Flexural response of FRP-strengthened lightweight RC beams: hybrid bond efficiency of L‐shape ribbed bars and NSM technique

Abstract

This paper presents the results of an experimental study on employing near surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement technique, and L‐shape ribbed bars, for flexural strengthening of lightweight reinforced concrete (RC) beams. 18 RC beams including 14 lightweight RC beams and four normal-weight concrete beams were designed. The beams were strengthened with glass fiber-reinforced polymer (GFRP) bars and carbon fiber-reinforced polymer (CFRP) laminate in bending tests. Test parameters included: (1) different FRP materials (glass bars and carbon sheets), (2) longitudinal steel reinforcement ratio, and (3) type of strengthening technique used (NSM reinforcement or hybrid). The ultimate tensile strength, deflection, compressive and tensile strain of concrete, and failure mode of the beams were examined under four-point flexural test. Results showed that the ultimate strength of all RC beams increased between 33 and 105% compared to the control beam. The ultimate strength of beams reinforced with CFRP in the mid-span region was 10% higher than that of beams strengthened at both ends, although the former exhibited 28% lower ultimate deflection. The ultimate strength and deflection of RC beams strengthened with combined steel reinforcing bars and GFRP bars were 10% and 108% higher, respectively, compared to those of RC beams strengthened with GFRP bars only. Hybrid L‐shape ribbed bars beams showed a considerably higher ductility (up to 170% increase in the ultimate deflection) compared to other beams. The comparison of the experimental results of the ultimate strength of the beams with ACI440-2R guidelines indicated a reasonable and conservative prediction of the code expression.

1 Introduction

The evolution of operating conditions and the need for repair and retrofit of structures have received a great deal of attention in different fields of civil engineering [1]. Structures deteriorate over time, and they become damaged in some cases. Indeed, change of use of building structures, the damage caused by natural and man-made hazards, and compliance with new regulations are some of the reasons that make renovation or restoration of structures inevitable [2]. Although attempts have been made to produce a durable concrete using novel materials and additives [3], concrete structures are prone to destruction and deterioration [4]. The use of fiber-reinforced polymer (FRP) composites has become a widely accepted way to retrofit or repair RC structures [5]. Such materials have been considered by many engineers and structural designers because of their outstanding features such as a high ratio of resistance to weight, resistance against corrosion, quick and easy installation [6]. Accordingly, the use of this materials as a promising technology to improve the mechanical properties of concrete, metal, wood members as well as masonry has been considered by industry and researchers. [7]. Changing design parameters such as increasing strength and stiffness, reducing displacement, and increasing ductility and energy absorption are pursued in structural retrofitting [8]. One of the objectives of the present study is the examination of such cases. However, some other parameters such as bond-dependent coefficient, and groove dimensions and position have been considered important for calculating the empirical and analytical models [9].

Reinforcing bars and FRP fabrics are used in the tension side to increase the flexural strength of RC beams. Externally bonding (EB) and near-surface-mounting (NSM) are the most widely used and recognized methods for FRP strengthening [10]. In the EB method, the FRP material capacity cannot be fully developed because of the debonding of FRP sheet before its rupture [11]. However, in some studies, [12] no signs of failure of concrete beams strengthened by EB system were observed. Many efforts have been made to overcome these weaknesses, the most successful of which is the NSM method [13]. Despite the numerous benefits of the reinforcing materials, such methods have some disadvantages. The early and sudden failure of flexural beams strengthened with these materials is an example of these problems. This is due to debonding of FRP from concrete [14]. Over the years, a large number of experimental and theoretical studies have been performed to understand and be able to prevent such failures. These studies have revealed that NSM method had a better performance than EB method in majority of the cases [15].

Many researchers [9, 15,16,17,19] have studied the performance of concrete beams or concrete slabs of retrofitted structures under bending or cutting pressures using the NSM method. Tanarslan [16] studied the shear capacity of CFRP-strengthened RC beams by NSM system under cyclic loads. He reported that in addition to increasing the shear capacity of the beams, no delamination and debonding was observed. In a similar study, Nanni et al. [18] evaluated the shear capacity of CFRP-strengthened-prestressed concrete bridge girder through NSM. Their results indicated that the proposed technique is effective solution to enhance shear strength.

Bianco et al. [17] and Rizzo et al. [19] also proposed theoretical models and, while successfully evaluating the NSM system, emphasized the complexity of the behavior of this technique. In 2001, De Lorenzis and Nanni [20] examined the effect of bonding length and groove size on the concrete-reinforced beams strengthened with NSM-FRP bars. They reported that when the bonding length and groove size increase, the maximum of the final load increases up to 2.5 times as compared to the control specimen. Another study [21] examined the effect of bonding length and type of epoxy matrix on the performance of RC concrete beams strengthened with FRP rebar. The results showed that application of different epoxy matrix has a negligible effect on the flexural strength of the beams, while the type of bonding significantly affects the performance of the beams. They claimed that the length of the reinforcement bars should be at least 80 times bigger than the diameter of the rebar.

EL-Gamal et al. [22] evaluated the effectiveness of the NSM technique for reinforced beams strengthened with FRP glass and carbon. Their results indicated that the reinforced beam strength increased from 31 to 133 percent compared to the control beam. Furthermore, carbon fiber-reinforced beams had higher strength compared to glass fiber reinforcements, while showing a more coherent behavior at debonding time. Sharaky et al. [23] investigated the effect of different variables (including FRP materials, number of bars, epoxy matrix and reinforcement arrangement) on the flexural response of RC beams strengthened with NSM-FRP. The results of the experiments showed that increased number of rebar had a small effect on the maximum load, caused by the separation of the concrete flexural cover from the rebar. The type of epoxy matrix did not affect the stiffness of the beams. In addition, load efficiency also largely depends on the area covered by the rebar and their debonding way. In Farghal’s research [24], the fatigue behavior of strengthened RC T-beams was investigated. He reported that despite the brittle failure, the strengthened beams (with U-jacket sheets) showed a significant increase in the ductility.

Major weakness of the NSM technique is the separation of the rebar from the concrete cover [25]. Therefore, the use of newer methods, such as a hybrid technique of NSM-EB and the anchor bolt system has been recently developed to increase the efficiency of reinforced elements [26]. Morsy and Mahmoud [27] developed a new technique for attaching FRP sheets to RC beams with steel rivets. Applying the riveting technique while helping to achieve the maximum flexural capacity of the beams delays the occurrence of sudden flexural failure to an acceptable level. In another study [28], the anchored FRP plate strengthening method was considered as a successful technique for strengthening of concrete members. In their study on the RC beams strengthened with CFRP plates, Mostofinejad and Moghaddas [29] showed that the combination of the Externally Bonded-Grooving method (EB-GM) increased the bearing capacity of the beams by 39%, and the FRP failure mechanism occurred. In another study [30], the effect of the number of anchor bolt was evaluated on the response to RC beams strengthened with GFRP plates. The results of the tests showed that the use of anchor bolt increased the load capacity of concrete beams from 22 to 34% compared to control beams. Jumaat et al. [31] studied the flexural strength of reinforced beams strengthened with NSM-CFRP/steel bars and end-anchorage CFRP sheet. Their results indicated that the strengthened beams of NSM-CFRP or steel bars increased the flexural capacity up to 96%. The use of end anchors improved the flexural strength of beams by 116% compared to the control specimen.

The use of lightweight concrete has increased in many structures, such as deck, girder, and beams of bridges, as well as residential buildings in the past few years [32]. The use of lightweight concrete in the girders increases the span and decreases the size of the foundation because of the reduced dead load [33, 34]. Pre-fabricated and lightweight concrete elements have been developed in North America in 1950 and widely used in many bridges [35]. Many studies have been conducted on material behavior of lightweight concrete; however, there are limited number of studies dealing with the performance of structures constructed with such concrete in large-scale. The bending strength of lightweight RC beams strengthened with CFRP plates was evaluated in Aljaafreh [36]. The results showed that the reinforced beams had a capacity increase of 126% compared to the control samples. In 2006, Tang et al. [37] studied the effect of concrete type (lightweight and normal), rebar type and bonding matrix on the performance of reinforced beams strengthened with NSM-GFRP. They reported that the ultimate flexural strength of the strengthened beams increased from 23 to 53 percent compared to non-reinforced specimens. In the study of Rahmanpour and Afshin [38], the combined strengthening of lightweight RC beams in near joint by the use of steel plates and CFRP sheets under cyclic loads was evaluated. Their results showed that the use of steel and CFRP sheets, while able to recover the hardness of the damaged specimens, also prevented the sudden drop in strength. Also, the bonding between CFRP and concrete was higher than the bonding between steel and CFRP, indicating faster absorption of carbon elements, resulting in higher initial hardness of CFRP-strengthened specimens. Another researcher [39] studied the flexure CFRP-strengthening of lightweight RC beams. In their research, three different methods of strengthening (NSM) and two different values of steel ratio were considered as variables. The results indicated that, CFRP-reinforced beams showed little improvement in their bending strength compared to the control beams. They showed a significant increase in stiffness, and initial cracking loads, and decreased mid-cracking deflection. Also, among the strengthening systems presented in their study, the CFRP jacketing was found to be the best method for enhancing the ultimate load capacity of the beams in bending. However, this method led to a reduced ductility, making the fracture brittle and sudden.

The current research studies the flexural behavior of lightweight RC beams strengthened with NSM FRP experimentally. In addition, it aims to understand the behavior of beams to conquer and delay their undesirable failure patterns, such as sudden failure, concrete cover debonding and pull-out of FRP bars, and to increase their bending load capacity. To achieve this, a new hybrid method (L‐shape ribbed bars and FRP-NSM) has been developed. FRP materials, i.e. glass bars and carbon laminate, longitudinal steel reinforcement ratio, and types of strengthening technique were the test parameters to investigate their influence in response to ultimate tensile strength, deflection, compressive and tensile strain of concrete, and failure mode of the strengthened beams.

2 Experimental program

2.1 Test specimens

18 rectangular RC beams, including 14 lightweight concrete beams and 4 normal-weight concrete beams, were constructed. Figure 1 shows the dimensions and configuration of the beams.

Fig. 1

Dimensions and configuration of reinforced concrete beams

The beams were designed to have much higher shear capacity than flexural strength to fail in bending. All beams had two 10 mm diameter ribbed steel bars in their compression side, and two 10 mm ribbed steel bars in their tension side. Also, all specimens were reinforced with 8-mm ribbed steel stirrups placed at 50 mm spacing. The relevant relationships between flexural and shear strength for beam design were added in the “Appendix 1”.

2.2 Materials

2.2.1 Concrete

In this research, two types of structural concrete, namely lightweight concrete and normal-weight concrete were casted. The details of the concrete mix design are shown in Table 1. The lightweight concrete was made of leca coarse aggregate and silica fume. The proportions of the materials used in both types of normal and lightweight concrete were such to achieve same 28-day strength. The 28-day compressive strength was 26 MPa which measured according to ASTM C39 [40].

Table 1 Mix details of lightweight concrete and normal-weight concrete (kg/m³)

2.2.2 Steel and FRP reinforcement

10 mm and 8 mm diameter ribbed steel bar for all beams were used as longitudinal and transverse reinforcements, respectively. The yield strengths of the bars were 450 and 360 MPa, respectively. GFRP bars with a nominal diameter of 10 mm were used as reinforcement in the NSM technique. The mechanical properties of FRP rebar were obtained in accordance with ACI 440.2R-08 [41], and the results are shown in Table 2.

Table 2 Characteristics of GFRP bars used

Carbon FRP sheets were used as unidirectional woven fabrics for EB reinforcement. The properties of the sheet supplied by the manufacturer are listed in Table 3.

Table 3 Characteristics of one layer of the CFRP laminate

2.2.3 Epoxy resin

An epoxy adhesive with an ultimate tensile strength of 55 MPa, ultimate elongation of 2.4%, and a compressive strength of 76 MPa was used in this study.

2.3 Preparation of the beams

The prefabricated reinforcements were transferred to the molds, and after the checking of the coverage which was the distance between the bars from the mold, the molds were filled with concrete. The beams were removed from their molds after 24 h and placed in the water pool for curing. After 28 days, all specimens were removed from the pool and kept in the laboratory for up to 30 days. After the completion of all stages of the preparation of the beams, before the strengthening of the specimens, the surfaces of the beams as well as the areas inside the grooves and holes were washed with high pressure water to remove dust.

2.4 Strengthening of the beams

To have a better comparison, the control specimens were not strengthened. The normal beams were reinforced with GFRP rebar in tension zone and lightweight beams with steel bar in compression zone both using NSM technique. One layer of unidirectional CFRP sheets were applied to the surface of beams at both ends of GFRP U-shaped rebar. In addition, a single layer of CFRP sheet with a length of 40 mm was used as a U-shaped spiral in the middle of the beam. Table 4 and Fig. 2 show the details of retrofitting.

Table 4 Details of control and strengthened beams

Fig. 2

Cross sections of the tested beams: a LB-REF and LP-REF, b LB-NG, c LB-NGS, d LB-NGS-CM, e LB-NGS-CE, f LB-NGS-A2 and g LB-NGS-A3

To control the debonding of the concrete beam cover, the hybrid-end L‐shape ribbed bars system was used. In this method, to increase the shear capacity of the coating (fabric) and also to improve the shear capacity between epoxy adhesive and concrete surface, the 8-grade steel rebars were planted in L-shape on the tensile side of the beam (at both ends and in the middle of the beam). For this purpose, holes were made at a depth of 70 mm and a diameter of 10 mm at both ends and in the middle of the GFRP bars in the tensile face of the beam between the shear rebar stirrups. Then, in each hole, a rebar with a nominal diameter of 8 mm and a length of 70 mm and a 50 mm leg size were placed with an epoxy adhesive.

2.5 Test set-up and instrumentation

All beams were tested under four-point bending at a loading rate of 1 mm/min, as shown in Fig. 3. A universal load control machine with a capacity of 200 kN was used for this purpose. LVDTs with a precision of 0.0001 inches, fixed by steel bolts to concrete surfaces or underneath the beam, were used to measure deflections and strains. The three LVDTs were installed at the mid-span of the beam to measure the mid-span deflection of the beams. In addition, two types of strain gauges were used to measure tensile and compressive strain. Strain gauges were attached to the top and bottom of the mid-span of beams to measure the concrete strain. All test data were recorded using a data logger and a computer at 1-s intervals.

Fig. 3

The schematic of four- point flexural test set-up

It should be noted that two nominally identical concrete beams were manufactured for each test and their average results were reported. Figure 3 depicts the schematic illustration of the four-point bending test.

3 Experimental results and discussion

3.1 Summary of the tested beams results

The test results of concrete beams are summarized in Table 5. For control beams (un-strengthened beams) which were categorized as Group 1 (LB-REF), the cracking load was approximately 10.5 kN. After the steel rebar reached the yield point corresponding to a load of 43 kN, the bending cracks grew vertically, leading to the failure. With increasing loading, concrete crushed in the compression zone under the load of 51.5 kN and the beams were broken. The deflection corresponding to the yield and ultimate load at the middle of the span were measured to be 3.6 mm and 8 mm, respectively.

Table 5 Summary of test results

The cracking load of the control beams and beams without extra compressive steel bar were 10.5 and 12kN, respectively. For the rest of the lightweight beams, the cracking load fluctuated from 17 to 20 kN. The cracking load of the normal-weight concrete also was roughly 15 kN. The minimum and maximum yielding load of the strengthened beams were measured to be 45 and 88 kN, respectively, that were associated with LB-NGS and LB-NGS-A3, respectively. This represents an increase of approximately 4.6% and 104% compared to the control beam (LB-REF). After retrofitting, the ultimate capacity of the beams compared with the control beam increased significantly by as high as 105% in the case of LB-NGS-A3. In addition, the strengthening of the beams considerably affected their ultimate deflection, which increased at least 9.6% and up to 170%, compared to the control beam, corresponding to LB-NG and LB-NGS-A2, respectively.

The second group of beams (conventional concrete) experienced almost the same cracking load which were measured to be 15 kN (PB-REF) and 15.5kN (PB-NG).

The cracking load of PB-REF beam was approximately 4 kN higher than LB-REF, whereas the ultimate tensile load of these tow beams was approximately the same. In addition, the yield load capacity of PB-NG was about 17% higher than that of PB-REF beam. The deflection at the span corresponding to the yield load was similar to the results of beams in group 1. The ultimate load capacity of the PB-REF beam was 58.5 kN, whereas that of PB-NG was 80 kN, representing an increase of 37%.

Experimental observations indicated that the strengthened beams experienced more cracks in such a way that in control beams (both groups) 7 cracks were observed, whereas in strengthened beams, there were between 9 and 17 cracks. The debonding of all tested beams, except for the LB-NG beam, occurred after the yielding of the steel rebars. General conditions for deflection of beams are shown in Table 5. It should be noted that the debonding of LB-NGS-CM beam was of a shear type, mainly due to the strengthening in the middle of the span and the weakness at the two ends of the support which the shear stress is higher at these points.

3.2 Control beams

The beams were designed in such a way that their shear capacity became much larger than their bending capacity. Figure 4 shows the results of the deflection at the middle of the span and strain of concrete in the compressive and tensile zone of non-reinforced (control) beams. Under static bending load, and by creating cracks in the middle one-third part of the span and the vertical growth of cracks, LB-REF and PB-REF beams had a bending failure. In these beams, when the plastic deformation of the tensile reinforcing bar began, no resistance was created practically against the loading, and the beams were markedly deflected with a slight increase in load.

Fig. 4

Mid-span deflection and concrete strain of: LB-REF or PB-REF (left) and LB-REF beams (right)

3.3 The effect of GFRP bars

According to Fig. 5, the capacity of the beams increased by reinforcing through GFRP rod. By the addition of GFRP, the ultimate capacity of LB-NG and PL-NG beams increased by 33% and 37.5%, respectively. Such beams were different in terms of the deflection mode. The LB-NG beam was subjected to crushing of compression zone before the plastic deformation of the tensile steel rebar. This is due to the increasing of flexural strength of the beam (an increase in the area of the tensile rebar), which resulted in a brittle deflection (see Fig. 6a).

Fig. 5

LB-NG or PB-NG beams: mid-span deflection (left), and concrete strain (right)

Fig. 6

Failure mode of: LB-NG (left), and PB-NG beams (right)

In the PL-NG beam, plastic deformation of steel rebar began first, and failure occurred after the sudden debonding of the GFRP bars. Figure 6b shows the debonding of the GFRP rebar. High stress concentration in these areas (the ends of the GFRP rebar) and the lack of shear reinforcement resulted in debonding. In the control beams, after the yielding of steel rebar, the failure of concrete in the compression zone caused their rupture.

As shown in Fig. 5a, after cracking of the reinforced beams, the strengthened beams experienced a greater stiffness than control beams. After yielding tensile bars, the stiffness of reinforced beam remained larger than the control beams.

Observations and experimental measurements showed that the width of the cracks decreased with the reinforcement of the beams. For example, in the load capacity of 15 kN (about service load), the maximum cracks width in the LB-REF, LB-NG, PB-REF and PB-NG beams were 0.32, 0.28, 0.23 and 0.18 mm, respectively. This shows that the application of GFRP rebar in lightweight and conventional concrete beams reduced crack width to 12.5% and 22% respectively, compared to the control beams. In some studies [22, 23] also reported that adding or increasing of FRP reinforcement decreased crack widths.

Figure 5b presents the load-strain diagram. It can be seen that the graphs include a three-step behavior: (1) linear behavior before the cracking, (2) linear behavior with low stiffness (this stage can be attributed to the cracking of concrete) and (3) known as the yield stage, happened before the plastic deformation of steel rebar, in which the higher strains are recorded. According to other studies [22, 42], the amount of the strain measured before the beginning of plastic deformation of steel rebar (yielding threshold) is significantly affected by the reinforcement of the structural elements. A similar behavior has been observed for the strengthened beams in this paper. Investigation of the tensile and compressive strains of concrete demonstrated that the tensile strain decreased to 18% for the LB-NG beam and the compressive strain increased by 66% compared with the control beam. The reduction of bending cracks is the main reason for the tensile strain decrease [22, 43].

3.4 The effect of steel reinforcement

To prevent the early failure of compression zone concrete of LB-NG beams, the compression zone of the beams was reinforced by a steel rebar, using NSM method. According to Fig. 7, after testing the LB-NGS beams, it was observed that the application of this technique prevents the early failure of the compression zone. As the loading increased, these beams broke down due to the debonding of the GFRP rebar from the groove (Fig. 8). It was found that the debonding of the GFRP rebar occurred suddenly from the inside of the groove. Therefore, in other reinforced beams, an appropriate reinforcement method should be taken into account. As shown in Fig. 7a, the load–deflection behavior of both LB-REF and LB-NGS beams was almost identical. Both beams broke down by reaching the yield load. However, they showed a different cracking, ultimate and stiffness load after cracking. The LB-REF beam broke down at an ultimate load of 51.5 kN, while the reinforced beams with steel rebar had a higher stiffness (after cracking or bearing the yield stress) and broke down at a load of 77 kN (with an increase in final capacity of up to 50%). The maximum deflection measured for the LB-NGS beam was 15.2 mm, indicating an increase of approximately two times of the ultimate deflection compared to the control beam. In addition, this illustrates the good ductility of the beam with the proper value of the steel ratio. The comparison between the two reinforced beams LB-NG and LB-NGS suggested that adding steel rebar had a significant effect on its ductility. In addition, it could improve the ultimate capacity somehow. The ultimate deflection and capacity of the LB-NGS beam, as compared to LB-NG, increased by 73.5% and 12%, respectively, while at the deflection corresponding to the yield range, a higher load was recorded for the LB-NG beam, which represents its lower ductility and higher stiffness. According to Fig. 7b, the concrete strain graph shows that strengthening with steel rebar increased both tensile and compression strain compared to the control beam.

Fig. 7

LB-NGS beams: mid-span deflection (left), and concrete strain (right)

Fig. 8

Steel bar placement in the compression side (left), and Failure mode of LB-NGS beam (right)

The application of steel bars in the LB-NGS beam had a significant effect on reducing the crack width. At a load of 15 kN (service load), the maximum crack width for the LB-REF beam was measured to be 0.32 mm, while for the LB-NGS beam, at the cracking load, the crack width decreased to 0.22 mm which indicates a reduction of about 31%.

3.5 The effect of CFRP sheet

In the LB-NGS beams, the debonding of the GFRP rebar from the inside of the groove caused a sudden failure. To solve this problem, a single unidirectional layer of CFRP sheet was used as a U-shape spiral at the edges of the beam (at the end of GFRP bar) to prevent the phenomenon of debonding, as well as to increase the shear capacity of the concrete coating in the tensile zone. As shown in Fig. 9a, the application of the U-shape layer had a negligible effect on the ultimate load of the beam and the debonding patterns did not change. However, using this technique, the yielding load increased to 64 kN, which represents an increase of about 42% in the ultimate tensile load compared to the LB-NGS beam. Similarly, the corresponding deflection of yielding load of the LB-NGS-CE beam was 5.22 mm, indicating an increase of 74% compared to the LB-NGS beam, which represents an improvement in the ductility. The ultimate deflection of the LB-NGS-CE beam was 16.3 mm, indicating an increase of about 7% compared to the LB-NGS. According to Fig. 9b, it was found that the same behavior took place for debonding, so that both the tensile and compression strains of LB-NGS-CE beam increased in comparison to the LB-NGS beam. Experimental observations indicated that by increasing the load, the bending cracks grew and penetrated into the compression zone, which results in the beam rupture.

Fig. 9

LB-NGS-CE beams: mid-span deflection (left), and concrete strain (right)

In the LB-NGS-CM beams, a single layer of CFRP unidirectional U-shaped sheet was used in the middle one-third of the beam. As shown in Fig. 10a, the use of CFRP in the middle of the beam increased the final capacity to 87kN, which shows an increase of 13% compared to the LB-NGS beam. The application of this technique increased the yield load up to 72.5 kN, which shows an increase of about 61% in the yield load compared to the LB-NGS beam. In addition, the ultimate deflection of the beam was 12.7 mm, which represents a 16.4% of the reduction in deflection compared to the LB-NGS beam. The above result, as well as the experimental observation of the beam failure indicates a diminished ductility, in such a way that the beams were subject to a sudden shear failure. Getting away from the flexure mode weakens this strengthening. Figure 11 depicts this condition. It is also clear from Fig. 10b that the stiffness of the LB-NGS-CM beam increased in comparison to the LB-NGS beam, so that it’s tensile and compression stain decreased to 54% and 72%, respectively. This behavior can be attributed to the brittle shear failure of the LB-NGS-CM beam. Figure 11 shows the failure condition and crack in the beam.

Fig. 10

LB-NGS-CM beams: mid-span deflection (left), and concrete strain (right)

Fig. 11

Failure mode of LB-NGS-CM beam

Comparison of the results of the two beams strengthened with CFRP suggests that the use of CFRP in the middle of the beam increased the yield and ultimate load by about 13% and 11%, respectively, and the ultimate deflection reduced to 28% (see Fig. 12a). In addition, such beams showed higher stiffness, and the tensile and compression strains of LB-NGS-CM reduced to 66% and 91% compared to LB-NGS-CE, as shown in Fig. 12b.

Fig. 12

Comparison between LB-NGS-CM and LB-NGS-CE beams; mid-span deflection (left), and concrete strain (right)

3.6 The effect of hybrid technique

Two or three L‐shape ribbed bars were planted on the edges of the beam to increase the shear capacity of the coating in the tensile zone and also to increase the shear capacity between the epoxy adhesive and the concrete surface (see Fig. 13).

Fig. 13

The hybrid beam: tow (left), and three anchour bolt (right)

Compared to the LB-NGS beams, the hybrid beams showed a higher ultimate and deflection strength. In addition, the failure condition was different from previous beams. Figure 14 shows the comparison between hybrids strengthened beams and LB-NGS. It can be seen that hybrid and LB-NGS beams exhibited very similar behavior before failure or yielding. With the debonding of GFRP after the yielding of the steel tension rebar, both the LB-NGS-A2 and LB-NGS-A3 hybrid beams were broken down. As shown in Fig. 14a, the yielding load of the hybrid beams with two or three bolts compared to the LB-NGS beam was 40% and 95%, respectively. Moreover, the maximum recorded loads for them were 92 and 105 kN, respectively, which shows an increase of about 19 and 37% compared to the LB-NGS beam. Furthermore, the ultimate deflection was measured to be 16 and 21 mm, respectively, representing an increase of about 6 and 40%. This proves the effectiveness of the L‐shape ribbed bar technique. On the other hand, the comparison between the two hybrid beams shows that the increase in the number of bolts to three bolts resulted in 15% increase in ultimate capacity and 34% increase in ultimate deflection. As shown in Fig. 14b, the ultimate tensile strain of the concrete did not significantly change, but the increase in stiffness and tension was considerable. It should be also noted that the compressive strain of hybrid beams was about 2.75 times higher than the LB-NGS beam compressive strain.

Fig. 14

LB-NGS-A2 beams: mid-span deflection (left), and concrete strain (right)

The maximum crack width for two and three bolted hybrid beams reduced to 0.14 and 0.12 mm compared to the LB-NGS beam, which indicates a reduction of about 40 and 48%.

To sum up, the hybrid system had a significant effect on the efficiency of strengthened beams compared with other techniques used in this paper. In addition, it is necessary to take measures to apply a finishing on the surface before installing the FRP material.

4 Conclusion

This paper determined the effect of using GFRP bars on flexural strength and ductility of lightweight RC beams and conventional concrete. In addition, some solutions were presented for preventing the debonding phenomenon of FRP bars with concrete cover and improving the flexural response of beams. According to the results of the experiments, the following conclusions are extracted:

• All strengthened beams with FRP materials had higher flexural ultimate bending capacity compared to the control beam. This increase was in the range of 33–105 percent.

• Steel/glass bars were more effective to increase the ultimate strength of the beams compared to the glass strengthened beam. However, such beams had more brittle behavior after the application of the ultimate load.

• Middle-CFRP-reinforced beams compared to end-CFRP beams showed an increase of 11% in the ultimate strength. However, their ultimate deflection of beams decreased to 28% percent and showed a more brittle behavior when they failed.

• The hybrid strengthening system showed very good ductility behavior, along with a higher deflection in the ultimate load (16.1 and 21.5 mm). Compared with the control beam, the ultimate strength of two- and three-bolted strengthened beams increased by 78 and 104%, respectively.

• The ultimate deflection of the hybrid beams was ranged from 101 to 170% compared to the control beam, which indicates the high potential of this technique for a warning before failure. Thus, it has the potential to be considered as a significant advantage in using the GFRP- L‐shape ribbed bar combined system, in NSM strengthening technique.

• The increase in the number of L‐shape ribbed bars from two to three will result in a 14.7% increase in ultimate strength and a 34% increase in ultimate deflection of the beam.

• The debonding of all tested beams (except LB-NG) occurred after the steel bars plastic deformation. General failure states were as follows: (a) crushing of concrete (such as the control beams of both groups), (b) debonding of the FRP materials, and (c) detachment of the FRP materials.

• Debonding is the most fundamental problem of strengthening of beams using the NSM technique. The effect of this phenomenon is reduced significantly in the study using the hybrid system. However, the debonding problem still remains in force for carbon/glass strengthened beams.

• The results of the tests and its comparison with the ACI 440 Guideline represents a logical and realistic prediction with an average difference of around 15.77 percent.

Appendices

Appendix 1: Building code requirements for structural concrete (ACI 318-14) [44]

1.1 Flexural analysis

Beam with tensile and compressive rebar (compression steel below yield stress):

Step 1: Eqs. (1)–(11) determine the nominal flexural strength of the section.

$$\frac{c}{{d^{\prime}}} = \frac{{\varepsilon_{u} }}{{\varepsilon_{u} - \varepsilon_{y} }}$$

(1)

Balanced reinforcement ratio:

$$\overline{\rho }_{{\text{b}}} = \rho_{{\text{b}}} + \rho^{\prime}\frac{{f_{{\text{s}}}^{\prime } }}{{f_{y} }}$$

(2)

where

$$f_{{\text{s}}}^{\prime } = E_{{\text{s}}} \varepsilon_{{\text{s}}}^{\prime } = E_{{\text{s}}} \left( {\varepsilon_{{\text{u}}} - \frac{{d^{\prime } }}{d}(\varepsilon_{{\text{u}}} + \varepsilon_{{\text{y}}} )} \right) \le f_{{\text{y}}}$$

(3)

$$\overline{\rho }_{\min } = 0.85\beta \frac{{d^{\prime } }}{d}\frac{{f_{{\text{c}}}^{\prime } }}{{f_{{\text{s}}} }}\frac{600}{{600 - f_{y}^{\prime } }} + \rho^{\prime}\frac{{f_{{\text{c}}}^{\prime } }}{{f_{{\text{s}}} }}$$

(4)

If tensile reinforcement ratio ρ ≤ ρ̄_b and ρ ≤ ρ̄_min, the tensile steel yields at failure and the compression steel does not reach the yield, if tensile reinforcement ratio meets ρ ≤ ρ̄_b and ρ ≤ ρ̄_min.

Force equilibrium:

$$T\, = \,C_{{\text{c}}} \, + \,C_{{\text{s}}}$$

(5)

$$A_{{\text{s}}} f_{{\text{y}}} = 0.85\beta f_{{\text{c}}}^{\prime } ab + A_{{\text{s}}}^{\prime } f_{{\text{s}}}^{\prime }$$

(6)

$$a = \frac{{A_{{\text{s}}} f_{{\text{y}}} - A_{{\text{s}}}^{\prime } f_{{\text{s}}}^{\prime } }}{{0.85\beta f_{{\text{c}}}^{\prime } b}}$$

(7)

$$f_{s}^{^{\prime}} = 600\frac{{a - \beta d^{^{\prime}} }}{a}$$

(8)

By placing relation (8) in relation (7), the following quadratic equation for a is obtained:

$$a^{2} + \frac{{600A^{\prime }_{{\text{s}}} - A_{{\text{s}}} f_{{\text{y}}} }}{{0.85f_{{\text{c}}}^{\prime } b}}a - \frac{{600A_{{\text{s}}}^{\prime } \beta d^{\prime } }}{{0.85f_{{\text{c}}}^{\prime } b}} = 0$$

(9)

By solving the quadratic Eq. (9), the value of a is obtained and then the value of $f_{{\text{s}}}^{\prime }$ is determined in relation (7). Finally, the value of the nominal flexural capacity of the section can be calculated from the following equation.

$$M_{{\text{n}}} = 0.85f_{{\text{c}}}^{\prime } ab\left( {d - \frac{a}{2}} \right) + A_{{\text{s}}}^{\prime } f_{{\text{s}}}^{\prime } \left( {d - d^{\prime } } \right)$$

(10)

By determining the value of M_n, the maximum bending moment created by the force P is obtained from the following equation.

$$M_{{\text{n}}} = \frac{PL}{8} \to P_{{\text{m - max}}} = \frac{{8M_{{\text{n}}} }}{L}$$

(11)

1.2 Shear analysis

The nominal shear strength of the cross section is as follows (V_n):

$$V_{{\text{n}}} \, = \,V_{{\text{c}}} \, + \,V_{{\text{s}}}$$

(12)

$$V_{{\text{c}}} = \frac{1}{6}\sqrt {f_{{\text{c}}}^{\prime } } b_{{\text{w}}} d$$

(13)

$$V_{{\text{s}}} = \frac{{A_{{\text{v}}} f_{{{\text{yt}}}} d}}{s}$$

(14)

For beams with hinged and roller supports, the maximum shear force is 0.5P.

$$V_{{{\text{max}}}} = 0.5P \to Vn = 0.5P \to P_{{\text{v - max}}} = 2V_{{\text{n}}}$$

After the calculations, the maximum shear force was greater than the maximum flexural force, and therefore the section cracks and then fails under the influence of the flexural moment.

Appendix 2: Guide for the flexural design of FRP-externally strengthened RC beams according to ACI 440 2R 08 [41]

Like normal RC beams, Committee ACI 440 uses a rectangular tension block in its calculations. Figure 

Fig. 15

Internal strain and stress distribution for FRP- strengthened RC beams [41]

15 shows the internal strain and stress distribution for a rectangular section of FRP- strengthened under flexure at ultimate stage.

Step 1: Eqs. (13)–(15) provide the tensile properties of FRP that should be used in all design equations.

$$f_{{{\text{fu}}}} \, = \,C_{{\text{E}}} f_{{{\text{fu}}}}^{*}$$

(13)

$$\varepsilon_{{{\text{fu}}}} \, = \,C_{{\text{E}}} \varepsilon_{{{\text{fu}}}}^{*}$$

(14)

$$E_{{\text{f}}} \, = \,f_{{{\text{fu}}}} /\varepsilon_{{{\text{fu}}}}$$

(15)

Step 2: Calculating the β (ratio of depth) and E_c (elasticity modulus) of concrete (and) according to ACI 318 code [44].

The strength design approach requires that the bending strength of a member should be more than factored moment at section Eq. (16).

$$\phi M_{{\text{n}}} \, \ge \,M_{{\text{u}}}$$

(16)

Step 3: Calculating the k_m of FRP (a bond-dependent coefficient).

This coefficient usually is taken from manufacturer. For the FRP bars used in this study, the k_m was 0.75. Equations (17) gives an expression for a bond-dependent coefficient k_m.

$$k_{{\text{m}}} = \begin{array}{*{20}l} {\left\{ {1/(60\varepsilon _{{{\text{fu}}}} )(1 - nE_{{\text{f}}} t_{{\text{f}}} /360000) \le 0.90\;{\text{for}}\,nE_{{\text{f}}} t_{{\text{f}}} \le 180000} \right\}} \hfill \\ {\left\{ {1/(60\varepsilon _{{{\text{fu}}}} )(90000/nE_{{\text{f}}} t_{{\text{f}}} ) \le 0.90\;{\text{for}}\,nE_{{\text{f}}} t_{{\text{f}}} \le 180000} \right\}} \hfill \\ \end{array}$$

(17)

Step 4: Calculating the strains in the FRP reinforcement and concrete using Eqs. (18) and (19).

$$\varepsilon_{\kappa } = 0.003\left( {\frac{{d_{{\text{f}}} - c}}{c}} \right) - \varepsilon_{{{\text{b1}}}} \le \kappa_{{\text{m}}} \varepsilon_{{{\text{fd}}}}$$

(18)

$$\varepsilon_{{\text{c}}} = \left( {\varepsilon_{{{\text{fd}}}} + \varepsilon_{{{\text{b1}}}} } \right)\left( {\frac{c}{{d_{{\text{f}}} - c}}} \right)$$

(19)

Step 5: Determining the stress value in the FRP and steel bars using Eqs. (20) and (21).

$$f_{{\text{s}}} = \, E_{{\text{s}}} \varepsilon_{{\text{s}}}$$

(20)

$$f_{{{\text{fe}}}} = E_{{\text{f}}} \varepsilon_{{{\text{fe}}}}$$

(21)

Step 6: Determine the resulting from internal force and verify equilibrium using Eqs. (22–25).

$$c = \frac{{A_{{\text{s}}} f_{{\text{s}}} + A_{{\text{f}}} f_{{{\text{fe}}}} }}{{\alpha_{1} f_{{\text{c}}}^{\prime } \beta_{1} b}}$$

(22)

$$\beta_{1} = \frac{{4\varepsilon^{\prime } - \varepsilon_{{\text{c}}} }}{{6\varepsilon_{{\text{c}}}^{\prime } - 2\varepsilon_{{\text{c}}} }}$$

(23)

$$\alpha_{1} = {{\left( {3\varepsilon_{{\text{c}}}^{\prime } - \varepsilon_{{\text{c}}}^{2} } \right)} \mathord{\left/ {\vphantom {{\left( {3\varepsilon_{{\text{c}}}^{\prime } - \varepsilon_{{\text{c}}}^{2} } \right)} {\left( {3\beta_{1} \varepsilon_{{\text{c}}}^{\prime 2} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {3\beta_{1} \varepsilon_{{\text{c}}}^{\prime 2} } \right)}}$$

(24)

$$\varepsilon_{{\text{c}}}^{\prime } = \, 1.7f_{{\text{c}}}^{\prime } /E_{{\text{c}}}$$

(25)

The nominal bending strength of the external FRP reinforcement section can be calculated from Eq. (26). A factor Ψ_f = 0.85 is recommended.

$$M_{{\text{n}}} = A_{{\text{s}}} f_{{\text{s}}} \left( {d - \frac{{\beta_{1} c}}{2}} \right) + \psi A_{{\text{f}}} f_{{{\text{fe}}}} \left( {h - \frac{{\beta_{1} c}}{2}} \right)$$

(26)