Determining sloped-load limits inside von Mises truss with elastic support

Abstract

The scientific novelty of this work lies in the description of the methods of calculating and analyzing the symmetrical stability loss of the von Mises truss in the case of sloped loads with an elastic support at the top of the truss. In this work, we consider a deformed layout of the von Mises truss with an elastic support under a concentrated load at the apex joint about the vertical axis. Numerical studies were carried out using the proposed methods. This work indicates the impact of the sloped load and elastic support on the truss' stability loss. We determined dependencies of critical external-load values on the rod's starting pitch for different situations. For each design situation, we obtained generalized expressions for determining critical force values for the truss' apex joint. We obtained dependencies and analytical expressions for determining the critical load on the dome structure, based on the initial geometrical parameters, taking into account the reaction of the elastic support at the apex joint and the direction of the external loads. Our studies show that increasing the support's stiffness increases the sustainability of the von Mises truss. Additionally, we obtained new results required for improving the stability of trusses under a sloped load with an angle of 10-40°about the vertical axis.

Tall von-Mises trusses' skew-symmetric deformation

“…The The equation (10.a) is a regularity that describes the truss' deformation in the vertical direction. Equation (10.a) is similar to the von-Mises truss' level of stability, which was obtained in [10]. The equation (10.b) is a regularity that describes the truss' deformation in the horizontal direction with the inclined loading taking into account the elastic support's horizontal reaction.…”

“…The efficiency of using spatial rod systems is due to construction volume approximation's possibility to the functional one on wellknown criterion [6]. Therefore, the stability problems study of rod spatial domes and shells, frame systems with constant and variable cross-section is aimed at creating economic structural systems [7,8,9,10,11,22]. The revealed aspects of calopstic nonlinear deformation of systems found a new direction for complex systems under the influence of destructive loads [12].…”

“…In general, the three-hinged systems, which type is shown at Fig. 1, could be assigned name the tall von-Mises trusses (Mises R. (Richard Edler von Mises) [10,15,25,26].…”

“…Equation (10.а) was well studied for sloped von-Mises trusses with the support racks' angle to the vertical axis α 0l ≥ 70°earlier at the scientific researches [10,15]. Equation (10.а) will became to the well-known equation [] when force's angle is absent β P =0, соsβ P = 1 (formula 11).…”

“…The skew-symmetric shape buckling possibility for the tall von-Mises trusses were investigated in works [10]. The tall von-Mises trusses' deformation with small vertical force's angles (Fig.…”