Stress Intensity Factor of Reinforced Concrete Beams in Bending
The stress values at the crack tip in bending reinforced concrete beams are considered. The stress state is analytically determined with an initial and propagating crack. Equations of the equilibrium of a part of the beam cut along the crack line are compiled. These equations are reduced to a system...
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2021-07-01
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doaj-c477ffa324d94a81b930bb943400c0632021-07-23T13:33:06ZengMDPI AGBuildings2075-53092021-07-011128728710.3390/buildings11070287Stress Intensity Factor of Reinforced Concrete Beams in BendingZhmagul Smagulovich Nuguzhinov0Zhetpisbay Bakirovich Bakirov1Nikolai Ivanovich Vatin2Madi Zhetpisbaevich Bakirov3Irina Alekseevna Kurokhtina4Daniyar Tokanovich Tokanov5Omirkhan Khabidolda6Kazakhstan Multidisciplinary Institute of Reconstruction and Development Republican State Enterprise on the Right of Economic Use, Karaganda 100027, KazakhstanMechanics Department, Building Materials and Technologies Department, Karaganda Technical University, Karaganda 100027, KazakhstanInstitute of Civil Engineering, Peter the Great Saint Petersburg Polytechnic University, 195251 Saint Petersburg, RussiaMechanics Department, Building Materials and Technologies Department, Karaganda Technical University, Karaganda 100027, KazakhstanMechanics Department, Building Materials and Technologies Department, Karaganda Technical University, Karaganda 100027, KazakhstanKazakhstan Multidisciplinary Institute of Reconstruction and Development Republican State Enterprise on the Right of Economic Use, Karaganda 100027, KazakhstanMechanics Department, Al Farabi Kazakh National University, Almaty 050040, KazakhstanThe stress values at the crack tip in bending reinforced concrete beams are considered. The stress state is analytically determined with an initial and propagating crack. Equations of the equilibrium of a part of the beam cut along the crack line are compiled. These equations are reduced to a system of two nonlinear algebraic equations using the plane-sections hypothesis. The equations determine the stress zone’s height and the nominal stress at the crack tip for a beam with an initial crack and the crack length. The rest of the stress state parameters are expressed regarding the zone stress height and the nominal stress or crack length. The same equation system determines the external moment starting from which the crack length increases. The analytical method for determining the stress intensity factor (SIF) with an initial and growing crack in bent reinforced concrete beams is proposed. The method is based on the assumption that the size of the stress concentration zone at the crack tip is determined by the equality of the nominal and local stresses at the end of this zone. The method determines the value of the external moment starting from which the crack length increases. The stress zone’s size is determined by the coincidence of the local stress with the nominal stress. The same problem is solved in a three-dimensional formulation by the FE method, considering the stress field’s peculiarities at the crack tip. The calculation results coincide with the analytical solutions.https://www.mdpi.com/2075-5309/11/7/287reinforced concretebeambendingcompressive sidecrackreinforcement |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhmagul Smagulovich Nuguzhinov Zhetpisbay Bakirovich Bakirov Nikolai Ivanovich Vatin Madi Zhetpisbaevich Bakirov Irina Alekseevna Kurokhtina Daniyar Tokanovich Tokanov Omirkhan Khabidolda |
spellingShingle |
Zhmagul Smagulovich Nuguzhinov Zhetpisbay Bakirovich Bakirov Nikolai Ivanovich Vatin Madi Zhetpisbaevich Bakirov Irina Alekseevna Kurokhtina Daniyar Tokanovich Tokanov Omirkhan Khabidolda Stress Intensity Factor of Reinforced Concrete Beams in Bending Buildings reinforced concrete beam bending compressive side crack reinforcement |
author_facet |
Zhmagul Smagulovich Nuguzhinov Zhetpisbay Bakirovich Bakirov Nikolai Ivanovich Vatin Madi Zhetpisbaevich Bakirov Irina Alekseevna Kurokhtina Daniyar Tokanovich Tokanov Omirkhan Khabidolda |
author_sort |
Zhmagul Smagulovich Nuguzhinov |
title |
Stress Intensity Factor of Reinforced Concrete Beams in Bending |
title_short |
Stress Intensity Factor of Reinforced Concrete Beams in Bending |
title_full |
Stress Intensity Factor of Reinforced Concrete Beams in Bending |
title_fullStr |
Stress Intensity Factor of Reinforced Concrete Beams in Bending |
title_full_unstemmed |
Stress Intensity Factor of Reinforced Concrete Beams in Bending |
title_sort |
stress intensity factor of reinforced concrete beams in bending |
publisher |
MDPI AG |
series |
Buildings |
issn |
2075-5309 |
publishDate |
2021-07-01 |
description |
The stress values at the crack tip in bending reinforced concrete beams are considered. The stress state is analytically determined with an initial and propagating crack. Equations of the equilibrium of a part of the beam cut along the crack line are compiled. These equations are reduced to a system of two nonlinear algebraic equations using the plane-sections hypothesis. The equations determine the stress zone’s height and the nominal stress at the crack tip for a beam with an initial crack and the crack length. The rest of the stress state parameters are expressed regarding the zone stress height and the nominal stress or crack length. The same equation system determines the external moment starting from which the crack length increases. The analytical method for determining the stress intensity factor (SIF) with an initial and growing crack in bent reinforced concrete beams is proposed. The method is based on the assumption that the size of the stress concentration zone at the crack tip is determined by the equality of the nominal and local stresses at the end of this zone. The method determines the value of the external moment starting from which the crack length increases. The stress zone’s size is determined by the coincidence of the local stress with the nominal stress. The same problem is solved in a three-dimensional formulation by the FE method, considering the stress field’s peculiarities at the crack tip. The calculation results coincide with the analytical solutions. |
topic |
reinforced concrete beam bending compressive side crack reinforcement |
url |
https://www.mdpi.com/2075-5309/11/7/287 |
work_keys_str_mv |
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