SUMMARY This paper is concerned with the superÿcial similarities and fundamental diierences betwe... more SUMMARY This paper is concerned with the superÿcial similarities and fundamental diierences between the os-cillatory response of a single-degree-of-freedom (SDOF) oscillator (regular pendulum) and the rocking response of a slender rigid block (inverted pendulum). The study examines the distinct characteristics of the rocking spectrum and compares the observed trends with those of the response spectrum. It is shown that the rocking spectrum reeects kinematic characteristics of the ground motions that are not identiÿable by the response spectrum. The paper investigates systematically the fundamental diierences in the dynamical structure of the two systems of interest and concludes that rocking structures cannot be replaced by 'equivalent' SDOF oscillators. The study proceeds by examining the validity of a simple , approximate design methodology, initially proposed in the late 1970s and now recommended in design guidelines to compute rotations of slender structures by performing iteration either on the true displacement response spectrum or design spectrum. This paper shows that the simple design approach is inherently awed and should be abandoned, in particular for smaller, less-slender blocks. The study concludes that the exact rocking spectrum emerges as a distinct intensity measure of ground motions.
This paper investigates the seismic response of freestanding equipment when subjected to strong e... more This paper investigates the seismic response of freestanding equipment when subjected to strong earthquake motions (2% probability of being exceeded in 50 years). A two-step approach is followed because the displacement limitations of the shake table do not permit full-scale experiments. First, shake table tests are conducted on quarter-scale wooden block models of the equipment. The results are used to validate the commercially available dynamic simulation software Working Model 2D. Working Model is then used to compute the response of the full-scale freestanding equipment when subjected to strong, 2% in 50 years hazard motions. The response is dominated by sliding, with sliding displacements reaching up to 70 cm. A physically motivated dimensionless intensity measure and the associated engineering demand parameter are identified with the help of dimensional analysis, and the results of the numerical simulations are used to obtain a relationship between the two that leads to ready-to-use fragility curves.
The seismic isolation code which must be used for all seismic isolated buildings in the United St... more The seismic isolation code which must be used for all seismic isolated buildings in the United States is conservative in many of its provisions. While seismic isolation is flourishing in other countries, it is underused in the United States. For static analysis and for the selection of time histories, the spectrum is constant-velocity for periods of one second and longer, leading to large displacements for long period systems and forcing the designer to use added damping to reduce these displacements. The damping systems used are hysteretic with the characteristic that damping decreases with increasing displacement. To achieve the damping needed to reduce these large displacements, expected from very rare seismic input, means that at smaller displacements, caused by realistic levels of seismic input, the damping will be very much higher, and there may be stiffening of the isolation system, meaning that the building may not act as isolated and there may be an impact on sensitive internal equipment. This paper shows how highly damped isolation systems are counterproductive to isolation and suggests an alternative approach that will conform to code requirements but ensure that, at moderate earthquake inputs, the equipment remains protected, and the large code-mandated displacements are kept to acceptable levels.
SUMMARY This paper is concerned with the superÿcial similarities and fundamental diierences betwe... more SUMMARY This paper is concerned with the superÿcial similarities and fundamental diierences between the os-cillatory response of a single-degree-of-freedom (SDOF) oscillator (regular pendulum) and the rocking response of a slender rigid block (inverted pendulum). The study examines the distinct characteristics of the rocking spectrum and compares the observed trends with those of the response spectrum. It is shown that the rocking spectrum reeects kinematic characteristics of the ground motions that are not identiÿable by the response spectrum. The paper investigates systematically the fundamental diierences in the dynamical structure of the two systems of interest and concludes that rocking structures cannot be replaced by 'equivalent' SDOF oscillators. The study proceeds by examining the validity of a simple , approximate design methodology, initially proposed in the late 1970s and now recommended in design guidelines to compute rotations of slender structures by performing iteration either on the true displacement response spectrum or design spectrum. This paper shows that the simple design approach is inherently awed and should be abandoned, in particular for smaller, less-slender blocks. The study concludes that the exact rocking spectrum emerges as a distinct intensity measure of ground motions.
This paper investigates the seismic response of freestanding equipment when subjected to strong e... more This paper investigates the seismic response of freestanding equipment when subjected to strong earthquake motions (2% probability of being exceeded in 50 years). A two-step approach is followed because the displacement limitations of the shake table do not permit full-scale experiments. First, shake table tests are conducted on quarter-scale wooden block models of the equipment. The results are used to validate the commercially available dynamic simulation software Working Model 2D. Working Model is then used to compute the response of the full-scale freestanding equipment when subjected to strong, 2% in 50 years hazard motions. The response is dominated by sliding, with sliding displacements reaching up to 70 cm. A physically motivated dimensionless intensity measure and the associated engineering demand parameter are identified with the help of dimensional analysis, and the results of the numerical simulations are used to obtain a relationship between the two that leads to ready-to-use fragility curves.
The seismic isolation code which must be used for all seismic isolated buildings in the United St... more The seismic isolation code which must be used for all seismic isolated buildings in the United States is conservative in many of its provisions. While seismic isolation is flourishing in other countries, it is underused in the United States. For static analysis and for the selection of time histories, the spectrum is constant-velocity for periods of one second and longer, leading to large displacements for long period systems and forcing the designer to use added damping to reduce these displacements. The damping systems used are hysteretic with the characteristic that damping decreases with increasing displacement. To achieve the damping needed to reduce these large displacements, expected from very rare seismic input, means that at smaller displacements, caused by realistic levels of seismic input, the damping will be very much higher, and there may be stiffening of the isolation system, meaning that the building may not act as isolated and there may be an impact on sensitive internal equipment. This paper shows how highly damped isolation systems are counterproductive to isolation and suggests an alternative approach that will conform to code requirements but ensure that, at moderate earthquake inputs, the equipment remains protected, and the large code-mandated displacements are kept to acceptable levels.
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Papers by Dimitrios Konstantinidis