Static analysis of a stepped main shaft in a mine hoist by means of the modified 1D higher-order theory

The analysis of a stepped main shaft by 1D refined beam theories in cylindrical coordinate system is presented. High-order displacement fields are achieved by employing the Carrera unified formulation (CUF), which takes direct implementation of any-order theory without the requirement of considering special formulations. The classical beam theories can be derived from the formulation as particular cases. The principle of minimum potential energy is used to obtain the governing differential equations and the related boundary conditions in a cylindrical coordinate system. These explicit terms of the stiffness matrices are exhibited and a global stiffness matrix is then obtained by matrix transformation. For the special working condition in a mining hoist and stepped shaft, the resulting global stiffness matrix and the loading vector are modified and applied with the boundary conditions in the static analysis of shaft parts. The accuracy of static analysis based on the refined beam theory is confirmed by comparing ANSYS solid theory and classical beam theories. An experiment for verifying the availability of the modified 1D refined beam model on the surface strain of segment 9 of the main shaft is conducted in a field experiment at Zhaojiazhai Coal Mine, China. Experimental results demonstrate the practicability of the present theory in predicting the strain field on the surface of the stepped main shaft of a mining hoist.