Seismic response of rocking frames with top support eccentricity

Abstract

Summary The seismic response of rocking frames that consist of a rigid beam freely supported on rigid freestanding rectangular piers has received recent attention in the literature. Past studies have investigated the special case where, upon planar rocking motion, the beam maintains contact with the piers at their extreme edges. However, in many real scenarios, the beam‐to‐pier contact lies closer to the center of the pier, affecting the overall stability of the system. This paper investigates the seismic response of rocking frames under the more general case which allows the contact edge to reside anywhere in‐between the center of the pier and its extreme edge. The study introduces a rocking block model that is dynamically equivalent to a rocking frame with vertically symmetric piers of any geometry. The impact of top eccentricity (ie, the distance of the contact edge from the pier's vertical axis of symmetry) on the seismic response of rocking frames is investigated under pulse excitations and earthquake records. It is concluded that the stability of a top‐heavy rocking frame is highly influenced by the top eccentricity. For instance, a rocking frame with contacts at the extreme edges of the piers can be more seismically stable than a solitary block that is identical to one of the frame's piers, while a rocking frame with contacts closer to the centers of the piers can be less stable. The concept of critical eccentricity is introduced, beyond which the coefficient of restitution contributes to a greater reduction in the response of a frame than of a solitary pier.

Dynamics of a sliding‐rocking block considering impact with an adjacent wall

“…Dar et al evaluated the ASCE 43‐05 seismic criteria for components vulnerable to overturning in nuclear facilities. There has also been notable interest in the seismic stability of structures consisting of rigid block assemblages, such as vertical block stacks (Allen et al; Psycharis; Spanos et al; Konstantinidis and Makris; Wittich and Hutchinson) and rocking frames (Makris and Vassiliou; DeJong and Dimitrakopoulos; Drosos and Anastasopoulos; Dar et al). The response of freestanding blocks in 3D has also been studied (Konstantinidis and Makris; Chatzis and Smyth; Zulli et al), albeit to a lesser extent than planar rocking becasue of the complexity involved.…”

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

“…Rocking has been proposed as a seismic isolation method for both bridges [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and buildings, [17][18][19][20][21] because uplift works as a mechanical fuse and limits the design forces of both the superstructure and the foundation. Unlike structures designed to yield, the free rocking rigid block 22 of Figure 1A,B exhibits negative post-uplift stiffness ( Figure 1C).…”

Rolling and rocking of rigid uplifting structures

“…Since then, a plethora of papers on rocking structures has been published studying these structures theoretically [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and experimentally. Their systematic study started after the 1960 Chilean earthquake, when Housner published his seminal paper 1 on the behavior of "inverted pendulum structures."…”

“…Their systematic study started after the 1960 Chilean earthquake, when Housner published his seminal paper 1 on the behavior of "inverted pendulum structures." Since then, a plethora of papers on rocking structures has been published studying these structures theoretically [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and experimentally. [17][18][19][20][21][22] The rocking oscillator has been used in bridge engineering, [23][24][25][26][27][28][29][30][31][32][33][34] as well as to model the behavior of masonry walls, [35][36][37][38][39][40] of ancient temples, [41][42][43] of unanchored equipment, and of museum artifacts.…”