41 Fib 2003 Full

SEISMIC DUCTILITY EVALUATION OF LARGE-SCALED BRIDGE PIERS BY THE QUASI-STATIC AND THE PSEUDO-DYNAMIC TEST

Youngsoo CHUNG 1 Changkyu PARK2 Jinyoung PARK 3

1 Professor, Dept. of Civil Engr., Chung-Ang University, KOREA 2 Ph. D. candidate, Dept. of Civil Engr., Chung-Ang University, KOREA 3 Master, Dept. of Civil Engr., Chung-Ang University, KOREA Keywords: circular reinforced concrete bridge piers, large–scale test specimens, pseudo dynamic test,

limited confinement ratio 1 INTRODUCTION

Even though earthquakes have severel economic, social, psychological and even political effects in the areas and the countries where they take place, most Korean thought a few years ago that Korea is located rather far away from the active fault area and immune from the earthquake hazard. Recently in the Korean peninsula, there has been occurred not a few of moderate earthquakes in above 5.0 Richter scale, which have increased much concern about probable strong earthquake. Seismic design provisions of Korea roadway bridge design code were newly introduced on 1992. These seismic design provisions are introduced from the AASHTO code which is appropriate for the strong seismicity region. There are many RC bridge piers that were nonseismically designed and constructed on the basis of the pre-1992 design code.

The objective of this research is to investigate the seismic performance of circular RC bridge piers which were designed and constructed based on the pre-1992 design code, and to propose pertinent seismic design provisions which are appropriate for low or moderate seismic region. Based on the pre-1992 design code, two large-scaled test specimens were made with 1.02% and 0.13% for the longitudinal steel ratio and the confinement reinforcement ratio, respectively. Other four test specimens were made with more confinement steel which was approximate 0.23 and 1.70 times the amount required by the new 1992 seismic design code and the pre-1992 design code, respectively. Further investigation was made for the relationship between structural displacement ductility factor and member ductility factor, which was expressed in curvature.

2 DESCRIPTION OF EXPERIMENT 2.1 Material properties

D19 deformed steel was used as longitudinal steel in RC test specimens, of which confinement steels had been laterally used with D10 deformed steel. Yield strength from the tensile coupon test is 3,500 kgf/cm2 for D19 deformed steel and 3,800 kgf/cm2 for D10 deformed steel. Table 1 shows the compressive strength of concrete which is based on the compression test on cm2010×φ concrete cylinders that were 100mm in diameter and 200mm in height. Max. size aggregate was 25mm.

Table 1 Mix proportion of concrete

Unit Weight (kg/cm3) Max. size Of Coarse Aggregate

(mm)

Slump (cm)

Air (%)

W/C (%)

s/a (%)

Water Cement Fine Aggregate

Coarse Aggregate AE.

Compressive Strength (kgf/cm2)

25 12 3.8 50 48 126 349 869 909 1.75 253

2.2 Test program

As shown on Table 2, six circular large-scaled test specimens were made 1200 mm in diameter and 4800 mm in height which was the aspect ratio of 4.0. They are three test specimens for the quasi-static test and other three test specimens for the pseudo-dynamic test, including two reference specimens. These two column models were made with 1.01% for the longitudinal steel ratio, and 0.13% for the confinement reinforcement ratio. Two reference specimens are reflected by considering

the existing bridge piers designed on the pre-1992 design code, and four other specimens are made with more confinement steels to develop the detailing provisions for the transverse steels which is appropriate in low or moderate seismicity region like Korea.

Further test parameters are the amount of lap splice for the starter bars and the type of the transverse steel in the plastic hinge region of test columns, which were shown in Fig. 1. All starter bars for two reference specimens are lap-spliced in the plastic hinge region by reflecting the actual status of existing bridge piers. Other four specimens are made with continuous for all the starter bars or lap-spliced only for 50% the starter bars. Similarly, Fig. 1 shows the detailing of the transverse steel, i.e HT1 for two reference models and HT4 for other four specimens.

HT1 HT4

250250

(c) Transverse steel type

Starter Bar

0.25D

100% L li 50% L li

0.25D

Column Bar

Starter Bar

Column Bar

(a) Non Seismic Design (b) Limited Ductile Design (d) Lap splice

Fig. 1. Details of Specimens Table 2 Test specimen description

Longitudinal Steel Transverse Steel

Test Specimen* Designation

Strength Steel Ratio (%)

Lap splice (%)

Strength Steel Ratio (%)

Space (cm)

Axial Force (tonf)

Load Type

NS-HT1-A-L2 100 0.13 20

MS-HT4-H-L2 50 Quasi-Static Test

MS-HT4-N-L2 0 0.22 11.5

Fig. 2

NP-HT1-A 100 0.13 20

MF-HT4-H 50 Pseudo- Dynamic

Test MF-HT4-N

SD30 1.01

0

SD30

0.22 11.5

gck AfP

=

0.1

(190) Fig. 3

* (1) NS·NP : Nonseismic, MS·MF : Limited ductile (2) HT1, HT4 : Transverse steel type (3) A, H, N : % of Lap splice

22@

150=

3300

0

4800

10@

115=

1150

2@60

=120

310

3@20

0=60

0100

SECTION A-A

AA

4800

A

701060

310 10

0

100

25@

200=

5000

A

120070 106070

120070

SECTION B-B

BB

2.3 Load procedure 2.3.1 Quasi-static Test

Quasi-static cyclic tests have been carried out in a displacement-controlled way. With the level of

axial load of gc Af. ′/070 , two constant cyclic loads have been applied in a sine wave at the top of test columns using 1000KN hydraulic actuator. Figure 2 shows the load pattern for lateral loading. The displacement-controlled test was conducted based on the drift level, starting from %.250± , %.50± ,

%.01± , %.51± , %.02± , %.52± , %.03± , %.04± , … and ending the final drift at failure. The drift level is computed as the ratio of the input displacement to the column height.

120

-12-24

-48

-72

-96

24

48

72

96

0 5 10 15 20 25 30 35 40 45-2.0

-1.5

-1.0

-0.5-0.250

0.250.5

1.0

1.5

2.0

1.0%

1.5%2.0%

0.5%0.25%

Number of Cycles

Drift

Lev

el (

% )

Disp

lacem

ent(m

m)

be continued

-400

-300

-200

-100

0

100

200

300

400

0 4 8 12 16 20 24

Time(sec)A

ccel

erat

ion

cm

/ sec

2

PGA = 0.2g

Dominant Frequency : 1.7 Hz

Fig. 2. Cyclic load pattern Fig. 3. Moderate artificial earthquake (T2) 2.3.2 Pseudo-dynamic test

The pseudo-dynamic test is similar to standard step-by-step nonlinear dynamic analysis procedures that the controlling computer software considers the response to be divided into a series of time step. Within each step the governing equation of motions are numerically solved for the incremental structural deformation. In the pseudo dynamic method, the ground motions as well as the structure’s inertial and damping characteristic are specified numerically in a conventional dynamic analysis. However, the structure’s restoring force characteristic is measured directly from the damaged specimen as the test progresses. Explicit Newmark’s β method is used for the algorithm of this pseudo-dynamic test, as shown on Fig. 4. And Figure 3 shows the input ground acceleration for the pseudo-dynamic test. Particularly for the pseudo-dynamic test, input ground acceleration is the artificial earthquake in 24 seconds duration which are developed based on rock soil condition and the Kanai Tajimi spectrum. Peak ground acceleration for input ground acceleration starts from 0.154g, 0.20g, 0.30g --- and ends at the final PGA at failure.

We used 1,000 KN hydraulic actuator for this pseudo-dynamic test. It’s maximum stroke is ±250mm. When lateral force will be imposed at the test specimen by the actuator, it is desirable to keep the axial force constant. A hydraulic axial force controller was mobilized to keep a constant axial load. The applied axial force was 190ton, which corresponds to gck Af.070 . Load rate is determined as 0.3mm/sec considering the effect of the strain rate Fig. 4. Pseudo dynamic test scheme for the pseudo-dynamic test.

2.4 Test setup and instrumentation The test setup was designed for testing column-footing assemblages subjected to the combining

axial and lateral loadings. The specimens were tested in a concrete reaction wall. Two independent loading systems were used to apply the load to the specimens. First, the axial load of 190 tonf corresponding axial load ratio 070.AP/f gck = was applied to the column by prestressing a pair of high-strength steel rods against the concrete floor of the loading frame. Next, the lateral forces were applied to the column by an 1,000 kN hydraulic actuator mounted on the reaction wall. Each column was instrumented to monitor the applied displacement and corresponding loads, strains, and deformations. Five instrumental equipments were used to measure various datas. These included:

a) the calibrated load cell and displacement transducer of the actuator, b) the clip gages and inclinometers mounted on the plastic hinge region of the column to

measure the curvature, c) the displacement transducers installed on the steel reference frame, d) electrical-resistance strain gages bonded to reinforcing bars, and e) photographic facilities for concrete cracks and failure modes.

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400

Displacement(mm)

Lat

eral

For

ce(t

onf)

NS-HT1-A-L2

0.25%~2.0%

-80

-60

-40

-20

0

20

40

60

80

-250 -200 -150 -100 -50 0 50 100 150 200 250Displacement(mm)

Lat

eral

For

ce (t

onf)

MF-HT4-HNP-HT1-A

0.154g ~ 0.40g

(a) NS-HT1-A-L2 (b) NP-HT1-A

MS-HT4-H-L2

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400Displacement (mm)

Lat

eral

forc

e (t

onf)

0.25%-4.0%

-80

-60

-40

-20

0

20

40

60

80

-250 -200 -150 -100 -50 0 50 100 150 200 250

Displacement(mm)

Lat

eral

For

ce (t

onf)

MF-HT4-HMF-HT4-H

0.154g ~ 0.70g

(c) MS-HT4-H-L2 (d) MF-HT4-H

MS-HT4-N-L2

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400

Displacement (mm)

Lat

eral

forc

e (t

onf)

0.25%-6.0%

-80

-60

-40

-20

0

20

40

60

80

-250 -200 -150 -100 -50 0 50 100 150 200 250Displacement(mm)

Lat

eral

For

ce (t

onf)

MF-HT4-HMF-HT4-N

0.154g ~ 0.80g

(e) MS-HT4-N-L2 (f) MF-HT4-N

Quasi-static test Pseudo-dynamic test

Fig. 5. Lateral force-displacement hysteresis loop

3 TEST RESULTS 3.1 Lateral force-displacement behavior

Figure 5 shows the relationship between lateral displacement and lateral force for six test specimens under the quasi-static cyclic load and the pseudo-dynamic load. The seismic performance of the specimens(NS-HT1-A-L2, NS-HT4-H-L2, NP-HT1-A, and MF-HT4-H) are determined to be very poor because of lap-splice for the starter bars and insufficient detailing of transverse steel. Other specimens(MS-HT4-N-L2, MF-HT4-N) shows much better seismic performance due to all continuous starter bars. Lap splice is the most important factor to ensure the statisfactory seismic performance.

It was observed from the test of lap-spliced specimens that the longitudinal reinforcement steel was buckled but not fractured even at the arrival of the ultimate displacement because of lap splice. However, the continuous longitudinal reinforcing steels for other specimens(MS-HT4-N-L2, MF-HT4-N) were buckled and fractured at failure. Flexure failure mode was observed for all specimens.

Fig. 6 shows the envelope curves of the hysteresis of all six specimens under the quasi-static test and the pseudo-dynamic test.

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400

Displacement(mm)

Lat

eral

For

ce(t

onf)

MS-HT4-N-L2MS-HT4-H-L2

NS-HT1-A-L2

Quasi-Static

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400Displacement(mm)

Lat

eral

For

ce (t

onf)

NP-HT1-AMF-HT4-NMF-HT4-H

Pseudo-Dynamic

(a) Quasi-static test (b) Pseudo-dynamic test

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400Displacement(mm)

Lat

eral

For

ce (t

onf)

NP-HT1-AMF-HT4-HNS-HT1-A-L2MS-HT4-H-L2

-80

-60

-40

-20

0

20

40

60

80

-400 -300 -200 -100 0 100 200 300 400Displacement(mm)

Lat

eral

For

ce (t

onf)

MF-HT4-NMF-HT4-HMS-HT4-N-L2MS-HT4-H-L2

(c) Confinement effect (d) Lap-splice effect

Fig. 6. Lateral force-displacement envelope curve

Seismic performance of RC bridge piers can be evaluated as a displacement ductility,

∆µ = u∆ / y∆ , which can be obtained from the envelope curves of Fig. 6. As shown in Figure 7, the yield displacement was calculated by two methods. The yield displacement of definition• was calculated by extrapolating the straight line between the origin and to the force-displacement point at 0.75Vi to the lateral loading Vi, which corresponds to the nominal flexural capacity of test specimen. And the yield displacement of definition• was corresponded to the intersection point which could be extended through the point as 75% of maximum lateral load, Vmax, form zero point. The ultimate displacement u∆ is determined as the value of the intersection point between Vi and strength envelope curve, which corresponds to about 0.80 Vmax. Table 3 shows the displacement ductility for all six specimens. As shown in Table 3, the moderate specimens(M series) have shown about 2-3 times the displacement ductility of the reference specimens(N series). Similarly, it is confirmed from Table 3 that lap splice of above 50% the starter bars for the specimens(MS-HT4-H-L2, MF-HT4-H) significantly decreases the displacement ductility.

¥ Äy

VV

Force

0.75i

i

Displacementu¥ Ä

Strength Envelope

0.8

Curve

maxV

maxV

Force

V0.8

Displacement¥ Ä

Strength Envelope

maxVmax

u

Curve

y¥ Ä

0.75 Vmax

(a) Definition • (b) Definition •

Fig. 7. Yield and ultimate definition

The Korea roadway bridge design code specifies the response modification factor, 12 −= ∆µR , as 3 for single column which gives 5 for the displacement ductility. Judging from the test result, the moderate specimens without lap splice should satisfy the seismic requirement.

Table 3 Displacement ductility

Definition • Definition •

Test Specimen Designation Yield

Displ. (mm)

Ultimate Displ. (mm)

Displ. Ductility

Yield Displ. (mm)

Ultimate Displ. (mm)

Displ. Ductility

NS-HT1-A-L2 23.10 81.54 3.53 35.90 81.54 2.27

MS-HT4-H-L2 26.95 105.88 3.93 35.47 105.88 2.98 Quasi-static Test

MS-HT4-N-L2 28.11 244.70 8.71 40.39 244.70 6.06

NP-HT1-A 22.94 51.07 2.22 27.67 51.07 1.85

MF-HT4-H 24.22 116.00 4.79 36.40 116.00 3.19 Pseudo Dynamic Test

MF-HT4-N 20.7 224.95 10.87 34.20 224.95 6.58 3.2 Moment-curvature behavior

The most convenient quantity to evaluate either the ductility imposed on a structure by an earthquake, or the structure’s capacity to develop ductility, is the displacement. But, the most common and desirable source of inelastic member deformations are rotation in plastic hinge region. Therefore, it is useful to relate the rotation per unit length, i.e., curvature to cause the bending moment. Figure 8 shows the relationship between the rotational curvature of the plastic hinge of the test column and the corresponding moment for six test specimens under the quasi-static cyclic load and the pseudo-dynamic load. It was observed from Fig. 8 that the shapes of the moment-curvature hysteresis were appeared to be similar to the force-displacement hysteresis of Fig. 5. The seismic performance of the specimens(NS-HT1-A-L2, NS-HT4-H-L2, NP-HT1-A, and MF-HT4-H) are determined to be very poor because of lap-splice for the starter bars and insufficient detailing of transverse steel. Other specimens,(MS-HT4-N-L2 and MF-HT4-N), show much better seismic performance due to all continuous starter bars.

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015Curvature (rad/cm)

Mom

ent (

tonf

.m)

0.25%~2.0%

NS-HT1-A-L2

-300

-200

-100

0

100

200

300

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015Curvature(rad/cm)

Mom

ent (

tonf

.m)

NP-HT1-A

0.154g~0.4g

(a) NS-HT1-A-L2 (b) NP-HT1-A

MS-HT4-H-L2

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Curvature (rad/cm)

Mom

ent (

tonf

-m)

0.25%-4.0%

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Curvature(rad/cm)

Mom

ent (

tonf

.m)

M F-HT4-H

0.154g ~ 0.70g

(c) MS-HT4-H-L2 (d) MF-HT4-H

MS-HT4-N-L2

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015Curvature (rad/cm)

Mom

ent (

tonf

-m)

0.25%-6.0%

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015Curvature(rad/cm)

Mom

ent (

tonf

.m)

MF-HT4-N

0.154g ~ 0.80g

(e) MS-HT4-N-L2 (f) MF-HT4-N

Quasi-static test Pseudo-dynamic test

Fig. 8. Moment-curvature hysteresis loop

Figure 9 shows the envelope curves of the hysteresis of the specimens under the quasi-static test and the pseudo-dynamic test which were obtained from Fig. 8. Similar to the displacement ductility, the curvature ductility is expressed as φµ = uφ / yφ , where uφ is the ultimate curvature and yφ is the yield curvature. The yield and ultimate curvature is defined as Fig. 7 for the definition of the yield and ultimate displacement.

Table 4 shows the curvature ductility for the specimens. As shown in Table 4, the moderate designed specimens(MS-HT4-H-L2, MS-HT4-N-L2, MF-HT4-H, MF-HT4-N) have shown that the curvature ductility enhanced by about 2-5 times the curvature ductility of the reference specimens,(NS-HT1-A-L2). This result is very similar to the result of the displacement ductility. It is also confirmed from Table 4 that lap splice of above 50% the starter bars for the specimens(NS-HT1-A-L2, MS-HT4-H-L2, NP-HT1-A, MF-HT4-H) significantly decreases the curvature ductility. Also, the curvature ductility of moderate specimens(MS-HT4-N-L2, MF-HT4-N) without lap splice, is above 7 which is required for minimum value of the limited ductile curvature in Eurocode 8. Therefore, it is thought that limited ductile design concept should be more desirable for the seismic preparedness of RC bridge piers in low or moderate seismicity region, in consideration of a good agreement between the displacement ductility and the corresponding curvature ductility for moderate test specimens(MS-HT4-N-L2, MF-HT4-N).

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Curvature(rad/cm)

Mom

ent (

tonf

.m)

MS-HT4-H-L2MS-HT4-N-L2NS-HT1-A-L2

Quasi-Static

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Curvature(rad/cm)

Mom

ent (

tonf

.m)

MF-HT4-HMF-HT4-NNP-HT4-A

Pseudo-Dynamic

(a) Quasi-static test (b) Pseudo-dynamic test

-400

-300

-200

-100

0

100

200

300

400

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Curvature(rad/cm)

Mom

ent (

tonf

.m)

MS-HT4-H-L2MS-HT4-N-L2MF-HT4-HMF-HT4-N

(c) Confinement effect (b) Lap-splice effect

Fig. 9. Moment-curvature envelope curve

Table 4 Curvature ductility

Definition • Definition •

Mode Specimen Yield Curvature (rad/cm)

Ultimate Curvature (rad/cm)

Curvature Ductility

Yield Curvature (rad/cm)

Ultimate Curvature (rad/cm)

Curvature Ductility

NS-HT1-A-L2 61E-6 207E-6 3.39 80E-6 207E-6 2.59

MS-HT4-H-L2 71E-6 365E-6 5.15 96E-6 365E-6 3.80 Quasi-static Test

MS-HT4-N-L2 65E-6 993E-6 15.32 88E-6 993E-6 11.28

NP-HT1-A 80E-6 226E-6 2.84 104E-6 226E-6 2.17

MF-HT4-H 88E-6 803E-6 9.18 127E-6 803E-6 6.32 Pseudo Dynamic

Test MF-HT4-N 74E-6 1214E-6 16.40 136E-6 1214E-6 8.92

3.3 Relationship between the displacement ductility and the curvature ductility The ductility is an essential property of structures responding inelastically during severe

earthquake. The term ductility defines the ability of a structure and selected structural components to deform beyond elastic limits without excessive strength or stiffness degradation. It is necessary to trace briefly specific source of ductility and to establish the relationship between different kinds of ductilities. Further investigation was made for the relationship between displacement ductility and curvature ductility in this research.

For a simple structural element, such as the vertical cantilever (like single column), the relationship between curvature and displacement ductilities can be expressed by integrating the curvatures along the member height. Thus

φµφφ

φ

φµ K

KK

dxxx

dxxx

y

u

yy

u ===∆∆

=∫∫

∆2

1

)(

)( (1)

where, )x(φ and )x(eφ are the curvature distributions at maximum displacement and at yield

displacement, respectively, 21 K,K and K are constant. Priestley et al. proposed the relation formula between curvature and displacement ductilities, such as Eq.(2).

−−+=∆ L

L.

LL)( pp 501131 φµµ (2)

where, ybp fd.L.L 0220080 += (MPa)

Our experimental results were plotted in Fig. 11(a) for both definition I and II of yield responses which by and large gave bigger values than the displacement ductility of Eq.(2) on the same curvature ductility. By the linear regression analysis on our results, Eq. (2) was modified into Eq. (3), of which the coefficient of correlation(R) and the coefficient of determination(R2) are obtained as 97% and 94%, respectively, as shown on Fig. 10(b).

−−+=∆ L

L.

LL)(. pp 57011551 φµµ (3)

where, ybp fd.L. 0220080 +=l (MPa)

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20Curvature Ductility

Dis

plac

emen

t D

uctil

ity

Eq. (2)µ¡ â=1+3(µΦ-1)(Lp/L)[1-0.5(Lp/L)]

Experimental Result

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20

Curvature Ductility

Dis

plac

emem

t Duc

tility

µ¡ â=1+5.5(µΦ-1)(Lp/L)[1-0.57(Lp/L)]R2=0.94

Eq. (3)

Linear Regression Analysis

(a) Experimental result (b) Linear regression analysis

Fig. 10. Relationship between displacement ductility and curvature ductility

4 CONCLUSIONS

For this research, following conclusions are drawn from the test : • Very low ductility was obtained for circular reinforced concrete bridge piers with lap-spliced

starter bars in the plastic hinge region, which were designed based on the pre-1992 design code. This is due to the debonding of lapped starter bars, resulting from insufficient detailing of transverse reinforcement.

• The specimens with continuous reinforcement through the plastic hinge region moderately improve the ductility even though poor detailing of transverse reinforcement. The column failure is induced by the buckling of longitudinal steels after the fracture of transverse reinforcing steels.

• Moderate specimens with more confinement steels in the plastic hinge region satisfied the requirements of the limited ductile design concept which should be desirable for low or moderate seismicity region.

• The result of quasi-static test is good agreement with the result of pseudo-dynamic test, which gives the sufficiency of the quasi-static test for single column test.

• It is thought that new formula for the relationship between curvature and displacement ductilities should be developed.

ACKNOWLEDEMENTS

This research was supported by Korea Highway Cooperation grants in 2001. This support is gratefully acknowledged. REFERENCES [1] Ministry of Construction and Transportation, " Korea Highway Bridge Design Specification,"

2000. [2] M.J.N. Priestley, F. Seible, and G. M. Calvi, “Seismic Design and Retrofit of Bridge,” JOHN

WILEY & SONS, Inc, 1996. [3] T. Paulay M., and J.N. Priestley, “Seismic Design of Reinforced Concrete and Masonry

Buildings,” JOHN WILEY & SONS, Inc, 1992. [4] Pui-shum B. Shing and Stephan A. Mahin, “Pseudo-Dynamic Test Method for Seismic

Performance Evaluation: Theory and Implementation,” Report No. UCB/EERC-83/12,1984. [5] European Committee for Standardization, “Design Provisions for Earthquake Resistant

Structure-Bridge,” Eurocode 8 Part 2, 1996.