REDUCTION AND DISTRIBUTION OF LATERAL SEISMIC INERTIA FORCES ON BASE ISOLATED MUL TISTOREY STRUCTURES

This paper presents some important results of a thorough investigation into the seismic behaviour of a wide range of Base Isolated multi storey structures. The benefits of implementing BI systems are highlighted. The reduction and distribution patterns of lateral inertia forces due to the inclusion of this isolation system are specifically discussed.

As a result the design practice at present still relies upon a series of deterministic time history analyses with direct step-by-step integration which are not only impractical for design purposes but appear unable to give the designer a clear insight into the seismic behaviour of BI multistorey structures.
It is understood that without a clear insight a structural designer will not be able to present an optimum design.
Realizing the above need, research was carried out at the University of Canterbury [ 4] .
Its first objective was into BI multi-storey structures to review the short-comings of current -design methods and to investigate in more detail the seismic behaviour of a wide variety of BI multistorey structures.
Then, based on the results obtained, the above research was directed to accomplish its second objective which is to develop a simple design procedure for this type of structure.
In this paper some important results of the above investigation are presented.The reduction and distribution patterns of lateral inertia forces due to the implementation of BI systems are specifically discussed.
In Sections 3 and 4, a single ground motion namely the El Centro 1940 N-S earthquake is considered while in Section 5, the effect of different ground motions is also discussed.
A proposed design approach is described in an accompanying paper( 5 l• 2.

ESSENTIAL CHARACTERISTICS AND BASIC PRINCIPLES
A desirable BI system should several essential characteristics.embody (a) Horizontal flexibility which is able to lengthen the fundamental natural period of the structure.Under earthquakes with acceleration response spectra that diminish at (b)

2.5
longer natural periods, this action will shift the structure out from the dominant earthquake energy region and thus will significantly reduce the inertia forces induced in the superstructure.
The capability of dissipating earthquake energy so as to resist excessive horizontal displacements at the base of the building.This additional hysteretic damping will reduce further the spectral acceleration and hence the forces.keff and the additional hysteretic damping, El). of the BI system at the maximum displacement, Xm~• Fig. 2 illustrates a typical hysteresis loop model.The initial and unloading stiffness is denoted by k 0 whereas the post-yield stiffness is expressed by ak 0 • FY denotes the yield force of the BI system which is reached at the yield displacement, xy.
This study assumes Keff to be the secant stiffness at Xmax and Eh is estimated from the area circumscribed by the hysteresis loop.
These two parameters, keff and Eh can be expressed in the following equations in terms of the initial stiffness, k 0 ; the ratio of the post-yield stiffness to the initial stiffness, a; and the ratio of the maximum displacement to the yield displacement,µ. where Factor R expressed in Eq.3 is the ratio of the bilinear hysteresis loop area to the area of its enclosing rectangle.
It is useful to introduce this factor since the fatness of the hysteresis loop can be estimated directly from it.R may vary from zero for a linear BI system to almost one for a very fat hysteresis loop.

EVALUATION OF THE SEISMIC RESPONSE
The implementation of a BI system is meant to protect a structure from the seismic In the two following parts of this section the influence of three important structural parameters on the seismic response of BI multistorey buildings with elastic superstructures are discussed.The three parameters are: where E is the elastic modulus of the structural materials, Ib and Ic are the beam and column moments of inertia, Lb and Lc are the length of the beam and column respectively.
Note a complete range of frame behaviour can be covered by simply varying € from € = o.0 for flexural "cantilever-beam" structures, in which the beams impose no restraint on joint rotation, to the "shear-beam" structures, where the joint rotation are completely restrained (€ = oo).
At the end of this section the effect of BI system on the inelastic response of the superstructure will be discussed briefly.

Lateral Storey Displacements
The typical lateral displacements of a four-storey uniform "shear beam" model with and without BI system are contrasted in Fig. 3 .
In BI multi storey structures larger displacements should be expected due to the horizontal flexibility provided by the BI system.
To avoid contact with adjacent buildings during earthquakes, a sufficient gap must be provided to accommodate these large lateral displacements.
Also flexible connections should be provided for services, such as water supply, drainage system, etc., into the building.Thus, there is a significant reduction in the interstorey drift which will considerably limit the damage to non-structural elements, such as partitions, plasterings, veneers, windows and equipment installed within the building.
Furthermore they imply reduced force response in the structural members.
These benefits will offset the disadvantages caused by the larger lateral movements.
The influence of the fundamental period • the superstructure, Tl(UI) on the maximum lateral storey displacements is shown in Fig. 4.
In this case the BI system has ka = However, the storey displacements of a BI structure relative to the base movement are much smaller when compared with the storey displacements of unisolated structures.
With regard to the influence of Tl(UI) on the interstorey drifts, it was found from the response history that the interstorey drifts of BI multistorey structures with stiff superstructures (say Tl(UI) 0.2 secs) are always in phase with each other revealing the dominance of the first mode.The drifts between the ground and first floors are always the maximum and followed in sequence by the drifts of the higher storeys in an almost constant ratio.
As the superstructure becomes more flexible, however, the interstorey drifts are no longer in phase due to the effect of the higher modes.
The maximum drifts may no longer occur in the first storey.
In an elastic unisolated structure this OJ ..c:.
The above phenomenon can be easily overlooked since the interstorey drifts of a BI structure are much smaller when compared to its base displacement.
The superstructure seems to move like a "rigid body" on top of a "spring" with a large horizontal flexibility.
Al though the other two structural parameters, namely the frame action and the BI system's parameters may also have si~nificant effects on the interstorey drifts the phenomena will be discussed implicitly while discussing the distribution patterns of the lateral inertia forces.
In the following only the effects of those parameters on base displacement will be discussed.
Figure 5 shows that the difference in maximum base displacement as affected by superstructure type are not significant especially for BI structures with Tl(UI) :-:; 0.8 secs.
Within this range the base displacements of BI structures with E = 0.0 ("cantilever-beam") and € = 0.l25 ( "typical moment resisting frame") differ less than l2% when compared to the base displacements of BI "shear-beam" structures ( E = oo) .For the whole considered range_ of T 1 (UI), i.e. up to 2. 0 seconds, the differences are less than 21%.
In the above evaluation all structures are mounted on a BI system with a fixed-set of parameters, namely k 0 = 10.0 W/m, ak 0 = 1.5 W/m and FY= 5%W where W is the total QJ 229 weight of the structure.It is also useful to discuss the effect of varying these parameters on the base displacement.For this purpose a four-storey "shearbeam" superstructure model with Tl(UI) = 0.4secs are used.
Results similar to those discussed below were found by Lee< 8 >.
First, k 0 and FY are varied from 2.5W/m to 25W/m and 1%W to 25%W, respectively, while ak 0 is kept constant at 1. 25 W/m.The effect of these parameter variations on the base displacement is shown in Fig. 6.a.It can be seen that a BI system with a stiffer k 0 tends to minimize the base displacement.
This is because to increase k 0 means widening the hysteresis loop which increases the effective damping and provides a stiffer system especially at high level of FY.
Hence it reduces the base displacement.
It is also shown in Fig. Ga

FIGURE 6b: THE EFFECT OF VARYING POST-YIELD STIFFNESS AND YIELD STRENGTH ON MAXIMUM BASE DISPLACEMENT
For a BI system with low k 0 , the base displacement increases again as the yield strength becomes greater than the "optimum" point, i.e. around 5%W.This type of BI system naturally has a small capacity for energy dissipation.
If ak 0 and F are now varied while k 0 is kept constant at 10.0 W/m, the maximum base displacement response varies as is shown in Fig. 6b.
In general the smaller the post-yield stiffness is the larger the base displacement.
However, the effect is not so dramatic as if k 0 is varied while ak 0 is kept constant.
At yield strength levels below 5%W, the base displacement increases rapidly as FY decreases especially for BI systems witn a small ak 0 • At this condition the effective stiffness becomes smaller as ak 0 decreases while at high levels of yield strength the effect of Fl become insignificant, since at these leve s the initial stiffness is more dominant.
The maximum base displacement of a linear BI system with lateral stiffness of 10. o W/m is also shown in Fig. 6b.
As expected, a relatively stiff linear BI system without energy dissipation capacity is able to keep the base displacement small (c.f. a much more flexible linear BI system shown in Fig. 6a), but at the expense of higher induced inertia forces as will be shown in the following subsection.

Reduction of Inertia Forces
From Fig. 7 it can be observed that the maximum base shear of an elastic unisolated structure changes dramatically with the value of Tl(UI) and it follows the pattern of the earthquake response spectra which, in this case, is for the El Centro 1940 N-S earthquake.
For BI structures, however the variation of Tl(UI) hardly effects the maximum base shear.This is caused by the shift of the period of the first mode, which dominates the base shear, to the plateau area of the acceleration response spectra.
It is obvious that a BI system will considerably reduce the base shear of short-period multi storey structures.
As the superstructure becomes more flexible (say Tl(UI) > 1. 2 secs) the reduction is less s1gnif icant, i.e. the degree of protection diminishes for structures with longer Tl(UI)" In this investigation a series of "shear-beam" structures mounted on The effect of varying the BI system's parameters on the base shear is depicted in Figs.9a and 9b.First, ak 0 is kept constant while varying k 0 • Secondly, k 0 is kept constant at 10. 0 W/m while ak 0 is varied from 0. 5 to 2. 5 W/m.
It can be seen from Figs. 9a and 9b that in general the base shear reaches its minimum value when F is around 3. 0 to 7. 0%W.
In this range lhe BI system provides the maximum energy dissipation capacity and reaches its optimium performance in reducing not only the base shear, but also the base displacement.
It was found that the upper-storey shears may not be reduced by the same degree as the base shear.
Fig. 10 shows the lateral inertia force distribution and the lateral storey shear envelopes of an unisolated structure and BI structures which are mounted on two types of BI system.
From these shear diagrams it can be seen that the upper-storey shears have a smaller Hence, the equivalent static lateral force distribution recommended by the loadings codes [9,10], which give a reasonable safety margin for the storey shears of unisolated structures, may underestimate the shears at the upper-storeys of BI structures especially if the BI system has a fat hysteresis loop, in this case due to a lower ak 0 • This is discussed in Section 4.

Reduction of Ductility Demands
In the previous discussions the superstructure was assumed to remain elastic.
Significant attenuation of the transmitted ground motion energy by a BI system enables the inertia forces to be reduced by factors of up to six.
Thus it is possible to expect the superstructure to behave elastically under the designlevel earthquakes.
It is important, however, to understand how a BI multistorey structure will behave under seismic load conditions beyond the design level.
For this purpose the inelastic responses of a six-storey frame structure, with and without BI systems, are compared and the effect of using BI systems with a different set of parameters is also studied.
The Both the unisolated and BI structures were subjected to El Centro 1940 N-S earthquake multiplied by 1. 4 so that the peak acceleration is O. 4g.Some researchers [ 3] have used this 1. 4 scaled El Centro 1940 N-S earthquake record to simulate an earthquake with a 450 year return period which is beyond the NZ Zone A's seismic design level [10).Ji.. 7.8   7.5 As can be seen in Fig. 11, the inclusion of a BI system which has lower post-yield stiffness and greater energy dissipating capacity or fatter hysteresis loops (k 0 = 10.0 W/m, a= 0.05, FY.= 5%W) further reduces the curvature ductility demand at most beam-ends.

2."JL
Some members of the frame never reach their yield strengths.It can be seen that the difference between the base shears of a multistorey structure mounted on two different BI systems, with initial stiffness of 2.5 and 25.0 W/m is only around 10%, while at the upper levels the shears may differ as much as 94%.
Low initial stiffness causes the hysteresis loop to narrow and the effect becomes similar to the one caused by a linear BI system, which deflects the input earthquake energy rather than absorbs it.As was pointed out by Kelly [16], in a vibrating linear system all modes tend to be mutually orthogonal.In this case, all higher modes will be orthogonal to the input motion so that the transmission of high energies of input ground motion at certain frequencies, which tend to excite the higher modes, will be minimized.Therefore, the structure response becomes first mode dominant and the lateral shear envelope 233 may even show a tendency of rigid body motion with equally distributed acceleration over the height of the superstructure.
An almost straight line lateral shear envelope is depicted in Fig .12a as the effect of this type of BI system.
An increase of initial stiffness, enhances the energy absorption capacity of the BI system.
The contributions of the higher modes become significant in the upper levels of the superstructure and a more bulged lateral shear envelope is encountered.
A similar effect is also found as the post-yield stiffness is decreased (Fig .12b) and as the yield strength level is increased (Fig. 12c).
As where V is the base shear, the floor weight and the respectively. (5) Wi and h:i, are floor height, In this section the correlations between these two factors for a wide range of BI structures, i.e. with Tl(UI) = 0.2, 0.4, 0.8 seconds and € = 0.0, 0.125, oo, are shown in Table 1 or Fig. 13.These correlations are based on the linear regression analyses [ 17] of data for the two variables, i.e.Rand p.
The range of the most likely used BI systems is covered by incorporating isolation systems with R from o .1 (thin loop) to o. 6 (fat loop).BI structures which have Tl(UI) equal to 0.8 secs but with R ~ 0.4 or Tl(UI) larger than 0.8 secs are not included since their shear envelopes become difficult to approximate using this approach.The range of the BI systems' yield strengths is 3.0 to 7.0% w.
This trend however, is not found for BI structures with T;I,(UI) = 0.4 secs.Since the modal contrioutions to the storey shears are also dependent on the likely irregular shape of the earthquake spectral acceleration as well as being affected by the inelastic behaviour of the BI system, the above phenomenon cannot be approximately evaluated using only their initial and pseudo post-yield linear modal properties [4].
In spite of this, the strong correlation Only some highlights of the results are reported here.
Figure 14 shows the correlations between the hysteresis loop ratio, R and the exponent p used in Eq. 5 for BI structures with Tl(UI) = o.8 secs subjected to group ground mo~ions.
It can be seen from this figure that the correlations between Rand p are earthquake dependent.Similar results for other "shear-beam" structures with different Tl(UI) are reported elsewhere [4].It can be seen in Fig. 15  As shown in Fig. 15, structures mounted _ on thin and moderately fat hysteresis loops have larger storey shears than their fixed-base counterparts.Some reductions can only be achieved by using BI systems with large energy dissipation capacities.
As expected, these reductions are still not so dramatic as observed in the El Centro 1940 N-S earthquake.
Any displacement-dependent BI system tends to lengthen the fundamental period of the structure and thus shifts it into a more dominant energy region of the Bucharest and Mexico City type earthquakes.Therefore the large energy dissipation capabilities become less effective.
For this particular case it is desirable to use a BI system which does not lengthen the fundamental period such as viscoelastic dampers [11].
The benefits of implementing a BI system have been demonstrated.Due to the inclusion of a BI system, the inertia forces and the interstorey drifts of a multistorey structure can be significantly reduced.As a result, the superstructure can be designed to behave elastically under design-level earthquakes.
The much smaller interstorey drifts prevent the early occurence of non-structural damage during moderate ground motions.

3.
Under earthquakes beyond the designlevel excitations, a superstructure monted on a BI system shows many fewer plastic hinges and has much lower ductility demands when compared with a conventionally designed ductile structure.
The In this case the equivalent lateral force are almost uniformly distributed over the entire height of the superstructure.
In contrast, if the BI system has a great energy dissipation capacity, indicated by a high hysteresis loop ratio R, the contributions of the higher modes become more significant, especially in the upper-storeys, and causes the lateral shear envelope to be more bulged.
As strong linear correlation was found between the hysteresis loop ratio Rand the shape of the lateral shear envelope.This correlation is dependent upon Tl-(UI), the beam-to-column stiffness ratio, € and the characteristics of the ground motion.

5.
For sites with ground motions which have peak spectral acceleration in longer periods the inclusion of a BI system may shift the fundamental period of the structure into that of a more dominant earthquake response.However, it seems possible to reduce the transmitted energy of this type of earthquake into the superstructure by using systems that provide large amounts of additional damping without increasing the fundamental period of the structure.

Fig
stiffness, ka, the postyield stiffness, aka and the yield strength, FY of the BI system. the frame action or the type of the superstructure which can be expressed in its joint-rotation index, €, as defined by Blume[7]  and which is based on the properties of beams and columns in the storey closest to the mid- It is worth noting that the base of a BI

FIGURE 3
FIGURE 3: TYPICAL LATERAL DISPLACEMENTS OF A MULTISTOREY UNIFORM STRUCTURE WITH AND WITHOUT BI SYSTEM FIGURE 4: MAXIMUM STOREY DISPLACEMENTS OF UNISOLATED AND BI MULTISTOREY STRUCTURES WITH VARIOUS Tl(UI) FIGURE 5: MAXIMUM BASE DISPLACEMENTS OF BI STRUCTURES WITH DIFFERENT Tl(UI) AND f FIGURE 6a: THE EFFECT OF VARYING INITIAL STIFFNESS AND YIELD STRENGTH ON MAXIMUM BASE DISPLACEMENT 15, and FY = 5%W were used as the analytical models.The influence of frame action on the base shear of the BI structures was found insignificant as demonstrated in Fig.B.For the entire range of evaluation (0.2 ~ T1 (UI l ~ 2. 0 sec) the maximum base shears of BI structures with € = o.o and 0.125 differ only less than 17% when compared to the maximum base shears of BI "shear-beam" structures which have€= oo.

FIGURE 7 :
FIGURE 7: THE EFFECT OF Tl(UI) ON MAXIMUM BASE SHEARS FIGURE 11: CURVATURE DUCTILITY DEMANDS AT BEAM ENDS AND COLUMN BASES UNDER 1.4 EL CENTRO 1940 N-S EARTHQUAKE Figure 12a illustrates the effect of varying the initial stiffness while keeping the post-yield stiffness and the yield strength level constant at 1. 25 W/m and 5% W, respectively.It can be seen that the difference between the base shears of a multistorey structure mounted on two different BI systems, with initial stiffness of 2.5 and 25.0 W/m is only around 10%, while at the upper levels the shears may differ as much as 94%.
FIGURE 12: THE EFFECT OF VARYING BI SYSTEM PARAMETERS ON LATERAL STOREY SHEARS

Fig . 13
Fig .13shows the values of the exponent p for different € diverge as R increases.It can also be seen that the slope of the correlation lines becomes steeper for BI structures with longer Tl(UI).As the value of exponent p increases, the lateral shear envelope becomes more bulged FIGURE 14: RELATIONSHIPS BETWEEN R AND £ FOR BI "SHEAR-BEAM" STRUCTURES WITH Tl{UI) = 0.8 SECS UNDER VARIOUS EARTHQUAKES

FIGURE 15 :
FIGURE 15: THE EFFECTS OF VARIOUS BI SYSTEMS ON THE LATERAL STOREY SHEARS OF STRUCTURES SUBJECTED TO DIFFERENT TYPES OF EARTHQUAKE INTRODUCTION

Table 1 :
correlations between the Hysteresis Loop Ratio and the Exponent p