Stress State in a Shaft Jumper due to Pressure at the Shock Wave Front

The development of coal deposits is accompanied by the release of methane from the destroyed coal and the formation of dust-gas-air mixtures predisposed to chemical reaction, manifested in the form of deflagration or detonation, as a result of which the shock waves are formed in the mine atmosphere, which in the conditions of coal mines can lead to catastrophic consequences. In order to prevent the propagation of shock waves and thermodynamic processes in the mine atmosphere at coal mines, various designs of shaft jumpers are used, for which the technological construction schemes were developed. However, scientifically substantiated and reliable methods for calculating jumpers have not yet been created. To date, the design parameters of the jumpers, primarily their thickness, are assigned on the basis of rather primitive strength calculations, which are based on the design scheme of a thin plate, the thickness of which, by definition, is significantly less than its other dimensions. The thickness of the shaft jumper is comparable to the dimensions of its cross section, which fundamentally contradicts the main requirement for the design scheme of a thin plate. In this regard, it can be said that the existing methods for determining the parameters of the jumpers based on the calculation scheme of a thin plate do not correspond to the actual operating conditions of the jumpers, therefore, they cannot be recommended to ensure the reliability of the shaft jumpers. This article discusses the stress-strain state in a shaft jumper with a circular cross section based on the classical theory of elasticity. The paper formulates a boundary value problem of the stress-strain state of a jumper in a linear formulation, constructs its solution, as a result of which the stress components in the jumper under the action of static pressure caused by a shock wave are found.