Method for determining spatial position of cable saddle of single main cable at inclined hoisting tower top of arch rib section of basket arch bridge

Abstract

The invention provides a method for determining the spatial position of a cable saddle of a single main cable at the inclined hoisting tower top of an arch rib section of a lifting basket arch bridge, and relates to the technical field of bracket-free installation of arch ribs of the lifting basket arch bridge, the technology comprises tower frames which are symmetrically arranged on river banks on two sides, cable saddles are arranged at the top ends of the tower frames, and a main cable is arranged between the cable saddles; the position of the cable saddle is determined through a cable saddle displacement calculation method, so that the single main cable is kept in the tangential direction of an arch rib section of the basket arch bridge. The cable saddle displacement calculation method comprises the steps that S1, the line shape of the arch axis of the basket arch bridge is determined; s2, projecting the arch axis in the horizontal direction; and S3, calculating the intersection point of the tangent line of the arch axis and the tower. Through the calculation method, the positions of the cable saddles on the two banks can be rapidly and accurately calculated, the cable saddles are transversely moved in advance, fine adjustment in the hoisting process is not needed, and accurate hoisting installation of arch ribs can be guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of bracket-free installation of arch ribs of a basket-handled arch bridge, and in particular to a method for determining the spatial position of a saddle of a single main cable on a top of an inclined suspension tower of an arch rib segment of a basket-handled arch bridge. Background Art

[0002] Basket arch bridges are highly favored in modern bridge engineering due to their light structure, beautiful appearance, good stability and other advantages. Most basket arch bridges are constructed by cable hoisting, but there are still technical difficulties in the installation of arch ribs. Among them, the "upright hanging construction method" proposed in "CN112779867A" is Figure 1 As shown in FIG. 1 , it is necessary to lay side cables and adjust the segment position with the help of side cables and hand winches so that the axis of the segment to be installed coincides with the axis of the installed segment. The construction process is complicated, and some basket arches are difficult to lay side cables due to the terrain of the bridge location, and the versatility is not strong; as shown in “CN108374347A”, “CN106702911A” and “CN101117795” Figure 2 As shown in the figure, although the inclined hanging arch rib method is adopted, there is no accurate algorithm for the corresponding saddle positioning, so the saddle on one side is only roughly moved to the tower, and the saddle on the other side is moved to the side of the tower. As a result, there is a deviation in the lateral position when the segment is in place, and it is still necessary to use a hand winch to fine-tune it to the designed position.

[0003] This patent is aimed at the installation of arch rib segments of basket arch bridges. It proposes a method for determining the spatial position of the single main cable saddle on the top of the inclined tower of the arch rib segment of the basket arch bridge. The spatial position of the saddle on the top of the tower on both sides can be accurately calculated before the segment is hoisted, so that the main cable and the arch rib axis are in the same direction. Without the need for side cable wind and hand winch, the positioning requirements of the basket arch bridge segment can be met. Figure 3 As shown, the construction is simple. Summary of the invention

[0004] The present invention provides a method for determining the spatial position of a single main cable saddle at the top of an inclined suspension tower of an arch rib segment of a basket-lift arch bridge, aiming to solve at least one technical problem existing in the prior art mentioned in the background technology.

[0005] The present invention provides the following technical solutions to achieve the above objectives:

[0006] A method for determining the position of a saddle on the top of a single-main-cable inclined tower of a basket-handled arch bridge comprises towers symmetrically arranged on two river banks, with saddles arranged on the tops of the towers and main cables arranged between the saddles. The saddle position is determined by a saddle displacement calculation method so that the single main cable is kept in the tangent direction of the arch rib segment of the basket-handled arch bridge.

[0007] Furthermore, the saddle displacement calculation method comprises the following steps:

[0008] S1. Determine the linear shape of the arch axis of the basket handle arch bridge;

[0009] S2, project the arch axis in the horizontal direction;

[0010] S3. Calculate the intersection of the tangent line of the arch axis and the tower.

[0011] Furthermore, the arch axis line shape includes a parabola and a catenary, and corresponding equations are established for the parabola and the catenary.

[0012] Furthermore, the steps of S2 are as follows:

[0013] S201, establishing a spatial coordinate system based on the center of the arch cross section of the basket handle arch bridge as the coordinate origin, with the along-bridge direction being the X direction, the transverse-bridge direction being the Z direction, and the vertical direction being the Y direction;

[0014] S202, establishing an arch axis equation based on the arch axis linear shape;

[0015] S203, based on the arch axis equation and the arch rib inclination angle θ, the three-dimensional equation of the arch axis is calculated by a three-dimensional coordinate rotation formula;

[0016] S204, projecting the three-dimensional equation of the arch axis in the horizontal plane direction to obtain the projection line equation.

[0017] Furthermore, the steps of S3 are as follows:

[0018] S301, segmenting the arch axis according to the number and length of the arch rib segments of the basket handle arch bridge;

[0019] S302, two front and rear hanging points are set on each arch rib segment, and the coordinates of the front hanging point and the rear hanging point in the horizontal direction are determined by the projection line equation;

[0020] S303, calculating the straight line equation of the main cable based on the coordinates of the front hanging point and the rear hanging point;

[0021] S304, calculating the coordinates of the saddle space point, that is, the saddle space position, by using the straight line equation.

[0022] Furthermore, the arch axis line shape is a parabola,

[0023] The parabola equation in S202 is:

[0024] The three-dimensional equation of the arch axis in S203;

[0025]

[0026] The projection line equation in S204

[0027] In S302, assuming that the front lifting point is Xa and the rear lifting point is Xb, then:

[0028] The coordinates of the front lifting point are

[0029] The coordinates of the rear lifting point are

[0030] The straight line equation of the main cable in S303;

[0031]

[0032] Transformed,

[0033]

[0034] In the above 304, the coordinate values ​​of the centers of the towers on both sides in the X direction are L1 and L2, and the coordinate values ​​of the saddles on the top of the tower in the Y direction are H1 and H2. Substituting them into the linear equation, the spatial coordinates of the saddles on the top of the tower on both sides are obtained as follows:

[0035] The spatial coordinates of the saddle on the left tower top are:

[0036]

[0037] The spatial coordinates of the saddle on the right tower top are:

[0038]

[0039] Furthermore, the linear shape of the arch axis is a catenary, and the catenary equation in S202 is:

[0040]

[0041] in,

[0042]

[0043] The three-dimensional equation of the arch axis in S203;

[0044]

[0045] The projection line equation in S204 is:

[0046]

[0047] In 302, it is assumed that the front hanging point is Xa and the rear hanging point is Xb. Then, the coordinates of the front hanging point are: The coordinates of the rear suspension point are The straight line equation of the main cable in 303;

[0048]

[0049] In the above 304, the coordinate values ​​of the centers of the towers on both sides in the X direction are L1 and L2, and the coordinate values ​​of the saddles on the top of the tower in the Y direction are H1 and H2. Substituting them into the linear equation, the spatial coordinates of the saddles on the top of the tower on both sides are obtained as follows:

[0050] The spatial coordinates of the saddle on the left tower top are:

[0051]

[0052] The spatial coordinates of the saddle on the right tower top are:

[0053]

[0054] Beneficial Effects

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] Compared with the traditional "straight hanging" method, the present invention requires additional design of arch rib side cable wind to adjust the axial position, and the construction process is complicated. The oblique hanging process is simple in construction method, can be quickly positioned, and does not need to set side cable wind to adjust the angle, which meets the requirements of arch rib hoisting and positioning of steel tube basket arch bridges. It is suitable for arch rib cable hoisting in canyon areas or where side cable wind cannot be arranged due to regional restrictions. Compared with the traditional oblique hanging scheme, this calculation method can quickly and accurately calculate the position of the saddles on both sides, and move the saddles horizontally in advance, without fine-tuning during the hoisting process, to ensure the accurate installation of the arch rib hoisting. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below only relate to some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative labor.

[0058] Figure 1 This is a schematic diagram of the hoisting arrangement of the main cable saddle in the prior art;

[0059] Figure 2 It is a schematic diagram of secondary lateral lifting of the arch rib segment of the basket arch bridge in the prior art;

[0060] Figure 3 It is the precise positioning and hoisting of the cable saddle on the top of the single main cable inclined hanging tower of the present invention;

[0061] Figure 4 This is the overall layout diagram of the basket arch of the present invention;

[0062] Figure 5 It is a plan view of the basket arch of the present invention;

[0063] Figure 6 This is a vertical layout diagram of the basket handle arch of the present invention;

[0064] Figure 7 It is a schematic diagram of the front and rear hanging points of the present invention; DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0066] It should be noted that in the present invention: the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or apparatuses; the directions or positional relationships indicated by the terms "upper", "lower", "left", "right", "front", "back", "top", "bottom", "inside", "outside", "middle", "vertical", "horizontal", "lateral", "longitudinal" and the like are based on the directions or positional relationships shown in the drawings. These The terms are mainly used to better describe the present invention and its embodiments, and are not used to limit the indicated devices, elements or components to have a specific orientation, or to be constructed and operated in a specific orientation; the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence; the terms "install", "set", "provided with", "connected", "connected", "sleeved", etc. should be understood in a broad sense; for example, it can be a fixed connection, a detachable connection, or an integral structure; it can be a mechanical connection, or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, or it can be an internal connection between two devices, elements or components. In addition, some terms can be used to express other meanings in addition to indicating orientation or positional relationships. For example, the term "on" may also be used to express a certain dependency or connection relationship in some cases. For those of ordinary skill in the art, the specific meanings of these terms in the present invention can be understood according to specific circumstances.

[0067] Embodiment 1. A method for determining the position of a saddle on the top of a single main cable inclined suspension tower of a basket-lift arch bridge comprises towers symmetrically arranged on both sides of the river bank, a saddle is arranged on the top of the tower, and a main cable is arranged between the saddles. The saddle position is determined by a saddle displacement calculation method to keep the single main cable in the tangent direction of the arch rib segment of the basket-lift arch bridge.

[0068] The saddle displacement calculation method comprises the following steps:

[0069] S1. Determine the linear shape of the arch axis of the basket handle arch bridge; the linear shape of the arch axis is a parabola.

[0070] S2. Project the arch axis horizontally:

[0071] S201, establishing a spatial coordinate system based on the center point of the arch line of the basket handle arch bridge as the coordinate origin, with the along-bridge direction being the X direction, the transverse-bridge direction being the Z direction, and the vertical direction being the Y direction;

[0072] S202. Establish the arch axis equation based on the arch axis line shape; the parabola equation is:

[0073] S203, based on the arch axis equation, taking into account the condition of the arch rib inclination angle θ, the three-dimensional equation of the arch axis is calculated by a three-dimensional coordinate rotation formula;

[0074]

[0075] S204. Project the three-dimensional equation of the arch axis horizontally to obtain the projection line equation

[0076] S3. Calculate the intersection point between the arch axis tangent and the tower:

[0077] S301, segmenting the arch axis according to the number and length of the arch rib segments of the basket handle arch bridge;

[0078] S302, two front and rear lifting points are set on each arch rib segment, and the coordinates of the front lifting point and the rear lifting point in the horizontal direction are determined by the projection line equation; assuming that the front lifting point is X a , the rear lifting point is X b but:

[0079] The coordinates of the front lifting point are

[0080] The coordinates of the rear lifting point are

[0081] S303, calculating the straight line equation of the main cable based on the coordinates of the front lifting point and the rear lifting point;

[0082]

[0083] Transformed,

[0084]

[0085] S304, the coordinates and heights of the towers on both sides are known, and the three-dimensional coordinates of the saddle are calculated by substituting them into the linear equation. The coordinates of the towers on both sides are L1, L2 and the height of the towers is H. Substituting them into the linear equation, the three-dimensional coordinates of the saddles at the top of the towers on both sides are obtained as follows:

[0086] The three-dimensional coordinates of the left saddle are:

[0087]

[0088] The three-dimensional coordinates of the right saddle are:

[0089]

[0090] The present invention is mainly used in the installation process of the arch rib segment of the basket arch bridge, and the installation process is as follows:

[0091] 1) When the arch axis line shape is a parabola, the coordinates of the cable saddle space points corresponding to the arch rib segments to be hoisted are calculated in sequence according to the above method;

[0092] 2) Before lifting, move the cable saddle to the aforementioned cable saddle space point coordinates. At this time, the main cable is in the tangent direction of the arch rib segment to be lifted;

[0093] 3) Connect the main cable to the front and rear lifting points on the arch rib segment to be hoisted and lift it. At this time, the position of the arch rib segment to be hoisted in the longitudinal and transverse directions of the bridge is determined. It is only necessary to adjust the position of the arch rib segment to be hoisted in the vertical direction to install the arch rib segment. Compared with the traditional "positive lifting and hanging" method, there is no need to use side cables to adjust the angle and the construction difficulty is reduced.

[0094] Embodiment 2. A method for determining the position of a saddle on the top of a single main cable inclined tower of a basket-lift arch bridge, comprising towers symmetrically arranged on both sides of the river bank, saddles arranged on the top of the towers, main cables arranged between the saddles, and the saddle position is determined by a saddle displacement calculation method to keep the single main cable in the tangent direction of the arch rib segment of the basket-lift arch bridge.

[0095] The saddle displacement calculation method comprises the following steps:

[0096] S1. Determine the linear shape of the arch axis of the basket handle arch bridge; the linear shape of the arch axis is a catenary.

[0097] S2. Project the arch axis horizontally:

[0098] S201, establishing a spatial coordinate system based on the center point of the arch line of the basket handle arch bridge as the coordinate origin, with the along-bridge direction being the X direction, the transverse-bridge direction being the Z direction, and the vertical direction being the Y direction;

[0099] S202. Establish an arch axis equation based on the arch axis line shape; the catenary equation is as follows:

[0100]

[0101] in,

[0102]

[0103] S203, based on the arch axis equation and taking into account the inclination angle of the arch rib, the three-dimensional equation of the arch axis is calculated by a three-dimensional coordinate rotation formula;

[0104]

[0105] S204, projecting the three-dimensional equation of the arch axis in the horizontal direction to obtain the projection line equation, which is as follows:

[0106]

[0107] S3. Calculate the intersection point between the arch axis tangent and the tower:

[0108] S301, segmenting the arch axis according to the number and length of the arch rib segments of the basket handle arch bridge;

[0109] S302, two front and rear lifting points are set on each arch rib segment, and the coordinates of the front lifting point and the rear lifting point in the horizontal direction are determined by the projection line equation; assuming that the front lifting point is X a , the rear lifting point is X b but:

[0110] The coordinates of the front lifting point are

[0111] The coordinates of the rear lifting point are

[0112] S303, calculating the straight line equation of the main cable based on the coordinates of the front lifting point and the rear lifting point;

[0113]

[0114] S304, the coordinates and heights of the towers on both sides are known, and the three-dimensional coordinates of the saddle are calculated by substituting them into the linear equation. The coordinates of the towers on both sides are L1, L2 and the height of the towers is H. Substituting them into the linear equation, the three-dimensional coordinates of the saddles at the top of the towers on both sides are obtained as follows:

[0115] The three-dimensional coordinates of the left saddle are:

[0116]

[0117] The three-dimensional coordinates of the right saddle are:

[0118]

[0119] The present invention is mainly used in the installation process of the arch rib segment of the basket arch bridge, and the installation process is as follows:

[0120] 1) When the arch axis line shape is a catenary, the coordinates of the saddle space points corresponding to the arch rib segments to be hoisted are calculated in sequence according to the above method;

[0121] 2) Before lifting, move the cable saddle to the aforementioned cable saddle space point coordinates. At this time, the main cable is in the tangent direction of the arch rib segment to be lifted;

[0122] 3) Connect the main cable to the front and rear lifting points on the arch rib segment to be hoisted and lift it. At this time, the position of the arch rib segment to be hoisted in the longitudinal and transverse directions of the bridge is determined. You only need to adjust the position of the arch rib segment to be hoisted in the vertical direction to install the arch rib segment.

[0123] Obviously, the above is only a part of the embodiments of the present invention, not all of the embodiments. The above embodiments are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and variations. Any combination, modification, equivalent replacement, improvement and all other embodiments that can be made by those of ordinary skill in the art within the spirit and principle of the present invention should be within the protection scope of the present invention.

Claims

1. A method for determining the spatial position of a single main cable saddle on the top of an arch rib segment of a basket arch bridge, comprising towers symmetrically arranged on both sides of the bridge, a cable saddle arranged on the top of the tower, and a main cable arranged on the cable saddle, characterized in that: The saddle position is determined by the saddle space point calculation method so that the main cable is located in the tangent direction of the arch rib of the basket arch bridge to be hoisted.

2. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 1 is characterized by: The saddle space point calculation method comprises the following steps: S1. Determine the arch axis line shape of the basket arch bridge; S2. Project the arch axis in the horizontal direction to obtain a projection line; S3. Calculate the intersection point between the tangent line of the projection line and the tower.

3. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 2 is characterized by: The arch axis line shape includes a parabola and a catenary, and corresponding equations are established for the parabola and the catenary.

4. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 3 is characterized by: The steps of S2 are as follows: S201, establishing a spatial coordinate system based on the center of the arch cross section of the basket handle arch bridge as the coordinate origin, with the along-bridge direction being the X direction, the transverse-bridge direction being the Z direction, and the vertical direction being the Y direction; S202, establishing an arch axis equation based on the arch axis linear shape; S203, based on the arch axis equation and the arch rib inclination angle θ, the three-dimensional equation of the arch axis is calculated by a three-dimensional coordinate rotation formula; S204, projecting the three-dimensional equation of the arch axis in the horizontal plane direction to obtain the projection line equation.

5. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 4 is characterized in that: The steps of S3 are as follows: S301, segmenting the arch axis according to the number and length of the arch rib segments of the basket handle arch bridge; S302, two front and rear hanging points are set on each arch rib segment, and the coordinates of the front hanging point and the rear hanging point in the horizontal direction are determined by the projection line equation; S303, calculating the straight line equation of the main cable based on the coordinates of the front hanging point and the rear hanging point; S304, calculating the coordinates of the saddle space point, that is, the saddle space position, by using the straight line equation.

6. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 5 is characterized by: The arch axis line shape is a parabola, The parabola equation in S202 is: The three-dimensional equation of the arch axis in S203; The projection line equation in S204 In S302, it is assumed that the front lifting point is X a , the rear lifting point is X b but: The coordinates of the front lifting point are The coordinates of the rear lifting point are The straight line equation of the main cable in S303; Transformed, In the above 304, the coordinate values ​​of the centers of the towers on both sides in the X direction are L1 and L2, and the coordinate values ​​of the saddles on the top of the tower in the Y direction are H1 and H2. Substituting them into the linear equation, the spatial coordinates of the saddles on the top of the tower on both sides are obtained as follows: The spatial coordinates of the saddle on the left tower top are: The spatial coordinates of the saddle on the right tower top are:

7. The method for determining the spatial position of the single main cable saddle of the arch rib segment inclined suspension tower top of the basket handle arch bridge according to claim 5 is characterized by: The arch axis line shape is a catenary, The catenary equation in S202 is: in, The three-dimensional equation of the arch axis in S203; The projection line equation in S204 is: In the above 302, it is assumed that the front suspension point is X a , rear hanging point is X b but: The coordinates of the front lifting point are The coordinates of the rear suspension point are The straight line equation of the main cable in 303; In the above 304, the coordinate values ​​of the centers of the towers on both sides in the X direction are L1 and L2, and the coordinate values ​​of the saddles on the top of the tower in the Y direction are H1 and H2. Substituting them into the linear equation, the spatial coordinates of the saddles on the top of the tower on both sides are obtained as follows: The spatial coordinates of the saddle on the left tower top are: The spatial coordinates of the saddle on the right tower top are:

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