Elastic design response spectra

Most seismic design is based on representing the earthquake actions in the for of an equivalent static force applied to the structure. hese forces are determined from the maximum acceleration response of the structure under the expected earthquake-induced ground shaking, hich is represented by the acceleration response spectrum. The starting point is an elastic response spectrum, which is subsequently reduced by factors that account for the capacity of the structure to dissipate the seismic energy through inelastic deformations. The definition of the elastic response spectrum and its conversion to an inelastic spectrum are presented in Chapter 3; this section focuses on how the elastic design response spectra are presented in seismic design codes, with particular reference to EC8.

The purpose of representing earthquake actions in a seismic design code such as EC8 is to circumvent the necessity of carrying out a site-specific seismic hazard analysis for every engineering project in seismically active regions. For non-critical structures it is generally considered sufficient to provide a zonation ap indicating the levels of expected ground otions throughout the region of applicability of the code and then to use the parameters represented in these zonations, together with a classification of the near-surface geology, in order to construct the elastic design response spectrum at any given site.

2.5.1 Uniform hazard spectra and code spectra

The primary output from a PSHA is a suite of hazard curves for response spectral ordinates for different response periods. design return period is then selected - often rather arbitrarily as noted previously (e.g. Bommer, 2006a) - and then the response parameter at this return period is determined at each response period and used to construct the elastic response spectrum. A spectrum produced in this way, for which it is known that the return period associated with several response periods is the same, is known as a uniform hazard spectrum (UHS) and it is considered an appropriate probabilistic representation of the basic earthquake actions at a particular location. he S ill often be an envelope of the spectra associated ith different sources of seismicity, with short-period ordinates controlled by nearby moderate-magnitude earthquakes and the longer-period part of the spectrum dominated by larger and more distant events. As a consequence, the otion represented by the S ay not be particularly realistic, if interpreted as being associated with some design scenario, and this becomes an issue hen the otions need to be represented in the for of acceleration time-histories, as discussed in Section 2.6. If the only parameter of interest to the engineer is the maximum acceleration that the structure will experience in its fundamental mode of vibration, regardless of the origin of this motion or any other of its features (such as duration), then the UHS is a perfectly acceptable format for the representation of the earthquake actions. In the following discussion it is assumed that the UHS is a desirable objective.

Until the late 1980s, seismic design codes invariably presented a single zonation map, usually for a return period of 475 years, showing values of a parameter that in essence was the PGA. This value was used to anchor a spectral shape specified for the type of site, usually defined by the nature of the surface geology, and thus obtain the elastic design spectrum. In many codes, the ordinates could also be multiplied by an importance factor, which would increase the spectral ordinates (and thereby the effective return period) for the design of structures required to perfor to a higher level under the expected earthquake actions, either because of the consequences of damage (e.g. large occupancy or toxic materials) or because the facility would need to remain operational in a post-earthquake situation (e.g. fire station or hospital).

A code spectrum constructed in this way would almost never be a UHS. Even at zero period, here the spectral acceleration is equal to P, the associated return period ould often not be the target value of 475 years since the hazard contours were simplified into zones with a single representative PGA value over the entire area. More importantly, this spectral construction technique did not allow the specification of seismic loads to account for the fact that the shape of response spectru varies ith earthquake agnitude as well as with site classification (Figure 2.11), with the result that even if the P anchor value as associated ith the exact design return period, it is very unlikely indeed that the spectral ordinates at different periods would have the same return period (McGuire, 1977). Consequently, the

Seismic Response SpectrumZero Period Acceleration

Figure 2.11 Median predicted response spectra, normalised to PGA, for a rock site at 10 km from earthquakes of different magnitudes from the Californian equations of Campbell (1997) and Boore et al. (1997)

objective of a S is not et by anchoring spectral shapes to the zero-period acceleration.

arious different approaches have been introduced in order to achieve a better approximation to the UHS in design codes, generally by using more than one parameter to construct the spectrum. The 1984 Colombian and 1985 Canadian codes both introduced a second zonation map for PGV and in effect used PGA to anchor the short-period part of the spectrum and PGV for the intermediate spectral ordinates. Since the zonation maps for the two parameters were different, the shape of the resulting elastic design spectru varied fro place to place, reflecting the influence of earthquakes of different agnitude in controlling the hazard. he 1997 edition of the Uniform Building Code (UBC) used two parameters, C and C , for the short- and intermediate-period portions of the spectra (with the subscripts indicating relations ith acceleration and velocity) but curiously the ratio of the two parameters was the same in each zone with the result that the shape of the spectrum did not vary except with site classification.

In the Luso-Iberian peninsula, seismic hazard is the result of moderate-magnitude local earthquakes and large-magnitude earthquakes offshore in the Atlantic. The Spanish seismic code handles their relative influence by anchoring the response spectru to P but then introducing a second set of contours, of a factor called the 'contribution coefficient', , that controls the relative amplitude of the longer-period spectral ordinates; high values of occur to the est, reflecting the stronger influence of the large offshore events. The Portuguese seismic code goes one step further and simply presents separate response spectra, with different shapes, for local and distant events. he Portuguese code is an interesting case because it effectively abandons the UHS concept, although it is noteworthy that the return period of the individual spectra is 975 years, in effect twice the value of 475 years associated with the response spectra in most European seismic design codes.

Within the drafting committee for EC8 there were extensive discussions about ho the elastic design spectra should be constructed, ith the final decision being an inelegant and almost anachronistic compromise to remain ith spectral shapes anchored only to P. In order to reduce the divergence from the target UHS, however, the code introduced two different sets of spectral shapes (for different site classes), one for the higher seismicity areas of southern Europe ( ype 1) and the other for adoption in the less active areas of northern Europe (Type 2). The Type 1 spectrum is in effect anchored to earthquakes of magnitude close to M ~7 whereas the Type 2 spectrum is appropriate to events of M 5.5 (e.g. Rey et al., 2002). (See Figure 2.12.) At any location where the dominant earthquake event underlying the hazard is different fro one or other of these agnitudes, the spectru ill tend to diverge fro the target 475-year S, especially at longer periods.

The importance of the vertical component of shaking in terms of the demand on structures is a subject of some debate (e.g. Papazoglou and

Ec8 Seismic Spectra
Figure 2.12 Median predicted spectral ordinates from the European ground-motion prediction equations of Ambraseys et al. (1996) for rock sites at 10 km from small and large magnitude events, compared with the EC8 Type 1 and 2 rock spectra anchored to the edian predicted P

Elnashai, 1996) but there are certain types of structures and structural elements, such as cantilever beams, for which the vertical loading could be important. Many seismic codes do not provide a vertical spectrum at all and those that do generally specify it as simply the horizontal spectrum with the ordinates reduced by one-third. Near-source recordings have shown that the short-period motions in the vertical direction can actually exceed the horizontal otion, and it has also been clearly established that the shape of the vertical response spectru is very different fro the horizontal components of motion (e.g. Bozorgnia and Campbell, 2004). In this respect, EC8 has some merit in specifying the vertical response spectrum separately rather than through scaling of the horizontal spectru; this approach as based on the work of Elnashai and Papazoglou (1997). As a result, at least for a site close to the source of an earthquake, the E8 vertical spectru provides a more realistic estimation of the vertical motion than is achieved in many seismic design codes (Figure 2.13).

2.5.2 The influence of near-surface geology on response spectra he fact that locations underlain by soil deposits generally experience stronger shaking than rock sites during earthquakes has been recognised for any years, both fro field studies of earthquake effects and fro recordings of ground otions. he influence of surface geology on ground otions is no routinely included in predictive equations. he nature of the near-surface deposits is characterised either by broad site classes, usually defined by ranges of shear-wave velocities (V), or else by the explicit value of the V over the uppermost 30 m at the site. Figure 2.14 shows the influence

Seismic Code Columns
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Responses

  • amaranth
    How to construct seismic response spectrum?
    8 years ago
  • celeste capon
    How to draw elastic response spectra?
    2 years ago
  • augusto
    How to draw resonse sectrum using eurocode?
    2 years ago
  • harry
    How to get design responce spectra from elastic responce spectra?
    1 year ago
  • anette
    How to construct UHS spectra?
    6 months ago

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