A Study of the Structural Behavior of Recycled-Concrete Haunched Beams with Web Opening

Reinforced Concrete Haunched Beams (RCHBs) are beams with varying depths along their length yet have a constant width. They are frequently used in continuous bridges, simply supported mid-rise framed buildings, and structural portal frames [1], as seen in Figure 1 The use of RCHB instead of the prismatic beam can allow for weight reduction and achieve larger spans without clearly degrading the load capacity [2]. Despite these advantages, few studies have been done so far on the behavior of RCHBs. Therefore, it is necessary to enhance the theoretical and experimental foundation for the mechanical behavior of RCHBs. However, it should be noted that the mechanical behavior and structural analysis of RCHBs differ from those of prismatic beams since the effective depth of RCHBs varies throughout their length. Debaiky and Elniema [3] conducted the first experimental study on the shear behavior of RCHBs.

Jebur [1] examined three beams: One prismatic and two Haunched Beams with varying haunch angles (α). In this work, reinforced concrete beams with different types of haunch angles and no shear reinforcement were studied. Researchers inferred that the shear strength of a beam decreases with the decrease of its depth near the support, and shear failure occurs at a 45° angle, which matches the test findings. Despite their failure in shear, Reinforced Concrete Haunched Beams appear to be more efficient compare with reinforced concrete prismatic beams, proved by Tena-Colunga et al. [4, 5]. A thicker concrete cover at the mid-span impacted the crack propagation, but it had nearly no impact on the shear capacity, according to Hou et al. [6]. As shown in research done by Tena-Colunga et al. [7, 8]. These studies have concluded that the Haunched Beams show a different cyclic shear behavior from the prismatic beams, where the Haunched Beams prefer an arching action in the length of the haunch as the main mechanism for preventing failure, which leads to smoother cracking patterns. To prevent the formation of plastic deformation in the steel bars, which would have an impact on the general behavior of the haunched reinforced concrete beams, a value of the complementary strain-energy limit is utilized to control it during the loading process proven by Rad et al. [9]. Recently, the use of Recycled Concrete Aggregate (RCA) instead of normal Aggregate (RA) in different proportions in beams to compare the shear strength of reinforced concrete has been widely studied for a variety of reasons, including being more effective, saving material, providing more height at the central span, and being more shear resistant. As shown in research done by Tabsh and Yehia [10], Fathifaz et al. [11], Pedro et al. [12], and Hamoodi et al. [13]. These studies have concluded that the use of RCA instead of RA in beams does not show major variations in mechanical or toughness between aggregates from controlled sources and those from precast rejects. According to Verian et al. [14], the use of partially saturated to fully saturated RCA, along with the appropriate mix design and mixing procedure, has been shown to increase the performance of concrete when compared to concrete batched using dry RCA. As noted by Sulaiman and Khudair [15], RCA not only reduces crack size and final loads but also results in the first crack and ultimate loading appearing earlier thanks to its lower stiffness than natural aggregate. According to Rahal and Alrefaei [16], the incorporation of recycled aggregates has been demonstrated to have less effect on beams reinforced with longitudinal and transverse reinforcement than on beams strengthened just with longitudinal rebar. The higher replacement ratio of RCA, the lower the ultimate load and the first cracking load, according to Khtar and Khudhair [17].

This article aims to evaluate the behavior of reinforced Haunched Beams made from recycled concrete aggregate with or without opening and to study the effect of inclination angle on shear strength. There are many studies on the presence of holes in all kinds of beams, and there are many studies on recycled concrete, but there is not enough presence research to connect all these effects and know most aspects of the behavior of Haunched Beams.

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(a) Bridges in Lisbon, Portugal [4]

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(b) Buildings [5]

Figure 1. Examples of RCHB use

The Finite Element (FE) method has become a significant and versatile tool for numerical solutions to many engineering problems. The FE technique has been used for linear and nonlinear analysis of reinforced concrete structures. The Abaqus Standard version 2020 is employed to simulate the finite element model. This section outlines the Abaqus/CAE 2020 program and the necessary steps to create and analyze the beams. The FE model represents the geometry, material properties, boundary conditions, and sample meshing.

3.1 Geometry

The geometry for the Abaqus simulation was chosen to match the actual size of experimental models. Figure 12 shows the geometric representation of prismatic beams and Haunched Beams.

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Figure 12. Geometric representation of prismatic beams and Haunched Beams

3.2 Material properties

Material properties must be specified for all elements. While obtaining high-quality material data might be difficult, particularly for complex material models, the accuracy and breadth of the material data impact the validity of Abaqus results. Material properties are defined by multiple input data for each element in the ABAQUS program. Materials used in this study included concrete and steel reinforcement. The following are the characteristics of each material:

3.2.1 Concrete properties

In this study, elastic and plastic behavior were used to define concrete material. For modeling the elastic behavior of NA and RCA, the parameters Poisson’s ratio (ν) and Young’s modulus (Ec) are used [28]. The CDP takes into account both isotropic compressive and isotropic tensile behavior to determine the plastic performance of concrete. Elastic properties. The Modulus of Elasticity for NA, R30 and R60 took from the Experimental Test, while the Poisson’s ratio (ν) was assumed =0.2 in this study as used by Tao and Chen [29]. The Elastic properties given in Table 3.

Table 3. The properties of elastic behavior

Properties	Value
Modulus of Elasticity	NA	28668
	R30	27915.38
	R60	24851.28
Poisson’s ratio	0.2

Concrete damage plasticty. The CDP modeling in ABAQUS consists of plasticty, tensile behavior and compressive behavior of concrete as following:

-Plasticity: Variables of plasticity include viscosity parameter (μ), eccentricity (e), surface yielding shape (Kc) factor, the relationship between the stress of initial biaxial compression yield and the stress of initial uniaxial compression yield (σbo/σco), and (ψ) dilation angle of NA and RCA [30]. The plasticity properties given in Table 4.

Table 4. The properties of plasticity [30]

Concrete Damage Plasticity
Dilation Angle	31
Eccentricity	0.1
fb0/fc0	1.66
K	0.667
Viscosity Parameter	0

-Compressive behavior: For simulating the compressive behavior of NA and RCA, the parameters Yield Stress and Inelastic Strain are used. 

The inelastic hardening strain in compression is calculated using the following equation, ε^in,h c:

$\varepsilon^{i n, h}=\varepsilon c-\frac{\sigma c}{E 0}$    (1)

where,

εc: nominal strain.

σc: nominal compressive stress.

E0: modulus of elasticity.

-Tensile behavior: Tensile behavior contains three methods: Stress-Strain, Stress-Displacement, and Strain Fracture Energy (GFI). After trying all the methods, the GFI method was chosen to simulate the tensile behavior of NC & RC in this research because it gave is closer to the practical results than other methods. There are two determinants of the GFI method, which are Yield Stress (ft) computed by splitting test, while fracture energy (GF) was counted utilizing CEB-FIP MC 90, as shown in the following equation:

Gϝ =Gϝο ((f_cm)/(f_cmo))^0.7 [31]       (2)

The fracture energy GF, which distinguishes the stress-strain curve’s softening branch, is the fundamental parameter of tensile concrete. The aggregate sizes have an impact on the fracture characteristics of concrete [31]. Where, Gϝ fracture energy (N/mm), GFo: fracture energy base value based on the maximum aggregate size Dmax: given in Table 5; fcm: concrete compressive strength (MPa); fcmo: compressive strength, 10 (MPa).

Table 5. The Gϝο fracture energy base value based on the maximum aggregate size Dmax

Dmax	[mm]	8	16	32
GFo	[N/mm]	0.025	0.03	0.058

A tensile behavior for reinforced concrete with (0%, 30% and 60%) of RCA, used in Abaqus is registered in the Table 6.

3.2.2 Steel properties

In contrast to concrete, steel's properties can more easily be determined through a tension experiment because of its homogeneous nature. Two types of steel sections were used in this study; bar and stirrup reinforcement. These materials were defined based on the elastic and plastic properties of steel reinforcement. The two elastic parameters, elastic modulus (Es) and Poisson’s ratio (ν) are needed in the elastic stage. While only one plastic parameter, the yield stress (fy), is required in the plastic stage. Steel plates were added to the finite element model at load and support positions to produce a uniform stress distribution over the loading and support regions. Table 7 indicates the reinforcing properties.

Table 7. The properties of reinforcing

Properties	Value
Modulus of Elasticity	NA	28668
	R30	27915.38
	R60	24322.01
Poisson’s ratio	0.3
fy	420

3.3 Load and boundary conditions

Supports and loading points are supplied by steel plates with dimensions (200x100x20) embedded into the model. The addition of loading plates will improve the load distribution across the structure. The loading plate was needed to facilitate the application of loads as point loads to the requisite nodes. Boundary conditions must be applied at sites where supports and loadings exist to guarantee that the model behaves similarly to the experimental beams. The beam's boundary condition was specified as a simply supported beam by defining one support as hinged support on one side and roller support as hinged support on one side and roller support on the other side, as shown in Figure 13.

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Figure 13. Details of hinged and roller support

The supports are attached to the bearing plates, not directly to the concrete element. The load distribution throughout the structure improves when the loading plates are introduced. Figure 14 show the load and boundary conditions of each model.

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Figure 14. Load and Boundary conditions for the models

3.4 Mesh

A rectangular mesh was utilized to get the best results from the model. The model was broken down into small elements. Since all beams had identical dimensions, the same mesh size was employed for all.

The mesh sizes employed in this study were three mesh sizes (30, 40, and 50) mm. A 30 mm mesh size gives a closer response to the load-deflection curve experimentally and is close to the mesh 40 curve. Therefore, the rest of the samples were analyzed numerical using a mesh size of 30 mm.

3.5 Numerical results

3.5.1 Ultimate load capacity and ultimate deflection

Compared to the experimental results, the findings of the nonlinear finite element analysis (FEM) of the tested beams in terms of ultimate load and deflection are discussed. Table 8 summarizes the ultimate load result and the deflections for experimental and FEM results. In this table, it is shown that the experimental results and the FE results agree well. In terms of percentage, the highest percentage divergence of the ultimate load is 8.41%, and the highest percentage divergence of deflection is 19.54%.

3.6 Beam behavior

According to ABAQUS software documentation, the damage region for tension and compression is described as substations parameters that are Concrete Compression Damage (dc) and Concrete Tension Damage (dt) in the Concrete Damage Plasticity Model (CDPM). The FE findings of crack patterns in the tension face of models that modeling in ABAQUS software gives good compatibility with the crack patterns obtained from the experimental findings after failure, as shown in Figures 15-17.

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Figure 15. Tension cracks for beam H6N

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Figure 16. Tension cracks for beam H6N-S

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Figure 17. Tension cracks for beam H6R30-C

3.7 Factors affecting beam behavior

Many factors affect the numerical simulation of the beams, such as the recycled concrete aggregate, the haunch angle, the spacing between stirrups, and the presence of openings. The use of recycled aggregate instead of ordinary aggregate affected the ultimate load. Therefore, when comparing samples with concrete mixes (the other factors remaining constant), it has been found that the final load of normal concrete was (3.26%-12.86%) greater than the ultimate load of RCA 30 samples. While the final load of RCA 60 was found to be lower than normal concrete by (15.16%-25.6%).

The difference in haunch angle also affects ultimate load, where the model with = 9.46° haunch angle is weaker than the model with α=6.34° haunch angle. For example, solid samples with normal concrete and α = 6.34° were stronger than solid samples with normal concrete and α=9.46° by 10.8% for the ultimate load.

Openings reduce the ultimate load, irrespective of the shape of the opening. Based on a comparison of samples with normal concrete, it was found that the solid samples were stronger than the samples with circular openings by 2.14% and 8% for samples with α=6.34° and samples with α=9.46°, respectively. However, the solid samples were stronger than samples with square openings by 6.7% and 23% for beams with α=6.34° and samples with α=9.46°, respectively.

3.8 Effect of mesh size on FE analysis of beam

It has been shown in several studies that mesh size affects the accuracy of findings obtained using FE Analysis in several studies. By varying element size and type, Liu et al. [32] obtained different results. Figures 18 show a comparison between three mesh sizes: 30, 40, and 50.

As mentioned earlier, it is clear from the graph of these models that a 30 mm mesh size gives a closer response to the load-deflection curve experimentally and is close to the mesh 40 curve. Therefore, the rest of the samples were analyzed numerically using a mesh size of 30 mm.

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(a) PN

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(b) H9R30-C

Figures 18. Load-Deflection curve for different mesh sizes

3.9 Load-deflection curve

The value of the mid-span deflection is measured at each load step, and the load versus deflection curves are plotted. During the entire loading process, all specimens pass through three behavior stages. The load mid-span deflection response behaves linearly during the first stage. The load increments rose gradually until the first cracking load. Therefore, the specimens remain elastic, and no visual cracks appear in the samples at this stage. However, when the second stage begins, diagonal and flexure cracks occur in the shear and flexure zones, and the curve shifts from linearity to nonlinearity behavior. Since this occurs as the load increases, the deflection rate is continuously rising with the load. Finally, in the third stage (failure stage), as an applied load reaches the vicinity of its ultimate value, deflections are increasing at a faster rate than the applied loads are increasing, thus causing samples to fail. The load-deflection responses of the current FE analysis and experimental findings are shown in Figures 19. As observed in these figures, the curves show a remarkable convergence between the FE and the experimental outcomes.

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(a) H6N

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(b) H9N

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(c) H6N-S

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(d) H6R30-S

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(e) H6R30-C

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(f) H6R60-C

Figures 19. Comparison between the FEM and experimental response to load-deflection

ABAQUS is a very accurate program that must have a good knowledge of all its aspects before use and choose the appropriate analysis methods for implementation.