A dynamic analysis procedure for hinge-controlled masonry arches subjected to horizontal acceleration profiles is developed. Constructed from the principle of energy conservation, the establishment of equivalent systems and the path independence of conservative work, a time-incremental analysis structure is established for kinematic propagation. Equivalent systems are defined through combining kinematic equilibrium with static deformations of the single degree of freedom mechanism through parametric plotting. This generates the minimum work required to propagate the arch towards collapse. For a constant acceleration above the static limit, energy conservation requires the transformation of excess work' into kinetic energy. The path independence of work creates a spatial kinetic energy equation that is used to establish the time domain of the system. Knowing the initial position and kinetic energy thus allows the final position and kinetic energy to be determined for the time increment. A new constant acceleration and timestep then propagates the behaviour through the acceleration profile.

中文翻译：

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铰链控制砌体拱的工作路径方法地震建模

开发了一种受水平加速度剖面影响的铰链控制砌体拱的动态分析程序。从能量守恒原理、等价系统的建立和守恒功的路径独立性出发，建立了运动学传播的时间增量分析结构。通过参数绘图将运动平衡与单自由度机构的静态变形相结合来定义等效系统。这产生了将拱形传播到塌陷所需的最小工作量。对于高于静态极限的恒定加速度，能量守恒需要将多余的功转化为动能。功的路径独立性创建了一个空间动能方程，用于建立系统的时域。因此，知道初始位置和动能允许确定时间增量的最终位置和动能。然后，新的恒定加速度和时间步长通过加速度曲线传播行为。