Граничний стан армованих двошарнірних арок двотаврового перерізу

Abstract

The method of determining the limit load for double-hinged arches is considered. The calculation is performed using the limit equilibrium method. The cross-section of the arch is taken in the form of a reinforced I-beam. The strain-deformed state of the I-beam material is described by the Prandtl diagram. But unlike the classical diagram, it has different yield points under tension and compression. The reinforcement material is described by the classic Prandtl diagram with the same yield strength in tension and compression.In most cases, the ultimate equilibrium of the cross-section is based on the use of one factor ˗ the plastic moment, upon reaching which the cross-section enters a plastic state with the possibility of unlimited deformation. But such an approach cannot be adopted for an arch, as significant longitudinal forces arise in its sections. Ignoring longitudinal forces leads to errors in determining the ultimate load. Therefore, for arches, when determining the limit state of the cross section, it is important to take into account both the bending moment and the longitudinal force. That is, for the transition of the section to the limit state, it is necessary to apply a limit moment to it, which corresponds to a certain longitudinal force. This leads to the concept of the region of cross-sectional strength, constructed in the coordinates of the bending moment - longitudinal force. The boundary of this region indicates the limit state of the cross-section and is described by the flow conditions, which can be obtained by considering the plastic equilibrium of the cross-section. Using the flow conditions, the equilibrium equation of the arch and some constraints, it is possible to formulate an optimization problem for finding the limit load. Limit load (objective function) is the smallest load that satisfies the arch equilibrium equation, yield conditions and constraints. The project variable is the coordinate of the cross-section that enters the plastic stage. The solution of this problem for arches of constant and variable stiffness was performed using electronic spreadsheets. Arch calculations were also performed in PC Lira-CAD. A comparison of the calculation results showed a satisfactory convergence.