Construction method for outward-tilting pylon cable-stayed bridge with collaborative construction of pylon, beam and cable

By segmenting the columns of the outer tilt upper tower columns and defining the number of cable-stayed cables, combining with the coordinated construction of the tower beam cable, the lateral component force of the cable-stayed bridge cable is used to solve the problem of excessive tensile stress on the outer tilt tower and the inner side, and the safety of the structure and construction efficiency are improved.

CN115538310BActive Publication Date: 2025-06-24CHINA RAILWAY BRIDGE SCI RES INST LTD +2
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Patent Information

Application Number
CN202211061884.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-08-31
Publication Date
2025-06-24
Estimated Expiration
2042-08-31

AI Technical Summary

Technical Problem

The tensile stress on the camber tower and the inner side is too large, resulting in structural cracking and transverse deformation, affecting the subsequent saddle installation positioning and cable-stayed cable tensioning.

Method used

By segmenting the bulging upper columns and defining the number of cable-stayed cables connected on each section, it is ensured that the sum of the tensile stress of the bulging upper column and the compressive stress of the cable-stayed cable does not exceed the concrete tensile strength design value. Combined with the coordinated construction of tower beam cables, the lateral component force of cable-stayed bridge cable force is used to exert the structural self-balancing characteristics.

Benefits of technology

It effectively solves the problem of excessive tension stress on the camber tower and the inner side, avoids structural cracking and lateral deformation, has no adverse impact on the subsequent saddle installation positioning and cable-stayed cable tensioning, and saves construction period and improves project progress and efficiency.

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Abstract

The invention discloses a construction method for an outward-tilting pylon cable-stayed bridge with coordinated tower, beam and cable construction, which relates to the field of bridge structure construction and control. The method comprises the following steps: segmenting the outward-tilting upper pylon from bottom to top and defining the number of stay cables connected to each segment; the sum of the tensile stress of the outward-tilting upper pylon and the compressive stress of all stay cables is less than or equal to the design value of the tensile strength of concrete; according to the above segmenting requirements, constructing the outward-tilting upper pylon section by section from bottom to top. After the construction of each segment of the outward-tilting upper pylon is completed, connecting the segment of the outward-tilting upper pylon to the corresponding section of the main beam through stay cables; fixing one end of each stay cable to the outward-tilting upper pylon and the other end to a section of the main beam. The invention can solve the problem of excessive tensile stress on the inner side of the outward-tilting pylon root without increasing the cost of temporary facilities, and avoid the adverse effects of structure cracking and large lateral deformation on the subsequent installation and positioning of saddle and stay cable tensioning.
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Description

Technical Field

[0001] The present invention relates to the field of bridge structure construction and control, and particularly relates to a construction method for an inclined pylon cable-stayed bridge with a canted pylon in which the tower, beam and cables are constructed in coordination. Background Art

[0002] With the development of the national transportation and infrastructure industries, long-span bridges, especially cable-stayed bridges, are becoming more and more common. The forms of the main towers of cable-stayed bridges are also becoming more diverse, among which there are canted cable towers. The canted concrete cable tower is a large cantilever structure during the construction process. Under the action of the self-weight of the cable tower and the formwork, the tensile stress inside the tower root is too large, and the tower root is prone to cracking and the structure is unsafe. Moreover, when the cable tower is capped, the lateral displacement at the top of the tower is too large, which has a serious adverse impact on the subsequent installation and positioning of the cable saddle and the tensioning of the stay cables.

[0003] In the related art, vertical prestress is usually set at the tower root, or when the canted double tower legs are in a Y-shaped tower structure, several active cross bracing rods are set during the construction of the main tower. However, the tower root structure is complex and the steel bars are densely arranged, making it difficult to operate the vertical prestress at the tower root, so this method is generally not used; moreover, the setting and tensioning processes of the active cross bracing rods are cumbersome, and the temporary structure will also increase additional costs, and the risk of high-altitude tensioning operation is high. Summary of the Invention

[0004] Aiming at the defects existing in the prior art, the technical problem solved by the present invention is: how to solve the problem of excessive tensile stress inside the canted tower root without increasing the cost of temporary facilities, and avoid the adverse effects of structural cracking and large lateral deformation caused by it on the subsequent installation and positioning of the cable saddle and the tensioning of the stay cables.

[0005] To achieve the above object, the present invention provides a construction method for an inclined pylon cable-stayed bridge with a canted pylon in which the tower, beam and cables are constructed in coordination. The canted pylon includes a bearing platform, a lower tower column and a canted upper tower column; the method includes the following steps:

[0006] S1: Segment the canted upper tower column from bottom to top and define the number of stay cables connected to each segment; the tensile stress of the canted upper tower column is less than or equal to the design value of the concrete tensile strength when summed with the compressive stress of all stay cables.

[0007] S2: Construct the bearing platform, the lower tower column and the 0# block of the main beam.

[0008] S3: Construct the cable-free section of the Y-shaped upper tower column and the cable-free section of the main beam.

[0009] S4: According to the segmentation requirements of S1, construct the canted upper tower column section by section from bottom to top. After the construction of each section of the canted upper tower column is completed, connect the section of the canted upper tower column to the corresponding section of the main beam through stay cables; one end of each stay cable is fixed to the canted upper tower column, and the other end is fixed to a section of the main beam.

[0010] On the basis of the above technical solution, when segmenting the outward-inclined upper tower column and defining the number of stay cables connected to each segment in S1, the following requirements need to be met:

[0011] Define the tensile stress of the i-th segment of the outward-inclined upper tower column as The number of stay cables on the i-th segment of the outward-inclined upper tower column is k, and the compressive stress of each stay cable is j represents the serial number of the stay cable;

[0012] The sum of the compressive stresses of k stay cables The calculation formula is:

[0013]

[0014] During the whole construction process, the sum of the tensile stresses of each segment of the outward-inclined upper tower column and the sum of the compressive stresses of the stay cables of each segment of the outward-inclined upper tower column need to be less than or equal to the design value f of the tensile strength of concrete t That is

[0015]

[0016] The tensile stress of the (i + 1)-th segment of the outward-inclined upper tower column Also needs to meet:

[0017]

[0018] On the basis of the above technical solution, the specific process of S4 includes: after completing the construction of a segment of the outward-inclined upper tower column, construct the corresponding main girder segment according to the number of saddles of this segment of the outward-inclined upper tower column; the number of saddles is the same as the number of stay cables required for this segment of the outward-inclined upper tower column designed in S1, and the number of main girder segments is the same as the number of saddles; after the construction of each main girder segment is completed, first connect it to the corresponding saddle with stay cables, and then construct the next main girder segment.

[0019] On the basis of the above technical solution, when the stay cables that can be tensioned on the i-th segment of the outward-inclined upper tower column are not enough to ensure that the tensile stress of the (i + 1)-th segment of the outward-inclined upper tower column does not exceed the limit, S4 also includes the following steps during the construction of the i-th segment of the outward-inclined upper tower column: over-tension the stay cables of the i-th segment of the outward-inclined upper tower column by 5% of the cable force, and release the over-tensioned cable force value after the stay cables of the (i + 1)-th segment of the outward-inclined upper tower column are tensioned.

[0020] On the basis of the above technical solution, the main girder in S4 is constructed symmetrically from the tower root to both sides in segments by the way of hanging basket cantilever casting or bridge erecting machine.

[0021] Compared with the prior art, the advantages of the present invention are:

[0022] It can be seen from this that according to the stress in S1, the segmentation of the out-of-inclination upper tower column and the number of stay cables are reasonably designed in the present invention. Then, combined with the subsequent coordinated construction of the "tower-beam-cable" (especially the steps in S4), the constructed out-of-inclination upper tower column will not exceed the design value of the concrete tensile strength. Therefore, compared with the prior art, the present invention makes full use of the lateral component force of the cable force of the cable-stayed bridge, gives play to the self-balancing characteristics of the structure, and can, without increasing the cost of temporary facilities, not only effectively solve the problem of excessive tensile stress on the inner side of the tower root of the out-of-inclination upper tower column, avoid the adverse effects of structural cracking and large lateral deformation on the subsequent installation and positioning of the saddle and the tensioning of the stay cables; but also save the construction period and improve the progress and benefits of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0024] Figure 1 It is a schematic diagram of the construction process of the out-of-inclination cable-stayed bridge in the embodiment of the present invention.

[0025] In the figure: 1 - caisson, 2 - lower tower column, 3 - out-of-inclination upper tower column, 4 - stay cable, 5 - main beam. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the scope of protection of the present application.

[0027] The flowcharts shown in the drawings are only illustrative examples, and do not necessarily include all the content and operations / steps, nor do they necessarily need to be executed in the described order. For example, some operations / steps can be decomposed, combined, or partially merged, so the actual execution order may change according to the actual situation.

[0028] See Figure 1 As shown, the out-of-inclination tower in the embodiment of the present invention includes a caisson 1, a lower tower column 2, and an out-of-inclination upper tower column 3 that are fixedly connected in sequence from bottom to top; on this basis, the construction method of the out-of-inclination cable-stayed bridge with coordinated construction of the tower-beam-cable in the embodiment of the present invention includes the following steps:

[0029] S1: Segment the outward-tilting upper tower column 3 from bottom to top, and define the number of stay cables 4 connected to each segment; the tensile stress generated by the construction load (such as self-weight and climbing formwork, etc. will generate construction loads) of the outward-tilting upper tower column 3 on the inner side of the tower root during the construction process is simply referred to as tensile stress; during the cable-hanging construction process of the main girder 5, the compressive stress generated by the lateral component force of the stay cable 4 on the inner side of the tower root is simply referred to as compressive stress; the sum of the tensile stress of the outward-tilting upper tower column 3 and the compressive stress of all stay cables 4 is less than or equal to the design value of the tensile strength of concrete.

[0030] The effect of S1 is: Before construction, the outward-tilting upper tower column 3 is segmented in advance, and the corresponding number of stay cables 4 is allocated to each segment, so that during subsequent normal construction (i.e., without the need to increase the cost of temporary facilities), the tensile stress of the outward-tilting upper tower column 3 and the compressive stress of the stay cable 4 will not exceed the design value of the tensile strength of concrete.

[0031] It should be noted that: The initial segment of the outward-tilting upper tower column 3 is a cable-free segment, that is, the segment without stay cables 4. The tensile stress of the cable-free segment must be less than or equal to the design value of the tensile strength of concrete (if it is greater, this invention is not applicable). The design of the cable-free segment is common knowledge for those of ordinary skill in the art. Each "segment" in the following text is a cable-bearing segment.

[0032] S2: Refer to Figure 1 As shown, construct the bearing platform 1, the lower tower column 2, and the 0# block of the main girder (this component is a conventional component and is known to those of ordinary skill in the art) in sequence.

[0033] S3: Refer to Figure 1 As shown, construct the cable-free segment of the Y-shaped upper tower column 3 and the cable-free segment of the main girder 5 respectively, and the working surfaces and processes of the two do not interfere with each other; the construction sequence is not in a specific order and can also be carried out simultaneously.

[0034] S4: Refer to Figure 1 As shown, according to the segmentation requirements of S1, use the climbing formwork method to construct the outward-tilting upper tower column 3 in sections from bottom to top. After each section of the outward-tilting upper tower column 3 is constructed, connect the section of the outward-tilting upper tower column 3 to the corresponding section of the main girder 5 through the stay cable 4; one end of each stay cable 4 is fixed to the outward-tilting upper tower column 3, and the other end is fixed to a section of the main girder 5.

[0035] In S4, the main girder 5 is constructed in sections symmetrically from the tower root to both sides by using the cantilever casting method with a hanging basket or a bridge erection machine; according to the structural design situation, the stay cable 4 can be tensioned only after the anchor fittings of the main girder 5 and the main tower saddles connected at both ends are constructed.

[0036] S5: Construct the closure segment.

[0037] S6: The secondary dead load, and the whole bridge is completed.

[0038] It can be seen from this that according to the stress in S1, the segmentation of the outward-tilting upper pylon 3 and the number of stay cables 4 are reasonably designed, and combined with the subsequent coordinated construction of the "pylon-girder-cable" (especially step S4), the completed outward-tilting upper pylon 3 will not exceed the design value of the concrete tensile strength. Therefore, compared with the prior art, the present invention makes full use of the lateral component force of the cable force of the cable-stayed bridge, gives play to the self-balancing characteristics of the structure, and can, without increasing the cost of temporary facilities, not only effectively solve the problem of excessive tensile stress on the inner side of the root of the outward-tilting upper pylon 3, avoid the adverse effects of its causing structural cracking and large lateral deformation on the subsequent installation and positioning of the cable saddle and the tensioning of the stay cables 4; but also can save the construction period and improve the progress and benefits of the project.

[0039] Preferably, the requirements and principles for the segmentation of the outward-tilting upper pylon 3 and the requirements and principles for the number of stay cables 4 connected to each segment of the outward-tilting upper pylon 3 in S1 include:

[0040] Define the tensile stress of the outward-tilting upper pylon 3 as σ t , and the tensile stress of the i-th segment of the outward-tilting upper pylon 3 is The compressive stress of the stay cable 4 is σ c , the number of stay cables 4 on the i-th segment of the outward-tilting upper pylon 3 is k, and the compressive stress of each stay cable 4 is where j represents the serial number of the stay cable 4.

[0041] On this basis, the sum of the compressive stresses of k stay cables 4 The calculation formula is:

[0042]

[0043] During the whole construction process, the sum of the tensile stresses of each segment of the outward-tilting upper pylon 3 and the sum of the compressive stresses of the stay cables 4 of each segment of the outward-tilting upper pylon 3 need to be less than or equal to the design value of the concrete tensile strength f t , that is

[0044]

[0045] Meanwhile, the tensile stress of the (i + 1)-th segment of the outward-tilting upper pylon 3 also needs to satisfy:

[0046]

[0047] On this basis, the process of segmenting the outward-tilting upper pylon 3 according to the above requirements and designing the length of each segment and the number of stay cables 4 on each segment can be completed by those of ordinary skill in the art using conventional means, and there are various methods. Taking the first segment as an example below, the design method of each segment of the outward-tilting upper pylon 3 in this embodiment will be described:

[0048] Calculate, in the order from bottom to top, whether the sum of the tensile stress of this section and the compressive stress of two stay cables 4 after tensioning one stay cable 4 on the outboard upper tower column 3 (it is default that one stay cable 4 has been initially tensioned, that is, the number of stay cables 4 after tensioning is two) is greater than f t If so, select the position where the upper stay cable 4 is tensioned as the first section; otherwise, loop through the above steps, that is, continue to increase the number of stay cables 4 by one and calculate again.

[0049] It can be seen from this that before construction, the outboard upper tower column 3 of the present invention is segmented in advance, and a corresponding number of stay cables 4 are allocated to each section, so that the tensile stress of the outboard upper tower column 3 and the compressive stress of the stay cables 4 will not exceed the design value of the tensile strength of concrete during subsequent normal construction (that is, without increasing the cost of temporary facilities).

[0050] Preferably, the specific process of S4 includes: After completing the construction of a section of the outboard upper tower column 3, construct the corresponding main girder 5 segment according to the number of saddles of this section of the outboard upper tower column 3; the number of saddles is the same as the number of stay cables 4 required for this section of the outboard upper tower column 3 designed in S1, and the number of main girder 5 segments is the same as the number of saddles. After the construction of each main girder 5 segment is completed, first connect it to the corresponding saddle with the stay cable 4, and then construct the next main girder 5 segment.

[0051] Specifically, refer to Figure 1 As shown, in this embodiment, the outboard upper tower column 3 in this embodiment has 5 segments, which are, from bottom to top, the cable-free tower segment, and Sections I to IV. Section I requires 2 stay cables 4, and the construction process of Section I is as follows:

[0052] Construct the first section of the outboard upper tower column 3 and the first main girder 5 independently. After completion, tension the 1# stay cable 4 of the first section of the outboard upper tower column 3. At this time, there are still saddle positions remaining on the first section of the outboard upper tower column 3, so continue to construct the second main girder 5 and tension the 2# stay cable 4 of the first section of the outboard upper tower column 3. Loop through the construction in the above manner until there are no exposed saddles on the first section of the outboard upper tower column 3. In this embodiment, the first section of the outboard upper tower column 3 requires 2 stay cables 4, so the number of saddle positions is 2.

[0053] The construction process of the remaining sections of the outboard upper tower column 3 is the same as that of Section I.

[0054] Preferably, during the segmentation process of S1, if the saddle position of the outboard upper tower column 3 is relatively high, and the stay cables 4 that can be tensioned on the i-th section of the outboard upper tower column 3 are not enough to ensure that the tensile stress of the (i + 1)-th section of the outboard upper tower column 3 does not exceed the limit, during the construction process of S4, the stay cables 4 of the i-th section of the outboard upper tower column 3 can be over-tensioned by 5% of the cable force, and the over-tensioned cable force value can be released after the stay cables 4 of the (i + 1)-th section of the outboard upper tower column 3 are tensioned.

[0055] Preferably, during the collaborative construction of the tower, beam, and cables, the most unfavorable tensile condition on the inner side of the tower root generally occurs when the Y-shaped cable tower is constructed to a certain height and the stay cable 4 cannot be tensioned in a timely manner. During the subsequent construction process, as the number of tensioned stay cables 4 increases, the growth rate of the lateral component force of the stay cable 4 is much greater than the growth rate of the self-weight of the Y-shaped cable tower limb and the climbing formwork. The inner side of the tower root gradually changes from tension to compression, which is more beneficial to the structural stress. By adjusting the length of the climbing formwork section of the cable tower, the number of stay cables 4 tensioned in the first section can be made sufficient, so that compressive stress can be reserved in advance on the inner side of the tower root, and the subsequent construction process is safer.

[0056] Preferably, in some embodiments, the i-th section of the cable tower is constructed by climbing formwork more than once. During the collaborative construction of the tower, beam, and cables, the stay cable 4 of the already installed cable saddle can be tensioned first, and then the (i + 1)-th section of the cable tower can be constructed by climbing up the formwork, which can reduce the tensile stress at the tower root during the climbing formwork construction of the cable tower.

[0057] Preferably, in some embodiments, the outwardly inclined upper tower column is the outward inclination of the tower limb of the double-tower limb cable tower; it can also be the outward inclination of a single tower column, so that the outwardly inclined upper tower column, the stay cable, and the main beam are not in the same plane; or for the construction of the cable tower of some curved girder cable-stayed bridges, due to the action of unbalanced forces, the inner side of the tower root is in tension, and the lateral component force of the stay cable can provide compressive stress on the inner side of the tower root. The cable-stayed bridge construction can also adopt the present invention.

[0058] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention 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, so it cannot be understood as a limitation of the present invention. 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 directly connected, or indirectly connected through an intermediate medium, and it can be the internal communication of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0059] It should be noted that in the present invention, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the said element.

[0060] The above are only specific embodiments of the present application, enabling those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but rather will be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A construction method for an outward-tilting pylon cable-stayed bridge with coordinated construction of tower, beam and cable. The outward-tilting pylon includes a bearing platform (1), a lower pylon column (2) and an outward-tilting upper pylon column (3); it is characterized in that, The method comprises the following steps: S1: Segment the outwards-inclined upper tower column (3) from bottom to top and define the number of stay cables (4) connected to each segment; the tensile stress of the outwards-inclined upper tower column (3) is less than or equal to the design value of the tensile strength of concrete when summed with the compressive stress of all the stay cables (4). S2: Construct the bearing platform (1), the lower tower column (2), and the main girder 0# block. S3: Construct the cable-free section of the Y-shaped upper tower column (3) and the cable-free section of the main girder (5). S4: Construct the outwards-inclined upper tower column (3) in segments from bottom to top according to the segmentation requirements of S1. After the construction of each segment of the outwards-inclined upper tower column (3) is completed, connect the segment of the outwards-inclined upper tower column (3) to the corresponding section of the main girder (5) through the stay cable (4); one end of each stay cable (4) is fixed to the outwards-inclined upper tower column (3), and the other end is fixed to a section of the main girder (5).

2. The construction method of the outward-tilting pylon cable-stayed bridge with coordinated construction of pylon, girder and cables according to claim 1, characterized in that When segmenting the outwards-inclined upper tower column (3) and defining the number of stay cables (4) connected to each segment in S1, the following requirements need to be met: Define the tensile stress of the i-th segment of the inclined upper tower column (3) as The number of stay cables (4) on the i-th segment of the inclined upper tower column (3) is k, and the compressive stress of each stay cable (4) is j represents the serial number of the stay cable (4); The sum of the compressive stresses of the k stay cables (4) The calculation formula is as follows: During the whole construction process, the sum of the tensile stresses of each segment of the outward-inclined upper tower column (3) and the sum of the compressive stresses of the stay cables (4) of each segment of the outward-inclined upper tower column (3) need to be less than or equal to the design value f of the concrete tensile strength t , that is The tensile stress of the (i + 1)-th outward-inclined upper tower column (3) shall also satisfy that:

3. The construction method of the outward-tilting pylon cable-stayed bridge with coordinated tower-beam-cable construction according to claim 2, characterized in that, The specific process of S4 includes: After the construction of a segment of the outwards-inclined upper tower column (3) is completed, construct the corresponding section of the main girder (5) according to the number of saddles of this segment of the outwards-inclined upper tower column (3); the number of saddles is the same as the number of stay cables (4) required for this segment of the outwards-inclined upper tower column (3) designed in S1, and the number of sections of the main girder (5) is the same as the number of saddles; after the construction of each section of the main girder (5) is completed, first connect it to the corresponding saddle with the stay cable (4), and then construct the next section of the main girder (5).

4. The construction method of the outward-tilting pylon cable-stayed bridge with coordinated construction of pylon, girder and cable according to claim 3, characterized in that: When the stay cables (4) that can be tensioned on the i-th segment of the outwards-inclined upper tower column (3) are not sufficient to ensure that the tensile stress of the (i + 1)-th segment of the outwards-inclined upper tower column (3) does not exceed the limit, the construction of the i-th segment of the outwards-inclined upper tower column (3) in S4 further includes the following steps: Over-tension the stay cables (4) of the i-th segment of the outwards-inclined upper tower column (3) by 5% of the cable force, and release the over-tensioned cable force value after the stay cables (4) of the (i + 1)-th segment of the outwards-inclined upper tower column (3) are tensioned.

5. The construction method of the outward-tilting pylon cable-stayed bridge with coordinated construction of pylon, girder and cable according to any one of claims 1 to 4, characterized in that: In S4, the main girder (5) is constructed symmetrically from the tower root to both sides in segments by means of hanging basket cantilever casting or a bridge erecting machine.

Citation Information

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