Effectiveness of Damping Devices on Coupling Beams of 15-story Building Based on Nonlinear Analysis Procedures
Galih Permana1*, Yuskar Lase1
1 Civil Engineering, Universitas Indonesia, Depok, Indonesia
*Corresponding Author: [email protected] Accepted: 15 December 2021 | Published: 31 December 2021
DOI:https://doi.org/10.55057/ijarei.2021.3.4.8
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Abstract: In recent years, damping device has been experimentally studied to replace diagonally reinforced coupling beams, to mitigate rebar congestion problem. This study focuses on evaluating the effectiveness of various damping devices in a high-rise building. Type of damping devices evaluated are Viscoelastic Damper (VCD) and Rotational Friction Damper (RFD), with study case of a 15-story reinforced concrete apartment building with a dual system (column-beam and shear walls). The analysis used is a nonlinear time history analysis with 11 pairs of ground motions matched to the Indonesian response spectrum based on ASCE 41-17 and ASCE 7-16. In this analysis, each damper will be varied with a different position, namely the first model, the damper will be installed on the entire floor and in the second model, the damper will be installed on the 5th floor to the 9th floor, which is the floor with the largest drift. The results show that the model using both dampers increase the level of structural performance globally and locally in the building, reducing the level of damage to the structural elements. But between the two dampers, the coupling beam that uses RFD is more effective than using VCD in improving building performance. The damper on the coupling beam has a good role in dissipating earthquakes and in terms of ease of installation.
Keywords: building, coupling beam, damper, nonlinear time history analysis
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1. Introduction
Earthquake-resistant buildings must be specially designed to minimize damage during an earthquake and at least not collapse while evacuating for occupants of the building. To minimize the damage, the strength and the stiffness of the building are the things that have an essential role. Based on the performance level of the building, it is explained that the building is allowed to get damage to certain elements (NIST, 2009). The structural elements that are permitted to be damaged are usually the beam elements. In high-rise buildings with earthquake- resistant elements using shear wall with coupling beams, if an earthquake occurs, it is expected that the most severe damage will happen to the coupling beam. The coupling beams have a function as a fuse member, which is an element that is expected to experience an inelastic phase first compared to other elements and become an energy dissipation element (Shoeibi, Kafi, &
Gholhaki, 2017). Ideally, this element can be replaced with a new one after the earthquake occurs if it is damaged; on the one hand, the other elements are still in an elastic phase condition. After changing these elements, the building can work according to the initial design plan. Based on the Indonesian Code, SNI 2847 (ACI 318), if the ratio of length and height is less than 2, the conventional concrete coupling beam must be reinforced with two intersecting groups of reinforcing bars placed diagonally symmetrically to the centre of the span (Badan
Standarisasi Nasional, 2019). Detailing of a coupling beam that is stated by the code is relatively difficult to do during construction because of the congestion of the reinforcement (Breña & Ihtiyar, 2011). This is also a consideration if the diagonally concrete coupling beam must be replaced after the earthquake occurs; it will not be easy. Based on this, the author tries to find another alternative to replace the diagonally concrete coupling beam by using a dissipation device RFD (Rotational Friction Damper) and VCD (Viscoelastic Damper).
2. Literature Review
2.1. Coupling Beam
The limitation of the diagonal reinforcement ratio in the coupling beam is based on the ratio of length to height (ln/h) and the shear ratio of the coupling beam (NIST, 2012), which can be seen in Figure 1.
Figure 1: Ratio of Coupling Beam Dimension and Shear Source: (NIST, 2012)
From the graph above, it consists of requirements for detailing that must be met if ratio ln/h <
2, 2 < ln/h < 4, ln/h > 4, and shear ratio to the capacity of the coupling beam, where diagonal reinforcement must be used when ratio ln/h < 2 and shear ratio of the coupling beam is greater than or equal to 4 (in MKS units). In the transition area, namely the ratio 2 < ln/h < 4, you can use ordinary or diagonal beam reinforcement, but it is advisable to continue using diagonal reinforcement because it is more stable when an earthquake occurs (Wight, 2016).
In 2000, the use of a new friction damper emerged, where the friction damper did not use a slotted type like the previous friction damper but instead used a rotating shaft which was called a Rotational Friction Damper (RFD), the results of which showed that the damper component produces a stable hysteresis curve and the ease of replacing the damper when it is plastic (Mualla, 2000).
The use of Viscoelastic Damper on coupling beam elements also shows good results regarding beam ductility compared to conventional coupling beams and provides damping in all lateral vibration modes (Montgomery & Christopoulos, 2015)
2.2. Damping Devices
Based on ASCE 41-17, the dissipation devices are divided into displacement-dependent devices and velocity-dependent devices. Displacement dependent device is a dissipation device where the dissipated energy is a function of the force and the relative displacement between the two ends of the device. In comparison, the velocity-dependent device is a dissipation device where the dissipated energy is a function of the relative velocity (excitation frequency) at both ends of the device (ASCE/SEI, 2017a). Examples of displacement-dependent devices are
friction dampers, while velocity-dependent devices are solid and fluid viscoelastic dampers. In simple terms, the relationship between force, displacement, and damping can be described in Figure 2.
Figure 2: Idealization of Dissipation Device Response Source: (NIST, 2012)
3. Methodology
3.1. Building Data
The building used in this analysis is a 15-story building with a dual system consisting of column-beams (Special Moment Frame) and special concrete shear walls. The description of the floor plan of the building to be analyzed can be seen in Figure 3, while the overall function of this building is an office building (SIDL = 1.5 kN/m2, LL = 2.4 kN/m2) and on the roof floor, there is an MEP load (SIDL = 2 kN/m2, LL = 4.79 kN/m2) and roof load (SIDL = 2 kN/m2, LL
= 2 kN/m2). The dimensions of the structural elements used in this building can be seen in Table 1.
Figure 3: Typical Floor Plan
Table 1: Properties of Elements
Element f'c (MPa) fy (MPa)
Fl. 2 s/d 5 - 950/950 Fl. 6 s/d 10 - 900/900 Fl. 11 s/d Roof - 850/850
Fl. 2 s/d 5 - 850/850 Fl. 6 s/d 10 - 800/800 Fl. 11 s/d Roof - 750/750
Shearwall 35 420
Coupling Beam 35 420
Slab 30 420
t = 400 b = 400, h = 1600, L =1500 primary - 400x800~500x950 secondary - 300x500~350x650
t = 130 Dimension (mm) C1
C2
Column 35 420
Beam 30 420
The modeling plan is to replace the coupling beam with VCD and RFD dampers in several positions. The analysis consists of 5 models where the first model is a model without a damper, the second model is a model with VCD on all floors, the third model is a model with VCD on the 5th-floor to 9th-floor, the fourth model is a model with RFD throughout the floor, and the fifth model is a model with an RFD on the 5th-floor to the 9th-floor according to Table 2.
Table 2: Type of Model
Figure 4: Coupling Beam (ND)
Figure 5: Viscoelastic Damper (VCD) Coupling Beam
No Model Damper Type Symbol
1 ND Without Damper ND
- All Floors RFD-A
- Fl. 5 to Fl. 9 RFD-B
- All Floors VD-A
- Fl. 5 to Fl. 9 VD-B
3 VD Viscoelastic Damper Position
Variabel 2 RFD Rotational Friction Damper Position
-
Figure 6: Rotational Friction Damper (RFD) Coupling Beam
3.2. Linear Modeling
3D linear mathematical modeling uses the ETABS 3D program to obtain reinforcement details which will be used for nonlinear modeling at the next step. The structural model is modeled with clamps at the base level, column and beam elements are modeled as frame elements, shear wall elements are modeled using shell elements, slabs are modeled as one-way slabs, and diaphragms are modeled as rigid diaphragms at each floor level. The element stiffness is input directly based on the lower limit strength of the material (f'c) and the size input, modifying the properties as suggested in ACI 318 to consider the crack section. The damping ratio for linear modeling is taken as 5% modal damping. The seismic design was carried out by modal response spectrum analysis procedure, Design-Based Earthquake (DBE), equal to 2/3 of 2%
probability of exceeding 50 years Maximum Considered Earthquake (MCER). DBE earthquake loading was applied according to the orthogonal combination procedure (Badan Standardisasi Nasional, 2019). The force demands are influenced by the response modification factor (R) and the importance factor (Ie). The displacement is influenced by the amplification factors of Cd and Ie (ASCE/SEI, 2017b).
3.3. Nonlinear Modeling
After obtaining the reinforcement details that meet the requirements of the Indonesia Code, SNI 2847 (ACI 318), it is evaluated using the PBSD (Performance-Based Seismic Design) approach. Each detailing of an element obtained is defined as a 3D mathematical nonlinear model using the Perform 3D program. This study used the nonlinear Dynamic Procedure (NDP) with Non-Linear Time History Analysis (NLTHA) according to the ASCE 41 tier 3 evaluation procedure. Based on ASCE 41, 11 pairs of ground motions must be used, which must be done with mean spectral matching following the response spectra of Jakarta, Indonesia, based on Code Indonesia, SNI 8899 (Badan Standardisasi Nasional, 2020). The results of the mean spectral matching of the 11 pairs of ground motions are shown in Figure 7.
Figure 7: Mean Spectral Matching 11 Pair of Ground Motions
The structural performance target is Collapse Prevention (CP) for buildings with category II risk with 2% MCER (Maximum Considered Earthquake) seismic risk within 50 years in the nonlinear dynamic procedure. Damping is modeled in the form of 2.4% modal damping and 0.5% Rayleigh damping at T/T1 to cover damping in high mode (LATBSDC, 2020). Nonlinear modeling considers the nonlinearity of each element through a force-deformation capacity curve of component or material stress-strain capacity curve. Structural elements are divided into deformation-controlled elements and force-controlled elements, which can be seen in Table 3.
Table 3: Component Model
The strength of the material used for the deformation-controlled elements is the expected material where the strength of the design material is multiplied by a factor of 1.50 for the compressive strength of concrete and a factor of 1.25 for the tensile and yield strength of reinforcing steel. In contrast, the force-controlled action capacity uses a lower bound (required strength). One example of defining beam elements based on ASCE 41 using a backbone curve is shown in Figure 8. The moment at point B is the yield moment (My); point C is the ultimate moment (Mu), equal to 1.13 My (ASCE, 2017); points D and E are calculated from the residual moment, c multiplied by My. The rotation is calculated based on the parameters “a” and “b”
adopted from Table 10-7 ASCE 41. The modeling parameters available in ASCE 41 have taken into account more significant strength degradation under cyclic loading. The deformation capacity is determined based on the recommendation of the acceptance criteria for Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) in ASCE 41.
Component Model Output Control Notes
Elastic Shear Force Demand/Capacity Ratio (DCR) must meet the requirements Fiber Axial &
Flexural Deformation
Stress-strain Diagram: Vertikal Reinforcement, Confined and
Unconfined Concrete Coupling Beam Concentrated
Hinge
Flexural &
Shear Deformation
Rigid-plastic shear hinge in the middle of the span or plastic hinges
at both ends of the beam.
Elastic Axial Force DCR must meet the requirements Elastic Shear Force DCR must meet the requirements Concentrated
Hinge
Interaction of Momen
& Aksial
Deformation Moment vs Rotation Diagram Shear Wall
Resistant Moment- Frames (Column-
Beam)
Figure 8: Backbone Curve Source: (ASCE/SEI, 2017a)
The VCD damper element modeling in the research uses a spring element that simulates a series of connection stiffness and Generalized Maxwell Models (GMM) elements (Pant, Montgomery, Christopoulos, Xu, & Poon, 2017), as shown in Figure 9. The properties used are obtained from VCD supplier company, while the RFD damper element is modeled as a shear hinge by including the backbone curves given from the RCD supplier company, as shown in Figure 10.
Figure 9: GMM Model and Properties VCD
Figure 10: Shear Hinges and Properties RFD
4. Result and Conclusion
4.1. Story Shears
The results of the analysis of the story shear comparison between coupling beams using dampers and without dampers show that in the VD-A model, there is an increase in story shear by 3% up to 6.5% for the X direction and 13% up to 18% for the Y direction. In the VD-B model, there is an increase in story shear about 3% up to 8.5% for the X direction and 9% up to 12% for the Y direction. While in the RFD-A model, there is an increase in story shear about 2% up to 5% for the X direction and a decrease of about -9% up to -15% for the Y direction.
In the RFD-B model, there is an increase in story shear about 3% up to 6% for the X direction and a decrease of about -4% up to -9% for the Y direction. Thus, there are quite significant increase and decrease seen in the Y direction, where the dampers are installed.
Figure 11: Story Shears
4.2. Story Drift
The results of the comparative analysis of story drift between coupling beams using dampers and without dampers show that in the VD-A model, there was an increase of approximately 1% up to 8% for the X direction while in the Y direction, the 2nd-floor to the 5th-floor increase about 2% up to 10%, the 6th- floor to the 11th- floor decrease about -0.5% up to -6.5% and on the 12th-floor to the roof floor, increase about 10% up to 50%. In the VD-B model, there is an increase of about 0.5% up to 7% for the X direction while the Y direction, on the 2nd-floor to the 5th-floor, increases about 3% up to 17%, the 6th-floor to the 10th-floor decrease about -3%
up to -11% and on the 12th-floor to the roof floor increase about 4% up to 25%. In the RFD-A model, there is an increase of about 0.5% up to 7% for the X direction, while the Y direction, on the 2nd-floor to the 8th-floor increase of about 0.5% up to 5%, the 9th-floor to the 11th-floor decrease about -1% up to -7% and on the 12th-floor to the roof floor decrease of about -10% up to -37%. In the RFD-B model, there is an increase of about 0.5% up to 5% for the X direction, while in the Y direction, on the 2nd-floor to the 5th-floor decrease about -0.2% up to -13%, the 6th-floor to the 10th-floor decrease about -2.5% up to -6% and on the 11th-floor to the roof floor decrease about -4% up to -22%. From these results, there is some increase in a drift on several floors using both VCD and RFD, but it is still below the allowable limit by ASCE 41, which is a drift ratio of 0.04 as shown in Figure 12.
Figure 12: Story Drifts
4.3. Component Action 4.3.1. Shear Walls
Based on ASCE 41, the deformation-controlled action of the shear wall is assessed from the strain that occurs in the concrete and steel to the concrete strain limits of 0.003 (IO), 0.0113 (LS), and 0.0150 (CP), while for steel strains 0.0026 (IO), 0.0375 (LS), and 0.050 (CP). The comparison of concrete strain between using damper and without damper shows that in the VD-A model for 2nd-floor to 7th-floor there is an increase about 9% up to 35% and the 8th-floor to the roof floor increases about 8% up to 20%. In the VD-B model, the 2nd-floor to the 7th- floor increased about 5% up to 25%, the 8th to 10th-floor decreases about -3% up to -7%, and the 11th-floor to the roof floor increase about 5% up to 16%. In the RFD-A model, almost all floors decrease -8% up to -24%, while RFD-B decreases -3% up to -13%. For strain steel, in the VD-A model for 2nd-floor to 8th-floor, there is an increase of about 17% up to 33%, and for 9th-floor to 15th-floor decreases about -2% up to -12%. In the VD-B model for 2nd-floor to 8th- floor, there is an increase of about 9% up to 20% and for 9th-floor to roof floor decrease about -3% up to -20%. In the RFD-A model, there is a decrease of about -8% up to -20% on the entire floor, while in the RFD-B model, decrease of about -6% up to -18%. From these results, there was an increase in the strain of both concrete and steel on several floors, but all of them were still below the CP limit. The force-controlled action in this paper is not discussed in detail because the deformation controlled is more decisive than force-controlled and the force that occurs is still below the existing capacity.
Figure 13: Concrete and Steel Wall Strain
4.3.1. Columns
The column element for deformation-controlled action is determined between the moment and the rotation that occurs in the column. The limits for CP, LS, and IO values are taken from table 10-8 in ASCE 41. From the analysis results for the most critical column compared to the model without a damper, the VD-A model for the 2nd-floor to the 3rd-floor has an increase of approximately 45%, while for the other floors, it is almost the same as the model without a damper. In the VD-B model, for the 2nd-floor to the 3rd-floor, there is an increase of approximately 35%, while the other floors are almost the same as the model without a damper.
For the RFD-A model, there is a decrease of approximately -9% for the 2nd- floor to the 3rd- floor, while for other floors, it is almost the same as the model without a damper. In the RFD- B model, on the 2nd-floor to the 3rd-floor decrease about -16%, while on the other floors it is almost the same as the model without a damper. From all these results, there are parts that experience an increase in performance but are still below the CP limit, as shown in Figure 14.
For force-controlled action in this paper, it is not discussed in detail because the controlled deformation is more decisive and the force that occurs is still below the required capacity.
Figure 14: Moment-Rotation Column Ratio
4.3.2. Beams
In beam elements for deformation-controlled action is determined by the moments and rotations that occur in the beam. The limits for CP, LS, and IO values are taken from table 10- 7 in ASCE 41. The presented beam is a beam that is parallel to the position of the damper and can represent the overall performance of the beam. The results of the analysis are compared with the model without damper; in the VD-A model, on the 2nd-floor to the 3rd-floor, there is an increase of about 3% up to 16%, the 4th-floor to the 11th-floor decrease about -6% up to - 13%, and the 12th floor to the roof floor increase about 10% up to 60%. In the VD-B model, the 2nd-floor to the 3rd-floor increase about 6% to 25%, the 4th-floor to the 10th-floor decrease - 2% up to -18%, and the 11th-floor to the roof floor increase about 9% up to 45%. In the RFD- A model, on the 2nd floor to the 9th floor, there is an increase of about 1% up to 6%, while the 10th-floor to the roof floor decrease about -10% up to -45%. In the RFD-B model, on the 2nd- floor to the 4th-floor, there is a decrease of about -4% up to -23%; on the 5th-floor to the 9th- floor, increase about 3% up to 8%, and on the 10th-floor to roof floor, it decreases about -5%
up to -25%. From all these results, there are parts that have increased performance but are still below the CP limit, as shown in Figure 15. The force-controlled action in this paper is not discussed in detail because the controlled deformation is more decisive and the force that occurs is still below the required capacity.
Figure 15: Moment-Rotation Beam Ratio
4.4. Conclusion
Based on story shear and story drift results in buildings that use dampers, both using viscoelastic dampers (VD-A and VD-B) or using rotational dampers (RFD-A and RFD-B), there is a decrease and increase, but it is still below the permit. For the results of the analysis on the elements, it is also seen that there is a significant decrease and increase, this needs to be considered if the building without dampers has a performance that is close to CP; if that happened, it needs to be retrofit if there is a significant performance improvement over CP performance. Based on story shear and story drift results in buildings that use dampers, both using viscoelastic dampers (VD-A and VD-B) or using rotational dampers (RFD-A and RFD- B), there is a decrease and increase, but it is still below the permit. For the results of the analysis on the elements, it is also seen that there is a significant decrease and increase, this needs to be considered if the building without dampers has a performance that is close to CP; if that happened, it needs to be retrofit when the performance over CP. In this building, the global performance (story shear and story drift) and local performance (element) are still below the limit criteria. Because of this, the use of damper elements on all floors or on floors 5 to 9 can make a solution related to the difficulty of installing diagonally coupling beam reinforcement by replacing it with this damper element. Furthermore, if there is damage to the damper element after the earthquake, it can be done easily without a long repair time when using conventional coupling beams.
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