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# **Purpose of this Application** ## Purpose of this Application
The Risk Targeted Ground Motion Calculator is used to calculate risk-targeted ground motion values in accordance with “Method 2” of 2010 ASCE 7 Standard Section 21.2.1.2. Users can input a hazard curve from a site-specific analysis to obtain a risk-targeted ground motion value.
# **Sample input** The Risk Targeted Ground Motion Calculator is used to calculate risk-targeted
ground motion values in accordance with "Method 2" of 2010 ASCE 7 Standard
Section 21.2.1.2. Users can input a hazard curve from a site-specific analysis
to obtain a risk-targeted ground motion value.
Application input can be user-provided or drawn from the [USGS Hazard Curve Data files](http://earthquake.usgs.gov/hazards/products/). The following example incorporates the 2008 USGS Lower 48 “Hazard Curve Data” file for “5Hz (0.2 Second)”. Specifically, the data for the coordinates (34.05, -118.25) in Los Angeles are used. ## Sample Input
Please note that all numeric input values should be comma separated as in the below example, and all units should be removed. In addition, users must provide an equal number of Spectral Response Acceleration values and Annual Frequency of Exceedance values. Application input can be user-provided or drawn from the [USGS Hazard Curve
Data files](http://earthquake.usgs.gov/hazards/products/). The following
example incorporates the 2008 USGS Lower 48 "Hazard Curve Data" file for
"5Hz (0.2 Second)". Specifically, the data for the coordinates (34.05, -118.25)
in Los Angeles are used.
## Curve Title Please note that all numeric input values should be comma separated as in the
This is an optional input. Users can input a string of characters (such as "Office Tower at 123 Main St.") to serve as a reminder of which output values correspond to a particular structure. below example, and all units should be removed. In addition, users must provide
an equal number of Spectral Response Acceleration values and Annual Frequency
of Exceedance values.
## Spectral Response Acceleration Values, in units of 'g' (corresponding to the x-axis on a hazard curve): **Curve Title**
This is an optional input. Users can input a string of characters (such as
`Office Tower at 123 Main St.`) to serve as a reminder of which output values
correspond to a particular structure.
**Spectral Response Acceleration Values, in units of 'g' (corresponding to the x-axis on a hazard curve)**
```
0.005, 0.0075, 0.0113, 0.0169, 0.0253, 0.038, 0.057, 0.0854, 0.128, 0.192, 0.288, 0.432, 0.649, 0.973, 1.46, 2.190, 3.28, 4.92, 7.38 0.005, 0.0075, 0.0113, 0.0169, 0.0253, 0.038, 0.057, 0.0854, 0.128, 0.192, 0.288, 0.432, 0.649, 0.973, 1.46, 2.190, 3.28, 4.92, 7.38
```
## Annual Frequency of Exceedance Values (corresponding to the y-axis on a hazard curve): **Annual Frequency of Exceedance Values (corresponding to the y-axis on a hazard curve)**
```
0.5855, 0.5208, 0.4389, 0.3515, 0.2679, 0.1953, 0.1376, 0.09335, 0.06027, 0.03659, 0.02096, 0.01146, 0.005985, 0.002934, 0.001287, 0.0004781, 0.0001411, 0.00003023, 0.000003828 0.5855, 0.5208, 0.4389, 0.3515, 0.2679, 0.1953, 0.1376, 0.09335, 0.06027, 0.03659, 0.02096, 0.01146, 0.005985, 0.002934, 0.001287, 0.0004781, 0.0001411, 0.00003023, 0.000003828
```
## Output
The application uses three iterations (briefly described here) to arrive at a
ground motion value corresponding to a 1% probability of collapse in 50 years.
For more information about the calculation procedure, please see the paper by
Luco, et al. noted in the References section.
# **Output** **First Iteration**
The application uses three iterations (briefly described here) to arrive at a ground motion value corresponding to a 1% probability of collapse in 50 years. For more information about the calculation procedure, please see the paper by Luco, et al. noted in the References section. 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.
## First Iteration Five plots illustrating the step-by-step process of calculating the
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. risk-targeted ground motion are briefly discussed below.
Five plots illustrating the step-by-step process of calculating the risk-targeted ground motion are briefly discussed below. 1. Hazard Curve
### Step 1: Hazard Curve 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/).
2. Fragility Curves
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/). These are generic fragility curves defined by a point corresponding to a
10% probability of structural collapse and a Beta (standard deviation)
value of 0.6.
### Step 2: Fragility Curves 3. Derivative of Fragility Curves
These are generic fragility curves defined by a point corresponding to a 10% probability of structural collapse and a Beta (standard deviation) value of 0.6.
### Step 3: Derivative of Fragility Curves These are simply the derivatives of each respective fragility curve. They
These are simply the derivatives of each respective fragility curve. They are provided as a reference for the next step in the calculation process. are provided as a reference for the next step in the calculation process.
### Step 4: Hazard Curve x Derivative of Fragility Curves 4. Hazard Curve x Derivative of Fragility Curves
Combining the hazard curve for the site with the derivative of each fragility curve produces a curve illustrating the annual collapse frequency density of a generic structure at the site of interest. This is provided as a reference for the next step in the calculation process.
### Step 5: Cumulative Integral of Hazard Curve x Derivative of Fragility Curves Combining the hazard curve for the site with the derivative of each
Integrating the hazard curve x derivative of each fragility curve produces the cumulative 50-year collapse probability of a generic structure at the site of interest. The "Final Iteration" is used to obtain the ground motion corresponding to a 1% probability of collapse in 50 years. fragility curve produces a curve illustrating the annual collapse frequency
density of a generic structure at the site of interest. This is provided as
a reference for the next step in the calculation process.
## Second Iteration 5. Cumulative Integral of Hazard Curve x Derivative of Fragility Curves
If the Conditional Probability of Collapse calculated during Iteration 1 exceeds 1%, the initial ground motion value is increased for Iteration 2. If on the other hand the probability of collapse calculated during Iteration 1 is less than 1%, the initial ground motion value is decreased for Iteration 2. Steps 2 through 5 are then repeated.
## Final Iteration Integrating the hazard curve x derivative of each fragility curve produces
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"). the cumulative 50-year collapse probability of a generic structure at the
site of interest. The "Final Iteration" is used to obtain the ground
motion corresponding to a 1% probability of collapse in 50 years.
**Second Iteration**
If the Conditional Probability of Collapse calculated during Iteration 1
exceeds 1%, the initial ground motion value is increased for Iteration 2. If,
on the other hand, the probability of collapse calculated during Iteration 1
is less than 1%, the initial ground motion value is decreased for Iteration 2.
Steps 2 through 5 are then repeated.
**Final Iteration**
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").
## Output Summary (yellow box)
## Output summary (yellow box)
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. 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.
# Frequently Asked Questions ## Frequently Asked Questions
### Does this calculator produce maximum-direction or geometric mean ground motion values?
If the hazard curve used as input is maximum-direction, then the resulting risk-targeted ground motion will also be maximum-direction. However, if the hazard curve is geometric mean, then the risk-targeted ground motion will also be geometric mean. - **Does this calculator produce maximum-direction or geometric mean ground
motion values?**
# **API Documentation** If the hazard curve used as input is maximum-direction, then the resulting
risk-targeted ground motion will also be maximum-direction. However, if the
hazard curve is geometric mean, then the risk-targeted ground motion will
also be geometric mean.
This page describes the process for creating a request and also defines the terms used in the response output. Additionally some examples are provided to help get you started. ## API Documentation
## Request API This section describes the process for creating a request and also defines the
terms used in the response output. Additionally some examples are provided to
help get you started.
### Request API
```
http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/x0,x1,...xN/y0,y1,...yN[/callback] http://earthquake.usgs.gov/hazards/apps/rtgm_calculator/service/x0,x1,...xN/y0,y1,...yN[/callback]
```
- x0,x1,...,xN
Comma-separated (no spaces) list of spectral acceleration values for the
hazard curve. Note: You must specify the same number of y-values and x-values.
- y0,y1,...,yN
Comma-separated (no spaces) list of annual frequency of exceedance values
for the hazard curve. Note: You must specify the same number of y-values
and x-values.
x0,x1,...,xN - callback
Comma-separated (no spaces) list of spectral acceleration values for the hazard curve. Note: You must specify the same number of y-values and x-values. Optional. If specified, the JSONP callback to call when the response is
y0,y1,...,yN returned. This is useful for application developers. Note: If this parameter
Comma-separated (no spaces) list of annual frequency of exceedance values for the hazard curve. Note: You must specify the same number of y-values and x-values. is specified, the response content-type header is changed from
callback "application/json" to "text/javascript".
Optional. If specified, the JSONP callback to call when the response is returned. This is useful for application developers. Note: If this parameter is specified, the response content-type header is changed from “application/json” to “text/javascript”
Note: All input hazard curve data must be adjusted with max-direction factors by the user before using the data in this application. Note: All input hazard curve data must be adjusted with max-direction
factors by the user before using the data in this application.
## Response API ### Response API
```
{ {
status: Response Code, status: Response Code,
rtgm: { rtgm: {
...@@ -91,56 +168,100 @@ Note: All input hazard curve data must be adjusted with max-direction factors by ...@@ -91,56 +168,100 @@ Note: All input hazard curve data must be adjusted with max-direction factors by
integrand: Annual Collapse Frequency Density, integrand: Annual Collapse Frequency Density,
integral: 50-Year Collapse Probability integral: 50-Year Collapse Probability
} }
,… ,...
], ],
originalHCMin: Minimum input SA value, originalHCMin: Minimum input SA value,
originalHCMax: Maximum input SA value originalHCMax: Maximum input SA value
} }
} }
```
status - **status**
Integer [_Integer_]
The HTTP Response Code for the request. A response of 200 indicates a successful request. Any other response code indicates an error. The HTTP Response Code for the request. A response of 200 indicates a
rtgm successful request. Any other response code indicates an error.
Number
- **rtgm**
[_Number_]
Risk Target Ground Motion Risk Target Ground Motion
uhgm
Number - **uhgm**
[_Number_]
Uniform Hazard Ground Motion Uniform Hazard Ground Motion
riskCoefficient
Number - **riskCoefficient**
RTGM divided by UHGM is equal to the Risk Coefficient (RTGM / UHGM = RiskCoefficient) [_Number_]
xs RTGM divided by UHGM is equal to the Risk Coefficient
Array of Numbers (RTGM / UHGM = RiskCoefficient)
Spectral response acceleration values upsampled from the input x-values. Upsampling may involve extrapolation at either (or both) end(s) of the hazard curve. Interpolated and extrapolated values are computed using linear interpolation in logarithmic space.
ys - **xs**
Array of Numbers [_Array of Numbers_]
Annual frequency of exceedance values upsampled from the input y-values. Upsampling may involve extrapolation at either (or both) end(s) of the hazard curve. Interpolated and extrapolated values are computed using linear interpolation in logarithmic space. Spectral response acceleration values upsampled from the input x-values.
cdf Upsampling may involve extrapolation at either (or both) end(s) of the
Array of Numbers hazard curve. Interpolated and extrapolated values are computed using linear
Conditional Collapse Probability. Data in this array correspond the the upsampled hazard curve x-values. interpolation in logarithmic space.
pdf
Array of Numbers - **ys**
Conditional Collapse Probability Density. Data in this array correspond the the upsampled hazard curve x-values. [_Array of Numbers_]
integrand Annual frequency of exceedance values upsampled from the input y-values.
Array of Numbers Upsampling may involve extrapolation at either (or both) end(s) of the
Annual Collapse Frequency Density. Data in this array correspond the the upsampled hazard curve x-values. hazard curve. Interpolated and extrapolated values are computed using linear
integral interpolation in logarithmic space.
Array of Numbers
50-Year Collapse Probability. Data in this array correspond the the upsampled hazard curve x-values. - **cdf**
originalHCMin [_Array of Numbers_]
Number Conditional Collapse Probability. Data in this array correspond to the
The smallest input spectral response acceleration value. This is useful for determining if a resulting spectral acceleration value in the upsampled hazard curve is based on extrapolation. upsampled hazard curve x-values.
originalHCMax
Number - **pdf**
The largest input spectral response acceleration value. This is useful for determining if a resulting spectral acceleration value in the upsampled hazard curve is based on extrapolation. [_Array of Numbers_]
Conditional Collapse Probability Density. Data in this array correspond to
the upsampled hazard curve x-values.
- **integrand**
[_Array of Numbers_]
Annual Collapse Frequency Density. Data in this array correspond to the
upsampled hazard curve x-values.
- **integral**
[_Array of Numbers_]
50-Year Collapse Probability. Data in this array correspond to the upsampled
hazard curve x-values.
- **originalHCMin**
[_Number_]
The smallest input spectral response acceleration value. This is useful for
determining if a resulting spectral acceleration value in the upsampled
hazard curve is based on extrapolation.
- **originalHCMax**
[_Number_]
The largest input spectral response acceleration value. This is useful for
determining if a resulting spectral acceleration value in the upsampled
hazard curve is based on extrapolation.
## Examples ## Examples
Example 1: JSON request, no callback is specified. Note the content-type header in the response. **Example 1**: JSON request, no callback is specified.
> Note the content-type header in the response.
```
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 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
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. ```
**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.
```
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 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
```
## References
# References Luco, N., B.R. Ellingwood, R.O. Hamburger, J.D. Hooper, J.K. Kimball &
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. C.A. Kircher (2007), "Risk-Targeted versus Current Seismic Design Maps for the
\ No newline at end of file Conterminous United States," Proceedings of the 2007 Structural Engineers
Association of California Convention, Lake Tahoe, CA, pp. 163-175.
\ No newline at end of file