ANALYSIS OF ARCH BRIDGE - Malaysian Public Works...
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Transcript of ANALYSIS OF ARCH BRIDGE - Malaysian Public Works...
ANALYSIS OF ARCH BRIDGE
-PARAMETRIC STUDY
BY:
ATIKAH ZAKARIA @ Y A
GS 14394
A Project Report Submitted in Partial Fulfillment of the Requirements for the Degree
of Master of Science in Structural Engineering and Construction in the Department
of Civil Engineering
University Putra Malaysia
Serdang, Selangorl Malaysia
2005
ABSTRACT
TI1e objective of this work is to develop a method enabling the optimal design of arch
bridges based on their modal characteristics. The relationship between the span to
rise ratio (H), monolithically connected together at the crown of the arch (M) and
arrangement of column was investigated. Based on two-dimensional analvtical
models of parabolic reinforced concrete arch bridges. the behavior of the arch with
regards to uniform load as dead load, superimposed dead load and HA and HB 30
unit live load were studied.
The load response for moment capacities. shear forces and axial forces of the arch
bridge as a behavior characteristic will be compared. Application of ST AADtt'ro
software has been used to model the arch bridge based on actual data to investigate
the effects of the span to rise ratio (H), monolithically connected together at the
crown of the arch (M) and arrangement of column.
ABSTRAK
Objckt1 f kaj1an ini di lakukan adalah untuk mem bina satu n1odel mendapatkan
rekabentuk yang optimal bagi jambatan gerbang. ITubungan di antara nisbah panjang
rentang kepada tingg1 jambatan (H), panjang sambungan binaan bersama di puncak
gcrbang yang mana di bina di antara rasuk/papak dan gerbang (M) dan susunan tiang
di selidiki. Berdasarkan model dua-dimensi, kelak.ukan jambatan gerbang konkrit
berbentuk parabohk yang berteraskan beban yang dikenakan iaitu bcban mati. beban
hidup di kaji.
Tindak balas beban seperti moment lentur, daya ricih and daya dalaman digunakan
sebagai pengukur sifat-sifat jambatan gerbang. Aplikasi perisian STAAD!Pro telah
digunakan untuk pen1odelan rekabentuk jan1batan gerbang untuk menyelidiki kesan
kriteria scperti nisbah panjang rentang kepada tinggi jambatan (H), panjang
sambungan binaan bersama di puncak gerbang yang mana di bina di antara
rasuk/papak dan gcrbang (M) dan susunan tiang.
LIST OF TABLES
CHAPTER 1 -INTRODUCTION
Table 1.1 Span Length for Various Type of Superstructure
CHAPTER 2 - LITERATURE REVIEW
Table 2.1
Table 2.2
Existing Bridge
Construction Sequence
CHAPTER 3- METHODOLOGY
Table 3.1
Table 3.2
Loads to be Taken in Each Combination With
Appropriate yfl
Beam Properties and Manual Calculation
CHAPTER 4- ANALYSTS AND RESULT
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Typical Cross-section
Section Properties
Modeling Proposal
Summary of odes, Elements and Element Dimension
Summary of Maximum Bending Moment , Shear Forces,
and Axial Forces at Deck, Arch, At Crown and Spandrel
Column Due to Effect of Span to Rise Ratio (H)
Summary of Maximum Bending Moments, Shear Forces
and Axial Forces at Deck, Arch, At Crown and Spandrel
Column Due lo Effect of Monolithic Integration at Crown
to the Deck ystem (M)
Summary of Maximum Bending Moments, Shear Forces
and Axial Force at Deck, Arch, and at Crown Due to
Effect of Arrangement of Spandrel Co lumn
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LIST OF FIGURES
CHAPTER 2 - LITERATURE REVIEW
Figure 2.1(a)
Figure 2.1(b)
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5(a)
Figure 2.5(b)
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9(a)
Figure 2.9(b)
Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 2.16
Figure 2.17
Figure 2.18(a)
Figure 2.18(b)
Figure 2.19
Behavior of Beam 8
Behavior of Arch 8
Multiple Span 9
Lines of Stress in a Skew Arch Bridge 10
Type of Arch Bridge 12
Terminology for Arch Bridge 16
Element in Arch Bridge 16
Arrangement of Arch Abutment for an Inclined Roadway 20
Reaction at a Point in an Arch 22
Forces in Arch 22
Axial Strain 24
Arch Shortening 24
No~tion 26
Arch Shown in Two Halves 27
Two-hinged Arch 30
Three-hinged Arch 32
The Relationship Between Resonant Frequencies and pan 35
to Rise Ratio (H)
The Relationship Between Total Mas and Span to Ri e 35
Ratio (H)
Crown Design 38
a) Arch and girder fushed together monolithically
b) Arch and girder separate
c) Suggested crown arrangement when arch and girder
fu hcd together
Optimum Topologies of Arch Bridge (a) UDL;
(b) ombined UDL and Moving Load
Centering nder Construction
Arch Con truction Using Cable Supports
Timber Centering Construction
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Figure 2.20 Pylon and Melan Method
CHAPTER 3- METHODOLOGY
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5(a)
Figure 3.4
Displacement for Beam Element
Forces for Beam Element
Bending Moment Diagram
Shear Force Diagram
Two-dimen ional Model
Three-dimensional Model
CHAPTER 4 - ANALYSIS AND RESULT
Figure 4.1
Figure 4.2
Figure 4.3(a)
Figure 4.3(b)
Figure 4.3(c)
Figure 4.3(d)
Figure 4.3(e)
Figure 4.3(f)
Figure 4.3(g)
Figure 4.3(h)
Figure 4.3(i)
Side Ele ation and Cross-section of BRl
Modeling for Arch Bridge
Modeling for Bridge BRl With Span to Rise Ratio
(H)= 7 Merged at Crown (M) = J/3 and arrangement
of Spandrel Column (C) =2
Modeling for Span to Rise Ratio (H) = 6
Modeling for Span to Rise Ratio (H) = 5
Modeling for pan to Rise Ratio (H) = 4
Modeling for Distance of Merged at Crown Equal to
~ of Span
Modeling for Distance of Merged at Crown Equal to
1/5 of pan
Modeling for Distance of Merged at Crown qual to
1/6 of Span
Modeling for o1umn Only at Springing Lines
Modeling for 3 Spans Between The Main Columns
and Merged
Location of 1 nit Load
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Figure 4 .5 Influence Line of Bending Moment and Shear Force for 76
Figure 4 .6
Figure 4. 7(a)
ode 40
Diagram howing the Placement of H B Loading Axle
Bending Moment Diagram for Bridge BR 1
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Figure 4.7(b)
Figure 4.8(a)
Figure 4.8(b)
Figure 4.8(c)
Figure 4.8(d)
Figure 4.8(e)
figure 4.8(t)
Figure 4.9(a)
Figure 4.9(b)
Figure 4.9(c)
Figure 4.9(d)
Figure 4.9(e)
Figure 4.9(t)
Figure 4.10(a)
Figure 4.1 O(b)
Figure 4.1 0( c)
Figure 4.10(d)
Figure 4.11(a)
Figure 4.11 (b)
Figure 4.11(c)
Figure 4.11(d)
Figure 4.11(e)
Figure 4.11(t)
Figure 4. I I (g)
Figure 4.11 (h)
Figure 4.11 (i)
Figure 4.12 (a)
Figure 4.12 (b)
Figure 4.13
Shear Force Diagram for Bridge BRl
Bending Moment Diagram due to H = 6, M = 1/3
Shear Force Diagram due to H = 6, M = 1/3
Bending Moment Diagram due to H = 5, M = 1/3
Shear Force Diagram due to H = 5 M = 113
Bending Moment Diagram due to H = 4 M = 1/3
Shear Force Dia!,rram due to H = 4 M = 1/3
Bending Moment Diagram due to H = 7, M = 1/4
Shear Force Diagram due to H = 7, M = 1/4
Bending Moment Diagram due to H = 7, M = 1/5
Shear Force Diagram due to H = 7, M = 1/5
Bending Moment Diagram due to H = 7, M = 116
Shear Force Diagram due to H = 7, M = 1/6
Bending Moment Diagram due to H = 7, SC = 1
Shear Force Diagram due to H = 7, SC = I
Bending Moment Diagram due to H = 7, SC = 3
Shear Force Diagram due to H = 7, SC = 3
Bending Moment Diagram at Deck
Bending Moment Diagram at Arch
hear Force Diagram at Deck
hear Force iagram at rch
Axial Force Diagram at Deck
Axial Force Diagram at Arch
Bending Moment Diagram at Cl and C2
Shear Force Diagram at Cl and C2
Axial Force Diagram at Cl and C2
Ma imum Moment Capacity at Different pan to Rise
Ratio for Deck and Arch (refer Table 4.5)
Maximum hear force at Different pan toRi e Ratio for
Deck and Arch refer Table 4.5)
The Relation hip Between Ma imum Bending Moment
and pan to Rise Ratio (H) at pandrel Column (Refer to
Table 4.5)
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Figure 4.14 The Relationship Between Maximum Shear Force and 92
Span to Rise Ratio (H) at Spandrel Column (Refer to
Table 4.5)
Figure 4.15 The Relationship Between Maximum Axial Force and 94
Span to Rise Ratio (H) at Deck (Refer to Table 4.5)
Figure 4.16 The Relationship Between Maximum Axial Force and 95
Span to Rise Ratio (H) at Arch (Refer to Table 4.5)
Figure 4.17 The Relationship Between Maximum Axial Force and 95
Span to Rise Ratio (H) at Crown (Refer to Table 4.5)
Figure 4.18(a) Bending Moment Diagram at Deck 97
Figure 4.18(b) Bending Moment Diagram at Arch 98
Figure 4.18( c) Shear Force Diagram at Deck 99
Figure 4.18( d) Shear Force Diagram at Arch 100
Figure 4.18(e) Axial Force Diagram at Deck 101
Figure 4.18(f) Axial Force Diagram at Arch 102
figure 4.18(g) Bending Moment Diagram at C1 and C2 103
Figure 4.18(h) Shear Force Diagram at C1 and C2 103
Figure 4.18(i) Axial Force Diagram at C1 and C2 104
Figure 4.19(a) Maximum Moment Capacity at Deck 105
Figure 4.19(b) Maximum Moment Capacity at Arch 105
Figure 4.19(c) Maximum Moment Capacity at Crown 106
Figure 4.19(d): Maximum Moment Capacity at Column Cl And C2 106
Figure 4.20(a) Maximum hear Force at Deck 107
Figure 4.20(b) Maximum Shear Force at Arch 107
Figure 4.20(c) Maximum Shear Force at Crown 108
Figure 4.20(d) Maximum Shear Force at Column C1 109
Figure 4.21 (a) Maximum Axial Force at Deck 110
Figure 4.21 (b) Maximum xial Force at Arch 111
Figure 4.21(c) Maximum Axial Force at Crown 111
Figure 4.2l(d): Maximum Axial Force at Column C1 111
Figure 4.22(a) Bending Moment Diagram at Deck 113
Figure 4.22(b) Bending oment Diagram at Arch 114
Figure 4.22(c) hear For e Diagram at Deck 115
Figure 4.22( d) Shear Force Diagram at Arch 116
rigure 4.22( e) Axial Force Diagram at Deck 117
Figure 4.22(f) Axial Force Diagram at Arch 118
Figure 4.23(a)) Maximum Bending Moment at Deck 120
Figure 4.23(b) Maximum Bending Moment at Arch 120
Figure 4.23( c) Maximum Bending Moment at Crown 120
Figure 4.23(d) Maximum Shear Force at Deck 121
Figure 4.23(e) Maxirnum Shear Force at Arch 121
Figure 4.23(f) Maximum Axial Force at Deck 122
Figure 4.23(g) Maximum Axial Force at Arch 123
Figure 4.23(h) Maximum Axial Force at Crown 123
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
ABSTRACT
ABSTRAK
LIST OF TABLES
LIST OF FIGURES
TABLE OF CO TE TS
CHAPTER 1: INTRODUCTIO
1.1 Introduction
1.2 Problems tatement
1.3 Research Objecti e
1.4 Outline Methodology
1.5 Project Scope and Limitation
1.6 Organization of Report
CHAPTER 2: LITERATURE REVIEW
2.1
2.2
2.3
2.4
2.5
2.6
2 .7
Introduction
The Beha ior of Arch
Multiple pan Arch
Skew Arch Bridge
Type of rch
2.5.1 Hingele of Arch
2 .5.2 pandrel Arch
Element of Arch Bridge
2 .6.1 Terminology
2.6 .2 Arch Rib
2.6.3 Deck I Girder
2.6.4 pandrel Columns
2.6.5 Foundation I abutment
Analysis pect
2 .7.1 Fixed Arch
2.7. 1.1 Flexural Movements
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2.7.1.2 Axial Strains or Arch Shortening
2.7.1.3 Temperature Change
2.7.1.4 Effect of Shrinkage and Creep
2.7.l.S Analysis of Parabolic Fixed Arch
2.7.1.6 Elastic Center
2.7 .2 Two- hinged Arch
2.7.3 Three- hinged rch
Design Aspects
2. 8.1 Span to Rise Ratio (H)
2 .8.2 Arch Shape
2.8.3 Monolithic Integration at the Crown to the
Deck System (M)
2.8.4 Arrangement of Spandrel Columns
2.8 .5 End Condition
2.9 Method Of on truction
2.9.1 Centering
2.9 .2 Cantilever Launching
C~TER3:METHODOLOGY
3.1 Introduction
3.2 TheRe earch Study
3.3
3.4
3.2.1 Preliminary Study
3 .2.2 Desk Study
3.2.2. 1 Proposed Idealization for Element
Analysis of Data
3.3.1 Loadings
Calibration of Program
3.4.1 Beam Element and Truss Element
3.4.2 Compari on Between Manual Calculation and
ST D-pro
3.4.3 Two-dimensional Model
3.4.4 Comparison Between Two-dimensional With
Three-dimensional Model
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CHAPTER 4: ANALYSIS AND RESULT
4.1
4.2
4.3
4.4
Project Background
Modeling
4.2.1 Mathematic Modeling
4.2.2 Discretization
4.2.3 Loading
Result of Analy is
4 .3.1 Span toRi e Ratio (H)
4.3.2 Monolithic integration at the Crown to the
Deck System (M)
4 .3 .3 Arrangement of Spandrel Column
Result Comparison and Discussions
4.4.1 Span to Rise Ratio (H)
4.4.1 .1 Moment Capacity and Shear Force
4.4.1.2 Axial Force
4.4.2 Merged at Crown (M)
4.4.2.1 Moment Capacity and Shear Force
4.4 .2.2 Axial Force
4.4.3 Arrangement of Spandrel Column
CHAPTER 5: DISCUSSIO AND CONCLUSION
5.1 Introduction
5.2 Effect of pan to rise ratio (H)
5.3 Effect of Mer ed at rown (M)
5.4 Effect of Arrangement of Spandrel Column
5.5 Recommendation for Future Researches
REFERENCES
APPENDIX A
APPENDIXB
DESIG r CALCULATION
1 rp T DATA FOR STAAD-pro
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CHAPTER 1 -INTRODUCTION
1.1 Introduction
Bridge stn1cture can be classified as the structure that needs thorough design
consideration and constnlction skills. Tt requires a handful of knowledge, experiences
and engineering judgment in order to accomplish the mo t outstanding structure in
tenns of performance, economical durability and aesthetical. The quality of a bridge
can be measured by its success in sati fying the basic objectives, functional ,
stnlctural, economic and ae thetic. Efficient structural design may be expected to
reduce construction cost and maintenance costs. It also improved the functionality of
the bridge by relaxing feasibility constraints by increa ing the service life and by
avoiding interruption in traffic due to maintenance. Excellence in tructural design
is based on a sound knowledge of structural theory, imagination and courage in the
development of new ideas and willingness to benefit from the experience of others.
Traditionally, bridge structure ere designed based on engineering theories and
previous experience, which would involved the preliminary design, structural
analysis and check against strength/stiffness/stability requirements. This is followed
by design modification, re-analysis and re-checking. Undoubtedly, such design
process is expensive and time-consuming. With the rapid development of ad anced
computer technologies, sophisticated optimum design approaches have gained
increasing popularity in recent year a they can significantly impro e the efficiency
of a design. Engineers are often confronted with the problem of choosing the correct
structural dimensions consistent with a safe, cost-effective, aesthetically appealing
balanced design .
The selection of material and structural fom1 for the main superstructure is a complex
problem and can only be determined with regard to all factors affecting the design of
a pmiicular bridge. The choice is a function of the span. It is also influenced by the
quality and cost of materials foundation condition, height to deck surface and
constraints placed by the site on erection. From the practical view, the range of span
for variou · types of superstructures as show in table 1.0
Table 1.1 : Span Lenf,rths for Various Type of Superstructure
Structural Type Range of span(m)
Slab 0 -12 Pseudo slab 10-20 Reinforced beam + slab 15 - 30 Prestressed beam + slab 20-40 Reinforced box girder 30 - 50 Pre tressed box girder 30- 100 Cable stayed 90-290 Concrete arch 90 -300 Steel arch 100 - 500 Suspension 300- 1400
The search for structures which cover long spans and large areas without
intermediate support and which do so using a minimum of materials, has long
occupied the structural engineering profession. The concrete arch bridge one of the
solutions in that problem. Therefore the arch bridge b come popular and more
favour to construct because their plea ing appearance and aesthetic elegance and also
econom1c. conomic in arch design can be achieved mainly by choosing a curve for
the centre line of the rib such that the bending moments due to loading and changes
of temperature and shrinkage is minimum.
Arch bridges are one of the olde t types of bridges and have great natural strength.
Instead of pushing stra ight do> n the weight of an arch b1idge is carried outward
along the curve of the arch to the supports at each end.
In Malaysia, roadways are the most common modes of transportation. These are the
principal form of tTansportation compare to the water and air transport. It is natural
that new roadways and consequently new bridge are being built as part of
infrastructure development work. Based on data from JK.R, the longest steel arch
bridge in Malaysia is Sultan Iskandar Bridge, comprising of seven spans with a total
length of 284m. This bridge was constructed in 1932 and was repaired in 1985.
The historical bridge and know as The Merdeka Bridge to commemorate Malava·s
independence was constructed using tied arch bridge system. where the main
material are concrete. This bridge has 13 spans with total length of 273m and was
reconstructed around 1957 after bombed during the Second World War.
The famous arches bridge is located at Route Bl5 (called as Putrajaya Bridge BRl)
where is a part of upgrading of the route B 15, to allow traffic access between the
road of B 15 and the LD P. the SKVE and Putrajaya which were design based on fixed
system and justified to construct because of their superior aesthetic qualities. The
bridge was completed construct in 1999 and will be chosen as a studying parameter
in this project.
