Dynamic response and impact energy loss in controlled rocking members

Abstract

Summary Unbonded posttensioning anchors a rocking structural member to its foundation and produces its controlled rocking response when the member undergoes seismic action. Unlike rocking of free‐standing bodies, little attention has been given to the dynamic behavior of these controlled rocking members. This paper utilizes experiments of concrete structural members with unbonded posttensioning, varying member geometries, and levels of initial posttensioning force to (a) characterize the associated impact energy loss and (b) improve modeling of controlled rocking motions. Experimental results show that impact energy loss in controlled rocking members can be captured accurately using the coefficient of restitution (r) approach of the modified simple rocking model (MSRM). Based on the MSRM, a controlled rocking model (CRM) is developed that additionally accounts for the variations in contact length at the member‐to‐foundation (rocking) interface. The CRM reproduces the experimental responses of controlled rocking members with good accuracy and is used to investigate controlled rocking motions under horizontal base excitations.

Seismic behavior of unbonded post-tensioned precast concrete members with thin rubber layers at the jointed connection

“…Using three precast concrete members representing columns and walls, Kalliontzis et al 9 quantified impact energy loss in terms of a coefficient of restitution r. 11 Accordingly, a generalized formula was developed, which assumes that the coefficient of restitution r is a function of the geometric properties of the precast concrete members and their pivot point locations just before and just after the impacts. A more recent study 10 showed that the experimental measurements of impact energy loss by Nazari et al 8 agreed with the generalized formula. 9 The same study 10 corroborated that precast concrete members with jointed connections may undergo large lateral drifts when subjected to horizontal ground motions.…”

“…F igure 1 shows a precast concrete member with a jointed connection at the foundation base that uses unbonded post-tensioning, a concept that has been used for precast concrete structures for the past two decades. [1][2][3][4][5][6][7][8][9][10] When subjected to lateral loads, the bottom corner of the member uplifts as it undergoes a rocking motion. During this motion, the member response is controlled by the axial force developed in the unbonded post-tensioning tendon, which recenters the member upon removal of the loads, concentrating inelastic deformations at its toes.…”

“…Several research studies [1][2][3][4][5][6][7] focused on the quasi-static behavior of these members, neglecting the impact energy loss. More recently, Nazari et al 8 and Kalliontzis et al 9,10 used shake table and free vibration tests, respectively, to investigate the impact energy loss. To achieve appropriate test conditions, the test specimens included no supplemental hysteresis elements (such as those used by Sritharan et al 6 and Twigden et al 7 ).…”

Uniform risk spectra for rocking structures

“…The only source of energy dissipation in the system is impact damping, which is assumed to happen instantaneously. This assumption is valid for rocking structures with protected ends and no extra damping mechanism but might deviate from reality when the column ends are not protected 62,63 . When the system is returning to its original position and its displacement equals to the uplift displacement ( u up ) (i.e., when the system is “downcrossing” u up ), the integration is halted, and its post‐impact velocity is calculated by a coefficient of restitution ( r c ): $$\begin{equation}{r_c} = \frac{{{{\dot u}_{post - impact}}}}{{{{\dot u}_{pre - impact}}}}\end{equation}$$…”

Review on the rocking wall systems as a self-centering mechanism and its interaction with floor diaphragm in precast concrete structures

“…However, this approach is not preferred as it mainly involves mathematical formulations. Hu et al (2018) and Kalliontzis et al (2020) are among the researchers who utilize the numerical analysis approach in their works. Together, some design guidelines, procedures, verification and validation document have been published by researchers on the rocking wall system.…”