Structural Behavior of a Long-Span Partially Earth ......cable-stayed bridges with long main span lengths of between 600 m and 1000 m constructed by the free cantilever construction

applied sciences

Article

Structural Behavior of a Long-Span PartiallyEarth-Anchored Cable-Stayed Bridge duringInstallation of a Key Segment byThermal Prestressing

Sang-Hyo Kim 1 and Jeong-Hun Won 2,*1 School of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro Seodaemun-gu,

Seoul 03722, Korea; [email protected] Department of Safety Engineering, Chungbuk National University, Chungdae-ro 1, Seowon-Gu,

Cheongju, Chungbuk 28644, Korea* Correspondence: [email protected]; Tel.: +82-43-261-2459

Academic Editor: Giuseppe LacidognaReceived: 4 July 2016; Accepted: 10 August 2016; Published: 17 August 2016

Abstract: This study investigated structural behavior of long-span partially earth-anchoredcable-stayed bridges with a main span length of 810 m that use a new key segment closing methodbased on a thermal prestressing technique. A detailed construction sequence analysis matchedwith the free cantilever method (FCM) was performed using a three-dimensional finite element (FE)model of a partially earth-anchored cable-stayed bridge. The new method offers an effective way ofconnecting key segments by avoiding large movements resulting from the removal of the longitudinalrestraint owing to the asymmetry of axial forces in the girders near the pylons. The new methoddevelops new member forces through the process of heating the cantilever system before installingthe key segment and cooling the system continuously after installing key segments. The resultingforces developed by the thermal process enhance the structural behavior of partially earth-anchoredcable-stayed bridges owing to decreased axial forces in the girders.

Keywords: structural behavior; partially earth-anchored cable-stayed bridge; key segment; thermalprestressing; FCM

1. Introduction

A partially earth-anchored cable system was developed by Gimsing to reduce peak compressiveforces in the girders of cable-stayed bridges [1]. In this type of bridge, tensile forces are developedin the main span, while the peak compressive forces in the girders near the pylons are decreased [1].Reducing the peak compressive forces in the girders facilitates construction of cable-stayed bridgeswith ultra-long main spans of over 1000 m [2–4]. However, in this bridge type, a special erectionmethod for the central parts of the girders in the main span is needed since a considerable tensile forceat mid-span is required [5].

It should be noted that the partially earth-anchored cable system can also be applied tocable-stayed bridges with long main span lengths of between 600 m and 1000 m constructed bythe free cantilever construction method (FCM). The FCM is a preferred construction method incable-stayed bridges where the deck is cantilevered from each pylon towards the center of the mainspan. In the FCM, construction is completed by connecting both ends of the deck in a cantilever state.The connection is made by installing and closing the final segment, which is called a key segment.Closure of the key segment is performed carefully since sufficient space should be provided for

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Appl. Sci. 2016, 6, 231 2 of 21

the installation of the key segment, and the bridge geometry should match in both the vertical andtransverse directions.

The process of a set back and reset back is widely used in ensuring sufficient space betweenthe key segment and adjacent segments in a cantilever state. However, in this process, tremendousforces for key segment closure are required because partially earth-anchored cable-stayed bridgesshow relatively large reactions at longitudinal restraints prior to the process of set back and reset back.The restraints are installed between the girders and the pylons to guarantee the stability of a bridge atthe start of the FCM. Owing to the difference of axial forces between the left and right side girders ofthe restraint devices, which are caused by earth-anchored cables, the release of the reaction forces justbefore the process of set back causes large movements (see the latter chapter 4.1). Thus, applicationof the general set back and reset back processes is not valid for long-span partially earth-anchoredcable-stayed bridges. However, in case of general self-anchored cable-stayed bridge where all of thecables are anchored to the pylon and the girder, there is little difference of axial forces between the leftand right side girders of restraint devices. Owing to the small reactions at longitudinal restraints, theset back and reset back can be done easily by hydraulic jacks controlling the space between the keysegment and adjacent segments.

This study focuses on the application of a partially earth-anchored cable system to along-main-span cable-stayed bridge constructed by the FCM where the application of set back andreset back process is not possible. A new type of key segment closing method is applied based onthe thermal prestressing technique [6], which provides an effective way of closing key segments bymeans of thermal expansion. To investigate structural behavior in the new closing method, a detailedconstruction sequence analysis was performed using a three-dimensional FE model of a partiallyearth-anchored cable-stayed bridge. The influence of the new method on the structural members wasexamined after construction was completed, and the variation of the member forces was checkedaccording to the specific construction stage during the thermal prestressing process.

2. Key Segment Closing Method

2.1. Partially Earth-Anchored Cable-Stayed Bridge

The stiffening girders of cable-stayed bridges can transmit tensile as well as compressiveforces. Figure 1 shows the axial force distributions of a partially earth-anchored cable-stayed bridge.The combination of supporting conditions and anchoring locations alters the axial force distributionsof the girders. Most cable-stayed bridges are constructed with a self-anchored cable system in which allof the cables are anchored to the pylon and the girder. Thus, a self-anchored cable system experiencescompression throughout the girders. In contrast, the partially earth-anchored cable system anchorssome cables to the ground outside of the girders and supports the girders by allowing longitudinalmovement at the pylons and the abutments or anchor piers. A partially earth-anchored cable systemundergoes compression in the girders near the pylons and tension at the mid-span.

Appl. Sci. 2016, 6, 231 2 of 21

installation of the key segment, and the bridge geometry should match in both the vertical and

transverse directions.

The process of a set back and reset back is widely used in ensuring sufficient space between the

key segment and adjacent segments in a cantilever state. However, in this process, tremendous forces

for key segment closure are required because partially earth‐anchored cable‐stayed bridges show

relatively large reactions at longitudinal restraints prior to the process of set back and reset back. The

restraints are installed between the girders and the pylons to guarantee the stability of a bridge at the

start of the FCM. Owing to the difference of axial forces between the left and right side girders of the

restraint devices, which are caused by earth‐anchored cables, the release of the reaction forces just

before the process of set back causes large movements (see the latter chapter 4.1). Thus, application

of the general set back and reset back processes is not valid for long‐span partially earth‐anchored

cable‐stayed bridges. However, in case of general self‐anchored cable‐stayed bridge where all of the

cables are anchored to the pylon and the girder, there is little difference of axial forces between the

left and right side girders of restraint devices. Owing to the small reactions at longitudinal restraints,

the set back and reset back can be done easily by hydraulic jacks controlling the space between the

key segment and adjacent segments.

This study focuses on the application of a partially earth‐anchored cable system to a long‐main‐

span cable‐stayed bridge constructed by the FCM where the application of set back and reset back

process is not possible. A new type of key segment closing method is applied based on the thermal

prestressing technique [6], which provides an effective way of closing key segments by means of

thermal expansion. To investigate structural behavior in the new closing method, a detailed

construction sequence analysis was performed using a three‐dimensional FE model of a partially

earth‐anchored cable‐stayed bridge. The influence of the new method on the structural members was

examined after construction was completed, and the variation of the member forces was checked

according to the specific construction stage during the thermal prestressing process.

2. Key Segment Closing Method

2.1. Partially Earth‐Anchored Cable‐Stayed Bridge

The stiffening girders of cable‐stayed bridges can transmit tensile as well as compressive forces.

Figure 1 shows the axial force distributions of a partially earth‐anchored cable‐stayed bridge. The

combination of supporting conditions and anchoring locations alters the axial force distributions of

the girders. Most cable‐stayed bridges are constructed with a self‐anchored cable system in which all

of the cables are anchored to the pylon and the girder. Thus, a self‐anchored cable system experiences

compression throughout the girders. In contrast, the partially earth‐anchored cable system anchors

some cables to the ground outside of the girders and supports the girders by allowing longitudinal

movement at the pylons and the abutments or anchor piers. A partially earth‐anchored cable system

undergoes compression in the girders near the pylons and tension at the mid‐span.

Figure 1. Axial force distribution of a partially earth‐anchored cable‐stayed bridge.

hh

qLs2h

q 2

8hLm -4Ls 2

qLs 2

2h

Ls LoLs

Lm

Lo Ls Ls

(-) Compression Tension(+)

Figure 1. Axial force distribution of a partially earth-anchored cable-stayed bridge.

Appl. Sci. 2016, 6, 231 3 of 21

For the partially earth-anchored cable system, the axial force diagrams can be obtained accordingto [1].

N(x) = −w Ls

xdN = −

w Ls

x(x/h)qdx =− q

2h(Ls

2 − x2) (1)

where x is the distance from the pylon, Ls is the length of the side span, h is the pylon height above thegirder, and q is uniform load along the length of the girder.

2.2. Thermal Prestressing Method

In bridge design, the thermal effect has been considered previously as merely a source ofundesirable forces. However, there have been recent studies on the thermal prestressing method(TPSM) indicating constructive uses of the thermal effect [7,8]. The basic concept of the thermalprestressing method is to convert the elastic deformation energy accumulated from temporary thermaldeflection into a prestressing force for a structural system. Thermal deflection is induced by a speciallydesigned heating system for heating certain portions of steel members. Like any other prestressingmethod, the thermal prestressing method can effectively reduce member stresses due to design loads.

The thermal prestressing method provides artificial heat to the pre-selected structural members,and can be categorized into three types according to the heating method as illustrated in Figure 2 [6].If the whole cross section of a member is subjected to a uniform temperature distribution by heating,the member is elongated in one direction without producing eccentricity (Figure 2a). After memberelongation reaches a pre-calculated length, the connection is fixed to unify the structural member andheating is then removed. When heating is removed, the member in the heated region (shadow area)tends to shrink. However, the connection restrains the contraction, thereby producing initial tensileforce throughout the member.

Appl. Sci. 2016, 6, 231 3 of 21

For the partially earth‐anchored cable system, the axial force diagrams can be obtained according

to [1].

2 2( ) ( / ) ( )2

s sL L

sx x

qN x dN x h qdx L x

h (1)

Where x is the distance from the pylon, sL is the length of the side span, h is the pylon height

above the girder, and q is uniform load along the length of the girder.

2.2. Thermal Prestressing Method

In bridge design, the thermal effect has been considered previously as merely a source of

undesirable forces. However, there have been recent studies on the thermal prestressing method

(TPSM) indicating constructive uses of the thermal effect [7,8]. The basic concept of the thermal

prestressing method is to convert the elastic deformation energy accumulated from temporary

thermal deflection into a prestressing force for a structural system. Thermal deflection is induced by

a specially designed heating system for heating certain portions of steel members. Like any other

prestressing method, the thermal prestressing method can effectively reduce member stresses due to

design loads.

The thermal prestressing method provides artificial heat to the pre‐selected structural members,

and can be categorized into three types according to the heating method as illustrated in Figure 2 [6].

If the whole cross section of a member is subjected to a uniform temperature distribution by heating,

the member is elongated in one direction without producing eccentricity (Figure 2a). After member

elongation reaches a pre‐calculated length, the connection is fixed to unify the structural member and

heating is then removed. When heating is removed, the member in the heated region (shadow area)

tends to shrink. However, the connection restrains the contraction, thereby producing initial tensile

force throughout the member.

(a) (b) (c)

Figure 2. Types of thermal prestressing methods. (a) Uniform temperature; (b) Temperature gradient;

(c) Thermally prestressed cover plate.

Another type of thermal prestressing can be observed in Figure 2b. If a member is subjected to

temperature gradient, it undergoes bending deformation (dashed line). When the temperature

gradient is removed, the ends are fixed after the bending deformation and the contracting force of

the heated part induces initial stresses in the member. The last type of thermal prestressing uses a

separate prestressing member (Figure 2c). A heated cover‐plate is attached to the member in need of

prestressing. The contracting force of the cover‐plate then induces prestressing in the member.

2.3. New Key Segment Closing Method

The process of set back and reset back is widely used for key segment closure of a cable‐stayed

bridge constructed with the FCM method. As shown in Figure 3a, after a predetermined spacing

between the key segment and the adjacent segments is obtained, the key segment is lifted for

connection. One side of the key segment is connected temporarily, and alignment of the girders is

checked vertically and transversely. Finally, the girder is reset back into position and the connection

is made. This method needs additional reinforcement of girders located near the pylons because it

involves jacking work at the pylons. In addition, changes in structural behavior must not occur

during the process.

Figure 2. Types of thermal prestressing methods. (a) Uniform temperature; (b) Temperature gradient;(c) Thermally prestressed cover plate.

Another type of thermal prestressing can be observed in Figure 2b. If a member is subjectedto temperature gradient, it undergoes bending deformation (dashed line). When the temperaturegradient is removed, the ends are fixed after the bending deformation and the contracting force ofthe heated part induces initial stresses in the member. The last type of thermal prestressing uses aseparate prestressing member (Figure 2c). A heated cover-plate is attached to the member in need ofprestressing. The contracting force of the cover-plate then induces prestressing in the member.

2.3. New Key Segment Closing Method

The process of set back and reset back is widely used for key segment closure of a cable-stayedbridge constructed with the FCM method. As shown in Figure 3a, after a predetermined spacingbetween the key segment and the adjacent segments is obtained, the key segment is lifted for connection.One side of the key segment is connected temporarily, and alignment of the girders is checked verticallyand transversely. Finally, the girder is reset back into position and the connection is made. This methodneeds additional reinforcement of girders located near the pylons because it involves jacking work atthe pylons. In addition, changes in structural behavior must not occur during the process.

Appl. Sci. 2016, 6, 231 4 of 21Appl. Sci. 2016, 6, 231 4 of 21

(a) (b)

Figure 3. Comparison of key segment closing methods. (a) Conventional set back and reset back

method; (b) new key segment closing method based on thermal prestressing.

However, it is difficult to apply such a process for a partially earth‐anchored cable system

because the presence of earth‐anchored cables requires tremendous forces for key segment closure, a

large number of hydraulic jacks, and substantial reinforcement of the girders for jacking. Unlike the

self‐anchored cable‐stayed bridges, the partially earth‐anchored cable‐stayed bridges show relatively

large reactions in the longitudinal restraints. Owing to the difference of axial forces between the left

and right side girders of the restraints, which are installed between the girders and the pylons to

guarantee stability during the construction sequence, large reactions occur in the restraints. The

release of the reaction forces, which should be done before the set back process, causes large

movements in bridges that use a partially earth‐anchored cable system. Thus, the set back process

cannot be applied to partially earth‐anchored cable‐stayed bridges.

A new key segment closing method using thermal expansion with uniform temperature (Figure

2a) is applied as an alternative method; it was verified in a partially earth‐anchored cable‐stayed

bridge with a medium span length of 344 m in the authors’ previous research [6]. A detailed

construction sequence for the new closing method is presented in Figure 3b. While a derrick crane

holds a key segment in position, certain girders are heated. After the key segment and the adjacent

segments make contact due to the elongation of the heated girder, the connection between the

segments is made. The longitudinal restraints that restrict the longitudinal movement at the pylon in

the cantilever state are then removed. Finally, the artificial heating is removed.

A feasible way of heating girders with large cross sections is to use large‐capacity industrial fan

heaters. By blocking one end of the diaphragm inside of a girder and blowing hot air from the other

Set backSet back

Lifting key-segment

Connecting one side & Matching alignment

Reset back & Connecting key-segmentReset backReset back

Set back work Lifting key-segment

Heating work

Remove longitudinal restraints at pylons

Matching alignment & Connecting key-segment

Heating Heating

Heat removal Heat removal

and then remove the heating source

Figure 3. Comparison of key segment closing methods. (a) Conventional set back and reset backmethod; (b) new key segment closing method based on thermal prestressing.

However, it is difficult to apply such a process for a partially earth-anchored cable system becausethe presence of earth-anchored cables requires tremendous forces for key segment closure, a largenumber of hydraulic jacks, and substantial reinforcement of the girders for jacking. Unlike theself-anchored cable-stayed bridges, the partially earth-anchored cable-stayed bridges show relativelylarge reactions in the longitudinal restraints. Owing to the difference of axial forces between the leftand right side girders of the restraints, which are installed between the girders and the pylons toguarantee stability during the construction sequence, large reactions occur in the restraints. The releaseof the reaction forces, which should be done before the set back process, causes large movements inbridges that use a partially earth-anchored cable system. Thus, the set back process cannot be appliedto partially earth-anchored cable-stayed bridges.

A new key segment closing method using thermal expansion with uniform temperature (Figure 2a)is applied as an alternative method; it was verified in a partially earth-anchored cable-stayed bridgewith a medium span length of 344 m in the authors’ previous research [6]. A detailed constructionsequence for the new closing method is presented in Figure 3b. While a derrick crane holds a keysegment in position, certain girders are heated. After the key segment and the adjacent segmentsmake contact due to the elongation of the heated girder, the connection between the segments is made.The longitudinal restraints that restrict the longitudinal movement at the pylon in the cantilever stateare then removed. Finally, the artificial heating is removed.

Appl. Sci. 2016, 6, 231 5 of 21

A feasible way of heating girders with large cross sections is to use large-capacity industrial fanheaters. By blocking one end of the diaphragm inside of a girder and blowing hot air from the otherend, the whole segment can be heated uniformly with ease. This kind of heating process by convectiveheating ensures a uniform temperature distribution within the girder section. In addition, the authors’previous research for the temperature distribution of a steel box girder in a cable-stayed bridge showedthat the temperature of the inner steel box is even at dawn [9]. From the temperature distributionresults, a heating schedule can be determined. The objective of this study is to examine the structuralbehavior of a partially earth-anchored cable-stayed bridge with a long main span during the new keysegment closing process. Thus, construction details such as operational details of a heating device, thepossible heating time during connection process, economic considerations, etc., will be studied further.

3. FE Model of a Bridge

3.1. Bridge Description

In order to investigate the response of partially earth-anchored cable-stayed bridges, a three-spancable-stayed bridge with a main span length of 810 m is designed preliminary. Its geometry anddimensions are presented in Figure 4. The girder section is composed of a steel box with a width of22.90 m. The pylon configuration is in an inverted Y-shape composed of concrete legs. The cables,composed of MS-type cables and arranged in a fan, have two planes in the transverse direction. In oneplane, there are 25 cables in the side span and in the main span for each pylon. In addition, it isassumed that earth-anchored cables are anchored to the abutments.

Appl. Sci. 2016, 6, 231 5 of 21

end, the whole segment can be heated uniformly with ease. This kind of heating process by

convective heating ensures a uniform temperature distribution within the girder section. In addition,

the authors’ previous research for the temperature distribution of a steel box girder in a cable‐stayed

bridge showed that the temperature of the inner steel box is even at dawn [9]. From the temperature

distribution results, a heating schedule can be determined. The objective of this study is to examine

the structural behavior of a partially earth‐anchored cable‐stayed bridge with a long main span

during the new key segment closing process. Thus, construction details such as operational details of

a heating device, the possible heating time during connection process, economic considerations, etc.,

will be studied further.

3. FE Model of a Bridge

3.1. Bridge Description

In order to investigate the response of partially earth‐anchored cable‐stayed bridges, a three‐

span cable‐stayed bridge with a main span length of 810 m is designed preliminary. Its geometry and

dimensions are presented in Figure 4. The girder section is composed of a steel box with a width of

22.90 m. The pylon configuration is in an inverted Y‐shape composed of concrete legs. The cables,

composed of MS‐type cables and arranged in a fan, have two planes in the transverse direction. In

one plane, there are 25 cables in the side span and in the main span for each pylon. In addition, it is

assumed that earth‐anchored cables are anchored to the abutments.

(a)

(b) (c)

(d)

P17.00

P27.00

3116@16=256

2616@24=384 16

300 405

2616@24=38416

405

A1 A2

3116@16=256

300

16256

37

55

4 1111

[email protected]=

36

A

B

C

E

F

DS=-2.000% S=-2.000%

1.00020.9001.00022.900

7.4007.850 7.850

2.771

3.000

T=80mm

23.100

wearing surface

7.00

6.00

0.452.001.10

2.000.45

1.0

05.00

1.00

SECTION A

7.7

6

6.00

5.100.45

6.76

0.5

0

0.45

0.50

SECTION B

SECTION C

SECTION D

SECTION ESECTION F

9.31

6.00

4.00

4.50

9.31

6.00

10.00

11.00

5.100.45

8.310

.50

0.45

0.50

2.501.00

2.00

1.00

1.00

1.00

4.800.60

8.110

.60

0.60

0.60

9.001.00

8.800.60

1.00

0.60

Figure 4. Cont.


(e)

Figure 4. Outline of the sample bridge (units: m). (a) Side view; (b) Cross‐section of the girder; (c)

Pylon; (d) Cross‐sections of the pylon; (e) Bearing conditions.

With regard to the supporting conditions of the girder, vertical and transverse movements are

fixed but longitudinal movement is free at the abutment. At the pylon, transverse and vertical

movements are restrained. The longitudinal movement of the girders at the pylons is free according

to the boundary conditions of the partially earth‐anchored cable system. However, in FCM

construction sequence analysis, the longitudinal movement of the girders at the pylons is constrained

before closing the key segment in order to satisfy construction stability. The main sectional and

material properties are given in Tables 1 and 2, respectively.

Table 1. Main sectional properties of a sample bridge.

Member Section area

ACS (m2)

Moment of Inertia

about strong axis

(Iy) (m4)

Moment of Inertia

about weak axis

(Iz) (m4)

Girder 1.022 42.946 1.254

Pylon United part 22.006–38.978 71.305–663.741 129.983–345.591

Separated part 12.097–30.230 65.054–544.107 102.823–395.802

Cable 0.0030–0.0150 ‐ ‐

Table 2. Material properties of a bridge.

Material Location

Elastic

modulus

(ECS, GPa)

Poisson ratio

() Weight density

(s, kN/m3)

Concrete (50 MPa) Pylon 31 0.167 24.53

Steel (SM520) Girder 210 0.300 77.00

Cable (1770 MPa) Stay cable 200 0.300 77.00

3.2. Bridge Models

The use of real structures and physical models is difficult to investigate structural behavior of

considered partially earth‐anchored cable‐stayed bridges with a new key segment closing method.

Instead of use of real structures, this study uses the finite element (FE) model, which can correctly

and reliably reproduce the real behavior of the structure. The method using FE model is frequently

applied for predicting the behavior of long‐span cable bridges in various fields [10–13].

Analysis of cable‐stayed bridges is much more complicated than that of conventional bridges

because of the former’s nonlinear structural behavior due to cable sag, large deflections, and

compression effects in the pylons and girders [14,15]. In the present study, RM Bridge, which is a

well‐known 3‐D finite element program for cable‐stayed bridges, is adopted to simulate the

complicated behavior of cable‐stayed bridges [16,17]. This program, which is widely used in

analyzing long‐span cable‐stayed, can simulate the cable nonlinear effect, P‐delta effect, and the

construction sequence of cable‐stayed bridges easily by simple beam elements and cable elements.

( )

( )

or

or

( )( )

A1 P1 P2 A2

Free in longitudinal and transverse directionFree in longitudinal direction

Free in transverse direction

Fixed in longitudinal and transverse direction

P1Partially earth-anchored cable system

Self-anchored cable system

Figure 4. Outline of the sample bridge (units: m). (a) Side view; (b) Cross-section of the girder;(c) Pylon; (d) Cross-sections of the pylon; (e) Bearing conditions.

With regard to the supporting conditions of the girder, vertical and transverse movements arefixed but longitudinal movement is free at the abutment. At the pylon, transverse and verticalmovements are restrained. The longitudinal movement of the girders at the pylons is free according tothe boundary conditions of the partially earth-anchored cable system. However, in FCM constructionsequence analysis, the longitudinal movement of the girders at the pylons is constrained before closingthe key segment in order to satisfy construction stability. The main sectional and material propertiesare given in Tables 1 and 2, respectively.

Table 1. Main sectional properties of a sample bridge.

Member Section AreaACS (m2)

Moment of Inertiaabout Strong Axis

(Iy) (m4)

Moment of Inertiaabout Weak Axis

(Iz) (m4)

Girder 1.022 42.946 1.254

Pylon United part 22.006–38.978 71.305–663.741 129.983–345.591Separated part 12.097–30.230 65.054–544.107 102.823–395.802Cable 0.0030–0.0150 - -

Table 2. Material properties of a bridge.

Material Location Elastic Modulus(ECS, GPa)

PoissonRatio (ν)

Weight Density(γs, kN/m3)

Concrete (50 MPa) Pylon 31 0.167 24.53Steel (SM520) Girder 210 0.300 77.00

Cable (1770 MPa) Stay cable 200 0.300 77.00

3.2. Bridge Models

The use of real structures and physical models is difficult to investigate structural behavior ofconsidered partially earth-anchored cable-stayed bridges with a new key segment closing method.Instead of use of real structures, this study uses the finite element (FE) model, which can correctly andreliably reproduce the real behavior of the structure. The method using FE model is frequently appliedfor predicting the behavior of long-span cable bridges in various fields [10–13].

Analysis of cable-stayed bridges is much more complicated than that of conventional bridgesbecause of the former’s nonlinear structural behavior due to cable sag, large deflections, andcompression effects in the pylons and girders [14,15]. In the present study, RM Bridge, which is awell-known 3-D finite element program for cable-stayed bridges, is adopted to simulate the complicated

Appl. Sci. 2016, 6, 231 7 of 21

behavior of cable-stayed bridges [16,17]. This program, which is widely used in analyzing long-spancable-stayed, can simulate the cable nonlinear effect, P-delta effect, and the construction sequenceof cable-stayed bridges easily by simple beam elements and cable elements. Girders and pylons aremodeled as beam elements based on beam theory. Stay cables are modeled as cable elements, whichconsider only normal forces and shear forces or bending moments cannot occur in cable elements.In addition, spring elements are used to model bearings and supports. In order to consider the curvedcable geometry (nonlinear deformation behavior of the cables), the stay cable nonlinear option of theprogram is used. The P-delta effect is also included in the analysis.

Figure 5 illustrates the configuration of the FE model with a partially earth-anchored cable system,where the partially earth-anchored cable-stayed bridge model has six pairs of earth-anchored cables atthe abutments (L-EA-6).

Appl. Sci. 2016, 6, 231 7 of 21

Girders and pylons are modeled as beam elements based on beam theory. Stay cables are modeled

as cable elements, which consider only normal forces and shear forces or bending moments cannot

occur in cable elements. In addition, spring elements are used to model bearings and supports. In

order to consider the curved cable geometry (nonlinear deformation behavior of the cables), the stay

cable nonlinear option of the program is used. The P‐delta effect is also included in the analysis.

Figure 5 illustrates the configuration of the FE model with a partially earth‐anchored cable

system, where the partially earth‐anchored cable‐stayed bridge model has six pairs of earth‐anchored

cables at the abutments (L‐EA‐6).

Figure 5. 3‐D FE model of the considered bridge. FE, finite element.

3.3. Load for Construction Sequence Analysis

The self‐weight, an additional dead load, and a construction working load are considered in

FCM construction sequence analysis. The self‐weight is calculated as follows:

CS sW A , (2)

Where is a coefficient that represents a connection, an anchorage, and a diaphragm, among others

(e.g., girder = 1.30, concrete pylon leg = 1.0, cable = 1.18); ACS is the section area, and is the weight

density (steel = 77.0 kN/m3, concrete = 24.5 kN/m3).

Additional dead loads of 55.45 kN/m are considered in order to consider the effects of pavement,

traffic barriers, railings, lights, spoilers, and utilities. During the construction sequence, the effects of

derrick crane operation (i.e., installation, movement, lifting, and removal) and of a construction

working live load (10 kN/m) are included.

3.4. Construction Sequence

To apply the new key segment closing method in the analysis, a detailed construction sequence

should be assumed. The applied construction sequence is presented in Table 3. The construction

sequence of cable‐stayed bridges can be modeled according to the backward or forward approaches

[18–20]. Even though the backward approach is much easier, this method can only approximate the

effects of time dependent effects. The forward approach, which follows the erection sequence, can

consider not only time dependent effects but also modification in design and tensioning strategy. In

this study, the forward approach is adopted to follow the assumed FCM sequence.

Earth-anchored

cable

Figure 5. 3-D FE model of the considered bridge. FE, finite element.

3.3. Load for Construction Sequence Analysis

The self-weight, an additional dead load, and a construction working load are considered in FCMconstruction sequence analysis. The self-weight is calculated as follows:

W = αACSγs, (2)

where α is a coefficient that represents a connection, an anchorage, and a diaphragm, among others(e.g., girder = 1.30, concrete pylon leg = 1.0, cable = 1.18); ACS is the section area, and γσ is the weightdensity (steel = 77.0 kN/m3, concrete = 24.5 kN/m3).

Additional dead loads of 55.45 kN/m are considered in order to consider the effects of pavement,traffic barriers, railings, lights, spoilers, and utilities. During the construction sequence, the effectsof derrick crane operation (i.e., installation, movement, lifting, and removal) and of a constructionworking live load (10 kN/m) are included.

3.4. Construction Sequence

To apply the new key segment closing method in the analysis, a detailed construction sequenceshould be assumed. The applied construction sequence is presented in Table 3. The construction sequenceof cable-stayed bridges can be modeled according to the backward or forward approaches [18–20].Even though the backward approach is much easier, this method can only approximate the effects oftime dependent effects. The forward approach, which follows the erection sequence, can consider notonly time dependent effects but also modification in design and tensioning strategy. In this study, theforward approach is adopted to follow the assumed FCM sequence.

Appl. Sci. 2016, 6, 231 8 of 21

Table 3. Construction sequence.

Stage Description of Stage Actions

1 Erect the lower legs of pylons P1 and P2 at the same time.2 Erect girders at the pylons and restrain the longitudinal movement of the girders at the pylons.3 Erect the upper pylon legs.4 Erect the girders using the free cantilever construction method (the cables are installed together).5 Lift the key segment.6 Heat the girders in the main span while the derrick crane holds the key segment.7 Connect the key segment to adjacent segments.8 Remove the longitudinal restraints and install permanent bearings.9 Remove the heating sources.

10 Re-adjust the cable tension forces on the side span.11 Cast the second additional concrete in side span girders and install the pavement, barrier, etc.

3.5. Simulation of the Heating and Heat Removal Processes

From the simple theoretical equation for thermal expansion, a heating temperature and a heatinglength can be calculated (∆L = α × ∆T × L; α = thermal coefficient; ∆T = temperature rise; L = heatinglength; ∆L = elongation length). However, the actual elongation extent does not match the theoreticalvalue since the cable-stayed bridge is a system supported by cables. Therefore, the heating temperaturerise should be calculated by an iterative analysis. To simulate the heating and heat removal processof the insides of box girders, constant-temperature loading is applied. In the program, the uniformtemperature load creates a thermal strain in the beam elements, and the thermal strain, which isconstant over the cross section, is given by the product of the thermal coefficient and temperaturerise to all selected elements. The heating process is modeled by applying the temperature rise (∆T)to elements within the heating length, whereas the heat removal process is modeled by applyinga negatives temperature (−∆T) to the elements within the heating length. Although the use of asimple beam element is insufficient for studying stress distributions or redistributions in a large steelbox section, global behaviors and force variations of major structural components can be estimatedsufficiently by using the beam element.

4. Results and Comparison

A detailed construction sequence analysis was performed using a three-dimensional FE model.The influence of a new closing method on the other structural members was investigated. The majorchanges of member forces are compared to their values for a completed construction, and the variationsof the member forces are also examined according to the detailed construction stages during the thermalprestressing process.

4.1. Verification of the Problem in the General Closing Method

For the sample bridge, the reaction force prior to the set back is examined. To compare theremaining reaction forces, the model for a self-anchored cable-stayed bridge (L-SE-1) is also analyzed.Table 4 shows the results of comparison. The remaining reaction forces are relatively small in bridgemodels with a self-anchored cable system (L-SE-1). However, the bridge model with a partiallyearth-anchored cable system shows relatively large reactions owing to the difference of axial forcesbetween the left and right side girders of the restraint device (L-EA-6). During the constructionsequence, in the bridge model with a partially earth-anchored cable system, the accumulated axialforces in the side span girder occurring via the inclined cables are different from those in the mainspan girders since some cables are anchored to the outside of the girders.

Appl. Sci. 2016, 6, 231 9 of 21

Table 4. Longitudinal restraint reactions before the set back process.

Bridge Model Reaction Force (kN)

Model with self-anchored cable system (L-SE-1) −289.3Model with partially earth-anchored cable system (L-EA-6) 31,541.0

The movements caused by the removal of longitudinal restraints are compared in Table 5. Owingto the release of the reaction forces, large movements occur in the bridge model with the partiallyearth-anchored cable system. Owing to tremendous movement, the process of reset back is impossible.In contrast, the bridge model with the self-anchored cable system shows relatively small movements.

Table 5. Movement caused by removal of the longitudinal restraints in set back.

Bridge Model Movement (mm) 1

Model with self-anchored cable system (L-SE-1) +97.1Model with partially earth-anchored cable system (L-EA-6) −2440.1

1 (+): movement from pylon to center of main span, (−): movement from pylon to abutment.

Therefore, it is difficult to apply the set back process for the partially earth-anchored cable systemowing to the large movements in the process of set back. Thus, the classical closing method of theset back and reset back processes is not valid. In contrast, the new method does not remove thelongitudinal restraints in a cantilever state but rather only after the connection of the key segment,which is in a continuous bridge state.

4.2. Heating Length and Temperature Rise

The horizontal displacement of the final segment in a cantilever state is calculated as 23 mm(toward the pylons) before lifting the key segment for the considered partially earth-anchoredcable-stayed bridge. Since this displacement does not give sufficient lifting space between the keysegment and the adjacent segments, it is assumed that the space should be 100 mm. This means thatthe key segment is made with a shortened length of 154 mm. Hence, the required elongation length tobe achieved by the heating process is 100 mm for each girder in a cantilever state.

In order to determine the optimal regions for long-span bridges, three cases are consideredwith the same heating length but different heated regions near the pylons (Case-L1), middle region(Case-L2), and near the center of the main span (Case-L3)). By iterative analysis giving the requiredelongation length of 100 mm, the heating length and temperature rise are determined (Table 6 andFigure 6).

Appl. Sci. 2016, 6, 231 9 of 21

Table 4. Longitudinal restraint reactions before the set back process.

Bridge model Reaction force (kN)

Model with self‐anchored cable system (L‐SE‐1) −289.3

Model with partially earth‐anchored cable system (L‐EA‐6) 31,541.0

The movements caused by the removal of longitudinal restraints are compared in Table 5.

Owing to the release of the reaction forces, large movements occur in the bridge model with the

partially earth‐anchored cable system. Owing to tremendous movement, the process of reset back is

impossible. In contrast, the bridge model with the self‐anchored cable system shows relatively small

movements.

Table 5. Movement caused by removal of the longitudinal restraints in set back.

Bridge model Movement (mm) 1

Model with self‐anchored cable system (L‐SE‐1) +97.1

Model with partially earth‐anchored cable system (L‐EA‐6) −2440.1 1 (+): movement from pylon to center of main span, (−):movement from pylon to abutment.

Therefore, it is difficult to apply the set back process for the partially earth‐anchored cable

system owing to the large movements in the process of set back. Thus, the classical closing method

of the set back and reset back processes is not valid. In contrast, the new method does not remove the

longitudinal restraints in a cantilever state but rather only after the connection of the key segment,

which is in a continuous bridge state.

4.2. Heating Length and Temperature Rise

The horizontal displacement of the final segment in a cantilever state is calculated as 23 mm

(toward the pylons) before lifting the key segment for the considered partially earth‐anchored cable‐

stayed bridge. Since this displacement does not give sufficient lifting space between the key segment

and the adjacent segments, it is assumed that the space should be 100 mm. This means that the key

segment is made with a shortened length of 154 mm. Hence, the required elongation length to be

achieved by the heating process is 100 mm for each girder in a cantilever state.

In order to determine the optimal regions for long‐span bridges, three cases are considered with

the same heating length but different heated regions near the pylons (Case‐L1), middle region (Case‐

L2), and near the center of the main span (Case‐L3)). By iterative analysis giving the required

elongation length of 100 mm, the heating length and temperature rise are determined (Table 6 and

Figure 6).

Table 6. Applied temperature rises (ΔT) and heating lengths (L).

Case Thermal coefficient (α) Heating length (L)Iterative analysis

Applied ΔT ΔL

Case‐L1, L2, L3 1.2 × 10−5/m/m/°C 160 m 54.9 °C 0.1 m

Figure 6. Heating regions for the verification example bridge.

Case-L1

Heating(160m)

Case-L1

Case-L2Case-L2

Case-L3 Case-L3

Heating(160m)

Heating(160m) Heating(160m)

Heating(160m)

Heating(160m)

Figure 6. Heating regions for the verification example bridge.

Table 6. Applied temperature rises (∆T) and heating lengths (L).

Case Thermal Coefficient (α) Heating Length (L)Iterative Analysis

Applied ∆T ∆L

Case-L1, L2, L3 1.2 × 10−5/m/m/◦C 160 m 54.9 ◦C 0.1 m

Appl. Sci. 2016, 6, 231 10 of 21

4.3. Thermal Prestressing Effect

4.3.1. Optimal Heating Region and Effects of the Closing Method

For the three cases, which have different heating regions, structural behaviors are examined usingthe new closing method. First, the girder moments are compared for the three cases. Figure 7a showsthe girder moments generated by the heating and heat removal processes. Case-L1 with the heatingregion near the pylons shows the smallest moments in the main span, while Case-L3, which has aheating region near the center of the main span, shows the largest moments. In the side span, the heatremoval process gives only the new member forces, and there is little difference among the threethermal cases.

Appl. Sci. 2016, 6, 231 10 of 21

4.3. Thermal Prestressing Effect

4.3.1. Optimal Heating Region and Effects of the Closing Method

For the three cases, which have different heating regions, structural behaviors are examined

using the new closing method. First, the girder moments are compared for the three cases. Figure 7a

shows the girder moments generated by the heating and heat removal processes. Case‐L1 with the

heating region near the pylons shows the smallest moments in the main span, while Case‐L3, which

has a heating region near the center of the main span, shows the largest moments. In the side span,

the heat removal process gives only the new member forces, and there is little difference among the

three thermal cases.

(a)

(b)

Figure 7. Girder moments according to the heating region. (a) Girder moments generated by heating

and heat removal processes; (b) Girder moments after completed construction.

For a completed construction state, the girder moments are compared with those in the case

without using the new closing method, which assumes only set back and reset back processes

ignoring the difficulty of the installation process. Case‐L3 shows the increase of girder moments in

the center of the main span, whereas Case‐L1 and Case‐L2 show similar moments to those in the case

without thermal prestressing effects (Figure 7b). In the side span, all cases with thermal prestressing

show similar or decreased moments resulting from the new member forces using the heat removal

process. The peak girder moment in the side span is reduced by about 23%.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

12000

10000

8000

6000

4000

2000

0

-2000

-4000

-6000

Mo

me

nt (

kNm

)

Heating process (Case-L1)Heat removal process (Case-L1)Heating process (Case-L2)Heat removal process (Case-L2)Heating process (Case-L3)Heat removal process (Case-L3)

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

40000

30000

20000

10000

0

-10000

-20000

-30000

-40000

-50000

Mo

me

nt (

kNm

)

Without thermal prestressing effectThermal prestressing Case-L1Thermal prestressing Case-L2Thermal prestressing Case-L3

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 7. Girder moments according to the heating region. (a) Girder moments generated by heatingand heat removal processes; (b) Girder moments after completed construction.

For a completed construction state, the girder moments are compared with those in the casewithout using the new closing method, which assumes only set back and reset back processes ignoringthe difficulty of the installation process. Case-L3 shows the increase of girder moments in the centerof the main span, whereas Case-L1 and Case-L2 show similar moments to those in the case withoutthermal prestressing effects (Figure 7b). In the side span, all cases with thermal prestressing showsimilar or decreased moments resulting from the new member forces using the heat removal process.The peak girder moment in the side span is reduced by about 23%.

Appl. Sci. 2016, 6, 231 11 of 21

Variations of axial forces according to the various heating regions are represented in Figure 8.As for the girders near the pylons, the three cases show similar axial forces generated by the heatingand heat removal processes. In the main span, Case-L3 with the heating region near the center of themain span shows the largest generated tensile force among the three cases. Thus, after construction iscompleted, Case-L3 shows the largest tensile force in the main span girder. Since tensile forces in thegirder generated by heat removal are accumulated in the bridge system, the peak compressive axialforce near the pylons is reduced in cases with thermal prestressing after construction. The peak valuesare reduced by about 3%.

Appl. Sci. 2016, 6, 231 11 of 21

Variations of axial forces according to the various heating regions are represented in Figure 8.

As for the girders near the pylons, the three cases show similar axial forces generated by the heating

and heat removal processes. In the main span, Case‐L3 with the heating region near the center of the

main span shows the largest generated tensile force among the three cases. Thus, after construction

is completed, Case‐L3 shows the largest tensile force in the main span girder. Since tensile forces in

the girder generated by heat removal are accumulated in the bridge system, the peak compressive

axial force near the pylons is reduced in cases with thermal prestressing after construction. The peak

values are reduced by about 3%.

(a)

(b)

Figure 8. Girder axial forces according to the heating region. (a) Axial forces generated by heating and

heat removal processes; (b) Axial forces after completed construction.

The cable forces are compared for the completed construction state (Figure 9). In the earth‐

anchored cables, the cable forces are increased by about 3% using the proposed method. However,

cables near the earth‐anchored cables show decreased cable forces. From the cable forces of the main

span, it is found that Case‐L3 shows the variation of cable forces, whereas Case‐L1 and Case‐L2 show

similar cable forces to those in the case without thermal prestressing.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

1600

1200

800

400

0

-400

Axi

al f

orc

e (

kN)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400

60000

40000

20000

0

-20000

-40000

-60000

-80000

Axi

al F

orc

e (k

N)

Without thermal prestressing effectThermal prestressing Case-L1Thermal prestressing Case-L2Thermal prestressing Case-L3

P1 P2

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

0.88

0.92

0.96

1

1.04

1.08

Fo

rce

Rat

io

Case-L1/Without thermal effectCase-L2/Without thermal effectCase-L3/Without thermal effect

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 8. Girder axial forces according to the heating region. (a) Axial forces generated by heating andheat removal processes; (b) Axial forces after completed construction.

The cable forces are compared for the completed construction state (Figure 9). In theearth-anchored cables, the cable forces are increased by about 3% using the proposed method. However,cables near the earth-anchored cables show decreased cable forces. From the cable forces of the mainspan, it is found that Case-L3 shows the variation of cable forces, whereas Case-L1 and Case-L2 showsimilar cable forces to those in the case without thermal prestressing.


(a)

(b)

Figure 9. Cable forces according to the heating region. (a) Cable forces after completed construction;

(b) Cable force ratio.

The deflections of the girders are compared. Figure 10 represents the girder deflections caused

by the heating and heat removal processes according to the heating region. Among the three cases,

Case‐L1 with the heating region near the pylons shows the smallest slope during the heating process,

while Case‐L3 with the heating region near the center of the main span has the steepest curve. In

addition, Case‐L1 shows the smallest variation of displacements during the heat removal process.

Table 7 represents the displacements at the end of the cantilever girder caused by the heating process.

Even though Case‐L3 has the smallest displacements, this case has the largest rotation because it has

the steepest curve. This is because the deflection occurs in a small region. Case‐L1 shows the smallest

value for the slope of the deflections and girder end rotation since it contains the large‐deflection

region.

Figure 10. Girder deflections generated by thermal prestressing for different heating regions.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Cable

Tensi

on (

kN)

.

Without thermal prestressing effect Thermal prestressing Case-L1

Thermal prestressing Case-L2 Thermal prestressing Case-L3

P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Forc

e ratio .

Thermal prestressing Case-L1/Without thermal prestressingThermal prestressing Case-L2/Without thermal prestressingThermal prestressing Case-L3/Without thermal prestressing

P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

300

200

100

0

-100

-200

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 9. Cable forces according to the heating region. (a) Cable forces after completed construction;(b) Cable force ratio.

The deflections of the girders are compared. Figure 10 represents the girder deflections caused bythe heating and heat removal processes according to the heating region. Among the three cases, Case-L1with the heating region near the pylons shows the smallest slope during the heating process, whileCase-L3 with the heating region near the center of the main span has the steepest curve. In addition,Case-L1 shows the smallest variation of displacements during the heat removal process. Table 7represents the displacements at the end of the cantilever girder caused by the heating process. Eventhough Case-L3 has the smallest displacements, this case has the largest rotation because it has thesteepest curve. This is because the deflection occurs in a small region. Case-L1 shows the smallest valuefor the slope of the deflections and girder end rotation since it contains the large-deflection region.

Appl. Sci. 2016, 6, 231 12 of 21

(a)

(b)

Figure 9. Cable forces according to the heating region. (a) Cable forces after completed construction;


The deflections of the girders are compared. Figure 10 represents the girder deflections caused

by the heating and heat removal processes according to the heating region. Among the three cases,

Case‐L1 with the heating region near the pylons shows the smallest slope during the heating process,

while Case‐L3 with the heating region near the center of the main span has the steepest curve. In

addition, Case‐L1 shows the smallest variation of displacements during the heat removal process.

Table 7 represents the displacements at the end of the cantilever girder caused by the heating process.

Even though Case‐L3 has the smallest displacements, this case has the largest rotation because it has

the steepest curve. This is because the deflection occurs in a small region. Case‐L1 shows the smallest

value for the slope of the deflections and girder end rotation since it contains the large‐deflection

region.


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Cable

Tensi

on (

kN)

.



P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Forc

e ratio .


P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

300

200

100

0

-100

-200

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~


Appl. Sci. 2016, 6, 231 13 of 21

Table 7. Displacements at the end of the cantilever girders caused by the heating process.

Case Bridge Axis (mm) Vertical (mm) Rotation (Radians × 10−3)

Case-L1 100.0 265.7 −0.52057Case-L2 100.0 273.8 −0.58151Case-L3 100.2 261.5 −1.92691

Thus, summarizing the results for moments, axial forces, and displacements of girders and cableforces, the advantages of the new method are not only that it provides an effective way to connectkey segments, but also that it reduces the peak compressive axial forces and moments of the girders.Among various heating regions, Case-L1 with the heating region near the pylons represents a betterway to apply the new method to large-span cable-stayed bridges.

4.3.2. Change of Elongation Length

Various elongation lengths are considered in order to examine the influence of the elongationlength in the new closing method. For Case-L1 selected from the previous section, which has anelongation length of 100 mm and the heating regions near the pylons, two additional cases withelongation lengths of 150 mm and 200 mm are added (Table 8 and Figure 11).

Appl. Sci. 2016, 6, 231 13 of 21

Table 7. Displacements at the end of the cantilever girders caused by the heating process.

Case Bridge axis (mm) Vertical (mm) Rotation (radians × 10−3)

Case‐L1 100.0 265.7 −0.52057

Case‐L2 100.0 273.8 −0.58151

Case‐L3 100.2 261.5 −1.92691

Thus, summarizing the results for moments, axial forces, and displacements of girders and cable

forces, the advantages of the new method are not only that it provides an effective way to connect

key segments, but also that it reduces the peak compressive axial forces and moments of the girders.

Among various heating regions, Case‐L1 with the heating region near the pylons represents a better

way to apply the new method to large‐span cable‐stayed bridges.

4.3.2. Change of Elongation Length

Various elongation lengths are considered in order to examine the influence of the elongation

length in the new closing method. For Case‐L1 selected from the previous section, which has an

elongation length of 100 mm and the heating regions near the pylons, two additional cases with

elongation lengths of 150 mm and 200 mm are added (Table 8 and Figure 11).

Table 8. Temperature rises and heating lengths for various elongation lengths.

Case Thermal coefficient α

(m/m/°C) Heating length L

(m) ΔT (°C)

Analysis results ΔL

(m)

Case‐L1 1.2 × 10−5 160 54.9 0.100

Case‐L4 1.2 × 10−5 240 54.9 0.150

Case‐L5 1.2 × 10−5 320 55.0 0.200

Figure 11. Heating regions for various elongation lengths.

Figure 12 represents the variations of the girder moments according to various elongation

lengths. As elongation length increases, positive moments generated at the side spans by the heat

removal process increase (Figure 12a). Thus, after construction is completed, the negative moments

at the side spans are reduced remarkably with increasing elongation length (Figure 12b). In the center

of the main span, there is a small increase in girder moments with increasing elongation length.

Case-L1

Case-L4

Case-L5

Heating(160m)

Heating(240m)

Heating(320m)

Case-L1

Case-L4

Case-L5

Heating(160m)

Heating(240m)

Heating(320m)

Figure 11. Heating regions for various elongation lengths.

Table 8. Temperature rises and heating lengths for various elongation lengths.

Case Thermal Coefficient α(m/m/◦C)

Heating Length L(m) ∆T (◦C) Analysis Results

∆L (m)

Case-L1 1.2 × 10−5 160 54.9 0.100Case-L4 1.2 × 10−5 240 54.9 0.150Case-L5 1.2 × 10−5 320 55.0 0.200

Figure 12 represents the variations of the girder moments according to various elongation lengths.As elongation length increases, positive moments generated at the side spans by the heat removalprocess increase (Figure 12a). Thus, after construction is completed, the negative moments at the sidespans are reduced remarkably with increasing elongation length (Figure 12b). In the center of the mainspan, there is a small increase in girder moments with increasing elongation length.


(a)

(b)

Figure 12. Girder moments for various elongation lengths. (a) Moments generated by heating and

heat removal processes; (b) Moments after completed construction.

The generated axial girder forces show increases in proportion to the elongation length (Figure

13a). For the state of completed construction, the ratio of the peak compressive axial force to that in

the case without using prestressing method is 0.97 for an elongation length of 100 mm, 0.96 for 150

mm, and 0.95 for 200 mm (Figure 13b).

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

24000

20000

16000

12000

8000

4000

0

-4000

Mo

me

nt (

kNm

)

Heating process (Case-L1: 100mm)Heat removal process (Case-L1: 100mm)Heating process (Case-L4: 150mm)Heat removal process (Case-L4: 150mm)Heating process (Case-L5: 200mm)Heat removal process (Case-L5: 200mm)

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

40000

30000

20000

10000

0

-10000

-20000

-30000

-40000

-50000

Mo

me

nt (

kNm

)

Without thermal prestressing effectThermal prestressing Case-L1: 100mmThermal prestressing Case-L4: 150mmThermal prestressing Case-L5: 200mm

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 12. Girder moments for various elongation lengths. (a) Moments generated by heating and heatremoval processes; (b) Moments after completed construction.

The generated axial girder forces show increases in proportion to the elongation length(Figure 13a). For the state of completed construction, the ratio of the peak compressive axial force tothat in the case without using prestressing method is 0.97 for an elongation length of 100 mm, 0.96 for150 mm, and 0.95 for 200 mm (Figure 13b).


(a)

(b)

Figure 13. Axial girder forces for various elongation lengths. (a) Axial forces generated by heating

and heat removal processes; (b) Axial forces after completed construction.

The variations of cable forces relative to the various elongation lengths are plotted in Figure 14.

Only in the side span do the cable forces show variation with changing elongation length. As the

elongation length increases, the earth‐anchored cables show increased tensile forces whereas the

cables anchored to the side span girders show decreased tensile forces.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

3000

2000

1000

0

-1000

Axi

al f

orc

e (

kN)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 140060000

40000

20000

0

-20000

-40000

-60000

-80000

Axi

al F

orc

e (k

N)

Without thermal prestressing effectThermal prestressing Case-L1: 100mmThermal prestressing Case-L4: 150mmThermal prestressing Case-L5: 200mm

P1 P2

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

0.80.840.880.920.96

11.041.081.12

Fo

rce

Rat

io

Case-L1/Without thermal effectCase-L4/Without thermal effectCase-L5/Without thermal effect

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Peak compression : -57794 kN : -56503 kN : -55857 kN

: -55204 kN

Figure 13. Axial girder forces for various elongation lengths. (a) Axial forces generated by heating andheat removal processes; (b) Axial forces after completed construction.

The variations of cable forces relative to the various elongation lengths are plotted in Figure 14.Only in the side span do the cable forces show variation with changing elongation length. As theelongation length increases, the earth-anchored cables show increased tensile forces whereas the cablesanchored to the side span girders show decreased tensile forces.


(a)

(b)

Figure 14. Cable forces for various elongation lengths. (a) Cable forces after completed construction;


For the state of completed construction, the deflections of the girders are plotted in Figure 15 for

various elongation lengths. The generated deflections increase in proportion to the elongation length

during the thermal prestressing procedure.

Figure 15. Girder deflections generated by heating and heat removal for various elongation lengths.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

6125

6123

6121

6119

6117

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6202

6204

6206

6208

6210

6212

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6222

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6325

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6317

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6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Cable

Tensi

on (

kN) .



P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

0.80

0.84

0.88

0.92

0.96

1.00

1.04

1.08

1.12

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

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6216

6218

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6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Rorc

e r

atio .


P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

600

400

200

0

-200

-400

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 14. Cable forces for various elongation lengths. (a) Cable forces after completed construction;(b) Cable force ratio.

For the state of completed construction, the deflections of the girders are plotted in Figure 15 forvarious elongation lengths. The generated deflections increase in proportion to the elongation lengthduring the thermal prestressing procedure.

Appl. Sci. 2016, 6, 231 16 of 21

(a)

(b)

Figure 14. Cable forces for various elongation lengths. (a) Cable forces after completed construction;


For the state of completed construction, the deflections of the girders are plotted in Figure 15 for

various elongation lengths. The generated deflections increase in proportion to the elongation length

during the thermal prestressing procedure.


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Cable

Tensi

on (

kN) .



P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

0.80

0.84

0.88

0.92

0.96

1.00

1.04

1.08

1.12

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Rorc

e r

atio .


P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

600

400

200

0

-200

-400

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~


Appl. Sci. 2016, 6, 231 17 of 21

Summarizing the results of major member forces for the various elongation lengths, the increaseof the target elongation length generates increased moments and axial forces in the girders and cableforces. In determining the elongation length for the closure of partially earth-anchored cable-stayedbridges, the elongation length is an important factor for enhancing the behavior of cable-stayed bridges.However, the condition of a construction site should be also considered.

4.3.3. Number of Earth-Anchored Cables

The influence of the number of earth-anchored cables on the effects of the new closing methodis examined. Three cases are compared: the case with six pairs of earth-anchored cables at the eachabutment (L-EA-6, Case-L1); the case with two pairs of earth-anchored cables (L-EA-2, Case-L6); andthe case with seven pairs of earth-anchored cables (L-EA-7, Case-L7). The heating length, heatingregion, and temperature rise are all the same of Case-L1.

The girder moments and axial forces generated by the heating and heat removal processesare represented in Figure 16. As the number of earth-anchored cables is increased, the generatedgirder moments in the side span increase while those in the main span decrease. In addition, thegenerated tensile forces in the girders decrease with the increment of the number of earth-anchoredcables. The deflections of the girders increase in the side span, but decrease in the main span with theincrement of the number of earth-anchored cables (Figure 17).

Appl. Sci. 2016, 6, 231 17 of 21

Summarizing the results of major member forces for the various elongation lengths, the increase

of the target elongation length generates increased moments and axial forces in the girders and cable

forces. In determining the elongation length for the closure of partially earth‐anchored cable‐stayed

bridges, the elongation length is an important factor for enhancing the behavior of cable‐stayed

bridges. However, the condition of a construction site should be also considered.

4.3.3. Number of Earth‐Anchored Cables

The influence of the number of earth‐anchored cables on the effects of the new closing method

is examined. Three cases are compared: the case with six pairs of earth‐anchored cables at the each

abutment (L‐EA‐6, Case‐L1); the case with two pairs of earth‐anchored cables (L‐EA‐2, Case‐L6); and

the case with seven pairs of earth‐anchored cables (L‐EA‐7, Case‐L7). The heating length, heating

region, and temperature rise are all the same of Case‐L1.

The girder moments and axial forces generated by the heating and heat removal processes are

represented in Figure 16. As the number of earth‐anchored cables is increased, the generated girder

moments in the side span increase while those in the main span decrease. In addition, the generated

tensile forces in the girders decrease with the increment of the number of earth‐anchored cables. The

deflections of the girders increase in the side span, but decrease in the main span with the increment

of the number of earth‐anchored cables (Figure 17).

(a)

(b)

Figure 16. Member forces generated by heating and heat removal with various numbers of earth‐

anchored cables. (a) Girder bending moments; (b) Girder axial forces.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

12000

10000

8000

6000

4000

2000

0

-2000

-4000

Mo

me

nt (

kNm

)

Heating process (L-EA-2,Case-L6)Heat removal process (L-EA-2,Case-L6)Heating process (L-EA-6,Case-L1)Heat removal process (L-EA-6,Case-L1)Heating process (L-EA-7,Case-L7)Heat removal process (L-EA-7,Case-L7)

P1P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

2000

1500

1000

500

0

-500

Axi

al f

orc

e (

kN)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Figure 16. Member forces generated by heating and heat removal with various numbers ofearth-anchored cables. (a) Girder bending moments; (b) Girder axial forces.


Figure 17. Displacements generated by heating and heat removal with various numbers of earth‐

anchored cables.

With regard to axial girder forces in the state of completed construction, the three cases show

decreased axial compressive forces compared with those in the case without using the new

prestressing method (Figure 18). The magnitude of the decreased axial forces is reduced with the

increment of the number of earth‐anchored cables, as is predicted in Figure 16(b). The ratio of the

decrease is small since the magnitudes of the peak axial forces are relatively large.

Figure 18. Axial girder forces with various numbers of earth‐anchored cables.

With regard to cable forces in the state of completed construction, the earth‐anchored cables

show increased cable forces when using the applied closing method (Figure 19). The other cables

anchored to the side span girders located near the earth‐anchored cables show decreased cable forces.

The increase of cable forces resulting from the effects of the new method is more notable in the case

with a small number of earth‐anchored cables.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

300

200

100

0

-100

-200

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375Element Number

50000

40000

30000

20000

10000

0

-10000

-20000

-30000

-40000

-50000

-60000

-70000

-80000

-90000

Axi

al F

orc

e (

kN)

L-EA-2: Without thermal prestressingL-EA-2: With thermal prestressingL-EA-6: Without thermal prestressingL-EA-6: With thermal prestressingL-EA-7: Without thermal prestressingL-EA-7: With thermal prestressing

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Peak compression : -80845 kN : -79102 kN : -57794 kN : -56503 kN : -53923 kN

: -52929 kN

Figure 17. Displacements generated by heating and heat removal with various numbers ofearth-anchored cables.

With regard to axial girder forces in the state of completed construction, the three cases showdecreased axial compressive forces compared with those in the case without using the new prestressingmethod (Figure 18). The magnitude of the decreased axial forces is reduced with the increment of thenumber of earth-anchored cables, as is predicted in Figure 16b. The ratio of the decrease is small sincethe magnitudes of the peak axial forces are relatively large.

Appl. Sci. 2016, 6, 231 18 of 21

Figure 17. Displacements generated by heating and heat removal with various numbers of earth‐

anchored cables.

With regard to axial girder forces in the state of completed construction, the three cases show

decreased axial compressive forces compared with those in the case without using the new

prestressing method (Figure 18). The magnitude of the decreased axial forces is reduced with the

increment of the number of earth‐anchored cables, as is predicted in Figure 16(b). The ratio of the

decrease is small since the magnitudes of the peak axial forces are relatively large.

Figure 18. Axial girder forces with various numbers of earth‐anchored cables.

With regard to cable forces in the state of completed construction, the earth‐anchored cables

show increased cable forces when using the applied closing method (Figure 19). The other cables

anchored to the side span girders located near the earth‐anchored cables show decreased cable forces.

The increase of cable forces resulting from the effects of the new method is more notable in the case

with a small number of earth‐anchored cables.

1000 1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400Element Number

300

200

100

0

-100

-200

DIs

pla

cem

en

t (m

m)


P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

1025 1050 1075 1100 1125 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375Element Number

50000

40000

30000

20000

10000

0

-10000

-20000

-30000

-40000

-50000

-60000

-70000

-80000

-90000

Axi

al F

orc

e (

kN)

L-EA-2: Without thermal prestressingL-EA-2: With thermal prestressingL-EA-6: Without thermal prestressingL-EA-6: With thermal prestressingL-EA-7: Without thermal prestressingL-EA-7: With thermal prestressing

P1 P2

1014 1095 1096 1198 1199 13011302 1383~ ~ ~ ~

Peak compression : -80845 kN : -79102 kN : -57794 kN : -56503 kN : -53923 kN

: -52929 kN

Figure 18. Axial girder forces with various numbers of earth-anchored cables.

With regard to cable forces in the state of completed construction, the earth-anchored cables showincreased cable forces when using the applied closing method (Figure 19). The other cables anchored tothe side span girders located near the earth-anchored cables show decreased cable forces. The increaseof cable forces resulting from the effects of the new method is more notable in the case with a smallnumber of earth-anchored cables.


(a)

(b)

Figure 19. Cable forces with various numbers of earth‐anchored cables. (a) Cable forces after

completed construction; (b) Cable force ratio.

From the results, it is clear that the number of earth‐anchored cables affects the applied key

segment closing method for a partially earth‐anchored cable‐stayed bridge with a long span.

However, the variation of the major member forces is relatively small.

5. Conclusions

This study examined the structural behavior of a partially earth‐anchored cable‐stayed bridge

with a long main span length when using a new key segment closing process utilizing the thermal

prestressing technique based on simple thermal expansion. The validity of the new key segment

closing method was demonstrated through a detailed construction sequence analysis. The main

contributions and conclusions of this study are summarized as follows:

(1) A new method utilizing the thermal prestressing technique offers an effective way to connect

key segments while avoiding large movements resulting from the removal of longitudinal restraints

arising from asymmetric of axial forces in girders near the pylons. The new method becomes more

effective with increasing span length since bridges with longer spans show substantial movement

with the removal of longitudinal restraints.

(2) The applied closing method develops new member forces through a heating process in the

cantilever system before closing the key segment and cooling the system continuously after closing.

The resulting forces developed by the new key segment closing method enhance the structural

efficiency of a partially earth‐anchored cable‐stayed bridge by reducing both the axial forces in the

girders. The application of the new closing method may change the bending moments in the girders.

However, these changes are not significant since the absolute values of the bending moments are

relatively small in relation to their capacities. With regard to cables, only earth‐anchored cables show

increased tensile forces, whereas other cables anchored to a side span show decreased tensile forces.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

6125

6123

6121

6119

6117

6115

6113

6111

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6107

6105

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6101

6202

6204

6206

6208

6210

6212

6214

6216

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6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Cable

Tensio

n (

kN

) .

Thermal prestressing Case-L6(L-EA-2)Thermal prestressing Case-L1(L-EA-6)Thermal prestressing Case-L7(L-EA-7)

P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

6125

6123

6121

6119

6117

6115

6113

6111

6109

6107

6105

6103

6101

6202

6204

6206

6208

6210

6212

6214

6216

6218

6220

6222

6224

6325

6323

6321

6319

6317

6315

6313

6311

6309

6307

6305

6303

6301

6402

6404

6406

6408

6410

6412

6414

6416

6418

6420

6422

6424

Element

Forc

e ratio .

Thermal prestressing Case-L1/Without thermal prestressing(L-EA-2)Thermal prestressing Case-L2/Without thermal prestressing(L-EA-6)Thermal prestressing Case-L3/Without thermal prestressing(L-EA-7)

P1 P2

6125 6101 6201 6225 6325 63016401 6425~ ~ ~ ~

Figure 19. Cable forces with various numbers of earth-anchored cables. (a) Cable forces after completedconstruction; (b) Cable force ratio.

From the results, it is clear that the number of earth-anchored cables affects the applied keysegment closing method for a partially earth-anchored cable-stayed bridge with a long span. However,the variation of the major member forces is relatively small.

5. Conclusions

This study examined the structural behavior of a partially earth-anchored cable-stayed bridgewith a long main span length when using a new key segment closing process utilizing the thermalprestressing technique based on simple thermal expansion. The validity of the new key segmentclosing method was demonstrated through a detailed construction sequence analysis. The maincontributions and conclusions of this study are summarized as follows:

(1) A new method utilizing the thermal prestressing technique offers an effective way to connectkey segments while avoiding large movements resulting from the removal of longitudinal restraintsarising from asymmetric of axial forces in girders near the pylons. The new method becomes moreeffective with increasing span length since bridges with longer spans show substantial movement withthe removal of longitudinal restraints.

(2) The applied closing method develops new member forces through a heating process in thecantilever system before closing the key segment and cooling the system continuously after closing.The resulting forces developed by the new key segment closing method enhance the structuralefficiency of a partially earth-anchored cable-stayed bridge by reducing both the axial forces in thegirders. The application of the new closing method may change the bending moments in the girders.However, these changes are not significant since the absolute values of the bending moments arerelatively small in relation to their capacities. With regard to cables, only earth-anchored cables showincreased tensile forces, whereas other cables anchored to a side span show decreased tensile forces.

Appl. Sci. 2016, 6, 231 20 of 21

(3) Parametric studies have shown that the elongation length is an important factor that canenhance the effects of the new method. The ratio of the peak compressive axial force is 0.97 for anelongation length of 100 mm elongation length, 0.96 for 150 mm, and 0.95 for a 200 mm.

There is latitude for additional research on the new applied key segment closing method,particularly concerning the operation of the heating device, the feasible heating times duringconnection, the enhancement of the economy of its operation, and other facets. In addition, furtherresearch is needed on the stress distribution created by the heat flow and in the cantilever state beforeclosing a key segment as well as on torsion and distortion of the box section.

Acknowledgments: This study has been supported by the Korea Agency for Infrastructure TechnologyAdvancement (KAIA) grant funded by the Ministry of Land, Infrastructure and Transport of the Koreangovernment (14CTAP-C078811-01).

Author Contributions: Sang-Hyo Kim proposed the topic of this study and designed the process. Jeong-Hun Wonperformed the analysis and wrote the paper. Sang-Hyo Kim and Jeong-Hun Won modified the final paper.

Conflicts of Interest: The authors declare no conflict of interest.

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http://dx.doi.org/10.1016/j.engstruct.2012.02.005

http://dx.doi.org/10.1016/j.engstruct.2012.02.022

http://dx.doi.org/10.1016/j.compstruc.2013.03.010

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Structural Behavior of a Long-Span Partially Earth ......cable-stayed bridges with long main span lengths of between 600 m and 1000 m constructed by the free cantilever construction