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Effect of SMA Braces in a Steel Frame Building

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Journal of Earthquake Engineering , 11: 326–342, 2007

Copyright © A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460601125763

326

UEQE1363-24691559-808XJournalof Earthquake Engineering, Vol.11, No. 3, February2007: pp. 1–31Journalof Earthquake Engineering

Effect of SMA Braces in a Steel Frame Building

Effectof SMA Braces in a Steel Frame BuildingR.L.Boroscheket al.

RUBEN L. BOROSCHEK, GLORIA FARIAS,

OFELIA MORONI, and MAURICIO SARRAZIN

Department of Civil Engineering, University of Chile, Santiago, Chile

Pull-back and shaking table test results on a simple model of a three-storey structure that includesshape memory alloys (SMA) copper-based dampers are presented and discussed. The model corre-sponds to a rigid-framed steel structure and the dampers to austenite CuAlBe wires inserted asbracing at each story. The inclusion of the dissipators in the structure increases the percentage of

critical damping from 0.59% for the bare case to 5.95% for the braced system. At the same time, thestructural stiffness increases making the first fundamental frequency change from 2.5–3.7 Hz (0.4– 0.27s). The net effect of these two factors is a 30–60% reduction of peak relative displacements compared to the ones obtained without dissipation devices when the structure is subjected to earthquakerecords. Depending on records frequency contents, a reduction of the peak accelerations to near 58% also can be obtained. Additionally, a crude nonlinear analytical model has been studied that can predict the earthquake responses reasonably well.

Keywords Shape Memory Alloys; Shake Table Test; Seismic Performance; Damping

1. Introduction

Shape memory alloys (SMA) are metallic alloys that can undergo large strains, while

recovering their initial configuration after unloading (superelastic effect) or by heating

(shape memory effect), without any permanent deformation. They dissipate energy in the

loading-unloading process, behavior that makes them suitable to be used as seismic dissi-

pation devices. In order to make this true, it is desirable that the superelastic behavior

occurs at ambient temperature. In addition, the material should dissipate substantial seismic

energy through repeated stable cycles at large strains with little degradation in properties

and low sensitivity to frequency in the 0.1–5 Hz range.

Although SMAs made of Nitinol (Ni-Ti), a binary alloy of nickel and titanium, have

received most of the commercial attention especially because of biomedical applications,

copper-based alloys may be more attractive for seismic applications because they are lessexpensive and easier to machine.

Thorough reviews concerning potential uses of Ni-Ti in earthquake engineering can

be found in DesRoches and Smith [2004a] and Wilson and Wesolowsky [2005]. Both

include state of the art information about modeling, design and testing of devices, as well

as theoretical and laboratory studies on their use in buildings and bridges. Janke et al.

[2005] discuss Ni-Ti and Fe-Mn-Si SMA potential applications on civil engineering. With

respect to copper-based SMA, most of the literature covers materials science aspects,

material models, and mechanical behavior of tertiary alloys such as CuZnAl, CuAlNi, and

CuAlBe. Studies on mechanical properties and energy dissipation capacity of copper-based

Received 28 November 2005; accepted 19 June 2006.

Address correspondence to Ruben L. Boroschek, Department of Civil Engineering, University of Chile,

Blanco Encalada 2002, Santiago, Chile; E-mail: [email protected]



Effect of SMA Braces in a Steel Frame Building 327

alloys can be found in Witting and Cozzarelli [1992] and Gillet et al. [1994]. More

recently, Casciati and Faravelli [2004] and Torra et al. [2005] studied CuAlBe alloy

towards its exploitation in passive control devices. Cyclic behavior depends on the type of

alloy, the thermo-mechanical processing which influences the grain size, the temperature

at which the material is used in relation to the phase transformation temperatures, sample

dimension, loading history, and loading rate. The influence of several of these factors on

Ni-Ti elements were studied within the MANSIDE project, Cardone et al. [1999]. DesRoches

et al. [2004b] also found that Ni-Ti wires show higher strength and damping compared

with bars and that increased loading rates lead to decreases in equivalent damping. Montecinos

et al. [2006] characterized two commercial batches of CuAlBe that differed in 1% Alumin-

ium and 0.1% Beryllium; although both alloys presented superelastic effect, important

differences were evident in terms of transformation phase temperatures, hysteresis loops

shapes and damping capacity.

In this study, a series of experiments were conducted on a model of a hypothetical

three-storey moment resistant steel frame building. Damping devices based on SMA

CuAlBe wires were installed in the longitudinal direction as braces. Pull-back and shakingtable tests were performed on the bare frame structure and on the braced one. The main

objectives were: (1) evaluation of the effectiveness of CuAlBe dampers during severe

seismic loads, and (2) evaluation of a simple analytical model for predicting earthquake

responses. The CuAlBe alloy was selected for this study because is actually available in

the world market at a reasonable cost and shows superelastic behavior at room tempera-

ture in tension cyclic tests.

2. Characteristics of SMA Braces

CuAlBe shape memory alloy wires (f

= 0.5 mm) were selected as energy dissipationdevices. Material was produced by Trefimetaux, France. Previously, in order to character-

ize their actual behavior, sinusoidal displacements were applied to pre-tensioned austenite

wire samples that were submitted to different thermal treatment, therefore, had different

grain sizes. Wires were heated at 717°C during different periods of time, followed by

water quenching and an aging process at 88°C for 20 h and at 96°C for 4 h. For compari-

son, an untreated wire was also tested.

Tests were performed at 1 Hz with displacement amplitude of 3.2 mm on wire sam-

ples that were 130 mm long. Strains were measured with a 2.5 cm length extensometer.

Figure 1 shows 20 cycles of the stress-strain relationship of the untreated wire and one that

was heated at 717°C for 225 s; the initial pre-tensioning loads were 100 and 51 N, respec-

tively, and the initial deformations were 3.8 and 9.1 mm, respectively. For comparisonpurposes, the initial deformations are not shown in the figure. Clearly, the untreated mate-

rial is much more rigid than the treated one, and in the latter case, less cycles are needed to

stabilize the stress-strain loops. In all cases, residual deformations were negligible.

Table 1 shows some results from the tests including secant stiffness, and energy loss

per cycle ED. The secant stiffness is defined as the difference between the maximum and

minimum load divided by the difference between the maximum and minimum deforma-

tion. The energy loss is the area enclosed by the hysteresis loop.

The Table shows variations in secant stiffness and energy dissipation capacity that

strongly depends on thermal treatment duration and strain. Wires with larger grain size

(heated for a longer period) are more flexible and with higher energy loss. Based on theseresults the wires installed in the structure were heated at 717°C for 225 s, followed by

water quenching and aging as explained earlier. However, due to the fact that the temperature

in the oven was not completely homogeneous, it was observed that the grain size changes



328 R. L. Boroschek et al.

along the length of the wire. This effect is more important when the wire is longer and has

a strong effect on the stiffness and energy dissipation capacity of the damper. Moreover,

to avoid intergranular brittle fracture, a small grain size is needed.

3. Description of the Model

Dimensions of the model are 120 cm high, 70 cm long, and 42 cm wide; the steel columns

(3 × 0.4 cm) are bolted to the beams which are welded to the floor slab. The model was

intended to work in the longitudinal direction, so four steel wires (f = 0.5 mm) were installedat each storey in the transverse direction to avoid torsion. Each floor weighs 180 N which

gives a total weight of 540 N (see Fig. 2) [Cerda, 2005]. The basis for selecting the dimension

of the test structure was the capacity of the shake table and available material dimensions.

FIGURE 1 Stress-strain relationship of CuAlBe untreated and thermal treated wire samples.

Characteristics of CuAlBe wires

Time of heating

at 717°C [sec]

Secant stiffness

[kN/m]

Energy loss ED

[N mm]

0 35.42 29.990 24.88 38.7135 25.36 37.1180 27.95 36.9225 21.48 41.0




Four SMA dampers were installed at each level. Details for each damper are shown in

Fig. 3. Each brace consists of a 45 cm long steel C angle 15 × 15 × 1.5 mm and a CuAlBe

wire (f = 0.5 mm) that is 40 cm long. The steel angle has at one extreme a longitudinal 3/8″

bolt that serves to tension the damper by means of a nut (top of the figure). The wire is

fixed to the steel angle and to the floor slab through a transverse 1/16″ bolt (bottom of the

figure).

FIGURE 2 Steel frame model.




4. Instrumentation and Experimental ResultsTwelve accelerometers that measure longitudinal and transverse accelerations were

installed in the bare structure. Additionally, in the damped structure, eight load-cells and

eight potentiometers were installed to measure forces and axial deformations in each

damper located at the first and second floor, as shown in Fig. 4.

Three pull-back tests were first performed with the bare structure to obtain the modal

parameters in the longitudinal direction. The structure was pulled and let it go manually

and also several initial velocities were produced by a soft impact on the structure corre-

sponding to different mode shape patterns. Shaking table tests were then performed using

5 min of white noise motion and amplitude and frequency scaled records from Sylmar

[1994] (with 0.36 g peak acceleration), Kobe [1995] (0.23 g), Taft [1952] (0.36 g),El Centro [1940] (0.21 g), and Llolleo [1985] (0.24 g) earthquakes; followed by three pull

back tests. The frequency scaling can have a strong effect on the response when the models

with and without diagonals are compared because of the change of predominant periods

and equivalent seismic demands. A similar sequence was used for the damped model, but

in this case the test series ended with 25 min of white noise motion. All tests were per-

formed at room temperature (≈ 20°C).

The shake table is a MOOG system, Model 6DOF2000E, with a load capacity of 10 kN

and approximately 25 cm of displacement capacity in three directions. Longitudinal as

well as simultaneous longitudinal and vertical components were applied.

The CuAlBe wires were pre-stressed with a tensile force of 30 N. This was performed

at the beginning of the tests, stressing first the wires on the east side and then those on

the west side. This sequence produced non uniform pre-strain, being they somewhat

larger at the west side. For each test the initial and final tensions were registered and

FIGURE 3 SMA Damper and connections.




FIGURE 4 Instrumentation of the model. (a) Detail of accelerometers; (b) Detail of load

cell and potentiometer.




some relaxation was noticed, but due to the test procedures no action could be taken to

restore the original 30 N.

Table 2 shows the frequencies and equivalent damping ratios obtained for the bare

model from the pull-back tests performed before and after shaking table tests. Analyses to

obtain natural frequencies and damping ratios were conducted using the Ibrahim Time

Domain Method [Ibrahim and Mikulcik, 1977]. Differences in frequencies are very small

for both set of test. Damping, although rather low, shows a larger variation in the first and

second mode that may be related to relaxation of some of the connections. Analytical

results obtained from a model using RUAUMOKO structural analysis program [Carr,

2000] are also included in Table 2.

Table 3 shows the first fundamental frequency and equivalent damping ratio for the

braced damped structure obtained from the pull-back tests, prior, and post shaking table

tests, and the analytical results from a RUAUMOKO model. In this case there is a range of

frequencies indicating nonlinear behavior of the wires. The logarithm decrement method

was used to determine an average damping. Equivalent damping increases from 0.59–5.95%

in the first mode. Due to very light initial damping the inclusion of braces, SMA wires,their connections and the measurement system contribute to increase the energy dissipat-

ing capacity of the system. The resulting damping is higher than the one obtained by

Aiken et al. [1993] for a similar model with Nitinol bracings.

Figure 5 presents the acceleration record at the top floor obtained from the pull-back

test prior to the shaking table tests, corresponding to an initial displacement close to the

first mode. Figure 6 shows the strong part of the same signal and the spectrogram, that is

the Short-Time Fourier Transform, in the frequency band of the first mode. For larger

amplitude the initial natural frequency of the mode is close to 3.5 Hz. After that, a smooth

transition is observed for lower amplitudes reaching a natural frequency of 4 Hz, i.e., a

softening effect is observed for higher amplitudes.Experimental data from shaking table tests show the effectiveness of the SMA dampers

in vibration reduction. The longitudinal accelerations at the third, second and first floor of

both buildings from the scaled Kobe record are compared in Fig. 7. Reduction in the

damped model response (right) with respect to the bare model (left) is as much as 58%.

TABLE 2 Frequencies and damping in bare model (pull-back tests)

Mode

Prior to shaking table test Post shaking table testRUAUMOKO

[Hz]Frequency [Hz] Damping [%] Frequency [Hz] Damping [%]

First 2.49 (0.40*) 0.59 2.50 (2.40) 0.40 2.49 (0.40)Second 7.25 (0.14) 0.35 7.20 (0.14) 0.54 6.49 (0.15)Third 10.95 (0.09) 0.44 10.90 (0.09) 0.45 9.80 (0.10)

*Period in seconds presented in parenthesis.

TABLE 3 First mode frequency and damping in damped model (pull-back tests)

Prior to shaking table test Post shaking table test

RUAUMOKO [Hz]Frequency [Hz] Damping [%] Frequency [Hz] Damping [%]

3.35–3.71 5.6 3.45–3.73 4.4 3.56




FIGURE 5 Acceleration record at top floor from pull-back test.

FIGURE 6 Spectrogram from acceleration record at the top floor, pull-back test.




The large reduction in acceleration is strongly influence by the different equivalent seismic

demand due to the change of structural period.

Figure 8 compares peak accelerations and peak relative displacements in each floor

for the bare and braced structure for all applied records. Calculation of the relative dis-

placements included: (1) filtering the absolute acceleration records to eliminate noise; (2)

obtaining relative acceleration in each floor by subtracting the absolute acceleration

record of the shake table; (3) integrating the relative acceleration records twice; and (4)

comparing the drifts with the horizontal components of the braces’ strains, that were measured

directly with potentiometers installed at the first and second floors. Sylmar and Llolleoscaled records caused the largest accelerations and relative displacements in the braced

structure while Llolleo and Kobe caused the largest accelerations and relative displace-

ments in the bare structure. Important reductions are apparent for all cases. The coinci-

dence of peak accelerations and absolute displacements at level 0 (shake table level) for

the bare and braced structures, respectively, confirms the similitude between the motions

applied to both cases.

The beneficial effects of the added SMA dampers can be related to two main reasons:

the increase in damping that reduced the amplitude and the strong motion duration and the

nonlinear skeleton curve that limits the stiffness of the system; initial stiffness is much

larger for small displacements.Figure 9 shows stress-strain relationship for all dampers located at the second and

first floor during the scaled Sylmar record. Some wires in the first floor underwent dis-

placement amplitudes up to 15 mm, which corresponds to approximately 3.75% total

FIGURE 7 Longitudinal acceleration for the time and frequency scaled Kobe earthquake

record.




strain. Secant stiffness of the wires on the east side differed from those on the west side.

Due to the procedure followed to pre-stress the wires, it is believed that differences in the

pre-strain from one side to the other may explain some variation in stiffness. In fact, Dolce

et al. [2000] tested Nitinol wires and bars for several different conditions and established,

among other conclusions, that the secant stiffness varies depending on the pre-strain.

Figure 10 presents a summary for different parameters that characterize the wires

behavior for the five records and a pull-back test performed previous to the shaking table

FIGURE 8 Peak acceleration and relative peak displacement for different records.




FIGURE 9 Wire force-deformation relationships for Sylmar earthquake.




tests. Figures 10a and 10b present the initial tension load at the first and second floor while

Figs. 10c to 10f show the maximum and minimum tension load attained at the same floors.

The first two bars correspond to the wires located at the east side of the structure (E-S and

FIGURE 10 Wire parameters at the first and second floor. Initial tension, maximum and

minimum load, maximum horizontal component deformation, and secant stiffness.




E-N), while the last two correspond to the wires located at the west side of the structure

(W-S and W-N). There could be some residual deformation and minor slipping in the

anchors that explains loosening that was detected in all wires especially at the east side of

the first floor and west side of the second floor. The 30 N initial load was insufficient to

avoid complete loss of preload at the first floor during the scaled Llolleo earthquake. Fig-

ures 10g and 10h present the horizontal components of the maximum wire deformation

and Figs. 10i and 10j present the wire secant stiffness corresponding to the maximum

strain at the first and second floor. Llolleo and Sylmar scaled records caused the largest

tension loads and wire deformations especially at the first floor. Differences between

secant stiffness are apparent indicating some problems with the thermal treatment applied

as can be verified through optical microscopy in Fig. 11. Grain size variation is quite

important between wires and also along the length of each wire. After 25 min of white

noise application, all wires showed fatigue problems and a dramatic reduction of stiffness.

Some of them fractured when tension loads were applied again. No appreciable difference

was detected when vertical components were included. Although the difference in wire

stiffness, movements in the transverse direction were negligible.

5. Analytical Model

The software RUAUMOKO [Carr, 2000], was adopted to conduct a dynamic analysis of

both the bare and braced frame structures. In the second case, a nonlinear behavior was

used for the dampers. Each floor was assumed to behave as a rigid plate. A modal critical

damping of 0.6% (the value obtained for the bare frame in the pull-back test) was used.

The SMA damper was modeled using the Hyst-18 element with the stress-strain rela-

tion shown in Fig. 12. This model was selected because it can produce an origin displaced

hysteric loop that can be adjusted using simple parameters. Input parameters are r, rsteep,rlower , and dxinit . The first three represent the stiffness variation in the loading and

unloading branches while dxinit defines the loading and unloading “yield” displacement.

Based on a SDOF system parametric analysis, it was concluded that increasing r increases

the slope after yielding, so maximum displacements are reduced and the maximum

stresses are increased. The hysteresis loop is insensitive to variation on rsteep. Reducing

rlower increases the loop area.

The values of these parameters were assigned by matching the area of the experimen-

tal and analytical hysteresis loops. Two simple alternative models were used. In Model 1,

all wires had the same properties obtained from the hysteresis loops of the heat-treated

wire test presented in Sec. 2, Fig. 13. In Model 2, wire properties in the first floor differ

FIGURE 11 Grain size variations from optical microscopy.




from the second and third floor. They were determined from the corresponding wire hys-

teresis loops obtained for each earthquake at the first and second level.

Figure 14 compares experimental and analytical accelerations (using model 2) time

histories at the three stories for the Sylmar record. Figure 15 contains maximum peak

accelerations and displacements determined experimentally and theoretically for both

models; showing a good agreement between them. The first model has up to 30% differ-

ence while the second one has only 10% difference.

FIGURE 12 Stress-strain curve Ruaumoko Hyst-18 element.

FIGURE 13 Parameters for Hyst-18 element from wire test.




6. Conclusions

A series of shaking table tests were conducted on a simple three-storey steel structure with

CuAlBe bracing. The weight of the model was 540 N and the volume of the braces was

0.942 cm3. Numerical simulations were carried out to reproduce the experiment. Based on

test results, the following conclusions can be drawn:

1. Inclusion of the braces produces a frequency increase of 44, 47, and 50% in the

first, second, and third mode, respectively.

2. Equivalent damping increases from 0.59% to 5.95% in the first mode.3. The balance of these two factors is a reduction of the peak accelerations and drifts

to near 60% compared to the ones obtained without dissipation devices.

4. During the seismic tests a deformation of up to 3.75% was obtained in the SMA

wires without rupture.

5. The thermal treatment of the copper-based SMA material resulted critical for

obtaining the desired superelastic properties, which is a complete recovery after

unloading and a wide loop in the load-unload cycles. Heating too long or non

homogenous may lead to large grain size and brittle fracture.

6. The analytical model reproduces the experimental results within reasonable error

limits.

7. In order to scale up these results to actual building structures, more research is

needed. Bars of CuAlBe alloy have shown lower damping than CuAlBe wires.

Alternatively, cables form by wires could be used in real structures.

FIGURE 14 Experimental and analytical (model 2) acceleration time history, Sylmar

records.




Acknowledgments

This project was sponsored by the University of Chile and Fondecyt Grant N°1030554.The authors are also grateful to Prof. Paul Roschke from Texas A&M University for his

helpful comments.

FIGURE 15 Peak acceleration and peak relative displacements from experiments and

numerical simulation.




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