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A practical design method to retrofit existing RC buildings with viscous dampers
Published in Günther Meschke, Bernhard Pichler, Jan G. Rots, Computational Modelling of Concrete Structures, 2018
R. Gobirahavan, A.C. Wijeyewickrema
The current earthquake design level is defined from U.S. Seismic design maps based on the provisions of IBC 2015 at the same location of the building. A total of seven far-fault ground motions (Table 1) are selected from the Pacific Earthquake Engineering Research Centre database (PEER 2017). In the selection process, the following criteria are employed: (i) magnitude of the earthquake MW ≥ 6.5; (ii) the closest distance to the fault rupture 10 < Rrup ≤ 100 km; (iii) the site class for recording station is D. The selected ground motions are scaled to the current earthquake design spectrum in the period range of 0.2T1 to 1.5T1 (Fig. 2). For the buildings considered in this study, the period range is 0.18 s to 3.38 s (the fundamental period T1 of the 4-, 8-, and 12-story buildings are 0.89 s, 1.74 s, and 2.25 s, respectively). The ground motions are applied in the N-S direction of the building.
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Published in Hojjat Adeli, Hongjin Kim, Wavelet-Based Vibration Control of Smart Buildings and Bridges, 2009
A pseudo frequency is defined corresponding to scale a, fa, (in Hz) as a function of the center frequency of wavelet,fc, in the following way (Abry, 1997): fa=fsfcawhere fs is the sampling frequency of the original signal. The inverse of the pseudo frequency is the pseudo period for any given scale a. There is a linear relationship between the pseudo-period and the scale a (representing the frequency of the signal), as noted in Eq. (4.12) and shown in Figure 4.6. Most building structures have a natural period of less than 10 seconds with the exception of very tall (super highrise building) and slender structures. Therefore, as Figure 4.6 indicates, it is sufficient to use scales 1 to 128, corresponding to the pseudo periods of 0.08 seconds to 10 seconds, respectively.
Audio Waveform
Published in Alexander U. Case, Sound FX, 2012
The amplitude versus time plot reveals fundamental information about audio waveforms. A pure-tone sine wave (see Figure 1.3) consists of a simple, never-changing pattern of oscillation. Measure the length of time associated with each cycle to determine the waveform's period. Count the number of times it cycles each second for a determination of its frequency. Period is the time it takes for exactly one cycle to occur, with units of seconds per dimensionless cycle, or simply seconds. Frequency describes the number of cycles that occur in exactly one second, with units of dimensionless cycles per second. Therefore, units for frequency live entirely in the denominator (per second, or/s) and have been given the alternative unit of hertz (Hz).
A Comparative Study on the Interpretation Procedure of Field Tests for Measuring the Dynamic Impedance of a Surface Footing
Published in Journal of Earthquake Engineering, 2023
F. de Silva, C. Amendola, D. Pitilakis, F. Silvestri
The main inertial effects of the dynamic soil-foundation structure (SFS) interaction consist in the elongation of the natural period, which depends on the swaying and rocking stiffness of the foundation, the generation of the radiation damping, accounting for the energy dissipated by the wave scattering from the foundation, and the generation of the hysteretic damping associated to the non-linear behavior of the soil beneath the foundation. The importance of the above effects increases with the foundation displacement and rotation (Karatzetzou and Pitilakis 2018). The period elongation and the wave scattering occur even when the foundation is close to its static equilibrium position and increase when the foundation motion induces significant shear straining in the soil. The hysteretic damping represents the energy loss due to the nonlinear soil response, thus becoming increasingly significant, if not dominant, at large foundation displacements (Gazetas 2015). The quantification of such effects is based on the accurate evaluation of the complex and frequency-dependent soil-foundation impedance, which integrates the stiffness and the damping ratio mobilized in the soil under the oscillating footing.
Investigation of Period-Lengthening Ratio for Single-Degree-of-Freedom Structures Using Dynamic Centrifuge Test
Published in Journal of Earthquake Engineering, 2021
Kil-Wan Ko, Jeong-Gon Ha, Heon-Joon Park, Dong-Soo Kim
Evaluating the natural period (T) of a structure is important for seismic design. As soil changes the period T, many researchers have studied the influence of soil on a structure during an earthquake to achieve sophisticated seismic design. The effect of soil on a structure is called the soil-structure interaction (SSI) or soil-foundation-structure interaction (SFSI). SFSI studies on the dynamic responses of structures have been conducted over the past four decades. For example, Veletsos and Meek [1974] have reported the effects of the SFSI on the dynamic response of a structure by assuming a single-degree-of-freedom (SDOF) structure on a fixed base for a structure on soil. They noted that a structure on soil has more degrees of freedom, such as those relevant to foundation rocking and swaying. In addition, Gazetas [1983] and [1991] has analyzed the dynamic responses of foundations to not only rocking and swaying motions, but also vertical and torsional motions. The additional motion of the foundation changes the dynamic characteristics of the structure; i.e., the T and damping of the structure increase, and these SFSI effects are known as period lengthening and damping increasing, respectively [Jennings and Bielak, 1973; Bielak, 1974; Veletsos and Meek, 1974].
Seismic site effect analysis for the city of Tehran using equivalent linear ground response analysis
Published in International Journal of Geotechnical Engineering, 2020
Reza Behrou, Fardad Haghpanah, Hamid Foroughi
Recorded bedrock motions in BHRC acceleration stations in Tehran are used as input bedrock motions. For this study, bedrock motions recorded during the 2004 Firozabad-Kojour earthquake are used. These motions were recorded in the following rocky stations: Emam zadeh Davood (EMD), Jamshideyeh Park (JAP) and Bibishahrbano (BSH). The recorded time histories in these rocky stations are shown in Figure 6. The acceleration time histories are normalised to the 475-year peak bedrock acceleration, and for each site, response spectrum considering 5% critical damping and site amplification factor, in period ranges of 0.1–0.5 s and 0.1–2.5 s are obtained. Period range of 0.1–0.5 s is considered as the dominant period of typical low-rise buildings (1–2 stories) in the study area, and period range of 0.1–2.5 s is considered as the dominant period of low-rise, high-rise and public buildings.