Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams
Abstract
:1. Introduction
2. Materials and Methods
2.1. Structural Elements Studied
2.2. Experimental Flexural Tests
2.3. Finite Element Modeling
2.3.1. Boundary Conditions
- RESTRICTIONS. At three levels: supports, symmetry and contact between elements.
- (a)
- Supports: a restriction is applied to the centerline of the support plate, coincident with the support point of the beam in the real test. The movement is restricted for the X and Y axes, avoiding that the piece moves vertically.
- (b)
- Symmetry: The simulation model is built for half a beam. On the face corresponding to the vertical symmetry axis, a restriction to the surface is introduced, restricting the movement in the X and Z axes. This allows to reproduce the symmetry of the model taking into account the continuity of the analyzed element.
- (c)
- Contacts: To ensure contact between the top and bottom faces of the beam with the corresponding surfaces of the support plates and of application of the load, it is applied contacts between these elements.
- LOADS.
- (a)
- External load application: the load step is introduced by means of a prescribed displacement in the vertical Y axis, applied at the center of the load plate.
- (b)
- Initial horizontal deformation due to prestressing: to simulate the effect of the initial prestressing force, an initial stretch deformation of 0.006375 mm/mm is applied.
- MONITORING POINTS
- (a)
- Control of the applied force: One at the same point of application of the prescribed displacement (center point of the load plate), to collect the output data of the Y-axis reactions.
- (b)
- Strain control in the center of the beam: located in the lower part of the central section of the beam.
- (c)
- Control of the deformation at the point of application of the load: which records the millimeters that the load arm descends during the analysis.
2.3.2. Materials
- CONCRETE. The specific concrete constitutive model CC3DNonLinCementitious2 was used. It reproduces the non-linear behavior of concrete, assuming a hardening regime prior to the compressive stress being reached, which is based on plastic fracture failure mechanisms combining constitutive models for tensile and compressive behavior. The parameters of the model were configured according to the corresponding strength classes in the experimentation, which are among those described in Eurocode 2 [20] for the actual compressive strength of elements. There are 22 parameters that define this material model, but the main ones are: compression strength, tensile strength, elasticity modulus, fracture energy and deformation to the highest peak compression.
- REINFORCEMENT. The reinforcement model used was 1DCCreinforcement, which follows the embedded reinforcement with bond approach described in [32]. This model was applied to linear elements crossing the volumetric finite elements corresponding to the concrete. Thus, the element for each reinforcement is described by the basic parameters of bar diameter, steel strength and modulus of elasticity, among others, which define its behavior, such as the type of bar (rebar or cable) or the bonding conditions of the reinforcement. There are a total of 15 basic parameters and 16 other parameters that define the adhesion conditions [30].
- STEEL IN AUXILIARY ELEMENTS. Small metallic elements were simulated at the load application points to avoid stress concentration on a node of the element. These elements without analytical interest were modelled by means of an elastic–linear material model with a modulus of elasticity of 210,000 MPa.
2.3.3. Meshing of the Joist
2.3.4. Configuration of the Analysis
2.3.5. Model Calibration
- Compressive strength. The initial compressive strength value was not modified in the tests, since, to calibrate the model, we used the actual values determined in the manufacturer’s quality control process, involving the corresponding concrete compressive strength tests.
- Initial modulus of elasticity. In addition to the previous parameter, the model response requires a small calibration of the first part of the curve, which is controlled by the modulus of elasticity of the concrete and for which no real data were available to incorporate into the model. Thus, we analyzed rates of 28,000, 32,000 and 36,000 N/ mm2.
- Tensile Strength and Energy Fracture. These characteristics of concrete affect the tensile strength of the elements. The tensile strengths analyzed were 2.8, 3.5 and 4.2 MPa, while the fracture energy values analyzed were 7.0, 9.5 and 13.0 GPa.
- Pre-stressing losses. The loss of the initial pre-stressing force was estimated according to the theoretical calculation results in simulations with a resistance higher than the actual resistance, both in highly reinforced and weakly reinforced elements. Thus, the pre-stressing losses were analyzed for 5 rates: 0% (no losses), 25%, 35%, 45% and 55%.
- Bond strength. As well as the response of the curve, another factor that determines the failure of the elements is the strength of the bond of the reinforcements to the concrete. Given the difficulty of experimentally determining this parameter, as in the previous case, the simulation of this factor was performed by changing variables with values of 4, 8 and 12 MPa.
3. Results and Discussion
3.1. Experimental Tests
3.2. Calibration
- Level of pre-stressing losses
- Modulus of elasticity
- Bond strength
3.3. Results of the Simulation of the Elements with the Parameters Obtained from the Calibration and Comparison with the Experimental Tests
- Joist T18-1.—This element lacks great strength, with an absolute difference in value between simulation and experiment of 1 kN-m. This difference is not particularly significant; it highlights the sensitivity in terms of the mean parameters considered in the calibration. The error with respect to the cracking moment was 5.8%.
- Tubular joist TB35-3 and TB35-6.—The elements are stronger, with the differences obtained in the maximum load being −10 y − 17 kN, respectively. Analyzing the overall fit of the load–deformation curve of each pair of elements, it can be seen that curve generated by the simulation shows a higher level of fit along its entire length compared to that of the experimental response. However, the deformation point at which the simulation obtains the rupture is similar to the experimental case.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Type | Repetitions | Length | Amount Reinforcement | Losses | Resistance Characteristics | |||
---|---|---|---|---|---|---|---|---|
(m) | Alower (‰) | Ahigher (‰) | Alower (%) | Ahigher (%) | Multimate (kN·m) | Mcracking (kN·m) | ||
T13.1 | 2 | 2.40 | 3.0 | 1.5 | 18.6 | 17.5 | 3.8 | 1.7 |
T13.2 | 3 | 2.40 | 4.5 | 1.5 | 20.3 | 18.5 | 4.6 | 2.3 |
T18.1 | 3 | 2.40 | 2.3 | 1.2 | 17.7 | 16.4 | 5.9 | 2.5 |
T18.3 | 2 | 2.40 | 4.7 | 1.2 | 21.6 | 16.5 | 9.8 | 5.0 |
T35.3 | 2 | 4.10 | 4.1 | 1.0 | 18.2 | 11.2 | 67.5 | 49.6 |
T35.4 | 3 | 2.03 | 5.1 | 1.0 | 20.3 | 11.2 | 76.1 | 56.8 |
T35.5 | 2 | 3.70 | 5.1 | 2.0 | 21.9 | 11.3 | 82.2 | 63.2 |
T35.6 | 2 | 3.26 | 6.1 | 1.0 | 22.7 | 10.9 | 86.0 | 66.2 |
T13-1 | T13-2 | T18-1 | T18-3 | T35-3 | T35-4 | T35-5 | T35-6 | ||
---|---|---|---|---|---|---|---|---|---|
Cracking | Force (kN) | 5.40 | 8.00 | 9.65 | 13.73 | 45.85 | 108.77 | 79.40 | 79.99 |
Deformation (mm) | 2.00 | 3.10 | 1.30 | 2.00 | 3.75 | 1.16 | 4.45 | 2.76 | |
Moment (kN·m) | 2.60 | 3.80 | 4.51 | 6.46 | 37.60 | 43.78 | 63.65 | 65.58 | |
Ultimate | Force (kN) | 11.20 | 15.90 | 17.35 | 26.90 | 81.05 | 177.77 | 117.10 | 137.90 |
Deformation (mm) | 29.50 | 22.80 | 25.27 | 17.08 | 23.83 | 4.73 | 16.45 | 13.94 | |
Moment (kN·m) | 5.30 | 7.50 | 8.15 | 12.64 | 66.45 | 71.57 | 96.45 | 113.10 | |
Crack spacing (mm) | 172 | 122 | 202 | 182 | 175 | 233 | 194 | 204 |
Parameter | Calibration Value |
---|---|
Compressive strength | 48 MPa |
Initial modulus of elasticity | 32,000 MPa |
Tensile strength | 3.5 MPa |
Fracture energy | 9.5 GPa |
Pre-stressing losses | 35% |
Bond strength | 12 MPa |
Element | Cracking Moment (kN·m) | Ultimate Moment (kN·m) | ||||||
---|---|---|---|---|---|---|---|---|
Exper. | Simul. | Difference | (%) | Exper. | Simul. | Difference | (%) | |
T13-1 | 2.60 | 2.99 | 0.39 | 15.00 | 5.30 | 5.19 | −0.11 | −2.08 |
T13-2 | 3.43 | 3.60 | 0.17 | 4.96 | 6.53 | 6.49 | −0.04 | −0.61 |
T18-1 | 4.51 | 4.25 | −0.26 | −5.76 | 8.15 | 7.14 | −1.01 | −12.39 |
T18-3 | 6.46 | 6.27 | −0.19 | −2.94 | 12.64 | 12.67 | 0.03 | 0.24 |
Overall joists | 7.17 | 3.83 | ||||||
TB35-3 | 37.60 | 36.14 | −1.46 | −3.88 | 66.45 | 58.55 | −7.90 | −11.89 |
TB35-4 | 43.78 | 50.12 | 6.34 | 14.48 | 71.57 | 73.88 | 2.31 | 3.23 |
TB35-5 | 63.65 | 61.20 | −2.45 | −3.85 | 96.45 | 92.70 | −3.75 | −3.89 |
TB35-6 | 65.58 | 63.72 | −1.86 | −2.84 | 113.10 | 98.56 | −14.54 | −12.86 |
Overall tubular joists | 6.26 | 7.97 | ||||||
Mean total | 6.71 | 5.90 |
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Montero, J.; Cervera-Gascó, J.; Gilarranz, C.; Laserna, S. Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams. Appl. Sci. 2023, 13, 7477. https://doi.org/10.3390/app13137477
Montero J, Cervera-Gascó J, Gilarranz C, Laserna S. Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams. Applied Sciences. 2023; 13(13):7477. https://doi.org/10.3390/app13137477
Chicago/Turabian StyleMontero, Jesús, Jorge Cervera-Gascó, Carlos Gilarranz, and Santiago Laserna. 2023. "Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams" Applied Sciences 13, no. 13: 7477. https://doi.org/10.3390/app13137477