DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

DEVELOPMENT OF A MODEL OF AN EQUAL STRESS CYLINDER BASED ON MOHR’S STRENGTH THEORY

Вестник МГСУ 5/2013
  • Chepurnenko Anton Sergeevich - Don State Technical University (DGTU) Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Yazyev Batyr Meretovich - Rostov State University of Civil Engineering (RSUCE) Doctor of Technical Sciences, Professor, Chair, Depart- ment of Strength of Materials; +7 (863) 201-91-09, Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya St., Rostov-on-Don, 344022, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 56-61

The authors have employed analytical methods to identify the nature of dependence of the elastic modulus distribution over the thickness of a cylinder, loaded by internal pressure p , if the equivalent stress is the same in all points, according to Mohr’s theory of strength. The problem in which dependence of an elastic modulus is to be identified along the radius, and the stress value is available, is called the inverse prob- lem. The idea of the method is that if a certain area of a body has the value of its elastic modulus lower than the one in the homogeneous material, stresses in this area are also reduced. The problem is solved for the case of plane strain and plane stress in the elastic formulation. It is proven that assurance of artificial heterogeneity reduces the maximal equivalent stress. Therefore, we have taken two variants of shells: one having inner radius a = 1 m and outer radius b = 2 m, the other one having inner radius a = 1 m and outer radius b = 0.52 m. The value of the maximal equivalent stress calculated using Mohr’s theory reduces almost two-fold in the first case and 1.5-fold in the second case. Moreover, the use of non-uniform thick-walled cylinders can significantly reduce their thickness with the value of the internal pressure being the same. In our case, the shell thickness reduces from 1 m to 0.52 m, which is almost 2 times. We also proven that the first, second and third strength theories in the case of an axisymmetric problem are the special cases of Mohr’s strength theory. This result coincides with well-known analytical and numerical solutions.

DOI: 10.22227/1997-0935.2013.5.56-61

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