Seismic Retrofit Case Study of Shear-Critical RC Moment Frame T-Beams Strengthened with Full-Wrap FRP Anchored Strips in a High-Rise Building in Los Angeles

Abstract

This paper discusses the iteration of a seismic retrofit solution for shear-deficient end regions of 19 reinforced concrete (RC) moment-resisting frame (MRF) T-beams located in a 12-story RC MRF building in downtown Los Angeles, California. Local strengthening with externally bonded (EB) fiber-reinforced polymer (FRP) fabric was chosen as the preferred retrofit strategy due to its cost-effectiveness and proven performance. The FRP-shear-strengthening scheme for the deficient end-hinging regions of the MRF beams was designed and evaluated through large-scale cyclic testing of three replica specimens. The specimens were constructed at 4/5 scale and cantilever T-beam configurations with lengths of 3.40 m or 3.17 m. The cross-sectional geometry was 0.98 × 0.61 m with a top slab of 1.59 m in width and 0.12 m in thickness. Applied to these specimens were three different retrofit configurations, tested sequentially, namely: (a) unanchored continuous U-wrap; (b) anchored continuous U-wrap with conventional FRP-embedded anchors at the ends; and (c) fully closed external FRP hoops made of discrete FRP U-wrap strips and FRP through-anchors that penetrate the top slab and connect both ends of the FRP strips, combined with intermediate crack-control joints. The strengthening concept with FRP hoops precluded the premature debonding and anchor pullout issues of the two more conventional retrofit solutions and, despite a more challenging and labor-intensive installation, was selected for the in-situ implementation. The proposed hooplike EB-FRP shear-strengthening scheme enabled the deficient MRF beams to overcome a 30% shear overstress at the end-yielding region and to develop high-end rotations (e.g., 0.034 rad [3.4% drift] at peak and 0.038 rad [3.8% drift]) at strength loss for a beam that, otherwise, would have prematurely failed in shear. These values are about 30% larger than the ASCE 41 prescriptive value for the Life Safety (LS) performance objective. Energy dissipation achieved with the fully closed scheme was 108% higher than that of the unanchored FRP U-wrap and 45% higher than that of the FRP U-wrap with traditional embedded anchors. The intermediate saw-cut grooves successfully attracted crack formation between the strips and away from the FRP reinforcement, which contributed to not having any discernable debonding of the strips up to 3% drift. This paper presents the experimental evaluation of the three large-scale laboratory specimens that were used as the design basis for the final retrofit solution.

1. Background

Non-ductile concrete moment-resisting frame (MRF) buildings are known to be susceptible to earthquake damage. As such, many buildings designed and erected under previous code recommendations are retrofitted to meet current seismic demands and to accommodate additional movement considered in today’s building codes. A five-year-long seismic upgrade program aimed at enhancing the strength and ductility of a 12-story reinforced concrete (RC) MRF building located in downtown Los Angeles, California, was developed to derive a creative, structural, and economical retrofit solution for a variety of structural and nonstructural components in the building. The retrofit implementation was completed in December 2021, allowing for subsequent dissemination of research insights.

The construction of the building (Figure 1) was completed in September 1998. The building’s structural design was based on code requirements of the 1996 City of Los Angeles Building Code (LABC) for an “essential facility” (i.e., importance factor I = 1.25). The superstructure holds 12 above-ground levels consisting of cast-in-place concrete special moment-resisting frames (SMRF) with precast concrete gravity frames, overlain by a cast-in-place concrete floor. The building’s concrete moment frames generally consist of beams with cross-sectional dimensions of 1.22 m (48 in) in depth and 0.76 m (30 in) in width and typical spans of 9.14 m (30′-0″) or 9.75 m (32′-0″) c.c. Only a few bays have shorter spans of 6.1 m (20′-0″) or 13 m (42′-8″) c.c. The foundation consists of isolated spread footings and perimeter wall footings. Following multiple repairs associated with shear cracking in several RC MRF beams between 2008–2010, a seismic structural evaluation of the lateral force-resisting system was conducted in 2011 by an external consulting engineering firm to assess potential structural deficiencies of the MRF design. The performance assessment was based on code-based structural checks and a 3D linear dynamic analysis model (i.e., response spectrum) considering two different seismic occupancy scenarios: the original essential-facility (I = 1.25) design criteria using codes and design parameters applicable at the time of design (1996 Los Angeles Building Code (LABC), 1995 California Building Code (CBC), and ACI 318-89 [1]) and a reduced occupancy category as an ordinary occupancy building (I = 1.0) using applicable code requirements in 2011 (i.e., International Building Code (IBC) 2006, ASCE 7-10 [2], and ACI 318-05 [3]) and modified seismicity. The basic performance objective for the building lateral force-resisting system (LFRS) required both Life Safety (LS) performance under the design basis earthquake (DBE) hazard level and Collapse Prevention (CP) performance under the maximum considered earthquake (MCE) hazard level. To note, an RC MRF building designed and detailed under the 1996 LABC is expected to behave in a ductile manner. However, the investigation revealed that the LFRS in this building was non-ductile and unable to achieve its intended seismic performance. Specifically, some of the MRF beams had insufficient shear capacity at the end-yielding regions (with a predicted overstress of up to 30%) and at sections with large rectangular web penetrations for passage of ductwork and pipes (with probable design shear demands ranging between two to four times larger than the available shear capacity). These shear deficiencies were attributed to a combination of inadequate detailing of the transverse reinforcement, with some of the MRF beams having only single hoops without intermediate crossties and/or noncompliant tie spacing around the openings, as well as an oversimplified estimation of the probable design shear demand, with the compression flange and compression reinforcement not being accounted for in the original design.

As part of this investigation, large-scale component testing of selected shear-deficient MRF beams was deemed necessary to assess the actual beam performance and aid in designing appropriate retrofit solutions. The testing program, sponsored by the building owner and conducted at the structural testing facility of the University of California, Irvine (SETH), was divided into two phases: Phase 1 focused on the performance assessment of representative, as-built, unstrengthened MRF beams with large rectangular web openings. Four 4/5-scale flanged beam (T-beam) specimens were tested in this phase. These tests were executed between March and June 2013 and published by Herrera et al. [4]. Phase 2 focused on the design and evaluation of retrofit schemes for the shear-deficient MRF beams at the end and opening regions using externally bonded (EB) fiber-reinforced polymer (FRP) and FRP anchors. Phase 2 consisted of three 4/5-scale FRP-strengthened T-beam specimens evaluated sequentially between Juny 2014 and November 2015. The retrofit schemes were designed collaboratively by the consulting engineer and the FRP specialists and tested at the Structural Laboratory at UC Irvine. The first two specimens, S1A and S1B, represented exact replicas of the unstrengthened specimen S1 from Phase 1. S1 was the only specimen to fail in shear at the opening region. Specimens S1A and S1B were externally strengthened with FRP at both the opening and the end-yielding regions and used to verify and optimize a retrofit concept around the web openings, as well as to relocate the plastic hinge to the beam ends by keeping the opening area elastic and damage-free. Results and discussions focusing on the beam openings are part of a previous publication by the authors [5] and won’t be repeated hereafter. A second objective for specimens S1A and S1B was to evaluate two low-effort and commonly used shear-strengthening schemes for the end-yielding region next to the support, where the shear overstress was estimated to be around 10%. The strengthening schemes consisted of a one-layer carbon FRP (CFRP) sheet U-wrap with no mechanical anchorage, applied to specimen S1A, and a similar CFRP U-wrap with embedded glass FRP (GFRP) anchors at the ends, installed on S1B. However, both tests revealed detailing issues of the FRP reinforcement at the beam ends, as discussed later in this paper. Specifically, complete detachment of a strip of the CFRP U-wrap occurred similarly for both S1A and S1B at 3% drift, accompanied by anchor pull-out at the location of the dominant flexural crack (S1B), followed by the sudden fracture of an adjacent CFRP strip and an abrupt loss in load-carrying capacity. In addition, both S1A and S1B exhibited wide cracks along the flange/web cold joint, indicative of horizontal shear transfer issues, as well as buckling of the top longitudinal reinforcement at large displacement levels. This can be attributed to the lack of intermediate vertical crossties, a detailing deficiency affecting multiple MRF beams in the building. Findings from specimens S1A and S1B pertaining to the beam end region were utilized to develop a third retrofit concept applied to another replica specimen, S5, tested several months after specimens S1A and S1B. The retrofit scheme for S5 consisted of fully closed external CFRP hoops supplemented with intermediate crack-control joints. Complete continuity of the shear-strengthening FRP wrap around the perimeter of the beam was achieved with continuous FRP splice anchors through the flanges and over the slab.

This case history documents the experimental research, design, and implementation of the full-wrap shear-strengthening concept that was experimentally tested on specimen S5 under fully reversed cyclic loading. A broader discussion on this retrofit project can be found in [6]. FRP design calculations and test results for specimens S1A, S1B, and S5 as they concern to the end-yielding regions are presented and discussed hereafter. The experimental load-deformation responses of the shear-strengthened MRF beam specimens are compared against analytical backbones and plastic rotation limits per Table 10–7 in ASCE 41-17 [7]. These tests were used to guide the design of the in-situ retrofit details applied to the end region of 19 MRF beams within the building.

2. Literature Review

2.1. Externally-Bonded FRP (EB-FRP)

Local retrofitting of reinforced concrete (RC) members with externally applied FRP composites is an extremely popular solution, the suitability of which is largely justified by its minimal weight, superior tensile strength, resistance to corrosion, and negligible impact on the mass or stiffness of the structure. FRP laminates are brittle materials with a linear-elastic, stress-strain relationship to failure. Compared to Grade 60 reinforcing steel, the stiffness of FRP is less than half (e.g., Young’s modulus of 13,900 ksi for carbon FRP vs. 29,000 ksi for reinforcing steel), and its ultimate tensile strength in the direction of the fibers is more than 50% larger (e.g., 143 ksi vs. 90 ksi for steel). The effectiveness of EB-FRP materials in increasing the strength and/or ductility of a structural member is proportional to the level of deformation (strain) that they can develop, which has been shown to be heavily dependent on the mode of failure [8]. EB-FRP materials often fail at stress levels significantly lower than their tensile capacity. This occurs for two main reasons. First, the bond between the FRP and the concrete substrate is weak compared to the FRP’s tensile capacity, making EB-FRP materials highly susceptible to premature debonding. This debonding is often followed by immediate and brittle failure due to the sudden load increase in the internal steel reinforcement. Second, the brittle nature of FRP materials makes them highly sensitive to stress concentrations. This sensitivity can lead to premature fracture due to bends (e.g., at corners), surface irregularities, or uneven stress distribution caused by the anchorage system. As a result, EB-FRP design guidelines prescribe strict limits on the maximum strain to be used when computing FRP strength contributions. ACI 440.2R-17 [9], the leading EB-FRP design and construction guideline in the United States, imposes a maximum effective strain value in the FRP of 0.4% for shear applications, about 40% of its typical ultimate (rupture) tensile strain. Prevention of stress concentrations is tackled with guidelines on surface preparation and corner rounding (minimum corner radius of 0.5 in [13 mm] on corners to be wrapped with FRP).

2.2. EB-FRP for Shear Strenghtening of T-Beams

Over the past three decades, numerous studies have investigated the use of EB-FRP laminates to shear-strengthen RC beams. Given the frequent lack of access to the top of beams with slabs (i.e., T-beams), the most typical FRP layout for shear-strengthening of T-beams consists of a three-sided jacket (also referred to as a “U-wrap” or “U-jacket”) of unidirectional FRP laminate, with fibers oriented perpendicular to the beam’s axis. For U-wrap applications, ACI 440.2R specifies an effective FRP strain that is inversely proportional to the number of FRP layers, with a maximum permissible design strain of 0.4%. Consequently, when multiple layers of FRP are applied, the strain in the FRP is reduced, thus decreasing the effectiveness of the FRP-strengthening scheme. EB-FRP shear reinforcement can take the form of a continuous sheet, completely covering the surface of the region to be strengthened, or equally spaced discrete strips. ACI 440.2R-08 [10] specifies a maximum center-to-center spacing for FRP strips of d/4, plus the width of the strip (with d being the effective depth of the concrete member). Continuous sheets provide more redundancy, but discrete strips allow for material optimization and cracking monitoring. Several experimental studies [11,12,13] indicated that CFRP U-strips achieved higher shear-strength contributions than continuous CFRP U-jackets.

When shear cracks develop and intersect the FRP U-wrap, local debonding of the FRP occurs at the shear crack location, and the FRP material is engaged in tension, with increasing strain as the crack widens. For unanchored U-wraps, axial demands in the FRP are only resisted by the bonded portion of fabric extending past the crack. Given the limited available development and bond lengths in shear U-wrap applications on T-beams, it has been experimentally shown that FRP laminates alone tend to peel off early, resulting in little enhancement on the ultimate load or the displacement capacity of T-beams and, in some cases, trigger even more brittle failure modes [14]. Hence, it is imperative to provide mechanical anchorage at termination points of the FRP laminate to keep it in place, provide a load path for the tensile forces after its complete detachment, and allow the development of higher tensile strains. ACI 440.2R recognizes that mechanical anchorage can be used in shear-strengthening applications to achieve higher strains in the FRP laminates, but current shear capacity equations do not account for it. The latest version of the ACI 440.2R guideline (published in 2017) states that properly anchored U-wraps can be designed to fail by FRP rupture, but in no case does it allow the use of an effective strain higher than the lesser of 0.004 or 0.75ε_fu, where ε_fu is the design rupture strain. The only EB-FRP design guidelines that incorporate the influence of mechanical anchorage in the shear design equations are those presented in NCHRP reports 655 [15] and 678 [16] by the Transportation Research Board (TRB), both of which are specific for concrete bridge members. ACI 440.2R and, similarly, all other EB-FRP design guidelines for strengthening concrete members only provide conceptual methods for mechanical anchorage but lack specific anchor design recommendations. Given the absence of an established anchorage design method, ACI 440.2R requires the performance of any anchorage system for FRP to be substantiated through testing.

2.3. FRP Anchors

Considering their corrosion resistance, compatibility with FRP fabric, and documented superior performance in shear-strengthening applications [14,17], FRP anchors (also referred to in the literature as “spike anchors”) were selected over steel anchors for the retrofit designs of the shear-deficient RC-MRF beams in the building. FRP anchors consist of a bundle of fibers saturated with epoxy, with one end (referred to as “dowel”) inserted into a predrilled hole filled with epoxy; the other end is splayed out in a fan shape and bonded to the FRP fabric, creating a load path to transfer tensile forces from the FRP laminate to the concrete member. The fan portion of FRP anchors (also referred to as “splay”) must cover the whole width of FRP fabric and overlap with adjacent anchor fans to ensure correct force transfer [18,19]. The load transfer mechanism in the dowel portion of the FRP anchor assimilates that of metallic adhesive anchors. For design purposes, anchors should not limit the strength of the EB-FRP system; therefore, all failure modes in the FRP anchors should be avoided. In this regard, FRP anchors can be designed for rupture of the FRP laminates, i.e., ultimate strain of the FRP fabric, or for the actual maximum expected load demand in the FRP fabric, i.e., design strain, which is limited to 0.004 by ACI 440.2R, as previously discussed. Obviously, the first approach produces considerably larger anchors.

FRP anchors are widely used by practicing engineers despite the absence of specific design guidance. At the time the FRP-strengthening schemes for the building were iterated (i.e., 2014–2015), FRP anchors were still a relatively new technique, and only limited experimental validation was available. FRP anchors were first studied in Japan [18]. Initial efforts to identify the failure modes of FRP anchors and the primary parameters affecting their tensile capacity focused on pullout tests of isolated straight-embedded FRP anchors [20,21,22]. However, early studies used handmade FRP anchors constructed using rolled FRP fabric, a very different configuration from the manufactured FRP anchors being used in real-life applications. Özdemir [20] reported that larger-diameter dowels resulted in stronger FRP anchors and identified an effective embedment length of 10 cm (4 in), beyond which the capacity of the straight FRP anchors did not increase. Ozbakkaloglu and Saatcioglu [21] identified three failure modes, namely, concrete cone failure, combined cone-bond failure, and anchor rupture. They also reported that the average bond strength between anchors and concrete decreases with both increasing anchor diameter and increasing embedment length but is not significantly affected by the strength of concrete.

Orton et al. [23] provided limited design recommendations for 90°-bent CFRP anchors based on test results of flexurally-strengthened beams using anchored CFRP laminates. Those included a minimum-dowel embedment depth of 13–15 cm (5–6 in), with at least 5 cm (2 in) into the core concrete and a cross-sectional area for FRP anchors designed to reach fracture of the FRP laminate of at least twice the area of the FRP laminate to be developed. The recommendation on the area of the FRP anchors was intended to overcome the loss of strength due to stress concentrations at the anchor bend, which can cause the anchor to rupture prematurely. It was also reported that the use of a larger number of smaller anchors with reduced spacing is more effective in developing the capacity of the FRP laminate than a few large anchors [23].

The first design model for FRP anchors, and the only available approach for this retrofit project, was developed by Kim and Smith [24] based on the failure modes and strength equations for adhesive metallic anchors and test data for straight CFRP anchors made from rolled carbon fiber sheets [20,21,22]. This model is only valid for straight anchors, and it does not consider the influence of the anchor size, the fan angle, or the fan-to-sheet failure mode. However, despite its limitations, this model is still widely accepted by practitioners. The corresponding anchor capacity equations are provided in Appendix B.

2.4. Similar Anchored EB-FRP Shear-Strengthening Applications

At the time of design for this retrofit project, studies on the use of FRP anchors for shear-strengthening FRP applications on flanged beams were somewhat limited [14,19,25,26,27,28]. Some of the strengthening concepts and design recommendations for the FRP laminates and FRP anchors in these studies were used by the authors as a reference for design. For example, both Jinno et al. [25] and El-Saikaly et al. [28] studied fully closed wrap schemes achieved using FRP splice anchors passing through either the flanges or the web-slab interface, respectively, and demonstrated the outstanding performance of these hooplike shear-strengthening concepts when compared to more traditional U-wrap solutions. Also, many of the design recommendations for FRP-embedded anchors provided in the Austin, Texas, report by Kim et al. [19] were incorporated in the retrofit design, as later discussed in Section 5.2. However, most of these studies (in fact, all except for Jinno et al. [25]) focused on the strengthening of gravity beams tested under monotonic loading, making their results not extractable to moment frame beams. To the author’s knowledge, tests of FRP-shear-strengthened RC MRF T-beams under large-amplitude, fully reversed cyclic loading had only been performed at the time by Jinno et al. [25], Anil [29,30], and Tzoura and Triantafillou [31]. Among these cyclic studies, only Jinno et al. [25] used embedded FRP anchors, and in all cases, the specimens were relatively small (specimens in [25] had depths of 400 mm [15.8 in], 500 mm [19.7 in], and 600 mm [23.6 in]; cross-sectional dimensions (depth × width) were 360 mm × 120 mm [14.2 in × 4.7 in] in [29] and [30], and 350 mm × 150 mm [13.8 in × 5.9 in] in [31]).

2.5. Research Posterior to Testing Program

After the completion of the authors’ testing program and retrofit design presented in this manuscript, a new version of ACI 440.2R was published (in 2017), and more research became publicly available, providing updated design recommendations and new design equations for FRP-embedded anchors [32,33] and further insight into the performance of RC T-beams with full-wrap FRP-strengthening applications [34]. Limited seismic-strengthening recommendations were added to ACI 440.2R-17 [9], which were not available at the time of design of the experimental program presented herein. Among these, the new guideline explicitly states that, for seismic shear-strengthening applications, FRP should be provided with complete continuity around the perimeter of the section to account for effects of stress reversal. A new report by the Austin, Texas, research group [32], published in 2017, complemented their previous work [19] with additional monotonic test results of full-scale RC bridge members strengthened in shear with bidirectional CFRP retrofit schemes. In their 2019 publication, del Rey Castillo et al. [33] provided the most comprehensive design methodology for FRP anchors to date. This paper presented improved capacity equations for both straight and 90°-bent anchors exhibiting fiber-rupture failure and incorporated the effect of anchor size and fan angle. Furthermore, it provided an additional load capacity equation for the fan-to-FRP laminate bond failure, which was not included in the model by Kim and Smith [24]. The work presented by El-Saikaly et al. [28] was also extended with a new publication in 2017 [34] evaluating an alternative full-wrap FRP-strengthening scheme with the CFRP rope anchors passing vertically through the flanges of the T-beam (somewhat similar to the concept tested by Jinno et al. [25] and implemented on specimen S5) instead of horizontally through the web. The two full-wrap schemes were compared in this paper, and a better performance was demonstrated using the anchors through the flanges.

Even though FRP is a popular solution for seismic retrofit of shear-deficient RC beams with a top slab, published performance data for this specific application under fully reversed cyclic loading is still very limited.

The findings and general recommendations on EB-FRP shear-strengthening of RC T-beams in the papers and national design guidelines available at the time this retrofit project was in progress were used as a reference for design. However, the unique combination of shear deficiency, T-beam configuration, large size, and cyclic load demands, together with the lack of anchorage-related FRP design provisions and the limited amount of experimental data, warranted the experimental assessment through large-scale testing of the retrofit schemes for the deficient MRF beams in the existing high-rise building.

3. Experimental Program

The two-phase experimental program pertinent to the shear-deficient MRF beams was carried out between March 2013 and November 2015 and consisted of seven 4/5-scale specimens. Phase 1 included four un-retrofitted beams with large rectangular web penetrations (S1 through S4). Test results were published in a prior paper by the authors [4]. Phase 2 included three specimens externally strengthened with FRP. The first two specimens (S1A and S1B) were replicas of specimen S1, a specimen with a large rectangular opening and the only specimen that failed prematurely at the opening region. These replicas were externally reinforced around the opening and at the end-yielding region next to the support using two slightly different FRP schemes (Figure 2 and Figure 3a,b). The objective of the third specimen (Specimen S5) in Phase 2 was to test an alternative retrofit solution for the end-hinging region that would overcome the performance deficiencies of the previously tested retrofit details. Specimen S5 was strengthened with a full-wrap FRP scheme achieved by using continuous FRP splice anchors penetrating the slab and connecting both ends of FRP U-strips. FRP reinforcement was supplemented with intermediate crack-control joints aimed at (1) mitigating flexural cracking behind the FRP strips to delay premature debonding due to stress concentration at crack locations, and (2) enhancing the beam’s ductility through distribution of the plastic rotations across the strengthened region.

3.1. Geometry and Internal Reinforcement

The test specimens were replicas of shear-deficient MRF beams located in an existing building in downtown Los Angeles. Utilizing the benefit of MRF beam symmetry between the columns, the actual test specimens were constructed as half-length cantilever beams. In addition, due to weight limitations of the crane in the UC Irvine structural laboratory, the specimens were scaled down to 80% (4/5 scale) in all dimensions and reinforcement sizing. All scaled specimens had consistent cross-sectional geometry of 0.98 m (38.4 in) × 0.61 m (24 in). The top slab had a thickness of 0.12 m (4.8 in) and a width of 1.59 m (62.4 in). Specimens S1A and S1B had a shear span of 3.40 m (134.0 in); S5 had a shear span of 3.17 m (124.8 in). Figure 2 and

Table 1. Internal steel reinforcement details at the end-yielding region.

Spec.	End Region Reinforcement (Section A)
	Top				Bottom				Hoops
	Main	Added Layer 1	Added Layer 2	Long. Reinf. Ratio	Main	Added Layer 1	Added Layer 2	Long. Reinf. Ratio	No. Sets-Size	Spac’g (cm)	Transv. Reinf. Ratio
S1A /S1B	4-#9	2-#9	2-#7	0.0087	4-#9	2-#9	─	0.0070	1-#4	12.1	0.0035
S5	6-#9	─	2-#9 + 2-#8	0.0117	4-#8	2-#8	2-#8	0.0075	2-#3	14.0	0.0033

provide details of the geometry and internal steel reinforcement for the Phase 2 specimens: S1A, S1B, and S5.

Unlike the rest of the specimens in the program, specimen S5 was not an exact replica of one of the in-situ beams; the internal reinforcement configuration was slightly adjusted to achieve a 30% shear overstress at the end-hinging region, representative of the maximum predicted shear-demand levels in the building. Crossties were added to preclude unwanted interferences in the performance of the FRP shear-strengthening from potential buckling of the longitudinal middle rebar.

3.2. FRP Reinforcement

The focus of this paper is the strengthening of the end-yielding region of shear-deficient MRF beams. This necessitated three iterations to devise a retrofit detail. The detail had to be effective not only in increasing shear strength to ensure flexural hinging but also in enhancing hinge ductility and delaying the buckling of the top longitudinal reinforcement. Figure 3 shows pictures of the FRP-strengthened specimens, S1A, S1B, and S5, prior to testing. For S1A and S1B, the CFRP wrap at the end-yielding region was painted white for easier monitoring of cracking in the fabric. Details on the geometry of the FRP shear-strengthening schemes on each specimen are provided below and depicted in Figure 4, Figure 5 and Figure 6. The FRP laminates and FRP anchors used in this project were manufactured and installed by Fyfe. Details on the installation procedure are provided in Section 8.

3.2.1. Specimen S1A

The FRP-strengthening detail at the end-yielding region consisted of a 45.7 cm (18 in)-wide U-jacket, installed 5.1 cm (2 in) away from the beam-column interface and constructed of one layer of 1.0 mm (0.04 in)-thick carbon FRP (CFRP) fabric with no anchors. Beam web corners and anchor hole edges were rounded to a minimum 1.9 cm (0.75 in) radius. A partial-depth layer of CFRP, with the fibers also oriented vertically, was added over the main U-wrap for additional strength at the corner areas, where stress concentrations occur. Specimen S1A was also retrofitted around the opening (see Figure 3) to prevent failure in that region, which is discussed in detail in a previous publication by the authors [5].

3.2.2. Specimen S1B

The retrofit scheme on specimen S1B was designed based on the results for S1A and represented an optimized version of the same retrofit concept. Specifically, the CFRP U-jacket at the end-yielding region was anchored at the top using embedded GFRP anchors with the same characteristics as those used at the opening regions of both S1A and S1B. Anchor splays were sandwiched with a 35.6 cm (14 in)-high patch of CFRP laminate with the fibers oriented vertically.

3.2.3. Specimen S5

As introduced in Section 1 and described in more detail in Section 6.1, the anchored U-wrap on S1B failed unexpectedly and undesirably by anchor pullout at around 3% drift. In light of the subpar performance of the traditional embedded anchors and the lack of space in the flange to lengthen the anchor dowels, external shear strengthening for specimen S5 was provided in the form of fully closed CFRP strips, as shown in Figure 6. This scheme was designed to overcome an analytically predicted 30% shear overstress at the end-yielding region and to mitigate buckling of the top longitudinal reinforcement by providing additional confinement. The FRP reinforcement consisted of two-layer U-strips made of 1.0 mm (0.04 in)-thick, 16.5 cm (6.5 in)-wide CFRP laminate, spaced at 27.9 cm (11 in) on center along a length from the fixed end of 1.5 times the effective depth of the beam. Each strip was developed with two 1.3 cm (0.5 in)-diameter CFRP splice anchors passing through predrilled holes across the flanges and connecting the ends of the U-wrap, thus providing complete continuity of the FRP around the perimeter of the beam. The over-the-top anchors were embedded into the slab along recessed grooves for a flat surface finish, as this was a requirement in the in-situ application to avoid tripping hazards. The anchor splays were detailed to fully cover the width of the FRP strip and have a length of 30.5 cm (12 in), resulting in a 16° fan angle. Anchor splays were sandwiched between the two layers of FRP. Beam web corners and anchor hole edges were rounded to a minimum radius of 1.27 cm (0.5 in) to reduce stress concentrations in the FRP. The CFRP anchors were designed for a maximum strain of 0.004. The FRP reinforcement was supplemented with 1.27 cm (0.5 in)-deep intermediate saw-cut grooves in between the FRP strips and along the beam’s soffit, sides, and slab, intended to act as crack-control joints to force an even distribution of thinner flexural cracks away from the FRP strips.

3.3. Material Properties

Concrete and steel material properties adopted for the test specimens were representative of the in-situ MRF beams. Given the quasi-static nature of the applied load, material properties were not scaled. A concrete design mix with an average compressive strength of 41.4 MPa (6 ksi), maximum aggregate size of 0.95 cm (0.375 in), and a slump of 7.62 cm (3 in) was used for all beams’ specimens. The average concrete compressive strengths at test date were 48.3 MPa (7.0 ksi) for S1A, 49.8 MPa (7.23 ksi) for S1B, and 46.1 MPa (6.69 ksi) for S5.

Reinforcing steel A615 Grade 60 was used for the longitudinal reinforcement and A706 Grade 60 for the transverse reinforcement. Steel material properties reported by mill certificates are summarized in

Table 2. Mechanical properties of steel reinforcing bars.

Bar Size	Diam.	Steel	Type	Nominal Yield Strength	Nominal Tensile Strength	Test Yield Strength	Test Tensile Strength	Elong. in 8″
	mm (in)			MPa (ksi)	MPa (ksi)	MPa (ksi)	MPa (ksi)	%
#3	9.5 (0.375)	A706/Gr60	Hoop	414 (60)	552 (80)	467 (67.8)	685 (99.4)	17.0%
#3	9.5 (0.375)	A615/Gr60	Long.	414 (60)	621 (90)	485 (70.4)	763 (110.7)	13.0%
#4	12.7 (0.50)	A706/Gr60	Hoop	414 (60)	552 (80)	440 (63.8)	636 (92.2)	15.0%
#7	22.2 (0.875)	A615/Gr60	Long.	414 (60)	621 (90)	445 (64.6)	734 (106.5)	15.0%
#8	25.4 (1.000)	A615/Gr60	Long.	414 (60)	621 (90)	458 (66.4)	761 (110.4)	16.0%
#9	28.7 (1.128)	A615/Gr60	Long.	414 (60)	621 (90)	462 (67.0)	738 (107.1)	18.0%

.

The properties of the FRP laminates and anchors utilized in this project were based on typical test and design values outlined in the Fyfe’s technical brochures available at the time of design (

Table 3. Mechanical properties of FRP composites.

Element Type	SEH-51A Laminate	SCH-41A Laminate	1/2″ SEH Anchor	1/2″ SCH Anchor
Fiber Type	glass	carbon	glass	carbon
Dry Fiber Minimum Weight	915 g/m2 (27 oz/yd2)	644 g/m2 (19 oz/yd2)	95.8 g/m (0.086 oz/in)	86.8 g/m (0.078 oz/in)
Nominal Thickness	1.3 mm (0.05 in)	1.0 mm (0.04 in)	-	-
Tensile Strength Typical/Design	575 MPa (83.4 ksi)/ 460 MPa (66.72 ksi)	986 MPa (143 ksi)/ 834 MPa (121 ksi)	575 MPa (83.4 ksi)/ 460 MPa (66.72 ksi)	986 MPa (143 ksi)/ 834 MPa (121 ksi)
Tensile Modulus Typical/Design	26.1 GPa (3.79 × 103 ksi)/ 20.9 GPa (3.03 × 103 ksi)	95.8 GPa (13.9 × 103 ksi)/ 82 GPa (11.9 × 103 ksi)	26.1 GPa (3.79 × 103 ksi)/ 20.9 GPa (3.03 × 103 ksi)	95.8 GPa (13.9 × 103 ksi)/82 GPa (11.9 × 103 ksi)
Elongation at Break Typical/Design	2.2%/1.76%	1.0%/0.85%	2.2%/1.76%	1.0%/0.85%

).

3.4. Test Procedure

Figure 7 shows a schematic and a picture of the test setup. Cyclic loading was applied in displacement control mode by means of a 1334 kN (300 kips) capacity hydraulic actuator and a U-shaped steel clamp connected to the specimen at 61 cm (24 in) from the tip via six post-tensioned horizontal Dywidag rods to facilitate an even, slip-free load distribution across the beam’s depth. The reaction block was fastened to the strong floor and strong wall via post-tensioned Dywidag bars and additionally secured with two shear plates in the front to restrict any block rotation or sliding.

The displacement histories applied to specimens S1A, S1B, and S5 are presented in Figure 8. Drift (i.e., chord rotation), applied tip displacement, and corresponding actuator forces in each loading direction are provided in

Table 4. Load protocol.

S1A	Drift	[%]	0.1	0.2	0.3	0.4	0.6	0.8	1.0	1.5	2.0	3.0	4.0	6.0
	Displ	[cm]	0.4	0.7	1.0	1.3	2.0	2.6	3.4	5.2	6.8	10.2	13.7	20.5
	Load Down	[kN]	111	211	295	364	470	568	606	654	682	722	698	392
	Load Up	[kN]	−92	−182	−272	−354	−468	−558	−574	−621	−656	−711	−695	−545
S1B	Drift	[%]	0.1	0.2	0.4	0.6	0.8	1.1	1.6	2.3	3.3	4.5	6.0
	Displ	[cm]	0.3	0.7	1.3	2.0	2.6	3.8	5.5	7.8	11.3	15.3	20.4
	Load Down	[kN]	134	202	322	448	541	617	668	713	749	562	400
	Load Up	[kN]	−177	−237	−369	−477	−552	−571	−624	−669	−715	−631	−552
S5	Drift	[%]	0.1	0.2	0.4	0.7	0.9	1.2	1.6	2.1	2.9	3.4	3.8	4.5	5.3
	Displ	[cm]	0.4	0.7	1.4	2.1	2.8	3.8	5.1	6.7	9.2	10.8	12.2	14.3	16.7
	Load Down	[kN]	199	302	491	705	805	856	886	926	979	986	971	646	431
	Load Up	[kN]	−233	−304	−464	−580	−624	−652	−664	−694	−735	−741	−734	−602	−406

. The test specimens were subjected to quasi-static fully reversed and monotonically increasing cyclic loading following the recommendations outlined in Chapter 5 of ACI 374.2R-13 [35] and in Section 10.3.2.1 of ASCE 41-13 [36]. Analytically estimated yield displacements were used as reference. Displacement levels were incrementally increased until complete structural failure was reached, which was defined as a drop in strength below 75% of the peak capacity in either loading direction. In general, three load cycles were applied at each displacement level up to the onset of strength loss; two cycles per increment were applied thereafter.

3.5. Instrumentation

Specimens S1A, S1B, and S5 were instrumented with a total of 68, 64, and 67 sensors, respectively. All specimens featured a similar instrumentation layout: LVDTs were mounted on the beams’ web, with 28 LVDTs on S1A and S1B and 30 on S5. Half of these LVDTs measured flexural deformations parallel to the beams’ longitudinal axis, while the other half were mounted in an X configuration to measure shear deformations. Additionally, five to seven string potentiometers (SP) were attached to the strong floor and connected along the beams’ soffit to capture beam deflection profiles. Two extra SPs were connected to the top and bottom of the reaction block to monitor potential displacements and rotations, which were found to be negligible. Finally, strain gauges (SGs) were installed along the main longitudinal top and bottom rebars, as well as on selected steel hoops, with 28 SGs on each specimen. In specimens S1A and S1B, only the end and middle small hoops within the chord members above and below the openings were instrumented (six hoops total); in S5, SGs were provided on the second and third stirrups within the end hinging region. Figure 9 provides a schematic of the instrumentation layout for specimens S1B and S5.

4. Beam Capacity Estimates

Expected flexural and shear capacities provided in this section were calculated using as-tested concrete compressive strengths, rebar yield and tensile stresses per mill certificates, typical test values of the FRP materials, and unity strength reduction factors to allow for direct comparison with the experimental results presented in Section 6.

4.1. Flexural Capacities

Table 5. Analytical flexural capacities.

Spec.	Load Dir.	First Yield			Effective Yield			Ultimate Strength
		My,0	ϕy,0	θy,0	My,eff	ϕy,eff	θy,eff	Mu	ϕu	θu
		[kN-m]	[rad/m]	[rad]	[kN-m]	[rad/m]	[rad]	[kN-m]	[rad/m]	[m/m]
S1A	down	1914	0.003	0.006	2248	0.004	0.007	3017	0.15	0.14
	up	1548	0.003	0.005	1844	0.004	0.006	2394	0.14	0.13
S1B	down	1871	0.003	0.006	2251	0.004	0.007	3018	0.15	0.14
	up	1512	0.003	0.005	1847	0.004	0.006	2395	0.14	0.13
S1A	down	2337	0.004	0.006	2588	0.004	0.006	3419	0.12	0.11
	up	1530	0.003	0.005	1989	0.004	0.006	2584	0.20	0.18

provides the specimen’s analytical flexural strength, curvature, and rotation capacity at first yield (M_y,0, ϕ_y,0, θ_y,0), effective yield (M_y,eff, ϕ_y,eff, θ_y,eff), and at ultimate point (M_u, ϕ_u, θ_u) in both loading directions. First yield and ultimate expected flexural capacities were obtained via moment-curvature (M-ϕ) analysis using the software XTRACT v3.08 [37] with as-tested concrete compressive strengths and rebar yield and ultimate stresses per mill certificates. Confinement provided by the transverse reinforcement was accounted for in terms of increased strength and ductility of the core concrete. No additional confinement provided by the FRP was considered. The material model proposed by Mander et al. [38] was used for both the unconfined and the confined concrete materials. Since the fibers in the FRP laminates were oriented perpendicular to the beam’s axis, it was assumed that the FRP did not provide any additional flexural capacity. The adopted strain values for the unconfined concrete associated with compression yield, peak strength, crushing, and spalling were 0.0014, 0.002, 0.004, and 0.006, respectively. The tensile strength of concrete was estimated as the modulus of rupture, in accordance with Equation 19.2.3.1 in ACI 318-14. A parabolic strain-hardening model was used for the reinforcing steel, assuming a hardening onset strain value of 0.012 and a failure strain equal to the corresponding experimental percent elongation at failure. The effective yield point was determined as the intersection of the secant line to the first yield point with the regression line fitted to the set of M-ϕ values within the inelastic hardening range of the curve. Rotation at yield (for both, first, and effective yield points) was derived from the corresponding curvature value at yield as: θ_y = ϕ_y L_s/2 (with L_s the shear span). Rotation at ultimate capacity was determined as: θ_u = θ_y,0 + (ϕ_u − ϕ_y,0)L_p, assuming a plastic hinge length (L_p) equal to the effective depth of the beam’s section (L_p = d). To note, the calculated M-ϕ relationships represent flexural strength and deformation capacities under monotonic loading, ignoring strength degradation due to cyclic loading and additional flexibility due to shear deformations and/or strain penetration at the support.

4.2. Shear Capacities

The nominal shear strength of the FRP-strengthened MRF beam specimens, V_n, was evaluated at the end flexural-yielding region using Equation (1), as described in ACI 440.2R-08. V_c, V_s, and V_f are the shear-strength contributions of concrete, reinforcing steel, and external FRP reinforcement, respectively. V_n was calculated using expected material properties and a value of 1.0 for the shear-strength reduction factor (ϕ_v), per ASCE 41-13 [36]. The additional strength reduction factor for the FRP, ψ_f, was taken as 0.85 for both U-wrap schemes applied to S1A and S1B, regardless of the anchorage, and as 0.95 for the full-wrap scheme on S5.

V_n = ϕ_v(V_c + V_s + ψ_fV_f)

(1)

V_c and V_s were computed per Section 22.5 in ACI 318-14 [39]. However, following the seismic provisions in Section 18.6.5 of the code for MRF beams, a reduced cyclic shear capacity, V_n,cyclic, was derived for the expected flexural-hinging region by eliminating the contribution of concrete (V_c = 0). For reference, ACI 318 and ACI 440.2R shear provisions are summarized in Appendix A.

Table 6. Analytical shear capacities.

Spec.	Load Dir.						Unstrengthened		FRP-Strengthened
		Vc	Vs	n	εfe	Vf	Vn	Vn,cyclic	Vn	Vn,cyclic
		[kN]	[kN]	[-]	[mm/mm]	[kN]	[kN]	[kN]	[kN]	[kN]
S1A	down	619	829	1	0.0019	281	1448	829	1687	1068
	up	638	853		0.0019	291	1491	853	1739	1101
S1B	down	629	829	1	0.0040	591	1458	829	1961	1331
	up	648	853		0.0040	612	1502	853	2022	1373
S5	down	596	824	2	0.0040	798	1420	824	2179	1582
	up	612	845		0.0040	819	1457	845	2235	1623

provides the computed V_c, V_s, V_f, V_n, and V_n,cyclic for the MRF beam specimens before and after the FRP-strengthening. In Table 6, n is the number of layers of FRP, and ε_fe is the effective strain used to calculate V_f.

5. Design of FRP Strengthening

Table 7. Design summary of the FRP retrofit schemes.

Spec.	Load Dir.	FRP Laminate Design						FRP Anchor Design
		Ve	Vn	Ve/Vn	Vf,req	nreq	N	εfe	wf	Freq	Kim and Smith (2010) [24]				del Rey Castillo et al. (2019D) [33]
											Ffr	Fcc	Fcb	DCR	Ffr	Fsd	DCR
		[kN]	[kN]	[-]	[kN]	[-]	[-]	[%]	[mm]	[kN]	[kN]	[kN]	[kN]	[-]	[kN]	[kN]	[-]
S1A	down	886	829	1.1	67.7	0.2	1	0.19	-	-	-	-	-	-	-	-	-
	up	703	853	0.8	0.0
S1B	down	887	829	1.1	68.1	0.1	1	0.4	102	39.6	43.0	68.9	46.0	0.92	24.3	50.4	1.63
	up	704	853	0.8	0.0
S5	down	1079	824	1.3	268.1	0.8	2	0.4	83	64.3	73.7	NA	NA	0.87	59.3	60.9	1.08
	up	815	845	1.0	0.0

summarizes the design capacities and demand-capacity ratios for the FRP laminates and the FRP anchors used for shear strengthening of the end yielding of specimens S1A, S1B, and S5. Details on the design approach are provided in Section 5.1 and Section 5.2 below. V_e is the design shear and represents the maximum shear demand that an MRF beam would experience if it developed flexural hinges at the ends. V_e was determined using the capacity design approach in § 18.4 of ACI 318-14; for the half-length cantilever test specimens, V_e = M_u/L_s, where M_u is the beam’s ultimate moment capacity evaluated for expected material properties (as reported in Table 5) and L_s is the shear span. To note, due to the higher longitudinal reinforcement ratio at the top face and the presence of the slab, the beams have a higher flexural capacity in the downward-loading direction, which, for the cantilever specimens, translates into a higher shear demand when loading down. V_n is the nominal shear capacity of the unstrengthened MRF beams at the end-yielding region for V_c = 0 (Table 6). V_f,req is the required FRP shear contribution (i.e., V_f,req = (V_e − V_n)/ϕ_v/ψ_f, with ϕ_v = 1.0). n_req is the required number of layers of FRP (i.e., n_req = V_f,req/(2t_fw_f ε_fe E_fd_fv/s_f), where t_f is the nominal thickness of each layer of FRP laminate, w_f is the width of FRP laminate, E_f is the tensile modulus of the FRP material, d_fv is the effective depth of the FRP shear reinforcement, and s_f is the center-to-center spacing of the FRP strips). n is the layers provided. F_req is the required tensile strength per anchor (i.e., F_req = E_f ε_few_f nt_f, where E_f is the tensile modulus of the FRP anchor and t_f is the nominal thickness of each layer of FRP laminate). F_fr, F_cc, F_cb, and F_sd are the anchor tensile capacities for the failure modes of anchor fracture, concrete cone, combined concrete cone and bond, and fan-to-FRP sheet debonding, respectively, per either Kim and Smith [24] or del Rey Castillo et al. [33], for which the equations are provided in Appendix B. DCR is the demand capacity ratio for the anchors (i.e., DCR = F_req/min (F_fr, F_cc, F_cb, F_sd)).

5.1. FRP Laminate

The FRP laminates in the shear-strengthening schemes applied to S1A, S1B, and S5 were designed according to the procedure outlined in ACI 440.2R-08 (see Appendix A) to resist the expected shear-capacity deficit at the end-yielding regions of the MRF specimens. For a given geometry of the FRP wrap (i.e., width and spacing for FRP strips), the required number of plies was determined based on design values of the tensile properties of the material (Table 3). One layer of FRP was found to be sufficient for all three applications, with predicted DCRs for S1A, S1B, and S5 (Table 7) of 0.2, 0.1, and 0.8, respectively. For precaution and additional conservativism, a partial-depth layer of the same laminate was added to strengthen the corner areas against premature rupture due to stress concentrations, but it was not accounted for strength purposes. Similarly, the number of layers for the strips applied to S5 was increased to two so the anchor fans could be sandwiched between the two layers of FRP. The width of the FRP wrap at the end-yielding region of specimens S1A and S1B was chosen based on the observed crack patterns next to the support for the original unstrengthened specimen from Phase 1 (specimen S1), which concentrated in a section of about 46 cm (18 in) measured from the face of the reaction block [4]. The width (w_f) and spacing (s_f) of the FRP strips for S5 were selected to achieve a redundant strengthening scheme with two anchors per strip, at least three strips intersected by a (45°) shear crack (i.e., d/s_f ≥ 3), and a maximum strip spacing below d/4 + w_f, as prescribed in ACI 440.2R-08.

5.2. FRP Anchors

Anchors were provided at the ends of the U-wrap fabric and as close as possible to the bottom of the slab to maximize the effective depth of the strengthening scheme. The embedded anchors used on the first two specimens, S1A and S1B, were inserted into the slab at an angle of 140° to 155° with respect to the laminate to guarantee an effective load transfer to the top reinforcement. The inclination and slab thickness (12.2 cm [4.8 in]) limited the available embedment length to 10 cm (4 in) for the 4/5 scale specimens (15.2 cm [6 in] for the in-situ beams). Anchor holes were drilled 25% larger than the anchor diameter (1.6 cm [0.625 in] holes for 1.3 cm [0.5 in] anchors), which provided a hole area-to-anchor area ratio of 1.6, larger than the 1.4 limit recommended in [19]. Anchor hole edges, same as web corners, were rounded to a minimum 1.9 cm (0.75 in) radius, exceeding the recommendation of 1.3 cm (0.5 in) in ACI 440.2R and the Austin, Texas, report by Kim et al. [19]. The goal was to minimize the risk of an anchor fracture due to stress concentrations at the bent, as this type of failure had been reported in [19] for their two-layer strip applications. The anchor fan geometries also satisfied and exceeded the recommendations by Kim et al. [19], with splay lengths above the 15.2 cm (6 in)-recommended minimum, full coverage of the FRP laminates, with overlap between adjacent anchors, and reduced fan angles below 60° to keep transverse stresses low. To prevent a bond failure at the splay, anchor fans were either sandwiched between two later of FRP or reinforced with a patch of the same FRP fabric, with the same fiber orientation as the main wrap.

FRP anchors were designed using the model by Kim and Smith [24] for straight anchors, provided in Appendix B. To note, the concrete cone and dowel pullout failure modes are not applicable to the splice anchors on S5; their capacity was calculated for anchor rupture in tension only. All FRP anchors were designed to develop the maximum design strain in the FRP laminates of 0.004 permitted by ACI 440.2R. The design examples in del Rey Castillo et al. [33] use the same criteria, as opposed to designing for the rupture strain of the FRP laminate, as done by [19,23,32]. Arguments to support the adopted design approach are discussed later. DCRs for the anchors at the end-yielding region were 0.92 for S1B and 0.87 for S5, both controlled by anchor fracture (Table 7). The DCR for a bond failure for S1B was 0.86. On the other hand, the updated strength model by del Rey Castillo et al. [33] (Appendix B), not available at the time of design, predicts anchor fracture failures in both cases, with an overstress of 63% for S1B and 8% for S5 (Table 7). However, the FRP anchors at the hinging region of S1B did not fracture. As described in Section 6, the anchors closest to the main flexural crack were pulled out at around 3% drift, which could have been caused by a combination of an underprediction of the tensile capacity of the anchors (due to either or both the conservatism of the design equation or higher ultimate tensile strength of the anchors than that reported in Fyfe’s technical brochures) and local strains in the FRP laminates higher than 0.004.

6. Experimental Results and Discussion

6.1. Experimental Damage Observations and Crack Patterns

For specimens S1A and S1B, crack patterns in the concrete were only visible in the area between the CFRP wrap next to the support and the GFRP wrap around the opening. The strengthened opening region remained basically elastic, with only minor hairline cracking starting at the opening corners, and thus is not going to be discussed in this section. The CFRP wrapping the end-yielding region was painted white for easier monitoring of cracks at the expected hinging region.

6.1.1. Specimen S1A

Figure 10 provides a photographic summary of the evolution of crack patterns and CFRP fabric damage at the end-yielding region of S1A. Local debonding of the CFRP at the hinging region started at 0.6% drift while loading downward and manifested itself in the form of a short vertical (flexural) hairline crack starting at the tip of the FRP U-wrap (i.e., web-slab interface), at the location of the dominant flexural-shear concrete crack. This crack expanded vertically during higher drift levels, creating a continuous vertical tear along the fabric at a distance of 15–20 cm (6–8 in) from the beam-column interface. The first yield of the longitudinal reinforcement was also recorded at 0.6% drift by the SGs closest to the support. Widening of this first vertical tear across the CFRP started at 1.5% drift (Figure 10a) and continued through successive cycles. Bulging of the concrete surface underneath the CFRP, resulting from extensive spalling of the cover concrete at the hinging region, eventually led to the complete detachment of a strip of the CFRP U-wrap during the second cycle at 3.0% drift, while loading downward (Figure 10c). This was closely followed, during the first cycle at 4.0% drift in upward loading, by a sudden fracture of the adjacent strip of CFRP at one of the web corners (Figure 10d). Detachment of the CFRP exposed widely open flexure-shear cracks in the concrete underneath (Figure 10e). Peak capacity was reached during the first cycle at 3.0% drift. Only 2% load-carrying capacity was lost in the downward direction following the detachment of the first strip of CFRP (between the second and third cycle at 3.0%), but the fracture of the second strip caused a very abrupt collapse with a dramatic 37% decrease in strength in the downward-loading direction accumulated during the three cycles at 4.0% drift. The cycles at 4.0% and 6.0% drift were characterized by progressively severe deterioration at the hinge, with intense crushing and abrasion of the core concrete, detachment of big concrete blocks, and buckling of the top and bottom longitudinal reinforcement.

6.1.2. Specimen S1B

Photographs of the crack patterns and CFRP fabric damage for S1B at the end-yielding region are provided in Figure 11. The first hairline vertical crack in the CFRP next to the support initiated at 0.4% drift while loading upward from the U-wrap corner (i.e., beam soffit) and largened slowly during higher drift levels. However, no cracks developed from the anchored tips of the U-wrap until reaching a downward-loading drift of 1.1% (Figure 11a). This occurred two displacement levels later (i.e., six additional cycles) than the unanchored CFRP U-wrap on S1A. The delayed debonding of the FRP U-wrap ends is attributed to the presence of the embedded GFRP anchors. It is important to note that anchorage is not expected to prevent debonding of the FRP laminate. Local debonding at locations where shear cracks cross the FRP laminate still needs to occur to effectively engage the FRP system. However, anchorage allows for the FRP laminate to carry load after debonding has occurred and develop higher strains. First yield of the longitudinal reinforcement next to the support was detected at 0.4% drift, earlier than for S1A. From this point on, despite the anchorage, cracking and failure development for S1B progressed similarly to that of S1A. The crack starting at the tip of the U-wrap underneath the slab at 1.1% drift extended downward during successive cycles to form a full-depth vertical tear at the location of the dominant flexural-shear concrete crack, at about 15 cm (6 in) from the support, which widened through the 1.6% and 2.3% drift cycles (Figure 11b). Sometime between the second and third cycles at 3.3% drift, the GFRP anchors located at the teared section of the wrap pulled out, and similarly to S1A, a strip of the CFRP wrap completely detached (Figure 11c). Again, the detachment of one strip was followed by the abrupt fracture of the adjacent strip of CFRP at one of the beam’s web corners during the first cycle at 4.5% drift while loading down (Figure 11d). Hinge deterioration progressed very quickly from this point on. In comparison to S1A, peak capacity was similarly achieved during the initial cycle at 3.3% drift for S1B. However, the strength loss accumulated during the three cycles at 3.3% drift before the fracture of the second strip was higher for S1B (15% downward) compared to S1A (4%). Fracture of the CFRP resulted in an additional 23% strength loss in the downward direction and accumulated during the two cycles at 4.5%. Further hinge deterioration during the cycles at 6% occurred similarly to S1A.

6.1.3. Specimen S5

Photographs of crack patterns in specimen S5 at selected drift levels are provided in Figure 12. The first flexural cracks appeared during the first downward-loading cycle at 0.1% drift and were located at the beam slab, specifically within the region reinforced with CFRP strips. During subsequent loading cycles, these initially short flexural cracks expanded progressively toward the web of the beam but did not affect the CFRP laminates. Cracks originating at the bottom face of the beam were difficult to discern because they developed along the saw-cut grooves. During the first cycle at 0.4% drift, long flexural-shear cracks developed outside of the FRP-reinforced region while loading in both directions. First yield of the main longitudinal reinforcement occurred at 0.4% drift next to the support. First yield of the transverse reinforcement within the end-yielding region was detected at 1.2% drift at the third hoop from the support. At 2.9% drift, the initial flexural cracks along the crack-control joints between the first two CFRP strips started widening (Figure 12a). Partial delamination of the second and third strips from the fixed-end support occurred during the second cycle at 2.9% drift (Figure 12b). The specimen’s peak capacity was reached during the next displacement level at 3.4% drift. Strength loss due to hinging started during the first cycle at 3.8% drift and was characterized by excessive widening of multiple vertical cracks at the beam-column interface and between the CFRP strips. Severe concrete crushing of the core throughout the sections at the two vertical cracks closer to the support was observed. Sudden fracture of the second-next CFRP strip adjacent to the support occurred at the beginning of the second cycle at 3.8% drift while loading up, with the strip tearing in half along the beam’s soffit and each half fracturing at opposite web corners (Figure 12c,d). During the next half-cycle downward (3.8% drift), one of the spliced CFRP anchors of the strip closest to the support fractured at one of the exit holes above the slab (Figure 12e), which resulted in a notable loss of strength in the downward-loading direction of 20% between the two cycles at 3.8% and an additional 17% between the second cycle at 3.8% and the first at 4.5%. Fracture of both anchors of the first CFRP strip adjacent to the support at opposite exit holes and complete detachment of the strip occurred during the first cycle at 4.5% drift (Figure 12g), accompanied by extensive damage at the hinging zone, which continued during the next two cycles at 4.5% and 5.3% drift, with massive spalling of core concrete pieces and buckling of the longitudinal reinforcement (Figure 12f,h,i).

6.2. Hysteretic Response

Experimental load-deformation results for specimens S1A, S1B, and S5 are summarized in

Table 8. Experimental hysteresis results.

Spec.	Load Dir.	First Cracks				First Yield				Effective Yield				Peak Strength				Onset of Strength Loss				Ductility	Shear Stress Ratio
		Mcr,f	Vcr,s	VY0	ΔY0	MY0	θY0	VYeff	ΔYeff	MYeff	θYeff	VP	ΔP	MP	θPt	θPp	VL	ΔL	ML	θLt	θLp	μ	α
		[kN-m]	[kN]	[kN]	[cm]	[kN-m]	[rad]	[kN]	[cm]	[kN-m]	[rad]	[kN]	[cm]	[kN-m]	[rad]	[rad]	[kN]	[cm]	[kN-m]	[rad]	[rad]	[cm/cm]	[-]
S1A	down	853	278	558	2.1	1806	0.006	650	2.5	2119	0.007	804	10.1	2643	0.030	0.023	775	13.0	2547	0.038	0.031	4.1	0.22
	up	489	288	411	2.0	1491	0.006	495	2.4	1775	0.007	650	10.1	2306	0.030	0.023	637	13.0	2261	0.038	0.031	4.2	0.17
S1B	down	1229	388	454	1455	1455	0.005	654	2.4	2134	0.007	818	11.0	2692	0.032	0.025	818	11.0	2692	0.032	0.025	4.6	0.22
	up	1121	302	293	1091	1091	0.003	480	1.8	1727	0.005	652	11.3	2311	0.033	0.028	652	11.3	2311	0.033	0.028	6.3	0.17
S5	down	749	570	563	1.4	1698	0.004	899	2.3	2765	0.007	1054	10.6	3255	0.034	0.027	1041	12.1	3215	0.038	0.029	4.6	0.29
	up	623	427	383	1.1	1301	0.004	546	1.5	1816	0.005	695	10.6	2288	0.034	0.029	687	11.6	2263	0.037	0.03	6.9	0.19

and shown on Figure 13 and Figure 14 in terms of hysteretic shear-displacement and moment-drift relationships, respectively. The hysteretic plots use the displacement history recorded by the string pot located at the section of load application. (See Figure 9). Shear was obtained by adding or subtracting the self-weight of the beam specimens (66.2 kN for S1A/S1B and 64.0 kN for S5) to the (cyclic) load applied at the free end. Moment was calculated at the fixed support of the cantilever beams and also accounts for the effect of the self-weight. Flexural and shear-cracking strengths are provided in Table 8 in terms of moment and shear loads, respectively (M_cr,f and V_cr,s), and were back-calculated from the applied load at the time-step when the first flexural and shear cracks were observed using video recordings during the test. Shear load, moment, total displacement (Δ), total rotation (θ or θ_t), and plastic rotation (θ_p) values are provided for the characteristic performance points of the experimental cyclic envelope: first yield of the main longitudinal reinforcement (V_Y0, Δ_Y0, M_Y0, θ_Y0), effective yield (V_Yeff, Δ_Yeff, M_Yeff, θ_Yeff), peak strength (V_P, Δ_P, M_P, θ_Pt, θ_Pp), and onset of strength loss (V_L, Δ_L, M_L, θ_Lt, θ_Lp). Rotation values were computed by dividing the beam’s deflection at the point of load application by the shear span (i.e., in this case, rotation is equivalent to drift). Plastic rotation values at peak (θ_Pp) and onset of strength loss (θ_Lp) were obtained by subtracting the rotation at the effective yield point from the total rotation values (θ_Pp = θ_Pt − θ_Yeff; θ_Lp = θ_Lt − θ_Yeff). The effective yield point was determined as the intersection of the secant line to the first yield point with the regression line fitted to the set of cycle peaks between the yield and peak points. The ductility capacity (μ) is evaluated by means of the peak-to-(effective) yield displacement ratio. Finally, the shear stress ratio at peak demand, i.e., $\mathsf{\alpha }={\mathrm{V}}_{\mathrm{P}}/{\mathrm{b}}_{\mathrm{w}}\mathrm{d}\sqrt{{\mathrm{f}}_{\mathrm{c}}^{\prime }}$, is provided (in SI units). To note, the shear stress ratio is in all cases below the limit prescribed in ACI 318 and ACI 440.2R (i.e., (${\mathrm{V}}_{\mathrm{c}}+{\mathrm{V}}_{\mathrm{s}}+{\mathrm{V}}_{\mathrm{f}})/(\sqrt{{\mathrm{f}}_{\mathrm{c}}^{\prime }}{\mathrm{b}}_{\mathrm{w}}\mathrm{d})$ ≤ 0.17 + 0.66 = 0.83 [SI units]), which is intended to prevent diagonal concrete-crushing failures.

In Figure 13 and Figure 14, positive values correspond to the downward-loading direction (i.e., slab in tension), while negative values correspond to upward-loading (i.e., slab in compression). The experimental load-deformation responses are compared with the analytical shear and moment capacity estimates presented in Section 4.

Figure 14 also provides the generalized backbone curve per Table 10–7 in ASCE 41-13, which accounts for cyclic degradation, for comparison with the experimental cyclic backbone. The plotted ASCE 41 backbones (in blue) assume a flexure-controlled performance, which is appropriate for all three FRP-strengthened specimens and the following modeling parameters: a = 0.025 rad; b = 0.05 rad; c = 0.20). The yield point was determined as the intersection of a line with slope m = M/θ = (2/Ls)*EI_flex, and the effective yield moment obtained from moment-curvature analysis is provided in Table 5. Hereby, M is the moment, θ is the chord rotation (i.e., equivalent to drift), and EI_flex is the prescriptive effective flexural stiffness for RC beams per Table 10–5 in ASCE 41-13 (i.e., EI_flex = 0.30E_cI_g). A 5% hardening slope was assumed to obtain the peak point. The acceptance criteria for the tested beams are also defined in Table 10–7 in ASCE 41-13 and consist of plastic rotation limits of 0.025 rad (i.e., 2.5.% drift) for the Life Safety (LS) performance objective (i.e., peak point of the ASCE 41 backbone) and 0.05 rad (i.e., 5.0% drift) for the Collapse Prevention (CP) performance objective (i.e., point of ultimate rotation and residual strength).

All three specimens showed a more flexible elastic response than predicted per the ASCE 41 backbone (Figure 14). This is mainly due to the fact that the analytical elastic stiffness used to construct the ASCE 41 backbone curve (i.e., EI_flex = 0.30E_cI_g) only accounts for flexural deformations. As discussed in Section 6.5, the contribution of shear deformations was derived from the LVDT readings and was found to be significant for all three specimens (up to 40% of the total tip deflection). None of the specimens reached the analytically predicted flexural capacity (M_u; Section 4.1), which may be partially explained by the fact that the M_u values correspond to monotonic loading; thus, they do not account for cyclic strength degradation. For specimens S1A and S1B, the deficit of the experimental ultimate moments with respect to the analytical predictions is three times larger in the downward-loading direction (for S1A, 12% down and 4% up; for S1B, 11% down and 4% up), which the authors attributed to the inefficacy of either of the U-wrap schemes in providing any shear strengthening to the beams in the downward-loading direction. Specimen S5 achieved a flexural capacity that was just 5% below the expected (monotonic) ultimate moment in the downward direction, but twice as much, 11%, in the upward direction. Furthermore, the proposed full-wrap EB-FRP-reinforcing scheme tested on specimen S5 enabled the development of considerably high rotation values—0.034 rad (3.4% drift) at peak and 0.038 rad (3.8% drift) at the onset of strength loss (due to FRP rupture) for an MRF beam that, otherwise, would have prematurely failed in shear (due to 30% shear overstress in the downward-loading direction, Figure 13c). This level of rotation is 30% and 27% higher than the LS (total) rotation limit per ASCE 41 in the downward- and upward-loading directions, respectively (e.g., total rotations at the ASCE 41 backbone peak points are 0.029 rad [2.9% drift] down and 0.030 rad [3.0% drift] up) (Figure 14c). In contrast, specimen S1A, strengthened at the end-yielding region with an unanchored FRP U-wrap, achieved rotation values at the onset of strength loss comparable to those predicted by the ASCE 41 backbone (Figure 14a); for specimen S1B, strengthened with an FRP U-wrap with embedded FRP anchors that failed due to anchor debonding, the increase rotation increase was only 6% downward and 12% upward (Figure 14b).

6.3. Strength and Stiffness Degradation

Figure 15 illustrates peak strength and secant stiffness deterioration versus specimen drift. Peak strength is presented as half-cycle peak loads, F_i, normalized by the load at the effective yield point, F_y,eff, and analogously, secant stiffness is computed in terms of half-cycle secant stiffness, K_i (with K_i = F_i/∆_i), normalized by the secant stiffness at the effective yield point, K_y,eff. As discussed in Section 6.1, similarly for all three specimens, peak strength cyclic degradation (i.e., strength loss due to repeated cycles at constant displacement level) ramped up after failure of the FRP and at a rate that increased with increasing displacement levels. Looking at the downward-loading direction, the load drop between the first two cycles at each displacement level after peak capacity amounted to: for S1A, 2% at 3% drift, 18% at 4.0% drift, and 50% at 6%; for S1B, 4% at 3.3% drift, 23% at 4.5% drift, and 41% at 6% drift; and for S5, 4% at 3.4% drift, 20% at 3.8% drift, and 26% at 4.5% drift. As shown in Figure 15, the secant stiffness degraded rapidly in both loading directions following an exponential decay. The ratio of the secant stiffness at peak capacity to the elastic secant stiffness at yield was: for S1A, 0.30 in both loading directions (peak capacity reached during the first cycle at 3.0% drift); for S1B, 0.27 downward and 0.21 upward (peak capacity reached during the first cycle at 3.3% drift); and for S5, 0.25 downward and 0.17 upward (peak capacity reached during first cycle at 3.4% drift).

6.4. Energy Dissipation

The history of normalized cumulative hysteretic energy (NHE) with respect to the drift level is presented in Figure 11. The NHE at a given cycle was computed as the summation of the dissipated hysteretic energies (HE) of the current and preceding cycles normalized by twice the elastic strain energy (computed at the effective yield point), where HE_i was determined as the area enclosed by the i^th hysteretic loop.

$${\mathrm{N}\mathrm{H}\mathrm{E}}_{\mathrm{i}}={\displaystyle \frac{{\sum }_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}}{\mathrm{H}\mathrm{E}}_{\mathrm{j}}}{2\left(\frac{1}{2}{\mathrm{F}}_{\mathrm{y},\mathrm{e}\mathrm{f}\mathrm{f}}{\Delta }_{\mathrm{y},\mathrm{e}\mathrm{f}\mathrm{f}}\right)}}={\displaystyle \frac{{\mathrm{H}\mathrm{E}}_1+{\mathrm{H}\mathrm{E}}_2+\cdots +{\mathrm{H}\mathrm{E}}_{\mathrm{i}}}{2\left(\frac{1}{2}{\mathrm{F}}_{\mathrm{y},\mathrm{e}\mathrm{f}\mathrm{f}}{\Delta }_{\mathrm{y},\mathrm{e}\mathrm{f}\mathrm{f}}\right)}}$$

(2)

Figure 16 reveals an exponential growth trend of the NHE. The NHE dissipated at peak capacity, which was reached at around 3% drift for all three specimens, accumulated to 24.9 for S1A, 35.7 for specimens S1B, and 51.6 for S5, which represents a 108% energy dissipation increase achieved with the full-wrap strengthening scheme with respect to the unanchored FRP U-wrap (S1A) and a 45% increase with respect to the FRP U-wrap with traditional embedded anchors (S1B).

6.5. Displacement Components

Table 9. Flexural, shear, and strain-penetration displacement components.

Drift	Displacement Component		S1A				S1B				S5
			Down (+)		Up (−)		Down (+)		Up (−)		Down (+)		Up (−)
1%	Δf	[cm]/[%]	1.3	38%	−1.4	41%	1.5	39%	−1.5	39%	2.0	53%	−1.6	41%
	Δs	[cm]/[%]	0.8	22%	−0.7	20%	0.9	24%	−0.7	19%	0.5	12%	−0.3	7%
	Δext	[cm]/[%]	0.1	3%	−0.3	10%	0.1	2%	0.0	1%	0.3	8%	−0.3	7%
	Δtotal	[cm]/[%]	3.4	100%	−3.4	100%	3.8	100%	−3.7	100%	3.8	100%	−3.8	100%
1.5%	Δf	[cm]/[%]	2.4	45%	−2.2	42%	2.4	44%	−2.3	42%	2.8	56%	−2.2	42%
	Δs	[cm]/[%]	1.0	19%	−0.8	17%	1.2	21%	−1.0	18%	0.7	13%	−0.4	8%
	Δext	[cm]/[%]	0.1	1%	−0.1	1%	0.0	1%	0.0	1%	0.4	8%	−0.3	6%
	Δtotal	[cm]/[%]	5.2	100%	−5.1	100%	5.5	100%	−5.5	100%	5.1	100%	−5.1	100%
2%	Δf	[cm]/[%]	3.2	47%	−3.0	44%	3.6	46%	−3.4	43%	3.8	57%	−2.7	41%
	Δs	[cm]/[%]	1.2	18%	−1.2	17%	1.5	19%	−1.5	19%	1.0	14%	−0.6	10%
	Δext	[cm]/[%]	0.1	1%	−0.1	1%	0.1	1%	0.0	0%	0.5	7%	−0.7	10%
	Δtotal	[cm]/[%]	6.8	100%	−6.8	100%	7.8	100%	−7.8	100%	6.7	100%	−6.7	100%
3%	Δf	[cm]/[%]	5.1	49%	−4.8	47%	5.2	46%	−4.9	43%	5.3	58%	−3.5	38%
	Δs	[cm]/[%]	1.6	16%	−1.9	18%	2.1	19%	−2.6	23%	1.4	15%	−1.1	12%
	Δext	[cm]/[%]	0.1	1%	−0.1	1%	0.1	1%	0.0	0%	0.2	3%	−0.3	3%
	Δtotal	[cm]/[%]	10.2	100%	−10.2	100%	11.3	100%	−11.4	100%	9.2	100%	−9.1	100%
4.0–4.5%	Δf	[cm]/[%]	7.0	51%	−7.4	54%	5.6	36%	−9.1	59%	9.8	68%	−5.6	39%
	Δs	[cm]/[%]	2.4	18%	−3.1	23%	3.6	24%	−4.2	28%	2.6	18%	−5.8	40%
	Δext	[cm]/[%]	0.3	2%	-	-	−0.1	0%	−0.2	1%	−0.1	−1%	−0.2	1%
	Δtotal	[cm]/[%]	13.7	100%	−13.7	100%	15.3	100%	−15.3	100%	14.3	100%	−14.3	100%

summarizes the individual deformation components at various drift ratios for specimens S1A, S1B, and S5. Δ_f, Δ_s, and Δ_ext are the deflection contributions at the section of load application of flexure, shear, and fixed-end rotation due to bar extension, respectively. Figure 17 shows the hysteretic loops corresponding to the flexural and shear-deformation components. The contributions of flexure and shear deformations to the overall beam deflection were derived from the LVDT displacement measurements. Fixed-end rotations due to bar extension (i.e., strain penetration) at the beam-column interface were estimated from the local strain measurements closest to the fixed-end section on the top and bottom main longitudinal reinforcement. The total deflection values presented in Table 9 were measured with a single-string potentiometer connected to the soffit of each beam specimen at the section of load application. Hence, these values do not equate to the sum of the three individual deflection components, estimated from different sensor readings, as described above. Data outliers shown as a dash are related to sensors located within the hinging region whose readings were not reliable or were disconnected during the test. The details on the computation of each individual deflection component can be found in a previous publication by the authors [4].

Although flexural deformations dominate the specimens’ response, the contribution of shear deformations is found to be significant for the tested MRF beams (ranging between 16% and 23% for S1A, 18% and 28% for S1B, and 7% and 40% for S5). This finding is consistent with the observed inclined cracks and the pinching of the hysteretic loops. In this regard, Figure 14 confirms that shear deformations are the sole cause behind pinching of the hysteretic loops prior to reaching peak capacity. As also discussed by the authors in [4], the displacement component analysis also reveals that the contribution of shear deformations increases with the applied drift level and with the number of cycles, even with repeated cycles at a constant drift level, as also described in Krawinkler and Popov (1973) [40].

6.6. Effective Stiffness

The effective stiffness of a structural member is calculated as the slope of the secant line to the point of first yield of the main longitudinal reinforcement. For a cantilever member, the normalized value of the overall effective stiffness can be computed from the load-deformation experimental data as follows:

$${\displaystyle \frac{{\mathrm{E}\mathrm{I}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l},\mathrm{e}\mathrm{f}\mathrm{f}}}{{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}}}={\displaystyle \frac{{{\mathrm{L}}_{\mathrm{s}}}^3}{{3\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}}}\left({\displaystyle \frac{{\mathrm{F}}_{\mathrm{y}0}}{{∆}_{\mathrm{y}0}}}\right)$$

(3)

where I_g is the gross inertia of the beam’s cross-section (the effect of the longitudinal reinforcement on the transformed section is not accounted for), E_c is the young modulus of concrete, L_s is the shear span, and F_y0 and ∆_y0 are the load and displacement values associated with first yield of the main longitudinal reinforcement, respectively. Analogously, the normalized values of the effective flexural and shear stiffnesses can be computed from measured flexural and shear displacement components at first yield (∆_f,y0 and ∆_s,y0) as follows:

$${\displaystyle \frac{{\mathrm{E}\mathrm{I}}_{\mathrm{f}\mathrm{l}\mathrm{e}\mathrm{x},\mathrm{e}\mathrm{f}\mathrm{f}}}{{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}}}={\displaystyle \frac{{{\mathrm{L}}_{\mathrm{s}}}^3}{{3\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}}}\left({\displaystyle \frac{{\mathrm{F}}_{\mathrm{y}0}}{{∆}_{\mathrm{f},\mathrm{y}0}}}\right)$$

(4)

$${\displaystyle \frac{{\mathrm{G}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}}}={\displaystyle \frac{\frac{\mathrm{F}}{{\mathsf{\gamma }}_{\mathrm{s}}}}{{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}}}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{s}}}{{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}}}\left({\displaystyle \frac{{\mathrm{F}}_{\mathrm{y}0}}{{∆}_{\mathrm{s},\mathrm{y}0}}}\right)$$

(5)

where A_w is the gross web area and G_c is the shear modulus of concrete, with G_c ≈ 0.4 E_c,

Normalized values of the total, flexural, and shear secant stiffnesses at first yield for specimens S1A, S1B, and S5 are summarized in

Table 10. Experimental effective stiffness values.

Specimen	Total Stiffness		Flexural Stiffness		Shear Stiffness
	EItotal,eff/EcIg		EIflex,eff/EcIg		GAeff/EcAw
	Down (+)	Up (−)	Down (+)	Up (−)	Down (+)	Up (−)
S1A	0.14	0.14	0.36	0.35	0.018	0.018
S1B	0.15	0.18	0.34	0.48	0.018	0.026
S5	0.18	0.2	0.35	0.37	0.07	0.15

. Compared to the prescriptive effective rigidity values for RC MRF beams in Table 10–5 of ASCE 41-13, where EI_flex,eff = 0.30E_cI_g and GA_eff = 0.40E_cA_w, the elastic experimental responses of all three specimens are found to be stiffer in flexure (i.e., >0.30) but much more flexible in shear (i.e., <0.40). Specifically, the experimentally derived flexural effective stiffness values in downward and upward directions are 20% and 17% higher than the ASCE 41 recommended value for S1A, respectively, 13% and 60% higher for S1B, and 17% and 23% higher for S5. On the other hand, the experimental shear effective stiffness values are between 63% and 96% lower than the ASCE 41 value.

7. Adjustments to the FRP Scheme

The results of the tests presented in this paper were the design basis for the in-situ retrofit details applied to the end region of 19 MRF beams within the building. Despite a more challenging and labor-intensive installation, the full-wrap strengthening concept tested on specimen S5 was selected for the in-situ application. Minimal adjustments were made based on the experimental observations described in Section 6.1. Namely: (1) the diameter of the anchors was increased from 1.27 cm (0.5 in) to 1.59 cm (0.625 in); (2) the anchors were not recessed into the existing slab but into an overlay layer of labeling concrete to prevent the inducement of flexural cracking in the slab at the FRP anchor locations; the flat floor finish was achieved by pouring a leveling layer of new concrete; (3) and an additional partial-depth layer of CFRP was added to the second strip closest to the column face (the strip that fractured during the test of S5), over the soffit and lower 61 cm (24 in) of the beam web. The intent of this additional layer was to strengthen the most highly stressed strip of FRP at the corner areas against premature fracture due to stress concentrations.

8. On-Site FRP Installation

Fyfe was also responsible for the manufacture and installation of the FRP laminates and FRP anchors used for the on-site retrofit applications in this project. The proper installation of FRP systems is critical to obtain the desired structural performance of the system. Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26 show photographs of the FPR materials and different installation stages in the building. For this project (and most others), the first step consisted of obtaining access to the beams, which included the temporary relocation (and replacement) of mechanical, plumbing, and electrical obstacles along with drop ceilings. Next, the beam section was scanned with ground-penetrating radar (GPR) to locate the existing reinforcing bars prior to drilling. Holes for the FRP anchors were drilled using a hammer drill with a carbide-tipped drill bit that was 0.25 in larger in diameter than the fiber anchor. To note, carbide-tipped drill bits allow for corrections in the hole trajectory if rebar is intersected. As opposed to standard embedded anchors installed from below the slab, drilling for the splice anchors through the slab was done from the top down to allow the holes to be right at the re-entrant corner between the beam and the bottom of the slab. Hereafter, the surfaces where the fiber laminates were to be installed were roughened to a minimum CSP-2 profile per ICRI Technical Guidelines No. 310.2R-2013 using a portable grinder equipped with a diamond cup wheel. Because of project specifications, the splice fiber anchors were recessed along the top of the beam to avoid any tripping hazards (Figure 19). For this purpose, an angle grinder was used to create a groove between the two holes. Beam web corners and anchor holes were rounded to a 0.5-in minimum radius to reduce stress concentrations. Prior to the FRP application, the anchor holes and surfaces receiving FRP were vacuumed to remove concrete dust and primed with a coat of epoxy. Anchor holes were filled with epoxy up to 75% using a syringe (Figure 20). FRP-composite laminates and anchors were manufactured following a standard wet layup process. The two-part epoxy was mixed and combined with the reinforcing fabric and fiber anchors in a controlled area. Saturation of the FRP fabric was done using a special saturator machine (Figure 21 (left), whereas the anchors were saturated manually with the help of a channel-shaped bath (Figure 21 (right)). The saturated fabric and anchors were then transported to the beams and installed as per the approved shop drawings (Figure 22, Figure 23, Figure 24 and Figure 25). A final protective coat of epoxy was then applied at fabric edges, termination points, and over-the-anchor holes. The cure time of the saturated FRP material is temperature-dependent, but in this interior application, at an average temperature of about 21 °C (70 °F), the installed system was hard to the touch and ready to accept any aesthetic finishes after about 24 h and could have taken potential design loads after approximately 72 h. This application was hidden behind the drop ceilings, and no finishes were required. Field quality control of the FRP materials included testing of samples of cured FRP fabric following ASTM D3039 [41] to verify the tensile properties of the material, weighing of the dry anchors to confirm their size, and weighing of the saturated anchors to ensure they had the required amount of epoxy (one-to-one ratio by weight ±10%). A minimum of two 30.5 cm × 30.5 cm (12 in × 12 in) FRP laminate samples were made for each day of production, as recommended by Fyfe. The samples had to achieve a minimum of 85% cure prior to testing (note that 85% cure corresponds to almost-full properties), which is achieved after approximately seven days at average temperature of 21 °C (70 °F). To note, there is no ASTM for field testing of FRP anchors to date. The installed FRP laminates and anchors were checked visually to ensure that all details matched the shop drawings.

9. Discussion

This section provides further explanation and discussion for the most relevant items in this study:

• FRP anchors were designed using the strength model by Kim and Smith (2010), the only available model at the time. Although those equations were calibrated using test data for CFRP anchors made from rolled carbon fiber sheets and are only strictly applicable to straight anchors, they constituted the best design model at the time and were considered appropriate for this project given the ample inclination angles adopted in both applications.
• FRP anchors were designed to develop the allowable design strain in the FRP laminates, that is, 0.004 for full-wrap and anchored U-wraps schemes per ACI 440.2R, as opposed to a design for FRP laminate rupture. The arguments supporting this specific design approach, which was also used by del Rey Castillo et al. [30], are twofold: first and foremost, FRP laminates used to strengthen the yielding region of an MRF beam in shear should not be designed to reach a strain level close to rupture, given the brittle nature of both FRP materials and shear failures and the catastrophic consequences of an MRF beam collapse. Second, anchors designed to fully develop the tensile strength of the FRP laminates are in many cases impractically large, with the drilling of large holes in RC members becoming a concern.
• The development of a full-wrap strengthening scheme for the end-yielding regions of the deficient MRF beams was justified by the following: (1) the ineffectiveness of the embedded FRP anchors added to S1B at the end-yielding region due to premature anchor pullout, resulting in S1A and S1B failing at a similar shear load and rotation demands, (2) the lack of intermediate vertical crossties affecting multiple MRF beams in the building, (3) the reversible nature of seismic demands, and (4) the consequent potential for buckling of the top flexural reinforcement if only a U-wrap were implemented.
• The saw-cut grooves on specimen S5 were intended to force the formation of an even distribution of thinner flexural cracks between the FRP strips to mitigate premature FRP debonding by minimizing concrete cracking behind the FRP reinforcement and, second, to enhance the ductility at the hinging region. Despite the limited data from only one specimen, the authors believe that the evenly spaced crack-control joints promoted a distribution of the plastic rotations across the hinging region that contributed to a more ductile behavior compared to a flexural failure with the plastic rotations concentrated at one dominant crack.
• Strains in the FRP reinforcement applied at the end-yielding regions were not monitored in any of the tests presented in this paper; thus, the adequacy of the prescriptive maximum allowable strain of 0.004 per ACI 440.2R cannot be discussed, and the shear contribution of the FRP (V_f) cannot be verified from the experimental data.
• Due to budget constraints and the high cost of each of these nearly full-scale tests, the performance of the retrofit concept on S5 had to be evaluated without a control specimen (i.e., identical to S5 but with no shear retrofit).

10. Conclusions and Results

This paper presents the design process, experimental evaluation, and in-situ implementation of a shear-strengthening solution applied to 19 shear-deficient RC-MRF T-beams in an existing 12-story building in downtown Los Angeles, California. The results of the experimental study presented herein served as a design basis for the in-situ retrofit, which was recently completed within the building. The shear-strength deficiency of these beams was up to 30% at the end-hinging region. The EB-FRP-strengthening scheme for the end region of the shear-deficient MRF beams was developed in three iterations, each of them evaluated experimentally via fully reversed cyclic testing of a 4/5-scale half-length cantilever specimen, replica of a representative beam in the building. Specifically, the following shear-strengthening concepts were tested: (a) specimen S1, strengthened with an unanchored continuous U-wrap; (b) specimen S1B, furnished with a continuous U-wrap anchored at the ends with embedded FRP anchors; and (c) specimen S5, strengthened with fully closed FRP hoops, achieved with discrete FRP U-wrap strips and spliced CFRP rope anchors through the beam flanges and supplemented with intermediate flexural crack-inducement joints. Results from testing the FRP-strengthening scheme at the end-yielding region of S1A and S1B were used to develop the strengthening scheme tested on S5. The FRP laminates were designed according to the procedure outlined in ACI 440.2R-08, whereas the FRP anchors were designed using the model by Kim and Smith (2010) for straight anchors and design recommendations found in literature.

With comparable (internal) transverse reinforcement ratios (0.0035 for S1A/S1B and 0.0033 for S5, Table 1) and unstrengthened shear capacities (Table 6), specimen S5, retrofitted with FRP hoops, outperformed the initial two specimens (S1A and S1B) constructed with conventional shear-strengthening solutions. Despite a more challenging and labor-intensive installation, requiring simultaneous access to the top and bottom of the beams, the fully closed FRP-strengthening scheme was selected for the in-situ implementation. The FRP hoops enabled the development of a ductile flexural failure with considerably high rotation values—0.034 rad (3.4% drift) at peak and 0.038 rad (3.8% drift) at strength loss for a beam that, otherwise, would have prematurely failed in shear (due to a 30% overstress at the beam end). The rotation at peak capacity was about 30% higher than the ASCE 41 rotation limit corresponding to the LS performance objective. Energy dissipation achieved with the fully closed scheme (S5) was 108% higher than that of the unanchored FRP U-wrap (S1A) and 45% higher than that of the FRP U-wrap with traditional embedded anchors (S1B). The intermediate saw-cut grooves successfully attracted crack formation at the desired locations, i.e., in between the strips and away from the FRP reinforcement, which contributed to not having any discernable debonding of the strips up to 3% drift. The FRP anchors, two per strip, were successful at developing the FRP reinforcement. Fracture of one of the second-next CFRP strips from the support, followed by fracture of one of the splice anchors on the first strip and subsequent substantial loss of strength, only occurred after complete plastic hinging during the second cycle at 3.8% drift (0.038 rad).

Although more disruptive than a U-wrap with FRP-embedded anchors, complete wrapping around the perimeter of the beam using FRP splice anchors through and over the slab is a better option for seismic applications on ductile regions of RC moment-resisting frame beams with a top slab (RC-MRF T-beams) given the reversible nature of the loading, and the only option when additional confinement is required, for example, to control premature buckling of the top reinforcement.

Detailed cyclic performance data of large-scale RC-MRF T-beams (i.e., including the effect of the slab) strengthened in shear with EB-FRP, as presented in this paper, fills vital data gaps in existing literature and is extremely valuable for the calibration of advanced simulation models of retrofitted RC-MRF beam members.