Installation diagram of the lattice truss with an arbitrary number of panels
Hereby the diagram of a flat statically determinate regular lattice truss with the parallel chords is proposed. The task is to obtain an analytical dependence of the truss deflection and forces in the most tension and compressed bars on the number of panels. In order to solve the problem, the Maple computing mathematical system is used. We have considered the case when the lower truss chord is subject to a uniform load. The forces are determined by the Method of Joint. The Maxwell-Mohr formula is used to determine the deflection. The solution obtained for a set of cases with different successively increasing numbers of panels is generalized to a random number of panels by method of induction. The special operators of the Maple system are used to prepare homogeneous linear recurrence relations that are satisfied with the sequences of coefficients in the required formula. It is shown that for the number of panels in the half-span that are divisible to three, the determinant of the equilibrium equation system is becoming zero. The truss is becoming kinematically changeable that is confirmed by the corresponding diagram of possible joint velocity. The algorithm for the truss installation diagram is described, where the cross bars are in different planes and are connected in the nodes so that the truss elements are not subjected to buckling. The solution of this problem is related to the correct edge coloring of graphs and hypergraphs.