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## DISCRETE CRACK MODEL OF BORCZ FOR CALCULATING THE DEFLECTIONS OF BENDING REINFORCED CONCRETE BEAM

• In the design of the reinforced concrete beams loaded by the bending moment, it is assumed that the structure can be used at a level of load, that there are local discontinuities - cracks. Designing the element demands checking two limit states of construction, load capacity and usability. Limit states usability include also the deflection of the element. Deflections in the reinforced concreteIn the design of the reinforced concrete beams loaded by the bending moment, it is assumed that the structure can be used at a level of load, that there are local discontinuities - cracks. Designing the element demands checking two limit states of construction, load capacity and usability. Limit states usability include also the deflection of the element. Deflections in the reinforced concrete beams with cracks are based on actual rigidity of the element. After cracking there is a local change in rigidity of the beam. The rigidity is variable in the element’s length and due to the heterogeneous structure of concrete, it is not possible to clearly describe those changes. Most standards of testing methods tend to simplify the calculations and take the average value of the beam’s rigidity on its entire length. The rigidity depends on the level of the maximal load of the beam. Experimental researches verify the value by inserting the coefficients into the formulas used in the theory of elasticity. The researches describe the changes in rigidity in the beam’s length more precisely. The authors take into consideration the change of rigidity, depending on the level of maximum load (continuum models), or localize the changes in rigidity in the area of the cracks (discrete models). This paper presents one of the discrete models. It is distinguished by the fact that the left side of the differential equation, that depends on the rigidity, is constant, and all effects associated with the scratches are taken as the external load and placed on the right side of the equation. This allows to generalize the description. The paper presents a particular integral of the differential equation, which allow analyzing the displacement and vibration for different rigidity of the silo’s walls, the flow rate and type of the flowing material.

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Document Type: Conference Proceeding Michal Musial, Mieczysław Kamiński, Andrzej Ubysz https://doi.org/10.25643/bauhaus-universitaet.2790Cite-Link https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27907Cite-Link http://euklid.bauing.uni-weimar.de/ikm2012 1611-4086 Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar Klaus GürlebeckGND, Tom LahmerORCiDGND, Frank WernerORCiDGND English 2017/03/03 2012/07/04 2017/03/14 Bauhaus-Universität Weimar Bauhaus-Universität Weimar Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar 11 Angewandte Informatik; Angewandte Mathematik; Computerunterstütztes Verfahren 000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme 500 Naturwissenschaften und Mathematik / 510 Mathematik 31 Mathematik / 31.80 Angewandte Mathematik 56 Bauwesen / 56.03 Methoden im Bauingenieurwesen Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 19. 2012 Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)