Spectral Analysis

Output Results

When a spectral analysis is done, all or some of the following quantities are computed:

Period, T (seconds)
Circular Frequency, w (rad/sec)
Ductility
Sd, spectral displacement (inch)
Sv, spectral velocity (inch/sec)
Sa, spectral relative acceleration (g)
Sat, spectral total acceleration (g)
PSv, pseudo-spectral velocity = Sd.w (inch/sec)
PSa, pseudo-spectral acceleration = Sd.w² (g)
Sfs, maximum spring force (Kips)
Sfd, maximum damping force (Kips)
Sfa, maximum inertia force = Sat x Mass (Kips)
R, the ratio of the peak elastic force to the yield capacity = F_elastic/F_y
Eta h, the normalized strength = Yield Force/ (Mass x PGA)

All of those quantities, plus period and/or frequency could be plot. Any two quantities could be plot at a time on the X and Y axes of the plot.

When the "Shake It" button is pressed, the "Spectral Analysis Results" dialog is called, and the analysis process starts. Two progress bars at the bottom of the dialog show the analysis progress. The lower progress bar shows progress of the whole analysis, while the upper one shows the state of the current batch.

For example, if spectral results are desired for a combination of 40 periods and 5 strengths, the lower progress bar can be imagined to start at 0 and progress uniformly to 200, while the upper one would go from 1 to 5 repeatedly, once for each period until all the periods are done, that is 40 times (See figure).

The program can construct linear spectra for an earthquake. The user has to specify the mass, the damping ratio, and the period range. The periods or frequencies to be used can be specified by the user as a range by specifying the minimum value, maximum value and number of periods. The user has control on how the values are generated as they can be evenly (linearly) spaced, or Logarithmically spaced, if it's desired to have more points at small periods/frequencies.

For nonlinear analysis, the program currently allows the specification of two parametric variables: Period/Frequency and Strength/Ductility allowing both "Constant Strength" and "Constant Ductility" spectral computations. That will result in a "matrix" of values for each of the result quantities. This is shown graphically on the plot by using different series to represent one of the parameters (either period/Frequency or strength/ductility). The other parameter is represented by the number of points in the series. Any of the two parameters could by chosen for the "series". This will mean that all the points in a series will share the same value of that parameter. In this way, if "period" and "strength" are the variables, the plots could be constructed as either "constant period series" or "constant strength series".

For the bidirectional case, those values can also be plot for each direction, as well as for the resultant (absolute maximum).
The 2 directions and the resultant could all be shown simultaneously if the data consists of only one series (constant strength spectra with 1 strength for example).

Note that ranges of strength and ductility are specified similarly to periods and frequencies, with the ability to specify linear or log spacing.

Results can be plot both in 2D and 3D.