Model of a spatial cantilever truss and formulas for calculating its deformations

The object of research is a spatial lattice statically determinate regular cantilever truss formed by connecting eight plane trusses. The truss is loaded at its nodes. The longitudinal stiffness of the bars is assumed to be equal. Formulas are derived for the dependence of the truss end deflection on its dimensions and the number of panels. Method. The forces in the bars are found in analytical form using computer mathematics methods by solving a system of algebraic equations. The Maxwell — Mohr formula is used. Generalization of the solutions to the case of an arbitrary number of panels is performed by induction. Results. The resulting formulas for the deflections have the form of polynomials in the number of panels. Formulas are derived for the forces in individual, most critical bars. Asymptotic forms of the solutions are found.