MECHANISMS OF PLASTIC DESTRUCTION OF ARCHES

The method of determining the limit load for double-hinged and hingeless arches of fixed and variable rigidity is considered. The calculation is performed using the limit equilibrium method. Arches under the influence of a vertical uniformly distributed load are considered. The cross section is taken in the form of a non-reinforced rectangle. The stress-strain state of an elastic-plastic material is described by the Prandtl diagram. The peculiarities of material deformation are that the yield limits in tension and compression are different. The determination of the limit load is based on taking into account only one factor - the bending moment. When a limiting moment occurs in the arch section, a plastic hinge is formed, which allows unlimited angular deformation without increasing the bending moment. When several plastic hinges are formed, the design diagram of the arch turns into a mechanism. Of course, this approach leads to inaccuracies in determining the limit load. However, at the first stage of the study, the task was to study in detail the features of the plastic mechanism of arch destruction. To study the limiting state of the arches, two methods were used - analytical calculation and numerical calculation using the finite element method. The use of two calculation methods allows you to control the results and increase their reliability. Using analytics, formulas were obtained to determine the limit load and coordinates of the sections where plastic hinges are formed. For arches of constant stiffness, formulas are written to determine the limit load, and for arches of variable stiffness, nonlinear equations are written, the solution of which allows us to find the limit load. For the numerical calculation, a simple method was used, when at each stage of the calculation the coordinate of the formation of the plastic hinge and the corresponding load were determined. The calculation program is written in APDL. As a result of the study, it was revealed that a hingeless arch, depending on the ratio of the lifting boom to the span, has three forms of plastic destruction, while a double-hinged arch has only one form of plastic destruction.