Number of Seismic Events Used

Some decades ago, when Earthquake Engineering started to develop, the amount and quality of the available recorded seismic events was limited. During those years, the "El Centro 1940" earthquake became the prototype of an intense event, and it was used by different researchers to do their investigations. Since the 70's the amount of recorded events has steadily increased. Nowadays, researchers have a large set of these recorded events. In this set, there are many events of much larger magnitude or duration than the "El Centro 1940" seismic record.

Older published papers and technical reports show results of analysis made using only one earthquake record. Parametric studies were done using single seismic events, and these results were, in some form, incorporated into the design codes of different countries. The problem with this research results is that the accumulated evidence demonstrates that different seismic events can have quite different characteristics. Dissertation Layout

To illustrate this point, in chapter 3 are presented the Fourier Spectra of the seismic events included in the data set used in this Dissertation. These Spectra show clearly that the frequency contents vary considerably for each event. There are other important parameters that differ, i.e., total duration of the event, magnitude, distance to the epicenter, etc. Nowadays, the research community recognizes the importance of using more than one seismic event for performing basic research. Thus, it has become the norm to use a set with many and diverse modified historic seismic events.

Number of Seismic Components Used.

The electronic devices used to record ground accelerations are capable of recording three orthogonal components of the ground acceleration. Two horizontal and one vertical. One or more of these components have been used to perform dynamic analysis of buildings. Historically, these seismic records were included in the mathematical model in three different variations:

1. Unidirectional seismic excitation Only one horizontal component of the seismic record is used for the time history analysis. 2. Bidirectional seismic excitation The two horizontal orthogonal components of the seismic record are used for the time history analysis.

3. Tridirectional seismic excitation The two horizontal and the vertical orthogonal components of the seismic record are used for the time history analysis. Many studies about torsional behavior of buildings were performed using unidirectional seismic excitations. Typically, the studied buildings have two or more parallel frames on one direction, X, and two or more parallel frames in the orthogonal direction, Y. To handle the fact that real earthquake ground motions have more than one component of acceleration, researchers have had to create peculiar concepts such as:

• Torsionally unrestrained is defined as a building where the unidirectional seismic action is on Y direction and the orthogonal frames (on the X direction) do not provide any opposition to the story rotation. The frames parallel to the earthquake action can behave non linearly.

• Torsionally restrained is defined as a building where the unidirectional seismic action is on Y direction and the orthogonal frames (on the X direction) provide opposition to the story rotation. The frames parallel to the earthquake action can behave non linearly and the orthogonal frames are in their elastic range of deformations.

These concepts were created to make sense of results obtained from unrealistic seismic excitations. Only in the context of unidirectional seismic actions these concepts make sense.

More recently, bidirectional seismic actions have been used to perform studies on torsional behavior of buildings. For this research, this is the type of seismic actions used. When bidirectional seismic actions are used, instead of unidirectional, the results obtained can be significantly different. One of the interesting implications of using bidirectional seismic actions is that the concepts of torsionally unrestrained and restrained are not necessary anymore. And, as it is demonstrated in chapter 8, new patterns of behavior can be observed. Patterns that cannot exist in buildings under unidirectional seismic actions. Of course, bidirectional seismic actions are closer to a realistic modeling of the seismic action than the unidirectional action.

The author did not find published research on torsional behavior of buildings, using Tridirectional seismic actions. However, in the near future, the inclusion of the vertical component of the ground acceleration will become a requisite, to allow the evaluation of changes of axial load in columns, due to the vertical accelerations, and their effects on the global response of the building.

Angle of Incidence of the Seismic Action. Seismology cannot provide to the designers with a reliable prediction of the direction where the ground waves will come from in the next earthquake. This direction is called the angle of attack, or the angle of incidence, of the seismic event. Therefore, for design or research purposes, a decision needs to be taken with respect to this parameter. Historically, there are three approaches used by researchers with respect to the selection of the angle of incidence used in their investigations: Dissertation Layout