CONVERGENCE OF THE NUMERICAL DIAGRAM METHOD OF NONLINEAR CALCULATION OF CORE REINFORCED CONCRETE ELEMENTS-Reference-Cited by-同舟云学术

CONVERGENCE OF THE NUMERICAL DIAGRAM METHOD OF NONLINEAR CALCULATION OF CORE REINFORCED CONCRETE ELEMENTS

Published:2022-04-07 Issue:7 Volume:7 Page:31-43
ISSN:2071-7318
Container-title:Bulletin of Belgorod State Technological University named after. V. G. Shukhov
language:en
Short-container-title:

Author:

Radaikin O.¹,Sabitov L.¹,Klyuev Sergey²,Hassoun M.³,Arakcheev T.⁴,Darvish A.¹

Affiliation:

1. Kazan State Energy University

2. Belgorod State Technological University named after V.G. Shukhov

3. Kazan State University of Architecture and Engineering

4. LLC «GC «EPC-Garant»

Abstract

Earlier, authors considered the under-examined question of accuracy (error) in the theory of the diagram method for calculating reinforced concrete core elements. The notion of convergence of the numerical implementation of the method under consideration is closely related to it, which has so far remained undisclosed. The article presents a theoretical justification of the convergence criterion of a numerical diagram method for calculating the strength of reinforced concrete bendable elements. The resulting criterion coincides in form with the Chebyshev norm. It implies a criterion for stopping the iterative calculation process and an estimate of the error of the numerical diagram method. Using the example of a reinforced concrete element with a rectangular cross section and double reinforcement, the issue of convergence of iterative strength calculation with varying concrete class and percentage of reinforcement is investigated. It is established that for all the considered design variants, the iterative calculation process converges after the 6th iteration at the initial curvature approximation and after the 4th iteration at , with a relative calculation error of δ<1 %. In addition, it is found that with an increase in the percentage of reinforcement, the convergence of the calculation improves: with the number of iterations equal to 4, the error in the design variant B60, µ = 0.5 % is 10.3 %, and with B35, µ = 3.0 %–0.98 %.

Publisher

BSTU named after V.G. Shukhov

Subject

Psychiatry and Mental health,Neuropsychology and Physiological Psychology

Reference15 articles.

1. Радайкин О.В., Сабитов Л.С., Клюев С.В., Ахтямова Л.Ш., Аракчеев Т.П., Дарвиш А. Точность численного диаграммного метода расчёта стержневых железобетонных элементов // Вестник БГТУ им. В.Г. Шухова. 2022. № 6. С. 25–34. DOI: 10.34031/2071-7318-2022-7-6-25-34, Radaykin O.V., Sabitov L.S., Klyuev S.V., Ahtjamova L.Sh., Arakcheev T.P., Darvish A. Accuracy of the numerical diagram method for calculating bar reinforced concrete elements. Bulletin of BSTU named after V.G. Shukhov. 2022. No. 6. Pp. 25–34. DOI: 10.34031/2071-7318-2022-7-6-25-34

2. Коваленко Г.В., Меньщикова Н.С. Учет физической нелинейности железобетона при оценке изменения изгибной жесткости конструкций со смешанным армированием // Системы, методы, технологии. 2010. №1. С. 63–67., Kovalenko G.V., Menshchikova N.S. Taking into account the physical nonlinearity of reinforced concrete when assessing changes in the bending stiffness of structures with mixed reinforcement [Uchet fizicheskoj nelinejnosti zhelezobetona pri ocenke izmeneniya izgibnoj zhestkosti konstrukcij so smeshannym armirovaniem]. Systems, methods, technologies. 2010. 2010. No. 1. Pp. 63–67. (rus)

3. Дыховичный А.А. Статически неопределимые железобетонные конструкции. Киев: Будiвельник, 1978. 104 с., Dykhovichny A.A. Statically indeterminate reinforced concrete structures [Staticheski neopredelimye zhelezobetonnye konstrukcii]. Kiev: Budivelnik. 1978. 104 p. (rus)

4. Сливкер В.И. Расчёт конструкций с нелинейными связями. В сб. «Исследования по теории сооружения». Вып. XVI. М.: Стройиздат, 1968., Slivker V.I. Calculation of constructions with nonlinear connections. Studies on the theory of construction [Raschyot konstrukcij s nelinejnymi svyazyami]. Issue XVI. M.: Stroyizdat. 1968. (rus)

5. Клованич С.Ф., Безушко Д.И. Метод конечных элементов в нелинейных расчетах пространственных железобетонных конструкций. Одесса: Издательство ОНМУ, 2009. 89 с., Klovanich S.F., Bezushko D.I. Finite element method in nonlinear calculations of spatial reinforced concrete structures [Metod konechnyh elementov v nelinejnyh raschetah prostranstvennyh zhelezobetonnyh konstrukcij]. Odessa: ONMU Publishing House. 2009. 89 p. (rus)