adfa, p. 1, 2011.

© Springer-Verlag Berlin Heidelberg 2011

On development of a new seismic base isolation system

Sanjukta Chakraborty (1)

Koushik Roy (2)

Chetan Chinta Arun (3)

and Samit Ray Chaudhuri (4)

Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, UP-208016, India

(1) sanjukta@iitk.ac.in, (2)koushik@iitk.ac.in (3) samitrc@iitk.ac.in

Abstract. Various base isolation schemes have been implemented to isolate a structure from intense base

excitations. In this paper, performance of a friction sliding bearing with nonlinear restoring mechanism is

studied on a three-storey steel moment-resisting frame building under varying seismic hazard conditions.

The performance of the proposed system is compared with that of the fixed-base and with only the fric-

tion sliding bearing. For this purpose, the effectiveness of the proposed isolation system is evaluated in

terms of the residual displacement, peak inter-storey drift and the maximum base displacement. It is en-

visioned that a system as proposed here, if optimized for a target hazard situation, will result in a cost-

effective solution.

Keywords: Non-linear spring, Friction sliding bearing,

1 Introduction

Seismic base isolation is becoming a cost effective way to mitigate the seismic vulnerability of various struc-

tures and bridges. Over the years, many types of base isolation devices have been proposed. Although these

devices have pros and cons, the selection of these devices is mainly decided based on their expected perfor-

mance under earthquake motions of various hazard levels and more importantly, their cost of installations.

Sliding base isolation system has widely been used as a cost effective choice to reduce seismic vulnerability

of the structures and bridges. While this type of isolation system is insensitive to dominant frequency of

ground motion, it does not possess a restoring mechanism. As a result, a structure isolated with this type of

device requires a large base plate to accommodate excessive base displacement in addition to end barriers to

prevent the structure from the falling of the plate. Further, high frequency shock waves are generated when

the isolator hits the barrier during strong earthquakes resulting in damage to non structural component s and

systems. In this study, the concept of nonlinear restoring mechanism is employed to improve the perfor-

mance of a conventional sliding isolation system. The nonlinear restoring mechanism has been achieved by

designing nonlinear springs for which the stiffness increases with an increase in displacement. An extensive

parametric study involving time history analysis of structure and subjected to a suite of ground motions with

different hazard levels is conducted to evaluate the effectiveness of the proposed isolation system. It is ob-

served from the results of the parametric study that the proposed isolation system ( Sliding bearing with

nonlinear spring) reduces the earthquake response of the structure in terms of residual and peak base dis-

placement demands while keeping the peak inters story drift within the safe limit. It is envisioned that the

proposed isolation system when tested experimentally, can be used as a better choice over the conventional

sliding bearing.

2 Spring Model

In this section a brief description of the spring model as well as the mathematical formulation is presented.

The desired behavior of the spring as described earlier can be achieved by a conical spring with uniform

pitch. The conical spring with increasing diameter towards the bottom provides a varying flexibility each

loop. Therefore the bottom loop grounds first as the force on the conical spring increases followed by other

loops with reducing diameter and also decrease in the active number of loops. Thus the stiffness of the

spring increases gradually along with the increase in displacement of the coil. Working characteristics can be

divided into two regions- working region with linear characteristics where no coil is grounded and working

region with progressive characteristics after the contact of the first active coil.

The variation of the loop diameter of the conical spring along with the length can be considered to be linear

or some other types of variation also can be assumed. Here two types of variations are studied. One spring is

considered with a linear reduction in the diameter along the length and other one having logarithmic spiral

type of variation in diameter along length.

Fig 1. A typical spring conical spring model showing different component

∫

∫

(1)

From Castigliano’s Theorem

∫

=

∫

(2)

The equation of logarithmic spiral is given by from equation

(3) For deflection in between two different angle θ1 and θ2 the deflection can be estimated from equation 2 as

below.

∫

(4)

[

] (5)

[

] (6)

Fig 2. The force displacement plot of the spring with logarithmic variation of diameter

Similarly the equation for the linear variation is given by

{

} (7)

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20.5

1

1.5

2

2.5

3

3.5x 10

4

Deflection (m)

Fo

rce

(N)

Stiffness plot

∫

{

(

)

}

(8)

Fig 3. The force displacement plot of the spring with linear variation of diameter

where d=diameter of the wire the spring made of steel, G= Shear modulus, N=Total number of loop, n1 and

n2 = the loop number the deflection to be calculated, Ds= Diameter of the tapered section, De= Diameter of

the larger side, and F=Force to be applied.

The two types of springs exhibited similar types of stiffness behavior with a very flat range at the beginning

and a very high stiffness at larger deformation. Both the plot of the springs as shown in Figure 2 and Figure

3 considered same parameters as stated above for the spring design. However the spring with linear diameter

variation is considered further because of its feasibility and higher stiffness at larger deformation as com-

pared to the spring with logarithmic variation.

3 Numerical Model

Steel moment resisting frame building with four storeys’s and originally with fixed base is considered. The

buildings consist of American standard steel sections with uniform mass distribution over their height and a

non uniform distribution of lateral stiffness. The beams and columns were assigned with various W sections

and the materials used were uniaxial material, `Steel01' with (kinematic) hardening ratio of 3%. All these

elements were modeled as Beam with hinges with length of plastic hinges taken as 10% of the member

length and each of the nodes were lumped with a mass of 16000 kg. The damping was given as 2% Rayleigh

damping for the first two modes. The base isolator was modeled using Flat slider bearing element. The non-

linear force deformation behavior is considered by using an elastic bilinear material with the properties as

per the spring design as mentioned earlier. The numerical modeling of the FSB isolation was done in Open-

Sees using flat slider bearing element, defined by two nodes. A zero length bearing element which is defined

by two nodes is used to model the same. These two nodes represent the flat sliding surface and the slider.

The bearing has unidirectional (2D) friction properties for the shear deformations, and force-deformation

behaviors defined by uniaxial materials in the remaining two (2D) directions. Coulomb’s friction model is

used with a friction coefficient equal to 0.05 yield displacement as 0.002. To capture the uplift behavior of

the bearings, user specified no-tension behavior uniaxial material in the axial direction is used. P-Delta mo-

ments are entirely transferred to the flat sliding surface. The numerical modeling of the nonlinear spring

element was done in OpenSees using zero length elements. The force-deformation behavior of element was

defined by 40 different Elastic bilinear materials.

This study utilizes 60 ground motions (SAC,2008) for the nonlinear time history analysis. Among these

ground motions, 20 represents a hazard level of 2% in 50 years, 20 of them represents a hazard level of 10%

in 50 years and remaining 20 represents a hazard level of 50% in 50 years. These ground motions include

both recorded as well as simulated one and scaled to match response spectrum of a particular hazard level.

They were mainly developed for the analysis of a steel moment resisting frames in Los Angeles area, USA.

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

4

Deflection (m)

Fo

rce

(N)

Stiffness Plot

These motions cover a broad range of peak ground accelerations (PGA) between 0.11g and 1.33g, peak

ground velocity (PGV) between 21.67cm/sec and 245.41 cm/sec, and peak ground displacements (PGD)

between 5.4 cm and 93.43 cm in addition to wide band frequency content and a wide range of strong motion

duration. Some of them even possess strong near fault pulse.

4 Result and Discussion

Nonlinear time history analysis of the structure with flat sliding bearing plus nonlinear spring is carried out

for a particular value of coefficient of friction (μ=0.05). The results obtained from the analysis are compared

with the nonlinear analysis results of the structure with fixed base and sliding base with no restoring mecha-

nism. The parameters used for the comparisons are -peak inter-storey drift ratio of the structure, residual

displacement of the structure and the maximum base displacement. Statistical comparison is performed to

observe the pattern of the above parameters. For this statistical comparison mean, maximum and the stand-

ard deviation values are calculated and are summarized in a tabular form. The results are further subcatego-

rized in three parts depending on the hazard level. These parameters are the measures of damage that a struc-

ture undergoes after an earthquake. FEMA-356 has specified three performance levels, these beings the im-

mediate occupancy (IO), the life safety (LS) and the collapse prevention (CP). These are associated with the

inter-storey drift limits of 0.7%, 2.5% and 5%, respectively. These limits are said to be appropriate for the

performance evaluation of pre-Northridge steel moment frames. FEMA-356 prescribes a basic safety objec-

tive (BSO), which comprises a dual-level performance objective. It requires LS performance for a 10% in

50-year event and CP performance level for a 2% in 50-year earthquake. According to these guidelines, the

drifts should be such that for LA01- LA20 ground motions, the structures should be safe in Life Safety;

LA21-LA40, the buildings should not be crossing the performance level of Collapse Prevention and Imme-

diate Occupancy in case of LA41-LA60. LA01-LA20, LA21-LA40 and LA41-LA60 are corresponding to

ground motion representing hazard level of 2%, 10% and 50% respectively.

Peak Inter-storey Drift Ratio- It is observed (Table) that the inter storey drift ratio is exceeding the allowable

range as prescribed by FEMA-356 for the fixed base building. At a particular coefficient of friction, the peak

inter-storey drift ratio of the structure having flat sliding bearing with nonlinear spring are almost similar

compared to the flat sliding bearing without nonlinear spring and this range is well inside the limit for a spe-

cific hazard level. . A rather decreasing pattern is observed for the case of sliding isolator with spring.

Residual displacement- This is an important parameter for this study to unfold the importance of the necessi-

ty of nonlinear spring in a sliding bearing. The residual displacement acts as an important measure of post-

earthquake functionality in determining whether a structure is safe and usable to the occupants. The large

residual displacement alters the new rest position of the structure which results in high cost of repair or re-

placement of non-structural elements. Restricting the large residual displacements also helps in avoiding the

pounding effect. From the results discussed above, it has been observed that the effect of sliding bearing

with and without nonlinear spring does not differ much. However there is a large reduction in the residual

displacement in all the hazards levels considered for the study. The range of reduction in residual displace-

ment when compared with sliding bearing without spring are 74% to 76% for hazard level of 2% in 50 years,

Table 1. Peak interstorey drift ratio at different hazard level for different base condition

Coefficient of

friction(μ)=0.05

Comparison of Peak inter-storey drift ratio in percentage

10% in 50 years (La01-

La20) 2% in 50 years (La21-La40)

50% in 50 years (La41-

La60)

Mean peak

inter-storey

drift (%)

Mean+SD of

peak inter-

storey drift (%)

Mean peak

inter-storey

drift (%)

Mean+SD of

peak inter-

storey drift(%)

Mean peak

inter-storey

drift (%)

Mean+SD of

peak inter-

storey drift (%)

FB 3.22 4.62 6.97 9.68 1.47 2.15

SI_no spring 0.411 0.493 0.478 0.571 0.349 0.411

SI_with spring 0.323

0.373

0.399

0.468

0.291

0.333

40% to 60% for hazard level of 10% in 50 years and 54% to 60 % for hazard level of 50% in 50 years.

Therefore the non-linear spring is found to be very effective for this factor. Thus the large reduction in the

residual displacement of the structure due to the incorporation of nonlinear springs in the sliding bearing

systems depicts its importance.

Base Displacement- The comparison of the base displacement at different hazard levels shows reduction in

displacement for the non-linear spring as compared with the case without nonlinear spring with sliding bear-

ing. The trend is same as that obtained for residual displacement. However the % of reduction is much less

here for all the three hazard level.

Table 2. Peak maximum residual displacement at different hazard level for different base condition

Coefficient of

friction(μ)=0.05

Comparison of maximum residual displacement

10% in 50 years (La01-La20) 2% in 50 years (La21-La40) 50% in 50 years (La41-La60)

Mean of peak

base displace-

ment

Mean+SD of

peak base

displacement

Mean of peak

base displace-

ment

Mean+SD of

peak base

displacement

Mean peak

inter-

storey drift

(%)

Mean+SD of

peak base

displacement

SI_no spring 0.149 0.269

0.478 0.887 0.082 0.205

SI_with spring 0.054

0.106

0.123

0.215

0.041

0.093

Table 3. Peak maximum base displacement at different hazard level for different base condition

Coefficient of

friction (μ)=0.05

Comparison of maximum base displacement

10% in 50 years (La01-La20) 2% in 50 years (La21-La40) 50% in 50 years (La41-La60)

Mean of peak

base

displacement

Means + SD

of peak base

displacement

Mean of peak

base dis-

placement

Mean + SD of

peak base

displacement

Mean peak

inter-storey

drift (%)

Mean + SD of

peak base dis-

placement

SI_no spring 0.327 0.459

0.774 1.158 0.136 0.249

SI_with

spring

0.194

0.329

0.725

1.121

0.118

0.200

Table 4. %reduction in the response by the provision of non-linear spring

% decrement in the residual displacement and maximum base displacement considering

non-linear spring along with sliding bearing with respect to the base with only sliding bearing

10% in 50 years

(La01-La20)

2% in 50 years

(La21-La40)

50% in 50 years

(La41-La60)

Residual dis-

placement 62% 75% 52%

Base displacement 35% 5% 16%

5 Conclusion

In this paper, the seismic performance of a steel moment-resisting frame structure resting on sliding type of

bearing with restoring force device as a conical non-linear spring is studied. The results showed that the

structure with fixed base is subjected to huge peak inter-storey drift outside the allowable range that needed

to be checked. The provision of sliding isolator is effective in reducing inter storey drift. However it results

into a large amount of residual and base displacement. The provision of a properly designed non-linear

spring with a very small stiffness at the beginning is found to be very effective in reducing residual

displacement to a great extent. The reduction in base displacement is also obtained at a lesser extent. The

peak storey drift also reduced to a very small extent by the provision of this kind of spring. The proposed

isolation system, if optimized for various target performance levels, will result in a cost-effective solution.

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