Post-earthquake survey and structural analysis prove that the vertical seismic action can damage buildings and bridges, even those with regular configuration. Moreover, there is evidence that one principal axis of ground motion may be not vertical. The inelastic demand to regular building structures is assessed here considering both uncorrelated and cross-correlated random seismic components, concurrent to deterministic weight. The method is conventional statistical equivalent linearization. Planar reinforced-concrete frames are analyzed parametrically varying the number of stories, the design ductility class, or the foundation ground type, as well as variance and cross-covariance of the vertical seismic component. Following a lumped plasticity approach, the bending moment-rotation relationship is a Bouc-Wen equation extended for asymmetry and interaction with axial force. Based on mean values, variances, and percentiles of response, the effect of uncorrelated vertical excitation is appreciable only on stress resultants of little practical consequence. Much more important is the effect of cross-correlated vertical excitation. As extreme results, the interstory drift demand increases up to four times. The rotation ductility demand to columns, less than 2 under uncorrelated excitations, rises to 5, meaning very likely yielding of columns designed as strong. The probability of axial force in the columns being tensile grows from negligible value to 8%. The beams may yield also around mid-span. The frame plastic mechanism worsens towards soft story, the peak deformation ductility being demanded more than the cyclic ductility. Not only variance of the vertical ground motion, but also cross-covariance with the horizontal one should be considered in the near field.
