This report investigates the transient rocking response of anchored electrical equipment and other anchored structures that can be approximated as rigid blocks. Practical issues that control over-turning, such as the effect of the vertical component of ground accelerations and the effect of the coefficient of restitution during impact, are also addressed.
The anchorages of equipment are assumed to have a pre-yielding linear behavior, a finite post-yielding strength, and some ductility. The nonlinear behavior of the restrainers in conjunction with the nonlinear dynamics of a rocking block yield a set of highly nonlinear equations which are solved numerically using a state-space formulation. The study uncovers that while for most of the frequency range, anchored blocks survive higher accelerations than free-standing blocks, there is a short frequency range where the opposite happens. This counterintuitive behavior is the result of the many ways that a block might overturn. It is shown that under a one-sine (Type-A) pulse or one-cosine (Type-B) pulse with frequency ωp, a free-standing block with fre- quency parameter has two modes of overturning; one with impact (mode 1), and one without impact (mode 2). The transition from mode 1 to mode 2 is sudden, and once ωp /p is sufficiently large, then a substantial increase in the acceleration amplitude of the one-sine pulse is needed to achieve overturning. When a block is anchored the transition from mode 1 to mode 2 happens at slightly larger values of ωp /p, and this results in a finite frequency range where a free-standing block survives acceleration levels that are capable of overturning the same block when it is anchored. The presence of restrainers is effective in preventing toppling of small, slender blocks. Prior to the transition from mode 1 to mode 2, the presence of restrainers has a destructive effect. When blocks overturn without impact (mode 2) the presence of restrainers has a marginal effect.
Furthermore, the investigation concludes that the effect of the vertical component of recorded ground motions is marginal and virtually does not affect the level of the horizontal acceleration needed to overturn an electrical equipment. An increasingly inelastic impact (smaller coefficient of restitution) results in smaller angles of rotation; however, the values of the impact velocities might be occasionally larger.
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