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The effect of the rotational inertia on the post-uplift dynamic stability of free-standing rocking columns and articulated frames

A half century ago G. Housner 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 post-uplift dynamic stability and explains that the enhanced seismic stability originates from the difficulty to mobilize 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 is sufficiently large, given that 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; yet, with larger size.

Author(s):

Nicos Makris    
University of Central Florida
United States