design of steel cable stayed bridges with low height tower

8/10/2019 Design of Steel Cable Stayed Bridges With Low Height Tower

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Design of Steel Cable-stayed Bridge with Low Height Towers

Summary

A large cable-stayed bridge with low height towers is planned crossing a canal near one of themajor airports in Japan. As a result of the low towers and since the angle between girder axis andcable is small, the increase of deflection of stiffening girder becomes a design issue for earthquakeand wind resistance performance. In addition, there is the issue of soil-liquefaction duringearthquake because the bridge is located in a reclaimed soft ground area. In order to solve theseissues, structural stability of the main structure was confirmed by FE analysis. For wind resistance

performance, the behavior of the bridge was examined by wind tunnel experiment, and forearthquake-resistance performance of the basement, the movement of the tower foundations waschecked by 2-D dynamic effective stress analysis of the ground.

Keywords:Cable-stayed Bridge; Low height towers; Ultimate strength; Earthquake resistanceperformance; Wind resistance performance; Soil liquefaction.

1. Introduction

The proposed cable-stayed bridge planned at a harbor adjacent to a major airport in Japan has lowtowers compared to ordinary cable-stayed bridges due to aviation control restriction by the airport.The structure overview of this bridge is shown in Figures 1 and 2, and Table 1. It is plannedto be a

Tomoo TOMODAGeneral Manager, NIPPON

KOEI CO., LTD., Tokyo,[email protected]

Hidenori TAKAHASHISenior Researcher, Port and

Airport Research Institute,Yokosuka, [email protected]

Hiroshi NAKAGAWADirector, Yokohama Research

and Engineering Office forPort and Airport, Yokohama,[email protected]

Yozo FUJINOProfessor, University ofTokyo, Tokyo, [email protected].

Hiroshi KATSUCHIProfessor, Yokohama

National University,Yokohama, [email protected]

Fig. 1: General view of cable-stayed Bridge (planned)

Fig. 2: Detail of stiffening girder (planned)

Table 1: Structure specifications (planned)

Items Specifications

Bridge type 5 spans cable-stayed bridge

Bridge length (Span length L) 1,035m (L=575.0m)

Tower height 95.5m (clearance 47.0m)

Superstructure

Girder type Flat 3 cells box girder (steel)

Tower type A-shaped form (steel)

Cable system Multi-cable system (Fan type)

SubstructurePier type RC hollow pier (P1,P2,P5,P6)Foundationtype

Pire foundation (P1,P6)Pneumatic caisson (P2-P5)

(Unit: mm)

26,000

23,2001,400

14,400

1,400

5,800 5,800

3,000

1,600

1,400

Sidewalk Roadway

Protective fenceFairing

95.5m

P4P1 P2 P3 P4 P5 P6

1,035.0m (95.0+135.0+575.0+135.0+95.0m)

47.0m

Aviation control restrictionComposite floor Composite floor

Sea route Reclaimedland

L/2 point L/4 point


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large cable-stayed bridge with 575.0 m span length and 47.0 m clearance needed to cross the route.Its unusual proportion of tower height above the girder to the main span length is 1:11, because thetowers are located in the restricted area of the airport. There was concern about degradation ofseismic and wind-resistance performance since the vertical supporting effect of cable is reduced duetolow towers, and deflection of the stiffening girder is larger than the cable-stayed bridge of thestandard tower height. There was also concern about decrease of the safety against overall buckling

since the axial force of stiffening girder increases. Furthermore, foundation movement due toliquefied and laterally spreading soils by a large-scale earthquake can be predicted because thetowers and piers will be constructed on soft ground reclaimed land.

In order to solve these bridge design issues, we studied placing the intermediate supports of the sidespan to decrease deflection of main span, employed multi-cable system using parallel wire strandsand the main structure by High Performance Steels in Japan, and confirmed ultimate strength byelasto-plastic FE analysis. In addition, for wind resistance stability, the wind-resistance behavior ofthe cable-stayed bridge with low height towers was verified by executing of wind tunnel experimentusing a girder section model and full aeroelastic bridge model. For foundation movement due toliquefied and laterally spreading soils by a large-scale earthquake, seismic performance of thefoundation was confirmed by 2-D dynamic effective stress analysis of the ground. In this paper, wereport some technical issues and the solutions of this bridge found in the early stages of planning.

2. Design of steel cable-stayed bridge

2.1 Static structure analysis

The proportions (the ratio of tower height to the main span length) of this cable-stayed bridge aredetermined by the condition of bridge construction area. Because tower height above the girder islow, the angle between girder axis and cable is small, so the effect of the vertical support of thestiffening girders decreases, and deflection for live load (vertical deformation) increases. In addition,the axial force of the stiffening girders increases, buckling of the stiffening girder is an issue for thedesign. Therefore, the entire static analysis using 3-D frame model was executed. Then cable layoutthat met the solution of those issues and cross-sections of the main structure were decided by

calculating the cross-sectional force of member of permanent load such as dead load, live load,influence of temperature change, wind load.

First, deflection for live load was confirmed by placing the intermediate supports (P2, P5) of theside span, decreasing in vertical deformation of center span. Next, by multistage placing of parallelwire strands, elastic modulus of which is higher than stranded rope or spiral rope, as twovertical cable plane fan system, deflection for live load is satisfied with allowable value ofdeflection (span L / 400 = 1438 mm) according to design criteria [1]. A comparison table of cablelayout is shown in Table 2. For the stiffening girder cross section, considering weight saving andhigh torsional rigidity, steel members were determined as flat three-cell box-girder section to avoid

Table 2: Comparison table of cable layoutCASE 1:4 cable planes (fan type) CASE 2:2 cable planes (fan type) CASE 3:4 cable planes (harp type)

Sketch

Layout 10 cables of 4 vertical planes 20 cables of 2 vertical planes 11 cables of 4 vertical planesCost Cost ratio:1.03 Cost ratio:1.00 Cost ratio:1.15

Review

1) Economy is no good.

2) Wind-resistance performanceis no good.

1) Economy is good.

2) Wind-resistance performanceis superior to others.

1) Economy is bad.

2) Wind-resistance performanceis no good.

P1 P2 P3P1 P2 P3

Parallel wire strandsParallel wire strandsParallel wire strands

P1 P2 P3


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local buckling.Also, steel-concrete compositefloor is adopted in the stiffening girders of theside span as the function of the counterweightin order to reduce the negative reaction of theend supportwith fully loaded in center span.

For the towers, considering reduction of impacton the port facilities adjacent to this bridge bycompact size of foundation and aesthetic designof the entire bridge, an A-shaped form withsmall lower part is adopted. The cross-sectionof tower columns and cross beams are designedas steel members to improve the earthquake-resistance performance in soft ground.

For the overall buckling in the stiffening girderand the tower resisting axial force and bendingmoment, buckling mode was calculated asshown in Figure 3 by elasto-plastic buckling

analysis applying effective buckling lengthmethod (Ef method). The safety of the cross-section is ensured by calculating the bucklingstrength using buckling length of each member.Furthermore, as shown in Figure 4, elasto-

plastic FE analysis was conducted using theentire model by calculating yield load andultimate strength of the whole structure of

bridge to check the validity of buckling design of Ef method.

From these studies, even for a cable-stayed bridge that haslow towers, it was found that the issue indeflection for live load could be solved by placing the intermediate supports of the side span andmulti-cable placement of parallel wire strands. The safety to overall buckling could be also

confirmed when the axial force of girder increases by horizontal component of cable.

2.2 Seismic analysis

In Japan, a number of civil engineering structures such as bridges and port facilities have beendamaged by the 1995 Great Hanshin Earthquake that occurred in Kobe and nearby cities. Hence,earthquake performance of this bridge was confirmed by 3-D non-linear time history responseanalysis. A waveform of the scenario earthquaketaking into account the ground property of thelocation point was used as target waveform in addition to the seismic waveforms (L1: middle scaleearthquake, L2: large-scale earthquake) which are big earthquake ever to strike in Japan [1]. Inaddition, the inspection by analysis method (dynamic substructure method) that takes into accountthe dynamic interaction of foundation and soil was executed because the towers and piers will beconstructed on the soft ground of reclaimed land.

From the results of 3-D non-linear time history response analysis, sectional force of the towers atL2 earthquake (perpendicular direction to the bridge axis) is greater than the sectional force by theentire static analysis. Hence, High Performance Steels (yield point = 500N/mm2)are adopted in the

base of the towers and corners of the crossbeams, where the sectional force is large because thesteel thickness of cross section members was equal to or greater than 100 mm by usingconventional steel. In addition, the response of the dynamic substructure method with the waveformof the scenario earthquake as the target is small compared to the time history response analysis asshown in Figure 5. This confirmed that the generated stress of the member is equal to or less thanthe allowable value.

In addition, from soft ground analysis during earthquake as shown in the next section, thefoundation of the tower P4 has been found to move about 32 cm on the route (to the center of the

span) according to liquefied and laterally spreading soils at L2 earthquake. As a countermeasure,cable anchor mechanism where cable tension after L2 earthquake can be readjusted, was adopted bystudying the adjustment amount of cable prestressing. Thisaims to equalize the distribution of the

Loading

condition

(D+L+PS)

D: Dead load, L: live load, PS: Prestress force

1steigenvalue = 2.59

Fig. 3: Elasto-plastic buckling analysis results

Fig. 4: Elasto-plastic FE analysis results

P1 P2 P3 P4 P5 P6Buckling length

le = 33.0m

=1.109

=1.273

=1.279

D+L+PS+SD2+D+LLoad: D+L+PS+SD (foundations displacement) + (D+L)

(1) Stiffening girder yielding (=1.109)

(2) Cable yielding (=1.273)

(3) Ultimate load (=1.273)


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bending moment of the stiffening girders, in order to reduce the sectional force that is added to thesuperstructure by the residual displacement with laterally spreading soils.

From these analyses, even when the cable-stayed bridge with low height towers is built in softground, it was found that cross-sectional thickness of tower could be designed economically byadopting High Performance Steels. Even if the residual displacement of the foundation occurs bylaterally spreading soils during a large-scale earthquake, the soundness of a cable-stayed bridgecould be also confirmed by the readjustment of cable prestressing.

2.3 Soft ground analysis during earthquake

There is a possibility that a large residual displacement will occur with liquefied and laterallyspreading soils in addition to the large fluctuations of the foundation in an earthquake, because this

bridge will be constructed around the embankment of the reclaimed land. Therefore, 2-D dynamiceffective stress analysis by the finite element method for the ground including the tower and pierfoundation was executed with examination of the ground behavior in and after an earthquake, andthe earthquake-resistance performance of the foundation was studied.

Foundation type is planned as pneumatic caisson for the towers (P3, P4) and the piers (P2, P5), aspile foundation for piers (P1, P6). Including these foundation, 2-D dynamic effective stress analysisby the finite element method was executed. For convenience of analysis, the bridge was modeled intwo parts with the bridge center point as the boundary.

From the results of the 2-D dynamic analysis, it was found that large earth pressure duringearthquake will act on the foundation by soil liquefaction of reclaimed land behind the embankment

protection and the lower layer of alluvial silt for L2 earthquake [1]. Therefore reinforcement forshear failure was executed at thefoundation where resistance is insufficient.The residual displacement at the crest of

foundation, shown in Table 3 and Figure 6,is large (about 32 cm) at the tower P4close to the embankment protection.Sincethis residual displacement seriouslyimpacts onsafety and soundness ofsuperstructure, countermeasures, such asincreasing the movable amount of bearingand structure of releasing internal stress,had to be taken.

From these studies, in this bridge to bebuilt in soft ground, it was found that thereis a need to consider earth pressure and the

lateral movement of the foundation by soilliquefaction during L2 earthquake.

Fig. 5: Comparison study of time history response analysis and dynamic substructure method

Table 3: Residual displacement of foundationsPier No. P1 P2 P3 P4 P5 P6Foundationtype Pire Pneumatic caisson PireResidualdisplacement

15cm 31cm 8cm 32cm 3cm -3cm

Fig. 6: Soil liquefaction at L2 earthquake

Moment of stiffening girder

Time history response analysis

Dynamic substructure method 413N/mm2

< y = 430N/mm2

498N/mm

< y =500N/mm2

Time historyresponse analysis

Dynamicsubstructuremethodresponseanalysis

-1,316,000 kN m -1,089,000 kN mP1 P3P2 P4 P5 P6800,000

200,000

400,000

600,000

-600,000

-400,000

-200,000

0.0

-200,000 (kN m) Moment of tower

P4Caisson

P5Caisson

P6Pire

32cm 3cm -3cm

-2m4m 2m 0mDisplacement direction


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3. Wind tunnel test

3.1 Girder section model

The bridge is planned with sidewalks. A protectivefence of falling objects will be installed to prevent

objects dropping or pedestrians deviating off thesidewalk.By this protective fence may reducing wind-resistance performance of the bridge. In addition, thecable is placed densely around the girder for the lowtowers. Therefore, wind tunnel experiment using agirder section model of the cable-stayed bridge withlow height towers was executed and the influence ofcable and protective fence (h=2.0m) was examined.

Modeling of cable and protective fence for the part ofcenter span of the stiffening girder which is connectedlargely to wind-resistance performance were executed(scale 1:70). The model is shown in Figure 7. The

extent of the influence by the cables was settled at thesame level to girder height (3 m) according to theresults of a preliminary experiment. Protective fenceis 2.0 m height and about 30% solidity ratio. Windtunnel experiment was executed at wind tunnel forstructures in Yokohama National University (testsection: 1.8 m height, 1.8 m width).

Relation between torsional maximum amplitude andwind speed (reduced velocity) is shown in Figure 8.Vortex induced vibration has not been identifiedregardless of the presence or absence of cables or

protective fence. However, for torsional flutter

vibration, critical flutter wind speed tended to be lowdue to the effect by cables and protective fence. Theextent of the influence tended to be the largest inwhen protective fence has been installed, and to belarger in span L/4, in which many cables are placed.Because critical flutter wind speed of divergentvibration is close with reference wind speed (Urf =69.3 m/s) of torsional flutter vibration when protectivefence has been installed, fairing shape is changed (toangle modernized type) to improve wind-resistance

performance.

3.2

Full aeroelastic modelIt was intended thatthe installation range of protectivefencewill be determined according to the usage ofpedestrians after the bridge is opened to traffic.However, the influence to wind-resistance

performance that depends on the installation rangewas verified by full aeroelastic bridge modelexperiment (scale 1:150) using the elastic model.From the experiment results of girder section model,cross section shape of the girder was settled as"fairing of angle modernized type + protective fence(h = 2.0 m)". Installation range of protective fence and

wind direction is shown in Figure 9.Wind tunnel experiment was executed at full span

Fig. 7: Girder section model (S=1:70)

Fig. 8: Torsion of girder and wind speed(smooth flow)

0.0

1.0

2.0

3.0

0 20 40 60 80 100

Torsionresponse(de

g)

Wind speed (m/s)

Girder

Girder+Cable (L/2 point)Girder+Cable (L/4 point)

Girder+Protective fence

Fairing type: primal type

Protective fence : h=2.0m

Urf = 69.3m/s

Fig. 10: Full aeroelastic model (S=1:150)

Fig. 9: Setting range of protective fence

Wind direction (Sidewalk side)

P1 P2 P3 P4 P5 P6

Case 2: One side of bridge

Case 3: Both sides of bridge

Case 3: Both sides of bridge

Case 1: Sidewalk part


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wind tunnel (test section 1.9 m height, 16.0 m width) inthe University of Tokyo. Smooth flow and turbulentflow (turbulent intensity 11.0%) were used [2]. Themodel is shown in Figure 10.

Relation between vertical amplitude of the stiffening

girders in the center span and wind speed (reducedvelocity) is shown in Figure 11. It indicates that there isno restriction by the installation range of protectivefence since the influence by the installation range of

protective fence is small and both smooth flow andturbulent flow are satisfied with prescribed wind-resistance performance. However, at full aeroelastic

bridge model, vortex induced vibration (8-9 m/s windspeed, about 400 mm half amplitude) was confirmed,and torsional flutter vibration which affects wind-resistance performance (more than 70 m/s wind speed)was not confirmed. For vortex induced vibrationconfirmed by full aeroelastic bridge model tests, we have verified by stress calculation that impact

does not occur to the structure itself since amplitude is small.

From these wind tunnel experiments, it was found that even if a protective fence is installed in thegirder that cable is closely placed, wind-resistance performance is confirmed by the aerodynamicsmeasures of fairing.

4. Conclusion

(i) Deflection for live load in cable-stayed bridge with low-height towers can be satisfied with thedesign allowable limit of deflection [1]byplacing the intermediate supports of the side spanand multi-cable placementof parallelwire strandsas two vertical cable plane fan system.

(ii) For the overall buckling in the stiffening girders where axial force and bending moment are high

compared to ordinary cable-stayed bridges, it was verified that safety on buckling resistance of thebridge can be ensured by a design utilizing elasto-plastic buckling analysis applying effectivebuckling length method (Ef method).

(iii) It was found that soil liquefaction during expected earthquake would generate large earthpressure on the foundation, and residual displacement would occur to the foundation by laterallyspreading of reclaimed soil. However, it is possible to ensure the soundness of this cable-stayed

bridge after a large-scale earthquake by the readjustment of cable prestressing.

(iv) For torsional flutter vibration, wind tunnel experiment confirmed that critical flutter wind speedtended to be low due to the effect by densely placed cables and protective fence. As acountermeasure, by reviewing the fairing shape of the stiffening girders it was confirmed that suchvortex induced vibration, which affects adversely to the structure itself or torsional flutter vibrationwhich becomes problem on wind-resistance performance, does not occur.

5. References

[1] Japan Road Association, SPECIFICATION FOR HIGHWAY BRIDGES 2002.

[2] Yasuaki Ito, Yozo Fujino, Hiroshi Katuchi, Hidenori Takahasi, Hiroshi Nakagawa, TomooTomoda, Tomonori Kawabe Study on wind-resistance behavior of cable-stayed bridgewith low height towers by full aeroelastic bridge model,Proceedings of the 22nd NationalSymposium on Wind Engineering, 2012, pp.275-280

Fig. 11: Torsion of girder and windspeed (smooth flow)

0

100

200

300

400

500

0 20 40 60 80 100

Verticalresponse(

mm)

Wind speed (m/s)

Case 1: Sidewalk part

Case 2: One side of bridge

Case 3: Both side of bridge

Fairing type:angle modernized type

Protective fence : h=2.0m

design of steel cable stayed bridges with low height tower

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