Earthquake Engineering Research - HKU Libraries - The University ...

472
investigated a base isolation system in which the isolation mechanism is purely sliding friction. Such
system utilizes pure friction to allow some parts of a structure to slide relative to the others.
A mathematical model was introduced by Qamaruddin [5] and Arya et al. [1] to compute the seismic
response of masonry building with friction base isolation. A new concept has been proposed for the
construction of brick building in which a clear smoothened surface is created just above the dampproof
course at plinth level without any mortar, and the superstructure simply rests at this level and is
free to slide except for frictional resistance. The concept of such system was further strengthened by
the damage studies made by Li Li[3] after the Xintai (1966), Bohai(1969) and Tangstan (1976)
earthquakes in which it was found that adobe buildings which were free to slide on their foundations
(by accident) survived with little or no damage whereas others which were tied on their foundations
collapsed. Researchers have made experimental and theoretical studies to incorporate such a system in
masonry buildings economically to achieve a collapse free if not a damage free performance during the
earthquakes. Further studies have also been made by Mostaghel et al. [4] and Qamaruddin et al. [6 and
7] with encouraging results.
2. MATHEMATICAL IDEALIZATION
2.1 Mathematical Model
A two-degree spring mass model shown in Fig. 2.1 represents the concept of multistory building with
restricted base sliding. A layer of suitable material of known coefficient of friction is laid between the
contact surfaces of the bond beam of the superstructure and plinth band of the substructure. The spring
action in the system is assumed to be provided by the shear walls. Internal damping is represented by a
dashpot that is parallel with the spring. The total mass of the superstructure of a multistory building,
i.e., the mass of all the stories, except the bottom half of the ground story is lumped at the top of the
system and the mass of the remaining bottom half portion of the ground story is lumped at the level of
the band beam. The lower mass is assumed to rest on a plane with dry frictional damping to permit
sliding of the system. Restricted base sliding can occur at the contact surface without overturning or
tilting. The building is subjected to only one horizontal component of ground shaking at a time, the
effect of vertical ground motion is not considered here. The stopper is considered as rigid.
2.2 Equations of Motions
Phase I: Initially, bottom mass moves with the base so long as sliding force does not overcome the
frictional resistance. So the building behaves as a single degree of freedom system and therefore
equation of motion is:
M t x t +C s (Z t -Z b )+K s (Z t -Z b ) = 0 (2.1)
orZ t -r2o)^(Z t -Z b )4-03 2 (Z t -Z b ) =-y(t) (2.2)
where, C s = coefficient of the viscous damper; K s = spring constant; M t = top mass; X{, Z{ =
absolute and relative acceleration of the top mass; y(t) = ground acceleration at time t; Z b, Z t =
lateral relative displacement of masses M b and M b respectively; M b - bottom mass; Z b , Zt =
relative velocity of masses M b and M t, respectively; co = natural frequency and £ = fraction of critical
damping.