The stress state of elliptical bottoms with centrally located branch pipes reinforced with a monolithic insert or cover ring is analyzed and experimentally investigated. Five zones of maximum stresses are exposed and examined in the designs employed for reinforcement of couplings. The advantage of the cover-ring design is established.Couplings, which are intended for the intake and discharge of a working medium and which differ in terms of dimensions and structural modification, are widely used structural elements of pressure vessels. According to regulatory documents in force [1,2], the reinforcing components of the coupling can be built in the form of a cover ring or monolithic insert (Fig. 1).In designing cylindrical housings or bottoms with couplings in accordance with effective standards based on the principle of area compensation, the opening cut into the wall of a shell is considered reinforced if the metal removed is compensated by supplementary metal of the branch pipe and housing [1][2][3][4]. Considering this, designs of couplings with a cover ring or monolithic insert are equivalent. The principle of area compensation is inadequate, however, to ensure cyclic or brittle strength of the design. The strength of a design with respect to stress state, which may differ considerably in designs with a cover ring and monolithic insert, is confirmed in accordance with modern standards [2,4,5]. And, although the zone where the ring is positioned is treated as a monolithic part when the stress state of an inlet coupling with a cover ring is analyzed in engineering practice, they are, in reality different structures, whose stress states should be calculated in accordance with different computational schemes.The company IrkutskNIIkhimmash performs stress-state analysis, and conducts experimental investigations and comparative analyses of the stress states of elliptical bottoms with central branch pipes built with two types of reinforcement -with a monolithic insert and with a cover ring -for different ratios of the branch-pipe and bottom diameters d/D.An elliptical bottom with an inside diameter of 450 mm, wall thickness of 6 mm, and height-diameter ratio of 0.25 was selected for numerical and experimental investigations of the stress state. Ratios d/D = 0.22, 0.33, and 0.44 were used to evaluate the level of stresses. In the experimental models, the bottoms were connected in pairs via a cylindrical insert.
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An engineering procedure is proposed for assessment of the stress state of elliptical bottoms with set-on nozzles as a function of their size. Diagrams and approximating equations to define stress-enlargement ratios, which are used to calculate brittle-fracture resistance and evaluate the cyclical strength of pressure vessels with nozzles are presented on the basis of alternative investigations.Statistical data in published literature indicate that more than one-third of the pressure vessels are taken out of service because of loss of strength in nozzle couplings. According to modern regulatory documents, the level of maximum stresses in the nozzle couplings of cylindrical, spherical, and elliptical shells must be known for evaluation of the strength and longevity of pressure vessels subject to static and cyclical loads.Approximate evaluation of the level of stresses in the area where a nozzle sets on an end is required for calculation of brittle-fracture strength [1]. For a calculated defect in the form of a surficial semi-elliptical crack, the meridional stresses in the end are tensile stresses.The notch-sensitivity index [1, 2], as determined from maximum equivalent stresses in the nozzle coupling, is used to calculate cyclical strength.An engineering method is proposed for evaluating the stress state in the zone of the coupling between a set-on nozzle and elliptical end as a function of the ratio of the dimensions of the nozzle and end. Approximating formulas derived on the basis of numerical calculations conducted for a large number of alternate schemes using the TUPROK software package founded on the theory of thin shells, are thought of as the backbone of the procedure [3]. A computational diagram of the design is shown in Fig. 1.In developing the procedure, a series of calculations were performed in the following range of ratios of the geometric dimensions of the nozzle and end:S/D = 0.01; 0.015; 0.025; 0.04; d/D = 0.05; 0.1; 0.25; 0.5; S 1 /S = 0.15; 0.2; 0.3; 0.5; 0.7; 1.0,where D is the inside diameter of the end, d is the inside diameter of the nozzle, S is the thickness of the end, and S 1 is the thickness of the nozzle. Two types of plots were constructed on the basis of results of the alternative investigations: 1) to evaluate the stress-enlargement factors (α σ ) in the elliptical end, disregarding the stress state in the nozzle; these factors can be used for calculating the brittle-fracture resistance (Fig. 2);
Results are presented for experimental investigations of the effect of fabrication inaccuracies in elliptical bottoms (EB) with branch-pipe assemblies on their stress state and strength.It is established that the design of a branch-pipe assembly of an EB with an overlain ring is preferable to one with a monolithic insert. The need to account for the actual shape of the components of the branch-pipe assembly of EB in analyzing the stress state, and the need for rational distribution of reinforcing metal in the branch-pipe assemblies to lower the level of the overall stress state and meet strength conditions are demonstrated.In designing elliptical bottoms (EB) with branch-pipe assemblies, it is assumed that the ideal EB will take on the form of an ellipsoid. This assumption is made in design analyses of the thickness of the bottom, and also in further analyses of the stress state when the bottoms are verified with respect to various strength criteria. One of the factors affecting the stress state of branch-pipe assemblies is fabrication inaccuracy, which causes noncorrespondence between usable shapes of design schemes and the actual shape of bearing components of the structure.We employed experimental and numerical models to investigate the influence exerted by fabrication inaccuracy of EB with branch-pipe assemblies on their stress state and strength.Investigations of the stress state were conducted for the entire (no branch pipe) EB (inside diameter of 450 mm, thickness of 6 mm, and height-to-diameter ratio of 0.25), and similar bottoms with branch pipes (ratio of inside diameter d of branch pipe to inside diameter D of bottom d/D = 0.22, 0.33, and 0.44). We used branch-pipe assemblies with reinforcing elements in the form of a monolithic insert or overlain ring, the dimensions of which were selected in accordance with current regulatory documents [1,2]. In the experimental models, the bottoms were connected in pairs via a cylindrical insert. The parameters of the bottom models investigated with a thickness of 6 mm are presented in Table 1.The stresses in the experimental models were determined by the strain-measurement method. Resistance strain gages with a 3-mm base were glued onto the outer surfaces of the bottoms, reinforcing elements, and branch pipes. Computational investigations of the stress state were conducted in accordance with the TUPROK program [3], which implements the finite-element method in the theory of thin shells.
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