The stability of low-pitched von Mises trusses with horizontal elastic supports

Abstract. Purpose. The work’s aim is to study the horizontal supports stiffness impact, which simulate the conditions for supporting the domes upper tier on the von Mises trusses' stability. Methodology. A three-hinged truss' deformed scheme under applying a concentrated vertical load in the ridge joint was considered. An analytical method was used to obtain a generalized equation for the three-hinged trusses' stability criterion to determine the critical load depending on the design system's parameters such as the rods' inclination angle, the rods' stiffness, and the horizontal elastic supports stiffness. A two transcendental equations' system for the dependence of the load on vertical and horizontal displacements taking into account the rods' compression was obtained. Such equations' system's analytical solution through a generalized parameter - a variable rods' angle tangent, made it possible to obtain one equation for the dependence of the vertical load on the vertical and symmetric horizontal supports' displacement. The truss' stability numerical studies were carried out depending on the structure's design geometry. Findings. An analytical expression of the dependence for the load on the structure, which was reduced to the rod’s stiffness depending on the rods’ angle to the horizontal stiffness of the supports, was obtained. The low-pitched double-rod three-hinged trusses' nonlinear deformation nature depending on the elastic supports' stiffness and the rods' angle was confirmed. It was found that with the two-rod low-pitched three-hinged systems’ nonlinear deformation nature the ridge joint's snap-through effect takes place. It was found that the relative reduced critical load value decreases along with the rods' inclination angle decrease depending on the horizontal supports' stiffness. Scientific innovation. On the theoretical studies basis of the three-hinged two-rod low-pitched trusses with elastic horizontal supports deformed scheme a generalized analytical equation for the such systems' solution was obtained. The generalized analytical solution models the dome system annular elements stiffness through the horizontal supports' stiffness and determines the general lower tier elements stiffness effect on the dome uppermost tier structural system stability. Practical value. The obtained analytical equation makes it possible to determine the dome annular elements rational design parameters to ensure the upper tier stability.