Earthquake response analysis of yielding structures coupled with vertically restrained rocking walls

Abstract

Summary This paper investigates the inelastic response of a yielding structure coupled with a vertically restrained rocking wall. The paper first derives the nonlinear equations of motion of a yielding oscillator coupled with a vertically restrained rocking wall, and the dependability of the one‐degree of freedom idealization is validated against the nonlinear time‐history response analysis of a well‐known nine‐story moment‐resisting steel frame that is coupled with a stepping, vertically restrained rocking wall. While, the coupling of weak building frames with rocking walls is an efficient strategy that controls inelastic deformations by enforcing a uniform interstory‐drift distribution, therefore, avoiding mid‐story failures, the paper shows that even for medium‐rise buildings the effect of vertical tendons on the inelastic structural response is marginal, with the exception of increasing the vertical reactions at the pivoting points of the rocking wall. Accordingly, the paper concludes that for medium‐rise to high‐rise buildings, vertical tendons in rocking walls are not beneficial.

Dynamic response and impact energy loss in controlled rocking members

“…More recently, these investigations were extended to analytically characterize the seismic responses of controlled rocking frame systems 40 and the behavior of controlled rocking walls coupled with monolithic building frames. 41 In all these cases, impact energy loss was obtained using SRM's r model. Following the above-referenced research on controlled rocking motions, this paper develops a CRM to address the following limitations pertaining to modeling of rocking structural members: during rocking motions, the contact between a structural member and the foundation base occurs over a finite length instead of a point at the member's bottom corner as evidenced in a number of controlled rocking experiments (eg, previous studies 7, 10,18,19,24,27 ).…”

“…This is illustrated in this section by comparing the CRM with experimental responses of the three controlled rocking members described above. To demonstrate these improvements, this section includes comparisons with the SRM's assumption used in previous analyses of controlled rocking members (eg,), suggesting that they pivot about their bottom corners (ie, NA → 0 for all values of θ ).…”

“…Controlled rocking motions were also investigated by Barthes et al and Vassiliou and Makris to account for the use of vertical unbonded tendons, as shown in Figure B. More recently, these investigations were extended to analytically characterize the seismic responses of controlled rocking frame systems and the behavior of controlled rocking walls coupled with monolithic building frames . In all these cases, impact energy loss was obtained using SRM's r model.…”

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).…”

Displacement‐based analysis and design of rocking structures

“…Makris and Vassiliou and Vassiliou and Makris have suggested that as the size of the rocking system increases, the restraining system can become obsolete and merely increases the design forces of both the superstructure and the foundation. In buildings, rocking walls have been suggested as a resilient design approach (Makris and Aghagholizadeh and Aghagholizadeh and Makris and references therein).…”