Behaviour and modelling of hybrid SMA-steel reinforced concrete slender shear wall

Engineering Structures 147 (2017) 77–89

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Behaviour and modelling of hybrid SMA-steel reinforced concrete slender shear wall Alaa Abdulridha a, Dan Palermo b,⇑ a b

Department of Civil Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa K1N 6N5, Canada Department of Civil Engineering, York University, 4700 Keele St., Toronto M3J 1P3, Canada

a r t i c l e

i n f o

Article history: Received 9 June 2016 Revised 15 December 2016 Accepted 9 April 2017

Keywords: Superelastic SMA Reinforced concrete shear walls Strain recovery Energy dissipation Hysteretic response Constitutive modelling Finite element analysis

a b s t r a c t Superelastic Shape Memory Alloys (SMAs) possess unique mechanical characteristics that make them appealing as alternative reinforcement for seismic applications; specifically, the capacity to recover large strains upon unloading, levels that would result in permanent deformations in steel reinforcement. An experimental study was conducted to assess the performance of a ductile, hybrid SMA-deformed steel reinforced concrete shear wall. A companion wall with deformed steel reinforcement only was also investigated. The walls were subjected to reverse cyclic displacements to failure. The results of the experimental program demonstrate that the hybrid SMA wall was significantly more effective at restoring resulting in marginal residual displacements after being subjected to drifts exceeding 4%. The hybrid SMA wall experienced similar lateral strength and displacement capacities to the steel reinforced wall. The hybrid SMA wall provided substantial, albeit less, energy dissipation and lower stiffness at yielding; the influence of these performance parameters on seismic behaviour is noted in the paper. A hysteretic constitutive model based on a trilinear envelope response, and linear unloading and reloading rules provided satisfactory simulations of behaviour of the SMA wall. Discrepancies in response are attributed to bond modelling of the smooth SMA bars. Furthermore, finite element analysis is also used to illustrate the effect of axial load on the re-centering capacity of the shear walls. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction In high seismic regions, reinforced concrete structures that are classified as normal importance, are designed to sustain severe damage and permanent deformations during design-level earthquakes, while preventing collapse and safeguarding against loss of life. This is generally achieved by assigning plastic hinges at pre-defined locations in a structure. The plastic hinges are designed to be controlled by flexural yielding, while preventing non-ductile modes of failure. Although the main performance objective may be achieved, the damage and permanent deformations could prevent a structure from being serviceable after a seismic event and, in addition, prohibit post-earthquake repairs. Due to these shortcomings, Shape Memory Alloys (SMAs) have attracted interest from researchers due, in most part, to their capability to recover displacements upon removal of stress (superelastic SMA) or with the application of heat (shape memory effect). In addition, SMAs can dissipate energy through hysteretic damping and provide strength and displacement capacities comparable to ⇑ Corresponding author. E-mail address: [email protected] (D. Palermo). http://dx.doi.org/10.1016/j.engstruct.2017.04.058 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

conventional deformed reinforcement. SMAs are also gaining popularity due to their high fatigue and corrosion resistances. SMAs have a number of structural applications [1–3], ranging from reinforcement in new construction or as a retrofitting material for existing structural elements, to serving as strands for prestressing and post-tensioning. In addition, other uses include SMA-based devices for passive, semi-active or active control of structures. Shortcomings of SMAs include the higher cost relative to traditional steel reinforcement; this leads to optimization of the material. Furthermore, the superelastic properties of SMAs are dependant on the operating temperature; the smooth bar surface results in a reduction in bond to the surrounding concrete leading to fewer, but larger cracks; and the lower elastic modulus (approximately 60 GPa) relative to steel reinforcement (200 GPa) results in larger displacements under service loads. A number of studies have focused on material characterization and on the mechanical properties of superelastic SMA bars and wires to evaluate their applicability for structural applications [4–6]. DesRoches et al. [7] highlighted that SMA in wire form experiences higher strength and damping properties compared to SMA bars; however, the form of the SMA does not influence the recentering capacity. McCormick et al. [8] investigated the behaviour

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A. Abdulridha, D. Palermo / Engineering Structures 147 (2017) 77–89

Notation As Ag Ei Es Esh P d f0 c funl fy h

area of flexural reinforcement gross cross sectional area of concrete section initial stiffness of reinforcement modulus of elasticity of reinforcement strain hardening stiffness of reinforcement axial load original length of displacement cable transducer concrete cylinder compressive strength unloading plateau stress of reinforcement yield stress of reinforcement height of displacement cable transducer

of large diameter superelastic SMA bars and concluded that decreasing the bar size results in an increase in re-centering capacity and equivalent viscous damping. Other studies [9–13] have concentrated on the cyclic response of SMA wires and large diameter bars with respect to strain amplitude, loading frequency, number of cycles, and ambient temperature. Limited experimental studies have focused on incorporating superelastic SMAs as reinforcement in concrete structural members. Deng et al. [14] investigated the capacity of embedded SMA wires to recover and reduce permanent deformations of concrete beams. Saiidi and Wang [15] studied the contribution of SMAs to reduce residual displacements in concrete columns reinforced with SMA bars in the plastic hinge area. The authors also evaluated the seismic performance and damage of an SMA reinforced column repaired using engineered cementitious composites. In another study [16], the seismic behaviour of columns reinforced with SMA bars and engineered cementitious concrete was investigated in an attempt to reduce permanent displacements and damage in columns subjected to strong earthquakes. Youssef et al. [17] investigated the seismic behaviour of a beam-column joint reinforced with superelastic SMAs in the plastic hinge region. Abdulridha et al. [18] investigated the response of large-scale concrete beams reinforced with SMAs in the critical region under monotonic, cyclic and reverse cyclic loadings. Each of the above experimental studies has demonstrated the effectiveness of SMAs to restore a structural member to its original position. Other experimental studies have included the combination of SMAs with fiber-reinforced polymers [19,20]. SMAs used as external reinforcement has also been investigated. A study by Ayoub et al. [21] investigated the behaviour of small-scale beams reinforced with externally anchored, superelastic SMA bars as the principal longitudinal reinforcement. The work of Effendy et al. [22] focused on external SMA diagonal bracing for squat concrete shear walls. While advancements have been made in the application of SMAs in structural members, there is a lack of knowledge on the behaviour of SMA reinforced shear walls, yet shear wall-type elements are routinely incorporated in the lateral force resisting systems of structures.

2. Research significance This paper investigates the performance of a concrete shear wall reinforced with superelastic SMAs in the plastic hinge area. SMAs are used only as the principal longitudinal reinforcement in the boundary zones, while the longitudinal reinforcement in the web region consists of deformed steel reinforcement, thus leading to a hybrid SMA-steel member. To the author’s best knowledge, this is the first study to use SMAs as internal reinforcement in

l Dy d

em ep er1 er2 esh eu ey cavg

length of displacement cable transducer yield displacement change in length of displacement cable transducer current maximum strain of reinforcement plastic offset strain of reinforcement first unloading strain second unloading strain the strain at the onset of strain hardening ultimate strain of reinforcement yield strain of reinforcement average shear strain

slender shear walls and to use a hybrid of SMA and steel along the critical section. In addition, this experimental study is used to provide a benchmark to develop modelling procedures and to corroborate a hysteretic constitutive model for superelastic SMAs based on linear unloading and reloading rules that explicitly considers accumulation of permanent straining and decaying of the unloading plateau stress.

3. Experimental program Two ductile shear walls were tested under reverse cyclic lateral loading. The walls were named W1-SR and W2-NR, where S and N distinguish between the steel reinforced and the hybrid NiTi SMAsteel reinforced walls, respectively. The NiTi SMA had a chemical composition of approximately 56% Nickel (Ni) and 44% Titanium (Ti) by weight. Details of the concrete and reinforcement are provided in Table 1. The shear walls had a rectangular cross section: 150 mm in thickness and 1000 mm in length. The height of the walls was 2200 mm resulting in an aspect ratio of 2.2, which was selected to promote ductile flexural response. The walls were designed according to the seismic detailing provisions for ductile walls prescribed by the Canadian Standards Association Standard A23.3-04 Design of Concrete Structures [23]. While no explicit provisions exist for SMA reinforced members, the design of the SMA wall followed that of the steel reinforced wall. The walls were reinforced with two layers of orthogonal steel reinforcement in the web. The vertical reinforcement consisted of three pairs of 10 M (100 mm2 and 11.3 mm diameter) deformed bars spaced uniformly at 150 mm, whereas the horizontal reinforcement consisted of fifteen pairs of 10 M bars spaced uniformly at 150 mm. As a result, each shear wall had the same web vertical and horizontal reinforcement ratio of 0.88%. The only difference between W1-SR and W2-NR was the longitudinal reinforcement used in the plastic hinge region within the end boundary zones. For W1-SR, four-10 M deformed steel bars were used; while for W2-NR, the deformed longitudinal bars were replaced with 12.7 mm-diameter superelastic SMA bars. The choice of SMA bar size was based on two factors: (1) readily available bar size; and (2) an equivalent Asfy to the deformed reinforcement used in the boundary zone of the steel reinforced wall. Mechanical couplers were used in W2-NR to connect the SMA bars with 15 M deformed steel bars (16 mm diameter and 200 mm2 area) extending above the plastic hinge region. The larger bar area above the plastic hinge was intended to prevent yielding of reinforcement outside this region. The total length of the SMA bars was 1200 mm. The length from the top of the foundation into the wall was 950 mm including the 150 mm length that extended into the couplers, while the remaining 250 mm extended into the foundation. The length of

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A. Abdulridha, D. Palermo / Engineering Structures 147 (2017) 77–89 Table 1 Material Properties. Specimens

Concrete

Vertical Reinforcement

e c  10

0

0

f c (MPa)

W1-SR W2-NR

30.5 31.6

3

Transverse Reinforcement

Web

2.7 2.6

Boundary

q (%)

fy (MPa)

q (%)

fy (MPa)

0.88 0.88

425 425

1.33 1.68

425 380(NiTi)

the SMA bars into the wall was based on the results of preliminary finite element analysis, which predicted the plastic hinge length to be approximately 760 mm. To prevent buckling of the principal reinforcement in the boundary zones, 10 M closed steel ties were provided along the full height of both walls. The ties were spaced at 75 mm within the plastic hinge region and 150 mm above the plastic hinge region. In addition, four sets of 10 M bars of 600 mm length were placed in the web section of the wall; 300 mm extended into the wall above the foundation and the remaining embedded into the foundation. These bars were solely added to increase the shear sliding resistance at the wallfoundation construction joint. Each wall was constructed with a heavily reinforced top beam, which distributed the applied lateral load uniformly along the top of the wall, and a heavily reinforced foundation. The dimensional details of the shear walls, and the reinforcement layout for W2-NR are provided in Fig. 1. A modified, single-barrel screw lock coupler used in W2-NR is illustrated in Fig. 2. The original form is manufactured with six sharp-end bolts in a single row. Tensile testing with this type of

400 mm

W2-NR 400 mm

400 mm

10M @ 200 mm 4 N0 15

15M 10M @ 150 mm

10M @ 150 mm

Couplers

15M @ 200 mm

15M @ 200 mm

500 mm

Couplers 1400 mm

1

(b)

1700 mm

(a) 40

120

190

1000 mm 150 150

190

120

150 mm

10M@75mm SMA

10M@ 150mm

10M

40

SMA

(c) Fig. 1. Reinforcement Details of Wall W2-NR: (a) Elevation View; (b) Section 1-1; and (c) Section 2-2.

500 mm

4 N0 10

300 mm

150 mm 10M @ 75 mm

300 mm

SMA (950 mm)

2200 mm

SMA

2

fy (MPa)

0.88 0.88

425 425

Fig. 2. Modified Mechanical Coupler Used in Wall W2-NR.

1

2

q (%)

80

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coupler with an SMA bar inserted in one end and a 15 M deformed steel bar inserted in the other end resulted in notable slip of the SMA bar. To improve performance, six additional sharp end bolts were distributed in two rows at each end of the coupler. Furthermore, the SMA bar was extended to the end of the coupler. In this configuration, all 18 bolts were used to secure the SMA bar to the coupler, while the 15 M steel bar was welded to the end of the mechanical coupler. With this modification, the SMA bar sustained its full strength capacity and strains in the range of 10%. This improved performance permitted optimization of the SMA over the plastic hinge region resulting in a more economical section given the high cost of SMA. The test setup consisted of a single hydraulic actuator that imposed the lateral loading along the center of the top beam (Fig. 3 (a)). The actuator was mounted to a reaction frame that, in turn, was fixed to the laboratory strong floor. Linear Variable Differential Transducers (LVDTs) and Displacement Cable Transducers

L9

L10

C2

C1, C9

(DCTs) were used to record displacements. Fig. 3 (b) illustrates the location of LVDTs (L) and DCTs (C). C1, C2, and C9 measured the lateral displacement of the top loading beam; C3 measured the lateral displacement at the mid-height of the wall; C5 and C6 measured the vertical displacement of the top loading beam, and C7 and C8 measured the diagonal displacements in the plastic hinge region. L1 and L2 measured sliding and uplift of the foundation, respectively; L3 and L4 measured the vertical displacement within the plastic hinge region; L5 and L8 measured base sliding and anchorage slip of the wall, respectively; and L9 and L10 measured out-ofplane displacements of the top loading beam. [Note C1 was used to construct the lateral load-lateral displacement responses.] Two types of strain gauges were used in the shear walls: general purpose (F-series) strain gauges for the deformed reinforcing steel, and post-yield (YF-series) strain gauges for the SMA bars. Additional information on the location of the strain gauges can be found elsewhere [24]. Lateral loading consisted of reverse cycles increasing incrementally at multiples of the yield displacement (Dy) according to ATC24 [25]. The walls were first loaded in three steps up to the yield load, which was determined from the theoretical monotonic lateral load-displacement response. The first and the second loading cycles targeted Dy/3 and 2Dy/3, respectively; while the third loading cycle aimed for the yield displacement. Three repetitions of loading were imposed at each displacement level. The post-yield lateral displacement history consisted of three repetitions at each displacement level to 5Dy and two repetitions thereafter. Successive displacement levels were increased by Dy for the steel reinforced wall while it was Dy/2 for the SMA wall. The predicted yield displacement of the SMA wall was significantly greater, thus the smaller displacement increments were intended to result in similar imposed drifts. One further modification during testing resulted in the displacement increments being increased to 2Dy and Dy for the steel and SMA walls, respectively, beyond 60 mm of displacement. Testing of W1-SR was initially terminated at 36 mm of displacement due to out-of-plane bending. Thereafter, a lateral supporting system (Fig. 3) was assembled and testing continued. This lateral supporting system was also used for W2-NR. No external axial load was imposed on the walls. The focus, herein, was on shear walls that are characterized by wide hysteretic response, which are typically accompanied with significant residual displacements. This type of behaviour arises in walls with light axial loading.

C6

C5

1200

4. Test results

L8 L4

L3 C7

L5

50

C8

750 mm

400

C3

L = LVDT

C = DCT

250

L1

L2

Fig. 3. Shear Wall Setup: (a) Loading System; and (b) Location of LVDTs and DCTs.

4.1. Material properties Tensile tests were performed on 300 mm-long samples of 12.7 mm diameter SMA bars to evaluate the mechanical properties. The ends of the SMA bars were connected to 15 M deformed steel bars with mechanical couplers to replicate the coupling system used in the shear walls. The NiTi sample was in compliance with ASTM F2516-07 [26]. Tensile tests were also conducted on 10 M deformed steel bars. The cyclic response of the two reinforcing bar types is illustrated in Fig. 4. The modulus of elasticity of the SMA bar was approximately 38 GPa, while the modulus of elasticity of the 10 M deformed bar was approximately 205 GPa. The SMA bar demonstrated a rounded response prior to yielding; therefore, the yield point was based on a 0.2% offset, resulting in an approximate stress of 380 MPa. The yield stress of the 10 M deformed steel was 425 MPa. The residual strains at the completion of unloading provide a clear differentiation between the SMA and deformed steel bars. During the last loading cycle, the SMA bar was strained to 8.4%, and upon unloading, the residual strain was

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81

4.3. Load-displacement response

Fig. 4. Cyclic Stress-Strain Response of Reinforcement.

0.72%, representing a 91% strain recovery capacity. During the last loading cycle to 8% strain, the 10 M bar sustained a permanent strain of approximately 7.5%, representing an approximate strain recovery of 6%. The SMA bar failed earlier than expected at the couplers. According to the specifications provided by the manufacturer, the minimum ultimate strain is 10% and the ultimate tensile strength is 1068 MPa. The cyclic response of the SMA is characterized by upper and lower stress plateaus. The upper plateau (forward transformation) is the stress-induced phase transformation from Austenite to Martensite. It resembles yielding in conventional deformed reinforcement. The lower plateau (reverse transformation) marks the return of the material from Martensite to Austeniste and induces the strain recovery. 4.2. Cracking characteristics The first flexural cracks in the steel (W1-SR) and SMA (W2-NR) reinforced shear walls surfaced near the base of the walls during the first load stage, corresponding to a lateral load of approximately 48 kN and displacement of 2.4 mm (0.1% of drift). The first diagonal shear cracks were evident at the end of the second load stage to 4.8 mm of displacement (0.2% drift) in both walls. With increased lateral loading, the flexural cracks in the SMA wall became wider and were spaced farther apart in comparison to the steel wall; while shear cracking was more prevalent in the web region of W1-SR than W2-NR. The crack patterns of W1-SR and W2-NR after yielding and after sustaining the peak lateral load, corresponding to 3% drift, are illustrated in Fig. 5. In general, cracking was widespread in W1-SR. The smooth surface of the SMA bars in W2-NR resulted in reduced bond to the surrounding concrete and wider spaced cracking. At lateral displacement of 48 mm (2% drift), a flexural crack located at a height of 350 mm from the base of the SMA wall extended across the entire length of the wall. This crack was located slightly above the starter bars in the web section of the wall and controlled the response up to failure. In the steel reinforced wall (W1-SR), a similar major flexural crack surfaced at a height of 380 mm from the base of the wall where significant damage and failure initiated. The residual crack widths demonstrated the capacity of the SMA wall to recover displacements. At yielding, the maximum flexural crack widths, near the base of the wall, were approximately 0.6 mm and 2.5 mm for W1-SR and W2-NR, respectively. At the completion of the unloading phase, the residual crack width and crack opening recovery were 0.45 mm and 25% for Wall W1-SR and 0.35 mm and 86% for Wall W2-NR. The average crack opening recovery capacity for the SMA wall was 88% throughout testing, whereas the average recovery capacity for the steel reinforced wall was only 24%.

The lateral load-displacement responses of W1-SR and W2-NR are illustrated in Fig. 6 (a) and (b), respectively, including the yield and ultimate displacements. Beyond the linear elastic range, there was more softening in the response of W2-NR than W1-SR. This was a result of yielding of the vertical deformed steel bars in the web portion of the wall prior to yielding of the SMA bars in the boundary zones. The yield displacement of the steel reinforced wall (W1-SR) was 9.4 mm (0.39% drift) corresponding to 116 kN of load, while the SMA wall (W2-NR) yielded at 26.4 mm (1.1% drift) of displacement corresponding to 112 kN of load. The yield displacement was calculated using the equivalent elasto-plastic system with a secant stiffness passing through the load-displacement response at 75% of the average nominal strength [27]. The yield displacements were established from the average of both directions of loading. The peak average load sustained by W1-SR was 156 kN, corresponding to an average displacement of 76 mm (3.2% drift). The average peak load in W2-NR was 133 kN, corresponding to 72 mm (3% drift) of lateral displacement. Therefore, at the peak load capacity, W1-SR and W2-NR experienced post-yield displacements of 66.6 mm and 45.6 mm, respectively. The lower post yield displacements in W2-NR was attributed to fracturing of the web vertical reinforcement. However, given that SMA reinforced sections experience larger yield displacements, it is more appropriate to compare the drift capacities. The hybrid SMA wall maintained the lateral load capacity up to the second repetition of loading to a displacement level of 72 mm (3% drift) in the positive direction. At this point, the wall experienced a sudden degradation in the lateral load capacity due to rupturing of one of the longitudinal deformed steel bars in the web. Three additional drops in load capacity are evident in the positive direction of the load-displacement response: during the second repetition of loading to a displacement level of 84 mm (3.5% drift); during the first repetition of loading to a displacement level of 94 mm (3.9% drift), and during the last loading cycle (4.5% drift). The drops at 84 mm (3.5% drift) and 94 (3.9% drift) mm were also associated with rupturing of the web vertical reinforcement. These fractures were observed along the major crack adjacent to the starter bars noted previously. At the end of testing, and after concrete was removed from the lower part of the wall, it became evident that one of the SMA bars had also fractured at the location of the mechanical coupler; a distance of approximately 800 mm above the base foundation. This phenomenon was responsible for the last drop in lateral load capacity. At this location, three sharp end bolts (Fig. 2) penetrated into the SMA bar causing a zone of weakness. In the negative direction of loading, there was a drop in the lateral load during the second repetition of loading to a displacement level of 94 mm (3.9% drift), which was caused by fracturing of a web vertical reinforcing bar. The wall sustained a reduced lateral load to a displacement level of 108 mm (4.5% drift) at which point testing was terminated. At this displacement, concrete crushing and buckling of the SMA bars was also evident at one boundary zone adjacent to the major crack at the termination height of the starter bars. In addition, the wall experienced sliding along this crack. By placing the SMA only in the boundary zones, a fuse was developed in the web section of the wall, where the longitudinal reinforcement fractured. Alternatively, SMA bars could be provided across the full length of the wall, which would provide additional drift capacity and result in failure initiating in the boundary zones. However, this would come at the expense of increased cost. More importantly, the hybrid wall tested herein sustained a drift capacity of 3%, which is greater that typical limits (2.5%) placed on structures of normal importance. From a design perspective, limits can be placed on the strain of the longitudinal reinforcement

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Fig. 5. Crack Patterns: (a) W1-SR at yielding; (b) W1-SR at 3% Drift; (c) W2-NR at yielding; and (d) W2-SR at 3% Drift.

to prevent localized fracturing prior to achieving the desired inelastic rotation demands. This is currently the approach used in seismic design [23]. Wall W1-SR exhibited a well-defined elastic loading branch followed by a yielding response with marginal post-yield stiffness. The lateral load capacity was maintained up to the first repetition of loading to a displacement of 84 mm (3.5% drift) where the wall experienced a 14% reduction in strength. The wall failed at a displacement of 94 mm (3.9% drift) in the negative direction of loading. During this cycle, the exterior longitudinal reinforcing bars in the boundary zone fractured and significant concrete crushing and longitudinal bar buckling was also visible at the opposite boundary zone. The unloading stiffness of Walls W1-SR and Wall W2-NR was similar to the initial loading stiffness for a significant portion of the response. Beyond 60 mm (2.5% drift) of lateral displacement, the unloading stiffness in the SMA wall (W2-NR) experienced degradation relative to the initial stiffness. This was partly attributed to fracturing of the longitudinal reinforcement in the web. The SMA wall experienced a rapid recovery of displacements when the SMA bars reached the reverse transformation stress (lower plateau

stress) during unloading. As a result, greater pinching is evident in the response of Wall W2-NR. The ability of the SMA wall to recover displacements was evident throughout testing. At an imposed displacement of 72 mm (3% drift), Wall W1-SR was capable of recovering only 28 mm, while Wall W2-NR recovered 64 mm. Table 2 provides the yield and peak lateral load capacities and corresponding displacements for W1-SR and W2-NR. Note that the ductility was based on the ultimate displacement; the displacement prior to the lateral load capacity of the wall dropping below 80% of the maximum load capacity or the displacement corresponding to fracturing of the reinforcement [27]. The ultimate displacements calculated from both directions of loading were used to determine the average ductility. 5. Discussion of experimental results 5.1. Strength and stiffness The envelope responses for the first repetition of loading are illustrated in Fig. 7. The envelope can be satisfactorily represented

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Fig. 7. Lateral Load-Drift Envelope Responses of Walls.

1.85 kN/mm, respectively. The lower stiffness at yield in the SMA wall does not necessarily imply a deficiency in behaviour. A lower stiffness would lead to an increase in the fundamental period used in seismic analysis, leading to reduced seismic forces. The full implication of a reduced stiffness requires nonlinear dynamic analysis. 5.2. Recovery capacity

Fig. 6. Lateral Load-Displacement Responses: (a) Wall W1-SR; and (b) Wall W2-NR.

by a bi-linear response for the steel reinforced wall; however, a trilinear representation is more appropriate for the hybrid SMA-steel wall. Degradation of strength in W2-NR of approximately 14% initiated at 3% drift due to rupturing of one longitudinal bar in the web. At lateral drift of 3.5%, a further 17% in strength degradation was recorded due to rupturing of another deformed steel bar in the web. In the steel reinforced wall, the first noticeable degradation in strength was at 3.5% drift where the wall experienced a 14% reduction due to the rupturing of the exterior longitudinal reinforcing bars in the boundary zone. The SMA wall experienced a lower initial pre-yielding stiffness and, consequently, higher yield deflection. At yielding, the average secant stiffness of W2-NR and W1SR were 4.24 kN/mm and 12.34 kN/mm, respectively. Therefore, the yield stiffness of the SMA wall was 35% of the yield stiffness of steel reinforced wall. At peak lateral load capacity, the average secant stiffness of W1-SR and W2-NR were 2.17 kN/mm and

The displacement recovery capacity for W1-SR and W2-NR is illustrated in Fig. 8 for the first repetition of loading. The reverse transformation phase that occurs in the SMA bars during unloading triggers the recovery of displacements in the SMA wall. Conversely, the linear unloading behaviour of the steel bars in W1-SR results in large permanent displacements. It is evident that the longitudinal SMA bars in the boundary zones had the capacity to overcome the resistance to re-centering of the steel reinforcement in the web section. Although the deformed steel in W2-NR yielded prior to the SMA bars, the wall recovered a minimum of 85% of the displacements up to 3% drift. This demonstrates that the SMA bars have the capacity to recover large displacements while other reinforcing bars are yielding. Between 3% and 4% drift, the recovery capacity of the SMA wall increased from 85% to 93%. This was a direct result of rupturing of the deformed steel in the web, which enabled the SMA to restore the wall more effectively. At the end of testing, the SMA wall was able to recover 92% of the imposed displacement, whereas the steel wall was only able to recover 31%. The recovery capacity of self-centering systems is intended to permit post-earthquake repairs. In addition, numerical studies have demonstrated that wall systems with flag-shaped hysteretic response are less prone to ratcheting under earthquake excitations in comparison to wall systems with typical wide hysteretic response [28]. In a structure where the only yielding component is the shear wall (main seismic force resisting system), recovery capacity is possible. However, an assessment of the influence on the recovery capacity of other yielding components not considered

Table 2 Load and Displacement Ductility Capacities. Wall

Yield

Peak

Load (kN)

Displacement (mm) (Drift%)

Load (kN)

Displacement (mm) (Drift%)

W1-SR

116

156

W2-NR

112

9.4 (0.39) 26.4 (1.1)

72 (3.2) 72 (3)

133

Ductility (Drift%)

8.9 (3.5) 2.76 (3)

84

A. Abdulridha, D. Palermo / Engineering Structures 147 (2017) 77–89

Fig. 8. Displacement Recovery Capacity-Lateral Drift Responses.

part of the seismic force resisting system is required. Alternatively, these other components should be designed to respond in the elastic range, similar to structures incorporating post-tensioned rocking wall systems.

Fig. 10. Energy Dissipation-Lateral Drift Responses.

shaped hysteretic behaviours, similar to that provided in Fig. 4 of the SMA bar, can match or improve the response relative to an elasto-plastic hysteretic behaviour similar to that of the traditional reinforcing steel. In addition, self-centering systems perform well at controlling peak responses.

5.3. Energy dissipation Fig. 9 provides the lateral load-displacement responses of W1-SR and W2-NR for the first repetition of loading at the peak lateral load resistance for the positive direction of loading of each wall corresponding to 72 mm of displacement (3% drift). At this drift level, the SMA wall (W2-NR) dissipated 7,750 Nm of energy; 60% of the energy dissipated by W1-SR. Fig. 10 provides the cumulative energy dissipated by W1-SR and W2-NR during the first repetition of loading. In general, W1-SR dissipated more energy than W2-NR by an average of 34%. There was noticeable increase in the cumulative energy dissipated by W1-SR at high drift levels. Above 2.5% drift, the energy dissipated by W2-NR varies linearly with drift; whereas the energy dissipation varies exponentially in W1-SR. At lateral drift of 3.5%, 55,600 Nm and 29,200 Nm of energy were dissipated by W1-SR and W2-NR, respectively; an increase of 90% for W1-SR. The reduced energy dissipation of Wall W2-NR was a result of the smaller hysteretic loops due to the reverse transformation that occurs in the SMA reinforcement during unloading. Although Wall W2-NR provided reduced energy dissipation, this does not suggest inferior seismic performance. Numerical studies by Christopoulos et al. [29] demonstrated that flag-

5.4. Rotation response The vertical displacements of the top beam at both ends of the wall were used to calculate the lateral load–rotation responses as illustrated in Fig. 11 (a) and (b). The rotation at yielding was 3.1  103 rads in W1-SR and 11.2  103 rads in W2-NR. The larger rotation in W2-NR is attributed to the larger displacement at yielding. At peak lateral load capacity, W1-SR and W2-NR experienced the same rotation of approximately 27.7  103 rads. [Note that the rotations at yield and peak lateral load capacities were based on the negative loading direction. The cable transducer experienced pinching during testing resulting in lower rotations in the positive direction of loading.] Therefore, the inelastic rotation of W1-SR and W2-NR at the peak lateral load capacity was 24.6  103 rad and 16.5  103, respectively. The rotation of the walls was also recorded over a height of 800 mm from the base of the wall, corresponding to the assumed plastic hinge region. At yielding and peak lateral load capacities, W1-SR experienced rotations of 4.0  103 rads and 18.6  103 rads, respectively; while W2-NR experienced rotations of 9.7  103 rads and 20.4  103 rads, respectively. Therefore, the two walls experienced similar total rotations within the plastic hinge region. A notable difference in responses is the capacity of Wall W2-NR to recover the large rotations experienced by the wall. 5.5. Shear strain An approximate average shear strain for each wall was calculated from displacements that were recorded by two DCTs placed diagonally on the walls over the assumed plastic hinge region following the approach suggested by Oesterle et al. [30]:

cav g ¼ ðd1 d1  d2 d2 Þ=2hl

Fig. 9. Hysteretic Responses of Walls at 3% Lateral Drift.

ð1Þ

where cav g is the average shear strain, d1 and d2 are the original lengths of the diagonal DCTs, d1 and d2 are the change in lengths of the diagonal DCTs, h is the height of the diagonal DCTs, and l is the length of the diagonal DCTs. For W1-SR and W2-NR, d1 and d2

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85

Fig. 12. Lateral Load-Shear Strain Responses: (a) Wall W1-SR; and (b) Wall W2-NR.

Fig. 11. Lateral Load-Rotation Responses: (a) Wall W1-SR; and (b) Wall W2-NR.

were 1265 mm, and h and l were 980 mm and 800 mm, respectively. The lateral load–shear strain responses are provided in Fig. 12 (a) and (b). The average shear strain of Wall W1-SR at yielding was 0.074  103 rads and 1.1  103 rads at the peak lateral load capacity. For Wall W2-NR, the shear strain at yielding and peak lateral load capacities were 0.35  103 rads and 1.1  103 rads, respectively. Therefore, the two walls experienced the same total shear strains. The shear strain responses provide notable differences. Wall W1-SR experienced a typical response for ductile steel reinforced shear walls. Large permanent straining was present at the end of unloading with significant pinching in the response. The pinching arises from a reduction in stiffness which is attributed to the shear cracks remaining open during load reversal. While the cracks remain open, there is a reduction in aggregate interlock and the resistance is primarily through dowel action. The latter is characterized with low stiffness. Once the cracks close, there is an increase in stiffness. Conversely, W2-NR experienced significantly smaller residual straining. This was partly a result of the SMA and partly a function of less diagonal shear cracking in the wall. Near the end of testing, the shear strains in W2-NR increased rapidly. This was associated with sliding along the main horizontal crack located slightly above the termination of the starter bars in the web.

6. Finite element modelling A hysteretic constitutive model for superelastic SMA bars was recently developed [18]. The model was implemented into Program VecTor2 [31], a nonlinear, two-dimensional finite element program applicable to concrete membrane structures. The superelastic SMA model is based on a trilinear envelope response, which is assumed to be identical to the monotonic response. The backbone includes: initial linear elastic loading; yielding (forward transformation); and strain hardening, which defines the stressinduced elastic response of Martensite. Improvements relative to other models [32–36] includes explicit consideration of permanent strains (Fig. 4); the degradation of the lower plateau stress (reverse transformation), which results from the recovery of strains; and a trilinear unloading response. Fig. 13 provides a schematic illustration of one complete cycle of the model. er1 and er2 are the first and second unloading strains, respectively, that define the lower plateau stress funl; em is the current maximum strain; and ep is the plastic offset strain. Abdulridha et al. [18] presented data from coupon testing of SMA bars that demonstrated the link between ep, er1, and funl with the current maximum strain em, as follows:

ep ¼ 0:0013ðem Þ2  0:025ðem Þ þ 0:71

ð2Þ

er1 ¼ 0:86ðem Þ  0:45

ð3Þ

f unl =f y ¼ 0:006ðem Þ þ 0:73

ð4Þ

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Stress fm fy

Esh

funl

ε

- m

ε

- r1

Ei

Ei

-εr2 -εp

Ei

εp εr2 -funl

εr1

εm Strain

-fy -fm Fig. 13. SMA Hysteretic Constitutive Model [18].

The second unloading strain, er2, is implicitly determined from the intersection of the lower plateau stress and the linear unloading branch to the plastic offset. The reloading response, following a full cycle, is linear originating from the plastic offset strain ep to the yield strain ey. Thereafter, the response follows the envelope curve. fy, Ei, Esh, ey, eu, and esh can be established from coupon testing or from specifications provided by an SMA supplier. The model successfully simulated the behaviour of SMA reinforced beams and a beam-column joint [18]. The analysis of the steel reinforced wall herein is intended to demonstrate the applicability of the finite element model and program, and the default constitutive models to provide successful simulations for typical steel reinforced slender walls. Similar procedures were then extended to the SMA reinforced wall with a focus to demonstrate the applicability of the SMA constitutive model to simulate the response of SMA reinforced shear walls, including the effect of the hybrid SMA-steel reinforcement in the critical section, and to provide modelling guidance. The finite element mesh of the SMA shear wall included 506 plane stress rectangular elements to model the concrete. The transverse shear reinforcement, the boundary zone confinement steel, and the vertical starter bars were modeled as smeared reinforcement in the concrete elements. The vertical reinforcement in the web portion of the wall, the longitudinal reinforcement in the boundary zones, and the couplers used between the SMA and deformed steel where modeled discretely by a total of 203 truss bar elements. The mesh consisted of 100 mm  100 mm rectangular elements throughout the wall, with the exception of the boundary zones. In this region, the mesh was discretized with 50 mm  100 mm elements. The mesh was divided into eight concrete zones to account for variation in concrete thicknesses and reinforcement ratios. Zones 1 and 2 correspond to the heavily reinforced foundation and top beam respectively; Zones 3 and 4 correspond to the boundary elements of the wall; and Zone 5 corresponds to the web portion of the wall. Zones 6, 7, and 8 have the same properties as Zone 5 with the addition of smeared vertical reinforcement to account for the starter bars, which were modeled with variable reinforcement ratios in each zone proportional to the development length of the bar. [Note that two zones were necessary in the boundary zones to account for the change in spacing of the anti-buckling/confinement reinforcement.] The deformed steel reinforcement and couplers were assumed perfectly bonded to the surrounding concrete. Bond-slip elements were used at the interface of the SMA truss elements and the rectangular concrete elements to model the bond characteristics of the SMA. The bond was based on the VecTor 2 constitutive model for smooth embed-

ded bars following the Eligehausen model. The bond stress-slip response is described by an ascending non-linear branch, a constant bond stress plateau, a linearly descending branch, and a residual stress branch. Further details can be found elsewhere [31]. The base of the shear wall was connected to the laboratory strong floor with four high strength bolts. This was simulated by restraining, in the vertical and horizontal directions, the six nodes around the location of each bolt at the base of the foundation. All other base nodes were considered free to move. A schematic representation of the finite element mesh for W2-NR is shown in Fig. 14. The steel reinforced wall was simulated with a similar model. The only difference was the replacement of the SMA bars in the boundary zones with deformed reinforcement that was fully bonded to the surrounding concrete elements. Additional information regarding the models is available elsewhere [24]. The default materials models of VecTor2 were selected for the analysis of the walls. The analyses followed the same loading protocol that was used during testing. The numerical load-displacement responses for W1-SR and W2NR are illustrated in Fig. 15 (a) and (b), respectively. In general, the predicted and recorded (Fig. 6) hysteretic responses were in satisfactory agreement in terms of yield and peak lateral load capacities, pre-yielding and post-yielding stiffness, and overall hysteretic behaviour. The unloading and reloading curves were well simulated. At the experimentally calculated yield displacement of 9.4 mm and 26.4 mm, respectively for W1-SR and W2NR, the numerical model predicted lateral loads of 118 kN and 130 kN. This corresponds to an overestimation of 1.7% and 16% for W1-SR and W2-NR. The predicted peak strength for W1-SR and W2-NR were similar at approximately 150 kN; an underestimation of only 3.8% for W1-SR and a slight overestimation of 12.8% for W2-NR. The corresponding lateral displacements of 72 mm (3% drift) and 82 mm (3.4% drift) were in close agreement with those recorded during testing. The analyses predicted ultimate displacements of 94 mm (3.9% drift) and 82 mm (3.4% drift) for W1-SR and W2-NR, respectively, which were in good agreement with the experimental results (Table 2). The predicted failure modes were consistent to those observed during testing. For W1SR, the analysis predicted rupturing of the exterior longitudinal

P

2

4

4

Regular Rein. 5

5 3

3

SMA

86

8 6

7

1

Fig. 14. Finite Element Mesh for Wall W2-NR.

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87

Fig. 16. Modified Numerical Load-Displacement Response of Wall W2-NR.

Fig. 15. Numerical Load-Displacement Responses: (a) Wall W1-SR; and (b) Wall W2-NR.

reinforcing bars in the boundary zones. For W2-NR, the numerical model captured fracturing of the longitudinal reinforcing bars in the web portion of the wall, while the SMA bars in the boundary zone remained intact. Discrepancies in the numerical and experimental unloading behaviours for Wall W2-NR are evident, including the larger residual displacements predicted by the analysis and the continual degradation of the reloading stiffness recorded during testing. Note that although the residual displacements are greater, the lateral load at zero displacement levels is accurately predicted. An additional analysis (Fig. 16) was conducted in which the SMA bars were fully unbonded from the surrounding concrete and connected to the concrete nodes at the foundation level and at the location of the couplers. The load-displacement response of the modified model more accurately captures the recovery capacity of the wall. However, a premature failure controlled by shear sliding of wall at the top of the starter bars was predicted. That is attributed to the loss of shear sliding resistance at the critical section since the SMA truss bars were connected only at the foundation and couplers. Therefore, the modified model illustrates that the constitutive SMA hysteretic model provides satisfactory simulations, and that the bond characteristics of the smooth SMA with the concrete is also critical to the analysis. In addition, an improved bond model would better capture the localized cracking and strain localization of the reinforcement along a predominant crack. The latter would

aid in capturing the gradual fracturing of the reinforcement in the web section of the wall. Further studies are required to develop a bond model specifically for smooth SMA bars. To assess the effect of axial load on re-centering, a preliminary study was conducted [37] that included varying the axial load ratio (P/Agf0 c) from 0–25%. Fig. 17 provides the results for W1-SR and W2-NR subjected to 10% axial load, which corresponds to shear walls in medium- to high-rise buildings. The axial load provides a re-centering effect. The residual displacements in W1-SR were reduced relative to the wall with no axial load (Fig. 6a)). At 3.5% drift, the residual displacement was 31 mm (1.3% drift) under the axial load compared to 54 mm (2.25% drift) recorded during testing with no axial load. The presence of the axial load resulted in negligible residual displacements in Wall W2-NR. This preliminary study suggested that hybrid SMA reinforced walls are significantly more effective at controlling permanent displacements for axial loads not exceeding 10%. However, for axial loads greater than 10%, there was no clear advantage in using SMAs. Furthermore, hysteretic responses of the hybrid SMA and steel reinforced walls were nearly identical for axial load levels of 20% and 25%. 7. Conclusions This study focused on the experimental performance of a hybrid SMA-steel reinforced ductile shear wall in comparison to a steel reinforced wall subjected to reverse cyclic loading. In addition, a recently developed hysteretic constitutive model for superelastic SMA was corroborated against the experimental results. The following conclusions are drawn from this research: 1. The load-displacement responses demonstrated the ability of walls to sustain large drifts (up to 3.5% for the steel reinforced wall and 3% for the SMA wall) without suffering a significant loss in load carrying capacity. 2. The SMA wall experienced similar yield load to the steel reinforced wall; however, the corresponding drift was substantially higher. The larger yield drift was a result of the lower modulus of elasticity of the SMA bars. 3. The peak lateral load capacity of the hybrid SMA wall was approximately 85% that of the steel reinforced wall; however, the peak capacity was recorded at a similar drift of approximately 3%. The lower strength in the SMA wall is attributed to rupturing of the longitudinal steel reinforcement in the web and one of the longitudinal SMA bars at the location of the coupler.

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same as the steel reinforced wall. Both the load-rotation and load-shear strain responses demonstrated the capacity of the hybrid SMA wall to recover various deformations in the wall. 9. The recently developed hysteretic constitutive model for superelastic SMA satisfactorily simulated the response of a shear wall with a hybrid reinforcement layout along the critical section. The predicted and recorded hysteretic responses were in good agreement, and the failure mode was accurately simulated. Discrepancies between the numerical and experimental results was attributed to the bond characteristics of the smooth SMA bars. Further studies are required to develop a bond model specifically for SMA bars.

Acknowledgements The research program was funded by the Public Works and Government Services Canada, and the Canadian Seismic Research Network (Grant: NETGP/350698-07). The authors wish to express their gratitude to both organizations. Furthermore, thanks are extended to SAES Smart Materials for providing support with the SMA material used in this study.

References

Fig. 17. Numerical Load-Displacement Responses Under Axial Load: (a) Wall W1SR; and (b) Wall W2-NR.

4. The displacement ductility capacity of the steel wall was much larger than the SMA wall; however, the drifts corresponding to the ultimate displacement were comparable (3.5% for the steel reinforced wall and 3% for the hybrid SMA wall). The lower displacement ductility in the hybrid SMA wall is a result of the much larger yield displacement. 5. The hybrid SMA wall demonstrated significantly greater capacity to recover displacements relative to steel reinforced wall. At the end of testing, the recovery capacity was 92% and 31% for the hybrid SMA and steel reinforced walls, respectively. 6. The secant stiffness at the yield point for the hybrid SMA wall was 35% of the yield stiffness of steel reinforced wall. 7. The steel reinforced wall dissipated more energy than the hybrid SMA wall. Numerical studies, however, have shown that flag-shaped hysteretic behaviours can match or improve the seismic response relative to an elasto-plastic hysteretic behaviour. Thus, the smaller energy dissipation capacity for flagshaped responses does not necessarily imply inferior seismic performance. 8. At the peak lateral load capacity, the hybrid SMA wall experienced the same total rotation as the steel reinforced wall. The shear strains experienced by the hybrid SMA wall over the plastic hinge region at the peak lateral load capacity was also the

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