An inductive method of calculation of the deflection of the truss regular type

Mikhail Kirsanov


In this paper, the author proposes a regular option of statically determinate flat truss with a lattice of Shukhov's type working under beam scheme. By induction, using Maple computer algebra system, the exact formula for the mid-span deflection under the action of the uniform load is obtained. The deflection of the elastic structure is defined by the formula of Maxwell – Mohr. Forces in the rods are found using cut nodes method with the composition of the management of the matrix of equations in vector form. The analysis of the coefficients in the truss evaluation with a different number of panels revealed the recurrence equation satisfied by these coefficients, and then the determined operators of a specialized package genfunc give a solution of the resulting equation that determines the required general formula. The case of a uniform load on the top horizontal zone is considered. The author obtained a simple asymptotic evaluation of this solution, proving the cubic nature of the growth of deflection for a fixed span length and a given nodal load. The solution found for an even number of panels and rods of the same cross-section, has a polynomial form; the dependence is non-monotonic and detects extremum, which allows optimizing the design.


truss, deflection, induction, exact solution, Maple

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