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Application of base isolation concept to soft first story buildings
-
Compureu
> Pergamon
& Svurruws Vol. 55, No. 5, pp. 883-896. 1995 CopyrIght 8cm1995 Elsewer Science Ltd Printed in Great Britain. All nghts reserved 0045.7949/95%9 50 + 0.00
0045-7949(94)00433-1 . _
APPLICATION
OF BASE ISOLATION CONCEPT FIRST STORY BUILDINGS
TO SOFT
Y. L. MO and Y. F. Chang Department
of Civil Engineering,
National (Receked
Cheng
Kung
7 September
University,
Tainan
70101, Taiwan
1993)
Abstract-A practical system that combines a flexible first story with sliding frictional interfaces is described. The system utilizes Teflon sliders at the top of the first story reinforced concrete framed shearwalls to carry a portion of the superstructure. Energy dissipation is provided by the first story ductile columns and by the Teflon sliders. Utilizing this concept the seismic response characteristics of a multistory frame are analyzed and discussed.
1. INTRODUCTION
dynamic response of the proposed system, parametric studies are performed, and the results are critically examined.
Base isolation can significantly reduce the damage of buildings produced by a strong earthquake [I]. To separate a building from the surrounding ground motion, two methods can theoretically be applied: (1) a soft first story concept; and (2) sliding/bearing system. However, their full utilization in practice is still questionable due to the following reasons. The soft first story concept [2] is an attempt to reduce accelerations in a building by allowing the first story columns to yield during an earthquake and produce energy-absorbing action. However, excessive drifts in the first story coupled with P -A effects on the yielded columns make buildings collapse [3]. Similarly. in the sliding/bearing systems there are risks of overturning, since no solid connections exist between the superstructures and the foundations. Also, lack of a solid connection may result in excessive displacement. Although horizontal dampers may be used to decrease the displacement, it is difficult to implement and maintain permanently. It is shown in this paper that a new approach is proposed, that combines the soft first story concept with a sliding frictional system. This approach is an attempt to minimize the disadvantages of the two methods discussed above while retaining their advantages in reducing the structural response and damage during an earthquake. In this approach, Teflon sliders are placed on the top of the first story reinforced concrete framed shearwalls. These shearwalls are framed by columns and beams and are designed to carry a portion of the weight of the superstructure and the lateral load determined by the frictional characteristics of the Teflon sliders. The remaining first story columns are designed for ductile behavior in order to accommodate large drifts. According to this proposed system, a dynamic response analysis is described. To determine the effects of variables on the (‘AS
55 s--J
2.
PROPOSED
SYSTEM
In the proposed system a major part of the weight of the building is carried by the Teflon sliders placed on top of the most heavily loaded shearwall of the first story. The least loaded columns on the first floor (termed ductile columns) are designed to accommodate large drifts. Figure I(a) shows a reinforced concrete seven-story frame. This structure is a hospital located in Tianjing City, China [4]. When the proposed system is applied to this structure, it becomes the form shown in Fig. l(b). A portion of the weight of the structure is carried by the first story shearwall which is fitted with Teflon sliders on top. The first story shearwall is designed for a lateral load determined by the frictional characteristics of the Teflon sliders [5]. The proposed system is also able to reduce P - A effects when a framed shearwall is used. The lateral force is shared by the ductile columns and the framed shearwall, which behave in distinctly different ways. Drift in the framed shearwall is very small and P -A effects are insignificant.
3. DYNAMIC
RESPONSE ANALYSIS
3.1. Equations of motion To illustrate the analytical model of the proposed system, the hospital mentioned previously is employed again. It should be noted that Fig. I(a) is a conventional frame structure; Fig. l(b) is a proposed system; Fig. l(c) is a detailing for the first story shearwall with Teflon sliders on top. The stiffness of the shearwall, k,, varies depending on stress level. The 883
Y. L. MO and Y. F. Chang
884
(a)
(b)
m
_-___r_l
Telfon
Slider
sheet ss steel
Fig. 1. Proposed system.
first story ductile columns have total initial stiffness K IDC and yield displacement Y,,, given by K ,oC=K,(l
-n)
nations of n and R result in systems with the characteristics of the proposed system. The equations of motion of the system are
(1)
Mt:+CI’+KY+P,=-Mj, Y IDC
=
Y,R
(3)
G-9
(4) in which n is the portion of weight carried by the sliders normalized by the total weight, K, and Y, are the initial stiffness and yield displacement, respectively, of the first story of the conventionally designed structure and R is a reduction factor applied to the yield displacement of the first story columns of the conventional design. The shearwall together with its beam is treated as an inelastic single-degree-of-freedom system with mass, m,. When R = 1 and n = 0 we have the conventional design. For n = 0, and R less than unity we have a conventional soft first story [2]. Other combi-
in which M, C, and K are the mass, damping and stiffness matrices, respectively; j, is the ground acceleration; Y, I’ and y are the floor displacement, velocity and acceleration vectors with respect to the ground, respectively; KY represents the vector of the restoring forces which will be described in the next section; m,, c, and k, are mass, damping and stiffness, respectively, for the shearwall; y,, 3, and j;, represent the displacement, velocity and acceleration of the top of the shearwall with respect to the ground, respectively; k,y, is the restoring force in the shearwall which
isolation concept and soft first story buildings
Base
be described later; Pf is the vector of frictional force which has one nonzero entry at the first floor level equal to pr; pr is the frictional force mobilized at the sliding interfaces, and will also be explained later. will
3.2. Frame elements 3.2.1. Stiffness matrix. To compute the tangent stiffness of a typical frame member, the element is subdivided into three regions [6] (Fig. 2): (1) an inelastic region of length Xi at node i, having the average stiffness (EZ)i; (2) an inelastic region of length Ti at modej, having the average stiffness (EI)i; and (3) a central region of length (L -XiX,), having the initial elastic stiffness (EI),. For the six planar degrees of freedom identified in Fig. 2, the tangent frame element stiffness can be written as
r
k,,
0
0
k,,
k 33
k, =
and reloading
curves
(12)
k,, = -k,, c,2
0
(13)
k,, =
Ol
k,,
0
Fig, 3. Unloading
(C,,G,
k,,
k,,
=
-
c,,
(k,,L
-
C22)
(14)
W
(5)
k,
Wm.)
0
0
k 55
’
k,,
=
(15)
-k2,
k,, Cl,
k 66
(16)
k”“=Gc22-C,2C2,Y
The coefficients
where
k,,=k,=
-k,4=-
EA A,, =-
L
’ [X,3(Q,-l,+(L-x,,‘(l-Q,, ~(EI ),
are assumed to remain constant. Using Castigliano’s theorem [7], the remaining coefficients can be derived as follows:
+ Q,L’l (17) A12
A22 kz2
=
@,,A22
-
-!-[X;(Q, 2tEIj,
ASI=
-
1)
(7) ~,2‘%1)
+(L
(8) 4, =
=
All
-Q,)+Q,L21
-x,)2(1
- 1) + (L - X,)(1 - Qj) +
A22 =L[X;(Q, (EI),
(18)
Q,Ll (19)
(9)
@,,A,,--A,,An)
M
1
c22 (10) k25
=
k,,
(C,zCzr
=
&,
-
I.
c,,
-
k.,
C,,)
1
(11)
*_.-
__--
__--
__-*
__--
__-- _-
CM,. a,)
,’ #’ Q,
<
Fig. 2. Inelastic
model for beam+olumn frame.
members
in plane Fig. 4. Average
stiffness
of unloading.
Y. L. MO and Y. F. Chang
886
(23)
Q2, =E
W),
(24)
Q,=,,,,,.
3.2.2. Hysteretic model. Under load reversals, the stiffness of a section experiences degradation due to the cracking of concrete and s!ip of reinforcing bars. The modified Takeda model [8], is used to simulate this degradation process. We distinguish four different kinds of branches (Fig. 3): (1) elastic loading and unloading, characterized by the slope CC@,, - Q,) (EI), = (EZ), of the first part of the primary A4 - 4 Fig. 5. Average stiffness of reloading. curve; (2) inelastic loading, with slope (EZ), = (EI), equal to that of the second part of the primary M - 4 - 1) f (L - X,))(l - Q) c,, = &x:(Q, curve; (3) inelastic unloading with slope (El),; and e (4) inelastic reloading, characterized by slope (EI), as + Q,L31(20)The stiffnesses (EZ), and (EI), are determined follows. Upon unloading, an auxiliary point with the folc,, = c,, = &W:'Q,- 1) lowing coordinates is introduced (Fig. 3): P
+@ -x,)*(1 - Qi,+Q&*1 (21)
M,=
&W4-“:I
(25)
&X(Q / J-l)+G ---x,)(1 -Q,)+Q,Ll c2*=(EI), (26)
(22) Et. I% ’
o,b cos a
HOR.DIR.
es
zb cot a
+---*
zb
YC
(b) element
(a) shearwall
A
CI [f-L_
b
. .
A _.__ _ P’ El-!-:. .
+
. . .
.
.
.
.
g
.-- q 04
_ ---. .
t
d (c) section
I-I
Fig. 6. Framed shearwall
c D
Base isolation
concept
and soft first story
Fig. 7. Softened stress-strain
buildings
887
curve of concrete
The length xi and stiffness ratio Qi of the plastic region at node i depend on the current branch of the M - 4 diagram. For elastic loading or unloading, we have
where M: is the maximum moment reached in the positive direction during the current load cycle. The inelastic unloading and reloadings stiffness follows then as
xi = 0
(30)
Qi= 1,
(31)
(27)
and while for inelastic
loading
’
4:=4%-(,)1
2, see Fig 3),
_Mi-M.y
‘y
(32)
M,+ Mi Q, = I
MO
(branch
(EI)e
(33)
0,’
(29)
,.
Upon inelastic unloading, A’, remains the maximum plastic region length reached in any previous inelastic loading cycle. The stiffness varies now over the length of the plastic region. Directly at node i it has to be equal to (EI),, while at the border line between the
is the residual curvature after a positive moment excursion, and M .;, 4 .; are the coordinates of the maximum previous excursion into the negative direction.
A
A B
BG
,/’
k
L
0
0
Deflection
Fig. 8. Three phases
/ / 2..
/
/
/
/’
C
.
%
..__....__......................... ~
D
I-
of load-deflection
relationship.
(a) Loading;
(b) unloading;
(c) reloading.
Y. L. MO and Y. F. Chang
888
plastic and elastic regions it is (EI), We approximate the variable stiffness by an average value, assumed to be constant over the length of the plastic region, and given by
(EI 1,=
Ml ~($1 - 9%) + (1 - c)M,l(~%’
(34)
where M,, 4, are the moment and curvature at the onset of unloading, and 4, is the residual curvature, Fig. 4. For the averaging coefficient c, a value of 0.75 has led to best comparisons with test results [7]. For
inelastic reloading, mated by
the average
is approxi-
where the definitions of M,, M,, 4,) 4, are illustrated in Fig. 5. It should be noted that the Takeda-type rules adopted for this study impose certain limitations on the model in its present form. In particular, “pinched” moment-curvature behavior, which may be caused by high shear and/or bond degradation, cannot be reproduced accurately.
I
Initialize
s=o,P-1
Set S=l.
_J
stiffness
No
I Yes Set P=2
e
1&z;:_
.
cl
Compute force from primary curve
Fig. 9. Algorithm for hysteresis loops (S = state, P = phase).
Base isolation concept and soft first story buildings Table 1. Parameters in model of friction of Teflon bearings Bearing pressure WPa)
Type of Teflon
6.9 13.8
Unfilled Unfilled
0.1193 0.0927 0.0870 0.0695
23.62 23.62
6.9
Glass filled at 15%
0.1461 0.1060
23.62
f map
analysis of framed this figure
a (s/m)
Df
889
shearwalls
can be derived
from
(J, = 0d cos.2 c( + pi,
(36)
sm a cos a,
(371
T,, =
od
where 3.3. ShearwaN element 3.3.1. Truss model theory. The truss model theory for framed shearwalls was first presented in Ref. (91. This theory was extended in Ref. [IO] to include vertical stresses. It consists of three parts and is briefly summarized in the following. Equilibrium conditions: Fig. 6 shows the equilibrium conditions of framed shearwalls. The following two basic equilibrium equations required for the
e, = normal stresses on element A in the I direction, T,, = shear stress on element A in the It coordinate, od= axial stress in the diagonal concrete struts, CL= angle of inclination of the concrete struts with respect to the longitudinal axis, p, = reinforcement ratios in the I directions, f; = steel stresses in the longitudinal bars.
Initialize
values 1.
Calculate
incremental
load for extended
1 time
Calculate
Find
effective
incremental
interval
incremental
displacement time
load for
for extended
interval
Calculate
incremental
acceleration
Calculate
incremental
acceleration
Calculate
incremental
velocity
for normal
and displacement
interval 1
Calculate
displacement
and velocity
at time ti+,i
1 Calculate
acceleration
at time ti+i
1 Output
time,
displacement
and force, ect.
Fig. 10. Algorithm for dynamic analysis.
Y. L. MO and Y. F. Chug
890
Compatibility conditions: the following two basic compatibility equations relating the shear distortion in the wall, 7, to the strains in the reinforcement and concrete, L, and t‘, can be derived using the compatibility condition
for
softened
f,,d
f,,:‘i.
concrete.
gli =
t, = t<,(1 - tan’ c()
(38)
)i,, = 2c, sin CLcos a,
(39)
For
1’: LYf,,:‘f,,)
-
while for the descending
the
ascending
(f,,if,,Yl,
j.
branch
branch
(40)
c,, > c,,:‘i..
(41) where L, = average strain of element A in the I direction. cd = average strain of element A in the d direction, y,, = average shear strains of element A in the It coordinate.
These two equations are plotted in Fig. 7. The quantity t,) is defined as the strain at maximum compressive stress of non-softened concrete and can be taken as 0.002. The factor i is a coefficient for softening effect and is suggested [Y] to bc
Material properties: the stress and strain of concrete in the strut direction are assumed to obey the following two equations proposed by Refs [ 1 I, 121
;. = lcos
2.
(42)
3 @ 305mm
I
1
I
1
1
1
1 3
1
1
2
2 3
3
As2
=
8.5
mm2
12.75
mm2
mass per floor = 0.227 N-sec2
/mm
3
4 2
4
type 4
4
7
= A Sl =
3
Mpa Mpa
3
2
2
350 31.1
f cy
2
4
3
=
3 2
2
2
2
3
3
0.268
3
2
2
0.0039
3
3
3
= =
2
2
2
Mpa Mpa
P,
3
3
3
= 20,733
P, f sy
3
2
2
= 200,000
EC 2 3
3
ES
3
2
2 3
3
3
3 2
3
3
3
3
3
3
3
3
3
77n
39mm
39mm
39mm
I
i
section Fig.
I I.
A IO-story
frame.
3
section
4
Base isolation The stress-strain relation for the longitudinal assumed to be elasto-perfectly plastic
where ES&, yield stress. respectively.
concept
and soft first story
bars is
f; = E,t, when t, < e,
(43)
.A =.f,,
(44)
when cl> e,,,
and c,, are the modulus of elasticity, the and the yielding strain of the bars,
3.3.2. Hpteretic model. To account for the continually varying stiffness and energy absorbing characteristics of framed shearwalls, the hysteresis loops model described in this section is needed. In other words, the force on a concrete shearwall is not only a function of the deflection, but also depends on other factors, such as whether the concrete has cracked, the direction in which the cracking first occurs. and the loading history. The rules to create the hysteresis loops model is described by Ref. [13] in detail. Let the relation V = CD,(6 ) describe the primary curve in Fig. 8(a). Let V = $(8) represent the un-
buildings
891
loading line BCDO, in Fig. 8(b), and let V = $(6 ) represent the reloading line EFG in Fig. 8(c). If reloading continues past the point G, (6, V) returns to the primary curve. In addition, let 3 be the direction (1 for positive and - 1 for negative) in which cracking first occurs (i.e. V exceeds V,,). Then the hysteresis loops for positive shear [sign(6 ) = -:I also apply to negative shear [sign(S ) = -z] with the modification that the primary curve V = @,,(6) is replaced by -@,(6/1.5) when (~6) ~0. To keep track of these factors, two auxiliary variables, state and phase, are used. The state variable indicates the cracking state of the wall: not yet cracked, cracked in one direction only, and cracked in both directions. The phase variable indicates the current point in the loading history: primary load-deflection curve, unloading, and reloading. The state and phase variables behave like finite state automata 1141 in the sense that the new state/phase is uniquely determined by the current state/phase together with an event which triggers a transition. See Fig. 9 for a flow chart describing the various possible state and phase transitions and the events which cause the transitions. 21868 We
:
R = a.5
:
D
=
0.3
Fig. 12. Restoring moment curvature loops of the first story ductile columns with R = 0.5.
Y. L. MO and Y. F. Chang
892
coefficient of friction at essentially zero velocity of sliding. For the case studies, bearing pressure is 6.9 MPa, for which ,fm,,, = 0.1193, Of = 0.0927 and a = 23.62 s rn--’ (see Table 1).
3.4. Teflon sliders pr is the frictional interfaces, and is equation [5]:
force mobilized at the sliding described by the following
3.5. Algorithm The theory presented in the previous cast into algorithm. Figure 10 summarizes ithm for the dynamic response analysis. algorithm, a computer program has been This program is used to perform the studies reported in this paper.
in which nW is the portion of the weight carried by the sliding bearings; Z is a parameter taking values in the range (- 1, 1) and p is the coefficient of sliding friction which is a function of the relative velocity between the first floor and the top of the shearwall; pr = p, - fS. For Teflon sliding against polished stainless steel of mirror finish, the sliding coefficient of friction is given by P =f,,,
-
of x exp(-al~r’,o.
4. PARAMETRIC
18888
l&Z00
R = 1.0 : 1
=
T
0.6
-(l
wI_
h
‘A-
1
‘-Ag
g
2
STUDIES
The primary concern of these studies is whether the energy dissipation and story drift in the upper storys of a building with the proposed system is significantly reduced in comparison with those in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4g, is used. The structure analyzed is as shown in Fig. 11. The properties of this structure is also shown in this figure. The shearwall used in these studies has the following properties: concrete com-
(46)
Experimentally determined parametersf&, Dfand a are given elsewhere [15]. It should be noted that these parameters depend on the condition of interface and bearing pressure. f,,, is the maximum value of the friction coefficient which is mobilized at large velocities. cf,,, - Of) represents the value of the
cam:
-1
0
“d iii _-
B_,
0
is
2
-12888
-12000
2
Curvature
( l/cm
IS@00
~~a:Rro.a:n=o.?,
Fig. 13. Restoring
n
moment
curvature
sections is the algorFrom this developed. parametric
loops of the first story ductile
columns
with n = 0.5
)
Base isolation concept and soft first story buildings
R = 1.0 ; n = 0.5
pressive strength, f: = 3 1.1 MPa; Iongitudinal steel yiefding stress, j;,, = 350 MPa; long~tudin~ steel ratio = 0.0025. The height, width and thickness are 27.9, 30.5 and Ucm, respectively. And the bearing pressure of Teflon sliders with unfilled sheet type keeps 6.9 MPa f4] for all the cases. Specific values considered are R = 1.0, 0.5, 0.3 and 0.1 and n = 0.0, 0.3, 0.5 and 0.8. For example, the case n = 0.5, R = 0.3corresponds to a design in which 50% of the superstructure’s weight is carried by shders and the yield displacement of the first story ductile columns
R = 0.3 ; n - 0.0
R = 0.3 ; n = 0.5
R = 0.5 ;n = 0.5
Fig. $4. Yielded locations in plane frame
R - 0.3 ; n - 0.3
Fig. 15. Yielded focations in plane frame
893
with
n = 0.5. (ef indicates “already
is haif tiond teretic drifts,
the yield displacement of the original convendesign. The results for moment~urvature hysloops, steel yielding locations, normalized and displacement history are discussed.
4. I _ ~o~e~f-~~~~~fur~ hy.rfere f ic kmps Figures f2 and X3 show the moment-curvature hysteretic loops of the exterior column in the first story. Figure 12 indicates the results for the cases when R = 0.5, and n varies, whife Fig. I3 shows those for n = 0.5 and R varies. It can be seen from Fig. 12
R - 0.3 ; n = 0.5
R * 0.3 ; n m0.8
R = 0.3. (0) indicates “akeadg yielded”.
Y. L. MO and Y. F. Chang
894
4.3. Normalized
that the energy dissipated by the momentxurvature hysteretic loops increases with increasing value of n. It can also be seen from Fig. I3 that for the case with R = I .O and n = 0.5, the moment-curvature relationship is linear (i.e. no energy dissipated), and the case with R = 0.5 and n = 0.5 has greater energy dissipations than the remaining cases.
drijrs
Figures 16 and I7 show the normalized story drifts. Again, it can be seen from these two figures that normalized story drifts are reduced with increasing the value of n (Fig. 16) and with decreasing value of R (Fig. 17).
4.2. Steel ,yielding locations 4.4. Displacement
Figures I4 and I5 show the steel yielding locations in the frame. Figure I4 indicates the results for the cases when n = 0.5 and R varies, while Fig. I5 shows those for R = 0.3 and n varies. It can be seen from Fig. I4 that the number of steel yielding locations decreases with decreasing value of R. It can also be seen from Fig. I5 that the number of steel yielding locations de&eases with increasing value of n. ( a ) R =
history
Figure I8 indicates the top-story displacement histories for both the elastic and inelastic analysis. It can be seen from this figure that stiffness degradation enlarges the displacement amplitudes and vibration periods when inelastic response occurs. The elastic vs inelastic displacement responses are very clearly compared in this figure. ( b ) R = 0.5
1.0
- oeeeo n = 0.0 - oeow n = 0.3 9- A-A.oaaP = 0.5 . +-a-t++ a = 0.8
9-
8
073 2 _ s 6w 5 4 3
Drift
( Normalized
to the
case
with
P =
a -0 1
Drift
( Normalized
to the
case
( d ) R = 0.1
( c ) R = 0.3
10 ) 9-
j 0-
0-
7-
3 72 s 6v, ?
2 s 6VJ : 5-
51
4-
4
3 3 i
4.!.sh... k00 0.20 Drift
.:
0.k’
( Normalized
‘l’--’
0.40
to the
0.b
.
case
.
.
..*...I 1.00 1.20
with
n = 0.0 )
Fig. 16. Story drifts of IO-story
structure
based
on plane frame model (n varies).
with
P =
0.0 )
Base isolation ( a
rsm -R
concept
895
and soft first story buildings (
f n = 0.0
b
) n = 0.3
( d
) n = 0.8
R = 0.3 = 0.1 8
6
( c ) n = 0.5 10
4 3
OeeeoR -R -It -R
z~.,.b,,..,,..,.,,..~...~ %.&!?3 8.28 8.48 Drift ( Normalized
= 1.0 -i 0.5 = 0.3 o 0.1
8.60 B.W l.ea 1.20 to the case with R = 1.0 )
-R
-R
= 0.3 = 0.1
Drift ( Normalized to the case with R E’
Fig. 17. Story drifts of IO-story structure based on plane frame model (R varies),
5. CONCLUSIONS
Fig. 18. Displacement histories of the roof level.
A new system for the design of earthquake-resistant buildings has been proposed. In this system, first story shearwalls are fitted with Teflon sliders while the remaining first story columns are designed with reduced yielding stress. With this system the energy dissipations may be increased and the number of steel yielding locations, normalized story drifts and placements in the superstructure may be significantly reduced.
Y. L. MO and Y. F. Chang
896 Acknowledgements-Support for this research tional Science Council, Taiwan, ROC, under 81-0410-E-006-573, is gratefullv acknowledged.
by the Nagrant NSC
REFERENCES review and 1. J. M. Kelly, A seismic base isolation: bibliography. Soil Dyn. Earthqu. Engng 5, 202-216 (1986). D. P. Clough and R. W. Clough, 2. A. K. Chopra, Earthquake resistance of buildings with a soft first story. Earthqu. Engng Struct. Dyn. I, 347-355 (1973). answer for seismic resist3. M. -Fintel, Shearwalls-an ance? Concr. Int. 13(7), 48-53 (1991). 4. Y. Q. Chen, and M.‘d. Constantinou, Use of Teflon sliders in a modification of the concept of soft first storey. Engng S!ruct. 12, 243-253 (1990). A. Mokha and A. M. Reinhorn, 5. M. C. Constantinou, Teflon bearings in base isolation. Part 2: modeling. /. Struct. Engng ASCE 116(2), 455474 (1990). 6. C. Meyer, M. S. L. Roufaiel and S. G. Arzoumanidis, Analysis of damaged concrete frames for cyclic loads. Earthqu. Engng Struct. Dyn. 11(2), 207-228 (1983). 1. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, 3rd SI edn. Chapman & Hall, London fi989). 8. T. Takeda, M. A. Sozen and N. N., Nielsen, Reinforced concrete response to simulated earthquakes. Proc. ASCE 96(STl2), 2557-2573 (1970).
9. T. C. Hsu and Y. L. MO, Softening of concrete in low-rise shearwalls. Research Report No. UHCE 84-8, Department of Civil Engineering, University of Houston (1985). Also in ACI J. Proc. 82(6j, 883-889 (1985). 10. S. T. Mau and T. T. C. Hsu, Shear behavior of reinforced concrete framed wall panels with vertical loads. ACZ Struct. J. &i(3), 228-234 (1987). Il. F. Vecchio and M. P. Colins, Stress-strain characteristics of reinforced concrete in pure shear. Final Report, IABSE Colloquium on Advanced Mechanics qf Reinforced Concrete, Delft, pp. 21 l-225. International Association for Bridge and Structural Engineering, Zurich (1981). 12. F. Vecchio and M. P. Colins, The response of reinforced concrete to in-plane shear and normal stresses. Publication No. 82-03, Department of Civil Engineering, University of Toronto, p. 332 (1982). 13. S. D. Jost and Y. L. MO. An algorithm for seismic analysis of lowrise structural walls. Nucl. Enanp ._ ., Des. 131,-2633270 (1991). 14. J. E. Hopcroft and J. D. Ullman. Introduction IO Automata _Theory, Languages and Computation, Addison-Wesley, New York (1979). 15. A. Mojkha, M. C. Constantinou and A. M. Reinhorn, Teflon bearings in base isolation. Part 1: testing. .I. Struct. Engng ASCE 116(2), 438454 (1990).
Compureu
> Pergamon
& Svurruws Vol. 55, No. 5, pp. 883-896. 1995 CopyrIght 8cm1995 Elsewer Science Ltd Printed in Great Britain. All nghts reserved 0045.7949/95%9 50 + 0.00
0045-7949(94)00433-1 . _
APPLICATION
OF BASE ISOLATION CONCEPT FIRST STORY BUILDINGS
TO SOFT
Y. L. MO and Y. F. Chang Department
of Civil Engineering,
National (Receked
Cheng
Kung
7 September
University,
Tainan
70101, Taiwan
1993)
Abstract-A practical system that combines a flexible first story with sliding frictional interfaces is described. The system utilizes Teflon sliders at the top of the first story reinforced concrete framed shearwalls to carry a portion of the superstructure. Energy dissipation is provided by the first story ductile columns and by the Teflon sliders. Utilizing this concept the seismic response characteristics of a multistory frame are analyzed and discussed.
1. INTRODUCTION
dynamic response of the proposed system, parametric studies are performed, and the results are critically examined.
Base isolation can significantly reduce the damage of buildings produced by a strong earthquake [I]. To separate a building from the surrounding ground motion, two methods can theoretically be applied: (1) a soft first story concept; and (2) sliding/bearing system. However, their full utilization in practice is still questionable due to the following reasons. The soft first story concept [2] is an attempt to reduce accelerations in a building by allowing the first story columns to yield during an earthquake and produce energy-absorbing action. However, excessive drifts in the first story coupled with P -A effects on the yielded columns make buildings collapse [3]. Similarly. in the sliding/bearing systems there are risks of overturning, since no solid connections exist between the superstructures and the foundations. Also, lack of a solid connection may result in excessive displacement. Although horizontal dampers may be used to decrease the displacement, it is difficult to implement and maintain permanently. It is shown in this paper that a new approach is proposed, that combines the soft first story concept with a sliding frictional system. This approach is an attempt to minimize the disadvantages of the two methods discussed above while retaining their advantages in reducing the structural response and damage during an earthquake. In this approach, Teflon sliders are placed on the top of the first story reinforced concrete framed shearwalls. These shearwalls are framed by columns and beams and are designed to carry a portion of the weight of the superstructure and the lateral load determined by the frictional characteristics of the Teflon sliders. The remaining first story columns are designed for ductile behavior in order to accommodate large drifts. According to this proposed system, a dynamic response analysis is described. To determine the effects of variables on the (‘AS
55 s--J
2.
PROPOSED
SYSTEM
In the proposed system a major part of the weight of the building is carried by the Teflon sliders placed on top of the most heavily loaded shearwall of the first story. The least loaded columns on the first floor (termed ductile columns) are designed to accommodate large drifts. Figure I(a) shows a reinforced concrete seven-story frame. This structure is a hospital located in Tianjing City, China [4]. When the proposed system is applied to this structure, it becomes the form shown in Fig. l(b). A portion of the weight of the structure is carried by the first story shearwall which is fitted with Teflon sliders on top. The first story shearwall is designed for a lateral load determined by the frictional characteristics of the Teflon sliders [5]. The proposed system is also able to reduce P - A effects when a framed shearwall is used. The lateral force is shared by the ductile columns and the framed shearwall, which behave in distinctly different ways. Drift in the framed shearwall is very small and P -A effects are insignificant.
3. DYNAMIC
RESPONSE ANALYSIS
3.1. Equations of motion To illustrate the analytical model of the proposed system, the hospital mentioned previously is employed again. It should be noted that Fig. I(a) is a conventional frame structure; Fig. l(b) is a proposed system; Fig. l(c) is a detailing for the first story shearwall with Teflon sliders on top. The stiffness of the shearwall, k,, varies depending on stress level. The 883
Y. L. MO and Y. F. Chang
884
(a)
(b)
m
_-___r_l
Telfon
Slider
sheet ss steel
Fig. 1. Proposed system.
first story ductile columns have total initial stiffness K IDC and yield displacement Y,,, given by K ,oC=K,(l
-n)
nations of n and R result in systems with the characteristics of the proposed system. The equations of motion of the system are
(1)
Mt:+CI’+KY+P,=-Mj, Y IDC
=
Y,R
(3)
G-9
(4) in which n is the portion of weight carried by the sliders normalized by the total weight, K, and Y, are the initial stiffness and yield displacement, respectively, of the first story of the conventionally designed structure and R is a reduction factor applied to the yield displacement of the first story columns of the conventional design. The shearwall together with its beam is treated as an inelastic single-degree-of-freedom system with mass, m,. When R = 1 and n = 0 we have the conventional design. For n = 0, and R less than unity we have a conventional soft first story [2]. Other combi-
in which M, C, and K are the mass, damping and stiffness matrices, respectively; j, is the ground acceleration; Y, I’ and y are the floor displacement, velocity and acceleration vectors with respect to the ground, respectively; KY represents the vector of the restoring forces which will be described in the next section; m,, c, and k, are mass, damping and stiffness, respectively, for the shearwall; y,, 3, and j;, represent the displacement, velocity and acceleration of the top of the shearwall with respect to the ground, respectively; k,y, is the restoring force in the shearwall which
isolation concept and soft first story buildings
Base
be described later; Pf is the vector of frictional force which has one nonzero entry at the first floor level equal to pr; pr is the frictional force mobilized at the sliding interfaces, and will also be explained later. will
3.2. Frame elements 3.2.1. Stiffness matrix. To compute the tangent stiffness of a typical frame member, the element is subdivided into three regions [6] (Fig. 2): (1) an inelastic region of length Xi at node i, having the average stiffness (EZ)i; (2) an inelastic region of length Ti at modej, having the average stiffness (EI)i; and (3) a central region of length (L -XiX,), having the initial elastic stiffness (EI),. For the six planar degrees of freedom identified in Fig. 2, the tangent frame element stiffness can be written as
r
k,,
0
0
k,,
k 33
k, =
and reloading
curves
(12)
k,, = -k,, c,2
0
(13)
k,, =
Ol
k,,
0
Fig, 3. Unloading
(C,,G,
k,,
k,,
=
-
c,,
(k,,L
-
C22)
(14)
W
(5)
k,
Wm.)
0
0
k 55
’
k,,
=
(15)
-k2,
k,, Cl,
k 66
(16)
k”“=Gc22-C,2C2,Y
The coefficients
where
k,,=k,=
-k,4=-
EA A,, =-
L
’ [X,3(Q,-l,+(L-x,,‘(l-Q,, ~(EI ),
are assumed to remain constant. Using Castigliano’s theorem [7], the remaining coefficients can be derived as follows:
+ Q,L’l (17) A12
A22 kz2
=
@,,A22
-
-!-[X;(Q, 2tEIj,
ASI=
-
1)
(7) ~,2‘%1)
+(L
(8) 4, =
=
All
-Q,)+Q,L21
-x,)2(1
- 1) + (L - X,)(1 - Qj) +
A22 =L[X;(Q, (EI),
(18)
Q,Ll (19)
(9)
@,,A,,--A,,An)
M
1
c22 (10) k25
=
k,,
(C,zCzr
=
&,
-
I.
c,,
-
k.,
C,,)
1
(11)
*_.-
__--
__--
__-*
__--
__-- _-
CM,. a,)
,’ #’ Q,
<
Fig. 2. Inelastic
model for beam+olumn frame.
members
in plane Fig. 4. Average
stiffness
of unloading.
Y. L. MO and Y. F. Chang
886
(23)
Q2, =E
W),
(24)
Q,=,,,,,.
3.2.2. Hysteretic model. Under load reversals, the stiffness of a section experiences degradation due to the cracking of concrete and s!ip of reinforcing bars. The modified Takeda model [8], is used to simulate this degradation process. We distinguish four different kinds of branches (Fig. 3): (1) elastic loading and unloading, characterized by the slope CC@,, - Q,) (EI), = (EZ), of the first part of the primary A4 - 4 Fig. 5. Average stiffness of reloading. curve; (2) inelastic loading, with slope (EZ), = (EI), equal to that of the second part of the primary M - 4 - 1) f (L - X,))(l - Q) c,, = &x:(Q, curve; (3) inelastic unloading with slope (El),; and e (4) inelastic reloading, characterized by slope (EI), as + Q,L31(20)The stiffnesses (EZ), and (EI), are determined follows. Upon unloading, an auxiliary point with the folc,, = c,, = &W:'Q,- 1) lowing coordinates is introduced (Fig. 3): P
+@ -x,)*(1 - Qi,+Q&*1 (21)
M,=
&W4-“:I
(25)
&X(Q / J-l)+G ---x,)(1 -Q,)+Q,Ll c2*=(EI), (26)
(22) Et. I% ’
o,b cos a
HOR.DIR.
es
zb cot a
+---*
zb
YC
(b) element
(a) shearwall
A
CI [f-L_
b
. .
A _.__ _ P’ El-!-:. .
+
. . .
.
.
.
.
g
.-- q 04
_ ---. .
t
d (c) section
I-I
Fig. 6. Framed shearwall
c D
Base isolation
concept
and soft first story
Fig. 7. Softened stress-strain
buildings
887
curve of concrete
The length xi and stiffness ratio Qi of the plastic region at node i depend on the current branch of the M - 4 diagram. For elastic loading or unloading, we have
where M: is the maximum moment reached in the positive direction during the current load cycle. The inelastic unloading and reloadings stiffness follows then as
xi = 0
(30)
Qi= 1,
(31)
(27)
and while for inelastic
loading
’
4:=4%-(,)1
2, see Fig 3),
_Mi-M.y
‘y
(32)
M,+ Mi Q, = I
MO
(branch
(EI)e
(33)
0,’
(29)
,.
Upon inelastic unloading, A’, remains the maximum plastic region length reached in any previous inelastic loading cycle. The stiffness varies now over the length of the plastic region. Directly at node i it has to be equal to (EI),, while at the border line between the
is the residual curvature after a positive moment excursion, and M .;, 4 .; are the coordinates of the maximum previous excursion into the negative direction.
A
A B
BG
,/’
k
L
0
0
Deflection
Fig. 8. Three phases
/ / 2..
/
/
/
/’
C
.
%
..__....__......................... ~
D
I-
of load-deflection
relationship.
(a) Loading;
(b) unloading;
(c) reloading.
Y. L. MO and Y. F. Chang
888
plastic and elastic regions it is (EI), We approximate the variable stiffness by an average value, assumed to be constant over the length of the plastic region, and given by
(EI 1,=
Ml ~($1 - 9%) + (1 - c)M,l(~%’
(34)
where M,, 4, are the moment and curvature at the onset of unloading, and 4, is the residual curvature, Fig. 4. For the averaging coefficient c, a value of 0.75 has led to best comparisons with test results [7]. For
inelastic reloading, mated by
the average
is approxi-
where the definitions of M,, M,, 4,) 4, are illustrated in Fig. 5. It should be noted that the Takeda-type rules adopted for this study impose certain limitations on the model in its present form. In particular, “pinched” moment-curvature behavior, which may be caused by high shear and/or bond degradation, cannot be reproduced accurately.
I
Initialize
s=o,P-1
Set S=l.
_J
stiffness
No
I Yes Set P=2
e
1&z;:_
.
cl
Compute force from primary curve
Fig. 9. Algorithm for hysteresis loops (S = state, P = phase).
Base isolation concept and soft first story buildings Table 1. Parameters in model of friction of Teflon bearings Bearing pressure WPa)
Type of Teflon
6.9 13.8
Unfilled Unfilled
0.1193 0.0927 0.0870 0.0695
23.62 23.62
6.9
Glass filled at 15%
0.1461 0.1060
23.62
f map
analysis of framed this figure
a (s/m)
Df
889
shearwalls
can be derived
from
(J, = 0d cos.2 c( + pi,
(36)
sm a cos a,
(371
T,, =
od
where 3.3. ShearwaN element 3.3.1. Truss model theory. The truss model theory for framed shearwalls was first presented in Ref. (91. This theory was extended in Ref. [IO] to include vertical stresses. It consists of three parts and is briefly summarized in the following. Equilibrium conditions: Fig. 6 shows the equilibrium conditions of framed shearwalls. The following two basic equilibrium equations required for the
e, = normal stresses on element A in the I direction, T,, = shear stress on element A in the It coordinate, od= axial stress in the diagonal concrete struts, CL= angle of inclination of the concrete struts with respect to the longitudinal axis, p, = reinforcement ratios in the I directions, f; = steel stresses in the longitudinal bars.
Initialize
values 1.
Calculate
incremental
load for extended
1 time
Calculate
Find
effective
incremental
interval
incremental
displacement time
load for
for extended
interval
Calculate
incremental
acceleration
Calculate
incremental
acceleration
Calculate
incremental
velocity
for normal
and displacement
interval 1
Calculate
displacement
and velocity
at time ti+,i
1 Calculate
acceleration
at time ti+i
1 Output
time,
displacement
and force, ect.
Fig. 10. Algorithm for dynamic analysis.
Y. L. MO and Y. F. Chug
890
Compatibility conditions: the following two basic compatibility equations relating the shear distortion in the wall, 7, to the strains in the reinforcement and concrete, L, and t‘, can be derived using the compatibility condition
for
softened
f,,d
f,,:‘i.
concrete.
gli =
t, = t<,(1 - tan’ c()
(38)
)i,, = 2c, sin CLcos a,
(39)
For
1’: LYf,,:‘f,,)
-
while for the descending
the
ascending
(f,,if,,Yl,
j.
branch
branch
(40)
c,, > c,,:‘i..
(41) where L, = average strain of element A in the I direction. cd = average strain of element A in the d direction, y,, = average shear strains of element A in the It coordinate.
These two equations are plotted in Fig. 7. The quantity t,) is defined as the strain at maximum compressive stress of non-softened concrete and can be taken as 0.002. The factor i is a coefficient for softening effect and is suggested [Y] to bc
Material properties: the stress and strain of concrete in the strut direction are assumed to obey the following two equations proposed by Refs [ 1 I, 121
;. = lcos
2.
(42)
3 @ 305mm
I
1
I
1
1
1
1 3
1
1
2
2 3
3
As2
=
8.5
mm2
12.75
mm2
mass per floor = 0.227 N-sec2
/mm
3
4 2
4
type 4
4
7
= A Sl =
3
Mpa Mpa
3
2
2
350 31.1
f cy
2
4
3
=
3 2
2
2
2
3
3
0.268
3
2
2
0.0039
3
3
3
= =
2
2
2
Mpa Mpa
P,
3
3
3
= 20,733
P, f sy
3
2
2
= 200,000
EC 2 3
3
ES
3
2
2 3
3
3
3 2
3
3
3
3
3
3
3
3
3
77n
39mm
39mm
39mm
I
i
section Fig.
I I.
A IO-story
frame.
3
section
4
Base isolation The stress-strain relation for the longitudinal assumed to be elasto-perfectly plastic
where ES&, yield stress. respectively.
concept
and soft first story
bars is
f; = E,t, when t, < e,
(43)
.A =.f,,
(44)
when cl> e,,,
and c,, are the modulus of elasticity, the and the yielding strain of the bars,
3.3.2. Hpteretic model. To account for the continually varying stiffness and energy absorbing characteristics of framed shearwalls, the hysteresis loops model described in this section is needed. In other words, the force on a concrete shearwall is not only a function of the deflection, but also depends on other factors, such as whether the concrete has cracked, the direction in which the cracking first occurs. and the loading history. The rules to create the hysteresis loops model is described by Ref. [13] in detail. Let the relation V = CD,(6 ) describe the primary curve in Fig. 8(a). Let V = $(8) represent the un-
buildings
891
loading line BCDO, in Fig. 8(b), and let V = $(6 ) represent the reloading line EFG in Fig. 8(c). If reloading continues past the point G, (6, V) returns to the primary curve. In addition, let 3 be the direction (1 for positive and - 1 for negative) in which cracking first occurs (i.e. V exceeds V,,). Then the hysteresis loops for positive shear [sign(6 ) = -:I also apply to negative shear [sign(S ) = -z] with the modification that the primary curve V = @,,(6) is replaced by -@,(6/1.5) when (~6) ~0. To keep track of these factors, two auxiliary variables, state and phase, are used. The state variable indicates the cracking state of the wall: not yet cracked, cracked in one direction only, and cracked in both directions. The phase variable indicates the current point in the loading history: primary load-deflection curve, unloading, and reloading. The state and phase variables behave like finite state automata 1141 in the sense that the new state/phase is uniquely determined by the current state/phase together with an event which triggers a transition. See Fig. 9 for a flow chart describing the various possible state and phase transitions and the events which cause the transitions. 21868 We
:
R = a.5
:
D
=
0.3
Fig. 12. Restoring moment curvature loops of the first story ductile columns with R = 0.5.
Y. L. MO and Y. F. Chang
892
coefficient of friction at essentially zero velocity of sliding. For the case studies, bearing pressure is 6.9 MPa, for which ,fm,,, = 0.1193, Of = 0.0927 and a = 23.62 s rn--’ (see Table 1).
3.4. Teflon sliders pr is the frictional interfaces, and is equation [5]:
force mobilized at the sliding described by the following
3.5. Algorithm The theory presented in the previous cast into algorithm. Figure 10 summarizes ithm for the dynamic response analysis. algorithm, a computer program has been This program is used to perform the studies reported in this paper.
in which nW is the portion of the weight carried by the sliding bearings; Z is a parameter taking values in the range (- 1, 1) and p is the coefficient of sliding friction which is a function of the relative velocity between the first floor and the top of the shearwall; pr = p, - fS. For Teflon sliding against polished stainless steel of mirror finish, the sliding coefficient of friction is given by P =f,,,
-
of x exp(-al~r’,o.
4. PARAMETRIC
18888
l&Z00
R = 1.0 : 1
=
T
0.6
-(l
wI_
h
‘A-
1
‘-Ag
g
2
STUDIES
The primary concern of these studies is whether the energy dissipation and story drift in the upper storys of a building with the proposed system is significantly reduced in comparison with those in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4g, is used. The structure analyzed is as shown in Fig. 11. The properties of this structure is also shown in this figure. The shearwall used in these studies has the following properties: concrete com-
(46)
Experimentally determined parametersf&, Dfand a are given elsewhere [15]. It should be noted that these parameters depend on the condition of interface and bearing pressure. f,,, is the maximum value of the friction coefficient which is mobilized at large velocities. cf,,, - Of) represents the value of the
cam:
-1
0
“d iii _-
B_,
0
is
2
-12888
-12000
2
Curvature
( l/cm
IS@00
~~a:Rro.a:n=o.?,
Fig. 13. Restoring
n
moment
curvature
sections is the algorFrom this developed. parametric
loops of the first story ductile
columns
with n = 0.5
)
Base isolation concept and soft first story buildings
R = 1.0 ; n = 0.5
pressive strength, f: = 3 1.1 MPa; Iongitudinal steel yiefding stress, j;,, = 350 MPa; long~tudin~ steel ratio = 0.0025. The height, width and thickness are 27.9, 30.5 and Ucm, respectively. And the bearing pressure of Teflon sliders with unfilled sheet type keeps 6.9 MPa f4] for all the cases. Specific values considered are R = 1.0, 0.5, 0.3 and 0.1 and n = 0.0, 0.3, 0.5 and 0.8. For example, the case n = 0.5, R = 0.3corresponds to a design in which 50% of the superstructure’s weight is carried by shders and the yield displacement of the first story ductile columns
R = 0.3 ; n - 0.0
R = 0.3 ; n = 0.5
R = 0.5 ;n = 0.5
Fig. $4. Yielded locations in plane frame
R - 0.3 ; n - 0.3
Fig. 15. Yielded focations in plane frame
893
with
n = 0.5. (ef indicates “already
is haif tiond teretic drifts,
the yield displacement of the original convendesign. The results for moment~urvature hysloops, steel yielding locations, normalized and displacement history are discussed.
4. I _ ~o~e~f-~~~~~fur~ hy.rfere f ic kmps Figures f2 and X3 show the moment-curvature hysteretic loops of the exterior column in the first story. Figure 12 indicates the results for the cases when R = 0.5, and n varies, whife Fig. I3 shows those for n = 0.5 and R varies. It can be seen from Fig. 12
R - 0.3 ; n = 0.5
R * 0.3 ; n m0.8
R = 0.3. (0) indicates “akeadg yielded”.
Y. L. MO and Y. F. Chang
894
4.3. Normalized
that the energy dissipated by the momentxurvature hysteretic loops increases with increasing value of n. It can also be seen from Fig. I3 that for the case with R = I .O and n = 0.5, the moment-curvature relationship is linear (i.e. no energy dissipated), and the case with R = 0.5 and n = 0.5 has greater energy dissipations than the remaining cases.
drijrs
Figures 16 and I7 show the normalized story drifts. Again, it can be seen from these two figures that normalized story drifts are reduced with increasing the value of n (Fig. 16) and with decreasing value of R (Fig. 17).
4.2. Steel ,yielding locations 4.4. Displacement
Figures I4 and I5 show the steel yielding locations in the frame. Figure I4 indicates the results for the cases when n = 0.5 and R varies, while Fig. I5 shows those for R = 0.3 and n varies. It can be seen from Fig. I4 that the number of steel yielding locations decreases with decreasing value of R. It can also be seen from Fig. I5 that the number of steel yielding locations de&eases with increasing value of n. ( a ) R =
history
Figure I8 indicates the top-story displacement histories for both the elastic and inelastic analysis. It can be seen from this figure that stiffness degradation enlarges the displacement amplitudes and vibration periods when inelastic response occurs. The elastic vs inelastic displacement responses are very clearly compared in this figure. ( b ) R = 0.5
1.0
- oeeeo n = 0.0 - oeow n = 0.3 9- A-A.oaaP = 0.5 . +-a-t++ a = 0.8
9-
8
073 2 _ s 6w 5 4 3
Drift
( Normalized
to the
case
with
P =
a -0 1
Drift
( Normalized
to the
case
( d ) R = 0.1
( c ) R = 0.3
10 ) 9-
j 0-
0-
7-
3 72 s 6v, ?
2 s 6VJ : 5-
51
4-
4
3 3 i
4.!.sh... k00 0.20 Drift
.:
0.k’
( Normalized
‘l’--’
0.40
to the
0.b
.
case
.
.
..*...I 1.00 1.20
with
n = 0.0 )
Fig. 16. Story drifts of IO-story
structure
based
on plane frame model (n varies).
with
P =
0.0 )
Base isolation ( a
rsm -R
concept
895
and soft first story buildings (
f n = 0.0
b
) n = 0.3
( d
) n = 0.8
R = 0.3 = 0.1 8
6
( c ) n = 0.5 10
4 3
OeeeoR -R -It -R
z~.,.b,,..,,..,.,,..~...~ %.&!?3 8.28 8.48 Drift ( Normalized
= 1.0 -i 0.5 = 0.3 o 0.1
8.60 B.W l.ea 1.20 to the case with R = 1.0 )
-R
-R
= 0.3 = 0.1
Drift ( Normalized to the case with R E’
Fig. 17. Story drifts of IO-story structure based on plane frame model (R varies),
5. CONCLUSIONS
Fig. 18. Displacement histories of the roof level.
A new system for the design of earthquake-resistant buildings has been proposed. In this system, first story shearwalls are fitted with Teflon sliders while the remaining first story columns are designed with reduced yielding stress. With this system the energy dissipations may be increased and the number of steel yielding locations, normalized story drifts and placements in the superstructure may be significantly reduced.
Y. L. MO and Y. F. Chang
896 Acknowledgements-Support for this research tional Science Council, Taiwan, ROC, under 81-0410-E-006-573, is gratefullv acknowledged.
by the Nagrant NSC
REFERENCES review and 1. J. M. Kelly, A seismic base isolation: bibliography. Soil Dyn. Earthqu. Engng 5, 202-216 (1986). D. P. Clough and R. W. Clough, 2. A. K. Chopra, Earthquake resistance of buildings with a soft first story. Earthqu. Engng Struct. Dyn. I, 347-355 (1973). answer for seismic resist3. M. -Fintel, Shearwalls-an ance? Concr. Int. 13(7), 48-53 (1991). 4. Y. Q. Chen, and M.‘d. Constantinou, Use of Teflon sliders in a modification of the concept of soft first storey. Engng S!ruct. 12, 243-253 (1990). A. Mokha and A. M. Reinhorn, 5. M. C. Constantinou, Teflon bearings in base isolation. Part 2: modeling. /. Struct. Engng ASCE 116(2), 455474 (1990). 6. C. Meyer, M. S. L. Roufaiel and S. G. Arzoumanidis, Analysis of damaged concrete frames for cyclic loads. Earthqu. Engng Struct. Dyn. 11(2), 207-228 (1983). 1. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, 3rd SI edn. Chapman & Hall, London fi989). 8. T. Takeda, M. A. Sozen and N. N., Nielsen, Reinforced concrete response to simulated earthquakes. Proc. ASCE 96(STl2), 2557-2573 (1970).
9. T. C. Hsu and Y. L. MO, Softening of concrete in low-rise shearwalls. Research Report No. UHCE 84-8, Department of Civil Engineering, University of Houston (1985). Also in ACI J. Proc. 82(6j, 883-889 (1985). 10. S. T. Mau and T. T. C. Hsu, Shear behavior of reinforced concrete framed wall panels with vertical loads. ACZ Struct. J. &i(3), 228-234 (1987). Il. F. Vecchio and M. P. Colins, Stress-strain characteristics of reinforced concrete in pure shear. Final Report, IABSE Colloquium on Advanced Mechanics qf Reinforced Concrete, Delft, pp. 21 l-225. International Association for Bridge and Structural Engineering, Zurich (1981). 12. F. Vecchio and M. P. Colins, The response of reinforced concrete to in-plane shear and normal stresses. Publication No. 82-03, Department of Civil Engineering, University of Toronto, p. 332 (1982). 13. S. D. Jost and Y. L. MO. An algorithm for seismic analysis of lowrise structural walls. Nucl. Enanp ._ ., Des. 131,-2633270 (1991). 14. J. E. Hopcroft and J. D. Ullman. Introduction IO Automata _Theory, Languages and Computation, Addison-Wesley, New York (1979). 15. A. Mojkha, M. C. Constantinou and A. M. Reinhorn, Teflon bearings in base isolation. Part 1: testing. .I. Struct. Engng ASCE 116(2), 438454 (1990).