Formulas for calculating the deflection and displacement of a planar truss support with short studs in a lattice

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The calculation of deformations of building structures is usually carried out by the finite element method in numerical form  [1]–[3]. Analytical methods are used much less often in engineering calculations. For regular trusses with periodically repeating structures in the lattice, in [4]–[7], together with operators of computer mathematics systems, the method of induction is used, which makes it possible to derive calculation formulas for an arbitrary order of structure regularity. Problems of regular statically determinate rod systems were dealt with by Hutchinson, R.G. and Fleck, N.A.   [8], [9]. Matrix methods and graph theory in the calculations of regular planar and spatial trusses in relation to their optimization were applied by  Kaveh A. [10]–[12]. In the papers [13]–[18], by induction in the Maple system, solutions were obtained for the problems of deflection of various planar  trusses with an arbitrary number of panels. An analytical estimate of the first natural frequency of oscillations of planar and spatial trusses was found in [19]–[21]. A two-sided estimate of the first frequency of a regular truss in an analytical form using the Maple system was obtained in [22]. The article [23] proposes a two-node method for predicting the effective elastic properties of a periodic cellular truss. The continuum representation for calculating a regular truss is used in [24]. In [25], in the problem of periodic truss networks based on the concepts of the quasi-continuum method, the decomposition of a regular truss lattice into simple Bravais lattices is used. To reduce computational costs while accurately taking into account the dominant deformation mechanisms, a homogenized continuum description of lattice trusses is introduced in [26], based on the application of the Cauchy–Born multilattice rule to a representative unit cell. The author's handbooks [27], [28] contain schemes of planar static determinate trusses and formulas for calculating their deflections and forces in characteristic rods. Analytical methods for calculating a regular truss in relation to the problem of optimization taking into account creep were also used in [29].