# Dynamics of rigid block structures

## by P.R. Lipscombe

This dissertation investigates the dynamic behaviour of structures which
consist of a small number of unbonded rigid blocks. These structures exhibit
an apparently simple rocking behaviour which, however, in the past has
proved difficult to analyse.

A review of available literature on rocking structures reveals that
the most popular model used to describe the dynamic rocking behaviour of
a single rigid block is G.W. Housner's classical theory. A study of published
experimental results reveals some discrepancies with this theory.

The accuracy and limitations of the classical theory are established
with the aid of experiments. A new theoretical model is developed to explain
the experimental behaviour, it allows the block to lose contact with the
foundation after impact. The predictions of the new 'bouncing' model match
the experimental results well. For slender blocks, the model coincides
with the classical theory. Any slight asymmetry significantly affects the
observed response.

The concepts developed for the 'bouncing' model are extended to develop
a three-dimensional model for a single block and a general model for multi-block
structures.

A series of random vibration experiments, on a shaking table indicate
that the rocking response of rigid structures is very difficult to predict
for any one particular simulation. However, statistical interpretation
of the results shows that the theory and experiments agree remarkably well.
An example is given, showing how the statistical interpretation may be
applied to a practical assessment of stability.

Keywords: Rigid block : Rigid body : Rocking : Structural dynamics :
Earthquake response.

[Cambridge University | CUED
| Division D | Structures
Group ]

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(last update 12th January 1998)