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Influence of Intermediate Hinge
Damage on Bridge Response and Modal
Parameters of Cantilever-Suspended
Girder Bridge
Aoi Hiraoka, Gen Hayashi & Takashi Yamaguchi
Citation

European Workshop on Structural Health Monitoring. 2022; 745-753.

Book series

Lecture Notes in Civil Engineering, vol 254.

Published2022-06-16

TypeTextversion

Conference paperAuthor© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG.
For Academic research only.

RightsThis is the accepted manuscript version. The formal published version is available athttps://doi.org/10.1007/978-3-031-07258-1_75.
See Springer Nature Accepted Manuscript Terms of Use:
https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms

DOI

10.1007/978-3-031-07258-1_75

Self-Archiving by Author(s)Placed on: Osaka City University

Hiraoka, A., Hayashi, G., Yamaguchi, T. (2023). Influence of Intermediate Hinge Damage on Bridge
Response and Modal Parameters of Cantilever-Suspended Girder Bridge. In: Rizzo, P., Milazzo, A.
(eds) European Workshop on Structural Health Monitoring. EWSHM 2022. Lecture Notes in Civil
Engineering, vol 254. Springer, Cham. https://doi.org/10.1007/978-3-031-07258-1_75

Influence of Intermediate Hinge Damage
on Bridge Response and Modal Parametersof Cantilever-Suspended Girder Bridge
Aoi Hiraoka1, Gen Hayashi2, and Takashi Yamaguchi2
1Osaka City Univ. 3-3-138 Sugimoto Sumiyoshi-ku, Osaka 558-8585 JAPANhiraoka@brdg.civil.eng.osaka-cu.ac.jp
2 Osaka City Univ. 3-3-138 Sugimoto Sumiyoshi-ku, Osaka 558-8585 JAPANhayashi-g@osaka-cu.ac.jp

Abstract. Cantilever-suspended girder bridges are provided with intermediatehinges to reduce the effects of support settlement, including damage to hinge
bearings caused by corrosion. To inspect, repair, and efficiently maintain thesebridges, it is necessary to develop a monitoring technology. Accordingly, research have been conducted on a bridge response health-monitoring technology.
In particular, the properties of bearings significantly influence the vibration characteristics of bridges. However, previous studies are yet to examine changes inbridge response due to the corrosion of hinge bearings. Using finite element analysis (FEA), this study aimed to investigate changes in the bridge response andmodal parameters of cantilever-suspended girder bridges due to the corrosion
damage levels of the hinge bearings. In the FEA, model-installed elastic spring
was used shell elements. Furthermore, static and eigenvalue analyses were conducted. Static analysis demonstrated that the target bridge type exhibited moreminor changes in its girder deflection due to bearing corrosion. In addition, theeffects were quantitatively determined by altering the corrosion position of thehinge bearing in the bridge.
Keywords: Cantilever-suspended Girder Bridge, Hinge Bearing, Corrosion,
Bridge Health Monitoring

1Introduction

Several bridges in Japan were constructed five decades ago. Considering that the number of bridges will continuously increase in the future, the maintenance of aging bridges
is a crucial issue. Hence, the revision of periodic inspection guidelines for bridges inJapan has made it necessary for road bridge inspections to be conducted periodically1).
However, the maintenance of these bridges has been conducted by engineers with specialized knowledge of visual and percussion inspections, which creates certain problems such as high human costs, shortage of engineers, and inspection inefficiencies.

2

Bridge health monitoring (BHM) is expected to be an efficient maintenance method.
BHM is a technology that evaluates performance and determines the existence of damage to a bridge based on the response of the bridge to various sensors placed on thebridge. In particular, damage detection by vibration-based health monitoring (VSHM)
adopts acceleration response. In previous studies, VSHM was applied to various steel
bridges such as truss, arch, and girder bridges2)–6). However, it is difficult to repair orreplace an existing bridge based on changes in its vibration characteristics alone. Therefore, BHM applications must consider the load-carrying capacity, which is importantin decision-making regarding vibration characteristics.
This study focused on a cantilever-suspended girder bridge, which is yet to be studied. Cantilever-suspended girder bridges are provided with intermediate hinges to reduce the effects of support settlement, and damage to hinge bearings caused by corrosion has been reported. However, previous studies are yet to examine changes in thevibration characteristics and load-carrying capacity due to the corrosion of hinge bearings.
In this study, to examine the applicability of the BHM technology, the effects of thelocation of the corroded hinges and corrosion level on the response of the bridge wereinvestigated analytically. Subsequently, the relationship between the vibration characteristics and the static response was clarified via eigenvalue analyses and static analyses.

2

Actual target bridge and analysis model

2.1

Actual target bridge

The actual target bridge, which was completed in 1959, is a cantilever-suspended nonsynthetic girder bridge with seven spans, including suspended-span and cantilevergirder lengths of 16.0 m and 40.8 m (6.2 m + 28.4 m + 6.2 m), respectively. Because
the target bridge is symmetrical, its general drawing can be obtained from the A2 abutment to its center, as illustrated in Fig. 1. The bridge bears a large amount of heavy
vehicular traffic daily. In the past, the slabs and main girders of its hinges were reinforced by a steel plate to prevent fatigue cracking.
2.2

Finite element method (FEM)In this study, entire bridge overviews of the models are presented in Fig. 2. The generalpurpose FEM software Abaqus/Standard 2020 was used for the analysis. To develop
the model, the main load transfer members, which include the slab, main girder, stringer
beam, and cross beam were modeled. The dimensions adopted are presented in Table 1and Fig. 3. The elastic moduli of the slab and girders were 30 GPa and 200 GPa, respectively. The boundary conditions were modeled as linear springs resisting the vertical and two horizontal directions so as to represent the rubber bearing of the bridge, asillustrated in Fig. 4. The spring constants were set as 1450 MN/m and 3.32 MN/m inthe vertical and horizontal directions, respectively. The spring constant was calculated

3P4-6, A2: Rubber bearing,

A2

Hinge bearinga):Wheel load

6.2m

:Reaction force(in (c))

28.4m

6.2m

Sym.

P4

G1
G2

G1
G3

Asphalt
Concrete Slab
t=220mm

500

1380

250

G1250

100

Center of road

8700
7700

500500Asphalt
Concrete Slab
t=220mm32014.2m

Hinge bearing1380b)

6.2m

P5P68700
7700

500

16.0m25016.0m

990

3@2240=6720

G1G1G1G3
G4G2G1756 728 756 756 728 756 756 728 756

G1G4990c)

990

3@2240=6720990

Fig. 1. General drawing of the actual bridge: (a) side view; (b) sectional view (girder end); and(c) sectional view (the central part)based on the road bridge bearing handbook7). In the eigenvalue analysis, the masses ofthe bridge were given as the material properties and densities of the members. The slabdensity was 23 kg/m3, while that of the girders was 77 kg/m3.

2.3

Finite element analysis (FEA) modelAll the members were modeled using four-node reduced-integral shell elements in theshell model. The element size was set to 100 mm × 100 mm for all the members. Fig.
5(b) and (c) present the method for modeling and constraining the hinges. In this model,
the reference points were set to the top surface of the upper flange in the main cantileverspan and the bottom surface of the lower flange in the suspended span of the half-joint.
These sets were joined to two nodes placed in the middle of the upper and lower surfaces of the half-joint. The double nodes are represented by pinning the two nodes.

Fig. 2. Overview of the entire bridge modeled using shell elements.

4Table 1. Dimensions of members
MemberSlabShape

Main girder

ICrossbeam,stringer beam

I

Dimension (Unit: mm)
B = 8700, hd = 220
Upper flange: Buf = 400, tuf = 28
Web: hg = 1380, tw = 9Lower flange: Buf = 440, tuf = 32
Upper flange, Lower flange: Buf = 200, tuf = 10
Web: hg = 630, tw = 9BuftuftwhgBa)

hdtlfb)

BlfFig. 3. Member section: (a) slab; and (b) girder

2.4c)Fig. 4. Rubber bearing of the model

Loading method and damage modeling

The load adopted for static analysis is a wheel load equivalent to the designed actualload mentioned in the Specifications for Highway Bridges (front axle weight: 122.6kN; rear axle weight: 122.6 kN). The distance between the front and rear axle weights
was 3.88 m for an actual vehicle. The loading position was at the top of the upper flangeof the main girder, just above the hinge in the end-suspended span section (hinge position 1 in Fig.2). The load distributed across the four main girders was calculated andloaded on each girder, assuming that the loading truck traveled in the center of one lane,
as illustrated in Fig. 1. In the analysis conducted on the sensitivity of the hinges tocorrosion, it is necessary to represent the corrosion of the hinges. Therefore, an elastic
rotational spring resisting at a position perpendicular to the bridge axis was introduced
to the hinges, and the corrosion was simulated by altering the spring constant.

a)b)Flange surface
Rotationpoint
spring kθ
Flange surfacec)

Fig. 5. Overview of the shell model: (a) entire view; (b) hinge bearing part; and (c) image ofthe hinge model

53

Effect of corrosion position

3.1

Analysis conditions

The relationship between the vibration characteristics and bridge response when thelocation of the corroded hinge was altered was investigated. This section examines thechange in the natural frequency when the spring constant increases by introducing
springs in all hinges. Fig. 6 presents the sensitivity analysis results. The hinge was intact
when the spring constant was small, thereby implying a rotational support. Conversely,
the hinge was corroded when the spring constant was large, thus implying a fixed state.
From Fig. 6, a transition interval is observed between the spring constants k = 107 Nmm
and 1014 Nmm.
Analysis results for this bridge retains the behavior of the cantilever-suspended
girder bridge even when the spring constant of the hinge spring increases, because thehinge is locally constrained. Therefore, this model accurately captures the behavior of
the actual bridge used in subsequent investigations. The analysis cases to be consideredwhen altering the corroded hinge position are presented in Table 2 and Fig. 2. In Table
2, the number following the "s" in the case name indicates the corroded position. The
number of corrosion locations under the hinges is presented in Fig. 2. The following
letters indicate the hinges in girders G1–G4 that were corroded. Eigenvalue and static
analyses were performed for the 12 cases.
3.2

Eigenvalue analysis

The eigenvalue analysis results for the 12 analyzed cases are presented in Fig. 7. The
maximum changes between the intact and fixed states of the first and second bending
modes of the first torsional mode were approximately 0.07 Hz and 0.20 Hz, respectively; in case of the second torsional mode, the values were 0.01 Hz and 0.07 Hz,
respectively. The most significant change was observed in the second bending mode,
whereas the changes in the other modes were negligible (less than 0.1 Hz). Focusing
on the second bending mode, the difference in case-s2-all between the intact and fixedstates was approximately 0.1 Hz, which is the next most significant change after cases123-all. case-s2-all corroded all bearings at hinge position-2. Hence, the changes ina)

051015
Spring constant log10 [Nmm]

14.7

nd

3.823.7b)

tortional [Hz]1 -shellnd
2 -shell

st

10.9
2.8

1 torsional [Hz]2.9

bending [Hz]

11.0

st

nd

3.0

11.1

2

st

1 -shellnd
2 -shellst

1 bending [Hz]3.1051015
Spring constant log10 [Nmm]

14.6

Fig. 6. Relationship between spring constant and natural frequency during total hinge corrosion:(a) bending mode; and (b) torsional mode

6Table 2. Analysis case
S123 S1
Case name -all -all
Corrodedposition
1,2,3 1Corroded
bearing
allallS2 S3 S123 S12S23S1S2S3S1 S2-all -all -G1G4 -G1G4 -G1G4 -G1G4 -G1G4 -G1G4 -G4 -G4
2

3

1,2,3

1,22,312312all

all

G1G4 G1G4 G1G4 G1G4 G1G4 G1G4 G4 G4case-s123-G1G4, case-s23-G1G4, and case-s3-all were relatively large at approximately 0.1 Hz.
In contrast, case-s1-all exhibited the least change among all cases. From these results,corroded hinge position-2 and position-3, which bear the suspended span, tend toemerge in the natural frequency. This is because the intermediate suspended span iswhere the modes tend to dominate, as shown in Fig.8. The bending mode shapes oscillated most dominantly at the mid-suspended span. A simple girder supported this spanon top of the overhanging beams on both sides. Hence, the vibration mode of this spanis dominant owing to the vibration of the anchorage span on both sides compared withthe end-suspended span, where one end is located on the bearing, as illustrated in Fig.
8.
Moreover, comparing the amount of change in case-a2-all, case-a2-G1G4, and casea2-G4 from the intact state yielded values of approximately 0.1 Hz, 0.05 Hz, and 0.25
Hz, respectively. The number of corroded hinges is proportional to the frequency of thesecond bending mode. This is because the second bending mode shape dominates atboth the hinges of the intermediate suspension girder, as illustrated in Fig. 8.
s2-all
s23-G1G4
s1-G4bending [Hz]s1-all
s12-G1G4
s3-G1G4

3.0

s3-all
s1-G1G4
s2-G4

11.1

11.0

nd2.9

2

st

1 bending [Hz]s123-alls123-G1G4
s2-G1G4

2.8a)

1015
Spring constant log10 [Nmm]

10.9b)

1015
Spring constant log10 [Nmm]c)

2nd torsional [Hz]st

1 tortional [Hz]

3.9

3.8

3.7
1015
Spring constant log10 [Nmm]

14.8

14.7

14.6d)

1015
Spring constant log10 [Nmm]Fig. 7. Results of eigenvalue analysis: (a) 1st bending mode; (b) 2nd bending mode; (c) 1sttorsional mode; and (d) 2nd torsional mode

7a)b)c)d)Fig. 8. Mode shape of the shell model: (a)1st bending mode (shell); (b) 2nd bending mode;(c) 1st torsional mode (shell); (d) 2nd torsional mode (shell).

3.3

Static analysis

Fig. 9 presents the static analysis results for the 12 cases. The vertical deflection wasmeasured at the bottom surface under the lower flange, directly below hinge position1 of G4. In all the analysis cases, the vertical deflection was smaller than that in theintact state. Consequently, the rotation is restricted by the spring at the hinge, stiffness
increases, while deflection decreases.
In case-s123-all, the change between the intact and fixed states was the most significant, 0.38 mm, followed by case-s1-all, where the change was 0.35 mm. The differencein change between cases-s1-all and cases-s123-all was 0.03 mm. This indicates that thechange in hinge properties at the loading position is primarily responsible for the response change. This is because the restriction of the rotating spring increased as thedeformation increased. The cases with the largest amount of change are case-s1-all,case-s123-G1G4, case-s12-G1G4, and case-s1-G4.

3.4

Relationship between frequency and deflection

The correlation between the eigenvalue analysis results in Section 3.2 and the static
analysis results in Section 3.3 is discussed in this subsection. Fig.10 presents the relationship between the vertical deflection and second bending mode with the mosts123-alls123-G1G4
s2-G1G4s1-all
s12-G1G4
s3-G1G4s2-all
s23-G1G4
s1-G4
1.00

4.9
4.8

Deflection [mm]5.0s3-all
s1-G1G4
s2-G4

4.70.96

4.6
4.5

1015
Spring constant log10 [Nmm]Fig. 9. Results of static analysis

0.92

0-0.08fINT - f [Hz]-0.16

Fig. 10. Relationship between the naturalfrequency of the 2nd bending mode anddeflections

8significant change in natural frequency due to the spring constant. The horizontal axisof Fig. 10 represents the difference between the natural frequency of the intact state andthe natural frequency of each case, while the vertical axis denotes the deflection of eachcase divided by the deflection of the intact state––a nondimensional quantity.
The vertical deflection changed significantly when the spring was introduced athinge position-1, just below the loading position. However, the natural frequencychanged significantly in the case of the spring presented at hinge position-2 and position-3, which are the bearings of the suspended span. Consequently, the corrosion of
the hinges in the middle-suspended span was detected based on the change in the natural
frequency of the second bending mode. Furthermore, the difference in the deflections
due to direct loading indicated the corrosion of the hinges of the end suspension girder.

4

Summary

Differences in vibration and static characteristics of cantilever-suspended girder
bridges due to the corrosion damage of the hinge bearings were investigated using FEA
modeling; the effects of the locations of the corroded hinges and corrosion levels on theresponse of the bridge were analytically studied for the constructed model.
1. The change in the natural frequency due to corroded bearing at all locations is about
0.2 Hz in the second bending mode among all vibration modes. In the case of partialcorroded bearing, the natural frequency change is about 0.12Hz in the corroded
bearing at the suspended span. In contrast, the no change in natural frequency withthe corrosion of the end-suspended span bearing.
2. The deflection just below the target hinge bearing is about 0.3 mm smaller thanintact case when a direct load is applied to a corroded hinge.
3. In the case of corroded bearing in suspended span, the natural frequency and deflection are correlated.
4. In the future, the relationship between corrosion and bridge response clarify bymoving load analysis, the effective parameters for BHM investigate.

Acknowledgements
This work was supported by Grants-in-Aid for Ueda Memorial FoundationReference
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