The constant of proportionality (for a 5 percent damping spectrum) is set at a standard value of 2.5 in both cases. 1 0 obj As shown in Table 8.2, performance requirements for sewer pipes under earthquake loading are broadly classified according to earthquake ground motion levels. For any given site on the map, the computer calculates the ground motion effect (peak acceleration) at the site for all the earthquake locations and magnitudes believed possible in the vicinity of the site. An accelerated mass induces a force that is proportional to the mass and the acceleration. Example: "The New Madrid Seismic Zone.". In this table, the exceedance probability is constant for different exposure times. This step could represent a future refinement. Also, in the USA experience, aftershock damage has tended to be a small proportion of mainshock damage. In a real system, the rod has stiffness which not only contributes to the natural period (the stiffer the rod, the shorter the period of oscillation), but also dissipates energy as it bends. This is a reasonable approximation for buildings or short bridges, but it may considerably alter the overall seismic response of more extended structures especially in the case where the local site conditions vary significantly with length (Deodatis et al., 2000; Der Kiureghian et al., 1997; Sextos et al., 2003b). Let r = 0.10, 0.05, or 0.02, respectively. Each of these magnitude-location pairs is believed to happen at some average probability per year. . Compare the results of the above table with those shown below, all for the same exposure time, with differing exceedance probabilities. V. Modeer, ... T. Cooling, in Innovative Bridge Design Handbook, 2016. .For purposes of computing the lateral force coefficient in Sec. For this ideal model, if the mass is very briefly set into motion, the system will remain in oscillation indefinitely. The maximum velocity can likewise be determined. That is, the probability of no earthquakes with M>5 in a few-year period is or should be virtually unaffected by the declustering process. Pounding is the main cause of damage to several buildings during almost every earthquake. Similarly for response acceleration (rate of change of velocity) also called response spectral acceleration, or simply spectral acceleration, SA (or Sa). However, the structural response based on different selection sets might still be different by using this approach. (This report can be downloaded from the web-site.) Also, other things being equal, older buildings are more vulnerable than new ones.). A.M. Cruz, ... S. Girgin, in Natech Risk Assessment and Management, 2017. Thus, in this case, effective peak acceleration in this period range is nearly numerically equal to actual peak acceleration. "…The EPA and EPV thus obtained are related to peak ground acceleration and peak ground velocity but are not necessarily the same as or even proportional to peak acceleration and velocity. x��}[s�ƒ���Ϳ��W�`pImm�c;���nb�$�:�$!�H���S����m_�� ��}�*���������旷:�=$/_���f���ח��O��C���U���W��^^��V��v�w����[������I��Jgu�d�����:����*O����o~�%O��������/ߴ��u��~�������&���Kxx��?��J�N�nEs��+�B��~x=��U߯�w��__^��>�*�4Oj��e�\�����vyQ,�vY-��b��Ū_�購0��&�nw�O��&�-����\$��d
��v�n��dE���O��Zn�ݱ��������'������W�=����)$� 5C�4iSF���2���V�/����i�#�yaZ���8�v�-/�Ŷ����W��B/4.6�? In areas of high seismicity, where contour values change rapidly, the website is the only accurate way to determine the MCE design parameters. The energy dissipation mechanism induces a force that is a function of a dissipation constant and the velocity. This suggests that, keeping the error in mind, useful numbers can be calculated. . Duration also plays a role in damage, and some argue that duration-related damage is not well-represented by response parameters. This conclusion will be illustrated by using an approximate rule-of-thumb for calculating Return Period (RP). where S0 = basic design acceleration response spectra in m/s2 and T = natural period. If we look at this particle seismic record we can identify the maximum displacement. The corresponding ground motion (peak acceleration) is said to have a P probability of exceedance (PE) in T years.The map contours the ground motions corresponding to this probability at all the sites in a grid covering the U.S. Click on a pin on the map to see more information. Any potential inclusion of foreshocks and aftershocks into the earthquake probability forecast ought to make clear that they occur in a brief time window near the mainshock, and do not affect the earthquake-free periods except trivially. In addition, © building codes use one or more of these maps to determine the resistance required by buildings to resist damaging levels of ground motion. This implies that for the probability statement to be true, the event ought to happen on the average 2.5 to 3.0 times over a time duration = T. If history does not support this conclusion, the probability statement may not be credible. Izuru Takewaki, in Critical Excitation Methods in Earthquake Engineering (Second Edition), 2013. The 1997 Uniform Building Code (UBC) (published in California) is the only building code that still uses such zones. From: Critical Excitation Methods in Earthquake Engineering (Second Edition), 2013, Zihai Shi, ... Hajime Kubo, in Structural Resilience in Sewer Reconstruction, 2018. THUS EPA IN THE ATC-3 REPORT MAP may be a factor of 2.5 less than than probabilistic peak acceleration for locations where the probabilistic peak acceleration is around 1.0 g. The following paragraphs describe how the Aa, and Av maps in the ATC code were constructed. 2020-04-29T17:30:17+05:302017-05-05T17:25:56ZMicrosoft® Office Word 2007 The broadened areas were denominated Av for "Effective Peak Velocity-Related Acceleration" for design for longer-period buildings, and a separate map drawn for this parameter. Response Spectrum Method. Since the earthquake force is a function of mass, the building shall be as light as possible consistent with structural safety and functional requirements. It does not have latitude and longitude lines, but if you click on it, it will blow up to give you more detail, in case you can make correlations with geographic features. They will show the probability of exceedance for some constant ground motion. Contour maps developed by the United States Geological Survey (USGS) are provided in Chapter 16 and provide values of Ss and S1 for all locations in the United States. The one we use here is the epicentral distance or the distance of the nearest point of the projection of the fault to the Earth surface, technically called Rjb. Answer: Let r = 0.10. SA would also be a good index to hazard to buildings, but ought to be more closely related to the building behavior than peak ground motion parameters. A earthquake strong motion record is made up of varying amounts of energy at different periods. To be a good index, means that if you plot some measure of demand placed on a building, like inter story displacement or base shear, against PGA, for a number of different buildings for a number of different earthquakes, you will get a strong correlation. By continuing you agree to the use of cookies. Definition: A site response spectrum graph plots the maximum response values of acceleration, velocity, and displacement against period and frequency. (London), in Earthquake-Resistant Structures, 2013. <>stream Generally, over the past two decades, building codes have replaced maps having numbered zones with maps showing contours of design ground motion. Rather, they are building code constructs, adopted by the staff that produced the Applied Technology Council (1978) (ATC-3) seismic provisions. The MCE design parameters are defined as those that have a 2% probability of exceedance in 50 years, but with deterministic limits in areas where earthquake sources and return periods are well known. Tall buildings have long natural periods, say 0.7 sec or longer. Aftershocks and other dependent-event issues are not really addressable at this web site given our modeling assumptions, with one exception. The maps can be used to determine (a) the relative probability of a given critical level of earthquake ground motion from one part of the country to another; (b) the relative demand on structures from one part of the country to another, at a given probability level. The building codes assume that 5 percent of critical damping is a reasonable value to approximate the damping of buildings for which earthquake-resistant design is intended. The detailed history can be found in Takewaki 2007. Tall buildings have long natural periods, say 0.7 sec or longer. If the probability assessment used a cutoff distance of 50 km, for example, and used hypocentral distance rather than epicentral, these deep Puget Sound earthquakes would be omitted, thereby yielding a much lower value for the probability forecast. Liquid sloshing and the resulting dynamic loading on the tank wall need to be taken into account in the design of storage tanks in earthquake-prone areas. When r is 0.50, the true answer is about 10 percent smaller. Spectral acceleration is a measure of the maximum force experienced by a mass on top of a rod having a particular natural vibration period. Thus, a map of a probabilistic spectral value at a particular period thus becomes an index to the relative damage hazard to buildings of that period as a function of geographic location. An attenuation function for peak velocity was "draped" over the Aa map in order to produce a spatial broadening of the lower values of Aa. Because of these zone boundary changes, the zones do not have a deeper seismological meaning and render the maps meaningless for applications other than building codes. php), where values are provided based on the latitude and longitude of the site. Table 8.2. Ground motions were truncated at 40 % g in areas where probabilistic values could run from 40 to greater than 80 % g. This resulted in an Aa map, representing a design basis for buildings having short natural periods.