Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations
Abstract
:1. Introduction
2. The Theory of Limited Residual Plastic Deformation Inside Steel Elements
- = actual stresses.
- and = actual strains and displacements.
- = fictitious stresses that would occur if the material were purely elastic.
- and fictitious elastic strains and displacements corresponding to .
- = actual residual stress distribution.
- = any arbitrary, time-independent self-stress distribution.
3. Optimization Problem
4. Models with Different Prestressing Tendon Numbers
4.1. Numerical Modelling of the Benchmarks
4.2. Results and Discussion of the Application of the Optimization Problem
5. Models with Different Prestressing Forces
5.1. Numerical Modelling of the Benchmarks
5.2. Results and Discussion of the Application of the Optimization Problem
6. Conclusions
- In most cases, an increase in the value of the allowable amount of energy will increase the corresponding loading values produced.
- The load– curve in the 2-PS model begins to take the direction of the horizontal line with lower loads than its counterpart in the 4-PS model, which can be explained by the fact that the 4-PS model contains more tendons, so the damages caused by internal stresses generated inside them are delayed in formation and accumulate more slowly compared to the other model.
- With a given value of allowed complementary strain energy, the corresponding load in the case of 2-PS will be smaller than in the case of 4-PS, implying that the yielded steel elements accumulate more in the first model, resulting in faster failure under lower loads.
- When the permissible complementary strain energy is almost zero, a reflection of general elastic behaviour is produced within the limits of the initial loads; however, as this value increases, the load– curves begin to take a path that leads to plastic behaviour, passing through the elasto-plastic region.
- When the provided allowable complementary strain energy value grows, so does the damage caused by high-stress intensity in steel and tension-damaged areas in concrete.
- Increasing the number of prestressed tendons results in higher load values for lower permissible complementary strain energy. This occurs as a result of the strengthening added by increasing the number of prestressed tendons, where increasing the number of these tendons would increase the required load to cause the yield inside the steel elements.
- The allowable complementary strain energy value produces an increase in the associated load values, indicating that a higher plasticity state has been achieved.
- When compared to a specific allowable complementary strain energy value, the 0%PSF model provides lower load values than the 100%PSF model. This may suggest that the steel used in the 0%PSF model experiences higher stresses under lower loads, which may reflect the general damage behaviour of the beams.
- The use of prestressed tendons in a 100%PSF model strengthened the beam and postponed the initiation of stresses within the steel elements, leading to higher load values and a smaller allowable complementary strain energy value. This is because the process of having yielded steel elements necessitates higher loads.
- Increasing the prestressing force inside the tendon strengthens the models, leading to an increase in the assumed allowable complementary strain energy value, which in turn leads to an increase in the load necessary to cause yield within the steel elements and a corresponding decrease in the corresponding allowable complementary strain energy value, which depends on the number of yielded elements.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
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Khaleel Ibrahim, S.; Movahedi Rad, M. Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations. Sustainability 2023, 15, 5742. https://doi.org/10.3390/su15075742
Khaleel Ibrahim S, Movahedi Rad M. Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations. Sustainability. 2023; 15(7):5742. https://doi.org/10.3390/su15075742
Chicago/Turabian StyleKhaleel Ibrahim, Sarah, and Majid Movahedi Rad. 2023. "Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations" Sustainability 15, no. 7: 5742. https://doi.org/10.3390/su15075742
APA StyleKhaleel Ibrahim, S., & Movahedi Rad, M. (2023). Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations. Sustainability, 15(7), 5742. https://doi.org/10.3390/su15075742