Analysis of the buckling of spatial truss with cross lattice
The construction of a beam type spatial truss is proposed. The truss consists of three plane trusses with a cross lattice. The supports of the structure are modeled at the four corner points. The simple analytical dependence of the structure deflection on its size, load and a number of panels has been found for the case of an even number of panels. In the case of an odd number of panels the system is kinematically changeable, which is evident from the zero determinant of the system of equilibrium equations. The system of Maple computer algebra and the method of induction, previously proposed and developed by the author when solving the problems of planar and spatial trusses has been used. A nonmonotonic dependence of the deflection on the number of panels and the expected increase in stiffness at the increased truss height and unexpected decrease in stiffness at an increased base width have been found. The forces in some members of the truss change the sign depending on the parity of the number of panels in half of a span. Asymptotes of the solution are detected. The features of the solution allow optimizing the size of the structure.