5 支承墊在無收縮水泥砂漿表面殘留的磨擦痕跡

第 5 屆美國橋樑地震工程研討會

(

5^th U.S. National Seismic Conference and Workshop for Bridges and Highways, 5NSC

)

報告人 張國鎮 台大土木系 一、參加會議經過

第五屆美國地震工程研討會於西元 2006 年 9 月 18 日至 20 日於 美國加州救舊金山(

San Francisco

)市舉行三天。此研討會雖以美國為 名，但世界其他國家橋樑及地震工程之專家學者參與者甚眾，包括來 自我國、日本、韓國等共兩佰餘人參與。本研討會每三年召開一次，

為地震工程界重要之盛會之一。

本 研 討 會 由 美 國 Multidisciplinary Center for Earthquake Engineering Research (MCEER)及美國聯邦工陸總暑(FHWA)共同主 辦。會議除每天早上有專題演講外，並有包括多主題一百餘篇論文報 告以及現場展示等，內容十分豐富。本人受邀於 9 月 20 日上午於會 議中發表 Key-note lecture“

Seismic Assessments of Bridges with Rubber Bearings during 1999 Taiwan Chi-Chi Earthquake

”，報告了台灣橋梁在民國 88 年 9 月 21 日集集大地震之反應及新發現，獲得與會專家熱烈之討論。

二、與會心得

本研討會最主要的特色之一為由三個美國國家科學基金會(NSF)

所成立之地震中心(PEER,MAE 及 MCREE)主任報告其中心主要研究

方向及預期目標，可供我國家地震中心未來發展之參考。另外一重要 特為介紹由 NSF 耗資千萬美金之網路地震工程實驗系統，NEES Program，將為未來世界地震工程研究之主流之一，值得我們更深入 之研究。

三、建議

由本研討會之內容可看出，地震工程之研究已由過去單獨領域之

研究擴大為多領域之整合研究，包括資訊科技之應用及社會層面之影

響等。國內應有能力發展類似 NEES Program 之計畫，以資訊科技整

合國家地震中心及各公私立大學之實驗及分析研究，使我國地震工程

水準更往上提昇。

Cover page

Title: Seismic Assessments of Bridges with Rubber Bearings during 1999 Taiwan Chi-Chi Earthquake

Authors: Kuo-Chun Chang (Contact person and Presenter)

Department of Civil Engineering, National Taiwan University No.1, Sec. 4, Roosevelt Road, Taipei, 106 Taiwan

Phone: +886-2-2363-8608

Fax: +886-2-2363-2975

E-Mail: [email protected]

Seismic Assessments of Bridges with Rubber Bearings during 1999 Taiwan Chi-Chi Earthquake

Kuo-Chun Chang

¹

ABSTRACT

The 921 Taiwan Chi-Chi Earthquake incurred tremendous disaster to the central region of the island. It was noticed that for those major damaged highway bridges located on or very close to the Chelungpu fault, they experienced collapsed spans in most cases. However, investigations from 1094 bridges in this area revealed that most bridge columns suffered none-to-minor damages while few are severe damaged due to large surface rupture passed through. One of the reasons for this unexpected performance is the construction method of rubber bearing – an unbolted design on the simply-supported bridge structure. Parameter studies have shown that the function of the bearing system, including rubber bearing, pot bearing, RC shear key and restrainer, plays an important role for the performance of the bridges during the earthquake. Therefore, this study proposes a three-year project started from 2004 to understand the influence of the bearing system on the seismic behavior of the bridge structure. Basic mechanical behaviors and performance levels in each bearing component and the interrelationship among the different components were tested to provide appropriate analytical models for numerical simulations. Besides, this project also applied the discrete-time state-space numerical integration processes to build up a real-time bridge simulator. Combined with the performance-based design concept, this project will develop design methodologies to provide sufficient capacity on the existing bridges and limit the damage level to be acceptable under a given seismic demand.

INTRODUCTION

A devastating earthquake with the magnitude of ML = 7.3 struck the central region of Taiwan in the early morning on September 21, 1999. It was known as the 921 or Chi-Chi Earthquake (NCREE, 1999). There are approximately 1,000 highway bridges spread on the provincial and county routes in Taichung, Nantou, Changhua, and Yunlin counties. Most of the bridges escaped from serious damage (Table I), while approximately 20% of them suffered minor-to-major damage due to fault rupturing, collapsed spans, landslides, soil settlement, slope failures, flexural and/or shear failures, and liquefaction. The construction completion dates of those bridges range from 1960 through 1999.

According to the preliminary bridge-disaster reconnaissance reports (A reconnaissance report 1999, A preliminary 1999), major damaged highway bridges have simply-supported, reinforced or prestressed concrete slab-and-girder superstructures.

Total of 26 bridges in the reports are regarded as severe damaged bridges, of which the peak ground accelerations (PGAs) measured in the east of or close to the Chelungpu fault are in the range of 400 gal to 980 gal.

Figure 1. shows a summary of comparison among 11 different damage modes. It is

seen that the ratios of damage of auxiliary facility (35.6%), abutment (32.5%), deck (26.3%), and approach slab (21.1%) are significantly larger than those of columns/pier (10.8%), and foundation (7.2%). For damage modes with high percentage, those can be related to the superstructure, and so to the bearing performance, since the “unbolt rubber bearing” (Figure 2 and 3) has been verified through an assessment of YanFeng bridge

(Chang et al., 2004) with well agreements to the field observations in the Chi-Chi

earthquake, and is taken as the main mechanism allowing friction/sliding movement of superstructure to pound on abutments, approach slabs and/or bridge decks. Moreover, the shear strength of bearing is found to be an important factor to explain the damages on the column – the minor cracks mainly appeared in the transverse direction rather longitudinal

(Figure 4). Compared to the case with fixed boundary condition, bridge

with unbolt rubber bearing, which provide a fuse-like function, can prevent column from failure because of little inertial force translated to the substructure. However, large movement induced by the friction movement should be limited.

TABLE I. DAMAGE LEVEL OF BRIDGE COMPONENT IN CHI-CHI EARTHQUAKE Damage Level

As A B C D Position

(falling) (major) (moderate) (slight) (none)

Sum

Superstructure 10 (0.9%) 3 (0.3%) 5 (0.5%) 58 (5.3%) 1018 (93.1%) 1094 (100%)

Bearing system 10 (0.9%) 3 (0.3%) 4 (0.4%) 44 (4.0%) 1033 (94.4%) 1094 (100%)

Sub structure 8 (0.7%) 2 (0.2%) 17 (1.6%) 75 (6.8%) 992 (90.7%) 1094 (100%)

26.3% 11. au xiliary facility

Figure 1. Percentage distribution of the 11 damaged

modes Figure 2. Construction for the rubber bearing

Figure 3. Bearing damage on Yeng-Feng bridge in Chi-Chi earthquake (sliding out of the pad seat)

Figure 4. Column damages on Chi-Lu bridge in Chi-Chi earthquake (cracks on the transversal direction)

A three-year (2004.8-2007.7) integrated project named “Seismic Assessment and Study of Bridges with Functional Bearing Systems” was proposed to understand the influence of bearing systems on the bridge structure. Experiments about rubber bearing in the friction coefficient test and pseudo-dynamic test were carried out and corresponding results were verified to provide appropriate numerical models, as well as the unseating prevention devices, such as shear key and restrainer in the cyclic loading tests. Based on this project, it is hope to reduce the seismic risk and repair/retrofit cost of highway bridges in future years in Taiwan.

EXPERIMENT PROGRAM

Friction Coefficient Test

Figure 5(a) shows the test setup of the friction coefficient test. In order to use same

bearings on the bridge model in shaking table test, the dimension of Steel-Reinforced Elastomeric Bearing specimen is determined to be 150mm¯150mm¯28mm. The Hardness IRHD of the rubber material is 60, and shape factor is 3.6. SS400 is used for the inner steel plate (144mm¯144mm¯1mm) inside of the bearing.

Total of six cases shown in Table Ⅱ are divided into two groups according to the contact material: group1 without PTFE and group2 with PTFE material on the top of the rubber bearing. For each group, three target displacements from 60mm, 90mm, to 120mm are selected as major parameter. The friction coefficient test was carried out according to the prEN-1337-5 and AASHTO 17^th version. Two vertical hydraulic actuators provide 26.6kN axial forces upon the two specimens, while friction force is measured through one horizontal hydraulic actuator as bearing slides against concrete pad in 15 cycles. The pad is made of concrete with compression strength equals to 25.51MPa.To get accurate friction force, a shear measuring device (Chang and Chen,

2005) with six steel plates is installed below each bearing pad. By measuring twelve

strain gages, the friction force resulting from axial and bending force can be recalculated with an assumption the steel plate is only in elastic range.

TABLE Ⅱ. SPECIMENS AND TEST RESULTS OF FRICTION COEFFICIENT TEST Group Case Rubber size

(mm)

Velocity (mm/sec)

Displacement

(mm) Friction coefficient

1

±

₆₀ 0.2871~0.3089 (RB-PTFE)

6

150¯150¯28 1.27

±

₁₅₀ 0.0833~0.1087

Figure 5(b) and Figure 5(c) show the test results. The definition of friction

coefficient is getting the sum of absolute force values (both positive and negative) on the force platform when corresponding displacement is close to zero, and then divided by the applied axial force. In Table.1, the friction coefficient ranges from 0.2 to 0.3 in group1 and 0.09 to 0.11 in group2, respectively. Compared with the friction coefficient for the moveable type of bearing in seismic design specification of bridge in Taiwan, test results will lead to a higher horizontal force to design the substructure.

-150 -120 -90 -60 -30 0 30 60 90 120 150 Displacement (mm)

-20

Horizontal force (kN)

RB1 RB2 RB3

-150 -120 -90 -60 -30 0 30 60 90 120 150 Displacement (mm)

-20

Horizontal force (kN)

PTFE1 PTFE2 PTFE3

(a) test frame (b) hysteresis loops in group1

(c) hysteresis loops in group2

Figure 5. Test setup of friction coefficient test

Pseudo-Dynamic Test (PDT)

In this study, pseudo dynamic tests are performed to simulate the friction under seismic wave. Test frame in Figure 6 is similar to that in the friction coefficient test in case1 to case6 (Chang et al., 2004), but with the new implementation of steel bars in case 7 to case 14(Chang and Chen, 2005), to represent the concrete shear keys. This frame is regarded as a single degree of freedom (SDOF) system with mass {M}, transmitted from vertical loads of two hydraulic jackets, damping force {C} taken value zero in the numerical model, and restoring force {R}, measured from the horizontal hydraulic jacket. To simulate the construction practices in most existing PCI-girder bridges in Taiwan, the test is divided by the boundary conditions: two-side-free for bearing placed directly between two substrate blocks (no any bolts on the upper or bottom face of the bearing), and one-side-free condition as used in the friction coefficient test. The diameter and yielding stress for each steel bar are 22mm and 274.68MPa, respectively. The gap spacing between steel bar and bearing pad is 40mm.

Newmark explicit integration algorithm is adapted to solve the equation of motion of this SDOF system. As regard to the input ground motions, acceleration record in TCU070 and EL-Centro are selected and adjusted to six PGA levels as shown in TABLE Ⅲ.

Figure 9 shows the test results. Obviously, only a few differences exist between

these two boundary conditions. That is, the friction coefficient used in the analytical model can be obtained directly from the friction coefficient test. For the case with same PGA, it is found bearing with PTFE is more likely to induce large displacement due to its low friction coefficient. In comparison with case 11 and 13, after installing the steel bars can reduce 50% displacement demand, for the reason of impact effect shown in

Figure 8

and Figure 10. The horizontal force turns to flat because bearings are sliding,

but impact force due to yielding at steel bar also provides additional force on the structure.

The test results are compared with the simulated results from an analytical model. In this model, bearing, steel bar, and gap are simulated by the nonlinear elements with appropriate material and section properties. Modification factor, say 0.8 to 0.85 for thicker bearing (case1 to 6, 38mm) and 0.9 to 0.95 for thinner bearing (case7 to 14, 25mm), about the nonlinear shear stiffness is needed to account for the warping effect (Figure 7) in large displacement of bearing. The friction coefficient is 0.205, 0.207, and 0.208, corresponding to the peak ground acceleration equals to 0.1g, 0.33g, and 0.4g.The friction coefficients for case 8 to 10 are 0.2988, 0.2407, and 0.1806; for case 12 to 14 are 0.1083, 0.0996 and 0.0902, respectively. In Figure 11, the propose analysis model can well predict the maximum displacement after bearings are sliding. It’s important to get this information and satisfies the support seat length in bridge design.

Table Ⅲ. EXPERIMENTAL CASES IN PSEUDO-DYNAMIC TEST Case Bearing type Name Input

ground motion PGA (gal) Steel bar Boundary condition

1 1F-010 98.1

2 1F-033 324

3 1F-040 392

one-side-free

4 2F-010 98.1

5 2F-033 324

6

RB

2F-040

TCU070

392

w/o

two-side-free

7 RB 500 w/o

8 RB-BAR1 300

9 RB-BAR2 500

10

RB

RB-BAR3 800 w/

11 PTFE 500 w/o

12 PTFE-BAR1 300

13 PTFE-BAR2 500

14

PTFE-RB

PTFE-BAR3

EL-Centro

800

w/

two-side-free

Figure 6. Test frame of the PDT Figure 7. Warping of the bearing Figure 8. Impact of the steel bar

0 10 20 30 40 50 60 70 80 90 Time (second)

-40

Displacement (mm)

Pseudo dynamic test _0.1g Test result (One-side-free) Test result (Two-side-free) Analytical result

0 10 20 30 40 50 60 70 80 90

Time (second) -100

Displacement (mm)

Pseudo dynamic test _0.33g Test result (One-side-free) Test result (Two-side-free) Analytical result

0 10 20 30 40 50 60 70 80 90

Time (second) -100

Displacement (mm)

Pseudo dynamic test _0.4g Test result (One-side-free) Test result (Two-side-free) Analytical result

(a) case1 and 4 (b) case2 and 5 (c) case3 and 6 Figure 9. Test and analytical results in the PDT (case1 to 6 )

-120 -90 -60 -30 0 30 60 90 120

Displacement (mm) -20

Horizontal force (kN)

Pseudo-dynamic test RB PTFE

-120 -90 -60 -30 0 30 60 90 120

Displacement (mm) -20

Horizontal force (kN)

Pseudo-dynamic test RB-BAR2 PTFE-BAR2

-120 -90 -60 -30 0 30 60 90 120

Displacement (mm) -20

Horizontal force (kN)

Pseudo-dynamic test RB-BAR3 PTFE-BAR3

(a) case7 and 11 (b) case 9 and 13 (c) case 10 & 14 Figure 10. Hysteresis curves in the PDT (case 7 to 14)

0 2 4 6 8 10 12 14 16

Time (second) -120

Displacement (mm) Experiment result

Analysis result

0 2 4 6 8 10 12 14 16

Time (second) -120

Displacement (mm)

Experiment result Analysis result

(a) case11 (PGA=500gal, w/o steel bar) (b) csse13 (PGA=500gal, w/ steel bar) Figure 11. Analysis results in the PDT

Shaking Table Test

Shaking table test was carried out in 2005 and 2006 to get realistic dynamic performance from two scale-down simply-supported bridge models, as shown in Figure

12 and Figure 14.

For the one-span bridge model (Chang and Chen, 2005), the superstructure consists of two girders and four diaphragms, supported by two CFT columns. PTFE-rubber bearings are placed on one column top to simulate the roller support, while the other column is equipped with rubber bearing as the hinge support. In addition, two steel bars representing a stopper are placed in front of the end-diaphragm about 20 to 25mm. The input ground motion is EL-Centro with its PGA ranges from 100 to 900 gal. Figure 12(b) shows the test results. With its low friction coefficient, PTFE-rubber bearing is more likely to slide than the rubber bearing since small PGA, and transfer little shear force to the column. However, the extensive large displacement resulted from the small friction force should be limited. After installing steel bars, in Figure

12(c), the distribution of

girder displacement has a turning point around 500 or 600gal. Though impact force on the steel bars will cause permanent displacement, they are capable of prohibiting superstructure from unseating in large earthquake event. Figure

13 shows the analysis

results when PGA equals 700 gal. Similar trend can be found from pseudo-dynamic test.

The prediction of maximum displacement is better than the residual displacement.

However, both velocity and acceleration results well satisfy the experiment results.

Two-span bridge model is similar to the previous one except of using shorter span of girders supported by three steel bents. Figure 14 shows the test specimen. Bent1 and bent3 are equipped with rubber and PTFE-rubber bearing, respectively. Only at bent2 can find both two types of bearings. The influence of using different kinds of bearings and distribution of superstructure weight can be found in Figure 14(b). The vertical axis represents the maximum strain on the side surface at the bottom end. Clearly, bent2 carries more weight and takes higher shear force than bent1 and bent3 does, phenomenon that gives highest values. On the other hand, the strain on bent3 is the lowest among three because of the PTFE-rubber bearing used as a roller bearing. When PGA level is greater than 400gal, there is a plateau in black line. As regard to the bent1, the stain distribution is linear, that is, the rubber bearing may stick to the concrete pad without any sliding even the PGA is 700gal. Other than that, both strains in bent1 and bent3 are almost the same under small PGAs. Figure

14(c) shows the analysis results

when PGA equals 700 gal. The prediction of maximum displacement is better than the residual displacement.

0 200 400 600 800 1000 Peak ground acceleration (gal) 0

Strain on the bottom column surface

PTFE bearing Rubber bearing

0 200 400 600 800 1000

Peak ground acceleration (gal) 0

Girder displacement (mm)

Without steel bar With steel bar

(a) test frame (b) strain on the columns (c) girder displacement Figure 12. shaking table test of the scaled-down one-span bridge

0 4 8 12 16 20

Time (second) -40

Girder displacement (mm)

Experiment result Analysis result

0 4 8 12 16 20

Time (second) -40

Girder velovity (cm/sec)

Experiment result Analysis result

0 4 8 12 16 20

Time (second) -500

Girder acceleration (cm^2/sec)

Experiment result Analysis result

(a) displacement (b) velocity (c) acceleration

Figure 13. Analysis results of girder (EL CENTRO, X=700gal, Z=100gal, with steel bar)

0.0 0.2 0.4 0.6 0.8

Peak ground acceleration (g) 0

Time (second) -20

Girder displacement (mm)

Experiment result Analysis result

Input ground motion: EL-centro PGA = 700gal

(a) test specimen (b) strain distribution (c) girder displacement Figure 14. shaking table test of the scaled-down two-span bridge

PROPOSED SIMPLIFIED SEISMIC EVALUATION METHOD

A simplified seismic evaluation method (Liu et al., 2006) to estimate maximum displacement on the girder is proposed in this paper based on the experiment results described above and Capacity-Spectrum Method (CSM) in ATC-40. The accuracy of the proposed method is also verified through the nonlinear dynamic analysis.

Seismic Demands

Total of seven ground acceleration records are chosen from Chi-Chi earthquake, and made them compatible with the design response spectrum in the draft Seismic Design Provision and Commentary for Highway Bridges in Taiwan, with PGA equals to 0.28g and 0.36g, corresponding to design level (DE) and maximum considerable earthquake (MCE) level, respectively.

TABLE Ⅳ. BASIC PARAMATERS FOR STRONG GROUND MOTION STATIONS

N

A

N

V

Strong ground motion stations S

SD

S

1D

F

a

F

v

DE MCE DE MCE TCU059, TCU061, TCU072, TCU074,

TCU078, TCU079,TCU109 0.7 0.4 1.0 1.3 1.0 1.0 1.0 1.0

Structural Capacity

The pushover curve which combines the friction and hinge mechanism is generated first and is transferred to the capacity spectrum later. Figure

15 shows the analytical

bridge model, a two-degrees-of-freedom system, in which the bearing is moveable controlled by the friction force, and the column hinge follows the pivot hysteresis rule that defines the strength degradation, stiffness reduction, and pinching effect. Moreover, to find the maximum displacement, the bearing is sliding without the presence of any displacement-restrained device. The friction coefficient is assumed 0.2. The fundamental period of this model is 1.168sec. Because friction force is smaller than the column yielding force, the pushover curve tends to be an elastic-perfect-plastic curve.

Figure 15. Analytical model for NDA

Nonlinear Dynamic Analysis (NDA)

Total of 14 cases in two PGA levels are analyzed. For each PGA level, the mean value shown in Table Ⅴ about the maximum displacement on the girder from seven nonlinear cases is used as a reference to compare the results from proposed method.

Proposed Equivalent Friction Damping

Currently, the equivalent damping model in the CSM represents the energy dissipation ability resulted from the yielding of structure members. For rubber bearing, an approach is developed to determine equivalent friction damping

β

_fri. Once the pushover curve of the bridge is governed by the friction force, ideally, the base shear is unchanged as top displacement increase. Therefore, according to the definition of equivalent damping, the expression can be simplified in the ADRS format, resulting in a equation which is only a displacement-related function. The unknown variables are displacements at yielding

d and performance point

_y

d . The total effective damping

_p

β

_eff

is sum of inherent damping

β

_fri, 5% for instance, and the friction damping in Equ 1. The spectrum reduction factors are shown in Equ 2 and 3 according to the regression analysis of data in Chi-Chi Earthquake.

( ) ( )

Estimation of the Performance Point

Table Ⅴand Figure 16show the numerical results by the proposed simplified seismic

evaluation method and nonlinear dynamic analysis (NDA). The propose method predicts the displacement demand with good accuracy, of which the difference in smaller than 5%. It is useful to determine the unseating length for the superstructure.

TABLE Ⅴ ANALYTICAL RESULTS IN THE NDA AND CSM

LONGITUDINAL DIRECTION

Displacement

(mean value) Displacement Difference Difference percentage

Equivalent damping NDA Proposed method (friction coefficient = 0.2)

Earthquake

level m m m % %

DE (0.28g) 0.1306 0.1307 0.0001 0.10 35.65 MCE (0.36g) 0.1745 0.1659 -0.0086 -4.91 44.03

TRANSVERSE DIRECTION Earthquake

level NDA Proposed method (Gap spacing = 0.2m)

DE (0.28g) 0.1306 0.1306 0 0 39.16

Demand spectrum - 5% damping Demand spectrum - 35.65% damping Capacity spectrum

Nonlinear dynamic analysis result

0.0

Demand spectrum - 5% damping Demand spectrum - 39.16% damping Capacity spectrum

Nonlinear dynamic analysis result

(a) DE level in the longitudinal direction (b) DE level in the transverse direction Figure 16 Analysis results of the proposed CSM method compared with NDA

PARAMETRIC STUDY OF BRIDGE PERFORMANCE RETROFITTED BY UNSEATING PREVENTION DEVICES

The major parameters studied in this paper include the design force and gap spacing for restrainers or concrete shear key, with allowable column damage in terms of displacement ductility under near-fault type earthquake events (Liu and Chang, 2006).

As listed in Table Ⅵ, the parameters of the restrainers and shear key were varied in the case study to examine the sensitivity and effectiveness of these pounding mitigation measures. Figure 17 and Figure 18 show the definition of the gap spacing. The design strength for the restrainer was varied with a bearing reaction from 1.0μRd, 1.0Rd, to 1.5Rd. The design strength for the shear key was assigned from 1/4, 1/2, to 1 plastic shear force of the column.

TABLE Ⅵ PARAMATERS OF UNSEATING PREVENTION DEVICE

Figure 17 Definition of gap for restrainer Figure 18 Definition of gap for concrete shear key

INPUT GROUND MOTIONS

Total of 7 near-fault type acceleration records were selected as the input ground motions from Chi-Chi earthquake. Based on the draft for a bridge site located in central Taiwan, the peak ground acceleration of each seismic wave was adjusted to 0.36g for the DE and 0.45g for MCE. Numerical results use the average value from each group.

Modeling of the Bridge

A typical simply-supported PCI-girder bridge approximately 40m in length and 10m in width with weighing 777.6kN was chosen as the benchmark model. The piers were designed according to the 1983 AASHTO Specifications for Highway Bridges with assumed height of substructure, diameter, nominal design strengths of concrete,

Longitudinal direction Transverse direction

Restrainer Concrete shear key Concrete shear key

Tension strength gap spacing Shear strength gap spacing Shear strength gap spacing

No.

412.02 MPa, and 274.68 MPa, respectively. In this paper, a friction-pendulum model of the rubber bearings was adopted for the supports of the bridge both in the longitudinal and transverse directions. The friction coefficient μ is 0.2 with a modification factor of 0.85 for the nonlinear shear stiffness. A pivot moment hinge model for the bridge column can be determined by considering cracking, yielding, and the ultimate point on the moment-rotation curve. The length of the plastic hinge zone is about 1m. Unseating prevention devices were simulated as bilinear models. The fundamental period of the analysis model is 0.9862 second.

Effect of Restrainer in the Longitudinal Direction

Figure 19 shows the results of the numerical analyses. The definition of strain ratio is

the difference of maximum girder displacement and gap spacing, divided by the length of the restrainer. For steel type A36 used in the restrainer, the ultimate strain was about 2.45%. If the ratio was larger than this limit, unseating or breaking of restrainers may happen when the impact force on the restrainer causes a large displacement, which exceeds its breaking strain. For the case in this study, the suitable combination was to use a gap spacing of 0.3m and a design force ratio of 1.0. Moreover, to ensure the safety, sufficient unseating length will be needed always.

Effect of Concrete Shear Key in the Transverse Direction

Concrete shear keys are usually installed in the transverse direction a short distance, say 2cm, to the girder and attached by rubber bumpers to absorb the impact force.

Clearly, in Figure 20, with shorter gap spacing or larger shear strength, the ductility demand of the column will increase. The proper combination can be determined while

Clearly, in Figure 20, with shorter gap spacing or larger shear strength, the ductility demand of the column will increase. The proper combination can be determined while

在文檔中 橋梁功能性支承系統耐震性能設計與評估補強方法之研究－總計畫暨子計畫:位移設計法於橋梁含功能性支承系統耐震性能設計方法之研究(III) (頁 176-195)