10.1002_stc.499 1vf2b

STRUCTURAL CONTROL AND HEALTH MONITORING

Struct. Control Health Monit. (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.499

Experimental studies on use of toggle brace mechanism fitted with magnetorheological dampers for seismic performance enhancement of three-storey steel moment-resisting frame model K. Rama Raju1,*,†, A. Meher Prasad2, K. Muthumani1, N. Gopalakrishnan1, Nagesh R. Iyer1 and N. Lakshmanan1 2

1 CSIR- Structural Engineering Research Centre, Chennai 600113, India Structures Division, Indian Institute of Technology, Madras 600036, India

SUMMARY The supplemental ive and semi-active dampers such as viscous fluid dampers and magnetorheological (MR) dampers normally placed in either Chevron or Toggle brace are increasingly used to provide enhanced seismic protection for new/retrofit existing buildings and bridges. The experimental nonlinear force–velocity relationships of MR dampers at different current inputs are fitted to fractional velocity power law. A three-storey quarter length scale steel moment-resisting frame model with two MR dampers fixed in upper toggle brace mechanism placed at ground floor level is designed and fabricated to study its seismic response characteristics. The natural frequencies and corresponding damping ratios of the model with MR damper at different current inputs are found. A procedure for modeling of MR dampers as nonlinear viscous fluid dampers is described. A methodology to find effective damping of the structural model is developed, using the formulations for nonlinear viscous fluid dampers given in literature. The methodology developed is used for finding the effective damping of structural model fitted with MR dampers in upper toggle bracing mechanism in different storeys of frame model. The model is subjected to two types of seismic excitations, and from studies of responses, it is found that the reduction in responses because of provision of MR dampers are to be quite significant. Copyright © 2011 John Wiley & Sons, Ltd. Received 1 October 2010; Revised 14 June 2011; Accepted 26 August 2011 KEY WORDS: seismic performance; magnetorheological dampers; toggle braces mechanism; dynamic characteristics; steel moment-resistant frame

1. INTRODUCTION Conventional seismic design of a frame structure relies on the inherent ductility of the structure to dissipate seismic-generated vibration energy while accepting a certain level of structural damage. An alternative approach to dissipate seismic energy and to prevent catastrophic failure of a frame structure is to install ive or active/semi-active devices within the structure. ive devices, such as viscoelastic damper, viscous fluid damper, friction damper, metallic damper, tuned mass damper, and tuned liquid damper can partially absorb structural vibration energy and reduce seismic response of the structure [1]. These ive devices are relatively simple and easy to be used as complementary structural appendages. However, the effectiveness of ive devices is always limited to combat the random nature of earthquake events. Different types of semi-active devices have been recently developed to equip ive control devices with actively controlled parameters forming a semi-active yet stable and low-power required damping system [2]. Among them, magnetorheological (MR) dampers and Electrorheological (ER) dampers are two typical types of smart (semi-active) dampers under active research. Addition of supplemental ive and semi-active energy dissipation devices such as viscous fluid dampers and MR dampers are considered to be viable strategies for enhancing the seismic performance of building structures. *Correspondence to: K. Rama Raju, Scientist, Structural Engineering Research Centre, CSIR Complex, Taramani, Chennai600113, India. † E-mail: [email protected]

Copyright © 2011 John Wiley & Sons, Ltd.

K. RAMA RAJU ET AL.

Viscous fluid dampers are increasingly used in new buildings or retrofitting the existing buildings in order to dissipate much of the earthquake-induced energy in elements not forming part of the gravity framing systems [3,4]. The philosophy behind the use of these elements is to limit or eliminate damage to the structural frame. The novelty and most interesting implementation of these energy dissipation devices is its configuration in the structural system. The configurations with a magnification factor larger than unity are very effective in enhancing the damping ratio with a reduced requirement for damper force. An iterative procedure using time history analysis is developed for finding the optimum number, capacity, and distribution of dampers fitted in different configuration in multistorey benchmark buildings and is described in references [3,5,6]. A review of several idealized mechanical models for controllable fluid dampers was carried out by Spencer et al. in 1997 [7], and they have developed a new model called phenomenological model for effectively modeling the behavior of a typical MR damper. Here, the behavior of MR damper is modeled as nonlinear viscous fluid damper at various current inputs. A new two-stage state control design approach has been developed by Ali and Ramaswamy [8] to monitor the voltage supplied to MR dampers for semi-active vibration control of the benchmark highway bridge. Choi et al. [9] numerically investigated the applicability of the MR damper-based smart ive control system with the electromagnetic induction part to the base-isolated building structures with nonlinear isolation systems such as friction pendulum bearings and lead–rubber bearings. Chang et al. [10] presented a semi-active control strategy for the seismic protection of the phase II smart base-isolated benchmark building subjected to near-fault earthquakes. In this paper, the effective damping of a frame model fitted with MR dampers in upper toggle bracing mechanism in the ground floor is experimentally evaluated. A procedure for modeling of MR dampers at different current inputs as nonlinear viscous fluid dampers is described. A methodology to find effective damping of the structural model is developed, using the formulations for nonlinear viscous fluid dampers given in literature. This methodology is used for finding the effective damping of structural model fitted with MR dampers in upper toggle bracing mechanism in different storeys of frame model. Experimentally, the sensitivity of the frame with MR damper in upper toggle bracing configuration to different current inputs is investigated. 2. DESCRIPTION OF EXPERIMENTAL MODEL A one-quarter scaled model of single bay three-storey steel moment-resisting frame (SMRF) is designed and fabricated as shown in Figures 1–3 [3,11]. The structure alignment and loading are

Figure 1. Frame model with upper toggle brace mechanism with magnetorheological dampers [3]. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM 1120

960 Steel Plate

Steel plate Concrete Slab

Concrete Slab ISLB100

ISLB100

ISLB100

ISLB100

ISLB100

700

700

ISLB 100

Steel Plate Concrete Slab

Steel Plate Concrete Slab

ISLB100

ISLB 100

2-- 1--

700

700

--1 --2

Steel Plate Concrete Slab

Steel Plate Concrete Slab

ISLB100

ISLB 100 50

200 422

--1 --2

1-2--

Pipe OD21/ID17

43

4 47

Pipe OD21/ID17

Pipe OD21/ID17

3

TS100x50x6

406

638 69

850

850

7 40

Damper

38

32

Base plate(300x300x10)

Base plate(300x300x10)

1.ISA 100x100x5 2.6 mm plate

All dimension are in mm

FRONT VIEW

SIDE VIEW

Figure 2. Plan and elevation of frame model with upper toggle brace mechanism and dampers [3].

1075

422

50

Steel Plate Concrete Slab

540

158

DAMPER

9 0°

43°

482

800

47 4

0 16

38

32°

3 69

7 40

638

50

1116

Figure 3. Connection details of upper toggle brace mechanism and damper to the frame model. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

chosen such a way that it gives response only in longer direction of structure. The weight at each floor including steel plate is 4.0 kN (excluding the tributary weight from beam and column). The three-storey SMRF model has a length of 1120 mm, width of 960 mm, and an overall height of 2250 mm as shown in Figures 1–3. The beams and columns are made of same type of sections (ISLB100@80 N/m). Six-millimeter thick gusset plates are used for connecting beams and columns. The are connected with bolts (eight, 10-mm high strength bolts with spring washer). The dimensions of base plates used near are 300 300 10 mm. The RC concrete slabs used in the model has dimension, 1120 960 100 mm. The inherent damping ratio of the structure is assumed to be 2%. The geometry, modal properties, and modal drifts of the structure are given in Table I. The model frame with masses are chosen in such a way that the fundamental period of the frame is in the flat region (0.1–0.4 s) of acceleration spectrum given in IS 1893–2002 corresponding to Type I soil stratum as shown in Figure 4. The experimental fundamental period of the model is found to be 0.25 s from sweep sine testing. Two MR dampers were placed at ground floor level by upper toggle brace configuration to the frame model. The toggle braces are tubular with 21 mm diameter and 4 mm thickness, and they are connected to each other with a pin connection. The toggle brace mechanisms and damper are connected to frame with a pin connection as shown in Figures 1–3. The values of θ1 = 32 and θ2 = 43 for toggle braces (Figure 3) and the orientation of the dampers in the upper toggle brace configuration were evolved iteratively by using the formula [12] for magnification factor given by Equation (1), such that it gives maximum magnification factor (varies from 2 to 5) and at the same time keeps the stroke length of the damper to its limiting value 53 mm. f ¼

sinθ2 þ sinθ1 cosðθ1 þ θ2 Þ

(1)

Here, θ1 and θ2 are 32 and 43 , respectively are the angles of inclinations of the bracings as shown in Figure 3. For the damper used, the limiting stroke length is 53 mm. In the final configuration, the values of θ1 and θ2 for toggle braces and the orientation of the dampers in the upper toggle brace configuration are 32 and 43 , respectively, as shown in Figure 3 and corresponding magnification factor is Table I. Geometric and modal properties of the structure (Figure 1). Floor no.

Mass (kg)

T (s)

Φ

Φr

400 400 400

0.25

1 0.85 0.59

0.15 0.26 0.59

3 2 1

Spectral Acceration Coefficient (sa/g)

Note: T is the first mode period in s, Φ is the first mode shape, and Φr is the modal drift between floors.

3 2.5 Type I (Rock, or Hard Soil)

2

Type II (medium Soil) Type III (Soft Soil)

1.5 1 0.5 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Periods (s)

Figure 4. Response spectrum for rock and soil sites for 5% damping. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM

3.16 and it is found from Equation (1). Here, the angles θ1 and θ2 vary under vibration and the magnification factor, f, also vary, but in practical design of toggle brace systems results in smaller rotations and the nonlinear are neglected [12]. 2.1. Details of test setup The three-storey steel frame was fabricated according to the details given in Figure 2 with suitable provision in base plate to connect the model with shake table. Concrete slab was cast separately and connected to beams through the bolts with washer. Circular opening of 20 mm diameter at center of slab are made by inserting polyvinyl chloride sleeves in the slab while casting. Additional mass of 200 kg is added to the model using 18-mm bolt with spring washer. The structure is fixed firmly with the shake table using bolts of 18 mm diameter inserted in each of the base plate sleeves. The accelerometers and the linear variable differential transformers (LVDTs) are fixed at each floor level with the LVDTs placed in an external steel frame kept outside the shake table. 2.2. Measurement of displacement An external frame outside the shaking table is provided to record the displacement history of the table. Accelerometers are attached on the table in order to check the accuracy of the reproduction of the input accelerogram. LVDTs of capacity 20 and 50 mm are used to measure the horizontal displacement at the floor levels 1, 2, and 3, respectively. All analog signals from instrument connected to the model and shake table are amplified, recorded, digitized, and stored. Graphic display and printer facilities are utilized using FFT analyzer. 2.3. Description of test procedure and results Free vibration tests are carried out using the shaking table in unidirectional way at Advanced Seismic Testing and Research Laboratory at Structural Engineering Research Centre, Council of Scientific & Industrial Research, India. The shake table is excited with low-level acceleration, and the corresponding data from the accelerometers placed side by side on the shake table is compared. In case, the output voltage of the accelerometers is not equal then; they are calibrated on an equal level by tuning their ratio to unity. Thus, it is possible to build the ratio between two measured accelerations. After the calibration, the accelerometers are installed at the required points, i.e. one at each floor level and two at the base plate of the shake table. One of the accelerometers at the base level is used to control the motion of the table, whereas the other is used for frequency response function analysis. The acceleration at the floor level was found from the accelerometer at the floor level. The accelerometer at the base gives the acceleration according to the input data of the shake table. The second accelerometer at the base is used to control the amplitude of the base acceleration to make it possible to keep the acceleration amplitude constant (in general, it is between 0.02 and 0.1 g). Each time, the frequency was increased with an increment of 0.1 Hz and corresponding frequency response function was noted up to the first three modes (i.e. up to 30 Hz) and it is as shown in Figure 5. 80

Amplitude Factor

70 60 50 40 30 20 10 0 0

5

10

15

20

25

30

Frequency (Hz)

Figure 5. Frequency response function. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

3. FREE VIBRATION STUDIES OF THE FRAME MODEL The equation of motion for the dynamic system with base excitation can be written as

:: :: Mx þ C x_ þ Kx ¼ -Mixg

(2)

where M, C, K, and i represent the mass, damping, stiffness, and influence matrices, respectively. The variation of real and imaginary parts of ratio of floor level acceleration to base acceleration for the three floors are obtained numerically increasing values of o2. Around the natural frequencies, the real part quickly changes from positive to negative or vice versa, whereas the imaginary part is positive or negative. The imaginary part of the transfer function for floor level acceleration to base acceleration at natural frequencies represents the mode shape to some scale Φi,j at the ith floor at jth natural frequency. The normalized mode shape is obtained as f’i;j = fi, j/|fi, j |max, where |fi, j |max is the maximum value of Φi,j at jth natural frequency. In the experimental program, after obtaining the natural frequencies through sweep sine testing, the structure was excited at the three natural frequencies namely 4.2, 12.5, and 19.5 Hz, and the imaginary parts of the transfer function of floor response acceleration to base acceleration were determined, and the experimental values for the mode shape vector are evaluated using the procedure given earlier. These are plotted in Figure 6. The mode shapes experimentally obtained satisfied both normality and orthogonality conditions within acceptable experimental error (5%), and the natural frequencies back worked using the above mode shapes matched well with experimental values. The amplitude of the sinusoidal displacement waveform was chosen for sine wave excitation keeping the acceleration amplitude constant 0.1 g. The forcing frequency is varied over a range that includes the natural frequency of the system. A frequency response curve in the form of acceleration amplitude (corresponding floor level) versus frequency is plotted directly from the measured data. The natural frequency can be determined from experimentally obtained frequency response curve. The above test procedure was carried out for the case of frame model with upper toggle bracing mechanism and dampers with the current inputs ranging from 0 to 1 A with an increment of 0.25 A. The natural frequencies of the frame model with upper toggle bracing mechanism and dampers with current inputs ranging from 0 to 1 A with an increment of 0.25 A for the first and second modes are determined by experiments. The natural frequencies for frame model with current inputs ranging from 0 to 1 A with an increment of 0.25 A are summarized in Table II. Mode I Exp. (4.2 Hz) Mode III Exp. (19.5 Hz) Mode II Ana (12.5 Hz)

Mode II Exp. (12.5 Hz) Mode I Ana (4 Hz) Mode III Ana (20 Hz)

3

Storey

2

1

0

-1.00

-0.50

0.00

0.50

1.00

Response Amplitude Factor

Figure 6. Mode shapes (experimental and analytical). Table II. Fundamental natural frequencies for frame model with and without current input. Sine wave excitation, 0.1 g Natural frequency (Hz) Current input (A) First mode Second mode

0 4.0 18.5

Copyright © 2011 John Wiley & Sons, Ltd.

0.25 4.5 18.0

0.5 4.5 17.5

0.75 4.5 17.5

1.0 4.5 17.5

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM

Theoretically, although addition of damper should not cause any change in frequency, a certain level of stiffening is noticed particularly at higher current levels. At 0 A current level, the frequency is 4 Hz, but at 0.25, 0.5, 0.75, and 1 A, the frequency is observed to be 4.5 Hz (Table II). The second frequency is significantly high compared with theoretical value but does not show variation for various current levels during testing. In the present study, it is assumed that the columns are fixed at the base. The natural frequencies of this frame model for the first three modes are determined by experimentally and analytically using SAP2000 software (Computers and Structures, Inc., Berkeley, CA, USA), and they are found to be 4, 12.5, 20, and 4.17, 12.84, 20 Hz, respectively. Two MR dampers were placed at ground floor level by upper toggle brace configuration to the frame model. The value of stiffness k, for the braces connecting the damper to the frame, is large enough to ensure that the element behaves as a pure damper. These braces were taken as tubular with 21 mm diameter and 4 mm thickness, and they are connected to each other with a pin connection. The pin has, three degrees of freedom, and they are Ux, Uz, and θY, and at base , it has only one degree of freedom, θY. The comparisons of experimental and analytical frequencies are given in Figure 6.

4. EFFECTIVE DAMPING RATIO OF THE MODEL FRAME

Frequency Response Amplitude, (x 0.1g)

The ratio of the third floor acceleration to base level acceleration, frequency response amplitudes, corresponding to the third floor level of three-storey steel frame with MR damper at different current inputs (A) and frequencies are recorded. The variation of frequency response amplitude with excitation frequency is plotted in Figure 7. From experimental frequency response curve, the damping ratios of the system is found at different current inputs to MR dampers and is given in Table III. It is observed that for the current input 0 and 0.25 A, the damping ratio, x, is in 0.11 and 0.1, respectively. However, with further increase in the current input, it is found that x is constant at about 0.07. From this, it can be concluded that at 0 A, the system is having maximum efficiency, and further increase in the current input beyond 0.25A, the efficiency decreases significantly. This is not in tune with the analytical expectation, i.e. increased damping with increase in current input. Experimental investigation becomes extremely important in view of the above observation. Frequency

6 0.25

0.5 A

0.75 A

1A

0A

5 4 3 2 1 0 3

3.5

4

4.5

5

5.5

6

6.5

7

Frequency

Figure 7. Frequency response function measured in the third floor at different current inputs. Table III. Damping using bandwidth method. Current input (A) 1.0 0.75 0.50 0.25 0.0

f1

f2

f2 Þ j ¼ ðð ff11 þ f2 Þ

3.6 3.85 4.05 4.1 4.1

4.5 4.7 4.7 4.7 4.75

0.074 0.07 0.07 0.1 0.11

Note: x is the damping ratio. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

4.1. Viscous damping provided by linear viscous dampers The damping ratio (x) provided by linear viscous dampers for a SDOF system subjected to one cycle of harmonic vibration is [13] WD (3) 4pWS where WD = the energy dissipated by linear viscous dampers in one cycle of harmonic vibration; WS = the strain energy. For MDOF systems, the energy dissipated by linear viscous dampers and the strain energy of the system for the primary mode can be computed as 2 X X 2p WD ¼ WD j ¼ pCj (4) uroof fmr;j fj Tm j j x¼

WS ¼

2p2 X m u 2 f2 i i roof mi Tm2

(5)

in which WDj = the energy dissipated by linear viscous damper j in one complete cycle loading; Cj = the damping coefficient for linear viscous damper j; Tm = the period of vibration of the primary mode; uroof = the maximum roof displacement; Φmr,j = the relative modal displacement of the primary mode between the ends of damper j along the axis of damper j; fj = magnification factor; mi = the mass of floor level i; Φmi = the modal displacement of the primary mode at floor level i. Substituting Equations (4) and (5) in Equation (3), the damping ratio (xd) provided by linear viscous dampers for the primary mode can be obtained. P Tm j C j f2mr;j fj2 (6) xd ¼ P 4p i mi f2mi 4.2. Equivalent viscous damping provided by nonlinear viscous dampers The energy dissipated by nonlinear viscous dampers for a SDOF system subjected to one cycle of harmonic vibration is [14]. a Z Z 2p u0aþ1 (7) WD ¼ Fd du ¼ CN u_ a du ¼ lCN Tm l ¼ 22þa

Γ2 ð1 þ a=2Þ Γ ð2 þ a Þ

(8)

where u = the displacement response of the SDOF system; u0 = the maximum value of u; CN = the damping coefficient of nonlinear viscous dampers; Γ = the gamma function. Equation (7) can be extended to MDOF systems as aj aj þ1 X X 2p WD;j ¼ lj CN;j uroof fmr;j fj (9) WD ¼ Tm j j Substituting Equations (9) and (5) in Equation (3), the equivalent viscous damping ratio (xm) provided by the nonlinear viscous dampers [11] for the primary mode can be obtained as aj 2 P aj 1 aj þ1 aj þ1 2p uroof fmr;j fj j lj CN;j Tm (10) xd ¼ P 2p i mi f2mi a j þ2

lj ¼ 2

Γ2 1 þ aj =2 Γ 2 þ aj

(11)

where CN,j = the damping coefficient for nonlinear viscous damper j; aj = the velocity exponent for nonlinear viscous damper j. If aj = 1 (i.e. the case of linear viscous damping), lj = p and then, Equation (10) becomes Equation (6). Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM

In this study, the equivalent (linear) viscous damping provided by nonlinear viscous dampers is basically derived from the assumption that the average energy dissipated by the linear and the nonlinear viscous dampers in a SDOF system subjected to all cycles of harmonic vibration is equal, i.e. 1 u0

Zu0

1 WDN du ¼ u0

0

1 u0



Zu0 lCN

0 a 1+a

2p Tm

Zu0 WDL du

(12)

0

a u

aþ1

1 du ¼ u0

Zu0



2p 2 pC u du Tm

(13)

0

where WDN = lCN(2p/Tm) u = the energy dissipated by nonlinear viscous dampers in one cycle of harmonic vibration; WDL = pC(2p/Tm)u2 = the energy dissipated by linear viscous dampers in one cycle of harmonic vibration. The left-hand side in Equation (12) is the average energy dissipated by nonlinear viscous dampers, and the right-hand side is the average energy dissipated by linear viscous dampers. Integrating Equation (13), the equivalent damping coefficient can be obtained as a1 3lCN T2pm u0a1 (14) C¼ pð2 þ aÞ Equation (14) is resulted from a SDOF system formulation. It can be extended to MDOF systems by replacing u0 with uroof Φmr,j fj as aj 1 aj 1 3lj CN;j T2pm uroof fmr;j fj Cj ¼ (15) p 2 þ aj Thus, the equivalent viscous damping ratio provided by nonlinear viscous dampers can be derived by substituting Equation (15) in Equation (6) as P lj CN;j 2p aj 2 aj 1 aj þ1 aj þ1 3 j 2þa uroof fmr;j fj ð j Þ Tm (16) xd ¼ P 2p i mi f2mi Although the functions of Equations (10) and (16) are similar, they are derived from different bases. Therefore, the results calculated from the two equations are somewhat different. In general, the equivalent viscous damping computed from Equation (10) is found to be smaller than that obtained from Equation (16).

5. CHARACTERIZATION OF MAGNETORHEOLOGICAL DAMPERS [3] A review of several idealized mechanical models for controllable fluid dampers was carried out by Spencer et al. in 1997, and they have developed a new model called phenomenological model for effectively modeling the behavior of a typical MR damper. Here, a MR damper is modeled as nonlinear viscous fluid damper at various current inputs. The dynamic response of the MR damper, RD-1005-3 subjected to sinusoidal excitation at 2 Hz with amplitudes of 3 mm was found experimentally. The characterization of MR damper is carried out by providing various (0, 0.25, 0.5, 0.75, and 1 A) current inputs by fitting experimental force– velocity relationships to fractional velocity power (FVP) law, and damper properties, damping coefficient, C0, and damping exponent, a, were found. The force–velocity relationship obtained experimentally shows that it behaves as nonlinear viscous damper at different current inputs. The MR damper with toggle brace mechanism is incorporated in a three-storey steel moment-resisting frame. The damping ratio obtained varies from 0.07 to 0.11 as given Table III. Theoretical expectation showed significant variation in damping ratio with input current. Hence, it is clear that individual performance as a damper, and in a structural scheme wherein there are other sub-assemblies also, could have an effect on efficiency of the damper performance. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

The force and velocity relation for nonlinear viscous fluid dampers can be expressed as a FVP law: (17) fD ¼ Co ju_ ja signðu_ Þ where fD is the damper output force, u_ is the velocity, and C0 is the damping coefficient with units of force per velocity; a is a real positive exponent. From the experimental values, the nonlinear relationships between force and velocity profile at 0, 0.25, 0.5, 0.75, and 1 A current inputs for the MR damper with different amplitudes of sinusoidal excitation are represented as the FVP law given in Equation (17), and they are shown in Figure 8. The damping coefficient, C0, and the real positive exponent, a, are found from FVP law using least square fit method and are tabulated in Table IV. The relationship between current inputs (A), damping coefficient (C0), and the exponent (a) in FVP law for the damper is given in Table V. Here, a is the current input, C(a) is the damping coefficient, and a(a) is the exponent in FVP law, and a is a real positive exponent. 6. DESIGN OF NONLINEAR VISCOUS DAMPING SYSTEM 6.1. Design coefficients of design basis earthquake as per IS: 1893–2002 Consider that the steel frame shown in Figure 2 is located in seismic Zone V. The soil conditions are medium stiff. Zone factor, Z = 0.36 for Zone 5, from Table 2 of IS: 1893–2002. The importance factor, I, is assumed to be 1, as per Table 6 of IS: 1893–2002. For medium stiff soil and 5% damping, from Figure 2 of IS: 1893–2002. For T = 0.33 s, Sa/g = 2.5. Response reduction factor, R = 5.0, as per Table 7 of IS: 1893–2002. DamperS.No:015918 for different current input and 2Hz frequency 2.5 2 1.5

0A-Exp 0.25A-Exp 0.50A-Exp 0.75A-Exp 1A-Exp

0A-FVP Law 0.25A-FVP Law 0.50A- FVP Law 0.75A-FVP Law 1A-FVP Law

Force (kN)

1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Velocity (m/s)

Figure 8. Damper S.No:015918 characterizations at different current inputs with experimental data fitted with fractional velocity power law. Table IV. Damper properties obtained from experiments. Current (A)

Damping coefficient C0 (N (s/m)a)

Exponent a

585 1632 2700 3150 4150

0.34 0.34 0.28 0.21 0.21

0 0.25 0.5 0.75 1 Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM

Table V. Variation of damper constants, a and C0 with current. C(a) = 2821a3 5045a2 + 5789.4a + 559.19 a(a) = 0.6933a3 1.0514a2 + 0.2281a + 0.3396 Note: a is the current input, a is the real positive exponent, C(a) and a(a) are the damping coefficient and exponents, respectively, in fractional velocity power law.

Horizontal seismic coefficient, Z I Sa ¼ 0:09 2R g The modal participation factor of the first mode, PF1 P mi fim 400 1 þ 400 0:85 þ 400 0:59 PF1 ¼ Pi ¼ ¼ 1:178 2 400 12 þ 400 0:852 þ 400 0:592 i mi fim Ah ¼

Floor acceleration, Ai1 Ai1 ¼ PF1 fi1 Ah Ai1 ¼ 1:178 1 0:09 9:81 ¼ 1:04 m=s2 Floor displacement, Δi1 Δi1 ¼

T 2 Ai1 2p

0:25 2 ð1:04Þð9810Þ ¼ 16:152 mm 2p Magnetorheological dampers at different current inputs are modeled as nonlinear viscous fluid dampers [3]. For different current inputs, the C0 and a, values were found as given in Table IV. Using these values, the equivalent viscous damping ratios, xd, are estimated using Equations (9) and (15), by provision of MR dampers at the first, first and second, and all three floors, are given in Tables VI and VII, uroof ¼ Δi1 ¼

Table VI. Effective damping (xd) values using Equation (9). xd considering dampers at Floor I Current (A) 0 0.25 0.50 0.75 1

C0(N (s/m)a)

a

Equation (9)

Experimental

Floors I and II

585 1632 2700 3150 4150

0.34 0.34 0.28 0.21 0.21

0.0145 0.0405 0.0695 0.0847 0.1116

0.11 0.1 0.07 0.07 0.07

0.02 0.0558 0.0969 0.1198 0.1578

Floors I, II, & III 0.0226 0.0631 0.1104 0.1378 0.1816

Table VII. Effective damping (xd) values using Equation (15). xd considering dampers at Floor I Current (A) 0 0.25 0.50 0.75 1

C0(N (s/m)a)

a

Equation (15)

Experimental

Floors I & II

585 1632 2700 3150 4150

0.34 0.34 0.28 0.21 0.21

0.0186 0.0520 0.0915 0.1150 0.1515

0.11 0.1 0.07 0.07 0.07

0.0256 0.0715 0.1275 0.1626 0.2143

Copyright © 2011 John Wiley & Sons, Ltd.

Floors I, II, & III 0.0290 0.0809 0.1453 0.1871 0.2465

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

respectively. From results, it is observed that addition of dampers at all floors increase the effective damping in structure at the given current inputs in MR dampers. From the results of effective damping ratio calculated, it can be observed that the dampers placed in the first floor contributes more to the effective damping ratio of the model comparing with the contribution of the dampers placed in all other floors. The effective damping contribution of dampers placed in the third floor is the least. Thus, effective damping contribution because of the dampers placed at the first and second floors is very significant. The effective damping estimated using Equation (15) is relatively more than the effective damping calculated using Equation (9). The more the current input (from 0 to 1 A) is, the more the effective damping in the model is. From Tables VI and VII, it can be observed that the analytical results using Equation (9) are closer to the experimental results. Here, it is to be noted that in analytical model of MR damper, the Hysteresis effect is neglected.

7. SEISMIC RESPONSE OF THE MODEL FRAME The model with and without dampers is subjected to two types of synthetic earthquake excitations exc1 and exc2 having PGAs of 0.2 and 0.4 g, and the same are as shown in Figure 9. The accelerometers are placed at all the floors levels of the model, and the accelerations are recorded. Analytically, the velocities and displacements are derived from the accelerations measured. The peak storey displacement, interstorey drifts, and interstorey shears of response time histories of the model without and with dampers at 0, 0.25, 0.5, 0.75, and 1 A current inputs are shown in Figures 10, 11, and 12, respectively. In all cases, provision of dampers at different current inputs, the performance enhancement in deformation, interstorey drifts, and base shear is observed except in few cases (Table VIII). For excitation exc1 current input beyond 0.25 A, an increase in interstorey drift in the first floor level is observed. Similarly, for excitation exc2, an increase in interstorey drift is observed at 0 A current input at the first floor level.

Earthquake excitation exc1 Acceleration (m/s2)

Acceleration (m/s2)

Earthquake excitation exc2

4

3 2 1 0 -1

2 0

-2

-2

-4

-3 0

5

10

15

20

25

30

35

40

45

50

55

60

0

5

10

15

20

25

30

35

40

45

50

55

60

Time

Time (s)

Figure 9. Excitations exc1 and exc2 considered on the experimental three-storey model.

2

Peak storey displacements of the frame subjected to

1 0

exc2 0A 0.75A

WOD 0.5A

0.25A 1A

3

Floor

Floor

Peak storey displacements of the frame subjected to exc1 WOD 0A 0.25A 0.5A 0.75A 1A 3

2 1 0

0

1

2

3

4

5

6

7

8

Displacements(mm)

9

10 11 12

0

2

4

6

8 10 12 14 16 18 20 22 24 26 28

Displacements(mm)

Figure 10. Storey displacements of the frame subjected to excitations exc1 and exc2. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

EXPERIMENTAL STUDIES ON USE OF TOGGLE BRACE MECHANISM

Inter-storey drifts of 3-storey frame subjected to exc2

Inter-storey drifts of 3-storey frame subjected to exc1 0A 0.75A

0.25A 1A

3

3

2

2

Floor

Floor

WOD 0.5A

1 0

WOD 0.5A

0A 0.75A

0.25A 1A

1 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Drift(mm)

Drift(mm)

Figure 11. Interstorey drifts of the frame subjected to excitations exc1 and exc2. Storey shears of the frame subjected to excitation exc1 WOD

0A

0.25A

0.5A

0.75A

Storey shears of the frame subjected to excitation exc2

1A

WOD

3

0A

0.25A

0.5A

0.75A

1A

3

2 Floor

Floor

2

1

1

0

0 1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

3

6

4

5

6

7

8

9

10

11

12

Shear(kN)

She ar(kN)

Figure 12. Storey shears of the frame subjected to excitations exc1 and exc2. Table VIII. Reduction in storey displacement, acceleration, and drift ratio in three-storey frame with provision of magnetorheological dampers at different current inputs. Storey displacements (mm) EQ

Current Configuration (A)

exc1 WOD WD

Reduction (%)

exc2 WOD WD

Reduction (%)

0.0 0.25 0.50 0.75 1.0 0.0 0.25 0.50 0.75 1.0 0.0 0.25 0.50 0.75 1.0 0.0 0.25 0.50 0.75 1.0

Interstorey drifts (mm)

First

Second

Third

First

26.57 9.15 7.63 2.82 15.86 11.76 65.56 71.28 89.39 40.31 55.74 21 8.36 7.07 8.63 8.55 7.66 60.19 66.33 58.90 59.29 63.52

11.57 1.73 3.85 3.39 3.58 3.63 85.05 66.72 70.70 69.06 68.63 17.02 9.65 6.45 5.97 5.5 5.86 43.30 62.10 64.92 67.69 65.57

8.86 2.08 3.3 3.01 3.15 4.8 76.52 62.75 66.03 64.45 45.82 26.57 7.15 5.71 2.55 15.86 11.76 73.09 78.51 90.40 40.31 55.74

2.8 2.5 1.9 3.7 3.9 6.2 10.71 32.14 32.14 39.29 121.43 4.76 6.04 4.33 3.07 3.31 3.54 26.89 9.03 35.50 30.46 25.63

Second Third 14.5 4.9 2.3 2.5 2.7 4.4 66.21 84.14 82.76 81.38 69.66 27.81 8.63 5.81 5.84 20.63 11.72 68.97 79.11 79.00 25.82 57.86

11.5 2.5 1.2 1 0.9 1.1 78.26 89.57 91.30 92.17 90.43 26.57 9.15 7.63 2.82 15.86 11.76 65.56 71.28 89.39 40.31 55.74

Storey shears (kN) First Second Third 5.802 3.583 3.062 3.418 3.565 3.607 38.25 47.24 41.10 38.57 37.84 11.376 7.184 5.836 7.896 7.994 8.080 36.85 48.69 30.59 29.73 28.98

4.673 2.813 2.692 3.004 3.091 3.102 39.80 42.40 35.72 33.86 33.62 8.858 5.407 4.689 5.878 6.330 6.483 38.96 47.07 33.65 28.55 26.82

2.646 1.537 1.954 2.115 2.161 2.179 41.90 26.14 20.07 18.34 17.65 5.030 3.644 3.633 4.792 4.863 4.963 27.56 27.78 4.74 3.33 1.33

Note: EQ stands for earthquake, WOD stands for without damper, and WD is with damper.

8. SUMMARY AND CONLUSIONS Based on the experimental studies reported in this paper with regard to the dynamic response of the MR damper, namely force–velocity relationship, it is inferred that it behaves as a nonlinear viscous damper at different current inputs. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2011) DOI: 10.1002/stc

K. RAMA RAJU ET AL.

A three-storey SMRF model was fabricated to carry out experimental studies. The MR damper with upper toggle brace mechanism is incorporated in a three-storey SMRF. The damping ratio obtained from experimental studies varies from 0.07 to 0.11 only, and for majority of the cases, the average value may be taken as 0.07. However, theoretical expectation showed significant variation in damping ratio with input current. Hence, it is clear that individual performance as a damper, and in a structural scheme wherein there are other sub-assemblies also, could have an effect on efficiency of the damper performance. In order to study the efficacy of provision of MR damper, the three-storey SMRF with damper assembly is also excited using two time history signals, exc1 and exc2. The reduction in maximum displacement, storey drift, acceleration, and base shear shows the effectiveness of dampers used with upper toggle brace configuration. The results show that provision of MR dampers with upper toggle bracing mechanism would act as vibration control device by dissipating energy at floor level where they are placed and controls the vibration levels of floors above. Experimentally, the sensitivity of the frame with MR damper in upper toggle bracing configuration to current input is investigated. It is observed that there is no performance enhancement in the system by transferring MR damper from ive to semi-active state. An attempt has been made to model the MR damper, with different current inputs, as nonlinear viscous damper. Using the formulations for nonlinear viscous fluid dampers given in literature, a methodology to find effective damping of the structural model is developed. This methodology is used for finding the effective damping of structural model fitted with MR dampers in upper toggle bracing mechanism in different storeys of frame model. By comparing the experimental effective damping with the analytical effective damping, it is noted that the results are found to be of the same order, but the variation of damping with current inputs is not following the same pattern. Further investigations are required to be carried out to find effectiveness of the system subjected to near-field earthquakes. ACKNOWLEDGEMENT

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Struct. Control Health Monit. (2011) DOI: 10.1002/stc