vestniktgasuВестник Томского государственного архитектурно-строительного университетаVestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture1607-18592310-0044Tomsk State University of Architecture and Building10.31675/1607-1859-2026-28-1-148-168vestniktgasu-2348Research ArticleСТРОИТЕЛЬНЫЕ КОНСТРУКЦИИ, ЗДАНИЯ И СООРУЖЕНИЯBUILDING AND CONSTRUCTIONТрещиностойкость и жесткость изгибаемых железобетонных конструкций на основе нелинейной деформационной моделиCrack Resistance and Rigidity of Bending Reinforced Concrete Structures Based on a Non-linear Deformation ModelОпбулЭрес Кечил-ооловичOpbulEres K.

Опбул Эрес Кечил-оолович, канд. техн. наук, зав. лабораторией, доцент, Петербургский государственный университет путей сообщения Императора Александра I; доцент, Тувинский государственный университет

190031, г. Санкт-Петербург, Московский пр., 9

667000, г. Кызыл, ул. Ленина, 36

Ehres K. Opbul, PhD, A/Professor, Emperor Alexander I St. Petersburg State Transport University; Tuvan State University

9, Moskovskii Ave., 190031, Saint-Petersburg

Lenin Str., 667000, Kyzyl, Republic of Tyva

pgupsopbul@mail.ruШируновГ. Н.ShirunovG. N.

Ширунов Гурий Николаевич, докт. техн. наук, профессор

191123, г. Санкт-Петербург, ул. Захарьевская, 22

Gurii N. Shirunov, DSc, Professor

8, Makarov Emb., 199034, Saint-Petersburg

guriyn@mail.ruКалдар-оолАнай-Хаак БугалдаевнаKaldar-oolAnai-Khaak B.

Калдар-оол Анай-Хаак Бугалдаевна, канд. техн. наук, доцент

667000, г. Кызыл, ул. Ленина, 36

Anai-Khaak B. Kaldar-ool, PhD, A/Professor

36, Lenin Str., 667000, Kyzyl, Republic of Tyva

oorzhaka-h@mail.ruСааяС. С.SaayaS. S.

Саая Светлана Сергеевна, канд. техн. наук

667000, г. Кызыл, ул. Ленина, 36

Svetlana S. Saaya, PhD

36, Lenin Str., 667000, Kyzyl, Republic of Tyva

sedip@list.ruПетербургский государственный университет путей сообщения Императора Александра I; Тувинский государственный университетРоссияEmperor Alexander I St. Petersburg State Transport University; Tuvan State UniversityRussian FederationВоенный институт (инженерно-технический) Военной академии материально-технического обеспечения имени генерала армии А.В. ХрулеваРоссияMilitary Engineering Institute of the Military Logistics AcademyRussian FederationТувинский государственный университетРоссияTuvan State UniversityRussian Federation202610032026281148168Copyright © Опбул Э., Ширунов Г.Н., Калдар-оол А., Саая С.С., 20262026Опбул Э., Ширунов Г.Н., Калдар-оол А., Саая С.С.Opbul E., Shirunov G.N., Kaldar-ool A., Saaya S.S.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/2348Актуальность

Актуальность. Деформационный метод расчета конструкций признается более точным и достоверным, поскольку базируется на опытных диаграммах деформирования материалов (бетон и арматура). При этом в практике проектирования пока отсутствуют развернутые примеры расчета трещиностойкости и жесткости изгибаемых железобетонных элементов с применением деформационной модели – несмотря на ее удобство и возможность быстрого получения результатов посредством итерационных процедур.

Цель

Цель. Выполнить практический деформационный расчет трещиностойкости и жесткости изгибаемого железобетонного элемента (вторая группа предельных состояний), используя расчетные параметры, полученные из расчета деформационной прочности конструкции (первая группа предельных состояний).

Методы

Методы. Исследование опирается на исходные данные и расчетные параметры, полученные при расчете прочности. Методика включает следующие этапы: определение момента трещинообразования путем суммирования внутренних усилий, возникающих от нормальных напряжений в каждом малом участке; вычисление базового расстояния между смежными трещинами с учетом площади растянутой зоны сечения в предельном состоянии; расчет ширины раскрытия трещин в зависимости от напряжений в растянутой арматуре; определение прогиба элемента с учетом максимальной кривизны, вычисленной с применением модуля деформаций.

В работе приведены принятые допущения и предпосылки, а также теоретические формулы с учетом расчетных предельных деформаций и напряжений (в том числе модулей деформаций).

Результаты

Результаты. Выполнен практический пример расчета и проведен сравнительный анализ с подсчетом процентного расхождения результатов между деформационным и нормативным (по предельным состояниям) методами. Сформулированы выводы исследования. Новизна работы заключается в разработке алгоритма практического расчета трещиностойкости и жесткости изгибаемого элемента на основе деформационной модели расчета конструкций.

The deformation method for the structural analysis is recognized as more accurate and reliable, as it is based on experimental deformation diagrams of materials (concrete and reinforcement). However, in practice, there are still no detailed examples of calculating the crack resistance and rigidity of bending reinforced concrete elements using a deformation model, despite its convenience and the ability to quickly obtain results through iterative procedures.

Purpose

Purpose: The aim is to calculate deformation of crack resistance and rigidity of bending reinforced concrete elements (service limit state), using design parameters obtained from calculating the deformation strength of the structure (ultimate limit state).

Methodology

Methodology: The study is based on initial data and design parameters obtained in the strength calculation. The methodology includes the following steps: determination of the crack formation moment by summing internal forces, arising from normal stresses in each small section; calculation of the distance between adjacent cracks, taking into account the tensile zone in the limit state; calculation of the crack opening width depending on stresses in tensile reinforcement. Determination of the element deflection taking into account the maximum curvature calculated using the deformation modulus.

The paper also presents the adopted assumptions and prerequisites, theoretical formulas with respect to calculated ultimate strains and stresses (including the strain modulus).

Research findings

Research findings: A practical calculation example was performed, and a comparative analysis was conducted, calculating the percentage difference in between the deformation and standard (limit state) methods.

Value

Value: The novelty of the paper lies in the algorithm development for practical calculation of the crack resistance and rigidity of bending element based on the deformation model for the structural analysis.

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