# General Information

SCAD has a capability of analyzing the behavior of structures under seismic actions described by given accelerograms. The accelerograms must be prepared in advance as files of a certain format which will be described later.

The accelerogram file format is simple and straightforward, so such files can be created and processed by any text editor or word processor. To further facilitate the accelerogram preparation process, SCAD Office has been supplemented with auxiliary software named Accelerogram Editor. Along with the common data editing functionality, this program enables you to perform an analysis of an accelerogram. Particularly, the following information can be obtained in both graphical and tabular form:

• an accelerogram (an acceleration vs. time relationship);
• a velocigram (a velocity vs. time relationship);
• a seismogram (a displacement vs. time relationship);
• an amplitude Fourier spectrum (absolute value of the accelerogram’s Fourier transform vs. frequency);
• a power spectrum (absolute value of the accelerogram’s Fourier transform squared vs. frequency);
• response spectra for given values of logarithmic decrements of oscillations;
• general properties (maximum and root-mean-square accelerations, velocities, and displacements).

# The following type of Fourier transfrom is used in the program: $\int f(t)e^{2\pi i\omega t}dt$.

Accelerograms usually contain errors, no matter whether they are instrumental (i.e. recorded with seismograph) or analytical (calculated on the basis of a measured seismogram). In analytical accelerograms the errors commonly arise because of the numerical differentiation. Most often, these errors will be great in magnitude for the high-frequency component of the action. In instrumental accelerograms, the errors will arise during the recording and digitizing. Most of the recorded accelerograms contain great errors in a long-period range. The Accelerogram Editor program does not offer any means for correcting instrumental errors of the baseline or signal frequency filtering. It is just assumed that such actions have been previously performed.

Another typical error commonly made in accelerograms is introducing an offset and a slope to the baseline (see [2] for examples). Let’s give an example borrowed from the book [4] that shows how even the smallest errors of this kind can enormously distort the depiction of displacements experienced by a designed structure. Suppose there is a given harmonic action $\ddot{{x}}(t)=w\sin (\omega t)$ subjected to a small perturbation in the form of a slope of the baseline of 0,001wt and an offset of the same line by -0,03w. The said perturbations are hardly noticeable on the accelerogram of $\ddot{{x}}(t)$, but they make the seismogram look utterly different from what it should be like; the equation of the latter becomes $x(t)=w(0,001\frac{t^{2}}{2}-0,03t-\frac{1}{\omega^{2}}\sin \omega t)$. The program suggests a capability of accelerogram balancing in order to be able to amend errors of this type.

Seismic analysis uses a suggestion that the half-space moves linearly and all points of it experience synchronous displacement. The time history of these displacements is defined by an accelerogram, i.e. a functional relationship between the ground acceleration and time. Thus the design model of a structure usable for the accelerogram-based analysis should have the accelerations in all supports modeling the soil-structure interaction.

The accelerograms are defined in points where the measuring devices are installed, and they are located on the ground surface (or close to it). Since a structure might have an embedded foundation, it is necessary to know the motion of points located below the ground surface. The Accelerogram Editor application can be also used to recalculate a standard accelerogram for a certain level shifted from the measurement surface.

Accelerogram files usually have the SPC extension and are plain text files. There is an arbitrary text (comment) at the beginning of each file, which is followed by a separator character # and three numbers (a factor for converting the given values to m/sec2, a number of points in the accelerogram, and a time step in seconds). It is assumed that the acceleration values were recorded at a constant time step. The listed data is followed by the acceleration values. The number of specified values must conform to the number of points. The accelerations, the time step, and the conversion factor are floating-point numbers with a period serving as a separator between their integer and fractional parts. All numbers in the file must be separated by spaces or start from a new line.