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Author: Admin | 2025-04-28
\varphi_{1} (x) + \theta_{0} \frac{1}{2\alpha }\varphi_{2} (x) - M_{0} \frac{{2\alpha^{2} }}{{kb_{2} }}\varphi_{3} (x) - Q_{0} \frac{\alpha }{{kb_{2} }}\varphi_{4} (x) + \frac{{q_{0} }}{{kb_{2} }}\left[ {1 - \varphi_{1} (x - x_{i} )} \right], \, x \in \left[ {x_{i} ,x_{i + 1} } \right] \hfill \\ y_{0} \varphi_{1} (x) + \theta_{0} \frac{1}{2\alpha }\varphi_{2} (x) - M_{0} \frac{{2\alpha^{2} }}{{kb_{2} }}\varphi_{3} (x) - Q_{0} \frac{\alpha }{{kb_{2} }}\varphi_{4} (x), \, x \in [0,x_{i} ] \hfill \\ \end{gathered} \right.$$ (28) where$$\left\{ \begin{gathered} \varphi_{1} (x) = {\text{ch}}\left( {\alpha x} \right)\cos \left( {\alpha x} \right) \hfill \\ \varphi_{2} (x) = {\text{ch}}\left( {\alpha x} \right)\sin \left( {\alpha x} \right) + {\text{sh}}\left( {\alpha x} \right)\cos \left( {\alpha x} \right) \hfill \\ \varphi_{3} (x) = {\text{sh}}\left( {\alpha x} \right)\sin \left( {\alpha x} \right) \hfill \\ \varphi_{4} (x) = {\text{ch}}\left( {\alpha x} \right)\sin \left( {\alpha x} \right) - {\text{sh}}\left( {\alpha x} \right)\cos \left( {\alpha x} \right) \hfill \\ \end{gathered} \right.$$ (29) 3.2.2 Rib pillar compression under dynamic loads of the mining haul truckSince the compression of the rib pillar under the dynamic loads of a fully-load truck is greater than that of a no-load truck, only the compression of the rib pillar under the dynamic load of a fully-loaded truck is discussed. As shown in Fig. 6, the rib pillar group between two permanent rib pillars is taken as the research object along the direction of the haulage bench in the end slope.Fig. 6Dynamic load of front and rear wheels of a mining haul truck under full loadFull size imageWhen calculating the compression of dynamic loads of a mining haul truck on the rib pillar, the rib pillar-roof model can be regarded as a plane strain model. In this model, displacement boundary conditions are adopted, and fixed boundary conditions are employed by the left and right sides. Combined with the Winkler elastic foundation
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