Experimental and Numerical Evaluation for Hybrid Reinforced T-Beam with Different Ratios of Recycled Rubberized Concrete

Abstract

The use of hybrid GFRP and steel bars as main reinforcement increases the flexural capacity of T-section concrete beams and reduces ductility. Adding recycled rubber to the concrete mix would further enhance the ductility of the hybrid system. Evaluation of the concrete's flexural capacity and ductility is the main goal of the current investigation using normal concrete (NC) and rubberized recycled concrete (RRC). Eight T-beams have been experimentally investigated in this research, two beams were reinforced with steel bars and GFRP bars with zero percentage of crumb rubber (C.R). The remaining beams were reinforced with different combinations of GFRP and steel bars with rubberized concrete mixes with partial substitution of sand with recycled crumb rubber by (0%, 7.5%, 10%, and 12.5% replacements by volume) particle size 1.0 to 2.0 mm. The ductility index for the tested hybrid rubberized T-beams (HRTB) BRH1, BRH3a, BRH5, BRH2, BRH4, and BRH6, were higher than BH1 and BH2 by 28.2%, 35.47%, 65.38%, 23.76%, 30.04%, and 56.95% indicating that increasing the percentage of C.R. has a direct effect on increasing the ductility index. The ultimate failure load for the tested HRTB BRH1, BRH3a, and BRH5, decreased by 11.68%, 14.29%, and 17.47% compared to the hybrid T-beam BH1. The energy dissipation decreased for HRTB BRH1, BRH3a, BRH5, BRH2, BRH4 and BRH6 by 7.88%, 12.36%, 17.17%, 8.12%, 12.96%, and 18.28 compared to hybrid T-beams BH1 and BH2. This indicates that the existence of the very weak C.R. was not able to dissipate the energy properly within the concrete matrix. Good agreement was found between the numerical model and experimental results in terms of crack pattern, ultimate loads and deflections.

1 Introduction

Reinforced concrete T-beams with steel bars, when compared to RC members reinforced with GFRP bars perform differently. Once cracking starts, the lower elastic modulus of FRP causes a significant decrease in the flexural stiffness of RC elements reinforced with FRP bars, leading to severe deformations under service loading circumstances. As a result, the design of RC components reinforced with FRP bars was significantly influenced by the serviceability limit condition. Tensile rupture of GFRP bars, which can occur at the applied point stress or in the mid-span area, is the main cause of flexural failure. The aim of this study was to combine the benefits of FRP bars regarding high strength and reduced cost with steel reinforcement regarding ductility and further enhancement of ductility was introduced using C.R. A significant diagonal crack inside the beam shear span is what causes the shear failure. The horizontal extension of this diagonal crack at the level of the GFRP bars indicated bond failure. The findings showed that the surrounding concrete and FRP reinforcing bars have a flawless connection. In addition, they demonstrate how simple it is to modify the ACI Code formulas for modeling deflection response, cracking-ultimate moments, and cracked-effective moments of inertia to simulate the flexural behavior of concrete beams reinforced with FRP reinforcing bars. The tension-stiffening component in Branson's original expression needed to be reduced to practical levels, which required the rational construction of suitable modification variables. With the proper modification factor, computed deflections using this method produce reasonable results that contrast favorably with a more comprehensive unified approach that includes a plausible tension-stiffening model. This approach is limited to rectangular sections and underestimates the deflection of aramid FRP-reinforced beams. The use of a straightforward modification factor that functions effectively for all varieties of FRP bar and beam cross-sectional shapes is suggested. In contrast to other analytical equations, the approach accurately predicts the load–deflection and the moment–curvature response, according to comparisons with experiments. For a variety of geometric and material features, as well as varied loading circumstances, parametric studies are carried out to examine the agreement of the various empirical equations with that of the present approach. (Ashour, 2006; Benmokrane et al., 2021; Bischoff, 2007; Kara & Ashour, 2012; Rasheed et al., 2004). The behavior of RC components reinforced with FRP bars should be better understood to use FRP reinforcement. Numerous studies have concentrated on RC beams using various types of FRP bars. ACI 440.1R-01 can be used. The deflections and fracture widths of six entire concrete beams reinforced with different GFRP reinforcement ratios were measured and compared to those predicted by the proposed models. The experimental findings were consistent with what the model predicted. (Razaqpur et al., 2000; Toutanji & Deng, 2003; Toutanji & Saafi, 2000; Vijay & Gangarao, 2001; Yost & Gross, 2002). The reuse of old tires in various civil engineering projects can have a positive on the environment. Several research studies Concentrated on the use of C.R. particles as a replacement for sand and aggregates at various ratios. (Oikonomou & Mavridou, 2009; Ozbay et al., 2010) The results revealed that as the % of rubber replacement increased in the concrete mix, the mechanical characteristics of concrete decreased and its workability decreased. (Najim & Hall, 2010, 2012; Zheng et al., 2008) The findings demonstrated that raising the C.R. seems to decrease the weight of concrete, decrease crack width and improve deformability under a given force. On the other hand, initial crack and ultimate flexural were significantly decreased when a high percentage of C.R. (above 15%) was used. (Ismail & Hassan, 2017; Mendis et al., 2018). According to test results, adding more rubber reduces the concrete's compressive strength and elastic modulus. Concrete mixes that are suitable for safety barriers made of concrete in places where strength, fracture toughness, and energy dissipation are required can be made by substituting up to 20–40% of the aggregates with crumb rubber. (Atahan & Yücel, 2012; Liu et al., 2012; Sukontasukkul et al., 2013) The critical crack mouth opening displacement (CMODcri) was also noticeably elevated by thermal damage resulting from heating from 25 to 600 ℃ (Guo et al., 2014). The findings show that when compared to regular NC concrete, reinforced recycled aggregate concrete RRAC with an appropriate rubber content exhibits good compressive behavior. Reinforced recycled aggregate concrete is also a more environmentally friendly alternative to normal rubber concrete for use in the flexural members of concrete structures (Xie et al., 2015). Load–displacement behavior was analyzed for the plain and hybrid concrete beams under static and impact loads were considered in previous studies. The results showed that most of the time hybrid beams were utilized, several characteristics improved, including stress, modulus of rupture, stiffness, failure pattern, and ultimate load. The strain capability of the RRC beams was raised (Ahmed, 2017; Alasmari et al., 2019; Al-Tayeb et al., 2012). The ultimate flexural loads and behavior of concrete slabs reinforced with BFRP were better than those of concrete slabs reinforced with steel reinforcement, according to the experimental test findings. In addition, the theoretical development of finite element models using the software ANSYS 2019-R1 was used to validate the structural behavior of the tested slabs, and in first cracking loads, load-carrying capacity, fracture pattern, and deflection. The effect of the hybrid reinforcement ratio on the flexural performance of concrete beams in both under and over-reinforced scenarios was examined using three-dimensional finite element models. When comparing standard steel-reinforced concrete with fiber-reinforced polymer (FRPRC), the former displays a more ductile behavior. The flexural performance of hybrid FRPRC is significantly influenced by the ratio, or Af/As, of hybrid reinforcement between steel and FRP (Erfan et al., 2021; Qin et al., 2017). The flexural performance of engineered cementitious composite (ECC) concrete beams reinforced with innovative hybrid bars was conducted using FRP or steel bars, proving that hybrid bars improved ultimate strength and ductility. According to the test results, ECC concrete beams reinforced with hybrid bars or hybrid schemes had significantly increased carrying loading capacity. The achieved enhancements are 12% and 27% for polyvinyl alcohol (PVA) ratio of 0.75% and 1.5%, respectively (Said et al., 2020). The results indicated that both the fracture toughness and fracture energy increased with the increase of the rubber content (Guo et al., 2014). A reduced number of wastes of recycled origin may be used in structural OPC concretes (Miraldo et al., 2021). Crumb rubber was substituted in multiples of 2.5% from 0 to 20%. These concrete samples underwent tests to ascertain the depth of carbonation, water absorption, compressive strength, weight change, and chloride penetration of these specimens under acid attack. It is clear from the test findings that high-strength rubberized concrete is extremely resistant to harsh situations (Thomas et al., 2015). By substituting micro-scale C.R. for sand, experiments have been conducted to preserve the electrical resistivity, damping qualities, Compressive, tensile, and flexural strengths of RRC with high strength. The findings of static and dynamic tests showed that certain recycled sign posts might make good substitutes for traditional wooden posts The compressive strength of reinforced self-consolidating rubberized concrete (SSCRC) mixtures was adversely influenced by increasing the proportion of C.R. (AbdelAleem et al., 2018; Atahan & Yucel, 2013; Kaewunruen et al., 2018; Onuaguluchi & Panesar, 2014). It was discovered that, in comparison to regular concrete, RRC is less ductile, more resilient to cracks, and has a lower compressive strength (Alam et al., 2015). When fine aggregates are replaced with C.R. to the extent of 5% and 10%, reinforced concrete beam performance is demonstrated to be satisfactory. Both the toughness and performance of rubber concrete with steel fibers increased as the proportion of rubber exceeded 10% (Eisa et al., 2020). Finite element analysis and concrete damage plasticity models are used to perform three-dimensional non-linear numerical simulations and parametric evaluations. The parametric study's findings allowed for a quantitative assessment of the degree of confinement offered by the transverse reinforcement as well as a direct evaluation of the inelastic behavior in terms of strength and deformation qualities. (Xu et al., 2020). Because GFRP is brittle, beams lose some of their flexibility. HRRC reinforcement has been suggested as a way to increase beam ductility while maintaining the high strength characteristic of GFRP bars. The ratio of GFRP to steel bars in the mid-span section and the effect of C.R. on the HRRC matrix were the main study parameters.

2 Experimental Program

The performance of hybrid reinforced T-beam with recycled rubberized concrete was investigated in this investigation, which was conducted at the Housing and Building National Research Centre in Dokki, Egypt. Estimating the ultimate loads, deflections, cracks, mode of failure, and ductility index for the tested beams was the aim of the study.

2.1 Specimens

The performance of eight concrete beam specimens containing hybrid reinforced concrete beams was investigated as listed in Table 1 and Fig. 1. The beams were simply supported and subjected to a two-point loading test and the schematic diagram for the eight beams and reinforcement along with the C.R value are represented in Fig. 2.

Table 1 Beams reinforcement and studied parameters

Fig. 1

The tested specimen’s reinforcement and dimensions

Fig. 2

Schematic longitudinal section of the tested specimen’s beam and dimensions

3 Materials

A control mix of normal concrete NC with a target compressive strength of 40 MPa and another mix for rubberized concrete with 35 MPa was used in developing rubberized concrete mixtures. A concrete mix of ordinary Portland cement with a relative density of 3.15 gm/ cm³, a 0.43 ratio of water to cement, potable water, natural crushed stone coarse aggregates with a relative density of 2.57 g/cm3 and a maximum size of 10 and 20 mm. And fine aggregates with a relative density of 2.60 gm/ cm3. A maximum size from 1 to 2 mm of crumb rubber with a relative density of 1.14 ± 0.02 gm/cm³ is shown in Fig. 3, Fig. 4, respectively. Superplasticizer (SikamentR-2004) was used with a density of 1200 kg/m3 (at 20 ℃ ASTM C 494/C494M-19e1) (ASTM, 2020) to reduce water and enhance workability, the mix NC with 0% C.R. and the concrete mix rubberized reinforced concrete (RRC) has the C.R. 7.5%, 10%, and 12.5% as partial replacement of sand by volume are listed in Table 2.

Fig. 3

Specific gravity of fine aggregate and the C.R

Fig. 4

a Fine aggregate (sand), b recycled fine crumb rubber sample—c size (1–2 mm) coarse aggregate and d HRWR (Sikament R2004)

Table 2 Mix proportions for concrete mixes with 0, 5%, 7.5%, 10%, 12.5, and 15% of sand replacement by recycled crumb rubber per cubic meter (kg/m³)

A 1000-kN capacity testing device applied the loads to the specimens as shown in Fig. 5 and Fig. 6. The maximum strain was determined similarly.

Fig.5

a Samples of GFRP fiber bars, b preparing samples of GFRP, FRP c steel bar, d testing of tensile strength for FRP and steel bars, e specimen after testing

Fig.6

Stress–strain curve for 10mm, 12mm steel and GFRP rebars

GFRP bars used in the experimental with 10mm and 12mm diameters with a tensile strength of (910–989) MPa. The steel rebar had a diameter of 10, and 12 mm with yield stress and tensile strength are 540 and 641 MPa, respectively, listed in Table 3; see Fig. 6. Tensile strength of GFRP bars was about 1.5 times that of reinforcing steel.

Table 3 Mechanical properties of reinforcement bars

Mixing concrete was performed using a concrete tilting drum mixer. The mixing time was about three minutes. The slump test was from 13 to 16 cm which was suitable for pouring reinforced concrete in beams The C.R. increased the workability of the concrete mix. The forms were constructed from clean wood, and their interior surfaces were coated with oil before casting. The concrete was compacted and physically placed using an internal electrical vibrator as shown in Fig. 7. After a day, the wood forms were removed, and the 28-day daily curing procedure started. Results for Young's modulus (E) are shown in Table 4, Fig. 8.

Fig.7

Specimen preparation: a preparation of cubes, b curing, c steel reinforcement, d casting the concrete, e finishing, f all finishing T-section beams

Table 4 Determination of Young's modulus for the differential type of concrete different concrete mixes

Fig.8

Specimen preparation for determine Young's modulus. a Preparing of cylinders. b, c Testing. d Measuring the load and strain

3.1 Test Setup

After 28 days of age, all beams were only supported and put through testing with a 500-ton testing device under a two-point static load. To convert the applied concentrated load into a two-point load on the tested beam, the applied load was transferred from the load cell to a steel I-beam plate, as shown in Fig. 9. A single longitudinal strain gauge was fastened to the specimens' center. The test machine's load cell measured the load. Differential transformers (LVDTs) were used to measure the deformation of the beams, where Strain gauges were used for measurement of the strain of GFRP and steel. The system of a data logger was employed to automatically gather the test data, as shown in Figs. 10, 11.

Fig.9

The test loading of the specimens, LVDT and strain gages for specimens

Fig.10

Hydraulic jack (5000 K N) on the loading plates

Fig.11

Test setup schematic diagram

4 Experimental Results

In this chapter, the effect of GFRP and steel bars with rubberized concrete mixtures including some substitution of sand with recycled C.R. by (0%, 7.5%, 10%, and 12.5% replacements by volume) were analyzed according to the recorded data. The test results of the specimens are presented.

The average concrete compressive strength was found by testing three cubes for each beam after 7 days and 28 days; see Table 5. The loss in compressive strength was more noticeable when the concrete specimens made with RRC were mixed with those made with the control mix (Thomas et al., 2015).

Table 5 Compressive strength fc (MPa) for cubes dimension 150*150mm for the different concrete mixes

Beams BH1, BH2, BRH1, BRH2, BRH3a, BRH4, BRH5 and BRH6 have ultimate loads of 269, 270, 237, 240, 230,234, 222, 227 kN, respectively. The deflection at ultimate load 50, 51, 53, 54, 55, 56, 58, 59 mm is listed in Table 6 (Moolaei et al., 2021). The mode of failure is flexural failure and the crack pattern of failure for the beams is listed in Table 7.

Table 6 Experimental results at cracking loads, yielding loads and ultimate loads of test specimens

Table 7 Experimental results of cracking load, yield load, ultimate load capacity, and mode of failure

Total load capacities for the tested hybrid rubberized T-beam BRH1, BRH3 and BRH5 (7.5%,10%, and 12.5% C.R) were decreased by 11.89%, 14.49%, and 17.47%, respectively, compared to the hybrid T- beam BH1(0% C.R as shown in Fig. 12.

Fig.12

First crack load, yield load and ultimate loads of test specimens

All beams were visually observed during the flexural test, and first crack have been observed and recorded relative to the corresponding loads, the yielding and ultimate loads, and the failure loads are listed in Table 6 and shown in Fig. 12.

The maximum and minimum deflation recorded 59 59.0mm, and 50.0 mm for BRH6 and BH1, respectively, as shown in Fig. 13. The deflections obtained for all tested beams are indicated in Fig. 14. This shows the effect of increasing the C.R. on increasing the deflection at the same level of reinforcement of the beams BH1 and BH2.

Fig. 13

Experimental load–deflection curve at mid-span

Fig.14

Corresponding deflections for the loads

Beams BH1 and BH2 flexural capacity increased compared to the other beams compared with the beams BRH1, BRH2, BRH3, BRH4, BRH5 and BRH6 due to the effect of increased percentage of C.R as listed in Table 6.

5 Discussion of Results

The effect of GFRP and steel bars with RRC mixes with partial substitution of sand with recycled C.R. by (0%, 7.5%, 10%, and 12.5%) replacements by volume were analyzed according to the recorded data. The test results of the specimens are presented.

5.1 Ultimate Load Comparisons

The ultimate flexure failure load for the tested hybrid rubberized T-beam BRH1, BRH3a and BRH5 (7.5%, 10%, and 12.5% C.R) decreased by 11.68%, 14.49%, and 17.47%, respectively, compared to the hybrid T-beam BH1(0% C.R) as shown in Fig. 15a. Also the ultimate flexure failure load for the hybrid rubberized T-beam BRH2, BRH4 and BRH6 (7.5%, 10%, and 12.5% C.R) were lower than the hybrid beam BH2 (0% C.R) by 13%, 15.72%, and 16%, respectively, as shown in Fig. 15b. This indicates that the load-carrying capacity of hybrid rubberized T-beams decreased compared to the reference hybrid T-beams as shown in Fig. 12 due to decreasing the compressive strength of the rubberized concrete specimens compared to NC specimens (AbdelAleem et al., 2018; Thomas et al., 2015). This was attributed to the effect of increasing the percentage of crumb rubber in the concrete mix; these results are compatible with the compressive strength results of concrete cubes (AbdelAleem et al., 2018; Thomas et al., 2015) as shown in Table 4. It was noted that increasing the diameter of GFRP bars from 10 to 12mm had minimal effect on the ultimate flexure failure load.

Fig. 15

The load capacity for beams

5.2 Deflection Discussions

The maximum deflection at mid-span for the tested hybrid rubberized T-beam BRH1, BRH3a and BRH5 (7.5%,10%, and 12.5% C.R) increased by 4.66%, 9.28%, and 15%, respectively, compared to the hybrid T- beam BH1(0% C.R) as shown in Fig. 14. Also the maximum deflection at mid-span for the tested hybrid rubberized T-beam BRH2, BRH4 and BRH6 (7.5%, 10%, and 12.5% C.R) increased by 5.26%, 9.16%, and 14.32, respectively, compared to the reference hybrid beam BH2 (0% C.R), as shown in Fig. 14 due to the effect of increasing the percentage of crumb rubber replacement to sand in the concrete mix. Compared to the hybrid beam, the RRC beam has improved the stress–strain curve, and ultimate deflection (Alasmari et al., 2019).

5.3 Ductility Index

The ductility of the structure refers to the deformation capacity from the start of yielding to the maximum bearing capacity or when the load does not significantly decrease after yielding (85% of the peak load) (Sun et al., 2019).

The maximum ductility index recorded was 4.32 for BRH1 mm and the minimum 2.23 mm for BH2 as listed in Table 8, Fig. 16. The ductility indices for the tested rubberized hybrid T-beams BRH1, BRH3a and BRH5 with 10-mm-diameter GFRP bars were higher than the beam BH1 by 28.2%, 35.47%, and 65.38%, respectively as shown in Fig. 17. This indicates that the ductility index of hybrid-rubberized RC T-beams increased with the increase in the percentage of rubber from 7.5% to 10%, and up to 12.5% C.R. The ductility of concrete mixes are increased by an appropriate rubber component (Guo et al., 2014). This trend was observed in GFRP bars 10 mm as shown in Fig. 16.

Table 8 Ductility index for test specimens

Fig.16

Specimen ductility index

Fig.17

Ductility index for the beams BH1, BRH1, BRH3 and BRH5

The ductility indices for the tested rubberized hybrid T-beams BRH2, BRH4 and BRH6 with 12-mm-diameter GFRP bars were higher than the beam BH2 by 23.76%, 30.04%, and 56.95%, respectively, indicating that the ductility index of hybrid-rubberized T-beams with 7.5%, 10%, and 12.5% C.R. showed a continuous increase in ductility index as the percentage of crumb rubber increased (Guo et al., 2014) as shown in Fig. 18. It was also noted that increasing the diameter of GFRP bars from 10 to 12 mm resulted in a decrease in the ductility index in all groups 7.5%, 10%, and 12.5%.

Fig. 18

Ductility index for the beams BH2, BRH2, BRH4 and BRH6

It should also be considered that increasing the diameter of GFRP bars from 10mm in BH1 to 12 mm in BH2 resulted in a decrease in the ductility index by 4.7%, yet the existence of C.R in BRH1 compared to BH1 resulted in regaining an increase in the ductility index by 28%. In terms of the stress–strain curve, ultimate deflection, ductility index, and strain as measured by the two gauges (steel bar and concrete), the rubberized beam performs better than the hybrid beam (Alasmari et al., 2019; Guo et al., 2014).

5.4 Energy Dissipation

The energy absorption of beams is a good criterion for calculating the energy dissipation of models. Based on the region beneath their load–displacement diagrams, the samples' energy absorption is measured up to 85% of the fiber-reinforced beams' ultimate strength (Moolaei et al., 2021). The energy dissipation of all samples has been computed as listed in Table 9. The lowest energy dissipation was recorded in sample BRH6. The highest energy dissipation for hybrid samples was BH2, meanwhile, the highest energy dissipation for hybrid-rubberized samples was BRH2; see Fig. 19. Also increased effective Af /As (bot.) ratios were associated with increased observed energy absorption in hybrid beams (Moolaei et al., 2021).

Table 9 Experimental results of the energy dissipation for test specimens

Fig.19

Tested beam’s energy dissipation

Energy dissipation decreased for hybrid-rubberized T-beams BRH1, BRH3a and BRH5 (7.5%, 10%, 12.5% C. R) by 7.88%, 12.36%, and 17.17%, respectively, compared to RC T-beam BH1 (0% C.R.); see Fig. 19. Energy dissipation decreased for hybrid-rubberized T-beams BRH1, BRH3a and BRH5 (7.5%, 10%, 12.5% C.R) by 7.88%, 12.36%, and 17.17%, respectively, compared to RC T-beam BH1 (0% C.R); see Fig. 20.

Fig.20

The energy dissipation for the T-beam BH1, BRH1, BRH3a and BRH5

The energy dissipation decreased for hybrid-rubberized T-beams BRH2, BRH4 and BRH6 with (7.5%, 10%, and12.5% C.R) by 8.12%, 12.96%, and 18.28% times, respectively, compared to RC T-beam BH2 (0% C.R); see Fig. 21. This indicates that the existence of the very weak crumb rubber was not able to dissipate the energy properly within the concrete matrix, which is an indication of slight lack of compatibility.

Fig.21

The energy dissipation for the T-beam BH2, BRH2, BRH4 and BRH6

6 Methodology and Numerical Model

Given the multitude of elements influencing the flexural behavior of hybrid rubberized concrete HRC reinforced with a combination of steel and glass fiber-reinforced polymer (GFRP) bars, a comprehensive parametric analysis was performed using the finite element analysis program (ANSYS 15). The finite element model’s results demonstrate that by carefully designing the hybrid reinforcement ratio, it is possible to achieve the required strength and ductility performance. (Qin et al., 2017). This research looked at the inelastic behavior of rubberized concrete reinforced using a hybrid of T-beams and glass fiber-reinforced polymer (GFRP) bars and steel. Finite element analysis was used to perform parametric evaluations and extensive three-dimensional non-linear numerical simulations. Additionally, it includes all the necessary instructions for building the hybrid rubberized concrete HRC and reinforced concrete models that were needed to analyze the flexural behavior and deflection. The analysis describes the failure modes, central deflection and ultimate load load-carrying of the beams. ANSYS version 15 was used to create a numerical model that was used to validate the results of the eight tested beams. Solid 65 components, which have non-linear properties and can crush in compression and fracture in tension, were used to model concrete. Eight nodes, each with three degrees of freedom, define the element (SAS IP, 1999). A typical element is shown in both local and global Cartesian coordinates in Fig. 22. It is defined in ANSYS by the linear behavior of concrete material with a poison's ratio of 0.2 and the modulus of elasticity derived from experimental tests by various concrete types and mixes. Furthermore, an open shear coefficient of 0.3 and a closed shear coefficient of 0.8 were used to characterize the non-linear behavior (SAS IP, 1999). The actual values of compressive strength fcu were obtained from the experimental program.

Fig.22

Solid 65 element (SAS IP, 1999)

The link180 element was used to model GFRP and steel rebars. With two nodes possessing three degrees of freedom, the element is a biaxial compression-tensile element. As seen in Fig. 23, it also featured plasticity, stress stiffness, and deflection.

Fig. 23

Discrete element link 180 (SAS IP, 1999)

The elasticity modulus of 200,000 MPa and a Poisson's ratio of 0.3 were the linear assumptions made for the material definitions of the steel element. Through experimental testing, the yield stress for flexural reinforcement was determined to be 540 MPa. The GFRP element’s material definitions were predicated on a linear elasticity modulus of 40,000 MPa and a poison’s ratio of 0.3. For the GFRP rebar, the yield stress was determined to be 910 MPa through experimental testing. Solid 45 elements were used to model the load plate and supports. Eight nodes with three degrees of freedom make up the element. For the concrete model, solid pieces were employed with a 50-mm mesh size. The study's concentrated load was applied at the top of a pair of transverse rollers and split into many loads at the top mesh joint in the y direction. In the concrete model, where there are two supports, two boundary conditions must be implemented (hinged and roller supports), as shown in Fig. 24.

Fig.24

Boundary conditions and loads applied to beams

SOLID 45: 3D load plate and supports: The solid 45 pieces are used as a model for the load plate and supports. Eight nodes make up the element, and each node has three degrees of freedom. Two transverse rollers were subjected to the concentrated load utilized in this investigation at their tops. At the top mesh junction, the force was divided into many loads in the y direction. In the concrete model, when there are two supports (hinged and roller supports), two boundary conditions must be implemented, as shown in Fig. 25.

Fig. 25

Solid 45 element in ANSYS (SAS IP, 1999)

7 Validation of Numerical Model

Validation was based on the experimental results with the analytical results using ANSYS. The numerical model with the application for finite element analysis (ANSYS 15) showed valuable results regarding the ultimate failure load, maximum central deflection, crack pattern and ductility.

7.1 Failure Load and Maximum Deflection at Mid-Span

The comparison of the greatest central deflection and ultimate loads is listed in Tables 10, 11. The results acquired by the numerical model were compared to the experimental results. A decrease in the ultimate failure load values of the numerical model by approximately 1% up to 6.5% compared to the experimentally acquired data was observed, and also decrease in the central deflection values by 1.4% up to 14.7% was obtained. The deflection results for all beams are listed in Table 11. It can be seen that all beams had linear behavior from initial loading up to the first crack, followed by a non-linear response after cracking.

Table 10 In contrast to the ultimate load results

Table 11 In contrast to the maximum mid-deflection results at the collapse

7.2 Crack Patterns

Fig. 26 shows the crack pattern after failure, acquired by both the analytical and experimental results for all beams. The load was applied progressively until the failure of the beam. The final failure occurred near the mid-span. The numerical results agree well with the experimental results recording the crack pattern.

Fig.26

Numerical and experimental crack patterns for beams

The results demonstrate that increasing the diameter of GFRP bars significantly increases the ultimate capacity and deflection of RC beams. The hybrid reinforcement ratio is investigated as a critical parameter to improve the flexural performance of hybrid rubberized concrete HRC reinforced with GFRP bars, and steel bars (Qin et al., 2017). The experimental results were validated and compared to those obtained from ANSYS software-based non-linear finite element analysis shown in Fig. 27a, d. The numerical results obtained from (ANSYS 15) agree well with the experimental results in terms of crack pattern as well as the ultimate load. The mid-deflection obtained using ANSYS matched the outcomes of the experiment for a lower range of load values for all beams. For higher loads, there was a slight deviation between the experimental and finite element results, as shown in Fig. 26e, l.

Fig. 27

Comparison of numerical and experimental results

7.3 In Contrast to the Experimental Results and the Numerical Results by ANSYS

The numerical results obtained from (ANSYS 15) correspond well with the experimental findings about the ultimate load and the crack pattern. The mid-deflection obtained using ANSYS matched the experimental results for a lower range of load values for all beams. For higher loads, there was a slight deviation between the experimental and finite element results, as shown in Fig. 26.

7.4 Ductility Index

The ductility index is calculated as:

Maximum deflection (85% of the peak load) / yield deflection equals the ductility index. The ductility index comparison is displayed in Table 12. The experiment's results and the numerical model’s obtained results diverge. It was found that the numerical model's ductility factor values were lower by about 8.3% when compared to the one obtained experimentally. The numerical results and the experimental results correspond well. The results of the finite element model show that the necessary strength and ductility performance may be obtained by appropriately engineering the hybrid reinforcement ratio. (Qin et al., 2017). It is shown that the proposed formulations yield reliable estimates of the strength and ductility of reinforced rubberized concrete members, which makes them suitable for use in both practical applications and codified norms (Xu et al., 2020).

Table 12 In contrast to the ductility factor results

8 Conclusion

Based on the experimental program's attained results, which were also contrasted with the results of non-linear finite element analysis performed with ANSYS software, the following conclusions were obtained:

• 1. The ultimate failure load for the tested hybrid rubberized T-beam BRH1, BRH3a and BRH5 (7.5%, 10%, and 12.5% C.R) decreased by 11.68%, 14.29%, and 17.47%, respectively, compared to the hybrid T-beam BH1(0% C.R). Also BRH2, BRH4 and BRH6 (7.5%, 10%, and 12.5% C.R) were lower than the hybrid beam BH2 (0% C.R) by 13%, 15.72%, and 15.99, respectively, indicating that the load capacity of hybrid rubberized-T RC beams decreased concerning hybrid T-beams with 0% C.R.

• 2. The mid-span maximum deflection for the tested hybrid rubberized T-beam BRH1, BRH3a and BRH5 (7.5%, 10%, and 12.5% C.R) increased by 4.66%, 9.28%, and 15%, respectively, compared to the hybrid T- beam BH1(0% C.R). Also for BRH2, BRH4 and BRH6 (7.5%, 10%, and 12.5% C.R) the mid-span deflection increased compared to BH2 (0% C.R) by 5.26%, 9.16%, and 14.32, respectively.

• 3. The ductility index for the tested rubberized hybrid T-beams BRH1, BRH3a and BRH5 were higher than BH1 by 28.2%, 35.47%, and 65.38%, respectively, indicating that increasing the percentage of C.R has a direct effect on increasing the ductility index. Also BRH2, BRH4, and BRH6 were higher than BH2 by 23.76%, 30.04%, and 56.95%, respectively, indicating that the ductility index of hybrid-rubberized RC T- beams with (7.5%, 10%, and 12.5% C.R) increased compared to hybrid normal R.C T-beams (0% C.R).

• 4. It was noted that increasing the diameter of GFRP bars from 10 to 12 mm resulted in a decrease in the ductility index (7.5%, 10%, and 12.5%). Increasing the diameter of GFRP bars from 10mm in BH1 to 12 mm in BH2 resulted in a decrease in the ductility index by 4.7% yet the existence of C.R in BRH1 compared to BH1 resulted in regaining an increase in the ductility index by 28%.

• 5. The energy dissipation decreased for hybrid-rubberized T-beams BRH1, BRH3a and BRH5 (7.5%, 10%, and 12.5% C.R) by 7.88%, 12.36%, and 17.17%, respectively, compared to T-beam BH1 (0% C.R). This indicates that the existence of the very weak crumb rubber was not able to dissipate the energy properly within the concrete matrix, which is an indication of a slight lack of compatibility. Also the BRH2, BRH4 and BRH6 with (7.5%, 10%, and 12.5% C.R) by 8.12%, 12.96%, and 18.28% times, respectively, compared to RC T-beam BH2 (0% C.R).

• 6. Regarding the final failure loads and the fracture pattern, the finite element calculations and the experimental data are in agreement. A decrease in the ultimate failure load values for the numerical model by approximately 1% up to 6.5% compared to the experimentally acquired data was observed.