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Phase 2: The sliding of the bottom mass begins when the sliding force overcomes the frictional
resistance at the plinth level. The force to cause sliding S t, is given by
S f = C s (Z t -Z b ) + K s (Z t -Z b )-M b X b (2.3)
Sliding of bottom mass occurs if | Sf | > JJL Mjg (2.4)
where, g = acceleration due to gravity; MT=Mb + M t and}x = friction coefficient. In this phase, the
building acts as two degree of freedom system shown by the following simplified equations of motion:
F =-y(t) (2.5)
Z, +2 2 (Z, -Z h ) = -X') (2.6)
where, F = |ig(l + 0)Sin(Z5); Z b = relative acceleration of bottom mass; Sin(Z b ) =+1 if (Z b )
is positive; Sin(Z b ) = -1 it (Zj-,) is negative and 0 = —— = mass ratio
M b
Phase 3: If the stopper is positioned in such a way that the peak displacement of the system is more,
then the system will strike the stopper at any time. Therefore, the motion of the system will be reversed
if the frictional resistance at the plinth level is overcome by the sliding force (S'f ) at the time of strike.
This force is given by:
n
M t
X b /p (2.7)
where, p=l/(2+0). The sliding of the bottom mass occurs backward if | S'f | > ^ M T g and the
equations of motion are given as follows:
Z b -2co^ep(Z t -Z b ) - (B 2 9|3(Z t -Z b ) + Fp = -y(t) (2.8)
Z t +2o^(Z t -Z b ) + 03 2 (Z t -Z b ) = -y(t) (2.9)
Phase 4: At any time during the motion of the system if | Sf | or | S'f j < JJL Mxg, then the sliding of
the bottom mass is stopped but the top mass continues to vibrate. Therefore, the system will behave as
single degree of freedom and its equation of motion is same as given in phase 1.
2.3 Solution of Equations of Motion
The equations of motion for the different phases are solved by Runga-Kutta fourth order method for
obtaining the complete seismic response. A computer program has been developed to compute the
time-wise earthquake response of multistory masonry building with restricted sliding base system.
3. PARAMETRIC STUDY
The parameters that are mainly considered in the study include the time period, mass ratio, dry
coefficient of friction and viscous damping for estimating realistic forces and displacements of
multistory building with restricted sliding type system. The response has been computed for two
actually recorded severe earthquakes viz., Koyna Earthquake (India) of December II, 1967
(longitudinal component) and El Centra Earthquake (USA) of May 18, 1940 (N-S component). The