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1、英文原文 A new way to design suspenders for through and half-through arch bridges R.J. Jiang, Y.Y. Chen, Q.M. Wu, W.M. Gai and D.M. PengShenzhen Municipal Design & Research Institute, Shenzhen, China1 ABSTRACT It is well-known that, in through and half-through arch bridges, the suspenders are important
2、components since they connect the bridge deck to the arch ribs. The collapse of bridge deck or arch ribs may be induced once one or more suspenders are broken. In this paper,the traditional design way of the suspenders in through and half-through arch bridges is discussed first. Based on the discuss
3、ion, a new way to design suspenders for arch bridges is then put forward. The reasonability of this new way is proved by numerical analysis examples. The impact effect of the remaining components of the arch bridge due to the breakage of one or more suspenders is obtained by appropriate simulation u
4、sing the comprehensive commercial software ANSYS. It can be concluded from the analysis in this paper that the new way to design the suspenders for the through and half-through arch bridges can assure the safety of the bridge effectively even though one or more suspenders happen to break.2 INTRODUCT
5、ION With the rapid development of new materials and construction technologies, the modern arch bridges are now entering a new era. The span length of the modern arch bridges is increasing,and the first two longest modern arch bridges are the Chaotianmen Yangtse River Bridge and the Lu pu bridge, res
6、pectively. The Chaotianmen Yangtse River Bridge built in 2008 is a tied steel truss arch bridge with a span length of 552m; and the Lupu Bridge built in 2003 is a steel box arch bridge with a central span length of 550m. They are both half-through arch bridges and respectively located in Chongqing a
7、nd Shanghai, China.Arch bridges can be classified into three categories according to the relative positions between the deck and the arch: deck-arch bridge, half-through arch bridge and through arch bridge (Cheng J. et al. 2003). For both half-through arch bridge and through arch bridge, the suspend
8、ers are the important components since they connect the bridge deck with arch ribs and transfer kinds of loads from bridge deck to arches, and finally to foundation. However, at the same time they are the vulnerable members to be damaged or ruined, because they usually work both in formidable natura
9、l environment and under fatigue-induced cycling loads (Li D.S.et al. 2007). It is a fact that the service life of the suspender is much shorter than that of the arch bridge, and the suspenders must be replaced timely (Tang H.C. 2005).The damage to the bridge deck or arches may be induced when one or
10、 more suspenders break, sometimes, even the collapse of the arch bridge may happen. In recent years, the accidents of arch bridges collapse caused severe casualties and huge economic loss (Li D.S.and Ou J.P. 2005 ). In order to know well about the health condition of suspenders, kinds of realtime mo
11、nitoring and diagnoses were conducted (Li D.S. et al. 2007). However, both the technologies and the materials for structural health monitoring and diagnose are not fully developed up to now (Li H.N. et al. 2008).In this paper, the traditional design way of suspenders in through and half-through arch
12、 bridges is discussed first. Based on the discussion, a new way to design the suspenders in through and half-through modern arch bridges is then put forward. With the application of this new way, the arch bridge will remain safe even though one or more suspenders happen to break.This new design way
13、is a different method from the health monitoring to control the safety of the modern arch bridges under the condition that the break of the suspender is uncontrollable.The reasonability and reliability of this new way is studied and proved by a numerical analysis example based on a real through arch
14、 bridge. The impact effect of the remaining components of the arch bridge due to the breakage of one or more suspenders is obtained by appropriate simulation using the comprehensive commercial software ANSYS. It can be concluded from the analysis in this paper that the new way to design the suspende
15、rs in modern arch bridges can assure the safety of the bridge effectively even though one or more suspend ers happen to break.3 DISCCUSION ON TRADITONAL DESIGN OF ARCH BRIDGE SUSPENDERSFor through-type and half-through-type arch bridges, the suspenders are anchored to arch ribs atone end and transve
16、rse beams at the other. Generally speaking, in the traditional arch bridge design the double-suspender anchorage (Fig.1) instead of the single-suspender anchorage is widely adopted in order to keep the arch bridge still safe and make the replacement of the suspenders more convenient when one suspend
17、er happens to break.Figure 1 : Double-suspender anchorage traditionally designed: (a) Parallel double-suspender anchorage,(b) Inclined double-suspender anchorage However, the two suspenders at the same anchorage are usually designed as the same both in material and cross sections; i.e., E1=E2, A1=A2
18、and 1=2, where E, A and are the elastic modulus, cross section area and inclined angles of the suspender, respectively. That means they have the same or similar stress and variation of stress in service. They are also under the same or similar corrosion environment since they are located at the same
19、 anchorage. Hereby, it can be concluded that the two suspenders at the same anchorage will fail at the same or similar time because of the almost equal level of both fatigue load and corrosion environment.Based on the discussion above, it can be seen that the double-suspender system designed in the
20、traditional way will not improve both the safety of the arch bridge and the convenience of suspenders replacement compared to the single-suspender system.4 A NEW WAY TO DESIGN ARCH BRIDGE SUSPENDERS In order to keep the remaining structure of arch bridge still safe when one suspender happens to brea
21、k, the double-suspenders must be designed with different service life. The only way to achieve this aim is to design the two suspenders at the same anchorage with different either material or cross section areas since they carry the same fatigue loads and are under the same corrosion environment.If
22、the two suspenders at the same anchorage are designed with different materials, the extra in convenience both in design and construction of the arch bridge will be induced. The better way is to make the two suspenders with different cross section areas A Fand AS(Fig.2)respectively. With different cr
23、oss section areas, the two suspenders at the same anchorage will have different stress levels and variation of stresses, that is to say, there are F,maxS,max, F,aF,a. max and a are the maximum stress and amplitude of the stress of the suspenders,respectively. Based on the basic theories of the mater
24、ial fatigue, the material or member has different service lives with different maximum stress and stress amplitude.Figure 2 : Double-suspender anchorage designed in new way : (a) Parallel double-suspender anchorage,(b) Inclined double-suspender anchorageThereupon, the two suspenders at the same anch
25、orage may have different service lives if they are appropriately designed with different cross section areas even though they are made of the same material and under the same fatigue loads and corrosion environment. During the service life of the arch bridge, the suspender with the larger cross sect
26、ion will still keep the arch bridge safe when the suspender with the smaller cross section at the same anchorage happens to break.The reasonability and reliability of this new way to consider the suspender design will be proved by numerical comparison study on a trough-type modern arch bridge, Shenz
27、hen North Railway Station Bridge, using comprehensive commercial software ANSYS in the following section in this paper.5 NUMERICAL ANALYSIS EXAMPLE5.1 Description of Shenzhen North Railway Station Bridge Shenzhen North Railway Station Bridge with a span length of 150m is a through-type modern concre
28、te-filled steel tubular arch bridge. It was built in 2000 and located at the Shenzhen North Railway Station, spanning all railways at that station. Rise-to-span ratio of this bridge is 1/4.5.The elevation view of the bridge is shown in Fig.3. The width of the general bridge deck is23.5m except at th
29、e end of the arch ribs with a bridge deck width of 28m. Horizontal cables in the steel box girders of the bridge deck are adopted to balance the horizontal force of the arch ribs. This bridge has two vertical arch ribs and each arch rib is composed of four concrete-filled steel tubes and thus has a
30、truss cross section of 2.0m in width and 3.0m in height. The material properties of the bridge are listed in Table 1. The more details about this bridge is found in Li etal. (2002).5.2 Finite element model of the example bridge A detailed finite element model (Fig.4) of the example bridge was develo
31、ped using the comprehensive commercial software ANSYS. In this 3 dimensional (3D) finite element model,every component is appropriately modelled.As mentioned above, each arch rib is composed of four concrete-filled steel tubes. These concrete-filled steel tubes are modelled by BEAM4 element. Since t
32、he concrete-filled steel tube is a composite member, the equivalent cross sectional properties and material properties are obtained first by editing an APDL file based on some equivalence rules, and then assign these equivalent cross sectional properties and material properties to the corresponding
33、beam elements. The equivalent cross sectional properties and material properties of the concrete-filled steel tubes are listed in Table 2.The BEAM4 element is also adopted to model the arch rib bracings, the longitudinal steel box girders, the steel tubes connecting the four concrete-filled steel tu
34、bes of the arch rib. The transverse steel girders of the bridge deck are modelled using BEAM188 element. The concrete plates on the top of the bridge deck are modelled as beam-grid using BEAM4 element. The suspenders are modelled by the LINK8 element. The cross section properties of these components
35、 except those of the transverse girders are listed in Table 3, BEAM188 element needs the cross section shape and dimensions as input information, the corresponding cross section properties will be calculated automatically by the program ANSYS. The connections between the longitudinal box girders and
36、 transverse girders, the concrete plates and the steel girders are all regarded as rigid and modelled by MPC184 elements. There are 4672 elements and 2448 nodes in total in this 3D finite element model.The boundary conditions of the 3D finite element model are also considered appropriately based on
37、the real situation of the bridge structure. In Shenzhen North Railway Station Bridge,the arches are fixed rigidly to the piers. The horizontal cables in the steel box girders of the bridge deck are adopted to balance the horizontal force at the fixed point connecting arch rib sand piers. Since the p
38、iers are not considered in this 3D finite element model, the ends of the arch ribs should be treated as fixed in all degrees of freedom, and the horizontal cables are ignored hereby. The two longitudinal steel box girders are supported on the transverse beams located at the inner side of the pier, t
39、he boundary conditions at these four ends of the two box girders are summarized in Table 4.There are two arch ribs in Shenzhen North Railway Station Bridge and 17 double-suspenders are anchored in each arch rib. For the convenience of the following analysis, the anchorages of each arch rib are numbe
40、red from 1 to 17 from west to east; the two suspenders at each anchorage are numbered as a and b for north arch rib, a and b for south arch rib, respectively.That is to say, the 34 suspenders in the north arch rib are marked as 1a, 1b, 2a, 2b, , 17a, and17b respectively; accordingly, those 34 suspen
41、ders in the south arch rib are 1a, 1b, 2a,2b, , 17a, and 17b (Fig.5) .5.3 Impact effect study due to the suspender break When one or more suspenders break, there will be impact effect on the remaining structure and its other components. It is very important to know well the impact effect. In this se
42、ction, the break of a suspender is appropriately simulated by assuming that two forces with equal value but opposite directions applied respectively to the broken suspenders anchorages on arch riband bridge deck decrease to 0 within a time slot t from the axial force value of that suspender.The impa
43、ct effect due to a suspenders break on the other components of the bridge is studied by carrying out time-history analysis based on the 3D finite element model in ANSYS. Of course, the impact effect due to a suspenders break on the other components of the bridge is closely related to the time slot t
44、 and the structural properties of the bridge. For a bridge in service, the impact effect is mainly dependent on the value of the time slot t. Here the impact coefficient is defined as the ratio of the structural response under both the impact and deal loads to that only under the deal loads. The str
45、uctural response of the bridge under kinds of loads refer to the stress, bending moment, axial force, displacement, and so on. In order to determine the appropriate value of the suspender break time slot t for the following analysis, the relationship between the impact coefficient and the suspender
46、breaktime slot tis studied based on different suspender break cases. Theoretically, when a suspender(a or a) breaks, the other suspender (b or b) at the same anchorage should be impacted mor strongly than other members of the bridge, such as bridge deck, arch rib, and so on. Because of the symmetric
47、 arrangement of the suspenders (Fig.5) in Shenzhen North Railway Station Bridge, the suspenders anchored to anchorage 1 to 9 are chosen to carry out the break simulation and impact effect analysis. At each anchorage, assuming the a (or b) suspender breaks, the curve to represent the relationship bet
48、ween the impact coefficient of the corresponding b (or a) suspender stress and the time slot tare obtained after the time-history analysis in ANSYS. The -t curves of four suspender break cases are plotted in Fig.6, shortest suspender 1a, second shortest suspender 1b, medium length suspender 5a and l
49、ongest suspender9a.From Fig.6, it can be seen that relatively larger variation of happens when the value of the time slot tin the range of (0.01s, 1.0s) . When the suspender break time tis longer than 1.0s,the impact effect is small and varies little with the increment of the break time. When the suspender break time tis shorter than 0.01s, the impact effect is obvious but varies little with the variation of the break time. So the impact effect d