This paper investigates the rocking response and stability analysis of an array of slender column... more This paper investigates the rocking response and stability analysis of an array of slender columns caped with a rigid beam which are vertically restrained with elastic prestressed tendons that pass through the centerline of the columns while anchored at the foundation and the cap-beam. Following a variational formulation, the nonlinear equation of motion is derived in which the stiffness and the prestressing force of the tendons are treated separately. In this way, the postuplift stiffness of the vertically restrained rocking frame can be anywhere from negative to positive depending on the axial stiffness of the vertical tendons. The paper shows that the tendons are effective in suppressing the response of rocking frames with small columns subjected to long-period excitations. As the size of the columns, the frequency of the excitations, or the weight of the cap-beam increases, the vertical tendons become immaterial given that most of the seismic resistance of tall rocking frames originates primarily from the mobilization of the rotational inertia of their columns. The paper concludes with the presentation and validation of an equivalent rigid-linear system so that the rocking response of vertically restrained rocking frames can be computed with popular open-source or commercially available software simply by employing existing elastic-mutilinear elements.
A half century ago, Housner (1963) explained that there is a safety margin between uplifting and ... more 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.
This paper investigates the rocking response and stability analysis of an array of slender column... more This paper investigates the rocking response and stability analysis of an array of slender columns caped with a rigid beam which are vertically restrained with elastic prestressed tendons that pass through the centerline of the columns while anchored at the foundation and the cap-beam. Following a variational formulation, the nonlinear equation of motion is derived in which the stiffness and the prestressing force of the tendons are treated separately. In this way, the postuplift stiffness of the vertically restrained rocking frame can be anywhere from negative to positive depending on the axial stiffness of the vertical tendons. The paper shows that the tendons are effective in suppressing the response of rocking frames with small columns subjected to long-period excitations. As the size of the columns, the frequency of the excitations, or the weight of the cap-beam increases, the vertical tendons become immaterial given that most of the seismic resistance of tall rocking frames originates primarily from the mobilization of the rotational inertia of their columns. The paper concludes with the presentation and validation of an equivalent rigid-linear system so that the rocking response of vertically restrained rocking frames can be computed with popular open-source or commercially available software simply by employing existing elastic-mutilinear elements.
A half century ago, Housner (1963) explained that there is a safety margin between uplifting and ... more 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.
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Papers by Nikos Upatras