influence of cable profiles on the performance of …cable-stayed bridges are performed by wang and...

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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


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


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.



• 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



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.



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.



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.



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.



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.



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.



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.



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



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.

influence of cable profiles on the performance of …cable-stayed bridges are performed by wang and...

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