Limit state of arches made of elastoplastic material.

This paper considers the application of the limit equilibrium method to the calculation of a double hinged circular arch loaded with a uniformly distributed vertical load. It is assumed that the arch has a rectangular cross-section made of a homogeneous elastic plastic material with different tensile and compressive yield strengths. The peculiarity of the limit state calculation is that the section works elastically until the transition to a plastic state of the entire section. If the action of the longitudinal force is not taken into account, in the limiting state a classical plastic joint is formed in the cross-section, which allows unlimited rotation relative to each other of the sections located infinitely close to the plastic joint. If the bending moment and the longitudinal force are taken into account simultaneously in the limit state, the possibility of unlimited rotation and unlimited linear displacement of the sections located infinitely close to the origin of the plasticity arises. In order to calculate the limit load for an arch, it is first necessary to obtain a dependence describing the strength area of the cross-section. This dependence relates the ultimate moment and ultimate longitudinal force for the section and is often referred to as the yield stress condition. In this paper the yield stress conditions for rectangular sections of arches with constant and variable stiffness are presented. Using yield conditions of the section and equations of balance of the arch it is possible to construct and solve an optimization problem for finding the minimum load which satisfies both equilibrium and yield equations. Thus, the target function of the problem is the value of ultimate load and the design variable is the coordinate of section which goes into the plastic stage. This problem was solved by means of spreadsheets. Also non-linear calculations of arches with constant and variable stiffness were performed in PC Lira-SAPR. Comparison of the calculation results showed their satisfactory convergence. [ABSTRACT FROM AUTHOR]