Experimental Methods in Earthquake Engineering - Dynamic Behavior of Concrete and Seismic Engineering - page 194

Depending on the tests and models, two laws of similarity are used for shaking
table seismic tests.
The first law of similarity is a speed law. It can be used when gravity does not
influence the model's behavior or when permanent stresses do not prevail. For the
same speed, the same stresses will also be found in the material. For a geometrical
reduction scale n, this involves applying a horizontal acceleration that is n times as
high as for scale-1 and is contracted in time by an n coefficient. As gravity remains
constant, the vertical acceleration (or gravity) is then n times as low as it should be.
For civil engineering tests, generally, the gravity effect is important. Therefore,
to get back to the normal loads and the stresses, it is necessary to apply a vertical
acceleration that will have the right horizontal acceleration ratio. As gravity cannot
be modified, another law of similarity called the acceleration law is used. In this
case, both horizontal and vertical acceleration levels applied are similar to scale-1
acceleration, and the signals are contracted in time by a factor n . In order to find
the right stresses, because the masses have to be in 1/n² (instead of 1/n 3 , if we keep
the same material), it is necessary to load the floors or the reduced-scale model with
additional masses.
5.7. Instrumentation
During seismic tests on civil engineering models, the following conventional
instrumentation is used:
- accelerometers (mainly controlled or piezo-resistive types to have the lowest
possible pass-band or a pass-band starting from zero);
- wire displacement transducers to allow measurement, even when the model has
transverse displacements, and to allow measurement of important displacements;
- LVDT-type displacement transducers to measure crack openings;
- strain gages stuck on the metallic frames during manufacturing or
stuck directly onto the concrete.
This instrumentation enables us to determine:
- the overall behavior of the model, by measuring the eigenfrequencies, the
eigenmodes, the overall displacements and the accelerations at different points of the
model; and
- the local behavior, by punctually measuring the strains and crack openings;
- the displacement transducers allow us to measure either the relative
displacements (if they are fitted to a supporting frame loaded on the table or directly