Equations of the Elastic of a Spatial Lattice from a Continuous Model

GUZMÁN, A. M.; GONZÁLEZ DEL SOLAR, G. A.; ROLDAN, V. A.

doi:10.5540/tcam.2022.024.01.00035

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Articles • Trends Comput. Appl. Math. 24 (1) • Jan-Mar 2023 • https://doi.org/10.5540/tcam.2022.024.01.00035 copy

Equations of the Elastic of a Spatial Lattice from a Continuous Model

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Within metal constructions there are structures made up of parallel members called legs, connected to each other by diagonals. Some of these structures, with a triangular cross section, turn out to be the guyed masts used in the communications industry, but also columns and beams used in metal structures. In the present work, the equations that allow obtaining the equations of the elastic of a spatial lattice of triangular cross section are developed, in which the legs are joined together by zig-zag diagonals. To do this, we start from an energy proposal in which the differential equations of equilibrium and the boundary conditions of the proposed problem are determined. Finally, examples are presented where results are obtained with the equations developed, and they are compared with the results obtained from the application of the expressions given in CIRSOC 303 Recommendation (1996) and from finite element models.

Keywords:
spatial lattice; static; strain energy; differential equations

Case	BC	Load	Proposed equation	Expression CIRSOC 303
A	simply supported	uniformly distributed (q)	$\frac{5}{384} \frac{q_{z} L^{4}}{E J_{z}} (1 + \frac{8}{15} φ)$	$\frac{5}{384} \frac{q_{z} L^{4}}{E J_{z}} (1 + \frac{9.6}{16} φ)$
B	cantilever	Concentrated at the free end (P)	$\frac{1}{3} \frac{P L^{3}}{E J_{z}} (1 + \frac{1}{6} φ)$	$\frac{1}{3} \frac{P L^{3}}{E J_{z}} (1 + \frac{3}{16} φ)$
C	cantilever	uniformly distributed (q)	$\frac{1}{8} \frac{q_{z} L^{4}}{E J_{z}} (1 + \frac{2}{9} φ)$	$\frac{1}{8} \frac{q_{z} L^{4}}{E J_{z}} (1 + \frac{3.1}{16} φ)$
D	fixed-fixed	uniformly distributed (q)	$\frac{1}{384} \frac{q_{z} L^{4}}{E J_{z}} (1 + \frac{8}{3} φ)$	-

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[1] *Corresponding author: Alberto Marcelo Guzmán - E-mail: mguzman@frm.utn.edu.ar