Finite Element Analysis of Normal Strength, High Strength and Hybrid Reinforced Concrete Beams

This paper presents the numerical study to simulate the flexural behavior of normal strength, high strength and hybrid reinforced concrete beams, under two points load with two different reinforcement ratio. The hybrid beam consists of two layers: the compressive layer is made of high strength concrete, and the tension layer is made of normal strength concrete. The simulation was done with a finite element model using the commercial finite element code, ANSYS (v.9.0). The concrete component material is modeled, the internal steel reinforcement modeled using ''LINK'' elements. The modeled behavior shown a good agreement with the experimental data. The maximum percentage difference in ultimate load-carrying capacity is 8% at the ultimate load level. Analytical study also included the effect of increasing the depth of the normal strength concrete for the hybrid reinforced concrete beam and the effect of increasing the compressive strength for high strength concrete and normal strength concrete respectively on the behavior and the load carrying capacity of the hybrid reinforced concrete beams.

). The results are presented in terms of ultimate load carrying capacity and deformationa characteristics. Finally, the accuracy and validity of the model were investigated.

3-1-Element types: 3-1-1 Concrete:
An eight-node solid element, Solid65, was used to model the concrete. Each node has three degrees of freedom in x, y, and z directions. Plastic deformation, cracking in three orthogonal directions, and crushing of the elements are allowable. Figure (2) show the geometry and node locations for this element. For reinforced concrete, ANSYS requires input data for material properties as follows:  Elastic modulus (E c ).
 Ultimate uniaxial tensile strength (modulus of rupture, f r ).
the modulus of elasticity, , can be calculated with a reasonable accuracy from the empirical formula (ACI code 318-2005) (4) .
The modulus of rupture f r is taken as ( ). A shear transfer coefficient (β) is introduced in order to estimate the ability of concrete to transfer shear force across the crack interface. This coefficient represents a shear strength reduction factor for concrete across the crack face (3) . The shear transfer coefficient used in this study were 0.2 and 0.3 for the case of open crack ( ) and closed crack ( ) respectively.
The uniaxial stress-strain relationship for concrete in compression is required by the program. The numerical expressions equations (2, 3, and 4) were used along to construct the uniaxial compressive stress-strain curve of concrete in this study (Desayi and Krishnan 1964) (5) , and stress-strain curve for normal weight concrete are shown in figure (3).  For the convergence nonlinear solution algorithm, the multi-linear curves were used. The summary of Material properties for all concrete types is shown in Table (1).

3-1.2 Steel reinforcement:
To model the steel reinforcement we used Link8 element. This element has two nodes with three degrees of freedom in nodal x, y and z directions and capable of plastic deformation. A perfect bond between the concrete and steel reinforcement is considered. Figure 4 shows the geometry and load locations of the element. The steel reinforcement was connected between nodes of each adjacent concrete solid element, so the two materials shared the same nodes. The steel reinforcement for the FE model is assumed to be elastic-perfectly plastic and identical in tension and compression as shown in Figure (5). Tables 2 reports material properties for the steel reinforcement for all beams models.

4-FINITE ELEMENT IDEALIZATION:
By taking advantage of the symmetry of the three beam's geometry and loading, a half of the entire model beam was used for the finite element analysis. In order to represent the concrete material, the reinforced concrete beams are modeled by (5760) 8node brick elements. While (2263) three-dimensional two-node bar elements (link8) were used to model the reinforcement bars which share with concrete elements in the same nodes. Perfect bond was assumed between normal and high strength concrete for hybrid reinforced concrete beams. The final step is applying the boundary conditions and the loads. There are two boundary conditions one for supports and the other for symmetry. For the support, the point of supports is constrained in the x and y-directions (hinge support). For the symmetry, one plane of symmetry exist, and at a plane of symmetry the displacement in the direction perpendicular to that plane was held at zero value (Uz=0). The external load is represented by equivalent nodal loads.
The boundary conditions and loading of hybrid reinforced concrete beam of the finite element mesh, are shown in Figure (  To carry out the nonlinear analysis, the calculation was conducted by using 8-point ( integration rule, and full Newton-Raphson method, and a convergence tolerance of (1%) is used.
For applying the external load we used the uniform increments load. The last applied load steps represents the final loads for the finite element models before the solution diverges due to numerous cracks and large deflections.

5-RESULTS AND DISCUSSION:
The validation of the FE models was conducted by comparing the modeled load carrying capacity and load-deflection with the experimental results for normal, high and hybrid reinforced concrete beams specimens. The finite element load-deflection response, obtained for the beams, BN, BH and BHY for two reinforcement ratios (1.43% and 3.95%) are shown in Figures (8), (9) and (10) respectively along with the corresponding experimental results. The behavior of the numerical models agrees well with the reported experimental observations throughout the whole loading process as can be seen from the loaddeflection curves, some differences between the experimental and finite element beams appeared in curves and this may be caused by several factors that lead to higher stiffness in the finite element models. The finite element analyses assumes the bond between the concrete and steel reinforcing is perfect, but in the reality the assumption would not be true because slip may occurs, therefore the composite action between the concrete and steel reinforcing is lost in the actual beams. Also the microcracks formed by drying shrinkage and handling are also may be present in the concrete to some degree. The aforementioned reasons would reduce the stiffness of the actual beams, while the finite element models do not take in consideration the microcracks which is not incorporated in the models. Also, the perfect bond between the two concrete types for hybrid beams which appeared especially after yield point may lead to different results. The experimental and the analytical load-carrying capacity for the beams and the ratio between them are shown in Table (3).

6-Effect of some parameters on behavior of hybrid beams
The behavior of a hybrid beams are affected by many parameters. In the current study the beams (BHY) have been employed in a numerical study to demonstrate the effects of some parameters on the nonlinear finite element solution. These parameters include the following:  The effect of changing depth of normal strength concrete.
 The Effect of Increasing Compressive Strength of Concrete.
The effects of each of the above-mentioned parameters are discussed below.

6-1 The Effect Of Changing The Depth Of Normal Strength
Concrete:  According to the results of the analysis, the following observation may be noted for BHY with 3ϕ25 (3.56% steel ratio): Increasing the depth of normal strength concrete for the hybrid reinforced concrete beam from (h=185mm) to (h= 200 mm), decreased the ultimate load by (7.2%).
Decreasing the depth of normal strength concrete for the hybrid reinforced concrete beam from (h=185mm) to (h= 137.5 mm) , decreased the ultimate load by (9.6%).
According to the results of the analysis, the following observation may be noted for HBY with 3ϕ16 (1.43% steel ratio): Increasing the depth of normal strength concrete for the hybrid reinforced concrete beam from (h=185mm) to (h= 200 mm), increased the ultimate load by (11.3%).
Decreasing the depth of normal strength concrete for the hybrid reinforced concrete beam from (h=185mm) to (h= 137.5 mm), increased the ultimate load by (1.67%).

Conclusion:
1. According to the results of the available experimental tests with comparison with the results obtained from the finite element analysis by (ANSYS) it is shown that the computer modeling can be used efficiently to predict the structural response and the load carrying capacity of such beams.
2. Increasing the depth of normal strength concrete for the hybrid concrete beam (with ρ=3.56%) by 8% cause a decrease of the ultimate load by (7.2%), while decreasing the depth of normal strength concrete by 25.6% cause a 9.6% decrease in the ultimate load caring capacity.
3. Increasing the depth of normal strength concrete for the hybrid concrete beam (with ρ=1.43%) by 8% cause a increase of the ultimate load by (11.3%), and decreasing the depth of normal strength concrete by 25.6% cause a 1.67% increase in the ultimate load caring capacity. 4. The finite element solution reveals that increasing the compressive strength of concrete causes an increase in the ultimate load carrying capacity. For the studied cases it is found that increasing c f ' of the normal strength concrete for the hybrid beams in the range of (34%-79%) causes an increasing in the load capacity by (3.9%-5.2%) and (1.67% -18.33%) for (ρ=3.56% and 1.43%) respectively .