vestniktgasuВестник Томского государственного архитектурно-строительного университетаVestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture1607-18592310-0044Tomsk State University of Architecture and Building10.31675/1607-1859-2022-24-4-110-129vestniktgasu-1272Research ArticleСТРОИТЕЛЬНЫЕ КОНСТРУКЦИИ, ЗДАНИЯ И СООРУЖЕНИЯBUILDING AND CONSTRUCTIONДеформационная модель прочности изгибаемого элемента в среде MatlabDeformation modeling of bending element strength in MATLABОпбулЭ. К.OpbulE. K.

Эрес Кечилоолович Опбул, канд. техн. наук, зав. лабораторией

190005

2-я Красноармейская ул., 4

Санкт-Петербург

Eres K. Opbul, PhD, Laboratory Head

190005

4, 2nd Krasnoarmeiskaya Str.

Saint-Petersburg

fduecnufce@mail.ruКалдар-оолА.-Х. Б.Kaldar-oolA.-Kh. B.

Анай-Хаак Бугалдаевна Калдар-оол, канд. техн. наук, ст. преподаватель

667000

ул. Ленина, 36

Республика Тыва

Кызыл

Anai-Khaak B. Kaldar-ool, PhD, Senoir Lecturer

667000

36, Lenin Str.

Tyva Republic

Kyzyl

 

oorzhaka-h@mail.ruХюиЛе КуангHuyLe Quang

Ле Куанг Хюи, аспирант

190005

2-я Красноармейская ул., 4

Санкт-Петербург

Le Quang Huy, Research Assistant

190005

4, 2nd Krasnoarmeiskaya Str.

Saint-Petersburg

lqh189@lqdtu.edu.vnСанкт-Петербургский государственный архитектурно-строительный университетРоссияSaint-Petersburg State University of Architecture and Civil EngineeringRussian FederationТувинский государственный университетРоссияTuvan State UniversityRussian Federation202225082022244110129Copyright © Опбул Э.К., Калдар-оол А.Б., Хюи Л.К., 20222022Опбул Э.К., Калдар-оол А.Б., Хюи Л.К.Opbul E.K., Kaldar-ool A.B., Huy L.Q.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.tsuab.ru/jour/article/view/1272

   В статье приводятся деформационные модели расчета прочности изгибаемых железобетонных элементов в программе Matlab. Универсальность деформационной модели заключается в возможности проведения контрольных тестов, например, верификации конструктивных расчетов в стадии проектирования. На основе нормативных диаграмм деформирования материалов и способа итерационных вычислений предлагаются два независимых друг от друга нелинейных расчёта. Одно из главных принятых условий методов заключается в том, что итерационные процессы начинаются при упругой работе элемента. Задачей итерационных вычислений является определение величины максимальной кривизны элемента и соответствующих ей деформаций. Критерием прочности методов являются расчетные деформации, величина которых не должна превышать допустимых значений, указанных в строительных нормах и правилах.

   The paper presents the strength analysis of bending reinforced concrete elements in the Matlab support package. The versatility of the deformation model is its ability to conduct control tests, for example, verification of structural analysis at the design stage. Based on the standard stress-strain state diagrams of materials and iteration procedures, two independent nonlinear analyses are suggested. One of the main accepted conditions is that iteration procedures occur at the elastic behavior of the member. Iteration procedures determine the maximum member curvature and its deformation. The strength criterion is theoretically calculated deformation, which must not exceed permissible values specified in construction codes and regulations. Calculation algorithms are given in flowcharts. In conclusion, the results of experimental data are presented. 

деформационная модельнелинейный расчетитерацияматрица жесткостидеформациинапряженияжелезобетонdeformation modelnonlinear strength analysisiteration proceduresstiffness matrixstress-strain statereinforced concreteReferencesMichał D., Jacek Ś. Design Aspects of the Safe Structuring of Reinforcement in Reinforced Concrete Bending Beams // Procedia Engineering. 2017. V. 172. P. 211–217. DOI: 10.1016/j.proeng.2017.02.051Michał D., Jacek Ś. Design aspects of the safe structuring of reinforcement in reinforced concrete bending beams. Procedia Engineering. 2017. V. 172. Pp. 211–217. DOI: 10.1016/j.proeng.2017.02.051Herranz J. P., Maria H. S., Gutiérrez S., Riddell R. Optimal Strut-and-tie models using full homogenization optimization method // ACI Structural Journal. 2012. V. 109(5). P. 605–613. DOI: 10.14359/51684038Herranz J. P., Maria H. S., Gutiérrez S., Riddell R. Optimal strut-and-tie models using full homogenization optimization method. ACI Structural Journal. 2012. V. 109. No. 5. Pp. 605–613. DOI: 10.14359/51684038Garstecki A., Glema A., Ścigałło J. Optimal design of reinforced concrete beams and frames // Computer Assisted Mechanics and Engineering Sciences. 1996. V. 3 (3). P. 223−231.Garstecki A., Glema A., Ścigałło J. Optimal design of reinforced concrete beams and frames. Computer Assisted Mechanics and Engineering Sciences. 1996. V. 3. No. 3. Pp. 223−231.Amin A., Gilbert R. I. Instantaneous Crack Width Calculation for Steel Fiber-Reinforced Concrete Flexural Members // Aci Structural Journal. 2018. V. 115. № 2. P. 535–542. DOI: 10.14359/51701116Amin A., Gilbert R. I. Instantaneous crack width calculation for steel fiber-reinforced concrete flexural members. ACI Structural Journal. 2018. V. 115. No. 2. Pp. 535–542. DOI: 10.14359/51701116Szeptyński P. Comparison and experimental verification of simplified one-dimensional linear elastic models of multilayer sandwich beams // Composite Structures. 2020. V. 214. P. 1–13. DOI: 10.1016/j.compstruct.2020.112088Szeptyński P. Comparison and experimental verification of simplified one-dimensional linear elastic models of multilayer sandwich beams. Composite Structures. 2020. V. 214. Pp. 1–13. DOI: 10.1016/j.compstruct.2020.112088Gao D. Y., Gu Z. qiang, Wu C. Bending Behavior and Deflection Prediction of High-Strength SFRC Beams under Fatigue Loading // Journal of Materials Research and Technology. 2020. V. 9. P. 6143−6159. DOI: 10.1016/j.jmrt.2020.04.017Gao D. Y., Gu Z. Qiang, Wu C. Bending behavior and deflection prediction of high-strength SFRC beams under fatigue loading. Journal of Materials Research and Technology. 2020. V. 9. Pp. 6143−6159. DOI: 10.1016/j.jmrt.2020.04.017Wu Z., Shi C., He W., Wu L. Effects of steel fiber content and shape on mechanical properties of ultra high-performance concrete // Construction and Building Materials. 2016. V. 103. P. 8–14. DOI: 10.1016/j.conbuildmat.2015.11.028Wu Z., Shi C., He W., Wu L. Effects of steel fiber content and shape on mechanical properties of ultra high-performance concrete. Construction and Building Materials. 2016. V. 103. Pp. 8–14. DOI: 10.1016/j.conbuildmat.2015.11.028Yoo D. Y., Banthia N., Yoon Y. S. Impact resistance of reinforced ultra-high-performance concrete beams with different steel fibers // ACI Structural Journal. 2017. V. 114 (1). P. 113–124. DOI: 10.14359/51689430Yoo D. Y., Banthia N., Yoon Y. S. Impact resistance of reinforced ultra-high-performance concrete beams with different steel fibers. ACI Structural Journal. 2017. V. 114 No. 1. Pp. 113–124. DOI: 10.14359/51689430Ulzurrun G. S. D., Zanuy C. Enhancement of impact performance of reinforced concrete beams without stirrups by adding steel fibers // Construction and Building Materials. 2017. V. 145. P. 166–182. DOI: 10.1016/j.conbuildmat.2017.04.005Ulzurrun G. S. D., Zanuy C. Enhancement of impact performance of reinforced concrete beams without stirrups by adding steel fibers. Construction and Building Materials. 2017. V. 145. Pp. 166–182. DOI: 10.1016/j.conbuildmat.2017.04.005Gali S., Subramaniam K.V.L. Investigation of the dilatant behavior of cracks in the shear response of steel fiber reinforced concrete beams // Engineering Structures. 2017. V. 152. P. 832–842. DOI: 10.1016/j.engstruct.2017.09.050Gali S., Subramaniam K. V. L. Investigation of the dilatant behavior of cracks in the shear response of steel fiber reinforced concrete beams. Engineering Structures. 2017. V. 152. Pp. 832–842. DOI: 10.1016/j.engstruct.2017.09.050Li Q., Huang B., Xu S., Zhou B., Yu R. C. Compressive fatigue damage and failure mechanism of fiber reinforced cementitious material with high ductility // Cement and Concrete Research. 2016. V. 90. P. 174–183. DOI:10.1016/j.cemconres.2016.09.019Li Q., Huang B., Xu S., Zhou B., Yu R. C. Compressive fatigue damage and failure mechanism of fiber reinforced cementitious material with high ductility. Cement and Concrete Research. 2016. V. 90. Pp. 174–183. DOI: 10.1016/j.cemconres.2016.09.019Butean C., Heghes B. Cost Efficiency of a Two Layer Reinforced Concrete Beam // Procedia Manufacturing. 2020. V. 46. P. 103–109. DOI: 10.1016/j.promfg.2020.03.016Butean C., Heghes B. Cost Efficiency of a two layer reinforced concrete beam. Procedia Manufacturing. 2020. V. 46. Pp. 103–109. DOI: 10.1016/j.promfg.2020.03.016Głowacki M., Kowalski R. An experimental approach to the estimation of stiffness changes in RC elements exposed to bending and high temperature // Engineering Structures. 2020. V. 217. P. 1–15. DOI: 10.1016/j.engstruct.2020.110720Głowacki M., Kowalski R. An experimental approach to the estimation of stiffness changes in RC elements exposed to bending and high temperature. Engineering Structures. 2020. V. 217. Pp. 1–15. DOI: 10.1016/j.engstruct.2020.110720Zhu H., Cheng S., Gao D., Neaz S. M., Li C. Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars // Construction and Building Materials. 2018. V. 161. Pp. 587–597. DOI: 10.1016/j.conbuildmat.2017.12.003Zhu H., Cheng S., Gao D., Neaz S.M., Li C. Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. Construction and Building Materials. 2018. V. 161. Pp. 587–597. DOI: 10.1016/j.conbuildmat.2017.12.003Song A., Wan S., Jiang Z., Xu J. Residual deflection analysis in negative moment regions of steel-concrete composite beams under fatigue loading // Construction and Building Materials. 2018. V. 158. P. 50–60. DOI: 10.1016/j.conbuildmat.2017.09.075Song A., Wan S., Jiang Z., Xu J. Residual deflection analysis in negative moment regions of steel-concrete composite beams under fatigue loading. Construction and Building Materials. 2018. V. 158. Pp. 50–60. DOI: 10.1016/j.conbuildmat.2017.09.075Fava G., Carvelli V., Pisani M. A. Remarks on bond of GFRP rebars and concrete // Composites Part B: Engineering. 2016. V. 93. P. 210–220. DOI: 10.1016/j.compositesb.2016.03.012Fava G., Carvelli V., Pisani M. A. Remarks on bond of GFRP rebars and concrete. Composites Part B: Engineering. 2016. V. 93. Pp. 210–220. DOI: 10.1016/j.compositesb.2016.03.012Aulia T. B., Rinaldi. Bending capacity analysis of high-strength reinforced concrete beams using environmentally friendly synthetic fiber composites // Procedia Engineering. 2015. V. 125. P. 1121–1128. DOI:10.1016/j.proeng.2015.11.136Aulia T. B., Rinaldi. Bending capacity analysis of high-strength reinforced concrete beams using environmentally friendly synthetic fiber composites. Procedia Engineering. 2015. V. 125. Pp. 1121–1128. DOI: 10.1016/j.proeng.2015.11.136Rabi M., Cashell K. A., Shamass R. Flexural analysis and design of stainless steel reinforced concrete beams // Engineering Structures. 2019. V. 198. P. 1–13. DOI: 10.1016/j.engstruct.2019.109432Rabi M., Cashell K. A., Shamass R. Flexural analysis and design of stainless steel reinforced concrete beams. Engineering Structures. 2019. V. 198. Pp. 1–13. DOI: 10.1016/j.engstruct.2019.109432Cramer S. D., Covino B. S., Bullard S. J., Holcomb G. R., Russell J. H., Nelson F. J., Laylor H. M., Soltesz S. M. Corrosion prevention and remediation strategies for reinforced concrete coastal bridges // Cement and Concrete Composites. 2002. V. 24. P. 101–117. DOI: 10.1016/S0958-9465(01)00031-2Cramer S. D., Covino B. S., Bullard S. J., Holcomb G. R., Russell J. H., Nelson F. J., Laylor H. M., Soltesz S. M. Corrosion prevention and remediation strategies for reinforced concrete coastal bridges. Cement and Concrete Composites. 2002. V. 24. Pp. 101–117. DOI: 10.1016/S0958-9465(01)00031-2Briz E., Biezma M. V., Bastidas D. M. Stress corrosion cracking of new 2001 lean-duplex stainless steel reinforcements in chloride contained concrete pore solution: An electrochemical study // Construction and Building Materials. 2018. V. 192. P. 1–8. DOI: 10.1016/j.conbuildmat.2018.10.108Briz E., Biezma M. V., Bastidas D. M. Stress corrosion cracking of new 2001 lean-duplex stain-less steel reinforcements in chloride contained concrete pore solution: An electrochemical study. Construction and Building Materials. 2018. V. 192. Pp. 1–8. DOI: 10.1016/j.conbuildmat.2018.10.108Yadollahi A., Shamsaei N., Thompson S. M., Elwany A., Bian L. Effects of building orientation and heat treatment on fatigue behavior of selective laser melted 17-4 PH stainless steel // International Journal of Fatigue. 2017. V. 94. P. 218–235. DOI: 10.1016/j.ijfatigue.2016.03.014Yadollahi A., Shamsaei N., Thompson S. M., Elwany A., Bian L. Effects of building orientation and heat treatment on fatigue behavior of selective laser melted 17-4 PH stainless steel. International Journal of Fatigue. 2017. V. 94. Pp. 218–235. DOI: 10.1016/j.ijfatigue.2016.03.014Hou Z., Chen S., Sun Q., Wei X., Lv W. Experimental research on fatigue characteristics of X12Cr13 stainless steel // Journal of Materials Research and Technology. 2020. V. 9. P. 3230−3240. DOI:10.1016/j.jmrt.2020.01.070Hou Z., Chen S., Sun Q., Wei X., Lv W. Experimental research on fatigue characteristics of X12Cr13 stainless steel. Journal of Materials Research and Technology. 2020. V. 9. Pp. 3230−3240. DOI: 10.1016/j.jmrt.2020.01.070Opbul E. K., Dmitriev D. A., Vedernikova A.A. Calculation of Bending of Steel-Fiber-Reinforced Concrete Members by a Nonlinear Deformation Model with the Use of Iteration Procedures // Mechanics of Composite Materials. 2018. V. 54 № 5. P. 1–24. DOI: 10.1007/s11029-018-9769-xOpbul E. K., Dmitriev D. A., Vedernikova A. A. Calculation of bending of steel-fiber-reinforced concrete members by a nonlinear deformation model with the use of iteration procedures. Mechanics of Composite Materials. 2018. V. 54 No. 5. Pp. 1–24. DOI: 10.1007/s11029-018-9769-xОпбул Э. К. Расчет прочности фиброжелезобетонных изгибаемых элементов с использованием трехлинейной диаграммы деформирования растянутой зоны / Э. К. Опбул, Э. Э. Ондар, А.-Х. Б. Калдар-оол // Научное обозрение. – 2016. – № 14. – С. 100−106.Opbul E. K., Ondar E. E., Kaldar-ool A.-Kh.B. Raschet prochnosti fibrozhelezobetonnykh izgibaemykh elementov s ispol'zovaniem trekhlineinoi diagrammy deformirovaniya rastyanutoi zony [Strength analysis of fiber-reinforced concrete bending elements using three-line stress-strain diagram of tension region]. Nauchnoe obozrenie. 2016. No. 14. Pp. 100−106. (rus)Опбул Э. К. Деформационные модели расчета прочности изгибаемых железобетонных элементов / Э. К. Опбул, Э. Э. Ондар, А.-Х. Б. Калдар-оол // Вестник Тувинского государственного университета. Технические и физико-математические науки. – 2020. – № 1 (58). – С. 6−22.Opbul E. K., Ondar E. E., Kaldar-ool A.-Kh.B. Deformatsionnye modeli rascheta prochnosti izgibaemykh zhelezobetonnykh elementov [Deformation models of strength of bending steel elements]. Vestnik Tuvinskogo gosudarstvennogo universiteta. Tekhnicheskie i fiziko-matematicheskie nauki. 2020. No. 1 (58). Pp. 6−22. (rus)Опбул Э. К. Практическое применение нелинейной деформационной модели в расчёте коротких железобетонных элементов, находящихся в косом внецентренном сжатии / Э. К. Опбул, А.-Х. Б. Калдар-оол // Вестник Тувинского государственного университета. Технические и физико-математические науки. – 2022. – № 1 (90). – С. 34−48.Opbul E. K., Kaldar-ool A.-Kh. B. Prakticheskoe primenenie nelineinoi deformatsionnoi modeli v raschete korotkikh zhelezobetonnykh elementov, nakhodyashchikhsya v kosom vnetsentrennom szhatii [Application of nonlinear deformation model for strength analysis of short reinforced concrete elements under oblique eccentrical compression]. Vestnik Tuvinskogo gosudarstvennogo universiteta. Tekhnicheskie i fiziko-matematicheskie nauki. 2022. No. 1 (90). Pp. 34−48. (rus)Munshi J. A. Design of prestressed flexural sections by the Unified Design Approach // PCI Journal. 1999. V. 46. P. 76–87. DOI:10.15554/pcij.09011999.72.81Munshi J. A. Design of prestressed flexural sections by the unified design approach. PCI Journal. 1999. V. 46. Pp. 76–87. DOI:10.15554/pcij.09011999.72.81Orozco C .E. Strain limits vs. reinforcement ratio limits - A collection of new and old formulas for the design of reinforced concrete sections // Case Studies in Structural Engineering. 2015. V. 4. P. 1–13. DOI: 10.1016/j.csse.2015.05.001Orozco C. E. Strain limits vs. reinforcement ratio limits − A collection of new and old formulas for the design of reinforced concrete sections. Case Studies in Structural Engineering. 2015. V. 4. Pp. 1–13. DOI: 10.1016/j.csse.2015.05.001ACI 318. Building Code Requirements for Structural Concrete and Commentary (ACI 318M-11). 2011. ISBN:9780870312649.ACI 318. Building Code Requirements for Structural Concrete and Commentary (ACI 318M-11). 2011. ISBN:9780870312649.Panfilov D. A., Pischulev A. A., Romanchkov V. V. The Methodology for Calculating Deflections of Statically Indeterminate Reinforced Concrete Beams (Based on Nonlinear Deformation Model) // Procedia Engineering. 2016. V. 153. P. 531–536. DOI: 10.1016/j.proeng.2016.08.183Panfilov D. A., Pischulev A. A., Romanchkov V. V. The methodology for calculating deflections of statically indeterminate reinforced concrete beams (based on nonlinear deformation model). Procedia Engineering. 2016. V. 153. Pp. 531–536. DOI: 10.1016/j.proeng.2016.08.183Gilbert R. I. The serviceability limit states in reinforced concrete design // Procedia Engineering. 2011. V. 14. P. 385–395. DOI: 10.1016/j.proeng.2011.07.048Gilbert R. I. The serviceability limit states in reinforced concrete design. Procedia Engineering. 2011. V. 14. Pp. 385–395. DOI:10.1016/j.proeng.2011.07.048Wróblewski R., Ignatowicz R., Gierczak J. Influence of Shrinkage and Temperature on a Composite Pretensioned - Reinforced Concrete Structure // Procedia Engineering. 2017. V. 193. P. 96–103. DOI: 10.1016/j.proeng.2017.06.191Wróblewski R., Ignatowicz R., Gierczak J. Influence of shrinkage and temperature on a composite pretensioned - Reinforced concrete structure. Procedia Engineering. 2017. V. 193. Pp. 96–103. DOI: 10.1016/j.proeng.2017.06.191

The authors declare that there are no conflicts of interest present.