In this work, the Theory of Plastic Mechanism Control (TPMC) is combined with a probabilistic method to account for the influence of random material variability. Reference is made to steel Moment Resisting Frames (MRFs) equipped with FREEDAM connections. FREEDAM connections are beam-to-column connections equipped with friction dampers to dissipate the seismic input energy. TPMC is used to guarantee that in case of destructive seismic events the structural members such as beams and columns remain undamaged. To this scope, the structure is designed to assure a collapse mechanism characterized by the activation of all the friction dampers of the beam ends and the formation of plastic hinges at the base of the first storey columns only. From the probabilistic point of view, the random uncertainties are given by the static friction coefficient of the contact surfaces and the preloading of the bolts of the friction dampers as well as the yielding resistance of the steel members. The failure domain is related to all the possible failure events, where the term “failure” concerns the development of an undesired mechanism different from the global one. Generally, the design conditions to prevent undesired collapse mechanisms are stochastic events within the framework of the kinematic theorem of plastic collapse. The limit state function corresponding to each event can be represented by a hyperplane in the space of random variables. Consequently, the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states of each single failure event. Since dissipative zones (member ends or friction dampers) in the frame members are common to many different mechanisms, the single limit state functions are correlated. Therefore, the probability of failure can be evaluated by means of the Bimodal or Ditlevsen bounds by assuming that the failure events are located in series. The output of the work is a simple relationship which provides the overstrength factor of FREEDAM connections to be considered in the column design phase to account for random material variability thus assuring a given level of reliability in the application of TPMC.

中文翻译：

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配备 FREEDAM 连接的钢抗弯框架的概率设计程序

在这项工作中，塑性机制控制理论 (TPMC) 与概率方法相结合，以解释随机材料变化的影响。参考配备 FREEDAM 连接的钢制力矩框架 (MRF)。 FREEDAM 连接是梁柱连接，配备摩擦阻尼器以消散地震输入能量。 TPMC 用于保证在发​​生破坏性地震事件时，梁、柱等结构构件不会损坏。在此范围内，该结构的设计旨在确保塌陷机制，其特征是梁端部的所有摩擦阻尼器均被激活，并且仅在第一层柱的底部形成塑料铰链。从概率的角度来看，随机不确定性由接触面的静摩擦系数、摩擦阻尼器螺栓的预紧力以及钢构件的屈服阻力给出。故障域与所有可能的故障事件相关，其中“故障”一词涉及与全局机制不同的不良机制的发展。一般来说，防止意外塌陷机制的设计条件是塑性塌陷运动学定理框架内的随机事件。每个事件对应的极限状态函数可以用随机变量空间中的超平面来表示。因此，失效域是由与每个单个失效事件的极限状态相对应的超平面相交而产生的表面。由于框架构件中的耗散区（构件端部或摩擦阻尼器）对于许多不同的机构来说是共用的，因此单个极限状态函数是相关的。因此，可以通过假设故障事件连续发生，通过双峰或 Ditlevsen 界限来评估故障概率。这项工作的输出是一个简单的关系，它提供了在塔设计阶段要考虑的 FREEDAM 连接的超强系数，以考虑材料的随机变化，从而确保 TPMC 应用中给定的可靠性水平。