Evaluating shear capacity in reinforced concrete deep beams with web openings strengthened using fiber-reinforced polymer and fiber-reinforced cementitious matrix

Abstract

This research systematically compares the effectiveness of Carbon Fiber-Reinforced Polymer (FRP) and Fabric-Reinforced Cementitious Matrix (FRCM) in shear strengthening of reinforced concrete (RC) deep beams featuring web openings. Through a comprehensive experimental program, six RC beams were subjected to shear tests, considering variations in the number of layers for both FRCM and FRP, employing a U-wrapping configuration. Recorded parameters include load-deflection curves, ultimate strength, cracking patterns, failure modes, and strains in steel bars, allowing a comprehensive comparison between strengthened and un-strengthened RC beams. The study compares observed shear strengths from experiments with shear capacities predicted by proposed models for RC beams strengthened with FRCM and FRP, following codes such as ACI 440.2R-17, CSA S806-12, Eurocode 2, and ACI 549.4R-20. Increasing layers enhanced shear strengths and post-elastic stiffness. The presence of substantial openings led to early shear cracks and reduced strength. CFRP improved shear strength by 13.99% (1-layer) and 18.12% (2-layer), while FRCM strengthened layers by 20.2% (1 layer) and 29.3% (2 layers). FRCM outperformed in strength and stiffness, while FRP excelled in ductility and concrete confinement. Experimental and calculated results varied based on ACI, CSA, and Eurocode, with ACI providing consistent and accurate results. CSA’s calculation surpassed experiments, emphasizing its consideration of effective fabric design strain.

Keywords

shear strengthening deep beam fabric-reinforced cementitious matrix carbon fiber-reinforced polymer opening

Introduction

Deep beams made of (RC) play a pivotal role in distributing loads effectively within high-rise buildings. Including openings in the web of these beams is common for accommodating utilities like air-conditioning, ventilation, and various cables. However, these openings can significantly weaken the beams, leading to stress concentration and diagonal cracks around their corners. The presence of these cracks results in elevated transverse strain, diminishing the effective strength of the diagonal strut in concrete. As structures evolve, the need to repurpose or modify RC deep beams may arise due to factors like concrete deterioration, changes in code requirements, or increased design loads. Strengthening, a preferred alternative to renewal for its cost and time efficiency, has been a research focus, particularly exploring advanced methods such as FRCM and FRP. The predominant approach for strengthening involves externally bonding FRP to concrete surfaces, with existing literature containing studies specifically addressing the effects of FRP application in beams with openings.

Mansour and El-Maaddawy (2021) investigated the effectiveness of near-surface-mounted carbon FRP (NSM-CFRP) in restoring shear strength to RC deep beams with openings. Allawi et al. (2021) used CFRP to enhance the performance of reinforced concrete deep beams with large web openings, noting a 20% to 47% increase in failure load compared to untreated beams. Jasim et al. (2020) numerically studied 16 RC deep beams with various opening sizes and shear span/depth ratios, demonstrating that FRP laminates increased the load required to initiate the first diagonal crack under certain conditions. Aksoylu et al. (2020) found that CFRP strengthening for shear-deficient RC beams with circular web openings is effective only up to a specific shear span/depth ratio. El-Maaddawy and Sherif (2009) observed a significant strength increase (up to 73%) in RC deep beams with web openings when externally bonded carbon FRP sheets were applied. Kumari and Nayak (2021) reported that externally bonded glass FRP sheets greatly improved shear capacity in RC deep beams without shear reinforcements and with web openings.

Nevertheless, FRP has some drawbacks, such as high costs, incompatibility with concrete surfaces, difficulty applying it in wet conditions, and sensitivity to high temperatures. For this reason, different composite materials, especially the FRCM, are becoming an alternative to FRP. FRCM combines a high-strength fabric embedded into inorganic materials such as cement-based mortars. In contrast to the epoxy resin found in FRP, the cementitious matrix utilized in FRCM boasts superior thermal capacity and demonstrates enhanced compatibility with the underlying concrete substrate (Awani et al., 2016). Recently, the FRCM has shown its potential in replacing FRP laminates in retrofitting and strengthening concrete structures. In recent decades, several researchers have focused on shear retrofitting and strengthening methods by utilizing FRCM. Triantafillou and Papanicolaou (2006) along with other researchers (Al-Salloum et al., 2012; Awani et al., 2016; Azam and Soudki, 2014; Blanksvärd et al., 2009; Guo et al., 2021; Loreto et al., 2015; Ombres, 2015; Tetta et al., 2018a; Trapko et al., 2015; Zhang et al., 2019; Aksoylu et al., 2020; Aljazaeri and Myers, 2017; Allawi et al., 2021; Al-Salloum et al., 2011, 2012; Blanksvärd et al., 2009; Brückner et al., 2008) conducted various experimental studies on the shear behaviors of RC beams strengthened using FRCM. Wakjira and Ebead (2019) demonstrated that FRCM significantly enhances the load capacities of RC deep beams, with near-surface embedded FRCM outperforming externally bonded FRCM and preventing debonding failures. The internal transverse reinforcement configuration has minimal impact, and a strut and tie model accurately predicts load capacities with less than a 6% error for both strengthening techniques. D’Antino et al. (2020) presented an analytical model for calculating the shear strength of RC members reinforced with FRCM composites, building upon existing models for FRP shear strengthening. Validation against experimental results demonstrates good accuracy, with further validation required for wider insights. Ombres and Verre (2022) investigated the structural response of U-wrapped SRG shear-strengthened RC beams, finding significant debonding effects on shear capacity and proposing analytical methods for prediction. Gonzalez-Libreros et al. (2017) provided a comprehensive literature review on shear strengthening of RC beams using FRCM composites, highlighting the significant increase in shear strength, effectiveness relative to matrix compressive strength. However, to date, no examination has been done on the utilization of FRCM for enhancing shear strength in RC beams with web openings.

This paper highlights a significant research gap concerning the lack of repair work on RC beams with openings. It acts as a catalyst for further investigations, shedding light on the comparative performance of FRCM and FRP in shear strengthening and prompting a comparative analysis of existing design approaches for RC beams with larger openings, thereby holding substantial implications for structural engineering and construction. This paper reports an experimental study on the shear performance of RC beams with web openings, examining the effectiveness of FRCM and FRP laminates in strengthening the shear capacities of six beams with rectangular openings. A three-point loading testing schema is conducted in this experimental campaign. Two un-strengthened beams with and without openings are used as the reference specimens. In this experimental program, the U-wrapping strengthening configuration is employed for both FRCM and FRP, focusing on exploring the impact of varying the number of fiber layers in each material. The research assesses the observed shear strengths obtained from experiments and contrasts them with shear capacities predicted by proposed models for RC beams strengthened using FRCM and FRP. The evaluation is conducted in accordance with standards such as ACI 440.2R-17, CSA S806-12, Eurocode 2, and ACI 549.4R-20.

Experimental program

Description of the tested specimens

All beams shared a consistent total length of 1300 mm and featured an identical cross-section measuring 150 mm × 500 mm. Six deep beams were built, each incorporating web openings of the same dimensions and placements, while one beam was constructed without any openings, serving as a solid reference. Openings were positioned at the specimens’ midpoint of the shear span, completely disrupting the inherent load path, specifically, the line connecting the bearing plates at the loading and support points. Web openings, commonly circular or rectangular, are prevalent in practical applications, often categorized as “small” or “large”. This study considered two 200 mm × 200 mm rectangular openings with a size-to-depth ratio of 0.4, classifying them as large openings (Mansur and Tan, 1999), as illustrated in Figure 1.

Table 1 provides information on the test matrix and the details of the test beams. The specimens were divided into three series based on the strengthening method. In the reference series, specimens “RB” and “RB-O” represent the reference beams that were not strengthened, without and with the openings. “FRCM” and “FRP” are beams series strengthened in shear by FRCM and FRP, respectively. The numerical labels “1” and “2” within the names of the tested beams indicate the respective number of reinforcement layers applied.

Table 1.

Summary of test specimens.

Series	Specimens	Stirrup configuration in sections with/without opening (mm)	Reinforcement ratio of FRP/fabric (%)	Strengthening configuration
Reference	RB	$ϕ$ 6-90	-	Reference without opening
Reference	RB-O	$ϕ$ 6-75/60	-	Reference with openings
FRCM strengthening	FRCM-1	$ϕ$ 6-75/60	0.141	U-wrapping one layer of FRCM
FRCM strengthening	FRCM-2	$ϕ$ 6-75/60	0.282	U-wrapping two layers of FRCM
FRP strengthening	FRP-1	$ϕ$ 6-75/60	0.148	U-wrapping one layer of FRP
FRP strengthening	FRP-2	$ϕ$ 6-75/60	0.296	U-wrapping two layers of FRP

The design strategy aimed to ensure that shear stirrups and longitudinal rebars failed in the shear before bending failure. Longitudinal reinforcement included deformed bars with diameters of 14 mm and 18 mm at the top and bottom, respectively, while shear reinforcement comprised smooth bars with a 6 mm diameter to prevent local cracks. Beam RB incorporates ϕ6 stirrups spaced at 90 mm intervals, contributing to a transverse reinforcement content of 0.42%. The transverse reinforcement comprises ϕ6 stirrups spaced at 60 mm in the section without the opening. In contrast, the regions above and below the opening consist of ϕ6 stirrups spaced at 75 mm, with corresponding reinforcement content of 0.63% and 0.5%, respectively. Furthermore, the longitudinal tension reinforcements include 3-ϕ18 and 2-ϕ14 reinforcements above and below the opening, as depicted in Figure 1.

Material properties

A local manufacturer supplied the concrete to guarantee that all specimens were cast in a single concrete batch, ensuring uniform mechanical properties. The average uniaxial compressive strength, determined from six cylinder samples measuring 150 mm × 300 mm, was 27.5 MPa. The concrete’s compressive strength was deliberately selected to be relatively low, falling within the typical range observed in older construction projects that recently require repair and strengthening. Eighteen bars with 18 mm, 14 mm, and 6 mm diameters underwent tensile testing to determine yield strength and elastic modulus. All steel bars’ mechanical characteristics and dimensions conform to ASTM A370 specifications (2022), as outlined in Table 2.

Table 2.

Properties of reinforced bars.

Rebar diamter (mm)	E_f (GPa)	f_y (MPa)	A_s (mm²)
18	203	364.5	254.5
14	201	358.2	153.9
6	201	279.8	28.3

Commercially available glass fabric and CFRP composite were utilized to strengthen the beams, as illustrated in Figure 2. The carbon FRP-strengthened beams incorporated a unidirectional dry fiber sheet, while the FRCM-strengthened beams utilized a bidirectional glass fabric. Table 3 compiles the manufacturer-reported values for overall area weight, elastic modulus, tensile strength, and thickness (or area per meter) of the carbon FRP sheet.

Table 3.

Characteristics of glass fabric and CFRP materials.

Type	Product name	E_F (GPa)	f_fu (MPa)	Area (mm²/m)	Weight (g/cm³)
Glass fibres	SITgrid200KE	120	1800	105.67	2.68
Carbon FRP	UT70-20G	230	4000	111	200

FRCM composites incorporate a bidirectional AR-glass fabric and a stabilized inorganic matrix, making them suitable for strengthening applications. The reinforcement involves intertwining alkali-resistant glass filaments into yarn to form the fabric structure. The fabric exhibits a uniform spacing of about 17.5 mm, a surface weight of 647 g/m², and an equal 50-50% weight distribution in both directions. Featuring a fine fineness of 2400 tex and styrene-butadiene rubber impregnation, the yarn within the fabric possesses a cross-sectional area of 105.67 mm²/m in each direction along its length. The yarn displays a tensile strength of 1800 MPa, and its elastic modulus is approximately 120 GPa. A cementitious matrix was formulated by mixing Portland cement, intermediate- and fine-size sand, fly ash, and water. Six 40 × 40 × 160 mm prismatic concrete samples were evaluated for compressive and flexural strength after 28 days, revealing values of 43.5 MPa and 4.5 MPa respectively. The evaluation was conducted according to ASTM C348-21 (2021) for flexural strength and ASTM C349-18 (2018) for compressive strength of hydraulic-cement mortars, utilizing sections of prisms broken in flexure.

Casting and strengthening procedures for RC beams

The reinforcement cage was constructed externally and later inserted into the formwork following the attachment of strain gauges to the designated individual rebars and stirrups (as illustrated in Figure 3). All six beams were poured at once with a single concrete batch, followed by the application of dampened burlap and plastic sheets to the concrete surface for curing. Before applying the FRP or FRCM system for reinforcement, the concrete surface underwent mechanical grinding to remove loose sand grains. The strengthening configuration, as depicted in Figure 4, featured a continuous U-wrapped pattern along the shear span, upgrading the chord section beneath the opening through a complete wrap.

Two specimens underwent external bonding with one and two CFRP composite sheets in this investigation. Before applying the CFRP sheets, a thorough cleaning was conducted on the concrete beam’s surface to eliminate dust, and weaker sections were ground away. To mitigate stress concentration, a 15 mm radius rounded the corner of the edge beam. The strengthening process involved external bonding around a web opening using FRP sheets arranged in a U-warp pattern on the tension side. Initially, a base layer of resin was applied to the dry concrete surface, and CFRP sheets were meticulously placed using a plastic roller to ensure thorough resin impregnation. To ensure continuity and avert shear delamination, the CFRP sheets were bonded to the bottom chord of the beam beneath the rectangular web opening, followed by the application of a second resin layer spread over the fibers using a plastic roller.

Following the guidelines specified in ACI 549.4R-20, the FRCM strengthening layer was applied to strengthened beams in a continuous U-wrapped configuration. The wrapping scheme for FRCM specimens resembled that of FRP-strengthened specimens, as illustrated in Figure 4. The process began with applying the cementitious matrix through trowelling and placing the fabric on top with slight pressure. The second matrix layer was applied onto the glass fabric while the first layer was still in its fresh state. In instances with multi-layer fabrics, the process was iterated, resulting in top and bottom cementitious matrix layers surpassing 5 mm, and a matrix overlay between fabrics measuring approximately 4-5 mm. The final step included trowelling the last matrix overlay and achieving a smooth surface. Note that, the lower chord section beneath the opening received full-wrap strengthening. All beams underwent a 28-day curing period under laboratory conditions following the strengthening process.

Experimental arrangement and instrumentation

The experimental program utilized a three-point bending test, and the setup is illustrated in both a photograph and a schematic view in Figure 5. A screw-type testing machine was used to exert the load, utilizing a steel cylindrical roller on a steel bearing block. The Linear Variable Differential Transformer (LVDT) was positioned at the mid-span bottom location of the beams to monitor vertical displacement, while Figure 6 illustrates the recorded strains in both transverse and longitudinal steel reinforcements throughout the tests.

Experimental results

Cracking patterns and modes of failure

Figures 7, 9, and 11 illustrate crack patterns observed on the specimens at failures. The crack patterns were notably similar among samples RB-O, FRCM1, and FRCM2, where concrete cracks were clearly visible at the surface. Despite the FRP sheet coverage on specimens FRP1 and FRP2, the crack patterns observed following the delamination of the FRP layer bore a resemblance to those found in specimens reinforced with FRCM. The RB specimens, which act as reference beams without openings, displayed a typical deep-beam crack pattern originating from the point of applied force to the support. All specimens exhibited nearly symmetrical cracks across the middle cross-section, with failure occurring on one side due to diagonal crack expansion, the strengthened layer’s delamination, or the compression strut’s concrete crushing.

References beams

Figure 7 depicts the cracking patterns and failure modes of two reference beams. Following the design process, these beams underwent failure characterized by a conventional diagonal tension mode and concrete crushing in the compression zone. For the reference beam RB (without an opening), an initial inclined crack emerged at an applied load of approximately 250 kN, extending from the loading point to the support as the load increased. Vertical cracks emerged at the beam’s centre at approximately 300 kN, extending to the bottom parts before coming to a halt. Furthermore, an additional shear crack formed and developed on the opposite side of the specimen, ultimately leading to the failure of reference beam RB at approximately 581.7 kN.

The presence of openings led to the early observation of the initial shear crack in beam RB-O, occurring at a load of approximately 125 kN. This diagonal crack has occurred at the corner of the opening on the left side. Limited and short flexural cracks then formed at the centre of the beam. The number of shear cracks continued to develop as the load increased. They propagated toward the loading point and two supports from the corners of openings. Compared to the RB beam, the damages appeared fewer at the centre of the beam. However, the shear cracks opened much more in RB-O, with the final failure occurring at approximately 329.6 kN. Figure 8 illustrates the distribution of a typical crack pattern, and the cracks are labelled for subsequent analysis.

Beams strengthened by FRP

Figures 9 and 10 illustrate the failure mode of the FRP-strengthened specimens, showcasing damage marked by FRP delamination, the propagation of inclined shear cracks, and concrete crushing at the upper chord. Noteworthy cracks, such as Cp1, Cp2, Ce4, and Ce7, are visible on the FRP-strengthened specimens. The Ce6 crack on the FRP specimens exhibits a smaller extension and is fainter than FRCM-strengthened specimens. Delamination occurs when the strengthened specimens reach their ultimate strength, leading to a decrease in applied load. As depicted in Figure 10, the delamination of two strips, DB1 and DB2, is noticeable. The initial strip, DB1, is located above the opening chord, whereas the second strip, DB2, is positioned beside the opening near the support. DB1 separates from the substrate concrete, while DB2 detaches due to delamination at the interfacial surface. This phenomenon is ascribed to the close proximity of DB1 to the applied force, resulting in increased local compression, evident from the presence of longitudinal cracks (Cp1) on the top surface of the beam.

Moreover, strip DB1, characterized by a short bonding length, experienced an inclined crack attributed to the passage of C4 shear, with the separation of strip DB1 occurring in the force range of 350-390 kN for FRP-1 and 380-420 kN for FRP-2. In contrast, strip DB2, located in the compression strut area to transmit force to the support, has a smaller compression force, and its anchor length is much larger than that of DB1. As a result, DB2 only delaminates when the Ce2 crack widens, indicating the loss of strength in the strengthened specimens. Even with FRP-2 strengthened with twice as many layers as FRP-1, both specimens display similar damage patterns (Figure 9), and the ultimate strength of FRP-2 does not show a substantial increase compared to FRP-1—426.3 kN and 396.2 kN, respectively (Figure 14). The specimen damage is not a result of FRP rupture but rather stems from FRP delamination, the expansion of inclined cracks, and the crushing of compressive struts in the concrete. Consequently, increasing the number of FRP layers only marginally enhances concrete strength, stiffness, and restraint in the bearing strips, leading to reduced deformation in tensile FRP layers and delayed delamination.

Beams strengthened by FRCM

Figure 11 illustrates the distributions of cracks in beams strengthened with FRCM. The crack pattern observed on the FRCM-strengthened specimens closely resembles that of the control sample. Compared to the reference specimens, the FRCM strengthening layer delays the formation of shear cracks until higher loads are applied. Initial cracks at the Ce2 and Ce3 corners manifest at forces ranging from 110 kN to 120 kN, followed by perpendicular bending cracks in the range of 160-200 kN. The last cracks to form and escalate into destructive ones are Ce4 and Ce5, which are emerging at a force level of about 300-350 kN. Damage in the FRCM-strengthened specimens is attributed to the expansion of shear cracks, resulting in the pulling-out of some yarns with short bonding lengths and the peeling off of concrete cover in certain areas (Figure 12). Notably, the delamination observed in the FRCM-strengthened beams closely resembles that in the FRP-upgraded specimens at the position of the DB1 strip.

Load-deflection curves, ultimate strength and stiffness

Load versus deflection relationships

Figure 13 depicts the comprehensive correlation between all test specimens’ applied load and midspan deflection. Figure 14 presents the relationship between the ultimate load obtained by the specimens and their strengthening ratio (defined as the ratio of the ultimate load of the strengthened specimens to the reference beam RB-O). It is evident that the reference beam RB (without an opening) exhibits the highest stiffness and strength, while the RB-O beam displays the lowest. The ultimate strengths of strengthened specimens fall within the range of values between the RB and RB-O specimens. The specimens’ behaviour can be classified into two stages—ascending and descending. Before reaching the maximum force, the force-deflection relationship tends to be linear. Despite the appearance of cracks, they do not induce abnormal points on the load-deflection curve. This performance indicates beams damaged by shear with small shear spans or influenced by the effect of deep beams where force transmission relies on the structure of compression struts. After reaching the maximum load, the descending segment of the load-deflection curves varies based on the structure of the specimens.

Figure 13 illustrates two reference beams, namely RB and RB-O. At deflection values below 8 mm, both specimens exhibit a linear load-deflection relationship. Subsequently, the beam RB tends to become more “rounded” as it reaches the maximum load, reflecting the effect of failure due to both shear and the concrete crushing in the compression zone. Specimen RB-O, immediately after reaching the ultimate strength, experiences a sudden decline in applied load, attributed to the abrupt expansion of the shear crack. The existence of openings (RB-O specimens with an opening ratio of 0.4) diminishes the shear strength by 76.5% and 53.3% of the stiffness at the ultimate load P_max compared to the reference specimen without openings. Both beams tend toward brittle failure and a dramatically decreased applied loads.

Figure 13 also shows the load-deflection relationship of FRP-strengthened beams in comparison to the reference beam RB-O, revealing that CFRP strengthening layers enhance shear strengths by 13.99% for 1-layer and 18.12% for 2-layer. However, the stiffness of the strengthened beams remains nearly unchanged compared to the control beam before reaching the maximum load. The beams lose their strength when the upgraded FRP sheet above the opening chords detaches. It is noteworthy that FRP-strengthened beams do not exhibit a sudden load drop compared to the reference beam RB-O. While FRP-2 beams do not significantly increase ultimate strength compared to FRP-1 beams, they exhibit better post-maximum load-bearing capacity. This is attributed to the strengthening of the lower chords of the opening in a closed form (full wrap), which confines the concrete chord and restricts crack expansion. As a result, the strength of the test specimens can be sustained after reaching the peak load.

The strengthening effectiveness of FRCM beams is illustrated in Figure 14. As evident in the load-deflection curves, the increased number of fabric layers has postponed shear failures in the tested beams. The beams experienced a 20.2% improvement in shear strength with one layer of fabric and a 29.3% enhancement with two layers. In contrast to the FRP specimens, strengthening with FRCM significantly increased the stiffness compared to the reference specimen. However, the increase was not linear, with a rapid rise of 66.5% for FRCM-1 and 86.5% for FRCM-2 specimens. The increased stiffness of FRCM specimens is also ascribed to the involvement of the cementitious matrix. After reaching the ultimate load, the FRCM specimens exhibited a significant decrease in strength, consistent with the observed failure pattern in the experimental tests. In particular, FRCM specimens displayed damage resulting from the extension of diagonal cracks in both the upper and lower chords of the opening. While the glass yarns did not rupture, their relatively small elastic modulus diminished their ability to restrict crack expansion and confine concrete.

The higher initial slope observed in the load-deflection curve of FRCM strengthened specimens, despite carbon fibers having a higher elastic modulus than glass in FRP, can be attributed to several factors (Figure 15). The interaction between the cementitious matrix and fibers in FRCM may enhance stiffness, with tension stiffening playing a significant role before cracking. Effective bonding between the fiber grid and cementitious matrix, coupled with interaction among cracks, results in a stiffness far exceeding that of the fabric alone. Additionally, differences in bonding mechanisms between FRCM and FRP could influence the structural response, potentially providing better load transfer mechanisms with FRCM. The enhancement of the beam cross-section through FRCM strengthening is notably superior to that achieved by FRP. These factors collectively contribute to the observed behavior in the load-deflection curves.

Energy dissipation and ductility

Figure 16 describes the dissipated energy regions in the tested specimens, including the elastic, maximum, and plastic failure energy. Figure 17 provides the dissipated energy and ductility values of the experimental specimens. FRP-strengthened beams typically demonstrate elevated ductility and the highest energy dissipation. Compared to the control beam RB-O, the ductility ranged from 39.7% to 72.7% higher. Meanwhile, FRCM-strengthened specimens only experienced an increase ranging from 5.8% to 17.4%. Regarding dissipated energy, FRP-strengthened specimens outperform opening beams, particularly in plastic energy dissipation, while the FRCM-strengthened beams exhibited comparable energy dissipation to the reference specimen.

Strains at critical locations

Figure 18 depicts the relationship between applied loads and strains in longitudinal steel bars, with strains showing a slight increase at loads below cracking loads, followed by a significant rise beyond the cracking loads. Comparatively, the deformation in longitudinal reinforcement at the same location does not significantly differ for beams with openings, indicating that the bending strength has a limited impact on the behaviour of the specimens. Notably, specimens without openings tend to experience larger deformation in longitudinal reinforcement, with beam RB showing yielding at position H4 (middle of the beam), consistent with the observed flexural failure.

While strains in longitudinal steel bars generally exhibit similar trends at the same locations, there is a notable distinction for strengthened beams compared to the control beam. Steel reinforcement in these beams experiences a slower increase in deformation compared to unstrengthened ones, especially evident in longitudinal reinforcement where the deformation is larger in unstrengthened beams for the same applied load. Essentially, the inclusion of FRP/FRCM layers contributes to load-bearing alongside the steel reinforcement. Additionally, the number of strengthened layers impacts deformation, with an increase in layers correlating to decreased deformation in the reinforcement. When comparing FRP and FRCM, the latter proves slightly more effective in reducing deformation in steel reinforcement than FRP.

Figure 19 illustrates the relationship between applied load and strain in the stirrups. While the deformation of stirrups at identical locations on the beams appears largely similar overall, closer inspection reveals distinct variations in stirrup strains among the specimens. For FRP-strengthened beams, the strain values are significantly reduced as shear cracks predominantly occur on the side of the opening without the strain gauge attached to the stirrup. Generally, both strengthening systems reduce deformation in stirrups under equivalent load levels. The number of strengthening layers also impacts the deformation of stirrup reinforcement. In particular, beams reinforced with multiple layers will experience a slower rate of deformation in the steel reinforcement. This effect is more pronounced with FRP than the FRCM layer, attributed to the higher elastic modulus of carbon FRP compared to the glass fabric used in FRCM. Contrary to the strains recorded in longitudinal reinforcement, most stirrups yielded as the specimens reached their ultimate capacities. This further confirms that shear failure dominated in these strengthened specimens.

When comparing V1 and V3 (the stirrups above and below the opening of the specimens strengthened with FRP), the deformation at position V1 is smaller than that at V3, indicating the restraining effect of full-wrap carbon FRP below the opening compared to U-wrap above the opening. However, for V1 and V3 on the FRCM specimens, the deformation at V1 is larger, which aligns with the wider inclined crack observed on the FRCM specimens below the opening, demonstrating that the restraining effect of FRCM is not as significant as that of FRP (also evaluated in the ductility of specimens strengthened with FRP).

Regarding strain position V2 (strain at the stirrup next to the opening, near the support) on the specimens, it shows the effect of the compression bar transmitting force to the supports. Initially, V2 experiences compression deformation, but as crack Ce6 forms and expands, the stirrup at this position undergoes tension, resulting in a quick increase in deformation.

For position V4 (strain at the stirrup next to the opening, near the applied load), this region experiences more tension than position V2. The strain diagram for V4 further illustrates the effectiveness of FRP in participating in tension with the stirrups, as the deformation of V4 on specimens strengthenedwith FRP is significantly smaller than those upgraded with FRCM.

Theoretical analysis and discussion

Given the lack of prior research on comparing existing design approaches for RC beams with larger openings strengthened with FRP and FRCM, this section necessitates a thorough examination through empirical tests. Experimental shear strengths are compared with predicted shear capacities for RC beams strengthened with FRP (following ACI 440.2R-17 (2017), CSA S806-12 (2012), Eurocode 2 (2023)) and for structures strengthened with FRCM (according to ACI 549.4R-20, 2020). It is crucial to emphasize that, as of the current date, there is no existing European standard specifically addressing key aspects such as load capacity or deflection for RC structures strengthened with FRCM. In such cases, designers commonly turn to the works by Triantafillou and Papanicolaou (2006), which adopts the design methodology of Eurocode 2 for FRCM-strengthened structures. Moreover, of the three codes, ACI and CSA codes consider shear strength as the combined strength of both concrete and steel stirrup, whereas Eurocode exclusively accounts for the strength of steel transverse reinforcement.

Designing shear according to code principles

The shear strength of a strengthened beam follows code guidelines, combining the shear contribution of RC beams with external reinforcement like FRP sheets or glass fabric.

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

(1)

where

V_{c} + V_{s}

is the RC beam’s initial strength, representing the strength attributed to the external reinforcement provided by the FRP sheet or glass fabric. Several suggestions exist for determining the value of

V_{f}

Shear capacity of RC beams strengthened by FRP

ACI 440.2R-17

As per (ACI 440.2R-17, 2017), the shear contribution of FRP sheets in RC beams is estimated like stirrups, assuming a 45° inclination angle for the main crack. The key difference is using the effective strain of FRP sheets, which can be smaller due to premature debonding. Guidelines for determining effective strain consider FRP properties, strengthening configuration, and concrete strength in estimating the shear contribution of FRP sheets.

V_{f} = \frac{A_{f v} f_{f e} (\sin α + \cos α) d_{f v}}{s_{f}}

(2)

Here, A_fv represents the area of FRP sheets (calculated as $A_{f v} = 2 n t_{f} w_{f}$ ), where n_f is the number of layers of FRP sheets, t_f is the thickness of the FRP sheets, and w_f is the width of the FRP sheets; Additionally, f_fe represents the effective tensile strength of FRP, determined by a calculation ( $f_{f e} = E_{f} ε_{f e}$ ) involving E_f (tensile modulus of elasticity of FRP) and ε_fe (FRP effective strain); d_fv stands for the effective depth of FRP; s_f, the spacing between FRP strips; $α$ , the angle of the main direction of FRP sheets to the longitudinal axis of the beam; ACI 440.2R-17 provides the recommended equation for ε_fe, factoring in concrete strength, shear strengthening configurations (complete wrapping, U-wrap, and two-side bonding), and FRP sheet stiffness. It is important to note that ACI sets a maximum limit of 0.004 for ε_fe.

CSA S806:12 (2012)

CSA S806-12 provides guidelines for building components with FRP. Its shear model simplifies the Modified Compression Field Theory, considering factors like shear span-to-depth ratio, axial stiffness, member size, and concrete strength. Equation (3) calculates shear capacity for concrete members without transverse reinforcement, cast from normal-strength concrete.

V_{f} = \frac{ϕ_{F} A_{F} E_{F} ε_{F} d_{v} (\sin θ + \cos α_{F}) \sin α_{F}}{s_{F}}

(3)

Hence, the formulas for assessing the strength contribution of FRP in RC structures share a common principle. Discrepancies among standards or recommendations arise from variations in the FRP sheet’s effective strain and whether the inclined crack’s angle is considered.

Eurocode 2 (2023)

Eurocode 2 standards for designing RC structures proposes equation (4) to estimate the shear contribution of FRP.

V_{f} = \frac{A_{f v} f_{f w d} d_{f v} (\sin θ + \cot α) \sin α}{s_{f}}

(4)

Shear capacity of RC beams strengthened by FRCM

ACI 549.4R-20 (2020)

As of now, ACI 549.4R-20 stands as the sole standard addressing FRCM and its use for reinforcing concrete structures. While Germany and Italy have released guidelines in this field, they are limited to technical guidelines.

V_{t} = n A_{f} f_{f v} d_{f}

(5)

where A_f represents the area of fabric reinforcement per unit width effective in shear; n is the number of fabric layers, and d_f denotes the effective depth of the FRCM shear reinforcement.

Eurocode 2 (Triantafillou and Papanicolaou, 2006)

Triantafillou developed a validated model for assessing the shear strength of FRCM-reinforced RC beams. It employs a strut and tie approach similar to that used for FRP-strengthened beams, assuming continuous fiber yarns in two directions inclined at an angle β_i relative to the beam’s axis (Figure 20). The formula for calculating the shear strength of the FRCM layer is as follows:

V_{T} = \sum_{i = 1}^{2} \frac{A_{t i}}{s_{i}} (ε_{t e, i} E_{f i b}) 0.9 d (\cot θ + \cot β_{i}) \sin β_{i}

(6)

Here, $ε_{t e, i}$ represents the effective strain of fiber yarns in direction i (usually about 0.8% for carbon fabric), $E_{f i b}$ is the elastic modulus of the fiber yarns in direction i, d is the effective depth of the cross-section, $A_{t i}$ is twice the cross-sectional area of each fiber yarn in direction i, $s_{i}$ is the distance between fiber bundles along the component axis, and $θ$ is the angle of inclination of the oblique crack to the component axis.

Evaluating shear strength determined based on code calculations

Note that CSA S806-12(CSA S806-12, 2012) and Eurocode 2 lack standards for FRCM materials. However, determining shear strength for fabric reinforcement involves multiplying the fabric area, effective tensile strength, and effective depth. The difference in standards primarily pertains to the effective strength of the fabric (i.e., the effective design strength of fabric reinforcement). By treating fabric reinforcement in the FRCM system like FRP sheet material and applying calculation formulas from CSA S806-12 and Eurocode 2 for FRCM, the shear strength of reinforced beams can be computed, as shown in Table 4.

Table 4.

Comparison between calculation models based on ACI, CSA, Eurocode 2, and experimental results.

Specimens	Ultimate load	ACI 318-19	ACI 318-19	ACI 440.2R-17		CSA A23.3:19	CSA A23.3:19	CSA S806:12		EN 1992-1-1:2023	EN 1992-1-1	EN 1992-1-1:2023
FRP Group		$V_{c} (k N)$	$V_{s} (k N)$	$V_{f} (k N)$	Exp./Total	$V_{c} (k N)$	$V_{s} (k N)$	$V_{f} (k N)$	Exp./Total	$V_{c} (k N)$	$V_{s} (k N)$	$V_{f} (k N)$	Exp./Total
RB-O	164.8	34.8	84.4	-	1.4	38.7	76		1.4	-	76		2.2
FRP-1	187.9	34.8	84.4	40.8	1.2	38.7	76	50.5	1.1	-	76	63	1.4
FRP-2	194.7	34.8	84.4	78.2	1.0	38.7	76	99.4	0.9	-	76	126.2	1.0
FRCM Group				ACI 549.4R-20								Triantafillou and Papanicolaou (2006)
FRCM-1	198.1	34.8	84.4	26.4	1.4	38.7	76	13.1	1.6	-	76	35.1	1.8
FRCM-2	213.1	34.8	84.4	52.9	1.2	38.7	76	31	1.5	-	76	70.3	1.5

ACI 440.2R-17	CSA S806:12	Eurocode 2 (EN 1992-1-1:2023)	ACI 549.4R-20
$V_{f} = \frac{A_{f v} f_{f e} (\sin α + \cos α) d_{f v}}{s_{f}}$	$V_{f} = \frac{ϕ_{F} A_{F} E_{F} ε_{F} d_{v} (\sin θ + \cos α_{F}) \sin α_{F}}{s_{F}}$	$V_{f} = \frac{A_{f v} f_{f w d} d_{f v} (\cot θ + \cot α) \sin α}{s_{f}}$	$V_{f} = V_{t} = n A_{f} f_{f v} d_{f}$
Full-wraps $ε_{f e} = 0.004 \leq 0.75 ε_{f u}$	$α_{F}$ represents the angle of inclination of the FRP sheet in relation to the beam’s axis	Full-wraps $f_{f w d} = 0.8 \times k_{r} \times f_{f u d}$	$ε_{f v} = ε_{f u} \leq 0.004$
U-wraps $ε_{f e} = κ_{v} ε_{f u} \leq 0.004$	$ε_{F}$ is calculated as:	U-wraps $f_{f w d} = \frac{2}{3} \frac{n s_{f}}{l_{b f, \max, k} \times [(\cot θ + \cot α_{f}) \sin α_{f}]} f_{b f R d}$	$f_{f v} = E_{f} ε_{f v}$
$κ_{v} = \frac{k_{1} k_{2} L_{e}}{11900} ε_{f u} \leq 0.75$	$ε_{F} = 0.006 < 0.75 {ε_{F}}_{u}$ for fully wrapped sections
$L_{e} \frac{23300}{{(n t_{f} E_{f})}^{0.58}}$	$ε_{F} = 0.005 < 0.75 {ε_{F}}_{u}$ for sections with U-shaped stirrups with a proven anchoring system
$k_{1} = {(\frac{{f^{'}}_{c}}{27})}^{\frac{2}{3}}$	$ε_{f e} = κ_{v} ε_{f u} \leq 0.004$ for sections with U-shaped stirrups without anchoring system
	In this case, the coefficient $κ_{v}$ is identical to ACI 440.2R-17

^aTotal = $V_{n} = V_{c} + V_{s} + V_{f}$

Comparing results between experimental data and calculation models based on ACI 440.2R-17, ACI 549.4R-20, CSA S806-12, and Eurocode 2 reveals variations in the accuracy of predictions. For reference beam RB-O, the difference ratio between experimental and ACI/CSA S806-1 calculations is 1.4, while Eurocode 2 exhibits a ratio of 2.2 due to its neglect of the shear contribution of the concrete beam.

The FRP group shows closer alignment with theoretical predictions than the FRCM group in strengthened beams. The ratio between experimental and ACI/CSA S806-1 calculations for the FRP group ranges from 0.9 to 1.2, while Eurocode results in a ratio of 1.0 to 1.4. In the FRCM group, the ratio ranges from 1.2 to 1.6 for ACI and CSA S806-1, and is 1.5 to 1.8 for Eurocode 2.

ACI codes consistently provides results closer to experimental data for FRP and FRCM-strengthened specimens. Notably, in the case of beam FRP-2, the calculated value according to CSA S806-1 surpasses the experimental results. This highlights CSA S806-1’s consideration of the effective design strain of the fabric in shear strength calculations, potentially exceeding values obtained from other codes. Nevertheless, it is crucial to note that if failure modes involve delamination or damage to the substrate concrete, the strengthened fabric may not reach the values permitted by CSA S806-1’s code.

Conclusions

In conclusion, this research systematically compared the effectiveness of FRCM and Carbon CFRP in shear strengthening of RC deep beams featuring web openings. Through a comprehensive experimental program, six RC beams were subjected to shear tests, considering variations in the number of layers for both FRCM and FRP, employing a U-wrapping configuration. Moreover, the investigation compared the observed shear strengths from experiments with the shear capacities anticipated by proposed models for RC beams reinforced with FRCM and FRP, adhering to standards like ACI 440.2R-17, CSA S806-12, Eurocode 2, and ACI 549.4R-20. Based on the test results and analytical analysis, the following conclusions can be derived:

(1) The presence of substantial openings in the deep beams led to the early detection of initial shear cracks, resulting in a reduction of shear strength by 76.5% and 53.3% of the stiffness at the ultimate load P_max compared to the reference specimen without openings.

(2) Regarding CFRP strengthening layers, a 1-layer wrapping showed a 13.99% improvement in shear strength, while a 2-layer wrapping demonstrated an 18.12% enhancement. Conversely, FRCM-strengthened layers exhibited a 20.2% and 29.3% increase in shear strength for beams with one and two layers of fabric, respectively.

(3) The experimental findings underscore that augmenting the number of layers in both FRCM and FRP significantly enhances the deep beams’ shear strengths and post-elastic stiffnesses. Notably, FRCM outperforms FRP in improving both strength and stiffness, showcasing its superior effectiveness in shear-strengthening applications. However, FRP offers a distinct advantage in improving ductility and, when properly anchored, effectively confines the concrete.

(4) Comparisons between experimental and calculated results based on ACI, CSA, and Eurocode standards reveal variations. For RB-O specimen, the ACI/CSA ratio stands at 1.4, while Eurocode yields a ratio of 2.2, disregarding the shear contribution from concrete.

(5) In strengthened beams, the FRP group closely aligns with theoretical predictions, with ACI consistently providing accurate results. Notably, CSA’s calculation for specimen FRP-2 surpasses experimental findings, highlighting its consideration of effective fabric design strain, although this may not hold in delamination scenarios.

Footnotes

Acknowledgments

The authors extend our sincere gratitude to the technical engineers at the Structural Laboratory of the University of Transport and Communication for their invaluable assistance and support. Huy-Cuong Nguyen was funded by the Postdoctoral Scholarship Program of Vingroup Innovation Foundation (VINIF), code VINIF.2023.STS.16.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Vietnam Ministry of Education and Training; B2023-GHA-07.

Correction (August 2024):

Article updated to correct the funding statement; see DOI: for details.

ORCID iDs

Huy Cuong Nguyen

Xuan Huy Nguyen

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