SEISMIC RESPONSE CONTROL OF A BUILDING INSTALLED …SAP2000 nonlinear time history analysis program was applied to investigate the effects on building such as normalized base shear,

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.II/ Issue III/July-September, 2011/246-256

Research Article

SEISMIC RESPONSE CONTROL OF A BUILDING

INSTALLED WITH PASSIVE DAMPERS Nitendra G Mahajan*1

and D B Raijiwala2

Address for Correspondence 1Research Scholar, Department of Structural Engineering, Sardar Vallabhbhai National

Institute of Technology, Surat 2Professor, Department of Structural Engineering, Sardar Vallabhbhai National

Institute of Technology, Surat

ABSTRACT: Seismic response control using passive dampers is most cost effective, satisfied the architectural requirement of opening and recent technique to control the vibrations of structures arising due to dynamic loading. This study investigates the influence of mechanical control on structural systems through strategically applying reliable dampers that can modulate the response of building. SAP2000 nonlinear time history analysis program was applied to investigate the effects on building such as normalized base shear, tip displacement, normalized acceleration and energy dissipation of damper element by varying different important parameters namely Earthquake time histories, location of dampers, damping coefficient, damper stiffness, no of story of building. Comparison study is also presented between building installed with dampers, building installed with diagonal bracing, combination of both and simple building to show importance of damping system for reduction of seismic quantities. Finally, the building installed with damping system is very effective and reliable solution to reduce very vital seismic quantities such as base shear, floor displacement, and floor acceleration and also mitigate architectural requirement which cannot be satisfied by shear walls.

KEYWORDS: structural control system, seismic response, Passive dampers, Non linear Time History, SAP2000.

1. INTRODUCTION 1.1 Need and Objectives of the Structural

Control The main objective of Structural engineering field

is to design and construct the safe and stable

structures. The massive earthquake that hit Japan

on March 11 and the tsunami it unleashed have

killed up to 28,000 people and crippled a nuclear

power plant near the northeastern town of

Fukushima that has leaked radiation virtually ever

since. Total damages have been estimated at $300

billion, making it the world's costliest natural

disaster. The disasters have also hurt the Japanese

economy, the world's third largest. Recent Japan

Earthquake of March 2011 has seriously

threatened the safety and property of the residents.

Various types of structural control technologies

have been developed to solve the safety and

functional problems for structures under the

excitation of external force. With current design

procedures, the structures are expected to suffer

significant damage but no collapse if the

earthquake scenario that was considered for its

design occurs. Although this philosophy has been

the standard for many decades, new design

procedures and novel devices are changing the

traditional approach. An example of the new

procedures is the one known as performance-

based design. This methodology will provide the

structural engineer with the tools to predetermine

the amount of damage that the user is willing to

tolerate and design the structure accordingly. On

the other hand, a number of modern mechanical

systems have been proposed in the last two

decades to reduce the structural response (and thus

the amount of damage). Figure 1.1 shows the

Annual earthquake death rate per million

populations in red; smoothed rates in grey. They

are known collectively as “protective devices” and

they include added viscoelastic dampers, viscous

fluid dampers, frictional dampers, hysteretic

dampers, tuned-mass dampers, and base isolation

systems. The devices themselves and their design

methodology are referred to as “passive control

systems”.

Figure 1.1 Annual earthquake death rate per

million.

1.2 Fundamental of Passive Structural Control 1.2.1 Passive Control Systems

Figure 1.1 shows the Conventional System. The

principal function of a passive energy dissipation

system is to reduce the inelastic energy dissipation

demand on the framing system of a structure. The

result is reduced damage to the framing system. A

passive control system (Figure 1.2) may be defined


IJAET/Vol.II/ Issue III/July-September, 2011/

as a system which does not require an external

power source for operation and utilizes the motion

of the structure to develop the control forces.

Control forces are developed as a function of

the response of the structure at the location of

the passive control system. The control system and

the structure do not behave as independent

dynamic systems but rather interact with each

other.

Figure 1.1 Conventional System.

Figure 1.2 Passive Control System.

1.2.2 Advantages of passive control system.

• It is usually relatively inexpensive.

• It consumes no external energy.

• It is inherently stable.

• It works even during a major earthquake.

1.2.3 Disadvantages of passive control systems.

The idea of passive control is to dissipate the

vibratory energy in the structural system.

However, this kind of control system provides no

extra assistance, so it cannot adapt to varying

loading conditions. Consequently its effect is

limited. The effectiveness (amount of control) of

passive devices is always limited due to the

passive nature of devices and the random nature of

earthquake events. The passive control does not

make any real time changes in the system.

1.3 Damping System.

The objective of utilizing dampers is to reduce

structure responses and to mitigate damage or

collapse of structures from severe earthquakes by

participating energy dissipations. As a successful

application, installation of dampers in an existing

building structure, which does not possess

sufficient lateral stiffness, enables control of the

story drift within the required limitation and

maintains its desired functions during an

earthquake event. Since the first application of

dampers in structural engineering took place in

1960s, abundant research work has been

conducted to study the mechanisms of dampers

and the behavior of damped structures. With the

invention of different types of damping devices,

improvement of modeling techniques and

development of new computational

methodologies, use of dampers has become a

mature technology in designing of new structures

and retrofitting of existing facilities.

1.3.1 Definitions:

1.3.1.1 Damping device:

A flexible structural element of the damping

system that dissipates energy due to relative

motion of each end of the device. Damping

devices include all pins, bolts, gusset plates, brace

extensions, and other components required to

connect damping devices to the other elements of

the structure. Damping devices may be classified

as either displacement dependent or velocity-

dependent, or a combination thereof, and may be

configured to act in either a linear or nonlinear

manner.

1.3.1.2 Damping System:

The collection of structural elements that includes

all the individual damping devices, all structural

elements or bracing required to transfer forces

from damping devices to the base of the structure,

and the structural elements required to transfer

forces from damping devices to the seismic force-

resisting system.

1.3.1.3 Displacement-dependent Damping

device:

The force response of a displacement-dependent

damping device is primarily a function of the

relative displacement, between each end of the

device. The response is substantially independent

of the relative velocity between each end of the

devices, and/or the excitation frequency.

1.3.1.4 Velocity- dependent Damping device:

The force-displacement relation for a velocity-

dependent damping device is primarily a function

of the relative velocity between each end of the

device, and could also be a function of the relative

displacement between each end of the device.

2. GOVERNING EQUATIONS AND

MATHEMATICAL MODEL OF MOTION 2.1Single-Degree-of-Freedom Motion Equations

A damping system is usually defined as a

collection of dampers, connections between

dampers and structural members, and structural

members transferring forces between damping

devices and the seismic force-resisting system or

the foundation. Figure 2.1 illustrates both

systems in a structural frame elevation. On the

basis of the location of the damping system, the

damping device can be classified as internal or

external.



Figure 2.1 damping device and damping system.

Development of single-degree-of-freedom (SDOF)

motion equations can be depicted from a single-story

building structure installed with a damping system,

which is schematically shown in Figure 2.2. The

mass of this structure, assuming it is simply lumped

at the roof level, is denoted as m. To consider the

nonlinear behavior of the building structure, a

general expression is utilized to define the structural

force, Q, instead of ksx, where ks is linear lateral

stiffness of the structure and x, simplified from x(t),

represents roof displacement or deflection of the

structure at any time t. The structural damping

coefficient is designated as cs. Force, P, is defined

along the movement of the damping device.

Accordingly, its horizontal component becomes D =

P cos φ , where angle, φ , relies on assembly

configurations of damping device and bracings. For

the damping devices connected by diagonal bracings

to the building structure, the angle, φ , represents the

damping device’s inclination to the horizontal

movement of the structure.

For common configurations of damping devices

assembled with diagonal or chevron bracings, the

axial stiffness of bracings is usually much stronger

than that of the damping device and the movement

or deformation of the damping system is

dominantly contributed by the damping device.

Accordingly, the bracings can be reasonably

assumed to be rigid components with infinite

stiffness.

Figure 2.2 Mathematical Model SDOF structures with damping devices.



On the basis of the assumption of infinite stiffness

of the bracings and the well-known equilibrium

condition, SDOF motion equation of the damped

structure is easily expressed as follows:

gs xmQDxcxm &&&&& −=+++

or

gs xmQPxcxm &&&&& −=+++ φcos …2.1

Where the structural acceleration, x&& , and the

ground acceleration, x&& g, are designated from

simplified notations of x&& (t) and x&& g(t),

respectively. On the basis of damper mechanical

properties, damping devices can be classified as

two major categories: (1) velocity dependent and

(2) displacement dependent. Velocity-dependent

damping devices include fluid viscous damper,

fluid viscoelastic damper, and solid viscoelastic

damper, whereas displacement dependent

damping devices consist of friction damper and

metallic yielding damper. Figure 2.3 represents

typical relations between the damping force and

its displacement of linear or nonlinear viscous

dampers, and solid or fluid viscoelastic dampers.

Supported by test results for linear fluid viscous

damper, the damping force, P, can be simply

depicted as a linear relation to its velocity:

lcp d&= ……2.2

Where cd is the damping coefficient of the fluid

viscous damper, while l& represents the relative

velocity of the damper in the direction of P. As

shown in Figure 3.2, l and x remain the

following relation.

φcosxl = and φcosxl && = ……2.3

Thus,

φcosxcP d&= , or φ2cosxcD d

&= …… 2.4

If the fluid viscous damper exhibits nonlinear

behavior to its relative velocity, then the force of a

nonlinear fluid viscous damper, P, has the

following relation to its movement

αα

φcos)sin( xcllcP dd&&& == or )sin(cos 1 xxcD d

&& φαα +=

……2.5

Where α is the velocity exponent. According to

mechanical properties of a solid viscoelastic

damper, the damper force features a function of

its relative velocity to displacement, which can

be simplified in terms of effective damping

coefficient, cd, and effective stiffness, kd:

φφ coscos xkxclklcP dddd +=+= && or φφ 22 coscos xkxcP dd += &

……2.6

Multiple-Degree-of-Freedom Motion Equations

A sketch of a multistory structure installed with

damping system is shown in Figure 2.3. Applying

the equilibrium conditions at the roof level n, and

using relative displacement, xn, the motion

equation due to the ground acceleration, , is

derived as

gnnnnnnsnn xmQDxxcxm &&&&&& −=++−+ − )( 1,.. 2.7

gnnnnnnnsnn xmQPxxcxm &&&&&& −=++−+ − φcos)( 1, ..2.8

where mn is the roof mass and cs,n is denoted as

the structural damping between the roof and the

story below the roof. xn , and xn−1 are utilized to

identify the relative displacement at the roof and

the story below. For the structural force between

the roof level and the story below, a general

expression of Qn , is also, used to represent elastic

or inelastic behavior of the seismic force-resisting

system. According to material properties of the

structure, Qn can be idealized as a linear model,

elastoplastic model, bilinear model, or other types

of models. In Equations 2.7 and 2.8, Pn and Dn are

used to define the axial force and its horizontal

component of damping devices between the roof

and the story below. The specific expression of

the damping force and its relative velocity or

relative displacement needs to be determined by

selected damping devices. φ n presents the angle

between the axial force and the horizontal

component of the damping device.

By applying the same methodology used for

Equation 3.5, the motion equation at story m is

identified as below:

.2.9..........…

)()(

11

11,1,

gnmmmm

mmmsmmmsmm

xmQQDD

xxcxxcxm

&&

&&&&&&

−=−+−

+−+−+

++

++−

or,

.2.10…coscos

*)()(

111

11,1,

gnmmmmm

mmmmsmmmsmm

xmQQP

Pxxcxxcxm

&&

&&&&&&

−=−+−

+−+−+

+++

++−

φφ

Where mm is the mass at the story m; cs,m+1 and

cs,m are the structural damping between story m +

1 and m, and between story m and m − 1,

respectively. xm+1 , xm , and xm−1 , are designated

as the relative displacement at story m + 1, m, and

m − 1. Qm+1 and Qm are denoted as the structural

force between story m + 1 and m, and between

story m and m − 1, respectively. Pm+1 , Pm , Dm+1 ,

and Dm represent the axial force and the

horizontal component of damping devices

between story m + 1 and m, and between story m



and m − 1. φ m+1 and φ m are angles between the

axial force, Pm+1 or Pm , and the horizontal

component Dm+1 or Dm of the damping devices.

Equations 2.9 and 2.9 form multiple-degree-of-

freedom (MDOF) motion equations. These

equations can be condensed in matrix notations

and symbolically shown as below:

}1]{[}1]{[}1]{[}]{[}]{[ MxQDxCxm g&&&&& −=+++ ..2.11

Where the mass matrix, [M], the structural

damping matrix, [C], the damping force matrix

[D], and the structural force matrix, [Q]. Once the

damping devices are identified and the

mechanical properties of the seismic force-

resisting system are selected, the damping force

matrix [D] and the structural force matrix [Q] can

be explicitly determined from the relation

between the damping force and the relative

velocity or displacement, as well as from the

relation between the structural force and its

deformation, respectively. Consequently, the

displacement, velocity, and acceleration of the

seismic force resisting system and the damping

system are explicitly computed from Equation

2.11 in accordance with the input of the ground

acceleration, gx&& .

3. NUMERICAL STUDY

The seismic response of 12-story model, 17-story

model, and 22-story model with different alternative

arrangement of viscous damper subjected to real

earthquake ground motion is investigated. The

response is investigated under different earthquake

ground motions as represented in Table 1. In this

report Comparative study between Buildings with

dampers, without dampers, with bracing system.

Caparison has been done for seismic response like

base shear, top floor displacement (top drift) and

acceleration. The mass at each floor is assumed to

be equal and the inherent damping of the frame is

considered 5%. SAP2000 nonlinear time history

analysis program was applied to investigate the

effects on building such as normalized base shear,

tip displacement, normalized acceleration and

energy dissipation of damper element by varying

different important parameters namely Earthquake

time histories, location of dampers, damping

coefficient, damper stiffness, no of story of building.

Figure 2.3 Mathematical Model of MDOF structures with damping devices.



Table 1. Details of earthquakes considered for the numerical study

Name Magnitude

Duration of

Earthquake

(sec)

PGA *

Value

(cm/sec2)

Time for

PGA

(sec)

Type

of

E.Q.

Koyna (1967,Maharashtra, INDIA)

6.5 7.02 54.1 2.606 Short

El Centro (1940, Imperial Valley Irrigation District)

7.1 31.18 142.18 0.29 Short

Bhuj (2001,Gujarat,INDIA) 7.6 109.995 103.82 46.940 Long Tohoku, Japan (2011, Undo) 9.0 639.99 152.055 107.79 Long

*PGA – Peak Ground Acceleration

3.1 Time History Plot of Earthquake Data

For engineering purposes, the time variation of

ground acceleration is the most useful way of

defining the shaking of ground during earthquake.

This ground acceleration is descriptive by

numerical values at discrete time intervals. This

plot for Koyna, EL Centro, Bhuj and Tohoku,

Japan earthquake are shown here

.

Fig 3.1 Acceleration (mm/sec

2) Vs Time (sec) Response for Koyna Earthquake


2) Vs Time (sec) Response for EL Centro Earthquake

Fig 3.3 Acceleration (m/sec

2) Vs Time (sec) Response for Bhuj Earthquake




2) Vs Time (sec) Response for Japan Earthquake

3.2 Effect on Normalized Base Shear

Figure 3.1 illustrates the Normalized Base Shear

response of the structure verses Time under the

Koyna (1967, Maharashtra) earthquake, El Centro

(1940, Imperial Valley Irrigation District), Bhuj

(2001, Gujarat) , Tohoku, Japan (2011, Undo) and

static earthquake analysis. It can be seen that in

Table 3.1 that the incorporation of the dampers

reduced the peak value of the Normalized Base. This

table is also showing that reduction in Base shear is

mainly depending on Earthquake acceleration and

No of story. These results are similar to the results

obtained for the 22-story, 17-story and 12-story

building but the percentage reduction is different for

different no of story. Figure 3.5, 3.6 and 3.7 easily

demonstrated that dampers can be used to improve

the mitigation of seismic forces. From the above

figure variation in Static analysis for base shear is

very less, which indicate the accuracy of Nonlinear

Time History method and results are very to

accurate results.

Table 3.1 Percentage reduction in Base Shear

due to Dampers.

Earthquakes 12-

Story

17-

Story

22-

Story

Koyna, 1967 18 % 43 % 25 %

El Centro, 1940 8 % 5 % 5 %

Bhuj, 2001 16 % 28 % 30 %

Tohoku, Japan, 2011 17 % 5 % 26 %

Figure 3.5 Normalized Base Shear for 22-Story





3.3 Generalized Effects of Adding Damping to a

Structure

The effects of added damping in a structure

subjected to earthquake transients is depicted in the

results obtained from SAP2000 Non-linear time

history analysis provided in Figure 3.8 to 3.15. The

tested structure was a 22-story, RCC building frame.

Figure 3.8 to 3.11 shows the response of the

structure under input of the Koyna, 1940 El Centro,

Bhuj and Japan earthquake for un-damped

condition. Note that a small hysteresis loop is

apparent in Figure 3.8 to 3.11 revealing that the test

structure was at the onset of yield. In comparison,

Figure 3.12 to 3.15 is the same structure with added

damping, obtained by the addition nonlinear fluid

dampers installed as diagonal brace elements. The

large energy dissipation of added damping is readily

apparent in the “football” shaped damping curve

superimposed over the structural spring rate curve.

Fig 3.8 Energy Dissipation for Undamped for

Koyna Earthquake (22-story) Fig 3.9 Energy Dissipation for Undamped for EL

Centro Earthquake (22-story)


Bhuj Earthquake (22-story)


Japan Earthquake (22-story)



Fig 3.12 Energy Dissipation for Damper for

Koyna Earthquake (22-story)

Fig 3.13 Energy Dissipation for Damper for EL

Centro Earthquake (22-story)

Fig 3.14 Energy Dissipation for Damper for Bhuj

Earthquake (22-story)

Fig 3.15 Energy Dissipation for Damper for

Japan Earthquake (22-story)

3.4 Effects on Base Shear and Story Drift.

It is clear that the characteristics of base shear is

completely depends on input type of Earthquake and

no of story. At very high stiffness of dampers, the

buildings behave as they are rigidly connected by

bracing. As a result, the relative displacements and the

relative velocities of the connected floors become

almost zero and the damper totally loses its

effectiveness. On the other hand, if the stiffness of

dampers is reduced to zero, the buildings return to the

unconnected condition like building without dampers

or un-damped condition, as a result dampers again

losses its effectiveness. Effectiveness of dampers is

also depends on no of storey. As no of story decreases

the overall stiffness of building increases to counter

act this thing damper stiffness was to be reduce

relative to higher no of story in this investigation.

Continuous decrease in effective stiffness of dampers

show increase in story drift as well as increased base

shear. Which clearly indicate that optimum effective

stiffness for particular no of story exist. The time

variation of the top floor displacement and base shear

responses of the 22-story buildings connected by

dampers at all the floors, is shown in Figures 3.16 to

3.23. These figures clearly indicate the effectiveness

of dampers in controlling the earthquake responses of

both the buildings. Similar types of results are

obtained for the 12-story building and 17-story

building but results for 22-story is presented over here.

Figure 3.16 Base Shear v/s Time for Koyna

Earthquake for 22 Story.

Figure 3.17 Base Shear v/s Time for El Centro for

22 Story.



Figure 3.18 Base Shear v/s Time for Bhuj


Figure 3.19 Base Shear v/s Time for Japan(2011)


Figure 3.20 Top Drift v/s Time for Koyna


Figure 3.21 Top Drift v/s Time for El Centro for

22 Story.

Figure 3.22 Top Drift v/s Time for Bhuj Earthquake

for 22 Story.

Figure 3.23 Top Drift v/s Time for Japan(2011)


4. DISCUSSION AND CONCLUSION

Comparison between Building with dampers and

Building with braces showed that dampers are

more significant to reduce seismic quantities with

same direction of placement as brace. Dampers

placed in the upper levels had little to no effect on

the structural response. The responses of the

structure were compared under different

earthquake records. There were significant

reductions in deflection and acceleration response

under all earthquake records. The reduction in

acceleration will lead to lesser inertia forces and so

increases the ability of the building to cope with

seismic events. The response however, varied with

the earthquake record indicating its dependence on

the intensity and frequency content of the

earthquake. The results showed that there was a

correlation between the amount of rigidity cut out

of the system and the stiffness and damping

coefficients of the damper replacing this. This

suggests that there is a need to balance these

parameters in order to obtain the optimum

improvement in seismic performance. The

investigations showed that significant reduction in

structure acceleration, deformation and Base shear

can be achieved by strategically placing the

dampers within the periphery of structure where

twisting deformation is significant and controlling

the reduction of stiffness within a reasonable

range. Problem of optimal damper placement in a



soil-structure interaction model including damper

support member systems would be of interest for

future research. Comparative investigation for

settlement of building installed with dampers and

other seismic resisting conventional frame

structure would be future work in this area.

Building installed with semi-active dampers and

active dampers would be the future investigation.

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Documents

SEISMIC RESPONSE CONTROL OF A BUILDING INSTALLED …SAP2000 nonlinear time history analysis program was applied to investigate the effects on building such as normalized base shear,