DYNAMIC RESPONSE OF SYMMETRICAL REINFORCED CONCRETE BUILDINGS
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Date
2004-03
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Addis Ababa University
Abstract
The effect of soil-structure interaction on the dynamic response of reinforced concrete
buildings of regular and symmetrical geometry is considered in this study. The structures
are presumed to be generally embedded in a homogenous soil formation underlain by very
stiff material or bedrock. The structure-foundation–soil system is excited at the base by an
earthquake ground motion.
The superstructure is idealized as a system with lumped masses concentrated at the floor
levels, and coupled with the substructure. The substructure system, which comprises of the
foundation and soil, is represented and replaced by springs and dashpots.
Frequency-dependent impedances of the foundation system are incorporated in the
discrete model in terms of the springs and dashpots coefficients. The excitation applied to
the model is field ground motions of actual earthquake records.
Modal superposition principle is employed to transform the equations of motion in
geometrical coordinates to modal coordinates. However, the modal equations remain
coupled with respect to damping terms due to the difference in damping mechanisms of
the superstructure and the soil. Hence, proportional damping for the coupled structural
system may not be assumed.
An iterative approach developed by Worku [13,14] is adopted and programmed to solve
the system of coupled equations of motion in modal coordinates to obtain the displacement
responses of the system.
Parametric studies for responses of building structures with regular and symmetric plans
of different structural properties and heights are made for fixed and flexible base
conditions, for different soil conditions encountered in Addis Ababa.
Soil borehole log data of three representative sites in Addis Ababa were used for the
computation of the stiffness and damping of the soil.
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The displacement, base shear and base overturning moments are used in the comparison of
different types of structures for various foundation embedment depths, site conditions and
height of structures. These values are compared against those of fixed base structure.
The study shows that the flexible base structures, generally exhibit different responses
from those structures with fixed base. Basically, the natural circular frequencies, the base
shears and the inter-story displacements for the flexible base are less than those of the
fixed base structures. This trend is particularly evident when the flexible soil has large
thickness. In contrast, the trend becomes less predictable, when the thickness of the
flexible soil decreases. Moreover, in the latter case, the iteration undulates significantly
making the prediction difficult. This is attributed to the highly jagged nature of the
impedance functions of frequencies for such formations. In this particular case, it is
difficult to conclude whether the conventional fixed-base approach yields conservative
design forces, as is the case for soil formations of large thickness.
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Keywords
Concrete; Buildings