Serviceability performance of fiber-reinforced lightweight aggregate concrete beams with CFRP bars

Abstract

Six lightweight aggregate concrete (LWC) beams reinforced with carbon fiber–reinforced polymer (CFRP) bars were tested under a four-point bending load with different steel fiber contents, reinforcement ratios, and clear span lengths to investigate their flexural behavior and serviceability performance. The test results showed that using steel fiber–reinforced lightweight aggregate concrete (SFLWC) and increasing the reinforcement ratio enhanced the serviceability performance of the beams. The incorporation of 0.6% by volume of steel fibers reduced the midspan deflection by 22.70%–36.87% at the same load level in service stage. At service load, all the CFRP-reinforced beams exhibited conservative deflections when compared to the deflection limits recommended by ACI 440.1 R and GB 50608, and satisfied the crack width limit of 0.7 mm. Comparing the measured maximum crack widths with the corresponding predictions revealed that the bond-dependent coefficient value of 1.4 specified in ACI 440.1 R was reasonable yet conservative. Moreover, an energy-based method was adopted to quantify the influence of the fibers on the beam stiffness. On this basis, a rational deflection model for SFLWC beams reinforced with CFRP bars was suggested.

Keywords

lightweight aggregate concrete fiber-reinforced polymer serviceability performance bond-dependent coefficient deflection model

Introduction

Deterioration of concrete structures due to corrosion of steel reinforcement incurs exorbitant maintenance costs. With regard to the inherent corrosion-resistant performance, fiber-reinforced polymer (FRP) bars are considered as a viable substitute for concrete reinforcement (Hassan and Deifalla, 2016; Wang et al., 2019). Aramid fiber–reinforced polymer (AFRP) and glass fiber–reinforced polymer (GFRP) bars are common options applied in construction field due to their price advantage. However, the low creep rupture strength and durability problems in alkaline prevent them from being widely used. Carbon fiber–reinforced polymer (CFRP) bars with advantages of high tensile strength, high creep rupture strength, and good durability in various environments have received considerable attention (Malvar et al., 2003). Many research efforts have been devoted to the behavior of composite structures with CFRP bars (Ashour and Family, 2006; Li et al., 2019; Rafi et al., 2008).

Lightweight aggregate concrete (LWC) has been increasingly applied in engineering construction because of their light weight, good heat insulation, and high sustainability (Suraneni et al., 2016; Wu et al., 2019a; Zhou and Brooks, 2019). In the light of the advantages of LWC and CFRP, their combined use in bridge architectures could significantly lower the internal force, improve the durability, and reduce the life cycle costs. The design of FRP-reinforced concrete (FRP–RC) beams is usually governed by the requirements in the serviceability limit state owing to the low elastic modulus of the FRP bars (Elgabbas et al., 2017; El-Nemr et al., 2013). Nevertheless, the drawbacks of LWC, including low crack resistance and poor bond behavior, would bring adverse impacts on both deflection and cracking behavior of the beam members.

Adding fibers to concrete has been proven to be effective in enhancing the deflection and crack width of FRP–RC beams. Gribniak et al. (2013) carried out flexural tests on five simply supported GFRP-reinforced beams and found that the post-cracking stiffness of the beams increased noticeably when steel fibers were used. Zhu et al. (2018) conducted an experimental study on flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. It was reported that the specimens with steel fibers in their tension zone experienced great benefit to the deflection and cracking behavior. Abed and Alhafiz (2019) investigated the effect of basalt microfibers on the flexural behavior of concrete beams reinforced with basalt fiber–reinforced polymer (BFRP) bars. They concluded that introducing basalt fibers to the concrete improved curvature ductility of the beams and helped restrain the opening of cracks.

Although extensive research work has been performed to characterize the cooperative working performance between CFRP reinforcements and concrete (Dong et al., 2019; Thamrin and Kaku, 2007; Thiagarajan, 2003), very few papers are available on the behavior of CFRP-reinforced fibrous LWC beams. Accordingly, in this study, six CFRP-reinforced beams fabricated using LWC and steel fiber–reinforced lightweight aggregate concrete (SFLWC) were tested under four-point bending to investigate their serviceability performance. The experimental midspan deflections and crack widths at service load were used to assess the accuracy of code provisions and previous models.

Experimental program

Material

Concrete

To assess the benefits of the steel fibers on the serviceability performance, the specimens were constructed using LWC and SFLWC. Table 1

Table 1.

Aggregate properties.

Type	Apparent density (kg/m³)	Bulk density (kg/m³)	Absorption at 24 h (%)	Aggregate size (mm)	Crushing strength (MPa)
Expanded shale aggregate	1363	750	2.9	5–16	4.2

summarizes the physical and mechanical properties of the grade 900 expanded shale aggregates used in this study. River sand with a fineness modulus of 2.56 and an apparent density of 2620 kg/m³ was used as fine aggregate. In addition to these materials, type I cement, fly ash, and superplasticizer were also used. Smooth steel fibers with a diameter of 200 μm and a length of 13 mm (Figure 1

Figure 1.

Appearance of steel fibers.

) were used as reinforcement materials for producing SFLWC. 0.6% by volume was selected to improve the concrete flexural toughness (Wu et al., 2019b). Table 2

Table 2.

Mix proportions (per m³).

Type	Aggregate (kg)	Sand (kg)	Cement (kg)	Fly ash (kg)	Superplasticizer (kg)	Water cement ratio	Steel fiber volume (%)
Lightweight aggregate concrete	616	700	400	100	4.3	0.3	0
steel fiber–reinforced lightweight aggregate concrete	616	700	400	100	4.3	0.3	0.6

details the mix proportions of the LWC and SFLWC. The compressive concrete strengths (f_cu) for each beam were carried out with three 100 × 100 × 100 mm³ cubes on the day of testing. The modulus of elasticity (E_c) and tensile strength (f_t) of the concrete are listed in Table 4 and Figure 2

Figure 2.

Uniaxial compressive stress–strain curves of LWC and SFLWC (Wu et al., 2021). Note: LWC: lightweight aggregate concrete; SFLWC: steel fiber–reinforced lightweight aggregate concrete.

displayed the uniaxial compressive stress–strain curves.

FRP bars

The CFRP bars used in this study were manufactured using carbon fibers impregnated in vinyl ester resin. The CFRP bars with a diameter of 8.65 mm had a helically wound fiber on their outside to produce grooved surface (Figure 3). Grade-400, 10.62 mm steel bars were used as transverse and top reinforcements in the specimens. The diameters and mechanical properties of the CFRP bars were determined by tests according to ACI 440.3R (ACI 2012). The CFRP bars behaved a linear elastic behavior in tension until failure and exhibited no yielding. The mechanical properties of the CFRP and steel bars are shown in Table 3.

Figure 3.

Appearance of carbon fiber–reinforced polymer bars.

Table 3.

Tensile properties of CFRP and steel bars.

Type	Diameter d_b (mm)	Elastic modulus E_f (GPa)	Tensile strength f_fu (MPa)	Ultimate tensile strain ε_fu (%)	Surface configuration
CFRP	8.65 ± 0.20	148	1705	1.16	Helically grooved
Steel	10.62 ± 0.05	E_s = 204	f_y = 445	ε_y = 2.28	Crescent-rib

Note: E_s: modulus of elasticity of the steel bars; f_y: yield strength of the steel bars; ε_y: yielding strain of the steel bars; CFRP: carbon fiber–reinforced polymer.

Specimens

Six simply supported beams with a cross-sectional dimension of 200 × 300 mm were fabricated and tested, as displayed in Figure 4. Two different reinforcement ratios (ρ_f) (0.75 and 1.03%) and three different lengths of clear span (L) (3, 3.6, and 4.2 m) were used. The total length of each specimen included two parts of 300 mm beyond the supports to prevent slippage of the CFRP reinforcements. In addition, the beams were provided with sufficient steel stirrups (10 mm at 100 mm) in the shear spans to avoid shear failure. To minimize the confining effect on the flexural behavior, the space of stirrups in the constant moment zone was increased to 200 mm. Table 4 provides the dimensions and reinforcement details of the tested beams. The specimens were labeled as follows: The beam types were identified as A–B–C. The symbols “LC” and “SLC” denote the type of the concrete, the second nomenclature identifies the reinforcement ratio, and the final nomenclature denotes the length of the clear span. For example, LC–1.03–3 indicates a lightweight aggregate concrete beam with a ρ_f of 1.03% and an L of 3 m.

Figure 4.

Specimen details (dimensions in mm).

Table 4.

Details of tested specimens.

Specimens Id	L (mm)	f_cu (MPa)	f_t (MPa)	E_c (GPa)	No. of carbon fiber–reinforced polymer (CFRP) bars	ρ_f (%)
LC–0.75–3	3000	44.6	4.3	28.0	6	0.75
LC–1.03–3	3000	43.5			8	1.03
SLC–0.75–3	3000	47.8	6.0	30.0	6	0.75
SLC–1.03–3	3000	49.5			8	1.03
SLC–0.75–3.6	3600	45.4			6	0.75
SLC–0.75–4.2	4200	40.6			6	0.75

Test setup and procedure

The specimens were tested under four-point bending with 4/15 L distances between loads. The schematic representation and actual laboratory test setup are shown in Figure 5. A 500 kN hydraulic jack applied the load to the specimens gradually through a rigid steel spreader beam. The specimens were supported on a hinged support and a roller support both with a size of 150 × 250 × 130 mm³. The beams were tested in force-control at a speed of 0.5 kN/min until cracking, and subsequently loaded in deformation-control at a rate of 1 mm/min until failure. A load cell was attached to the underside of the hydraulic actuator to monitor the applied force. To monitor beam deformation comprehensively, linear variable displacement transducers (LVDTs) were installed at midspan, loading point, and middle of the shear span, respectively. Furthermore, midspan strains of the CFRP bars were captured using strain gauges with a length of 5 mm. At the end of each load increment (4 min), crack widths were measured using hand-held optical microscopes and all the data were fed into a data acquisition system.

Figure 5.

Test setup: (a) Schematic representation; (b) Actual laboratory test setup.

Test results

Cracking moment

In the initial stages of loading, the specimens were observed visually for crack appearance. The moments and midspan deflections at first cracking of the tested beams are summarized in Table 5. The specimens with steel fibers exhibited higher cracking moments (M_cr) compared to the corresponding LWC beams since this parameter was mainly controlled by the f_t. The presence of steel fibers resulted in an average increase of 25.63% in the M_cr. As expected, test results indicated that the ρ_f and L had no evident effect on the M_cr.

Table 5.

Experimental results.

Specimens Id	M_cr (kN·m)	Δ_cr (mm)	M_u (kN·m)	Failure mode^a	Δ_s (mm)	Δ_s/L	Δ_max (mm)	Δ_max/L	w_s (mm)
LC–0.75–3	9.32	0.38	65.88	B.F	9.89	1/303	52.97	1/57	0.62
LC–1.03–3	9.97	0.37	72.25	C.C	7.71	1/389	63.12	1/48	0.41
SLC–0.75–3	11.21	0.79	79.04	FRP.R	9.94	1/302	57.85	1/52	0.52
SLC–1.03–3	13.06	0.83	102.30	FRP.R	10.88	1/276	61.79	1/49	0.63
SLC–0.75–3.6	12.31	1.24	68.85	C.C	10.48	1/344	126.52	1/28	0.44
SLC–0.75–4.2	12.67	1.37	64.09	C.C	10.39	1/404	150.41	1/28	0.26

^aB.F. denotes balanced failure; C.C. denotes concrete crushing; and FRP.R denotes FRP rupture.

Comparing beams LC–0.75–3 and LC–1.03–3, which had the same concrete type and L, revealed close midspan deflections at M_cr (Δ_cr). Similar results were observed for SFLWC beams SLC–0.75–3 and SLC–1.03–3. Beams SLC–0.75–3, SLC–0.75–3.6, and SLC–0.75–4.2 with the same concrete type and ρ_f gave an indication of the effect of L. As expected, the Δ_cr tended to increase with increasing L.

Failure mode

The tested beams exhibited three different failure modes. The first was concrete crushing observed in specimens LC–1.03–3, SLC–0.75–3.6, and SLC–0.75–4.2. The second was FRP rupture observed in specimens SLC–0.75–3 and SLC–1.03–3. The third was defined as balanced failure where compressive concrete failure followed immediately by rupture of the FRP bars and it was observed in beam LC–0.75–3.

Typical failure shapes are presented in Figure 6. As can be seen, for beams failed by concrete crushing, cracks through the lightweight aggregates (LWAs) were observed at the broken surface, which could be attributed to the low compressive strength of the LWAs. The LWC beam LC–1.03–3 (Figure 6(a)) experienced explosive spalling of concrete in the compression zone, while no serious disintegration occurred in the SFLWC beams SLC–0.75–3.6 and SLC–0.75–4.2 (Figures 4(b) and (c)), owing to the contribution from the steel fibers. In addition, the range of the crushed concrete was larger in beam SLC–0.75–3.6 than that in beam SLC–0.75–4.2, although both of them experienced concrete crushing.

Figure 6.

Failure modes: (a) LC–1.03–3; (b) SLC–0.75–4.2; (c) SLC–0.75–3.6; (d) LC–0.75–3; and (e) SLC–0.75–3 (Wu et al., 2021).

As shown in Figure 6(d), for beam LC–0.75–3 that failed by balanced failure, concrete crushing occurred with a small scale in the compression zone. In addition, both FRP rupture and balanced failure modes were characterized by a large vertical crack in the constant moment region (Figures 6(d) and (e)). The CFRP bars were fractured and the fiber bundles which wound around the bars were snapped. Horizontal cracks at the level of the CFRP reinforcement were typical behaviors seen in these failure modes. The formation of these cracks could be a result of the slip between the CFRP bars and the surrounding concrete. Moreover, the deformations of the specimens partly recovered after unloading, even in beams failed by FRP rupture, indicating that the CFRP bars did not rupture simultaneously. It could be deduced that the strength of the CFRP bars was of high discreteness.

Moment–deflection relationship

The moment–midspan deflection responses of the specimens are depicted in Figure 7. All the tested beams yielded typical bilinear relationships before the peak load, namely, a steep linear stage that described the uncracked condition and a basically linear stage that represented the reduced post-cracking stiffness. This result complimented the findings of Issa et al. (2011) for FRP-reinforced normal weight concrete (NWC) beams with and without fibers. Additionally, for specimens experienced concrete crushing (LC–1.03–3, SLC–0.75–3.6, and SLC–0.75–4.2), a nonlinear stage that corresponded to the crushing process was observed after the peak load. In this stage, the load progressively decreased with increasing deformation. The inelastic deformations near failure lent a degree of ductility for this failure mode, which was in agreement with the results reported for GFRP-reinforced NWC beams with and without fibers (Yang et al., 2012).

Figure 7.

Moment–deflection relationships: (a) Specimens with an L of 3 m; (b) steel fiber–reinforced lightweight aggregate concrete beams with a ρf of 0.75%.

Figure 7(a) indicates that increasing the ρ_f enhanced the post-cracking stiffness of the beams, regardless of the concrete type. Given the same ρ_f, using SFLWC resulted in lower deflections at the same load level. This could be attributed to the fact that the steel fibers inhibited the formation and development of the cracks. Gribniak et al. (2013) also reported the benefit offered by fibers achieved in stiffness for FRP-reinforced NWC beams. From component size point of view, a greater increase in the deflection was found in the portion from three to 3.6 m compared to that within the 3.6–4.2 m.

Midspan deflection

At service load

The design of FRP–RC beams is usually governed by the serviceability limit state requirements due to the low elastic modulus (E_f) of the FRP bars. Based on Bischoff et al. (2009) recommendation, 30% of the ultimate moment (M_u) was considered a service load (M_s) for FRP–RC beams. The midspan deflections at M_s (Δ_s) of the specimens are given in Table 5 and are represented by filled points on the curves in Figure 7.

Comparing specimens LC–0.75–3 and LC–1.03–3 revealed lower Δ_s in specimens with higher ρ_f. However, in regard to the SFLWC beams, the Δ_s of specimen SLC–1.03–3 was higher than that of specimen SLC–0.75–3. The conflicting results could be attributed to the fact that increasing the ρ_f had both positive and negative influences on the Δ_s, more specifically, improving the M_s as well as lowering the deflection simultaneously. For similar reasons, no clear effect of the incorporation of the steel fibers on the Δ_s was observed. To assess the benefit offered by the steel fibers, deflections of LWC and SFLWC beams with the same ρ_f were compared. At 19.76 kNm (service load of beam LC–0.75–3), the midspan deflection of beam SLC–0.75–3 was 36.87% lower than that of its plain counterpart LC–0.75–3. Similarly, at 23.71 kNm (service load of beam LC–1.03–3), specimen SLC–1.03–3 yielded 22.70% lower deflection when compared to beam LC–1.03–3.

Experimental results also showed that increasing the L did not significantly increase the Δ_s. This could be a result of the lower M_u of specimens SLC–0.75–3.6 and SLC–0.75–4.2 compared to that of beam SLC–0.75–3.

GB 50608 (GB, 2010) provided a deflection limit of L/200 for FRP–RC beams, namely, 18 mm for SLC–0.75–3.6, 21 mm for SLC–0.75–4.2, and 15 mm for the rest of the specimens, as illustrated in Figure 7. ACI 440.1 R (ACI, 2015) recommended an allowable deflection of L/240. On the basis of these specifications, the Δ_s of the CFRP-reinforced beams were relatively conservative. Moreover, CSA S806 (CSA, 2012) specified a stricter limit of L/360 and only two specimens (LC–1.03–3 and SLC–0.75–4.2) fulfilled this requirement.

At failure

After the peak load, the beams that were damaged by concrete crushing continued to sustain loads with increasing deformation. Thus, in order to evaluate the deformability, the maximum deflection (Δ_max) of these specimens was defined as the deflection at the residual load corresponding to 85% of the M_u, as shown in Figure 7. Table 5 presents the Δ_max of all the CFRP-reinforced beams. The ratios of Δ_max/L of the specimens with an L of 3 m varied from 1/57 to 1/48. Comparing beams LC–0.75–3 and LC–1.03–3 revealed higher Δ_max/L in beam with greater ρ_f. The same trend was seen in the case of the SFLWC beams. Moreover, specimens SLC–0.75–3.6 and SLC–0.75–4.2 yielded fairly higher Δ_max/L in comparison to their short-span counterpart SLC–0.75–3, which could be explained by their more gradual failure mode.

Strain in reinforcement

Figure 8 shows the midspan tensile strains in the FRP bars (ε_f) versus the applied moment. It should be noted that the ε_f at ultimate stage were not monitored due to the invalidating of the strain gauges. The shapes of the moment–ε_f responses were analogous with respect to the first two stages of their moment–midspan deflection relationships. This was consistent with the findings of Gribniak et al. (2013) and Kassem et al. (2011) for FRP-reinforced NWC beams with and without steel fibers, respectively. Furthermore, the effects of steel fibers and ρ_f on the moment–ε_f responses were in agreement with those on the moment–midspan deflection relationships.

Figure 8.

Moment–midspan fiber-reinforced polymer strain relationships.

Additionally, as presented in Figure 8, increasing the L while maintaining the ρ_f increased the ε_f at the same load level. Since the curves presented in the figure reflected the ε_f at the location of the gauges, based on the assumption that L had a marginal effect on the tensile strains of the FRP bars at the location of cracks (GB, 2010), it could be deduced that increasing the L delivered a more uniform deformation of the CFRP bars, and consequently a higher ε_f.

Cracking behavior

Figure 9 illustrates the relationships between the applied moment and the maximum crack width (w_max) of the tested beams. To highlight the stage of interest, the maximum service loads of the specimens are also plotted in Figures 9(a) and (b). As shown in Figure 7(a), the w_max of beam SLC–0.75–3 was smaller than that of beam LC–0.75–3 during the entire loading period. In regard to beams with a ρ_f of 1.03%, adding steel fibers decreased the w_max before the moment of 30.69 kNm (M_s of beam SLC–1.03–3). However, at high load levels, the benefit offered by the steel fibers became invalid with respect to the size of the crack widths since the fibers at the crack surfaces pulled out successively with increasing load. Similar observations were reported for the cracking characteristics of GFRP-reinforced LWC beams with short steel fibers (Wu et al., 2019a).

Figure 9.

Moment–crack width relationships: (a) Specimens with an L of 3 m; (b) steel fiber–reinforced lightweight aggregate concrete beams with a ρf of 0.75% (Liu et al., 2020).

Furthermore, for specimens with and without steel fibers, increasing the ρ_f was favorable for reducing the w_max before 30.69 kNm (M_s of beam SLC–1.03–3). The influence of the L and the reason behind it have been presented by the authors (Liu et al., 2020).

The maximum crack widths at M_s (w_s) of the specimens are given in Table 5 and are represented by black symbols on the curves in Figure 9. As can be seen, specimens with larger L exhibited smaller w_s. The benefit of increasing the L was especially true when comparing specimens SLC–6#8–3.6 and SLC–6#8–4.2, which attained comparable M_s.

Since the FRP reinforcement is noncorrodible, flexural crack width limits specified in the FRP–RC design codes were more relaxed than those for steel-reinforced elements. GB 50608 (GB, 2010) allowed crack widths of 0.5 mm for both interior and exterior exposure. ACI 440.1 R (ACI, 2015) and CSA S806 (CSA, 2012) recommended same crack width limits, namely, 0.5 mm and 0.7 mm for exterior and interior exposure, respectively. It can be seen from Table 5 that half of the specimens yielded w_s higher than 0.5 mm, while all the beams satisfied the crack width criteria of 0.7 mm.

Evaluation of design code predictions

Cracking moment

The M_cr for FRP-reinforced beams were calculated from equation (1) for both ACI 440.1 R (ACI, 2015) and CSA S806 (CSA, 2012). The modulus of rupture of the concrete f_r was expressed by equation (2) for the CSA code and equation (3) for the ACI code. Taking into account the negative effect of lightweight aggregates on the tensile strength of the concrete, the reduction factor λ=0.85 was employed as recommended by ACI 318 (ACI, 2019)

M_{c r} = \frac{f_{r} I_{g}}{y_{t}}

(1)

f_{r} = 0.62 λ \sqrt{f_{c}^{'}}

(2)

f_{r} = 0.6 λ \sqrt{f_{c}^{'}}

(3)

where f_c’ is the cylinder compressive strength of concrete.

The experimental-to-predicted cracking moment ratios (M_cr,Exp/M_cr,Pred) for the tested beams are listed in Table 6. Considering the overall average of both LWC and SFLWC beams, the M_cr,Exp/M_cr,Pred obtained from ACI 440.1R (ACI, 2015) and CSA S806 (CSA, 2012) were 1.21 ± 0.16 and 1.25 ± 0.16, respectively. For the LWC beams, the predictions according to ACI 440.1R (ACI, 2015) and CSA S806 (CSA, 2012) were in good agreement with the experimental results. In regard to the SFLWC beams, both codes provided conservative estimations, which implied that the f_r obtained using

\sqrt{f_{c}^{'}}

was not adequate for the SFLWC.

Table 6.

Experimental-to-predicted cracking moment ratios and experimental-to-predicted deflection ratios.

Specimens Id	M_cr,Exp/M_cr,Pred			Δ_Exp/Δ_Pred
Specimens Id	ACI 440.1R-15	CSA S806-12	GB 50608 2010	CSA S806-12	ACI 440.1R-15	Proposed model
LC–0.75–3	0.99	1.03	2.17	1.12	1.45	1.04
LC–1.03–3	1.08	1.11	1.52	0.95	1.20	1.18
SLC–0.75–3	1.18	1.22	1.94	0.95	1.24	0.81
SLC–1.03–3	1.32	1.37	1.55	0.95	1.17	1.06
SLC–0.75–3.6	1.27	1.31	1.63	0.83	1.26	0.98
SLC–0.75–4.2	1.42	1.46	1.36	0.67	1.11	0.75
Average	1.21	1.25	1.70	0.91	1.24	0.97
Standard deviation	0.16	0.16	0.30	0.15	0.12	0.16
COV, %	13	13	18	16	9	17

Deflection

Review of existing deflection models

In CSA S806 (CSA, 2012), moment–curvature method was employed to calculate the deflection of cracked FRP–RC members. For a beam under four-point bending, the midspan deflection was expressed as

Δ = \frac{P L^{3}}{24 E_{c} I_{c r}} {[3 (\frac{a}{L}) - 4 {(\frac{a}{L})}^{3} - 8 (1 - \frac{I_{c r}}{I_{g}}) (\frac{L_{g}}{L})]}^{3}

(4)

where

Δ

is the midspan deflection,

p

is the applied load,

I_{c r}

is the cracked moment of inertia, a is the beam shear span,

I_{g}

is the gross moment of inertia, and

L_{g}

is the uncracked beam length.

ACI 440.1R (ACI, 2015) recommended an effective flexural stiffness method to estimate the deflection of FRP–RC beams, in which an effective moment of inertia (I_e) expression incorporating tension stiffening (equation (5)) was provided

I_{e} = \frac{I_{c r}}{1 - γ_{1} {(M_{c r} / M_{a})}^{2} [1 - (I_{c r} / I_{g})]}

(5)

where

M_{a}

is the actual bending moment and

γ_{1}

is the reduction factor as follows

γ_{1} = 1.72 - 0.72 (\frac{M_{cr}}{M_{a}})

(6)

In GB 50608 (GB, 2010), the deflection prediction entailed the calculation of the short-term stiffness B_s

B_{s} = \frac{E_{f} A_{f} d^{2}}{1.15 ζ + 0.2 + 6 α_{f E} ρ_{f}}

(7)

where

B_{s}

is the short-term stiffness,

A_{f}

is the area of the FRP bars, d is the beam effective depth,

α_{f E}

is the ratio of modulus of elasticity of FRP bars to modulus of elasticity of concrete, and

ζ

is the nonuniformity coefficient of strain as follows

ζ = 1.1 - 0.65 \frac{f_{t}}{ρ_{t e} ε_{f} E_{f}}

(8)

where

ρ_{t e}

is the reinforcement ratio of the FRP bars on the basis of the effective cross-sectional area of concrete.

Comparison of experimental and predicted deflections

The experimental midspan deflections were used to assess the accuracy of the code provisions and previous models. Table 6 presents the experimental-to-predicted deflection ratios (Δ_Exp/Δ_Pred) for the specimens at M_s and Figure 10 compares the measured and predicted deflections at various load levels. At M_s, CSA S806 (CSA, 2012) gave reasonable yet conservative estimations, on average, with a Δ_Exp/Δ_Pred of 0.91 ± 0.15. ACI 440.1R (ACI, 2015) slightly underestimated the deflection predictions with average Δ_Exp/Δ_Pred of 1.24 ± 0.12. Furthermore, very unconservative theoretical deflections were obtained when calculated by GB 50608 (GB, 2010), with an average Δ_Exp/Δ_Pred of 1.70 ± 0.30.

Figure 10.

Comparison of moment–deflection curves obtained from experiments and predictions: (a) LC–0.75–3; (b) LC–1.03–3; (c) SLC–0.75–3; (d) SLC–1.03–3; (e) SLC–0.75–3.6; and (f) SLC–0.75–4.2.

In addition, the Δ_Exp/Δ_Pred based on GB 50608 (GB, 2010) tended to decrease with increasing L. In the case of CSA S806 (CSA, 2012) and ACI 440.1R (ACI, 2015), the change in the L had no significant influence on the accuracy of the predictions.

As displayed in Figure 10, when the load exceeded the M_cr, ACI 440.1R (ACI, 2015) yielded transition stages that were very similar with the experimental responses since the I_e in equation (13) continuously changed from I_g with increasing load. While each of GB 50608 (GB, 2010) and CSA S806 (CSA, 2012) exhibited an obvious increase in the deflection at M_cr, which led to an overestimation of the deflections at this load level. In the second stage, the moment–deflection relationships obtained using the deflection equations followed the same trend. However, the slopes of the experimental curves were lower than those predicted by the calculation models for all the tested beams. At service load levels, the estimated values were relatively close to the experimental results. However, at high load levels, the specimens yielded fairly larger deflections than the estimated values.

Crack width

Review of existing crack width models

The crack width formulas recommended by ACI 440.1R (ACI, 2006) and ISIS-M03 (ISIS, 2007), as presented in equations (9) and (10), respectively, were both modified by the theoretical formulas proposed by Gergely and Lutz (1968). With respect to the parameters that were used to describe the interaction between concrete and FRP bars, bar spacing s was used by ACI 440.1R (ACI, 2006) and the effective tension area of the concrete surrounding each bar A was adopted by ISIS-M03 (ISIS, 2007). Moreover, a more conservative bond-dependent coefficient (k_b) was recommended by ACI 440.1R (ACI, 2006) than ISIS-M03 (ISIS, 2007)

w = 2 \frac{f_{f}}{E_{f}} \frac{h_{2}}{h_{1}} k_{b} \sqrt{d_{c}^{2} + {(\frac{s}{2})}^{2}}

(9)

w = 2.2 k_{b} \frac{f_{f}}{E_{f}} \frac{h_{2}}{h_{1}} {(d_{c} A)}^{1 / 3}

(10)

where f_f is the tensile stress in the FRP bars, h₁ and h₂ are the distances from the centroid of the tension reinforcement and the extreme tension surface to the neutral axis, respectively, and d_c is the concrete cover measured from the centerline of the flexural reinforcement to the extreme tension surface.

Comparison of experimental and predicted crack widths

Table 7 provides a comparison between the experimental and predicted values for the maximum crack widths at M_s. The average experimental-to-predicted crack width ratios (w_Exp/w_Pred) obtained from ACI 440.1R (ACI, 2006) and ISIS-M03 (ISIS, 2007) were 0.94 ± 0.23 and 1.06 ± 0.26, respectively, which supported the validity of these two procedures.

Table 7.

Experimental-to-predicted crack width ratios and predicted k_b values.

Specimens Id	w_Exp/w_Pred		k _b
Specimens Id	ACI 440.1R-06	ISIS-M03-07	ACI 440.1R-06	ISIS-M03-07
LC–0.75–3	1.32	1.43	1.85	1.71
LC–1.03–3	0.90	1.11	1.26	1.33
SLC–0.75–3	0.92	1.00	1.29	1.20
SLC–1.03–3	0.99	1.21	1.39	1.45
SLC–0.75–3.6	0.89	0.97	1.25	1.16
SLC–0.75–4.2	0.61	0.66	0.85	0.79
Average	0.94	1.06
Standard deviation	0.23	0.26
COV, %	24	24

As shown in Table 7, the k_b calculated using the measured crack widths ranged from 0.85 to 1.85 for ACI 440.1R (ACI, 2006), and from 0.79 to 1.71 for ISIS-M03 (ISIS, 2007). The results also indicated that the k_b value of 1.4 specified in ACI 440.1R (ACI, 2006) was conservative for all the specimens except for beam LC–6#8–3. Furthermore, the 1.2 value assumed in ISIS-M03 (ISIS, 2007) was slightly unconservative for specimens with an L of 3 m while it was seen to be conservative for specimens with L of 3.6 and 4.2 m. According to both ACI 440.1 R (ACI 2006) and ISIS-M03 (ISIS 2007), the calculated k_b was lower in beams with larger L. This finding corroborated with the experimental results discussed earlier that increasing the L tended to decrease the w_max at low load levels.

Figure 11 shows a comparison between the experimental moment–w_max responses and those predicted with ACI 440.1R (ACI, 2006) and ISIS-M03 (ISIS, 2007). The theoretical curves passed through the origin since the crack width was assumed to be in proportion to the applied moment, while the experimental curves started from M_cr where the first cracking actually occurred. Hence, the code procedures showed conservative estimations at low load levels. Similar to the case of the deflection prediction discussed earlier, the increase rates of the measured crack widths were generally higher than those of the predicted values. Consequently, the w_max of the beams were underestimated by the codes at high load levels, except for beam SLC–0.75–3, for which the experimental moment–w_max relationship followed the same trend with the theoretical curve based on ACI 440.1R (ACI, 2006). Moreover, it could be observed that the degree of underestimation was higher for specimens with larger L.

Figure 11.

Comparison of moment–crack width curves obtained from experiments and predictions: (a) LC–0.75–3; (b) LC–1.03–3; (c) SLC–0.75–3; (d) SLC–1.03–3; (e) SLC–0.75–3.6; and (f) SLC–0.75–4.2.

Proposed deflection model

Deflection equation based on strain in FRP reinforcement

Wu et al. (2019a) specified the strain and stress conditions of FRP–RC elements at service load and established a deflection model based on the relationship between the average tensile strain of the FRP bar ${\bar{ε}}_{f}$ and the curvature (equation (11))

Δ = \frac{3 L^{2} - 4 a^{2}}{24} \cdot \frac{{\bar{ε}}_{f}}{d - c}

(11)

where c is the neutral axis depth from the top compression fiber.

The ${\bar{ε}}_{f}$ can be approximated as equation (12) as recommended by Wu et al. (2021)

{\bar{ε}}_{f} = \frac{M_{a}^{2} - M_{c r}^{2}}{(d - (c / 3)) M_{a} E_{f} A_{f}}

(12)

For NWC beams, the M_cr can be calculated by the equations recommended by ACI 440.1R (ACI, 2015).

Modification to average strain in FRP reinforcement

The experimental results showed that the concrete properties have significant impact on the beam stiffness. A modified version of ${\bar{ε}}_{f}$ accounting for the influence of the aggregate type and the fibers, ${\bar{ε}}_{f, SLC}$ , is proposed

{\bar{ε}}_{f, SLC} = \frac{{\bar{ε}}_{f}}{λ β}

(13)

where

λ

denotes the influence of the aggregate type and

β

represents the influence of the fibers.

For NWC beams, the elicited value of the λ = 1. For specimens cast using LWC, λ is equivalent to 0.85 owing to the low tensile strength of the concrete (ACI, 2019). Incorporating steel fibers improved the properties of the LWC, and thus helped restrain the stiffness degradation of the beams post-cracking. With this in mind, the ratio of energy density released and absorbed by concrete failure under uniaxial compression (A₂/A₁) is selected to reflect the contribution of the concrete from the definition of toughness (Figure 12), and thus β can be determined using

β = \frac{A_{2, SC}}{A_{1, SC}} \frac{A_{1, C}}{A_{2, C}}

(14)

where A_1,C and A_1,SC are the areas enclosed by the compressive stress–strain curves before the peak points of NWC and fiber-reinforced NWC, respectively; A_2,C and A_2,SC are the areas enclosed by the compressive stress–strain curves between the peak points and the corresponding points of 3 times peak strain of NWC and fiber-reinforced NWC, respectively.

Figure 12.

Schematic of A1 and A2.

Furthermore, it has been proved that specimens with higher reinforcement amount gained less benefit from fibers (Abed and Alhafiz, 2019; Wu et al., 2021). In order to reflect this influence, factor ρ_fb/ρ_f is introduced and an alternative expression of β is given in equation (15)

β = 1 + \frac{ρ_{f b}}{ρ_{f}} (\frac{A_{2, SC}}{A_{1, SC}} \frac{A_{1, C}}{A_{2, C}} - 1)

(15)

where

ρ_{f b}

is the balanced reinforcement ratio of FRP-reinforced concrete beam.

Vertification

Table 6 and Figure 10 compare the estimations calculated from the proposed equations and the measured results. The theoretical deflections according to the proposed model were in agreement with the experimental results at low load levels. At M_s, the proposed model gave the most accurate predictions among all the models studied herein, with an average Δ_Exp/Δ_Pred of 0.97 ± 0.16.

Moreover, the accuracy of the proposed model was further checked based on Wu et al. (2019a) experimental deflections for GFRP-reinforced LWC and SFLWC beams at M_s. The ratios of Δ_Exp/Δ_Pred of the members collected and tested in this study are shown in Figure 13. Considering the overall results, the proposed model realistically estimated the deflections for the LWC beams with an average Δ_Exp/Δ_Pred of 1.02 ± 0.13, and yielded conservative predictions for the SFLWC ones with an average Δ_Exp/Δ_Pred of 0.84 ± 0.13.

Figure 13.

Comparison of service deflections obtained from experiments and predictions.

Conclusion

The main aim of this study was to investigate the flexural behavior and serviceability performance of CFRP-reinforced beams conducted using LWC and SFLWC. On the basis of the experimental results and prediction models presented herein, the following conclusions are drawn:

Increasing the FRP reinforcement ratio was shown to be effective in enhancing the serviceability performance of the CFRP-reinforced LWC beams. The incorporation of 0.6% by volume of steel fibers reduced the midspan deflection by 22.70%–36.87% at the same load level in service stage.

At service load, all the CFRP-reinforced beams exhibited conservative deflections when compared to the deflection limits recommended by ACI 440.1R (ACI, 2015) and GB 50608 (GB, 2010). However, only two specimens fulfilled the requirement specified in CSA S806 (CSA, 2012). In regard to crack width, half of the beams yielded maximum crack widths higher than 0.5 mm at service load, while all the specimens satisfied the criteria of 0.7 mm.

Generally, the bond-dependent coefficient value of 1.4 specified in ACI 440.1R (ACI, 2006) was reasonable yet conservative for CFRP-reinforced LWC specimens with and without steel fibers. Moreover, the 1.2 value assumed in ISIS-M03 (ISIS, 2007) was slightly unconservative for specimens with a clear span length of 3 m but was conservative for those with clear span lengths of 3.6 and 4.2 m.

At service load, CSA S806 (CSA, 2012) and ACI 440.1R (ACI, 2015) gave reasonable estimations with average Δ_Exp/Δ_Pred of 0.91 ± 0.15 and 1.24 ± 0.12, respectively. Considering the influence of the aggregate type as well as the fibers, the proposed model gave accurate predictions with an average Δ_Exp/Δ_Pred of 0.97 ± 0.16.

Footnotes

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 National Natural Science Foundation of China (No. 51878054 and 52078042).

ORCID iDs

Yijia Sun

Tao Wu

References

Abed

Alhafiz

(2019) Effect of basalt fibers on the flexural behavior of concrete beams reinforced with BFRP bars. Composite Structures 215: 23–34.

ACI (2006) ACI 440.1R-06: Guide for the Design and Construction of Concrete Reinforced with FRP Bars. Farmington Hills, MI: American Concrete Institute.

ACI (2012) ACI 440.3R-12: Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures. Farmington Hills, MI: American Concrete Institute.

ACI (2015) ACI 440.1R-15: Guide for the Design and Construction of Structural Concrete Reinforced with Fiber-Reinforced Polymer (FRP) Bars. Farmington Hills, MI: American Concrete Institute.

ACI (2019) ACI 318-19: Building Code Requirements for Structural Concrete and Commentary. Farmington Hills, MI: American Concrete Institute.

Ashour

Family

(2006) Tests of concrete flanged beams reinforced with CFRP bars. Magazine of Concrete Research 58(9): 627–639.

Bischoff

Gross

Ospina

(2009) The story behind proposed changes to ACI 440 deflection requirements for FRP-reinforced concrete. ACI Special Publication 264: 53–76.

CSA (2012) CSA S806-12: Design and Construction of Building Components with Fibre-Reinforced Polymers. Mississauga, Canada: Canadian Standards Association.

Dong

Zhou

Wang

(2019) Flexural performance of concrete beams reinforced with FRP bars grouted in corrugated sleeves. Composite Structures 215: 49–59.

10.

Elgabbas

Ahmed

Benmokrane

(2017) Flexural behavior of concrete beams reinforced with ribbed basalt-FRP bars under static loads. Journal of Composites for Construction 21(3): 04016098.

11.

El-Nemr

Ahmed

Benmokrane

(2013) Flexural behavior and serviceability of normal- and high-strength concrete beams reinforced with glass fiber-reinforced polymer bars. ACI Structural Journal 110(6): 1077–1087.

12.

GB (2010). GB 50608:2010: Technical code for infrastructure application of FRP composites. Beijing, China: Ministry of Housing and Urban-Rural Development of the People’s Republic of China.

13.

Gergely

Lutz

(1968) Maximum crack width in reinforced concrete flexural members. ACI Special Publication 20: 87–117.

14.

Gribniak

Kaklauskas

Torres

, et al. (2013) Comparative analysis of deformations and tension-stiffening in concrete beams reinforced with GFRP or steel bars and fibers. Composites Part B: Engineering 50: 158–170.

15.

Hassan

Deifalla

(2016) Evaluating the new CAN/CSA-S806-12 torsion provisions for concrete beams with FRP reinforcements. Materials and Structures 49(7): 2715–2729.

16.

ISIS (2007) ISIS-M03-07: Reinforcing Concrete Structures with Fiber-Reinforced Polymers—Design Manual No. 3. Intelligent Sensing for Innovative Structures. Manitoba, Canada: Intelligent Sensing for Innovative Structures.

17.

Issa

Metwally

Elzeiny

(2011) Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars. Engineering Structures 33(5): 1754–1763.

18.

Kassem

Farghaly

Benmokrane

(2011) Evaluation of flexural behavior and serviceability performance of concrete beams reinforced with FRP bars. Journal of Composites for Construction 15(5): 682–695.

19.

Bian

(2019) Flexural behaviour of RC beams strengthened with combinations of two CFRP systems and P-SWRs. Magazine of Concrete Research 71(14): 749–760.

20.

Liu

Sun

, et al. (2020) Flexural cracks in steel fiber-reinforced lightweight aggregate concrete beams reinforced with FRP bars. Composite Structures 253: 112752.

21.

Malvar

Cox

Cochran

(2003) Bond between carbon fiber reinforced polymer bars and concrete. I: Experimental study. Journal of Composites for Construction 7(2): 154–163.

22.

Rafi

Nadjai

Ali

, et al. (2008) Aspects of behaviour of CFRP reinforced concrete beams in bending. Construction and Building Materials 22(3): 277–285.

23.

Suraneni

Anleu

PCB

Flatt

(2016) Factors affecting the strength of structural lightweight aggregate concrete with and without fibers in the 1,200-1,600 kg/m(3) density range. Materials and Structures 49(1–2): 677–688.

24.

Thamrin

Kaku

(2007) Bond Behavior of CFRP bars in simply supported reinforced concrete beam with hanging region. Journal of Composites for Construction 11(2): 129–137.

25.

Thiagarajan

(2003) Experimental and analytical behavior of carbon fiber-based rods as flexural reinforcement. Journal of Composites for Construction 7(1): 64–72.

26.

Wang

Uji

, et al. (2019) Experimental investigation of stress transfer and failure mechanism between existing concrete and CFRP grid-sprayed PCM. Construction and Building Materials 215: 43–58.

27.

Sun

Liu

, et al. (2019a) Flexural behavior of steel fiber-reinforced lightweight aggregate concrete beams reinforced with glass fiber-reinforced polymer bars. Journal of Composites for Construction 23(2): 04018081.

28.

Yang

Wei

, et al. (2019b) Mechanical properties and microstructure of lightweight aggregate concrete with and without fibers. Construction and Building Materials 199: 526–539.

29.

Sun

Liu

, et al. (2021) Comparative study of the flexural behavior of steel fiber-reinforced lightweight aggregate concrete beams reinforced and prestressed with CFRP tendons. Engineering Structures 233: 111901.

30.

Yang

Min

Shin

, et al. (2012) Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars. Composites Part B: Engineering 43(3): 1077–1086.

31.

Zhou

Brooks

(2019) Thermal and mechanical properties of structural lightweight concrete containing lightweight aggregates and fly-ash cenospheres. Construction and Building Materials 198: 512–526.

32.

Zhu

Cheng

Gao

, et al. (2018) Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. Construction and Building Materials 161: 587–597.