vestnikcstroyВестник НИЦ «Строительство»Bulletin of Science and Research Center of Construction2224-94942782-3938АО «НИЦ «Строительство»10.37538/2224-9494-2026-1(48)-56-73DTRWDFvestnikcstroy-618Research ArticleСТРОИТЕЛЬНЫЕ КОНСТРУКЦИИ, ЗДАНИЯ И СООРУЖЕНИЯBUILDING CONSTRUCTIONS, BUILDINGS AND STRUCTURESКоэффициент градиента эквивалентного момента при плоской форме потери устойчивости балок двутаврового сечения с переменной высотой стенкиEquivalent moment gradient factor for lateral- torsional buckling of web-tapered i-section beamsИльюшенковА. О.IlyushenkovA. O.

Александр Олегович Ильюшенков, инженер промышленного и гражданского строительства

Уссурийский бульвар, д. 2, г. Хабаровск, 680000

Alexander O. Ilyushenkov, Civil and Industrial Engineer

Ussuriysky Blvd., 2, Khabarovsk, 680000

revivaltree@gmail.comАО «Территориальный проектный институт «Хабаровскпромпроект»РоссияTerritorial Design Institute Khabarovskpromproekt JSCRussian Federation2026250520264815673Copyright © Ильюшенков А.О., 20262026Ильюшенков А.О.Ilyushenkov A.O.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.cstroy.ru/jour/article/view/618Введение

Введение. Исследуется устойчивость симметричных двутавровых балок с переменной высотой стенки, подверженных действию неравных концевых моментов. Влияние угла конусности, которое играет главную роль в поведении балки с переменной высотой стенки при изгибно-крутильной потери устойчивости, исследовано путем уточнения дифференциальных уравнений технической теории Власова открытых тонкостенных стержней. Аналитические решения уточненных дифференциальных уравнений приводятся на основе метода Бубнова – Галеркина через закон изменения момента инерции поперечного сечения балки вдоль ее оси. Окончательное бифуркационное уравнение упругого критического момента содержит новые члены, включающие коэффициенты редукции поперечного сечения. Эквивалентный коэффициент градиента момента для всего диапазона значений определяется и приводится в замкнутой форме относительно угла наклона поясов. Сравнительные графики показывают согласование аналитических и численных решений. Эти результаты могут быть использованы для формулирования критериев потери устойчивости для призматических и конических двутавровых балок и могут быть интегрированы в текущие методы проектирования.

Цель

Цель. Разработать единое уравнение для коэффициента градиента эквивалентного момента. Уточнить техническую теорию Власова для балок с конической стенкой двутаврового сечения.

Материалы и методы

Материалы и методы. В работе использована уточненная техническая теория Власова и аналитический метод Бубнова – Галеркина.

Результаты

Результаты. На основе полученных уточнений получено замкнутое решение упругой изгибно-крутильной потери устойчивости двутавровой балки с переменной высотой стенки. Представлен аналитический метод расчета. Результаты показывают отличное согласие численных и аналитических решений. Уравнения представлены в замкнутом виде, аналогичном случаю постоянного поперечного сечения, но с дополнительными коэффициентами, что позволяет интегрировать разработанное решение в существующие методы расчета.

Выводы

Выводы. В представленной теоретической работе разработан единый метод расчета упругого критического момента и коэффициента градиента эквивалентного момента для балок с конической стенкой двутаврового сечения при изгибно-крутильной потере устойчивости.

Introduction

Introduction. This paper studies the stability of symmetrical web-tapered I-beams subjected to unequal end moments. Taper angle, which plays a main role in the lateral-torsional buckling behavior of web-tapered beams, is investigated through refinement of differential equations of the original Vlasov technical theory for thin-walled bars. Analytical solutions of refined differential equations are given based on the Bubnov – Galerkin method through the law of change of moment of inertia of the cross section of the beam along its axis. The final bifurcation equation of elastic critical moment contains new terms that includes reduction coefficients of cross-section. Equivalent moment gradient factor for the full range of values is determined and given in closed form with respect to taper angle. Comparative graphs show alignment between analytical and numerical solutions. These results can be used to formulate efficient buckling criteria for prismatic and non-prismatic I-section beams and can be integrated into the current design methods.

Aim

Aim. To develop a unified equation for the equivalent moment gradient factor. Refine Vlasov technical theory for web-tapered I-section members.

Materials and methods

Materials and methods. Refined Vlasov technical theory and Bubnov – Galerkin method were used in the work.

Results

Results. Based on given refinements, a closed form of elastic lateral-torsional buckling solution of a webtapered beam was obtained. Analytical calculation method is introduced.

Conclusions

Conclusions. The presented theoretical work introduces a unified design method for elastic critical moment and equivalent moment gradient factor determining for lateral-torsional buckling of web-tapered I-section beams. Results show an excellent agreement between numerical and analytical solutions. Equations are given in closed form similar to a constant cross-section but with additional factors and coefficients, that makes it possible to integrate the developed solution into existing calculation methods.

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