• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• Journal of The Korean Astronomical Society
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• v.56 no.2
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• pp.169-185
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• 2023

The GMT-Consortium Large Earth Finder (G-CLEF) is the first instrument for the Giant Magellan Telescope (GMT). G-CLEF is a fiber feed, optical band echelle spectrograph that is capable of extremely precise radial velocity measurement. G-CLEF Flexure Control Camera (FCC) is included as a part in G-CLEF Front End Assembly (GCFEA), which monitors the field images focused on a fiber mirror to control the flexure and the focus errors within GCFEA. FCC consists of an optical bench on which five optical components are installed. The order of the optical train is: a collimator, neutral density filters, a focus analyzer, a reimager and a detector (Andor iKon-L 936 CCD camera). The collimator consists of a triplet lens and receives the beam reflected by a fiber mirror. The neutral density filters make it possible a broad range star brightness as a target or a guide. The focus analyzer is used to measure a focus offset. The reimager focuses the beam from the collimator onto the CCD detector focal plane. The detector module includes a linear translator and a field de-rotator. We performed thermoelastic stress analysis for lenses and their mounts to confirm the physical safety of the lens materials. We also conducted the global structure analysis for various gravitational orientations to verify the image stability requirement during the operation of the telescope and the instrument. In this article, we present the opto-mechanical detailed design of G-CLEF FCC and describe the consequence of the numerical finite element analyses for the design.