TO DETERMINATION OF STRESS-STRAIN STATE FOR A ROD OF ARBITRARY CROSS SECTION UNDER TORSION USING MECHANICS OF MATERIALS

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.

Download Full-text

CALCULATION OF BENDING ELEMENTS OF WOOD AFTER THE ACTION OF LOW-CYCLE REPEATED LOADS ON THE CRITERION OF DEFORMATION DESTRUCTION

Ресурсоекономні матеріали, конструкції, будівлі та споруди ◽

10.31713/budres.v0i37.335 ◽

2020 ◽

pp. 106-117

Author(s):

E M Babich ◽

S S Gomon

Keyword(s):

Bearing Capacity ◽

Cross Section ◽

Strain State ◽

Repeated Loading ◽

Building Structures ◽

Deformation Method ◽

Stress Strain ◽

Stress Strain State ◽

Layer Deformation

Existing norms of design for wooden constructions valid in different countries including Ukraine entirely disregard the effect of low-cycle repeated loadings during the operation of buildings and structures. The article deals with development of the bearing capacity computation of the bending elements manufactured from solid and glue-laminated wood exposed to repeated loadings in accordance with the deformation model.Equilibrium equations for computing the bending element made of wood after being exposed to repeated loadings are presented in the article. The deformation method is proposed for the computation of the rectangular wooden beams manufactured from solid and glued laminated wood with allowance for the occurrence of folds in the compression zone.The results of the research allow designing the solid and glue-laminated wooden constructions taking into consideration the possibilities of the material and peculiar features of the performance of the element, which in turn will allow choosing the cross-section of the elements of building structures more economically.On the basis of the study of the process of layer deformation by section height and the determination of the characteristics of the stress-strain state of these layers under the effect of repeated loading, it is possible to fulfill more accurate computation of the elements manufactured from wood at different stages of the stress-strain state through destruction.

Download Full-text

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

Collection of Research Papers of the National Mining University ◽

10.33271/crpnmu/64.166 ◽

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.

Download Full-text

Stress-strain state of enclosing rock mass around an arbitrary cross-section excavation by measurement of displacements of the excavation walls

Journal of Mining Science ◽

10.1134/s1062739114010037 ◽

2014 ◽

Vol 50 (1) ◽

pp. 18-24 ◽

Cited By ~ 5

Author(s):

A. I. Chanyshev ◽

I. M. Abdulin

Keyword(s):

Rock Mass ◽

Cross Section ◽

Strain State ◽

Arbitrary Cross Section ◽

Stress Strain ◽

Stress Strain State

Download Full-text

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

Structural Mechanics of Engineering Constructions and Buildings ◽

10.22363/1815-5235-2019-15-4-261-270 ◽

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.

Download Full-text