Civil Engineering Reference
In-Depth Information
5.1.4.
Comparison with shaking tables
At this stage, we can already compare the advantages and drawbacks of reaction
wall PSD tests with shaking table dynamic tests.
Advantages
: the PSD tests are carried out on real scale or only slightly reduced
models, which are easy and cheap to build without any scale effect of the basic
materials. The tests are carried out slowly, so they can be carefully observed. As
they can be stopped at any time, the models can be loaded to failure and it is
possible to potentially add instrumentation where it is necessary. It is also possible
to use the sub-structuration method with them.
Disadvantages:
PSD tests are carried out more slowly than they would be in real
time, which does not suit all material types. We only drive few nodes in the
structure, which is not an accurate situation when the mass is too widely distributed.
Usually we can only control the model in the horizontal plane, which prevents the
vertical components of earthquakes being taken into account.
5.2. The conventional pseudo-dynamic method
5.2.1.
Algorithms
The basic hypothesis of the PSD method is that the dynamic behavior of a
structure can be represented using a discrete model with a small number of degrees
of freedom (dof). The motion equations of this idealized structure are expressed as a
system of second order differential equations:
Mat
()
Cvt
()
rdt
( ())
f t
()
[5.1]
where
M
and
C
are respectively the mass and damping matrices,
a(t), v(t)
and
d(t)
the acceleration, speed and displacement vectors,
r(d(t))
the originally non-viscous
internal forces and
f(t)
the external forces applied to the structure.
An approximation of the solution to equation [5.1] can be obtained using a step
by step direct integration method. The solution at each time step is obtained
according to the values obtained at the previous time step, in order to have the
displacement of the structure submitted to any external loading. From this point
onwards, the time interval
0.
T
ª
¬ ¼
on which the integration has to be effected is
divided into equal time steps of size
'
.
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