The MP and VP are used to check the foundation base shown in Figure 4-3.
Herein because MPO, equal to 1.3M (n 1.376025=98833kNm), is more than M (87320P kN m), the further evaluation for foundation is not required.
6 CONCLUSION
Seismic effect is a very complex and specific activity for design of bridge structures and other architecture structures. In Taiwan, the study of seismic design code and technology are not as early as in the United States and Japan but the study has been advanced recently due to the special geographic location of Taiwan. Especially after the Chi-Chi earthquake, the bridge design requirements become more rigid to cater for seismic scenario. On the other hand, for the safety of existing bridges, a pragmatic economical evaluation approach is mandatory. This study tries to explore the SDSHB 2000 with viewpoint from the displacement-based ductility to establish an economical procedure to assess the existing bridges at Taiwan.
(a) SDSHB 2000 requires designer to consider the effect of vertical seismic force, which is one of the major design parameters for the calculation of plastic moment. However, the definition is ambiguous on the component associated with the vertical seismic force and the situation that requires to be undertaken. As the result, all design will have to consider the vertical seismic force. Furthermore, it is an uneconomical construction so a clear definition about the requirement for vertical seismic force demand is necessary.
(b) The material properties used for the nominal design strength to evaluate the existing bridge are conservative. They will result in the actual strength capacity of existing pier stronger than the design capacity. The plastic hinge can not serve its protection function when the earthquake occurs. Therefore, an expected material property is employed to evaluate the component capacity instead of material nominal property.
On the other hand, for the evaluation of existing bridges, it is strongly recommended to adopt the actual material test data of bridge on site.
Thus the evaluation result can be more accurate.
(c) In ductility design, the moment capacity of plastic hinge is a major element. It is suggested to calculate the plastic moment via the moment-curvature analysis associated with the definition of material strain. Thus the capacity of plastic moment can be accurately estimated under the ductility requirement.
(d) Although the expected material properties are recommended for evaluating the moment capacity, it is suggested to calculate the shear
capacity conservatively with the nominal design material strength to prevent the shear damage during the performance of plastic hinge.
(e) The bearing assembly is allowable as a fuse in the study. Nevertheless the displacement of bearing must be limited to prevent loss of span.
Despite the fusing activity can effectively reduce the force demand for the substructure, some technical conditions need to verify before to launch the actual evaluation.
i. The actual ultimate force capacity of bearing.
ii. The friction coefficient for sliding
(f) The purpose of study is to evaluate the existing bridge at Taiwan to make sure it is safe for operation. The evaluation result reveals that under the new seismic demand, the existing bridge structures probably can be considered as safety with the displacement ductility analysis.
Hence the effect of the displacement ductility should be considered when the seismic design code in Taiwan is modified in future.
7 REFERENCE DOUCUMENTS
(1) Design Specification for Highway Bridges, Ministry of Transportation and Communications, 1987.
(2) Seismic Design Specification for Highway Bridges, Ministry of Transportation and Communications, 1995.
(3) Seismic Design Specification for Highway Bridges, Ministry of Transportation and Communications Revised Edition, 2000
(4) Jun-Shian,Wu, ”Effect of Vertical Earthquake on Seismic Analysis and Design of Bridge, NTU Master Degree，1996.
(5) Caltrans Seismic Design Criteria Version 1.2, California Department of Transportation, 2001.
(6) 20-1 Seismic Design Methodology, California Department of Transportation, 1999.
(7) Mander, Priestley, Park, “Theoretical Stress- Strain Model for Confined Concrete”, J. Struct. Eng., ASCE, 1988.
(8) Mander, J. B., M. J. N. Priestley, and R. Park,“Observed Stress-Strain Behavior of Confined Concrete,” Journal of the Structural Division, ASCE, 1988.
(9) Silva, P., Megally, S., and Seible, F., “Seismic Performance of Sacrificial Shear Keys,” Western Bridge Conference, 2002.
(10) Priestley, M. J. N., F. Seible, G. M. Calvi, Seismic Design and Retrofit of Bridges, John Wiley & Sons, Inc. 1996.
(11) Comprehensive Specification for the Seismic Design of Bridges, Nation Cooperative Highway Research Program (NCHRP) Project 12-49, 2001.
(12) Blume, J.A.,N.M. Newmark, and L.H.Corning, “Design of Multistory Reinforced Concrete Building for Earthquake Motion”, Portland Cement Association , Chicago, 1961.
(13) Housner, G.W., “The Continuing Challenge - The Northridge Earthquake of January 17,1994, (Report to Director, California Department of Transportation)”, Sacramento, California, 1994.
(14) Report No.SSRP-99/08, ”Performance Library of Concrete Bridge Components, Sub-assemblies, and System under Seismic Loads”, University of California, San Diego, 1999.
(15) BART Seismic Retrofit Program – Design Criteria, San Francisco Bay Area Rapid Transit District, 2002.
(16) Center for Research on Earthquake Engineering, “Seismic safety Assessment and Retrofit Specification for Telecommunication and Transportation”, CEER-R85-01, 1996.
(17) Central Geological Survey, MOEA, Active Technical Research – Active Fault Map, 2004.
(18) Zheng-Mu Lin, “An Investigation on Seismic Evaluation of Performance-Based Design for RC Structure, CYU, 2003.
(19) Dowell, R.K., and Hines, E.M., “Plastic Hinge Length of Reinforced Concrete Bridge Columns,” Proceedings of the Third National Seismic Conference and Workshop on Bridges and Buildings, 2002.
(20) Seyed-Mahan, M., 1996, Procedures in Seismic Analysis and Design of Bridge Structures, release II draft, Caltrans Division of Structures.
California Department of Transportation, Sacramento, California.
(21) Nadim I. Wehbe, M. Saiidi and David H. Sanders, “Confinement of Rectangular Bridge Columns for Moderate Seismic Areas”, MCEER Bulletin, Vol. 12, No. 1, 1998.
(22) Directorate General of Highway, MOTC, Bridge Investigation Report for 921 Chi-Chi Earthquake, Taiwan, 1999.Priestley, M. J. N., R.
Verma, and Y. Xiao, “Seismic Shear Strength of Reinforced Concrete Columns,” Journal of Structural Engineering, ASCE, Vol. 120, No. 8, pp. 2310-2329, 1994.
(23) Thomas R. Cooper, Joseph I. Showers, “Strategies For Developing a High Performance Structure With Typical Bridge Design Features on a Design-Build Project”, Legacy Parkway Seismic Design, Parsons Brinckerhoff, 2002.
Appendix A: Figure
Figure 2-1 : Design Ground Acceleration Coefficient Zone - 1995
Figure 2-2 : Difference on Seismic Zone
Figure 2-3 : Axial Force-Moment Curve
Moment
A x ia l F o rc e
φMn Mn Pn
φPn
0.1Ag fc'
Figure 3-1a : Displacement Demand of Fixed footing
Figure 3-1b : Displacement Demand of Foundation Flexibility
Figure 3-2 : Steel Stress-Strain Model
Figure 3-3 : Concrete Stress-Strain Model
Figure 3-4 : Moment Curvature Curve
Figure 3-5 : Equivalent Static Vertical Loads & Moments
Figure 4-1 : Distribution of Taiwan Faults
Figure 4-2 : Effective Stiffness of Reinforced Concrete Section
Figure 4-3 : Displacement Performance for Pier
Figure 4-4 : Elevation of Bridge in the Transverse Direction
M s
Figure 4-5 : Foundation Force Equilibrium
Figure 4-6 : Moment Curvature Curve for Bilinear Response
φP
Figure 4-7 : Fuse Performance of Bearing Displacement
Force
FF
FS
FF= Ultimate capacity of bearing
FS= Frictional sliding force of bearing (interface friction force)
Figure 4-8 : Moment-Curvature Analysis of Column Section
Figure 4-9 : Moment-Curvature Analysis with Various Axial Forces
0 20000 40000 60000 80000 100000 120000 140000
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02
Curvature (1/m)
Moment(kN-m)
P=0 kN P=20000 kN P= 40000 kN P=60000 kN P=80000 kN
Figure 5-1 : Stress-Strain Diagram of Unconfined Concrete
Figure 5-2 : Stress-Strain Diagram of Confined Concrete
(0.014)
Figure 5-3 : Stress-Strain Diagram of Reinforce Steel
Figure 5-4 : Cross Section of Pier
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02
Curvature (1/m)
M o m en t (k N -m )
Figure 5-5 : Moment-Curvature Curve
Figure 5-6 : Force Displacement by Substitute Structure Analysis Diagram
A
yi0 2000 4000 6000 8000 10000 12000
0 20 40 60 80 100 120 140 160
displacement (mm)
Force(KN)
( Δyi=55) (ΔD=90) (ΔA=148)
(Fyi=8290) (FA=8735)
Appendix B: Table
Table 2-1 : Horizontal Normalised Acceleration Response Spectrum Coefficient for Different Soil and period
C
Period Short Period Moderate Period Long Period
Type III T<0.03sec 1.0
Taipei Basin T<0.03sec 1.0
Table 2-2 : Vertical Normalised Acceleration Response Spectrum Coefficient for Different Soil and period
C
Period Short Period Moderate Period Long Period
Type I T<0.03sec 1.0
Type II T<0.03sec 1.0
Table 2-3 : Property Factor of Structure System, R*
Type Substructure R*
1 Wall-Type Pier 2
2 Single Pier 3
3 Multiple Pier Frame 5
4
RC Pile-Type Pier : Vertical Pile
Inclined Pile
3 2 5
Steel Pile/ Steel-Concrete Pile : Vertical Pile
Inclined Pile
5 3
Table 4-1 : Seismic Performance Criteria of Bridge Issued by SSRP-99/08,UCSD.
I No Barely visible
Cracking No Repair Fully Operation Onset of hairline cracks Elastic, <1
II Minor Cracking Possible
Repair Operation
Theoretical first yield of Longitudinal
reinforcement
1 to 2
III Moderate Open Cracking Onset of Spalling
Minimum
Repair Life safety
Initiation of inelastic deformation, Onset of concrete spalling
Development of Diagonal cracks
2 to 4
IV Major
Very wide cracks extended concrete spalling
Repair Near Collapse
Wide Crack
widths/spalling over Full location mechanism region
4 to 8
V Local Failure /Collapse
Bucking of main
reinforcement Rupture of transverse reinforcement
>8
Table 4-2 : Comparison of column response of fused vs. non-isolated strategies for a typical bent of a multi-span, multi-column structure on the Legacy Parkway Project.
Non-Fused Fused Bearings
Bearing properties Pinned Fuse at 40%g
Governing Column Moment demands (kips-ft)
38,000 8400
Column Plastic Moment Capacity (1.5% rebar, Kips-ft)
13249 13249
Foundation Size (footing, no. of piles) Seismic Load Design
21.3‘ x 21.3‘
25-150 Ton Piles
20’x 20’
12-150 Ton Piles Foundation Size (footing, no. of 150
ton piles)
Service Load Design
18’x 18’
8-150 Ton Piles
18’x 18’
8-150 Ton Piles
Table 5-1 : Data of Moment Curvature
Confined Concrete
Strain Steel Strain Mxx Kxx
No.
strain strain kN-m 1/m
1 -7.59E-05 0 0 -8.98E-21
2 -3.67E-04 3.44E-04 1.92E+04 2.53E-04
3 -5.93E-04 8.30E-04 3.01E+04 5.06E-04
4 -8.10E-04 1.33E-03 4.05E+04 7.59E-04
5 -1.03E-03 1.82E-03 5.06E+04 1.01E-03
6 -1.25E-03 2.31E-03 6.04E+04 1.27E-03
7 -1.45E-03 2.82E-03 6.65E+04 1.52E-03
8 -1.62E-03 3.36E-03 7.02E+04 1.77E-03
9 -1.78E-03 3.91E-03 7.28E+04 2.02E-03
10 -1.94E-03 4.47E-03 7.47E+04 2.28E-03
11 -2.09E-03 5.03E-03 7.62E+04 2.53E-03
12 -2.65E-03 7.14E-03 7.96E+04 3.48E-03
13 -3.20E-03 9.26E-03 8.10E+04 4.43E-03
14 -3.75E-03 1.14E-02 8.17E+04 5.38E-03
15 -4.30E-03 1.35E-02 8.24E+04 6.33E-03
16 -4.86E-03 1.56E-02 8.32E+04 7.28E-03
17 -5.42E-03 1.77E-02 8.41E+04 8.23E-03
18 -5.99E-03 1.98E-02 8.50E+04 9.18E-03
19 -6.55E-03 2.19E-02 8.59E+04 1.01E-02
20 -7.13E-03 2.40E-02 8.67E+04 1.11E-02
21 -7.72E-03 2.61E-02 8.75E+04 1.20E-02
22 -8.31E-03 2.82E-02 8.83E+04 1.30E-02
23 -8.91E-03 3.03E-02 8.90E+04 1.39E-02
24 -9.52E-03 3.23E-02 8.97E+04 1.49E-02
25 -1.01E-02 3.44E-02 9.04E+04 1.58E-02
26 -1.08E-02 3.64E-02 9.10E+04 1.68E-02
27 -1.14E-02 3.85E-02 9.16E+04 1.77E-02
28 -1.20E-02 4.05E-02 9.22E+04 1.87E-02
29 -1.27E-02 4.25E-02 9.28E+04 1.96E-02
30 -1.33E-02 4.46E-02 9.33E+04 2.06E-02
31 -1.40E-02 4.66E-02 9.38E+04 2.15E-02
Table 5-2 : Data of Substitute Structure Analysis
No. 1 2 3 4 5 6 7 8
Force(kN) 9795 9511 9072 8910 8755 8607 8607 8607 Δ (mm)
65 74 80 85 88 89 90 90
K(kN/m) 150730 128270 113260 105120 99220 96000 94970 93970
T(S) 0.68 0.73 0.75 0.77 0.79 0.79 0.79 0.79