Static analysis of cable-stayed bridge with CFT arch ribs-外文翻译原文.pdf

Journal of Constructional Steel Research 65 2009 776 783 Contents lists available at ScienceDirect Journal of Constructional Steel Research journal homepage Static analysis of cable stayed bridge with CFT arch ribs Shun ichi Nakamuraa Hiroyasu Tanakab Kazutoshi Katoa aDepartment of Civil Engineering Tokai University 1117 Kitakaname Hiratsuka 259 1292 Japan bDesign Section Bridge Division Kawada Industry Co Takinogawa Kita ku Tokyo Japan a r t i c l ei n f o Article history Received 29 February 2008 Accepted 18 May 2008 Keywords Arch bridge Cable stayed bridge Concrete filled steel tube a b s t r a c t A new type of cable supported bridge cable stayed CFT arch bridge was proposed and its static strength was studied in this paper Arch ribs consist of concrete filled steel tubes CFT CFTs have high resistance against bending moments and compressive axial forces and are ideal as arch ribs A cable stayed CFT arch bridge with a main span of 300 m was designed and the safety of its structural members was checked by the limit state design method Large deformation analysis was used to obtain sectional forces The CFT arch ribs and the steel box girders and towers of the designed bridge satisfied the required safety criteria for ultimate design loads The applied loads were further increased until the bridge collapsed when the arch ribs buckled The amount of steel required for the cable stayed CFT arch bridge was significantly lower than that for the cable stayed bridge It has been found that the proposed cable stayed CFT arch bridge is feasible and potentially economical 2008 Elsevier Ltd All rights reserved 1 Introduction The authors have proposed new types of bridges using concrete filled steel tubes CFT 1 4 One of the ideas was adopted and actually constructed for a railway bridge 3 as shown in Fig 1 The CFT girder has many advantages First it has large axial and bending strength due to the confined effects of the concrete inside the steel tubes 5 Second levels of noise and vibration caused by trains and vehicles are much lower in the CFT girders than in the steel girders 3 This is particularly advantageous for railway bridges Third assteelpipesareproducedatsteelmills theamount of work in welding and assembling of the CFT girders in the fabrication process is much smaller than that for conventional plate girders Fourth as steel tubes work as moulds for concrete pouring the concrete filling work is easy Fig 2 is another idea a suspension CFT arch bridge 3 The arch rib is CFT which has large resistance against axial compression and bending moments These CFT arch ribs are suspended by the suspension cables This bridge is basically a mixed structure of suspension bridge and CFT arch bridge Fig 3 is a cable stayed bridge using the pipe girder 4 The girder consists of a large center pipe girder and two small edge pipe girders with an orthotropic steel deck Concrete is poured inside the pipes in the side spans and tower positions to increase resistance against axial compressive forces and to restrain uplifts The cable stayed CFT arch bridge Fig 4 is proposed and its static strength is studied in this paper The arch ribs consist of CFT Corresponding author Tel 81 463 58 1211 fax 81 463 5045 E mail address snakamu keyaki cc u tokai ac jp S Nakamura Fig 1 CFT girder bridge andaresuspendedbycablestays Asimilarbridgewasconstructed in Malaysia with arch ribs consisting of steel box sections 6 It is expected that the CFT arch ribs have higher resistance againstaxialcompressionandbendingmomentsandalsoaremore economical than steel box sections Horizontal thrusts exist at the arch supports of the proposed bridge It is assumed in this bridge that the ground is hard and strong enough to bear these horizontal thrusts In this paper large deformation structure analyses are con ducted to obtained design sectional forces and then the safety of structuralmembers are checked for ultimate loads The global buckling strength of the structure is also found Approximate con struction cost is also evaluated to compare a cable stayed CFT arch bridge with a conventional steel cable stayed bridge 0143 974X see front matter 2008 Elsevier Ltd All rights reserved doi 10 1016 j jcsr 2008 05 005 第95页 共102页 S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783777 Fig 2 Suspension bridge with CFT arch ribs Fig 3 Cable stayed bridge with CFT girders Fig 4 Cable stayed bridge with CFT arch ribs 2 Dimensions of the assumed cable stayed CFT arch bridge The layout of the assumed cable stayed CFT arch bridge is shown in Figs 5 and 6 The center span is 300 m with two side spans of 100 m each The tower is an inverse Y shape 91 0 m high The girder is a steel box girder with orthotropic deck Fig 7 with a width of 32 0 m accommodating six lanes The deck is 12 mm thick the web is 2000 mm high and 19 mm thick and the lower flange is 19 mm thick The diaphragms are arranged at every 5 0 m All of the steel plates are assumed to have a yield stress of 355 MPa and a tensile strength of 490 MPa The arch rib consists of a steel pipe with a diameter of 1700 mm and a thickness of 20 mm filled with concrete Fig 8 The same steel grade of the girder is assumed for the steel pipe Light aggregate concrete with a unit weight of 15 kN m3is used for the concrete filling It is well known that concrete filling improves resistance against local bucking of steel plates and therefore increases resistance against resistance axial and bending moments 5 The cross section of the tower is rectangular in the lower part and square in the upper part as shown in Fig 9 This is because the stays are anchored at the upper part and the upper column is separated into two columns at the lower part to let the girder go through Cross beams connect the two side arch ribs and rolled H beams with a height of 700 mm and a width of 250 mm are used Parallel wire strands consisting of 7 mm diameter high strength wires with a tensile strength of 1570 MPa are used for stays and hangers The numbers of wires are decided by the design tensile forces 3 Static structural analyses Static structural analyses are conducted to obtain design sectional forces The structural model is three dimensional as shown in Fig 10 where all of the elements are beam elements As theassumedbridgeisalongspanarchbridge theanalysisincludes the non linearity of geometric deformation Pre stress forces are introduced into the stay cables so that the bending moments of the girder and tower due to dead loads are flattened Five patterns of live loads are considered as shown in Fig 11 The live loads consists of the concentrated load 10 kN m2with 10 m long and the distributed load 3 0 kN m2 Axial forces and bending moments of the arch rib are shown in Figs 12 and 13 respectively Three load cases are shown The first case is the result due to the dead load and cable pre stress forces multipliedbytheloadfactorof1 1 Thiscaseisfortheserviceability check The second case is the first case result added to the result due to the maximum live load multiplied by the load factor of 1 98 This is for the ultimate safety check The third case is the first case result added to the result due to the minimum live load multiplied by the load factor of 1 98 This is also for the ultimate safety check Fig 12 shows that axial forces are overall in compression and are minimum at the span center Fig 13 shows that there are positive and negative bending moments depending on the live load cases and the value is maximum at the quarter point A L 4 instead of at the center point B Axial forces and bending moments of the girder are shown in Figs 14 and 15 respectively Three load cases are also shown Fig 14 shows that axial forces are overall in compression and are maximum at the tower positions Fig 15 shows that there are positiveandnegativebendingmomentsdependingontheliveload cases and the positive bending moments are maximum at the side spanofpointCandatthemainspanofpointE Thesebehaviorsare the same as those of conventional steel cable stayed bridges Axial forces and bending moments of the tower are shown in Figs 16and17respectively Threeloadcasesarealsoshown Fig 16 shows that axial forces are in compression and increase from the top to the base Fig 17 shows that bending moments have two peaks at the cable anchor position F and at the base point G On this cable stayed CFT arch bridge the girder is suspended by the cables and the arch ribs It is therefore expected that this bridge shows intermediate characteristics between the cable stayed bridge and the arch bridge The deflection due to live loads can be smaller than that of the conventional steel cable stayed bridge To validate this a steel cable stayed bridge with same dimension of the cable stayed CFT arch bridge is designed The deflection due to fully distributed live load LC1 of the cable stayed CFT arch bridge is 362 mm whereas that of the conventional cable stayed bridge is 747 mm This suggests that the applied loads are sustained by both the cable system and the arch system on the 第96页 共102页 778S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783 Fig 5 Layout of cable stayed CFT arch bridge Fig 6 Layout of tower cable stayed CFT arch bridge and therefore it has higher bending rigidity with less deflection than the steel cable stayed bridge Although it is difficult to show an accurate fraction of the total load shared by the cable stayed system and the arch system this particular case study shows the fraction of both the systems is about half 4 Safety check of members for ultimate state 4 1 Basic equations In this chapter safety of the arch ribs and the girder and tower steel sections are checked for the ultimate design loads The basic equation for the check of ultimate state is Eq 1 7 i Sd Rd 51 0 1 where iis the structure factor 1 1 and Sdis the response expressed by Eq 2 Sd aS Fk f f 2 Fig 8 CFT arch rib Fig 9 Cross section of steel towers where Fkis the nominal design load athe analysis factor 1 0 fthe load factor 1 1 for dead load 1 2 for live load and f the modified load factor 1 65 for live load Rdis the resistance expressed by Eq 3 Rd R fk m b 3 where fkis the nominal material strength mthe material factor 1 05 for steel 1 3 for concrete and bthe member factor 1 1 for steel member 1 3 for concrete member These factors are adopted from the Japanese Specification for Steel Concrete Composite Structures 7 4 2 Safety check of CFT arch ribs The safety check of CFT arch ribs is carried out by Eq 4 i Md Mud 51 0 4 Fig 7 Steel box girder with orthotropic decks 第97页 共102页 S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783779 Fig 10 Analytical model Fig 11 Design live loading cases Fig 12 Axial force of CFT arch ribs where Mdis the design bending moment and Mudthe ultimate strength of bending moments Mudis a function of axial compres sive force To find Mudthe steel pipes and filled concrete of CFT is divided into fiber elements Figs 18 and 19 show the stress and strain relations of steel and concrete used for this analysis When the design bending moment is within the curve shown in Figs 20 and 21 it satisfies Eq 4 The CFT arch rib must also satisfy Eq 5 i N0 d N 0 oud 51 0 5 where N0dis the design axial compression and N0oudthe ultimate buckling strength It is understood from Figs 20 and 21 that N0d is within N0oud Table 1 shows the safety check of the arch ribs at Point A quarter span and Point B centre span which satisfies the Eqs 4 and 5 Fig 13 Bending moment of CFT arch bridge Fig 14 Axial force of girder Fig 15 Bending moment of girder 4 3 Safety check of girder and tower steel sections Thegirderandthetowerhavesteelboxsectionsandtheirsafety check is carried out by Eq 6 i Nsd Nrd Msdz Mrdz Msdx Mrdx 51 0 6 where Nsdis the design axial compression Nrdthe ultimate buckling strength Msdzthe design bending moment in the longitudinal direction Mrdzthe ultimate strength of bending moments in the longitudinal direction Msdzthe design bending 第98页 共102页 780S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783 Fig 16 Axial forces of tower columns Fig 17 Bending moments of tower columns Fig 18 Stress strain relation of steel moment in the transverse direction and Mrdzthe ultimate strength of bending moments in the transverse direction These equations must be satisfied for both upper and lower flanges Table 2 shows safety check of the steel girder at points C D and E Table 3 shows safety check of the steel tower at points F and G The buckling strength is found by the elastic buckling analysis It is foundbythesefiguresthatallofthesevaluesofEq 6 aresatisfied It is understood from this chapter that the assumed cable stayed CFT arch bridge is feasible Fig 19 Stress strain relation of concrete Table 1 Safety check of CFT arch ribs Point A at quarter span Md kN m 10 913N0d kN 33 999 Mud kN m 26 304N0oud kN 45 877 i Md Mud 0 46 i N0d N0oud 0 82 Point B at half span Md kN m 6173N0d kN 33 153 Mud kN m 23 988N0oud kN 52 551 i Md Mud 0 28 i N0d N0oud 0 69 第99页 共102页 S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783781 Table 2 Safety check of girders Point C in side span Nsd 11 401Nrd 293 795Nsd Nrd0 04 Msdz93 743Mrdz338 107Msdz Mrdz0 28 Msdx 36 319Mrdx 67 056Msdx Mrdx0 54 Nsd Nrd Msdz Mrdz Msdx Mrdx 0 94 Point D at tower Nsd 16 995Nrd 323 444Nsd Nrd0 05 Msdz 77 877Mrdz 338 107Msdz Mrdz0 23 Msdx26 986Mrdx46 622Msdx Mrdx0 58 Nsd Nrd Msdz Mrdz Msdx Mrdx 0 95 Point E in main span Nsd 10 466Nrd 310 107Nsd Nrd0 03 Msdz85 789Mrdz338 107Msdz Mrdz0 25 Msdx16 783Mrdx42 000Msdx Mrdx0 40 i Nsd Nrd Msdz Mrdz Msdx Mrdx 0 76 Nsd Design Axial Force kN Nrd Axial Resistant Force kN Msdz Design Longitudinal Bending Moment kN m Mrdz Longitudinal Resistant Bending Moment kN m Msdx Design Transverse Bending Moment kN m Mrdx Transverse Resistant Bending Moment kN m Table 3 Safety check of tower columns Point F in upper part Nsd 28 107Nrd 117 570Nsd Nrd0 24 Msdz39 308Mrdz109 984Msdz Mrdz0 36 Msdx671Mrdx 100 032Msdx Mrdx0 01 i Nsd Nrd Msdz Mrdz Msdx Mrdx 0 66 Point G in lower part Nsd 25 270Nrd 72 875Nsd Nrd0 35 Msdz13 121Mrdz62 427Msdz Mrdz0 21 Msdx 8 998Mrdx 42 984Msdx Mrdx0 21 i Nsd Nrd Msdz Mrdz Msdx Mrdx 0 84 Notations are the same as Table 2 Fig 20 Safety check of CFT arch rib at quarter span A 5 Global buckling strength In this chapter global buckling strength of the cable stayed CFT arch bridge is evaluated using the analysis including non linear geometric deformation The calculation is carried out as follows First dead load and cable pre stress forces with a load factor of 1 1 and live load with a load factor of 1 98 is applied Two live load cases LC1 and LC5 as shown in Fig 22 are considered Then 5 0 of the live load is incrementally applied until the bridge collapses Fig 23 shows the vertical displacement versus applied load at thequarterpositionandFig 24showsthehorizontaldisplacement Fig 21 Safety check of CFT arch rib at half span B at the same position It is understood from Fig 24 that for the live load case LC1 the horizontal displacement sharply increases at a total load of 2826 kN m Fig 23 shows the vertical displacement alsosignificantlyincreasesatthisload ItisunderstoodfromFig 24 that for the live load case LC5 the horizontal displacement sharply increases at a total load of 2475 kN m Fig 23 shows the vertical displacement also significantly increases at this load Fig 25 shows the vertical displacement versus applied load at the center position and Fig 26 shows the horizontal displacement at the same position It is understood from Fig 26 that for the live loadcaseLC1thehorizontaldisplacementsignificantlyincreasesat 第100页 共102页 782S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783 Fig 22 Design live loadings for buckling analysis Fig 23 Vertical displacements of CFT arch ribs at quarter span Fig 24 Horizontal displacements of CFT arch ribs at quarter span a total load of 2826 kN m Fig 25 shows the vertical displacement sharply increases at this load It is understood from Fig 26 that for the live load case LC5 the horizontal displacement sharply increases at a total load of 2475 kN m Fig 23 shows the vertical displacement also significantly increases at this load Fig 27 and Fig 28 show deformation shapes due to LC1 at a load of 2826 kN m indicating that the arch rib buckles vertically in a half sine wave and horizontally in two sine waves Figs 29 and Fig 25 Vertical displacements of CFT arch ribs at half span Fig 26 Horizontal displacements of CFT arch ribs at half span Fig 27 Vertical deformation due to LC1 Fig 28 Horizontal deformation due to LC1 Fig 29 Vertical deformation due to LC5 Fig 30 Horizontal deformation due to LC5 30 show deformation shapes due to LC5 at a load of 2475 kN m indicating that the arch rib buckles vertically and horizontally on the half span asymmetrically The deformation shapes agree with the results of Figs 23 26 The load intensity of 2826 kN m in LC1 corresponds to 1 1 D PS 6 05 1 98L and that of 2475 kN m 第101页 共102页 S Nakamura et al Journal of Constructional Steel Research 65 2009 776 783783 Table 4 Required amount of steel for cable stayed CFT arch bridge MembersCable stayed CFT arch bridgeCable stayed steel bridge Girders46 04253 566 Towers8 76720 722 Cables1 0911 296 CFT Arch ribs5 199 Arch hangers69 Cross beams1 005 Total62 17375 584 indicate rate 0 82 1 0 unit kN in LC5 corresponds to 1 1 D PS 5 25 1 98L This means that the assumed bridge has a sufficient resistance against global bucking 6 Construction cost and method Required amounts of steel for the proposed cable stayed CFT arch bridge and the conventional steel cable stayed bridge are shown in Table 4 The cable stayed CFT arch bridge needs a significantlysmalleramountofsteelforthegirderandtowersthan the steel cable stayed bridge Although the CFT bridge needs extra steel for the steel tube arch ribs cross beams and arch hangers the total steel amount is 18 less than for the conventi