Abstract
AbstractThe statically defined truss is triangular in plan and is supported on three sides by vertical posts. One of the corners supports is a spherical joint, the other is a cylindrical joint. The truss panels are regular triangular pyramids with pivoting rods. The task is to obtain a formula for the dependence of the deflection of the truss on the number of panels, the load, and the distribution of the stiffness characteristics of the rods. The regularity property of the construction is used to output the formula. The coefficients in the calculation formula are calculated by induction, the form of which does not depend on the number of panels. The operators of the Maple computer mathematics system, the knot - cutting method for calculating forces in rods, and the Maxwell-Mohr's formula for finding deflection are used. To determine the general terms of the coefficient sequences the linear homogeneous recurrent equations are compiled and solved. The solution is obtained in polynomial form. Formulas for the reactions of supports and forces in the most compressed and stretched rods are obtained. A horizontal asymptote is found that restricts the deflection dependence on the number of panels from below, and it is inclined to curves of deflection dependence on the height of the structure.KeywordsSpatial trussInductionDeflectionAnalytical calculationMaxwell-Mohr's formula
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