Effect of Supplemental Hysteretic and Viscous Damping on Rocking Response of Free-Standing Columns

Dynamic rocking response of a rigid planar block on a nonlinear hysteretic Winkler foundation

“…Figure 8A illustrates the scollop-shaped failure envelope in the non-dimensional V-H-M space, which is symmetric about the planes of = 0 and = 0, as is also seen in Figure 8B. Figure 8C shows that without rocking moment, Equation (27) reduces to an semielliptical bounding surface of 2 + 2 = 1 with negative cutoff, which takes the same functional form as Equation ( 26), due to the self-similarity between the mesoscopic point-wise shearcompression behavior and the macroscopic sliding-settlement foundation response. Figure 8D shows that Equation (27) coincides with the classical Meyerhof's solution of = − 2 to the bearing capacity of foundations under combined vertical and rotational loading.…”

“…Figure 8C shows that without rocking moment, Equation (27) reduces to an semielliptical bounding surface of 2 + 2 = 1 with negative cutoff, which takes the same functional form as Equation ( 26), due to the self-similarity between the mesoscopic point-wise shearcompression behavior and the macroscopic sliding-settlement foundation response. Figure 8D shows that Equation (27) coincides with the classical Meyerhof's solution of = − 2 to the bearing capacity of foundations under combined vertical and rotational loading. It is shown that the normalized ultimate foundation rocking moments are lower at low regions due to the uplifting-dominated response where geometrical nonlinearity arising from loss of contact results in localized soil plasticity within a small contact region.…”

“…Of practical interests are small-to-medium sized slender objects such as storage tanks, [18][19][20] electrical equipment, [14,16,21] and building contents. [17,22,23] Attempts have also been made to suppress overturning potential using restrainers, [24,25] control devices, [26][27][28][29] or the combination of both, [30][31][32] in order to reduce or exploit rocking motions in a controlled manner. It has been shown that the seismic rocking response is so sensitive to the imperfections of the rocking objects, the supporting surface, and the details of the excitation that perfectly repeatable testing results are practically not possible; however, the peak rocking rotation demand is generally predictable using the Housner's model [3] in a statistical sense.…”

Response analysis of yielding structures coupled to rocking walls with supplemental damping

“…When the dampers are attached at the pivoting points of the rocking wall ( and ), they become essentially zero‐length elements (as is the configuration of the torsionally yielding steel beam dampers installed in the piers of the South Rangitikei Rail Bridge 6,44 ), Equations () and () simplify to: while with .…”

Seismic control of flexible rocking structures using inerters

“…Dimitrakopoulos and DeJong 13 studied the response of rigid blocks connected to linear viscous dampers (VDs) and showed that supplemental damping can efficiently improve the seismic stability of rocking structures. A similar approach was later applied by Makris and Aghagholizadeh 14 to the protection of free‐standing bridge piers. Alternative passive approaches have also been proposed by a number of researchers.…”