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根据砌体梁理论，上覆岩层破断以后仍可以形成能够承受载荷的稳定岩体结构，因此老顶通常以给定变形的方式作用于直接顶。这使得在老顶给定变形下直接顶成为一个混合边界条件的复杂力学问题，其位移至今尚未给出。根据“砌体梁”理论的支架一围岩整体力学模型，运用能量变分方法对老顶给定变形情况下直接顶的变形进行了初步求解，进而探讨了顶板下沉量、支架工作阻力、直接顶高度、直接顶弹性模量及老顶回转角之间的相互关系。
According to the masonry beam theory, the overlying strata can still form stable rock mass structure capable of withstanding load after the overburden is broken, so the old roof usually acts on the direct roof in a given deformation. This makes it a complicated mechanical problem that the direct top becomes a hybrid boundary condition given a given deformation of the roof and the displacement has not been given so far. According to the overall mechanical model of the surrounding rock of “Masonry beam” theory, the energy deformation method is used to solve the deformation of the direct roof under a given deformation of the roof. Then the roof subsidence, work resistance, Direct top height, direct top elastic modulus and the relationship between the old top slew angle.