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R E P O R T
Hamilton
Telephone
+64 7 856 4849
Facsimile
+64 7 856 2397
Internet Address
www.holmesgroup.com
Unit 1b
300 Grey Street
PO Box 4283
Hamilton East
Hamilton 3247
New Zealand
Offices in
Auckland
Wellington
Christchurch
Queenstown
San Francisco
MASHAD CRISIS CENTRE
DESIGN AND EVALUATION OF SEISMIC ISOLATION SYSTEM
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R E P O R T
Hamilton
Telephone
+64 7 856 4849
Facsimile
+64 7 856 2397
Internet Address
www.holmesgroup.com
Unit 1b
300 Grey Street
PO Box 4283
Hamilton East
Hamilton 3247
New Zealand
Offices in
Auckland
Wellington
Christchurch
Queenstown
San Francisco
CONTENTS
1
INTRODUCTION.......................................................................................1
2 PROJECT REQUIREMENTS
.........................................................................
2
2.1 REFERENCES
..................................................................................
2
3 ISOLATION SYSTEM
DESIGN.....................................................................
3 3.1 S ELECTION OF ISOLATOR
TYPE............................................................. 3
3.2 S EISMIC PARAMETERS
.......................................................................
4 3.3 ISOLATOR LAYOUT
...........................................................................
6 3.4 ISOLATOR LOADS
............................................................................
7 3.5 ISOLATION S YSTEM PERFORMANCE
....................................................... 7 3.6 S
UMMARY OF PERFORMANCE
........................................................... 11
4 LEAD RUBBER BEARING DESIGN
PROCEDURE..........................................13 4.1
DEFINITIONS
...............................................................................
13 4.2 VERTICAL STIFFNESS AND LOAD C APACITY
............................................ 14
4.2.1 VERTICAL STIFFNESS
................................................................ 14
4.2.2 C OMPRESSIVE RATED LOAD C APACITY
.......................................... 15 4.2.3 TENSILE RATED
LOAD C APACITY ..................................................
16 4.2.4 BUCKING LOAD C APACITY
....................................................... 17
4.3 LATERAL STIFFNESS AND H YSTERESIS PARAMETERS FOR BEARING
................... 18
5 BEARING DESIGN CALCULATIONS
..........................................................21 5.1 M
ATERIAL PROPERTIES
.....................................................................
21 5.2 DESIGN LOADS
............................................................................
21 5.3 BEARING D IMENSIONS
...................................................................
21 5.4 BEARING PROPERTIES
.....................................................................
22 5.5 S ERVICEABILITY LOAD LIMIT STATE
........................................................ 23 5.6 S
EISMIC LOAD LIMIT STATE
............................................................... 24
5.7 VERTICAL STIFFNESS
.......................................................................
25 5.8 S PRING PROPERTIES FOR ETABS ANALYSIS
............................................ 26
6 ANALYSIS OF ISOLATED
BUILDINGS........................................................27
6.1 EQUIVALENT LINEAR ANALYSIS
........................................................... 27
6.1.1 ETABS ANALYSIS
..................................................................
27 6.1.2 CHECK FOR
UPLIFT..................................................................
27 6.1.3 VERTICAL LOAD DISTRIBUTION
.................................................... 28 6.1.4 M
AXIMUM VERTICAL LOADS
....................................................... 31
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P A G E 3
7 SUMMARY OF ISOLATION DESIGN AND PERFORMANCE
........................32
LIST OF FIGURES
FIGURE 3-1 5% DAMPED ACCELERATION
SPECTRUM........................................4 FIGURE 3-2 5%
DAMPED DISPLACEMENT SPECTRUM
........................................ 5 FIGURE 3-3 ISOLATOR
LAYOUT
........................................................................
6 FIGURE 3-4 INDIVIDUAL ISOLATOR HYSTERESIS
..............................................10 FIGURE 4-1 : LEAD
RUBBER BEARING
HYSTERESIS............................................19
LIST OF TABLES
TABLE 3-1 MATERIAL PROPERTIES FOR
DEVICES.................................................3 TABLE 3-2
ISOLATOR
LOADS.............................................................................7
TABLE 3-3 UBC AND AASHTO DAMPING
COEFFICIENTS...................................9 TABLE 3-4
ESTIMATED SEISMIC
PERFORMANCE...............................................12 TABLE
5-1: ISOLATOR DIMENSIONS
(MM).......................................................22 TABLE
5-2: BEARING PROPERTIES (KN, MM UNITS)
.......................................... 22 TABLE 5-3: GRAVITY
LOAD LIMIT
STATE...........................................................23
TABLE 5-4: SEISMIC LIMIT STATE DESIGN BASIS LOAD
..................................... 24 TABLE 5-5: SEISMIC LIMIT
STATE FOR MAXIMUM CAPABLE LOAD.....................25 TABLE 5-6
VERTICAL STIFFNESS (UNITS KN,
MM).............................................25 TABLE 5-7 ETABS
PROPERTIES (UNITS
KN,MM).................................................26 TABLE 6-1
DBE ISOLATION SYSTEM
PERFORMANCE........................................27 TABLE 6-2
VERTICAL LOADS
............................................................................29
TABLE 6-3 SUMMARY OF VERTICAL
LOADS......................................................31
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O f f i c e s i n
Wel l ing ton
C h r i s t c h u r c h
Q u e e n s t o w n
A u s t r a l i a
A u c k l a n d
Te lephone
6 4 9 5 2 2 4 5 9 6
Facs imi le
6 4 9 5 2 2 4 5 7 2
E m a i l A d d r e s s
[email protected]
67 Davis Crescent
P O B o x 9 9 - 4 5 0
N e w m a r k e t
A u ck la nd
N e w Z e a l a n d
P A G E 1
1 INTRODUCTION
This report presents the design and evaluation of a seismic
isolation system forMashad Crisis Centre.
Design is generally in accordance with the United States Uniform
Building Code(UBC) except for parameters such as level of seismic
load which are taken from theIranian earthquake code.
The building is a 1 storey with 1 basement floor structure.
Details of the building layout and structural system are provided
in a separate report.
The design process for the seismic isolation system was
iterative, with a number of configurations and isolation system
designs considered. This report details only the final isolation
system selected.
The structural design was based on an equivalent linear elastic
analysis using thecomputer program ETABS.
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P A G E 2
2 PROJECT REQUIREMENTS
2.1 REFERENCES
A complete reference list is as provided in the project
specifications. Referencesused in these calculations are:
[1] Iranian Code of Practice for Seismic Resistant Design of
Buildings 3rd Edition , Ministry of Housing and Urban Development,
Islamic Republic of Iran
[2] Uniform Building Code Appendix Division III Earthquake
Regulations for Seismic- Isolated Structures , UBC, American
Association of Building Officials, Whittier,CA, 1997.
[3] Guide Specifications for Seismic Isolation Design , AASHTO,
American Associationof State Highway Transportation Officials,
Washington D.C, 1991 and 1999.
[4] SAP2000 - Integrated Finite Element Analysis References
Manual , A Habibullah,Computers and Structures, Inc. Berkeley, CA
1997 and later revisions.
[5] Teflon Bearings in Aseismic Base Isolation : Experimental
Studies and Mathematical Modeling , A Mokha, M C Constantinou and A
M Reinhorn, State University of New York at Buffalo, Technical
Report NCEER-88-0038, December,1988.
[6] Base Isolation of Structures Design Guidelines,Holmes
Consulting Group,Revision 0, July 2001
[7] Seismic Isolation for Designers and Structural Engineers, T
E Kelly, R I Skinner andB W.H. Robinson, 2010
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P A G E 3
3 ISOLATION SYSTEM DESIGN
3.1 S ELECTION OF ISOLATOR TYPE
The isolation system selected was based on lead-rubber bearings.
These devicesare compact, cost effective and provide variable
damping within a single compactunit.
The building has a fixed base period of about 0.8 seconds which
was a little bithigher than expected to a 2 storey structure, but
the building is situated in a highlevel of relative seismic hazard
zone and is an essential government facility which
will make it suitable for base isolation.
Material properties of the devices used are listed in Table
3-1.
TABLE 3-1 MATERIAL PROPERTIES FOR DEVICES
Elastomer Properties KN,mm MPaShear Modulus 0.0004 0.4Ultimate
Elongation 6.5 6.5Material Constant, k 0.87 0.87Elastic Modulus, E
0.00135 1.35Bulk Modulus 1.5 1500Damping 0.05 0.05Lead Yield
Strength 0.008 8.00
Teflon Coeff of Friction 0.1 0.10Gravity 9810 9810
TFE Properties Vertical Stiffness 5000 5000000Lateral Stiffness
2000 2000000Coeff of Friction - Lo Vel 0.04 0.04Coeff of Friction -
Hi Vel 0.1 0.10Coefficient a 0.9 0.9
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P A G E 4
3.2 S EISMIC PARAMETERS
The site specific response spectra provided by the client was
based on the IranianCode. It was assumed that the code defined the
Design Basis Earthquake (DBE).
The Maximum Capable Earthquake (MCE) was assumed to be equal to
1.5 x DBE.
Figures 3-1 and 3-2 plot the acceleration and displacement
spectra for 5% damping for DBE and MCE. These curves formed the
basis of the isolation system design.
FIGURE 3-1 5% DAMPED ACCELERATION SPECTRUM
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 1.00 2.00 3.00 4.00
Period (seconds)
Ac
ea
on
gDBEMCE
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P A G E 5
FIGURE 3-2 5% DAMPED DISPLACEMENTSPECTRUM
0
200
400
600
800
1000
1200
1400
0.00 1.00 2.00 3.00 4.00
Period (seconds)
Dispa
me
mm)
DBE
MCE
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P A G E 6
3.3 ISOLATOR LAYOUT
Various configurations for the building were investigated and
the final layout of isolator types was as shown in Figures 3-3. The
building has 60 lead-rubberbearings (LRBs) in total.
FIGURE 3-3 ISOLATOR LAYOUT
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P A G E 7
3.4 ISOLATOR LOADS
The design and evaluation of the performance of the isolation
system is a functionof:
1. The number of isolators of each type.
2. The total seismic load on isolators of each type. The total
seismic load isbased on dead load plus seismic live load, which is
G+0.2Q for thesebuildings.
For individual isolator evaluation, the maximum loads under
gravity conditions andseismic conditions are also required. Table
3-2 lists the loads of the buildings.
TABLE 3-2 ISOLATOR LOADS
Type LRBNumber of Bearings 60Number of Prototypes 2
Average DL + SLL 780Maximum DL + LL 1262Maximum DL + SLL + EQ
1156
Total Seismic Weight 46800
3.5 ISOLATION S YSTEM PERFORMANCE
The isolation system design is an iterative process whereby
isolator properties areadjusted to obtain the performance required
of the system.
For these buildings, the performance objective was to minimise
design base shear.For a building with low wind loads, the base
shear design coefficient is the higherof two values:
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P A G E 8
1. The yield force of the isolation system times 1.5.
2. The elastic base shear coefficient under DBE load divided by
the StructuralBehaviour Factor, R. For isolated buildings R=2 to
ensure essentially elasticresponse.
The most effective design will be one in which the design shear
coefficient required
by each of these conditions are approximately equal. The design
and evaluation of the isolation system is based on the total
stiffness anddamping values of the system. The steps involved in
this evaluation are:
Step 1.
Select isolator plan sizes based on maximum gravity load. Set a
trial number of rubber layers and lead core size.
Step 2.
The shear force in the bearing at a specified displacement is:+=
r K dm QF
where Qd is the characteristic strength and K r the yielded
stiffness. For a leadrubber bearing these are a function of the
rubber thickness and lead core size. Fora sliding bearing Qd = P
and K r = 0.0, where is the coefficient of friction and Pthe
vertical load.
From the maximum forces an average, or effective, stiffness can
be calculated as:
=m
eff
FK
Step 3.
The sum of the effective stiffness of all bearings allows the
period of response tobe calculated as:
eff e K g
W T
= 2
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P A G E 9
Step 4
The effective damping is calculated from the hysteresis loop
area. For lead rubberbearings the hysteresis area is calculated at
displacement levelm as:
y mdh 4Q A =
For slider bearings, Qd is equal to the friction force and the
loop area is
m= d h 4QA
from which the equivalent viscous damping is calculated as:
=
2eff
h
K
A
21
The damping then allows the damping coefficient, B, to be
obtained from UBC, as
shown in Table 3-3:
TABLE 3-3 UBC AND AASHTO DAMPING COEFFICIENTS
50%B 0.8 1.0 1.2 1.5 1.7 1.9 2.0
Step 5.
The isolator displacement can be calculated from the effective
period, equivalent
viscous damping and spectral acceleration as:
B
T S ea
m 2
2
4 =
The displacement calculated from the effective period and
damping in Step 5 isthen compared with the displacement assumed in
calculation of stiffness propertiesin Step 2. Values are adjusted
until convergence is obtained.
Once convergence is achieved, the performance of the system is
evaluated and, if necessary, the isolator details in Step 1 are
modified and the process repeated.
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P A G E 1 0
Figure 3-4 shows the form of the hysteresis loops provided by
the isolator.
FIGURE 3-4 INDIVIDUAL ISOLATOR HYSTERESIS
-300
-200
-100
0
100
200
300
-400 -300 -200 -100 0 100 200 300 400
SHEAR DISPLACEMENT (mm)
S H E A R F O R C E ( K N )
LRB
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P A G E 1 2
TABLE 3-4 ESTIMATED SEISMIC PERFORMANCE
Block ADBE MCE
Effective Period T D TM 1.74 1.97Displacement D D DM 160 306
Total DisplacementsD TD D TM
184 352
Force Coefficient V b / W 0.213 0.317Force Coefficient V s / W
0.1061.5 x Yield Force / W 0.146
Wind Force / W 0.000Governing Design Coefficient 0.146Base Shear
Force 6833Damping eff 26.6% 18.6%Damping Coefficients BD BM 1.62
1.44Restoring Force at D D 0.245
at 0.5DD 0.122Difference (to be > 0.025) 0.123
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P A G E 1 3
4 LEAD RUBBER BEARING DESIGN PROCEDURE
The design procedure described in the previous section of the
report was based onlead-rubber bearing properties calculated using
the procedures given in this section.
On completion of the design, these procedures were also used to
check thecapacity of the isolators, as described in the following
section.
4.1 DEFINITIONS
Ab = Bonded area of rubber Ag = Gross area of bearing, including
side cover Ah = Area of hysteresis loop
(Also termed EDC = energy dissipated per cycle) Apl = Area of
Lead core Ar = Reduced rubber areaB = Overall plan dimension of
bearing E = Elastic modulus of rubber
= 3.3 to 4.0 G depending on hardnessEb = Buckling ModulusEc =
Effective Compressive ModulusE = Bulk Modulus (usually assumed as
290 ksi)f = Factor applied to elongation for load capacity
= 1 / (Factor of Safety)Fm = Force in bearing at specified
displacementg = Acceleration due to gravity G = Shear modulus of
rubber (at shear strain )H r = Height free to buckleI = Moment of
Inertia of Bearing k = Material constant (0.65 to 0.85 depending on
hardness)K d = Yielded stiffness of lead rubber bearing = K r K eff
= Effective StiffnessK r = Lateral stiffness after yieldK u =
Elastic Lateral stiffnessK v = Vertical stiffness of bearing K vi =
Vertical stiffness of layer in = Number of rubber layersp = Bonded
perimeter
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P A G E 1 4
P = Applied vertical loadPcr = Buckling LoadP = Maximum rated
vertical loadQd = Characteristic strength
(Force intercept at zero displacement)Si = Shape factor for
layer iti = Rubber layer thicknesstsc = Thickness of side covertsh
= Thickness of internal shims
Tpl = Thickness of mounting plates Tr = Total rubber thickness W
= Total seismic weight
= Applied lateral displacementm = Maximum applied displacementy
= Yield displacement of lead rubber bearing = Equivalent viscous
damping
u = Minimum elongation at break of rubberc = Compressive
Strainsc = Shear strain from applied vertical loadssh = Shear
strain from applied lateral displacementsr = Shear strain from
applied rotationu = Minimum elongation at break of rubber = Applied
rotationy = Lead yield stress
4.2 VERTICAL STIFFNESS AND LOAD C APACITY
The dominant parameter influencing the vertical stiffness, and
the vertical loadcapacity, of an elastomeric bearing is the shape
factor. The shape factor of aninternal layer, Si, is defined as the
loaded surface area divided by the total free tobulge area:
ii 4t
BS = for square and circular bearings
4.2.1 VERTICAL STIFFNESS
The vertical stiffness of an internal layer is calculated as
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P A G E 1 5
i
rc vi t
AEK =
where the apparent compressive modulus, E c, is a function of
the shape factor andmaterial constant as follows:
2ic 2kS1EE +=
In the equation for vertical stiffness, a reduced area of
rubber, A r, is calculatedbased on the overlapping areas between
the top and bottom of the bearing at adisplacement, , as
follows:
=
B AA br 1 for square bearings
( )22
12 sin
=
=
B
where B
B0.5A r
for circular bearings
When the effective compressive modulus, E c, is large compared
to the bulk modulus E (generally about 2000MPa or 290 ksi) then the
vertical deformationdue to the bulk modulus is included by dividing
E c by 1 + (E c /E ) to calculatethe vertical stiffness. This
effect is used to calculate vertical deformations in thebearing but
not the shear strains due to vertical load.
4.2.2 C OMPRESSIVE RATED LOAD C APACITY
The vertical load capacity is calculated by summing the total
shear strain in theelastomer from all sources. The total strain is
then limited to the ultimateelongation at break of the elastomer
divided by a the factor of safety appropriate tothe load
condition.
The shear strain from vertical loads, sc , is calculated as
cisc S 6=
where
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P A G E 1 6
i vic tK
P=
If the bearing is subjected to applied rotations the shear
strain due to this is
ri
2
sr T2t
B =
The shear strain due to lateral loads is
rsh T
=
For service loads such as dead and live load the limiting strain
criteria are
scuf where f = 1/3 (Factor of safety 3)
And for ultimate loads which include earthquake
displacements
shscu +f where f = 1.0 (Factor of safety 1)
Combining these equations, the maximum vertical load, P , at
displacement canbe calculated from:
( )i
shui vi
Sf tK 6
=P
4.2.3 TENSILE RATED LOAD C APACITY
For tension loads, the stiffness in tension depends upon the
shape of the unit, as incompression, and is approximately the same
as the compression stiffness.
Therefore, the same equations are used as for compressive loads
except that thestrains are the sum of absolute values.
When rubber is subjected to a hydrostatic tension of the order
of 3G cavitationmay occur. This will drastically reduce the
stiffness. Although rubbers with very poor tear strength may
rupture catastrophically once cavitation occurs, immediatefailure
does not generally take place. However, the subsequent strength of
thecomponent and its stiffness may be effected. Therefore, the
isolator design is
generally based on ensuring that tensile stresses do not exceed
3G under any loadconditions.
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P A G E 1 7
4.2.4 BUCKING LOAD C APACITY
For bearings with a high rubber thickness relative to the plan
dimension the elasticbuckling load may become critical. The
buckling load is calculated using theHaringx formula as
follows:
The moment of inertia, I is calculated as
12B
I 4
= for square bearings
64
4BI
= for circular bearings
The height of the bearing free to buckle, that is the distance
between mounting plates, is
shir 1)t(n )(ntH +=
An effective buckling modulus of elasticity is defined as a
function of the elasticmodulus and the shape factor of the inner
layers:
)0.742SE(1E 2ib +=
Constants T, R and Q are calculated as:
r
r
b TH
IET =
r
rg
H
TGAR =
rHQ
=
From which the buckling load at zero displacement is:
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P A G E 1 8
+= 10
R 4TQ
12R
P 2
cr
For an applied shear displacement the critical buckling load at
zero displacement isreduced according to the effective "footprint"
of the bearing in a similar fashion tothe strain limited load:
g
r0crcr A
APP =
The allowable vertical load on the bearing is the smaller of the
rated load, P, or thebuckling load.
4.3 LATERAL STIFFNESS AND H YSTERESIS PARAMETERS FOR BEARING
Lead rubber bearings, and elastomeric bearings constructed of
high damping rubber, have a nonlinear force deflection
relationship. This relationship, termedthe hysteresis loop, defines
the effective stiffness (average stiffness at a
specifieddisplacement) and the hysteretic damping provided by the
system. A typicalhysteresis for a lead-rubber bearing is as shown
in Figure 3.1.
For design and analysis this shape is usually represented as a
bilinear curve with anelastic (or unloading) stiffness of K u and a
yielded (or post-elastic) stiffness of K d.
The post-elastic stiffness K d is equal to the stiffness or the
elastomeric bearing alone, K r. The force intercept at zero
displacement is termed Q d, thecharacteristic strength.
ply d AQ =
The theoretical yield level of lead, y , is 1.5 ksi but the
apparent yield level isgenerally assumed to be 1.15 to 1.4 ksi,
depending on the vertical load and leadcore confinement.
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P A G E 1 9
FIGURE 4-1 : LEAD RUBBER BEARING HYSTERESIS
The post-elastic stiffness, K d, is equal to the shear stiffness
of the elastomericbearing alone:
r
rr T
AGK =
The shear modulus, G , for a high damping rubber bearing is a
function of the
shear strain , but is assumed independent of strain for a
lead-rubber bearing manufactured from natural rubber and with
standard cure.
The elastic (or unloading) stiffness is defined as:
ru K K = for elastomeric bearings
+=
r
plru A
AK K
1215.6
for lead-rubber bearings
ru 25K K =
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P A G E 2 0
For lead rubber bearings, the first formula for K u was
developed empirically in the1980s to provide approximately the
correct stiffness for the initial portion of theunloading cycle and
to provide a calculated hysteresis loop area whichcorresponded to
the measured areas.
The bearings used to develop the original equations generally
used rubberlayers and dowelled connections. By the standard of
bearings now used, they were
poorly confined. A database of test results from more recent
projects has shownthat the latter formula for K u provides a more
realistic estimate.
The shear force in the bearing at a specified displacement
is:
+= r K dm QF
from which an average, or effective, stiffness can be calculated
as:
= meff
FK
The sum of the effective stiffness of all bearings allows the
period of response tobe calculated as:
eff e K g
W T
= 2
Seismic response is a function of period and damping. High
damping and leadrubber bearings provide hysteretic damping. For
high damping rubber bearings,the hysteresis loop area is measured
from tests for strain levels, , and theequivalent viscous damping
calculated as given below. For lead rubber bearingsthe hysteresis
area is calculated at displacement levelm as:
y mdh 4Q A =
from which the equivalent viscous damping is calculated as:
=
221
eff
h
K A
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P A G E 2 1
5 BEARING DESIGN CALCULATIONS
The lead rubber bearings used in the building have the same
dimensions andinternal construction. Design of these are described
in this section of the report.
5.1 M ATERIAL PROPERTIES
The detailed design of the isolation system was performed using
an EXCELspreadsheet based on the design procedures given in the
preceding section. Theproperties of the elastomer used were as
listed in Table 3-1.
5.2 DESIGN LOADS
The design vertical loads are the load combinations listed in
Table 3-2. Therequirements for bearing design (based on AASHTO
Specifications) are for afactor of safety of 3.0 under gravity
loads, 1.33 under DBE loads and 1.0 underMCE loads.
5.3 BEARING D IMENSIONS
The bearing dimensions are as given in Table 5-1. The plan
dimensions, internalconstruction and lead core sizes were set to
meet dimensional limitations andprovide the specified stiffness and
energy dissipation. All isolators are circle inplan shape.
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P A G E 2 2
TABLE 5-1: ISOLATOR DIMENSIONS (MM)
TypicalLead-Rubber
IsolatorPlan Dimension 620Layer Thickness 10Number of Layers
18Lead Core Size 110
Total Height 274
5.4 BEARING PROPERTIES
The properties of each bearing were calculated using the
formulas from Section 4and are as listed in Table 5-2.
TABLE 5-2: BEARING PROPERTIES (KN, MM UNITS)
TypicalLead-Rubber
IsolatorGross Area, Ag 301907Bonded Dimension 600Bonded Area
282743Plug Area 9503Net Bonded Area 273240
Total Rubber Thickness 180Bonded Perimeter 1885Shape Factor
14.5Characteristic Strength, Qd 76.0Shear Modulus (50%) 0.0004
Yielded Stiffness Kr 0.65For LRB, Coefficient on Kr 6.50
Coefficient on Ap/Ar 12.00Elastic Stiffness Ku 5.99
Yield Force 85.3 Yield Displacement 14.25Moment of Inertia
6.362E+09
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P A G E 2 3
TypicalLead-Rubber
IsolatorHeight Free to Buckle 214.0Effective Buckling Modulus
0.212Constant T 1.602E+09Constant R 95.1
Constant Q 0.0147
5.5 S ERVICEABILITY LOAD LIMIT STATE
The vertical stability criteria require a factor of safety on
the elongation at break of at least 3 under maximum vertical loads.
Table 5-4 summarises the calculation of the maximum strain in the
rubber under the load condition of DL+LL.
TABLE 5-3: GRAVITY LOAD LIMIT STATE
LRBFactor on Eu 0.33
Applied Vertical Load 1262 Applied Displacement 0 Applied
Rotation 0Shape Factor, Si 14.5Constant k 0.87Elastic Modulus, E
0.0014Compressive Modulus, Ec 0.495Reduced Area 282743
Vertical Stiffness, Kvi 13994Compressive Strain, ec
0.009Compressive Shear Strain, esc 0.78Displacement Shear Strain,
esh 0Rotational Shear Strain, esr 0
Total Strain 0.78 Allowable Strain 2.17Buckling Load, Pcr
5684Status OK
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P A G E 2 4
5.6 S EISMIC LOAD LIMIT STATE
The seismic displacement is used to evaluate the seismic load
limit state in thebearings. The total shear strain is calculated
from compression plus the strain dueto applied displacements. A
factor is applied to the ultimate elongation, e u, equalto the
reciprocal of the safety factor.
Tables 5-4 and 5-5 list the calculations for the seismic
displacement from DBE andMCE earthquakes respectively.
TABLE 5-4: SEISMIC LIMIT STATE DESIGN BASIS LOAD
LRB Applied Vertical Load 1156DBE Displacement, DD 160.3Factor
on DD 1.15
Applied Displacement 184.3 Applied Rotation 0Shape Factor, Si
14.5Constant k 0.87Elastic Modulus, E 0.0014Compressive Modulus, Ec
0.495Reduced Area 173913
Vertical Stiffness, Kvi 8608Compressive Strain, ec
0.013Compressive Shear Strain, esc 1.17Displacement Shear Strain,
esh 1.02Rotational Shear Strain, esr 0
Total Strain 2.19 Allowable Strain 4.88Buckling Load, Pcr
3496Status OK
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P A G E 2 5
TABLE 5-5: SEISMIC LIMIT STATE FOR MAXIMUM CAPABLE LOAD
LRB Applied Vertical Load 1156MCE Displacement, DD 305.9
Factor on DD 1.15 Applied Displacement 351.8 Applied Rotation
0Shape Factor, Si 14.5Constant k 0.87Elastic Modulus, E
0.0014Compressive Modulus, Ec 0.495Reduced Area 84489
Vertical Stiffness, Kvi 4182Compressive Strain, ec
0.028Compressive Shear Strain, esc 2.4Displacement Shear Strain,
esh 1.95
Rotational Shear Strain, esr 0 Total Strain 4.36 Allowable
Strain 6.50Buckling Load, Pcr 1698Status OK
5.7 VERTICAL STIFFNESS
Table 5-6 lists the calculation of the vertical stiffness for
each bearing type.
TABLE 5-6 VERTICAL STIFFNESS (UNITS KN, MM)
TypicalLead-Rubber
IsolatorKvi 13994Kv 777Bulk Modulus Kb 1.5
Vertical Stiffness, Kv 585
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P A G E 2 6
5.8 S PRING PROPERTIES FOR ETABS ANALYSIS
The calculated properties of the isolators were used to assemble
springs propertiesto be used as input for analysis using the ETABS
computer program, as listed in
Tables 5-7, 5-8 and 5-9 for the three buildings.
For the lead-rubber isolators (ISOLATOR1) , the vertical, K1,
the elastic stiffness,K2 and K3, and the ratio of elastic to
yielded stiffness, RK2 and RK3 arecalculated as part of the design
procedure, see Tables 5-2 and 5-6.
For an equivalent linear analysis an effective stiffness, KE2,
and effective damping,DE2, are defined. The effective stiffness and
damping are defined at the estimatedDBE displacement (Table 3-4)
using the equations provided in Section 4 of thisreport.
Damping is reduced by 5% to account for the damping incorporated
in the modalanalysis.
TABLE 5-7 ETABS PROPERTIES (UNITS KN,MM)
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P A G E 2 7
6 ANALYSIS OF ISOLATED BUILDINGS
The analysis and design of the isolated building was based on an
equivalent elasticanalysis using the computer program ETABS and
spring properties as listed in thepreceding section.
6.1 EQUIVALENT LINEAR ANALYSIS
6.1.1 ETABS ANALYSIS
Calculations and design of the superstructure from the ETABS
analysis arereported separately. Only the results which are used to
verify the design of theisolation system are reported here.
Table 6-1 compares the centre of mass displacements (D D ),
maximumdisplacements including torsion (D TM ) and base shear force
from the ETABSanalysis for each building with the equivalent values
predicted by the designprocedure.
In all cases the results are very close, which indicates that
the assumption of a rigidbuilding on a flexible isolation system is
reasonable for the building.
TABLE 6-1 DBE ISOLATION SYSTEM PERFORMANCE
ETABSX
Direction
ETABS Y
Direction
DesignProcedure(Table 3-4)
Displacement D D (mm) 157 157 160 Total Displacements D TD (mm)
176 177 184Base Shear Force (KN) 7578 7579 6842
6.1.2 CHECK FOR UPLIFT
Initial run of the ETABS analysis for the un-isolated structure
showeduplift/tensile forces on the perimeter of the buildings
foundation. The problem
with uplift forces is that lead-rubber bearings were not ideal
for tension because of the limitation of rubber to resist tensile
stresses, thus, we run a check on theisolated structure to verify
the presence of uplift forces in the bearings.
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P A G E 2 8
6.1.3 VERTICAL LOAD D ISTRIBUTION
Tables 6-2 list the axial load on each isolator for the
building. The table lists thefollowing load combinations from the
ETABS analyses:
1. G+0.2Q-E. This is the most likely load minimum load (tension)
on theisolators, based on the dead load plus seismic live load plus
earthquake upward
load.2. G+0.2Q+E. This is the most likely load maximum load
(compression) on the
isolators, based on the dead load plus seismic live load plus
earthquakedownward load.
3. 0.8G-E. This is the extreme minimum load (tension) expected
on any isolator, based on UBC combinations.
4. 1.2G+1.0Q+E. This is the extreme maximum load (compression)
expectedon any isolator, based on UBC combinations.
The loads listed in Tables 6-2 are for the MCE, taken as 1.5
times the ETABSresults for the DBE.
As seen in the tables, the ETABS analysis shows no uplift forces
present on theisolated structure. Even though in reality there may
be a probability of sometensile/uplift forces in some of the
bearings, the LRBs have its inherent propertiesto resist those
minimal forces.
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P A G E 2 9
TABLE 6-2 VERTICAL LOADS
Col G+0.2Q E G+0.2Q+E 0.8G E 1.2G+Q+E1 216 512 135 626 2 595 755
456 961 3 601 751 463 955 4 601 751 463 955 5 595 754 456 959 6 215
512 134 625 7 187 501 110 610 8 831 848 638 1142 9 999 1010 763
1380
10 997 1008 762 1377 11 997 1008 762 1377
12 998 1009 763 1379 13 842 860 645 1157 14 215 511 134 624 15
567 744 432 946 16 971 999 740 1365 17 993 995 758 1363 18 995 998
760 1368 19 995 998 760 1368 20 992 994 758 1362 21 998 1010 763
1380 22 596 754 457 959 23 662 841 507 1068 24 1059 1098 807 1492
25 963 983 732 1351 26 915 951 693 1320 27 915 951 693 1320 28 962
983 732 1351 29 998 1009 763 1379 30 600 750 463 954
31
661
840
507
1067
32 1060 1097 808 1490
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P A G E 3 0
33 888 926 677 1261 34 672 675 509 945 35 672 675 509 945 36 888
924 677 1259 37 999 1008 764 1378 38 600 750 463 954 39 595 754 457
960 40 999 1011 763 1382 41 962 983 731 1351 42 915 950 692 1319 43
915 950 692 1319 44 962 983 731 1351 45 1000 1010 764 1381 46 596
753 457 958 47 214 511 133 624
48
842
860
645
1158
49 1000 1010 764 1381 50 1000 1008 764 1379 51 1000 1008 764
1379 52 1000 1010 764 1381 53 842 860 645 1158 54 215 511 134 624
55 215 511 134 625 56 595 755 456 960 57 601 751 463 955
58 601 750 463 954 59 595 754 456 959 60 215 512 134 625
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P A G E 3 1
6.1.4 M AXIMUM VERTICAL LOADS
The detailed results listed above in Tables 6-2 are used to
derive maximum loadson each isolator type, as listed in Table 6-3.
These are for the MCE level of load.
1. Maximum compression on any lead-rubber bearing 1492 KN for
ETABS.
2.
Maximum tension on any lead-rubber bearing 0 KN for ETABS.
TABLE 6-3 SUMMARY OF VERTICAL LOADS
G+0.2Q E G+0.2Q+E 0.8G E 1.2G+Q+E MIN MAX MIN MAX 187 1098 110
1492
The aim of the isolation system configuration was to avoid
tension on the lead-rubber bearings at DBE levels of load and allow
only small tensions under MCEloads.
Applied tension tests on elastomeric bearings have shown that
the bearings tensilestiffness was approximately linear to a strain
of 10% (5.6 mm elongation) at a stressof 4.0 MPa. The stiffness
then reduced due to cavitation and failure occurred at astrain of
150% (84 mm elongation) and stress of 5.5 MPa.
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P A G E 3 2
7 SUMMARY OF ISOLATION DESIGN AND PERFORMANCE
The Mashad Crisis Centre have a number of characteristics which
make them wellsuited to isolation, in particular, their location on
a stiff soil profile, relatively short
natural period, and building importance category. This makes for
a straight-forward seismic isolation design.
The squat configuration of the building (low height & large
footprint) makes it anideal structure for lead-rubber bearings
wherein the probability of uplift forces
would be minimal. The isolation system used comprised mainly
lead-rubberbearings.
The isolation system design set a target of an isolated period
of approximately 2seconds. On a stiff soil site there is little
benefit to be gained by a longer isolatedperiod as the design base
shear force is governed by the yield level of the
isolationsystem.
The system as designed provided isolation periods under the
design earthquake of 1.74 seconds, which produced displacements of
184 mm. The elastic base shearcoefficients (R = 1) was 0.213, about
20% the elastic base shear coefficient of 1.0for a non-isolated
building on the same site. An isolated structural behaviourfactor
of R = 2 was used for design of the superstructure, providing a
design baseshear coefficient of 0.146 for the building.
The building analysis procedure used the equivalent elastic
analysis procedure,based on a response spectrum approach using
effective linear spring values for theisolators.
The building analysis also checks the likelihood of an uplift
force during a MCEevent level of earthquake and found out that the
possibility was nil (where MCE was defined as a seismic load 1.5
times the design earthquake level).
Although tension forces are not desirable in lead-rubber
bearings, tests have shownthat they are linear elastic in tension
to stresses of 4 MPa, which corresponds to1131 for the 620 mm
square bearings used in this project.
We conclude from these calculations and analyses that the
isolation system asdesign for the Mashad Crisis Centre provides a
safe and effective method of improving the earthquake performance
of the structures.
