In-plane shear strengthening of reinforced concrete diaphragms using fiber reinforced polymer composites

Abstract

Reinforced concrete (RC) diaphragms play a fundamental role in seismic resistance of RC buildings. In addition to transferring the gravity loads to the beams and columns, diaphragms need to be sufficiently rigid with high shear capacity to resist and distribute the earthquake loads to the lateral force resisting system. Despite the large building inventory with under designed diaphragms to resist the shear loads from earthquakes, the number of studies investigating possible approaches to increase the in-plane shear capacity of diaphragms is limited. External equally distributed narrow strips of fiber-reinforced polymers (FRP) providing additional shear strength for RC diaphragms is proposed in this study. Five full scale RC diaphragms with overall dimensions of 4.5 m long by 1.5 m wide by 0.1 m thick were built and tested under cyclic shear loading. One out of the five specimens was tested as a reference with no strengthening, while the remaining four were strengthened with external glass or carbon fiber-reinforced polymer (GFRP or CFRP) composites. The test results showed that the FRP strengthening system effectively enhances the in-plane shear capacity of the RC diaphragms. Compared to the reference specimen, the FRP layout used for testing increased the shear capacity by up to 40%. This paper presents the test specimens, strengthening systems, and in-plane shear response of tested diaphragms in terms of failure modes, strength, and deformation. The experimental results were also compared to theoretical values determined according to the evaluation criteria in the International Code Council (ICC)-Evaluation Services (ES), Acceptance Criteria (AC) 125.

Keywords

Reinforced concrete diaphragm shear strength fiber reinforced polymer composites cyclic testing

Introduction

Utilizing fiber reinforced polymers (FRP) is a method that has been established as an effective means to strengthen, or repair, the flexural and shear resistance of reinforced concrete (RC) structures. Having a high-tensile strength and being lightweight, FRP composites can be easily applied to increase structural capacity. The effectiveness of FRP composites applied on reinforced concrete structures depends on the orientation, type, and thickness of FRP, and anchorage details (Wu et al., 2017). Fiber reinforced polymer composite application has the potential to improve the shear capacity of concrete diaphragms; however, there is limited information about this application because it requires validation through testing of representative size samples. Failure modes and the FRP strains depend on the testing and clear methods to prediction FRP strains for diaphragms are yet to be developed. Nonlinear models developed to predict shear failure patterns of FRP strengthened RC structures need to incorporate complex behavior such as bonding and delamination between FRP and concrete in order to obtain accurate results (Ferreira et al., 2013).

Inadequate shear reinforcement is the main cause of in-plane shear failure in RC structures. There are a variety of difficulties with increasing steel reinforcement ratio in structural elements such as the need to increase the overall size of the member, intensive labor, and pouring concrete in a congested space without compromising its quality. FRP strips act as shear reinforcement as they carry tensile and shear forces (Alsayed et al., 2010; Shrestha et al., 2009). Smith and Kim (2009) investigated the use of FRP composites to strengthen one-way RC slabs with and without central cutouts subjected to dynamic loads. Their tests included six simply supported one-way slabs 3400 mm in length, 160 mm in thickness, with a 3200 mm span between the supports. Four of the slabs were 2500 mm wide and had a central cutout 900 mm wide by 1200 mm long. The other two slabs were 800 mm wide and had no cutout. Two of the slabs with cutout and one of the slabs without cutout served as control specimens and the rest were strengthened with FRP composites. Each slab was loaded along two lines at 1800 mm distance parallel to the width at a monotonic rate of 80 N/sec. The strengthened specimens showed about 50% higher load carrying capacity compared to the control specimens. The failure mode of all the strengthened slabs was debonding at intermediate cracks and the major crack lines in the specimens with central cutout were oriented diagonal from the corners of the cutout (Smith and Kim, 2009). Researchers also investigated the applications of FRP composites in RC slabs for purposes other than in-plane shear strengthening. Farghaly and Ueda (2011) evaluated the efficiency of FRP composites to strengthen two-way slabs against punching shear. Three RC slabs with 1600 mm square dimensions and 120 thickness were built and tested under a monotonic central load while being simply supported around the four edges such that the corners were allowed lift. One specimen was used as the control specimen and the other two specimens were retrofitted through bonding carbon FRP (CFRP) composites in the perpendicular directions on the tension face of the slabs. Results showed an increase of up to 40% in the punching shear capacity of the strengthened slabs compared to the control specimen (Farghaly and Ueda, 2011). Fiber-reinforced polymer composites can also be used to strengthen precast prestressed hollow-core (PHC) concrete slabs, which are one of the most common load-bearing concrete systems globally. These slabs are commonly used in the floors and roofs of a variety of buildings plus bridge decks because of their economy. PHC slabs have multiple voids, which decrease their weight and fabrication costs. However, the manufacturing of PHC does not allow for shear reinforcement, e.g., stirrups. This means that PHC slabs rely on the shear strength of the concrete alone to resist the shear stresses. Typical solutions to shear capacity result in added cost and weight of the system, which defeat the purpose of using PHCs. Externally bonding FRP composites to PHC has been determined to be an effective measure to help support or restore the flexural and shear strength (Wu et al., 2017).

Literature on enhancing the shear capacity of diaphragms against in-plane seismic loading is very limited (Smith and Kim, 2009) but there are studies on strengthening the RC shear walls which have similar in-plane shear behavior to RC diaphragms and these results can be extrapolated to the diaphragm performance. Unlike diaphragms that carry out-of-plane gravity loads in addition to the in-plane shear loads, shear walls only resist axial gravity and in-plane shear loads. In terms of in-plane shear behavior, the performance of diaphragms and shear walls is similar, but the diaphragms distribute the earthquake shear loads between horizontal elements of the floors while the shear walls transfer the shear loads from floors to the foundation. Cruz-Noguez et al. (2015) performed an experimental study to investigate the efficiency of externally bonded carbon FRP composites to strengthen RC shear walls against brittle in-plane shear failures. The response of seven RC shear wall specimens with FRP composites was evaluated in the vertical direction and both vertical and horizontal directions under lateral in-plane loading until failure. Two different anchoring systems, angle and tube, were used to transfer the loads from the FRP composites to the supporting elements of the wall. The response of these walls was compared with two reference specimens. Using the FRP composites for in-plane shear strengthening of the walls led to an increased initial stiffness and shear capacity of the walls and prevented brittle shear failures by inducing a ductile behavior. The maximum load carried by the FRP strengthened specimens was up to 2.4 times that of the reference specimen for the angle anchoring system and up to 2.5 times that of the reference specimen for the tube anchoring system. Moreover, diagonal and horizontal cracking and spalling observed in reference specimens at maximum load was not seen in the specimens with FRP strengthening (Cruz-Noguez et al., 2015). El-Sokkary and Galal (2013) tested three RC shear walls including a control specimen and two CFRP strengthened specimens under constant axial and in-plane cyclic loading. The walls were 1045 mm tall, 1290 mm wide and 80 mm thick, and the load was applied 1850 mm above the foundation level. One of the retrofitted walls was covered by horizontal CFRP wraps on both faces in addition to 200 mm wide vertical CFRP strips at the wall ends with FRP anchors to the foundation and the cap beam. The other wall was retrofitted with 200 mm deep horizontal CFRP strips on the top and bottom of the wall and 280 mm wide diagonal strips with FRP anchors. As a result, flexural and shear strengths of the retrofitted walls were improved compared to the control specimen. The control specimen sustained a lateral displacement ductility of 10 with no degradation at a load of 59 kN. The first and the second retrofitted specimens respectively showed 46% and 19% higher load capacity at yield than the control specimen and yielding happened at 7% higher displacement compared to the control specimen (El-Sokkary and Galal, 2013). Deng et al. (2018) investigated the seismic performance of slotted RC shear walls strengthened with glass FRP (GFRP) wraps. Two conventional and two FRP retrofitted slotted walls were tested. The walls were 4000 mm high, 1500 mm wide, 200 mm thick and had two 150 mm slots along the height and an anchorage system at every quarter of the height. The GFRP wraps were installed at the bottom 850 mm of the two wall boundaries. The walls were tested under constant axial and in-plane cyclic loading. The FRP strengthened walls showed 1:30 drift ratio tolerance without damage while the walls without FRP reached their ultimate deformation at about 1:50 drift ratio (Deng et al., 2018).

To better understand the effectiveness of external CFRP and GFRP strengthening of RC diaphragms against in-plane shear failure, in this study, five full scale RC diaphragms were built and tested. One of the specimens served as the reference. The specimens were then subjected an in-plane cyclic shear loading representing earthquake loads, and the results of the tests are presented in terms of shear strength, deformation, and failure modes. The experimental results were also compared against the predicted values according to International Code Council (ICC)-Evaluation Services (ES) Acceptance Criteria for Concrete and Reinforced and Unreinforced Masonry Strengthening Using Externally Bonded Fiber-Reinforced Polymer (FRP) Composite Systems (AC125) (2020).

Experimental program

Specimens and test matrix

Five RC diaphragms with overall dimensions of 4570 mm long by 1525 mm wide by 102 mm thick were prepared. The specimen dimensions were selected based on a full-scale diaphragm supported by girders spaced at 4570 mm in both directions and supported by middle beams in one direction spaced at 1525 mm with each other and the girders. The ends of the specimens were enlarged to form the boundaries as shown in Figure 1. Each diaphragm was reinforced with one layer of 9.5 mm diameter bars (US #3 Grade 60) placed at 305 mm on center in the longer direction of the diaphragm and same size bars placed at 203 mm on center in the shorter direction of the diaphragm. The horizontal bars were anchored into the end members to mimic continuity of diaphragm bars in real applications. The vertical bars had a 90-degree hook at each end, oriented in the plane of the diaphragm. The diaphragm chord elements, which are located along the top and bottom of the section were reinforced with three 28.65 mm bars (US #9 Grade 75) placed 76 mm apart and anchored into the enlarged end elements using 90-degree hooks. The enlarged end elements at the supports had nominal dimensions of 1829 mm by 203 mm by 508 mm and were reinforced with four 16 mm diameter longitudinal bars (US #5 Grade 60) and 9.5 mm diameter transverse bars (US #3 Grade 60) at 152 mm on center. All the same size and same grade rebar were from the same lot. Accordingly, there were three rebar lots, one for each of 9.5 mm diameter bar (US #3 Grade 60), 16 mm diameter bar (US #5 Grade 60) and 28.65 mm diameter bar (US #9 Grade 75), and from each lot three rebar specimens were tested under uniaxial tension to determine mechanical properties. The coupons prepared from the steel rebar were 457 mm long and the strain was measured using an extensometer with a gauge length of 203 mm. The specimen preparation and testing were conducted following applicable sections of ASTM A615/A615M-20 (2020), ASTM A370-20 (2020), and ASTM E8/E8M-21 (2021). The average yield and ultimate strength values were obtained as shown in Table 1.

Figure 1.

Specimen geometry (all dimensions shown are in mm).

Table 1.

Rebar test results.

Bar type	ASTM A370-18 (2020) method to determine yield point	Average yield strength (MPa)	Average ultimate strength (MPa)
9.525 mm diameter (US #3 Grade 60)	Autographic diagram	520	800
15.875 mm diameter (US #5 Grade 60)		478	745
28.65 mm diameter (US #9 Grade 75).		560	705

Figure 2 shows the preparation of the specimens. Concrete strength at 28 days and at the day of testing (313 days of age) was 28.5 MPa and 36.4 MPa, respectively, averaged from three 100 mm by 200 mm cylinder samples tested according to ASTM C39/C39M-21 (2021).

Figure 2.

Specimen preparation: (a) rebar cage in form, (b) pouring and placing concrete, and (c) finishing concrete.

The test matrix is provided in Table 2. The variables were the type of FRP reinforcement, the width of the FRP plies, and whether one or both sides of the specimens were strengthened. As an example, the strengthening scheme of 3-G-2 specimen is shown in Figure 3. Average properties of different FRP types including high strength carbon fiber fabric, C200H, high modulus carbon fiber fabric, C200HM, and high strength glass fiber fabric, EG50, are presented in Table 3 as reported by the manufacturer.

Table 2.

Test matrix (1 in. = 25.4 mm).

Specimen ID	28 days concrete strength, MPa	Concrete strength at testing, MPa	FRP designation	Strengthening scheme	FRP (T: Top, B: Bottom)
3-0	28.5	36.4	None	None	None
3-H-1			C200H	1 ply 76 mm wide at 610 mm on center	T
3-H2-1			C200HM	1 ply 76 mm wide at 610 mm on center	T
3-G-1			EG50	1 ply 152 mm wide at 610 mm on center	T
3-G-2			EG50	1 ply 152 mm wide at 610 mm on center	T&B

FRP: fiber-reinforced polymer.

Figure 3.

Strengthening details of 3-G-2 specimen (all dimensions shown are in mm).

Table 3.

Average properties of different fiber-reinforced polymer types.

Fiber-reinforced polymer type	Fiber material	Thickness, mm	Strength per unit width, kN/mm	Tensile strength, MPa	Modulus of elasticity, MPa	Elongation at break, %
C200H	Carbon	1.02	1.26	1,240	73,770	1.7
C200HM	Carbon	1.02	1.26	1,241	98,181	1.27
EG50	Glass	1.016	0.58	567	26,680	2.13

Test setup and instrumentation

An experimental setup was designed and fabricated to ensure controlled test conditions as shown in Figures 4 and 5. To investigate the in-plane shear performance of the diaphragms a third-point loading configuration was adopted along the width of the diaphragms reinforced with the shear stirrups and the FRP wraps perpendicular to the longitudinal reinforcement. This represents the actual load carrying mechanism of a diaphragm in a building where the forces are resisted in the in-plane direction. The specimens were placed vertically along the width to be aligned with a servo hydraulic actuator hanging from a vertical frame to apply the loading in the middle of the specimens. Vertical arrangement of the specimens rather than horizontal was merely to facilitate easy handling of specimens without cracking them and did not alter the actual conditions. At the loading location, a fixture was used at the top and bottom of the diaphragm, which were connected to each other using high strength steel threaded bars. The top fixture at the loading point was bolted to the actuator to allow a reversed cyclic load application. At the loading point, flexible lead plates were inserted between the top and bottom loading fixtures and the specimen to ensure a uniform application of the loading. The specimen ends were placed on two pin supports attached to the strong floor and they were clamped between the top fixture and the pin support using high strength steel threaded bars. The supports were connected to the strong floor with four high strength bolts and the top steel fixtures were clamped to the supports by applying a post-tensioning force in the high strength steel threaded bars.

Figure 4.

Actual test setup and instrumentation.

Figure 5.

Schematic test setup and instrumentation (all shown dimensions are in mm).

In terms of instrumentation, two string potentiometers were used at the bottom of diaphragms, shown in Figure 5, to measure the mid-span deflection based on their average reading. In each span between the loading point and the supports, on the face of the specimens, linear potentiometers or a combination of linear and string potentiometers were used to measure the shear deformations. Other instrumentation included strain gauges installed on the steel reinforcement, as shown in Figure 6, and strain gauges installed on the FRP composites of the strengthened specimens, as shown in Figure 7. The rebar strain gauges, shown in Figure 6, included six gages on the shear reinforcement and one gauge in the middle of the top longitudinal reinforcement.

Figure 6.

Steel reinforcement strain gauges (all shown dimensions are in mm).

Figure 7.

FRP composite strain gauges (all shown dimensions are in mm).

Loading protocol

The loading protocol is shown in Figure 8. For the load-controlled steps, 1 to 8, P_nc indicates the design strength of the control sample and it is taken equal to 400 kN. For the deformation-controlled cycles, $μ_{u}$ is taken from the last cycle in step 8 in the pull and push directions during the actual test of each specimen. Details of the loading protocol and rates are shown in Table 4. This loading protocol conforms to lateral load procedure presented in section 5.8.1.2 of AC125 (2020) for seismic strengthening of horizontal diaphragms. In conformance with the section 5.8.1.2 of AC125, the specimens were loaded until the strengthening systems is damaged, the specimen capacity is reached, or the desired limit states are achieved. It is noted that when the specimen failed in one direction during any of the loading steps the test was completed by pushing or pulling the specimen to failure in the other direction.

Figure 8.

Loading protocol.

Table 4.

Loading protocol and loading rates.

Control mode	Loading step	Applied load	Number of cycles	Loading rate
Load control	1	0.25 Pnc	1	1.1 kN/min
	2	0.5 Pnc	1	1.1 kN/min
	3	0.75 Pnc	1	2.2 kN/min
	4	Pnc	3	2.2 kN/min
	5	1.15 Pnc	3	3.3 kN/min
	6	1.3 Pnc	3	4.4 kN/min
	7	1.45 Pnc	3	4.4 kN/min
	8	1.6 Pnc	3	6.6 kN/min
Deformation control	9	1.25 $μ_{u}$	3	0.127 mm/sec
	10	1.5 $μ_{u}$	3	0.254 mm/sec
	11	1.75 $μ_{u}$	3	0.254 mm/sec
	12	2.0 $μ_{u}$	3	0.508 mm/sec
	13	2.25 $μ_{u}$	3	0.508 mm/sec
	14	2.5 $μ_{u}$	3	0.508 mm/sec

Results from experimental program

The shear capacity of the control specimen (3-0) was 592 kN and 514 kN in the push and pull directions, respectively. With no exception, the FRP strengthened diaphragms showed larger peak load carrying capacity in both directions under cyclic loading compared to the control specimen. The shear failure of the FRP strengthened diaphragms occurred either due to delamination of the FRP sheets followed by concrete diagonal shear failure or concrete crushing under the load application point. As shown in Figure 9, the failure of the control specimen 3-0 was concrete diagonal shear. As seen in Figures 10–12, the failure modes of specimens 3-H-1, 3-H2-1, and 3-G-1 were FRP delamination followed by concrete diagonal shear. The failure mode of the 3-G-2 diaphragm was local concrete crushing under loading points in push and pull directions, as shown in Figure 13. It is noted that unlike the other strengthened specimens which had FRP composites applied only on one side, specimen 3-G-2 had FRP on both sides. The overlap of the FRP plies, shown in Figure 3, made it much more difficult for the FRP delamination to occur starting from the edges. This strengthening scheme provided specimen 3-G-2 with a full FRP wrap that prevented diagonal shear cracks to develop. This resulted in the high shear strength of the specimen, which led to the stresses under the loading fixture to exceed the compressive strength of concrete. This may be considered as a local failure mode.

Figure 9.

Specimen 3-0 cyclic shear test failure mode: concrete diagonal shear.

Figure 10.

Specimen 3-H-1 cyclic shear test failure mode: Fiber-reinforced polymer delamination followed by concrete diagonal shear.

Figure 11.

Specimen 3-H2-1 cyclic shear test failure mode: Fiber-reinforced polymer delamination followed by concrete diagonal shear.

Figure 12.

Specimen 3-G-1 cyclic shear test failure mode: Fiber-reinforced polymer delamination followed by concrete diagonal shear.

Figure 13.

Specimen 3-G-2 cyclic shear test failure mode: concrete crushing under loading points.

Figure 14 shows the cyclic load versus mid-span displacement responses of all the diaphragm specimens. The peak load values and the corresponding displacements as well as the dissipated energy throughout the entire load cycles are summarized in Table 5. A negative load indicates the push direction (downwards) and a positive load indicates the pull direction (upwards) of the actuator. As seen in Table 5, in the push direction, the shear capacity of specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2 was respectively 26%, 32%, 23%, and 40% higher than that of the reference specimen. In the pull direction, specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2 respectively showed 38%, 39%, 47%, and 33% higher strength than that of the reference specimen. In terms of the shear capacity, specimens 3-H-1, 3-H2-1, and 3-G-1 were more symmetric in the push and pull directions with respectively 5%, 9%, and 5% difference between the results of the two directions compared to the reference specimen with 15% difference between the peak push and pull loads. This shows that these specimens not only have a higher shear capacity compared to the reference specimen but also show a smaller reduction in shear capacity after the failure of the diaphragm in one loading direction. On the other hand, specimen 3-G-2, despite showing higher shear capacity in both directions compared to the reference specimen and a higher shear capacity in the push direction compared to the other strengthened specimens, had a higher reduction in the shear capacity in the pull direction compared to the push direction, about 20%, which resulted in a lower shear capacity in the pull direction compared to the rest of strengthened specimens. This is because, as seen in Figure 13, unlike concrete crushing under the loading point in the push direction, concrete crushing in the pull direction resulted in the local softening and penetration of the bottom loading point into the specimen that prevented further capacity of the specimen to develop. This is again considered a local failure mode without developing the full strength of the specimen. Specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2 had respectively 59%, 97%, 132%, and 123% higher energy dissipation compared to the reference specimen. This significant increase in the energy dissipation due to FRP strengthening compared to the reference specimen is due to both the increase in the load-displacement area inside the cycles and the number of cycles that the specimen could sustain prior to failure. The higher energy dissipation in the GFRP strengthened specimens compared to the CFRP strengthened specimens is attributed to the double width of the GFRP strips compared to the CFRP strips. It is noted that applying GFRP on both sides of 3-G-2 did not result in higher energy dissipation compared to 3-G-1 with GFRP applied to one side. As it will be discussed in the next paragraph, the wider strips of FRP strengthening while resulting in higher energy dissipation resulted in a lower increase in the ductility of the specimens compared to narrower strips.

Figure 14.

Applied load versus mid-span displacement response of (a) 3-0, (b) 3-H-1, (c) 3-H2-1, (d) 3-G-1, and (e) 3-G-2.

Table 5.

Results of cyclic diaphragm tests.

Specimen ID	Peak push load (kN)	Peak pull load (kN)	Displacement at peak push load (mm)	Displacement at peak pull load (mm)	Energy dissipation (kN.mm)	Failure mode
3-0	591	514	11.7	9.3	12,127	Concrete diagonal shear
3-H-1	742	710	12.8	11.9	19,331	FRP delamination followed by concrete diagonal shear
3-H2-1	781	715	11.7	14.0	23,912
3-G-1	724	758	9.7	13.5	28,086
3-G-2	825	685	13.1	9.1	26,988	Concrete crushing under loading points both in push and pull directions

The mid-span displacements presented in Table 5 for strengthened specimens correspond to higher peak loads compared to the reference specimen. Therefore, in most cases these displacements are higher in strengthened specimens compared to the reference specimen. In order to further investigate this, Figure 15 compares the load versus mid-span displacement envelope curves and Table 6 presents the results of initial stiffness, yield point displacement and ductility in the push and pull loading directions. The ductility is calculated by dividing the peak displacements presented in Table 5 by the yield point displacements presented in Table 6. The yield point was calculated by fitting a line to the peak load values of the first three cycles and finding the intersection of that line with a second line fitted to the peak values of the remaining load cycles in each direction. The initial stiffness was calculated as the slope of this first line.

Figure 15.

Load versus mid-span displacement envelope curves.

Table 6.

Initial stiffness, yield point, and ductility results.

Specimen ID	Initial stiffness in push direction(kN/mm)	Initial stiffness in pull direction(kN/mm)	Yield displacement in push direction (mm)	Yield displacement in pull direction (mm)	Ductility in push direction	Ductility in pull direction
3-0	121.34	118.68	2.45	2.64	4.78	3.52
3-H-1	147.49	120.74	1.64	1.94	7.80	6.13
3-H2-1	122.16	157.68	2.55	2.06	4.59	6.80
3-G-1	125.94	120.54	2.90	2.81	3.34	4.80
3-G-2	133.60	131.51	2.49	2.73	5.26	3.33

As expected, the results of Table 6 show that the strengthened specimens all had higher initial stiffnesses compared to the reference specimen in the push and pull directions. However, the difference in the initial stiffness of the strengthened specimens with the reference specimens is not significant in all cases. The CFRP strengthened specimens showed higher initial stiffness values compared to the GFRP strengthened specimens because of the higher elastic modulus of CFRP material compared to GFRP as presented in Table 3. CFRP strengthened specimens 3-H-1 and 3-H2-1 respectively showed 22% increase of the initial stiffness in the push direction and 33% increase of the initial stiffness in the pull direction compared to the reference specimen. Subsequently, the increase in the initial stiffness for GFRP strengthened 3-G-2 specimen with respect to the reference specimen, 10% in the push direction and 11% in the pull direction, was notable as this specimen was strengthened on both sides unlike others. With regards to ductility, specimen 3-H-1 showed higher values compared to the reference specimen in the push direction, by 63%, and pull direction, by 74%. Specimens 3-H2-1 and 3-G-1 had higher ductility in the pull direction, by 93% and 36% respectively, and specimen 3-G-2 had higher ductility in the push direction, by 10%, compared to the reference specimen. In summary, all the strengthened specimens increased the ductility in one or both loading directions compared to the reference specimen. This increase in the ductility was more noticeable in the CFRP strengthened specimens than the GFRP strengthened specimens because the GFRP strips in 3-G-1 and 3-G-2 had double the width size of CFRP strips in 3-H-1 and 3-H2-1 specimens. Additionally, 3-G-2 specimen, which was strengthened on both sides unlike the other specimens, showed the lowest increase in ductility with respect to the reference specimen. This is a result of higher yield point of GFRP strengthened specimens (due to lower modulus of GFRP).

Figure 16 presents the individual diaphragm cyclic load versus reinforcement strain responses in microstrains (με) for the strain gauges on the steel reinforcement. According to Figure 16, strain in the middle shear reinforcement bar of the North span, SG-R04, exceeded 2% in the reference specimen; however, the recorded strain of the transverse reinforcement in the strengthened specimens was limited to about 1% before failure. This value for specimen 3-G-2 was limited to 0.5%. Therefore, while according to Figure 14 and Table 5, the strengthened diaphragms tolerated higher shear loads and deflections, the transverse reinforcement experienced a lower strain compared to the reference specimen due to the contribution of external FRP reinforcement. Figure 17 shows the individual diaphragm cyclic load versus FRP strain responses. According to Figure 17, while the carbon FRP strains of specimens 3-H-1 and 3-H2-1 were limited to 0.5%, the glass FRP strains of specimens 3-G-2 reached 0.75% due to the lower modulus of elasticity of glass fibers compared to carbon as presented in Table 3. Moreover, the results in Figures 16 and 17 indicate that that unlike the other strengthened specimens, applying the FRP composites on both sides of specimen 3-G-2 resulted in up to 50% higher strains in the FRP and up to 50% less steel reinforcement strains. It is noted that the FRP composite strain values for 3-G-1 specimen are not shown in Figure 17 as this data was not captured during the experiment.

Figure 16.

Applied load versus reinforcements strain cycles of (a) 3-0, (b) 3-H-1, (c) 3-H2-1, (d) 3-G-1, and (e) 3-G-2.

Figure 17.

Applied load versus FRP strain cycles of (a) 3-H-1, (b) 3-H2-1, and (c) 3-G-2.

To obtain the average shear deformation in the North and South shear spans of each diaphragm, the parallelogram layout of the sensors, as shown in Figure 18, was used to obtain the angle using equation (1) at each loading point in the test. This parallelogram analysis assumes that the flexural deformations are negligible. This assumption is confirmed because the cracks shown in Figures 9–13 are diagonal shear cracks not flexural cracks and the longitudinal rebar strain SG-R07 at maximum moment location shown in Figure 16 is within the linear range until the specimen failure. The applied load versus shear deformation of the North and South spans are shown in Figure 19. The N1 to N4 and S1 to S4 angles in these plots are defined in Figure 5 and δ corresponds to the change in angle or deformation. A comparison of the strengthened specimens with the reference specimen shows that the contribution of the external FRP reinforcement allows the diaphragms to undergo larger shear loads and deformations. It is noted that for specimens 3-H-1, 3-H2-1 and 3-G-1 that failed due to FRP delamination followed by concrete diagonal shear, the shear deformations are more dominant in the span that failed as also shown in Figures 10–12. On the other hand, the shear deformations of the North and South panels for specimen 3-G-2 are more consistent because this specimen failed due to concrete crushing under the loading point.

α = \cos^{- 1} (\frac{D_{1}^{2} - a^{2} - b^{2}}{2 a b})

(1)

Figure 18.

Layout of sensors to measure shear deformations.

Figure 19.

Applied load versus shear deformation of (a) 3-0 South span, (b) 3-0 North span, (c) 3-H-1 South span, (d) 3-H-1 North span, (e) 3-H2-1 South span (δS1 and δS2 are not shown due to a sensor failure), (f) 3-H2-1 North span, (g) 3-G-1 South span, (h) 3-G-1 North span, (i) 3-G-2 South span, and (e) 3-G-2 North span.

Comparison with AC125 predictions

In this section, the of results of the shear tests are compared against the ICC ES Acceptance Criteria for Concrete and Reinforced and Unreinforced Masonry Strengthening Using Externally Bonded Fiber-Reinforced Polymer (FRR) Composite Systems (AC125). According to section 5.8.1.2 of AC125 (2020), the ratio of the peak experimental results before failure to the theoretical values calculated according to section 7.3.2.7.1 of AC125 (2020), shall exceed 1. In order to calculate the corresponding predicted values of the diaphragm samples tested in this study according to AC125, equation (2) is used.

V_{n} = V_{c} + V_{s} + V_{f}

(2)

In equation (2),

V_{n}

is the nominal shear strength of the specimen and

V_{c}

V_{s}

, and

V_{f}

are the contributions of concrete, steel reinforcement, and FRP strengthening system, respectively. The contribution of FRP strengthening system is calculated according to equations (3)–(5).

V_{f} = Ψ_{f} . A_{f v} . f_{f e}

(3)

A_{f v} = n_{s} . n . t_{f} . w_{f}

(4)

f_{f e} = k_{s} . ε_{f e} . E_{f} \leq 0.75 ε_{f u} . E_{f}

(5)

In equations (3)–(5),

A_{f v}

is the area of FRP shear reinforcement,

f_{f e}

is the effective stress in the FRP at failure,

n_{s}

is the number of diaphragm sides with FRP,

n

is the number of FRP plies (equal to one for all the specimen in this study),

t_{f}

is the nominal design thickness of one ply of the FRP,

w_{f}

is the width of the FRP strip,

ε_{f e}

and

ε_{f u}

are respectively the effective and ultimate strain of FRP, and

E_{f}

is the elastic modulus of FRP. The reduction factor of

Ψ_{f} = 0.85

is specified for both one and two-sided strengthening scenarios. The efficiency factor,

k_{s}

, is equal to 1.0 and 0.75, respectively, for two-sided and one-sided strengthening applications. It is noted that the equations above and the parameters from AC125 (2020) are the same as those in ACI 440.2 R (Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures) (2017). Table 7 presents the results of the ratio of the experimental strength to the theoretical strength. It is noted that the presented results in Table 7 is only for one shear span of the specimens while the results in Section 3 considered both shear spans. Results in Table 7 confirm that AC125 (2020) conservatively predicts the strength of FRP reinforced diaphragms. This conservatism, the normalized difference between AC125 (2020) strength predictions and the experimental results, is about twice for the diaphragms with FRP compared to the reference RC specimen.

Table 7.

Nominal strength calculations according to AC125 (2020) and ACI 440.2R (2017) and comparison with experimental results.

Specimen	V_c (kN)	V_s (kN)	V_f (kN)	V_n (kN)	V_exp (kN)	V_exp/V_n
3-0	181.3	78.3	0	259.5	295.5	1.14
3-H-1	181.3	78.3	36.3	290.4	371.0	1.28
3-H2-1	181.3	78.3	41.2	294.6	390.5	1.33
3-G-1	181.3	78.3	37.2	291.2	379.0	1.30
3-G-2	181.3	78.3	82.6	329.8	412.5	1.25

Conclusions

This study was performed to provide additional data and advance the understanding of structural behavior of RC diaphragms externally strengthened using FRP wraps. Five full-scale RC diaphragms including one reference specimen, 3-0, two specimens strengthened with carbon FRP on one side, 3-H-1 and 3-H2-1, one specimen strengthened with glass FRP on one side, 3-G-1, and one specimen strengthened with glass FRP on both sides, 3-G-2, were tested under cyclic shear loading. It is noted that the width of the applied GFRP strips on 3-G-1 and 3-G-2 was double the width of CFRP strips on 3-H-1 and 3-H2-1. The main findings are summarized here.

1. With no exception, the FRP strengthened diaphragms showed a higher shear capacity in both directions under cyclic loading with respect to the control specimen. The shear capacity of the control specimen, 3-0, was 592 kN and 514 kN in the push and pull directions, respectively. In the push direction, the specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2, respectively, showed 26%, 32%, 23%, and 40% higher strength compared to the reference specimen. In the pull direction, the specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2, respectively, showed 38%, 39%, 47%, and 33% higher strength compared to the reference specimen.

2. Specimens 3-H-1, 3-H2-1, 3-G-1, and 3-G-2 respectively showed 59%, 97%, 132%, and 123% higher energy dissipation before failure compared to the reference specimen.

3. The CFRP and the GFRP strengthened specimens respectively increased the ductility by up to 93% and 36% compared to the reference specimen in one or both loading directions. The double width of GFRP strips compared to the CFRP strips was the reason for the ductility difference between strengthened specimens. Additionally, 3-G-2, which was strengthened on both sides unlike other specimens, showed the lowest increase in ductility, 10% in the push direction, compared to the reference specimen.

4. The control specimen failed due to concrete diagonal shear cracks. The FRP strengthened diaphragms also formed diagonal shear cracks during testing but their failure was either due to delamination of the FRP composite followed by concrete diagonal shear failure or concrete crushing under the load application point. The specimens 3-H-1, 3-H2-1, and 3-G-1 failed due to FRP delamination followed by concrete diagonal shear, but the failure mode of the specimen 3-G-2 was concrete crushing under loading point in the push and pull directions.

5. While the shear reinforcement strains of the reference specimen exceeded 2%, the same strains of the strengthened specimens were limited to about 1%. This value for specimen 3-G-2 was limited to 0.5%.

6. During the cyclic tests, the carbon FRP strains of the specimens 3-H-1 and 3-H2-1 were limited to 0.5% but the strains in specimen 3-G-2 reached 0.75% due to lower modulus of the glass fibers and higher contribution of the FRP reinforcement.

7. The predicted values of shear strength of specimens according to AC125 (2020) were conservative by 14%–33%.

In this study the FRP wraps were not anchored. In the case of FRP on one face, the FRP was bent like a C-shape at the ends of diaphragm and bonded through the diaphragm thickness. In the case of FRP on both faces, the FRP on one side was bent like a C-shape at the ends of the diaphragm and overlapped with the FRP from the other side along the diaphragm thickness. FRP delamination was observed in most failure cases. The ends of diaphragms may not always be accessible in the buildings. Therefore, the performance of different FRP anchoring systems for concrete diaphragms is recommended for future research.

Footnotes

Declaration of conflicting interests

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: The last author of this paper is a representative of the company that has provided the strengthening materials for testing. However, he was not directly involved in the analysis of the test results, nor he has asked for any changes to the reported results during the paper preparation process.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Bora Gencturk

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