SUMMARYThe result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning.

SUMMARYThe results of an experimental investigation on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. It is shown that two common types of steady state response are harmonic and 1/3 subharmonic response. The measured steady state response amplitudes correlate well with theoretical predictions for both harmonic and 1/3 subharmonic responses. Within each type of steady state response, theoretical studies show that the system may respond in either a symmetric or an unsymmetric mode. A symmetric mode denotes that the block oscillates about a mean zero position while an unsymmetric mode implies the mean position of oscillation is at an inclined position. One form of unsymmetric response was observed in the experiment. In addition, almost periodic responses were also observed in the experiment, although their existence has not been reported in theoretical studies.

Dynamic analysis is in general accepted as the best method to obtain the seismic load distribution for buildings with a setback. However, most building codes require the base shear obtained by dynamic analysis to be calibrated by the static base shear obtained using the code's equivalent static load procedure. In obtaining the code static base shear, two issues often arise among the design professionals. First, it is unclear whether the code static base shear is applicable for buildings with setbacks because the period prescribed by the code to be used in the base shear formula is in general not pertinent to buildings with setbacks. Second, it is uncertain whether the higher mode period should be used in computing the base shear when the modal weight of a higher mode is larger than that of the fundamental mode -a case often encountered in designing buildings with setbacks. This paper is an attempt to resolve the above issues. For the first issue, modification factors were derived for adjusting the code period formula so that it can provide a more reasonable estimate for the period of a building with a setback. For the second issue, it was demonstrated in this paper that for cases where the modal weight of a higher mode is larger than that of the fundamental mode, using the higher mode period for base shear calculation will result in unnecessarily conservative design.Key worcls: earthquake, seismic, irregular buildings, setback, dynamic analysis.Regle gCnCrale, I'analyse dynamique est reconnue comme la meilleure mCthode pour obtenir la rkpartition de la charge sismique des bitiments qui ont des dCcrochements. Cependant, la plupart des codes du bltiment exigent que le cisaillement h la base obtenu h l'aide de I'analyse dynamique soit calibre en fonction du cisaillement statique h la base obtenu en utilisant la procCdure de charge statique Cquivalente du code. En calculant le cisaillement statique h la base, les concepteurs font face h deux problemes. D'une part, il n'est pas certain que le cisaillement statique h la base soit applicable aux bltiments ayant des dCcrochements car la pCriode qui doit Etre utilisCe dans la formule de cisaillement h la base ne s'applique pas aux bitiments avec dCcrochements. D'autre part, il n'est pas certain qu'il faille utiliser la periode des modes plus ClevCe dans le calcul du cisaillement h la base lorsque le poids modal du mode plus ClevC est supCrieur h celui du mode fondamental, une situation h laquelle sont souvent confrontis les concepteurs de bitiments avec dCcrochements. Cet article tente d'apporter une rCponse h ces questions. Dans le premier cas, des coefficients de modification ont CtC calculCs afin d'ajuster la formule de periode du code de maniere h obtenir une estimation plus raisonnable de la pCriode d'un bitiment ayant des dCcrochements. Dans le second cas, il est dCmontrC que, lorsque le poids modal du mode plus ClevC est superieur h celui du mode fondamental, l'utilisation de la pCriode des modes plus ClevCe dans le calcul du cisaillement a la base se traduira par ...

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