Overturning instability of a two-rigid block system under ground excitation

The rocking response of a freely standing two-rigid block 2-DOF system under ground excitation is comprehensively presented. The highly nonlinear governing equations of motion, properly established, under certain conditions may be linearised leading after integration to closed form solutions. The analysis is based on the assumption that friction at the interface between the two-rigid blocks or the lower block and the ground is sufficient to prevent sliding. All possible configuration patterns exhibited by the two-rigid block system during rocking motion are examined in detail. Attention is focused on the determination of the minimum amplitude ground acceleration among all patterns which leads the system to overturning instability. The effect of week damping is included in the analysis by reducing the relative angular velocity after impact. Conditions for overturning instability with or without impact, either between the two blocks or between the lower block and the ground, associated with an escaped motion in the phase-plane portrait, are thoroughly discussed. It is found that for moderately large values of excitation frequencies overturning instability occurs after impact. Beyond these values overturning instability without impact prevails. In case of overturning instability without impact, surprisingly enough, it was also found that there are ranges of values of excitation frequencies in which a monolithic rigid block as a 1-DOF system becomes more stable when divided into two equal rigid blocks, acting as a 2-DOF system. The rocking response of a freely standing two-rigid block 2-DOF system under ground excitation is comprehensively presented. The highly nonlinear governing equations of motion, properly established, under certain conditions may be linearised leading after integration to closed form solutions. The analysis is based on the assumption that friction at the interface between the two-rigid blocks or the lower block and the ground is sufficient to prevent sliding. All possible configuration patterns exhibited by the two-rigid block system during rocking motion are examined in detail. Attention is focused on the determination of the minimum amplitude ground acceleration among all patterns which leads the system to overturning instability. The effect of week damping is included in the analysis by reducing the relative angular velocity after impact. Conditions for overturning instability with or without impact, either between the two blocks or between the lower block and the ground, associated with an escaped motion in the phase-plane portrait, are thoroughly discussed. It is found that for moderately large values of excitation frequencies overturning instability occurs after impact. Beyond these values overturning instability without impact prevails. In case of overturning instability without impact, surprisingly enough, it was also found that there are ranges of values of excitation frequencies in which a monolithic rigid block as a 1-DOF system becomes more stable when divided into two equal rigid blocks, acting as a 2-DOF system. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Mathematical micromodeling of infilled frames:state of the art

The in-plane contribution of infill walls on the structural response of infilled frame structures is an important problem and many research initiatives, via experimental and numerical methods, have been conducted in order to investigate it thoroughly. As a result, the need to consider these research findings on the structural performance has been acknowledged in the latest generation of structural design codes. However, due to the uncertainties concerning the behavior of masonry at the material and structural level, these elements are usually ignored during practical structural analysis and design. They are overtly considered only when there is suspicion that their influence is detrimental to the overall structural response or to the behavior of individual load bearing elements or when it is necessary to justify an improvement in the overall load-carrying capacity or structural performance in general. In this paper, a thorough overview of the different micromodels proposed for the analysis of infilled frames is presented, and the advantages and disadvantages of each micromodel are pointed out (this paper follows our recent review paper on the state-of-the-art of the mathematical macromodeling of infilled frames, thus completing the overview of both macro- and micro- models in the field). Practical recommendations for the implementation of the different models are also presented