BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

ON THE EFFECT OF EFFORT REGULATION BY MEANS OF TEMPORARY CONTINUITYIN SPLIT SPAN STRUCTURES OF STEELREINFORCED CONCRETE BRIDGES

The publication shows the effectiveness of applying the principle of temporary continuity by combining split span structures into acontinuous couplingusing a temporary joint. The method can be viewed as an option for effort regulation, creating abearing capacity reserveinload-bearing constructions within the span structures of bridges. The calculations provided show the effect on stress rate and bending moment in split span structurescombined into a double-spancontinuous coupling by a temporary joint.

ESTIMATION OF THE POWDER-ACTUATED SHEAR CONNECTORS TESTS

The shear connector design should be executed according to the SP 266.1325800.2016. For the different typed of welded connectors are there analytic dependences, which could be used for shear connection strength estimation. The design code also allows to use powder-actuated Z-shape shear connectors. Their bearing capacity should be proved by tests according to the GOST R 58336-2018. Inasmuch the GOST doesn't consist the test estimation approach, the authors offer the method. For the test estimation methods the test results of 15 series specimen had been used. The results were compared with estimation according to the European standard for the verification.

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.

CALCULATION OF EFFORTS RIPS FOUNDATION BOLTS IN THE BCALCULATION OF EFFORTS RIPS FOUNDATION BOLTS IN THE BASES OF CENTRAL AND ECCENTRIC COMPRESSION COLUMNASES OF CENTRAL AND ECCENTRIC COMPRESSION COLUMN

An engineering technique for calculating the tearing forces in the foundation bolts in the bases of centrally compressed columns is proposed. The calculation of the forces is based on the calculation of extra-centrally compressed rods, taking into account: the influence of the cross-section shape; the initial curvature of the neutral axis of the column; random eccentricity; nonlinear steel work. The calculation of the attachment forces (Nult and Mfic) of columns on the foundation edge is based on the method of practical calculations of centrally compressed elements using the stability coefficients at central compression φ (longitudinal bending coefficients), which are calculated depending on the flexibility l. The calculation of the attachment forces for rods with different reduced flexibility was performed by FEM in the FEMAP software package, as well as analytically using fictitious forces in centrally compressed rods. To calculate the tearing forces in the foundation bolts, a calculation model is made taking into account the contact interaction of the base and the reinforced concrete base. Graphs of the effect of the flexibility of the centrally compressed rod on the tearing force in the foundation bolts at the stage of exhaustion of the bearing capacity of the column when calculating its stability as an element of a continuous section under central compression are constructed.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

EQUATION OF STATE OF A WIRE IN THE PARAMETRIC FORM OF A CHAIN LINE

The "equation of state of the wire" is presented for the parametric representation of a chain line as a system of nonlinear equations. The classical equation of state of a wire is a special case of the presented system of nonlinear equations. The concept of the "initial" state of the wire is introduced, which is used to show the solution of the parametric "equation of state of the wire".

STRUCTURAL RELIABILITY ANALYSIS OF STEEL TRUSS ELEMENTS ON BUCKLING USING PBOX APPROACH

The reliability of load-bearing structural elements is one of the indicators of structural safety. The article presents methods for steel trusses bars reliability analysis according to the buckling criterion using p-boxes. A p-box consists of two boundary probability distribution functions that form the area of possible distribution functions. Such model used for modeling random variables in conditions of incomplete statistical data by quantity or quality. An algorithm for summing p-boxes of random load models is demonstrated on the example of a probabilistic estimate of the force in the truss bar. The result of reliability analysis using p-boxes is presented in interval form. The use of p-boxes makes it possible to obtain a more cautious assessment of reliability in case of incomplete statistical data. To increase the informativity of the reliability analysis result, it is necessary to obtain more statistical data about random variables in design mathematical models of limit state, which will allow forming p-boxes with narrower boundary distribution functions.

DEDETERMINATION OF THE LOGARITHMIC DECREMENT OF NATURAL VIBRATIONS OF BUILDINGS AND STRUCTURESTERMINATION OF THE LOGARITHMIC DECREMENT OF NATURAL VIBRATIONS OF BUILDINGS AND STRUCTURES

For the passport of buildings and structures, it is required to determine the logarithmic damping decrement. The proposed expressions [1, 2] to determine the decrement use the value of the Q-factor, however, an expression is known in which the damping decrement is determined through the logarithm of the ratio of the amplitudes of the damped signal. Comparison of the formulas for calculating the logarithmic decrement of vibrations was carried out using the example of data obtained when testing a beam with reinforcement.

DEVELOPMENT OF TESTING METHODS FOR BRICK AND MASONRY SAMPLES, CONSIDERING THE BIAXIAL STRESS STATE

The article contains a brief description about the addition of the test program of the walls from masonry and the processing of results of experimental studies. It'll make the processing of the results so much easier and improve their accuracy.