Civil Engineering Association

SDOF Elastic Response Spectrum Time History

The archive contains the following:

Excel files with macro (visual basic script) that computes elastic response spectrum for a given time history record, and SDOF response (acceleration, velocity, displacement):
Elastic Response Spectrum.xls Elastic Response Spectrum.xlsm

The same functions are inside the Mathcad V.14:
Elastic Response Spectrum.xmcd

For verification sap V14.2.4 model files are provided:
pendulum.SDB; pendulum.$2k

The reference article, timehist.pdf, containing the algorithm in MATLAB for SDOF, MDOF timehistory and additional information. Based on this article the above files were written.

AccData.txt contains time history data first column is time is seconds, second column is acceleration in m/s^2

Functions available in excel:
=SpectrumPeriodAcceleratioVelocityDisplacement(r, dT, xi, Optional Tmax, Optional noPoints)
Function returns a matrix with:
first column - periods
second column - accelerations
third column - velocity
fourth column - dispalcements

=TimeAccelerationVelocityDisplacement(r, T, xi, dT)
Function returns a matrix with:
first column - time
second column - accelerations
third column - velocity
fourth column - dispalcements

Input parameters:

r is range like B1:B2008, a single column with accelerations from time history recoding
dt is time step for time history recording like 0.02 seconds
xi is critical damping ratio usually 0.05 in codes
Optional Tmax is the maximum value for period in spectrum calculation default value 4 seconds
Optional noPoints is the number of periods to use when calculating spectrum default value 200.
Response spectrum is computed starting for 0 sec to Tmax sec at equal step size of Tmax/noPoints.
T is the period for the pendulum when computing time history response.

User can use any measurement units. Output tested with SeismoSignal and Sap2000, no differences. Only for response spectrum when T<0.1s.

Note on how to work in excel with matrix:
Select multiple cells, click in formula bar, write the formula, press ctrl+shift+enter to finish.
To modify the formula: select all cells that are part of the matrix, modify formula, press ctrl+shift+enter
To erase: select all cells that are part of the matrix, modify formula to nothing, press ctrl+shift+enter
To select an entire matrix place currenc cell inside that table press ctrl+a.
If still in trouble search google for: excel matrix.

Request: if somebody manages to understand how this code can be used for MDOF (see article), please send me private message. I've all ready tried that in mathcad with matrix as input instead of values for xi, p, w but I don't understand the results.
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