Numerical Simulations on the Flexural Responses of Rubberised Concrete
Abstract
:1. Introduction
1.1. Current Researches
1.2. Significance of This Study
2. Geometric Properties of the Numerical Models
2.1. Mechanical Properties of the Materials
2.2. Assumptions
3. Finite Element Modelling
- Determining the locations of the nodes and entering their coordinates to form the models, which were rectangle prisms with the cross-sectional dimensions of 530 mm × 150 mm × 150 mm.
- Determining the positions of the steel plate at the supports of the model and the applied loading points to avoid sudden failure, with the element sizes set as 50 mm × 10 mm, as shown in Figure 4.
- After deciding the geometries of the models, carrying out the meshing for the rectangular concrete beam and the supporting steel plates by specifying the properties and selecting the elements for individual materials, e.g., concrete and steel plates, and then dividing the models to small 10 mm element sizes in a homogeneous or heterogeneous manner, i.e., the concrete was represented by the solid element 187, and the steel plates were modelled by using the solid element 185, see Figure 5, Figure 6 and Figure 7.
- Imposing a correlation between all the simulated components in the ANSYS program [25] by assuming a full bonding between the concrete and rubber parts.
- Determining the tolerance criterion as a constraint when analysing the model, e.g., the tolerance used for deflection was 0.05.
- Designating the applied loads from the previous studies [37,38] in the top–middle regions of the models to obtain true behaviours for the simulated models, where the right support of the models was simulated as the roller support by restraining the movement in the vertical loading direction, while the left support was restrained in two directions against the movements in the vertical direction and in the direction parallel to the axis of the models as a pinned support. Hence, the applied loads were simulated gradually to be identical to the experimental loads.
- In the analysis of the nonlinear behaviours of the models, the open and closed shear coefficients were defined as 0.2 and 0.7, with the splitting tensile modulus within the ANSYS program, [25] as stated in the references [42,43,44], with the details of the simulated beam models shown in Figure 6 and Figure 7. Hence, these parameters were defined for the simulated models as constants for the purpose of analysis.
4. Results and Discussion
5. Conclusions
- The numerical analysis with appropriate assumptions can be used as an effective tool to predict the structural behaviours of the rubber concrete beam models through validating the obtained numerical results with the results from the experimental investigations.
- The behaviours of the homogeneous models were closer to those experimental behaviours than those of the heterogeneous models due to the adopted meshing methods in the individual models.
- The mid-span deflections of the rubberised concrete beam models at the failure loadings increased with the increasing rubber content by 5% to 35% when the rubber replacement ratios varied between 20% and 40%. The variances of the deflections at the failure loadings between the numerical and experimental results ranged from 2% to 7% for the rubberised concrete beams under flexural loading.
- The flexural resistance of the numerical rubberised concrete beam models was largely degraded with the increasing content of added rubbers that replaced the coarse aggregates. The flexural strength or the modulus of rupture decreased with the increasing rubber replacement ratio by 15–49%. The numerical and experimental results of the modulus of rupture agreed very well and the differences ranged from 5% to 9% for the homogeneous and heterogeneous rubber concrete beam models and experimental studies.
- The statistical analysis of the arithmetic means and standard deviations of the modulus of rupture, as well as the deflection of the rubberised concrete beam models at the failure loadings, indicated larger convergences between the results from the numerical analysis and experimental investigations. However, the current study is only validated for the considered materials and rubber replacement ratios. Additionally, the used numerical models can be improved and used for other investigations by modifying the relevant factors and adopting the models in the ANSYS program [25].
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Content | (0% Rubber) | 20% | 40% | 60% | 80% | 100% |
---|---|---|---|---|---|---|
* W (kg) | 250 | 250 | 250 | 250 | 250 | 250 |
C (kg) | 500 | 500 | 500 | 500 | 500 | 500 |
* S (kg) | 850 | 850 | 850 | 850 | 850 | 850 |
* G (kg) | 500 | 450 | 175 | 125 | 25 | 0.00 |
* C.R. (kg) | 0.00 | 50 | 200 | 250 | 300 | 350 |
Stress (MPa) | Strain (mm/mm) |
---|---|
7.65 | 0.00033 |
11.68 | 0.00091 |
15.26 | 0.00135 |
18.76 | 0.00160 |
20.17 | 0.00220 |
20.17 | 0.00300 |
Mix No. | Experimental [37,38] | Numerical (Homogeneous Models) | Numerical (Heterogeneous Models) | |||
---|---|---|---|---|---|---|
fr (MPa) | Defl. (mm) | fr (MPa) | Defl. (mm) | fr (MPa) | Defl. (mm) | |
0 | 3.760 | 1.016 | 3.450 | 0.992 | 3.410 | 0.990 |
20 | 3.109 | 1.397 | 2.930 | 1.343 | 2.890 | 1.341 |
40 | 2.730 | 1.067 | 2.590 | 1.045 | 2.580 | 1.044 |
60 | 2.488 | 0.914 | 2.340 | 0.890 | 2.320 | 0.888 |
80 | 2.248 | 0.813 | 2.135 | 0.780 | 2.095 | 0.778 |
100 | 1.874 | 0.991 | 1.776 | 0.935 | 1.762 | 0.926 |
Mix No. | Experimental [37,38] | Numerical Homogeneous | Num./Exp. | Numerical Heterogeneous | Num./Exp. | |||||
---|---|---|---|---|---|---|---|---|---|---|
fr (MPa) | Defl. (mm) | fr (MPa) | Defl. (mm) | fr % | Defl. % | fr (MPa) | Defl. (mm) | fr % | Defl. % | |
0 | 3.760 | 1.016 | 3.450 | 0.992 | 91.76 | 97.64 | 3.410 | 0.990 | 90.69 | 97.44 |
20 | 3.109 | 1.397 | 2.930 | 1.343 | 94.24 | 96.13 | 2.890 | 1.341 | 92.96 | 95.99 |
40 | 2.730 | 1.067 | 2.590 | 1.045 | 94.87 | 97.94 | 2.580 | 1.044 | 94.51 | 97.84 |
60 | 2.488 | 0.914 | 2.340 | 0.890 | 94.05 | 97.37 | 2.320 | 0.888 | 93.25 | 97.16 |
80 | 2.248 | 0.813 | 2.135 | 0.780 | 94.97 | 95.94 | 2.095 | 0.778 | 93.19 | 95.69 |
100 | 1.874 | 0.991 | 1.776 | 0.935 | 94.77 | 94.35 | 1.762 | 0.926 | 94.02 | 93.44 |
Mean | 94.11 | 96.56 | 93.10 | 96.26 | ||||||
STD | 1.10 | 1.24 | 1.20 | 1.47 |
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Al-Balhawi, A.; Muhammed, N.J.; Mushatat, H.A.; Al-Maliki, H.N.G.; Zhang, B. Numerical Simulations on the Flexural Responses of Rubberised Concrete. Buildings 2022, 12, 590. https://doi.org/10.3390/buildings12050590
Al-Balhawi A, Muhammed NJ, Mushatat HA, Al-Maliki HNG, Zhang B. Numerical Simulations on the Flexural Responses of Rubberised Concrete. Buildings. 2022; 12(5):590. https://doi.org/10.3390/buildings12050590
Chicago/Turabian StyleAl-Balhawi, Ali, Nura Jasim Muhammed, Haider Amer Mushatat, Hadi Naser Ghadhban Al-Maliki, and Binsheng Zhang. 2022. "Numerical Simulations on the Flexural Responses of Rubberised Concrete" Buildings 12, no. 5: 590. https://doi.org/10.3390/buildings12050590