MODELING OF STRUCTURES SEISMICALLY ISOLATED BY FRICTION BEARINGS

MINISTRY OF EDUCATION AND TRAINING

DANANG UNIVERSITY

NGUYEN VAN NAM

MODELING OF STRUCTURES SEISMICALLY
ISOLATED BY FRICTION BEARINGS

MAJOR
CODE

: MECHANICAL ENGINEERING
: 62.52.01.01

SUMMARY OF DOCTOR OF ENGINEERING DISSERTATION

Danang - 2017


The work was finished at
University of Science and Technology - Danang University

Science Advisor:
1. Assoc. Prof. Dr. HOANG PHUONG HOA
2. Assoc. Prof. Dr. PHAM DUY HOA

Reviewer 1: Prof. Dr. PHAN QUANG MINH
Reviewer 2: Assoc. Prof. Dr. LUONG VAN HAI
Reviewer 3: Dr. NGUYEN THE DUONG

This Dissertation was defended at The Doctor of Engineering
committee at Danang University on 17 of 4, 2017

For the detail of the dissertation, please contact:
- Information and Library Center of Danang University.
- National Library of Vietnam.


1

INTRODUCTION
1. Motivation of Study
Earthquake is one of the serious disasters caused by natural for
human life, constructions and economy in general. Throughout
history, the world has seen occuring of many strong earthquakes,
killed a lot of human lifes, destroyed a lot of buildings and lost
millions of dollars in economic each year due to the earthquakes.
Although Vietnam is not in the dangerous zone of the
epicenter of strong earthquakes in the world, it is still a country
located in areas with high seismic hazard. It is reported by scientists
at the International Workshop "Dangerous earthquake, tsunami and
the early warning system for Asia - Pacific" hold by the Institute of
Geophysics - Institute of Science and Technology Vietnam within
two days (5 and 6-9.2011). Some large urban areas are currently
located on the fault zone and are possible to get very strong
earthquakes such as Hanoi located on the Hong river fault zone,
Chay river, Ma river, Son La river is forecasted to suffer level 8
concussions according to the Richter scale.
Recently, the vibration caused by earthquakes appeared in
many provinces and cities, especially Hanoi, Ho Chi Minh City and

Danang where have of a large number of buildings, large bridges
and demands of construction of large projects are growing in number
as well as in height. Those are very sensitive to ground acceleration
of earthquakes.
With these facts as above, the constructions should have
seismic resistant design, particularly modern seismic resistant design
standpoint associated with the term "structural vibration control" and
is still new in Vietnam. Therefore, the research about them is


2

essential, has scientific meaning and high practice. This is also the
motivation for the author to research the title: “Modeling of
structures seismically isolated by friction bearings” to provide a
solution to reduce the harm caused by earthquakes for constructions.
2. Purpose of Study
Research the numerical modeling for base isolated structures
with the friction pendulum bearings including SFP, DFP and TFP
bearings subjected to earthquake load. Evaluate the seismic reduction
effectiveness of the base isolation bearings for constructions. From
there, application research of TFP bearings for high-rise buildings
built in Hanoi, Vietnam.
3. Object and Scope of Study
The objects of the study in dissertation are the friction
pendulum bearings including SFP bearing, DFP bearing and TFP
bearing.
The scope of the study including: Research response of
structures with single bearing (don’t consider the work together of
many bearings in a construction), ignoring torsion; The superstructure

behavior is linear and the bearing behavior is nonlinear.
4. Dissertation content
- Identify the structure, working principle of the seismic
isolation bearings: SFP, DFP and TFP.
- Numerical modeling for base isolated structures with the
friction pendulum bearings above subjected to earthquake. Evaluate
the

seismic

reduction

effectiveness

of

these

bearings

for

constructions.
- Research to develop a new model for TFP bearing.
- Application research of TFP bearing for high-rise buildings


3

in Vietnam according to ASCE 7-2010 Standard design.

5. Methodology of study
Investigate a theoretical model, the research results were
simulated by Matlab and compared to an experimental model results
of other authors have been published by NEES (Network for
Earthquake Engineering Simulation) to verify.
6. Contributions of the dissertation
- Numerical modeling for base isolated structures with the
friction pendulum bearings: SFP, DFP and TFP. Evaluate the seismic
reduction effectiveness of these bearings for constructions.
- Improve the TFP bearings model. Via improved model,
details of each slider displacement on the spherical surfaces and
effects of vertical component of ground acceleration are also clearly
calculated for TFP bearings.
- Propose the optimal parameters of TFP bearings for high-rise
buildings in Hanoi and evaluate the seismic reduction effectiveness
of them.
7. Dissertation layout
The Dissertation consists of the introduction, four chapters and
conclusion, the recommendations, all content of the dissertation is
contained in 133 A4 pages and is organized as follows:
Introduction
Chapter 1. Overview
Chapter 2. Modeling of friction bearings
Chapter 3. Improved model of triple friction pendulum bearing
Chapter 4. Seismic reduction effectiveness of TFP bearings for
high-rise buildings in Ha Noi
Conclusions and recommendations


4

Chapter 1
OVERVIEW
1.1. Overview of earthquakes and earthquake resistant design
1.1.1. Earthquakes
An earthquake is a very strong shaking phenomenon of the
surface of the earth when large energy are released in a very short
time due to the sudden cracked in the crust or in the upper mantle of
the earth [10], [ 62].
Earthquakes

have

the

following

original:

Earthquake

originated from plate tectonics, from the faults; Other originals: from
the expansion in the hard rock crust of the earth, by explosions,
volcanic activity,…
The important parameters of ground motion in seismic
resistant design including: the largest amplitude, duration of strong
motion, frequency content, magnitude earthquake, the distance to the
fault, soil conditions at site.
1.1.2. Approachs of earthquake resistant design
Earthquake resistant design of structures is a required duty, a

major challenge for structural engineers. There are two earthquake
resistant design perspective: traditional earthquake resistant design
and modern earthquake resistant design.
Earthquake resistant design with modern standpoint associated
with the structural vibration control engineering with 3 main groups
as follows: passive control, active control and semi-active control.
1.2. Seismic base isolation technology
1.2.1. Concept of seismic base isolation
Seismic base isolation is a passive control technique for
structure and very effective in earthquake resistant design. The main


5

idea of this technique is the isolation between superstructure and
basement by using the soft bearings, called seismic isolation bearings.
1.2.2. Types of isolation devices
The types of bearing used in seismic base isolation technique
usually involves two common types: rubber bearings (elastic bearing,
Figure 1.6) and friction bearings made from stainless steel.
Friction bearings 3 main categories:
- Single friction pendulum bearings: structure shown in Fig. 1.7,
including 1 spherical surface with radius R, 1 slider slides on spherical
surface with friction coefficient  and ability of displacement is d.
R, 

a. Cutaway view

d

b. Cross section

Figure 1.7. Single friction pendulum bearings (EPS, 2011)
- Double friction pendulum bearings: structure shown in Fig.
1.8, including spherical surfaces 1 and 2 and a slider inside.

a. Cutaway view

b. Cross section

Figure 1.8. Double friction pendulum bearings (Fenz, 2008e)
Triple friction pendulum bearings: Structure shown Fig 1.9,
including 4 spherical surfaces with the radius R1, R2, R3 and R4. Inside,
3 sliders slide on 4 spherical surfaces with friction coefficient i.


6

a. Cutaway view

b. Cross section

Figure 1.9. Triple friction pendulum bearings (Fenz, 2008e)
1.2.3. Brief history of seismic base isolation technology application
Seismic base isolation technology has been studied and
applied in recent decades. However, the idea appeared more than 100
years ago by the invention of the Touaillon. In recent years, the
application of this techniques for structure subjected to earthquakes
becomes popular in the US, Japan, New Zealand,... and some
countries in Europe.

1.3. Overview of research for isolated friction bearings
1.3.1. The studies outside the country
- The studies of SFP bearings: the first study is published in
1987 by Zayas. The outstanding studies are published by other
authors: Mokha, Constantinou, Reinhorn, Nagarajaiah, Mosqueda,...
The studies focused on analysis structure and movement of the SFP
bearing. Effectiveness of reduce seismic of bearings was evaluated
through theoretical and experimental models.
- The studies of DFP bearings: Tsai and Constantinou research
groups are considered systematically. In addition, many individual
studies on this bearing also should concern such as Kim and Yun
(2007), Malekzadeh (2010),...
- The studies of TFP bearings: TFP bearing with it’s


7

advantages began to be produced around the year 2007. The
outstanding studies can mention such as Constantinous and Fenz
(University of Buffalo); Steve Mahin, Troy Morgan and Tracy
Becker (UC Berkeley); Ryan’s research group (University of
Nevada, Reno), The latest publication of TFP bearing almost belongs
to this group, the publication can be listed as: Dao [36], [37, [38],
Okazaki [80], Ryan [86], [87], [88]. In addition, some studies of
other authors on the TFP bearing also published as: Fadi [41],
Ghodrati [52], Moeindarbari [67], Sarkisian [89], Tsai [103], [104].
1.3.2. The studies inside the country
In Vietnam, base isolation was mentioned in Vietnam design
standards 375: 2006 in 2006. The study is very limited, the
outstanding studies such as: Nguyen Van Giang and Chu Quoc

Thang (2006), Tran Tuan Long (2007), Le Xuan Huynh et al (2008),
Do Kien Quoc (2009), Le Xuan Tung (2010, 2012).
1.4. Comments, the need of new findings
- Earthquake resistant design is a necessary requirement.
Using seismic isolation bearings in the structural vibration control
technology subjected to earthquakes is new perspective bringing high
efficiency, should be studied and more widely applied.
- The studies of friction sliding bearing need to be
implemented in this dissertation as follows: indicate the mumerical
model and evaluate the sseismic reduction effectivenes of SFP, DFP
and TFP bearing; research to develop a improved model of TFP
bearing from the simple model of previous studies. This model must
have the reliability and improve than the existing models; A
application research on TFP bearing for high-rise buildings built in
the ground conditions in Hanoi need been implemented.


8

Chapter 2
MODELING OF FRICTION BEARINGS
2.1. Basis of the theory
2.1.1. Basis of earthquake resistant design for buildings
- Numerical model: with these assumptions in structural
dynamics, numerical model of an n-storey building subjected to
earthquakes will be presented as shown in Figure 2.1.
Nth storey

kn

mn

cn

2nd storey

k2

1st storey

k1
a.

ug

b.

m2

c2

u1

m1

c1
ug

u2

k1

k2

c1

m1 c2

c.

un
kn

m2

cn

mn

ug

a. N-storey frame; b. Ideal numerical model;
c. Equivalent model
Fig. 2.1. Multiple DOFs structure model subject to earthquakes
- Equations of motion: the differential equations of motion of
the structural model are established by displacement method
(stiffness matrix method) as Equation 2.1.
- Determination method of structural response: this study will
use the direct integration method (time-history analysis). This
method is the most accurate results, reflect nature of the dynamic

problem, is suitable for research problems.
2.1.2. The choice of numerical method in research
System of differential equations of motion of seismic isolated
structures subjected to earthquakes in this research is complex. We


9

have to use the numerical method to solve them. Runge – Kutta
method will be selected in this study with the it’s advantages.
2.1.3. Calculation model of friction force in friction bearings
Friction force in motion with the laws of nature is relatively
complex. It depends on many factors such as surface material,
pressure, sliding velocity and load history,... There are many models
established to determine the dynamic friction force. The model used
in the study of friction sliding bearing such as: Coulomb model,
modified Coulomb model, plasticity model (Viscoplasticity model,
Bouc - Wen model). In particular, the plasticity model give the most
accurate results, used in this study.
2.2. Modeling of single friction pendulum (SFP) bearings
2.2.1. The relationship between force and horizontal displacement
The general equation of motion of SFP bearings represents the
relationship between force and the horizontal displacement of the
bearings as Equation 2.25, hysteresis loop shown in Figure 2.5.
W
(2.25)
F  u  WZ  Fr
R
where: 1st component of the equation is the restoring force, the 2nd
component is the friction force, the force of impact is the 3rd.

F/W



1/R



u

Figure 2.5. Hysteresis loop of SFP bearings
2.2.2. Modeling of seismic isolated structure with SFP bearings
The model is presented as Figure 2.6.


10
SFP bearing

kb

mb

c1

m1

un

u2
k2

k1


d

u1

ub

kn
m2

c2

mn

cn

ug

Fig. 2.6. The model of seismic isolated structure with SFP bearing
System of differential equations of motion including (n + 1)
equations subjected to ground acceleration is written as Equation
2.26 (according to the d'Alembert principle).
2.3. Modeling of double friction pendulum (DFP) bearings
2.3.1. The relationship between force and horizontal displacement
DFP bearing is structured as Fig. 1.8. The motion including 3
different sliding stage. Stage I: sliding begins on surface 1 (surface 2
not yet sliding). Stage II: surface 2 will slide together with surface 1

(sliding on surface 1 and 2). Stage III: Slider on restrainer of surface
1, sliding on surface 2. Equations of motion show the relationship
between force and displacement in the stages expressed as Eq. 2.30,
2.35 and 2.36. Hysteresis loop of the stages shown in Fig. 2.8.
f=F/W

uII
2

2

2

1

uI

u
uIII =d 1+d 2

Figure 2.8. Hysteresis loop of DFP bearings (----: stage I, II)
2.3.2. Modeling of seismic isolated structure with DFP bearings
The model of seismic isolated structures subjected to earthquake
is presented as Fig. 2.9. System of differential equations of motion is


11

written as Eq. 2.42 (according to the d'Alembert principle).
DFP bearing

k b1

ub1 k b2



d2

un

u2
k2

k1


mb1

d1

u1

ub2

m1

mb2 c1

c2

kn
m2

mn

cn

ug

Fig. 2.9. The model of seismic isolated structure with DFP bearing
2.4. Modeling of triple friction pendulum (TFP) bearings
2.4.1. The relationship between force and horizontal displacement
The motion of bearings including 5 stages are described in
detail by Fenz and Morgan. Stage I: sliding on surface 2 and 3 only;
Stage II: sliding on surface 1 and 3; Stage III: sliding on surface 1
and 4; Stage IV: sliding on surface 2 and 4; Stage V: sliding on
surface 2 and 3. Motion equation corresponding stage as Eq. 2.51,
2.55, 2.59, 2.63 and 2.67. Hysteresis loop shown in Fig. 2.11.

2

2

uIV
uIII

f=F/W
uII

4

2

2

1

uI
u
uV

Figure 2.11. Hysteresis loop of TFP bearings (----: stage I to IV)
2.4.2. Modeling of seismic isolated structure with TFP bearings
The model of seismic isolated structures with TFP bearings
subjected to earthquakes such as Fig 2.12 shows. System of
differential equations of motion is written as Eq. 2.84.


12
TFP bearing

k b1 ub1 k b2 ub2 k b3

 e

 e
mb1

d 1e

 e
mb2

d 2e

d 3e

u1

ub3
mb3 c1

m1

un

u2
k2

k1

c2

kn
m2

cn

mn

ug

Fig. 2.12. The model of seismic isolated structure with TFP bearing
2.5. Analysis of numerical example
To illustrate the results of study, an example of a 5-storey
structure was isolated by different friction bearings include: SFP, DFP
and TFP bearing subjected to earthquake is analyzed. Examples will
illustrate the value of the physical characteristics of the structure,
seismic isolation bearings and structural response.
- The 5-storey structure: the same mass per floor mi= 450/g
(kN.s2/mm), stiffness ki = 80 kN/mm and damping ratio %,
fundamental period of structure T1 = 0.529 s.
- Parameters of the bearing: dimensions and parameters of the
bearings are presented as Figure 2.13.
- Ground acceleration parameters: including 7 real acceleration
data of different earthquakes found from the Pacific Earthquake
Engineering Research Center (PEER), as shown in Table 2.1
- Analysis results:
Analysis results including hysteresis loop (Fig. 2.14 to 2.20),
effectiveness of reduce shear for 1st floor (Fig. 2.21 to 2.27) and
reduce absolute acceleration 5th floor (Fig. 2.28 to 2.34). Results of
displacement of bearing is according to relative displacement spectra
and effectiveness of reduce seismic of the bearings is approximately
80% (suitable for previous studies). Comparing the effects of three


13

bearings SFP, DFP and TFP presented in the Fig. from 2.35 to 2.41.

The results show that the effectiveness of TFP bearing is the best.
2.6. Conclusion of Chapter 2
The research results including: 1. Indicate basis of calculation of
earthquake resistant structure; 2. Present the principle of motion SFP,
DFP and TFP bearings and modeling seismic isolated structures with
SFP, DFP and TFP bearings subjected to earthquake; 3. Present an
example to illustrate the results of research. Via the analysis of the
example, the seismic reduction effectiveness is evaluated detailly,
results is suitable for previous studies. In this example, the advantages
of TFP bearing is considered better than the SFP and DFP bearings.

Chapter 3
IMPROVED MODEL OF TFP BEARING
3.1. Introduction
In the Chapter 3 of the dissertation, an improved model for
TFP bearing is studied. The behaviors not yet mentioned in previous
studies of TFP bearing will be analyzed in this model.
3.2. Establishing improved model
The improvements of the model shown in the following: a.
The model considers movement in three-dimensional (two horizontal
x, y and vertical z) of ground acceleration; b. The friction force is
calculated according to a general model, the friction coefficient
depends on sliding velocity and surface pressure of bearing.
Nonlinear behavior of friction force is governed by modified BoucWen model; c. The model can check the position of the slider on the
surface at each time; d. The accuracy of the model will be validated
by experimental results on many different ground acceleration data.


14

3.2.1. Numerical model
One-dimensional behavior (1D): 1D movement of the TFP
bearing including 5 stages is modeled by Fenz [47], [50] with three
groups of friction elements connected as shown in Figure 3.1. The
physical parameters of the model as Tables 3.1.
F/W

k b1

k b2

k b3

 1e

 2e

 3e

d 1e

d 2e

d 3e

F/W

Figure 3.1. The series model of TFP bearings (Fenz, 2008a)
Developing model: The general model of seismic isolated
structure with TFP bearings subjected to movement of ground in 2

dimensions x and y is shown in Figure 3.2
TFP bearing

 e

mb2

d 2e

d 3e

ms

csx

mb3

csy

k sy

d 1e

usx
k sx

 e

 e
mb1

ub3x

usy

k b1

ub1x k b2 ub2x
k b3

mb3

ugy
d 1e

 e

mb1

d 2e

 e

mb2

d 3e

 e

ub2y

k b2
k b1

ub1y

x

TFP bearing

y

k b3

ub3y

ugx

Figure 3.2. The general model of seismic isolated structure with
TFP bearing


15

From the model shown in Figure 3.2, the system of differential
equations of motion of structure isolated by TFP bearing subjected to
ground acceleration in each direction established on the basis of the
d'Alembert principle (Equation 3.1 and 3.2). Friction coefficient of
the movement in both 2 directions is calculated by Equation 3.3,
where the hysteresis variable Z is determined according to Equation
3.5. The vertical component of ground acceleration will be calculated

according to Equation 3.7 and included in the model through the total
weight of superstructure.
3.2.2. Model verification
Theoretical model simulated by Matlab is verified by
experimental results performed by Ryan et al in 2013 [87]. The
experimental full-scale model is a 5-storey building having a total
weight of over 5000 kN (Figure 3.3 to 3.6), is isolated by 9 TFP with
1.4 m in size (Figure 3.7) subjected to 19 different ground
acceleration data. Extracted from some of verify results such as the
following figure.

a. Results of displacement bearing in the x and y directions


16

b. Results of hysteresis loop in the x and y directions
Figure 3.13. Comparing the analytical result to experimental
result subjected to 90TAB motion

a. Results of displacement bearing in the x and y directions

b. Results of hysteresis loop in the x and y directions
Figure 3.26. Comparing the analytical result to experimental
result subjected to 115TAK motion


17

3.3. Detailed calculation slider displacements

Slider displacements on 4 surfaces are calculated as follows:
Reff 1

u1  ( F  Ff 1  Fr1 )
W

R
u2  ( F  Ff 2  Fr 2  W u1 ) eff 2

Reff 1
W
(3.9)

Reff 3
W
u3  ( F  Ff 3  Fr 3 
u4 )
Reff 4
W


Reff 4
u4  ( F  Ff 4  Fr 4 )
W

Where the force components are determined from solving the
system of differential equations of motion.
3.4. Effects of the vertical component of ground acceleration
The model considering of the effects of vertical component of
ground acceleration is verified with the model of Dao [36]. Analysis

of 5-storey building model with 7 different ground acceleration data
in 2 cases with/without vertical component. The results showed that
displacement bearing has not changed much but absolute
acceleration and shear force in the floor were increased significantly.
Therefore, we can not ignore this component as previous studies.
Figure 3.46 and 3.47 illustrate a case with 88RRS motion.

a. Absolute acc.
b. Shear
Figure 3.46. Structural behavior with 88RRS motion


18

Hình 3.47. Hysteresis loop of bearing with 88RRS motion
3.5. Conclusion of Chapter 3
Developing a new model for seismic isolated structure with
TFP bearing from the one-dimensional (1D) equivalent model of
Fenz et al (2008). Via this model, the displacement of the slider on
surface is calculated in detail and affect of vertical component of
ground acceleration is evaluated clearly.

Chapter 4
SEISMIC REDUCTION EFFECTIVENESS OF TFP
BEARING FOR HIGH-RISE BUILDINGS IN HA NOI
4.1. Introduction
As predicted, Hanoi may occur earthquake level 8. Earthquake
resistant design of buildings for this area is required in the recent
constructions. However, seismic resistant design method is still
traditional. In the study of this chapter, seismic resistant design

method with seismic base isolation technology by TFP bearing for
high-rise buildings was implemented.
4.2. Analysis of the effectiveness of TFP bearings for high-rise
buildings in Hanoi
4.2.1. Structure parameter
The 9-storey reinforced concrete building, assuming the
absoluted hard slab, mass and stiffness of the floor the same


19

assumptions, including: mass mi = 100 N.s2 /mm, stiffness ki = 150
kN/mm, damping ratio fundamental period of structure T1 =
1 s (suitable for various projects).
4.2.2. Selection of analyzed ground acceleration parameters
With performance - based seismic design and time history
analysis, ground acceleration are selected according to the provisions
of ASCE 7-2010 including 7 acceleration data and each motion is
recorded both 2 directions. Structure is analyzed and evaluated with 3
different levels of earthquakes including SLE (Service Level
Earthquake) level, DBE (Design Base Earthquake) level and MCE
(Maximum Considered Earthquake) level. The magnitude of data for
each level is adjusted by SF coefficient as Eq. 4.3. Results acceleration
data is selected as the Table 4.1 and SF coefficient is calculated as
Table 4.2. Fig. 4.2 and 4.3 illustrate the average of SRSS spectra
acceleration and target spectra magnitude after adjustment.
T2

SF 

f ( SF )   SSRSS 1.3Sa dT
T1

(4.3)

T2

S

2
SRSS

dT

T1

Figure 4.2. Target spectra MCE compare to the average of SRSS
in isolated base structure


20

Figure 4.3. Target spectra MCE compare to the average of the
SRSS in fixed base structure
4.2.3. The choice of the optimal parameters for TFP bearing with
ground conditions in Hanoi
As structure, there will be 7 parameters of bearing need be
chosen icluding: 2  3 ; Reff 2  Reff 3 ; d2  d3 ; 1; 4; Reff1 = Reff4; d1
= d4 ensuring sliding must occur on 5 stages. The criteria to select the
optimal parameters are given: 1. Adapt many earthquake levels; 2. The

structural response is the smallest. Process of choosing the optimal
parameters for TFP bearing is performed as schematic in Figure 4:24.
The results of the optimal parameters of bearing following: R2 = R3
=500 mm; R1 = R4 = 4000 mm; 2 = 3 = 0.01 - 0.02; 1 = 0.02 - 0.06;

4 = 0.04 – 0.08; d2 = d3 = 40 mm; d1 = d4 = 170 mm.
4.2.4. Seismic reduction effectiveness of the bearing for buildings
We analyze the structure of the two cases: fixed base and
isolated base with TFP bearing. Seismic reduction effectiveness is
evaluated through absolute acceleration and relative displacement of
the floors. With MCE level, the results shown in Figure 4.20 and
4.21. SLE and DBE levels for the same results. Displacement of
bearing, base shear in 2 cases and seismic reduction effectiveness of


21

TFP bearing is calculated in detail in Table 4.4.

Figure 4.20. Absolute acceleration in the floors, MCE level

Figure 4.21. Relative displacement in the floors, MCE level
Table 4.4. Displacement bearing and effectiveness of reducing
base shear in isolated base 9-storey structures with TFP bearings

Level

Disp bearing, ub
(mm)

Base shear, Fb (kN)

Fixed
base

Isolated
base

Fixed
base

Isolated
base

Effectiveness
(%)

SLE

0

65.8

2415

697

71

DBE

0

176

5183

1103

79

MCE

0

311

7791

1451

81

From the results of structural response, the horizontal force
conditions in the bearing (in 17.2.4.4, ASCE 7-2010) and the initial
assumption parameters are tested satisfactorily.


22
- Size of structure

- Construction site

Design spectrum
Assume TD
and TM

1. Structural parameters calculation.
2. Choice of parameters for bearing:
- According to experience: Reff2 = Reff3 ; d2 = d3;

2 = 3

Choose and adjust
ground accl.

- Preliminary: d1 = d4
- Preliminary: Varied Reff1 = Reff4.
- Preliminary: Varied 1 < 4.

Fixed Reff1 = Reff4, analyze with varied 1 < 4

- Determine the reasonable 1 < 4
- Analyze varied Reff1 = Reff4 with 1 < 4 above
- Determine the reasonable Reff1 = Reff4
- Determine the parameters fully

-

-

Calculate and check
TD and TM

Analyze structure with
parameters above

Check horizontal
force conditions

+

+
Optimal parameters

Fig. 4.24. Determining schematic the parameters for TFP bearing
4.3. Conclusion of Chapter 4
TFP bearing device is very effective in performance-based
seismic design. Application TFP bearing for high-rise buildings
subjected to earthquake in Hanoi according to ASCE 7-2010 bring high
efficiency (about 70% - 80%). A determining method of the optimum
parameters for TFP bearing is presented. Accordingly, the optimal
parameters used for high-rise building in Hanoi were found.


23

CONCLUSIONS AND RECOMMENDATIONS
1. Conclusions
Within the scope of the dissertation, conclusions are drawn as
follows:

1. Based on the the structure and movement principles of the
friction bearings including: SFP, DFP and TFP bearings from
previous studies, dissertation established the model of isolated base
structures with the bearings subjected to earthquakes. Contents
including: indicate numerical model, establish differential equations
of motion and suggest methods to solve them to find out the response
of structures. Dissertation performed a simulation example of the
structure subjected to different ground acceleration data to evaluate
the effectiveness of the devices. The results show that the bearings
are very effective in seismic reduction. From the results of
simulation examples, the advantages of TFP bearing is considered
the best in comparison to SFP and DFP bearing.
2. With the advantages of TFP bearings evaluated, the
dissertation established an improved model for TFP bearings. The
reliability of the model was verified with experimental results.
3. From improved model, the calculation of each slider
displacement inside the bearing is performed. The results are
evaluted detailly of each location of slider at each time of the
movement. The significance of this work is to determine precisely
the surphus displacement of each slider at the end of the earthquake.
4. Effects of vertical component of ground acceleration on
response of the structures isolated by TFP bearings is carefully
analyzed in the dissertation. This result shows that, with some
earthquakes having large peak value or large vertical acceleration