A methodology of design for seismic performance enhancement of buildings using viscous fl uid dampers
K. Rama Raju*,†, M. Ansu and Nagesh R. Iyer
Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India
SUMMARY
A methodology of design for seismic performance enhancement of buildings by using linear viscousfluid dampers (VFDs) is proposed. It also gives the procedure for arriving at an efficient distribution of VFDs in the building. The peak base shear and inter-storey drifts determined from a time history analysis of the building subjected to design basis earthquake (DBE) are used for satisfying the Uniform Building Code 1997 specified target performance criteria for base shear and inter-storey drifts. The methodology proposed is used for designing the linear VFDs to increase the effective damping with chevron, upper toggle, and scissor jack mechanisms in a 20-storey bench- mark building subjected to DBE to meet the performance criteria. The time histories of the N–S component of El Centro, N–S component of Kobe, N–S component of Northridge, and S–E component of Taft scaled to a PGA of 0.2gare considered to be representatives of DBE for the place where the 20-storey benchmark building is located. It is observed that the optimum location of the dampers with different mechanisms in the building is the groundfloor or thefirst few storeys from the groundfloor. Copyright © 2013 John Wiley & Sons, Ltd.
Received 17 May 2012; Revised 8 January 2013; Accepted 19 February 2013
KEY WORDS: buildings; viscousfluid dampers; damper configurations; optimum distribution of dampers; energy dissipation devices; chevron; toggle brace and scissor jack mechanisms; steel moment resistant frame
1. INTRODUCTION
The seismic design of framed structures relies on their inherent ductility to dissipate seismic vibration energy while accepting a certain level of structural damage. To keep the vibration of framed structures within the functional and serviceability limits and to control and reduce structural and architectural damage caused by extreme loads, an alternative approach is to dissipate seismic energy by installing different passive, semi-active, active, and hybrid devices [1]. In buildings with viscousfluid dampers (VFDs), it is found that the damper configuration has significant effect on the structural response under earthquake excitation [2]. For many building structures, optimal configuration of energy dissipation devices may provide considerable performance improvement or cost saving. Here, a methodology for efficient use of VFDs in buildings for seismic performance enhancement is proposed.
Constantinou et al. [3] used a half-length scale single-storey steel model to test a novel energy dissipation system configuration termed thetoggle brace damper, described the concept and theoretical development, and presented experimental and analytical results. Scheller and Contantinou [4] carried out an analytical study of a three-storey quarter-length scale steel model using SAP2000, and results were compared with other programs, 3D BASISandANSYS, and experimental results. They found, in general, that the use of SAP2000 produced results that are in good agreement with other programs and also with experimental results. Contantinouet al. [5] presented new configurations such as toggle
*Correspondence to: K. Rama Raju, Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India.
†E-mail: [email protected]
Published online 17 April 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.1568
and scissor jack mechanisms to substantially magnify the effect of damping devices so that they can be utilized effectively in the application of small structural drift.
Hahn and Sathiavageeswaran [2] made several parametric studies on the effects of damper distribu- tion on the earthquake response of a shear building and showed that for short buildings, thefirst-storey damped case effectively reduces the response. It was shown that the behavior of tall buildings is generally more sensitive than that of short buildings to changes in distribution of dampers. Lopez Garcia [6] simplified the sequential search algorithm for the design of optimal damper configuration and made it attractive to practicing engineers. The same approach of Lopez Garcia has been adopted using both stiffness and damping coefficient optimization and compared with other methods by Cimellaro and Retamales [7]. Takewaki [8], Takewaki and Yoshitomi [9], and Takewakiet al. [10]
suggested a gradient-based algorithm for the optimum design of viscous damping by minimizing the sum of the amplitudes of drifts’ transfer functions evaluated at the undamped fundamental natural frequency of the structure subjected to a constraint on the total added damping. Singh and Moreschi [11] used a gradient-based algorithm for optimal design of viscous and viscoelastic dampers to achieve their best response reduction in structures. Singh and Moreschi [12] have determined both the optimal number and optimal distribution of dampers for seismic response control of a 10-storey linear building structure.
Wongprasert and Symans [13] proposed a methodology for optimum distribution of VFDs with chevron bracing mechanism by minimizing four different frequency-domain objective functions. Each of the resulting optimized damper configurations provided an improvement in the seismic response of the 20-storey benchmark building as compared with the uncontrolled building. For the four optimized damper configurations, the maximum damper forces used were found to vary from 200 to 400 kN.
However, in their study, the actual damper capacities used corresponding to damper locations were missing. The limits on performance indices were not prescribed. Yoshida and Dyke [14] proposed a semi-active control system for the same 20-storey benchmark building. Northridge earthquake was used to determine the number of 1000-kN semi-active control devices (magnetorheological dampers) on eachfloor, because it requires the largest control forces in the structure. The methodology used was based on the parametric studies with the assumption that the number of devices employed on each floor has equal weighing on the forces of each floor. Liu et al. [15] proposed a new optimization strategy for configuring energy dissipation devices in the building structures based on the performance objectives. The optimization is based on three different performance indices: (i) maximum inter-storey drift, (ii) absolute acceleration, and (iii) device cost with the same level of drift performance. It was found that the optimum configuration of Energy Dissipation Device (EDD) depends on the perfor- mance index selected. Lavan and Levy [16] presented a methodology for optimal design of supplemen- tal viscous dampers for framed structures.
The integrated design of civil engineering structures with control systems was described by Cimellaroet al. [17]. Cimellaro [18] studied the variation of the optimal stiffness, and damping place- ment using a generalized objective function that simultaneously considers displacements, absolute accelerations, and base shear is presented. A design strategy for the control of buildings experiencing inelastic deformations during seismic response is formulated by Cimellaro et al. [19]. The strategy involves using weakened, and/or softened, elements in a structural system while adding passive energy dissipation devices (e.g., viscous fluid devices) in order to simultaneously control acceleration and deformation responses during seismic events.
Ohtori et al. [20] presented 3-, 9-, and 20-storey benchmark control problems for seismically excited nonlinear buildings designed for the SAC project for Los Angeles, California, region. The objective of considering these problems is to provide a common basis for comparing the efficiency of various control strategies with passive, active, and/or semi-active control devices or a combination thereof. These structures meet seismic code requirements and represent typical low-, medium-, and high-rise buildings designed for Los Angeles, California, region.
In buildings with VFDs, it is found that the VFD configuration has significant effect on the struc- tural response under earthquake excitation [2,13]. The addition of fluid dampers to a structure does not significantly alter its natural period, but it increases damping of structure from 2% to 5% critical (which is usual for structures) to anywhere between 20% and 30%. It is important to note that damping beyond 30% critical damping results in small decrease in response, and such increases would not, in
general, lead to economical use of dampers [21]. For many buildings, optimal configuration of energy dissipation devices may provide considerable performance improvement and cost saving. The current codes of practices do not provide procedures or guidelines for optimal configuration of energy dissipa- tion devices. However, systematic design procedures for optimal sizing and placement of these device systems in structural systems are needed, but they are not yet available [22].
In the present study, a methodology is presented for finding the number, location, and capacity of VFDsfitted in different types of mechanisms such as chevron, upper toggle, and scissor jack (Table I) for a 20-storey benchmark building [20]. The building is subjected to design basis earthquake (DBE) and needs to satisfy the Uniform Building Code (UBC) 1997 [23] specified performance criteria for base shear and inter-storey drifts (Table II). The base shear and peak inter-storey drifts are found by carrying out a linear time history analysis using the SAP2000 software (Computers and Structures Inc., Berkeley, CA, USA). The time histories of the N–S component of El Centro, N–S component of Kobe, N–S component of Northridge, and S–E component of Taft scaled to a PGA of 0.2gare considered to be representatives of DBE. Thus, for DBE, the PGAs are 0.57 times the El Centro, 0.34 times the Kobe, 0.24 times the Northridge, and 1.28 times the Taft. The allowable limits of storey drift ratio (%) and base shear for a 20-storey building as per UBC 1997 with the variables assumed in Table II are found to be 0.40 and 1789.62 kN, respectively, and the same are given Table III.
The paper begins with Section 1, where the review of literature and the purpose of the present study are given. This section is followed by Section 2, which gives the details of the benchmark problem considered, damper mechanisms used in the benchmark building, and performance indices used for evaluation. Section 3 gives the details of the modeling and analysis of the benchmark frame without
Table I. Magnification factors for different damper configurations.
f= 1 f¼ cosðsinθ1θþ2θ2Þþ sinθ1 f¼ cosctanθ
Table II. Allowable limits of inter-storey drift and base shear.
Storey drift/height (UBC 97 Section 1630.2.2.) Design base shear/weight (UBC 97 Section 1630.2) 0.005 forT<0.7 s, 0.004 forT>0.7 s, and the building
periodT=Cth3/4, whereCtis a coefficient = 0.085 andh is the total height of the building = 80.77 m.
Base shear/weight WV¼CRTvI, where seismic coefficient Cv= 0. 64, importance factor I= 1, and ductility factorR= 8.5.
Table III. Allowable limits for a 20-storey building as per UBC 1997.
S. No. Parameters
Limits
GS RS
1 Allowable drift ratio (%) 0.40 0.40
2 Allowable base shear (kN) 1789.62
UBC, Uniform Building Code; GS, ground storey; RS, remaining storey.
and with dampers for four cases of damper distributions given by Wongprasert and Symans [13]. In Section 4, a methodology on the design and distribution of dampers is described. Critical observations based on the results of design cases considered for study and comparison of the same with the other damper placements referred in literature are the topics of Section 5. Section 6 deals with criteria for approximate selection of dampers from the available dampers based on the study carried out. Section 7 deals with the summary and conclusions of the study carried out.
2. TWENTY-STOREY BENCHMARK BUILDING
A 20-storey building [20] is taken for the present study, and it is 80.77 m (265 ft) tall and is rectangular in plan with bay spacing of 6.10 m (20 ft) on the center in both the N–S (five bays) and E–W (six bays) directions. The first three natural frequencies of the building are 0.261, 0.753, and 1.30 Hz. The fundamental period of the building, T1, is 3.035 s. The first mode shape is f1= [0.023 0.029 0.034 0.037 0.038 0.042 0.045 0.050 0.053 0.053 0.054 0.054 0.057 0.058 0.0595 0.058 0.059 0.059 0.058 0.077]. Seismic masses are 5.63e05 kg in the first floor, 5.52e05 kg in the 2nd–19th floor, and 5.84e05 kg in the 20th floor.
2.1. Damper mechanisms used in 20-storey benchmark building
When the earthquake excitation is given to a building fitted with dampers, the energy dissipation capacity depends on the magnification factor of the damper. The magnification factor depends on the angle of inclination and placement of dampers. Magnification factor is defined as the ratio of damper displacement to inter-storey drift. The magnification factors for chevron, upper toggle, and scissor jack mechanisms are calculated using the formulae given in Table II [5].
Upper toggle bracings for the 20-storey building in the ground floor and remaining floors are designed as shown in Figures 1 and 2. The magnification factor,f, is found using the formula given in Table II. The anglesθ1andθ2in the upper toggle brace are assumed to be 40and 37, respectively, in the groundfloor of the building as shown in Figure 1. For the remainingfloors of the building, the anglesθ1andθ2in the upper toggle brace are assumed to be 30 and 50, respectively, as shown in Figure 2. For the upper toggle mechanisms in the ground floor and other floors of the building, the magnification factors are calculated as 3.318 and 4.725, respectively.
The scissor jack mechanisms for the 20-storey building in the groundfloor and remainingfloors are designed as shown in Figures 3 and 4, respectively. The anglescandθin the scissor jack mechanism in the groundfloor of the building are assumed to be 63and 8, respectively, as shown in Figure 3. For the remainingfloors of the 20-storey building, the anglescandθin the scissor jack mechanism are
All dimensions are in Metres Pin (u2,u3,r1,r2,r3)
Pin (u2,r1,r3)
Pin (u2,r1,r3) 2.45
3.56 1.74
90°
Lever Arm Damper
40°
0.80 6.10
20-Storey Benchmark Building Pin
(u2,r1,r3) 2.01
37°
5.49
Figure 1. Upper toggle brace configuration in groundfloor.
assumed to be 56 and 9, respectively, as shown in Figure 4. The magnification factor,f, is found using the formula in Table II. For the scissor jack mechanisms in the ground floor and otherfloors of building, the magnification factors are calculated as 3.23 and 3.53, respectively.
All dimensions are in Metres Pin (u2,u3,r1,r2,r3)
Pin (u2,r1,r3)
Pin (u2,r1,r3) 1.95 50°
3.05 2.25
90°
3.96
Lever Arm Damper
30°
0.80 6.10
20-Storey Benchmark Building Pin
(u2,r1,r3) 2.01
Figure 2. Upper toggle configuration forfloors above groundfloor.
6.10 2.8
63°
8°
5.49
2.78
0.81 Damper
0.3 0.28
0.3 All dimensions are in Metres
Pin(r2)
Figure 3. Scissor jack in groundfloor.
6.10 2.6
56°
9°
3.96
2.07
0.64 Damper
0.3 0.28
0.3 All dimensions are in Metres
Pin(r2)
Figure 4. Scissor jack configuration forfloors above groundfloor.
2.2. Performance evaluation indices used for 20-storey building
To form a common basis for evaluating the effectiveness of different structural control strategies, the seismic benchmark problem utilizes common building structure and structural performance evaluation criteria [20]. The nondimensional performance indices considered for the model are peak drift ratio (J1), peak level acceleration (J2), and peak base shear (J3). A detailed description of the evaluation criteria was provided by Ohtoriet al. [20]. As an example, thefirst evaluation criterion J1is deter- mined as follows: the ratio of maximum inter-storey drift ratio of the controlled structure to the maximum inter-storey drift ratio of the uncontrolled structure computed for each of the earthquake considered. Then,J1is defined as the maximum of these ratios. Similarly,J2andJ3can be interpreted.
These performance indices are defined as given in Equations (1)–(3).
Peak drift ratio; J1¼
El Centro Kobe Northridge
Taft
Max max
t;i
│di tð Þ│
hi dmax
8
<
:
9
=
; (1)
Peak level acceleration; J2¼
El Centro Kobe Northridge
Taft
Max max
t;i│€x ai tð Þ│
€xmax a
n o
(2)
Peak base shear; J3 ¼
El Centro Kobe Northridge
Taft
Max maxij
P
imi €x ai tð Þ Fmax
b
n o
(3)
whereirepresents the number of the storey; di(t) is the inter storey drift for the frame over the time history of each earthquake; hi is the height of each of the associated storeys;dmaxis the maximum inter-storey drift ratio of the bare frame without dampers calculated from maxt;i di tð Þ=hi
€xaið Þ;t €xmaxa are the absolute acceleration of theith level with and without dampers, respectively;miis the seismic mass of theith level; andFbmaxis the maximum base shear of the bare frame. It is noted from the afore- mentioned definitions that smaller values of performance indices are desirable.
3. MODELING AND ANALYSIS OF THE BENCHMARK BUILDING WITH VFDs Viscousfluid dampers provide a force that always resists the structural motion. This force is propor- tional to the relative velocity between the ends of the dampers. This force is expressed as follows:
fD¼C0j ju_ asgnð Þu_ (4)
wherefDis the damper output force,u_is the velocity,C0is the damping coefficient with units of force per velocity, a is a real positive exponent (with typical values in the range of 0.35–1) for seismic applications, and‘sgn( )’is the signum function. In Equation (4), when a= 1, fD¼C0u, and this_ represents a linear VFD.
In controlling nonlinear systems, one often treats the controlled system as linear for design purposes.
Although the building can experience plastic deformation during severe earthquakes, which results in a nonlinear model, the approach adopted herein for designing the damper distribution is based on the linear model of the building. In this study, the linear time history analysis with modal superposition for 20-storey buildings is carried out using SAP2000. For modeling linear dampers, theNlinkelement in SAP2000 is used. The inputs for the same are effective stiffness (ke) and effective damping (Ce).
For the time history analysis, aminimum of three acceleration time histories are required for the given project site, generated by a geotechnical expert [24]. Guidelines given in 1993 by the Passive Energy Subcommittee of the Structural Engineers of Northern California require the engineer to use
the worst of the three events in design (or maximum stress and deflection case). The 20-storey bench- mark building considered in this study is subjected to four different earthquakes [20]: (i) the N–S component of El Centro, (ii) the N–S component of Kobe, (iii) the N–S component of Northridge, and (iv) the S–E component of Taft. The absolute peak acceleration for these earthquake records are 3.417, 5.79, 8.268, and 1.520 m/s2, respectively. The benchmark buildings are assumed to be located in a region for which the PGA corresponding to DBE is 0.2g.
The time history analysis of the 20-storey benchmark building bare frame model (case 1) is carried out as described earlier. The inter-storey drift ratios along the height of the bare frame and base shears for this case are found out and are shown in Figures 5 and 6, respectively. From Figure 5, it is clear that, except for El Centro, for all other load cases, the inter-storey drift ratios are crossing the UBC specified limit (0.4%). The base shear of the bare frame (Figure 6) is exceeding the UBC specified limit of 1789.62 kN.
The results of the four optimized damper configurations arrived by Wongprasert and Symans [13]
for a benchmark building is provided in Table IV. It is noted that they [13] did not consider limits on performance indices. The four cases, namely, 2–5, considered in the present study are equivalent to the cases considered by Wongprasert and Symans [13]. The arrangements of dampers for these four cases, 2–5, are presented in Table V, and the corresponding values of damping coefficients per damper are given in Table VI.
The time history analysis of the 20-storey frame model with the four cases (2–5) of damper distri- butionfitted with chevron mechanism is carried out as described previously. For all the four cases, the
0 2 4 6 8 10 12 14 16 18 20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Floor
Drift ratio(%)
Bare Frame EC KO NR TA limit
Figure 5. Inter-storey drift ratios for bare frame. EC, El Centro; KO, Kobe; NR, Northridge; TA, Taft.
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000
Base Shear (kN)
Elcentro Kobe Northridge Taft bare frame Upper Toggle Chevron Scissor jack 1789.62kN
Figure 6. Base shears for the frame.
peak base shears and peak inter-story drifts are found from the analysis (Table VII). The inter-storey drifts ratios are within the prescribed limit (4%), but the base shears are exceeding the limit prescribed by UBC 1997 (1780.62 kN)
4. METHODOLOGY FOR DESIGN AND DISTRIBUTION OF DAMPERS
From the results of the analysis presented in Section 3, it is found that there is a need to evolve a proce- dure for the design and distribution of dampers that explicitly satisfy the performance criteria (Table I).
Table IV. Damper distribution obtained from the genetic algorithm [13].
Storey
TND
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
ND 12 6 12 6 4 4 — — — — — — — — — — — 2 4 50
6 6 8 2 4 — — — — — — — — 4 4 — 6 4 6 50
46 — — 2 — — 2 — — — — — — — — — — — — 50
18 — — — — — — — — — — — — 2 12 — 10 8 — 50
Each damper is a linear viscous damper having a damping coefficient of 970.7 kNs/m.
ND, number of dampers; TND, total number of dampers.
Table V. Damper placements for a 20-storey building.
Storey
Mechanism
Chevron Upper toggle Scissor jack
Case
2 3 4 5 6 7 8 9 10 (NL) 11 12 13
1 5A 5C 5G 5I 5K 10L 3M 5N 5B 3O 5O 5P
2 — 1D 2E — 3K — 3M — — 3O - 2P
3 — 2D 2H — 1K — 1M — — 1O - 1P
4 2B 2E 2B — — — — — — — — —
5 - 2F 2F — — — — — — — — —
6 - 2F — — — — — — — — — —
7 2B — — — — — — — — — — —
8 — — — — — — — — — — — —
9 — — — — — — — — — — — —
10 — — — — — — — — — — — —
11 — — — — — — — — — — — —
12 — — — — — — — — — — — —
13 — — — — — — — — — — — —
14 — — 2F 2B — — — — — — — —
15 — — 2F 2D — — — — — — — —
16 — — — — — — — — — — — —
17 — — 2E 2J — — — — — — — —
18 — 2B 2F 2H — — — — — — — —
19 — 2F 2F — — — — — — — — —
TND 9 18 23 13 9 10 7 5 5 7 5 8
Characteristics of dampers A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, and P are given in Table VI.
TND, total number of dampers.
Table VI. Damping coefficients of the dampers (kNs/m).
DD A B C D E F G H I J K L M N O P
DC 9200 1000 2400 6000 3000 2000 1200 4000 3600 5000 15,000 13,500 1400 650 3300 2500 DD, damper designation; DC, damping coefficient.
From the preliminary parametric studies carried out by Rama Rajuet al. [25,26], it was found that for a 20-storey benchmark building, placement of dampers in thefirst few storey from the ground was most efficient, because inter-storey drifts and velocities are maximum in thesefloors. In the present study, nine cases (6–13) of damper distributions are used, and the arrangements of dampers for the same are as given in Table V. It may be noted that the damper configurations chosen satisfy the obser- vation made by Rama Rajuet al. [25,26].
Recognizing that the higher-mode responses will be highly suppressed when sufficient dampers are incorporated into a building, in the design provisions of Federal Emergency Management Agency (FEMA) 273 [27] and FEMA 356 [28], the damping ratio of a building with added linear dampers is approximated by thefirst-mode vibration in the direction of excitation considered. This simplification is considered to be acceptable for the preliminary design of the supplemental dampers in buildings [29].
The proposed methodology of designing buildings with linear VFDs by using FEMA 273/274 [27]
and FEMA 356 [28] provisions is presented in Table VIII. It is to be noted that the methodology is a trial-and-error method. The developed methodology is used for designing the linear viscous dampers to the required effective damping in the buildings with chevron, upper toggle, and scissor jack brace
Table VII. Peak responses in a 20-storey building.
Case a TotalC0(kNs/m) Inter-storey drift (%) Base shear (kN) Acceleration (mm/s2)
1 1 0.595 3630 2379
Chevron 2 1 50,000 0.397 2503 2040
3 1 50,000 0.381 2447 2176
4 1 50,000 0.359 2266 2134
5 1 50,000 0.374 2235 2021
6 1 135,000 0.27 1764 1856
7 1 135,000 0.267 1724 1727
Upper toggle 8 1 9800 0.341 1698 1710
9 1 3250 0.358 1768 1830
10 0.5 5000 0.326 1772 1758
Scissor jack 11 1 23,100 0.273 1784 1757
12 1 16,500 0.273 1784 1732
13 1 20,000 0.277 1787 1740
a= damping exponent.
The values exceeding the limits prescribed by the Uniform Building Code 1997 are underlined.
Table VIII. Methodology for design building with VFDs.
1. Choose a damper configuration: (i) chevron, (ii) upper toggle, or (iii) scissor jack.
2. Calculate the magnification factor:
ð Þi chevron;f ¼1; ð Þii upper toggle; f ¼cossinðθ1θþ2θ2Þþ sinθ1; ð Þiii scissor-jack; f¼ cosctanθ:
3. Assume damping in structure, x0, to be 0.2. Choose the additional effective damping required by the provision of VFDs, xd, to be 0.28. Effective damping ratio is xeff=x0+xd.
4. Input the characteristics of the building: fundamental period T1, mode shape f1, and storey masses mi, i= 1,. . .,n,, wherenis number of storeys.
5. Choose the number of dampers and their distribution in the differentfloors of the building.
6. Calculate the damping constant (Cj) of dampers at eachfloor by using the Equation (5).
7. Assign the damping coefficient,Cj, to the dampers in the differentfloors of the building.
8. Find the inter-storey drift and base shear limits as given in Table I, and for the 20-storey building, they are as given in Table III.
9. Carry out a time history analysis of the building subjected to four types of earthquake loads (representing DBE) andfind the maximum inter-storey drift and base shears.
10. Check whether inter-storey drifts and base shear exceeds the limits calculated. If they exceed the limits, increase the Cjvalue and go back to step 7; otherwise, decrease theCjvalue till it becomes the smallest one that satisfies the limits.
VFD, viscousfluid damper.
damper configurations. The design formula for calculating the supplemental damping ratio [5,28] for the primary mode is specified by Equation (5):
xd ¼ T1X
jCjf2jgf2rj 4pX
iWif2i (5)
where T1 is the natural period of thefirst mode of vibration, Cj is the damping coefficient of the damper j, frj= (fj fj 1) is the first-mode relative displacement between the ends of the devices j in the horizontal direction, fj and fj 1 are, respectively, the horizontal modal displacements of thejth and (j 1)th storey in the kth mode of vibration,Cjare the damping coefficients of the dampers at thejth storey,fjis the magnification factor for the damping system containing the damping device (fj= cosθj, if the angle of inclination of damperjto horizontal isθj),Wiis the relative weight offloor levelI, andgis the acceleration due to gravity.
In the present procedure, initially, to increase the structural damping approximately to 28% by the provision of VFDs, the supplemental damping ratio (xd) is assumed to be 0.28.
After the damping is provided, it is required tofind the peak inter-storey drift ratio and base shear, and those values should be less than the prescribed limits for the building (for this problem, the allow- able drift ratio is 0.4%, and the allowable base shear is 1782.62 kN). The number of iterations is required forfinding the smallest damping constantCjfor the given damper distribution, which satisfies the limits prescribed as described in Table VIII. Following this procedure, thefinal damping coeffi- cients (Cj) of the dampers in differentfloors are found for the nine cases (6–13), and the same are given in Table VI.
5. CRITICAL OBSERVATIONS BASED ON THE RESULTS OF DESIGN CASES From the analysis, the peak inter-storey drift ratio, base shear, and maximum storey acceleration for all cases (1–13) are found, and the same are given in Table VII. The damping coefficient,C0; the percent- age of reduction in inter-storey drift; the base shear; the acceleration due to the provision of dampers;
and the performance indices for maximum inter-storey drift ratio, base shear, and maximum storey acceleration for the 12 cases (2–13) are given in Table IX.
In linear dampers, the only one variable varying is the damping coefficient,C0. In cases 6 and 7, the dampers in the building are with chevron bracings. Between cases 6 and 7, case 7 is the most efficient because the percent reduction, inter-storey drift, and base shear are maximum and the value of the
Table IX. Reduction in peak responses as % and performance evaluation indices.
Case a
TotalC0
(kNs/m)
% Reduction
Performance evaluation indices Inter-storey
drift Base shear Acceleration J1 J2 J3
Chevron 2 1 50,000 33.3 31.0 14.2 0.67 0.86 0.69
3 1 50,000 36.0 32.6 8.5 0.64 0.92 0.67
4 1 50,000 39.7 37.6 10.3 0.60 0.89 0.62
5 1 50,000 37.1 38.4 15.0 0.63 0.85 0.62
6 1 135,000 54.6 51.1 22.0 0.45 0.78 0.49
7 1 135,000 55.1 52.5 27.4 0.45 0.73 0.48
Upper Toggle 8 1 9800 42.7 53.2 28.1 0.57 0.72 0.47
9 1 3250 39.8 51.3 23.1 0.60 0.77 0.49
10 0.5 5000 45.2 51.2 26.1 0.55 0.74 0.49
Scissor jack 11 1 23,100 54.1 50.9 26.1 0.46 0.74 0.49
12 1 16,500 54.1 50.9 27.2 0.46 0.73 0.49
13 1 20,000 53.4 50.8 26.9 0.47 0.73 0.49
a= damping exponent.
performance indices,J1,J2, andJ3,are minimum. In cases 8–10, the dampers in the building frame are fitted in upper toggle mechanisms. Among these cases, it is in case 9 that the damping coefficient used in the dampers is minimum and at the same time satisfying the inter-storey drift and base shear limits. In case 10, the building frame is fitted with a nonlinear damper with damping exponent, a= 0.5 (ain Equation (4)). For this case, even though the performance indices,J1,J2, andJ3, are small in comparison with those in case 9, the damping coefficient, C0, value is higher. In cases 11–13, the dampers in the building frame arefitted with scissor jack mechanisms. Among these cases, it is in case 12 that the damping coefficient used is minimum and the value of the performance indices,J1,J2, and J3, are minimum. Thus, in the nine cases (6–13) studied, the most efficient cases are case 7 (chevron), case 9 (upper toggle), and case 12 (scissor jack). This can be observed from theC0values and the performance indices given in Table IX. In all the three cases (7, 9, and 12), the dampers are placed in the groundfloor. The maximum inter-storey drift ratios from the time history analysis for cases 7, 9, and 12 are shown in Figures 7–9, respectively. The corresponding base shear values for these three cases are shown in Figure 6. From thesefigures, it can be observed that the peak inter-storey drift ratios and base shear for all the three configurations are well below the prescribed limits.
5.1. Comparison of damper placement with other references
Wongprasert and Symans [13] distributed 50 passive dampers (fixed in chevron configuration) over the height of the 20-storey benchmark building as given in Table IV. The equivalent practical placements of the dampers are in cases 2–5 of the present study as given in Table V. The total damping coefficient used in all the four cases is 50,000 kNs/m.
0 2 4 6 8 10 12 14 16 18 20
0.00 0.10 0.20 0.30 0.40
Floor
Drift Ratio(%) Chevron
EC KO NR TA Limit
Figure 7. Inter-storey drift ratios for chevron. EC, El Centro; KO, Kobe; NR, Northridge; TA, Taft.
0 2 4 6 8 10 12 14 16 18 20
0.00 0.10 0.20 0.30 0.40
Floor
Drift Ratio(%)
Upper Toggle EC KO NR TA Limit
Figure 8. Inter-storey drift ratios for upper toggle. EC, El Centro; KO, Kobe; NR, Northridge; TA, Taft.
In present study, the optimum configurations are found to be cases, 7, 9, and 12. In all these cases, the dampers are placed in the groundfloor with chevron, upper jack, and scissor jack configurations, respectively, as given in Table V. The details of the same are given in Table XI.
Even though in cases 2–5, the damping coefficient used (50,000 kNs/m) is much smaller than in the present optimum case, case 7 (135,000 kNs/m), it is to be noted that cases 2–5 do not satisfy the base shear constraint of the problem.
In case 9 (with toggle brace configuration), the total damping coefficient of 3250 kNs/m is used for dampers. It is the most optimum and is more superior to all other cases considered in the present study.
The second best configuration is case 12 (with scissor jack configuration), in which the total damping coefficient of 16,500 kNs/m is used. This shows the importance of the type of damper configuration used for placement in the building.
In a 20-storey benchmark building, Yoshida and Dyke [14] used 1000-kN capacity semi-active dampers as chevron and placed four dampers in thefirst eight storeys, three dampers in the next nine storeys, and two dampers in the top three storeys.
Here, it is to be noted that the actual dampers available in the market are nonlinear. The only information known from the manufacturers of dampers is the capacity and stroke length of the damper.
6. APPROXIMATE METHOD TO CHOOSE DAMPERS IN BUILDING
The maximum forces and displacements are found for nine cases, 6–13, and they are given in Table X.
For these cases, the damper capacity and stroke lengths are chosen from the Taylor devices correspond- ing to the maximum damper force and displacements in different dampers in the building frame found from the analysis, and the same are also given in Table X. Among these cases, cases 7, 9, and 12 are the most efficient and are given in Table XI. In cases 7, 9, and 12, all dampers are placed at groundfloor
0 2 4 6 8 10 12 14 16 18 20
0.00 0.10 0.20 0.30 0.40
Floor
Drift Ratio (%)
Scissor Jack EC KO NR TA
Figure 9. Inter-storey drift ratios for scissor jack. EC, El Centro; KO, Kobe; NR, Northridge; TA, Taft.
Table X. Damper force and damper displacement.
Case
C0value/
damper (kNs/m)
Damper force (kN)
Damper displacement
(mm)
Damper capacity from Taylor devices (kN)
Stroke length from Taylor devices (mm)
Chevron 6 15,000 1417 12.95 1467.913 101.6
7 13,500 1267 12.84 1467.913 101.6
Upper toggle 8 1400 520.9 51.59 733.96 101.6
9 650 316.4 73.5 489.304 101.6
10 1000 476 65.57 489.304 101.6
Scissor jack 11 3300 1262 30.32 1467.913 101.6
12 3300 1018 42.47 1467.913 101.6
13 2500 775.4 42.31 978.6087 101.6
only. In groundfloor, the maximum velocity and inter-storey drifts are present. From Tables X and XI, it can be observed that even though the same type of dampers are chosen for chevron and scissor jack, for scissor jack, the damping coefficient (C0) value is less and the damper displacements are high.
7. SUMMARY AND CONCLUSION
A methodology of design for seismic performance enhancement of buildings by using linear VFDs is proposed. It is based on the consideration of locating the dampers at points where the inter-storey velocities and drifts are highest. It also gives the procedure for arriving at an efficient distribution of VFDs in the building. The peak base shear and inter-storey drifts determined from the time history analysis of the building subjected to DBE are used for satisfying the UBC 1997 specified target perfor- mance criteria for base shear and inter-storey drifts. The proposed methodology is used for designing the linear VFDs to increase the effective damping with chevron, upper toggle, and scissor jack mech- anisms in a 20-storey benchmark building subjected to DBE to meet the performance criteria. The time histories of the N–S component of El Centro, N–S component of Kobe, N–S component of Northridge, and S–E component of Taft scaled to a PGA of 0.2gare considered to be representatives of DBE for the place, that is, where the 20-storey benchmark building is located. It is observed that the optimum location of the dampers with different mechanisms in the building is the groundfloor or thefirst few storeys from the groundfloor. Among the mechanisms studied, the toggle brace mechanism is found to be most efficient for the distribution of VFDs in the buildings. The second best configuration for the distribution of dampers in a building is the scissor jack mechanism.
The developed methodology can be used forfinding the capacity and distribution of VFDsfitted in different mechanisms in buildings located at any place. For this, an ensemble of earthquakes is required to prescribe a DBE representative of the location of the building.
ACKNOWLEDGEMENT
This paper is being published with the kind permission of the Director of CSIR Structural Engineering Research Centre, Chennai 600113, India.
REFERENCES
1. Soong TT, Spencer BF. Supplemental energy dissipation: state-of-the-art and state-of-the-practice.Engineering Structures 2002;24:243–259.
2. Hahn GD, Sathiavageeswaran KR.“Effects of added-damper distribution on the seismic response of buildings”.Computers and Structures1992;43:No.5:941–950.
3. Constantinou MC, Soong, TT, Dargush GF. Passive energy dissipation systems for structural design and retrofit, MCEER, University of Buffalo, Red Jacket Quadrangle, Baffalo, Ny, 14261, 1998.
4. Scheller, J and Contantinou, MC. Response history analysis of structures with seismic isolation and energy dissipation systems: verification examples for program SAP2000, Technical Report MCEER-99-0002, 1999.
5. Constantinou MC, Tsopelas P, Hammel, W, Sigaher AN. Toggle-brace-damper seismic energy dissipation systems.Journal of Structural Engineering ASCE2001;127:No.2,105–112.
6. Lopez GD. A simple method for the design of optimal damper configurations in MDOF structures.Earthquake Spectra 2001;17(3):387–398.
7. Cimellaro GP, Retamales R. Optimal softening and damping design for buildings.Journal of Structural Control and Health Monitoring2007;14:831–857.
8. Takewaki I. (1997). Optimal damper placement for minimum transfer functions.Earthquake Engineering and Structural Dynamics2007;26(11):1113–1124.
Table XI. Damper force and damper displacement for the most efficient cases.
CaseConfiguration
C0value per damper (kNs/m)
Damper force (kN)
Damper displacement (mm)
Damper capacity from Taylor devices (kN)
Stroke length from Taylor devices (mm)
7 Chevron 13,500 1267 12.84 1467.913 101.6
9 Upper toggle 650 316.4 73.5 489.304 101.6
12 Scissor jack 3300 1018 42.47 1467.913 101.6
9. Takewaki I, Yoshitomi S. Effects of support stiffnesses on optimal damper placement for a planar building frame.The Structural Design of Tall Buildings1998;7:323–336.
10. Takewaki I, Yoshitomi S, Uetani K, Tsuji M. Non-monotonic optimal damper placement via steepest direction search.
Earthquake Engineering and Structural Dynamics1999;28(6):655–670.
11. Singh MP, Moreschi LM. Optimal seismic response control with dampers. Earthquake Engineering and Structural Dynamics2001;30(4):553–572.
12. Singh MP, Moreschi LM. Optimal placement of dampers for passive response control. Earthquake Engineering and Structural Dynamics2001;31:No.4,955–976.
13. Wongprasert N, Symans MD. Application of genetic algorithm for optimal damper distribution within the nonlinear seismic benchmark building.Journal of Engineering Mechanics ASCE2004;130:No. 4,401–406.
14. Yoshida O, Dyke SJ. Seismic control of a nonlinear benchmark building using smart dampers.Journal of Engineering Mechanics ASCE2004;130:No. 4,386–392.
15. Liu W, Tong M, Lee, GC. Optimization methodology for damper configuration based on building performance indices.
Journal of Structural Engineering ASCE2005;131:No. 11,1746–1756.
16. Lavan O, Levy R. Optimal design of supplemental viscous dampers for linear framed structures.Earthquake Engineering and Structural Dynamics2006;35(3):337–356.
17. Cimellaro GP, Soong TT, Reinhorn AM. Integrated design of controlled linear structural systems.Journal of Structural Engineering ASCE2009;135(7):853–862.
18. Cimellaro GP. Simultaneous stiffness-damping optimization of structures with respect to acceleration, displacement and base shear.Engineering Structures2007;29(11):2853–2870.
19. Cimellaro GP, Lavan O, Reinhorn AM. Design of passive systems for controlled inelastic structures.Earthquake Engineer- ing and Structural Dynamics2009;38(6):783–804.
20. Ohtori Y, Christenson RE, Spencer Jr., BF. Benchmark control problems for seismically excited nonlinear buildings.
Journal of Engineering Mechanics ASCE2004;130:No.4,366–385.
21. Hanson RD, Soong TT. Seismic design with supplemental energy dissipation devices,EERI Publication No.MNO-8, 2001.
22. Rama Raju K, Hemant GG, Rekha KS, Iyer NR. Seismic design of buildings with viscousfluid dampers—a methodology.
Journal of Institution of Engineers(India)2011;92:44–54.
23. Uniform Building Code. Volume 1 and 2, 1997 edition, Published by International Conference of Building Officials 24. Haskell G, Lee, D. “Fluid viscous damping as an alternative to base isolation” 2007; http://www.taylordevices.com/
FluidViscousDamping.htm accessed on 7.05.2007.
25. Rama Raju K, Meher Prasad A, Muthumani K, Lakshmanan N, Jagadish DR. Amuthasheela.“Optimum distribution of viscousfluid dampers in multi-storied buildings”,The 3rdInternational Conference on Structural Stability and Dynamics, June 19–22,2005,Kissimmee,Florida
26. Rama Raju K, Mehar Prasad A, Lakshmanan N, Muthumani K, Jagadish DR, Amuthasheela R.“Optimum Distribution of Viscous Fluid Dampers in structural systems”. Journal of The Institution of Engineers (India)2005; 86: November 2005,103–108.
27. Federal Emergency Management Agency (FEMA). NEHRP guidelines for the seismic rehabilitation of buildings 1997;
Rep. No. 273/274, Building Seismic Safety Council, Washington, D.C.
28. Federal Emergency Management Agency (FEMA). Pre-standard and commentary for the seismic rehabilitation of buildings 2000; FEMA 356, Washington, D.C.
29. Hwang JS, Huang YN; Yi SL, Song YH. Design formulations for supplemental viscous dampers to building structures.
Journal of Structural Engineering ASCE2008;134:No. 1,22–31.
