experimental flexural performance of concrete beams

Engineering Structures 226 (2021) 111348

Available online 12 October 20200141-0296/© 2020 Elsevier Ltd. All rights reserved.

Experimental flexural performance of concrete beams reinforced with an innovative hybrid bars

Mohamed Said a, Ali S. Shanour a, T.S. Mustafa a, Ahmed H. Abdel-Kareem b, Mostafa M. Khalil a,*

a Faculty of Engineering (Shoubra), Benha University, Egypt b Benha Faculty of Engineering, Benha University, Egypt

A R T I C L E I N F O

Keywords: Concrete beams Flexural performance Hybrid reinforcement bars Finite element analysis Nominal flexural strength

A B S T R A C T

Twelve half-scale concrete beams were tested to investigate the flexural performance of concrete beams rein-forced with locally produced hybrid bars and hybrid schemes. The variables are the reinforcement bar type (hybrid, GFRP, and steel) and the reinforcement ratios (0.85%, 1.26%, 1.70%, 1.8, and 2.13%). The test results showed a significant enhancement in the maximum load-carrying capacity due to increasing the hybrid rein-forcement ratio. The capacities were increased by 109% and 167% respectively for hybrid reinforcement ratio of 1.26% and 1.7%. Also, the strain of reinforcing bars exceeds the yield level. Accordingly, using hybrid reinforced bars or hybrid schemes exhibited more ductility for concrete beams. Non-linear finite element analysis (NLFEA) was carried out using ANSYS Software. The analysis adequately reflected the trend of experimental results, the overall average value of the ratio between experimental and NLFEA ultimate capacity is 1.01. Additionally, parametric studies have been performed in order to investigate the effect of concrete compressive strength, hybrid reinforcement ratio and shear-span to depth ratio on the performance of hybrid reinforcement concrete beams. Nominal flexural strength was assessed with the experimental test results and 38 reinforced concrete beams from the literature. The comparison proved that assessment of the nominal flexural strength performs well in predicting the flexural capacity. The average value of the ratio between experimental and nominal flexural strength is 1.011.

1. Introduction

The rapid corrosion of steel reinforcement bars is considered one of the main causes for reducing the service life of reinforced concrete structures. For example, dams, tanks, and bridges exposed to moisture, chlorides, and de-icing salts which caused the corrosion of steel rein-forcement. To achieve the requirement of ultimate limit state and durability for these structures, steel reinforcement bars should be replaced or coated with non-corrosive materials. Over the last four de-cades, fiber-reinforced polymer (FRP) bars were used as an alternative material to resolve the corrosion problem of steel reinforcement bars. The common types of fibers are carbon, glass, and aramid. FRP bars provide high specific strength and also good resistance to corrosion.

Investigations on the behaviour of concrete beams reinforced with FRP bars were studied [1–6]. Adam et al. [1] presented an experimental investigation for concrete beams reinforced with GFRP bars. The

deflection behaviour, cracking, and the load-carrying capacity of the tested beams were evaluated. The reinforcement ratio and concrete compressive strength were the main studied variables. Significant reduction in crack widths and deflection were observed by increasing the reinforcement ratio. Also, the observed failure modes were concrete crushing and GFRP rupture. FRP bars have linear stress–strain behaviour under tension and up to failure with a lower elastic modulus and no ductility compared to steel reinforcement bars [7]. This behaviour causes large deflections, crack widths, and brittle failure. Moreover, the observed investigated failure modes from the experimental test results [8–11] were compression failures. Based on these results, FRP rein-forcement is not recommended for moment resistance frames.

To enhance the ductility, flexural capacity, and to provide more corrosion protection for RC structures, some researchers have proposed the concept of combining steel bars with FRP bars (hybrid schemes) in RC structures [12–15]. In the hybrid schemes, FRP bars are located at the corners of the concrete elements and steel reinforcement bars are

* Corresponding author. E-mail addresses: [email protected] (M. Said), [email protected] (A.S. Shanour), [email protected] (T.S. Mustafa),

[email protected] (A.H. Abdel-Kareem), [email protected] (M.M. Khalil).

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

https://doi.org/10.1016/j.engstruct.2020.111348 Received 24 February 2020; Received in revised form 17 September 2020; Accepted 18 September 2020

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placed inside the element for more protection. The steel reinforcement bars are having a large margin of ductility. Accordingly, utilizing proper reinforced ratios for these bars will enforce the section to fail by yielding of the steel bars and consequently in a ductile failure preventing the occurrence of the compression failure. At the same time, the FRP bars increase the load-carrying capacity of the RC structures [16–20]. An experimental investigation on the hybrid reinforced beams was pre-sented by Qu et al. [12]. The reinforcement ratio was the main inves-tigated parameter. The hybrid schemes of steel and GFRP bars enhanced the ductility of the tested beams. Also, increasing the reinforcement ratio improved the flexural capacity. Leung et al. [20] studied the

flexural performance of the hybrid concrete beams reinforced with GFRP and steel bars. The hybrid reinforced beams showed higher flexure strength than the steel or GFRP reinforced beams. Also, enhancement in the stiffness of hybrid reinforced beams was observed after the steel bars were yielded.

An innovative reinforcing material for a flexural structural element is created which called hybrid reinforcement bars. A less common area of research relates to investigating the potential of using two different materials (FRP or steel) together as reinforcement in a hybrid bar [21–24]. These systems seek to capitalize on the higher axial stiffness of one material like conventional steel, while still benefitting from the

Nomenclature

Ac area of the compression zone. Af the reinforcing area of FRP bars in tension Ahr area of the hybrid reinforcement bars As the reinforcing area of steel reinforcement bars in tension a depth of the rectangular stress block b width of the cross-section C depth of compression zone in concrete Cc the compression force of concrete DF ductility factor DFB1 ductility factor of beam B1 DFB6 ductility factor of beam B6 DFexp. experimental ductility factor DFNL. predicted ductility factor from NLFEA d depth of the beam d’ distance from the center of the tension bars to the concrete

tension edge E Modulus of elasticity fcu cubic compressive strength of the concrete fc’ cylindrical compressive strength of the concrete ff tensile strength of FRP bars fhr tensile strength of the hybrid bar fu ultimate strength of the reinforcing bars fy yield strength of the reinforcing bars I energy absorption IB1 energy absorption of beam B1 IB6 energy absorption of beam B6 Iexp. experimental energy absorption INL. predicted energy absorption from NLFEA K initial stiffness K-B1 initial stiffness of beam B1 K-B6 initial stiffness of beam B6 K-exp. experimental initial stiffness K-NL. predicted initial stiffness from NLFEA k1 constant value = 3 × 108

k2 constant value = 107

k3 constant value = 1.46 × 105

L length of the beam Lcl-cl length of the beam between the centers of the supports M exp. experimental moment strength Mn. nominal flexural strength Pcr cracking load Pcr-B1 cracking load of beam B1 Pcr-B6 cracking load of beam B6 Pcr-exp. experimental cracking load Pcr-NL. predicted cracking load from NLFEA Pu ultimate load-carrying capacity Pu-B1 the ultimate load-carrying capacity of beam B1 Pu-B6 the ultimate load-carrying capacity of beam B6 Pu-exp. experimental load-carrying capacity

Pu-NL. predicted load-carrying capacity from NLFEA Py load at the yield level Py-B1 load at the yield level of beam B1 Py-B6 load at the yield level of beam B6 Py-exp. experimental load at the yield level Py-NL. predicted load at the yield level from NLFEA Ts tension force of steel reinforcement bars Tf tension force of FRP bars Thr tension force of hybrid bars t depth of the cross-section X flexural shear span α coefficient depends on the design code β factor relating depth of equivalent rectangular

compressive stress block to neutral axis depth εc the compressive strain in the concrete εco the compressive strain in the concrete, while the stress up

to compressive strength εcu the ultimate compressive strain in the concrete εhr the tensile strain of the hybrid bar εhry the tensile strain of the hybrid bar at the yield level εhru the tensile strain of the hybrid bar at the ultimate level εt the tensile strain of the reinforcing bars at the ultimate

level εt , exp. the experimental tensile strain of the reinforcing bars at the

ultimate level εt,NL. predicted ultimate tensile strain of the reinforcing bars

from NLFEA εt,N. the nominal ultimate tensile strain of the reinforcing bars

from NLFEA εy the tensile strain of the reinforcing bars at the yield level μs strain ductility μs, NL. predicted strain ductility from NLFEA μs, n. nominal strain ductility ρbhr, min. minimum balanced reinforcement ratio of hybrid bars ρbhr, max. maximum balanced reinforcement ratio of hybrid bars ρf reinforcement ratio of GFRP bars = (Af/b.d) ρhr reinforcement ratio of hybrid bars = (Ahr/b.d) ρs reinforcement ratio of steel reinforcement bars = (As/b.d) ρt total reinforcement ratio = (ρs + ρf + ρhr) δu deflection at the ultimate level δu-B1 deflection at the ultimate level of beam B1 δu-B6 deflection at the ultimate level of beam B6 δu-exp. experimental deflection at the ultimate level δu-NL. predicted deflection at the ultimate level from NLFEA δy deflection at the yield level δy-B1 deflection at the yield level of beam B1 δy-B6 deflection at the yield level of beam B6 δy-exp. experimental deflection at the yield level δy-NL. predicted deflection at the yield level from NLFEA ơc effective compressive strength of concrete

M. Said et al.


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corrosion resistance of FRP. Forty-eight specimens of the hybrid rein-forcement bars were experimentally tested under uniaxial tensile test by Minkwan et al. [21] to predict the tensile strength and the elastic modulus of the hybrid bar. The test results showed a higher modulus of elasticity than the GFRP bar. The mentioned previous research works were limited to investigate the behaviour of the hybrid bars only. For that reason, the investigation of the performance of concrete members reinforced with hybrid bars is required.

This paper aims to introduce the production of innovative hybrid bars to overcome the corrosion problems and the brittle behaviour of the concrete beams reinforced with FRP bars. The fundamental mechanical

properties of the hybrid bars were evaluated and verified with the other works. Twelve half-scale concrete beams reinforced with hybrid bars and hybrid schemes were experimentally tested. The main key param-eters were the types of reinforcement bars and the reinforcement ratios. The cracking load, load-carrying capacity, and load–deflection curves were discussed. Also, the load–strain curves of the reinforcing bars were presented. Moreover, the cracks pattern and failure modes were observed. NLFEA was performed to simulate the tested beams. ANSYS software [25] was used to develop the models. Additionally, parametric studies have been performed in order to investigate the effect of concrete compressive strength, hybrid reinforcement ratio and shear-span to depth ratio on the performance of hybrid reinforcement concrete beams. Finally, the nominal flexural strength of hybrid reinforced concrete beams was assessed with the experimental results.

2. Test program

2.1. Manufacturing and testing of hybrid bars

The hybrid bars and GFRP bars were locally produced by the authors using a steel bar (steel core) of 10 mm diameter, E-glass fiber roving, and vinyl-ester resin. Up to 70 E-glass fibers roving to manufacture GFRP

(a) 14 mm Hybrid Bars

(b) Ribbed 12 mm GFRP Bars

Fig. 2. Produced GFRP and Hybrid Bars.

Fig. 3. Uniaxial Tensile Test of Hybrid Specimen.

Fig. 1. Double Set Mold.

Table 1 Technical data for E-glass fibers roving.

Property Value

Density (g/cm3) 2.60 Tensile Strength (MPa) 2250 Elastic Modulus (GPa) 75 Glass Softening Point (◦C) 850

Table 2 Mechanical Properties for the Vinyl-ester Resin.

Material Model Tensile Strength (MPa) Elastic Modulus (MPa)

Resin HETRON-911 88 3270

M. Said et al.


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bars with 12 mm nominal diameter were used while, 22 E-glass fibers roving were used to manufacture the outer GFRP surface of the hybrid bar with 14 mm nominal diameter. The direct roving is produced by pulling individual fibers directly from the bushing and then winding them into a roving package. The uniform distribution of a proprietary sizing system assures an excellent resin-to-glass binding through uni-form distribution of the binding agent. Table 1 lists the technical data for E-glass fiber roving. Vinyl ester resin (HETRON-922) was used to pro-duce the GFRP bars. Vinyl-ester resins have the following advantages of corrosion resistance to a wide range of acids, bases, chlorides, solvents, and oxidizers. The mechanical properties of the vinyl-ester resin are presented in Table 2. Double sets of plastic mold were produced at a private workshop to manufacture 3.0 m length of hybrid bars and GFRP bars. As shown in Fig. 1, the mold inner faces of the two sets were crescent-shaped lugs. The produced hybrid bar of 14 mm diameter and GFRP ribbed bar of 12 mm diameter are shown in Fig. 2.

The fundamental mechanical properties of the six hybrid bars, GFRP bars and steel bars were investigated by a machine of 1000 kN capacity as shown in Fig. 3. The tensile stress–strain curves for six hybrid bars are presented in Fig. 4. Comparison between the tensile stress–strain curves for a steel bar, GFRP bar and the average tensile stress–strain curve for six hybrid bars are shown in Fig. 5. The average tensile stress–strain curves showed a bi-linear behaviour and acceptable ductility against the brittle failure of GFRP bars. Moreover, higher elastic modulus and lower tensile strength were recorded for hybrid bars when compared to GFRP bars.

The idealized stress–strain curve for the six hybrid bars has been assumed to simulate the bilinear best fitting of the experimental tensile stress–strain curves for the hybrid bars. The idealized tensile stress of the hybrid bar can be calculated by the following formula:

fhr = k1εhr3 − k2εhr

2 + k3εhr (1)

The values of the constants k1, k2, and k3 have been obtained from the regression analysis using Datafit software [26], these values are (3 ×108), (107), and (1.46 × 105) respectively. The idealized tensile stress–strain curves for the hybrid bars were verified with the tensile test results from the literature [21,23], as shown in Fig. 6. The comparison showed good agreements between the produced hybrid bars in this research and the test results from the literature [21,23].

2.2. Test specimens

Twelve half-scale RC beams were designed as a simply supported span with an adequate amount of longitudinal and shear reinforcement. The study investigated the influence of the main parameters on the flexural behaviour of concrete beams. The investigated parameters include the type of the reinforcing bars and tension reinforcement ratios. Two concrete beams were reinforced with steel bars as control speci-mens for comparison. Four concrete beams were reinforced with different longitudinal hybrid reinforcement ratios and presented in Group A. The other six concrete beams present Group B were reinforced with hybrid schemes (steel and GFRP) bars, (steel and hybrid) bars, and (GFRP and hybrid) bars. For all beams, two 8 mm steel bars were used as top reinforcement to hold stirrups and 8 mm diameter stirrups @ 100 mm c/c spacing were used as shear reinforcement. Five different tensile reinforcement ratios (ρt) (0.85%, 1.26%, 1.70%, 1.8% and 2.13%) were used. The mechanical properties of the used reinforcing bars and the coefficient of variation (C.O.V) for the properties of GFRP bars and hybrid reinforcement bars are presented in Table 3.

The layout of the tested beams is detailed in Fig. 7 and summarized in Table 4.

The concrete strength depends primarily on the properties of the constituent materials (Portland cement, sand, coarse aggregate, and

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02 0.025 0.03

Sample-1 Sample-2Sample-3 Sample-4Sample-5 Sample-6

Tensile Strain (mm/mm)

Tens

ile S

tres

s (M

Pa)

Fig. 4. Tensile Stress-Strain Curves for the Hybrid Bars.

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02 0.025 0.03

Hybrid Bar [Predicted]Hybird Bar [21]Hybird Bar [23]


Tens

ile S

tres

s (M

Pa)

Fig. 6. Comparison of the Idealized Tensile Stress-Strain Curves for the Hybrid Bars.

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02 0.025 0.03

Hybird BarSteel BarGFRP Bar


Tens

ile S

tres

s (M

Pa)

Fig. 5. Tensile Stress-Strain Curves for Steel Bar, GFRP Bar and Hybrid Bar.

Table 3 Mechanical Properties of the Reinforcing Bars.

Reinforcement Type

Diameter (mm)

Yield Strength (fy) N/mm2

Ultimate Strength (fu) N/mm2

Young’s Modulus (E) (GPa)

MS 8 240 350 200 HTS 10 400 600 200 HTS 12 400 600 200 GFRP 12 — 850 42.5 C.O.V for GFRP — — 5.70% 5.40% HRB 14 380 700 140 C.O.V for HRB — 4.80% 4.40% 4.20%

Note: MS = mild steel bar, HTS = high tensile steel bar and HRB = hybrid reinforcement bar.

M. Said et al.


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water), their mix proportions and the method of their preparation, placing, compacting and curing. The target cubic compressive strength of the concrete (fcu) was 45 MPa. Table 5 presents the mix design for the concrete in the present work. (Sikament®-R4PN) high range water reducer (HRWR) and slump retaining concrete admixture were used in the mix design.

2.3. Test setup

The beams were tested in a machine of 1000 kN capacity. The load was distributed on two plates kept 400 mm apart. The two loads were symmetrical to the centreline of the beam. The beams were tested under load control. Strain gauges were fixed at the longitudinal reinforcement bars to measure the strain of the bars as illustrated in Figs. 8 and 9. The

deflection at the centreline was recorded for every 0.5 kN increment of load using a linear variable differential transformer (LVDT) fitted at the center. The cracks were mapped out during loading stages until the failure.

3. Experimental results and discussion

3.1. Crack load and ultimate load

All beams were visually observed until the appearance of the first crack with the recording of the corresponding first crack load. Tables 6 and 7 summarizes the observed test results for Group A and Group B respectively. The test results showed that the first crack load (Pcr) and the load at the ultimate level (Pu) were enhanced by increasing the

2100850 850400

1

1100 100100100

2300

300

8@100

Longitudinal Section for the Tested Beams

150

300

2Ø8

3Ø12

Ø8@100

B1150

300

2Ø8

Ø8@100

B2150

2Ø8

Ø8@100

B3

150

300

2Ø8

Ø8@100

2H14

150

300

2Ø8

Ø8@100

B5150

2Ø8

Ø8@100

B6

3G12+2Ø10

150

300

2Ø8

Ø8@100

B4

150

300

2Ø8

2H14+2G12

Ø8@100

B9150

300

2Ø8

Ø8@100

B10150

2Ø8

Ø8@100

B11

3G12+1H14 2H14+3G12

300

3H14

150

300

2Ø8

2H14+2Ø10

Ø8@100

B7 B8

LEGEND

HTS (Ø)

GFRP (G)

HRB (H)

300

300

4H14

5H14 4Ø12+1Ø10

150

2Ø8

Ø8@100

B12

2H14+4G12

300

Fig. 7. Tested Beams Geometry and Details.

M. Said et al.


6

hybrid reinforcement ratio (ρhr). For Group A and with reference to beam B1, using the same tension

reinforcement ratio for the hybrid concrete beam B2 led to enhance the crack load (Pcr) by 12% and the ultimate load (Pu) by 71%. Moreover,

increasing the hybrid reinforcement ratio (ρhr) increased the crack load (Pcr) by 23%, 31%, and 42% respectively for B3, B4, and B5. At the ul-timate level, the load-carrying capacity was improved by 109%, 167%, and 203% respectively for B3, B4, and B5. Consequently, the hybrid bars displayed a basic contribution to improve the flexural capacity for the concrete beams. This enhancement in the load-carrying capacity of the

HRB beams is due to the high tensile strength of the outer layers of the GFRP in addition to the tensile strength of the internal layer of steel reinforcement.

For Group B, comparing the test results with the control beam B6,

P/2Upper Steel

Applied Load (P)

Load Cell

Spreader Beam P/2

Loading Plate

ALVDT

Roller &

Testing Machine Bed

Supporting PlateHinge & Supporting Plate

B

2100 100100

850100 850 100400

Strain Gauge

300

Fig. 8. Testing Setup Details.

Table 4 Details of the Tested Beams.

Group Beam Bottom RFT Bottom RFT Ratios

As HTS Af

GFRP Ahr

HRB ρs % ρf % ρhr

% ρt %

Group A

B1 3∅12 — — 0.85 — — 0.85 B2 — — 2H14 — — 0.85 0.85 B3 — — 3H14 — — 1.26 1.26 B4 — — 4H14 — — 1.70 1.70 B5 — — 5H14 — — 2.13 2.13

Group B

B6 4∅ 12 + 1∅ 10

— — 1.26 — — 1.26

B7 2∅ 10 — 2H14 0.41 — 0.85 1.26 B8 2∅ 10 3G12 — 0.41 0.85 — 1.26 B9 — 2G12 2H14 — 0.42 0.85 1.27 B10 — 3G12 1H14 — 0.85 0.42 1.27 B11 — 3G12 2H14 — 0.85 0.85 1.70 B12 — 4G12 2H14 — 0.95 0.85 1.80

Fig. 9. Typical Beam during Testing.

Table 5 Concrete Mix Proportions per One Cubic Meter.

Quantity required for 1 m3 (kg)

Cement Sand Coarse aggregate Water HRWR

500 620 1180 210 10

Table 6 Experimental Results of the Tested Beams for Group A.

Group Beam Experimental Test Results Relative Experimental Results to the Control Beam (B1)

Pcr

(kN) Py

(kN) δy

(mm) Pu

(kN) δu

(mm) K (kN/ mm)

I (kN. mm)

DF Pcr

Pcr− B1

Py

Py− B1

δy

δy− B1

Pu

Pu− B1

δu

δu− B1

KKB1

IIB1

DFDFB1

Group A

B1 26 84.5 8 92 34 10.38 3150 4.30 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 B2 29 135 10 157 61 13.46 8300 5.87 1.12 1.60 1.32 1.71 1.79 1.30 2.63 1.36 B3 32 155 9 193 67 16.76 11,800 7.19 1.23 1.83 1.17 2.09 1.96 1.61 3.75 1.67 B4 34 220 12 246 73 17.29 16,900 6.33 1.31 2.60 1.46 2.67 2.15 1.67 5.37 1.47 B5 37 260 15 279 83 17.57 20,900 5.61 1.42 3.08 1.87 3.03 2.44 1.69 6.63 1.30

M. Said et al.


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using hybrid schemes with the same tension reinforcement ratio for B7 (hybrid and steel bars) and B9 (hybrid and GFRP bars) improved the crack load (Pcr) by 10% and 13% for B7 and B9 respectively. Also, the load-carrying capacity was enhanced by 23% and 34% for B7 and B9 respectively. No significant enhancement was observed for the cracking load of B8 (steel and GFRP bars) and B10 (GFRP and hybrid bars) when compared with beam B6. However, enhancement in the maximum load was observed by 13% and 31% for B8 and B10 respectively. The crack load was enhanced by 17% and 20% for B11 and B12. Also, the maximum load was increased by 61% and 68% for B11 and B12 respectively. The improvement in the load-carrying capacity occurred due to the role of GFRP bars in resisting loads after the yielding of steel reinforcement. This is attributed to the fact that the steel reinforcement bars cannot resist higher loads after yielding. Furthermore, increasing

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

B3 (3H14)B2 (2H14)B1 (3 12)

Deflection (mm)

Load

(kN

)

(a)

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

B5 (5H14)

B4 (4H14)

B1 (3 12)

Deflection (mm)

Load

(kN

)

(b)

Fig. 10. Load-Deflection Curves of the Tested Beams for Group A.

Table 7 Experimental Results of the Tested Beams for Group B.

Group Beam Experimental Test Results Relative Experimental Results to the Control Beam (B6)

Pcr

(kN) Py

(kN) δy

(mm) Pu

(kN) δu

(mm) K (kN/ mm)

I (kN. mm)

DF Pcr

Pcr− B6

Py

Py− B6

δy

δy− B6

Pu

Pu− B6

δu

δu− B6

KKB6

IIB6

DFDFB6

Group B

B6 30 133 8 152 46 16.02 6500 5.54 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 B7 33 159 9 187 51 17.26 9100 5.68 1.10 1.20 1.08 1.23 1.11 1.08 1.40 1.02 B8 29 170 26 171 40 6.54 5900 1.54 0.97 1.28 3.13 1.13 0.87 0.41 0.91 0.28 B9 34 197 25 203 55 7.88 9800 2.20 1.13 1.48 3.01 1.34 1.20 0.49 1.51 0.40 B10 29 190 30 200 50 6.44 7400 1.69 0.97 1.43 3.55 1.31 1.09 0.40 1.14 0.31 B11 35 230 21 245 66 9.27 14,100 3.12 1.17 1.73 2.56 1.61 1.44 0.58 2.17 0.56 B12 36 250 27 255 69 9.43 14,500 2.60 1.20 1.88 3.19 1.68 1.50 0.59 2.23 0.47

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

B10 (1H14+3G12)B9 (2H14+2G12)B6 (4 12+1 10)

Deflection (mm)

Load

(kN

)

(b)

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

B12 (2H14+4G12)

B11 (2H14+3G12)

B6 (4 12+1 10)

Deflection (mm)

Load

(kN

)

(c)

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

B8 (3G12+2 10)B7 (2H14+2 10)B6 (4 12+1 10)

Deflection (mm)

Load

(kN

)

(a)

Fig. 11. Load-Deflection Curves of the Tested Beams for Group B.

M. Said et al.


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the reinforcement ratio of GFRP bars exhibited an enhancement in the load-carrying capacity. Consequently, the hybrid schemes showed an improvement in the maximum load-capacity compared with RC beams reinforced with steel reinforcement bars only.

3.2. Load-deflection curves

The experimental load–deflection curves for Group A and B are plotted in Figs. 10 and 11 respectively. Generally, the load–deflection curves consisted of three main branches, the first branch is linear that specifies the response until the initial cracks and the second branch is

linear fitting that represents the response until the yield of longitudinal reinforcement. After the yielding of reinforcement, increasing the deflection took place for successive loads. It was observed that the tested beams of Group A exhibit higher deflection before failure with extended ductile plateau more than the control beam as shown in Fig. 10. For beams with hybrid schemes, the inclusion of steel reinforcement bars or HRB with GFRP bars exhibited residual ductility for the tested beams up to concrete crushing. The experimental results confirm the effectiveness of steel reinforcement and HRB in improving the ductility of hybrid schemes beams. Based on the plotted load–deflection curves, the following measurements can be evaluated as follows:

a. Initial Stiffness (K)

0

50

100

150

200

250

300

0 2.5 5 7.5 10 12.5 15 17.5 20

B3 (3H14)B2 (2H14)B1 (3 12)

Reinforcing-Strain (x10-3)

Load

(kN

)

(a)

0

50

100

150

200

250

300

0 2.5 5 7.5 10 12.5 15 17.5 20

B5 (5H14)B4 (4H14)B1 (3 12)


Load

(kN

)

(b)

Yield Level of HRB Bars


Fig. 12. Load-Reinforcing Strain of the Tested Beams for Group A.

Table 8 Experimental Reinforcing Strain of the Tested Beams.

Group Beam Type of Bar

Reinforcing Strain at Yield Level, (εy)

Reinforcing Strain at the Ultimate level, (εt)

Strain Ductility,

μs =εt

εy

Group A

B1 HTS 0.002 0.0198 10.42 B2 HRB 0.0025 0.0148 5.90 B3 HRB 0.0025 0.0112 4.48 B4 HRB 0.0026 0.0074 2.85 B5 HRB 0.0025 0.005 2.00

Group B

B6 HTS 0.0020 0.0142 7.10 B7 HRB 0.0022 0.012 5.45 B8 HTS 0.0020 0.0064 3.20 B9 HRB 0.0024 0.0075 3.10 B10 HRB 0.0026 0.0057 2.19 B11 HRB 0.0024 0.0048 2.00 B12 HRB 0.0024 0.004 1.67

Where: HTS: high tensile steel bar and HRB: hybrid reinforcement bar.

0

50

100

150

200

250

300

0 2.5 5 7.5 10 12.5 15 17.5 20

B8 (3G12+2 10)B7 (2H14+2 10)B6 (4 12+1 10)


Load

(kN

)

(a)

0

50

100

150

200

250

300

0 2.5 5 7.5 10 12.5 15 17.5 20

B10 (1H14+3G12)B9 (2H14+2G12)B6 (4 12+1 10)


Load

(kN

)

(b)



0

50

100

150

200

250

300

0 2.5 5 7.5 10 12.5 15 17.5 20

B12 (2H14+4G12)B11 (2H14+3G12)B6 (4 12+1 10)


Load

(kN

)

(c)


Fig. 13. Load-Reinforcing Strain of the Tested Beams for Group B.

M. Said et al.


9

Utilizing hybrid bars as tension reinforcement exhibit an improve-ment in the stiffness (K) which can be defined as the ratio between load at yield level (Py) to the corresponding displacement (δy) [27]. For Group A, compared with B1, the stiffness was enhanced for B2, B3, B4, and B5 respectively by 30%, 61%, 67%, and 69%. Accordingly, using hybrid reinforcement bars displayed an enhancement in the stiffness compared with steel reinforcement beams.

For Group B, compared with B6, no significant change in the stiffness for B7 (hybrid and steel bars) was observed. On the other hand, a sig-nificant reduction in the stiffness was observed for beams B8, B9, B10,

B11, and B12 respectively by 59%, 51%, 60%, 42%, and 41%. The reduction in the stiffness of the hybrid schemes beams compared with steel reinforcement bars occurred due to the existence of GFRP bars which have a lower modulus of elasticity.

b. Energy Absorption (Toughness)

Energy absorption (I) is defined as the area under the load–deflection curve. It is a function of the ultimate load (Pu) and the corresponding ultimate deflection (δu) [27]. Accordingly, it can be a good indication to

B1

B2

B3

B4

B5

Fig. 14. Cracks Pattern for Group A.

M. Said et al.


10

measure the ductility of the beams. Generally, energy absorption improved by increasing hybrid bars reinforcing ratio. For Group A, the energy absorption for B2, B3, B4, and B5 was higher than B1 respec-tively by 163%, 275%, 437%, and 563%.

For Group B, compared with steel reinforcement concrete beam (B6), a slight change in the toughness was observed for beams B8 (0.85% GFRP + 0.41% steel) and B10 (0.85% GFRP + 0.42% HRB). The in-clusion of HRB with higher reinforcement ratios for beams B9, B11, and B12 provided more ductile behaviour for the tested beams. Conse-quently, significant improvement in the toughness was observed by 51%, 117%, and 123% respectively with reference to B6. Finally, using HRB is an effective way to enhance the toughness of the RC beams.

c. Ductility Factor (DF)

Ductility factor (DF) for tested beams can be defined as the ratio between the deflection at the ultimate level (δu) to the deflection at the yield level (δy) [28]. The inclusion of hybrid bars provides more ductile performance for the tested beams. For Group A, comparing with beam

B1, the DF improved by 36%, 67%, 47%, and 30% respectively for B2, B3, B4, and B5. For Group B, the DF of the beams displayed lower values than Group A due to the brittle behaviour of GFRP bars. With reference to B6, the DF degraded respectively by 72%, 60%, 69%, 44%, and 53% for B8, B9, B10, B11, and B12. Based on the recorded test results, the inclusion of hybrid reinforcement bars with enhanced the flexural per-formance of concrete beams compared with steel reinforcement bars.

3.3. Strains in the hybrid bars

Strain gauges were fixed at the tension reinforcement bars to mea-sure the strain as illustrated in Fig. 8. For beams reinforced with steel reinforcement bars or hybrid reinforcement bars, the strains were fixed in the middle of these bars. For beams reinforced with hybrid schemes (steel + GFRP) bars or (hybrid + GFRP) bars, the strain gauges were fixed for each bar type. The strains of the steel reinforcement bars and hybrid bars at the ultimate level (εt) were recorded in Table 8. Also, the load- strain curves for steel reinforcement bars and the hybrid bars of Group A and Group B are plotted in Figs. 12 and 13 respectively. A close

B6

B7

B8

B9

Fig. 15. Cracks Pattern for Group B.

M. Said et al.


11

examination of the strain measurements reveals that the strain of the tension reinforcement bars at the ultimate level (εt) exceeds the strain at the yield level (εy) for all beams. Accordingly, all beams have been failed in a ductile manner. The recorded tensile reinforcement strains for GFRP bars in Group B at the ultimate level for specimens B8, B9, B10, B11, and B12 was 0.013, 0.0115, 0.011, 0.0105, and 0.01 respectively. These strains are lower than the ultimate tensile strain of GFRP bars. Accord-ingly, the GFRP bars did not rupture at the failure of beams. Generally, based on the strain measurements, the bond failure was not observed in all the test specimens. Based on the measured mechanical properties of the hybrid bars in Section 2.1, the possible failure modes could occur as follows:

1. Concrete crushing (CC) before hybrid reinforcement bars yielding (over-reinforced case). In which (εc = εcu) and (εhr < εhry).

2. Yielding of hybrid reinforcement bars (HRB) followed by concrete crushing (ductile case). In which (εc = εcu) and(εhry ≤ εhr < εhru).

3. The strain of hybrid bars reaches the ultimate strain before concrete crushing. In which (εc < εcu) and(εhr = εhru).

As can be shown in Fig. 12 and Table 8, the strain in the hybrid reinforcement at the ultimate level is laying between the yield and ul-timate strain values(εhry ≤ εhr < εhru). Accordingly, the failure mode of case-2 has been observed for the test beams. To avoid the failure modes of case 1 and 3, upper and lower limits for the balanced ratios of the hybrid reinforcement should be defined. The maximum and minimum balanced ratios of the hybrid reinforcement could be defined as follows

[29]:

ρbhr,min =fc’fhr,u

×εcu − (εco/3)

εcu + εhr,u(2)

ρbhr,max =fc’fhr,y

×εcu − (εco/3)

εcu + εhr,y(3)

In the current study, the values of ρbhr, min. and ρbhr, max are 0.48% and 3.64% respectively and the hybrid reinforcement ratios for the tested beams ranged between these values. Accordingly, yielding of HRB fol-lowed by concrete crushing was indicated.

From the load-reinforcing strain curves, the strain ductility (μs) was evaluated as the ratio between strain in the longitudinal bars at the ul-timate level to the strain at the yield level (μs= εt /εy) [30]. As observed in Table 8, the measured strain at the ultimate level (εt) decreased as the ratio of the hybrid reinforcement bars (ρhr) increased. Accordingly, the strain ductility values decreased as ρhr increased. For Group A, compared with B1, the strain ductility was decreased by 40% and 58% respectively for B2 and B3. For Group B, using hybrid schemes is an effective way to solve the brittle behaviour of GFRP concrete beams. The inclusions of steel bars or hybrid reinforced bars with GFRP bars provides more ductile behaviour for the beams.

3.4. Failure modes and cracks pattern

Tracing the cracks with recording the corresponding causing loads at different load levels is one of the most powerful procedures to identify

B10

B11

B12

Fig. 15. (continued).

M. Said et al.


12

the failure mechanism and highlighting the related effect of the exper-imental variables. The crack patterns for Group A and B were the same as presented in Figs. 14 and 15 respectively for Group A and Group B. Generally, initial crack for all tested beams appeared in the beam mid- span at the flexural region followed by consecutive cracks away from this region in the direction of supports with increasing load increments. Increasing load values led to deeper and widened cracks with a major flexural crack in the maximum moment area at the failure load level.

For Group A, using hybrid bars for beams B2, B3, B4, and B5 delayed the appearance of the first crack with reference to the beam with steel reinforcement B1. Increasing the hybrid reinforcement ratios delayed the appearance of the first crack by 23% and 31% respectively for beams B3 and B4. Moreover, at failure load, using hybrid bars resulted in less spread cracks and less visual crack width.

For Group B, reinforcing the beams with a combination of steel or hybrid bars with GFRP bars increased the cracking loads and reduced

(a) Concrete Element; Solid65

(b) Reinforcing Bar Element; Link8Fig. 16. Finite Element Simulation Models for the Tested Beams.

M. Said et al.


13

the crack propagation when compared with beam B6 reinforced only with steel reinforcement bars. Beams B8 and B10 showed almost similar cracking loads with no significant deviation in cracks pattern. Addi-tionally, the inclusion of hybrid reinforcement bars for beams B7, B9, B10, and B12 had an acceptable improvement in limiting the crack width and propagation.

The observed failure mode for the concrete beams reinforced with steel reinforcement bars was conventional ductile flexural failure (flexural-tension failure). This failure mode occurred due to yielding of the tensile steel reinforcement (SY) followed by concrete crushing (CC). Also, observed failure mode for the concrete beams reinforced with HRB

was yielding of HRB followed by CC, as discussed in Section 3.3. In addition, for concrete beams reinforced with hybrid schemes, the failure mode was characterized by yielding of steel reinforcement followed by concrete crushing, before the rupture of FRP reinforcement. This case is similar to the under-reinforced section of RC beams (flexural-tension failure).

4. Non-Linear Finite Elements Analysis (NLFEA)

NLFEA was performed to simulate the tested concrete beams. The commercially available finite element (FE) analysis software package

(a) At Cracking Load, Pcr

(b) At Failure

Fig. 17. Cracks Propagation for Beam B2.

M. Said et al.


14

ANSYS (ANSYS release 12.1) [25] was used. The load–deflection curve is an important aspect of verifying the behaviour of beams. It includes beneficial parameters such as: cracking loads (Pcr), the load at yield point (Py), the corresponding deflection (δy), the ultimate load (Pu), the corresponding ultimate deflection (δu), the initial stiffness (K), the

ductility factor (DF), and energy absorption (I). Also, the predicted strain ductility (μs, NL.) was defined. Accordingly, comparing the extracted load–deflection curves from the idealized models with the experimental test results considered is an efficient method to validate the models.

0

25

50

75

100

0 5 10 15 20 25 30 35 40

ExperimentalNumerical

Deflection (mm)

Load

(kN

)

B1

0.0

50.0

100.0

150.0

0 10 20 30 40 50 60 70


Deflection (mm)

Load

(kN

)

B2

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B3

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B4

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B5

Fig. 18. Comparison of Predicted Deflections with Experimental Values of Group A.

M. Said et al.


15

0

50

100

150

200

250

0 10 20 30 40 50 60


Deflection (mm)

Load

(kN

)

B9

0

50

100

150

200

250

0 10 20 30 40 50 60

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B10

0

50

100

150

0 10 20 30 40 50

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B6

0

50

100

150

200

0 10 20 30 40 50 60

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B7

0

50

100

150

200

0 10 20 30 40 50

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B8

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B11

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

Experimental

Numerical

Deflection (mm)

Load

(kN

)

B12

Fig. 19. Comparison of Predicted Deflections with Experimental Values of Group B.

M. Said et al.


16

4.1. Finite element geometric and material idealization

The structural element types used for the geometric idealization of the different materials are Solid 65 for concrete as its capability to the plastic deformation, cracking and crushing in three directions. 3-D spar elements (Link 8) was used for idealized reinforcing bars and stirrups. It has two nodes and three DOF. Also, it has the capability of plastic deformation. Solid 45 was idealized at the location of loading and supports in the concrete beams to avoid stress concentration problems. Hawileh [31] used the same elements and procedures for modelling concrete beams reinforced with hybrid schemes bars. The predicted results showed reasonable agreement comparing the experimental test results.

For concrete in compression, the Hognestad-Popvics stress–strain curve [32] was used. For concrete in tension, a linear-tension curve was used [33]. The bilinear stress–strain curve was adopted for steel rein-forcement in tension and compression [34], while a linear elastic behaviour was used for the GFRP bars. The idealized stress–strain curve for the hybrid bars shown in Fig. 6 was used in the idealization. Perfect bond was assumed between the concrete and bars. The 3-D model for a typical beam is presented in Fig. 16.

4.2. NLFEA model verification

NLFEA results were verified with the experimental test results. First, cracks appeared at the maximum tension zone in the mid-span. Then, the cracks propagated in an upward direction through the depth of the beam. New cracks occurred in the shear region due to increasing the load, as shown in Fig. 17.

All beams exhibited similar patterns of crack development and propagation. NLFEA showed the first formation of vertical cracks in the mid-span at load levels of 27–35 kN. The predicted cracking loads (Pcr-

NL.) were close to experimental crack loads (Pcr-exp.). The average value of the ratio (Pcr-exp./Pcr-NL.) is 1.05 with a standard deviation of 0.048 and the coefficient of variation equal 4.54%.

4.3. Load-deflection comparison

The analytical results for all beams were very close to the experi-mental results. Generally, the load–deflection curves for the tested beams displayed similar features. A comparison of the load–deflection curves extracted from ANSYS and test results for all the beams are plotted in Figs. 18 and 19 for Group A and Group B respectively and listed in Table 9. The comparison evinced that, at the yield level, the overall average ratio [Py, exp./Py, NL.] is 1.053. Also, the average yield deflection ratio [δ y, exp./δy, NL.] is 1.05. At the ultimate level, the average ratio [Pu, exp./Pu, NL.] for all beams is 1.01 and the average value of deflection ratio [δ u, exp./δu, NL.] is 1.03. The average stiffness ratio [Kexp./ KNL.] for all beams is 0.98. Moreover, the average energy absorption ratio [I exp./INL.] for all beams is 1.06.

4.4. Parametric studies

To advance the knowledge and further investigate the effect of different factors in the structural response of hybrid reinforced concrete beams, a parametric study is designed and conducted herein. The vari-ables of the parametric study are concrete compressive strength (fcu), the ratio of the hybrid reinforcement bars (ρhr), and shear-span to depth ratio (X/d). In the parametric study, the validated specimen B2 will be the reference beam. Table 10 presents the input parameters and analysis results of the analyzed specimens in the parametric study.

4.4.1. Effect of concrete strength The effect of the concrete compressive strength (fcu) on the flexural

performance of hybrid reinforced concrete beams is investigated. Two additional finite element models were developed with concrete Ta

ble

9 Co

mpa

riso

n of

Exp

erim

enta

l Res

ults

with

NLF

EA R

esul

ts.

Beam

Ex

peri

men

tal R

esul

ts

NLF

EA R

esul

ts

Expe

rim

enta

l Res

ults

/ N

LFEA

Res

ults

P cr

(kN

) P y

(kN

) δ y

(m

m)

P u (

kN)

δ u (

mm

) K

(kN

/mm

) I (

kN.m

m)

DF

P cr

(kN

) P y

(kN

) δ y

(m

m)

P u (

kN)

δ u (

mm

) K

(kN

/mm

) I (

kN.m

m)

DF

P cr−

exp.

P cr−

NL.

P y−

exp.

P y−

NL.

δ y−

exp.

δ y−

NL.

P u−

exp.

P u−

NL.

δ u−

exp.

δ u−

NL.

Kex

p.

KN

L.

I exp

.

I NL.

DF e

xp.

DF N

L.

B1

26

84.5

8

92

34

10.3

8 31

50

4.30

27

79

7.

25

84.5

31

.2

10.9

0 29

10

4.30

0.

96

1.07

1.

09

1.09

1.

09

0.95

1.

08

1.00

B2

29

13

5 10

15

7 61

13

.46

8300

5.

87

28

122

10.9

8 15

0.1

66.1

12

.30

8420

6.

02

1.04

1.

11

0.95

1.

05

0.92

1.

09

0.99

0.

97

B3

32

155

9 19

3 67

16

.76

11,8

00

7.19

30

15

0 8.

6 20

0 68

.0

17.4

4 12

,600

7.

91

1.07

1.

03

1.08

0.

96

0.98

0.

96

0.94

0.

91

B4

34

220

12

246

73

17.2

9 16

,900

6.

33

32

204

11

260

77.3

18

.55

17,1

50

7.02

1.

06

1.08

1.

05

0.95

0.

95

0.93

0.

99

0.90

B5

37

26

0 15

27

9 83

17

.57

20,9

00

5.61

35

24

0 13

.75

294.

5 85

.0

17.4

5 22

,000

6.

18

1.06

1.

08

1.08

0.

95

0.98

1.

01

0.95

0.

91

B6

30

133

8 15

2 46

16

.02

6500

5.

54

29

128

7.57

6 14

7 42

.0

16.9

0 58

20

5.54

1.

03

1.04

1.

10

1.03

1.

10

0.95

1.

12

1.00

B7

33

15

9 9

187

51

17.2

6 91

00

5.68

31

15

7 9.

1 18

2.2

56.0

17

.80

9180

6.

15

1.06

1.

01

0.99

1.

03

0.91

0.

97

0.99

0.

92

B8

29

170

26

171

40

6.54

59

00

1.54

31

16

0 25

16

8.5

37.0

6.

40

5310

1.

48

0.94

1.

06

1.04

1.

01

1.08

1.

02

1.11

1.

04

B9

34

197

25

203

55

7.88

98

00

2.20

32

19

4 23

19

8.25

52

.0

8.43

86

80

2.26

1.

06

1.02

1.

09

1.02

1.

06

0.93

1.

13

0.97

B1

0 29

19

0 30

20

0 50

6.

44

7400

1.

69

27

175

27

189.

5 47

.2

6.48

69

80

1.75

1.

07

1.09

1.

09

1.05

1.

06

0.99

1.

07

0.97

B1

1 35

23

0 21

24

5 66

9.

27

14,1

00

3.12

32

22

0 20

24

3.25

60

.5

10.0

0 12

,500

3.

03

1.09

1.

05

1.06

1.

01

1.10

0.

93

1.13

1.

03

B12

36

250

27

255

69

9.43

14

,500

2.

60

33

248

27.1

5 25

3.5

63.4

9.

13

13,2

00

2.34

1.

09

1.01

0.

98

1.01

1.

09

1.03

1.

10

1.12

A

vera

ge

1.05

1.

053

1.05

1.

01

1.03

0.

98

1.06

0.

98

Stan

dard

dev

iati

on

0.04

8 0.

032

0.04

9 0.

041

0.06

9 0.

048

0.07

5 0.

061

Coef

fici

ent

of v

aria

tion

4.

54%

3.

08%

4.

64%

4.

09%

6.

74%

4.

92%

7.

12%

6.

26%

M. Said et al.


17

compressive strengths of 30 and 60 MPa and designated as B2a and B2b, respectively. The load–deflection response results of these beams are shown in Fig. 20 and Table 10. The comparison between the given re-sults indicates that increasing fcu leads to an enhancement in load- carrying capacity by 18% and 34% along with an increase of 35% and 57% in the associated mid-span deflection for specimens B2 and B2b respectively when compared to B2a. The calculated strain ductility (µs) is 3.6, 6.29, and 7.32 for B2a, B2, and B2b respectively. Then, the strain ductility (µs) has been increased due to an increase in the concrete compressive strength (fcu). Significant enhancement in the toughness (I) which calculated as the area under the load–deflection curve is observed due to the increase of fcu. Toughness is enhanced by 55% and 117% for specimens B2 and B2b respectively compared to specimen B2a. Finally, the crack patterns are shown in Fig. 21 for B2a, B2, and B2b. As illus-trated in this figure, that increasing (fcu) increases cracks propagation at the beam length and depth.

4.4.2. Effect of hybrid reinforcement ratio Three beams were analyzed with different hybrid reinforcement ra-

tios (ρhr) of values (0.85%, 1.7%, and 3.85%) respectively for beams (B2, B2c, and B2d). Fig. 22 presents the predicted load–deflection response for the analyzed beams. It is clear that increasing ρhr improves the load- carrying capacity of the specimens by 73% and 106% for B2c and S2d with respect to B2. Also, the toughness (I) is improved by increasing ρhr. The toughness is enhanced by 104% and 129% respectively for beams B2c and B2d compared with B2. On the other hand, increasing the

hybrid reinforcement ratio decreases the hybrid strain at the ultimate level (εt). Compared with B2, the hybrid strain at the ultimate level is decreased by 52% and 86% respectively for B2c and B2d. Furthermore, the hybrid strain at the ultimate level does not exceed the strain at the yield level for beam B2d due to the over-reinforcement ratio. The pre-dicted values of strain ductility are 6.92, 3.0, and 0.91 for specimens B2, B2c, and B2d. The predicted crack patterns for B2, B2c, and B2d are shown in Fig. 23. As shown in the predicted crack patterns, increasing the hybrid reinforcement ratio spreads cracks more widely and gradu-ally along the span and depth of the beams.

4.4.3. Effect of shear-span to depth ratio Three specimens are studied with different shear span to depth ratio

(X/d) values. The used shear-span to depth ratios are 2.18, 2.55, and 3.1 for specimens B2e, B2f, and B2 respectively. The predicted load–deflection curves for the specimens are plotted in Fig. 24. Gener-ally, increasing (X/d) reduces the load-carrying capacity of the beams. Increasing (X/d) for specimens B2f and B2 decreases Pu by 18% and 29% respectively compared with B2e. Increasing (X/d) decreases slightly the toughness (I). As shown in the predicted load–deflection curves, the toughness is decreased for specimens B2f and B2 by 4% and 9% respectively. Also, the strain ductility (μs) is increased by increasing (X/ d). The values of (μs) are 4.2, 4.7, and 6.29 for B2e, B2f, and B2 respectively. The cracking patterns of the analyzed beams (B2e, B2f, and B2) are also shown in Fig. 25. The figure illustrated that, the amount of vertical and inclined cracks increases with the increase of (X/d) ratio.

5. Nominal flexural strength

The experimental moment strength (M exp.) for each beam was calculated (using the relation P/2*X, where P is the failure load and X is the flexural-shear span = 0.85 m). To compare the experimental results with the nominal flexural strength (Mn.), the strain compatibility method was performed. The nominal flexural strength is estimated for a single hybrid concrete rectangular beam of cross-section (b × t). The proposed equation of the current research is an enhancement equation of ACI Code 318–14 [35]. The main assumptions to predict the nominal flexural strength were considered. Moreover, the idealized stress–strain curve for the hybrid bar presented in Eq. (1) was used. Fig. 26 presents the simplified rectangular stress block. Accordingly, the nominal flex-ural strength, the equilibrium equation can be expressed as follows:

Cc = Ts + Tf +Thr (4)

The compression force of concrete (Cc) can be estimated depending

Table 10 Input Parameters and Analysis Results of the Analyzed Specimens.

Input Parameters Analysis Results

Beam fcu (MPa) ρhr (%) X/d Studied Parameter Pcr (kN) Py (kN) δy (mm) Pu (kN) δu (mm) K (kN/mm) I (kN.mm) εt μs, N.L

B2a 30 0.85 3.1 fcu 21 108 9.8 127 49 11.02 5435 0.009 3.6 B2 45 0.85 3.1 28 122 10.98 150 66.1 12.30 8420 0.0137 6.29 B2b 60 0.85 3.1 32 148 11.1 170 77 13.33 11,812 0.0183 7.32 B2 45 0.85 3.1 ρhr 28 122 10.98 150 66.1 12.30 8420 0.0137 6.29 B2c 45 1.7 3.1 32 204 11 260 77.3 18.55 17,150 0.0072 3.0 B2d 45 3.85 3.1 34 246 10.25 310 68 23.2 19,300 0.0023 0.91 B2e 45 0.85 2.18 X/d 31 155 12.2 210 54 12.70 9233 0.0105 4.2 B2f 45 0.85 2.55 29 138 11.2 172 60 12.32 8863 0.0118 4.72 B2 45 0.85 3.1 28 122 10.98 150 66.1 12.30 8420 0.0137 6.29

0.0

50.0

100.0

150.0

200.0

0 10 20 30 40 50 60 70 80

B2b (fcu=60 MPa)B2 (fcu=45 MPa)B2a (fcu=30 MPa)

Deflection (mm)

Load

(kN

)

Fig. 20. Effect of Concrete Compressive Strength on the Load-Deflection Response of HRC Beams.

M. Said et al.


18

on the rectangular stress block which, calculated generally as:

Cc = σc*Ac (5)

The compressive strength of concrete (ơc) can be defined as:

σc = α.fc’ (6)

The coefficient (α) assumed to be 0.85, according to ACI-code 318–14 [35]. Also, the cylindrical compressive strength of the con-crete (fc’) was considered as (0.8 fcu). Additionally, the area of compression zone (Ac) was defined as:

Ac = b.a (7)

The depth of the rectangular stress block (a) was estimated as:

a = β.C (8)

Factor (β) should not exceed 0.85 but shall not be taken less than

a) B2a

b) B2

c) B2b

Fig. 21. Predicted Crack Pattern for Beams B2a, B2 and B2b.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

0 10 20 30 40 50 60 70 80 90

B2d (ρh=3.85%)B2c (ρh=1.7%)B2 (ρh=0.85%)

Deflection (mm)

Load

(kN

)

Fig. 22. Effect of Hybrid Reinforcement Ratio on the Load-Deflection Response of HRC Beams.

M. Said et al.


19

a) B2

b) B2c

c) B2d

Fig. 23. Predicted Crack Pattern for Beams B2, B2c and B2d.

M. Said et al.


20

0.65 [35]. It can be calculated as:

β = 0.85 − 0.05[

f ’c − 28

7

]

(9)

Conclusively, Cc can be defined as:

Cc = 0.85*f ’c *b*a (10)

For under reinforced section, the tension force of reinforcing bars Ts, Tf and Thr can be calculated as follows:

Ts = fy*As (11)

Tf = ff *Af (12)

Thr = fhr*Ahr (13)

Based on the rectangular stress block and the equilibrium equation, (a) and (C) can be predicted. Accordingly, Mn. can be estimated as:

Mn. =[(

Asfy + Af ff + Ahrfhr)(

d −a2

) ](14)

The analysis procedure for calculating Mn. can be easily implemented by hand calculations or a spreadsheet. Mn. was calculated for all beam specimens using Eq. (14). Table 11 presents a comparison between the experimental and nominal flexural strength. It can be concluded that good agreements between the experimental and nominal flexural strength were achieved. The average ratio of [Mu, exp./Mn.] for the tested beams is 1.037 with 0.043 standard deviation, and the coefficient of variation equal 4.10%. Moreover, Table 11 includes a comparison with 38 reinforced concrete beams tested [1,12,14,18]. The nominal flexural strength generally performs well in predicting the flexural strength. The overall average value of the ratio [Mu, exp./Mn.] is 1.01 with a standard deviation of 0.08, and the coefficient of variation equals 7.57%.

Table 12 presents the comparison between the strain in the tension reinforcement at the ultimate level measured from the experimental test results (εt , exp.) with the predicted strain in the tension reinforcement from ANSYS (εt , NL.) and with the nominal strain (εt ,n.) which defined as following [35]:

εt,n. = 0.003(

dc− 1

)

(15)

Also, the strain ductility (μs) was calculated. Comparing the test re-sults with NLFEA and nominal strain ductility, good agreements were achieved, the overall average value of the ratio [μs, exp./μs, NL.] is 1.04 with a standard deviation of 0.091, and the coefficient of variation equals 8.75%. Also, the overall average value of the ratio [μs, exp./μs, n.] is 1.095 with a standard deviation of 0.07, and the coefficient of variation

equals 6.41%.

6. Conclusions

The flexural behaviour of concrete beams reinforced with locally produced hybrid bars was investigated. Based on the experimental re-sults and the comparison with the NLFEA and nominal flexural strength in this study, the main conclusion points can be drawn as follows:

1) Generally, the provision of the hybrid reinforcement bars enhanced the flexural behaviour of RC beams compared with steel-reinforced concrete beams in terms of the cracking load, load-carrying capac-ity, ductility, and energy absorption.

2) The locally produced hybrid bars showed bi-linear behaviour indi-cating an enhancement in the ductility against the brittle failure of GFRP bars. These bars displayed reasonable mechanical properties compared with the results from the literature.

3) The design of RC beams with hybrid reinforcement bars should consider the steel yielding prior to concrete crushing or FRP rupture in case of hybrid schemes to ensure adequate deformation in the beams.

4) For RC beams with HRB bars, the enhancement in the load-carrying capacity occurred due to the high tensile strength of the outer layers of the GFRP in addition to the tensile strength of the internal layer of steel reinforcement. Also, the improvement in the load-carrying ca-pacity for RC beams with hybrid schemes was observed because of the role of GFRP bars in resisting loads after the yielding of steel reinforcement.

5) Hybrid bars exhibited an improvement in the stiffness of the concrete beams compared with steel reinforcement beams. On the other hand, a reduction in the stiffness was observed for concrete beams rein-forced with hybrid schemes due to the lower elastic modulus of GFRP bars.

6) All hybrid-reinforced beams with (ρbhr, min. < ρhr < ρhr, max.) failed in a favorable ductile manner due to concrete crushing after yielding of HRB reinforcement.

7) The application of NLFEA to the tested beams yielded acceptable load-carrying capacities and load–deflection curves. The analysis adequately reflected the trend of experimental results. At the ulti-mate level, the overall average ratio [Pu, exp./Pu, NL.] was 1.013. Accordingly, the developed models can be used by researchers as an analytical tool to investigate the performance of RC beams reinforced with HRB or hybrid schemes of GFRP and steel reinforcement bars.

8) Increasing concrete compressive strength (fcu) enhanced the load- carrying capacity and the toughness of HRC beams. On the other hand, increasing the shear-span to depth ratio reduced the load- carrying capacity and the toughness of the beams.

9) The nominal flexural strength for hybrid concrete beams proved to be a successful analytical tool for predicting flexure strength (Mn.). The nominal flexure strength predictions for 50 experimental test results were on the safe side and gives consistent predictions.

CRediT authorship contribution statement

Mohamed Said: Conceptualization, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration. Ali S. Shanour: Conceptualization, Software, Valida-tion, Formal analysis, Investigation, Resources, Data curation, Writing - review & editing, Visualization, Supervision, Project administration. T. S. Mustafa: Conceptualization, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - review & editing, Visualization, Supervision, Project administration. Ahmed H. Abdel- Kareem: Resources, Writing - review & editing, Supervision, Project administration. Mostafa M. Khalil: Software, Validation, Formal anal-ysis, Investigation, Resources, Data curation, Writing - original draft,

0.0

50.0

100.0

150.0

200.0

250.0

0 10 20 30 40 50 60 70

B2e (X/d=2.18)B2f (X/d=2.55)B2 (X/d=3.10)

Deflection (mm)

Load

(kN

)

Fig. 24. Effect of Shear-Span to Depth Ratio on the Load-Deflection Response of HRC Beams.

M. Said et al.


21

a) B2e

b) B2f

c) B2

Fig. 25. Predicted Crack Pattern B2, B2e and B2f.

M. Said et al.


22

b

t

FRP bars

d'd

a) General Cross Section b) Stress Distribution c) Rectangle Stress Block

a=ßC

c

Cc

Ts+Tf+ThrC

c

N.A

Hybrid bars

Steel bars

Mn.

Ts+Tf+Thr

d-(a

/2)

Fig. 26. Cross Section Stress Distribution for Hybrid Concrete Beams.

Table 11 Experimental and Nominal Flexural Strength.

Authors Beam fcu Geometrical Parameters Bottom RFT Experimental moment, Mexp.

Nominal flexural strength, Mn.

Mexp.

Mn.b d L CL-

CL

X As fy Af ff Ahr fhr ρt

MPa (mm) (mm) (mm) (mm) HTS MPa FRP MPa HRB HRB % (kN.m) (kN.m)

Present B1 45 150 275 2100 850 3∅ 12 400 — — — — 0.85 39.1 36.75 1.064 B2 45 150 275 2100 850 — — — — 2H14 630 0.85 66.73 60.35 1.106 B3 45 150 275 2100 850 — — — — 3H14 630 1.26 81.813 82.45 0.992 B4 45 150 275 2100 850 — — — — 4H14 630 1.7 104.55 102.85 1.017 B5 45 150 275 2100 850 — — — — 5H14 630 2.13 118.58 120.28 0.986 B6 45 150 275 2100 850 4∅

12 +1∅ 10

400 — — — — 1.26 64.64 58.65 1.102

B7 45 150 275 2100 850 2∅ 10 400 — — 2H14 630 1.26 79.48 73.10 1.087 B8 45 150 275 2100 850 2∅ 10 400 3G12 850 — — 1.26 72.68 69.70 1.043 B9 45 150 275 2100 850 — — 2G12 850 2H14 630 1.27 86.28 84.15 1.025 B10 45 150 275 2100 850 — — 3G12 850 1H14 630 1.27 84.78 81.13 1.045 B11 45 150 275 2100 850 — — 3G12 850 2H14 630 1.7 103.95 102.43 1.015 B12 45 150 275 2100 850 — — 4G12 850 2H14 630 1 108.38 111.35 0.973

Adam, et al. [1]

A25 25 120 275 2500 1100 — — 3G12 + 1G8

650 — — 0.92 40.81 37.5 1.088

A25- 1

25 120 275 2500 1100 — — 2G8 650 — — 0.33 25.245 23.01 1.097

A25- 2

25 120 275 2500 1100 — — 1G12 + 1G8

650 — — 0.56 22.385 23.86 0.938

A25- 3

25 120 275 2500 1100 — — 2G12 + 1G8

650 — — 0.89 41.36 38 1.088

A45- 1

45 120 275 2500 1100 — — 1G12 + 1G8

650 — — 0.54 30.69 28.98 1.059

A45- 2

45 120 275 2500 1100 — — 2G12 + G18

650 — — 0.92 45.045 47.2 0.954

A45- 3

45 120 275 2500 1100 — — 4G12 650 — — 1.46 60.39 62 0.974

A70- 1

70 120 275 2500 1100 — — 2G12 + 1G8

650 — — 0.92 46.53 43.8 1.062

A70- 2

70 120 275 2500 1100 — — 4G12 650 — — 1.56 72.985 69.2 1.055

A70- 3

70 120 275 2500 1100 — — 6G12 650 — — 2.48 79.805 87.5 0.912

Authors Beam fcu

(MPa) Geometrical Parameters Bottom RFT Experimental

moment, Mexp.


Mexp.

Mn.b d L CL-

CL


(continued on next page)

M. Said et al.


23

Table 11 (continued )

Authors Beam fcu


moment, Mexp.


Mexp.

Mn.b d L CL-

CL


(mm) (mm) (mm) (mm) HTS MPa FRP MPa HRB HRB % (kN.m) (kN.m)


Qu, et al. [12]

B1 30.95 180 220 1800 600 4∅ 12

363 — — — — 1.14 32.37 31.9 1.015

B2 30.95 180 220 1800 600 — — 4G12 782 — — 0.29 43.89 40.2 1.092 B3 33.1 180 220 1800 600 2∅

12 363 2G12 782 — — 0.71 38.28 41.2 0.929

B4 33.1 180 220 1800 600 1∅ 16

336 2G16 755 — — 0.71 39.66 42.5 0.933

B5 34.4 180 220 1800 600 2∅ 16

336 2G10 778 — — 1.08 36.36 39.8 0.914

B6 34.4 180 220 1800 600 2∅ 16

336 2G12 782 — — 1.16 42.57 45.01 0.946

B7 40.65 180 220 1800 600 1∅ 10

363 2G10 778 — — 0.35 23.55 22.8 1.033

B8 40.65 180 220 1800 600 6∅ 16

336 2G16 755 — — 3.49 63.3 66.5 0.952

El Refai, et al. [14]

B1 40 230 275 3700 1250 — — 2G12 1000 — — 0.38 49 48.7 1.006 B2 40 230 275 3700 1250 — — 3G12 1000 — — 0.64 53.7 60 0.895 B3 40 230 275 3700 1250 — — 3G16 1000 — — 1.12 69 72 0.958 B4 40 230 275 3700 1250 1∅

10 520 2G12 1000 — — 0.51 47.6 50 0.952

B5 40 230 275 3700 1250 2∅ 10

520 2G12 1000 — — 0.55 53.5 58.4 0.916

B6 40 230 275 3700 1250 2∅ 12

520 2G12 1000 — — 0.67 58 64 0.906

B7 40 230 275 3700 1250 2∅ 10

520 2G16 1000 — — 0.85 68.6 78.5 0.874

B8 40 230 275 3700 1250 2∅ 12

520 2G16 1000 — — 0.96 64.7 69 0.938

B9 40 230 275 3700 1250 2∅ 16

520 2G16 1000 — — 1.13 83.5 82.5 1.012

Authors Beam fcu


moment, Mexp.


Mexp.

Mn.b d L CL-

CL



Lau, et al. [18]

G0.8 39 280 255 4200 2100 — — 4G16 593 — — 0.81 158.8 152.52 1.041 G2.1 41.3 280 255 4200 2100 — — 4G25 528 — — 1.98 238 218.21 1.091 G0.4 42.3 280 255 4200 2100 — — 3G12 603 — — 0.34 79.5 68.09 1.167 G0.5 42.5 280 255 4200 2100 — — 4G12 603 — — 0.46 107 89.97 1.189 G2.1 34 280 255 4200 2100 — — 1G25 205 — — 0.49 220 200.05 1.100 G0.3 40 280 255 4200 2100 2∅

25 336 1G20 588 — — 1.27 150 153.18 0.979

G1.0- T0.7

39.3 280 255 4200 2100 2∅ 20

579 2G25 582 — — 1.62 261 255.85 1.020

G0.6- T1.0

40 280 255 4200 2100 2∅ 25

550 2G20 558 — — 1.56 229 252.20 0.908

MD1.3 39 280 255 4200 2100 4∅ 20

340 — — — — 1.26 147.4 141.84 1.039

MD2.1 45.9 280 255 4200 2100 4∅ 25

340 — — — — 1.98 250 216.60 1.154

T0.2 35.3 280 255 4200 2100 2∅ 12

507 — — — — 0.23 44 39.93 1.102

Number of Specimens 50 Average 1.01 Standard deviation 0.08 Coefficient of variation 7.57%

M. Said et al.


24

Writing - review & editing, Visualization, Supervision, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Table 12 Reinforcing Strain of the Tested Beams.

Group Beam Exp. Results NLFEA Results Nominal Results μs,exp.

μs,NL

μs,exp.

μs,n.εy , exp. εt , exp. μs, exp. εt , N.L μs, N.L εt , N. μs, n

Group A B1 0.0019 0.0198 10.42 0.0198 9.00 0.0190 10.10 1.16 1.03 B2 0.0025 0.0148 5.90 0.0158 6.29 0.0137 5.46 0.94 1.08 B3 0.0025 0.0112 4.48 0.0126 5.04 0.0100 4.06 0.89 1.10 B4 0.0026 0.0074 2.85 0.0078 3.00 0.0072 2.77 0.95 1.03 B5 0.0025 0.005 2.00 0.0052 2.10 0.0048 1.92 0.96 1.09

Group B B6 0.0020 0.0142 7.10 0.0135 6.75 0.0120 6.02 1.05 1.18 B7 0.0022 0.012 5.45 0.0126 5.73 0.0108 4.91 0.95 1.11 B8 0.0020 0.0064 3.20 0.006 3.00 0.0069 2.85 1.07 1.12 B9 0.0024 0.0075 3.10 0.0065 2.69 0.0063 2.60 1.15 1.19 B10 0.0026 0.0057 2.19 0.005 1.92 0.0058 2.23 1.14 0.98 B11 0.0024 0.0048 2.00 0.0045 1.88 0.0043 1.79 1.07 1.12 B12 0.0024 0.004 1.67 0.004 1.67 0.0039 1.65 1.00 1.01

Average 1.04 1.095 Standard deviation 0.091 0.07 Coefficient of variation 8.75% 6.41%

M. Said et al.

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experimental flexural performance of concrete beams

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