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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]

A nonlinear hardening rule that defines a yield surface translation for homogeneous frame member materials is proposed. The rule is defined as a nonlinear constitutive relationship that examines material behavior through a postelastic perspective. The gradual development of the postelastic states of a beam along its length and through its section thickness is analyzed. The model uses a hardening index parameter to guide the nonlinear stress–strain relationship, and a smooth function to model the web–flange intersection of frame members. As such, nonlinear curvature distributions with continuous derivatives are determined along the length of the member, which enables lateral displacements to be accurately predicted. Plastic hinge lengths and finite-element displacements are subsequently determined, and a nonlinear stiffness is derived. The model is formulated on a constitutive level and applies a smoothed-over cross section to derive a single internal moment expression for any postelastic state. Results are verified through experimental published literature. [ABSTRACT FROM AUTHOR]