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The application uses three iterations to arrive at a ground motion value corresponding to a 1% probability of collapse in 50 years.
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## First Iteration
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The application begins by using the ground motion with a 2% probability of being exceeded over a 50 year time period. This value is obtained during Step 1 and is used to arrive at an initial Probability of Collapse in 50 years in Steps 2 through 5.
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The application begins by using the uniform hazard ground motion (UHGM) with a 2% probability of being exceeded over a 50 year time period. This value is obtained during Step 1 and is used to arrive at an initial Probability of Collapse in 50 years in Steps 2 through 5.
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Five plots illustrating the step-by-step process of calculating the risk-targeted ground motion are briefly discussed below.
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### Step 1: Hazard Curve
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This is simply a graphical representation of the Spectral Response Acceleration Values (x-axis) and Annual Frequency of Exceedance Values (y-axis) provided by the user. For more information on these values, users are referred to the Documentation for the 2008 Update of the [USGS National Seismic Hazard Model] (http://pubs.usgs.gov/of/2008/1128/).
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This is simply a graphical representation of the spectral response acceleration values (x-axis) and their annual frequencies of exceedance (y-axis) provided by the user. For more information on these values, users are referred to the Documentation for the 2008 Update of the [USGS National Seismic Hazard Model] (http://pubs.usgs.gov/of/2008/1128/).
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### Step 2: Fragility Curves
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These are generic fragility curves defined by a point corresponding to a 10% probability of structural collapse and a Beta (standard deviation) value of 0.8.
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## Final Iteration
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With the First and Second Iterations bracketing the target probability of collapse (1%), the ground motion for the Final Iteration can be precisely selected during Step 1 to result in Steps 2 through 5 to correspond to a 1% probability of structural collapse. This ground motion value is referred to as the risk-targeted ground motion, or "RTGM". The Risk Coefficient, or "RC", is simply the ratio of the RTGM divided by the uniform hazard ground motion ("UHGM").
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For more information about the calculation procedure, please see the paper by Luco, et al. in the References section.
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## Output summary (yellow box)
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This section provides the risk-targeted ground motion (RTGM) corresponding to a 1% probability of collapse in 50 years. The uniform hazard ground motion (UHGM) used as a starting point for the calculations is provided, as is the Risk Coefficient (RC) representing the ratio of RTGM to UHGM for the site of interest.
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http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/0.01,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.4,1.7,2/0.5696,0.088335,0.02925,0.01229725,0.00564925,0.00275075,0.001385175,0.000733875,0.0003984225,0.0002205625,0.0001235975,6.881825E-5,3.82493775E-5,1.13329875E-5,1.34645E-6,6.4884E-8
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Example 2: JSONP request, a callback is specified. Note the content-type header in the response. The response for this request is wrapped in the specified javascript callback.
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http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/0.01,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.4,1.7,2/0.5739,0.09486,0.032775,0.0143475,0.00689675,0.00349925,0.001878025,0.0010358,0.00059415,0.00034517,0.0002041625,0.00012253,7.213325E-5,2.5567215E-5,4.81976025E-6,7.196E-7/processData
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# References
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Luco, N., B.R. Ellingwood, R.O. Hamburger, J.D. Hooper, J.K. Kimball & C.A. Kircher (2007), “Risk-Targeted versus Current Seismic Design Maps for the Conterminous United States,” Proceedings of the 2007 Structural Engineers Association of California Convention, Lake Tahoe, CA, pp. 163-175. |
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