The Role of the Rotational Inertia on the Seismic Resistance of Free-Standing Rocking Columns and Articulated Frames

A half century ago, Housner (1963) explained that there is a safety margin between uplifting and overturning of slender, free-standing columns and that as the size of the column or the frequency of the excitation increases, this safety margin increases appreciably to the extent that large, free-standing columns enjoy ample seismic stability. This paper revisits the important implications of this postuplift dynamic stability and explains that the enhanced seismic stability originates from the difficulty of mobilizing the rotational inertia of the free-standing column. As the size of the column increases, the seismic resistance (rotational inertia) increases with the square of the column size, whereas the seismic demand (overturning moment) increases linearly with size. Accordingly, in theory, a slender, free-standing column can survive any ground shaking provided that the column is sufficiently large, because a quadratic term eventually dominates over a linear term. The same result applies to the articulated rocking frame given that its dynamic rocking response is identical to the rocking response of a single free-standing column with the same slenderness but larger size.