Analysis of the buckling of spatial truss with cross lattice

Kirsanov, Mikhail

doi:10.5862/mce.64.5

Cited by 18 publications

(13 citation statements)

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“…A rare feature of this solution is the presence of the number of panels n in the denominator of the formula. All known solutions [10][11][12][13][15][16][17][18][19][20] have the form of polynomials of different degrees. The calculation of a series of trusses reveals sequences of coefficients for 3 a , 33    is obtained.…”

Section: Resultsmentioning

confidence: 99%

“…The search for schemes of statically determinate trusses was carried out by R. G. Hutchinson and N. A. Fleck [15]. In [16][17][18][19], the induction method solved more complex problems for spatial constructions, in [19] for the problem of a pile foundation with a regular arrangement of piles. In [20], the method of double induction (based on the number of panels in height and the number of panels along the length of the span) was used to calculate the planar truss.…”

Section: Introductionmentioning

confidence: 99%

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Analytical calculation of the combined suspension truss

2019

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An algorithm is given for obtaining the formula for the dependence of the deflection of a regular planar truss of an arched type with a suspended lower belt on the number of panels. The cases of uniform loading of the nodes of the upper and lower belts by a vertical load are considered. To generalize a number of solutions obtained in the system of computer mathematics Maple to an arbitrary case, an induction method was applied. For this purpose, for a sequence of coefficients of the particular solutions found, a common term is determined which is a solution of the recurrence equation. The deflection was determined with the help of Mohr's integral, which depends on the forces in the rods. Forces in a statically determinate construction were performed by cutting out nodes from the solution of a system of equations written in a matrix form. The analytical dependence of displacement of the mobile support on the number of panels is found.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical calculation of the combined suspension truss

2019

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“…These solutions and their combinations can be used for assessment of accuracy and reliability of the numerical results obtained in specialized packages of structural mechanics (Samofalov, Ziukas, 2015). Compact analytical solutions by induction method on the basis of the program (Kirsanov, 2012) were obtained in (Ilin, Kirsanov, 2016;Kirsanov, 2016a;Kirsanov, 2016b;Ponamareva, 2016;Dong, Kirsanov, 2016;Voropai, Kazmiruk, 2016;Voropai, 2016;Shipaeva, 2016;Bolotina, 2016). The comparative review of some analytical solutions is given in (Tinkov, 2015).…”

Section: Resultsmentioning

confidence: 99%

The Mathematical Model of Dome Covering Industrial Facility

Kirsanov

Astahov

2017

AEJ

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A statically determinate flat truss models the industrial facility's arch. To derive dependence of structural deflection on the number of panels in a span, the Maxwell-Mohr equation, computer mathematics system Maple and the induction method are applied. Forces in the rods are determined by the method of cutting nodes. Several cases of loading are considered: uniformly distributed along the top and bottom chords, uniformly distributed along the lateral surface, and by concentrated force. For analytical assessment of the structural strength, equations for forces in the most compressed and tensioned rods and equation for support displacement are derived. Asymptotics of the solution for the number of panels at the fixed span length, and total load is found.

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“…The proposed method is based on algorithms of nonlinear analysis of structures implemented and tested in the computer program PRINS for other types of structures [9]. The results obtained by the authors of this article earlier [10][11] and the domestic [12][13][14][15][16][17] and foreign [18][19][20][21] experience in the development of nonlinear methods of hinge-rod systems analysis were used.…”

Section: Introductionmentioning

confidence: 99%

Calculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method

Агапов

Golovanov

Aidemirov

2017

IOP Conf. Ser.: Earth Environ. Sci.

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PAPER • OPEN ACCESSCalculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method Abstract. The technique of calculation of prestressed reinforced concrete trusses with taking into account geometrical and physical nonlinearity is considered. As a tool for solving the problem, the finite element method has been chosen. Basic design equations and methods for their solution are given. It is assumed that there are both a prestressed and nonprestressed reinforcement in the bars of the trusses. The prestress is modeled by setting the temperature effect on the reinforcement. The ways of taking into account the physical and geometrical nonlinearity for bars of reinforced concrete trusses are considered. An example of the analysis of a flat truss is given and the behavior of the truss on various stages of its loading up to destruction is analyzed. A program for the analysis of flat and spatial concrete trusses taking into account the nonlinear deformation is developed. The program is adapted to the computational complex PRINS. As a part of this complex it is available to a wide range of engineering, scientific and technical workers IntroductionThe design of prestressed reinforced concrete structures, including reinforced concrete trusses, is currently conducted using empirical and semi-empirical formulas [1]. These formulas do not take into account all the features of the work of prestressed systems associated with the nonlinearity of deformation, with loading, unloading and possible reloading (change in the direction of deformation) due to a sharp redistribution of forces in the event of failure of one or another element. Recommendations for accounting for the nonlinearity of the deformation of concrete and reinforcement [2], which are given in the building norms and acts and annexes to them, carry conventional character. In addition, the normative documents practically do not contain recommendations for taking into account the geometric nonlinearity. Therefore, the development of methods for analysis of prestressed reinforced concrete structures, taking into account physical and geometrical nonlinearity, which makes it possible to determine the load-bearing capacity of structures, is a vital task. This work is devoted to the analysis of prestressed reinforced concrete trusses taking into account the nonlinearity of deformation by the finite element method. A prerequisite for the successful solution of this problem is the general theory of truss analysis, the foundations of which were laid in the nineteenth century [3] and developed later in the works of domestic and foreign scientists [4][5][6][7][8].

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Analysis of the buckling of spatial truss with cross lattice

Cited by 18 publications

References 0 publications

Analytical calculation of the combined suspension truss

Analytical calculation of the combined suspension truss

The Mathematical Model of Dome Covering Industrial Facility

Calculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method

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