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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">firesmi</journal-id><journal-title-group><journal-title xml:lang="ru">Пожаровзрывобезопасность/Fire and Explosion Safety</journal-title><trans-title-group xml:lang="en"><trans-title>Pozharovzryvobezopasnost/Fire and Explosion Safety</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0869-7493</issn><issn pub-type="epub">2587-6201</issn><publisher><publisher-name>ФГБОУ ВО «Национальный исследовательский Московский государственный строительный университет»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22227/0869-7493.2024.33.03.57-66</article-id><article-id custom-type="elpub" pub-id-type="custom">firesmi-1381</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>БЕЗОПАСНОСТЬ ЗДАНИЙ, СООРУЖЕНИЙ, ОБЪЕКТОВ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SAFETY OF BUILDINGS, STRUCTURES, OBJECTS</subject></subj-group></article-categories><title-group><article-title>Аппроксимационная формула для расчета огнестойкости незащищенных стальных конструкций</article-title><trans-title-group xml:lang="en"><trans-title>Approximation formula for calculating fire resistance of unprotected steel 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/0009-0009-4334-7526</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Маликов</surname><given-names>Ю. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Malikov</surname><given-names>Yu. K.</given-names></name></name-alternatives><bio xml:lang="ru"><p>МАЛИКОВ Юрий Константинович, канд. техн. наук, директор научно-исследовательского центра</p><p> 620002, г. Екатеринбург, ул. Мира, 19</p><p>РИНЦ AuthorID: 134294, Scopus: 6603995452</p></bio><bio xml:lang="en"><p>Yuri K. MALIKOV, Cand. Sci. (Eng.), Head of Research Center</p><p>Mira St., 19, Ekaterinburg, 620002</p><p>RISC AuthorID: 134294, Scopus: 6603995452</p></bio><email xlink:type="simple">uma66p@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3778-7033</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Титаев</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Titaev</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ТИТАЕВ Александр Анатольевич, канд. техн. наук, доцент</p><p>620002, г. Екатеринбург, ул. Мира, 19</p><p>РИНЦ AuthorID: 546224, Scopus: 26649649000</p></bio><bio xml:lang="en"><p>Aleksandr A. TITAEV, Cand. Sci (Eng.), Associate Professor</p><p>Mira St., 19, Ekaterinburg, 620002</p><p>RISC AuthorID: 546224, Scopus: 26649649000</p></bio><email xlink:type="simple">a.a.titaev@urfu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0004-7129-3418</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Серебренников</surname><given-names>В. О.</given-names></name><name name-style="western" xml:lang="en"><surname>Serebrennikov</surname><given-names>V. O.</given-names></name></name-alternatives><bio xml:lang="ru"><p>СЕРЕБРЕННИКОВ Вячеслав Олегович, магистрант</p><p>620002, г. Екатеринбург, ул. Мира, 19</p></bio><bio xml:lang="en"><p>Vyacheslav O. SEREBRENNIKOV, Master’s Student</p><p>Mira St., 19, Ekaterinburg, 620002</p></bio><email xlink:type="simple">v.o.serebrennikov@urfu.me</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Уральский федеральный университет имени первого Президента России Б.Н. Ельцина</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural Federal University named after the First President of Russia B.N. Yeltsin</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2024</year></pub-date><volume>33</volume><issue>3</issue><fpage>57</fpage><lpage>66</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Маликов Ю.К., Титаев А.А., Серебренников В.О., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Маликов Ю.К., Титаев А.А., Серебренников В.О.</copyright-holder><copyright-holder xml:lang="en">Malikov Y.K., Titaev A.A., Serebrennikov V.O.</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.fire-smi.ru/jour/article/view/1381">https://www.fire-smi.ru/jour/article/view/1381</self-uri><abstract><sec><title>Введение</title><p>Введение. При проектировании зданий требуется оценить фактические пределы огнестойкости незащищенных стальных конструкций. Удобным инструментом для получения такой оценки являются номограммы. Практическая необходимость интеграции «ручной» технологии и современных средств автоматизации проектирования делает актуальной задачу «оцифровки» номограмм путем создания вычислительных моделей данных.</p></sec><sec><title>Цели и задачи</title><p>Цели и задачи. Целью работы было получение достаточно простой формулы для расчета передела огнестойкости незащищенных стальных конструкций. Были решены следующие задачи: сопоставление литературных данных по пределам огнестойкости с результатами расчетов по нормативному документу по пожарной безопасности ВНПБ 73–18; расчет четырехзначной таблицы пределов огнестойкости для последующей аппроксимации функциональной зависимости.</p></sec><sec><title>Методы</title><p>Методы. Таблица значений огнестойкости вычислена с четырьмя верными знаками с помощью многошагового метода Адамса переменного порядка. Формула для расчета передела огнестойкости незащищенных стальных конструкций получена методом последовательной аппроксимации табличных данных сначала по одной переменной (приведенная толщина), а затем по другой (критическая температура).</p></sec><sec><title>Результаты и обсуждение</title><p>Результаты и обсуждение. Расчет по методике ВНПБ 73–18 дает пределы огнестойкости, близкие к реперным значениям, которые были опубликованы А.И. Яковлевым в 1985 г. Принятые в методике ВНПБ 73–18 значения конвективного и радиационного коэффициентов теплоотдачи соответствуют испытаниям на огнестойкость согласно ГОСТ 30247.0–94 (ИСО 834–75).</p></sec><sec><title>Выводы</title><p>Выводы. Получена аппроксимационная формула, вычисления по которой дают те же самые пределы огнестойкости, что и расчеты по методике ВНПБ 73–18. Относительная погрешность аппроксимации не превышает 0,5 % в диапазоне изменения параметров: критическая температура — от 500 до 700 °C; приведенная толщина — от 3 до 12 мм.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. When designing buildings it is necessary to estimate the actual fire resistance limits of unprotected steel structures. Nomograms are a convenient tool for obtaining such an assessment. Practical necessity of integration of “manual” technology and modern means of design automation makes the task of “digitization” of nomo­grams by creating computational data models urgent.</p></sec><sec><title>Goals and objectives</title><p>Goals and objectives. The purpose of the work was to obtain a rather simple formula for calculating the fire resistance limits of unprotected steel structures. The following tasks were solved: comparison of the literature data on fire resistance limits with the results of calculations according to the normative document on fire safety “VNPB 73–18”; calculation of a four-digit table of fire resistance limits for the subsequent approximation of functional dependence.</p></sec><sec><title>Research methods</title><p>Research methods. The table of fire resistance values is calculated with four correct digits using the Adams multistep method of variable order. The formula for calculation of fire resistance limit of unprotected steel structures was obtained by successive approximation of tabular data first by one variable (thickness, i.e. reciprocal of the section factor) and then by another (critical temperature).</p></sec><sec><title>Results and discussion</title><p>Results and discussion. Calculation according to the methodology VNPB 73–18 gives the fire resistance limits close to the reference values, which were published by A.I. Yakovlev in 1985. The values of convective and radiation heat transfer coefficients adopted in the VNPB 73–18 method correspond to the fire resistance tests according to GOST 30247.0–94 (ISO 834–75).</p></sec><sec><title>Conclusions</title><p>Conclusions. An approximation formula was obtained, the calculations according to which give the same fire resistance limits as the calculations according to the VNPB 73–18 method. Relative error of approximation does not exceed 0.5 % in the range of parameters change: critical temperature — from 500 to 700 °C; thickness — from 3 to 12 mm.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>металлические конструкции</kwd><kwd>пределы огнестойкости</kwd><kwd>математическое моделирование</kwd><kwd>эмпирические зависимости</kwd><kwd>номограмма</kwd></kwd-group><kwd-group xml:lang="en"><kwd>metal structures</kwd><kwd>fire resistance limits</kwd><kwd>mathematical modelling</kwd><kwd>empirical relations</kwd><kwd>nomogram</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Авторы выражают признательность А.Ю. Маликову за помощь в обзоре эволюции граничных условий для теплотехнических расчетов.</funding-statement><funding-statement xml:lang="en">The authors express their gratitude to A.Yu. 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