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6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
266
Seismic Performance Evaluation of Steel Moment Resisting
Frames Equipped with Tuned Liquid Damper
Sareh Akbarpoor1, Seyed Mehdi Dehghan Banadaki2, Mohammad Ali
Hadianfard3.
1- Graduate Student, Civil & Environmental Eng. School, Shiraz University of Technology
s.akbarpoor@sutech.ac.ir
2- Assistant Professor, Civil & Environmental Eng. School, Shiraz University of Technology
smdehghan@sutech.ac.ir
3- Associate Professor, Civil & Environmental Eng. School, Shiraz University of Technology
hadianfard@sutech.ac.ir
Abstract
A common approach to mitigate the structures` response under dynamic loading is to attach a dynamic
vibration absorber such as Tuned Liquid Damper (TLD) to the structure. A TLD is a passive control
system, which reduces the structures` response utilizing the fluid sloshing motion to dissipate the lateral
excitation energy. For rehabilitation of existing intermediate steel moment resisting frames in this
study, the TLD is modelled as an equivalent Tuned Mass Damper that Yu developed. This paper aims
at investigating the efficiency of TLD in improving seismic performance of existing intermediate steel
moment resisting frames based on nonlinear dynamic analysis.
Keywords: Passive Control, Tuned Liquid Damper, Seismic Performance, Rehabilitation, Steel
Moment Resisting Frame.
1. Introduction
Passive structural control techniques are generally used as seismic rehabilitation and
retrofit methodologies of existing structures [1]. Passive control mechanisms operate without
using any external energy supply. Passive control systems such as dampers can be used to
reduce vibration motion of structures due to dynamic loadings, such as wind and earthquake.
The main function of a passive damping device is to dissipate a portion of the input energy
associated with external dynamic excitations acting on a structure, thus avoiding or reducing
structural damages.
One of these passive systems is Tuned Liquid Damper (TLD). The TLD damper consists
of one or multiple rigid tanks, partially filled with a liquid, which is typically water that is
allowed to slosh as the structure experiences dynamic motions. The basic principle of TLD to
absorb kinetic energy of the main structure is same as Tuned Mass Damper (TMD). TLD is
simply constructed and easily maintained which make the device very cost efficient [2]. The
damping is achieved by the physical properties of the system and no external force is needed.
Vibration mitigation of the structure is achieved due to the transference of the structural
vibrational energy to the liquid when the natural frequency of the liquid motion is tuned to
the structural frequency. Tuning the fundamental linear sloshing frequency of the TLD to the
structure's natural frequency causes large amount of sloshing and wave breaking at the
resonant frequencies of the combined TLD-structure system that dissipates a significant
amount of energy [3]. The force of the sloshing fluid, as shown in Figure 1, resists the
motion of the structure, which reduces the structural response.
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
267
Figure 1 - TLD damper
Many experimental and numerical research studies were done over past years to illustrate
the effectiveness of a TLD as a vibration control device for structures subjected to harmonic,
wind and earthquake excitations. The use of TLDs designed to suppress wind-induced
structural vibrations experienced in tall buildings, e.g. the 105 m high Hobart Tower in
Tasmania and the 158 m Gold Tower in Japan, were studied by Kareem et al [4]. Full-scale
measurements of four buildings were conducted by Tamura et al. to verify the efficiency of
the TLD under wind excitations [5]. A number of papers [5-9] have been presented about the
studying of TLDs to effectively control the wind response of structures. Vancliver et al. [10],
Sun et al. [11], Banerji et al. [3] and Reed et al. [12] were among the first to study the use of
TLD as an earthquake response controlling device. Fujino et al. [13] have developed 2D
rectangular model of the tuned liquid damper (TLD) to reduce the dynamic response of
structures. Experiments were performed to make out the characteristics of TLD and the
interaction between the TLD and structure using the shaking table test with a harmonic
external loading. Banerji et al. [3] have shown through numerical studies that if the design
parameters of a TLD are set appropriately, that TLD can be very effective in controlling
earthquake response of structures. The results showed the TLD was effective for controlling
earthquake response.
Different approaches are proposed for numerical modeling of the TLD. Sun introduced a
model to solve nonlinear Navier-Stokes and continuity equations. A combination of
boundary layer theory and shallow water wave theory is employed and resulting equations
were solved using numerical methods and this model considers wave breaking under large
excitations by means of two empirical coefficients [14]. Yu employed equivalent Tuned
Mass Damper (TMD) concept that can capture the TLD behavior under large amplitude
excitations and during wave breaking. An equivalent Nonlinear-Stiffness-Damping (NSD)
model is proposed through an energy matching procedure when the dissipated energy by the
equivalent NSD model is matched by that of the TLD [15]. Tait developed an equivalent
linear mechanical model that accounts for the energy dissipated by the damping screens for
both sinusoidal and random excitation [16, 17]. Effect of employing TLD for seismic
response control has been studied [3, 18]. In fact, a rectangular TLD can allow sloshing to
occur in any direction and, when properly designed, its inherent behavior properties under
dynamic loading can make it a good solution in the reduction of earthquake demands in
buildings.
In this paper, an attempt has been made to study the effectiveness of Tuned Liquid
Damper for improving seismic performance and controlling seismic vibration of existing
intermediate steel moment resisting frames. Etabs Nonlinear 15.1 software is used to model
the structure and the TLD. The TLD is modelled as an equivalent Tuned Mass Damper for
rehabilitation of existing intermediate steel moment resisting frames following ASCE 41-13
provisions [19]. In this study, 2D 4-story and 8- story, 3-bay frame structures were
considered in Tehran. Nonlinear response history analysis has been performed under 5
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
268
earthquake records for seismic design hazard level, namely a return period of 475 years.
Effect of introducing TLD damper on seismic performance is evaluated considering
parameters of the TLD damper (such as damper mass and tuning damper frequency).
2. Yu`s Model [15]
Yu (1997) and Yu et al. (1999) modelled the TLD as a solid mass damper that can
capture nonlinear stiffness and damping of the liquid motion. This mechanical model can
capture the behavior of the TLD in a broad range of excitation amplitudes and can be a good
TLD design tool. An equivalent Nonlinear-Stiffness-Damping (NSD) model is proposed
through an energy matching procedure when the dissipated energy by the equivalent NSD
model is matched by that of the TLD. Figure 2 shows the characterized schematic SDOF
model of the TLD; , and refer to the stiffness, damping coefficient, and mass of
the NSD model, respectively.
Figure 2- Schematic of the a) TLD and b) Equivalent NSD Model [15].
The TLD behavior is described by NSD parameters, which have been obtained from
experimental investigations on TLDs. An equivalent interaction force is introduced to
simulate the forces exerted by liquid sloshing inside the tank as shown in Figure 2.
Considering the TLD as an equivalent linear system, this force has been characterized by its
amplitude and phase. The results are analyzed through two ratios: frequency shift ratio and
stiffness hardening ratio.
The main parameters for NSD model are based on following [15]:
1-Non-dimensional value of the amplitude was found to be the most suitable parameter to
describe the stiffness and damping ratio. This value is described as:
Λ
1
where is the amplitude of excitation and L is the length of the tank in the direction of
motion.
2- Yu obtained the damping ratio as:
0.5Λ.2
3- is the linear fundamental natural frequency of the liquid and can be found as[14]:
1
2
tanh
3
where is the height of the water and g is the gravitational constant.
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
269
4- Under larger amplitude of base excitations the fundamental frequency of TLD, is
larger than , the value derived from Eq (3). This increase in fundamental frequency has
been incorporated in Eq (4) by introducing a term ‘frequency shift ratio’. The equivalent
nonlinear frequency of the TLD is presented as:
2
tanh
4
5- Based on experimental observations and by energy matching procedures is
quantified as:
1.038Λ.0.03waekwavebreaking5.
1.59Λ.Λ0.03strongwavebreaking5.
6- The stiffness of the NSD model is obtained by introducing a stiffness hardening ratio.
6
where 2.
7-The stiffness hardening ratio is defined as:
1.075.0.03waekwavebreaking7.
2.52.Λ0.03strongwavebreaking7.
3. Analysis
3.1 Model Definition
In this study, 2D 4-story and 8- story, 3-bay existing steel structures are considered in
Tehran. The elevations of the frames are shown in Figure 3. The buildings utilize a structural
system with intermediate steel moment resisting frames. Height of the first story is 3.6 meter
and other stories are considered 3.2 meter height.
Figure 3: 4-story and 8- story intermediate steel moment resisting frames
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
270
In this research, and are assumed 1.631 and 0.577, respectively. According to
ASCE 7-10 [20] for soil type D, and are equal with 1.1 and 0.6, respectively. The
program Etabs Nonlinear is employed to model the structure. Furthermore, HEA sections for
beams and HEB sections for columns are used. The building is designed for gravity and
seismic loads. A uniformly distributed live load of 2 kN/m2 and a uniformly distributed dead
load of 8 kN/m2 are considered for all floors. Snow load of 1.05 kN/m2 is considered for roof
level. The steel is ST-37 type with Fy=250 MPa.
Evaluation of seismic bearing of these buildings is performed according to ASCE 41-13
provisions [19]. The fundamental period of the structure, determined from linear analysis.
3.2 Selecting Earthquake Ground Motions
To investigate the effectiveness of TLD in reducing damage to the structure induced by
ground excitation, five earthquake records are employed as the input ground motions.
Characteristics of selected records are shown in table 1.
Table 1: Characteristics of selected records
ID Earthquake Name Year Station Name Magnitude
1 "Duzce Turkey" 1999 "Bolu" 7.14
2 "Imperial Valley-06" 1979 "El Centro Array #11" 6.53
3 "San Fernando" 1971 "LA - Hollywood Stor FF" 6.61
4 "Superstition Hills-02" 1987 "Poe Road (temp)" 6.54
5 "Manjil Iran" 1990 "Abbar" 7.37
In Figure 4, the comparisons of design response spectra according to ASCE7-10 [20]
with response spectra of the five earthquakes records are represented.The ground motions
are scaled such that the average value of the 5 percent damped response spectra for the suite
of motions is not less than the design response spectrum for the site for periods ranging from
0.2T to 1.5T where T is the natural period of the structure in the fundamental mode for the
direction of response being analyzed [20]. Based on ASCE7-10, scale factors of this set of
earthquake records are listed in table 2.
Figure 4: Comparison of response spectrum of selected records with ASCE7-10.
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
271
Table 2: Scale factors of selected records
Earthquake ID 8 - story 4 - story
1 1 1.1
2 1 1.2
3 1.8 1.8
4 1.6 1.6
5 1 0.9
3.3 Design and modeling of the TLD
In this research, to investigating the TLDs effect on seismic performance of structures,
TLDs are modelled based on YU approach [15] that presented in section 2. It is assumed that
length of TLDs are 1 m. Four cases of TLDs are considered that the TLD mass is 1%, 2%,
3%, and 4% of total mass of the structure. TLDs properties such as stiffness and damping
coefficient are determined by YU model. The structures with and without the TLD are
analyzed through nonlinear response history subjected to each scaled ground motion records,
where the structure model includes nonlinear hinges [19]. The TLDs are simulated as a mass-
spring-dashpot system through connecting a point mass by appropriate Link element in Etabs
Nonlinear software.
The procedure of determining the TLD properties are as follow:
1- With tuning the linear frequency of the TLD with frequency of structure first mode,
the length and width of the tank are determined.
2- Non-dimensional value of the amplitude (Λ) is calculated from Eq (1) for each
motion records.
3- The damping ratio of the TLD is determined using Eq (2).
4- The stiffness of the TLD is determined by Eq (6).
4. Results
In this section, the results of modelling structures with and without TLD in Etabs
Nonlinear 15.1 program are presented. The results include maximum roof displacement,
maximum drift story, maximum base shear, and maximum roof residual displacement. The
max drift story for 4 cases of TLD and without TLD are compared as a graph.
4.1 Results of 4-Story Frame
Average maximum story drift in % are compared in Figure 5. Maximum base shear is
presented in Table 3. Maximum roof displacement is listed in Table 4. Roof residual
displacement at the end of ground motion record is tabulated in Table 5.
Table 3- Maximum Base Shear
Max Base Shear (kN)
Record ID 1 2 3 4 5 Avg
1% 2078.51 1519.60 1494.72 1600.21 1526.97 1644.00
2% 2045.45 1435.18 1353.20 1493.16 1571.33 1579.66
3% 2003.37 1361.99 1282.01 1390.62 1575.51 1522.70
4% 1970.50 1304.84 1215.42 1339.42 1540.71 1474.18
Without TLD 2111.75 1599.44 1700.33 1702.86 1570.94 1737.06
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
272
Employing the TLD reduces the maximum base shear 5 to 15%, while the maximum roof
displacement is reduced 4 to 10%. Residual displacement decreased 40 to 55%.
Figure 5: Maximum Drift Story for 4-story.
Table 4- Maximum roof displacement
Max roof displacement
1% 2% 3% 4% No TLD
Record ID m m m m m
1 0.4058 0.3922 0.3792 0.3663 0.4197
2 0.2876 0.2836 0.2801 0.2779 0.2907
3 0.3387 0.3220 0.3193 0.3180 0.3692
4 0.2209 0.2074 0.2043 0.2109 0.2349
5 0.3038 0.3062 0.3038 0.3007 0.3187
MAX 0.4058 0.3922 0.3792 0.3663 0.4197
AVG 0.3114 0.3023 0.2973 0.2948 0.3266
Table 5- Roof residual displacement
Roof residual displacement
1% 2% 3% 4% No TLD
Record ID m m m m m
1 0.0335 0.0367 0.0421 0.0489 0.0261
2 0.0008 0.0006 0.0010 0.0009 0.0044
3 0.0017 0.0044 0.0054 0.0059 0.0029
4 0.0260 0.0015 0.0017 0.0014 0.0808
5 0.0026 0.0066 0.0063 0.0056 0.0020
MAX 0.0335 0.0367 0.0421 0.0489 0.0808
AVG 0.0129 0.0100 0.0113 0.0125 0.0232
4.2 Results of 8-story Frame
Average maximum story drift in % are compared in Figure 6. Maximum base shear is
presented in Table 6. Maximum roof displacement is listed in Table 7. Roof residual
displacement at the end of ground motion record is tabulated in Table 8.
Employing the TLD reduces the maximum base shear 6 to 17%, while the maximum roof
displacement is reduced 4 to 10%. Residual displacement decreased 14 to 40%.
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
273
Figure 6: Maximum Story Drift for 8-story
Table 6- Maximum Base Shear
Max Base Shear (kN)
Record ID 1 2 3 4 5 AVE
1% 2874.98 2400.24 2538.30 2710.38 2297.15 2564.21
2% 2773.19 2179.09 2310.24 2671.05 2241.47 2435.00
3% 2680.60 1997.80 2108.17 2694.70 2396.79 2375.61
4% 2584.24 1835.98 1817.58 2705.01 2407.52 2270.07
Without TLD 2989.17 2661.63 2785.34 2802.88 2377.44 2723.29
Table 7- Maximum roof displacement
Max roof displacement
1% 2% 3% 4% No TLD
Record ID m m m m m
1 0.2282 0.2292 0.2280 0.2263 0.2282
2 0.3678 0.3509 0.3374 0.3264 0.3892
3 0.4989 0.4855 0.4707 0.4593 0.5074
4 0.4378 0.4187 0.3977 0.3761 0.4582
5 0.3489 0.3715 0.3938 0.4075 0.3903
MAX 0.4989 0.4855 0.4707 0.4593 0.5074
AVG 0.3763 0.3712 0.3655 0.3591 0.3946
Table 8- Roof residual displacement
Roof residual displacement
1% 2% 3% 4% No TLD
Record ID m m m m m
1 0.0512 0.0567 0.0581 0.0562 0.0426
2 0.0269 0.0160 0.0110 0.0084 0.0384
3 0.0034 0.0144 0.0185 0.0201 0.0256
4 0.1153 0.0873 0.0445 0.0107 0.0983
5 0.0021 0.0175 0.0336 0.0417 0.0253
MAX 0.1153 0.0873 0.0581 0.0562 0.0983
AVG 0.0398 0.0384 0.0331 0.0274 0.0461
6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
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4.2 Using two TLDs for 8-story Frame
In this section, using two TLD for 8-story frame is presented. The total mass ration of
TLDs are 2% of total mass of frame and the TLDs are tuned to 1st and 2
nd mode of the
8-story frame using YU model. The results of two TLDs are slightly better than one TLD of
the same mass ratio, as shown in Figure 7 and summarized in Table 9.
Figure 7: Max Story Drift (%)
Table 9- Reduction of average maximum story drifts
Reduction percent of max story drifts of all stories
1% 2% 3% 4% 2-TLD
7.3 13.3 18.8 23.1 12.5
5. Conclusion
In this research, it is observed that TLD dampers can be utilized as seismic response
mitigation device, so they can be employed for seismic rehabilitation of existing steel
structures. With increasing mass ratio of the TLD, the reduction in maximum drift story,
maximum base shear, and maximum roof displacement are increased. The TLD is more
efficient for 8-story frame. It is observed that using two TLDs tuned to 1st and 2nd mode of
the structures can improve slightly seismic response slightly comparing to TLD of same
mass ratio tuned to 1st mode of the structure.
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6th International Conference on Earthquake & Structures
October 14-15, 2015, ACECR of Kerman, Kerman, Iran
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