New Pet in Gongqiao: Net -shaped boom arch
In 2014, Russia was built into the Bugrinsky Bridge (Figure 1), a road tie arch bridge, two -way 6 lanes, 36.9m in the bridge, and 380m in the main cross! The Jinan Qilu Yellow River Bridge, which is under construction in my country, is a three -span -tie arched bridge designed by the same level of public rails, two -way 8 lanes, a bridge width of 60.7m, and a maximum span of 420m!
Figure 1 The New Siberian Buglinsk Bridge (2014)
Why is a seemingly conventional rod arch bridge, why is there such a considerable leapfrog ability? If you look closely, you can find that the arrangement of these arch bridges is different from the conventional rod arch bridge. This is the network -shaped boom arch bridge (net arch) discussed in this article.
From traditional rod arch to mesh booth arch
This topic should start with the tie arch. As we all know, the level of arch of arch depends on a solid foundation. When the local base is not suitable for the horizontal force, a horizontal flexible tie (called a rod) can be added between the two arched toe (arch feet) of the same arch to form a rod arch; It is called a beam or a rigid beam) to bear the horizontal force. In this way, the horizontal force of the arch does not need to bear it.
按现在的惯常说法,对采用竖吊杆布置的系杆拱,根据其拱肋和系杆（梁）的相对刚度大小,可分为柔性系杆刚性拱（图2a,即系杆拱）、 Rigid rod flexible arch (Figure 2B) and rigid rod rigid arch (Figure 2C). The latter two are actually arched-beam combined structures.
Figure 2 Various types of tie arched bridges (red line represents tie rods or beams)
The concept of the tie arch bridge has a long history. As early as 1482, Da Vinci painted the sketch of the arched bridge. In the book “New Machine” of European scholars Veranzio (1551-1617), you can also see the imagination composition of the tie arch bridge. As for the engineering application of the tie arch bridge, according to the author’s clumsy opinion, it starts in the first half of the 19th century.
In 1849, British engineer Bruner used cooked iron to build a 62M Windsor Railway Bridge. The structure of this bridge is similar to Figure 2B, but the cross -crossing rod is added between the vertical rods. In 1841, American engineer WHIPPLE obtained the patent of the bow string truss bridge. The so -called bow string truss means that the upper string rod is arc -shaped, the lower string flexible rod is arranged horizontally, and the truss of several vertical rods and interval cross -diagonal rods is arranged. The Hewell Iron Bridge (Figure 3) was built in 1869, with a span of 33.5m and a bridge width of 7m. It can be seen that the bridge is slightly transformed (remove the cross -diagonal rod and let the vertical rod hang directly to the bridge surface) is a modern rod arch bridge.
Figure 3 American HP Iron Arch Bridge (1869)
The flexible arch of the rigid rod is also known as Langele arch, named after Austrian engineer Langer. In 1858, Langer proposed that flexible arch was added to the top surface of the high steel plate beam (setting hinge vertical boom); because flexible arch is used to stigmatize steel beams (instead of rigid beams to serve flexible arch), this structure is Also called Langel Liang. In 1883, the first Langel Liangqiao was built. By the way, the self -anchor suspension bridge was also the earliest proposed by Langle in 1859.
The rigid rod rigid arch is also known as Luoze arch, named after the name of German engineer Lohse. In the second half of the 19th century, the upper and lower string rods were arc -shaped truss bridges, called dual -convex mirror trusses or fish belly beams, and used the patent proposed by German engineer Paoli in 1865. The SmithField street bridge (above Figure 4) built in Pittsburgh in 1883 is a typical bridge. Luo Ze changed the lens truss to the upper and lower arches of the bow -shaped truss, and the structure of only vertical rods was arranged in the middle. This structure looks like the structure characteristics of fish abdomen beams and rod arch. However, how it evolved into “rigid rod rigid arches” later, it remains to be explored.
Figure 4 American Smithfield Street Bridge (Part 1, 1883) and Burger Beiti Beihe Bridge in Hamburg (below, 1872)
In addition to the vertical boom, the bipping rod of the tie arch bridge can also be used in other layouts (such as fan -shaped layout, oblique layout, etc.). The most representative is Danish engineer Nielsen, which was proposed by the sloping boom (no vertical boom, see Figure 2D) proposed in 1926, and later called the Nielsen arch or Nielsen system. The facade layout of the oblique boom may not cross (shown in the solid line in the figure); or only once (that is, add Figure 2d medium dotted part).
Imagine the half span of the tie tie arches loaded. For the vertical booth arches, several vertical boils near the arched toe will exit work due to relaxation, which leads to the increase in the arched and beams of the corresponding parts; For Nielson arch, half spans that are not loaded have only partially distributed diagonal booms withdrawing out of work. It can be seen that with a sloping birch instead of the vertical boom, although the axis of the arched rib and the beam will not change significantly, the bending moment and vertical deflection can be reduced. In addition, the sloping boom also enhances the overall stiffness and stability of the tie arch bridge, and the frequency of vibration of the structure is improved.
In 1933, the Castelmoron Bridge built in France (Figure 5), a steel concrete arch bridge without a cross -inclined biploma with 140m span, was the most similar bridge span at that time. However, due to the constraints of the boom materials and calculation methods, for a long period of time, the Nielsen arch bridge with a cross -inclined crane was not built.
Figure 5 French Castelmoron Bridge (1933)
The world’s large span Nielsen arched with cross -diagonal booms began in Japan in the 1970s and 1980s. In Japan, such a bridge is called the Nielson-Luoze Bridge. Typical bridges include: OUNOURA Bridge (span 195m, 1972), UTSUMI bridge (span 219.6m, 1988), etc. For more than 10 years, the Nielsen arch bridge has received more attention. In 2013, the Netherlands was built into the De Oversteek Highway Bridge with a length of 285m. my country ’s high -speed rail has also built a number of steel pipe concrete Nielsen arch span of about 100 meters, such as the Hujiajia Bay Bridge of Wudang House and the Beijing -Shanghai high -speed rail.
If the slashing lever is encrypted again, will the force of the tie arches be better? In fact, the Germans tried before the Nielsen system came out. In 1878, a railway arched bridge was built in Risa, a eastern city of Germany (Figure 6). However, it is conceivable that in that era, the computing and design difficulties of such a complex bridge structure, complicated construction construction, and difficult to be competitive. As a result, such innovative practice can only be tasted.
Figure 6 The Railway Bridge of the Railway Railway, Germany (1878)
By 1955, Professor PER TVEIT of the University of Norwegian University proposed the concept of a mesh boom arch (Figure 2E) in his then master’s dissertation. The pole and other slanting bars are crossed at least twice.
The significant stressing characteristics of mesh -like arches are the small bending moment that the arches and the beams are, and the distribution is more uniform. Figure 7 shows the comparison of the three boom arrangement methods, as well as its arched ribs and tiered beams affecting the line in L/2, L/4. In contrast, the arched ribs of the mesh arch and the bending moment of the tiered beam affect the line value of the line, and the decrease is obvious. This means that the mesh bipper can largely reduce the bending moment of the arched ribs and the beams. As a result, the arched ribs and tiered beams can be designed more slender, the structure is more transparent and light, and the materials will be used less. In this way, the economic and aesthetic effects appear.
Figure 7 The comparison of the tie arched bending moment of different boom arranges
According to the author’s understanding, the significant structural characteristics of the mesh arch can be regarded as a means of adjusting the architectural behavior (including stability and dynamic behavior) to adjust the arch structural behavior. The mesh boom is not only a simple transmission component, but also an important part of the structural system. Therefore, such arch bridges shown in Figure 2C, whether it is a subordinate arch arched or a medium -ended arch, a basket arch or an outer tilt arched, a regular arch or a alien arch, a single material arch You can achieve good results through the optimization layout of a mesh boom. According to Professor PER TVEIT, if the design and construction is well -designed, the mesh arch is usually saved 40%of the construction cost compared to the traditional tie arch.
Since the 1960s, about 30 countries in the world (mainly Japan, Germany, Norway, the United States, etc.) have built more than 120 mesh arch bridges (including several railway bridges), most of which are in the past 20 years. Constructed. The first mesh arch is the Norwegian Steinkjer Highway Bridge participated in the design of Professor TVEIT. It was completed in 1963 and was completed in 1963. In the same year, the German Fermarn Strait Bridge has a span of 248m and a two -purpose public iron. It is a classic representative of the early mesh arch bridge. See Figure 8.
Figure 8 Norwegian Steinkjer Bridge (left) and the Fermarn Strait Bridge (right) in Germany
The following table lists the top ten mesh arch bridges in the world. After the completion of the Jinan Qilu Yellow River Bridge in China, its span ranked first in the world.
The rigid rod arch shown in FIG. 2F belongs to an external ultra -static small thrust combination system. Limited to space, here is omitted.
Conditional arch bridge structure and instance
The main structural characteristics of the mesh arch bridge are briefly divided into the following.
The arched ribs are mostly steel boxes and steel pipe structures, or steel pipe concrete structures, rarely use steel concrete. Because the curved moment of the arched ribs and the tiered beam is small, this has largely reduced the structural self -weight, and the axis of the arch decreased. Therefore, the arched ribs are more slender than the conventional arch bridge. In addition, the arches are mostly arc -shaped, and the radius within a certain length range of both ends can be appropriately reduced, and the span ratio is roughly 1/7 to 1/5.
A variety of forms can be steel beams, or concrete beams, or combination beams. Because the main beam of the main beam is not large, Liang Gao can be far less than the conventional arch bridge.
Flexible boons made of round steel, strip steel, high -strength steel wire (including sealing steel cables), steel twisted wires and other materials, most of which are round steel (convenient connection and easy maintenance). In 2020, the Stugart light rail -shaped arch bridge built in Germany, span 107m, used a CFRP boom for the first time. The diameter of the boom is only 32mm, and the cross -sectional area is not 1/4 of the traditional steel boom. According to the type of boom, the connection between the boom and the arch rib and the beam can be hinged, welded, anchoring and other methods.
The number of mesh booms is usually 2 to 4 times that of other types of rod arch. If the number of booms is too large, not only waste materials, but the effect may also be greatly reduced. According to the existing engineering practice, the spacing of the lower end of the boom is generally between 2 and 5m. There are literatures that give up the number of reasonable booms of single arches: when the span is 100m, the number of boils is 36 to 46; when the span is 150m, it is 38 to 48; when the span is 200m, it is 40-50.
The layout of the boom is diverse. Several common methods are: (1) Constant inclination: The lower end of the boom is distributed by the span of span, and the siphon rod and the main beam Cheng Cheng constant angle α (45 ° ≤ ≤ 75 °); (2) increasing (minus) Ending angle: The upper point of the boom is distributed along the arched axis, and the angle of the boom and the main beam gradually increases (decrease); The method of the rod and the arch axis is constant angle α; (4) the lower end point spacing gradient: the upper end of the boom is distributed along the arched axis, and the distance between the lower end of the boom is gradually changing. In addition, the scattered arrangement of the anchor head at both ends of the boom (see Figure 10) is conducive to the repairs of the boom.
Figure 10 Basic arrangement
Live loads such as vehicles and horizontal winds can easily cause vibration of soft booms, which may cause each boom to collide in the intersection. According to the results of the power analysis, the vibration reduction device can be set at the intersection of the boom depending on the situation to prevent the boom from colliding with each other, reducing the vibration of the boom, and reducing fatigue and damage. Common vibration reduction devices are shown in Figure 9.
Figure 9 The shock -reducing device set at the intersection of the mesh boom poles
Most of the stent construction methods of the first beam and then arched, and the construction of the cable buckle can also be constructed (such as the Fermarn Bridge in Germany). There are applications from the top push method, including the top push of the beams, the arch ribs pushed along the arched axis (such as the Buglinsk Bridge in Russia) or the whole cross -top push. When conditions permit, large -scale assembly, overall floating or upgrading can also be adopted.
Limited to space, only introduce the Brandangersundet Highway Bridge (Figure 11) built in 2010. The main bridge is 220m, and the bridge width is 7.6m; the arched ribs use two outer diameters of 711mm, wall thickness 40mm (increased to 60mm near the arched toe), and the height is 33m; 5mm; the beam is two 0.4m thick stress concrete beams, with a thickness of 0.25m thick in the middle lane; 35M and 30M cross -crossing are also provided with the prestressed concrete beam of 1.2m height; In the vertical surface of the rib, it is roughly arranged by the “French lines and other angle” methods. The structure layout is shown in Figure 10.
The main cross -structure of the bridge weighs only 1860T. First pour the concrete beams on the shore bracket and pull the stress. After 5 months (in order to reduce the impact of the concrete Xu change), the arched ribs are lifted in three major sections and opened the boil; Putting on position (below Figure 11).
Figure 11 BRANDANGERSUNDET Bridge (2010)
Can meship arches be used for high -speed rail bridges?
The mesh arch bridge can be applied to highway bridges and conventional railway bridges. The high -speed rail bridge pays more attention to the dynamic behavior of the structure, and the deformation of dynamic deflection is also directly related to the smoothness of the track and driving comfort. Therefore, the high -speed railway bridge must have sufficient vertical, horizontal, and twisted stiffness.
In order to examine the feasibility of mesh arch bridges for high -speed railway bridges, the author has carried out trial planning research on the high -speed rail arch bridge (dual -line, maximum speed of 250km/h) of the high -speed rail high -speed rail arch bridge (dual -line, maximum speed of 250km/h). The selection is as follows.
FIG. 12 shows the three -dimensional sign of the trial bridge structure and the facade of the boom. Under the combined structure of the undercut, Q345Q steel, Taoist bridge, span 128m. The arched ribs adopt the form of a basket, with an inclination angle of 9 °. The arched axis is an arc, with 21.76m, and 0.17 span ratio. The whole bridge is set with a round steel boom with a diameter of 80mm in diameter, and the lower end of the booth is distributed by the cross -band of the band, and the inclination angle is between 55 ° and 80 °.
Figure 12 Test the three -dimensional sign of the design bridge and the facade layout of the boom
In the section layout, the two arched ribs and the tiered beams are box -shaped sections. During the case, the box -shaped end beam and T -shaped middle beam are set up. The main size is shown in Figure 13. The cross height of the arched rib and the beam is only 2m, which is about 60%of the size of the corresponding span steel arched bridge of the current high -speed rail of the domestic high -speed rail.
FIG. 13 Test the component section and size diagram of the design bridge (unit: MM)
Based on the “Specification of High-speed Railway Design” (TB 10621-2014), Midas/Civil software modeling is adopted, and static analysis and calculations are performed according to the ZK live load and 13 load combinations. The indicators are less than the specification limit. Adopt Midas/Civil software and Southwest Jiaotong University bridge structural power analysis software BDAP modeling, conducting power behavior analysis and calculation, the contemporary frequency of structure, the indicators of the bridge coupling analysis (cross -medium vertical horizontal vibration displacement and acceleration, acceleration, acceleration, acceleration, acceleration, acceleration. The derailment coefficient, reduction rate, horizontal force, vertical acceleration, comfort, etc.) of the vehicle meet the standard limit.
Compared with the steel volume of a domestic special line, a steel tie arch bridge (using a rigid vertical boom, a span 128m). The results show that the use of a mesh arch bridge scheme can save about 22%of steel, reaching more than 600 tons.
Despite further optimization, the above -mentioned trial design results have indicated that the mesh arch bridge has a considerable potential for high -speed rail bridges.
The development of the tie arch bridge has more than one and a half centuries. Looking at the context of its development, you can see the continuous efforts of bridge engineers to pursue more reasonable structures, more materials saving, and more beautiful shapes.
The mesh arch is born in the Nielsen arch, which has the advantages of good stressfulness, strong structural stiffness, saving materials, light and beauty, etc. This is due to the mechanical behavior of the mesh arch bridge.
The mesh arch bridge can not only be used in highways and railway bridges, but also have potential to try in the field of high -speed rail bridge.
The mesh arch bridge is not new. In the past, there were not many construction, and it may be restricted by the traditional concept of steady design. In the past 20 years, it has been built more. Bridge engineers pursue the enthusiasm of light and beautiful arch bridges.
(Author’s note: This article is revised according to the WeChat article “Yadong Bridge 20: What is a network boom arch bridge?”. During the writing process, refer to many documents and materials, which are not listed one by one, thank you here!)
This article is published / “Bridge” magazine 2021, issue 53, Issue 103
Author / Li Yadong
Author Unit / Southwest Jiaotong University