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In the framework of seismic design of structures, response spectrum analysis (RSA) is the most commonly used approach in practice. The most popular combination rule is the complete quadratic combination (CQC) which is also prescribed by the most of seismic design codes and is based on the assumptions that the seismic acceleration is a white noise process and the peak factor ratios associated to the total and modal responses are unitary. Recently, the damping adjusted combination (DAC) rule has been developed for base-isolated structures to overcome the aforementioned simplified assumptions. Although it has been proved that the simplifications about peak factors lead to noticeable errors in the case of base-isolated structures, the accuracy gain of DAC with respect to CQC in the case of fixed-base structures is still unknown. Therefore, the paper presents an in-depth study on the RSA of three-dimensional frame structures, aimed to evaluate the accuracy of the above methods. Two reference classes of frame structures having different degree of complexity are considered. Average interstorey drift and floor torsion responses, obtained from a set of Time History Analyses are compared with those of the modal combination rules. Lognormal joint probability density functions of the predictive errors from CQC and DAC are finally evaluated for a reliability assessment of the two combination rules under bidirectional seismic excitations.

Infill masonry walls in framed structures make a significant contribution to the response under seismic actions. With special regard to reinforced concrete (RC) structures, it is known that internal forces modifications caused by the frame–infill interaction may be not supported by the surrounding frame because of the additional shear forces arising at the ends of beams and columns. Such additional forces may lead to the activation of brittle collapse mechanisms and hence their prediction is basic in capacity assessment, especially for structures that disregard the details for seismic zones. In this paper a parametric study is carried out addressed to the prediction of the shear forces mentioned before. The results of this study can be used as a support when the simplified model is adopted consisting in the substitution of infill with an equivalent pin jointed concentric strut, because in this case the structural analysis fails in the prediction of the shear forces in question. Through the paper, in which existing RC infilled frames designed only for vertical loads are discussed, analytical laws, depending on the level of the axial force arising in a concentric strut equivalent to infill, are proposed, the above analytical law allowing to correct the local shear forces in the frame critical sections, which are not predictable in the case of substitution of infill with an equivalent concentric strut.