The influence of direction of the nodal load on stability of the von Mises truss with elastic supports on the example of ribbed domes with rings of steel

Purpose. The aim of this work is to study the influence of the oblique force and elastic resistance of supports that located at the ridge node of truss on stability of von Mises truss. Methodology. In this paper the scheme of deformation of threehinged truss under impact of load that concentrated at the apex of truss at an angle to the vertical axis with the presence of elastic supports was considered. A generalized equation for determining the critical force level of buckling depending on the parameters of calculation scheme was obtained. Numerical studies of truss stability depending on the initial geometry of structure were conducted. A proposed algorithm of detection of the maximum force value using the method of the tangent lines by Newton makes possible to detect the regularities with the different inclination angles of rods, stiffness of elastic supports in the apex of truss and in depending of inclination angle of the concentrated load. Findings. Confirmed the nonlinear deformation of von Mises truss depending on the angles of application force in node, stiffness of elastic supports at the apex of truss. It is shown that the elastic supports increases the critical levels of force. At sufficient rigidity of elastic supports and decreasing of the inclination angle to the horizontal axis of rods buckling of trusses may not occur. This is important to take into account when calculating buckling of dome the nodes of whose are placed between the support and central vertical axis of symmetry. The relative values of critical load have been obtained for a number of structural forms of trusses and it is shown an influence of angle of slope of rods, the values of load and the stiffness of elastic supports in the apex of truss on stability loss of the von Mises truss. Scientific innovation. Based on theoretical studies was obtained generalized analytical equation of balance the function of force which placed at the apex of truss and depends from the displacement of node. This equation of balance is enables to describe the impact on the stability of node of design features of dome and placement of nodes. Equation shows the displacements of the node in space due to the reaction elastic supports. The equation of balance also shows the compression of elements of the truss considering deformations and displacements. Practical value. The obtained analytical equations allows us to determine the limiting rational angles of slope of rods depending from the load and the placement of node in the dome, take account of the features of shape of structure and the scheme of force application.