A PROBABLISTIC APPROACH TO EVALUATION OF THE ULTIMATE LOAD ON FLEXURAL RC ELEMENT ON CRACK LENGTH
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Abstract
The fracture mechanics of concrete and reinforced concrete is a promising direction in the development of methods for reinforced concrete structural elements design and inspection. At the same time, probabilistic methods of design and behavior analysis of structural elements are of particular interest. The article describes a probabilistic approach to load-bearing capacity and reliability analysis of flexural reinforced concrete elements based on the crack length criterion. The functional relationship between the critical stress intensity coefficient of concrete and the design compressive strength of concrete is given. The article presents a method for the reliability analysis of flexural reinforced concrete elements at the operational stage with limited statistical data about the critical stress intensity coefficient of concrete. The ultimate value of the failure probability (or reliability index) should be set for each object individually based on the value of the acceptable risk.
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Solovyev, S. (2020). A PROBABLISTIC APPROACH TO EVALUATION OF THE ULTIMATE LOAD ON FLEXURAL RC ELEMENT ON CRACK LENGTH. International Journal for Computational Civil and Structural Engineering, 16(1), 98–105. https://doi.org/10.22337/2587-9618-2020-16-1-98-105
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REFERENCES
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2. Melchers R. E., Beck A. T. Structural reliability analysis and prediction. John Wiley & Sons. 2018. 497 p.
3. Piradov K.A., Savickij N.V. Mekhanika razrusheniya i teoriya zhelezobetona [Fracture mechanics of concrete and reinforced concrete]. Beton i zhelezobeton. 2014. No. 4. pp. 23-25. (in Russian)
4. Tung N.D., Tue N.V. A fracture mechanics-based approach to modeling the confinement effect in reinforced concrete columns. Construction and Building Materials. 2016. Vol. 102. pp. 893-903
5. Yehia N.A.B. Fracture mechanics approach for flexural strengthening of reinforced concrete beams. Engineering Structures. 2009. Vol. 31. Issue 2. pp. 404-416
6. Sau N., Medina-Mendoza J., Borbon-Almada A.C. Peridynamic modelling of reinforced concrete structures. Engineering Failure Analysis. 2019. Vol. 103. pp. 266-274.
7. Zajcev Yu.V. Mekhanika razrusheniya dlya stroitelej [Fracture mechanics for structural engineers]. Moscow: Vysshaya shkola. 1991. 287 p. (in Russian)
8. Gvozdev A.A. Novoe v proektirovanii betonnyh i zhelezobetonnyh konstrukcij [New in concrete and reinforced concrete structures design]. Moscow: Strojizdat. 1978. 208 p. (in Russian)
9. Carpinteri A., Carmona J.R., Ventura G. Propagation of flexural and shear cracks through RC beams by the bridged crack model. Magazine of concrete research. 2007. No. 10. Pp. 743-756.
10. Piradov K.A. Teoreticheskie i eksperimental'nye osnovy mekhaniki razrusheniya betona i zhelezobetona [Theoretical and experimental foundations of concrete and reinforced concrete fracture mechanics]. Tbilisi: Energiya, 1998. 355 p. (in Russian)
11. Wang P., Zhang J., Zhai H., Qiu J. A new structural reliability index based on uncertainty theory Chinese Journal of Aeronautics. 2017. Vol. 30. Issue 4. pp. 1451-1458.
12. Van Coile R., Hopkin D., Bisby L., Caspeele R. The meaning of Beta: background and applicability of the target reliability index for normal conditions to structural fire engineering. Procedia Engineering. 2017. Vol. 210. pp. 528-536.
13. Roudak M.A., Shayanfar M.A., Barkhordari M.A., Karamloo M. A new three-phase algorithm for computation of reliability index and its application in structural mechanics. Mechanics Research Communications. 2017. Vol. 85. pp. 53-60
14. Li H., Nie X. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence. 2018. Vol. 67. pp. 91-99.
15. Utkin V.S., Solovyev S.A., Kaberova A.A. Znachenie urovnya sreza (riska) pri raschete nadezhnosti nesushchih elementov vozmozhnostnym metodom [Cut (risk) level in reliability analysis of structural elements by possibilistic methods]. Stroitel'naya mekhanika i raschet sooruzhenij. 2015. No. 6. pp. 63-67. (in Russian)
16. Trbojevic V. M. Another look at risk and structural reliability criteria. Structural Safety. 2009. Vol. 31. Issue 3. pp. 245-250.
17. Zhu B., Frangopol D.M. Reliability, redundancy and risk as performance indicators of structural systems during their life-cycle. Engineering Structures. 2012. Vol. 41. pp. 34-49.
18. Crespo L.G., Kenny S.P., Giesy D.P. Staircase predictor models for reliability and risk analysis. Structural Safety. 2018. Vol. 75. pp. 35-44.
СПИСОК ЛИТЕРАТУРЫ
1. Elishakoff I. Probabilistic Methods in the Theory of Structures: Strength of Materials, Random Vibrations, and Random Buckling. – World Scientific Publishing Co. 2017. 400 p.
2. Melchers R. E., Beck A. T. Structural reliability analysis and prediction. John Wiley & Sons. 2018. 497 p.
3. Пирадов К.А., Савицкий Н.В. Механика разрушения и теория железобетона // Бетон и железобетон. 2014. № 4. С. 23-25.
4. Tung N.D., Tue N.V. A fracture mechanics-based approach to modeling the confinement effect in reinforced concrete columns. Construction and Building Materials. 2016. Vol. 102. pp. 893-903
5. Yehia N.A.B. Fracture mechanics approach for flexural strengthening of reinforced concrete beams. Engineering Structures. 2009. Vol. 31. Issue 2. pp. 404-416
6. Sau N., Medina-Mendoza J., Borbon-Almada A.C. Peridynamic modelling of reinforced concrete structures. Engineering Failure Analysis. 2019. Vol. 103. pp. 266-274.
7. Зайцев Ю.В. Механика разрушения для строителей. 1991. М.: Высшая школа. 287 с.
8. Гвоздев А.А. Новое в проектировании бетонных и железобетонных конструкций. М.: Стройиздат. 1978. 208 с.
9. Carpinteri A., Carmona J.R., Ventura G. Propagation of flexural and shear cracks through RC beams by the bridged crack model // Magazine of concrete research. 2007. No. 10. Pp. 743-756.
10. Пирадов К.А. Теоретические и экспериментальные основы механики разрушения бетона и железобетона. Тбилиси: Энергия, 1998. 355 с.
11. Wang P., Zhang J., Zhai H., Qiu J. A new structural reliability index based on uncertainty theory Chinese Journal of Aeronautics. 2017. Vol. 30. Issue 4. pp. 1451-1458.
12. Van Coile R., Hopkin D., Bisby L., Caspeele R. The meaning of Beta: background and applicability of the target reliability index for normal conditions to structural fire engineering. Procedia Engineering. 2017. Vol. 210. pp. 528-536.
13. Roudak M.A., Shayanfar M.A., Barkhordari M.A., Karamloo M. A new three-phase algorithm for computation of reliability index and its application in structural mechanics. Mechanics Research Communications. 2017. Vol. 85. pp. 53-60
14. Li H., Nie X. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence. 2018. Vol. 67. pp. 91-99.
15. Уткин В.С., Соловьев С.А., Каберова А.А. Значение уровня среза (риска) при расчете надежности несущих элементов возможностным методом // Строительная механика и расчет сооружений. 2015. №6. С. 63-67.
16. Trbojevic V. M. Another look at risk and structural reliability criteria. Structural Safety. 2009. Vol. 31. Issue 3. pp. 245-250.
17. Zhu B., Frangopol D.M. Reliability, redundancy and risk as performance indicators of structural systems during their life-cycle. Engineering Structures. 2012. Vol. 41. pp. 34-49.
18. Crespo L.G., Kenny S.P., Giesy D.P. Staircase predictor models for reliability and risk analysis. Structural Safety. 2018. Vol. 75. pp. 35-44.
1. Elishakoff I. Probabilistic Methods in the Theory of Structures: Strength of Materials, Random Vibrations, and Random Buckling. World Scientific Publishing Co. 2017. 400 p.
2. Melchers R. E., Beck A. T. Structural reliability analysis and prediction. John Wiley & Sons. 2018. 497 p.
3. Piradov K.A., Savickij N.V. Mekhanika razrusheniya i teoriya zhelezobetona [Fracture mechanics of concrete and reinforced concrete]. Beton i zhelezobeton. 2014. No. 4. pp. 23-25. (in Russian)
4. Tung N.D., Tue N.V. A fracture mechanics-based approach to modeling the confinement effect in reinforced concrete columns. Construction and Building Materials. 2016. Vol. 102. pp. 893-903
5. Yehia N.A.B. Fracture mechanics approach for flexural strengthening of reinforced concrete beams. Engineering Structures. 2009. Vol. 31. Issue 2. pp. 404-416
6. Sau N., Medina-Mendoza J., Borbon-Almada A.C. Peridynamic modelling of reinforced concrete structures. Engineering Failure Analysis. 2019. Vol. 103. pp. 266-274.
7. Zajcev Yu.V. Mekhanika razrusheniya dlya stroitelej [Fracture mechanics for structural engineers]. Moscow: Vysshaya shkola. 1991. 287 p. (in Russian)
8. Gvozdev A.A. Novoe v proektirovanii betonnyh i zhelezobetonnyh konstrukcij [New in concrete and reinforced concrete structures design]. Moscow: Strojizdat. 1978. 208 p. (in Russian)
9. Carpinteri A., Carmona J.R., Ventura G. Propagation of flexural and shear cracks through RC beams by the bridged crack model. Magazine of concrete research. 2007. No. 10. Pp. 743-756.
10. Piradov K.A. Teoreticheskie i eksperimental'nye osnovy mekhaniki razrusheniya betona i zhelezobetona [Theoretical and experimental foundations of concrete and reinforced concrete fracture mechanics]. Tbilisi: Energiya, 1998. 355 p. (in Russian)
11. Wang P., Zhang J., Zhai H., Qiu J. A new structural reliability index based on uncertainty theory Chinese Journal of Aeronautics. 2017. Vol. 30. Issue 4. pp. 1451-1458.
12. Van Coile R., Hopkin D., Bisby L., Caspeele R. The meaning of Beta: background and applicability of the target reliability index for normal conditions to structural fire engineering. Procedia Engineering. 2017. Vol. 210. pp. 528-536.
13. Roudak M.A., Shayanfar M.A., Barkhordari M.A., Karamloo M. A new three-phase algorithm for computation of reliability index and its application in structural mechanics. Mechanics Research Communications. 2017. Vol. 85. pp. 53-60
14. Li H., Nie X. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence. 2018. Vol. 67. pp. 91-99.
15. Utkin V.S., Solovyev S.A., Kaberova A.A. Znachenie urovnya sreza (riska) pri raschete nadezhnosti nesushchih elementov vozmozhnostnym metodom [Cut (risk) level in reliability analysis of structural elements by possibilistic methods]. Stroitel'naya mekhanika i raschet sooruzhenij. 2015. No. 6. pp. 63-67. (in Russian)
16. Trbojevic V. M. Another look at risk and structural reliability criteria. Structural Safety. 2009. Vol. 31. Issue 3. pp. 245-250.
17. Zhu B., Frangopol D.M. Reliability, redundancy and risk as performance indicators of structural systems during their life-cycle. Engineering Structures. 2012. Vol. 41. pp. 34-49.
18. Crespo L.G., Kenny S.P., Giesy D.P. Staircase predictor models for reliability and risk analysis. Structural Safety. 2018. Vol. 75. pp. 35-44.
СПИСОК ЛИТЕРАТУРЫ
1. Elishakoff I. Probabilistic Methods in the Theory of Structures: Strength of Materials, Random Vibrations, and Random Buckling. – World Scientific Publishing Co. 2017. 400 p.
2. Melchers R. E., Beck A. T. Structural reliability analysis and prediction. John Wiley & Sons. 2018. 497 p.
3. Пирадов К.А., Савицкий Н.В. Механика разрушения и теория железобетона // Бетон и железобетон. 2014. № 4. С. 23-25.
4. Tung N.D., Tue N.V. A fracture mechanics-based approach to modeling the confinement effect in reinforced concrete columns. Construction and Building Materials. 2016. Vol. 102. pp. 893-903
5. Yehia N.A.B. Fracture mechanics approach for flexural strengthening of reinforced concrete beams. Engineering Structures. 2009. Vol. 31. Issue 2. pp. 404-416
6. Sau N., Medina-Mendoza J., Borbon-Almada A.C. Peridynamic modelling of reinforced concrete structures. Engineering Failure Analysis. 2019. Vol. 103. pp. 266-274.
7. Зайцев Ю.В. Механика разрушения для строителей. 1991. М.: Высшая школа. 287 с.
8. Гвоздев А.А. Новое в проектировании бетонных и железобетонных конструкций. М.: Стройиздат. 1978. 208 с.
9. Carpinteri A., Carmona J.R., Ventura G. Propagation of flexural and shear cracks through RC beams by the bridged crack model // Magazine of concrete research. 2007. No. 10. Pp. 743-756.
10. Пирадов К.А. Теоретические и экспериментальные основы механики разрушения бетона и железобетона. Тбилиси: Энергия, 1998. 355 с.
11. Wang P., Zhang J., Zhai H., Qiu J. A new structural reliability index based on uncertainty theory Chinese Journal of Aeronautics. 2017. Vol. 30. Issue 4. pp. 1451-1458.
12. Van Coile R., Hopkin D., Bisby L., Caspeele R. The meaning of Beta: background and applicability of the target reliability index for normal conditions to structural fire engineering. Procedia Engineering. 2017. Vol. 210. pp. 528-536.
13. Roudak M.A., Shayanfar M.A., Barkhordari M.A., Karamloo M. A new three-phase algorithm for computation of reliability index and its application in structural mechanics. Mechanics Research Communications. 2017. Vol. 85. pp. 53-60
14. Li H., Nie X. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence. 2018. Vol. 67. pp. 91-99.
15. Уткин В.С., Соловьев С.А., Каберова А.А. Значение уровня среза (риска) при расчете надежности несущих элементов возможностным методом // Строительная механика и расчет сооружений. 2015. №6. С. 63-67.
16. Trbojevic V. M. Another look at risk and structural reliability criteria. Structural Safety. 2009. Vol. 31. Issue 3. pp. 245-250.
17. Zhu B., Frangopol D.M. Reliability, redundancy and risk as performance indicators of structural systems during their life-cycle. Engineering Structures. 2012. Vol. 41. pp. 34-49.
18. Crespo L.G., Kenny S.P., Giesy D.P. Staircase predictor models for reliability and risk analysis. Structural Safety. 2018. Vol. 75. pp. 35-44.