Required response spectrum

This is a response spectrum obtained during a test in a laboratory while exciting the shake table with ground movements as in the RRS. The test object is mounted on the shake table. The test object should respond normally during such movements. The test conditions (i.e. TRS) should closely overlap the required seismic conditions (i.e. RRS) of Figure 14.25. 

This is the duration sufficient to simulate seismic conditions. It depends upon the algorithm used to find time history from the reqtiired response spectrum (RRS). The minimum duration of a strong movement, as recommended by IEEE 344, is 15 seconds as illustrated in Figure 14.24(b). This will require a total duration of the order of 20 seconds, including the movement s times of rise and time of decay. A duration of 20.48 seconds, as noted in the figure, is typical of a test conducted at University of Rorkee. The following tests may be conducted ... 

However, the argument that the cyclic nature of the perturbation ehminates the intrusion of heat effects must be treated with caution. For both p-xylene and 2-butyne in silicalite Shen and Rees [31,32] observed a bimodal response spectrum and they interpreted the two peaks as indicative of two different transport processes corresponding to diffusion through the straight and sinusoidal channels. There is some NMR evidence to support the view that such molecules cannot easily reorient themselves at the channel intersections, and for silicalite-2, which contains only straight channels of similar dimensions, only a single response peak is observed so this hypothesis is certainly plausible. However, Sun and Bourdin [34] have shown that an alternative explanation is also possible. If the heat balance equations are included in the theoretical model, the predicted response assumes a bimodal form and the heat-transfer parameter required to match the experimental data appears to be quite reasonable. 

These tests are standardized (e.g. see USNRC, 1988). These standards require that a component is placed on a vibrating table and that it is submitted to a higher vibratory load than that characterized by the floor response spectrum. In some cases, if necessary, the component is even verified for operation during the test. The components are tested together with their support structure to avoid a further uncertainty in the calculation of the dynamic load at the level where they are located. The excitation must include all three axes, unless S5unmetry conditions exist. 

A sinusoidal or sinusoidal beat motion can be used for the qualification testing of stiff systems at a frequency significantly lower than the first mode frequency of the system. This should result in a test response spectrum that envelops the reference response spectrum required to qualify the item. If no adequate shaking device is available, a sinusoidal motion can be used at resonance to obtain the necessary quahfying level of response of the item. 

When the system has one or more vibrational resonances in the frequency range of interest, the test input motion should have a response spectrum not smaller than the required design basis response spectrum. This can be achieved... 

When the natural frequencies of the item are well separated, independent tests can be made, for example with a suitably scaled sinusoidal input at the given frequenqr with a half-sine or other time envelope of interest. However, such tests should be made with two or more time histories or natural time histories whose response spectra are not lower than the required design basis response spectrum. The use of several different time histories helps to overcome any deficiencies that could arise from the peculiarities of a single time history. 

An alternative nonlinear static procedure was proposed by Aydinoglu (2003). The procedure, called Incremental Response Spectrum Analysis (IRSA) does not properly belong to the pushover methods. The procedure is displacement-based, it uses the equal displacement rule and the structure nonlinear behavior is modeled as piece-wise linear. The initial modes are computed and the elastic response spectrum for the initial structure is carried out. In the first stop the spectral ordinates are scaled to the formation of the first plastic hinge, which corresponds in the piece-wise linear capacity curve, to the first change of stiffness. The updated modal quantities are computed and additional spectral ordinates are computed up to the formation of the second plastic hinge. The procedure continues until the entire spectral ordinates are applied. The method does not require any transformation to an equivalent SDOE system. 

In the framework of this study, the RC building has been optimally designed to meet the Eurocode (EC2 and ECS) or the PBD requirements. According to ECS the lateral forces were derived from the design response spectrum (5%-damped elastic spectrum divided by the behaviour factor q) at the fundamental period of the building. Concrete of class C20/25 (nominal cylindrical strength of 20 MPa) and class S500 steel (nominal yield stress of 500 MPa) are assumed. The base shear is obtained from the response spectrum for soil type A (stiff soil 0= 1.0, with characteristic periods T1 =0.10 sec and T2 = 0.40 sec) and a PGA of 0.31 g. Moreover, the importance factor yi was taken... 

Since the design time histories meet response spectrum enveloping requirement and power spectral density function requirement and the components of design time histories in each direction are statistically independent, the deisgn time histories are acceptable. The critical damping values are consistent with Reg. Guide 1.61 and ASME Code Case N-411-1. 

The conditional spectrum (CS) is a target response spectrum (with mean and variance) for ground motion selection to perform nonlinear dynamic analysis. The computation of the CS requires (1) input earthquake parameters of magnitude, distance, relevant seismological and site characteristics (e.g., fault type and soil type) ... 

In ECS the earthquake motion at a site is represented by an elastic response spectmm in terms of spectral acceleration values (Annex A of ECS Part 1 additionally represents seismic action in the form of an elastic displacement response spectrum). The shape of the elastic response spectrum for each country may be found in its National Aimex, and it is the same for the two levels of seismic performance, i.e., for the no-collapse requirement as well as for the damage limitation requirement. It is also noted that in selecting the appropriate shape of the spectrum, consideration should be given to the magnitude of earthquakes that contribute most to the seismic hazard as defined in PSHA, rather than on conservative upper limits (e.g., the maximum credible earthquake). Regarding magnitude, two types of spectra are recommended,... 

A d5mamic (response-history) analysis, linear or nonlinear, requires as input acceleration time-histories of the ground motion. These time-histories should conform on average with the 5 %-damped elastic response spectrum defining the seismic action. 

Response spectrum analysis (RSA) is a method widely used for the design of buildings. Conceptually the method is a simplification of modal analysis, i.e., response history (or time history) analysis (RHA) using modal decomposition, that benefits from the properties of the response spectrum concept. The purpose of the method is to provide quick estimates of the peak response without the need to carry out response history analysis. This is very important because response spectrum analysis (RSA) is based on a series of quick and simple calculations, while time history analysis requires the solution of the differential equation of motion over time. Despite its approximate nature, the method is very useful since it allows the use of response spectrum, a very convenient way to describe seismic hazard. 

Deodatis (1996) proposed a general iterative procedure to determine quasi-stationary response-spectrum-compatible ground motion vector process. The procedure requires the initial selection of the modulating functions and coherence functions representative of a given site. The procedure starts assuming the stationary power-spectral density function constant for every location ... 

Knowing Go(VF) and the transferring function (Hsdof) of a single-degree-of-freedom system (SDOF), the SDOF Spectra Power Density is evaluable (see Eq. 2) and the related Response Spectrum is the required FRS. 

The safety factor for all load components to be combined with seismic loading shall be set equal to 1.0. The ground acceleration shall be evaluated for a 475-year recurrence period based on ground acceleration and response spectrum requirements as defined in local building codes. If a local building code is not available or does not provide ground acceleration and response spectrum, an appropriate evaluation of these parameters shall be carried out. 

Derivation of the (inelastic) design spectrum requires the correction of the elastic response spectrum to account for the ability of the... 

Application of the exact continuum analysis of dispersion forces requires significant calculations and the knowledge of the frequency spectmm of the material dielectric response over wavelengths X = 2irc/j/ around 10-10 nm. Because of these complications, it is common to assume that a primary absorption peak at one frequency in the ultraviolet, j/uv. dominates the dielectric spectrum of most materials. This leads to an expression for the dielectric response... 

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