Calculation of deformations of a cantilever-frame planar truss model with an arbitrary number of panels

Buka-Vaivade, Karina; Kirsanov, Mikhail; Serdjuks, Dmitrijs

doi:10.22227/1997-0935.2020.4.510-517

Cited by 12 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We set the task to determine in an analytical form the deflection of the cantilever and the horizontal displacement of the top. We use a program written in the language of computer mathematics Maple to calculate the forces in the rods [7]. Nodes and rods are numbered.…”

Section: Solution Method Truss Schemementioning

confidence: 99%

See 1 more Smart Citation

Formulas for Calculating Deformations of Power Line Supports

Astakhov¹,

Kirsanov²,

Vorob′yev³

2022

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

In this work, we investigate the static deformations of the spatial model of a statically determined truss of a power line support. The tetrahedral truss has a pyramidal extension at the base and a cross-shaped lattice. Brackets for attaching the supporting cables are located at the top of the truss. A spherical support hinge, a cylindrical one, and two vertical posts are located at the four corners of the structure base. We consider two types of loads: wind, and force. Horizontal forces applied to the nodes of one face model the wind load. The horizontal force is applied to the top of the structure. We aim to derive formulas for the dependence of the deflections of the truss on the number of its panels. We use the Maxwell-Mohr formula to determine the deflection. We find the efforts in the structural elements and the reactions of the supports from the general system of linear equations of equilibrium of all nodes of the truss. A series of solutions for trusses with different numbers of panels are summarized by the induction method in the Maple computer mathematics system. The sought formulas for the dependence of the vertical deflection of the console and the displacement of the top of the mast on the number of panels were obtained in the form of polynomials in the number of panels of degree not higher than the fourth. Some asymptotics of solutions is found in the work.

show abstract

Section: Solution Method Truss Schemementioning

confidence: 99%

“…This allows the engineer to select the optimal variant of the designed structure in an analytical form. One of the methods for solving this problem is the induction method [7]. A number of solutions for the statics of flat arches were obtained by this method [8,9].…”

Section: Introductionmentioning

confidence: 99%

Formulas for Calculating Deformations of Power Line Supports

Astakhov¹,

Kirsanov²,

Vorob′yev³

2022

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

show abstract

“…Here the choice was made in favour of the Maple system [21], which has a more intuitive interface. In the language of this system, there is a software for calculating forces in the truss rods [22]. We use this software to calculate the proposed coverage.…”

Section: Methodsmentioning

confidence: 99%

“…Using data on the structure and coordinates of nodes, guiding cosines of forces that make up the matrix of the system of equilibrium equations for all nodes are calculated. This system also includes support reactions as unknown values [22].…”

Section: Methodsmentioning

confidence: 99%

Analytical calculation of deformations of a truss for a long span covering

Kirsanov

2020

Vestnik MGSU

Self Cite

View full text Add to dashboard Cite

Introduction. The method of induction based on the number of panels is employed to derive formulas designated for deflection of a square in plan hinged rod structure, which has supports on its sides and which consists of individual pyramidal rod elements. The truss is statically determinable and symmetrical. Some features of the solution are identified on the curves constructed according to derived formulas. Materials and methods. The analysis of forces arising in the rods of the covering is performed symbolically using the method of joint isolation and operators of the Maple symbolic math engine. The deflection in the centre of the covering is found by the Maxwell–Mohr’s formula. The rigidity of truss rods is assumed to be the same. The analysis of a sequence of analytical calculations of trusses, having different numbers of panels, is employed to identify coefficients, designated for deflection and reaction at the supports, in the final design formula. The induction method is employed for this purpose. Common members of sequences of coefficients are derived from the solution of linear recurrence equations made using Maple operators. Results. Solutions, obtained for three types of loads, are polynomial in terms of the number of panels. To illustrate the solutions and their qualitative analysis, curves describing the dependence of deflection on the number of panels are made. The author identified the quadratic asymptotics of the solution with respect to the number of panels. The quadratic asymptotics is linear in height. Conclusions. Formulas are obtained for calculating deflection and reactions of covering supports having an arbitrary number of panels and dimensions if exposed to three types of loads. The presence of extremum points on solution curves is shown. The dependences, identified by the author, are designated both for evaluating the accuracy of numerical solutions and for solving problems of structural optimization in terms of rigidity.

show abstract

Model and Analytical Calculation of a Spatial Truss

Kirsanov

2021

Lecture Notes in Civil Engineering

View full text Add to dashboard Cite

Calculation of deformations of a cantilever-frame planar truss model with an arbitrary number of panels

Cited by 12 publications

References 15 publications

Formulas for Calculating Deformations of Power Line Supports

Formulas for Calculating Deformations of Power Line Supports

Analytical calculation of deformations of a truss for a long span covering

Model and Analytical Calculation of a Spatial Truss

Contact Info

Product

Resources

About