SEISMIC ISOLATION FOR MEDIUM RISE REINFORCED CONCRETE
FRAME BUILDINGS
Himat T Solanki*, Consultant, Sarasota, Florida, USA
Vishwas R Siddhaye, Emeritus Professor, College of Engineering, Pune, India
Gajanan M Sabnis, Emeritus Professor, Howard University, Washington, DC, USA
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SEISMIC ISOLATION FOR MEDIUM RISE REINFORCED CONCRETE
FRAME BUILDINGS
Himat T Solanki*, Consultant, Sarasota, Florida, USA
Vishwas R Siddhaye, Emeritus Professor, College of Engineering, Pune, India
Gajanan M Sabnis, Emeritus Professor, Howard University, Washington, DC, USA
Abstract
During January 2001 earthquake many reinforced concrete buildings and other structures were
damaged and/or collapsed in Ahmedabad, State of Gujarat. After this natural disastrous event, some
deficiencies of these buildings became evident. It also taught the engineering community some
lessons to minimize such losses by improving the seismic design codes and practice. Recognizing the
influence of high shear forces, alternate design methods for buildings and other structures and its
components including the use of isolation bearings should be investigated.
Various techniques are readily available having them used in the United States for the seismic
rehabilitation of structures. These techniques include adding cross bracings, structural shear walls,
base isolation systems etc. The cross bracings and structural/shear walls help reduce the drift and
increase the ductility of the structures. To enhance structural safety and integrity against severe
earthquakes, more effective technique for aseismic design of structures based on structural control
concepts are desired. Among the structural controls, aseismic base isolation is one of the most
promising alternatives. It can be adopted for new structures as well as the retrofit of existing
structures. The base isolation system with considerable lateral flexibility help in reducing the
earthquake forces by changing the structure’s fundamental period to avoid resonance with
predominant frequency contents of the earthquake.
In this paper the base isolation systems have been considered for the reinforced concrete frame
structures supported on isolation bearings. Analytical procedure is presented in-depth for a reinforced
concrete frame buildings. This study is based on a single degree of freedom (SDOF) with appropriate
hysteretic properties. Different geometries, variation of bearing stiffness, foundation flexibility and
ground motion are considered. Inelastic behavior by increasing the effective natural period of
vibration and the damping ratio of frame was considered. The viscous damping coefficient and
hysteretic damping ratio for isolation bearings were considered from the shear load deflection
relationship of isolation bearings.
A simplified step-by- step design procedure based on the static analysis is considered for the
preliminary practical design of a base isolated reinforced concrete frame buildings. This procedure is
adequate for designing the building structures with fair geometrical regularities.
INTRODUCTION
During January 2001 earthquake (Fig. 1a and Fig. 1b) many reinforced concrete buildings and other
structures were damaged and/or collapsed in Ahmedabad, State of Gujarat. The structure including its
foundation subjected to earthquake should be theoretically modeled by representing its behavior and
expected ground motion at the site. The theoretical model system of the structure should be idealized
into a spring-mass-dashpot system. In multistory frame structure, the masses are assumed to be
concentrated at floor levels and that floors are assumed to be rigid and the flexibility is provided by
the columns.
The damping is usually chosen based on the strain in the materials and is usually assumed to be
viscous for convenience in solution of vibration. The percentage of damping for various materials is
in the following ranges: Concrete and Masonry – 5% to 10%, Steel and Timber - 2% to 5% and soil
10% to 30%. These values are for estimation of ground motion and idealization of spring-massdashpot of a system. For the preliminary design and/or the codified design, empirical values are used.
The earthquake resistant design is a combined philosophies of a structure that may be designed to
withstand frequent moderate earthquake under elastic condition and may be permitted inelastic
deformation under the effect of the severest earthquake.
For routine design, the dynamic analysis of structures under elastic condition is cumbersome and
inelastic analysis is very tedious which would require a digital computer. Based on numerous scale
model and analytical series of deterministic dynamic inelastic time history (sets of forces and
displacements) studies, a simplified/codified seismic design provision is developed in various
countries including India. In seismic building codes, the structures are designed to resist specific static
lateral forces related to the properties of structures and the seismicity of the region.
An alternate technique to mitigate the seismic effect is the base isolation system. Worldwide
numerous buildings using base isolation systems are increasing. It is generally accepted that a base
isolation building will perform better than a conventional building in moderate and strong earthquake,
because it reduces the seismic forces transmitted to the superstructure and reduces the floor
acceleration induced by the earthquake.
In this paper, a simplified procedure is considered for both conventional method based on Indian
Standard Code IS 1893 (Part I): 2002 (1) and the lead –rubber isolated bearings based on
International Building Code (IBC) 2006 (2) for multistory buildings by considering it as a single
degree of freedom(SDOF) system with the inertial mass equal to the total mass equal to the total
building (assuming to be rigid body) and the spring stiffness equal to the effective stiffness.
DESIGN CRITERIA FOR EARTHQUAKE RESISTANT BUILDINGS: BUILDING CODES
Conventional Method (IS 1893 (Part I): 2002))
A.
The structures are designed to resist specified static lateral force related to the properties of structures
and zone seismicity (Fig. 2). Based on the formulae specified, an estimate for the fundamental natural
vibration period, base shear and the distribution of base shear, can be computed. Static analysis of the
building for lateral forces provides including shear and overturning moments for various stories.
Assumptions
•
•
•
Fundamental natural vibration period and amplitude lasting for small duration due to
impulsive ground motion.
Earthquake will not occur simultaneously with wing and/or maximum flood and/or maximum
sea wave action.
Elastic modulus of materials is considered same as that for static analysis
Permissible Stresses and Load Factors
•
•
•
No stresses increase is allowed in the Limit State Design Method
Ultimate State Design Method, the yield stress of steel limited to 80% of ultimate strength or
0.2 percent proof stress whichever is smaller.
For Limit State Design Method, a partial safety factor can be taken as per
IS 456:2000 (3) provided that premature failure due to shear and/or bond will not occur.
The percentage of allowable bearing pressure of soil can be increased depending upon the
type of foundations (Table- 1)
Seismic Design Coefficient Methods
For determining the seismic design forces, the structures depend on its own dynamic characteristics
and the ground motion due to earthquake. There are two methods: (1) Seismic Coefficient Method
and (2) Response Spectrum Method
1. Seismic Coefficient Method:
This method is simple and may be used for simple structures where Response Spectrum Method is not
warrant. In this method, the seismic forces can be computed on the basis of importance of the
structures and its soil- foundation systems. The horizontal seismic coefficient, αh , can be computed
as :
where:
αh
=
β I α0
(1)
β
I
α0
=
=
=
a coefficient depending upon the foundation system (Table -3 )
a factor depending upon the Importance of the structure (Table- 3A )
basic horizontal seismic coefficient (Table- 2)
2. Response Spectrum Method
In this method, first the response acceleration coefficient for the natural vibration period and damping
of the structure are required. Based on these values, the horizontal seismic coefficient, αh, can be
computed as :
αh
=
Z ISa/2Rg
(2)
where,
R
=
I
Z
Sa/g
=
=
=
performance factor depending upon the structural Framing system
and/or ductility of construction(Table-2A )
a factor depending upon the Importance of the structure (Table- 3A)
Seismic Zone Factor for average acceleration spectra (Table- 2)
average acceleration coefficient based on appropriate natural periods
and damping of the structure (Fig. 3 or Fig. 3(a)).
Fundamental Period of Building
Fundamental period of time, T for moment resisting frames building without bracing or shear walls
can be calculated as (IS 1893(Part I): 2002))
T
=
0.075 h 0.75
(3a)
T
=
0.09h/d 0.5
(3b)
h
d
=
=
height of building, in m.
base dimension of building at the plinth level in m. along the
or
where
considered direction of the lateral force.
Professor Goel and Professor Chopra ( 4 ) suggested the following equation for RCMRF buildings:
T
=
0.016 h 0.90
(4a)
T
=
0.023h 0.90
(4b)
and
Crowley and Pinho(5 ) suggested the following equation for cracked infilled RC frame buildings
T
=
0.055h
(5)
Inelastic Behavior
In order to take into account the effect of inelastic behavior of structure, Iwan (6 ) suggested the
following relationships:
(a)
Period of vibration
Tinelastic =
(b)
(6)
Damping
+
0.0587(µ∆ - 1) 0.371
=
ζ0
µ∆
k
=
=
(k2 + 1)
structural behavior factor OR response reduction factor, R, (Table 2-
ζ0
=
normal viscous damping and is equal to 0.05
ζinelastic
where
Telastic(1 +0.121(µ∆ - 1 ) 0.939)
(7)
A)
Effective Period of System
The fundamental vibration period, Teff, of the building, considering soil-structure interaction, is given
by the following equation (7 ):
T eff
where
=
T [1 + (k/Kx){ 1 + (Kxh2/Kθ)}] 0.50
Kx
Kθ
h
k
=
=
=
=
(9)
dynamics translation stiffness of the foundation in harmonic motion
dynamics rocking stiffness of the foundation in harmonic motion
effective height of building
lateral stiffness supported through a foundation of mass at the surface
Design Criteria for Multistory Building
Design Lateral Force
•
•
•
•
Building Design as a whole for seismic force (Rigid Diaphragm action)
Frame Building with tributary masses for seismic force (Diaphragm without Rigid action)
Table 5 outlines the recommendations of design method for various Building height located in
various seismic zones.
Drift should be checked for building greater than 40m and torsion for irregular Building floor
plan and/or elevation.
Base Shear
Base shear, Vb, is calculated as:
Vb
=
CαhW
(10)
where C
αh
W
Table- 4)
=
=
=
a coefficient depending upon the fundamental time period, T (Fig.4 )
design seismic coefficient (Eq. 2)
Dead Load (as specified in IS 875:1987 (8)) + Live Load (as defined in
Distribution of Forces along with Height of the Building
The distribution of forces along with height of the building can be expressed as:
where
Wihi2
Vb ---------i=n
∑ Wihi2
i=1
Q
=
(11)
Q
Vb
Wi
hi
=
=
=
=
lateral force at floor i
base shear
load (DL + LL ( as specified in Table- 4)) of the roof or any floor i
height measured from the base of the building to the roof or any floor
n
=
number of story including basement
i
Fig. 5 shows the force and shear distribution of a typical multistory building.
B.
Base Isolation System
Conventional method for Earthquake resistant design of building structures is primarily based on a
ductility design concept. Based on major earthquake this concept has been proved unsatisfactory.
Ductility design concept is primarily attributed to (Fig. 6):
1. The desired “Strong Column Weak Beam” concept may not be realistic due to existence of
walls
2. Shear failure of a column or short column effect
3. Construction difficulties especially at beam-column connections
To minimize the above problems, seismic isolation is one of the most promising alternatives. Seismic
isolation may reduce the earthquake induced forces by factor of 3 to 8 from those that an elastic,
conventional fixed base structure would experience.
The design of an isolated structure cannot be carried out by the following the design technique for
ductile structures (i.e. Conventional Design Method). The IBC guidelines provide a direction
regarding the analysis procedure for determining the dynamic response of isolated structures. There
are two approaches. The first procedure is the static formula for the displacements and forces to be
considered in the isolation system. The displacement and forces are a function of the seismic zone,
distance from active fault, soil profile, isolated system period and damping. The second procedure
uses the dynamic analysis. This paper addresses the static procedure. In static procedure, the
maximum displacement calculated from the elastic analysis and that maximum design forces obtained
from elastic analysis are considered in the overall design concepts and methodology.
Static Analysis
The static analysis procedure represents an upper bound estimate of seismic design loads and isolator
displacements. This concept is a useful tool for preliminary design.
IS 1893 (Part I):2002 allows modal analysis using response spectrum method for seismic Zones I, II,
and III and up to 90 m. building height.
The statically equivalent seismic force, V,
where
in which
V
=
keff di
(12a)
keff
di
keff
di
Si
=
=
=
=
=
B
T
=
=
g
W
A
=
=
=
4 π2W/T2g
10ASiT/B
isolator system stiffness
displacement across the isolation bearing
dimensionless site coefficient for isolator Design for the given soil
profile (Table-7 )
coefficient for the elastic damping ratio (Table-6)
period of vibration and it could be taken as
1/3[Telastic (Eq 3) + Tinelastic(Eq. 6) + Teff (Eq. 9)]
gravitational force
total weight of the structure
acceleration coefficient based on 5% Damping (Fig. 3a)
The maximum base isolation system shear force,
where
NOTE: Visol
Visol
=
[ASi/TB] W
(12b)
Visol
A
B
T
=
=
=
=
Si
=
isolation base shear force
spectral acceleration coefficient at 5 percent damping (Fig.3a )
damping coefficient (Table- 6)
Period of vibration and it could be taken as
1/3[Telastic (Eq 3) + Tinelastic(Eq. 6) + Teff (Eq. 9))]
site coefficient based on soil type (Fig 3a)
≥ seismic design load and yield level of isolation system
Design Procedure
The design of an isolated structure cannot be carried out by following the design technique for ductile
structures. To determine the dynamic response of the isolated structure, the procedure outlined is the
static formula for the displacements and forces to be considered in the design of isolation system; the
displacement and forces are a function of the seismic zone, distance from active faults, soil profile,
isolated period and damping.
In this paper a step- by- step design procedure is outlined and accompanies by a design example of
RC frame building.
Step by Step Design Procedure for Isolated RC Frame Building
1. Determine total weight of the building
2. Layout the bearing locations and determine the number of bearings (Fig.7)
3. Determine the maximum vertical load on each bearing using vertical column load
4. Based on the load capacity provided by the manufacturers, determine the plan dimension
of the bearings
5. Determine the fundamental period of the non-isolated superstructure
(IS 1893 (Part I): 2002 or Goel and Chopra (Ref.4 ) or Crowley and Pinho(5 ) method
can be used to estimate the fundamental period of fixed base superstructure).
6. The fundamental period of non-isolated superstructure can be modified to take account the
soil-structure interaction as suggested by Veletsos (7 )
7. In order to take into account the effect of inelastic behavior of the structure, the Iwan (6 )
approach can be used.
8. Make trial selection of the base Isolation System base on initial stiffness, post yield
stiffness and its yield strength and maximum allowable horizontal displacements at
working load and ultimate load levels.
In order to account for possible torsional effects, it is recommended that the average
displacement be increased by 10%.
9. Assume ductility ratio
10. Obtain the effective stiffness of the base isolation system at the maximum base shear
displacement from Force-Displacement relationship for Isolators
11. Determine the increase in damping due to hysteretic behavior of the base Isolation
system. To calculate the effective damping of the structure as a sum of the inherent
damping (5%) and the additional hysteretic damping.
12. Determine/modify the effective fundamental period of the base Isolation multistory
structure based on effective stiffness of isolation and the fundamental period of fixed base
structure.
13. Based on the effective fundamental period and the effective damping of the structure
calculate the maximum base isolation system shear force from the appropriate elastic
acceleration spectra and the maximum base displacement and the maximum ductility ratio.
14. If the difference between the calculated maximum displacement ductility ratio and the
assume maximum displacement ductility ratio is unacceptable repeat in step 9 through 13
until the two values converge.
15. Design Base Isolation system.
(a) Determine the maximum yield strength for lead plugs
(b) Calculate the core diameter
(c) Calculate the height of bearings
16. Determine the base shear and lateral inertia force distribution over the entire height of the
multistory structure as per Clause 7.7.1 of IS 1893(Part I): 2002.
The above procedure is adequate for medium rise base isolated multistory structures which
have a uniform mass and stiffness.
DESIGN EXAMPLE:
Fig. 8- shows building dimensions for six story superstructure (after Jury, 1978)(Ref.9 )
Fig. 9 - shows Predicted equivalent static lateral story shear
CONCLUSIONS:
1. The inelastic behavior of most typical buildings supported on isolation bearing can be
reasonably represented by an elastic SDOF structures
2. Properly designed isolation bearing system are highly effective in attenuating the ground
acceleration transmitted to superstructure and in reducing the structural displacement
3. The lead rubber bearing combined with elastomeric bearings are generally better than
building supported on elastomeric bearings.
4. The elastic performance of buildings is generally better with taller bearings. The use of
taller bearing results in greater effective period shift and greater amount of damping. The
maximum height of the bearing should be limited to a “roll-out” failure or vertical load
capacity at maximum displacement.
5. Based on Fig. 9, it can be seen that there is no significant difference between the step by
step procedure and the time history dynamic analysis.
6. Based on Fig. 9, it can be seen that the proposed procedure for designing buildings with
lead rubber bearings provide good results and appears to be a simple and straight forward
method.
7. This procedure can be used even in case of non-linear behavior of medium rise building.
REFERENCES
1. IS 1893(Part I): 2002, “Criteria for Earthquake Resistant Design of Structures: Part I
General Provisions and Buildings,” (Fifth Revision), Bureau of Indian Standards, New
Delhi, February 2006.
2. International Code Council, “International Building Code(IBC) 2006”, Fall Church, VA
2006.
3. IS 456: 2000, “Plain and Reinforced Concrete- Code of Practice,” (Forth Revision),
Bureau of Indian Standards, New Delhi, November 2005.
4. Goel, R. and Chopra, A.K., “Period Formulas for Moment- Resisting Frame Buildings”,
Journal of Structural Engineering, ASCE Vol. 123, No. 11, November 1997, pp. 14541461
5. Crowley H. and Pinho, R., “Simplified Equations for Estimating the Period of Vibration
of Existing Buildings”, Paper No. 1122, First European Conference on Earthquake
Engineering and Seismology, 3-8 September 2006, Geneva, Switzerland.
6. Iwan, W.D., “Estimating Inelastic Response Spectra from Elastic Spectra,” Earthquake
Engineering and Structural Dynamics, Vol. 8, 1980, pp. 375-388.
7. Veletsos, A.S., “Dynamics of Structure Foundation Systems,” In: Structural and
Geotechnical Mechanics, Ed. By. W.J. Hall, Prentice – Hall, Englewood Cliff, NJ, 1977,
pp. 333-361.
8. IS 875:1987, “Code of Practice for Design Loads (other than Earthquake ) for Buildings
and Structures: Part I Dead Loads- Unit Weight of building Materials and Stored
Materials” (Second Revision) , Bureau of Indian Standards, New Delhi, August 2001.
9. Jury, R.D., “Seismic Load Demands of Columns of Reinforced Concrete Multistorey
Frame,” Report 78-12, Department of Civil Engineering, University of Canterbury,
Christchurch, NZ 1980.
10. Sharma, H.K. and Agrawal, G.L., “Earthquake Resistant Building Construction,” ABD
Publishers, Jaipur, 302 003 (India), 2001.
Table 2- Value of Basic Seismic Coefficients and Seismic Zone Factors in Different Zones
_______________________________________________________________________________
Method
__________________________________________________________
Serial
Zone
Seismic Coefficient
Response Spectrum
No.
No
Method
Method
__________________________________________________________
Basic Horizontal
Seismic Zone Factor, Z, for
Seismic Coefficient
Average Acceleration Spectra
α0
(Fig.1 or Fig.4)
(1)
(2)
(3)
(4)
_________________________________________________________________________________
___
i
V
0.08
0.36
ii
IV
0.05
0.24
iii
III
0.04
0.16
iv
II
0.02
0.10
v
I
0.01
0.05
__________________________________________________________________________________
Table 3 - Values of β for Different Soil-Foundation
Systems( Ref.10 )
Table 4 – Percentage of Imposed Load to be considered in
Seismic Weight Calculation (IS 1893 (Part I): 2002)
____________________________________________________
Imposed Uniformly Distributed
Percentage of Imposed
Floor Loads (kN/m3)
Load
Upto and including 3.0
Above 3.0
25
50
Table 2(a) – Response Reduction Factor, R, for Building Systems
IS 1893 (Part I): 2002 Table-7
Table 5 - Recommendation of design method for a various
Building height located in various seismic zones (Ref.10 ).
Table 6 – Isolation System
___________________________________________________________
Isolation System
Damping Coefficient System Damping
“B”
________________________________________________________
5%
10%
1.0
1.2
High Damping
Rubber
20%
1.5
30%
1.7
Lead Rubber
40%
1.9
50%
2.0
_______________________________________________________
Table 7 - Site Coefficient
__________________________________________
Soil Type
S
__________________________________________
Type I (rock or hard soil)
1.0
(SPT N > 30)
Type II (medium soil)
1.2
(STP N 30 > N > 10)
Type III ( soft soil)
1.5
(STP N < 10 )
___________________________________________
Note: STP
=
Standard Penetration Test
N
=
number of blows per 150 mm penetration
Table 3A – A Factor Depending Upon the Importance
of the Structure (Ref. 10)
Fig. 1a- Gujarat Earthquake
Fig. 1b - Location of Earthquake
Fig. 2. – Seismic Zones in India
(IS 1893(Part I): 2002)
Fig. 3 – Average Acceleration Spectra (Ref.10)
Fig. 3a. – Response Spectra for Rock and Soil Sites for 5% Damping
(IS 1893(Part I): 2002)
Fig. 4 – C Versus Fundamental Time Period, T (Ref. 10)
Fig. 5 – Force and Shear Distribution of a Typical Multistory Building
(Ref. 10)
Fig. 6 – Deformation Pattern in Structures during an Earthquake (Ref. 10)
Fig. 7 – Lead-Rubber Hysteretic Bearing (NZ Systems)
Fig. 8 – Building Dimensions for Six Story Superstructure
(After Jury 1978)
Fig. 9 – Predicted Equivalent Static Lateral Story Shear