基于薄板理论的空区顶板稳定性分析

考虑作用于顶板上的均布载荷及作用于顶板上方中心处的集中载荷情况下,基于四边固支矩形薄板的纳维叶解法,分别导出了均布载荷与集中载荷作用下矩形顶板的挠度方程与应力表达式.分析得到四边固支矩形板在均布载荷和集中载荷作用下的高应力主要出现在板的中心以及长边的中点处,影响应力的因素主要包括厚度、载荷大小、板的尺寸以及泊松比.依据第一强度理论建立均布载荷和集中载荷共同作用下的顶板安全性控制方程,并求解得到其安全临界顶板厚度,并通过工程实例验证了该控制方程的正确性.

Analysis on Roof Stability of Gob Area Based on Thin Plate Theory

Gob area in open-pit mine directly influences safe production of operating personnel and large equipment. Based on Navier's solving method of rectangular thin plate with completed clamped supported, deflection equation and stress expressions under uniform load and concentrated load were derived separately, which turns out that the high stress under uniform load and concentrated load is mainly concentrated at the center of the plate and the midpoint of the long side. The factors that influence the stress are thickness, loading condition, dimension and Poisson ratio of the plate. In accordance with the first strength theory, the roof safety equations under uniform load and concentrated load were established, and the critical safety roof thickness was calculated. At last, the correctness of the equations was verified by engineering examples.