Optimized design of bi-rocking steel braced frames via changing the second rocking joint location

After an earthquake, plastic deformation of structural elements can render repairing uneconomical, thus necessitating the adoption of low-damage systems that mitigate the residual drift of structures. Among these, self-centering rocking-core systems have been extensively explored. However, due to the geometric nonlinearity of such systems, higher modes dominate their seismic responses, which necessitates the incorporation of secondary rocking joints to minimize their effects. Nevertheless, identifying the optimal location of such joints is challenging, given the redistribution of internal forces between the rocking plates. In this context, a bi-rocking steel braced frame is designed using the modified modal superposition method (MMS), accounting for higher mode effects. Subsequently, the secondary joint is moved floor by floor to determine its optimal location that minimizes shear, overturning moment, peak floor acceleration, and drift. To represent damage to non-structural components, peak floor acceleration and drift are chosen as key parameters. Three sets of seven ground motions, namely Far-Field (FF), Near-Field-Pulse (NF-Pulse), and Near-Field-no-Pulse (NF-No Pulse), are considered for frames of 12, 18, and 24 stories, modeled using OpenSees software in 2-dimensional frameworks. A total of 1071 non-linear time-history analyses are carried out, and the results indicate that the conventional practice of placing the secondary joint in the mid-height is inadequate for the 12-story frame under NF-Pulse records, causing a 15.1% deviation from the optimal state of overturning moment. In most cases, placing the joint at 40% height reduces all four demands. To evaluate demand sensitivity, the standard deviation of their percentage difference with the optimal state is computed, with higher values indicating greater unpredictability. Among the sets of records, FF and among demands, overturning moment exhibit the highest sensitivity to the location of the secondary joint, with changes in overturning moment being correlated with shear. Therefore, we suggest selecting overturning moment as an optimization objective function.