scholarly journals Theory of “dissolution” and “condensation” of the physical geometric characteristics of an arbitrary cross-section under the action of torsion with bending

2019 ◽  
Vol 15 (4) ◽  
pp. 261-270
Author(s):  
Vladimir I. Kolchunov ◽  
Aleksej I. Demyanov ◽  
Nikolay V. Naumov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Large Circle ◽  
Stress Strain ◽  
Cross Sectional ◽  
Tangential Stresses ◽  
Stress Strain State

Aim of research - to continue the development of methods for determining the stress-strain state of rods during torsion using materials resistance methods. Methods. A new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance, is proposed. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Results. Three theorems have been formulated, the first of which relates the accumulation of tangential stresses (increments) from the edges of a rectangle to the middle of a rectangular section with the formula for determining tangent stresses for round sections. The second theorem allows to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows to remove the need to use special tables for the calculation and not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.

The movement investigation of an axisymmetric rotation body under the action of electromagnetic fields

2020 ◽  
Vol 2 (103) ◽  
pp. 67-77
Author(s):  
O. Hrevtsev ◽  
N. Selivanova ◽  
P. Popovych ◽  
L. Poberezhny ◽  
O. Shevchuk ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Cross Section ◽  
Variable Thickness ◽  
Structural Damage ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Stress Strain ◽  
Coordinate Time ◽  
Stress Strain State ◽  
Natural Time

Purpose: To ensure an adequate level of accuracy, it is rational to study the ponderomotor forces of the ring, which drive a hollow disk of variable thickness, hung on the ring. Design/methodology/approach: The solution of the motion problem of a hollow disk of variable thickness suspended on a force ring of rectangular cross section is based on the method of solving the equations of the theory of thermoelasticity. The stress-strain state, as well as the motion of the specified body of rotation, the disk, in studies in a cylindrical coordinate system, under the action of ponderomotor forces. Findings: The motion equation of a hollow disk hung on a force ring-torus is made, exact solutions of the motion equations of a ring in the torus form of rectangular cross section are found. New component expressions of ponderomotor forces, which appear from the action of the ring's own electromagnetic field and cause the motion of a hollow disk, have been found on the basis of Maxwell's equations. It is proved that at high speeds and low natural accelerations the stress - strain state of the disk material does not cause the destruction of the structure. Research limitations/implications: Calculations of ponderomorphic forces are valid for the ring, which drives a hollow disk of variable thickness, hung on the ring. Practical implications: It is proved that at high velocities and small natural accelerations the stress-strain state of the disk medium does not cause structural damage. It is determined that the rotation in the direction of movement at an angle of 90 degrees changes only the direction of the acceleration vector without increasing its value. Originality/value: The dependences between own time and coordinate time are formulated. It is proved that a small change in the natural time for the studied disk can significantly change the coordinate time, and the pulsed electromagnetic field provides the ability to cover infinitely large distances over finite periods of time.

scholarly journals A transient dynamic process in a structural nonlinear system “beam – two-parameter foundation”

2020 ◽  
Vol 310 ◽  
pp. 00007
Author(s):  
Vladimir Gordon ◽  
Pavel Morrev ◽  
Olga Pilipenko
Keyword(s):  
Cross Section ◽  
Strain State ◽  
Shear Stiffness ◽  
Arbitrary Cross Section ◽  
Forced Oscillations ◽  
Stiffness Parameter ◽  
Stress Strain ◽  
Stress Strain State ◽  
Internal Forces ◽  
Two Parameter

A method for analytical assessment of dynamic added stress in elastic loaded beam resting on elastic two-parameter Pasternak’s foundation due to sudden destruction a part of foundation is proposed. Equations of static bending, natural and forced oscillations are written in a matrix form using state vectors including deflection, rotational angles, bending moments, and shear forces at arbitrary cross section of a beam and also using the matrices of the initial parameters influence on the stress-strain state in arbitrary cross section. The influence of foundation failure on beam’s stress-strain state, taking into account a relation between the stiffness parameters of foundation, is analyzed. The condition of smallness for the shear stiffness parameter (Pasternak’s parameter) in comparison with the stretching-compressing stiffness parameter (Vinkler’s parameter) is accepted. It is shown that the accounting of Pasternak’s parameter reduces the level of dynamic added stress in a beam when sudden destructing of a foundation. The factor of sudden defect occurrence in the system “beam – foundation” increases considerably the internal forces in a beam in comparison with quasistatic formation of the same defect.

scholarly journals DETERMINATION OF STRESS-STRAIN STATE OF A THREE-LAYER BEAM WITH APPLICATION OF CONTACT LAYER METHOD

Vestnik MGSU ◽  
2016 ◽  
pp. 17-26 ◽  
Author(s):  
Vladimir Igorevich Andreev ◽  
Robert Alekseevich Turusov ◽  
Nikita Yur’evich Tsybin
Keyword(s):  
Experimental Data ◽  
Edge Effect ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Contact Layer ◽  
Theory Of Elasticity ◽  
Stress Strain ◽  
Tangential Stresses ◽  
Stress Strain State ◽  
Layer Method

The article deals with the solution for the stress-strain state of a multilayer composite beam with rectangular cross-section, which is bended by normally distributed load. The intermolecular interaction between layers is accomplished by the contact layer, in which the substances of adhesive and substrate are mixed. We consider the contact layer as a transversal anisotropic medium with such parameters that it can be represented as a set of short elastic rods, which are not connected to each other. For simplicity, we assume that the rods are normally oriented to the contact surface. The contact layer method allows us to solve the problem of determining the concentration of tangential stresses arising at the boundaries between the layers and the corner points, their changes, as well as to determine the physical properties of the contact layer basing on experimental data. Resolving the equations obtained in this article can be used for the solution of many problems of the theory of layered substances. These equations were derived from the fundamental laws of the theory of elasticity and generally accepted hypotheses of the theory of plates for the general case of the bending problem of a multilayer beam with any number of layers. The article deals with the example of the numerical solution of the problem of bending of a three-layer beam. On the basis of this solution the curves were obtained, which reflect the stress-strain state of one of the layers. All these curves have a narrow area of the edge effect. The edge effect is associated with a large gradient tangential stresses in the contact layer. The experimental data suggest that in this zone the destruction of the samples occurs. This fact allows us to say that the equations obtained in this article can be used to construct a theory of the strength layered beams under bending.

scholarly journals Influence of breakages of cable groups on strength ofrubber-cable tractive-transporting element

2021 ◽  
Vol 64 ◽  
pp. 166-174
Author(s):  
I Belmas ◽  
D Kolosov ◽  
O Dolgov ◽  
H Tantsura ◽  
S Onyshchenko
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Elastic Shell ◽  
Practical Significance ◽  
Analytical Determination ◽  
Shear Stresses ◽  
Stress Strain ◽  
Stress Strain State

Purpose. Development and justification of a method of analytical determination of a stress-strain state of a flat rubber-cable tractive-transporting element with breakages of continuity of cable groups in different cross-sections. Methodology of research is in development of a mathematical model of interaction of tractive-transporting element parts considering breakages of groups of random cables, construction of analytical solutions for determining dependencies of force distribution between cables and shear stresses in an elastic shell of a tractive-transporting element with random locations of breakages of cable groups in different cross-sections. Findings. A model of a flat rubber-cable tractive-transporting element with random locations of breakages of cable groups in different cross-sections is developed. Expressions that allow determining a stress-strain state of a flat rubber-cable tractive-transporting element of a hoisting and transporting machine with random locations of breakages of cable groups in different cross-sections are obtained analytically in a closed form. Strength conditions are formulated. Scientific novelty is in establishment of dependencies of interaction of disturbance fields of a stress-strain state of a rubber-cable tractive-transporting element with breakages of continuity of random cable groups in different cross-sections. It is established that disturbance fields caused by breakages of adjacent cables overlap when the breakages are located in one cross-section and there are less than three whole cables located between the broken cables. Disturbance fields also overlap when the same cable or the adjacent cable is broken in both cross-sections and the distance between cross-sections of breakage does not exceed the value, which depends on the design of a flat rubber-cable tractive-transporting element and mechanical properties of its components. Practical significance. The obtained algorithms and strength conditions allow determining a stress-strain state and preventing the breakage of the entire flat rubber-cable tractive-transporting element with breakages of cable groups in different cross-sections. These cross-sections can be: cross-section of the edge of a butt joint, where cables have breakages of continuity; cross-section, which includes the edge of an area of partial restoration of a tractive ability of the element, lost due to breakage of a cable; cross-section of cable or cable group breakage during operation. A possibility of establishing a stress-strain state and the strength conditions of a tractive-transporting element under such conditions allows reasonable determination of a possibility of its further operation in a hoisting and transporting machine.

scholarly journals Stress-strain state of the storage silos under the action of the asymmetric load

2018 ◽  
Vol 230 ◽  
pp. 02018 ◽  
Author(s):  
Nataliia Makhinko
Keyword(s):  
Cross Sections ◽  
Strain State ◽  
Wind Load ◽  
Exponential Dependence ◽  
Engineering Practice ◽  
Stress Strain ◽  
Cross Sectional ◽  
Stress Strain State ◽  
Construction Design ◽  
Cross Section Area

This paper deals with the investigation of work of the vertical steel cylindrical storage silos for grain with the different thickness of casing sheets and stiffeners at different height sunder the asymmetric wind load. Construction is designed using the analytical method involving decomposition of load into the completed trigonometric series and adding separate stress-strain states of k influence. The construction design model is a thin-walled cylindrical shell reinforced with vertical stiffeners. According to the shell theory, all unknown elements of the stress-strain states from the wind load components are expressed by unknown function ξk (x). In the analysis, the introduced hypotheses were used, which provides for using exponential dependence to describe the thickness changing law of the casing sheets and stiffeners and the equality of the change rate of these characteristics. The obtained results for silos with corrugated wall showed that the desired function which characterizes the stress-strain state of the construction is determined by ratio of the total cross-section area of all stiffeners to the cross-sectional area of the silo provided this ratio is constant at all heights. Represented calculation formulas for radial, circular and longitudinal displacements, and for strains in cross-sections are simple enough for using in the engineering practice.

scholarly journals Influence of the Cross-Sectional Shape of a Reinforced Bimodular Beam on the Stress-Strain State in a Transverse Impact

Buildings ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 248
Author(s):  
Alexey Beskopylny ◽  
Elena Kadomtseva ◽  
Besarion Meskhi ◽  
Grigory Strelnikov ◽  
Oleg Polushkin
Keyword(s):  
Reinforced Concrete ◽  
Stress State ◽  
Cross Section ◽  
Strain State ◽  
Transverse Impact ◽  
Stress Strain ◽  
Cross Sectional ◽  
Stress Strain State ◽  
The Cross ◽  
The Impact

The paper considers the stress-strain state of a reinforced concrete beam, as a bimodular material, under the action of an impact. The behavior of bimodular concretes with different moduli of elasticity in tension and compression has not been studied enough. At the same time, taking into account the bimodularity of concrete makes it possible to design a more economical structure, especially for dynamic load. In this article, the impact is considered as an absolutely plastic impact of an absolutely rigid body on an elastic system. The stress state is investigated for beams of rectangular, T-section and I-sections, and is compared with and without the bimodularity of reinforced concrete. The analysis of the dependence of the stress state on the shape, cross-sectional dimensions, and the location of reinforcing bars in the compressed and tensioned zones was carried out for lightweight concrete (Et < Ec) and for heavy concrete (Et > Ec) under the action of shock load with and without regard to the mass of the beam. The numerical study shows that taking into account the mass of the beam upon impact significantly decreases the magnitude of the normal stresses in both the tensioned and compressed zones. Beams of rectangular cross-section have the highest load-bearing capacity when the cross-section height is equal for both light and heavy concrete. An increase in the size of the flange of the I-beam in the stretched zone leads to a sharp decrease in normal tensile stresses and a slight increase in normal compressive stresses. The proposed engineering method makes it possible to numerically study the effect on the stress-strain state of a beam under the action of a concentrated impact of various geometric characteristics of the cross-section, bimodularity of the material, size, number and location of reinforcement.

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