### Earthqauke design of buildings. Rotations in the soil motions

*Alberto Castellani*

Ultima modifica: 2022-08-29

#### Sommario

**Abstract **

In the present paper, the set of records collected at a dense array of recorders are represented through an interpolation function of the surface coordinates of the instruments. Rotation is measured as a function of space and time, free from any model of propagation. Propagation models hold in fact at some distance from the source, i.e. at distances where the source mechanism can be represented as a point source.

The way to take into account earthquakes in a building design is originally dictated by G. W. Housner (1956). It is based on the description of the soil motion through a *Response spectrum.* In the design specification of buildings, this quantity is established in regions of suitable extension. It is affected by a few parameters that take into account the local soil condition.

Some other items affect the Response spectrum, and in general the buildings behavior. One is the fact that soil motion can be affected by rotation besides the translations, which only are represented by the Response spectrum. In particular, the couple of rotations around two orthogonal axes in an horizontal plane, ¶a_{x}/¶y and ¶a_{y}/¶x, where a_{x} and a_{y }are soil acceleration along x and y axis.

In order to check these assumption, some dense arrays of instruments have been installed since a few decades. The most important of them is the dense array of Smart 1 [ ] and that of Smart 2. . The present study is devoted to analyze the record of some earthquakes, in order to establish the relevance of difference of soil motion at short distances, and thus of rotations.

A few investigations on this subject have been undertaken. The scope of the present investigation is to rely as much as possible on the records collected by the dense array during one earthquake. The scope of the investigation is twofold:

- The power spectrum of the rotation signal shows that the dominant frequencies for rotation are in the range of 3-11 cps. Excitation provided by rotation may thus be meaningful for common buildings but mainly for chimneys, tall buildings, and bridge pears.

-On the basis of dw/dx and dw / dy, one cannot evaluate the max rotation component, (see for instances.as defined in the Flugge Handbook)

It is established that rotations can be favorable or unfavorable with respect to a building acted by the appropriate Response spectrum.

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