Stressed State of the Axisymmetric Adhesive Joint of Two Cylindrical Shells under Axial Tension

The research of the deflected mode of the construction, composed of two coaxially-glued cylindrical pipes, is done. Pipes are considered as thin-walled axisymmetric shells, which are joined by adhesive layer of a certain thickness. The shearing stresses in the glue are considered to be constant over the thickness of the adhesive layer, and normal stresses are linearly dependent on the radial coordinate. The shearing stresses in the adhesive layer are considered to be proportional to the difference in the longitudinal displacements of the shell sides that are faced to the adhesive layer. Normal stresses are proportional to the difference in radial displacement of the shells. It is supposed that the change in the adhesive layer thickness under deformation does not affect the stress, that is, the linear model is considered. The problem of the joint deflected mode finding is reduced to the system of four ordinary differential equations relative to the radial and longitudinal displacements of the layers. The system is solved by the matrix method. Displacements of layers outside of the adherent area can be found by the classical theory of axisymmetric shells. Satisfaction of boundary conditions and conjugation conditions leads to a system of twenty two linear equations with twenty two unknown coefficients. The model problem is solved; the results are compared with the computation made by the finite element method. The tangential and normal stresses in the glue reach the maximum values at the edges of the adhesive line. It is shown that the proposed model describes the stressed state of the joint with high accuracy, and this joint has an influx of glue residues at the ends of the adhesive line but can not be applied in the absence of adhesive influxes. Because in this case, the tangential stresses due to the parity rule reach maximum values not on the edge, but at some distance from the edge of the line. As a result, the distribution of normal stresses at the edge of the line also substantially changes. Thus, the proposed model with certain restrictions has sufficient accuracy for engineering problems and can be used to solve design problems.

EXPERIMENTAL INVESTIGATION OF DEFLECTED MODE OF THE RIENFORCED CONCRETE BEAMS WITH ORGANIZED CRACKS UNDER LONG-TERM LOADING

Introduction. Evaluation of the influence level of the pre-organized cracks in tensile zone of the reinforced concrete beams on their crack resistance, deformability under long-term loading is investigated in the article.Materials and methods. Concrete for specimen was produced in laboratory and factory on portland cement of the 500-grade at W/C=0,71; concrete composition 1:1,9:4 (by weight); strength of cube at 28th days – 13,85 MPa; strength of prism with dimensions 10/10*40 cm – 11,48 MPa; span calculation – 78 cm; steel rebar grade – A400 with diameter of 10 mm. Organized crack was formed by installing plate with thickness of 0,5 mm and height of 30 mm on the rebar in the zone of maximum moments.Results. The experiments confirmed the hypothesis about the beams rigidity with pre-organized cracks in comparison with stochastic cracks under the influence of long-term loading. As a result, the beams with pre-organized cracks provide the smaller deflection after long-term period than the beams without organized cracks. Thus, the proposed method of the deflections calculation of the reinforced concrete beams with pre-organized cracks under the long-term loading helps to reduce deflection to 33%.Discussion and conclusion. The findings of this study suggest that the presence of pre-organized cracks reduces the beams deflections in comparison with the specimens of section, and such method actually regulates the stress-strain state of reinforced concrete structures and leads to the smooth deformation at all stages under the influence of long-term loading.

On the analytical solution of one creep problem

The analytical solution of one initial value problem for the system of two ordinary differential equations describing the fracture process of metal structures in deflected mode at creep conditions is considered in the paper. Similar problems arise when calculating the strength characteristics and estimating residual deformations in the design of nuclear reactors, in building and aerospace industries and in mechanical engineering. The solvability of the creep constitutive equations’ system is of great practical importance. The possibility of obtaining an exact analytical solution makes it possible to significantly simplify both the identification of creep characteristics and the process of model examination. Necessary and sufficient integrability conditions imposed on the parameters of the model are obtained for the initial problem using Chebyshev's theorem on the integration of a binomial differential. The recommendations for the numerical solution of the considered problem are given.

On the analytical solution of one creep problem

The analytical solution of one initial value problem for the system of two ordinary differential equations describing the fracture process of metal structures in deflected mode at creep conditions is considered in the paper. Similar problems arise when calculating the strength characteristics and estimating residual deformations in the design of nuclear reactors, in building and aerospace industries and in mechanical engineering. The solvability of the creep constitutive equations’ system is of great practical importance. The possibility of obtaining an exact analytical solution makes it possible to significantly simplify both the identification of creep characteristics and the process of model examination. Necessary and sufficient integrability conditions imposed on the parameters of the model are obtained for the initial problem using Chebyshev's theorem on the integration of a binomial differential. The recommendations for the numerical solution of the considered problem are given.