Alcan Structural Engineering

Acceleration timehistories

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Although seismic design invariably begins with methods of analysis in which the earthquake actions are represented in the form of response spectra, some situations require fully dynamic analyses to be performed and in these cases the earthquake actions ust be represented in the for of acceleration time-histories. Such situations include the design of safety-critical structures, highly irregular buildings, base-isolated structures, and structures designed for a high degree of ductility. For such projects, the simulation of structural response using a scaled elastic response spectrum is not considered appropriate and suites of accelerograms are required for the dynamic analyses. The guidance given in the majority of seismic design codes on the selection and

scaling of suites of acceleration tie-histories for such purposes is either very inadequate or else so prescriptive as to make it practically impossible to identify realistic accelerograms that meet the specified criteria (Bommer and Ruggeri, 2002). A point that cannot be emphasised too strongly is that time-histories should never be matched to a uniform hazard spectrum, but rather to a spectru corresponding to a particular earthquake scenario. In the case of codes, this may be difficult since the code generally provides an approximation, albeit a crude one, to the UHS and offers no possibility to generate a disaggregated event-specific spectrum.

There are a number of options for obtaining suites of acceleration time-histories for dynamic analysis of structures, including the generation of spectrum-compatible accelerograms from white noise, a method that is no idely regarded as inappropriate because the resulting signals are so unlike earthquake ground otions. he ost popular option is to use real accelerograms, which can be selected either on the basis of having response spectra similar, at least in shape, to the elastic design spectrum, or else matching an earthquake scenario in terms of magnitude, source-to-site distance and possibly also site geology (Bommer and Acevedo, 2004). The latter approach, however, is generally not feasible in the context of seismic design code applications, because information regarding the underlying earthquake scenarios is usually not available to the user. Selecting records fro earthquakes of appropriate agnitude is only an issue if the duration of the shaking is considered an important parameter in determining the degree of seismic demand that the records impose, which is an issue of ongoing debate in the technical literature (Hancock and Bommer, 2006).

nce a suite of records has been selected, hether on the basis of the spectral shape or an earthquake scenario, the next question for the design engineer to address is how many records are needed. Most of the seismic design codes that address this issue, including EC8, specify that a minimum of 3 records should be used, and that if less than 7 records are used then the maximum structural response must be used as the basis for design, whereas if 7 or more time-histories are employed then the average structural response can be used. The use of the maximum inelastic response obtained from dynamic analyses may never be appropriate since the input accelerograms will in some sense have been adjusted to approximate to the elastic design spectrum, which, if determined from a probabilistic hazard assessment, will already include the influence of the ground-motion variability. The largest dynamic response will probably correspond to a record that is somewhat above the target spectrum, and in a sense the ground-motion variability is therefore being taken into account twice.

The key question then becomes how many records are required to obtain a stable estimate of the mean inelastic response, which will depend on how the records are adjusted so that their spectral ordinates approximate to those of the elastic design spectrum: the more closely the adjusted records match the target elastic design spectrum, the fewer analyses will be needed.

Period (seconds) Period (seconds)

Figure 2.18 Comparison of the difference bettveen scaled and matched spectra. Modified from Hancock et al. (2006)

Period (seconds) Period (seconds)

Figure 2.18 Comparison of the difference bettveen scaled and matched spectra. Modified from Hancock et al. (2006)

Options include scaling the records to match the design spectrum at the natural period of the structure or scaling to match or exceed the average ordinates over a period range around this value, the extended range accounting for both the contributions to the response fro higher odes and also for the elongation of response period due to inelastic deformations. Scaling the records in amplitude is legitimate given that whilst the amplitude of the motion is highly dependent on distance - especially within a few tens of kilometres from the source - the shape of the response spectrum is actually rather insensitive to distance over the range of distances of normal engineering interest (Bommer and Acevedo, 2004). Although scaling limits of a factor of 2 were proposed at one time, and became embedded in the 'folklore' of engineering practice, much larger scaling factors can be applied ^atson-Lamprey and Abrahamson, 2006). Adjusting records by scaling the time axis, however, is to be avoided.

An alternative to linear scaling of the records is to make adjustments, using Fast Fourier Transform or wavelet transformations, to achieve a spectral shape that approximates to that of the target design spectrum (Bommer and Acevedo, 2004). The most elegant way to achieve this is using the wavelet transformation, which minimises the alteration of the original accelerogram but at the same time can achieve a very good spectral match (Hancock et al., 2006). An example of the difference between linearly scaling a record and matching spectra through wavelet transformations is given in Figure 2.18.

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