ERECTION STAGE DYNAM IC BEHAVIOR OF CABLE STAYED …d.researchbib.com/f/6nnJSyoJHhL29gY01up3EypxSxoJyhY0ciqKWhLJksqKOfo… · International Journal of Civil Engineering and Technology

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International Journal of Civil Engineering and Technology (IJCIET)Volume 8, Issue 4, April 2017, pp.

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ISSN Print: 0976-6308 and ISSN Online: 0976

© IAEME Publication

ERECTION STAGE DYNAM

CABLE STAYED BRIDGE

CONSTRUCTION STAGE A

M. Tech. Structural Engg, SCALE,

VIT University,Vellore,Tamil Nadu, India

Professor, Department of Civil and Structural Engg, SCALE,

VIT University, Vellore, Tamil Nadu, India

Senior Technical Manager, Mida

ABSTRACT

There are various means and methods available in the construction industry for

the erection of bridges. The Cantilever Method is the most widely used erection

method for the construction of the cable stayed brid

analysis, the geometrical and boundary changes as well as the material properties

changes must be considered. However, considerable stresses are produced due to the

construction loads in the continuous structure. To determi

forces, the initial equilibrium state for dead load at the final stage must be determined

first. However, in order to obtain the desired cable force which satisfies the suitable

range of displacement and member forces, the enginee

numerous trial & error procedures. To find the cable pretension loads, the unit load

method is used in this study. For verification, the Finite Element software (Midas

Civil) is used to determine the cable forces using the functio

Also the construction stage analysis for the cable stayed bridge is explained using

software. Various parameters are influenced on the cable forces as well as pylon

forces. These are back span to main span ratio

Geometry, Cable system arrangements are varied, results are validated and all the

details are given in this paper.

Key words: Cable forces, Unknown Load Factor,

IJCIET/index.asp 252 [email protected]

International Journal of Civil Engineering and Technology (IJCIET) 2017, pp. 252–264 Article ID: IJCIET_08_04_032

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=3

6308 and ISSN Online: 0976-6316

Scopus Indexed

ERECTION STAGE DYNAMIC BEHAVIOR

CABLE STAYED BRIDGE USING

CONSTRUCTION STAGE ANALYSIS

Prataprao Jadhav

M. Tech. Structural Engg, SCALE,

VIT University,Vellore,Tamil Nadu, India.

Dr. G. Mohan Ganesh


VIT University, Vellore, Tamil Nadu, India.

Vinayagamoorthy M.

Senior Technical Manager, Midas IT, Mumbai, Maharashtra, India,



method for the construction of the cable stayed bridges. For this type of structural



construction loads in the continuous structure. To determine the cable installation



range of displacement and member forces, the engineers need to go through the



Civil) is used to determine the cable forces using the function Unknown Load Factor.



back span to main span ratio, pylon height to deck span ratio,


details are given in this paper.

Cable forces, Unknown Load Factor, Construction stage Analysis

[email protected]

asp?JType=IJCIET&VType=8&IType=3

BEHAVIOR OF

USING

NALYSIS


s IT, Mumbai, Maharashtra, India,



ges. For this type of structural



ne the cable installation



rs need to go through the



n Unknown Load Factor.



span ratio, Pylon


Construction stage Analysis

Prataprao Jadha V., G. Mohan Ganesh and Vinayagamoorthy M,

http://www.iaeme.com/IJCIET/index.asp 253 [email protected]

Cite this Article: Prataprao Jadha V., G. Mohan Ganesh and Vinayagamoorthy M,

Erection Stage Dynamic Behavior of Cable Stayed Bridge Using Construction Stage

Analysis, International Journal of Civil Engineering and Technology, 8(4), 2017, pp.

252–264.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=3

INTRODUCTION

A cable stayed bridge is a type of bridge whose deck superstructure is supported by multiple

cables that run down to the main girder from one or more towers. The cable stayed bridges

are specially suited in the span range of 100 to 1000 m and thus provides a transition between

the continuous box girder bridges and the stiffened suspension bridges. It was developed in

Germany in the post war years in an effort to save steel which was then in short supply. Since

then many cable stayed bridges have been built all over the world. The cable stayed bridges

are economical over a wide range of span lengths and they are aesthetically attractive. The

wide application of the cable stayed bridge has been greatly facilitated in recent years by the

availability of high strength steels, the adoption of orthotropic decks using advanced welding

techniques and the use of electronic computers in conjunction with rigorous structural

analysis of highly indeterminate structures. The beauty and visibility of a cable stayed bridges

are mainly constructed using steel for stay cables, deck and towers. In some of the recent

constructions, the deck and towers has been constructed in structural concrete or a

combination of steel and concrete.

The cables are prestressed by introducing additional tensile force in the cables in order to

improve the stress in the main girder and tower at the completion stage, to prevent the

lowering of rigidity due to sagging of cable, and to optimize the cable condition for the

erection. The magnitude of the prestress is determined by taking into consideration the factors

such as the horizontal components of each cable tension is balanced such that there is no in-

plane bending of the tower due to unbalanced horizontal force due to dead load at the

completion stage, and the net force on the main girder at the connection of the cable at the

completion stage be assumed to be in certain limit.

The major issue of the design and erection of the cable-stayed bridges are to determine

and achieve the initial equilibrium configuration at the completed state. The initial

equilibrium configuration in case of cable-stayed bridges is the equilibrium condition due to

combined effect of dead load and tension forces in the stay cables.

There are various methods to determine the cable forces; these are classified as below;

1. Traditional "Zero Displacement" method

2. Force Equilibrium method

3. Force method

4. Unit Load method

In “Traditional Zero Displacement Method”, it is assumed as roller support at the cable

anchorage location of deck without cable and determines cable forces referring to the reaction

which is vertical component of cable force. Major concept of design is reducing bending

moment in tower and girders due to dead load.

In “Force Equilibrium Method”, it is assumed that all the cable support and tower

connection as fixed supports. The target bending moment distribution is obtained. The

condition is arrived as there would be zero moment in the pylon. In this case, nonlinearity due

to cable sag effect is ignored and pretension of cable at each end is assumed to be identical.

Force Equilibrium method considers the effect of this horizontal force.

Erection Stage Dynamic Behaviour of Cable Stayed Bridge Using Construction Stage Analysis


In “force method”, we can assume the member force by converting the structure as

determinate structure. Using the member forces due to live loads, member forces due to dead

loads can be obtained.

In “Unit Load Method”, to determine the unknown forces in each stay cables and to

achieve the ideal state, a unit pretension load is applied in each cable. By performing a linear

analysis, the influence on the structure due to each unit tension load is determined. In the

Unknown Load method, the unit load cases are created as a pretension Load. The structural

constraints e.g. moment or displacement values, which are to be realized through the load

factors in the combined load case, must be defined (Figure.1.1).

Figure. 1.1 Unit Load Method

2. LITERATURE REVIEW

Camara had proposed the parametric analysis for main span length, cable system

arrangement, tower geometry, the height and width of deck as well as soil conditions. After

that author suggested the contribution of transverse modes of vibration to the seismic

response, which is strongly influenced by the main span length. Also he suggested as more

the inclined legs above the deck, the larger will be transverse stiffness of tower.

Fabbrocino had attempted for calculating the optimal prestress design for composite cable

stayed bridges. First a target bending moment distribution over longitudinal beam was

identified and further Algorithm for the computation of optimal pre-tension forces had been

formulated.

Xudong Shao discussed about a new cable stayed bridge type named as partial ground

anchored cable stayed bridge with crossing stay cables. He concluded that as the pylon height

to span length ratio is reduced the horizontal pressure in main girder also the cost reduced to

11.8% than suspension bridge. Also the size of ground anchors reduced by 30% than

suspension bridge.

Yutaka Okamoto carried out research on steel double box section filled with the concrete.

He proposed that filled concrete increases the strength because of confined effect and steel

plates increases the resistance against local buckling because of the deformation resisted by in

filled concrete. The towers with three different heights are also studied and how it will affects

deformation and bending moment are classified.

3. OBJECTIVES

Based on the above literatures a number of initial studies are conducted to ensure the

accuracy and suitability of the modelling and following objectives are formulated for this

paper.

(1) Modeling of cable stayed bridge for initial pretension and carry out analysis using 3D

Finite Element Software (Midas Civil)



(2) Optimize the behavior of the cable stayed bridge under unit load method

(3) To arrive at maximum dynamic response of the bridge for the optimum pretension load

and determine cable forces

(4) Verification of results with analytical method.

(5) Carry out the construction stage analysis and determine the optimum cable forces in each

stage

4. WORK METHODOLOGY

To arrive the above objectives following stepwise methodology is adopted (Figure.4.1).

Figure. 4.1 Flow chart for work methodology

5. MODEL STUDY

The following modelling data is used for the calculations of example model. A simple 2D

Cable stayed model is chosen to clarify main considerations in modelling and to determine

the cable forces. Figure.5.1 shows a schematic representation of the cable stayed bridge. The

structure is modelled using the following data considerations (Refer Table 5.1 to Table5.3).

Table 5.1. Material data of the model

Classification Modulus of Elasticity (kN/m2) Poisson’s Ratio

Deck 2.7386e+007 0.2

Pylon 2.7386e+007 0.2

Cable 2.0500e+008 0.3

Defining Scope of work

Data consideration

Modelling using Midas Civil

Analysis

Numerical Analysis

Results & Discussion

Conclusion



Classification Cross

Deck

Pylon Top

Pylon Bottom

Cable

Table 5.3

Classification

Dead load

Cable pretension 1

Cable pretension 2

Cable pretension 3

Cable pretension 4

A concrete deck having grade M40 consists of span of 10m is considered and is

with conventional beam element. A P

7.5m is also modelled as bea

modelling as they cannot take

(Figure.5.1).

Figure. 5.1 Example Bridg

The results shows that, the bending moment profile (

equilibrium condition, is unit pretension forces and the displacements are checked for

condition as shown in table 5.4.

The procedure adopted to get the final cable forces is formulated using Finite Element

software (Midas Civil). The steps required to get cable forces are explained using following

figures (Figure 5.3 to Figure 5.6)

5m

A B



Table 5.2. Section data of the model

Cross-section Area (m2) Moment of Inertia(m

0.0225 7.11 e-5

0.04 2.25 e-4

0.07 5.184 e-4

3.15 e-4

1.57 e-8

Table 5.3. Loading data of the model

Load Type Load

Self weight -1(Factor)

Cable pretension 1 Pretension Loads 1 kN

pretension 2 Pretension Loads 1 kN



A concrete deck having grade M40 consists of span of 10m is considered and is

ment. A Pylon having grade M40 consists of overall height of

am element. For cables, the truss type of element is used for

cannot take the effects such as sag effect and non linear effects

Example Bridge model Figure. 5.2 Bending moment envelope

, the bending moment profile (Figure. 5.2) will be arrived for i

unit pretension forces and the displacements are checked for

table 5.4.



figures (Figure 5.3 to Figure 5.6)

4.5m

3m5m

C D


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Moment of Inertia(m4)

4

1(Factor)

A concrete deck having grade M40 consists of span of 10m is considered and is modelled

grade M40 consists of overall height of

the truss type of element is used for

the effects such as sag effect and non linear effects

Bending moment envelope

5.2) will be arrived for initial

unit pretension forces and the displacements are checked for these





Table 5.4 Displacement resul

Node No Self

Dx

17 0.025

19 -0.001

22 0.001

2 -0.025

Node No Pretension 3

Dx

17 0.006

19 0.002

22 0

2 0

Figure 5.3 Unknown Load Factor

Figure 5.6



Table 5.4 Displacement results for bridge model (m)

Self-Weight Pretension 1 Pretension 2

DZ Dx Dz Dx

-0.214 -0.005 -0.06 0.001

0.001 -0.201 0 0.049 0.001

-0.201 -0.001 0.033 0

0.025 -0.214 -0.001 0.069 0.005

(Continue)

Pretension 3 Pretension 4 Pretension 5

DZ Dx Dz Dx

0.164 0 -0.017 0.027

0.012 0 -0.008 0.002

-0.008 -0.002 0.0112 -0.002

-0.017 -0.006 0.164 -0.027

oad Factor Figure 5.4 Constraints in terms of displacements (m)

Figure 5.5 Unknown Load values

Figure 5.6 Optimized cable pretension loads


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ts for bridge model (m)

Pretension 2

Dz

0.069

0.033

0.049

-0.06

Pretension 5

Dz

-0.059

-0.115

-0.115

-0.059

Constraints in terms of displacements (m)



6. ANALYTICAL METHOD (STIFFNESS MATRIX METHOD)

The method used for optimization of tensions of cables at the initial equilibrium position of a

cable structure is unit load method. The initial cable forces are calculated by considering the

constraints such as displacement, moment, etc. and satisfy the constraints. If we use the

unknown load factor of FEM software, we can minimize the trials to determine the optimized

pretension forces. In this function, by defining the constraint condition of

displacement/reaction/member force in a certain range, we can determine the unknown cable

pretension forces.

The following procedure explains the analysis for finding the jack-up loads at Points A, B

as shown in Figure 1.1

• Apply a pretension load in the direction of the unknown jack-up loads as shown in Figure

1.1, one at a time. The number of unit load conditions created should be equal to the

number of the unknown loads.

• Carry out a static analysis for the given loadings. Loading condition is self weight load in

this case.

• Formulate Equality conditions using the Constraints imposed.

Using linear algebraic equations, these equality conditions can be solved. If the numbers

of the unknown loads and equations are exactly equal, the solution can be readily obtained

from the matrix method or the linear algebra method also. �� + �� + �� + �� + �� = �� Eq. (1) �� + �� + �� + �� + �� = �� Eq. (2) �� = displacement at point A due to the unit load applied at P1 direction �� = displacement at point B due to the unit load applied at P2 direction �� = displacement at point A due to the design loading condition �� = displacement at point B due to the design loading condition �� = displacement at point A due to the design loading condition and unknown loads �� = displacement a point B due to the design loading condition and unknown loads

For the current model, to find the initial cable tension loads T1, T2, T3 & T4 that limits the

lateral at point A which is less than δA and vertical displacements a displacement points B, C

and D which are greater than zero for the given loading condition (Figure 5.1).

Using the constraints the equality conditions are formulated. T1, T2, T3 & T4 are Unknown

Load factors or Optimized Cable Forces. Following equations are used to form the influence

matrix. �� + �� + �� + �� + �� = �� Eq. (3) �� + �� + �� + �� + �� = �� Eq. (4) �� + �� + �� + �� + �� = �� Eq. (5) �� + �� + �� + �� + � = � Eq. (6)

If the numbers of the unknown loads and equations are exactly equal, the solution can be

obtained from simultaneous equation method or the matrix method also.



��After putting all the values, we get following simultaneous equations.��0.06�� + �0.069�� + �0.164�0.049�� + �0.033�� + �0.012�0.033�� + �0.049�� + ��0.008�0.069�� + ��0.06�� + ��0.017Solving the equations (7) to (10)��= 0.991985, ��= 1.018489,

7. CONSTRUCTION STAGE ANALYSIS

To determine the cable forces that are introduced at cable installation

equilibrium condition for dead load at the final stage must be determined first. Then,

construction stage analysis according to the sequence

general, with forward construction stage analysis, we cannot obtain cable pretension loads for

each stage which satisfy the initial equilibrium at the final stage.

The Bhim Gowda Bridge

span Steel composite cable-sta

deck is of 13.6 m wide. It consists

beams at spacing of 3 m and a

stayed section is supported by

of configuration on each side

Each reinforced concrete pylon co

supporting the deck. Figure. 7.1 shows

view. A model of the completed

in Figure. 7.1 considering the geometrical and material

Figure. 7.1 Bhim Gowda cable



� = ��

putting all the values, we get following simultaneous equations. � 164�� + ��0.017�� + ��0.214� = ��0.059� � 012�� + ��0.008�� + ��0.201� = ��0.115� � 008�� + �0.0112�� + ��0.201� = ��0.115� � 017�� + �0.164�� + ��0.214� = ��0.059� (7) to (10), the unknown cable forces are calculated

= 1.018489, �"= 0.983432, �#= 1.002321

STAGE ANALYSIS

cable forces that are introduced at cable installation

for dead load at the final stage must be determined first. Then,

construction stage analysis according to the sequence of construction

with forward construction stage analysis, we cannot obtain cable pretension loads for

each stage which satisfy the initial equilibrium at the final stage.

at Haridwar is used for modelling in this paper

ayed bridge with overall length of 130m (65m

consists two longitudinal steel girders 2.5 m

a reinforced concrete slab of 250 mm deep.

supported by a total of 14 cables. The cables are arranged

side of the pylon, in two planes on either side of

lon comprises one tower and two cross bea

7.1 shows a schematic representation of the bridge

leted Bhim Gowda cable-stayed bridge in FEM software

geometrical and material properties.

Bhim Gowda cable-stayed bridge at completed stage


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�

Eq. (7)

Eq. (8)

Eq. (9)

Eq. (10)

the unknown cable forces are calculated,

cable forces that are introduced at cable installation time, the initial

for dead load at the final stage must be determined first. Then,

of construction is performed. In

with forward construction stage analysis, we cannot obtain cable pretension loads for

is used for modelling in this paper consists of 2-

m+ 65m each). The

m deep, transverse

The deck of cable-

arranged in semi-fan type

side of the bridge deck.

ams, the lower one

e bridge with elevation

bridge in FEM software is shown

at completed stage



7.1 Construction Stage Analysis Model using FEM software

For the given bridge the Forward type of analysis used to reflects the real construction

sequence. We can examine the structural behaviour of the analytical model and the changes

of cable tensions, displacements and moments.

The following steps are included in each construction stage:

• Activation and deactivation of elements with certain concrete maturities (ages)

• Activation and deactivation of loadings at certain points with time

• Changes in boundary conditions as per time

The analytical sequence of forward construction stage analysis is as shown in Figure.7.2

In forward Construction stage analysis the bridge is modelled stage wise as per the real type

construction shown in Figure.7.2, starting from the construction of substructure to the final

stage at completed state. These stages are shown in the figure.

Stage 1 Tower Installation Stage 2 Install 1st segment Stage 3 Pretension 1

st set of

cables

Stage 15 Pretension 7th

set of cables Stag 16 Install final segment

Figure 7.2 Sequence of forward construction stage analysis



8. RESULTS INTERPRETATION

The parameters used for studying construction stage analysis are Displacement contour,

bending moment diagram, reactions at supports, unknown load factors.

8.1 Deformation Contour

Figure 7.3 Deformation at final construction stage

The maximum resultant displacement at deck portions are shown in the Figure. (7.3) which is

45.61 mm from legend.

8.2 Bending Moment Diagram

Figure. 7.4 Bending Moment Diagram final construction stage

The Bending moment diagram at completed stage (Figure.7.4) is same as the target

bending moment diagram which is assumed to be for initial conditions. The resultant bending

moment diagram is shown which are equally distributed and have permissible moments at

final stage.

8.3 Reaction Diagram

The reactions at all the supports are calculated as shown in Figure.7.5. The axial compression

resultant reactions are shown at pier bottom through pylon, as well as the outer reactions are

considered for design of abutments.



Figure

8.4 Unknown Load Factors

Figure 7.6 Unknown Load Factors for final construction stage

The cable forces in terms of unknown load factors are found using the Finite Element

software (Midas Civil) for the initial pretension cable forces at

8.5. Parametric Analysis

Various parameters are influenced on the cable forces as well as pylon forces. These

parameters are back span to main span ratio

Geometry

Side span L

Main span L$%&'Ratio

Pylon Force (kN)

From Table 7.1 it is observed that

pylon compressive forces are increases considerably.

Table 7.2 shows that, for different types of tower geometry, the pylon axial compressive

forces are varying considerably.

properties the single pylon tower and two plane tower are effective in load transfer.



Figure. 7.5 Reactions at final construction stage

8.4 Unknown Load Factors

Unknown Load Factors for final construction stage


software (Midas Civil) for the initial pretension cable forces at completed stage


span to main span ratio, pylon height to deck span ratio

Table 7.1 Result – Pylon Forces

Side span LS (m) 3.5 5 7.5

Main span LM (m) 15 15 15

0.25 0.33 0.5

Pylon Force (kN) 172.60 214.70 224.80

From Table 7.1 it is observed that, as the ratio of side span to main span increases, the

pylon compressive forces are increases considerably.

for different types of tower geometry, the pylon axial compressive

considerably. It is found that for the same geometrical and material



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Unknown Load Factors for final construction stage


completed stage (Figure.7.6).


ylon height to deck span ratio, tower / Pylon

as the ratio of side span to main span increases, the

for different types of tower geometry, the pylon axial compressive

It is found that for the same geometrical and material




Table 7.2 Result – Pylon Forces

Geometry Type Pylon Forces (kN)

Single Plane Tower 382.5

Two Plane Tower 520.2

A-frame or inverted Y-shape 142.20

Diamond configuration 144.35

Table 7.3 Result – Cable Forces & Pylon Forces

Height of Pylon(m) 3 4 5 6 7 7.5

Main Span(m) 15 15 15 15 15 15

)*+,-./0123450-%65- Ratio 0.2 0.266 0.333 0.4 0.466 0.5

Cable Force (kN) 240.69 206.08 185.288 171.87 162.67 158.50

Pylon Force (kN) 216.87 215.93 214.98 214.01 213.29 206.66

From Table 7.3 it is observed that, as the ratio of height of pylon to main span increases,

the pylon compressive forces as well as cable forces are reduces apparently .But compared to

the pylon forces there is considerable decrease in cable forces for the same material and

geometrical properties.

8. CONCLUSION

After the examination of the construction stage analysis, the given model shows the

importance of the consideration of changing configuration at each stage. Here, the activation

to a deformed or undeformed deck and the cables will lead to a wrong estimation of cable

forces. The ideal cable forces are determined to achieve an optimal structural performance

due to its permanent loads. For the construction stage analysis, 17 various stages are modelled

using Finite Element Software so that they allow to include each erection stage.

Most of the calculated cable forces are equal to the final forces of the compared data with

the software. In the performed analysis, the initial stressing of the cables is applied in terms of

pretension load which is not a basic parameter. Therefore, the construction loads must be

accurately define to obtain the initial cable forces. The model does not include any geometric

as well as material non-linearity in the analysis of construction stage. A final calculation

should be done to consider these effects into account as they may optimize the cable forces.

Complete understanding of a structure is necessary to use the above optimization

techniques for finding design variables. The parameters like back span to main span ratio,

pylon height to deck span ratio, pylon geometry, cable system arrangements are compared

and results are drawn as bridge with back span to main span ratio lies between 0.25 and 0.5,

the height of pylon lies between L/8 to L/15, the inverted ‘Y’-shaped towers and diamond

configuration are less effective in load transfer than two plane tower.



ACKNOWLEDGEMENT

The authors wish to thank the supports provided by the VIT University Vellore. Also they

would like to special thank to the entire team from Midas IT, R&D, Mumbai, Maharashtra for

their valuable support.

REFERENCES

[1] A.Camara, E. Efthymiou,Deck–tower interaction in the transverse seismic response of

cable-stayed bridges and optimum configurations, Engineering Structures, 124, (2016)

494–506

[2] F. Fabbrocino, M. Modano, I. Farina, G. Carpentieri, F. Fraternali, Optimal prestress

design of composite cable-stayed bridges, Journal of Composite Structures, (2016),1-6

[3] Xudong Shao,Jia Hu, Lu Deng,and Junhui, Conceptual Design of Superspan Partial

Ground-Anchored Cable-Stayed Bridge with Crossing Stay Cables, Journal of Bridge

Engineering, 1, (2014),11-15

[4] Yutaka Okamoto,Shunichi Nakamura, Static and seismic studies on steel/concrete hybrid

towers for multi-span cable-stayed bridges, Journal of Constructional Steel Research,67,

(2011), 203–210

[5] M.Vinayagamoorthy, Dr. G. Mohan Ganesh, Dr. A.S. Santhi, Secondary analysis for Pile

foundation by P-∆ Method, International Journal of Applied Engineering Research,11,

(2016),1579-1582

[6] D.Johnson Victor, Essentials of Bridge Engineering, Oxford and IBH Publications, Sixth

Edition, (2007)

[7] N. Krishna Raju, Design of Bridges, Third Edition, (2007)

[8] IRC: 6-2014, Code of Practice for Concrete Road Bridges, (2011)

[9] Midas Civil Help and Analysis Manual

[10] Suhas S Vokunnaya, Ravindranatha and Tanaji.Thite, Construction Stage Analysis of

Segmental Cantilever Bridge. International Journal of Civil Engineering and Technology,

8(2), 2017, pp. 373–382.

[11] G. M. Savaliya, Prof. (Dr.) A. K. Desai and Prof.(Dr.) S. A. Vasanwala. The Effect of

Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported

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of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable

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Documents

ERECTION STAGE DYNAM IC BEHAVIOR OF CABLE STAYED …d.researchbib.com/f/6nnJSyoJHhL29gY01up3EypxSxoJyhY0ciqKWhLJksqKOfo… · International Journal of Civil Engineering and Technology