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http://www.iaeme.com/IJCIET/index.asp 1136 [email protected]
International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 5, May 2018, pp. 1136–1148, Article ID: IJCIET_09_05_127
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=5
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
INFLUENCE OF CABLE PROFILES ON THE
PERFORMANCE OF CABLE STAYED BRIDGE
Nithesh. K
Post-Graduate Student, Department of Civil Engineering, Manipal Institute of Technology,
Manipal Academy of Higher Education, Manipal, Karnataka, India
Kiran K. Shetty
Professor, Department of Civil Engineering, Manipal Institute of Technology, Manipal
Academy of Higher Education, Manipal, Karnataka, India
Premanand Shenoy
Managing Partner, Roy & Shenoy Consultancy, Mangalore, Karnataka, India
ABSTRACT
Cable stayed bridges have good stability, optimum use of structural materials,
aesthetic, relatively low design and maintenance costs, and efficient structural
characteristics. Therefore, this type of bridges is becoming more and more popular and
are usually preferred for long span crossings compared to suspension bridges. A cable
stayed bridge consists of one or more towers with cables supporting the bridge deck. In
terms of cable arrangements, the most common type of cable stayed bridges are fan,
harp, and semi fan bridges. Because of their large size and nonlinear structural
behavior, the analysis of these types of bridges is more complicated than conventional
bridges. In this Paper, detailed study of cable stayed bridge is carried out. The objective
of paper is to find the initial shape of cable stayed bridges under the action of dead load
of girders and pretension force in the inclined cable. All three types of longitudinal
arrangements are modeled in STAAD.PRO. These models are analyzed for various
loads as per the guidelines of Indian Road Congress. Finally, comparative study is
carried out for semi-fan, harp and fan type cable arrangements of Cable Stayed Bridge
in terms of cable force, axial force, shear force, bending moment, displacement to get
the efficient cable arrangement of Cable Stayed Bridge.
Key words: Cable Profile Arrangement, Semi-fan, Harp and Fan, Types of Pylon, Bay
length.
Cite this Article: Nithesh. K, Kiran K. Shetty and Premanand Shenoy, Influence of
Cable Profiles On The Performance of Cable Stayed Bridge, International Journal of
Civil Engineering and Technology, 9(5), 2018, pp. 1136–1148.
http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=5
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
http://www.iaeme.com/IJCIET/index.asp 1137 [email protected]
1. INTRODUCTION
A cable-stayed bridge has one or more pylons, from which cables support the bridge deck. A
distinctive features are the cables which run directly from the tower to the deck, normally
forming a fan-like pattern or a series of parallel lines. This is in contrast to the modern
suspension bridge, where the cables supporting the deck are suspended vertically from the main
cable, anchored at both ends of the bridge and running between the towers. The cable-stayed
bridge is optimal for spans longer than cantilever bridges, and shorter than suspension bridges.
This is the range where cantilever bridges would rapidly grow heavier if the span were
lengthened, while suspension bridge cabling would not be more economical if the span were
shortened.
During the past decade cable-stayed bridges have found wide application, especially in
Western Europe, and to a lesser extent in other parts of the world. The renewal of the cable-
stayed system in modern bridge engineering was due to the tendency of bridge engineers, to
obtain optimum structural performance from material which was in short supply during the
post-war years. Cable-stayed bridges are constructed along a structural system which comprises
an orthotropic deck and continuous girders which are supported by stays, i.e. inclined cables
passing over or attached to towers located at the main piers.
The idea of using cables to support bridge spans is by no means new, and a number of
examples of this type of construction were recorded a long time ago. Unfortunately, the system
in general met with little success, due to the fact that the statics were not fully understood and
that unsuitable materials such as bars and chains were used to form the inclined supports or
stays. Stays made in this manner could not be fully tensioned and in a slack condition allowed
large deformations of the deck before they could participate in taking the tensile loads for which
they were intended. Wide and successful application of cable-stayed systems was realized only
recently, with the introduction of high-strength steels, orthotropic type decks, development of
welding techniques and progress in structural analysis. The development and application of
electronic computers opened up new and practically unlimited possibilities for the exact
solution of these highly statically indeterminate systems and for precise static analysis of their
three-dimensional performance.
In the world, research is going on the torsional behavior, impact and stability analysis of
cable stayed bridges and also on the parametric study of cable stayed bridge with their optimal
design. Wang et al., (1993) has done work on initial shape of cable stayed bridges under the
action of dead load of girders and pretension in inclined cables. Also, parametric studies on
cable-stayed bridges are performed by Wang and Yang (1996) for investigating the individual
influence of different sources of nonlinearity in such bridges. Chena et al., (2000) calculated
the initial cable forces in a prestress concrete cable-stayed bridge for a vertical profile of deck
under its dead load by utilizing of idea of force equilibrium method. Mozosa and Aparicio
(2010) considered the limit state of failure in the design of cable stayed bridges to determine
the safe level.
There is huge potential in India also for the research work in cable stayed bridges. Agrawal
(1997) and Raheem et al., (2013) has done work on the parametric study of cable stayed bridge
for investigating the individual influence of different sources of nonlinearity. Nadkarni et al.,
(2015) performed parametric investigation on cable stayed bridge using macro based program.
These studies are still going out by taking various factors in the account to get best suitable
configuration.
In the present study, the focus is given on cable arrangements such as fan, harp, and semi
fan. To obtain the best suitable configuration of cable stayed bridge, cable forces are an
important task and plays a major role in the analysis and design of cable stayed bridges.
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
http://www.iaeme.com/IJCIET/index.asp 1138 [email protected]
1.1 Objective of the Study
The present study aim is to find the initial shape of cable stayed bridges under the action of
dead load of the girders and pretension force in the inclined cable. Also comparative study is
carried out for semi-fan, harp and fan type cable arrangements of Cable Stayed Bridge in terms
of cable force, axial force, shear force, bending moment, displacement to get the efficient cable
arrangement of Cable Stayed Bridge.
2. METHODOLOGY
In this paper analysis of two span double plane cable stayed bridge is performed. A complex
Structural linear analysis is carried out with the help of STAAD PRO software. For linear
analysis IRC class AA is considered as moving load on bridge.
2.1. Determination of Initial Cable Shape by Force Equilibrium Method.
In the force equilibrium method, the cable-stayed bridge is modeled as a planer structure. The
method works as an evolving substructure eventually comprising of the bridge deck and towers,
and searches for a set of cable forces which will give raise to desirable bending moments at
selected locations of the substructure. As the method works on the equilibrium forces rather
than deformation, there is no need to deal with non-linearity caused by cable sag and other
effects. First of all, certain sections of bridge deck and tower are chosen as control sections
where the bending moments are adjusted by varying the cable forces. To establish the design
bending moments, only the bridge deck is considered. All supports cables and towers are
replaced by rigid simple supports. The bending moments caused by dead load in the bridge deck
under such modified support conditions are taken to be the design bending moments. These
design bending moments are adopted because the effects of creep and shrinkage of concrete
tend to change the bending moments can be controlled at the same time, the scheme of initial
cable forces is reasonably stable.
The cable forces are taken as independent variables for adjustment of bending moments at
the control sections. Normally the bending moment at each deck section where a cable is
anchored is treated as a control parameter. It should be pointed out that wherever a model
consists of a back-stay anchored at the deck above an end pier, where the deck carries no
bending moment, the corresponding cable force can be treated as an additional variable to
improve the structural efficiency further. For example, the bending moment at the deck-tower
junction or that at the tower base may be taken to be an additional control parameter as they are
critical sections affecting the long term behavior. The target bending moments at the deck
sections are those obtained and the target bending moment at the chosen tower section is
normally set as zero.
2.2. Analysis of Cable Stayed Bridge Using Staad Pro
Analysis of cable-stayed bridge can be done in many methods. Here we have considered most
conventional method of analysis as influence line diagram method. In this method we first
consider cable stayed as planer structure as in force equilibrium method. After that all cable
connections are replaced by roller supports and vertical deflections at these control sections are
considered as zero.
Following steps involved in analysis of cable stayed bridge by influence line diagram;-
• First choose symmetric cable stayed arrangement.
• Consider one of the symmetric sections of the bridge.
• Model it as planner structure as force equilibrium method.
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
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• Replace connections with roller supports.
• Consider supports as control section as displacement at these points in vertical direction is zero.
• Beams with roller supports are constructed in STAAD Pro
• By applying loads (equivalent uniformly distributed force of self weight of slab cross girder
longitudinal girder) we can get reactions and bending moments at each support.
• By defining a load car in STAAD Pro and moving it along the model constructed earlier we can
get reactions and bending moments.
• Once we know the reactions it is resolved into components to get forces in cables and
compression in the deck.
2.3. Problem Statement
For a present study, a two-span cable stayed is considered. The total span of bridge is 70 m with
a side span of 35 m. Total height of pylon is 28 m, height of pylon above deck is 20 m and
below deck is 8 m. Girder Consist of bay length of 3.5m.
2.4. Types of Model Considered For Study
There are 3 models which are considered for the present study.
1. Model 1: Semi fan type arrangement of Cable Stayed Bridge
2. Model 2: Harp type arrangement of Cable Stayed Bridge
3. Model 3: Fan type arrangement of Cable Stayed Bridge
Figure 1 Semi fan type arrangement of CSB with 3.5 m bay span
Figure 2 Harp type arrangement of CSB with 3.5 m bay span
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
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Figure 3 Fan type arrangement of CSB with 3.5 m bay span
3. RESULTS AND DISCUSSION
The linear analysis is carried out to analyze the present study models under IRC 6(2014) loads.
The results are compared in terms of:
• Initial Cable force (Due to dead load)
• Final Cable force (Due to Combination of Loads)
• Axial force
• Shear force
• Bending Moment
• Displacement
• Weight of cables
3.1. Initial Cable Force
Figure 4 Initial Cable Forces of CSB with 3.5m Bay Span
Figure 4 shows that the maximum initial cable forces are occurred in harp type of
arrangement i.e. 918.58 kN, followed by semi-fan and fan arrangement.
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
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3.2. Final Cable Force
Figure 5 shows the comparative study between semi-fan, harp and fan type of cable stayed
bridge in terms of cable forces, due to combination of loads i.e dead load and live load, which
are occurred in fan type of arrangement followed by semi-fan and harp type of arrangements.
The maximum cable force arrived in Harp type of cable stayed bridge is of 1832.57 kN,
followed by semi-fan and fan arrangement. Maximum Cable forces occurred in Harp type of
CSB which are 99.5% more than the initial forces.
Figure 5 Final Cable Forces of CSB with 3.5m Bay Span
3.3. Axial Forces in Deck Elements
Figure 6 Axial Forces in Deck Element of CSB with 3.5 m Bay Span
Figure 6 shows maximum axial forces generated in the deck elements of semi-fan, harp and
fan arrangement which are compressive in nature. The maximum axial force is occurred in harp
type of arrangement followed by semi-fan and fan. The axial forces of harp arrangement are
44.67% more than the semi-fan type arrangement and 71.27% more than the fan type of
arrangement of cable stayed bridge.
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
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3.4. Shear Forces in the Cable Stayed Bridge
Figure 7 shows the comparison between semi-fan, harp and fan type of cable stayed bridge in
term of shear force. The maximum shear force occurred in Harp type of cable stayed bridge.
Semi-fan and fan type has 4.5% and 6.03% lesser values than that of harp type.
Figure 7 Shear Force of CSB Structure with 3.5 m Baby span
3.5. Bending Moment in Deck
Figure 8 Bending Moment in Deck of CSB with 3.5 m Bay Span
Figure 8 shows the maximum sagging and hogging bending moments of deck. The sagging
bending moment is maximum in harp type of cable stayed bridge also the hogging bending
moment is maximum in Harp type of arrangement. Semi-fan has 0.67% and 15.93% lesser
values than maximum values of sagging and hogging bending moments.
3.6. Displacement in Deck
In terms of displacement of deck, the comparison is made between semi-fan, harp and fan type
of cable stayed bridge. Figure 9 shows the maximum displacement in the deck .The maximum
displacement of deck is occurred in harp type of cable stayed bridge. Semi-fan and fan type has
10.10% and 14.3% lesser values than that of harp type.
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
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Figure 9 Displacement in Deck of CSB with 3.5 m Bay Span
3.7. Cables weight
Figure 10 Total Weight of Cables
Figure 10 shows the variation of cable weight of semi-fan, harp and fan arrangement of
CSB where deck of bridges have different bay span. The maximum cable weight is occurred in
harp type of arrangement followed by fan and semi-fan for all values of bay span. The maximum
cable weight of harp arrangement are 7.48% more than the semi-fan type arrangement and
6.48% more than the fan type of arrangement of cable stayed bridge.
3.8. Fan type of cable stayed bridge with different bay span
Figure 11 & 12 shows the fan type of cable stayed bridge with different bay span which is
considered for the study. Initially we considered bridge girder with 3.5m bay span (Figure 3)
and further length of bay were increased from 3.5m to 5m then to 7m.
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
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Figure 11 Fan type arrangement of CSB with 5 m bay span
Figure 12 Fan type arrangement of CSB with 7 m bay span
3.9. Initial Cable Force
Figure 13 Initial Cable Forces of Fan type of CSB
Figure 13 shows that the variation of cable forces of the fan type of cable arrangement along
the length of the bridge with varying bay span. The maximum initial cable forces of fan type of
arrangement with 7m Bay span is 1557.105kN, followed by CSB with 5 m and 3.5m Bay Span.
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
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The maximum cable force decreases with increase in number of cables. It decreases by 83.14%
and 34.53% for 20 cables per plane as compare to 10 and 14 cables per plane.
3.10. Final Cable Force
Figure 14 Final Cable Forces of Fan type of CSB
Figure 14 shows the comparative study between fan type of cable stayed bridge in terms of
cable forces, due to combination of loads i.e dead load and live load, which are occurred in fan
type of arrangement. The maximum cable force arrived in Fan type of cable stayed bridge with
7m bay span is of 2488.274 kN, followed by bridge with 5m and 3.5m bay span. Maximum
Cable forces occurred in Fan type of CSB with 7m bay span, which are 59.80% more than the
initial forces.
3.11. Axial Forces in Deck Elements
Figure 15 Axial Forces in Deck Element of Fan type of CSB
Figure 15 shows maximum axial forces generated in the deck elements of fan type of
arrangement which are compressive in nature. The maximum axial force is occurred in fan type
of CSB with 3.5m bay span followed by 5m and 7m bay span. The maximum axial force in
girder increases with decrease in number of cables. It increases by 1.54% and 3.077% for 20
cables per plane compare to the 14 and 10 cables per plane.
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
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3.12. Shear Forces in the Cable Stayed Bridge
Figure 16 Shear Force of Fan type of CSB Structure
Figure 16 shows the variation of shear force of fan type of cable stayed bridge with different
bay span. The maximum shear force occurred in fan type of cable stayed bridge with 7m bay
span. The maximum shear force of the girder decreases with increase in number of cable. It
decreases by 23.20% and 55.28% for 20 cables per plane compare to 14 and 10 cables per plane.
3.13. Bending Moment in Deck
Figure 17 Bending Moment in Deck of Fan type of CSB
Figure 17 shows variation of bending moments of deck. The bending moment is maximum
in fan type of cable stayed bridge with 7m bay span. Fan type of cable stayed bridge with 5m
and 3.5m bay span has 14.97 and 21.59% lesser values than maximum values of bending
moments. Figure it shows that maximum bending moment in girder decreases with increase in
number of cables or decrease in bay length.
Influence of Cable Profiles On The Performance of Cable Stayed Bridge
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3.14. Displacement in Deck
Figure 18 Displacement in Deck of Fan type of CSB
In terms of displacement of girder, the comparison is made between fan type of cable stayed
bridge with different bay span. Figure 18 shows the maximum displacement in the deck .The
maximum displacement of girder is occurred in fan type of cable stayed bridge with 7m bay
span. The maximum deflection of the girder decreases with increase in number of cables. It
decreases by 2.294% and 2.55% for 20 cables per lane compare to 14 and 10 cables per lane.
4. CONCLUSION
From the results and discussion we have come to following conclusion.
• The engineering parameters like cable force, axial and shear force, bending moment which are
considered for the present study have the minimum values in case of fan type of cable stayed
bridge compare to harp and semi-fan type of cable stayed bridge. Thus, it can be concluded
that fan type of cable stayed bridge is most efficient structure than harp and fan type of cable
stayed bridge for shorter spans.
• As number of cables along the span increases, there is a decrease in maximum cable forces and
maximum bending moment in the girder. This leads to decrease in the weight of girder.
• As the number of cables increases along the length of the bridge, total weight of the cable
element increases. As a result of this the efficiency of cable stayed bridge depends on the type
of material used for the cable.
REFERENCES
[1] Wang, P. H., Tseng, T. C., and Yang, C. G. "Initial Shape of Cable-Stayed Bridges." Journal
of Computers and Structures, 41(1), 1993, pp. 111-123.
[2] Wang, P. H., and Yang, C. G. "Parametric Studies on Cable-Stayed Bridges." Journal of
Computers and Structures, 60(2), 1996, pp. 243-260.
[3] Chena, D. W., Au, F. T. K., Cheng, Y. S., Cheung, Y. K. , and Zheng, D. Y. "Determination
of Initial Cable Forces in Prestressed Concrete Cable- Stayed Bridges for Given Design
Deck Profiles using The Force Equilibrium Method." Journal of Computers and Structures,
74, 2000, pp. 1-9.
[4] Mozosa, C. M., and Aparicio, A. C. "Parametric Study on The Dynamic Response of Cable
Stayed Bridges to The Sudden Failure of A Stay; Part I: Bending Moment Acting On The
Nithesh. K, Kiran K. Shetty and Premanand Shenoy
http://www.iaeme.com/IJCIET/index.asp 1148 [email protected]
Deck; Part II: Bending Moment Acting On The Pylons And Stress Onthe Stays." Journal
of Engineering Structures, 32, 2010, pp. 3288-3312.
[5] Agrawal, A. P."Cable-Stayed Bridges-Parametric Study." Journal of Bridge Engineering,
American Society of Civil Engineers, 2(2), 1997, pp. 61-67.
[6] Raheem, S. E. A., Shafy, Y. A., Seed, F. K. A., and Ahmed, H. H. "Parametric Study on
Nonlinear Static Analysis of Cable Stayed Bridges." Journal of Engineering Sciences,
41(1), 2013.
[7] Nadkarni, P. R., Salunke, P. J., and Narkhede, T. N. "Parametric Investigation of Cable
Stayed Bridge Using Macro Based Program." International Journal of Research in
Engineering and Technology, 4(9), 2015, pp.207-210.