Longitudinal-transverse bending of physically nonlinear reinforced concrete beams

В работе рассматриваются экспериментальные диаграммы деформирования бетонов марок B10, B30, B50. Методом наименьших квадратов приведены аппроксимации диаграмм деформирования полиномами второго и третьего порядка. Указанные расчеты выполнены как для случая одинаковых коэффициентов для зон растяжения и сжатия, так и различных. Приведен алгоритм решения задачи продольно-поперечного изгиба балки в случае использованных данных аппроксимаций диаграмм. The paper considers experimental deformation diagrams of concrete grades B10, B30, B50. The approximation of the deformation diagrams by polynomials of the second and third order is given by the least squares method. The calculations were performed both for the case of the same coefficients for the zones of tension and compression, and different ones. An algorithm for solving the problem of longitudinal-transverse bending of a beam in the case of the used data of approximations of diagrams is given.

Computer Modeling Deformation of Porous Elastoplastic Materials and Identification their Characteristics Using the Principle of Three-dimensional Similarity

It is proposed to numerically model large deformations of porous specimens, using the 3D- similarity principle in structural elements, which makes it possible to account for the inhomogeneity of the stress-strain state due to the presence of pores and allows one to vary the number of representa- tive volumes without changing porosity values and dimensions of the specimens. A methodology for determining true deformation diagrams of materials, using the results of compression tests, has been de- veloped. The efficiency of using the 3D-similarity principle is demonstrated by comparing the numerical and experimental results for the example analyzing compression of porous specimens of an aluminum alloy with free lateral surfaces and fixed in a rigid cartridge

Resistance of Structural Materials to Deformation in the Case of Linear and Flat Stresses

Annotation: The deformation resistance properties of structural materials in the case of linear and flat stresses are given on the basis of experimental results. The method of estimating the mechanical properties of the material based on the initial deformation diagrams is described. Keywords: Stress, deformation, longitudinal force, internal pressure, stress state, deformation diagram, initial deformation, Yung modulus, Poisson's ratio, anisotropy, strength, yield strength

Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.

DETERMINATION OF CRACK RESISTANCE OF PRESTRESSED REINFORCED CONCRETE BEAMS OF TRAPEZOIDAL CROSS-SECTION

Beams of a trapezoidal cross-section with a wide upper edge with prestressed reinforcement combine positive qualities in terms of strength, crack resistance, deformability and resource saving, which allows them to cover significant spans of multi-storey buildings. To develop a method for calculating the moment of cracking in these structures, a nonlinear deformation model was adopted, which includes equilibrium equations, conditions for the linear distribution of relative deformations along the height of the element section, and refined deformation diagrams of concrete and reinforcement. Concrete state diagrams are assumed to be nonlinear without a falling branch. To describe the deformation diagrams of high-strength and conventional reinforcement, a universal dependence is adopted, consisting of one linear and two nonlinear equations, in which the calculation of individual parameters is performed using different formulas. For the initial stage of the crack formation process, a design scheme is presented, in accordance with which the necessary equations and ratios are drawn up in relation to the considered prestressed reinforced concrete beam of a trapezoidal cross-section. The purpose of the study, in addition to developing a calculation methodology, was also the development of an algorithm and a computer calculation program. To obtain and analyze the results, a numerical experiment was carried out, the results of which are presented in tabular form. Due to the fact that the calculation method was built without involving empirical dependencies, the possibility of its application to determine the crack resistance of prestressed reinforced concrete beams of trapezoidal cross-section for any class of concrete and reinforcement was confirmed.

Study of the properties of materials under complicated conditions of low cycle deformation

Operational integrity of structures under complex combined modes of a loading depends on a significant number of combinations of operational parameters of thermomechanical impacts in part of loads, temperatures, duration, number of cycles, and deformation rates. The main laws governing the deformation of structural materials under complex loading are determined in conditions of combined standard, unified and special tests in laboratories. Using representative substantiations of physical and mechanical models for deformation diagrams in a wide range of loading conditions, taking into account the different scales of models, the structure of materials and the responsibility of structures, a stepwise consideration of the corresponding types of deformation is proposed: elastic, sign-variable flow, progressing accumulation of strains and their combination. At the same time, calculations of the structures can be carried out in the form of a hierarchical system in which each next level specifies the boundaries of permissible impacts towards expansion of the range of acting loadings, temperatures, rates and modes of deformation, which entails an increase in the bulk of the required initial data and complicates the calculations. The proposed methods of schematization of the physicomechanical properties and types of the equations of state for description of the deformation curves take into account the requirements of compactness of the initial data and the need of using both standard and unified methods for determining the characteristics of cyclic inelastic deformation and special methods as well. To describe the kinetics of deformation diagrams under aforementioned conditions both from the theoretical point of view and from the point of view of practical applications, power equations appeared most suitable; to reflect the role of the temperature factor exponential dependences should be used; whereas power dependences are useful to take into account time factors, strain rate, and conditions of two-frequency loading. The refined calculations at the higher and more complicated steps of the considered hierarchy providing the maximum possible use of the deformation and strength reserves of the materials and structures are to be based on the kinetic laws describing processes of low cycle deformation under complex modes of loading.

INITIAL AND RESIDUAL RESOURCE OF RUBBER-CORD SHELLS OF CONNECTING DEVICES OF ROLLING STOCK

In article the basic settlement dependences of a resource rubber-cord environments are given on the basis of the received results of experimental researches of integrated characteristics in view of quasi-elastic, not elastic and total deformation. Diagrams of dependence of durability of environments from a corner of a twisting and the specified kinds of deformation are constructed.

Investigation of Integral and Differential Characteristics of Variatropic Structure Heavy Concretes by Ultrasonic Methods

The article develops methods and methodology for experimental studies of centrifuged and vibro-centrifuged concrete products of annular cross-section. They assess the real variatropy of the structure and confirm the correctness of the accepted research. An original technique for experimental studies of the variatropy of the cross-sections of vibrated, centrifuged and vibro-centrifuged concretes is proposed to determine their integral (common) and differential (differing in layers) strength and strain characteristics and deformation diagrams. It has been proved that with vibro-centrifugation it becomes possible to obtain concretes with improved structure and higher characteristics compared with centrifugation and vibration techniques. Experimental studies of the differential characteristics of centrifuged and vibro-centrifuged concretes under compression and tension revealed that the outer layer of concrete had the best characteristics after centrifugation and vibro-centrifugation, and the inner layer had the worst ones. The three-layer model of the variatropic structure for centrifuged and vibro-centrifuged concrete has been experimentally confirmed. The concrete of the outer layers had the highest strength and modulus of elasticity and the least deformability; the concrete of the inner layers had the lowest strength and modulus of elasticity and the highest deformability; and the concrete of the middle layers had average characteristics. The deformation diagrams of centrifuged and vibro-centrifuged concretes were also differentiated by layers, confirming the variatropy of the structure of such concretes. The deformation diagrams for the outer concrete layer demonstrated the highest strength; the diagrams for the inner concrete layer showed the lowest strength; and the diagrams for the middle concrete layer corresponded to mean characteristics.

MACLOCYCLE FATIGUE OF STRUCTURAL ELEMENT UNDER SOFT LOADING.

In the article the method of calculation of capacity for work construction element of low – cycle deformation diagrams with considering of cyclic instability and unilateral accommodation of plastic deformation.

DIFFERENTIAL EQUATIONS OF EQUILIBRIUM OF IDEALLY ELASTOPLASTIC CONTINUOUS MEDIUM FOR PLANE ONE-DIMENSIONAL DEFORMATION IN APPROXIMATION OF CLOSING EQUATIONS BY BIQUADRATIC FUNCTIONS

The present article considers the construction of differential equations of equilibrium of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of one-dimensional plane deformation, when the diagrams of volumetric and shear deformation are approximated by biquadratic functions. The construction of physical dependencies is based on calculating the secant moduli of volumetric and shear deformation. When approximating the graphs of the volumetric and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volumetric expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volumetric and shear deformation, the secant shear modulus is a fractional (rational) function of the shear strain intensity; the secant modulus of volumetric expansion-compression is a fractional (rational) function of the first invariant of the strain tensor. Based on the assumption of independence, generally speaking, from each other of the volumetric and shear deformation diagrams, five main cases of physical dependences are considered, depending on the relative position of the break points of the graphs of the diagrams volumetric and shear deformation. On the basis of received physical equations, differential equations of equilibrium in displacements for continuous medium are derived under conditions of plane one-dimensional deformation. Differential equations of equilibrium in displacements constructed in the present article can be applied in determining stress and strain state of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of plane one-dimensional deformation, closing equations of physical relations for which, based on experimental data, are approximated by biquadratic functions.