Fabricated viaduct adopting improved small box girders and swingable piers

Abstract

The utility model relates to an assembly type viaduct adopting an improved small box girder and a swingable pier, the viaduct comprises a pile foundation, a bearing platform, an anti-shear pin, a prestress stranded wire, an energy consumption assembly, a stand column, a cover beam, a simply supported small box girder and a diaphragm beam, the bearing platform, the stand column and the cover beam are sequentially arranged on the pile foundation, the prestress stranded wire is arranged in the bearing platform, the stand column and the cover beam in a penetrating mode, and the energy consumption assembly is arranged on the diaphragm beam. The two ends of the prestress stranded wire are anchored to the top of the cover beam, a swing interface is formed by the contact faces of the stand column, the bearing platform and the cover beam, and a shear pin and an energy dissipation assembly are arranged on the swing interface. Simply-supported small box girders are arranged on the cover beam, transverse partition beams are arranged at the two ends of a single span below the simply-supported small box girders, and inspection manholes are formed in the transverse partition beams combined below the transversely adjacent simply-supported small box girders. Compared with the prior art, the internal force response of the pier and the foundation under the action of an earthquake is remarkably reduced, effective energy dissipation capacity and self-resetting capacity are provided, prestress detection, maintenance or replacement are facilitated, and rapid repair after the earthquake is achieved.

Description

Technical Field

[0001] The utility model belongs to the technical field of bridges and relates to an assembled viaduct adopting an improved small box beam and swingable bridge piers. Background Art

[0002] In recent years, with the continuous development and improvement of urban transportation, the continuous advancement of industrialized bridge construction technology, and people's increasing attention to environmental protection, the prefabrication and assembly technology of bridge piers has developed rapidly. The full prefabrication and assembly technology of both the upper and lower structures, which are prefabricated in the factory and assembled on site, has been vigorously promoted and applied in newly built urban viaducts. Among them, "prefabricated small box girder + support + prefabricated large cantilever cap beam double column pier" is the most typical structural form.

[0003] At present, the connection of prefabricated bridge piers mostly adopts the same cast-in-place connection method, including grouting sleeve connection, grouting bellows connection, socket connection, wet joint connection, etc. The engineering application is mainly concentrated in non-seismic areas and medium and low intensity areas, and there are few related research and applications in medium and high intensity areas. In a small number of application cases in medium and high intensity areas, seismic isolation bearings are basically used to prevent the pier-column connection area from entering plasticity. However, seismic isolation will bring greater main beam displacement and post-earthquake residual displacement. In high seismic areas, it is difficult to meet the deformation requirements by relying solely on seismic isolation bearings. The above factors have seriously restricted the promotion and application of prefabricated bridge piers in medium and high intensity areas.

[0004] Prefabricated bridge piers can also be connected by post-tensioning prestressing. The joints are easy to open and close. If the joints at the bottom of the pier are set as rocking interfaces to isolate the input of seismic energy, a rocking system can be formed. Its deformation mainly depends on the rigid body rotation caused by the opening of the joints. The pier body basically maintains elasticity. The pier has the ability to self-reset under the action of prestress and self-weight, with small residual displacement, self-reset, low damage, and easy repair. It is of great significance for the construction of resilient cities and has become a hot topic in the current bridge engineering field. However, most of them are based on theoretical analysis and experimental research of simple models, lacking consideration of many aspects such as design, construction and post-maintenance. The model construction is quite different from the actual project, and it is difficult to put it into engineering application. For example, unbonded prestressing is the key self-reset component of rocking bridge piers. It may experience large stress changes under the action of earthquakes and may produce large stress losses during long-term use. It is necessary to conduct regular prestress testing and, if necessary, perform re-tensioning, repair or replacement.

[0005] Patent CN113718634A discloses a fully prefabricated bridge swing self-resetting shock-absorbing structure system for an inverted T-shaped cap beam, comprising two groups of prefabricated main beams, a prefabricated inverted T-shaped cap beam, a cap, a prestressed steel bundle, two prefabricated piers and a pile foundation, wherein the top surface of the pile foundation is fixedly connected to the bottom surface of the cap, the prefabricated pier is vertically arranged on the cap, the bottom surface of the prefabricated inverted T-shaped cap beam is respectively fixedly connected to the top surfaces of the two prefabricated piers, the two groups of prefabricated main beams are respectively arranged at the shoulders on both sides of the prefabricated inverted T-shaped cap beam, U-shaped prestressed pipes are arranged in the prefabricated piers, the prefabricated inverted T-shaped cap beam and the cap, the prestressed steel bundle is arranged in the U-shaped prestressed pipe, the end of the prestressed steel bundle extends out of the U-shaped prestressed pipe and is fixedly connected to the prefabricated inverted T-shaped cap beam, and a swing interface is formed between the contact surfaces of the prefabricated piers and the cap.

[0006] However, this patent has the following problems:

[0007] (1) It is only applicable to the case of inverted T-beams, but not to the case of conventional rectangular-shaped beams. Due to its large size and weight, the inverted T-beam usually needs to be hoisted and spliced ​​in sections, which brings certain troubles to the construction; while the rectangular beam has a relatively light weight and is more adaptable to hoisting and transportation equipment. It can generally be hoisted as a whole, and has a higher proportion in actual engineering applications;

[0008] (2) The double-column pier with a large cantilever cap beam is a transverse frame structure. Under the action of a transverse earthquake, a large bending moment will be generated at the junction of the pier top and the cap beam, which is also a potential plastic hinge area. Large plastic damage may occur, which is not conducive to rapid post-earthquake repair.

[0009] (3) The unbonded prestressed anchor is fixed at the top of the inverted T-beam, which makes it possible to inspect, repair or replace the prestressed material. However, it is still necessary to remove the bridge deck pavement and dismantle the groove sealing anchor device, which will have some adverse effects on the normal traffic on the bridge deck. Utility Model Content

[0010] The purpose of the present invention is to overcome at least one defect of the above-mentioned prior art and to provide an assembled viaduct using an improved small box girder and swingable piers. The present invention significantly reduces the internal force response of the piers and foundations under earthquake action, provides effective energy dissipation capacity and self-resetting capacity, and facilitates prestress detection, maintenance or replacement, thereby achieving rapid post-earthquake repair.

[0011] The purpose of the utility model can be achieved through the following technical solutions:

[0012] One of the technical solutions of the utility model is to provide an assembled viaduct using an improved small box girder and a swingable bridge pier, the viaduct comprising a pile foundation, a cap, a shear pin, a prestressed strand, an energy dissipation component, a column, a cap beam, a simply supported small box girder and a diaphragm, the pile foundation is provided with a cap, a column and a cap beam in sequence, the cap, the column and the cap beam are provided with a prestressed strand, the two ends of the prestressed strand are anchored at the top of the cap beam, the contact surface of the column with the cap and the cap beam forms a swing interface, the swing interface is provided with a shear pin and an energy dissipation component;

[0013] A simply supported small box beam is arranged on the cap beam, and a cross beam is arranged at both ends of a single span under the simply supported small box beam, and a maintenance manhole is opened on the combined cross beam under the transversely adjacent simply supported small box beams.

[0014] As a preferred technical solution, the rocking interface is reinforced with a high-performance material selected from steel plates and ultra-high performance concrete (UHPC) to avoid local pressure damage.

[0015] As a preferred technical solution, the energy dissipation component includes an energy dissipation steel rod, a mild steel damper or a viscous damper.

[0016] Furthermore, a longitudinal limit block is provided at the top of the cap beam, and transverse limit blocks are provided at both ends of the top of the cap beam to prevent the simply supported small box beam from uncontrolled displacement or even falling and damage.

[0017] Furthermore, buffer pads are pasted on the inner sides of the longitudinal limit blocks and the transverse limit blocks to avoid or reduce structural damage caused by the collision between the simply supported small box girder and the limit blocks when large deformation occurs.

[0018] As an optimal technical solution, a certain gap is reserved between the buffer pad and the simply supported small box girder. On the one hand, it can adapt to the bearing deformation requirements caused by temperature changes, braking force, etc. under normal use conditions; on the other hand, it can also adapt to the bearing deformation requirements under small and medium earthquake conditions.

[0019] Furthermore, bridge deck joints are reserved between transversely adjacent simply supported small box girders, and transverse diaphragm joints are reserved between transversely adjacent transverse diaphragm joints. Concrete is poured laterally on the bridge deck joints and transverse diaphragm joints, and inspection manholes are provided on the combined transverse diaphragm joints under the transversely adjacent simply supported small box girders.

[0020] Furthermore, a continuous bridge deck layer is reserved between the joints of two longitudinally adjacent spans of simply supported small box girders and the bridge deck, and the continuous bridge deck layer is cast with concrete, so that the entire bridge deck is continuous.

[0021] Furthermore, a support is provided on the top of the cap beam, and the simply supported small box beam is arranged on the cap beam through the support.

[0022] Furthermore, an anchor groove is provided at the top of the cap beam, an anchor plate is provided in the anchor groove, and the prestressed stranded wire is anchored in the anchor groove through the anchor plate.

[0023] As a preferred technical solution, the transverse beams are located on both sides of the central axis of the cap beam, the longitudinal limit blocks are arranged outside the simply supported small box beam, and the longitudinal limit blocks are arranged on the central axis of the cap beam between the transverse beams.

[0024] Furthermore, a cap shear pin reserved hole is provided at the top of the cap, a column shear pin reserved hole is provided at the top and bottom of the column, a cap beam shear pin reserved hole is provided at the bottom of the cap beam, and the shear pins are buried in the cap shear pin reserved holes and the column shear pin reserved holes, as well as the column shear pin reserved holes and the cap beam shear pin reserved holes.

[0025] As a preferred technical solution, the shear pin reserved holes are located on the central axis of the pedestal, column and cap beam.

[0026] Furthermore, a prestressed pipe is provided in the pedestal, a prestressed pipe is provided in the column, and a prestressed pipe is provided in the cap beam. The prestressed strands are buried in the prestressed pipes of the pedestal, the columns and the cap beam, and the prestressed strands are buried outside the shear pins.

[0027] Furthermore, the energy dissipation components are circumferentially arranged at the top and bottom of the column.

[0028] The working principle of the utility model is as follows:

[0029] Under normal use conditions, the bridge piers do not sway. The deformation of the bearings can adapt to the horizontal forces generated by temperature changes and vehicle braking, thereby reducing the internal forces of the bridge piers.

[0030] Under the conditions of small and moderate earthquakes, the bridge piers do not sway, and the earthquake force transmitted to the bridge piers and foundations is reduced through bearing deformation;

[0031] Under major earthquake conditions, when the bearing deformation reaches the limit value of the limit device, the seismic force increases. When the bending moment of the rocking interface exceeds the critical bending moment, the bridge enters a rocking state, further extending the bridge structure period and limiting the increase in the internal force response of the piers and foundation, so that it basically remains elastic.

[0032] Compared with the prior art, the utility model has the following beneficial effects:

[0033] (1) The utility model improves the simply supported small box girder. The cross beams of two adjacent longitudinal span small box girders are respectively moved toward the mid-span direction, thereby increasing the distance between the two longitudinal cross beams of the single-span small box girder. The area between the two cross beams is used as an operating space for prestressing inspection, maintenance or replacement. At the same time, a maintenance manhole is opened on the cross beam to allow personnel, materials and equipment to enter and exit the operating space.

[0034] (2) The joint surfaces between the cap and the column bottom, and between the column top and the cap beam of the utility model are designed as rocking interfaces, which reduces the bending moment caused by longitudinal and transverse earthquakes, avoids plastic hinge damage, and facilitates rapid repair after earthquakes;

[0035] (3) The conventional prestressing test of the utility model is carried out within the operating space and does not affect the traffic of vehicles on the bridge deck. Temporary control of the traffic on the bridge deck is only required when the prestressing is supplemented or replaced. The prestressing anchor is at the top of the cap beam, and the prestressing anchor is moved from the bridge deck to under the bridge deck, which greatly reduces the impact on the traffic on the bridge deck. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic cross-sectional structure diagram of a plurality of transversely adjacent small box girders and piers of an assembled viaduct adopting improved small box girders and swingable piers in an embodiment of the utility model;

[0037] Figure 2 It is a schematic diagram of the side-standing structure of two adjacent longitudinal spans of small box girders and piers of an assembled viaduct using improved small box girders and swingable piers in an embodiment of the utility model;

[0038] Figure 3 It is a schematic diagram of the top plane structure of the support platform in the embodiment of the utility model.

[0039] Description of the markings in the figure:

[0040] 1—pile foundation, 2—cap, 201—preserved hole for shear pin of cap, 202—prestressed pipe of cap, 3—shear pin, 4—prestressed strand, 5—energy dissipation component, 6—column, 601—swing interface, 602—prestressed pipe of column, 7—cap beam, 701—anchor groove, 8—anchor pad, 9—support, 10—longitudinal limit block, 11—transverse limit block, 12—buffer pad, 13—simply supported small box girder, 1301—bridge deck joint, 14—diaphragm, 1401—manhole for maintenance, 1402—diaphragm joint. DETAILED DESCRIPTION

[0041] The present invention is described in detail below in conjunction with specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and a specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0042] In the description of the present utility model, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present utility model and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present utility model. In addition, the terms "first", "second", "third" and the like are used to describe common objects, and only refer to different instances of the same object, and are not intended to imply that the objects described in this way must adopt a given order, whether in time, space, order or any other manner.

[0043] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0044] Example:

[0045] An assembled viaduct using an improved small box girder and swingable piers, such as Figure 1 and Figure 2 As shown, it is composed of pile foundation 1, cap 2, shear pin 3, prestressed strand 4, energy dissipation component 5, column 6, cap beam 7, anchor plate 8, support 9, longitudinal limit block 10, transverse limit block 11, buffer pad 12, simply supported small box beam 13 and transverse diaphragm 14;

[0046] A cap 2, a column 6 and a cap beam 7 are sequentially arranged on the pile foundation 1. Prestressed strands 4 are inserted into the cap 2, the column 6 and the cap beam 7. Both ends of the prestressed strands 4 are anchored at the top of the cap beam 7. The contact surfaces of the column 6, the cap 2 and the cap beam 7 form a swing interface 601. A shear pin 3 and an energy dissipation component 5 are arranged at the swing interface 601.

[0047] A plurality of simply supported small box beams 13 are arranged on the cap beam 7, and a transverse diaphragm 14 is arranged at both ends of a single span (above the cap beam 7) under the simply supported small box beams 13, and a maintenance manhole 1401 is opened on the transverse diaphragm 14 combined under the transversely adjacent simply supported small box beams 13;

[0048] A longitudinal limit block 10 is provided at the top of the cap beam 7, and transverse limit blocks 11 are provided at both ends of the top of the cap beam 7 to prevent the simply supported small box beam 13 from losing control of displacement or even falling and being damaged;

[0049] Buffer pads 12 are attached to the inner sides of the longitudinal limit blocks 10 and the transverse limit blocks 11 to avoid or reduce structural damage caused by the collision between the simply supported small box beam 13 and the limit blocks when large deformation occurs;

[0050] A certain gap is reserved between the buffer pad 12 and the simply supported small box beam 13, which can adapt to the deformation requirements of the support 9 caused by temperature changes, braking force, etc. under normal use conditions, and can also adapt to the deformation requirements of the support 9 under small and medium earthquake conditions;

[0051] A bridge deck joint 1301 is reserved between the transversely adjacent simply supported small box girders 13, a transverse diaphragm joint 1402 is reserved between the transversely adjacent transverse diaphragm beams 14, the bridge deck joint 1301 and the transverse diaphragm joint 1402 are poured with concrete, and a maintenance manhole 1401 is opened on the transversely adjacent simply supported small box girders 13 and the transverse diaphragm joint 1402;

[0052] A bridge deck continuous layer is reserved between two longitudinally adjacent spans of simply supported small box girders 13 and the bridge deck joint 1301, and the bridge deck continuous layer is cast in situ with concrete, so that the entire bridge deck is continuous;

[0053] A support 9 is provided on the top of the cap beam 7, and a simply supported small box beam 13 is provided on the cap beam 7 through the support 9;

[0054] An anchor groove 701 is provided at the top of the cap beam 7, an anchor plate 8 is provided in the anchor groove 701, and the prestressed strand 4 is anchored in the anchor groove 701 through the anchor plate 8;

[0055] In this embodiment, five simply supported small box girders 13 are arranged transversely, and the number of supports 9 corresponds to the number of simply supported small box girders 13. One is arranged at each end of a single span of the simply supported small box girder 13. A pair of longitudinal limit blocks 10 are arranged outside the second and fourth simply supported small box girders 13, and the longitudinal limit blocks 10 are arranged between two adjacent spans of the simply supported small box girders 13 in the longitudinal direction.

[0056] like Figure 3 As shown, a cap shear pin reserved hole 201 is provided at the top of the cap 2, a column shear pin reserved hole is provided at the top and bottom of the column 6, a cap beam shear pin reserved hole is provided at the bottom of the cap beam 7, and the shear pin 3 is buried in the cap shear pin reserved hole 201 and the column shear pin reserved hole, as well as in the column shear pin reserved hole and the cap beam shear pin reserved hole;

[0057] A cap prestressed pipe 202 is provided in the cap 2, a column prestressed pipe 602 is provided in the column 6, a cap beam prestressed pipe is provided in the cap beam 7, and the prestressed stranded wire 4 is buried in the cap prestressed pipe 202, the column prestressed pipe 602 and the cap beam prestressed pipe, and the prestressed stranded wire 4 is buried outside the shear pin 3;

[0058] The energy dissipation components 5 are arranged at the top and bottom of the column 6 along the circumferential direction;

[0059] In this embodiment, one shear pin 3 is provided at each rocking interface 601 , and a total of four holes are provided outside the shear pin 3 for the prestressed strand 4 . The shear pin reserved holes are located on the central axis of the pedestal 2 , the column 6 and the cap beam 7 .

[0060] The rocking interface 601 is reinforced with high-performance materials such as steel plates or ultra-high performance concrete (UHPC), and in this embodiment, UHPC is preferred to avoid local pressure damage.

[0061] The energy dissipation component 5 is an energy dissipation steel rod, a mild steel damper or a viscous damper, and in this embodiment, the energy dissipation steel rod is preferred.

[0062] In this embodiment, the prestressed strand 4 adopts unbonded prestressed steel strand, the column 6 adopts prefabricated column, the cap beam 7 adopts prefabricated rectangular cap beam, the support 9 adopts rubber support, the buffer pad 12 adopts buffer rubber pad, the simply supported small box beam 13 adopts prefabricated simply supported small box beam, and the cross beam 14 adopts prefabricated cross beam.

[0063] The working principle of this embodiment is as follows:

[0064] Under normal use conditions, the bridge pier does not sway, and the deformation of the support 9 can adapt to the horizontal force generated by temperature changes and vehicle braking, thereby reducing the internal force of the bridge pier;

[0065] Under the conditions of small and medium earthquakes, the bridge piers do not sway, and the earthquake force transmitted to the bridge piers and foundation is reduced by the deformation of the bearing 9;

[0066] Under a large earthquake condition, when the deformation of the support 9 reaches the limit value of the limit device, the seismic force increases, and when the bending moment of the rocking interface 601 exceeds the critical bending moment, it enters a rocking state, further extending the bridge structure period, limiting the increase in the internal force response of the piers and foundation, and keeping it basically elastic.

[0067] This embodiment uses swingable piers, which can significantly reduce the internal force response of the piers and foundations under earthquake action, provide effective energy dissipation capacity and self-resetting capacity, and improve the prefabricated small box girders to facilitate prestressed inspection, maintenance or replacement, thereby achieving rapid post-earthquake repair.

[0068] The above description of the embodiments is to facilitate the understanding and use of the utility model by those skilled in the art. It is obvious that those familiar with the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the utility model is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the utility model without departing from the scope of the utility model should be within the scope of protection of the utility model.

Claims

1. An assembled viaduct using an improved small box girder and swingable piers, characterized in that: The viaduct comprises a pile foundation (1), a cap (2), a shear pin (3), a prestressed strand (4), an energy dissipation component (5), a column (6), a cap beam (7), a simply supported small box beam (13) and a diaphragm (14); the pile foundation (1) is provided with a cap (2), a column (6) and a cap beam (7) in sequence; the cap (2), the column (6) and the cap beam (7) are provided with a prestressed strand (4); both ends of the prestressed strand (4) are anchored at the top of the cap beam (7); the contact surface between the column (6) and the cap (2) and the cap beam (7) forms a swing interface (601); the shear pin (3) and the energy dissipation component (5) are provided at the swing interface (601); A simply supported small box beam (13) is arranged on the cap beam (7), and a cross beam (14) is arranged at both ends of a single span under the simply supported small box beam (13), and a maintenance manhole (1401) is opened on the cross beam (14) combined under the transversely adjacent simply supported small box beams (13).

2. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: A longitudinal limit block (10) is arranged at the top of the cap beam (7), and transverse limit blocks (11) are arranged at both ends of the top of the cap beam (7).

3. The assembled viaduct using improved small box beams and swingable piers according to claim 2, characterized in that: Buffer pads (12) are pasted on the inner sides of the longitudinal limit block (10) and the transverse limit block (11).

4. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: A bridge deck joint (1301) is reserved between transversely adjacent simply supported small box girders (13), and a transverse diaphragm joint (1402) is reserved between transversely adjacent transverse diaphragm beams (14). Concrete is poured into the bridge deck joint (1301) and the transverse diaphragm joint (1402) laterally. A maintenance manhole (1401) is provided on the transverse diaphragm beam (14) combined under the transversely adjacent simply supported small box girders (13) and the transverse diaphragm joint (1402).

5. The assembled viaduct using improved small box beams and swingable piers according to claim 4, characterized in that: A bridge deck continuous layer is reserved between two longitudinally adjacent spans of simply supported small box girders (13) and the bridge deck joint (1301), and the bridge deck continuous layer is cast-in-place with concrete.

6. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: A support (9) is provided on the top of the cap beam (7), and the simply supported small box beam (13) is arranged on the cap beam (7) through the support (9).

7. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: An anchor groove (701) is provided at the top of the cap beam (7), an anchor pad (8) is provided in the anchor groove (701), and the prestressed strand (4) is anchored in the anchor groove (701) through the anchor pad (8).

8. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: The top of the pedestal (2) is provided with a pedestal shear pin reserved hole (201), the top and bottom of the column (6) are provided with a column shear pin reserved hole, the bottom of the cap beam (7) is provided with a cap beam shear pin reserved hole, and the shear pin (3) is buried in the pedestal shear pin reserved hole (201) and the column shear pin reserved hole, as well as in the column shear pin reserved hole and the cap beam shear pin reserved hole.

9. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: The pedestal (2) is provided with a pedestal prestressed pipe (202), the column (6) is provided with a column prestressed pipe (602), the cap beam (7) is provided with a cap beam prestressed pipe, the prestressed stranded wire (4) is buried in the pedestal prestressed pipe (202), the column prestressed pipe (602) and the cap beam prestressed pipe, and the prestressed stranded wire (4) is buried outside the shear pin (3).

10. The assembled viaduct using improved small box beams and swingable piers according to claim 1, characterized in that: The energy dissipation components (5) are arranged at the top and bottom of the column (6) along the circumferential direction.

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