STIFFENING GIRDER ERECTION METHOD OF GROUND-ANCHORED SUSPENSION BRIDGE

Abstract

A stiffening girder erection method of a ground-anchored suspension bridge is provided. Clips for all hanger rods of a space main cable suspension bridge are installed such that design center lines of the clips are located in a vertical plane. A first stiffening girder section is installed at a position away from a first tower at a preset distance in a longitudinal direction. A second stiffening girder section is installed at a position away from a second tower at the preset distance along the longitudinal direction. A plurality of third stiffening girder sections are installed one by one in a direction respectively from the first stiffening girder and the second stiffening girder toward a mid-span until a mid-span closure is completed. An azimuth angle of a main cable around a central axis thereof at each of the clips is measured.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority from Chinese Patent Application No. 202410141583.3, filed on Jan. 31, 2024. The content of the aforementioned application, including any intervening amendments made thereto, is incorporated herein by reference in its entirety.

TECHNICAL FIELD

This application relates to connectors, and more particularly to a stiffening girder erection method of a ground-anchored suspension bridge.

BACKGROUND

Ground-anchored suspension bridges using space main cables have begun to emerge in recent years to improve the wind resistance of long-span suspension bridges. In existing methods for erecting stiffening girders of ground-anchored suspension bridges with space main cables, the two main cables are first pushed (or pulled) to close to or reach the transversal position of the completed bridge, and then the stiffening girders are erected, which inevitably increases the temporary facilities and processes required to push the two main cables apart or pull the two main cables closer together, resulting in an increased cost and construction period. For bridges with large transverse inclination angles of cable systems in the completed state, a plurality of temporary pushing (or pulling) facilities are commonly arranged along the longitudinal direction of the bridge. During the process of the main cable being temporarily pushed (or pulled), torques occur since the force exerted by each temporary pushing (pulling) facility on the main cable is difficult to completely pass through the cross-sectional center of the main cable, and even the direction of torques may be reversed, thus causing a large torsion of the main cable. Moreover, the torsion angles along the main cable axis are different or even reversed, causing trouble for subsequent construction.

SUMMARY

An object of the disclosure is to provide a stiffening girder erection method of a space main cable ground-anchored suspension bridge without temporary push (or pull) movement of a main cable.

In order to achieve the above object, the following technical solutions are adopted.

This application provides a stiffening girder erection method of a ground-anchored suspension bridge, comprising:

• • step (1) installing clips for all hanger rods of a space main cable suspension bridge such that design center lines of the clips are coincident with center lines of the hanger rods, respectively; wherein the design center lines of the clips are located in a vertical plane, such that a lateral pre-deflection angle of each of the clips is configured as a lateral inclination angle of a corresponding one of the hanger rods in a bridge complete state;
  • step (2) installing a first stiffening girder section at a position away from a first tower at a preset distance along a longitudinal direction, and installing a second stiffening girder section at a position away from a second tower at the preset distance along the longitudinal direction; and installing a plurality of third stiffening girder sections one by one in a direction respectively from the first stiffening girder and the second stiffening girder toward a mid-span until a mid-span closure is completed; wherein an azimuth angle of a main cable around a central axis thereof at each of the clips is measured after one or more of the plurality of third stiffening girder sections are installed; and a lateral deflection angle of each of the clips is calculated as a lateral inclination angle of each of the plurality of the hanger rods minus the azimuth angle of the main cable around the central axis thereof at each of the clips;
  • step (3) installing a plurality of fourth stiffening girder sections one by one respectively from the first stiffening girder section toward the first tower and from the second stiffening girder section toward the second tower until a stiffening girder is closed at mid-span; and step (4) measuring an azimuth angle of the central axis of the main cable at each of the clips.

In some embodiments, the step (4) is performed through steps of:

• • measuring an azimuth angle of the central axis of the main cable at a hanger rod among the hanger rods corresponding to an uninstalled fourth stiffening girder section; comparing a measured value and a theoretical value of a change of an azimuth angle of the central axis of the main cable at a certain stage; modifying a prediction model of an azimuth angle change value of the central axis of the main cable at the hanger rod corresponding to the uninstalled fourth stiffening girder section; determining an adjustment of a lateral deflection angle of a clip of the hanger rod corresponding to the uninstalled fourth stiffening girder section followed by adjustment; and installing the uninstalled fourth stiffening girder section.

In some embodiments, it is assumed that two points E and F on each of the clips in the bridge complete state are located on a tangent line of a configuration of a corresponding hanger rod at an upper endpoint thereof, an angle between an EF connection line in another state and an EF connection line in the bridge complete state is configured as a lateral deflection angle of each of the clips in the another state, and the lateral pre-deflection angle of each of the clips is a lateral deflection angle achieved during installation and adjustment.

In some embodiments, the lateral inclination angle of each of the hanger rods is an angle between a tangent line of a configuration of each of the hanger rods at an upper endpoint thereof and a vertical line in a projection of each of the hanger rods on a vertical plane perpendicular to a bridge central axis in the bridge complete state.

In some embodiments, it is assumed that an angle between a top-bottom connecting line AB of a section of the main cable in a tightened state and a line AB of a section of the main cable in a certain state is an azimuth angle of the section of the main cable around the central axis thereof in the certain state; and the azimuth angle of the section of the main cable around the central axis thereof is the azimuth angle of the main cable around the central axis thereof.

In some embodiments, in step (2), the preset distance is not less than 60 times a diameter of the main cable, and a girder section which not adjacent to the two main towers is located at the preset distance.

In some embodiments, the theoretical value of the lateral deflection angle of each of the clips is calculated through simulation analysis using a modified finite element model, a modified linear or a modified nonlinear model.

In some embodiments, in step (4), the adjustment of the lateral deflection angle of each of the clips is calculated through simulation analysis using a modified finite element model, a modified linear or a modified nonlinear model.

In some embodiments, the stiffening girder is a steel box girder, a steel truss girder or a steel-concrete composite girder.

In some embodiments, a rise-to-span ratio f_h/L of a plane projection of the main cable in the bridge complete state in a transverse direction is greater than 1/175.

Compared to the prior art, this application has the following beneficial effects.

In the stiffening girder erection method of the present disclosure, there is no need to push (pull) the main cable before installing the stiffening girder, which eliminates a required process and device or facility for pushing (pulling) the main cable, thus saving the cost and construction period. Moreover, an additional torsion caused by the temporary push (or pull) of the main cable can be avoided. During the installation of the stiffening girder, the prediction model is modified based on an actual measurement of the change in the azimuth angle of the main cable around the central axis, so as to determine the adjustment amount of the lateral deflection angle of the clip, thereby reducing a deviation between the lateral inclination angle and a designed lateral inclination angle of the clip in the bridge complete state, resulting in favorable stress on the main cable, the clip and the hanger rod. In addition, the problem that when tower side girder sections are installed first, the large pre-deflection angle of the clip of these girder sections results in unfavorable stress on the main cable, the clip and the hanger rod can be avoided, which is caused by a large deviation between a predicted (calculated) value and an actual value of the azimuth angle change of the main cable around the central axis thereof at a clip within a certain distance along the longitudinal direction of the two main towers and at a first clip in an early installation stage of the stiffening girder. At the same time, this facilitates the avoidance of the problem of a large gap between a corresponding hanger rod installation state and the bridge complete state when first installing girder sections close to the mid-span, which leads to difficulty or inability to meet construction requirements.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to illustrate the technical solutions in the embodiments of the present disclosure or in the prior art more clearly, the drawings needed in the description of embodiments or the prior art will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can be obtained based on these drawings without exerting creative efforts.

FIG. 1 is a schematic diagram of an azimuth angle β of a main cable around a central axis thereof and a lateral inclination angle α of a hanger rod in accordance with an embodiment of the present disclosure;

FIG. 2 illustrates a rise-to-span ratio of a space main cable in a transverse direction in accordance with an embodiment of the present disclosure;

FIG. 3 is a schematic diagram of a space main cable suspension bridge in accordance with an embodiment of the present disclosure;

FIG. 4 illustrates an elevation of the space main cable suspension bridge in accordance with an embodiment of the present disclosure;

FIG. 5 is a plan view of the space main cable suspension bridge in accordance with an embodiment of the present disclosure;

FIG. 6 illustrates an elevation of a main tower of a main bridge in accordance with an embodiment of the present disclosure;

FIG. 7 is a side view of the main tower in accordance with an embodiment of the present disclosure;

FIG. 8 shows a dimensional layout of a main girder in accordance with an embodiment of the present disclosure;

FIG. 9 is a cross-sectional view of a U rib and a straight plate rib of the main girder (single width) in accordance with an embodiment of the present disclosure;

FIG. 10 is a schematic diagram of a diaphragm of the main girder in accordance with an embodiment of the present disclosure;

FIG. 11 illustrates a layout of a crossbeam and the diaphragm in accordance with an embodiment of the present disclosure;

FIG. 12 is a schematic diagram of a perimeter plate of the diaphragm in accordance with an embodiment of the present disclosure;

FIG. 13 illustrates a layout of the perimeter plate, the diaphragm and a stiffeners in accordance with an embodiment of the present disclosure;

FIG. 14 illustrates a vertical component distribution of a force exerted on the hanger rod in accordance with an embodiment of the present disclosure;

FIG. 15 is a schematic diagram of a finite element model of the main bridge (hidden front view) in accordance with an embodiment of the present disclosure;

FIG. 16 illustrates a vertical displacement of the main cable at a mid-span of a main span during an entire process of hoisting the main girder from the main tower to both sides (without any temporary cross brace) in accordance with an embodiment of the present disclosure;

FIG. 17 illustrates a longitudinal displacement at a top of a left tower during the entire process of hoisting the main girder from the main tower to both sides (without any temporary cross brace) in accordance with an embodiment of the present disclosure;

FIG. 18 illustrates a stress of a tower root during the entire process of hoisting the main girder from the main tower to both sides (without any temporary cross brace) in accordance with an embodiment of the present disclosure;

FIG. 19 illustrates a structural condition to be met during an upcoming installation stage and a subsequent hoisting stage of the hanger rod in accordance with an embodiment of the present disclosure;

FIG. 20 is a schematic diagram of a test model and a loading tool in accordance with an embodiment of the present disclosure; and

FIGS. 21a-f illustrates a process of installing the stiffening girder in accordance with an embodiment of the present disclosure.

The realization of the purpose, functional features and advantages of the present disclosure will be further described with reference to the embodiments and the accompanying drawings.

DETAILED DESCRIPTION OF EMBODIMENTS

The technical solutions of the present disclosure will be clearly and completely described below in conjunction with the accompanying drawings and embodiments. Obviously, described below are only some embodiments of the present disclosure, instead of all embodiments of the present disclosure. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the scope of the present disclosure.

It should be noted that all directional indications (such as up, down, left, right, front, back . . . ) in the description of the embodiments are merely intended to explain a relative positional relationship, movement, etc. between components in a specific posture (as shown in the accompanying drawings). When the specific posture changes, the directional indication changes accordingly.

In addition, descriptions involving “first”, “second”, etc. in this application are only descriptive, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, features defined as “first” and “second” can explicitly or implicitly include at least one of the features. In addition, “and/or” in the entire specification includes three solutions. For example, A and/or B includes technical solution A, technical solution B, and technical solutions that satisfy both A and B. Moreover, technical solutions in the embodiments can be combined with each other, but must be based on what can be achieved by those of ordinary skill in the art. When the combination of technical solutions appears to be contradictory or cannot be realized, it should be deemed that such combination of technical solutions does not exist and is not within the scope of the present disclosure defined by the appended claims.

A space main cable suspension bridge of the present disclosure refers to a suspension bridge in which a rise-to-span ratio f_h/L in a transverse direction in a plane projection of a main cable in a bridge complete state is greater than 1/175. When the rise-to-span ratio f_h/L is 0, the space main cable suspension bridge degenerates into a planar main cable suspension bridge.

As shown in FIGS. 1-2 and 21a-f, this application provides a stiffening girder erection method of a ground-anchored suspension bridge, which includes the following steps.

(S1) Clips for all hanger rods of a space main cable suspension bridge are installed such that design center lines of the clips are coincident with center lines of the hanger rods, respectively. The design center lines of the clips are located in a vertical plane, such that a lateral pre-deflection angle of each of the clips is configured as a lateral inclination angle of a corresponding one of the hanger rods in a bridge complete state.

(S2) A first stiffening girder section is installed at a position away from a first tower at a preset distance along a longitudinal direction. A second stiffening girder section is installed at a position away from a second tower at the preset distance along the longitudinal direction. A plurality of third stiffening girder sections are installed one by one in a direction respectively from the first stiffening girder and the second stiffening girder toward a mid-span until a mid-span closure is completed. An azimuth angle of a main cable around a central axis thereof at each of the clips is measured after one or more of the plurality of third stiffening girder sections are installed. A lateral deflection angle of each of the clips is calculated as a lateral inclination angle of each of the plurality of the hanger rods minus the azimuth angle of the main cable around the central axis thereof at each of the clips.

(S3) A plurality of fourth stiffening girder sections are installed one by one respectively from the first stiffening girder section toward the first tower and from the second stiffening girder section toward the second tower until a stiffening girder is closed at mid-span.

(S4) An azimuth angle of the central axis of the main cable at each of the clips is measured.

In the stiffening girder erection method of the present disclosure, there is no need to push (pull) the main cable away before installing the stiffening girder, which eliminates the process of pushing (pulling) the main cable apart, thereby avoiding additional torsion of the main cable caused by the main cable being pushed (pulled) apart, thus reducing a deviation between a torsion angle and a preset optimal torsion angle of the main cable. In addition, when installing the stiffening girder, the azimuth angle of the main cable around the central axis thereof at the hanger rod of the upcoming installed stiffening girder section is first measured, which is the lateral deflection angle of the clip, and then the measured value of the lateral deflection angle of the clip is compared with the theoretical value to determine the adjustment amount of the lateral deflection angle of the clip. After adjustment, the stiffening girder is installed. The azimuth angle of the main cable around the central axis thereof is continuously adjusted during the installation of the stiffening girder to make it closer to the theoretical value, thereby further reducing the deviation between the torsion angle and the preset optimal torsion angle of the main cable.

In this embodiment, the process of pushing (pulling) the main cable apart in advance is omitted, thereby improving efficiency. In addition, a temporary facility required to push (pull) the main cable laterally can be eliminated, which facilitates fewer required facilities and lower cost.

The step (4) is performed through the following steps.

An azimuth angle of the central axis of the main cable at a hanger rod among the hanger rods corresponding to an uninstalled fourth stiffening girder section among the plurality of fourth stiffening girder sections is measured. A measured value and a theoretical value of a change of an azimuth angle of the central axis of the main cable at a certain stage are compared. A prediction model of an azimuth angle change value of the central axis of the main cable at the hanger rod corresponding to the uninstalled fourth stiffening girder section is modified. An adjustment of a lateral deflection angle of a clip of the hanger rod corresponding to the uninstalled fourth stiffening girder section is determined and adjusted. An uninstalled fourth stiffening girder section is installed.

Specifically, the installation of the stiffening girder sections has the same operation. During the installation of the stiffening girder section, the azimuth angle of the main cable around the central axis thereof is continuously adjusted to make it closer to the theoretical value, thereby further reducing the deviation between the torsion angle and the preset optimal torsion angle of the main cable.

As shown in FIG. 1, two points E and F on each of the clips in the bridge complete state are located on a tangent line of a configuration of a corresponding hanger rod at an upper endpoint thereof. An angle between an EF connection line in another state and an EF connection line in the bridge complete state is configured as a lateral deflection angle of each of the clips in the another state, and the lateral pre-deflection angle of each of the clips is a lateral deflection angle achieved during installation and adjustment. Specifically, relative to the bridge complete state, when the point F with a larger elevation in other states moves away from the center line of the bridge, the lateral deflection angle is positive. Otherwise, the lateral deflection angle is negative.

As shown in FIG. 1, the lateral inclination angle of each of the hanger rods is an angle α between a tangent line of a configuration of each of the hanger rods at an upper endpoint thereof and a vertical line in a projection of each of the hanger rods on a vertical plane perpendicular to a bridge central axis in the bridge complete state.

Specifically, a configuration of a hanger rod is a catenary line, which can generally be regarded as a straight line. FIG. 1 refers to a situation when the hanger rod in the bridge complete state is viewed as a straight line.

As shown in FIG. 1, an angle β between a top-bottom connecting line AB of a section of the main cable in a tightened state and a line AB of a section of the main cable in a certain state is configured as an azimuth angle of the section of the main cable around the central axis thereof in the certain state, i.e., the azimuth angle of the main cable around the central axis thereof. Specifically, a rotation of point A relative to the movement of the empty cable toward the center line of the bridge is positive, and vice versa is negative. Determination of the connection line AB: A connection between the highest point A of the section of the main cable and the lower edge point B of the section of the main cable on a plumb line passing through point A is the connection line AB.

For the space main cable suspension bridge, the empty cable is in a vertical plane under its own weight. Under an external force with horizontal and vertical components (provided by the hanger rods, a temporary cross brace, a temporary cable, etc., which are commonly difficult to completely pass through the center of the section of the tightened main cable), not only the main cable is displaced, but also each section of the main cable may be twisted. Obviously, the azimuth angle of each section of the empty cable in the vertical plane around the central axis of the main cable is 0.

In some embodiments, in step (S2), the preset distance is not less than 60 times a diameter of the main cable.

Specifically, this method uses component forces of the hanger rod generated by the weight of the stiffening girder to gradually pull the main cable apart or close, gradually forming a spatial shape of the bridge. In this way, the shortcomings of increased temporary facilities and corresponding processes for the main cable being pushed (pulled) apart laterally caused by pushing (pulling) the main cable apart first and then installing the stiffening girder can be overcome. A risk of twisting the main cable section due to an axial force not passing through the center of the main cable section in a transverse push (pull) state can be avoided. Compared to a traditional solution of first erecting the girder section at the mid-span, a maximum lifting height of the stiffening girder is reduced, leading to a reduced capacity requirement of a lifting device. Compared to a traditional solution of first erecting the girder section at the mid-span or near the mid-span (that is, not erecting the girder section near the two main towers first), this application is easier to meet a structural compatibility condition, due to a shorter distance between an upper end position of the hanger rod and a complete position when each girder section is installed, and fewer structural restrictions on a location of an anchor point of the hanger rod and a diameter of a casing of the hanger rod.

In some embodiments, the theoretical value of the lateral deflection angle of each of the clips is calculated through finite element simulation analysis. Specifically, the finite element simulation analysis is performed using an ANSYS software.

In some embodiments, in step (S4), the adjustment of the lateral deflection angle of each of the clips is calculated through finite element simulation analysis. Specifically, the finite element simulation analysis is performed using an ANSYS software.

Specifically, a finite element stiffness of a clip is calculated based on the measured value of the lateral deflection angle of the clip and the theoretical value, and the adjustment amount of the lateral deflection angle of the clip is calculated based on the finite element stiffness.

In some embodiments, the stiffening girder is a steel box girder, a steel truss girder or a steel-concrete composite girder.

An overall process of the stiffening girder installation is shown in FIGS. 21a-f.

1.1 Analysis Object

1.1.1 Overall Layout of the Bridge

The analysis object is the space main cable suspension bridge of a certain passageway, Lingding Channel, as shown in FIG. 3. The space main cable suspension bridge has a span layout of 165 (left anchor span)+688 (=37+26*24+27, left side span)+1658 (=37+66*24+37, middle span)+688 (=37+26*24+27, right span)+165 m (right anchor span), a hanger rod with a spacing in a longitudinal direction of 24 m, a main girder at a mid-span with a top elevation of 88 m, a slope point set at the mid-span, a longitudinal slope from the mid-span to both sides with a gradient of 2.7% and a vertical curve radius of 56139.25 m. FIGS. 4-7 shows a bridge layout with only the span layout (the main span is only enlarged by 2 m) and the spacing of the hanger rod changed.

The stiffening girder is designed as two steel box sub-girders connected by a crossbeam, as shown in FIG. 8. Four traffic lanes with a width of 3.75 m are arranged in each side. A distance between the two steel box girders in the transverse direction is 16.6 m. A full width of each steel box girder at the main span in the transverse direction is 64 m. Each main cable is composed of 252 strands. Each strand is composed of 127 parallel steel wires Φ5.3 with a tensile strength of 1990 MPa (referring to the Nansha Bridge with a main span of 1688 m). The rise-to-span ratio of the main cable is 1/9.26. A main cable holder is provided above a pier at the side span to improve the stiffness of the main girder at the side span. An arc radius of a main cable saddle is 8.2 m (referring to the Xihoumen Bridge with a main span of 1650 m). A theoretical vertex elevation of the main cable at the top of the two main towers is 270.050 m. Double hanger rods are used on one side in the transverse direction. A single hanger rod is temporarily composed of 199 parallel steel wires with a diameter of 7 mm and an area of 0.007658417 m².

Each of the two main towers has an elevation of a top of a cap platform (i.e. a bottom of a tower column) of −7.8833 m, an elevation of a top of the tower column of 265.5461 m, and a total height of the tower column of 273.4294 m. Based on the design experience of similar projects, a 5 m-section of the tower column near the cap platform within an elevation range of −7.8833 m to −2.8833 m is set as a round-end solid section, a 89.3354 m-section within an elevation range of −2.8833 m to 86.4521 m is set as a round-end hollow section with a wall thickness of 2.2 m, a 80 m-section within an elevation range of 86.4521 m to 166.4521 m is set as a round-end hollow section with a wall thickness of 1.6 m, a 80 m-section within an elevation range of 166.4521 m to 257.5461 m is set as a round-end hollow section with a wall thickness of 1.2 m, and a 8 m-section within an elevation range of 257.5461 m to 265.5461 m is set as a round-end solid section.

1.1.2 Main Girder Design and Second Phase Dead Load

1) Main Girder and Diaphragm Thereof

According to an overall dimension of the stiffening girder (with a height of 5 m and a width of 23.7 m, as shown in FIG. 9) and similar engineering design experience, dimensions of each plate in a cross section of the main girder is proposed, as shown in Table 1 and FIG. 10, so as to obtain the cross-sectional characteristics of the main girder (single width) shown in Table 2.

TABLE 1
Thickness, dimensions and spacings of each plate in
the cross section of the main girder (single width)
of the main bridge of the Lingding Channel between
Shenzhen and Zhongshan Passageway (Unit: mm)
Thickness of top plate           16
Thickness of U rib at top plate  8
Dimensions of U rib at top plate Bottom width 300-height 280-top
                                 width 170-horizontal spacing 600
Thickness of inclined web        20
Thickness of straight web        20
Thickness of base plate          12
Thickness of U rib at base plate 8
Dimensions of U rib at base plate Bottom width 400-height 260-top
                                 width 250-horizontal spacing 800
Dimensions of stiffeners at      Height 120-thickness 10
straight plate

TABLE 2
Cross-sectional characteristics of the main girder (single width)
Area (m2)	1.105967802
	Distance from center of	X	−12.2480	11.4511
	inertia to each end (m)	Y	−3.3842	1.6108
	Moment of inertia (m4):	X	2.7572
		Y	53.1220

Based on the experience of similar projects, a plurality of diaphragms are provided with a spacing of 3 m. A thickness of a diaphragm at a non-hanger rod area is 10 mm. A thickness of a diaphragm at the hanger rod position is 12 mm. The number of the plurality of diaphragms of each steel box girder is 8 (7 diaphragms with a thickness of 10 mm and 1 diaphragm with a thickness of 12 mm). A peripheral stiffening plate is provided on the diaphragm close to the top plate, bottom plate and web. A vertical plate stiffening rib is provided vertically in the peripheral stiffening plate, which has a spacing of 1200 mm in the transverse direction. A horizontal plate stiffening rib is provided between longer vertical plate stiffening ribs. 2 cable holes and 1 manhole are provided on each diaphragm. A layout of the stiffening rib, cable hole and manhole of the diaphragm is shown in FIG. 10. The dimensions and thickness of the peripheral stiffening plate, vertical plate, horizontal plate, manhole and cable hole are shown in Table 3.

TABLE 3
Thickness and width of peripheral stiffening plate, vertical plate,
horizontal plate, and peripheral plate of manhole and cable hole
Peripheral stiffening plate	Width/mm	140	Thickness/mm	10
Vertical plate	Width/mm	120	Thickness/mm	10
Horizontal plate	Width/mm	100	Thickness/mm	10
Peripheral plate of manhole	Width/mm	120	Thickness/mm	10
and cable hole

It is calculated that a total mass of diaphragms of each steel box girder (single width) is 48879.53 kg. According to similar projects, a structural mass of a cable anchor of each steel box girder is 3000 kg. Therefore, a total mass of a single steel box girder per segment (excluding welds) is 260243.8649 kg, and a total mass of a single steel box girder per segment (including welds) is 264147.523 kg. Based on a cross-sectional area of the peripheral stiffening plate of the steel box girder, an equivalent density of each section of the single steel box girder (including welds) is calculated as 9951.597843 kg/m³.

2) Crossbeam Between Main Girder

The crossbeam is provided on the main girder with a gap of 12 m. The crossbeam has a height of 5 m (as shown in FIG. 11) and a width (along the longitudinal direction) of 4 m. The stiffeners (as shown in FIG. 12) of the peripheral stiffening plate and the straight plate, and the diaphragm with a spacing of 2.1 m are used for stiffening, thereby avoiding local buckling. A horizontal straight plate stiffening rib, a vertical straight plate stiffening rib and the manhole are provided on the diaphragm (as shown in FIG. 13).

After calculation, the cross-sectional characteristics of the crossbeam are obtained, as shown in Table 4.

TABLE 4
Cross-sectional characteristics of the crossbeam
Area (m2)	0.41888
	Distance from center of	X	−2	2
	inertia to each end (m)	Y	−2.5	2.5
	Moment of inertia (m4):	X	1.5212
		Y	1.1833

According to statistics, a total mass of each crossbeam at the main span is 91852.324 kg. Based on the finite element simulation, the crossbeam has a length of 39.5021 m and a cross-sectional area of 0.41888 m². A volume of the crossbeam is 16.54665523 m³, and thus a density of the crossbeam is 5551.111229 kg/m³.

3) Second Phase Dead Load

A single main girder has a bridge deck pavement width of 18.75 m, a thickness of 0.075 m, a bulk density of 25000 N/m³ and a load concentration caused by the pavement of 35156.25 N/m. A total mass of a railing, a curb, an inspection vehicle track, a water pipe, etc. is initially planned to be 1300 kg per meter, corresponding to the resulting load concentration of 12747.8 N/m. Therefore, a total load concentration of the second phase dead load is 47904.05 N/m.

1.1.3 Bridge Complete State

1) Preliminary Determination of a Vertical Component Force of the Hanger Rod in the Bridge Complete State (Rigid Support Continuous Girder Method)

Based on the span, hanger rod layout, cross-sectional characteristics of the main girder and crossbeam, the equivalent bulk density and the second phase dead load in the previous two sections (sections 1.1.1 and 1.1.2), the ANSYS software is used to establish a finite element model of a rigid support continuous girder spatial rod system, which only include the main girder and imposed vertical constraints on a girder end, a tower-girder junction and a suspension point of the hanger rod. After calculation, the vertical component force at the lower end of each hanger rod (one side) is shown in Table 5. A distribution of the vertical component force of the hanger rod is shown in FIG. 14.

TABLE 5
Calculated value of the vertical component force
of the hanger rod in the bridge complete state
		Vertical component	Vertical component
		force of the hanger	force of the hanger
	Number	rod (before averaging	rod (after averaging
Number of	description	three hanger rods	three hanger rods
hanger rod	of hanger rod	at span end)	at span end)
1	Left side span	4419.7	4511.0
	1#hanger rod
2	Left side span	4786.5	4511.0
	2#hanger rod
3	Left side span	4326.7	4511.0
	3#hanger rod
4	Left side span	4433.3	4433.3
	4#hanger rod
5	Left side span	4421.8	4421.8
	5#hanger rod
6	Left side span	4435.1	4435.1
	6#hanger rod
7	Left side span	4443.3	4443.3
	7#hanger rod
8	Left side span	4452.6	4452.6
	8#hanger rod
9	Left side span	4461.7	4461.7
	9#hanger rod
10	Left side span	4470.9	4470.9
	10#hanger rod
11	Left side span	4480.0	4480.0
	11#hanger rod
12	Left side span	4489.2	4489.2
	12#hanger rod
13	Left side span	4498.3	4498.3
	13#hanger rod
14	Left side span	4507.6	4507.6
	14#hanger rod
15	Left side span	4516.7	4516.7
	15#hanger rod
16	Left side span	4525.9	4525.9
	16#hanger rod
17	Left side span	4535.1	4535.1
	17#hanger rod
18	Left side span	4544.3	4544.3
	18#hanger rod
19	Left side span	4553.6	4553.6
	19#hanger rod
20	Left side span	4562.9	4562.9
	20#hanger rod
21	Left side span	4572.0	4572.0
	21#hanger rod
22	Left side span	4582.8	4582.8
	22#hanger rod
23	Left side span	4585.4	4585.4
	23#hanger rod
24	Left side span	4628.2	4628.2
	24#hanger rod
25	Left side span	4479.4	4548.8
	25#hanger rod
26	Left side span	5250.7	4548.8
	26#hanger rod
27	Left side span	3916.3	4548.8
	27#hanger rod
28	Main span	3947.2	4575.4
	1#hanger rod
29	Main span	5266.6	4575.4
	2#hanger rod
30	Main span	4512.3	4575.4
	3#hanger rod
31	Main span	4669.0	4669.0
	4#hanger rod
32	Main span	4635.7	4635.7
	5#hanger rod
33	Main span	4642.3	4642.3
	6#hanger rod
34	Main span	4640.7	4640.7
	7#hanger rod
35	Main span	4640.8	4640.8
	8#hanger rod
36	Main span	4640.7	4640.7
	9#hanger rod
37	Main span	4640.6	4640.6
	10#hanger rod
38	Main span	4640.6	4640.6
	11#hanger rod
39	Main span	4640.5	4640.5
	12#hanger rod
40	Main span	4640.5	4640.5
	13#hanger rod
41	Main span	4640.5	4640.5
	14#hanger rod
42	Main spar	4640.4	4640.4
	15#hanger rod
43	Main span	4640.4	4640.4
	16#hanger rod
44	Main span	4640.4	4640.4
	17#hanger rod
45	Main span	4640.4	4640.4
	18#hanger rod
46	Main span	4640.3	4640.3
	19#hanger rod
47	Main span	4640.3	4640.3
	20#hanger rod
48	Main span	4640.3	4640.3
	21#hanger rod
49	Main span	4640.3	4640.3
	22#hanger rod
50	Main span	4640.3	4640.3
	23#hanger rod
51	Main span	4640.3	4640.3
	24#hanger rod
52	Main span	4640.3	4640.3
	25#hanger rod
53	Main span	4640.2	4640.2
	26#hanger rod
54	Main span	4640.2	4640.2
	27#hanger rod
55	Main span	4640.2	4640.2
	28#hanger rod
56	Main span	4640.2	4640.2
	29#hanger rod
57	Main span	4640.2	4640.2
	30#hanger rod
58	Main span	4640.2	4640.2
	31#hanger rod
59	Main span	4640.2	4640.2
	32#hanger rod
60	Main span	4640.2	4640.2
	33#hanger rod
61	Main span	4640.2	4640.2
	34#hanger rod
62	Main span	4640.2	4640.2
	35#hanger rod
63	Main span	4640.2	4640.2
	36#hanger rod
64	Main span	4640.2	4640.2
	37#hanger rod
65	Main span	4640.2	4640.2
	38#hanger rod
66	Main span	4640.2	4640.2
	39#hanger rod
67	Main span	4640.2	4640.2
	40#hanger rod
68	Main span	4640.2	4640.2
	41#hanger rod
69	Main span	4640.2	4640.2
	42#hanger rod
70	Main span	4640.3	4640.3
	43#hanger rod
71	Main span	4640.3	4640.3
	44#hanger rod
72	Main span	4640.3	4640.3
	45#hanger rod
73	Main span	4640.3	4640.3
	46#hanger rod
74	Main span	4640.3	4640.3
	47#hanger rod
75	Main span	4640.3	4640.3
	48#hanger rod
76	Main span	4640.3	4640.3
	49#hanger rod
77	Main span	4640.4	4640.4
	50#hanger rod
78	Main span	4640.4	4640.4
	51#hanger rod
79	Main span	4640.4	4640.4
	52#hanger rod
80	Main span	4640.4	4640.4
	53#hanger rod
81	Main span	4640.5	4640.5
	54#hanger rod
82	Main span	4640.5	4640.5
	55#hanger rod
83	Main span	4640.5	4640.5
	56#hanger rod
84	Main span	4640.6	4640.6
	57#hanger rod
85	Main span	4640.6	4640.6
	58#hanger rod
86	Main span	4640.7	4640.7
	59#hanger rod
87	Main span	4640.8	4640.8
	60#hanger rod
88	Main span	4640.7	4640.7
	61#hanger rod
89	Main span	4642.3	4642.3
	62#hanger rod
90	Main span	4635.7	4635.7
	63#hanger rod
91	Main span	4669.0	4669.0
	64#hanger rod
92	Main span	4512.3	4575.4
	65#hanger rod
93	Main span	5266.6	4575.4
	66#hanger rod
94	Main span	3947.2	4575.4
	67#hanger rod
95	Right side span	3916.3	4548.8
	27#hanger rod
96	Right side span	5250.7	4548.8
	26#hanger rod
97	Right side span	4479.4	4548.8
	25#hanger rod
98	Right side span	4628.2	4628.2
	24#hanger rod
99	Right side span	4585.4	4585.4
	23#hanger rod
100	Right side span	4582.8	4582.8
	22#hanger rod
101	Right side span	4572.0	4572.0
	21#hanger rod
102	Right side span	4562.9	4562.9
	20#hanger rod
103	Right side span	4553.6	4553.6
	19#hanger rod
104	Right side span	4544.3	4544.3
	18#hanger rod
105	Right side span	4535.1	4535.1
	17#hanger rod
106	Right side span	4525.9	4525.9
	16#hanger rod
107	Right side span	4516.7	4516.7
	15#hanger rod
108	Right side span	4507.6	4507.6
	14#hanger rod
109	Right side span	4498.3	4498.3
	13#hanger rod
110	Right side span	4489.2	4489.2
	12#hanger rod
111	Right side span	4480.0	4480.0
	11#hanger rod
112	Right side span	4470.9	4470.9
	10#hanger rod
113	Right side span	4461.7	4461.7
	9#hanger rod
114	Right side span	4452.6	4452.6
	8#hanger rod
115	Right side span	4443.3	4443.3
	7#hanger rod
116	Right side span	4435.1	4435.1
	6#hanger rod
117	Right side span	4421.8	4421.8
	5#hanger rod
118	Right side span	4433.3	4433.3
	4#hanger rod
119	Right side span	4326.7	4511.0
	3#hanger rod
120	Right side span	4786.5	4511.0
	2#hanger rod
121	Right side span	4419.7	4511.0
	1#hanger rod

2) Configuration and Tension Force of the Main Cable in the Bridge Complete State (Analytical Method)

According to main control geometric parameters of the main cable proposed in section 1.1.1, it is easy to determine a theoretical vertex mileage and an elevation of a main cable saddle and a loose cable saddle at a side pier, coordinates of an anchor point of the main cable (the theoretical vertex of the loose cable saddle is temporarily taken as the anchor point and the elevation of the main cable), a material and a cross-sectional size of the main cable, a material and a cross-sectional characteristics of the hanger rod, and the obtained vertical component force of the hanger rod. Referring to a quality of a clip of similar bridges, a numerical analysis calculation software of the space main cable suspension bridge cable system is used to perform iterative calculations, and the configuration and an internal force state of the cable system in the bridge complete state are obtained. The obtained node coordinates of the main cable, unstressed length of the main cable section (without considering the saddle arc correction), cable force of the cable segment and safety factor obtained according to an ultimate strength of 1860 MPa are shown in Table 6. It can be seen from Table 6 that the safety factor of the main cable in the dead-load state has a minimum value of 2.45 and a maximum value of 2.68, which will be reduced after considering a live load effect. It is calculated that an increment of a tension in the main cable section caused by a live load of a vehicle is approximately 10% of the dead load. Therefore, after considering the live load of the vehicle, the minimum safety factor of the main cable can reach 2.22. When using parallel steel wires with an ultimate strength of 1990 MPa, the minimum safety factor can reach 2.37.

TABLE 6
Node coordinates, cable section tension force and safety factor of the main cable in the bridge complete state
					Unstressed
					length of
					main cable
					section
					(without
					considering		breaking
					the arc	Tension	force of	Safety
					correction	of cable	main	factor in
Node	Node		Transverse		at the	section	cable	dead-
number	description	Mileage	direction	Elevation	saddle)	N	N	load state
1	Theoretical	−1682.000	−28.500	27.500
	vertex of left
	loose cable
	saddle
2	Theoretical	−1517.000	−24.198	67.450	169.226	4.90E+08	1.313E+09	2.68
	vertex of left
	cable saddle for
	steering
3	Left side span	−1490.000	−23.967	70.851	27.119	4.91E+08	1.313E+09	2.68
	1#hanger rod
4	Left side span	−1466.000	−23.725	74.178	24.146	4.91E+08	1.313E+09	2.67
	2#hanger rod
5	Left side span	−1442.000	−23.445	77.796	24.188	4.92E+08	1.313E+09	2.67
	3#hanger rod
6	Left side span	−1418.000	−23.129	81.706	24.233	4.93E+08	1.313E+09	2.66
	4#hanger rod
7	Left side span	−1394.000	−22.777	85.903	24.281	4.94E+08	1.313E+09	2.66
	5#hanger rod
8	Left side span	−1370.000	−22.390	90.389	24.333	4.95E+08	1.313E+09	2.65
	6#hanger rod
9	Left side span	−1346.000	−21.969	95.164	24.388	4.96E+08	1.313E+09	2.65
	7#hanger rod
10	Left side span	−1322.000	−21.513	100.229	24.446	4.97E+08	1.313E+09	2.64
	8#hanger rod
11	Left side span	−1298.000	−21.023	105.585	24.508	4.99E+08	1.313E+09	2.63
	9#hanger rod
12	Left side span	−1274.000	−20.500	111.232	24.573	5.00E+08	1.313E+09	2.63
	10#hanger rod
13	Left side span	−1250.000	−19.943	117.172	24.642	5.01E+08	1.313E+09	2.62
	11#hanger rod
14	Left side span	−1226.000	−19.353	123.406	24.715	5.03E+08	1.313E+09	2.61
	12#hanger rod
15	Left side span	−1202.000	−18.730	129.935	24.791	5.05E+08	1.313E+09	2.60
	13#hanger rod
16	Left side span	−1178.000	−18.074	136.759	24.870	5.06E+08	1.313E+09	2.59
	14#hanger rod
17	Left side span	−1154.000	−17.386	143.881	24.953	5.08E+08	1.313E+09	2.59
	15#hanger rod
18	Left side span	−1130.000	−16.666	151.300	25.040	5.10E+08	1.313E+09	2.58
	16#hanger rod
19	Left side span	−1106.000	−15.914	159.019	25.130	5.11E+08	1.313E+09	2.57
	17#hanger rod
20	Left side span	−1082.000	−15.130	167.037	25.224	5.13E+08	1.313E+09	2.56
	18#hanger rod
21	Left side span	−1058.000	−14.315	175.358	25.321	5.15E+08	1.313E+09	2.55
	19#hanger rod
22	Left side span	−1034.000	−13.468	183.981	25.422	5.17E+08	1.313E+09	2.54
	20#hanger rod
23	Left side span	−1010.000	−12.590	192.907	25.527	5.20E+08	1.313E+09	2.53
	21#hanger rod
24	Left side span	−986.000	−11.681	202.139	25.635	5.22E+08	1.313E+09	2.52
	22#hanger rod
25	Left side span	−962.000	−10.742	211.678	25.747	5.24E+08	1.313E+09	2.51
	23#hanger rod
26	Left side span	−938.000	−9.772	221.524	25.862	5.26E+08	1.313E+09	2.49
	24#hanger rod
27	Left side span	−914.000	−8.771	231.680	25.982	5.29E+08	1.313E+09	2.48
	25#hanger rod
28	Left side span	−890.000	−7.740	242.144	26.103	5.31E+08	1.313E+09	2.47
	26#hanger rod
29	Left side span	−866.000	−6.680	252.916	26.228	5.34E+08	1.313E+09	2.46
	27#hanger rod
30	Closed clip	−842.000	−5.590	263.998	26.356	5.37E+08	1.313E+09	2.45
31	Theoretical	−829.000	−5.000	270.050	14.297	5.37E+08	1.313E+09	2.45
	vertex of left
	main tower
32	Closed clip	−816.000	−5.676	264.528	14.087	5.29E+08	1.313E+09	2.48
33	Main span	−792.000	−6.925	254.391	25.985	5.29E+08	1.313E+09	2.48
	1#hanger rod
34	Main span	−768.000	−8.144	244.565	25.865	5.26E+08	1.313E+09	2.49
	2#hanger rod
35	Main span	−744.000	−9.333	235.047	25.749	5.24E+08	1.313E+09	2.51
	3#hanger rod
36	Main span	−720.000	−10.492	225.838	25.637	5.22E+08	1.313E+09	2.52
	4#hanger rod
37	Main span	−696.000	−11.620	216.941	25.526	5.20E+08	1.313E+09	2.53
	5#hanger rod
38	Main span	−672.000	−12.717	208.353	25.420	5.17E+08	1.313E+09	2.54
	6#hanger rod
39	Main span	−648.000	−13.783	200.074	25.317	5.15E+08	1.313E+09	2.55
	7#hanger rod
40	Main span	−624.000	−14.818	192.103	25.218	5.13E+08	1.313E+09	2.56
	8#hanger rod
41	Main span	−600.000	−15.820	184.439	25.122	5.11E+08	1.313E+09	2.57
	9#hanger rod
42	Main span	−576.000	−16.791	177.082	25.030	5.09E+08	1.313E+09	2.58
	10#hanger rod
43	Main span	−552.000	−17.729	170.031	24.942	5.08E+08	1.313E+09	2.59
	11#hanger rod
44	Main span	−528.000	−18.634	163.285	24.857	5.06E+08	1.313E+09	2.60
	12#hanger rod
45	Main span	−504.000	−19.506	156.843	24.776	5.04E+08	1.313E+09	2.60
	13#hanger rod
46	Main span	−480.000	−20.345	150.705	24.698	5.03E+08	1.313E+09	2.61
	14#hanger rod
47	Main span	−456.000	−21.150	144.870	24.624	5.01E+08	1.313E+09	2.62
	15#hanger rod
48	Main span	−432.000	−21.921	139.338	24.554	5.00E+08	1.313E+09	2.63
	16#hanger rod
49	Main span	−408.000	−22.657	134.108	24.487	4.98E+08	1.313E+09	2.64
	17#hanger rod
50	Main span	−384.000	−23.358	129.180	24.424	4.97E+08	1.313E+09	2.64
	18#hanger rod
51	Main span	−360.000	−24.024	124.553	24.365	4.96E+08	1.313E+09	2.65
	19#hanger rod
52	Main span	−336.000	−24.654	120.226	24.309	4.95E+08	1.313E+09	2.66
	20#hanger rod
53	Main span	−312.000	−25.247	116.199	24.257	4.94E+08	1.313E+09	2.66
	21#hanger rod
54	Main span	−288.000	−25.804	112.472	24.209	4.93E+08	1.313E+09	2.67
	22#hanger rod
55	Main span	−264.000	−26.322	109.043	24.164	4.92E+08	1.313E+09	2.67
	23#hanger rod
56	Main span	−240.000	−26.802	105.914	24.123	4.91E+08	1.313E+09	2.68
	24#hanger rod
57	Main span	−216.000	−27.243	103.083	24.086	4.90E+08	1.313E+09	2.68
	25#hanger rod
58	Main span	−192.000	−27.643	100.551	24.052	4.89E+08	1.313E+09	2.68
	26#hanger rod
59	Main span	−168.000	−28.002	98.316	24.023	4.89E+08	1.313E+09	2.69
	27#hanger rod
60	Main span	−144.000	−28.319	96.379	23.996	4.88E+08	1.313E+09	2.69
	28#hanger rod
61	Main span	−120.000	−28.592	94.739	23.974	4.88E+08	1.313E+09	2.69
	29#hanger rod
62	Main span	−96.000	−28.819	93.397	23.955	4.87E+08	1.313E+09	2.69
	30#hanger rod
63	Main span	−72.000	−28.999	92.351	23.940	4.87E+08	1.313E+09	2.70
	31#hanger rod
64	Main span	−48.000	−29.129	91.602	23.929	4.87E+08	1.313E+09	2.70
	32#hanger rod
65	Main span	−24.000	−29.208	91.150	23.921	4.87E+08	1.313E+09	2.70
	33#hanger rod
66	Main span	0.000	−29.235	90.999	23.917	4.87E+08	1.313E+09	2.70
	34#hanger rod
	(mid- span of
	Main span)
67	Main span	24.000	−29.208	91.150	23.917	4.87E+08	1.313E+09	2.70
	35#hanger rod
68	Main span	48.000	−29.129	91.602	23.921	4.87E+08	1.313E+09	2.70
	36#hanger rod
69	Main span	72.000	−28.999	92.351	23.929	4.87E+08	1.313E+09	2.70
	37#hanger rod
70	Main span	96.000	−28.819	93.397	23.940	4.87E+08	1.313E+09	2.70
	38#hanger rod
71	Main span	120.000	−28.592	94.739	23.955	4.87E+08	1.313E+09	2.69
	39#hanger rod
72	Main span	144.000	−28.319	96.379	23.974	4.88E+08	1.313E+09	2.69
	40#hanger rod
73	Main span	168.000	−28.002	98.316	23.996	4.88E+08	1.313E+09	2.69
	41#hanger rod
74	Main span	192.000	−27.643	100.551	24.023	4.89E+08	1.313E+09	2.69
	42#hanger rod
75	Main span	216.000	−27.243	103.083	24.052	4.89E+08	1.313E+09	2.68
	43#hanger rod
76	Main span	240.000	−26.802	105.914	24.086	4.90E+08	1.313E+09	2.68
	44#hanger rod
77	Main span	264.000	−26.322	109.043	24.123	4.91E+08	1.313E+09	2.68
	45#hanger rod
78	Main span	288.000	−25.804	112.472	24.164	4.92E+08	1.313E+09	2.67
	46#hanger rod
79	Main span	312.000	−25.247	116.199	24.209	4.93E+08	1.313E+09	2.67
	47#hanger rod
80	Main span	336.000	−24.654	120.226	24.257	4.94E+08	1.313E+09	2.66
	48#hanger rod
81	Main span	360.000	−24.024	124.553	24.309	4.95E+08	1.313E+09	2.65
	49#hanger rod
82	Main span	384.000	−23.358	129.180	24.365	4.96E+08	1.313E+09	2.65
	50#hanger rod
83	Main span	408.000	−22.657	134.108	24.424	4.97E+08	1.313E+09	2.64
	51#hanger rod
84	Main span	432.000	−21.921	139.338	24.487	4.98E+08	1.313E+09	2.64
	52#hanger rod
85	Main span	456.000	−21.150	144.870	24.554	5.00E+08	1.313E+09	2.63
	53#hanger rod
86	Main span	480.000	−20.345	150.705	24.624	5.01E+08	1.313E+09	2.62
	54#hanger rod
87	Main span	504.000	−19.506	156.843	24.698	5.03E+08	1.313E+09	2.61
	55#hanger rod
88	Main span	528.000	−18.634	163.285	24.776	5.04E+08	1.313E+09	2.60
	56#hanger rod
89	Main span	552.000	−17.729	170.031	24.857	5.06E+08	1.313E+09	2.60
	57#hanger rod
90	Main span	576.000	−16.791	177.082	24.942	5.08E+08	1.313E+09	2.59
	58#hanger rod
91	Main span	600.000	−15.820	184.439	25.030	5.09E+08	1.313E+09	2.58
	59#hanger rod
92	Main span	624.000	−14.818	192.103	25.122	5.11E+08	1.313E+09	2.57
	60#hanger rod
93	Main span	648.000	−13.783	200.074	25.218	5.13E+08	1.313E+09	2.56
	61#hanger rod
94	Main span	672.000	−12.717	208.353	25.317	5.15E+08	1.313E+09	2.55
	62#hanger rod
95	Main span	696.000	−11.620	216.941	25.420	5.17E+08	1.313E+09	2.54
	63#hanger rod
96	Main span	720.000	−10.492	225.838	25.526	5.20E+08	1.313E+09	2.53
	64#hanger rod
97	Main span	744.000	−9.333	235.047	25.637	5.22E+08	1.313E+09	2.52
	65#hanger rod
98	Main span	768.000	−8.144	244.565	25.749	5.24E+08	1.313E+09	2.51
	66#hanger rod
99	Main span	792.000	−6.925	254.391	25.865	5.26E+08	1.313E+09	2.49
	67#hanger rod
100	Closed clip	816.000	−5.676	264.528	25.985	5.29E+08	1.313E+09	2.48
101	Theoretical	829.000	−5.000	270.050	14.087	5.29E+08	1.313E+09	2.48
	vertex of right
	main tower
102	Closed clip	842.000	−5.590	263.998	14.290	5.37E+08	1.313E+09	2.45
103	Right side span	866.000	−6.680	252.916	26.358	5.37E+08	1.313E+09	2.45
	27#hanger rod
104	Right side span	890.000	−7.740	242.144	26.229	5.34E+08	1.313E+09	2.46
	26#hanger rod
105	Right side span	914.000	−8.771	231.680	26.104	5.31E+08	1.313E+09	2.47
	25#hanger rod
106	Right side span	938.000	−9.772	221.524	25.983	5.29E+08	1.313E+09	2.48
	24#hanger rod
107	Right side span	962.000	−10.742	211.678	25.863	5.26E+08	1.313E+09	2.49
	23#hanger rod
108	Right side span	986.000	−11.681	202.139	25.747	5.24E+08	1.313E+09	2.51
	22#hanger rod
109	Right side span	1010.000	−12.590	192.907	25.636	5.22E+08	1.313E+09	2.52
	21#hanger rod
110	Right side span	1034.000	−13.468	183.981	25.527	5.20E+08	1.313E+09	2.53
	20#hanger rod
111	Right side span	1058.000	−14.315	175.358	25.423	5.17E+08	1.313E+09	2.54
	19#hanger rod
112	Right side span	1082.000	−15.130	167.037	25.322	5.15E+08	1.313E+09	2.55
	18#hanger rod
113	Right side span	1106.000	−15.914	159.019	25.224	5.13E+08	1.313E+09	2.56
	17#hanger rod
114	Right side span	1130.000	−16.666	151.300	25.130	5.11E+08	1.313E+09	2.57
	16#hanger rod
115	Right side span	1154.000	−17.386	143.881	25.040	5.10E+08	1.313E+09	2.58
	15#hanger rod
116	Right side span	1178.000	−18.074	136.759	24.953	5.08E+08	1.313E+09	2.59
	14#hanger rod
117	Right side span	1202.000	−18.730	129.935	24.870	5.06E+08	1.313E+09	2.59
	13#hanger rod
118	Right side span	1226.000	−19.353	123.406	24.790	5.05E+08	1.313E+09	2.60
	12#hanger rod
119	Right side span	1250.000	−19.943	117.172	24.714	5.03E+08	1.313E+09	2.61
	11#hanger rod
120	Right side span	1274.000	−20.500	111.232	24.642	5.01E+08	1.313E+09	2.62
	10#hanger rod
121	Right side span	1298.000	−21.023	105.585	24.573	5.00E+08	1.313E+09	2.63
	9#hanger rod
122	Right side span	1322.000	−21.513	100.229	24.508	4.99E+08	1.313E+09	2.63
	8#hanger rod
123	Right side span	1346.000	−21.969	95.164	24.446	4.97E+08	1.313E+09	2.64
	7#hanger rod
124	Right side span	1370.000	−22.390	90.389	24.387	4.96E+08	1.313E+09	2.65
	6#hanger rod
125	Right side span	1394.000	−22.777	85.903	24.332	4.95E+08	1.313E+09	2.65
	5#hanger rod
126	Right side span	1418.000	−23.129	81.706	24.281	4.94E+08	1.313E+09	2.66
	4#hanger rod
127	Right side span	1442.000	−23.445	77.796	24.233	4.93E+08	1.313E+09	2.66
	3#hanger rod
128	Right side span	1466.000	−23.725	74.178	24.187	4.92E+08	1.313E+09	2.67
	2#hanger rod
129	Right side span	1490.000	−23.967	70.851	24.146	4.91E+08	1.313E+09	2.67
	1#hanger rod
130	Theoretical	1517.000	−24.198	67.450	27.120	4.91E+08	1.313E+09	2.68
	vertex of right
	cable saddle for
	steering
131	Theoretical	1682.000	−28.500	27.500	169.226	4.90E+08	1.313E+09	2.68
	vertex of right
	loose cable
	saddle

3) Force, Safety Factor and Unstressed Length of the Hanger Rod (Analytical Method)

According to the designed suspension point coordinates of the main girder, the vertical component force of the hanger rod in the bridge complete state determined in Table 5, the coordinates of the upper end of the hanger rod and the material and cross-sectional size of the hanger rod are determined in Table 6 (the coordinates of the main cable), a component force in the transverse direction and a vertical component force at the lower end, the force, the safety factor and the unstressed length of the hanger rod in the bridge complete state can be calculated by the numerical analysis method, as shown in Table 7 (unstressed length is not shown).

TABLE 7
Force and safety factor of the hanger rod in the bridge complete state
				Total
				force
		Transverse	Vertical	of		safety
		component	component	hanger	Breaking	factor of
		force of	force of	rod in	force	hanger
Number		hanger rod	hanger rod	dead	of	rod in
of	Number	in dead load	in dead load	load	hanger	dead
hanger	description of	state	state	state	rod	load
rod	hanger rod	kN	kN	kN	kN	state
1	Left side span	769.8	4511.0	4576.2	28947.4	6.33
	1#hanger rod
2	Left side span	748.1	4511.0	4572.6	28947.4	6.33
	2#hanger rod
3	Left side span	736.1	4511.0	4570.7	28947.4	6.33
	3#hanger rod
4	Left side span	715.0	4433.3	4490.6	28947.4	6.45
	4#hanger rod
5	Left side span	706.8	4421.8	4477.9	28947.4	6.46
	5#hanger rod
6	Left side span	701.0	4435.1	4490.2	28947.4	6.45
	6#hanger rod
7	Left side span	696.0	4443.3	4497.5	28947.4	6.44
	7#hanger rod
8	Left side span	690.8	4452.6	4505.9	28947.4	6.42
	8#hanger rod
9	Left side span	684.8	4461.7	4514.0	28947.4	6.41
	9#hanger rod
10	Left side span	680.7	4470.9	4522.4	28947.4	6.40
	10#hanger rod
11	Left side span	676.3	4480.0	4530.8	28947.4	6.39
	11#hanger rod
12	Left side span	672.0	4489.2	4539.2	28947.4	6.38
	12#hanger rod
13	Left side span	667.8	4498.3	4547.6	28947.4	6.37
	13#hanger rod
14	Left side span	664.4	4507.6	4556.3	28947.4	6.35
	14#hanger rod
15	Left side span	661.1	4516.7	4564.8	28947.4	6.34
	15#hanger rod
16	Left side span	657.8	4525.9	4573.4	28947.4	6.33
	16#hanger rod
17	Left side span	654.8	4535.1	4582.1	28947.4	6.32
	17#hanger rod
18	Left side span	652.2	4544.3	4590.9	28947.4	6.31
	18#hanger rod
19	Left side span	649.7	4553.6	4599.7	28947.4	6.29
	19#hanger rod
20	Left side span	647.1	4562.9	4608.5	28947.4	6.28
	20#hanger rod
21	Left side span	645.3	4572.0	4617.3	28947.4	6.27
	21#hanger rod
22	Left side span	643.9	4582.8	4627.8	28947.4	6.26
	22#hanger rod
23	Left side span	642.0	4585.4	4630.1	28947.4	6.25
	23#hanger rod
24	Left side span	646.2	4628.2	4673.1	28947.4	6.19
	24#hanger rod
25	Left side span	633.9	4548.8	4592.8	28947.4	6.30
	25#hanger rod
26	Left side span	629.3	4548.8	4592.1	28947.4	6.30
	26#hanger rod
27	Left side span	618.5	4548.8	4590.7	28947.4	6.31
	27#hanger rod
28	Main span	614.6	4575.4	4616.5	28947.4	6.27
	1#hanger rod
29	Main span	632.2	4575.4	4618.9	28947.4	6.27
	2#hanger rod
30	Main span	639.2	4575.4	4619.8	28947.4	6.27
	3#hanger rod
31	Main span	654.3	4669.0	4714.6	28947.4	6.14
	4#hanger rod
32	Main span	652.0	4635.7	4681.3	28947.4	6.18
	5#hanger rod
33	Main span	655.0	4642.3	4688.3	28947.4	6.17
	6#hanger rod
34	Main span	658.0	4640.7	4687.1	28947.4	6.18
	7#hanger rod
35	Main span	661.9	4640.8	4687.8	28947.4	6.18
	8#hanger rod
36	Main span	666.4	4640.7	4688.3	28947.4	6.17
	9#hanger rod
37	Main span	670.9	4640.6	4688.8	28947.4	6.17
	10#hanger rod
38	Main span	676.1	4640.6	4689.6	28947.4	6.17
	11#hanger rod
39	Main span	681.2	4640.5	4690.2	28947.4	6.17
	12#hanger rod
40	Main span	687.1	4640.5	4691.1	28947.4	6.17
	13#hanger rod
41	Main span	693.4	4640.5	4692.0	28947.4	6.17
	14#hanger rod
42	Main span	699.8	4640.4	4692.9	28947.4	6.17
	15#hanger rod
43	Main span	707.1	4640.4	4694.0	28947.4	6.17
	16#hanger rod
44	Main span	714.8	4640.4	4695.1	28947.4	6.17
	17#hanger rod
45	Main span	723.0	4640.4	4696.4	28947.4	6.16
	18#hanger rod
46	Main span	732.2	4640.3	4697.7	28947.4	6.16
	19#hanger rod
47	Main span	742.5	4640.3	4699.3	28947.4	6.16
	20#hanger rod
48	Main span	753.3	4640.3	4701.0	28947.4	6.16
	21#hanger rod
49	Main span	765.6	4640.3	4703.0	28947.4	6.16
	22#hanger rod
50	Main span	779.6	4640.3	4705.3	28947.4	6.15
	23#hanger rod
51	Main span	794.8	4640.3	4707.9	28947.4	6.15
	24#hanger rod
52	Main span	813.1	4640.3	4711.0	28947.4	6.14
	25#hanger rod
53	Main span	832.5	4640.2	4714.3	28947.4	6.14
	26#hanger rod
54	Main span	857.5	4640.2	4718.8	28947.4	6.13
	27#hanger rod
55	Main span	883.5	4640.2	4723.6	28947.4	6.13
	28#hanger rod
56	Main span	916.3	4640.2	4729.8	28947.4	6.12
	29#hanger rod
57	Main span	951.9	4640.2	4736.8	28947.4	6.11
	30#hanger rod
58	Main span	991.2	4640.2	4744.9	28947.4	6.10
	31#hanger rod
59	Main span	1029.2	4640.2	4753.0	28947.4	6.09
	32#hanger rod
60	Main span	1057.6	4640.2	4759.2	28947.4	6.08
	33#hanger rod
61	Main span	1074.0	4640.2	4762.9	28947.4	6.08
	34#hanger rod
62	Main span	1057.6	4640.2	4759.2	28947.4	6.08
	35#hanger rod
63	Main span	1029.2	4640.2	4753.0	28947.1	6.09
	36#hanger rod
64	Main span	991.3	4640.2	4744.9	28947.4	6.10
	37#hanger rod
65	Main span	952.1	4640.2	4736.9	28947.4	6.11
	38#hanger rod
66	Main span	916.5	4640.2	4729.8	28947.1	6.12
	39#hanger rod
67	Main span	883.8	4640.2	4723.6	28947.4	6.13
	40#hanger rod
68	Main span	856.9	4640.2	4718.7	28947.4	6.13
	41#hanger rod
69	Main span	832.0	4640.2	4714.2	28947.4	6.14
	42#hanger rod
70	Main span	813.4	4640.3	4711.0	28947.4	6.14
	43#hanger rod
71	Main span	795.0	4640.3	4707.9	28947.4	6.15
	44#hanger rod
72	Main span	779.7	4640.3	4705.3	28947.4	6.15
	45#hanger rod
73	Main span	765.7	4640.3	4703.1	28947.4	6.16
	46#hanger rod
74	Main span	753.5	4640.3	4701.1	28947.4	6.16
	47#hanger rod
75	Main span	742.6	4640.3	4699.3	28947.4	6.16
	48#hanger rod
76	Main span	731.8	4640.3	4697.6	28947.4	6.16
	49#hanger rod
77	Main span	722.6	4640.4	4696.3	28947.4	6.16
	50#hanger rod
78	Main span	714.9	4640.4	4695.2	28947.4	6.17
	51#hanger rod
79	Main span	707.3	4640.4	4694.0	28947.4	6.17
	52#hanger rod
80	Main span	699.9	4640.4	4692.9	28947.4	6.17
	53#hanger rod
81	Main span	693.5	4640.5	4692.0	28947.4	6.17
	54#hanger rod
82	Main span	687.2	4640.5	4691.1	28947.4	6.17
	55#hanger rod
83	Main span	681.2	4640.5	4690.2	28947.4	6.17
	56#hanger rod
84	Main span	676.1	4640.6	4689.6	28947.4	6.17
	57#hanger rod
85	Main span	670.8	4640.6	4688.8	28947.4	6.17
	58#hanger rod
86	Main span	666.5	4640.7	4688.3	28947.4	6.17
	59#hanger rod
87	Main span	661.9	4640.8	4687.8	28947.4	6.18
	60#hanger rod
88	Main span	658.1	4640.7	4687.1	28947.4	6.18
	61#hanger rod
89	Main span	655.1	4642.3	4688.3	28947.4	6.17
	62#hanger rod
90	Main span	652.0	4635.7	4681.3	28947.4	6.18
	63#hanger rod
91	Main span	654.3	4669.0	4714.6	28947.4	6.14
	64#hanger rod
92	Main span	639.2	4575.4	4619.8	28947.4	6.27
	65#hanger rod
93	Main span	632.1	4575.4	4618.9	28947.4	6.27
	66#hanger rod
94	Main span	614.5	4575.4	4616.5	28947.4	6.27
	67#hanger rod
95	Right side span	618.5	4548.8	4590.7	28947.4	6.31
	27#hanger rod
96	Right side span	629.2	4548.8	4592.1	28947.4	6.30
	26#hanger rod
97	Right side span	633.9	4548.8	4592.8	28947.4	6.30
	25#hanger rod
98	Right side span	646.1	4628.2	4673.1	28947.4	6.19
	24#hanger rod
99	Right side span	642.0	4585.4	4630.1	28947.4	6.25
	23#hanger rod
100	Right side span	643.9	4582.8	4627.8	28947.4	6.26
	22#hanger rod
101	Right side span	645.3	4572.0	4617.3	28947.4	6.27
	21#hanger rod
102	Right side span	647.1	4562.9	4608.5	28947.4	6.28
	20#hanger rod
103	Right side span	649.7	4553.6	4599.7	28947.4	6.29
	19#hanger rod
104	Right side span	652.2	4544.3	4590.9	28947.4	6.31
	18#hanger rod
105	Right side span	654.8	4535.1	4582.1	28947.4	6.32
	17#hanger rod
106	Right side span	657.8	4525.9	4573.5	28947.4	6.33
	16#hanger rod
107	Right side span	661.1	4516.7	4564.8	28947.4	6.34
	15#hanger rod
108	Right side span	664.4	4507.6	4556.3	28947.4	6.35
	14#hanger rod
109	Right side span	667.8	4498.3	4547.6	28947.4	6.37
	13#hanger rod
110	Right side span	672.1	4489.2	4539.2	28947.4	6.38
	12#hanger rod
111	Right side span	676.3	4480.0	4530.8	28947.4	6.39
	11#hanger rod
112	Right side span	680.7	4470.9	4522.4	28947.4	6.40
	10#hanger rod
113	Right side span	684.8	4461.7	4514.0	28947.4	6.41
	9#hanger rod
114	Right side span	690.8	4452.6	4505.9	28947.4	6.42
	8#hanger rod
115	Right side span	696.0	4443.3	4497.5	28947.4	6.44
	7#hanger rod
116	Right side span	701.0	4435.1	4490.2	28947.4	6.45
	6#hanger rod
117	Right side span	706.8	4421.8	4477.9	28947.4	6.46
	5#hanger rod
118	Right side span	715.1	4433.3	4490.6	28947.4	6.45
	4#hanger rod
119	Right side span	736.1	4511.0	4570.7	28947.4	6.33
	3#hanger rod
120	Right side span	748.1	4511.0	4572.6	28947.4	6.33
	2#hanger rod
121	Right side span	769.9	4511.0	4576.2	28947.4	6.33
	1#hanger rod

4) Replication of Bridge Complete State Through Full Bridge Model

The main girder and main tower are divided into a beam element, the main cable is divided into a cable element (the unstressed length of each cable section is known), and the hanger rod is configured as the cable element (the unstressed length of the hanger rod is known). A geometric nonlinear finite element model of the full bridge that considers large displacement and stress stiffening effects is established using node positions in the bridge complete state, the corresponding cross-sectional characteristics of the elements, the dead load, and the second-stage dead load (the ANSYS model of full bridge is shown in FIG. 15), so as to obtain displacement results. A maximum longitudinal displacement of the whole bridge is 0.0165 m, which is located at the top of the tower. A maximum transverse displacement of the whole bridge is 0.058 m, which occurs in the main cable at a quarter of the main span. A maximum vertical displacement of the whole bridge is 0.051 m, which occurs in the main cable and main girder at the mid-span. This shows that the finite element simulated three-dimensional displacements of the whole bridge under dead-load are less than 6 cm, indicating that the resulting geometric position of the space main cable ground-anchored suspension bridge with a main span of 1658 m has a deviation of no more than 6 cm from the design. Such finite element model can be used to simulate a construction process.

1.1.4 Empty Cable State and Saddle Pre-Offset

On the basis of the finite element model of the bridge complete state, (after considering the geometric nonlinear analysis of large displacement and stress stiffening), the main girder, hanger rod (and the second-stage dead load thereon), and the clip load on the main cable are removed. A saddle top of the main cable is pushed to the top of the main tower, such that an offset is basically 0, so as to obtain the empty cable state and the pre-offset of the main cable saddle. The obtained pre-offset of the empty cable saddle is 220 cm. Compared with the completed bridge, the empty cable has a displacement in the mid-span along the transverse direction of 24.235 m and a mid-span lift of 15.727 m.

1.2 Comparison of Stiffening Girder Erection Technical Solution without Temporary Pushing (Pulling) of the Main Cable1.2.1 Technical Solution for First Installing Girder Section at the Mid-Span without Temporary Pushing (Pulling) of the Main Cable

When the cable is empty, a distance between two main cables in the transverse direction of the main span is 10 m, that is, a distance between the two main cables in the transverse direction is only 5 m from the center line in the longitudinal direction. A designed unstressed length of the hanger rod in the girder section at the main span is only 3.8466 m. A distance between the hanger rod on both sides of the stiffening girder in the transverse direction is 60.21 m. When the girder section at the mid-span is installed first, and no measures are taken to temporarily push (pull) the main cable laterally, even if the girder section at the mid-span is lifted until its top surface is flush with the bottom of the main cable, and a distance between the anchor point of the lower end of the hanger rod (on the girder section) on one side of the girder section at the mid-span and the anchor point of the upper end of the hanger rod (on the main cable) is the unstressed length of the hanger rod, it is impossible to make the distance between the anchor point of the lower end of the hanger rod (on the girder section) on the other side of the girder section at the mid-span and the anchor point of the upper end of the hanger rod (on the main cable) less than or equal to the unstressed length of the hanger rod. Therefore, the technical solution for first installing girder section at mid-span without temporary pushing (pulling) of the main cable is not valid.

1.2.2 Technical Solution for Installing the Stiffening Girder Section by Section from the Main Tower to the Mid-Span without Temporary Pushing (Pulling) of the Main Cable

A finite element simulation calculation is performed on an entire process of hoisting the main girder from the main tower to both sides without cross braces for the main cable at the main span (that is, without using temporary cross braces to prop up the main cable first). A vertical displacement of the main cable in the main span, a deflection of a tower top and a stress of a tower root are shown in Table 8 and FIGS. 16-18. An angle between a line connecting the upper and lower suspension points of the hanger rod and a horizontal line in the transverse direction during the entire process of each hanger rod at the main span from to be installed to the completion of hoisting is obtained, as shown in Table 9.

TABLE 8
Vertical displacement of the main cable at the mid-span during an entire
process of hoisting the main girder from the main tower to both sides
				Stress	Stress
		Vertical		on side	on main
		displacement	Deviation	span of	span of
Construction		of main	of left	tower	tower
phase		cable at mid-	tower top	root	root
number	Construction content	span (m)	(m)	(Mpa)	(Mpa)
1	Installing clip and hanger	16.494	−0.098	−4.82	−6.03
	rod
2	Hoisting girder section	16.871	−0.044	−4.62	−6.38
	corresponding to main span
	1#, 67#hanger rod
3	Hoisting girder section	17.469	0.041	−4.29	−6.84
	corresponding to main span
	2#, 66#hanger rod
4	Pushing the main cable	17.301	−0.207	−5.48	−5.66
	saddle for the first time
	(with a pushing amount of
	30 cm)
5	Hoisting girder section	18.060	−0.101	−5.07	−6.21
	corresponding to main span
	3#, 65#hanger rod
6	Hoisting girder section	18.940	0.026	−4.58	−6.84
	corresponding to main span
	4#, 64#hanger rod
7	Pushing the main cable	18.788	−0.225	−5.78	−5.65
	saddle for the second time
	(with a pushing amount of
	30 cm)
8	Hoisting girder section	19.730	−0.086	−5.24	−6.32
	corresponding to main span
	5#, 63#hanger rod
9	Hoisting girder section	20.692	0.066	−4.65	−7.06
	corresponding to main span
	6#, 62#hanger rod
10	Pushing the main cable	20.559	−0.190	−5.89	−5.83
	saddle for the third time
	(with a pushing amount of
	30 cm)
11	Hoisting girder section	21.507	−0.030	−5.27	−6.59
	corresponding to main span
	7#, 61#hanger rod
12	Hoisting girder section	22.392	0.137	−4.64	−7.38
	corresponding to main span
	8#, 60#hanger rod
13	Hoisting girder section	23.173	0.306	−4.00	−8.18
	corresponding to main span
	9#, 59#hanger rod
14	Pushing the main cable	22.932	−0.306	−6.96	−5.23
	saddle for the fourth time
	(with a pushing amount of
	70 cm)
15	Hoisting girder section	23.601	−0.139	−6.35	−6.01
	corresponding to main span
	10#, 58#hanger rod
16	Hoisting girder section	24.112	0.027	−5.74	−6.79
	corresponding to main span
	11#, 57#hanger rod
17	Hoisting girder section	24.449	0.191	−5.14	−7.55
	corresponding to main span
	12#, 56#hanger rod
18	Pushing the main cable	24.344	−0.167	−6.89	−5.82
	saddle for the fifth time
	(with a pushing amount of
	40 cm)
19	Hoisting girder section	24.502	−0.010	−6.33	−6.55
	corresponding to main span
	13#, 55#hanger rod
20	Hoisting girder section	24.469	0.143	−5.80	−7.26
	corresponding to main span
	14#, 54#hanger rod
21	Pushing the main cable	24.427	−0.029	−6.64	−6.42
	saddle for the sixth time
	(with a pushing amount of
	20 cm)
22	Hoisting girder section	24.206	0.118	−6.14	−7.10
	corresponding to main span
	15#, 53#hanger rod
23	Hoisting girder section	23.999	0.196	−5.98	−7.57
	corresponding to left side
	span 27#, main span
	16#, 52#, right side span
	27#hanger rod
24	Hoisting girder section	24.318	0.095	−6.45	−7.23
	corresponding to left side
	span 26#, right side span
	26#hanger rod
25	Hoisting girder section	24.739	−0.037	−7.03	−6.76
	corresponding to left side
	span 25#, right side span
	25#hanger rod
26	Hoisting girder section	25.269	−0.201	−7.74	−6.15
	corresponding to left side
	span 24#, right side span
	24#hanger rod
27	Hoisting girder section	25.154	−0.214	−7.93	−6.25
	corresponding to left side
	span 23#, main span 17#,
	51#, right side span
	23#hanger rod
28	Hoisting girder section	24.880	−0.236	−8.15	−6.31
	corresponding to left side
	span 22#, main span 18#,
	50#, right side span
	22#hanger rod
29	Hoisting girder section	24.457	−0.265	−8.40	−6.34
	corresponding to left side
	span 21#, main span 19#,
	49#, right side span
	21#hanger rod
30	Hoisting girder section	23.861	−0.294	−8.65	−6.38
	corresponding to left side
	span 20#, main span 20#,
	48#, right side span
	20#hanger rod
31	Hoisting girder section	23.108	−0.322	−8.89	−6.41
	corresponding to left side
	span 19#, main span 21#,
	47#, right side span
	19#hanger rod
32	Hoisting girder section	22.201	−0.347	−9.12	−6.46
	corresponding to left side
	span 18#, main span 22#,
	46#, right side span
	18#hanger rod
33	Hoisting girder section	21.145	−0.367	−9.33	−6.52
	corresponding to left side
	span 17#, main span 23#,
	45#, right side span
	17#hanger rod
34	Hoisting girder section	19.976	−0.384	−9.52	−6.60
	corresponding to left side
	span 16#, main span 24#,
	44#, right side span
	16#hanger rod
35	Hoisting girder section	18.636	−0.390	−9.67	−6.72
	corresponding to left side
	span 15#, main span 25#,
	43#, right side span
	15#hanger rod
36	Hoisting girder section	17.166	−0.387	−9.79	−6.87
	corresponding to left side
	span 14#, main span 26#,
	42#, right side span
	14#hanger rod
37	Hoisting girder section	15.562	−0.374	−9.86	−7.05
	corresponding to left side
	span 13#, main span 27#,
	41#, right side span
	13#hanger rod
38	Hoisting girder section	13.835	−0.352	−9.90	−7.28
	corresponding to left side
	span 12#, main span 28#,
	40#, right side span
	12#hanger rod
39	Hoisting girder section	12.038	−0.323	−9.91	−7.51
	corresponding to left side
	span 11#, main span 29#,
	39#, right side span
	11#hanger rod
40	Hoisting girder section	10.071	−0.279	−9.86	−7.81
	corresponding to left side
	span 10#, main span 30#,
	38#, right side span
	10#hanger rod
41	Hoisting girder section	7.991	−0.223	−9.77	−8.14
	corresponding to left side
	span 9#, main span 31#,
	37#, right side span
	9#hanger rod
42	Hoisting girder section	5.801	−0.156	−9.64	−8.52
	corresponding to left side
	span 8#, main span 32#,
	36#, right side span
	8#hanger rod
43	Hoisting girder section	3.511	−0.077	−9.46	−8.93
	corresponding to left side
	span 7#, main span 33#,
	35#, right side span
	7#hanger rod
44	Hoisting girder section	2.509	−0.085	−9.56	−8.96
	corresponding to left side
	span 6#, main span 34#,
	right side span 6#hanger
	rod
45	Hoisting girder section	2.829	−0.177	−9.91	−8.64
	corresponding to left side
	span 5#, right side span
	5#hanger rod
46	Hoisting girder section	3.099	−0.254	−10.20	−8.37
	corresponding to left side
	span 4#, right side span
	4#hanger rod
47	Hoisting girder section	3.315	−0.315	−10.44	−8.15
	corresponding to left side
	span 3#, right side span
	3#hanger rod
48	Hoisting girder section	3.466	−0.358	−10.60	−8.00
	corresponding to left side
	span 2#, right side span
	2#hanger rod
49	Hoisting girder section	3.644	−0.410	−10.79	−7.82
	corresponding to left side
	span 1#, right side span
	1#hanger rod

TABLE 9
Angle between a line connecting the upper and lower suspension points of the hanger rod and a horizontal line in the transverse
direction during the entire process of each hanger rod at the main span from to be installed to the completion of hoisting
	Construction on phase number
				4
				Pushing			7
				the			Pushing
			3	main	5		the main	8
		2	Hoisting	cable	Hoisting	6	cable	Hoisting	9
		Hoisting	girder	saddle	girder	Hoisting	saddle	girder	Hoisting
		girder	section	for the	section	girder	for the	section	girder
		section	corresponding	first	corresponding	section	second	corresponding	section
	1	corresponding	to	time	to	corresponding	time	to	corresponding
	Installing	to main	main	(with a	main	to main	(with a	main	to main
	clip	span	span	pushing	span	span	pushing	span	span
	and	1#,	2#,	amount	3#,	4#,	amount	5#,	6#,
Construction	hanger	67#hanger	66#hanger	of 30	65#hanger	64#hanger	of 30	63#hanger	62#hanger
content	rod	rod	rod	cm)	rod	rod	cm)	rod	rod
1#	81.7	81.8	81.8	81.8	81.9	81.9	81.9	82.0	82.0
2#		81.2	81.3	81.3	81.4	81.5	81.5	81.6	81.7
3#				80.8	80.9	81.1	81.1	81.2	81.3
4#					80.3	80.5	80.5	80.7	80.8
5#							79.8	80.1	80.3
6#								79.4	79.7
7#
8#
9#
10#
11#
12#
13#
14#
15#
16#
17#
18#
19#
20#
21#
22#
23#
24#
25#
26#
27#
28#
29#
30#
31#
32#
33#
34#
35#
36#
37#
38#
39#
40#
41#
42#
43#
44#
45#
46#
47#
48#
49#
50#
51#
52#
53#
54#
55#
56#
57#
58#
59#
60#
61#
62#								79.4	79.7
63#							79.9	80.1	80.3
64#					80.3	80.5	80.5	80.7	80.9
65#				80.8	80.9	81.1	81.1	81.2	81.3
66#		81.3	81.4	81.4	81.5	81.5	81.5	81.6	81.7
67#	81.7	81.8	81.8	81.8	81.9	81.9	81.9	82.0	82.0

TABLE 9
Angle between the line connecting the upper and lower suspension points of the hanger rod and the horizontal line in the transverse direction
during the entire process of each hanger rod at the main span from to be installed to the completion of hoisting (continued-1)
	Construction phase number
	10				14
	Pushing				Pushing				18
	the		12	13	the				Pushing
	main	11	Hoisting	Hoisting	main	15	16	17	the main
	cable	Hoisting	girder	girder	cable	Hoisting	Hoisting	Hoisting	cable
	saddle	girder	section	section	saddle	girder	girder	girder	saddle
	for the	section	corresponding	corresponding	for the	section	section	section	for the
	third	corresponding	to	to	fourth	corresponding	corresponding	corresponding	fifth
	time	to	main	main	time	to	to	to	time
	(with a	main	span	span	(with a	main	main	main	(with a
	pushing	span	8#,	9#,	pushing	span	span	span	pushing
	amount	7#,	60#h	59#h	amount	10#,	11#,	12#,	amount
Construction	of 30	61#hanger	anger	anger	of 70	58#hanger	57#hanger	56#hanger	of 40
content	cm)	rod	rod	rod	cm)	rod	rod	rod	cm)
1#	82.0	82.0	82.1	82.1	82.1	82.1	82.2	82.2	82.2
2#	81.7	81.8	81.8	81.9	81.9	81.9	82.0	82.0	82.0
3#	81.3	81.4	81.5	81.6	81.6	81.7	81.8	81.8	81.8
4#	80.8	81.0	81.1	81.3	81.3	81.4	81.5	81.6	81.6
5#	80.3	80.5	80.7	80.9	80.9	81.0	81.2	81.3	81.3
6#	79.7	79.9	80.2	80.4	80.4	80.6	80.8	81.0	81.0
7#	78.9	79.2	79.5	79.8	79.8	80.1	80.4	80.6	80.6
8#		78.4	78.8	79.2	79.2	79.5	79.8	80.1	80.1
9#			77.9	78.4	78.4	78.8	79.2	79.5	79.5
10#					77.4	77.9	78.4	78.9	78.9
11#						76.9	77.5	78.0	78.1
12#							76.4	77.1	77.1
13#									75.8
14#
15#
16#
17#
18#
19#
20#
21#
22#
23#
24#
25#
26#
27#
28#
29#
30#
31#
32#
33#
34#
35#
36#
37#
38#
39#
40#
41#
42#
43#
44#
45#
46#
47#
48#
49#
50#
51#
52#
53#
54#
55#									75.9
56#							76.4	77.1	77.1
57#						76.9	77.5	78.1	78.1
58#					77.4	78.0	78.5	78.9	78.9
59#			77.9	78.4	78.4	78.8	79.2	79.6	79.6
60#		78.4	78.8	79.2	79.2	79.5	79.8	80.1	80.1
61#	78.9	79.3	79.6	79.9	79.9	80.1	80.4	80.6	80.6
62#	79.7	80.0	80.2	80.4	80.4	80.6	80.8	81.0	81.0
63#	80.3	80.5	80.7	80.9	80.9	81.0	81.2	81.3	81.3
64#	80.9	81.0	81.2	81.3	81.3	81.4	81.5	81.6	81.6
65#	81.3	81.4	81.5	81.6	81.6	81.7	81.8	81.8	81.8
66#	81.7	81.8	81.8	81.9	81.9	81.9	82.0	82.0	82.0
67#	82.0	82.1	82.1	82.1	82.1	82.2	82.2	82.2	82.2

TABLE 9
Angle between the line connecting the upper and lower suspension points of the hanger rod
and the horizontal line in the transverse direction during the entire process of each hanger
rod at the main span from to be installed to the completion of hoisting (continued-2)
	Construction phase number
									27
					23				Hoisting
					Hoisting				girder
					girder				section
					section	24	25	26	corres-
			21		corres-	Hoisting	Hoisting	Hoisting	ponding
			Pushing		ponding	girder	girder	girder	to
	19	20	the	22	to	section	section	section	left side
	Hoisting	Hoisting	main	Hoisting	left side	corres-	corres-	corres-	span
	girder	girder	cable	girder	span	ponding	ponding	ponding	23#,
	section	section	saddle	section	27#,	to left	to left	to left	main
	corre-	corres-	for the	corres-	main	side	side	side	span
	sponding	ponding	sixth	ponding	span	span	span	span	17#
	to	to	time	to	16#,	26#,	25#,	24#,	51#,
	main	main	(with a	main	52#,	right	right	right	right
	span	span	pushing	span	right	side	side	side	side
	13#,	14#,	amount	15#,	side span	span	span	span	span
Construction	55#hanger	54#hanger	of 20	53#hanger	27#hanger	26#hanger	25#hanger	24#hanger	23#hanger
content	rod	rod	cm)	rod	rod	rod	rod	rod	rod
1#	82.2	82.2	82.2	82.3	82.3	82.3	82.3	82.3	82.3
2#	82.1	82.1	82.1	82.1	82.2	82.2	82.2	82.2	82.2
3#	81.9	81.9	81.9	82.0	82.0	82.0	82.0	82.0	82.1
4#	81.7	81.8	81.8	81.8	81.9	81.9	81.9	81.9	81.9
5#	81.4	81.5	81.5	81.6	81.7	81.7	81.7	81.7	81.8
6#	81.1	81.3	81.3	81.4	81.5	81.5	81.5	81.5	81.6
7#	80.8	81.0	81.0	81.1	81.3	81.3	81.3	81.2	81.4
8#	80.4	80.6	80.6	80.8	81.0	81.0	81.0	81.0	81.1
9#	79.9	80.1	80.1	80.4	80.6	80.6	80.6	80.6	80.8
10#	79.3	79.6	79.6	79.9	80.2	80.2	80.2	80.2	80.5
11#	78.5	79.0	79.0	79.4	79.8	79.7	79.7	79.7	80.0
12#	77.7	78.2	78.2	78.7	79.2	79.2	79.1	79.1	79.5
13#	76.6	77.3	77.3	77.9	78.5	78.4	78.4	78.4	78.9
14#	75.3	76.	76.1	76.9	77.6	77.6	77.6	77.5	78.1
15#			74.7	75.7	76.5	76.5	76.5	76.5	77.2
16#				74.1	75.2	75.1	75.1	75.1	76.0
17#								73.4	74.6
18#									72.7
19#
20#
21#
22#
23#
24#
25#
26#
27#
28#
29#
30#
31#
32#
33#
34#
35#
36#
37#
38#
39#
40#
41#
42#
43#
44#
45#
46#
47#
48#
49#
50#									72.7
51#								73.4	74.6
52#				74.1	75.2	75.2	75.1	75.1	76.0
53#			74.7	75.7	76.5	76.5	76.5	76.5	77.2
54#	75.3	76.2	76.2	76.9	77.6	77.6	77.6	77.6	78.2
55#	76.6	77.3	77.3	77.9	78.5	78.5	78.4	78.4	78.9
56#	77.7	78.2	78.2	78.7	79.2	79.2	79.2	79.1	79.5
57#	78.6	79.0	79.0	79.4	79.8	79.8	79.7	79.7	80.0
58#	79.3	79.6	79.6	80.0	80.3	80.2	80.2	80.2	80.5
59#	79.9	80.2	80.2	80.4	80.7	80.6	80.6	80.6	80.8
60#	80.4	80.6	80.6	80.8	81.0	81.0	81.0	81.0	81.1
61#	80.8	81.0	81.0	81.1	81.3	81.3	81.3	81.3	81.4
62#	81.1	81.3	81.3	81.4	81.5	81.5	81.5	81.5	81.6
63#	81.4	81.5	81.5	81.6	81.7	81.7	81.7	81.7	81.8
64#	81.7	81.8	81.8	81.8	81.9	81.9	81.9	81.9	81.9
65#	81.9	82.0	82.0	82.0	82.1	82.0	82.0	82.0	82.1
66#	82.1	82.1	82.1	82.1	82.2	82.2	82.2	82.2	82.2
67#	82.2	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3

TABLE 9
Angle between the line connecting the upper and lower suspension points of the hanger rod
and the horizontal line in the transverse direction during the entire process of each hanger
rod at the main span from to be installed to the completion of hoisting (continued-3)
	Construction phase number
			30						36
		29	Hoisting	31	32	33	34	35	Hoisting
	28	Hoisting	girder	Hoisting	Hoisting	Hoisting	Hoisting	Hoisting	girder
	Hoisting	girder	section	girder	girder	girder	girder	girder	section
	girder	section	corre-	section	section	section	section	section	corre-
	section	corre-	sponding	corre-	corre-	corre-	corre-	corre-	sponding
	corre-	sponding	to	sponding	sponding	sponding	sponding	sponding	to
	sponding	to left	left	to left	to left	to left	to left	to left	left
	to left	side	side	side	side	side	side	side	side
	side	span	span	span	span	span	span	span	span
	span	21#,	20#,	19#,	18#,	17#,	16#,	15#,	14#,
	22#,	main	main	main	main	main	main	main	main
	main	span	span	span	span	span	span	span	span
	span	19#,	20#,	21#,	22#,	23#,	24#,	25#,	26#,
	18#,	49#,	48#,	47#,	46#,	45#,	44#,	43#,	42#,
	50#,	right	right	right	right	right	right	right	right
	right	side	side	side	side	side	side	side	side
	side	span	21#hanger	span	span	span	span	span	span
Construction	span	22#hanger	20#hanger	19#hanger	18#hanger	17#hanger	16#hanger	15#hanger	14#hanger
content	rod	rod	rod	rod	rod	rod	rod	rod	rod
1#	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.4
2#	82.2	82.2	82.2	82.3	82.3	82.3	82.3	82.3	82.3
3#	82.1	82.1	82.2	82.2	82.2	82.2	82.2	82.2	82.2
4#	82.0	82.0	82.1	82.1	82.1	82.1	82.2	82.2	82.2
5#	81.8	81.9	81.9	82.0	82.0	82.1	82.1	82.1	82.1
6#	81.7	81.7	81.8	81.9	81.9	82.0	82.0	82.0	82.1
7#	81.5	81.6	81.7	81.7	81.8	81.9	81.9	81.9	82.0
8#	81.3	81.4	81.5	81.6	81.7	81.7	81.8	81.8	81.9
9#	81.0	81.1	81.3	81.4	81.5	81.6	81.7	81.7	81.8
10#	80.7	80.9	81.0	81.2	81.3	81.4	81.5	81.6	81.7
11#	80.3	80.6	80.8	81.0	81.1	81.3	81.4	81.5	81.6
12#	79.9	80.2	80.4	80.7	80.9	81.1	81.2	81.3	81.4
13#	79.3	79.7	80.0	80.3	80.6	80.8	81.0	81.1	81.3
14#	78.7	79.1	79.5	79.9	80.2	80.5	80.7	80.9	81.1
15#	77.9	78.4	78.9	79.4	79.8	80.1	80.4	80.7	80.9
16#	76.9	77.6	78.2	78.8	79.3	79.7	80.1	80.4	80.6
17#	75.6	76.5	77.3	78.0	78.6	79.2	79.6	80.0	80.3
18#	74.0	75.1	76.2	77.1	77.8	78.5	79.1	79.6	80.0
19#	72.0	73.4	74.7	75.8	76.8	77.7	78.4	79.0	79.5
20#		71.2	72.8	74.3	75.5	76.6	77.5	78.3	79.0
21#			70.3	72.2	73.8	75.2	76.4	77.4	78.2
22#				69.5	71.6	73.4	74.9	76.3	77.3
23#					68.6	71.0	73.0	74.7	76.1
24#						67.6	70.4	72.7	74.5
25#							66.6	69.8	72.4
26#								65.7	69.3
27#									64.8
28#
29#
30#
31#
32#
33#
34#
35#
36#
37#
38#
39#
40#
41#									64.8
42#								65.7	69.3
43#							66.6	69.8	72.4
44#						67.6	70.4	72.7	74.6
45#					68.6	71.0	73.0	74.7	76.2
46#				69.5	71.6	73.4	75.0	76.3	77.3
47#			70.4	72.2	73.9	75.2	76.4	77.4	78.3
48#		71.2	72.8	74.3	75.5	76.6	77.5	78.3	79.0
49#	72.0	73.4	74.7	75.9	76.8	77.7	78.4	79.0	79.5
50#	74.0	75.2	76.2	77.1	77.8	78.5	79.1	79.6	80.0
51#	75.6	76.5	77.3	78.0	78.6	79.2	79.6	80.0	80.3
52#	76.9	77.6	78.2	78.8	79.3	79.7	80.1	80.4	80.6
53#	77.9	78.4	79.0	79.4	79.8	80.2	80.4	80.7	80.9
54#	78.7	79.1	79.6	79.9	80.2	80.5	80.7	80.9	81.1
55#	79.3	79.7	80.0	80.3	80.6	80.8	81.0	81.2	81.3
56#	79.9	80.2	80.4	80.7	80.9	81.1	81.2	81.3	81.4
57#	80.3	80.6	80.8	81.0	81.1	81.3	81.4	81.5	81.6
58#	80.7	80.9	81.1	81.2	81.3	81.5	81.6	81.6	81.7
59#	81.0	81.2	81.3	81.4	81.5	81.6	81.7	81.8	81.8
60#	81.3	81.4	81.5	81.6	81.7	81.8	81.8	81.9	81.9
61#	81.5	81.6	81.7	81.8	81.8	81.9	81.9	82.0	82.0
62#	81.7	81.8	81.8	81.9	81.9	82.0	82.0	82.0	82.1
63#	81.9	81.9	82.0	82.0	82.0	82.1	82.1	82.1	82.1
64#	82.0	82.0	82.1	82.1	82.1	82.2	82.2	82.2	82.2
65#	82.1	82.1	82.2	82.2	82.2	82.2	82.2	82.2	82.3
66#	82.2	82.2	82.3	82.3	82.3	82.3	82.3	82.3	82.3
67#	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.4	82.4

TABLE 9
Angle between the line connecting the upper and lower suspension points of the hanger rod
and the horizontal line in the transverse direction during the entire process of each hanger
rod at the main span from to be installed to the completion of hoisting (continued-4)
	Construction phase number
					41	42
	37	38	39	40	Hoisting	Hoisting	43	44
	Hoisting	Hoisting	Hoisting	Hoisting	girder	girder	Hoisting	Hoisting
	girder	girder	girder	girder	section	section	girder	girder
	section	section	section	section	corre-	corre-	section	section	45
	corre-	corre-	corre-	corre-	sponding	sponding	corre-	corre-	Hoisting
	sponding	sponding	sponding	sponding	to	to	sponding	sponding	girder
	to left	to left	to left	to left	left	left	to left	to	section
	side	side	side	side	side	side	side	left	corre-
	span	span	span	span	span	span	span	side	sponding
	13#,	12#,	11#,	10#,	9#,	8#,	7#,	span	to
	main	main	main	main	main	main	main	6#,	left
	span	span	span	span	span	span	span	main	side
	27#,	28#,	29#,	30#,	31#,	32#,	33#,	span	span
	41#,	40#,	39#,	38#,	37#,	36#,	35#,	34#,	5#,
	right	right	right	right	right	right	right	right	right
	side	side	side	side	side	side	side	side	side
	span	span	span	span	span	span	span	span	span
Construction	13#hanger	12#hanger	11#hanger	10#hanger	9#hanger	8#hanger	7#hanger	6#hanger	5#hanger
content	rod	rod	rod	rod	rod	rod	rod	rod	rod
1#	82.4	82.4	82.4	82.3	82.3	82.3	82.3	82.3	82.3
2#	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3
3#	82.3	82.3	82.3	82.2	82.2	82.2	82.2	82.2	82.2
4#	82.2	82.2	82.2	82.2	82.2	82.2	82.2	82.2	82.2
5#	82.1	82.1	82.1	82.1	82.1	82.1	82.1	82.1	82.1
6#	82.1	82.1	82.1	82.1	82.1	82.1	82.0	82.0	82.0
7#	82.0	82.0	82.0	82.0	82.0	82.0	82.0	82.0	82.0
8#	81.9	81.9	81.9	81.9	81.9	81.9	81.9	81.9	81.9
9#	81.8	81.9	81.9	81.9	81.9	81.8	81.8	81.8	81.8
10#	81.7	81.8	81.8	81.8	81.8	81.8	81.7	81.7	81.7
11#	81.6	81.7	81.7	81.7	81.7	81.7	81.6	81.6	81.6
12#	81.5	81.6	81.6	81.6	81.6	81.6	81.6	81.5	81.5
13#	81.4	81.4	81.5	81.5	81.5	81.5	81.5	81.4	81.4
14#	81.2	81.3	81.4	81.4	81.4	81.4	81.4	81.3	81.3
15#	81.0	81.2	81.2	81.3	81.3	81.3	81.2	81.2	81.2
16#	80.8	81.0	81.1	81.1	81.2	81.2	81.1	81.1	81.1
17#	80.6	80.8	80.9	81.0	81.0	81.0	81.0	81.0	81.0
18#	80.3	80.5	80.7	80.8	80.9	80.9	80.9	80.8	80.8
19#	79.9	80.2	80.5	80.6	80.7	80.7	80.7	80.7	80.7
20#	79.5	79.9	80.2	80.4	80.5	80.5	80.5	80.5	80.5
21#	78.9	79.4	79.8	80.1	80.3	80.3	80.3	80.3	80.3
22#	78.2	78.9	79.4	79.8	80.0	80.1	80.1	80.1	80.1
23#	77.3	78.2	78.9	79.4	79.7	79.8	79.9	79.9	79.9
24#	76.1	77.3	78.2	78.8	79.3	79.5	79.6	79.6	79.6
25#	74.4	76.1	77.3	78.2	78.8	79.1	79.3	79.3	79.3
26#	72.1	74.4	76.1	77.3	78.2	78.7	78.9	79.0	79.0
27#	68.9	72.0	74.4	76.1	77.3	78.1	78.5	78.6	78.6
28#	64.1	68.7	72.0	74.5	76.3	77.3	78.0	78.1	78.1
29#		63.6	68.6	72.3	74.8	76.4	77.3	77.6	77.6
30#			63.5	69.0	72.7	75.1	76.6	77.0	76.9
31#				64.4	69.9	73.5	75.7	76.3	76.3
32#					66.2	71.5	74.7	75.7	75.6
33#						69.2	73.8	75.2	75.1
34#							73.1	75.0	74.9
35#						69.2	73.8	75.2	75.1
36#					66.2	71.5	74.7	75.7	75.6
37#				64.4	69.9	73.5	75.7	76.3	76.3
38#			63.5	69.0	72.7	75.1	76.6	77.0	76.9
39#		63.6	68.6	72.3	74.8	76.4	77.3	77.6	77.6
40#	64.1	68.7	72.0	74.5	76.3	77.4	78.0	78.1	78.1
41#	68.9	72.0	74.4	76.1	77.3	78.1	78.5	78.6	78.6
42#	72.2	74.4	76.1	77.3	78.2	78.7	78.9	79.0	79.0
43#	74.4	76.1	77.3	78.2	78.8	79.	79.3	79.3	79.3
44#	76.1	77.3	78.2	78.8	79.3	79.5	79.6	79.6	79.6
45#	77.3	78.2	78.9	79.4	79.7	79.8	79.9	79.9	79.9
45#	78.2	78.9	79.4	79.8	80.0	80.1	80.1	80.1	80.1
46#	78.9	79.5	79.8	80.1	80.3	80.3	80.4	80.3	80.3
47#	79.5	79.9	80.2	80.4	80.5	80.6	80.5	80.5	80.5
48#	79.9	80.2	80.5	80.6	80.7	80.7	80.7	80.7	80.7
49#	80.3	80.5	80.7	80.8	80.9	80.9	80.9	80.8	80.8
50#	80.6	80.8	80.9	81.0	81.0	81.0	81.0	81.0	81.0
51#	80.8	81.0	81.1	81.2	81.2	81.2	81.1	81.1	81.1
52#	81.0	81.2	81.2	81.3	81.3	81.3	81.3	81.2	81.2
53#	81.2	81.3	81.4	81.4	81.4	81.4	81.4	81.3	81.3
54#	81.4	81.5	81.5	81.5	81.5	81.5	81.5	81.4	81.4
55#	81.5	81.6	81.6	81.6	81.6	81.6	81.6	81.5	81.5
56#	81.6	81.7	81.7	81.7	81.7	81.7	81.7	81.6	81.6
57#	81.7	81.8	81.8	81.8	81.8	81.8	81.7	81.7	81.7
58#	81.8	81.9	81.9	81.9	81.9	81.8	81.8	81.8	81.8
59#	81.9	81.9	81.9	81.9	81.9	81.9	81.9	81.9	81.9
60#	82.0	82.0	82.0	82.0	82.0	82.0	82.0	82.0	82.0
61#	82.1	82.1	82.1	82.1	82.1	82.1	82.0	82.0	82.0
62#	82.1	82.1	82.1	82.1	82.1	82.1	82.1	82.1	82.1
63#	82.2	82.2	82.2	82.2	82.2	82.2	82.2	82.2	82.2
64#	82.3	82.3	82.3	82.3	82.3	82.2	82.2	82.2	82.2
65#	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3	82.3
66#	82.4	82.4	82.4	82.4	82.4	82.3	82.3	82.3	82.3
(The bold items in the tables indicate a value of a to-be-installed hanger rod)

TABLE 9
Angle between the line connecting the upper and lower suspension points
of the hanger rod and the horizontal line in the transverse direction
during the entire process of each hanger rod at the main span from
to be installed to the completion of hoisting (continued-5)
	Construction phase number
	46	47	48	49
	Hoisting	Hoisting	Hoisting	Hoisting
	girder section	girder section	girder section	girder section
	corresponding	corresponding	corresponding	corresponding
	to left side	to left side	to left side	to left side
	span 4#, right	span 3#, right	span 2#, right	span 1#, right
Construction	side span	side span	side span	side span
content	4#hanger rod	3#hanger rod	2#hanger rod	1 #hanger rod
1#	82.3	82.3	82.3	82.3
2#	82.3	82.3	82.3	82.3
3#	82.2	82.2	82.2	82.2
4#	82.2	82.2	82.2	82.2
5#	82.1	82.1	82.1	82.1
6#	82.0	82.0	82.0	82.0
7#	82.0	81.9	81.9	81.9
8#	81.9	81.9	81.9	81.9
9#	81.8	81.8	81.8	81.8
10#	81.7	81.7	81.7	81.7
11#	81.6	81.6	81.6	81.6
12#	81.5	81.5	81.5	81.5
13#	81.4	81.4	81.4	81.4
14#	81.3	81.3	81.3	81.3
15#	81.2	81.2	81.2	81.2
16#	81.1	81.1	81.1	81.1
17#	81.0	81.0	80.9	80.9
18#	80.8	80.8	80.8	80.8
19#	80.7	80.7	80.6	80.6
20#	80.5	80.5	80.5	80.5
21#	80.3	80.3	80.3	80.3
22#	80.1	80.1	80.1	80.1
23#	79.9	79.8	79.8	79.8
24#	79.6	79.6	79.6	79.6
25#	79.3	79.3	79.3	79.3
26#	78.9	78.9	78.9	78.9
27#	78.5	78.5	78.5	78.5
28#	78.1	78.1	78.0	78.0
29#	77.5	77.5	77.5	77.5
30#	76.9	76.9	76.9	76.9
31#	76.2	76.2	76.2	76.2
32#	75.6	75.6	75.5	75.5
33#	75.1	75.1	75.0	75.0
34#	74.9	74.9	74.8	74.8
35#	75.1	75.1	75.0	75.0
36#	75.6	75.6	75.5	75.5
37#	76.2	76.2	76.2	76.2
38#	76.9	76.9	76.9	76.9
39#	77.5	77.5	77.5	77.5
40#	78.1	78.1	78.1	78.0
41#	78.5	78.5	78.5	78.5
42#	79.0	78.9	78.9	78.9
43#	79.3	79.3	79.3	79.3
44#	79.6	79.6	79.6	79.6
45#	79.9	79.9	79.9	79.8
46#	80.1	80.1	80.1	80.1
47#	80.3	80.3	80.3	80.3
48#	80.5	80.5	80.5	80.5
49#	80.7	80.7	80.7	80.7
50#	80.8	80.8	80.8	80.8
51#	81.0	81.0	81.0	81.0
52#	81.1	81.1	81.1	81.1
53#	81.2	81.2	81.2	81.2
54#	81.3	81.3	81.3	81.3
55#	81.4	81.4	81.4	81.4
56#	81.5	81.5	81.5	81.5
57#	81.6	81.6	81.6	81.6
58#	81.7	81.7	81.7	81.7
59#	81.8	81.8	81.8	81.8
60#	81.9	81.9	81.9	81.9
61#	82.0	82.0	82.0	82.0
62#	82.0	82.0	82.0	82.0
63#	82.1	82.1	82.1	82.1
64#	82.2	82.2	82.2	82.2
65#	82.2	82.2	82.2	82.2
66#	82.3	82.3	82.3	82.3
67#	82.3	82.3	82.3	82.3

It can be seen from the structure of the steel box girder (as shown in FIG. 19) that installation and construction conditions that the hanger rod needs to meet during the installation to the completed bridge are as follows. 1) The hanger rod must not be bent at an outer roof plate and outer anti-collision rail of the steel box girder in the transverse direction (structural compatibility condition). 2) A distance between the upper and lower suspension points before installation along the transverse direction must be less than the unstressed length of the hanger rod (the installation condition without temporary pushing or pulling of the main cable).

It can be seen from Table 9 that when the stiffening girder is installed section by section from the main tower to both sides without temporary pushing or pulling of the main cable, the entire process satisfies the structural compatibility condition and the installation condition of the main cable without temporary pushing or pulling, resulting in a generally established technical solution. However, when the main cable is transformed from a vertical plane state of the empty cable to the empty cable state of the bridge, the torsion of the main cable is constrained by the cable saddle to a certain extent, where the constraint is difficult to simulate accurately. Therefore, during the installation process of the above stiffening girder, it is necessary to reasonably determine the lateral pre-deflection angle of the clip (or the azimuth angle of the installation axis) to minimize the additional stress on the steel wire caused by torsion. Therefore, it is necessary to investigate the torsional characteristics of the main cable.

1.3 Conclusion on Spatial Torsion Characteristics Test of the Main Cable

The test results of the torsion characteristics of the main cable are obtained through a 1:15 main cable torsion indoor model test. After analyzing the experimental results and arguments of this application, main conclusions can be summarized as follows.

(1) When a final value of the hanger rod force is constant, an installation pre-deflection angle of a certain clip is changed, such that the torsion angle of the main cable changes the most at said clip, and is almost unchanged at an adjacent clip and beyond. A torsion angle between the clip and the adjacent clip changes almost linearly with a distance from the clip.

(2) The torsion angle of the main cable at the clip is close to a final value under the hanger rod force at a first level, with a small later change. A torsion direction of the section of the main cable adjacent to the clip under hanger rod forces at all levels is the same, which increases as the hanger rod force increases, and a rate of increase gradually decreases.

(3) Due to complex influencing factors and mechanisms of the restraint of the cable saddle on the torsion of the main cable strands, there is no rule to follow in the magnitude and even direction of the torsion angle of the main cable near the cable saddle (a range along a span direction does not exceed 80 times or less of the diameter of the main cable, with 60 times in this application).

1.4 Technical Solution of this Application

Through the above investigation and analysis, the stiffening girder erection method is performed as follows.

Step (1) Each hanger rod and clip are installed. The design center line of the clip (coincident with the center line of the hanger rod) is allowed to be located in the vertical plane. The lateral pre-deflection angle of the clip is the lateral inclination angle of the hanger rod in the bridge complete state (the design corresponds to the lateral inclination angle of the hanger rod).

Step (2) The stiffening girder is installed section by section from a certain distance in the longitudinal direction of the two main towers (not less than 60 times the diameter of the main cable, and not a girder section adjacent to the two main towers). The stiffening girder sections are installed one by one in the direction toward the mid-span. Each time one or several girder sections are installed, the azimuth angle of the main cable around the central axis thereof at the clip (especially at the clip near the bridge tower) until the installed stiffening girders are closed at the mid-span.

Step (3) The azimuth angle of the main cable around the central axis thereof at the hanger rod corresponding to the uninstalled girder section near the two main towers (i.e., the lateral deflection angle of the clip) is measured. The theoretical value and the measured value of the lateral deflection angle are compared to determine the adjustment amount of the lateral deflection angle of the clip of the immediately adjacent uninstalled girder section (the installed girder section in the mid-span). The lateral deflection angle of the clip of the immediately uninstalled girder section is adjusted. The stiffening girder installation is performed on the adjacent girder section.

Step (4) The step (3) is repeated until the stiffening girder erection is completed.

The embodiments described above are merely illustrative of the present disclosure, and are not intended to limit the patent scope of the present in disclosure. Any equivalent structural transformation or direct/indirect application in other related technical fields made using the description and drawings of the present disclosure without departing from the concept of the disclosure shall fall within the scope of the disclosure defined by the appended claims.

Claims

1. A stiffening girder erection method of a ground-anchored suspension bridge, comprising: step (1) installing clips for all hanger rods of a space main cable suspension bridge such that design center lines of the clips are coincident with center lines of the hanger rods, respectively; wherein the design center lines of the clips are located in a vertical plane, such that a lateral pre-deflection angle of each of the clips is configured as a lateral inclination angle of a corresponding one of the hanger rods in a bridge complete state;step (2) installing a first stiffening girder section at a position away from a first tower at a preset distance along a longitudinal direction, and installing a second stiffening girder section at a position away from a second tower at the preset distance along the longitudinal direction; and installing a plurality of third stiffening girder sections one by one in a direction respectively from the first stiffening girder and the second stiffening girder toward a mid-span until a mid-span closure is completed; wherein an azimuth angle of a main cable around a central axis thereof at each of the clips is measured after one or more of the plurality of third stiffening girder sections are installed; and a lateral deflection angle of each of the clips is calculated as a lateral inclination angle of each of the plurality of the hanger rods minus the azimuth angle of the main cable around the central axis thereof at each of the clips;step (3) installing a plurality of fourth stiffening girder sections one by one respectively from the first stiffening girder section toward the first tower and from the second stiffening girder section toward the second tower until a stiffening girder is closed at mid-span; andstep (4) measuring an azimuth angle of the central axis of the main cable at each of the clips.

2. The stiffening girder erection method of claim 1, wherein the step (4) is performed through steps of: measuring an azimuth angle of the central axis of the main cable at a hanger rod among the hanger rods corresponding to an uninstalled fourth stiffening girder section among the plurality of fourth stiffening girder sections; comparing a measured value and a theoretical value of a change of an azimuth angle of the central axis of the main cable at a certain stage relative to an azimuth angle before the first stiffening girder section and the second girder section are installed; modifying a prediction model of an azimuth angle change value of the central axis of the main cable at the hanger rod corresponding to the uninstalled fourth stiffening girder section; determining an adjustment of a lateral deflection angle of a clip of the hanger rod corresponding to the uninstalled fourth stiffening girder section followed by adjustment; and installing the uninstalled fourth stiffening girder section.

3. The stiffening girder erection method of claim 1, wherein assuming that two points E and F on each of the clips in the bridge complete state are located on a tangent line of a configuration of a corresponding hanger rod at an upper endpoint thereof, an angle between an EF connection line in another state and an EF connection line in the bridge complete state is configured as a lateral deflection angle of each of the clips in the another state, and the lateral pre-deflection angle of each of the clips is a lateral deflection angle achieved during installation and adjustment.

4. The stiffening girder erection method of claim 1, wherein the lateral inclination angle of each of the hanger rods is an angle between a tangent line of a configuration of each of the hanger rods at an upper endpoint thereof and a vertical line in a projection of each of the hanger rods on a vertical plane perpendicular to a bridge central axis in the bridge complete state.

5. The stiffening girder erection method of claim 1, wherein assuming that an angle between a top-bottom connecting line AB of a section of the main cable in a tightened state and a line AB of a section of the main cable in a certain state is an azimuth angle of the section of the main cable around the central axis thereof in the certain state; and the azimuth angle of the section of the main cable around the central axis thereof is the azimuth angle of the main cable around the central axis thereof.

6. The stiffening girder erection method of claim 1, wherein in step (2), the preset distance is not less than 60 times a diameter of the main cable.

7. The stiffening girder erection method of claim 2, wherein the theoretical value of the lateral deflection angle of each of the clips is calculated through simulation analysis using a modified finite element model, a modified linear model or a modified nonlinear model.

8. The stiffening girder erection method of claim 2, wherein in step (4), the adjustment of the lateral deflection angle of each of the clips is calculated through simulation analysis using a modified finite element model, a modified linear model or a modified nonlinear model.

9. The stiffening girder erection method of claim 1, wherein the stiffening girder is a steel box girder, a steel truss girder or a steel-concrete composite girder.

10. The stiffening girder erection method of claim 1, wherein a rise-to-span ratio fh/L of a plane projection of the main cable in the bridge complete state in a transverse direction is greater than 1/175.