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The random vibration analyses of gradually yielding shear-frame buildings are considered using a recently proposed constitutive model that is used to calculate the detailed degradation of the stiffness of structures which permits the prediction of their global responses, as well as the states of stress in their members. It is shown that the detailed stress degradation model can also be used in connection with a global force-displacement model, such as the Bouc and Wen model, to predict the time evolution of the various stress-related variables and time passages to failure. The two models are applied in separate analyses and are exemplified using both a single-story building and a four-story building subjected to artificial ground motions. The corresponding probability density functions of the various stress-related responses, including the strains and plastic hinge lengths, and the first time passages to failure are presented and discussed. [ABSTRACT FROM AUTHOR]