis was performed to obtain the initial stress state in structure members, which served as the initial state of nonlinear dynamic analysis. Meanwhile, a modal analysis was conducted to get the natural vibration characteristics of the structure. Then, the optimal design of the FPTMD with varying friction coefficients and radius of friction pendulum under seismic excitations was carried out. The overall seismic responses and the effect of seismic reduction of the structure were also investigated as well.
To verify the accuracy of the model transformation from NosaCAD to Perform-3D, an initial judgment was made on the fundamental dynamic characteristic of the structure. The first three periods and vibration mode shapes obtained from NosaCAD and Perform-3D are listed and shown in Table
Natural vibration characteristic.
Number | Period (s) | Description | |
---|---|---|---|
NosaCAD | Perform-3D | ||
1 | 5.791 | 5.740 | Translation in direction |
2 | 3.880 | 3.845 | Translation in direction |
3 | 3.596 | 3.555 | Torsion |
The first three vibration modes: (a) 1st vibration mode, (b) 2nd vibration mode, and (c) 3rd vibration mode.
According to the CSDB, the site soil in this project belongs to type III, which is defined that the overlaying thickness of the site soil is more than 50 m and the average velocity of shear wave in the soil layer is between 150 m/s and 250 m/s, or the thickness is between 15 m and 80 m and the average velocity of shear wave is not more than 150 m/s. It is specified in the TSCSTB that no less than two earthquake records and a synthetic accelerogram should be selected for elastoplastic time-history analysis. According to the power spectral density properties of type III site soil, three different ground motions were chosen as ground input accelerations to the model: (a) the L0689 series record; (b) the L0223 series record; and (c) the L6501 series record, which is formed artificially according to the CSDB. The parameters of the three records are shown in Table
Parameters of the earthquake records.
Label of the record | Component | Label of the direction | Recoding time interval (s) | Recording time (s) |
---|---|---|---|---|
L0689S | L0689 | Primary | 0.02 | 40 |
L0688 | Secondary | |||
L0690 | Vertical | |||
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L0223S | L0223 | Primary | 0.02 | 40 |
L0224 | Secondary | |||
L0225 | Vertical | |||
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L6501S | L6501 | Primary | 0.02 | 40 |
L6502 | Secondary | |||
L6503 | Vertical |
L0689 series accelerogram. Time history of acceleration in (a) secondary direction (L0688), (b) primary direction (L0689), and (c) vertical direction (L0690). (d) Response spectrums compared with the design spectrum in CSDB.
According to the CSDB, buildings in seismic regions should be designed to sustain earthquakes of frequent, moderate, and rare levels, which correspond to 63.2%, 10%, and 2% probability of being exceeded in 50 years, and return period of 50, 475, and about 2475 years, respectively. That is to say, when buildings are designed to be subjected to the influence of frequently occurring earthquakes with an intensity of less than the design intensity, the buildings will not be damaged, or will be only slightly damaged and will continue to be serviceable without repair; when they are subjected to the influence of earthquakes equal to the design intensity, they may be damaged but will still be serviceable after ordinary repair or without repair; when they are subjected to the influence of expected rare earthquakes with an intensity higher than the design intensity, they will neither collapse nor suffer damage that would endanger human lives. According to earthquake safety assessment, the peak ground accelerations (PGA) corresponding to the earthquakes of minor, moderate, and major levels are specified to be 0.027, 0.075, and 0.175 g, respectively.
Since seismic reduction performance under rare earthquake was mainly investigated in this paper, the peak ground acceleration (PGA) of the selected earthquake accelerograms was scaled to 0.175 g, corresponding to earthquakes of major levels. During the analysis, the three earthquake records were inputted in three principal directions simultaneously (direction X, Y, and Z in Figures
As specified by the TSCSTB, a damping ratio of 0.04 for SRC frame-RC core wall structure system was adopted, and Rayleigh damping was used in integration equation.
In order to achieve maximum vibration reduction for the structure, the design parameters of the FPTMD should be optimized. Usually, the minimum structural responses under earthquake are used as the optimization target. In this paper, the displacement responses of the top floor of the 4 towers were taken as the basis for the optimization of the parameters. When the frequency of a tuned mass damper (TMD) is tuned to be close to the fundamental frequency of the primary structure, the dynamic energy will be transferred to the TMD. However, there are more vibration modes participating in seismic response in the high-rise building structure, and the damage in the structure will also cause a change in the structural dynamic characteristics, so it is not suitable to simply set the frequency of FPTMD to the frequency of the first mode of the primary structure. The determination of FPS parameters needs to be searched by a series of calculations. The relationship between the pendulum period of the FPS and the radius of curvature of the spherical surface is as follows:
According to formula (
The relationship between the periods of FPTMD and the radii of curvature of the FPB spherical surface.
|
|
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3000 | 3.476 |
3500 | 3.755 |
4000 | 4.014 |
4500 | 4.258 |
5000 | 4.488 |
6000 | 4.916 |
By the elastoplastic time-history analysis of the structure which has been installed with FPBs with different radii and friction coefficients between tower and sky corridor bridge, the maximum displacement responses of the top of the towers T2 and T4S under different seismic load cases are shown in Figures
The maximum top displacement of T2 tower with
The maximum top displacement of T2 tower with
The maximum top displacement of T2 tower with
The maximum top displacement of T2 tower with
The maximum top displacement of T2 tower with
The maximum top displacement of T2 tower with
The maximum top displacement of T4S tower with
The maximum top displacement of T4S tower with
The maximum drift of T4 tower with
The maximum drift of T4S tower with
The maximum top displacement of T4S tower with
The maximum top displacement of T4S tower with
Although FPS has its own energy dissipation capacity, in order to prevent its sliding displacement too large to exceed the design limit, viscous dampers are set in FPTMD as shown in Figure
The maximum top displacement of T2 tower with FPBs (
The maximum top displacement of T2 tower with FPBs (
The maximum top displacement of T4S tower with FPBs (
The maximum top displacement of T4S tower with FPBs (
The trace of the shear force to sliding displacement of FPB No. 15 in the X and Y direction under L0689S wave is shown in Figures
The trace of the shear force to sliding displacement of FPB15 (Figure
The trace of the shear force to sliding displacement of FPB15 (Figure
The trace of the axial force to axial deformation of damper D9 under L0689S wave.
The trace of the axial force to axial deformation of damper D10 under L0689S wave.
Since the effect of seismic reduction is close to the best when the radius of the curvature of the FPB spherical surface parameters is taken as 4500 mm and friction coefficient of the FPB is 0.02, the damper exponent is equal to 0.3 and the viscous damping coefficient is equal to 100 kN/mm/s, and the comparison of the structure seismic responses between the model having FPS with aforementioned parameters and the model having no FPS was carried out as follows.
The comparison of the maximum interstory drift of the structure with and without FPS is shown in Table
Maximum interstory drift of the structure.
Wave | Tower | X direction (rad) | Y direction (rad) | ||||
---|---|---|---|---|---|---|---|
No FPS and no damper | With FPS and damper | Reduction rate (%) | No FPS and no damper | With FPS and damper | Reduction rate (%) | ||
L0689S | T2 | 1/183 | 1/257 | 28.79 | 1/252 | 1/331 | 23.87 |
T3S | 1/176 | 1/246 | 28.46 | 1/223 | 1/318 | 29.87 | |
T4S | 1/167 | 1/230 | 27.39 | 1/232 | 1/333 | 30.33 | |
T5 | 1/192 | 1/251 | 23.51 | 1/287 | 1/379 | 24.27 | |
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L0223S | T2 | 1/325 | 1/385 | 14.92 | 1/342 | 1/423 | 19.15 |
T3S | 1/317 | 1/367 | 13.62 | 1/328 | 1/395 | 16.96 | |
T4S | 1/303 | 1/352 | 13.92 | 1/349 | 1/419 | 16.71 | |
T5 | 1/299 | 1/388 | 22.94 | 1/354 | 1/413 | 14.29 | |
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L6501S | T2 | 1/275 | 1/335 | 17.91 | 1/345 | 1/424 | 18.63 |
T3S | 1/270 | 1/337 | 19.88 | 1/367 | 1/443 | 17.16 | |
T4S | 1/281 | 1/324 | 13.27 | 1/344 | 1/401 | 14.21 | |
T5 | 1/261 | 1/319 | 18.18 | 1/357 | 1/429 | 16.78 |
Interstory drift of T2 tower in the X direction under L0689S wave.
Interstory drift of T2 tower in the Y direction under L0689S wave.
Interstory drift of T4S tower in the X direction under L0689S wave.
Interstory drift of T4S tower in the Y direction under L0689S wave.
The comparison of the maximum absolute acceleration on the top of the towers with and without FPS is shown in Table
Maximum absolute acceleration on the top of the towers.
Wave | Tower | X direction (mm/s2) | Y direction (mm/s2) | ||||
---|---|---|---|---|---|---|---|
No FPS and no damper | With FPS and damper | Reduction rate (%) | No FPS and no damper | With FPS and damper | Reduction rate (%) | ||
L0689S | T2 | 3366.8 | 2759.5 | 18.04 | 2557.8 | 2359.3 | 7.76 |
T3S | 3251.2 | 2572.2 | 20.88 | 2512.6 | 2306.8 | 8.19 | |
T4S | 3184.8 | 2551.7 | 19.88 | 2224.6 | 2218.3 | 0.28 | |
T5 | 3007.1 | 2624.7 | 12.72 | 2167.5 | 2120.1 | 2.19 | |
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L0223S | T2 | 3428.7 | 2993.7 | 12.69 | 2200.0 | 2024.9 | 7.96 |
T3S | 3147.7 | 2965.3 | 5.79 | 2451.7 | 2102.3 | 14.25 | |
T4S | 3272.3 | 2805.5 | 14.27 | 2314.1 | 2160.0 | 6.66 | |
T5 | 3397.3 | 2840.7 | 16.38 | 2437.4 | 2275.8 | 6.63 | |
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L6501S | T2 | 2955.6 | 2682.3 | 9.25 | 2125.4 | 2050.3 | 3.53 |
T3S | 2844.2 | 2664.7 | 6.31 | 2308.9 | 2125.5 | 7.94 | |
T4S | 2862.9 | 2649.2 | 7.46 | 2296.7 | 2130.5 | 7.24 | |
T5 | 3067.5 | 2737.4 | 10.76 | 2339.1 | 2194.2 | 6.19 |
Figures
Damage patterns under L0689S wave (no PFS and no damper). (a) Beam yielding. (b) Column yielding.
Damage patterns under L0689S wave (FPS and damper). (a) Beam yielding. (b) Column yielding.
The base shear forces of the sky corridor bridge acting on the top of T4S tower in the X and Y direction under L0689S wave are shown in Figures
The base shear of the sky corridor bridge acting on the top of T4S tower in the X direction under L0689S wave.
The base shear of the sky corridor bridge acting on the top of T4S tower in the Y direction under L0689S wave.
The time history of the energy distribution in the structure with or without FPS and viscous damper under L0689S wave are shown in Figures
The time history of the energy distribution in the structure under L0689S wave (no FPS and no damper).
The time history of the energy distribution in the structure under L0689S wave (FPS and damper).
The rate of the FPS energy dissipation in the total nonlinear energy dissipation under L0689S wave (FPS and damper).
The amount of the energy dissipation by the viscous damper was relatively small (Figure
In order to reduce the earthquake responses and the member forces of a connected multitower structure, a passive control strategy with a friction pendulum tuned mass damper (FPTMD) was employed. Based on the analytical results, conclusions can be drawn as follows: The friction pendulum tuned mass damper (FPTMD) composed of friction pendulum bearing, viscous damper, and sky corridor bridge can effectively reduce the seismic response of the structure, including deformation of the structure and damage extent of the structure members. In theory, when the frequency of a tuned mass damper (TMD) is tuned to be close to the fundamental frequency of the primary structure, the effect of seismic reduction will be the best. However, there are many factors that affect the effect of seismic reduction, such as more vibration modes of the primary structure participating in earthquake response, damping leads the FPTMD frequency change, and the damage of structure causes the change of the dynamic property of the primary structure. Therefore, it is unsuitable to simply set the frequency of FPTMD to the frequency of the first mode of the tower. The determination of FPS parameters needs to be searched by a series of calculations to reach the better effect of seismic reduction2. When the sky corridor bridge and towers are rigidly connected, the relative displacement among the towers caused by the earthquake will lead to larger interaction force between sky corridor bridge and towers. The isolation device set between the bridge and the towers can reduce the interaction remarkably, and the members of the sky corridor bridge can keep in elastic state even under the action of large earthquake. Compared with the friction pendulum, the viscous damper has less energy dissipation. However, the viscous damper can reduce the horizontal slip displacement of the friction pendulum and limit the slip displacement within the design value. Neither columns nor walls reached the ultimate state. The structure meets the requirement in Chinese Design Codes of “no collapse under rare earthquake.” In addition to that, the deformation of the structure stays inside the limitation stipulated in Chinese Design Codes as well.
The written data used to support the findings of this study are included within the article. The digital data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors are grateful for the financial support received from Scientific Research Program of Shanghai Science and Technology Committee (Grant no. 17DZ1203200).