Experimental study on shear strengthening of shear critical RC beams using iron-based shape memory alloy strips

Engineering Structures 200 (2019) 109680

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Experimental study on shear strengthening of shear critical RC beams using iron-based shape memory alloy strips

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Luis A. Montoya-Coronado , Joaquín G. Ruiz-Pinilla, Carlos Ribas, Antoni Cladera Department of Physics. University of Balearic Islands, Palma de Mallorca, Spain

A R T I C LE I N FO

A B S T R A C T

Keywords: Iron-based shape memory alloy (Fe-SMA) Shear strength Reinforced concrete Strengthening Experimental test

Shape memory alloys (SMAs) have been introduced into structural engineering in recent years. This paper presents research results about developing a new methodology to actively strengthen reinforced concrete (RC) beams by low-cost iron-based SMA strips (Fe-SMA). These strips can transversally prestress, or confine, the crosssection of beams thanks to the shape memory effect of Fe-SMA, without having to apply prestressing force. Activation of strips is carried out by heating them up to 160 °C and then cooling them. An experimental campaign was carried out at two levels: characterization of Fe-SMA strips, and the practical application of the strengthening technique on small-scale beams without internal stirrups. The retrofitted beams with activated strips failed by bending, and the appearance of shear cracks was clearly delayed. Meanwhile, the reference beams failed due to shear.

1. Introduction Structural design is moving toward performance-based design (PBD) methods to optimize structures by controlling different failure mechanisms. To increase sectional ductility, controlling the flexural failure mechanism is necessary to avoid brittle failures, such as shear. This is why the shear strengthening of existing structures is often needed, especially in structures subjected to seismic actions or where new loads are expected. Moreover, shear behavior is a highly controversial topic that is continuously being investigated by many different research groups given the numerous parameters involved [1–6]. In the last few years, several proposals of shear retrofitting systems have appeared with different materials and techniques. Adhikary and Mutsuyoshi [7] studied various techniques for the shear strengthening of RC beams, including steel brackets, steel plates, vertical strips and externally anchored stirrups. Chalioris et al. [8] experimentally verified the high efficiency of using thin RC layers (with self-compacted concrete) as jacketing. Colajanni et al. [9,10] presented a new retrofitting method based on using longitudinal steel angles and prestressed stainless-steel ribbons. Steel ribbons were able to confine concrete by improving the deformation capacity and shear strength of retrofitted beams. Different references about applying fiber-reinforced polymers (FRPs) to critical shear beams confirm their applicability in a wide range of cases. For example, Foster et al. [11] used externally bonded FRP fabric to transfer shear forces across a diagonal crack. El-Hacha and

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Soudki [12] presented a review on the near mounted surface (NMS) of FRP reinforcement and showed advantages of this specific method over other FRP techniques, such as occurrence of debonding and exposure to the external environment. Soroushian et al. [13] used Fe-SMA rods as a component of a shear repair system for a concrete bridge beam. The anchorage system for the prestrained Fe-SMA rods was developed by steel angles, and was verified by a laboratory testing one beam. Zerbe et al. [14] recently studied the use of Fe-SMA strips as shear external reinforcement to retrofit reinforced concrete (RC) T-beams. This study showed how the shear strength of retrofitted beams increased. However, tests were influenced by the adopted anchorage system and the results were not conclusive. While testing, diagonal cracks in members with activated Fe-SMA strips started to appear at the anchorage system location. However, as most of the previously cited shear strengthening methodologies are passive technologies, the deformation of a strengthened structure is needed to increase and to reach a certain level of damage before the strengthening material can begin to contribute. Alternatively, excess load must be removed, and then the strengthening material can contribute as soon as the additional load is applied. The technology proposed herein uses the shape memory effect (SME) to actively confine and prestress the strengthened concrete member. In this way, the strengthening material immediately begins working upon installation and activation, and does not need to introduce high forces

Corresponding author at: Department of Physics, University of the Balearic Islands, Ctra. Valldemossa, Km 7.5, Palma, Balearic Islands, Spain. E-mail address: [email protected] (L.A. Montoya-Coronado).

https://doi.org/10.1016/j.engstruct.2019.109680 Received 14 December 2018; Received in revised form 7 August 2019; Accepted 12 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Different atomic behaviors on SMA. Adapted from [20].

researches. This paper also presents a comprehensive characterization of these commercially available Fe-SMA strips, and compares the results with recently research works available in the literature. These Fe-SMA strips have been used to externally retrofit small-scale beams without shear reinforcement, and with a different anchorage to those used by Zerbe et al. [14]. This paper presents the different behaviors of the reference beams (without shear reinforcement), the retrofitted beams (with the activated strips fully wrapping beams to generate recovery stresses), and beams with externally placed strips, but without activation. The retrofitted beams with activated strips failed by bending and the appearance of shear cracks was clearly delayed. Meanwhile, the reference beams failed due to shear.

by using hydraulics jacks or similar tools for prestressing. Shape memory alloys (SMAs) are unique materials that can achieve major deformations and return to a predefined shape after unload or upon heating [15]. In structural engineering terms, SMAs possess three key properties: superelasticity (or pseudoelasticity), SME and damping capacity. Superelasticity is the phenomenon whereby SMAs can undergo major inelastic deformations and, notwithstanding, they return to their original shape upon unloading. The SME refers to the phenomenon whereby SMAs are capable of returning to a predefined shape upon heating. Damping capacity, linked to pseudoelasticity and SME, is due to the possibility of reducing a structure’s movements or vibrations thanks to mechanical energy being converted into the thermal energy of SMAs. All these properties are in fact the result of martensitic transformation, a reversible phase transformation [15]. Moreover, some of these SMAs also display very high ductile behavior upon failure. A good introductory review on martensitic transformation from an engineering perspective is presented in [16]. Comprehensive reviews about applying SMAs to structural engineering have also been published [17–21]. Some previously used SMAs are quite expensive for civil engineering applications, but can be very useful for special cases, e.g., in retrofitting, when the cost of strengthening materials may be insignificant compared to either the retrofitted structure’s real value or the social and/or economic cost of having an infrastructure out of service. However, the alloy used for the shear strengthening technique developed herein is a low-cost SMA developed at Empa. It is competitive and can be used regularly in civil engineer applications [21]. Its composition is as follows: Fe–17Mn–5Si–10Cr–4Ni–1(V, C) (mass%) [22]. Note that around 63% of its composition in mass is Fe, which is a relatively cheap mineral. Although superelasticity is not relevant to this alloy given incomplete martensitic transformation, the SME and high ductility are still significantly present. In recovered strain terms, the SME is considerably lower (up to 1% of shape recovery) than other SMAs (i.e. 6–8% of shape recovery in Ni-Ti alloys). However, the SME presents a singular application when shape recovering capacity is restrained. In this situation, shape cannot be recovered, and SMA develop internal “recovery stresses” that can be used as prestraining forces [20]. The SME of the employed Fe-SMA suffices to generate enough recovery stresses (up to 350 MPa) when heated at around 160 °C. This temperature enables Fe-SMA to be combined with concrete structures without concrete being affected by any crucial damage due to the high temperatures. Furthermore, this SMA type has a significantly higher modulus of elasticity than most SMA alloys, which is desirable for retrofitting applications. Recently, Fe-SMA strip production has started on an industrial scale, and the experimentally determined properties of such industrially produced Fe-SMA strips have been reported in [23]. On the other hand, the one-way and two-way ribbed structural floors and other type of structural elements are allowed (in some countries) to have no stirrups due to the repetition of the structural elements, due to the possibility of transversely redistributing the load in case of failure of one single rib. However, this modus operandi is not extended in some other countries. In any case, this research starts with beams without stirrups in order to develop a new shear-strengthening technology eliminating several variables that should be studied in later

2. Fundamentals of the shape memory effect in Fe-SMAs The martensitic transformation is a diffusionless, solid state displacive transformation in which the atoms move cooperatively [15]. The new phase is constituted through small coordinated displacements of the atoms, where the displacements of neighboring atoms are smaller than their original interatomic distances. Martensitic transformation takes place through the lattice deformation that modifies the crystal structure of the parent austenite phase to the martensite phase, but the deformation mechanism differs from the slip of crystals by dislocations. During martensitic transformation, the lattice is distorted without atoms being reorganized (neighbors stay neighbors). During plastic deformation, atoms are rearranged by slip (neighbors change). Reverse martensitic transformation takes place in the opposite direction, when the martensite phase is transformed into the austenite phase (see Fig. 1). The transverse prestressing effect of strengthening strips was obtained in this research by initial forward martensitic transformation (prestraining of the material to generate the stress-induced martensite phase), and by installing the prestrained strips wrapping the RC beam specimens (impelling the shortening of strips) to finally produce reverse martensitic transformation by an increment of temperature, generating recovery stresses due to the strain constraint of strips. Austenite phase formation in reverse martensitic transformation, and in the absence of applied stresses, began at temperature As (austenite start) and finished at temperature Af (austenite finish). Fig. 2 summarizes the conceptual procedure. More information on the main actions in SMA application for longitudinally or transversally prestressing RC members, and in relation to the fundamentals of martensitic transformation, can be found in [20–23]. 3. Fe-SMA strips characterization Fe-SMA strips were provided in the form of a coil, manufactured by re-fer AG. The manufacturing process and the detailed production procedure of the Fe-SMA material and strips are described in [24], while recommendations for the characterization test setup and protocols are detailed in [25]. Strips with two different thicknesses were 2

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Fig. 2. Schematic illustration of Fe-SMA behavior. Adapted from [23].

performed (approx. 80) in order to prestrain samples (to create martensite in strips), which would be used later for strengthening the RC beam specimens. The mean modulus of elasticity came close to 195 GPa (Fig. 4b), and was computed between 100 and 300 MPa. This value was slightly higher than the 160 GPa reported in [23], determined within a stress range of 20–200 MPa. The mean 0.2% proof stress, obtained by the off-set method, came close to 475 MPa (Fig. 4b), and was also similar to the 500 MPa proof stress for the strip with a 1.5-mm thickness reported by [23]. If semi-cyclic tests were performed (Fig. 4a), the modulus of elasticity lowered in each semi-cycle after six semi-cycles (160.4, 134.8, 122.0, 106.5, 97.6, 98.1 GPa to the number of semi-cycles), but seemed to converge at around 100 GPa. The previous results corresponded to the mean of three semi-cycle tests up to failure. In any case for the application envisaged herein, the material was not exposed to cycles in the as-provided form, and further research is needed to confirm these data.

3.2. Recovery stress tests

Fig. 3. The Fe-SMA strips installed in a Zwick Z100 universal testing machine equipped with an extensometer over a length of 35 mm.

The recovery stress tests included three different steps (see Fig. 5). First, it was necessary to pre-strain strips, as shown in Fig. 4b and as previously mentioned, to generate martensite inside strips. Second, the pre-strained sample was once again placed in the universal testing machine, and an initial pre-load of around 40 MPa was applied. Third, the strip was heated using a heat-gun up to approximately 160 °C and was then cooled. During the heating and cooling processes, sample deformation was prevented by forcing to maintain constant the strain level measured by the extensometer, and the load cell measured the generated stresses to maintain the extensometer position constant. As the sample tended to shorten due to reverse martensitic transformation when heated, the tensile stress in the sample increased (blue in Fig. 5a and b). Heating and cooling were measured by five thermocouples placed at an equal distance on one side of the sample (see Fig. 3), and heating was performed with the heat-gun on the opposite side. The two thermocouples near the clamps were placed 5 mm away from each clamp. Afterward, the initial pre-load of around 40 MPa was performed, displacement was restrained and the sample was activated as homogeneously as possible by a heat-gun until more than 160 °C was achieved in the five different installed thermocouples to allow it to recover ambient temperature (see Fig. 5b). The maximum average temperature was slightly higher than 160 °C (172 °C in the test shown in Fig. 5b). The tests accomplished recovery stresses of around 350 MPa.

manufactured (0.5 and 1.5 mm), and the thinner strip (0.5 mm) was used for this experimental campaign. The Fe-SMA strip coil was provided in the austenite phase (γ) with no initial prestraining. To obtain this material’s mechanical properties, several tests were performed in a Z100 Zwick universal tensile machine with a 100 kN load cell. Typical samples were tested with the original strip width (50 mm), a free length equal to 150 mm, and 15 mm inside each clamp to grip the sample to avoid sliding. However, as the intention was to use strips as the strengthening material for small-scale beams, the original strips were cut into narrower strips (25 and 12.5 mm). Fig. 3. represents a test with a sample free length that equaled 75 mm and an extensometer base length that equaled 35 mm. 3.1. Tensile tests in the as-provided samples (austenite phase) The ultimate strength of the as-provided Fe-SMA strip was approximately equal to 950 MPa, which corresponded to 45% of the strain (Fig. 4a) tested at a displacement rate of 7.5 mm/min up to failure. These results are similar to those provided by [23], who reported stresses at failure between 960 and 1000 MPa and minimum ultimate strains of 47% for a 0.5 mm-thick Fe-SMA strip. Numerous one-semi cycle tests (loading and unloading) were 3

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Fig. 4. Stress-strain curves.

cycle. After each activation, a mean value of the shape recovery equal to 1% was obtained, which corresponded to 0.85%, 1.06%, 1.07%. 1.08%, 1.05% of free shape recovery, respectively, for each semi-cycle, which means that the prestrain level does not affect the percentage of shape recovery. The measured 0.2% proof stress remained between 487 MPa and 463 MPa. A reduction in stress of less than 5% was observed after five thermal-stress cycles. Fig. 6b shows all the cycles with their start normalized to zero. This figure also illustrates how the modulus of elasticity significantly lowered from 170 GPa to 94 GPa after the first semi-cycle. Nevertheless, it is noteworthy that after the first back and forward transformation temperatures (in blue in Fig. 6), the 0.2% proof stress and the modulus of elasticity maintained their mechanical properties during all the semi-cycles. Note that the modulus of elasticity indicated in Fig. 4b is the mean value of 80 tests, while the result shown in Fig. 6b is merely the result obtained in one individual test.

This value of recovery stresses is completely compatible with the recovery stresses reported in [23], and that for the 0.5- and 1.5-thick strips heated up to 160 °C obtained recovery stresses between 303 and 349 MPa. Interestingly, the authors also obtained recovery stresses up to 388 MPa when strips were heated up to 195 °C. Monotonic tests were also carried out up to failure following the recovery stress test (see Fig. 5a). The tangent modulus of elasticity after the generation of recovery stresses was 86 GPa. However, the modulus of elasticity measured between the stresses of 450 and 550 MPa in a monotonic tensile test after generating recovery stresses was 34.4 GPa.

3.3. Free shape recovery tests Free shape recovery tests were also performed to determine the shape recovery capacity of strips. The free shape recovery test included two different steps. First, it was necessary to prestrain strips as shown in Fig. 4b. and as previously discussed. Second, the prestrained sample was once again placed in the universal testing machine (or remained in it if not removed), and was heated using a heat-gun up to approximately 160 °C and then cooled. No initial preload was used in this test. The process was repeated several times via multi-thermal cyclic activation, as shown in Fig. 6a. The strain in the first cycle was taken up to 4% and up to 6%, 8%, 10% and 12% of the total strain in each next

4. Experimental campaign on small-scale RC beams In this experimental campaign, 10 small-scale beams were tested and analyzed. These experimental tests were designed to show the feasibility of using external Fe-SMA strips to strengthen shear critical RC beams. Since this research has been developed studying very small

Fig. 5. Prestraining test, recovery stress, and final monotonic test up to failure. 4

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Fig. 6. Free recovery tests with multiple thermal activations. Blue represents the first cycle, while the next cycles are denoted by a gradient red color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

To fulfill this aim, a post-processing digital image correlation (DIC) analysis was run to guarantee the maximum possible shear crack width. These two pre-cracked beams were strengthened and tested with narrow strips (12.5 mm-wide), and with no activation in test Cr1-SPn1, but with activated strips in test Cr2-SAn1. It is important to highlight that using Fe-SMA with no previous activation in beam specimens SP1, SP2, SPn1, and Cr1-SPn1 was performed only for academic purposes to study the influence of recovery stresses on shear behavior. In real practice, however, using Fe-SMA with no activation would make no practical sense.

beams, further investigation should be carried out in order to clarify whether the results of these experimental campaign can be reasonably scaled up. An overview of the test program is presented in Table 1. The RC beam specimens were 80-mm wide (b), and 150-mm deep (h), as shown in Fig. 7. The total length of beam specimens was 900 mm. All the beams were loaded in a three-point bending test scheme with a 760-mm span between the axes of the supports. Shear span a equaled 340 mm, with a/d approximately equaling 2.68, where d is the effective depth of beams (d = 127 mm). All the beams were longitudinally reinforced with a 16-mm corrugated bar with welded end plates at both ends to ensure correct anchorage in such small beam specimens. Two beams (R1/R2) were designed and tested as the reference beams, but did not include any shear reinforcement. Beams SP1 and SP2 were strengthened by the Fe-SMA strips (25-mm wide), but without activating them. Beams SA1 and SA2 were identical to the previous beams, but strengthening strips were activated before testing the beams. Note that two identical beams were tested for the three previously mentioned configurations (R1/R2, SP1/SP2, SA1/SA2) to ensure the repeatability of the results. Then four beam specimens were strengthened using 12.5 mm-wide strips. Beams SPn1 and SAn1 were strengthened with narrow strips (12.5 mm): in the first case without activating strips (SPn1), and strips were activated before testing the beam in the second case (SAn1). Finally to simulate a real case of strengthening previously cracked beams, two beam specimens, Cr1 and Cr2, were subjected to a pre-cracked that corresponded to 29.73 and 27.78 kN, respectively, to ensure the formation of critical shear cracks.

4.1. Strengthening procedure The active strengthening method proposed herein comprises these steps: (1) prestraining Fe-SMA strips to create martensite through initial forward martensitic transformation (this prestaining could be done directly by the manufacturer); (2) placing the pre-strained strips wrapping the RC beam specimens; (3) anchoring strips against themselves and to RC beams; (4) producing reverse martensitic transformation by incrementing temperature (activation process) and generating recovery stresses due to the strain constraint of strips. For the small-scale beams used in this proof-of-concept research, it is very important to avoid gaps between strips and the concrete surface due to the relatively low shape recovery strain capacity of this material (see Fig. 8a and b). To develop full recovery stresses, it is necessary to reduce any possible gap. For this reason, a strip-tensioning device is used to confer pretension only to close the gaps between strips and the

Table 1 Detail of the beam specimen and test. Beam specimen

Age at testing [days]

fcm [MPa]

fsp [MPa]

Strip spacing [mm]

Strip width [mm]

Fe-SMA state

Vtest [kN]

δtest at Vtest [mm]

Comment

R1 R2

172 172

30.1 30.1

2.80 2.80

– –

– –

– –

17.95 15.82

3.24 1.53

Reference beam Reference beam

SP1 SP2

173 173

30.1 30.1

2.80 2.80

88.9 88.9

25 25

Non activated Non activated

29.51 31.01

7.88 9.34

Full strip Full strip

SA1 SA2

174 175

30.1 30.1

2.80 2.80

88.9 88.9

25 25

Activated Activated

31.69 31.64

6.52 5.83

Full strip Full strip

SPn1 SAn1

221 221

30.5 30.5

2.91 2.91

88.9 88.9

12.5 12.5

Non activated Activated

25.18 27.55

7.05 4.14

Narrow strip Narrow strip

Cr1-SPn1

251

31.0

3.03

88.9

12.5

Non activated

29.75

6.65

Cr2-SAn1

251

31.0

3.03

88.9

12.5

Activated

29.15

4.69

Precracked in test Cr1. Narrow strip Precracked in test Cr2. Narrow strip

5

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Fig. 7. Detail of a strengthened beam specimen with a 25 mm-wide strip.

structural element (see Fig. 8a). A handmade buckle was employed as a passive anchor, which was combined with shot nails. Industrial buckles for narrow strips are available on the market, and were used herein. 4.2. Concrete and steel properties All the beam specimens, concrete cubes and cylinders were cast from a single batch. A maximum aggregate size of 14 mm was used. Standard 150 mm cubes and 150 × 300 mm cylinders were employed to obtain mean compressive strength fcm, and splitting strength fsp, respectively. The mean fcm(28) and fsp(28) at 28 days was 23 MPa and 2.5 MPa, respectively. The fcm and fsp estimations found in Table 1 at the age when testing beams were derived from the results obtained from 23 cube tests for compressive strength, and from 25 cylinder tests for splitting strength. Cylinders and cubes remained under the same environmental conditions as the beam specimens until testing began. Longitudinal reinforcement was composed of a 16 mm (∅16) standard B500SD rebar (As = 201 mm2, and a characteristic yielding strength of 500 MPa). The actual mechanical properties of these 16 mm rebars were: fy = 550 MPa, fu = 649 MPa, and εu = 27% (mean value of two reported tests). 4.3. Test setup The experimental campaign was carried out at the University of the Balearic Islands (UIB; Spain). The simply supported small-scale beams were tested in a three-point bending test with a concentrated load at the center span (see Figs. 7 and 9–11). Tests were run with displacement control using a hydraulic actuator with a maximum load capacity of

Fig. 9. Test setup.

Fig. 8. Comparison before and after activating shear strengthening strips. 6

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Fig. 10. Beam instrumentation.

4.5. Experimental results

100 kN. The length of the supporting plates was 60 mm on the beam’s longitudinal axis, and that of the loading plate was 110 mm. Load was applied by two cylinders, whose centers were spaced 80 mm on the same loading plate. A sliding pin bearing was placed at the Westside and a fixed pin bearing on the Eastside (see Fig. 7). The displacement at the loading plate was monotonically increased until beam failure.

4.5.1. Crack patterns and failure modes Fig. 12 presents the crack pattern of beams at failure. Photographs were taken with two cameras on each side of the load application point, and were merged to obtain a complete view of the beam specimens. DIC was followed to observe the crack patterns on beams. Images show the post-peak cracks for a load that equaled 80% of maximum load. The failure mechanism of reference beams R1 and R2 was characterized by the presence of a well-developed unique critical shear crack (see Fig. 12a and b). However, the strengthened beams present more vertical cracks and well-distributed in all its length. The beams strengthened with the 25 mm-wide strips failed by bending, with spalling occurring in the compression chord at the mid-span after some clearly marked shear cracks had formed. The shear crack patterns of the beams with the non-activated 25 mm-wide strips (Fig. 12c and d) differed from the shear crack patterns of the beams with the activated strips with the same width (Fig. 12e and f). Note that more distributed shear cracks appeared along the length of the beam specimens in the beams with the non-activated strips, and that shear cracks appeared more closely to the supports than for the beams with the activated 25 mm-wide strips. In contrast, when the 12.5 mm-wide strips were used (Fig. 12g–j), shear cracks were more visible for the beams strengthened with or without activation. In fact these four beams failed due to shear. To perform the last two tests on pre-cracked beams, the beams were initially preloaded to (around) 15 kN before strengthening them. Cracks widths were measured with the DIC obtaining a maximum crack width of 0.05 mm near mid-span. During the pre-loading operation, one crack (the bigger one) was visually detected, nevertheless the DIC analysis was able to show and measure many other cracks not visually detected. It allowed to verify that crack openings remained in a normal service range to ensure that the test approximately reproduced an actual case where an existing shear-cracked structure could be strengthened.

4.4. Instrumentation To monitor the behavior of all the tested beam specimens, the applied load, displacements, and the strain at the discrete points on the flexural reinforcement and on strips were measured by a load cell, magnetostrictive transducers (LVDT) (see Figs. 9 and 10a), rotatory encoder transducers, laser displacement sensors (see Fig. 10b) and strain gauges. The instrumentation to measure deflections (LVDTs, encoders, and lasers) was redundant to ensure the goodness of measures; two encoders were located on each support (Encoders 1 and 3, and Encoders 2 and 4 on the opposite side) to measure the supports’ rotation and vertical displacement. At each end of the beam, one LVDT was located and fixed to the end-plates of the longitudinal bar (LTVDT 3 and 4), even though no relevant information was obtained from these LVDTs, and they are omitted in Figs. 10 and 11. Strain gauges are named TSG (located at strips) or LSG (located at longitudinal reinforcement); see Fig. 11. The employed numbering followed a sequential order from left to right in the frontal view. In the longitudinal bars, strain gauges were placed at the bottom of the bar. For stirrups, most strain gauges were attached to the back of the beam (the name that finishes in “B”), but some were attached to the top face (T). All the parameters were monitored continuously by a data acquisition system. Digital image correlation (DIC) was used to confirm and post-process several specimen’s behavior details. Two cameras took pictures on the front face during the test (opposite face to the strain gauges on strips).

Fig. 11. Strain gauges on both longitudinal reinforcement and strengthening strips (rear view). 7

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Fig. 12. Photograph of the state of the tested beams after maximum load.

offers the results of the reference beams and beam specimens strengthened with narrow strips (12.5 mm). Horizontal axes correspond to the difference between the displacements at the mid-span and the support displacements (see Fig. 10). Vertical axes represent the shear force at the support (half the load measured by the load cell).

4.5.2. Shear strength and displacement-shear force curves Fig. 13 presents the general behavior of all the beam specimens when referring to shear strength, initial stiffness and post-peak behavior. Fig. 13a depicts the results of the reference beams and beam specimens strengthened with the 25 mm-wide strips, while Fig. 13b 8

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Fig. 12. (continued)

reinforcement doubled shear strength by reaching values of 29.51 and 31.01 kN for the specimens with the 25 mm-wide non activated strips (SP1/SP2), and of 31.68 and 31.64 kN for those with activated strips (SA1/SA2). The four beam specimens strengthened with the 25 mmwide strips failed by bending, but load was slightly greater for the beam with the activated strips.

It can be observed that the response of the pairs of specimens R1/ R2, SP1/SP2 and SA1/SA2 (Fig. 13a) is similar. Since reference beam specimens R1 and R2 had no shear reinforcement, they presented brittle shear failure, and fast strength degradation became evident after maximum load. The shear strength of specimens R1 and R2 reached 17.95 and 15.82 kN, respectively. The use of Fe-SMA strips as external

Fig. 13. Shear force-displacement curve at the mid-span of the tested beam specimens. 9

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initiated after yielding longitudinal reinforcement. This behavior was observed for specimens SP1, SP2, SA2, and SA1 (in SA1, gauge LSG02 was damaged while testing and the reading was interrupted). In contrast, longitudinal reinforcement did not yield at the mid-span for reference beams R1 and R2. The beam specimens strengthened with narrow strips (SPn1, SAn1, Cr1-SPn1, and Cr2-SAn1) failed immediately before or slightly after yielding longitudinal reinforcement at the mid-span. Note also the change in slope in gauge LSG02 for all the tests (except for pre-cracked beams Cr1-SPn1 and CR2-SAn1) at approximately 4 kN, which corresponded to the load of the cracking bending moment. Gauges LSG01 and LSG03, located at the beginning of the supporting plates, presented a symmetric behavior to one another, and rose to a certain value when readings presented bifurcation. This happened when a shear crack appeared on one side of the beam. In some graphs, particularly in the beams failing upon shear with external strips (see the behavior of SPn1 and SAn1), LSG01 or LSG03 measured compression strain, which differing to that expected. This could be due to the dowel effect on the bar as the strain gauge was located on the bottom side of longitudinal reinforcement. The compression strain could be due to the negative moment induced locally at this point on the longitudinal bar. This was much more relevant for the beams with activated strips (compare SAn1 and Cr2-SAn1 with SPn1 and Cr1-SPn1), which indicates that the dowel effect genuinely improved given the external confinement of the Fe-SMA activated strips.

In those specimens reinforced with the 12.5 mm-wide Fe-SMA strips, all failures were due to shear, and greater ultimate loads were achieved compared to the reference beams: 25.18 kN for SPn1, 27.53 kN for SAn1, 29.75 kN for Cr1-SPn1, and 29.15 kN for Cr2-SAn1. Note that the increase in the shear strength of the precracked elements could be due to the beams without transversal reinforcement developing a flatter critical shear crack than those that initially had transversal reinforcement (deduced from [26]). This can lead to a greater contribution of transversal reinforcement to shear strength. By comparing the shear strength of specimens SP1/SP2/SA1/SA2 with SPn1/ SAn1, it is possible to appreciate the difference in the ultimate load reached due to the lower amount of transversal reinforcement employed. It should be remarked that all specimens had almost the same stiffness at the initial behavior of the test, and this slope changed when shear cracking load was achieved. At that time, a difference was observed between the specimens with the external reinforcement activated and not activated. The beams with activated strips were stiffer and clearly displayed lower deflection for maximum load (see Table 1). 4.5.3. Strains in longitudinal reinforcement As previously mentioned, longitudinal reinforcement was instrumented by strain gauges at three locations (see Fig. 11): at the midspan and at each end (at the beginning of the supporting plate). The strains measured during the tests are illustrated in Fig. 14. For some of the included figures, a yield at the mid-span is evident (strain gauge LSG02), which demonstrates that a flexural failure mechanism was

Fig. 14. Strain measured on the longitudinal bar of beams. 10

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Fig. 14. (continued)

in all the strips in beams SP1, SP2, SA1, and SA2 were relatively low at failure, and the behavior of the strips on both sides of the load application point was similar, with only slightly higher strains on one side in some cases (as in beams SP1, SP2, and SA1). Fig. 16 shows the strain in the strips for the beams strengthened with the 12.5 mm-wide strips. These beams (SPn1, SAn1, Cr1-SPn1, and Cr2-SAn1) failed due to shear. In this case, the strains measured in strips were higher, especially on the side of the beam where shear failure took place. The strips with a generally more marked deformation

4.5.4. Strain in external strips All the external strips were instrumented by one strain gauge at the middle height to monitor its behavior. Note there was no bonding between strips and concrete. So strains had to remain constant through vertical segments. Figs. 15 and 16 show the curves that relate the unit strain of the instrumented strips and shear force. Fig. 15 illustrates the strain in the strips for the beams strengthened with the 25 mm-wide strips. The strains measured in strips confirmed the previously mentioned failure mode (bending failure) as the strains 11

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Fig. 15. Strains in the strips measured on the beams strengthened with the 25 mm-wide strips.

increment due to the applied load. Strips started to work when shear cracks appeared. In the beam specimens strengthened with activated strips, the strain in strips began to increase for a higher load (approximately 23 kN) than for the beams with the non activated strips

were those on the central length (TSG02 and TSG03 on the left, and TSG06 and TSG07 on the right). As observed in all the curves, there was a zero strain, while shear force increased from 0. This meant that the strains of strips did not 12

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Fig. 16. Strains in the strips measured on the beams strengthened with the 12.5 mm-wide strips.

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the predicted shear strength was higher than V(MR), the last value has been considered. The predictions made by the CCCM model are excellent, with an average value for the Vtest/VR ratio that equals 1.10 and a coefficient of variation of 7.98%. Note that in column Vtest/VR the value in brackets is when bending strength is lower than shear strength. The predictions made by current Eurocode 2 [27] are also presented in Table 3. EC 2 presents two different models for elements with and without stirrups: an empirical equation for beams without stirrups, and a variable angle truss model (with no concrete contribution) for beams with stirrups. The predictions made by EC-2 are more conservative and present higher scatter than the CCCM predictions. The average value of the Vtest/VR ratio equals 1.24, with a coefficient of variation of 17.3% for EC-2 predictions. In any case, note that model EC2 is not intended for calculating the shear strength of externally strengthened beams. However, it is remarkable that both the CCCM and EC-2 satisfactorily predict the failure mode.

Table 2 Summary of the basic CCCM formulation particularized for reinforced concrete beams with a rectangular cross-section. Equations

Expressions

Shear strength

confinement VR = Vcu + V cu + Vsu ≤ VR, max

Strut crushing Concrete contribution

VR, max = αcw bzν1 fcm

Vcu = 0.3ζ

1 + cot2θ

x 2/3 f bd d cm

(3)

Contribution of external vertical shear reinforcement Increase in concrete contribution due to confinement by external shear reinforcement

confinement V cu = Vsu ΔVcu

Factors

Expressions

Size and slenderness effect

Vsu =

Asw f (d s y

2

ζ=

1+

Relative neutral axis depth Non dimensional confinement factor Crack inclination

d0 200

x d

(4)

− x )cotθ

(5)

(6)

d 0.2 a

()

= αe ρl ⎛−1 + ⎝ x ΔVcu = ζ

(1) (2)

cotθ

1+

2 α e ρl

⎞ ⎠

(7)

6. Conclusions (8)

d

cotθ =

0.85d d−x

≤ 2.5

An experimental campaign used to assess the feasibility of strengthening shear critical beams by using Fe-SMA strips is presented. Fe-SMA strips, already available on the construction market, have been fully characterized as-provided and after activating the material to create recovery stresses. The mean 0.2% proof stress of Fe-SMA strips comes close to 475 MPa, ultimate strength approximately equals 950 MPa and corresponds to 45% of strain, with similar values for the as-provided material or after activating the material. However, the modulus of elasticity is highly nonlinear, and lowers as tensile stress increases. For this reason, the modulus of elasticity for the as-provided strips comes close to 195 GPa, computed between 100 and 300 MPa, but lowers to 86 GPa after generating recovery stresses (tangent modulus of elasticity), and to 34.4 GPa in the last case, but computed between 450 and 550 MPa. The recovery shape capacity of the Fe-SMA alloys is around 1%. The 10 tests carried out in small-scale beams showed a clear increase in the shear strength of the retrofitted beams by validating the new anchorage system. The reference beams failed in shear, but the beams strengthened with the 25 mm-wide strips failed due to bending for an 83% higher load, by changing the failure mode and showing high ductility. The beams strengthened with the 12.5 mm-wide strips failed due to shear with an average increase in shear strength of 65% compared to the reference beams. For the beams strengthened with activated strips, the appearance of shear cracks was delayed, there were fewer shear cracks, and the deflections of beams were significantly lower, which reveal the benefits of active technology: the shear strengthening material started to work upon installation and activation, unlike other passive shear strengthening technologies. The instrumentation used to monitor the behavior of beams was redundant, and allowed to well ensure the failure modes and behavior of beams. Further investigation is needed in real-scale elements to contrast whether the good results obtained in this experimental campaign are applicable to actual structures with or without stirrups. The maximum shear force of the tested beam specimens was compared with the predictions made by the CCCM and Eurocode 2. It is remarkable that both models correctly predicted the failure mode (shear or bending), but the shear strength predictions made by the model, and included in Eurocode 2, were excessively conservative and presented a high scatter. However, the CCCM was perfectly able to predict the shear strength of the reference and strengthened beams presented herein.

(9)

(approximately 18 kN). This indicates that the activation of external strengthening confers the cross-section confinement, which delays the appearance of shear cracks at service loads. 5. Comparison of the experimental results with the Compression Chord Capacity Model (CCCM) and Eurocode 2 predictions The Compression Chord Capacity Model (CCCM) [1] is a designoriented model for the shear strength of reinforced and prestressed concrete beams, derived as a simplification of the Multi-Action Shear Model (MASM) [4]. Both models are based on classic mechanics, but the MASM proposes explicit equations for the different shear transfer actions: shear transferred by the uncracked concrete in the compression chord, by residual tensile stresses in the cracked concrete web, by the dowel effect of longitudinal reinforcement, and by shear reinforcement, if it exists. However, the CCCM was derived for simplicity, whose main premise is that the shear transferred by the compression chord is the main resisting action in the considered failure state. The main CCCM expressions governing shear strength are summarized in Table 2 for the particular case of RC beams with a rectangular cross-section, vertical shear reinforcement, and by considering average laboratory values for the material strength parameters, and not design values. Moreover for externally strengthened RC beams, it is appropriate to write the strength increment of the compression chord in an independent equation due to externally strengthening wires (Vcuconfinement, Eq. (5)). See Ref. [1] for a detailed description of each expression and all the factors. In fact the CCCM was not initially derived to consider externally added strengthening reinforcement, but may be used conveniently because it explicitly takes into account the increment of the shear resisted by concrete caused by the stirrup confinement in the compression chord, with the term ΔVcu. Table 2 presents the exact equations presented in the original CCCM publication [1], with only some terms rearranged to clarify this specific case. The predictions made by the CCCM are presented in Table 3. The concrete compression strength in the cylinder specimens equaled 0.9·fc,cube. The compression strength varied slightly depending on the age of testing (see Table 1). No safety partial coefficients were used in the presented calculations. The yielding strength of material fy was substituted for the measured 0.2% proof stress; i.e., 475 MPa, as seen before (see Fig. 4). The spacing of vertical strips was constant on the tested beams (nominal spacing, 90 mm; real spacing, 88.9 mm). Column V(MR) in Table 3 shows the predicted shear force at flexural failure. If

Declaration of Competing Interest The authors declared that there is no conflict of interest. 14

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Table 3 Predictions by the CCCM and EC2. Beam no.

S1-R1 S1-R2 S1-SP1 S1-SP2 S1-SA1 S1-SA2 S1-SPn1 S1-SAn2 S1-Cr1-SPn1 S1-Cr2-SAn1

Vtest (kN)

17.95 15.82 29.51 31.01 31.69 31.64 25.18 27.55 29.75 29.15

V (MR) (kN)

29.94 29.94 29.94 29.94 29.94 29.94 30.01 30.01 30.16 30.16

Compression Chord Capacity Model

Eurocode 2

Observed and predicted failure for CCCM and EC2

Vcu (kN)

confinement V cu (kN)

Vs (kN)

VR (kN)

Vtest VR

Vcu (kN)

Vsu (kN)

VR (kN)

Vtest VR

14.1 14.1 14.1 14.1 14.1 14.1 14.2 14.2 14.4 14.4

– – 7.4 7.4 7.4 7.4 3.7 3.7 3.7 3.7

– – 14.4 14.4 14.4 14.4 7.2 7.2 7.2 7.2

14.1 14.1 36.0 36.0 36.0 36.0 25.1 25.1 25.3 25.3

1.26 1.11 (0.99) (1.04) (1.06) (1.06) 1.00 1.09 1.21 1.15

13.8 13.8 – – – – – – – –

– – 38.17 38.17 38.17 38.17 19.08 19.08 19.08 19.08

13.8 13.8 38.17 38.17 38.17 38.17 19.08 19.08 19.08 19.08

1.30 1.15 (0.99) (1.04) (1.06) (1.06) 1.32 1.44 1.56 1.53

Average Standard deviation Coefficient of Variation (%)

1.10 0.09 8.0

Acknowledgements

Vsu

This research was conducted as part of Project HORVITAL-sp2 “Development of strengthening techniques with advanced materials for concrete structures and their mechanical behavior models to extend their lifetime” – BIA2015-64672-C4-3-R (AEI – FEDER, UE). The authors appreciate the contribution of the re-fer AG Strengthening Solution Company, which kindly provided the memory steel (Fe-SMA strips).

Vtest αcw

αe σy,0.02 ν1

Notations a

shear span, the distance from the support to the resultant of the loads that produced shear at that support b width of the cross-section d effective depth of the cross-section fcm mean compressive strength of concrete using 150-mm cubes fcm,cyl mean compressive strength of concrete using 150 × 300 mm cylinders, considered to equal 0.9fcm fsp mean splitting strength of concrete using 150 mm × 300 mm cylinders fy mean yield strength of shear reinforcement h overall depth of a cross-section s spacing of shear reinforcement x neutral axis depth of the cracked section, obtained by assuming zero concrete tensile strength z inner lever arm. In the shear analysis of the reinforced concrete members without axial force, the approximate value z ≈ 0.9d can normally be used Asw cross-sectional area of shear reinforcement (internal or external) Ecm secant modulus of elasticity of concrete, Ecm = 22, 000(fcm /10)0.3≯39 GPa Es modulus of elasticity of reinforcing steel V(MR) reaction at the support due to the maximum moment Vcu concrete contribution to the shear resistance of the member Vcuconfinement increment of the concrete contribution to the shear resistance of the member due to the confinement of the concrete compression chord caused by the externally strengthening wires VR shear resistance of the member when considering average laboratory values for the material strength parameters VR,max the maximum shear force value that can be sustained by the member, limited by the crushing of struts, when considering average laboratory values for the material strength parameters

cotθ ρl ζ ΔVcu

Shear failure Shear failure Flexural failure Flexural failure Flexural failure Flexural failure Shear failure Shear failure Shear failure Shear failure

1.24 0.22 17.3

contribution of internal or external shear reinforcement to the shear resistance of the member experimental shear strength of a tested beam coefficient by taking account the state of stress in struts: α cw = 1 for non prestressed structures; α cw = 1 + σcp/ fcd for 0 ≤ σcp ≤ 0.25fcd ; α cw = 1.25 for 0.25fcd < σcp ≤ 0.50fcd ; and α cw = 2.5(1 − σcp/ fcd ) for 0.50fcd < σcp ≤ fcd modular ratio, α e = Es / Ecm proof yield stress at 0.2% strength reduction factor for the concrete cracked in shear, ν1 = 0.6 for fck ≤ 60 MPa and ν1 = 0.9 − fck/200 for fck > 60 MPa angle between the concrete compression strut and the beam axis perpendicular to shear force, given by Eq. (9) longitudinal tensile reinforcement ratio referring to effective depth d and width b combined size and slenderness effect factor, given by Eq. (6) non dimensional confinement factor that considers the increment in shear resisted by concrete caused by the stirrup confinement in the compression chord, see Eq. (8)

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