Finite Element Modeling Concrete Reinforced

European Journal of Scientific ResearchISSN 1450-216X Vol.30 No.1 (2009), pp.177-186 © EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/ejsr.htm Finite Element Modeling of Continuous Reinforced Concrete Beam with External Pre-stressed Amer M. Ibrahim Asst. prof, College of engineering Diyala University, Iraq Huda M. Mubarak Structure Engineering, Huda Mohammed Diyala University, Iraq Abstract This paper deals with the behavior of externally pre-stressed continuous concrete beams, subjected to symmetrically static loading. A numerical model based on the finite element method using computer program ANSYS (version 10.0). The behavior of the beam- tendon system is ruled by the nonlinearity of materials and by geometric nonlinear effects. The relevance of the geometric effects in evaluating the failure load of externally pre-stressed concrete continuous beams by considering the tendon eccentricity variation. The comparison between the experimental tests from previous researches and numerical analyses is showing good agreement. Keywords: ANSYS, Externally pre-stressed; Finite element; Nonlinear behavior; Reinforced concrete continuous beam. 1. Introduction External post-tensioning has long recognized as effective means of strengthening existing concrete structures. External pre-stressing as a strengthening method for beams or girders has become popular due to advantages such as construction speed and the possibility of monitoring, future re-tensioning, and replacement of tendons, reduction in web thickness due to elimination of tendons within the concrete, resulting in reduced construction cost and light weight structures, and enhanced construction processes combined with the precast segmental method of construction. The behavior of externally pre-stressed members is conceptually similar to the behavior of members with internal unbounded tendons, except for one major difference. When beams with internal unbonded tendons deflect under applied load, the internal tendons remain in contact with the surrounding concrete, and hence, their eccentricity practically does not change throughout the response. On the other hand, in externally pre-stressed members, the external tendons are able to displace freely relative to the beam axis with increasing deflection, giving rise to second- order effects. The second- order effects may lead to inferior flexural strength capacities in externally pre-stressed members as compared with internally unbonded ones, and become particularly significant when no deviators are used in the critical region of the member. An experimental investigation carried out to study the flexural behavior and strength characteristics of continuous concrete beams pre-stressed using external tendons. Aravinthan et al., span continuous beams externally pre-stressed T-beams.0. A three dimensional element was used to representation the structure. Harajli et al. due to the limited increase in shear capacity.Finite Element Modeling of Continuous Reinforced Concrete Beam with External Pre-stressed 178 carried out an experimental study on two. and each node has three degree of freedom translation in the (X. f c = ε Ec 0 ≤ ε ≤ ε1 for (1) fc = ε Ec ⎛ε ⎞ 1 + ⎜⎜ ⎟⎟ ⎝ ε° ⎠ ε1 ≤ ε ≤ ε ° ε° = where 2 for for ε1 ≤ ε ≤ ε ° ε ° ≤ ε ≤ ε cu (2) (3) ' c 2f Ec (4) ƒc= stress at any strain ε.span continuous beams with highly eccentric external tendons. It must satisfy Hooke’s law: E = σ/ε (5) ' σ = 0. taking into consideration the influence of the second. Y and Z direction). An analytical study is presented to explain and further examine the phenomenon in beams strengthened with eight variations of tendon profiles. and confinement reinforcements on the flexural strength and stress in external tendons. the results demonstrated that the strengthened beam could fail in shear particularly at the high.order effects. Tan and Tjandra. The compressive uniaxial stress-strain relationship for concrete model is obtained by using the following equations to compute the multi-linear isotropic stress-strain curve for the concrete as shown in figure 1. and develop analytical approach to predicate their ultimate flexural response. rotation capacity in the plastic region.shear region near the interior support. the ANSYS computer program was used for analyzing the continuous pre-stressed concrete beams with external tendon. N/mm2 ε◦ =strain at the ultimate compressive strength f′c. The concrete is assumed to be homogeneous and initially isotropic.strain implemented requires the first point of the curve to be defined by the user. The multi-linear curves were used to help with convergence of the nonlinear solution algorithm. test four two.order effects using computer program ANSYS 10. The element has eight corner nodes. This study was carried out to investigate the behavior of continuous externally pre-stressed members by develop analytical model to predict the ultimate flexural response. loading pattern. Finite Element Model In this study.3 f c (6) . The results of this investigation discuss the effect of tendon layout.3 f c The multi-linear isotropic stress. examine the behavior of continuous externally pre-stressed members experimentally. taking into consideration the influence of the second. Finite Element Model of concrete The three dimensional 8-node brick element (Solid 65 reinforced concrete solids) is used for model of concrete.. casting method. 2. The crack modeling depends on smeared cracking modeling. εcu= ultimate compressive strain ' ε1=strain corresponding to 0. perfectly plastic as shown in Figure 2. The reinforcement in the discrete model uses bar or beam elements that are connected to concrete mesh nodes. as shown in Figure (3). the discrete representation is used to model the steel reinforcements by using the (3D spar Link8 element). Ibrahim and Huda M.1. The stress-strain relationship for ordinary reinforcing steel is a bilinear relationship assumed to be elastic. bilinear elastic-plastic with hardening is the relationship of stress-strain. .Strain Curve for Concrete 3.179 Amer M. The modulus of the strainhardening portion is assumed to (2%) of the modulus of elasticity of steel. External Pre-stressed Tendon The pre-stress in finite element is applying as real pre-stress to the tendon with initial conditions. Finite Element Model of Reinforcement In the present study. Mubarak Figure 1: Simplified Compressive Uniaxial Stress. Figure 2: Constitutive Law for Steel Reinforcement 3. The pre-stressing stress was taken as the initial value and equal to the effective stress and appears in the analysis as initial strain in link element. For pre-stressing tendons. 1400. the profile of the external tendons.3. and 206850 N/mm2 respectively. Anchorages and Steel Plates The anchorage zone used as the steel plate the tendon element is connected to it. J. M. Analytical Model Nine specimens. and 582 N/mm2. M.wire strands.Haji. for the 5 mm wires. taking into consideration the influence of the second -order effect. by develop a general analytical approach to predict the ultimate flexural response.. B12D2 and B10S1A are with deviators at their mid-spans. and 195129 N/mm2 respectively.Finite Element Modeling of Continuous Reinforced Concrete Beam with External Pre-stressed 180 Figure 3: Constitutive Law for Pre-stressing Steel 3. Al. for the 8 mm strands. The element is defined with 8-nodes and at each node three degrees of freedom. respectively. Also steel plates are added at the support and loading location to avoid stress concentration problems. were tested by Harajli. and the specimen B10S1B is without deviators at their mid-spans. The ultimate strength. In this study. continuous over two spans. 3. Small concrete blocks were cast monolithically with the specimen to serve as deviators for the external tendons. 10. Mabsout. and 1986. yield strength and modulus of elasticity were 1607. five specimens were selected to investigate the behavior of continuous externally prestressed members. The accuracy and validity of the finite element models is determined by ensuring that failure modes are correct. The external pre-stressing steel consisted of 5 mm wires or 8mm seven. The typical dimensions and reinforcement details of the test specimen are shown in Figure (4). 568. Y. The ordinary bonded steel consisted of 6. B6D2. The solid element (solid 45) was used for the steel plates. .. The specimens were loaded with two concentrated point loads applied simultaneously at the middle of the spans. The shear reinforcement in the outer shear spans (Av in Figure (4)) consisted of 6 mm stirrups spaced at 150 mm for specimen B6D2 and at 100 mm for the remaining specimens. The test variables included the areas of the external pre-stressing steel and ordinary bonded reinforcement. and Z directions. translations in X. and the configuration of the deviators. 12 mm bars having yield strengths of 347.2. 1669. A summary of the materials properties of the selected specimens are listed in Table (1). The specimens B6D1.. the ultimate load is reasonably predicted in comparison with the available experimental investigations. The boundary conditions need to be applied at points of symmetry and where the supports and loading exist. boundary condition and loading arrangement are shown in Figure (5). only one half of the beam in longitudinal direction has been used in the finite element analysis.7 41.181 Amer M.8 2(8mm)74.8 2(5mm)38. The finite element mesh.1 42 By taking advantage of symmetry. Ibrahim and Huda M.8 2(5mm)38.9 41.8 2(8mm)74.4 37.8 932 1112 1056 916 921 dp midspan mm 142 142 142 100 100 dp internal support mm 150 150 150 100 100 ƒ′c N/mm2 38. Mubarak Figure 4: Typical dimensions and reinforcement details Table 1: Beam B6D1 B6D2 B12D2 B10S1A B10S1B Summary of Material properties As mid-span and internal support mm2 2(6 mm) 56 2(6 mm) 56 2(12 mm) 226 2(10 mm) 157 2(10 mm) 157 External pre-stressing steel Ap mm2 fpe N/mm2 2(5mm)38. . Figure 6: Load. 25. 7.deflection curves obtained for five beams are shown in Figures (6. B12D2.Deflection Curve for B6D1 .Finite Element Modeling of Continuous Reinforced Concrete Beam with External Pre-stressed 182 Figure 5: Finite Element Mesh. 55. Figure (11) show the first crack in beam B6D2. B10S1B) respectively. good agreement is in loaddeflection relation prior to cracking load. 8. The experimental and numerical load. 30. B6D2. Discussion Results of the Analysis The results include the total ultimate applied load and average measured mid-span deflection. 25) percent of the ultimate load for beams (B6D1. 9. The first flexural cracks in all of the specimens developed at the interior support on either side of the deviator (3). These figures show good agreement in finite element analysis with the experimental results (3) throughout the entire range of behavior and failure mode.5. For all beams. 10). Boundary conditions and loading arrangement 4. It was found that the first flexural cracks occurred at approximately (49. B10S1A. Deflection Curve for B10S1A . Mubarak Figure 7: Load.183 Amer M.Deflection Curve for B12D2 Figure 9: Load.Deflection Curve for B6D2 Figure 8: Load. Ibrahim and Huda M. For the specimens B12D2. Figure 12: Crack Pattern in Beam B6D1 The summary of measured resistance of all beams from the cracking to the ultimate together with average mid-span deformation is summarized in Table (2). B10S1A and B10S1B. After the yield of internal reinforcing bars. The specimen with straight tendon profiles and without deviators at its mid-spans (B10S1B) experienced a reduction in the eccentricity (or depth) of the external tendons with increasing deflection as shown in Figure (13). and approximately linear post-cracking stage up to yield of the internal bonded reinforcement.Finite Element Modeling of Continuous Reinforced Concrete Beam with External Pre-stressed 184 Figure 10: Load.Deflection Curve for B10S1B Figure 11: First Crack in Beam B6D2 As the load increased. the load deflection response from finite element analysis was stiff comparison to experimental data. the deflection increased nonlinearly with the slight increase in load until the ultimate resistance. The corresponding reduction was practically equal the magnitude of the mid-span deflection at all loads levels during the response. The numerical load for all beams is slightly smaller than experimental load. and a post yield stage until the ultimate load. additional cracks developed simultaneously at the interior support and mid-span sections as shown in Figure (12). . Finite element model was develop based on computer program ANSYS (10. Conclusions This study was carried out to evaluate the behavior of continuous concrete beams pre-stressed using eternal tendons.4 190.5 320 166.7 194 19 Pcrack kN 58.7 47.4 96 96 47. Ibrahim and Huda M.4 15.8 118 155.1 8.8 Max. .4 7.5 10. Mubarak Figure 13: Deflected Shape for Beam B10S1B at Ultimate load Table 2: Beams B6D1 B6D2 B12D2 B10S1A B10S1B Summary of Experimental and Analytical Results Pcrack kN 60 100 83.order effects in externally pre-stressed members. As a consequence of the second-order effects associated with the change in depth of the pre-stressed steel with increasing deflection.7 208 20 264 307 9 169.8 Analytical Results P yield kN Pu kN 97.def mm 15.17 5.2 174.185 Amer M.8 166 188. member with undeviated external tendons (B10S1B) mobilized lower deflections at failure load than those with deviated tendons.def mm 100 130 23 178.0) to predict the ultimate load and maximum deflection at mid-span for two spans of beam.3 191 28 168.3 49 50 Experimental Results P yield kN Pu kN Max.4 289. This model accounts for the influence of the second. The results predicted by the model were in good agreement with experimental data. Al-Haji. May 1. Ramos G.... Vol.engstruct. Tjandra. 1.1061/(ASCE)0733-9399(2007)133:1(117).Doi:10.1061/(ASCE)0733-9445(2003)129:1(96). 1. “Flexural Behavior of Two.. "Effects of Existing Shear Damage on Externally Posattensioned Repair of Bent Caps" Journal of Structural Engineering ASCE. ELSEVIER. A. 99. 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