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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">mgssuvest</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник МГСУ</journal-title><trans-title-group xml:lang="en"><trans-title>Vestnik MGSU</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1997-0935</issn><issn pub-type="epub">2304-6600</issn><publisher><publisher-name>Moscow State University of Civil Engineering (National Research University) (MGSU)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22227/1997-0935.2026.3.333-349</article-id><article-id custom-type="elpub" pub-id-type="custom">mgssuvest-923</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Проектирование и конструирование строительных систем. Строительная механика. Основания и фундаменты, подземные сооружения</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Construction system design and layout planning. Construction mechanics. Bases and foundations, underground structures</subject></subj-group></article-categories><title-group><article-title>Использование регрессионного анализа для совершенствования методики расчета железобетонных конструкций на действие поперечной силы</article-title><trans-title-group xml:lang="en"><trans-title>Application of regression analysis to improve the shear design method for reinforced concrete structures</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0004-5304-8507</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Зенин</surname><given-names>С. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zenin</surname><given-names>S. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сергей Алексеевич Зенин — кандидат технических наук, заведующий лабораторией теории железобетона и конструктивных систем</p><p>109428, г. Москва, 2-я Институтская ул., д. 6</p><p>РИНЦ AuthorID: 326794, Scopus: 6603820715, ResearcherID: LRV-1545-2024</p></bio><bio xml:lang="en"><p>Sergei A. Zenin — Candidate of Technical Sciences, Head of the Laboratory of Theory of Reinforced Concrete and Structural Systems</p><p>6, 2nd Institutskaya st., Moscow, 109428</p><p>RSCI AuthorID: 326794, Scopus: 6603820715, ResearcherID: LRV-1545-2024</p></bio><email xlink:type="simple">lab01@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бударин</surname><given-names>А. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Budarin</surname><given-names>A. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Александр Михайлович Бударин — главный специалист отдела расчетных обоснований</p><p>125993, г. Москва, Волоколамское шоссе, д. 2</p></bio><bio xml:lang="en"><p>Alexander M. Budarin — chief specialist of the Department of Calculation Justifications</p><p>2 Volokolamskoe shosse, Moscow, 125993</p></bio><email xlink:type="simple">alex.budarin01@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Редикульцев</surname><given-names>Е. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Redikultsev</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Евгений Александрович Редикульцев — аспирант</p><p>620002, г. Екатеринбург, ул. Мира, д. 19</p></bio><bio xml:lang="en"><p>Evgeny A. Redikultsev — postgraduate student</p><p>19 Mira st., Yekaterinburg, 620002</p></bio><email xlink:type="simple">e.a.redikultsev@urfu.ru</email><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Научно-исследовательский, проектно-конструкторский и технологический институт бетона и железобетона (НИИЖБ) им. А.А. Гвоздева АО «НИЦ «Строительство»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Research, Design and Technological Institute of Concrete and Reinforced Concrete named after A.A. Gvozdev of Research Center for Construction</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт Гидропроект</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Institute Hydroproject</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Уральский федеральный университет имени первого Президента России Б.Н. Ельцина (УрФУ)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural Federal University named after the First President of Russia B.N. Yeltsin (UrFU)</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>30</day><month>03</month><year>2026</year></pub-date><volume>21</volume><issue>3</issue><fpage>333</fpage><lpage>349</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Зенин С.А., Бударин А.М., Редикульцев Е.А., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Зенин С.А., Бударин А.М., Редикульцев Е.А.</copyright-holder><copyright-holder xml:lang="en">Zenin S.A., Budarin A.M., Redikultsev E.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.vestnikmgsu.ru/jour/article/view/923">https://www.vestnikmgsu.ru/jour/article/view/923</self-uri><abstract><sec><title>Введение</title><p>Введение. Механизм разрушения железобетонных конструкций от действия поперечной силы — объект исследования отечественных и зарубежных ученых на протяжении многих десятилетий. Повышенный интерес к этому механизму разрушения обусловлен его опасностью — разрушение конструкций от действия поперечной силы зачастую имеет хрупкий, внезапный характер. Несущая способность и характер разрушения железобетонной конструкции в рамках данного механизма зависят от множества конструктивных параметров, что значительно усложняет его изучение. В качестве основных конструктивных параметров, оказывающих влияние на несущую способность в рамках указанного механизма разрушения, можно выделить: прочность бетона, геометрические характеристики сечения, величину относительного пролета среза конструкции, содержание продольной арматуры растянутой зоны и интенсивность поперечного армирования конструкции. Также к таким параметрам можно отнести масштабный энергетический эффект, понятие которого раскрыто в работе. Методика расчета железобетонных конструкций по наклонным сечениям на действие поперечной силы, представленная в СП 63.13330.2018, только косвенно учитывает влияние содержания продольной арматуры растянутой зоны и не учитывает масштабный энергетический эффект, что оказывает влияние на ее точность. Актуальной является задача модификации расчетной методики за счет учета данных конструктивных параметров.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Для получения коэффициентов уточненной методики использовался регрессионный анализ, выполненный методом наименьших квадратов с применением алгоритма Левенберга – Марквардта.</p></sec><sec><title>Результаты</title><p>Результаты. Представлена уточненная методика расчета железобетонных конструкций по наклонному сечению на действие поперечной силы, учитывающая влияние процента продольного армирования растянутой зоны конструкции, а также масштабного энергетического эффекта. Приведено сопоставление уточненной методики и оригинальной методики из СП 63.13330.2018 с результатами лабораторных испытаний 958 образцов. Образцы разделены на группы в соответствии с величинами конструктивных параметров.</p></sec><sec><title>Выводы</title><p>Выводы. Уточненная методика расчета железобетонных конструкций по наклонному сечению на действие поперечной силы более точная, чем нормативная методика, представленная в СП 63.13330.2018. Применение уточненного метода расчета позволит корректно оценивать несущую способность наклонных сечений при действии поперечных сил, что в ряде случаев приведет к сокращению расхода поперечной арматуры.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. The mechanism of failure of reinforced concrete structures from the action of shear force has been the object of research of Russian and foreign scientists for many decades. This failure mechanism garners significant attention due to its danger — the shear failure is often brittle and sudden. The bearing capacity and the type of failure of reinforced concrete structure within this mechanism depends on a variety of design parameters, which greatly complicates its study. Key parameters influencing load-bearing capacity in shear failure include the strength of concrete, geometric characteristics of the cross-section, span-to-depth ratio, percentage of tensile reinforcement and the transverse reinforcement intensity. Also, to such parameters can be attributed the energetic size effect which concept is disclosed in the paper. The shear design method, presented in building code SP 63.13330.2018 only indirectly accounts percentage of tensile reinforcement. It also does not consider the energetic size effect, which impacts its accuracy. It is urgent to modify the design method by taking into account these design parameters.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. To obtain the coefficients of the refined design method, the regression analysis performed by the least squares method using the Levenberg – Marquardt algorithm was used.</p></sec><sec><title>Results</title><p>Results. The paper presents a refined method for shear design of reinforced concrete structures which takes into account the influence of the percentage of tensile reinforcement and energetic size effect. A comparison of the refined design method and the original methodology from SP 63.13330.2018 with the results of laboratory tests of 958 specimens is presented. The specimens are divided into groups according to the values of the design parameters.</p></sec><sec><title>Conclusions</title><p>Conclusions. The refined design method for shear design of reinforced concrete structures is more accurate than the normative method presented in SP 63.13330.2018. The application of the refined calculation method will allow to correctly assess the load-bearing capacity of inclined sections under the action of shear forces, which in some cases will lead to a reduction in the consumption of transverse reinforcement.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>железобетон</kwd><kwd>расчет</kwd><kwd>прочность</kwd><kwd>наклонные сечения</kwd><kwd>поперечная сила</kwd><kwd>регрессионный анализ</kwd><kwd>метод наименьших квадратов</kwd><kwd>алгоритм Левенберга – Марквардта</kwd></kwd-group><kwd-group xml:lang="en"><kwd>reinforced concrete</kwd><kwd>strength</kwd><kwd>inclined sections</kwd><kwd>shear force</kwd><kwd>regression analysis</kwd><kwd>least squares</kwd><kwd>Levenberg – Marquardt algorithm</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Leonhardt F., Walther R. The Stuttgart Shear Tests // CACA Translation. 1961. 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