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Structural Behavior of High-Strength Concrete Slabs Reinforced with GFRP

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DOI: 10.3390/polym13172997

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Article

Structural Behavior of High-Strength Concrete Slabs

Reinforced with GFRP Bars
Maher A. Adam, Abeer M. Erfan, Fatma A. Habib and Taha A. El-Sayed *

Department of Structural Engineering, Reinforced Concrete Structures, Shoubra Faculty of Engineering,

Benha University, 108 Shoubra St., Shoubra, Cairo 11629, Egypt; maher.adam@feng.bu.edu.eg (M.A.A.);
abeer.erfan@feng.bu.edu.eg (A.M.E.); Fatma.Habiba@feng.bu.edu.eg (F.A.H.)
* Correspondence: taha.ibrahim@feng.bu.edu.eg

Abstract: In this manuscript, structural testing was conducted on high-strength concrete slab spec-
imens to investigate the behavior of such specimens when reinforced with a locally produced GFRP
reinforcement. Subsequently, a finite element model (FEM) was constructed and validated against
the experimental results. In the experimental phase, a total of eleven specimens (nine were rein-
forced with GFRP, while two were reinforced with conventional steel) were constructed and tested.
The slabs dimensions are 700 mm × 1750 mm with variable thickness from 100 mm to 150 mm and
different reinforcement ratios using different diameters. The structural behavior of the tested slabs
was investigated in terms of ultimate load, ultimate deflection, load–deflection relationship, and
crack pattern. Additionally, a nonlinear finite element model using the software ANSYS 2019-R1
was constructed to simulate the structural behavior of slabs reinforced with GFRP bars. The results
obtained from the finite element analysis are compared with experimental results. The outcomes
Citation: Adam, M.A.; Erfan, A.M.; showed that the contribution of GFRP rebars in concrete slabs improved slab ductility and exhibited
Habib, F.A.; El-Sayed, T.A. higher deflection when compared with traditional steel rebars. Good agreement between experi-
Structural Behavior of High-Strength mental and nonlinear analysis was obtained.
Concrete Slabs Reinforced with
GFRP Bars. Polymers 2021, 13, 2997. Keywords: structural performance; exponential study; GFRP bars; high-strength concrete (HSC),
https://doi.org/10.3390/ nonlinear analysis; ANSYS 2019-R1
polym13172997

Academic Editor:
Abdel-Hamid I. Mourad
1. Introduction
Received: 18 August 2021 Corrosion of steel reinforcing bars is one of the major problems that shorten the life-
Accepted: 2 September 2021 time serviceability of reinforced concrete (RC) structures [1–4]. This has led to the devel-
Published: 3 September 2021 opment of new concrete-reinforcing materials. With their high strength and good corro-
sion resistance, fiber-reinforced polymers (FRPs) represent a good alternative. In compar-
Publisher’s Note: MDPI stays neu- ison to steel, the distinctive properties of FRP materials are high strength, relatively low
tral with regard to jurisdictional elastic modulus, and elastic response to failure. Given these different properties, the be-
claims in published maps and insti-
havior of concrete elements reinforced with FRP is likely to differ markedly from those
tutional affiliations.
that employ conventional steel reinforcement. This difference is characterized not only by
a different load–deflection response but also by a change in the mode of failure. The fail-
ure mechanism of FRP-reinforced concrete elements is due to them being relatively brittle,
even in flexure. This gives rise to major concerns by structural engineers who are more
Copyright: © 2021 by the authors.
familiar with the under-reinforced design philosophy developed for steel RC structures,
Licensee MDPI, Basel, Switzerland.
This article is an open access article
which ensures a ductile failure to give plenty of warning. However, Ospina and Nanni
distributed under the terms and
[5] concluded that different deflections can be predicted for members reinforced with FRP
conditions of the Creative Com- bars that have similar stiffness but different ultimate tensile strength. Because deflection
mons Attribution (CC BY) license is a problem associated with the serviceability limit state, the procedure should not be
(http://creativecommons.org/li- linked to ultimate limit state parameters [6–8]. Lately, the flexural performance of FRP-
censes/by/4.0/). RC elements has been widely studied. Benmokrane et al. [9] conducted an experimental
and theoretical evaluation of the flexural performance of RC beams reinforced with glass

Polymers 2021, 13, 2997. https://doi.org/10.3390/polym13172997 www.mdpi.com/journal/polymers

Polymers 2021, 13, 2997 2 of 24

FRP and steel. Masmoudi et al. [10] investigated the effects of reinforcement ratio on
cracking patterns, deformation, flexural capabilities, and failure mechanisms of GFRP and
steel-reinforced concrete beams. They evaluated the impact of compression reinforcement
when calculating the final flexural capacity of the beams. Nonetheless, the impact was
dismissed as insignificant. FRP and steel-reinforced concrete parts react differently in
terms of serviceability. Alsayed et al. [11] found that GFRP beams could precisely antici-
pate flexural capabilities using the ultimate theory of designs. Toutanji and Saafi [12]
changed the factor of the power in the equation of Branson to account for its experimental
results with the elasticity of the bar and the ratio of reinforcement. Toutanji and Deng [13]
demonstrated that ACI 440.1R-01 can successfully estimate deflections and crack width in
one-layer FRP-bar beams with crack width. However, ACI 440.1R-01 may be employed
once some parameters have been changed when FRP bars are arranged in two layers. Thi-
agarajan [14] reported the findings of an experimental and analytical investigation com-
paring the flexural performance of RC beams reinforced with sandblasted carbon basalt
fiber rods composite rods. He studied 12 beams comprising three control steel beams that
were evaluated for features of deformation and strength. Experimental results from
pullout testing revealed that bonding of sandblasted rods is not a serious problem. The
effective inertia prediction moment of the FRP-RC beam was investigated by Moussavi
and Esfahani [15]. This article presents new equations based on evolutionary algorithms
and experimental data to estimate the effective time of FRP-RC beams in inertia. The test-
ing results were highly associated with the expected values using the suggested equa-
tions, particularly with high strengthening ratios and high load-levels. Rashid et al. [16]
reported the flexural behavior of 10 HSC beams reinforced with aramid-fiber-reinforced
polymers (AFRPs). The study recommended that ductility measurement for FRP beams is
useful. The necessity to reduce the maximum distances between the stirrups as defined in
the existing code has also been recognized, and recommendations have been given for
sections with high shear forces coupled with considerable bending moments. Ashour [17]
presented the flexural and shear capacity of 12 GFRP beams. Comparisons between the
flexural capacity derived from theoretical analysis and those determined experimentally
indicate satisfactory consent. Nayal and Rasheed [18] proposed a model investigating the
tension stiffening of RC beams reinforced with steel and FRP bars. The study’s findings
give useful model parameters for steel and FRP-RC beams. According to Kara and Ashour
[19–21], the low elastic modulus of FRP bar results in significant crack width and deflec-
tions when compared with steel bars. Kassem et al. [22] investigated the serviceability of
FRP beams reinforced with various types and reinforcement ratios. To assess the accuracy
of such prediction models according to ACI Committee 440-H., the experimental results
were compared with CSA 2002 and ACI Committee 440 2006 accessible models. Al-Sunna
et al. [23] showed high ultimate capacities of moment compared obtained from nearly all
codes. Barris et al. [24] evaluated the deflections and cracking in 14 GFRP RC beams for
typical predicted models. The impact of the important factors was examined, and the ap-
propriateness of various predicted models and the empirical coefficient modification were
explored. Mahroug et al. [25,26] examined continuous concrete slabs strengthened with
basalt and carbon FRP bars. The combined flexure–shear collapse mechanism was seen in
all slabs. Furthermore, they demonstrated that increasing the bottom reinforcement of
slabs is more successful than increasing the top reinforcement in enhancing load-carrying
capacity and reducing midspan deflections. Dundar et al. [27] reported the load–displace-
ment conduct of FRP and steel multispan RC beams. The deflection of FRP or steel RC
beams was determined using a numerical technique. This study can offer a helpful
method for calculating deflection for any type of reinforcement. Wang et al. [28] assessed
the polymer tendons under sea conditions in both the prestressed basalt and hybrid fiber-
reinforced tendons. The interior corrosive steel wires caused basalt and steel wire to de-
grade considerably more quickly. Chenggao et al. [29] investigated the distribution in a
pultruded glass or carbon hybrid bar and absorption of water under temperatures and
hydraulic pressures. The increased temperatures and hydraulic pressure accelerated the
Polymers 2021, 13, 2997 3 of 24

water diffusion in the hybrid bar. Demakos et al. [30] provided a numerical and experi-
mental study for a structured curved frame. The thin-arched ultimate load achieved val-
ues similar to those seen for the mortar compressive strength employed. There was good
agreement between experimental and numerical results. In an optimal design of a steel
building, Papavasileiou and Pnevmatikos [31] submitted an investigation against an
earthquake and the gradual cord collapse. This study indicates that the gradual collapse
can bring the whole structure to failure locally by a structural component. The findings of
this research show the promising cable potential as a way of increasing the building’s
progressive resistance to collapse.
This paper presents the flexural behavior of one-way concrete slabs reinforced with
locally manufactured GFRP bars. Currently, experimental data conducted for HSC slabs
reinforced with GFRP bars are scarce. So, an experimental study was done to study the
behavior of HSC slabs reinforced with GFRP bars with different reinforcement ratios var-
ying from 0.8 µb to 1.2 µb (balanced reinforcement ratio) using different bars diameters.
Eleven slabs 1750 mm in length, 700 mm in width, and 100 mm to 150 mm in depth were
loaded and tested until failure. Nonlinear finite element analysis was conducted using
ANSYS 2019-R1 to verify the obtained experimental results in terms of load–deflection
curves, deflection, and crack pattern for all tested slabs.

2. Experimental Program
The experimental study was investigated in the Housing and Building National Re-
search Center (HBNRC), Giza, Egypt. This study was performed to study the structural
performance of HSC slabs reinforced with GFRP bars under flexural load. The ultimate
load, ultimate deflection, concrete and GFRP bar strains, and crack pattern was obtained.

2.1. Experimental Study

2.1.1. Concrete Mix
The concrete mix of 60 MPa at 28 days compressive strength was used. Table 1 shows
the weights of materials used. Concrete cubes were poured during pouring of the concrete
slabs, as shown in Figure 1.

Table 1. Material weights.

Per m3 of Concrete
Materials
(fcu = 60 MPa)
Cement 575 kg/m3
Coarse aggregate 1100 kg/m3
Fine aggregate 580 kg/m3
Water 138 kg/m3
Silica fume 50 kg/m3
Superplasticizer 18 kg/m3

Figure 1. Concrete cubes.

Polymers 2021, 13, 2997 4 of 24

2.1.2. Compressive Strength Test

Concrete cubes of 150 × 150 × 150 mm dimensions were tested after 28 days under a
universal testing machine of 2000 kN capacity for compression, according to ECP’2018
[32], as shown in Figure 2. Table 2 shows the compressive strength of the tested cubes.

Figure 2. Concrete cubes under testing machine.

Table 2. Compressive strength test results.

Compressive Strength (MPa)

Cubes
28 days
C−1 63.9
C−2 68.2
C−3 66.7
Average 66.3

2.1.3. GFRP Bars

The tensile strength of used GFRP bars varied between 490, 650, and 750 MPa for
diameters of 8 mm, 10 mm and 12 mm, respectively, as shown in Table 3. This tensile
strength for nominal diameters of 8 mm, 10 mm, and 12 mm was tested in the Housing
and Building National Research Center (HBNRC), as shown in Figure 3, according to
ECP’2018 [32].

Table 3. GFRP bar tensile stresses.

Diameter (mm) Tensile Strength (MPa)

8 490
10 650
12 750
Polymers 2021, 13, 2997 5 of 24

(a) (b)

(c)
Figure 3. Tensile test: (a) steel bar; (b) GFRP bar of Φ 10 mm; (c) different bar diameters of Φ8, 10,
and 12 mm.

2.1.4. Description of Tested Slabs

The experimental program consists of four groups of concrete slabs with dimensions
of 1750 mm in length and 700 mm in width and different heights from 100 mm to 150 mm.
All tested slabs have the same 60 MPa compressive strength. The first group (SP1 and SP2)
represents control slabs with balanced steel reinforcement ratios of 0.16 and 0.24, respec-
tively, and concrete height of 100 mm. The second group is “Group I” (SP3, SP4, and SP5),
with balanced fiber reinforcement ratios of 0.80, 1.00, and 1.20, respectively, and concrete
height of 100 mm. The third group is “Group II” (SP6, SP7, and SP8), with balanced fiber
reinforcement ratios of 1.20 and concrete height of 120 mm. The final group is “Group III”
(SP9, SP10, and SP11), with balanced fiber reinforcement ratios of 1.20 and concrete height
of 150 mm. Table 4 and Figure 4 showed the details for the tested slabs.

Table 4. Specimen details.

Specimen Thickness Reinforcement

Specimen Group Diameter (mm) RFT. Type
ID (mm) Ratio %
Group I Control

SP1 100 8 0.16 µb Steel

SP2 100 10 0.24 µb Steel
SP3 100 8 0.80 µfb GFRP
SP4 100 8 1.00 µfb GFRP
SP5 100 8 1.20 µfb GFRP
Polymers 2021, 13, 2997 6 of 24

SP6 120 8 1.20 µfb GFRP

Group II
SP7 120 10 1.20 µfb GFRP
SP8 120 12 1.20 µfb GFRP
SP9 150 1.20 µfb GFRP

Group III
8
SP10 150 10 1.20 µfb GFRP
SP11 150 12 1.20 µfb GFRP

Figure 4. Slab dimensions and reinforcement.

2.2. Test Setup

Eleven HSC slabs were examined under two-point load with a 500 mm load distance,
as in Figure 5. The test was performed in the National Building Research Center under a
universal testing machine with a maximum capacity of 5000 KN. Outputs were recorded
using LVDTs and strain gauges.

(a) (b)
Polymers 2021, 13, 2997 7 of 24

(c)
Figure 5. Test setup: (a) slab details, (b) flexural test setup, (c) LVDT and strain gauge locations.

3. Experimental Results and Discussion

The results obtained from the experimental test were given in terms of ultimate load,
ultimate deflection, load–deflection curves, crack pattern, and load strains for concrete
and reinforcement rebars as follows.
Concrete cracking and tension (CCT) cracks, GFRP rupture (GR), flexural failure (FF).

3.1. Ultimate Load

Table 5 shows the ultimate load for all slabs. The ultimate load for the control group
(SP1 and SP2) was 148.00 kN and 139.00 kN, respectively. This is due to the decreased
diameter of bars and increased bonding between the concrete and steel bars, which agrees
with the results recorded by Janus et al. [33].

Table 5. Experimental results.

Ultimate Deflec-
Specimen First Crack Ultimate Load
Specimen ID tion Δu Mode of Failure
Group (kN) (kN)
(mm)
Con-

SP1 75 148.00 6.75 FF

trol

SP2 75 139.00 4.89 FF

Group II Group I

SP3 50 87.85 2.74 GR

SP4 80 149.30 4.91 GR + TF
SP5 85 154.40 3.72 CCT
SP6 100 180.70 7.91 CCT
SP7 120 149.30 4.91 GR
SP8 125 129.30 4.79 GR
SP9 100 313.75 11.03 GR
Group
III

SP10 150 256.02 6.55 CCT

SP11 200 212.10 7.80 CCT

For Group I (SP3, SP4, and SP5), Slab SP3 recorded the lowest ultimate load of 87.85
kN, which was also lower than the control slabs by a decreasing ratio of 39.0%. This is due
to the small reinforcement ratio, which led to rupture of GFRP bars. However, for SP4 and
SP5, the ultimate loads were 149.30 kN and 154.40 kN, respectively.
For Group II (SP6, SP7, and SP8), Slab SP6 recorded the highest ultimate load of 180.70
kN, which was higher than Slabs SP7 and SP8, in which the ultimate loads were 149.30 kN
and 154.40 kN, respectively. It was recorded that a smaller diameter indicated high perfor-
mance with concrete slabs as in SP6, which recorded an ultimate load of 180.70 kN, higher
than that obtained from Slabs SP7 and SP8, which recorded 149.30 kN and 129.3 kN, respec-
tively.
Polymers 2021, 13, 2997 8 of 24

Slabs (SP9, SP10, and SP11) of Group III recorded a higher ultimate load compared
to the second group “Group II” because of increased concrete thickness. The ultimate
loads were 313.75 kN, 256.02 kN, and 212.10 kN for SP9, SP10, and SP11, respectively.
Slab SP9 recorded an enhanced ultimate load with respect to all other slabs due to
the concrete thickness and the small diameter Φ8 of the GFRP reinforcement.

3.2. Ultimate Deflection

Table 5 shows the ultimate deflection for all slabs. For the control group, the ultimate
deflation recorded was 6.75 mm and 4.89 mm for SP1 and SP2, respectively. This shows
the effect of increasing the reinforcement ratio in decreasing deflection.
For Group I, Slab SP5 recorded the lowest deflection value of 3.72 mm compared to
SP3 and SP4 and control slabs. The slabs SP3 and SP4 recorded a deflection of 2.47 mm
and 4.91 mm, respectively.
For Group II, Slab SP6 recorded a higher deflection of 7.91 mm with an ultimate load-
carrying capacity of 180.70 kN compared to Slabs SP7 and SP8, which recorded lower
deflection values of 4.91 mm and 4.79 mm and an ultimate load of 149.30 kN and 129.30
kN, respectively, which agrees with Achillides and Pilakoutas [34].
For Group III, Slab SP9 recorded the highest deflection of 11.03 mm with the highest
ultimate load-carrying capacity of 313.75 kN compared to slabs of all groups. This indi-
cated that the GFRP bars enhanced the loading-carrying capacity, deflections. and ductil-
ity when using small diameters, which increased the bond between concrete and bars, as
shown in Figure 6 through the load–deflection curves for all slabs.

(a) (b)

(c) (d)
Figure 6. Load–deflection curves: (a) slabs with Φ8 in control and Group I; (b) slabs with the same reinforcement ratio
with different diameter (ts = 120 mm); (c) slabs with the same reinforcement ratio with different diameter (ts = 150 mm);
(d) slabs with the same reinforcement ratio and different diameter (ts).
Polymers 2021, 13, 2997 9 of 24

3.3. Crack Pattern and Mode of Failure

Figure 7 shows the crack propagation for all slabs. Additionally, Table 5 shows the
mode of failure for all slabs. Crack pattern for the control slabs SP1 and SP2 was propa-
gated in the tension zone, as shown in Figure 7a, and the mode of failure was tension
failure (TF). The behavior of Slabs SP3, SP6, and SP9 was the same. Although the concrete
capacity was still able to carry load, the GFRP bars could not, so rupture failure (RF) oc-
curred in the GFRP bars. For Slabs SP4, SP7, and SP10, the concrete and bars failed, to-
gether with compression and rupture failure (CC and RF, respectively). However, for
Slabs SP5, SP8, and SP11, a decrease in crack number and propagation was noticed, as
shown in Figure 8, and the mode of failure occurred as tension cracks and GFRP rupture
failure.

(a) Slab SP1

(b) Slab SP2

(c) Slab SP3

Polymers 2021, 13, 2997 10 of 24

(d) Slab SP4

(e) Slab SP5

(f) Slab SP6

(g) Slab SP7

Polymers 2021, 13, 2997 11 of 24

(h) Slab SP8

(i) Slab SP9

(j) Slab SP10

(k) Slab SP11

Figure 7. Crack pattern for all slabs.
Polymers 2021, 13, 2997 12 of 24

(a) (b)
Figure 8. Crack pattern: (a) rupture of GFRP bars; (b) tension failure with concrete crushing.

4. Nonlinear Finite Element Analysis (NLFEA)

A finite element model was created to validate the experimental study using the AN-
SYS 2019-R1 [35] program. The Solid-65 element was employed for the representation of
concrete, and the LINK-180 element was employed for steel and GFRP bar representation.
Figure 9 indicates the Solid-65 and LINK-180 elements’ geometry.

Figure 9. Element geometry: (a) Solid-65; (b) Link-180.

4.1. Modeling
The NLFE model was used to investigate the structural performance of HSC slabs
reinforced with GFRP bars using ANSYS2019-R1 software, as indicated in Figure 10. in
terms of ultimate load, ultimate deflection, and crack pattern for the modeled slabs.
Polymers 2021, 13, 2997 13 of 24

(a)

(b)
Figure 10. NLFEA model: (a) slab modeling; (b) restraints and applied loads.

4.2. NLFE Ultimate Load

Table 6 shows the ultimate loads obtained from NLFEA. For the control slabs SP1
and SP2, the ultimate load was 133.30 kN and 118.40 kN, respectively. For Slabs SP3, SP4,
and SP5, the ultimate load was 76.42 kN, 119.40 kN, and 138.92 kN, respectively. For Slabs
SP6, SP7, and SP8 the ultimate load was 153.60 kN, 134.40 kN, and 112.40 kN, respectively.
For Slabs SP9, SP10, and SP11, the ultimate load was 247.86 kN, 215.05 kN, and 193.10 kN,
respectively.

Table 6. NLFEA results.

Specimen First Crack Ultimate Load

Specimen ID ΔNLFA (mm)
Group (kN) (kN)
Con-

SP1 50 133.30 6.10

trol

SP2 50 118.40 4.15

Group II Group I

SP3 50 76.42 2.38

SP4 50 119.40 3.92
SP5 50 138.92 3.35
SP6 70 153.60 6.72
SP7 70 134.40 4.41
SP8 70 112.40 4.16
ou
Gr

III

SP9 82 247.86 8.71

p
Polymers 2021, 13, 2997 14 of 24

SP10 82 215.05 5.50

SP11 82 193.10 7.10

The enhancement in ultimate load for Slab SP9 compared with the control slabs led
to concrete compressive strength and concrete thickness. The enhanced ratio is slightly
low due to the small values of strain and the Young’s modulus of GFRP bars.

4.3. NLFE Deflection

The NLFE deflections obtained are indicated in Table 6. Generally, the recorded de-
flection improved due to the use of GFRP bars with respect to control slabs. The deflection
of SP1 was 6.10 mm at failure load, but it recorded an enhancement that varied between
60.0% and 45.0% for SP3, SP4, and SP5. For the second group, the deflections recorded
were 6.72 mm, 4.41 mm, and 4.16 mm for SP6, SP7, and SP8, respectively. The enhance-
ment was apparent in Slab SP8, which had the least compressive load with a ratio of 1.2
µfb. This indicates the behavior of GFRP bars in enhancing the deflections, as shown in
Figure 11.

Figure 11. Sample of NLFEA deflection.

4.4. Crack Pattern and Mode of Failure

The crack pattern of the control group featured crack propagation in the tension zone,
as shown in Figure 12a. Additionally, the mode of failure was tension failure (TF) due to
reinforcement failure. The behavior of SP3 and SP6 was the same, while the reinforcement
was less than 0.8 µb. So, the concrete capacity was still able to carry load, but the GFRP
bars could not. Rupture occurred in GFRP bars, which was sudden rupture due to the
brittle nature of GFRP bars, so there was RF in the bars. The mode of failure for the first
group is the same for the second group in crack propagation and mode of failure. For slabs
that had a reinforcement ratio of 1.2 µfb, the failure was a combination of concrete cracks
in the compression zone and rupture in the GFRP bars, as shown in Figure 12d.
Polymers 2021, 13, 2997 15 of 24

(a)

(b)

(c)
Polymers 2021, 13, 2997 16 of 24

(d)
Figure 12. NLFE crack pattern: (a) control slabs; (b) Group I slabs; (c) Group II slabs; (d) Group III slabs.

5. Comparisons between Experimental and NLFEA Results

There was good agreement between the experimental and ANSYS results. Compari-
sons were made between ultimate load, deflection, the first crack load, and crack pattern.

5.1. Comparison between Experimental and NLFE Ultimate Loads

Figure 13 shows good agreement between the experimental and analytical load–de-
flection curves. Comparisons between the obtained results for the different groups are
shown in Table 7. Pu NLFEA/Pu exp. had an average ratio of 0.86. Group II of concrete rein-
forced with GFRP of the same diameter but different reinforcement ratios for SP3, SP4,
and SP5, respectively, has an average of 0.86. Finally, for Group II and Group III, the av-
erage ratio of agreement for all specimens is 0.87 and 0.84. The variance of 0.0015 and
standard deviation of 0.04 show the effect of using NLFEA in predicting the behavior of
the tested slabs, as shown in Table 7 and Figure 14.

(a) SP1
Polymers 2021, 13, 2997 17 of 24

(b) SP2

(c) SP3

(d) SP4
Polymers 2021, 13, 2997 18 of 24

(e) SP5

(f) SP6

(g) SP7
Polymers 2021, 13, 2997 19 of 24

(h) SP8

(i) SP9

(j) SP10
Polymers 2021, 13, 2997 20 of 24

(k) SP11
Figure 13. Comparisons between experimental and NLFE load–deflection curves for all slabs.

Table 7. Comparisons between experimental and NLFEA results.

Experimental Load Analytical Load ( )

Δ (mm)
Specimen (kN) (kN) ( ) ( )
Spec. ID
Group First First ( )
First Crack Ult. Load Ult. Load Δexp ΔNLFE Ult. Load
Crack Crack
Con-

SP1 75 148.00 50 133.30 6.75 6.10 0.67 0.90 0.90

trol

SP2 75 139.00 50 118.40 4.89 4.15 0.67 0.85 0.84

Group II Group I

SP3 50 87.85 50 76.42 2.74 2.38 1.0 0.87 0.87

SP4 80 149.30 50 119.40 4.91 3.92 0.62 0.80 0.79
SP5 85 154.40 50 138.92 3.72 3.35 0.59 0.90 0.90
SP6 100 180.70 70 153.60 7.91 6.72 0.70 0.85 0.85
SP7 120 149.30 70 134.40 4.91 4.41 0.58 0.90 0.89
SP8 125 129.30 70 112.40 4.79 4.16 0.56 0.87 0.87
SP9 100 313.75 82 247.86 11.03 8.71 0.82 0.79 0.79
Group
III

SP10 150 256.02 82 215.05 6.55 5.50 0.55 0.83 0.84

SP11 200 212.10 82 193.10 7.80 7.10 0.41 0.91 0.91
Average 0.65 0.86 0.86
Variance 0.019 0.0015 0.0016
Standard Deviation 0.15 0.04 0.041
Polymers 2021, 13, 2997 21 of 24

Figure 14. Comparisons between experimental and NLFE ultimate load.

5.2. Comparison between Experimental and NLFE Deflections

Figure 15 shows the obtained deflections for all groups for both experimental and
analytical studies. The load–deflection curves for the tested slabs and analytical results
show good agreement, with an average of agreement of 86.0%. Table 7 shows a deflection
ratio ∆u NLFEA/∆u exp. of the control group of 0.87, but for Group I, the ratios are 0.87, 0.79,
and 0.90 for SP3, SP4, and SP5, respectively, and the average ratio of agreement is 0.85.
This indicates that the analytical models provided an acceptable load–deflection response,
as shown in Table 7. For all groups, the average of ∆u NLFEA/∆u exp is equal to 0.86, with a
coefficient of variance and standard deviations of 0.0016 and 0.041, respectively.

Figure 15. Comparisons between experimental and NLFE deflections.

5.3. Comparison between Experimental and NLFE Crack Patterns and Mode of Failure
The crack pattern for the control slab with a steel reinforcement started with crack
propagation in the tension zone for the experimental and analytical slabs, as shown in
Figure 16a, showing tension failure (TF).
Polymers 2021, 13, 2997 22 of 24

However, for Slabs SP5 to SP11 reinforced with the same reinforcement ratio, a
higher ultimate load, lower deflection, and decreased cracks were obtained, showing ten-
sion cracks with low propagation, as obtained from the experimental patterns. The crack
patterns show good agreement between the NLFEA and experimental results.

(a)

(b)
Figure 16. Comparisons between experimental and NLFE crack patterns: (a) slabs reinforced using steel bars; (b) slabs
reinforced using GFRP.
Polymers 2021, 13, 2997 23 of 24

6. Conclusions
Based on the experimental and the analytical studies, the following conclusions can
be drawn:
1. Using reinforcement areas of the GFRP bars less than or equal to µb led to brittle fail-
ure in GFRP bars and concrete crushing with rupture GFRP bars, respectively.
2. The behavior of the tested GFRP-reinforced slabs was bilinear elastic until failure.
3. There was an enhancement in deflections and crack patterns for slabs reinforced us-
ing GFRP bars, especially for equal reinforcement areas.
4. The NLFEA obtained an acceptable agreement with the experimental study in terms
of the ultimate loads, ultimate deflection, and crack pattern.
5. The agreement between the experimental and analytical study was approximately
86.0% with a standard deviation of 0.04 and a coefficient of variance of 0.0015.

Author Contributions: Conceptualization, M.A.A., A.M.E., F.A.H. and T.A.E.-S.; Data curation,
F.A.H. and T.A.E.-S.; Formal analysis, A.M.E., F.A.H. and T.A.E.-S.; Funding acquisition, F.A.H.;
Investigation, A.M.E., F.A.H. and T.A.E.-S.; Methodology, A.M.E., F.A.H. and T.A.E.-S.; Project ad-
ministration, A.M.E., F.A.H. and T.A.E.-S.; Resources, A.M.E., F.A.H. and T.A.E.-S.; Software,
F.A.H. and T.A.E.-S.; Supervision, M.A.A., A.M.E. and T.A.E.-S.; Validation, A.M.E., F.A.H. and
T.A.E.-S.; Visualization, A.M.E., F.A.H. and T.A.E.-S.; Writing – original draft, A.M.E., F.A.H. and
T.A.E.-S.; Writing – review & editing, M.A.A., A.M.E., F.A.H. and T.A.E.-S. All authors have read
and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All data included in this study are available upon request by contact
with the corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.

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