### ANALYTICAL STUDY ON THE RIGIDITY OF STATICALLY DETERMINATE SPATIAL TRUSS

Pages 165-171

Beamlike spatial two-layer symmetric truss is formed by four plane trusses connected by the long sides, and rests on four corner points. Stresses in truss components are defined in a symbolic manner by the method of joint isolation using the Maple computer algebra system. Matrix of the set of equilibrium equations is formed in a cycle according to the number of bars of the truss. For calculation of deflection the Maxwell-Mohr formula is used. The solution is framed for the case of various bar sectional areas and is generalized to an arbitrary number of panels by the method of induction. Operators for formation and solution of recurrence equations are involved for determination of general terms of sequences of coefficients. Certain limit performance and asymptotic characteristics of the structure are found. Formulas for stresses in the most compressed and stretched truss components are derived. Model of statically determinate spatial two-layer truss is proposed. Exact analytical expression for deflection of the truss under action of a concentrated force is found. The used algorithm allows to expand the solution to an action of other loads and methods of supporting. Inhomogeneous distribution of material throughout the structure bars is taken into account in the solution. It enables a designer to choose the most optimal combination of design parameters without making numerical calculations in specialized packages. The proposed two-layer trusses may find practical use in roofs of buildings and structures where a natural interior volume creates additional thermal protection, herewith providing an improvement of strength.

DOI: 10.22227/1997-0935.2017.2.165-171