Large scale testing of nitinol shape memory alloy ... - Semantic Scholar
IOP PUBLISHING
SMART MATERIALS AND STRUCTURES
Smart Mater. Struct. 17 (2008) 035018 (10pp)
doi:10.1088/0964-1726/17/3/035018
Large scale testing of nitinol shape memory alloy devices for retrofitting of bridges Rita Johnson1 , Jamie E Padgett2 , M Emmanuel Maragakis1 , Reginald DesRoches3 and M Saiid Saiidi1 1
Department of Civil and Environmental Engineering, University of Nevada, Reno, 89557-0258, USA 2 Department of Civil and Environmental Engineering, Rice University, Houston, TX 77005, USA 3 School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355, USA E-mail: [email protected], [email protected], [email protected], [email protected] and [email protected]
Received 19 December 2007, in final form 1 March 2008 Published 18 April 2008 Online at stacks.iop.org/SMS/17/035018 Abstract A large scale testing program was conducted to determine the effects of shape memory alloy (SMA) restrainer cables on the seismic performance of in-span hinges of a representative multiple-frame concrete box girder bridge subjected to earthquake excitations. Another objective of the study was to compare the performance of SMA restrainers to that of traditional steel restrainers as restraining devices for reducing hinge displacement and the likelihood of collapse during earthquakes. The results of the tests show that SMA restrainers performed very well as restraining devices. The forces in the SMA and steel restrainers were comparable. However, the SMA restrainer cables had minimal residual strain after repeated loading and exhibited the ability to undergo many cycles with little strength and stiffness degradation. In addition, the hysteretic damping that was observed in the larger ground accelerations demonstrated the ability of the materials to dissipate energy. An analytical study was conducted to assess the anticipated seismic response of the test setup and evaluate the accuracy of the analytical model. The results of the analytical simulation illustrate that the analytical model was able to match the responses from the experimental tests, including peak stresses, strains, forces, and hinge openings. (Some figures in this article are in colour only in the electronic version)
alloys to limit the susceptibility to bridge collapse and improve the seismic response of bridges.
1. Introduction During earthquake events, bridges are susceptible to unseating and collapse due to excessive longitudinal motion at in-span hinges or supports. Such damage to bridges can cause significant disruptions to the transportation network, posing a threat to emergency response and recovery as well as resulting in severe direct and indirect economic losses for a region. Bridges may be retrofitted, or rehabilitated, in order to overcome their seismic vulnerabilities. This paper examines a new approach for bridge retrofit using nitinol shape memory 0964-1726/08/035018+10$30.00
1.1. Unseating at in-span hinges The seismic vulnerability resulting from large relative displacements between adjacent bridge spans has been illustrated worldwide as in the 1971 San Fernando (US), 1989 Loma Prieta (US), 1994 Northridge (US), 1999 ChiChi (Taiwan), and 1999 Kocaeli (Turkey) earthquakes, among others. Figure 1(a) exemplifies this failure mode at an 1
© 2008 IOP Publishing Ltd Printed in the UK
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 1. Unseating at in-span hinge during the 1994 Northridge earthquake for (a) an existing bridge and (b) bridge retrofit with traditional steel restrainer cables (NISEE Collection).
in-span hinge of the I-5/Highway 14 interchange during the 1994 Northridge earthquake (NISEE 1997). Such unseating typically occurs when adjacent bridge frames displace outof-phase. Hence, retrofits that target improving performance typically include response modification devices or restraining elements placed between adjacent frames to reduce the potential for unseating. Following the 1971 San Fernando earthquake, the California Department of Transportation (Caltrans) implemented a state-wide bridge retrofit program to systematically address the deficiencies of existing structures, including potential span unseating (Caltrans 2003). Other states such as Washington, Oregon, and Tennessee have established similar programs to install restrainer cables on bridges with short seat widths. There are a number of potential unseating prevention devices which have been examined by previous researchers or are now used in practice to prevent unseating (Saiidi et al 2001, Hipley 1997, DesRoches and Fenves 2000, Keady et al 2000). However, some of the limitations of traditional approaches have been highlighted (Andrawes and DesRoches 2005). For example, traditional steel restrainer cables can transfer large forces to adjacent bridge components, or upon yielding may accumulate plastic deformations in repeated loading cycles (DesRoches and Muthukumar 2002). This can ultimately result in large hinge openings and subsequent span unseating, such as seen in the 1999 Chi-Chi and 1994 Northridge earthquakes when bridges retrofit with restrainer cables collapsed (figure 1(b)). The challenge of reducing the potential for deck collapse due to excessive longitudinal movement continues to be an issue faced by designers. A new bridge retrofit device capitalizing on the unique properties of shape memory alloys (SMAs) may overcome some of the limitations of traditional devices.
strains, and the formation of a stress-plateau limiting force transmission. One of the defining qualities of superelastic SMAs that is particularly attractive for seismic design and retrofit is the recentering capability, or the ability to return to their original undeformed shape upon returning to a state of zero stress after loading. In addition, hysteretic damping is associated with the energy requirements in the austenite– martensite phase transition in stressed SMA. Previous work has focused on the optimization of SMA properties for use in seismic applications (DesRoches et al 2004, McCormick et al 2007, Tyber et al 2007), illustrating that with proper heat treatment, nearly ideal superelastic properties can be obtained for both wires and bars. Andrawes and DesRoches (2005) identified key characteristics of nitinol SMAs that are conducive to restraint of bridge decks, and analytically evaluated the use of superelastic nitinol SMA restrainer cables placed at in-span hinges of multi-frame bridges. They found that the devices were highly effective in reducing hinge opening between adjacent frames. A subsequent analytical study compared their performance to other retrofit measures (steel restrainers or metallic dampers), concluding that the SMA restrainers had a similar impact on column drifts but were superior in reducing hinge openings for multi-frame box girder bridges (Andrawes and DesRoches 2007b). While the use of shape memory alloy restrainer cables has been proposed as a potential seismic retrofit approach for bridges, their viability had not been validated through experimental testing. This study presents the experimental findings of large scale testing of shape memory alloy devices for seismic bridge retrofit. A series of tests were conducted at the University of Nevada Reno’s (UNR) Large Scale Structures Laboratory to determine the effect of SMA restrainers on the seismic performance of in-span hinges using a representative multipleframe concrete box girder bridge. Additionally, the results are compared to data from a previous study conducted at UNR to assess the bridge structure response using traditional steel restrainer cables (Sanchez-Camargo et al 2004). An analytical evaluation of the representative frame and SMA system is conducted in order to refine and validate the model against the experimental test data.
1.2. Shape memory alloys Several past researchers have indicated the unique properties of shape memory alloys (SMAs) which may be beneficial for applications in the field of earthquake engineering (Aiken et al 1993, Dolce et al 2000, Dolce and Cardone 2001, Baratta and Corbi 2002, Han et al 2003, DesRoches et al 2004, Saiidi and Wang 2006, Dolce and Cardone 2006, Choi et al 2006). Characteristics of superelastic SMAs desirable for seismic applications include their hysteretic damping, excellent lowand high-cycle fatigue properties, strain hardening at large 2
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
et al 2000, Sanchez-Camargo et al 2004) to simulate an inspan hinge within a multi-span concrete box girder bridge. Dimensions of the specimen are based on superstructure dimensions of representative Caltrans bridges. The two box girder cells represent adjacent bridge spans at expansion joints. Block A, seen as the right block in figure 2(a), is the lighter of the concrete cells, with a weight of 92.5 kN; block B, the left block in figure 2(a) with additional lead added, is the heavier cell with a weight of 128.3 kN. A close-up of block B with additional weight is shown in figure 2(b). Elastomeric bearing pads, which support the box girder cells and transfer loading from the shake table, simulate the substructure stiffness (figure 2(c)). Block A is supported by bearings with a collective stiffness of 1302 kN m−1 , and block B, the heavier of the frames, by bearings with a collective stiffness of 683 kN m−1 . This resulted in individual frame periods of 0.53 and 0.87 s and a block period ratio of 0.6. Figure 3 shows the system design with the 25 mm gap between blocks, the location of the elastomeric pads, and the cable restrainers located on the outside of the cells. The east side of the test specimen, seen in figure 3(a), shows the heavier of the blocks on the left and the lighter on the right, leading to anticipated out-of-phase motion when excited by the shake table. A close-up of the SMA restrainer cable is seen in figure 3(b). The 84-wire SMA restrainers were constructed of eighty four 0.584 mm (0.023 in) diameter wires and the 130-wire SMA restrainers consisted of one hundred thirty 0.584 mm (0.023 inch) diameter wires. All of the wire snubbers were contained within thin walled amber latex tubing for ease of handling, and the loose ends of the wire were tied together using a 180◦ bend back and twist with a heat set to hold the ends. The effective length of both the 84 and 130-wire restrainers was 1.16 m. The wire restrainer cables were all made with superelastic nitinol with a composition of
Figure 2. SMA restrainer test setup.
2. Experimental test setup This section presents the specimen and test parameters used in this study. The specimen and parameters are the same as those used in the steel restrainer studies previously noted (Sanchez-Camargo et al 2004), in order to provide a means of comparison between the steel and SMA systems. The most critical scenario from the previous UNR experiments, in which the steel restrainers either had significant displacements, or failed, established the controlling study parameters to use in the SMA restrainer experiments. These parameters helped provide the criteria for the SMA restrainer design and test protocol. 2.1. Test specimen The test specimen, seen in figure 2, was designed and used during the UNR steel restrainer experiments (Vlassis
Figure 3. Schematic of the test setup and SMA restrainer cable.
3
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
2.2. Parameters of study The critical parameters of this study as determined from previous steel restrainer tests are: (a) frame period ratio, (b) restrainer stiffness, (c) restrainer slack, (d) and earthquake input motion. Likeness of all four of these factors was required for comparisons between the responses of SMA cable restrainers and the steel cable restrainers that were previously tested. The following section details each parameter as it is defined for the series of tests conducted on the SMA restrainers. (a) A frame period ratio of 0.6 between the two adjacent bridge frames was determined to result in large out-of-phase motions. This ratio between the structural periods is taken as the period of the stiffer frame over the period of the more flexible frame. During the Sanchez-Camargo restrainer studies, a frame period ratio of 0.6 between the two adjacent bridge frames had been determined to produce significant restrainer demands. The same physical test specimen and frame period ratio was used in the SMA restrainer tests. (b) Comparable restrainer stiffness is essential to equate the relative properties of two sets of restrainer systems. Each test set consisted of steel cable restrainers and ‘equivalent’ SMA cable restrainers with the same effective stiffness as the steel restrainers. In the previous restrainer tests, (3) and (5) cable steel restrainers were tested. The 84- and 130-wire SMA restrainers were equivalent in stiffness to the steel restrainers tested. In the first set, each cable system had stiffness equal to 0.42 kN mm−1 . In the second, each system had stiffness equal to 0.7 kN mm−1 . The stiffness of the restrainers was determined based on geometric properties (length and crosssectional area), elastic modulus, and number of cables used. The 6% strain that was used for the basis of the design stiffness of the restrainers was also used in the calculation of the chord modulus (Johnson et al 2004). (c) Restrainer slack is the amount of relative hinge displacement necessary to engage the cables in tension. The testing matrix consisted of two different values of restrainer slack, 12.7 and 0 mm. In the steel restrainer tests, zero slack was used for the restrainer with a stiffness of 0.42 kN mm−1 , while a slack of 12.7 mm was used for the stiffer (0.7 kN mm−1 ) steel cables. These combinations of slack and stiffness were determined to produce the maximum responses in the case of the steel restrainers. As such, these testing parameters were repeated in the experiments for the SMA restrainers.
Figure 4. SMA cable restrainer used in shake table tests.
51.0 at.% nickel. Nitinol in its austenitic phase has thermal expansion coefficient of 11 × 10−6 ◦ C−1 and a Poisson’s ratio of 0.33. Its material properties include a martensite start ( Ms ), martensite finish ( Mf ), austenite start ( As ), and austenite finish ( Af ) temperatures of Ms = −50 ◦ C (−58 ◦ F), Mf = −70 ◦ C (−94 ◦ F), As = −10 ◦ C (14 ◦ F), and Af = 10 ◦ C (50 ◦ F) respectively. The approximate stress loading and unloading plateaus are 503 and 276 MPa, and the elastic modulus is 31.7 GPa. Each set of brackets had a steel strength of 248 MPa and were designed to be bolted through both sides of each frame element. The 84-wire cable had a total cross-sectional area of 22.58 mm2 (0.035 in2 ), while the 130-wire cable had a cross-sectional area of 34.84 mm2 (0.054 in2 ). The wires of the looped end of the SMA cables, seen in figure 4, were spread over a 19.05 mm diameter steel pin that was part of a yoke system welded to one side of the plates. A piece of leather was placed between the steel pin and cable ends to reduce stress concentrations and prevent cutting action on the wires that could lead to early failure. The larger of the plates held the load cell to measure force in the restrainers. Figure 5 shows the complete instrumentation plan. The experiment was performed on one of the 50-ton capacity biaxial shake tables at UNR. Three linear displacement transducers were placed on the east, west and topside of the hinge section. These three transducers (LWG-225 Novotechnik), seen in figure 5, directly measured the relative displacement at the hinge. Absolute displacement of the blocks was measured with two string potentiometers. These instruments measured the displacement between the specimen and a fixed frame. Accelerometers centrally located on the blocks measured impact accelerations, and a load cell measured the force in the restrainer cables.
Figure 5. Instrumentation used in shake table tests.
4
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 6. Input ground motion scaled to a peak ground acceleration of 0.25g . Table 1. Peak displacements and maximum forces for the east side restrainer. (Note: peak disp includes the initial slack in the cables, and is not a direct measure cable deformation.)
Run
SMA PGA cable ( g ) size
Peak Cable Max Max cable Slack disp strain force stress (mm) (mm) (%) (kN) (MPa)
1 2 3 (caseA) 4 5 6 7 8 (case B) 9 (case C) 10
0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25
0 0 0 0 0 12.7 12.7 12.7 12.7 12.7
84-wire 84-wire 84-wire 84-wire 84-wire 130-wire 130-wire 130-wire 130-wire 130-wire
9.5 15.8 23.0 28.4 37.2 21.2 28.7 32.1 38.9 45.2
0.81 1.35 1.97 2.43 3.18 0.72 1.37 1.66 2.25 2.78
4.6 8.4 10.5 11.1 11.0 4.7 12.0 17.5 18.9 18.8
206 373 465 492 487 134 345 503 542 540
Figure 7. Stress–strain hysteresis for the 84-wire SMA cable with increasing earthquake motion ((a)–(c)).
(d) The synthetic earthquake input motion used for the steel restrainer testing was developed based on the Applied Technology Council ATC32-E (soft soil) motion (California Department of Transportation 2001) design spectrum. This motion, ATC32-E, is based on the expected magnitude of the earthquake (6.5), soil type of the site (E or soft soil), and peak ground acceleration (PGA). Previous tests have shown that soil type E produced the largest out of phase motion and resulted in frequent restrainer engagement during shake table testing (Sanchez-Camargo et al 2004). Five levels of shake table input ground motion with peak ground accelerations between 0.05g and 0.25g were used in the SMA cable testing. An example of the input ground motion scaled to a peak ground acceleration (PGA) of 0.25g is shown in figure 6. The loading is applied to the bridge by use of a shake table supporting the test specimen, which simulates the earthquake ground motion. The period difference between the blocks representing results in out-of-phase motion when excited by the shake table, and produces a hinge opening that is targeted for reduction with restrainer cables. The test parameters described above, along with the experimental results, will be discussed in section 3. In total, ten tests were conducted. The series of tests performed with the 84-wire cables had a slack of 0 mm, while the tests with the 130-wire cables had a 12.7 mm slack. These reflect the cases from the steel restrainer testing which proved to have large hinge openings and indicate the need for an improved restraining system.
3. Experimental results 3.1. SMA restrainers Table 1 shows the peak displacement and maximum forces that were recorded during the shake table tests as well as the calculated stresses and strains. The recorded hinge displacement for the larger SMA cable includes the initial 12.7 mm slack. The first column of the table shows the run number. Case A, B and C are SMA restrainer shake table runs that are directly equivalent to the previous steel restrainer experiments. These runs are used to compare the behavior of the SMA and steel cable restrainers. Consistent with intuition, increasing displacement was recorded as ground acceleration amplitude increased. Figures 7(a)–(c) show the SMA response with incremental increases of ground acceleration of 0.05g . This illustrates the stress–strain relationships for the 84-wire cable for run 3, with a PGA of 0.15g , through run 5, with a PGA of 0.25g . The superelastic effect of this material is evident through repeated deformation cycles with minimal accumulation of residual strain. The typical flag-shaped hysteresis characteristic of the superelastic SMA becomes apparent by run 5 (figure 7(c)). The recentering ability of the SMA is most visible at the larger accelerations. At a maximum PGA of 0.25g , seen in figure 7(c), the stress in the 84-wire cable is approximately 483 MPa and the corresponding strain is approximately 3%. 5
R Johnson et al
Total Restrainer Force (kN)
Smart Mater. Struct. 17 (2008) 035018
Figure 9. Block acceleration time histories for equivalent SMA and steel restrainer cables (PGA = 0.20g ).
Relative Hinge Disp.(mm)
Figure 8. Force–displacement relationship for 84 and 130-wire cable restrainers under maximum earthquake motion.
capabilities are evident. In order to evaluate the nitinol restrainers in relation to the past research performed on steel restrainers with comparable stiffness, the test parameters were duplicated.
The usable strain range for this material is 6–8%. In figures 7(a) (PGA of 0.15g ), a maximum stress of 465 MPa (67.4 ksi) and a corresponding strain of 1.97% were reached. Figure 7(b) (PGA of 0.2g ) shows an opening of the hysteretic loop that is characteristic of the superelastic effect of SMAs. The maximum stress and strain associated with a PGA of 0.2g are 492 MPa and 2.43%, respectively. Due to the large displacement of the elastomeric bearings, and the effectiveness of the SMAs in limiting the relative hinge displacement, a strain of 6% in the SMAs was not achieved during dynamic testing. The largest strain realized for the SMA restrainers during the experiment was 3%, as seen in figure 7(c) (PGA of 0.25g ). Even at this strain, the SMA hysteresis that results from its mechanical ability to recover deformation after stress removal is clearly evident in the typical flag shape loop that is synonymous with SMA’s superelasticity.
3.3.1. Block acceleration. The acceleration history of block B (the soft block) from the SMA experiment was compared to the block B acceleration histories from the previous steel restrainer tests for cases A, B and C. During the seismic loading tests, all three cases produced lower acceleration in the blocks with SMA restrainers compared to those being restrained by steel. In case A, the maximum block B accelerations for the SMA versus steel restrainer shake table tests were 2.7g versus 6.3g , respectively. There were similar results for case B and C. In Case C, the acceleration of Block B was more than 3.5 times larger (11.6g versus 3.2g ) when restrained by the steel restrainers than the block acceleration with SMA restraining devices, as shown in figure 9. The decreased block accelerations seen in the SMA versus steel restrainer experiments is most likely the result of the reduction of displacement and velocity due to the unique recentering properties of the shape memory alloys.
3.2. 84- versus 130-wires A comparison of the relative hinge displacement between blocks and total restrainer force for both the 84-wire and 130-wire SMA cables at a PGA of 0.25g is illustrated in figure 8. The initial slack in the larger restrainer is evidenced by the lack of force transmitted through the cable until a hinge displacement of 12.7 mm is reached. After deducting the initial slack from the relative hinge displacement, the restrainer elongation is 32.5 mm for the 130-wire cable versus 37.2 mm for the smaller 84-wire cable restrainer. At a PGA of 0.25g , the calculated force in the 84-wire SMA restrainer is 11 kN while the calculated force in the 130-wire restrainer is almost 19 kN. Similar to the stress–strain relationship seen in figure 7, the force–displacement relationship seen in figure 8 reveals the recentering capabilities of SMA to return to its point of origin with minimal residual elongation. The number of wires per cable did not appear to affect the ability of the SMA restrainer to recenter.
3.3.2. Hinge opening. Figure 10 shows the force– displacement relationships for the SMA restrainer cases A, B, and C and their equivalent cases from the past steel restrainer tests. The restrainer force–displacement relationships seen in figure 10 reveal fairly equivalent steel and SMA restrainer force but a larger relative hinge displacement for the steel restrainers. The data collected during these experiments measuring maximum restrainer force and maximum relative hinge displacement for these three cases is summarized in table 2. The maximum hinge displacements for steel in case A and B are nearly double that of the SMA restrainers. In case A, the 3-cable steel restrainer has an elongation of 43 mm while the equivalent 84-wire SMA restrainer has an elongation of 23 mm. The maximum hinge displacement for the larger 5cable steel restrainer and 130-wire SMA restrainer in case B is 61 and 32 mm, respectively. As listed in table 1, case A and B are tested at a peak ground acceleration of 0.15g . Figure 10(c) reveals an extremely large relative hinge displacement in the 5-cable steel restrainer at a PGA of 0.20g . As shown in this
3.3. SMA versus steel restrainer As stated earlier, nitinol SMAs possess the desirable properties for seismic resistant design and retrofit of structures. The large elastic strain capacity, hysteretic damping, and the recentering 6
Total Force (kN)
Relative Hinge Disp (mm)
Total Force (kN)
R Johnson et al
Total Force (kN)
Smart Mater. Struct. 17 (2008) 035018
Relative Hinge Disp (mm)
Relative Hinge Disp (mm)
Figure 10. Total restrainer force and relative hinge displacement for cases A, B, and C.
Table 2. Max force and displacement and total energy dissipation for cases A, B, and C. Total force (kN)
Max disp (mm)
Energy dissipation (kN mm)
Case A Steel SMA
27 21
43 23
307 249
Case B Steel SMA
30 31
61 32
112 263 Figure 11. Uniaxial constitutive model used for nitinol shape memory alloys.
Case C Steel SMA
36 35
120 39
2111 448
lower than traditional civil engineering dampers (DesRoches et al 2004).
figure for case C, there was a restrainer failure in two of the five cables in the steel restrainer resulting in a maximum restrainer displacement three times greater than in the steel cable. The displacement of the steel cable restrainer in case C is 120 mm while that of the SMA cable restrainer is 39 mm. Figure 10(c) also reveals that while the steel restrainer has failed, the SMA restrainer has only reached yield, beyond which the SMA can undergo large elastic deformation with reversibility.
4. Analytical evaluation An analytical study conducted to assess the anticipated seismic response of the test setup and evaluate the analytical models’ capability to duplicate the response of the shape memory alloy restrainer cables. The results of the analytical simulation are compared to the experimental results for the in-span hinge of adjacent frames retrofit with large and small SMA cables. 4.1. Analytical model of the shape memory alloy restrainer cable
3.3.3. Energy dissipation. Table 2 shows a comparison of the energy dissipation between the SMA restrainers and steel restrainer cables. It is interesting to note that in most cases, the steel restrainer cables dissipate more energy than the SMA restrainers. In fact, in case C, the steel restrainers dissipate approximately five times as much energy as the SMA restrainers. The energy dissipation in steel cables is a result of yielding in the cable, which also results in large maximum hinge displacements and large permanent (residual) displacements in the cables. The results from this study are consistent with previous studies of SMAs which have shown that their ability to limit hinge opening is due to their recentering capability, rather than their ability to dissipate energy (Andrawes and DesRoches 2007a, 2007b). In general, SMAs have equivalent viscous damping values which are much
The superelastic behavior of the SMA restrainers is developed using a uniaxial constitutive model, as shown in figure 11. The model, which is a modification of the model proposed by Auricchio and Saco (1997), is capable of capturing the material behavior under non-uniform loading typically found in earthquake excitations, where the response is primarily composed of sub-hysteresis loops internal to the main loop associated with the phase transformation. The model formulation relies on the assumption that the relationship between stresses and strains is represented by a series of straight lines whose form is determined by the extent of the transformation experienced. Further assumptions include no strength degradation during cycling (Bernardini 7
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
and Brancaleoni 1999), and that the austenite and martensite branches have the same modulus of elasticity. Previous studies have shown that these parameters have little effect on the global response of structural systems, such as the bridge system studied in this paper (Andrawes and DesRoches 2008, 2007b). The model works with one scalar internal variable, ξs , representing the martensite fraction, and with two processes which may produce its variation: the conversion of austenite to martensite and the conversion of martensite to austenite. For both processes, linear kinetic rules are chosen to describe the evolution in time of the martensite fraction. Limiting the discussion to the small deformation regime, we assume the following additive decomposition of the total strain ε :
ε = εe + ε L ξ S sgn(σ ), where ε e is the elastic strain, ε L is the maximum residual strain, and sgn(·) is the sgn function. Finally, the elastic strain is assumed to be linearly related to stress as follows:
Figure 12. Experimental and analytical stress–strain response of the 84-wire shape memory alloy restrainer cable under 0.25g loading.
The shape memory alloy devices were modeled as described in the section above. Gaps elements represented the initial slack in the cables. The series of tests with 130-wire cables were specified to have 12.7 mm slack and zero slack for the 84-wire runs. A slight additional slack of 2.54 mm was defined in the analytical model to capture the inability to precisely obtain zero gap in the test specimen.
σ = Eεe , where E is the elastic modulus of both the austenite and martensite branch. The modified constitutive model used in this study was implemented in OpenSees by Auricchio et al (2006). The primary advantages of the model adopted for this study are the robustness and simplicity of implementation, ease in obtaining material parameters from typical uniaxial tests conducted on wires or bars, and the ability to reproduce partial (i.e. sub-loops) and complete transformation patterns (i.e. from fully austenite to fully martensite) in both tension and compression. The model does not account for rate and temperature dependency. However, for the moderate loading rates typically observed during earthquakes, this does not appear to be an important parameter.
4.3. Comparison with experimental results Run 5 is used to compare the analytical and experimental results for the test setup with 84-wire SMA cables subjected to the ground motion scaled to a peak ground acceleration of 0.25g . The loading is simulated by applying the ground motion as an input acceleration to the base of the modeled structure. Figure 12 shows the stress–strain plot for the dynamic response of the SMA restrainer. The results indicate that the analytical model is able to capture the sub-looping, and the loading and unloading plateau. The peak strain from the analysis is 2.89%, and stress is 471 MPa, which is within 1% of the experimental results. The modeling assumption of zero strain accumulation during cycles reasonably predicts the hysteretic response of the SMA cable recorded in the experiment. Figure 13 shows an experimental versus analytical comparison of the time history response of the hinge opening between the blocks. The experimental plot is the average of the measured opening from the displacement transducers on either side of the in-span hinge. The analytical simulation represents the dynamic response of the in-span hinge reasonably well. The peak hinge openings are 33.8 and 33.9 mm for the experimental and analytical studies, respectively. Table 3 presents a comparison of the peak responses for low (0.15g ) and high (0.25g ) PGAs, and the small (84-wire) and large (130-wire) cables. The calculated peak strains and hinge openings differ by 1%–22% relative to the experimental results, and the stresses differ by 1%–13%. In general, the model more accurately captures the response at the larger amplitude motions. Inconsistencies between the analytical and experimental response are attributed to some sticking
4.2. Analytical model of the bridge system A two degrees-of-freedom model is developed in OpenSees (McKenna and Fenves 2005) to capture the out-of-phase motion of the blocks representing the multi-frame concrete bridge. The substructure and frame stiffness for blocks A and B were modeled with elastic springs having a stiffness of 1303 and 683 kN m−1 , respectively, based on the measured collective bearing stiffness. The nodal block masses are 0.787 and 1.09 kg. In addition to 1.5% damping, energy is dissipated during vibration through friction. A hysteretic friction element was placed between the blocks with a yield force of 2.9 kN based on Fy = μN , where the coefficient of friction was assumed to be 0.3 and the normal force at overlap was approximated as 7.5% of the block B weight. Impact was modeled between the decks using a bi-linear contact element based on the recommendations by Muthukumar (2003). The proposed hysteretic model reflects the energy dissipated during pounding. However, a gap of 10 mm was provided between the blocks before the impact element engages based on the test setup and experimental data. 8
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 13. Time history of hinge opening from analysis (peak of 33.5 mm) plotted relative to the experimental test data. Table 3. Comparison of peak responses from the analytical and experimental studies. Peak from experimental
Peak from analytical
Per cent difference
PGA Opening Strain Force Stress Opening Strain Force Stress (mm mm−1 ) (kN) (MPa) (mm) (mm mm−1 ) (kN) (MPa) Run ( g ) (mm) 3 5 8 10
0.15 0.25 0.15 0.25
21.5 33.8 31.8 40.0
0.0186 0.0292 0.0275 0.0346
10.27 10.90 15.72 17.34
450.3 477.9 450.6 497.0
16.8 33.5 28.8 36.8
0.0145 0.0289 0.0249 0.0319
between the blocks as well as slight rotation of the blocks which are not captured by the analytical model. However, the proposed model adequately captures the seismic response of the simplified bridge system retrofit with SMA restrainer cables. The analytical model was used to determine the relative performance of the system before and after retrofit. Using run 5 as an example, the as-built response of the dual-frame system was evaluated at a PGA of 0.25g , in order to estimate the improvement realized by using the shape memory alloy devices. The SMA retrofit was found to reduce the peak hinge openings by 48%. This reveals the considerable benefit of retrofitting the bridge in order to improve the seismic response and limit the potential for unseating at the in-span hinge.
8.78 10.62 13.60 17.08
Opening (%)
389.6 −22 471.2 −1 389.9 −9 489.5 −8
Strain (%)
−22 −1 −9 −8
Force (%)
−15 −3 −13 −2
Stress (%)
−13 −1 −13 −2
(3) The forces in the SMA and steel restrainers were comparable. However, the SMA cable restrainers had minimal residual strain after repeated loading cycles and exhibited the ability to undergo many cycles of loading with little strength and stiffness degradation. This would negate the need to replace them after a major seismic event unlike traditional steel restrainers. (4) The proposed analytical model was capable of reasonably predicting and reproducing the dynamic characteristics of the representative multi-frame bridge retrofit with SMA restrainer cables. Peak stresses, strains, forces, and hinge openings were well matched. (5) Utilizing the analytical model, comparisons between the as-built and retrofitted system could be made, and the results revealed that using SMA restrainer cables reduced the peak hinge openings by nearly 50% for some cases.
5. Conclusions The potential advantages of using nitinol shape memory alloys in the seismic restraint of bridges have been realized and illustrated as a part of this large scale testing and analytical study. The results of the experimental testing have revealed that the SMA restrainers not only served as effective bridge retrofits, but also result in superior performance relative to equivalent traditional steel restrainer systems. Key conclusions from the study are summarized below. (1) The SMA restrainers were effective in limiting relative hinge displacements compared to steel restrainers. This would reduce the possibility of unseating of frames at the in-span hinge of bridges during a seismic event. (2) SMA restrainers produced lower block accelerations during earthquake excitation compared to equivalent steel restrainers.
Acknowledgments This work was funded by the California Department of Transportation. This financial support is gratefully acknowledged. Special thanks to Patrick Laplace and Paul Lucas for all of the effort required to put the test specimen in place, for instrumentation of the experiments and for operating the experiment with successful acquisition of the data reported in this study.
References Aiken I D, Nims D K, Whittaker A S and Kelly J M 1993 Testing of passive energy dissipation systems Earthq. Spectra 9 335–70
9
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Dolce M and Cardone D 2006 Theoretical and experimental studies for the application of shape memory alloys in civil engineering Trans. ASME, J. Eng. Mater. Technol. 128 302–11 Han Y-L et al 2003 Structural vibration control by shape memory alloy damper Earthq. Eng. and Struct. Dyn. 32 483–94 Hipley P 1997 Bridge retrofit construction techniques 2nd National Seismic Conf. on Bridges and Highways (Sacramento, CA) Johnson R, Maragakis M, Saiidi M, DesRoches R and Barbero L 2004 Experimental evaluation of seismic performance of SMA bridge restrainers Report CCEER 04-2 Center for Civil Engineering Earthquake Research, University of Nevada, Reno Keady K I, Alameddine F and Sardo T E 2000 Seismic retrofit technology Bridge Engineering Handbook (Boca Roton, FL: CRC Press) McCormick, Tyber J, DesRoches R, Gall K and Maier H 2007 Structural engineering with NiTi part II: mechanical behavior and scaling ASCE J. Eng. Mech. 133 1019–29 McKenna F and Fenves G L 2005 Open System for Earthquake Engineering Simulation Version 1.5.2, Pacific Earthquake Engineering Research Center Muthukumar S 2003 A contact element approach with hysteresis damping for the analysis and design of pounding in bridges PhD Thesis School of Civil and Environmental Engineering, Georgia Institute of Technology NISEE 1997 National Information Service for Earthquake Engineering Highway Bridges http://nisee.berkeley.edu/ northridge/highway bridges.html Saiidi M, Randall M, Maragakis E A and Isakovic T 2001 Seismic restrainer design methods for simply supported bridges J. Bridge Eng. 6 307–15 Saiidi M and Wang H 2006 Exploratory study of seismic response of concrete columns with shape memory alloys reinforcement ACI Struct. J. 103 436–43 Sanchez-Camargo F, Maragakis E M, Saiidi M S and Elfass S 2004 Seismic performance of bridge restrainers at in-span hinges Report CCEER 04-4 Center for Civil Engineering Earthquake Research, University of Nevada, Reno Tyber J, McCormick J, Gall K, DesRoches R, Maier H and Maksoud A 2007 Structural engineering with NiTi Part I: basic materials characterization ASCE J. Eng. Mech. 133 1009–18 Vlassis A G, Maragakis E M and Saiidi M S 2000 Experimental evaluation of seismic performance of bridge restrainers Technical Report MCEER-00-00123 Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY
Andrawes B and DesRoches R 2005 Unseating prevention of bridges using superelastic restrainers Smart Mater. Struct. 14 60–7 Andrawes B and DesRoches R 2007a Effect of hysterestic properties of shape memory alloys on the seismic performance of structures Struct. Control Health Monitoring J. 14 301–20 Andrawes B and DesRoches R 2007b Effect of ambient temperature on the hinge openings in bridges with shape memory alloy seismic restrainers Eng. Struct. 29 2294–301 Andrawes B and DesRoches R 2008 Sensitivity of seismic applications to different shape memory alloy models ASCE J. Eng. Mech. 134 173–83 Auricchio F, Fugazza D and DesRoches R 2006 Earthquake performance of steel frames with nitinol braces J. Earthq. Eng. 10 45–66 Auricchio F and Saco E 1997 A one-dimensional model for superelastic shape memory alloys with different elastic properties between austenite and martensite Int. J. Non-Linear Mech. 32 1101–14 Baratta A and Corbi O 2002 On the dynamic behaviour of elastic–plastic structures equipped with pseudoelastic SMA reinforcements Comput. Mater. Sci. 25 1–13 Bernardini D and Brancaleoni F 1999 Shape memory alloys modelling for seismic applications Proc. Final Workshop of MANSIDE Project—Memory Alloys for New Seismic Isolation and Energy Dissipation Devices (Roma, Italy) pp 73–84 Caltrans (California Department of Transportation) 2001 Caltrans Seismic Design Criteria Version 1.2 Engineering Service Center Earthquake Engineering Branch, California Caltrans 2003 Seismic Retrofit Program www.dot.ca.gov/hq/pa airs/ about/retrofit.htm Choi E, Nam T H, Oh J T and Cho B S 2006 An isolation bearing for highway bridges using shape memory alloys Mater. Sci. Eng. A 438–440 1081–4 DesRoches R and Fenves G L 2000 Design of seismic cable hinge restrainers for bridges ASCE J. Struct. Eng. 126 500–9 DesRoches R, McCormick J and Delemont M 2004 Cyclic properties of superelastic shape memory alloy wires and bars J. Struct. Eng. 130 38–46 DesRoches R and Muthukumar S 2002 Effect of pounding and restrainers on the response of multiple-frame bridges ASCE J. Struct. Eng. 128 860–9 Dolce M et al 2000 Implementation and testing of passive control devices based on shape memory alloys Earthq. Eng. Struct. Dyn. 29 945–68 Dolce M and Cardone D 2001 Mechanical behaviour of shape memory alloys for seismic applications 2. Austenite NiTi wires subjected to tension Int. J. Mech. Sci. 43 2657–77
10
SMART MATERIALS AND STRUCTURES
Smart Mater. Struct. 17 (2008) 035018 (10pp)
doi:10.1088/0964-1726/17/3/035018
Large scale testing of nitinol shape memory alloy devices for retrofitting of bridges Rita Johnson1 , Jamie E Padgett2 , M Emmanuel Maragakis1 , Reginald DesRoches3 and M Saiid Saiidi1 1
Department of Civil and Environmental Engineering, University of Nevada, Reno, 89557-0258, USA 2 Department of Civil and Environmental Engineering, Rice University, Houston, TX 77005, USA 3 School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355, USA E-mail: [email protected], [email protected], [email protected], [email protected] and [email protected]
Received 19 December 2007, in final form 1 March 2008 Published 18 April 2008 Online at stacks.iop.org/SMS/17/035018 Abstract A large scale testing program was conducted to determine the effects of shape memory alloy (SMA) restrainer cables on the seismic performance of in-span hinges of a representative multiple-frame concrete box girder bridge subjected to earthquake excitations. Another objective of the study was to compare the performance of SMA restrainers to that of traditional steel restrainers as restraining devices for reducing hinge displacement and the likelihood of collapse during earthquakes. The results of the tests show that SMA restrainers performed very well as restraining devices. The forces in the SMA and steel restrainers were comparable. However, the SMA restrainer cables had minimal residual strain after repeated loading and exhibited the ability to undergo many cycles with little strength and stiffness degradation. In addition, the hysteretic damping that was observed in the larger ground accelerations demonstrated the ability of the materials to dissipate energy. An analytical study was conducted to assess the anticipated seismic response of the test setup and evaluate the accuracy of the analytical model. The results of the analytical simulation illustrate that the analytical model was able to match the responses from the experimental tests, including peak stresses, strains, forces, and hinge openings. (Some figures in this article are in colour only in the electronic version)
alloys to limit the susceptibility to bridge collapse and improve the seismic response of bridges.
1. Introduction During earthquake events, bridges are susceptible to unseating and collapse due to excessive longitudinal motion at in-span hinges or supports. Such damage to bridges can cause significant disruptions to the transportation network, posing a threat to emergency response and recovery as well as resulting in severe direct and indirect economic losses for a region. Bridges may be retrofitted, or rehabilitated, in order to overcome their seismic vulnerabilities. This paper examines a new approach for bridge retrofit using nitinol shape memory 0964-1726/08/035018+10$30.00
1.1. Unseating at in-span hinges The seismic vulnerability resulting from large relative displacements between adjacent bridge spans has been illustrated worldwide as in the 1971 San Fernando (US), 1989 Loma Prieta (US), 1994 Northridge (US), 1999 ChiChi (Taiwan), and 1999 Kocaeli (Turkey) earthquakes, among others. Figure 1(a) exemplifies this failure mode at an 1
© 2008 IOP Publishing Ltd Printed in the UK
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 1. Unseating at in-span hinge during the 1994 Northridge earthquake for (a) an existing bridge and (b) bridge retrofit with traditional steel restrainer cables (NISEE Collection).
in-span hinge of the I-5/Highway 14 interchange during the 1994 Northridge earthquake (NISEE 1997). Such unseating typically occurs when adjacent bridge frames displace outof-phase. Hence, retrofits that target improving performance typically include response modification devices or restraining elements placed between adjacent frames to reduce the potential for unseating. Following the 1971 San Fernando earthquake, the California Department of Transportation (Caltrans) implemented a state-wide bridge retrofit program to systematically address the deficiencies of existing structures, including potential span unseating (Caltrans 2003). Other states such as Washington, Oregon, and Tennessee have established similar programs to install restrainer cables on bridges with short seat widths. There are a number of potential unseating prevention devices which have been examined by previous researchers or are now used in practice to prevent unseating (Saiidi et al 2001, Hipley 1997, DesRoches and Fenves 2000, Keady et al 2000). However, some of the limitations of traditional approaches have been highlighted (Andrawes and DesRoches 2005). For example, traditional steel restrainer cables can transfer large forces to adjacent bridge components, or upon yielding may accumulate plastic deformations in repeated loading cycles (DesRoches and Muthukumar 2002). This can ultimately result in large hinge openings and subsequent span unseating, such as seen in the 1999 Chi-Chi and 1994 Northridge earthquakes when bridges retrofit with restrainer cables collapsed (figure 1(b)). The challenge of reducing the potential for deck collapse due to excessive longitudinal movement continues to be an issue faced by designers. A new bridge retrofit device capitalizing on the unique properties of shape memory alloys (SMAs) may overcome some of the limitations of traditional devices.
strains, and the formation of a stress-plateau limiting force transmission. One of the defining qualities of superelastic SMAs that is particularly attractive for seismic design and retrofit is the recentering capability, or the ability to return to their original undeformed shape upon returning to a state of zero stress after loading. In addition, hysteretic damping is associated with the energy requirements in the austenite– martensite phase transition in stressed SMA. Previous work has focused on the optimization of SMA properties for use in seismic applications (DesRoches et al 2004, McCormick et al 2007, Tyber et al 2007), illustrating that with proper heat treatment, nearly ideal superelastic properties can be obtained for both wires and bars. Andrawes and DesRoches (2005) identified key characteristics of nitinol SMAs that are conducive to restraint of bridge decks, and analytically evaluated the use of superelastic nitinol SMA restrainer cables placed at in-span hinges of multi-frame bridges. They found that the devices were highly effective in reducing hinge opening between adjacent frames. A subsequent analytical study compared their performance to other retrofit measures (steel restrainers or metallic dampers), concluding that the SMA restrainers had a similar impact on column drifts but were superior in reducing hinge openings for multi-frame box girder bridges (Andrawes and DesRoches 2007b). While the use of shape memory alloy restrainer cables has been proposed as a potential seismic retrofit approach for bridges, their viability had not been validated through experimental testing. This study presents the experimental findings of large scale testing of shape memory alloy devices for seismic bridge retrofit. A series of tests were conducted at the University of Nevada Reno’s (UNR) Large Scale Structures Laboratory to determine the effect of SMA restrainers on the seismic performance of in-span hinges using a representative multipleframe concrete box girder bridge. Additionally, the results are compared to data from a previous study conducted at UNR to assess the bridge structure response using traditional steel restrainer cables (Sanchez-Camargo et al 2004). An analytical evaluation of the representative frame and SMA system is conducted in order to refine and validate the model against the experimental test data.
1.2. Shape memory alloys Several past researchers have indicated the unique properties of shape memory alloys (SMAs) which may be beneficial for applications in the field of earthquake engineering (Aiken et al 1993, Dolce et al 2000, Dolce and Cardone 2001, Baratta and Corbi 2002, Han et al 2003, DesRoches et al 2004, Saiidi and Wang 2006, Dolce and Cardone 2006, Choi et al 2006). Characteristics of superelastic SMAs desirable for seismic applications include their hysteretic damping, excellent lowand high-cycle fatigue properties, strain hardening at large 2
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
et al 2000, Sanchez-Camargo et al 2004) to simulate an inspan hinge within a multi-span concrete box girder bridge. Dimensions of the specimen are based on superstructure dimensions of representative Caltrans bridges. The two box girder cells represent adjacent bridge spans at expansion joints. Block A, seen as the right block in figure 2(a), is the lighter of the concrete cells, with a weight of 92.5 kN; block B, the left block in figure 2(a) with additional lead added, is the heavier cell with a weight of 128.3 kN. A close-up of block B with additional weight is shown in figure 2(b). Elastomeric bearing pads, which support the box girder cells and transfer loading from the shake table, simulate the substructure stiffness (figure 2(c)). Block A is supported by bearings with a collective stiffness of 1302 kN m−1 , and block B, the heavier of the frames, by bearings with a collective stiffness of 683 kN m−1 . This resulted in individual frame periods of 0.53 and 0.87 s and a block period ratio of 0.6. Figure 3 shows the system design with the 25 mm gap between blocks, the location of the elastomeric pads, and the cable restrainers located on the outside of the cells. The east side of the test specimen, seen in figure 3(a), shows the heavier of the blocks on the left and the lighter on the right, leading to anticipated out-of-phase motion when excited by the shake table. A close-up of the SMA restrainer cable is seen in figure 3(b). The 84-wire SMA restrainers were constructed of eighty four 0.584 mm (0.023 in) diameter wires and the 130-wire SMA restrainers consisted of one hundred thirty 0.584 mm (0.023 inch) diameter wires. All of the wire snubbers were contained within thin walled amber latex tubing for ease of handling, and the loose ends of the wire were tied together using a 180◦ bend back and twist with a heat set to hold the ends. The effective length of both the 84 and 130-wire restrainers was 1.16 m. The wire restrainer cables were all made with superelastic nitinol with a composition of
Figure 2. SMA restrainer test setup.
2. Experimental test setup This section presents the specimen and test parameters used in this study. The specimen and parameters are the same as those used in the steel restrainer studies previously noted (Sanchez-Camargo et al 2004), in order to provide a means of comparison between the steel and SMA systems. The most critical scenario from the previous UNR experiments, in which the steel restrainers either had significant displacements, or failed, established the controlling study parameters to use in the SMA restrainer experiments. These parameters helped provide the criteria for the SMA restrainer design and test protocol. 2.1. Test specimen The test specimen, seen in figure 2, was designed and used during the UNR steel restrainer experiments (Vlassis
Figure 3. Schematic of the test setup and SMA restrainer cable.
3
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
2.2. Parameters of study The critical parameters of this study as determined from previous steel restrainer tests are: (a) frame period ratio, (b) restrainer stiffness, (c) restrainer slack, (d) and earthquake input motion. Likeness of all four of these factors was required for comparisons between the responses of SMA cable restrainers and the steel cable restrainers that were previously tested. The following section details each parameter as it is defined for the series of tests conducted on the SMA restrainers. (a) A frame period ratio of 0.6 between the two adjacent bridge frames was determined to result in large out-of-phase motions. This ratio between the structural periods is taken as the period of the stiffer frame over the period of the more flexible frame. During the Sanchez-Camargo restrainer studies, a frame period ratio of 0.6 between the two adjacent bridge frames had been determined to produce significant restrainer demands. The same physical test specimen and frame period ratio was used in the SMA restrainer tests. (b) Comparable restrainer stiffness is essential to equate the relative properties of two sets of restrainer systems. Each test set consisted of steel cable restrainers and ‘equivalent’ SMA cable restrainers with the same effective stiffness as the steel restrainers. In the previous restrainer tests, (3) and (5) cable steel restrainers were tested. The 84- and 130-wire SMA restrainers were equivalent in stiffness to the steel restrainers tested. In the first set, each cable system had stiffness equal to 0.42 kN mm−1 . In the second, each system had stiffness equal to 0.7 kN mm−1 . The stiffness of the restrainers was determined based on geometric properties (length and crosssectional area), elastic modulus, and number of cables used. The 6% strain that was used for the basis of the design stiffness of the restrainers was also used in the calculation of the chord modulus (Johnson et al 2004). (c) Restrainer slack is the amount of relative hinge displacement necessary to engage the cables in tension. The testing matrix consisted of two different values of restrainer slack, 12.7 and 0 mm. In the steel restrainer tests, zero slack was used for the restrainer with a stiffness of 0.42 kN mm−1 , while a slack of 12.7 mm was used for the stiffer (0.7 kN mm−1 ) steel cables. These combinations of slack and stiffness were determined to produce the maximum responses in the case of the steel restrainers. As such, these testing parameters were repeated in the experiments for the SMA restrainers.
Figure 4. SMA cable restrainer used in shake table tests.
51.0 at.% nickel. Nitinol in its austenitic phase has thermal expansion coefficient of 11 × 10−6 ◦ C−1 and a Poisson’s ratio of 0.33. Its material properties include a martensite start ( Ms ), martensite finish ( Mf ), austenite start ( As ), and austenite finish ( Af ) temperatures of Ms = −50 ◦ C (−58 ◦ F), Mf = −70 ◦ C (−94 ◦ F), As = −10 ◦ C (14 ◦ F), and Af = 10 ◦ C (50 ◦ F) respectively. The approximate stress loading and unloading plateaus are 503 and 276 MPa, and the elastic modulus is 31.7 GPa. Each set of brackets had a steel strength of 248 MPa and were designed to be bolted through both sides of each frame element. The 84-wire cable had a total cross-sectional area of 22.58 mm2 (0.035 in2 ), while the 130-wire cable had a cross-sectional area of 34.84 mm2 (0.054 in2 ). The wires of the looped end of the SMA cables, seen in figure 4, were spread over a 19.05 mm diameter steel pin that was part of a yoke system welded to one side of the plates. A piece of leather was placed between the steel pin and cable ends to reduce stress concentrations and prevent cutting action on the wires that could lead to early failure. The larger of the plates held the load cell to measure force in the restrainers. Figure 5 shows the complete instrumentation plan. The experiment was performed on one of the 50-ton capacity biaxial shake tables at UNR. Three linear displacement transducers were placed on the east, west and topside of the hinge section. These three transducers (LWG-225 Novotechnik), seen in figure 5, directly measured the relative displacement at the hinge. Absolute displacement of the blocks was measured with two string potentiometers. These instruments measured the displacement between the specimen and a fixed frame. Accelerometers centrally located on the blocks measured impact accelerations, and a load cell measured the force in the restrainer cables.
Figure 5. Instrumentation used in shake table tests.
4
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 6. Input ground motion scaled to a peak ground acceleration of 0.25g . Table 1. Peak displacements and maximum forces for the east side restrainer. (Note: peak disp includes the initial slack in the cables, and is not a direct measure cable deformation.)
Run
SMA PGA cable ( g ) size
Peak Cable Max Max cable Slack disp strain force stress (mm) (mm) (%) (kN) (MPa)
1 2 3 (caseA) 4 5 6 7 8 (case B) 9 (case C) 10
0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25
0 0 0 0 0 12.7 12.7 12.7 12.7 12.7
84-wire 84-wire 84-wire 84-wire 84-wire 130-wire 130-wire 130-wire 130-wire 130-wire
9.5 15.8 23.0 28.4 37.2 21.2 28.7 32.1 38.9 45.2
0.81 1.35 1.97 2.43 3.18 0.72 1.37 1.66 2.25 2.78
4.6 8.4 10.5 11.1 11.0 4.7 12.0 17.5 18.9 18.8
206 373 465 492 487 134 345 503 542 540
Figure 7. Stress–strain hysteresis for the 84-wire SMA cable with increasing earthquake motion ((a)–(c)).
(d) The synthetic earthquake input motion used for the steel restrainer testing was developed based on the Applied Technology Council ATC32-E (soft soil) motion (California Department of Transportation 2001) design spectrum. This motion, ATC32-E, is based on the expected magnitude of the earthquake (6.5), soil type of the site (E or soft soil), and peak ground acceleration (PGA). Previous tests have shown that soil type E produced the largest out of phase motion and resulted in frequent restrainer engagement during shake table testing (Sanchez-Camargo et al 2004). Five levels of shake table input ground motion with peak ground accelerations between 0.05g and 0.25g were used in the SMA cable testing. An example of the input ground motion scaled to a peak ground acceleration (PGA) of 0.25g is shown in figure 6. The loading is applied to the bridge by use of a shake table supporting the test specimen, which simulates the earthquake ground motion. The period difference between the blocks representing results in out-of-phase motion when excited by the shake table, and produces a hinge opening that is targeted for reduction with restrainer cables. The test parameters described above, along with the experimental results, will be discussed in section 3. In total, ten tests were conducted. The series of tests performed with the 84-wire cables had a slack of 0 mm, while the tests with the 130-wire cables had a 12.7 mm slack. These reflect the cases from the steel restrainer testing which proved to have large hinge openings and indicate the need for an improved restraining system.
3. Experimental results 3.1. SMA restrainers Table 1 shows the peak displacement and maximum forces that were recorded during the shake table tests as well as the calculated stresses and strains. The recorded hinge displacement for the larger SMA cable includes the initial 12.7 mm slack. The first column of the table shows the run number. Case A, B and C are SMA restrainer shake table runs that are directly equivalent to the previous steel restrainer experiments. These runs are used to compare the behavior of the SMA and steel cable restrainers. Consistent with intuition, increasing displacement was recorded as ground acceleration amplitude increased. Figures 7(a)–(c) show the SMA response with incremental increases of ground acceleration of 0.05g . This illustrates the stress–strain relationships for the 84-wire cable for run 3, with a PGA of 0.15g , through run 5, with a PGA of 0.25g . The superelastic effect of this material is evident through repeated deformation cycles with minimal accumulation of residual strain. The typical flag-shaped hysteresis characteristic of the superelastic SMA becomes apparent by run 5 (figure 7(c)). The recentering ability of the SMA is most visible at the larger accelerations. At a maximum PGA of 0.25g , seen in figure 7(c), the stress in the 84-wire cable is approximately 483 MPa and the corresponding strain is approximately 3%. 5
R Johnson et al
Total Restrainer Force (kN)
Smart Mater. Struct. 17 (2008) 035018
Figure 9. Block acceleration time histories for equivalent SMA and steel restrainer cables (PGA = 0.20g ).
Relative Hinge Disp.(mm)
Figure 8. Force–displacement relationship for 84 and 130-wire cable restrainers under maximum earthquake motion.
capabilities are evident. In order to evaluate the nitinol restrainers in relation to the past research performed on steel restrainers with comparable stiffness, the test parameters were duplicated.
The usable strain range for this material is 6–8%. In figures 7(a) (PGA of 0.15g ), a maximum stress of 465 MPa (67.4 ksi) and a corresponding strain of 1.97% were reached. Figure 7(b) (PGA of 0.2g ) shows an opening of the hysteretic loop that is characteristic of the superelastic effect of SMAs. The maximum stress and strain associated with a PGA of 0.2g are 492 MPa and 2.43%, respectively. Due to the large displacement of the elastomeric bearings, and the effectiveness of the SMAs in limiting the relative hinge displacement, a strain of 6% in the SMAs was not achieved during dynamic testing. The largest strain realized for the SMA restrainers during the experiment was 3%, as seen in figure 7(c) (PGA of 0.25g ). Even at this strain, the SMA hysteresis that results from its mechanical ability to recover deformation after stress removal is clearly evident in the typical flag shape loop that is synonymous with SMA’s superelasticity.
3.3.1. Block acceleration. The acceleration history of block B (the soft block) from the SMA experiment was compared to the block B acceleration histories from the previous steel restrainer tests for cases A, B and C. During the seismic loading tests, all three cases produced lower acceleration in the blocks with SMA restrainers compared to those being restrained by steel. In case A, the maximum block B accelerations for the SMA versus steel restrainer shake table tests were 2.7g versus 6.3g , respectively. There were similar results for case B and C. In Case C, the acceleration of Block B was more than 3.5 times larger (11.6g versus 3.2g ) when restrained by the steel restrainers than the block acceleration with SMA restraining devices, as shown in figure 9. The decreased block accelerations seen in the SMA versus steel restrainer experiments is most likely the result of the reduction of displacement and velocity due to the unique recentering properties of the shape memory alloys.
3.2. 84- versus 130-wires A comparison of the relative hinge displacement between blocks and total restrainer force for both the 84-wire and 130-wire SMA cables at a PGA of 0.25g is illustrated in figure 8. The initial slack in the larger restrainer is evidenced by the lack of force transmitted through the cable until a hinge displacement of 12.7 mm is reached. After deducting the initial slack from the relative hinge displacement, the restrainer elongation is 32.5 mm for the 130-wire cable versus 37.2 mm for the smaller 84-wire cable restrainer. At a PGA of 0.25g , the calculated force in the 84-wire SMA restrainer is 11 kN while the calculated force in the 130-wire restrainer is almost 19 kN. Similar to the stress–strain relationship seen in figure 7, the force–displacement relationship seen in figure 8 reveals the recentering capabilities of SMA to return to its point of origin with minimal residual elongation. The number of wires per cable did not appear to affect the ability of the SMA restrainer to recenter.
3.3.2. Hinge opening. Figure 10 shows the force– displacement relationships for the SMA restrainer cases A, B, and C and their equivalent cases from the past steel restrainer tests. The restrainer force–displacement relationships seen in figure 10 reveal fairly equivalent steel and SMA restrainer force but a larger relative hinge displacement for the steel restrainers. The data collected during these experiments measuring maximum restrainer force and maximum relative hinge displacement for these three cases is summarized in table 2. The maximum hinge displacements for steel in case A and B are nearly double that of the SMA restrainers. In case A, the 3-cable steel restrainer has an elongation of 43 mm while the equivalent 84-wire SMA restrainer has an elongation of 23 mm. The maximum hinge displacement for the larger 5cable steel restrainer and 130-wire SMA restrainer in case B is 61 and 32 mm, respectively. As listed in table 1, case A and B are tested at a peak ground acceleration of 0.15g . Figure 10(c) reveals an extremely large relative hinge displacement in the 5-cable steel restrainer at a PGA of 0.20g . As shown in this
3.3. SMA versus steel restrainer As stated earlier, nitinol SMAs possess the desirable properties for seismic resistant design and retrofit of structures. The large elastic strain capacity, hysteretic damping, and the recentering 6
Total Force (kN)
Relative Hinge Disp (mm)
Total Force (kN)
R Johnson et al
Total Force (kN)
Smart Mater. Struct. 17 (2008) 035018
Relative Hinge Disp (mm)
Relative Hinge Disp (mm)
Figure 10. Total restrainer force and relative hinge displacement for cases A, B, and C.
Table 2. Max force and displacement and total energy dissipation for cases A, B, and C. Total force (kN)
Max disp (mm)
Energy dissipation (kN mm)
Case A Steel SMA
27 21
43 23
307 249
Case B Steel SMA
30 31
61 32
112 263 Figure 11. Uniaxial constitutive model used for nitinol shape memory alloys.
Case C Steel SMA
36 35
120 39
2111 448
lower than traditional civil engineering dampers (DesRoches et al 2004).
figure for case C, there was a restrainer failure in two of the five cables in the steel restrainer resulting in a maximum restrainer displacement three times greater than in the steel cable. The displacement of the steel cable restrainer in case C is 120 mm while that of the SMA cable restrainer is 39 mm. Figure 10(c) also reveals that while the steel restrainer has failed, the SMA restrainer has only reached yield, beyond which the SMA can undergo large elastic deformation with reversibility.
4. Analytical evaluation An analytical study conducted to assess the anticipated seismic response of the test setup and evaluate the analytical models’ capability to duplicate the response of the shape memory alloy restrainer cables. The results of the analytical simulation are compared to the experimental results for the in-span hinge of adjacent frames retrofit with large and small SMA cables. 4.1. Analytical model of the shape memory alloy restrainer cable
3.3.3. Energy dissipation. Table 2 shows a comparison of the energy dissipation between the SMA restrainers and steel restrainer cables. It is interesting to note that in most cases, the steel restrainer cables dissipate more energy than the SMA restrainers. In fact, in case C, the steel restrainers dissipate approximately five times as much energy as the SMA restrainers. The energy dissipation in steel cables is a result of yielding in the cable, which also results in large maximum hinge displacements and large permanent (residual) displacements in the cables. The results from this study are consistent with previous studies of SMAs which have shown that their ability to limit hinge opening is due to their recentering capability, rather than their ability to dissipate energy (Andrawes and DesRoches 2007a, 2007b). In general, SMAs have equivalent viscous damping values which are much
The superelastic behavior of the SMA restrainers is developed using a uniaxial constitutive model, as shown in figure 11. The model, which is a modification of the model proposed by Auricchio and Saco (1997), is capable of capturing the material behavior under non-uniform loading typically found in earthquake excitations, where the response is primarily composed of sub-hysteresis loops internal to the main loop associated with the phase transformation. The model formulation relies on the assumption that the relationship between stresses and strains is represented by a series of straight lines whose form is determined by the extent of the transformation experienced. Further assumptions include no strength degradation during cycling (Bernardini 7
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
and Brancaleoni 1999), and that the austenite and martensite branches have the same modulus of elasticity. Previous studies have shown that these parameters have little effect on the global response of structural systems, such as the bridge system studied in this paper (Andrawes and DesRoches 2008, 2007b). The model works with one scalar internal variable, ξs , representing the martensite fraction, and with two processes which may produce its variation: the conversion of austenite to martensite and the conversion of martensite to austenite. For both processes, linear kinetic rules are chosen to describe the evolution in time of the martensite fraction. Limiting the discussion to the small deformation regime, we assume the following additive decomposition of the total strain ε :
ε = εe + ε L ξ S sgn(σ ), where ε e is the elastic strain, ε L is the maximum residual strain, and sgn(·) is the sgn function. Finally, the elastic strain is assumed to be linearly related to stress as follows:
Figure 12. Experimental and analytical stress–strain response of the 84-wire shape memory alloy restrainer cable under 0.25g loading.
The shape memory alloy devices were modeled as described in the section above. Gaps elements represented the initial slack in the cables. The series of tests with 130-wire cables were specified to have 12.7 mm slack and zero slack for the 84-wire runs. A slight additional slack of 2.54 mm was defined in the analytical model to capture the inability to precisely obtain zero gap in the test specimen.
σ = Eεe , where E is the elastic modulus of both the austenite and martensite branch. The modified constitutive model used in this study was implemented in OpenSees by Auricchio et al (2006). The primary advantages of the model adopted for this study are the robustness and simplicity of implementation, ease in obtaining material parameters from typical uniaxial tests conducted on wires or bars, and the ability to reproduce partial (i.e. sub-loops) and complete transformation patterns (i.e. from fully austenite to fully martensite) in both tension and compression. The model does not account for rate and temperature dependency. However, for the moderate loading rates typically observed during earthquakes, this does not appear to be an important parameter.
4.3. Comparison with experimental results Run 5 is used to compare the analytical and experimental results for the test setup with 84-wire SMA cables subjected to the ground motion scaled to a peak ground acceleration of 0.25g . The loading is simulated by applying the ground motion as an input acceleration to the base of the modeled structure. Figure 12 shows the stress–strain plot for the dynamic response of the SMA restrainer. The results indicate that the analytical model is able to capture the sub-looping, and the loading and unloading plateau. The peak strain from the analysis is 2.89%, and stress is 471 MPa, which is within 1% of the experimental results. The modeling assumption of zero strain accumulation during cycles reasonably predicts the hysteretic response of the SMA cable recorded in the experiment. Figure 13 shows an experimental versus analytical comparison of the time history response of the hinge opening between the blocks. The experimental plot is the average of the measured opening from the displacement transducers on either side of the in-span hinge. The analytical simulation represents the dynamic response of the in-span hinge reasonably well. The peak hinge openings are 33.8 and 33.9 mm for the experimental and analytical studies, respectively. Table 3 presents a comparison of the peak responses for low (0.15g ) and high (0.25g ) PGAs, and the small (84-wire) and large (130-wire) cables. The calculated peak strains and hinge openings differ by 1%–22% relative to the experimental results, and the stresses differ by 1%–13%. In general, the model more accurately captures the response at the larger amplitude motions. Inconsistencies between the analytical and experimental response are attributed to some sticking
4.2. Analytical model of the bridge system A two degrees-of-freedom model is developed in OpenSees (McKenna and Fenves 2005) to capture the out-of-phase motion of the blocks representing the multi-frame concrete bridge. The substructure and frame stiffness for blocks A and B were modeled with elastic springs having a stiffness of 1303 and 683 kN m−1 , respectively, based on the measured collective bearing stiffness. The nodal block masses are 0.787 and 1.09 kg. In addition to 1.5% damping, energy is dissipated during vibration through friction. A hysteretic friction element was placed between the blocks with a yield force of 2.9 kN based on Fy = μN , where the coefficient of friction was assumed to be 0.3 and the normal force at overlap was approximated as 7.5% of the block B weight. Impact was modeled between the decks using a bi-linear contact element based on the recommendations by Muthukumar (2003). The proposed hysteretic model reflects the energy dissipated during pounding. However, a gap of 10 mm was provided between the blocks before the impact element engages based on the test setup and experimental data. 8
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Figure 13. Time history of hinge opening from analysis (peak of 33.5 mm) plotted relative to the experimental test data. Table 3. Comparison of peak responses from the analytical and experimental studies. Peak from experimental
Peak from analytical
Per cent difference
PGA Opening Strain Force Stress Opening Strain Force Stress (mm mm−1 ) (kN) (MPa) (mm) (mm mm−1 ) (kN) (MPa) Run ( g ) (mm) 3 5 8 10
0.15 0.25 0.15 0.25
21.5 33.8 31.8 40.0
0.0186 0.0292 0.0275 0.0346
10.27 10.90 15.72 17.34
450.3 477.9 450.6 497.0
16.8 33.5 28.8 36.8
0.0145 0.0289 0.0249 0.0319
between the blocks as well as slight rotation of the blocks which are not captured by the analytical model. However, the proposed model adequately captures the seismic response of the simplified bridge system retrofit with SMA restrainer cables. The analytical model was used to determine the relative performance of the system before and after retrofit. Using run 5 as an example, the as-built response of the dual-frame system was evaluated at a PGA of 0.25g , in order to estimate the improvement realized by using the shape memory alloy devices. The SMA retrofit was found to reduce the peak hinge openings by 48%. This reveals the considerable benefit of retrofitting the bridge in order to improve the seismic response and limit the potential for unseating at the in-span hinge.
8.78 10.62 13.60 17.08
Opening (%)
389.6 −22 471.2 −1 389.9 −9 489.5 −8
Strain (%)
−22 −1 −9 −8
Force (%)
−15 −3 −13 −2
Stress (%)
−13 −1 −13 −2
(3) The forces in the SMA and steel restrainers were comparable. However, the SMA cable restrainers had minimal residual strain after repeated loading cycles and exhibited the ability to undergo many cycles of loading with little strength and stiffness degradation. This would negate the need to replace them after a major seismic event unlike traditional steel restrainers. (4) The proposed analytical model was capable of reasonably predicting and reproducing the dynamic characteristics of the representative multi-frame bridge retrofit with SMA restrainer cables. Peak stresses, strains, forces, and hinge openings were well matched. (5) Utilizing the analytical model, comparisons between the as-built and retrofitted system could be made, and the results revealed that using SMA restrainer cables reduced the peak hinge openings by nearly 50% for some cases.
5. Conclusions The potential advantages of using nitinol shape memory alloys in the seismic restraint of bridges have been realized and illustrated as a part of this large scale testing and analytical study. The results of the experimental testing have revealed that the SMA restrainers not only served as effective bridge retrofits, but also result in superior performance relative to equivalent traditional steel restrainer systems. Key conclusions from the study are summarized below. (1) The SMA restrainers were effective in limiting relative hinge displacements compared to steel restrainers. This would reduce the possibility of unseating of frames at the in-span hinge of bridges during a seismic event. (2) SMA restrainers produced lower block accelerations during earthquake excitation compared to equivalent steel restrainers.
Acknowledgments This work was funded by the California Department of Transportation. This financial support is gratefully acknowledged. Special thanks to Patrick Laplace and Paul Lucas for all of the effort required to put the test specimen in place, for instrumentation of the experiments and for operating the experiment with successful acquisition of the data reported in this study.
References Aiken I D, Nims D K, Whittaker A S and Kelly J M 1993 Testing of passive energy dissipation systems Earthq. Spectra 9 335–70
9
Smart Mater. Struct. 17 (2008) 035018
R Johnson et al
Dolce M and Cardone D 2006 Theoretical and experimental studies for the application of shape memory alloys in civil engineering Trans. ASME, J. Eng. Mater. Technol. 128 302–11 Han Y-L et al 2003 Structural vibration control by shape memory alloy damper Earthq. Eng. and Struct. Dyn. 32 483–94 Hipley P 1997 Bridge retrofit construction techniques 2nd National Seismic Conf. on Bridges and Highways (Sacramento, CA) Johnson R, Maragakis M, Saiidi M, DesRoches R and Barbero L 2004 Experimental evaluation of seismic performance of SMA bridge restrainers Report CCEER 04-2 Center for Civil Engineering Earthquake Research, University of Nevada, Reno Keady K I, Alameddine F and Sardo T E 2000 Seismic retrofit technology Bridge Engineering Handbook (Boca Roton, FL: CRC Press) McCormick, Tyber J, DesRoches R, Gall K and Maier H 2007 Structural engineering with NiTi part II: mechanical behavior and scaling ASCE J. Eng. Mech. 133 1019–29 McKenna F and Fenves G L 2005 Open System for Earthquake Engineering Simulation Version 1.5.2, Pacific Earthquake Engineering Research Center Muthukumar S 2003 A contact element approach with hysteresis damping for the analysis and design of pounding in bridges PhD Thesis School of Civil and Environmental Engineering, Georgia Institute of Technology NISEE 1997 National Information Service for Earthquake Engineering Highway Bridges http://nisee.berkeley.edu/ northridge/highway bridges.html Saiidi M, Randall M, Maragakis E A and Isakovic T 2001 Seismic restrainer design methods for simply supported bridges J. Bridge Eng. 6 307–15 Saiidi M and Wang H 2006 Exploratory study of seismic response of concrete columns with shape memory alloys reinforcement ACI Struct. J. 103 436–43 Sanchez-Camargo F, Maragakis E M, Saiidi M S and Elfass S 2004 Seismic performance of bridge restrainers at in-span hinges Report CCEER 04-4 Center for Civil Engineering Earthquake Research, University of Nevada, Reno Tyber J, McCormick J, Gall K, DesRoches R, Maier H and Maksoud A 2007 Structural engineering with NiTi Part I: basic materials characterization ASCE J. Eng. Mech. 133 1009–18 Vlassis A G, Maragakis E M and Saiidi M S 2000 Experimental evaluation of seismic performance of bridge restrainers Technical Report MCEER-00-00123 Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY
Andrawes B and DesRoches R 2005 Unseating prevention of bridges using superelastic restrainers Smart Mater. Struct. 14 60–7 Andrawes B and DesRoches R 2007a Effect of hysterestic properties of shape memory alloys on the seismic performance of structures Struct. Control Health Monitoring J. 14 301–20 Andrawes B and DesRoches R 2007b Effect of ambient temperature on the hinge openings in bridges with shape memory alloy seismic restrainers Eng. Struct. 29 2294–301 Andrawes B and DesRoches R 2008 Sensitivity of seismic applications to different shape memory alloy models ASCE J. Eng. Mech. 134 173–83 Auricchio F, Fugazza D and DesRoches R 2006 Earthquake performance of steel frames with nitinol braces J. Earthq. Eng. 10 45–66 Auricchio F and Saco E 1997 A one-dimensional model for superelastic shape memory alloys with different elastic properties between austenite and martensite Int. J. Non-Linear Mech. 32 1101–14 Baratta A and Corbi O 2002 On the dynamic behaviour of elastic–plastic structures equipped with pseudoelastic SMA reinforcements Comput. Mater. Sci. 25 1–13 Bernardini D and Brancaleoni F 1999 Shape memory alloys modelling for seismic applications Proc. Final Workshop of MANSIDE Project—Memory Alloys for New Seismic Isolation and Energy Dissipation Devices (Roma, Italy) pp 73–84 Caltrans (California Department of Transportation) 2001 Caltrans Seismic Design Criteria Version 1.2 Engineering Service Center Earthquake Engineering Branch, California Caltrans 2003 Seismic Retrofit Program www.dot.ca.gov/hq/pa airs/ about/retrofit.htm Choi E, Nam T H, Oh J T and Cho B S 2006 An isolation bearing for highway bridges using shape memory alloys Mater. Sci. Eng. A 438–440 1081–4 DesRoches R and Fenves G L 2000 Design of seismic cable hinge restrainers for bridges ASCE J. Struct. Eng. 126 500–9 DesRoches R, McCormick J and Delemont M 2004 Cyclic properties of superelastic shape memory alloy wires and bars J. Struct. Eng. 130 38–46 DesRoches R and Muthukumar S 2002 Effect of pounding and restrainers on the response of multiple-frame bridges ASCE J. Struct. Eng. 128 860–9 Dolce M et al 2000 Implementation and testing of passive control devices based on shape memory alloys Earthq. Eng. Struct. Dyn. 29 945–68 Dolce M and Cardone D 2001 Mechanical behaviour of shape memory alloys for seismic applications 2. Austenite NiTi wires subjected to tension Int. J. Mech. Sci. 43 2657–77
10
