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4.1. The decision of a problem of a bending down of physically nonlinear girder of a variable thickness

We investigate the is intense-deformed condition of physically nonlinear girder of a variable thickness. For an estimation of influence on intense - a state of strain of a girder of variable geometrical characteristics, we will consider a girder of a rectangular cross-section from nelinejno - the deformable material which thickness is function of its length.

Initial data for a girder, including the warping chart, we will accept same as in point 3.1. For approximation of experimental data of a nonlinear curved line of a warping it is used cubic splines [13]. Function of a variable thickness of a girder we will accept in the form of a square parabola of a sort (85). The decision of a problem of a bending down of a girder of a variable thickness we will carry out in a dimensionless sort.

For research of the is intense-deformed condition of physically nonlinear girder of a variable thickness it is necessary to solve inkrementalnoe the differential equation (92) under corresponding boundary conditions and variable rigidness of a sort (89).

Let's consider a problem of a bending down of physically nonlinear girder of a variable thickness, boundary conditions on which both ends correspond to conditions of a rigid jamming (99). The girder is under the influence of a uniformly distributed lateral load. In this research it is necessary to estimate influence of a variable thickness of a girder on its is intense-deformed condition, in this connection as variable parametre allowing

To operate the is intense-deformed condition of a girder we accept parametre of a relative thickness λ.nizhe in drawing 73 are resulted epjury girder deflections at various parametre values of a relative thickness λ, and for an estimation of qualitative changes in drawing 74 are resulted same epjury deflections, but normirovannye in unit in the girder centre.

Drawing 73. Epjury deflections at are various parametre values λ

Drawing 74. Epjury deflections, normirovannye to unit in the centre

The results of calculation resulted in drawing 73 show, that with growth of parametre of a relative thickness proishodit essential increase in deflections in the girder centre. From results resulted in drawing 74 it is visible, that besides essential growth of peak values of deflections, in epjurah also there are also qualitative changes on which it is visible, that with parametre increase progiby in girder quarters decrease. However if to compare reduction of deflections in quarters to their increase in the centre these changes are insignificant.

For a better and detailed estimation of change it is intense - a state of strain of a girder more low in drawings 75, 76 are resulted epjury girder moments of flexion at various parametre values of a relative thickness λ.

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From the analysis of results resulted in drawing 75 it is visible, that growth of parametre of a relative thickness proishodit essential redistribution of moments of flexion from the central part of a girder to rigidly restrained edges in this connection at great values of parametre v the central part of a girder there is practically bezmomentnaja a working area.

For more detailed estimation of change of moments of flexion of a girder depending on parametre privedem, in a percentage parity, a difference at λ = 0 (a girder of a constant thickness). Reduction of moments of flexion in the central part of a girder makes: at λ = 0,3 - 25,53 %, at λ = 0,5 - 45,25 %, and at λ = 0,7 - 66,88 %. The increase in moments of flexion in a basic part of a girder (rigid zadelka) makes: at λ = 0,3-14,10 %, at λ = 0,5 - 25,08 %, and at λ = 0,7 - 37,29 %. Thus, it is necessary to notice, that reduction of moments of flexion in the girder centre goes faster, than their growth in a basic working area.

In drawing 77 the schedule of dependence of the maximum pressure in a girder σiот parametre of a relative thickness λ is resulted. On the schedule following marking-offs are resulted: 1 - a curved line of change of the maximum pressure in a basic part of a girder (in rigid zadelke), 2 - a curved line of change of the maximum pressure in the girder centre. In drawing 78 the schedule of change of the maximum pressure in extreme bottom fibres (ζ =-1) on length of a girder is resulted.

From the analysis of the schedule resulted in drawing 77 it is visible, that to growth of parametre of a relative thickness there is a substantial growth of the maximum pressure. Also from the schedule σi (λ) it is visible, that growth of pressure in a basic part of a girder has strongly pronounced linear character, thus in the central part of a girder this dependence accepts strongly pronounced nonlinear character. Also it is necessary to notice, that in a point with λ ≈ 0,56 there is a crossing of schedules from what follows, that in the centre of a girder and in a basic part of pressure accept identical values.

By results resulted in drawings 77 and 78 it is visible, that at the further increase in parametre of a relative thickness λ, that is at λ> 0,56, there is a redistribution of the maximum pressure from a basic part of a girder in its centre. From the analysis of schedules resulted in drawing 78 it is visible, that with parametre growth λ, on length girders limits ξ = 0 - 0,35, occurs vygibanie a stress curve therefore at great values λ pressure in this working area are displaced on distance ≈ 0,1 from zadelki. However despite it the maximum pressure fall to the central part of a girder. At λ = 0,7 pressure in the central part of a girder exceed pressure in a point ξ = 0,1 on 18,25 %.

For more detailed estimation of influence on tensely-state of strain physically nonlinear girder of variable geometrical characteristics, we will consider also a problem of a bending down of physically nonlinear girder of a variable thickness, under the influence of a uniformly distributed lateral load, boundary conditions on which both ends correspond to conditions sharnirnogo opiranija (100).

In drawing 79 are resulted epjury deflections sharnirno opertoj girders at various parametre values λ, and for an estimation of qualitative changes in drawing 80 are resulted same epjury, but normirovannye in unit in the girder centre.

Drawing 79. Epjury deflections at are various parametre values λ

Drawing 80. Epjury deflections, normirovannye to unit in the centre

From epjur resulted in drawing 79 it is visible, that with growth of parametre of a relative thickness proishodit essential increase in deflections in the girder centre, and it is necessary to notice, that the difference between peak values of deflections at ravnom 0,5 and 0,7 is much more than between 0,3 and 0,5. By results resulted in drawing 80 it is visible, that qualitative changes in epjurah deflections are insignificant, and at comparison of these changes with deflection increase in the girder centre, it is possible to tell, that they prenebrezhimo are small.

For the better and detailed analysis of influence of a variable thickness on intense-state of strain sharnirno opertoj girders

Let's consider, resulted more low in drawings 81, 82, epjury moments of flexion at various parametre values of a relative thickness λ.

Drawing 81. Epjury moments of flexion at are various parametre values λ

Drawing 82. Epjury moments of flexion,

normirovannye to unit in the centre

From the analysis of the results resulted in drawings 81 it is visible, that influence of a variable thickness on moments of flexion in sharnirno opertoj to a girder is insignificant. From drawing 81 it is visible, that with parametre growth proishodit increase in moments of flexion in the centre of a girder which at λ = 0 makes: at λ = 0,3-0,35 %, at λ = 0,5-1,49 %, and at λ = 0,7-6,57 %. From the analysis normirovannyh epjur, resulted in drawing 82, it is visible, that qualitative changes in epjurah moments of flexion are small and are shown only at great values of parametre λ.

Let's consider change of the maximum pressure in sharnirno opertoj to a girder at various parametre values of a relative thickness. More low drawing 83 the schedule of dependence of the maximum pressure in a girder σi from parametre λ is resulted. For more detailed analysis of change of the maximum pressure we will consider also, resulted on drawing 84, the schedule of change of the maximum pressure in extreme bottom fibres (ζ =-1) on length of a girder.

The analysis of the schedule resulted in drawing 83 shows, that change of the maximum pressure in the centre of a girder depending on parametre nosit strongly pronounced nonlinear character. Also from the schedule σi (λ) it is visible, that to value λ ≈ 0,45 maximum pressure in the girder centre grow slowly and in regular intervals, however at λ> 0,45 their sharp increase is observed. By results resulted in drawing 84 it is visible, that with growth of parametre of a relative thickness λ, on length of a girder, redistribution of pressure does not occur, their peak value in the girder centre increases only.

4.2.

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A source: MISHCHENKO Roman Viktorovich. CALCULATION of NON-UNIFORM PHYSICALLY NONLINEAR THIN-WALL SPATIAL DESIGNS of the VARIABLE THICKNESS. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. Saratov - 2018. 2018

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