Method for determining the position and posture of the main beam of a suspension bridge with short overhanging span in the state of waiting for closure

Abstract

The present invention discloses a method for determining the position and posture of the main beam of a suspension bridge with a short overhang span in a state to be joined, comprising the steps of: 1. determining basic unknowns used to describe the structural state of the suspension bridge with a short overhang span in a state to be joined, taking into account the number and position of hinge points; 2. establishing a control equation group; 3-5. expressing the non-basic unknowns in the control equation group as functions of the basic unknowns; 6. solving all basic unknowns; and 7. determining the position and posture of the main beam of the suspension bridge with a short overhang span in a state to be joined, taking into account the number and position of hinge points. The method of the present invention takes into account the deformation of the main beam due to the number and position of hinge points, the pre-deflection of the main cable saddle, and the inclination and elongation of the hanger, and can accurately determine the position and posture of the main beam of the suspension bridge with a short overhang span in a state to be joined. The method is easy to use, and the results are accurate and reliable, and can be used for structural analysis and construction scheme design of suspension bridges with short overhang spans in a state to be joined.

Description

Technical Field

[0001] The present invention relates to the field of bridge analysis theory, in particular to a method for determining the position and posture of a main beam of a suspension bridge with a short overhanging span in a state to be closed. Background Art

[0002] With economic development and changes in transportation modes, the demand for high-speed rail is increasing. To ensure smooth crossings of rivers and canyons, suspension bridges, with their strong spanning capacity and superior construction methods, have emerged as a popular bridge type. To meet track smoothness requirements and avoid large beam end rotations under live train loads, suspension bridges with short overhangs have emerged. This type of bridge features a traditional single-span suspension bridge with a stiffening girder extending outward from the tower by one or more spans. The short overhang and main span girder form a continuous beam, suspended only by hangers at the main span. This structural change allows for a gentle transition from deformation at the ends of the original main span to the short overhang. Examples of this type of bridge include the Shimotsui Seto Bridge, the Tsing Ma Bridge, the Jinsha River Bridge on the Lixiang Railway, and the Wufengshan Yangtze River Bridge.

[0003] Analysis during the construction phase of a suspension bridge has a significant impact on the performance of the structure. As a key step in the installation of the superstructure, the jointing of the stiffening beams has drawn particular attention from designers and constructors. For suspension bridges with short overhangs, the short overhanging span main beams lack hangers, making it impossible to construct the short overhanging span beam sections using the hoisting method. Currently, the more common method in China is to erect the short overhanging span main beams using the full-frame scaffolding method. After all segments of the main span main beams are hoisted, the short overhanging span main beams are jack-pushed and joined to the main span main beams at the bridge towers. To ensure the accuracy of the joint closure, the position and inclination of the joints when the main span main beams are waiting to be joined must be calculated in advance. This allows the short overhanging span main beams to be erected in the appropriate position and posture until all the main span main beams are hoisted into place, allowing for a single joint. This shortens the construction period and greatly improves construction efficiency.

[0004] To ensure the integrity of the main beam after closure, the accuracy of the closure must be strictly controlled. The position and end face inclination of the short span closure are determined by the closure of the main span girder, and the position and end face inclination of the main span girder closure are affected by the main span girder alignment. Therefore, the alignment of the main span girder in the closed state becomes the focus of research. It should be noted that the alignment of the main span girder in this state is different from that in the completed bridge for three reasons:

[0005] (1) The bridge deck pavement and ancillary facilities have not yet been installed, so the loads are different.

[0006] (2) The main cable saddle at the top of the tower has not been pushed into place.

[0007] (3) The connection method between beam segments is different from that in the completed bridge state.

[0008] During construction, the different connection methods between beam segments significantly impact the main beam's alignment. Furthermore, to avoid excessive stress in the main beam during the process of lowering the entire beam to its official support after closure, the main span beam typically retains hinged connections between some segments while awaiting closure. This effectively reduces the amount of rigid connection required for the entire main span beam. This effectively relieves excess construction stress during beam lowering. Clearly, the main span beam's alignment, beam end coordinates, and end face inclination angles during the closure phase are affected by the number and location of hinge points.

[0009] In order to accurately calculate the position and posture of the main beam of a suspension bridge with a short overhang span in the state of being ready for closure, taking into account the number and position of the hinge points, a calculation method needs to be invented. Summary of the Invention

[0010] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and to provide a method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in the state to be joined. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in the state to be joined can quickly and accurately obtain the main beam line shape, the end face position of the joint mouth and the internal force of the structure in the state to be joined.

[0011] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0012] A method for determining the position and posture of the main beam of a suspension bridge with a short overhang span in a state to be closed includes the following steps.

[0013] Step 1: Determine the basic unknown quantities to be connected: The main beam of a suspension bridge with short overhang spans includes the main span beam and the short overhang span beams on both sides of the main span beam; there are g hinge points in the main span beam, numbered from left to right as J1, J2, ... J g The main span beam is divided into g+1 main span beam segments by g hinge points, which are the 1st, 2nd,…, g+1 main span beam segments from left to right.

[0014] When the main span girder and the short outrigger are in the state of being connected, the main span girder is connected to the main cable located directly above through n hangers; the left end point G of the main span girder is L and the right endpoint G R are in a free state; by determining the left endpoint G L and the right endpoint G R The spatial coordinates in the global coordinate system (X GL , Y GL ) and (X GR , Y GR ), the position and posture of the main beam of the main span to be joined can be obtained; therefore, the basic unknown quantities to be joined include X GL 、Y GL , and calculate X GRand Y GR The 2n+2g+11 basic unknown quantities related to the rotation involved; among them, the global coordinate system is a coordinate system established with the intersection of the left pylon and the main beam when the suspension bridge with a short overhang span is in the completed state as the origin, the length direction of the main span main beam as the X direction, and the height direction of the main span main beam as the Y direction.

[0015] Step 2: Establish a control equation group: Based on the conservation of the stress-free length of each section of the main cable, the coordination of the force and deformation of each hanger, the closure of the span and height difference of each span, and the force balance of the main beam, a control equation group containing 2n+2g+13 equations is established.

[0016] Step 3: Analyze the deformation of the main cable and express the non-basic unknowns related to the deformation of the main cable in the control equations as functions of the basic unknowns.

[0017] Step 4: Analyze the deformation of the main beam and express the non-basic unknowns related to the deformation of the main beam in the control equations as functions of the basic unknowns;

[0018] Step 5: Analyze the relationship between the main cable and the main beam, and express the non-basic unknowns related to the relationship between the main cable and the main beam in the control equations as functions of the basic unknowns.

[0019] Step 6: Use the planning solution method to solve the control equations and obtain the values ​​of 2n+2g+13 basic unknown quantities at one time.

[0020] Step 7: Determine the position and posture of the main span beam to be connected: GL and Y GL , directly get the left end point G of the main span main beam L The spatial coordinates of GL 、Y GL , and 2n+2g+11 basic unknowns related to the rotation angle, the right end point G of the main beam of the main span is obtained R The spatial coordinate X GR and Y GR , and then the position and posture of the main span girder to be connected considering the number and position of the hinge points are obtained.

[0021] In step 1, n hangers are used to divide the main cable of the main span into n+1 main cables of the main span segment.

[0022] Then the basic unknown quantities related to the 2n+2g+11 corners are:

[0023] Horizontal projection length L of the left span main cable L , horizontal projection length of n+1 main span segment main cables l1~l n+1 , horizontal projection length L of the main cable on the right side R .

[0024] Catenary parameter a of the left span main cableL , the main cable catenary parameter a1 of the first section of the main span, the main cable catenary parameter a of the right span R .

[0025] The horizontal force H1 of the main cable in the first section of the main span, the axial force P1~P n .

[0026] Left tower main cable saddle pre-deflection Δp L , right tower main cable saddle pre-deflection Δp R .

[0027] The integral constant C of the rotation angle expression corresponding to the g+1 main span beam segments in sequence 1,1 ~C g+1,1 .

[0028] The integral constant D of the deflection expression corresponding to g+1 main span beam segments in sequence 1,1 ~D g+1,1 .

[0029] In step 2, the control equation group includes three span closure equations, three span height difference closure equations, n+3 main cable unstressed length equations, n hanger force and deformation coordination equations, two main beam force equilibrium equations, g+1 hinge point moment equations, and g+1 hinge point deformation continuity equations. The method for establishing the control equation group includes the following steps:

[0030] Step 2-1, establish three span closed equations, the specific expressions are:

[0031] L′ L =L L +Δp L (2-1)

[0032]

[0033] L′ R =L R +Δp R (2-3)

[0034] Where L′ L The horizontal projection length of the main cable of the left span when the bridge is completed is a known quantity.

[0035] L′ M The horizontal projection length of the main cable of the main span when the bridge is completed is a known quantity.

[0036] L′ R The horizontal projection length of the main cable of the right span when the bridge is completed is a known quantity.

[0037] l j The horizontal projection length of the main cable of the j-th segment of the main span is a basic unknown quantity; where j = 1, 2, …, n + 1.

[0038] Step 2-2: Establish three closed equations for the height difference. The specific expressions are:

[0039] Δy L =Y B′ -Y A (2-4)

[0040]

[0041] Δy R =Y C′ -Y D (2-6)

[0042] Where Y A 、Y B '、Y C' 、Y D They are the elevations of the left span anchorage point A, the left tower vertex B', the right tower vertex C', and the right span anchorage point D when the bridge is in the completed state, all of which are known quantities.

[0043] Δy L It is the height difference between the left and right end points of the left span main cable when it is ready to be connected.

[0044] Δy j It is the height difference between the left and right end points of the main cable of the jth section of the main span when it is ready to be connected.

[0045] Δy R This is the height difference between the left and right end points of the main cable on the right side when the cable is ready to be connected.

[0046] Step 2-3: Based on the conservation of the stress-free length of each main cable segment, establish n+3 stress-free length equations of the main cable. The specific expression is:

[0047] S L =S′ L (2-7)

[0048] S j =S′ j ,j=1,2,...,n+1 (2-8)

[0049] S R =S′ R (2-9)

[0050] Where S′ L is the unstressed length of the main cable of the left span when the bridge is completed, a known quantity.

[0051] S L It is the unstressed length of the main cable of the left span when it is ready for closure.

[0052] S′ jis the unstressed length of the main cable of the jth section of the main span when the bridge is in the completed state, a known quantity.

[0053] S j It is the stress-free length of the main cable of the jth section of the main span in the state of waiting for closure.

[0054] S′ R is the unstressed length of the main cable of the right span when the bridge is completed, a known quantity.

[0055] S R It is the stress-free length of the main cable on the right side when the joint is ready to be connected.

[0056] Step 2-4: According to the coordination between the force and deformation of each boom, establish n boom force and deformation coordination equations. The specific expression is:

[0057]

[0058] in:

[0059] ΔL h,i =|L h,i -L′ h,i | (2-10a)

[0060]

[0061] L′ h,i =Y O′i -Y G′i (2-10c)

[0062] ΔP i =P i -P′ i (2-10d)

[0063] Where, E h and A h are the elastic modulus and cross-sectional area of ​​the hanger, respectively, both of which are known quantities.

[0064] ΔL h,i is the elongation of the i-th hanger from the state to be connected to the completed bridge state.

[0065] L h,i is the length of the i-th boom in the state to be connected.

[0066] L′ h,i is the length of the i-th hanger in the completed bridge state.

[0067] X Oi and X Gi are the global horizontal coordinates of the upper and lower hanging points of the i-th boom in the state to be closed.

[0068] Y Oiand Y Gi are the global vertical coordinates of the upper and lower hanging points of the i-th boom in the state to be closed.

[0069] Y O′i and Y G′i are the global vertical coordinates of the upper and lower hanging points of the i-th hanger when the bridge is in the completed state, and both are known quantities.

[0070] ΔP i is the axial force increment of the i-th hanger from the ready-to-connect state to the completed bridge state.

[0071] P i is the axial force of the i-th hanger in the state to be connected, which is a basic unknown quantity.

[0072] P i ′ is the axial force of the i-th hanger in the completed bridge state, which is a known quantity.

[0073] Step 2-5: Establish two main beam force balance equations. The specific expressions are:

[0074]

[0075]

[0076] Where, P i,x and P i,y are the horizontal and vertical components of the force on the i-th boom in the state of being connected.

[0077] q is the deadweight of the main beam per meter, kN / m, a known quantity.

[0078] L G is the total length of the main span girder, a known quantity.

[0079] Step 2-6, establish the moment equations of g+1 hinge points: suppose the number of suspenders on the 1st, 2nd, ..., k-1, k, ..., g+1 main span beam segments are s1, s2, ..., s k-1 、s k ,…,s g+1 ; Among them, k=2,3,…,g; Then, take the left end point G of the main span main beam as the L A local coordinate system is established with the origin as the x-direction, the length direction of the main span main beam as the x-direction, and the height direction of the main span main beam as the y-direction. Then, in the local coordinate system, based on the zero moment of each hinge point, the expression of the moment equation of g+1 hinge points is established as follows:

[0080]

[0081]

[0082]

[0083] in:

[0084]

[0085]

[0086] Where, It is the algebraic sum of the moments of all forces on the hinge point J1 of the first main span beam in the state to be connected.

[0087] When the joint is ready to be connected, the hinge point J1 is connected to the left end point G of the main beam of the main span. L The horizontal distance is a known quantity.

[0088] t is the cross-sectional distance of the main span main beam along the x-direction. When t=0, it represents the left end face of the main span main beam.

[0089] q(t) is the deadweight of the main span main beam section t.

[0090] x i The distance from the i-th hanging point to the left end point G of the main beam of the main span in the state of being connected L The horizontal distance is a known quantity.

[0091] The total forces on the main span beam segments from k-1 to k in the state of being joined to the hinge point J k The algebraic sum of moments of .

[0092] The hinge point J is in the state of being joined k-1 To the left end point G of the main span main beam L The horizontal distance is known as k = 2, 3, ..., g;

[0093] The hinge point J is in the state of being joined k To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0094] m is the serial number of the small segment after the main span beam segment is further divided by the lower hanging point. It is distinguished from k for the convenience of statistics.

[0095] s m is the number of hangers on the mth main span beam segment.

[0096] It is the sum of the total number of hangers on the 1st to k-1th main span beam segments and the number of i hangers on the kth main span beam segment.

[0097] When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main spanL The horizontal distance is a known quantity.

[0098] When the joint is ready to be connected The vertical component of the hanger force.

[0099] M g+1 (L G ) is the moment of the g+1th main span beam segment in the state of being connected.

[0100] It is the sum of the total number of hangers on the 1st to gth main span beam sections and the number of i hangers on the g+1th main span beam section.

[0101] When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main span L The horizontal distance is a known quantity.

[0102] When the joint is ready to be connected The vertical component of the hanger force.

[0103] F (k-1)Y is the hinge point J (k-1) The vertical force at .

[0104] F gY is the hinge point J g The vertical force at .

[0105] The hinge point J is in the state of being joined g To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0106] Step 2-7: Based on the continuity of deformation of each hinge point, establish the deformation continuity equation of g+1 hinge points. The specific expression is:

[0107]

[0108] Y1(0)=Y GL (2-17)

[0109] Where, J is the upper hinge point of the kth main span beam segment in the state of being connected k The global vertical coordinate of .

[0110] The upper hinge point J of the k+1th main span beam segment in the state to be connected k The global vertical coordinate of .

[0111] Y1(0) is the upper left end point G of the first main span beam segment in the state of being connectedL The global vertical coordinate of .

[0112] In step 3, the non-basic unknowns related to the main cable deformation are Δy L , Δy j , Δy R 、S L 、S j and S R , then the method of expressing it as a function of the basic unknown quantity includes the following steps:

[0113] Step 3-1, Δy j and S j Expression: According to the catenary equation of each main span segment main cable, Δy j and S j All are expressed as the basic unknowns H1, a1, l1~l n+1 function.

[0114] Step 3-2, Δy L and S L Expression: According to the catenary equation of the left span main cable, Δy L and S L are expressed as the basic unknown quantities H1, a L and L L function.

[0115] Step 3-3, Δy R and S R Expression: According to the catenary equation of the main cable on the right, Δy R and S R are expressed as the basic unknown quantities H1, a R and L R function.

[0116] In step 4, by analyzing the deformation of the main beam, the lower hanging point G of the i-th hanger on the main span main beam is obtained. i And the right end point G of the main span main beam R The spatial coordinates of the right end point G of the main span main beam L The spatial coordinates of have the following relationship:

[0117] X Gi =X GL +x i ,i=1,2,...,n (4-1)

[0118] Y Gi =Y GL -w(x i )+Y Gi,0 (4-2)

[0119] XGR =X GL +x R (4-3)

[0120] Y GR =Y GL -w(x R )+Y GR,0 (4-4)

[0121] Where x i The lower lifting point G is in the state of waiting for closure. i To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0122] Y Gi,0 The lower lifting point G when the bridge is completed i Modeling coordinates of , known quantities.

[0123] x R The right end point G of the main beam of the main span in the state of waiting for closure R To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0124] Y GR,0 The right end point G of the main beam of the main span when the bridge is completed R Modeling coordinates of , known quantities.

[0125] w(x i ) is the lower lifting point G when the joint is ready for closure i deflection.

[0126] w(x R ) is the right end point G of the main beam of the main span when it is ready for closure R deflection.

[0127] w(x i ) and w(x R ) has the integral constant C of the rotation angle expression k,i+1 and D k,i+1 , which is expressed as the basic unknown quantity C 1,1 ~C g+1,1 and D 1,1 ~D g+1,1 The specific conversion analogy formula is:

[0128]

[0129]

[0130] In step 5, the non-basic unknown quantity P related to the relationship between the main cable and the main beam is i,x and P i,y are expressed as the basic unknown quantity Pi The function of is:

[0131] P i,x =P i sinα i (5-1)

[0132] P i,y =P i cosα i (5-2)

[0133] in:

[0134]

[0135]

[0136]

[0137] X B =X B′ +Δp L (5-6)

[0138] Y B =Y B′ (5-7)

[0139] Where, α i is the angle between the boom force direction of the i-th boom and the vertical direction in the state of being connected;

[0140] X B It is the global horizontal coordinate of the intersection point B between the main cable and the left tower in the state of waiting for closure.

[0141] l j The horizontal projection length of the main cable of the j-th segment of the main span is a basic unknown quantity; where j = 1, 2, …, n + 1.

[0142] Y B It is the global vertical coordinate of the intersection point B between the main cable and the left tower when the joint is ready.

[0143] X B′ is the global horizontal coordinate of the intersection point B between the main cable and the left tower when the bridge is completed, a known quantity.

[0144] Y B′ is the global ordinate of the intersection point B between the main cable and the left tower when the bridge is completed, a known quantity.

[0145] In step 6, the 2n+2g+13 control equations established in step 2 are all rewritten into a function form of f()=0, and then solved using the planning solution method to obtain the values ​​of all basic unknown quantities at one time.

[0146] The present invention has the following beneficial effects: the present invention takes into account factors such as the deformation of the main beam due to the number and position of hinge points, the pre-deflection of the main cable saddle, the inclination and elongation of the hanger, and is closer to the actual construction of the short overhanging span waiting to be connected; it relies on an equal number of basic unknowns and control equations for solution, has clear ideas and clear physical meaning, has strong versatility and practicality, and can provide ideas for construction status analysis and plan formulation for this type of suspension bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0147] Figure 1 It is a schematic diagram of the full bridge in the bridge state in a specific embodiment.

[0148] Figure 2 It is a schematic diagram of the main beam in the bridge-building state in a specific embodiment.

[0149] Figure 3 Schematic diagram of the main cable in a state ready for closure in a specific embodiment.

[0150] Figure 4 Schematic diagram of the side span main cable in the state of being connected in a specific embodiment; wherein (a) is the left span main cable; (b)

[0151] It is the main cable on the left side.

[0152] Figure 5 It is a schematic diagram of the main beam in the state of being ready for closure in a specific embodiment.

[0153] Figure 6 It is a schematic diagram of the deformation of the main beam in the state of being ready for closure in a specific embodiment.

[0154] Figure 7 Schematic diagram of the forces acting on the upper and lower hanging points in a specific embodiment; (a) is the completed bridge state; (b) is the state to be joined.

[0155] Figure 8 It is a force diagram of the upper hanging point in the state of waiting for closure in a specific embodiment.

[0156] Figure 9 It is a schematic diagram of a suspension bridge with a short overhanging span in a specific embodiment in a state ready for closure. DETAILED DESCRIPTION

[0157] The present invention will be further described in detail below with reference to the accompanying drawings and specific preferred embodiments.

[0158] like Figure 9 As shown, the method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be connected includes the following steps.

[0159] Step 1: Determine the basic unknown quantities to be joined

[0160] like Figure 1and Figure 2 As shown in the figure, when the main span main beam of the suspension bridge is in the completed state, the main beam is rigidly connected as a whole. However, when the short span is closed, the main beam of the main span with full rigid connection will produce excessive stress. Therefore, it is necessary to retain the hinge connection points between some beam sections, which are referred to as point hinges. The hinge point position can be set at the place with greater stress according to the needs of the main beam construction. It can generally be set at the midpoint, third point or fourth point of the main span main beam, such as Figure 5 shown.

[0161] The main girder of a suspension bridge with short overhang spans consists of the main span girder and the short overhang span girders on both sides of the main span girder. There are g hinge points in the main span girder, numbered J1, J2, ... J from left to right. g The main span beam is divided into g+1 main span beam segments by g hinge points, which are the 1st, 2nd,…, g+1 main span beam segments from left to right.

[0162] When the main span girder and the short outrigger are in the state of being connected, the main span girder is connected to the main cable located directly above through n hangers; the left end point G of the main span girder is L and the right endpoint G R are in a free state; by determining the left endpoint G L and the right endpoint G R The spatial coordinates in the global coordinate system (X GL , Y GL ) and (X GR , Y GR ), the position and posture of the main beam of the main span to be joined can be obtained; therefore, the basic unknown quantities to be joined include X GL 、Y GL , and calculate X GR and Y GR The 2n+2g+11 basic unknown quantities related to the rotation involved; among them, the global coordinate system is a coordinate system established with the intersection of the left pylon and the main beam when the suspension bridge with a short overhang span is in the completed state as the origin, the length direction of the main span main beam as the X direction, and the height direction of the main span main beam as the Y direction.

[0163] Assume that n hangers divide the main cables of the main span into n+1 main span segment cables. Then the basic unknown quantities related to the 2n+2g+11 rotation angles are:

[0164] Horizontal projection length L of the left span main cable L , horizontal projection length of n+1 main span segment main cables l1~l n+1 , horizontal projection length L of the main cable on the right side R .

[0165] Catenary parameter a of the left span main cable L , the main cable catenary parameter a1 of the first section of the main span, the main cable catenary parameter a of the right span R.

[0166] The horizontal force H1 of the main cable in the first section of the main span, the axial force P1~P n .

[0167] Left tower main cable saddle pre-deflection Δp L , right tower main cable saddle pre-deflection Δp R .

[0168] The integral constant C of the rotation angle expression corresponding to the g+1 main span beam segments in sequence 1,1 ~C g+1,1 .

[0169] The integral constant D of the deflection expression corresponding to g+1 main span beam segments in sequence 1,1 ~D g+1,1 .

[0170] Step 2: Establish a control equation group: Based on the conservation of the stress-free length of each section of the main cable, the coordination of the force and deformation of each hanger, the closure of the span and height difference of each span, and the force balance of the main beam, a control equation group containing 2n+2g+13 equations is established.

[0171] The above-mentioned control equation group includes 3 span closure equations, 3 span height difference closure equations, n+3 main cable unstressed length equations, n hanger force and deformation coordination equations, 2 main beam force equilibrium equations, g+1 hinge point moment equations and g+1 hinge point deformation continuity equations; the method for establishing the control equation group includes the following steps.

[0172] Step 2-1, establish three span closed equations, the specific expressions are:

[0173] L′ L =L L +Δp L (2-1)

[0174]

[0175] L′ R =L R +Δp R (2-3)

[0176] Where L′ L The horizontal projection length of the main cable of the left span when the bridge is completed is a known quantity.

[0177] L′ M The horizontal projection length of the main cable of the main span when the bridge is completed is a known quantity.

[0178] L′ R The horizontal projection length of the main cable of the right span when the bridge is completed is a known quantity.

[0179] lj The horizontal projection length of the main cable of the j-th section of the main span is a basic unknown quantity; where 1≤j≤n+1.

[0180] Step 2-2: Establish three closed equations for the height difference. The specific expressions are:

[0181] Δy L =Y B′ -Y A (2-4)

[0182]

[0183] Δy R =Y C′ -Y D (2-6)

[0184] Where Y A 、Y B' 、Y C' 、Y D They are the elevations of the left span anchorage point A, the left tower vertex B', the right tower vertex C', and the right span anchorage point D when the bridge is in the completed state, all of which are known quantities.

[0185] Δy L It is the height difference between the left and right end points of the left span main cable when it is ready to be connected.

[0186] Δy j It is the height difference between the left and right end points of the main cable of the jth section of the main span when it is ready to be connected.

[0187] Δy R This is the height difference between the left and right end points of the main cable on the right side when the cable is ready to be connected.

[0188] Step 2-3: Based on the conservation of the stress-free length of each main cable segment, establish n+3 stress-free length equations of the main cable. The specific expression is:

[0189] S L =S′ L (2-7)

[0190] S j =S′ j ,j=1,2,...,n+1 (2-8)

[0191] S R =S′ R (2-9)

[0192] Where S′ L is the unstressed length of the main cable of the left span when the bridge is completed, a known quantity.

[0193] S LIt is the unstressed length of the main cable of the left span when it is ready for closure.

[0194] S′ j is the unstressed length of the main cable of the jth section of the main span when the bridge is in the completed state, a known quantity.

[0195] S j It is the stress-free length of the main cable of the jth section of the main span in the state of waiting for closure.

[0196] S′ R is the unstressed length of the main cable of the right span when the bridge is completed, a known quantity.

[0197] S R It is the stress-free length of the main cable on the right side when the joint is ready to be connected.

[0198] Step 2-4: According to the coordination between the force and deformation of each boom, establish n boom force and deformation coordination equations. The specific expression is:

[0199]

[0200] in:

[0201] ΔL h,i =|L h,i -L′ h,i | (2-10a)

[0202]

[0203] L′ h,i =Y O′i -Y G′i (2-10c)

[0204] ΔP i =P i -P′ i (2-10d)

[0205] Where, E h and A h are the elastic modulus and cross-sectional area of ​​the hanger, respectively, both of which are known quantities.

[0206] ΔL h,i is the elongation of the i-th hanger from the state to be connected to the completed bridge state.

[0207] L h,i is the length of the i-th boom in the state to be connected.

[0208] L′ h,i is the length of the i-th hanger in the completed bridge state.

[0209] X Oi and X Giare the global horizontal coordinates of the upper and lower hanging points of the i-th boom in the state to be closed.

[0210] Y Oi and Y Gi are the global vertical coordinates of the upper and lower hanging points of the i-th boom in the state to be closed.

[0211] Y O′i and Y G′i are the global vertical coordinates of the upper and lower hanging points of the i-th hanger when the bridge is in the completed state, and both are known quantities.

[0212] ΔP i is the axial force increment of the i-th hanger from the ready-to-connect state to the completed bridge state.

[0213] P i is the axial force of the i-th hanger in the state to be connected, which is a basic unknown quantity.

[0214] P i ′ is the axial force of the i-th hanger in the completed bridge state, which is a known quantity.

[0215] Step 2-5: Establish two main beam force balance equations. The specific expressions are:

[0216]

[0217]

[0218] Where, P i,x and P i,y are the horizontal and vertical components of the force on the i-th boom in the state of being connected.

[0219] q is the deadweight of the main beam per meter, kN / m, a known quantity.

[0220] L G is the total length of the main span girder, a known quantity.

[0221] Step 2-6, establish the moment equations of g+1 hinge points: suppose the number of suspenders on the 1st, 2nd, ..., k-1, k, ..., g+1 main span beam segments are s1, s2, ..., s k-1 、s k ,…,s g+1 ; Among them, k=2,3,…,g; Then, take the left end point G of the main span main beam as the L A local coordinate system is established with the origin as the x-direction, the length direction of the main span main beam as the x-direction, and the height direction of the main span main beam as the y-direction. Then, in the local coordinate system, based on the zero moment of each hinge point, the expression of the moment equation of g+1 hinge points is established as follows:

[0222]

[0223]

[0224]

[0225] in:

[0226]

[0227]

[0228] Where, It is the algebraic sum of the moments of all forces on the hinge point J1 of the first main span beam in the state to be connected.

[0229] When the joint is ready to be connected, the hinge point J1 is connected to the left end point G of the main beam of the main span. L The horizontal distance is a known quantity.

[0230] t is the cross-sectional distance of the main span main beam along the x-direction. When t=0, it represents the left end face of the main span main beam.

[0231] q(t) is the deadweight of the main span main beam section t.

[0232] x i The distance from the i-th hanging point to the left end point G of the main beam of the main span in the state of being connected L The horizontal distance is a known quantity.

[0233] The total forces on the main span beam segments from k-1 to k in the state of being joined to the hinge point J k The algebraic sum of moments of .

[0234] The hinge point J is in the state of being joined k-1 To the left end point G of the main span main beam L The horizontal distance is known as k = 2, 3, ..., g;

[0235] The hinge point J is in the state of being joined k To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0236] m is the serial number of the small segment after the main span beam segment is further divided by the lower hanging point. It is distinguished from k for the convenience of statistics.

[0237] s m is the number of hangers on the mth main span beam segment.

[0238] It is the sum of the total number of hangers on the 1st to k-1th main span beam segments and the number of i hangers on the kth main span beam segment.

[0239] When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main span L The horizontal distance is a known quantity.

[0240] When the joint is ready to be connected The vertical component of the hanger force.

[0241] M g+1 (L G ) is the moment of the g+1th main span beam segment in the state of being connected.

[0242] It is the sum of the total number of hangers on the 1st to gth main span beam sections and the number of i hangers on the g+1th main span beam section.

[0243] When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main span L The horizontal distance is a known quantity.

[0244] When the joint is ready to be connected The vertical component of the hanger force.

[0245] F (k-1)Y is the hinge point J (k-1) The vertical force at .

[0246] F gY is the hinge point J g The vertical force at .

[0247] The hinge point J is in the state of being joined g To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0248] Step 2-7: Based on the continuity of deformation of each hinge point, establish the deformation continuity equation of g+1 hinge points. The specific expression is:

[0249]

[0250] Y1(0)=Y GL (2-17)

[0251] Where, J is the upper hinge point of the kth main span beam segment in the state of being connected k The global vertical coordinate of .

[0252] The upper hinge point J of the k+1th main span beam segment in the state to be connected kThe global vertical coordinate of .

[0253] Y1(0) is the upper left end point G of the first main span beam segment in the state of being connected L The global vertical coordinate of .

[0254] Step 3: Analyze the deformation of the main cable and express the non-basic unknowns related to the deformation of the main cable in the control equations as functions of the basic unknowns.

[0255] The above non-basic unknowns related to the main cable deformation are Δy L , Δy j , Δy R 、S L 、S j and S R , then the method of expressing it as a function of basic unknown quantities includes the following steps.

[0256] Step 3-1, Δy j and S j Expression: According to the catenary equation of each main span segment main cable, Δy j and S j All are expressed as the basic unknowns H1, a1, l1~l n+1 function.

[0257] (1) Figure 3 As shown in the figure, the height difference Δy between the left and right end points of the main cable of the main span in the jth section of the catenary cable is analyzed when the main cable is in the state of being connected. j Expressed as:

[0258]

[0259] in:

[0260] c j =-H j / q (3-2)

[0261] Where H j is the horizontal component of the main cable of the jth section of the main span in the state of being connected, kN;

[0262] c j is the horizontal component of the deadweight of the main cable of the jth section of the main span per meter when the main span is in the state of being connected;

[0263] a j are the catenary equation parameters of the main cable of the jth segment of the main span in the state to be connected.

[0264] l j It is the horizontal projection length of the main cable of the jth section of the main span in the state to be connected, which is a basic unknown quantity.

[0265] The stress-free length S of the main cable of the jth segment of the main span in the state of being connected j Expressed as:

[0266]

[0267] Where, E c and A c are the elastic modulus and cross-sectional area of ​​the main cable, respectively.

[0268] The above H j and a j They are functions of the basic unknown quantities H1 and a1 respectively. The specific solution process is as follows.

[0269] For hanging point O j Perform force analysis and obtain the following according to the static equilibrium condition:

[0270] H j+1 +P j,x =H j (3-4)

[0271]

[0272] Where, and Corresponding to the hanging point O j The inclination of the main cables on the left and right sides.

[0273] H j+1 It is the horizontal component of the main cable of the j+1th section of the main span in the state of being connected.

[0274] P j,x and P j,y are the horizontal and vertical components of the j-th boom force in the state of being connected;

[0275] By using formula (3-5), we can obtain:

[0276]

[0277]

[0278] Then we can obtain:

[0279]

[0280] Step 3-2, Δy L and S L Expression: According to the catenary equation of the left span main cable, Δy L and S L are expressed as the basic unknown quantities H1, a L and L L function.

[0281] Height difference Δy between the left and right end points of the main cable on the left side L and the unstressed length S of the left span main cable L The expression is:

[0282]

[0283]

[0284] in:

[0285]

[0286] Where H L is the horizontal component of the main cable in the left span when the joint is ready to be connected, kN.

[0287] a L It is the parameter of the catenary equation of the left span main cable in the state to be connected, which is a basic unknown quantity.

[0288] L L It is the horizontal projection length of the main cable of the left span when the joint is ready to be connected, which is a basically unknown quantity.

[0289] like Figure 4 As shown, in the left span, a coordinate system is established with point A as the local coordinate origin, with the x-axis horizontally pointing to the left and the y-axis vertically downward. The main cable of the side span in the state to be closed is analyzed. According to the horizontal component force balance relationship at point B, it can be obtained:

[0290] H L =H1 (3-12)

[0291] Step 3-3, Δy R and S R Expression: According to the catenary equation of the main cable on the right, Δy R and S R are expressed as the basic unknown quantities H1, a R and L R function.

[0292]

[0293]

[0294] in:

[0295]

[0296] Where H R is the horizontal component of the main cable on the right side when the joint is ready to be connected, kN.

[0297] a RIt is the parameter of the catenary equation of the main cable on the right side when the joint is ready to be connected, which is a basic unknown quantity.

[0298] L R It is the horizontal projection length of the main cable on the right side when the joint is ready to be connected, which is a basically unknown quantity.

[0299] like Figure 4 As shown, on the right side, a coordinate system is established with point C as the origin, with the x-axis pointing horizontally to the left and the y-axis pointing vertically downward. According to the horizontal component force balance relationship at point C, we can obtain:

[0300] H R =H n+1 (3-16)

[0301] Where H n+1 It is the horizontal component of the tail section of the main cable in the main span, which can be calculated using formula (3-4).

[0302] Step 4: Analyze the deformation of the main beam and express the non-basic unknowns related to the deformation of the main beam in the control equations as functions of the basic unknowns.

[0303] like Figure 5 As shown, considering the main beam calculation model, the single main beam calculation model is only affected by the boom force that is always in the upward direction and the gravity that is always in the downward direction. The single structure is a geometric variable relative to the ground reference system, and its absolute coordinates relative to the ground cannot be calculated. However, if the main beam is placed in the full bridge model, the full bridge model is an over-static structure, and the absolute coordinates relative to the ground can be calculated. Therefore, in order to calculate the absolute coordinates of each hanging point of the main beam, first use the leftmost end GL of the full beam as the origin of the local coordinates, establish a local coordinate system, calculate the relative deflection and rotation angle of the full beam hanging point relative to the left endpoint GL, and then obtain the absolute coordinates of the main beam hanging point through the global coordinates of the left endpoint GL and the coordinates of the main beam when it is in the bridge state, that is, Figure 6 The present invention obtains the lower hanging point G of the i-th suspension rod on the main span main beam by analyzing the deformation of the main beam. i And the right end point G of the main span main beam R The spatial coordinates of the right end point G of the main span main beam L The spatial coordinates of have the following relationship:

[0304] X Gi =X GL +x i ,i=1,2,...,n (4-1)

[0305] Y Gi =Y GL -w(x i )+Y Gi,0 (4-2)

[0306] XGR =X GL +x R (4-3)

[0307] Y GR =Y GL -w(x R )+Y GR,0 (4-4)

[0308] Where x i The lower lifting point G is in the state of waiting for closure. i To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0309] Y Gi,0 The lower lifting point G when the bridge is completed i Modeling coordinates of , known quantities.

[0310] x R The right end point G of the main beam of the main span in the state of waiting for closure R To the left end point G of the main span main beam L The horizontal distance is a known quantity.

[0311] Y GR,0 The right end point G of the main beam of the main span when the bridge is completed R Modeling coordinates of , known quantities.

[0312] w(x i ) is the lower lifting point G when the joint is ready for closure i deflection.

[0313] w(x R ) is the right end point G of the main beam of the main span when it is ready for closure R deflection.

[0314] In the present invention, the bending moment expression of each main beam section is:

[0315]

[0316]

[0317]

[0318] Where:

[0319]

[0320]

[0321] Where x i is the i-th boom force P iis the horizontal distance from the point of action to the origin of the local coordinate system, and x is the horizontal distance from the control surface to the origin of the local coordinate system.

[0322] According to material mechanics, the main span main beam is relative to the left end point G L The rotation and deflection equations can be expressed as:

[0323]

[0324]

[0325]

[0326]

[0327]

[0328]

[0329] Where, E b is the elastic modulus of the main beam, I b (x) is the moment of inertia of the cross section, the rotation angle is counterclockwise and the deflection is downward; and are all undetermined constants on each section of the main beam. There is a recursive relationship between the undetermined constants of adjacent sections on the kth main beam section:

[0330]

[0331]

[0332] At this point, the undetermined constants of the remaining sections of the kth beam segment can be transformed into the basic unknown quantity C k,1 and D k,1 The formula.

[0333] Step 5: Analyze the relationship between the main cable and the main beam, and express the non-basic unknowns related to the relationship between the main cable and the main beam in the control equations as functions of the basic unknowns.

[0334] Analyze the relationship between the main cable and the main beam connected by the same suspender in the completed bridge state and the state to be connected (such as Figure 7 shown)

[0335] (1) When the bridge is completed, the suspender is vertical, so the horizontal force P′ on the lower suspending point is i,x and vertical force P′ i,y They are:

[0336] P′ i,x =0 (5-1)

[0337] P′i,y =P′ i (5-2)

[0338] (2) When the joint is ready to be closed, the axial force of the boom is P i , and the angle between the direction of the boom force and the vertical direction is α i (like Figure 8 As shown), the horizontal force P on the lower hanging point is i,x and vertical force P i,x Expressed as

[0339] P i,x =P i sinα i (5-3)

[0340] P i,y =P i cosα i (5-4)

[0341] in:

[0342]

[0343]

[0344]

[0345] X B =X B′ +Δp L (5-8)

[0346] Y B =Y B′ (5-9)

[0347] Where, α i is the angle between the boom force direction of the i-th boom and the vertical direction in the state of being connected;

[0348] X B It is the global horizontal coordinate of the intersection point B between the main cable and the left tower in the state of waiting for closure.

[0349] l j The horizontal projection length of the main cable of the j-th segment of the main span is a basic unknown quantity; where j = 1, 2, …, n + 1.

[0350] Y B It is the global vertical coordinate of the intersection point B between the main cable and the left tower when the joint is ready.

[0351] X B′ is the global horizontal coordinate of the intersection point B between the main cable and the left tower when the bridge is completed, a known quantity.

[0352] YB′ is the global ordinate of the intersection point B between the main cable and the left tower when the bridge is completed, a known quantity.

[0353] Step 6: Use the planning solution method to solve the control equations and obtain the values ​​of 2n+2g+13 basic unknown quantities at one time.

[0354] In this embodiment, the 2n+2g+13 control equations established in step 2 are all rewritten as a function form with f()=0, and all the control equations in the state to be fused are combined into the following objective function:

[0355]

[0356] The objective function is solved using the planning and solving method to solve the values ​​of the 2n+2g+13 basic unknown quantities in the first step, so that the 2n+2g+13 control equations in step 2 are valid at the same time.

[0357] Step 7: Determine the position and posture of the main span beam to be connected

[0358] A. Through X GL and Y GL , directly get the left end point G of the main span main beam L The spatial coordinates of .

[0359] B. Through X GL 、Y GL , and 2n+2g+11 basic unknowns related to the rotation angle, the right end point G of the main beam of the main span is obtained R The spatial coordinate X GR and Y GR , and lifting point G i The spatial coordinate X Gi and Y Gi , and then the position and posture of the main span girder to be connected considering the number and position of the hinge points are obtained.

[0360] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. A method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed, characterized by: The steps include: Step 1: Determine the basic unknown quantities to be connected: The main beam of a suspension bridge with short overhang spans includes the main span beam and the short overhang span beams on both sides of the main span beam; there are g hinge points in the main span beam, numbered from left to right as J1, J2, ... J g , the main span beam is divided into g+1 main span beam segments by g hinge points, which are the 1st, 2nd, ..., g+1 main span beam segments from left to right; When the main span girder and the short outrigger are in the state of being connected, the main span girder is connected to the main cable located directly above through n hangers; the left end point G of the main span girder is L and the right endpoint G R are in a free state; by determining the left endpoint G L and the right endpoint G R The spatial coordinates in the global coordinate system (X GL , Y GL ) and (X GR , Y GR ), the position and posture of the main span girder to be connected can be obtained; Therefore, the basic unknown quantities to be fused include X GL 、Y GL , and calculate X GR and Y GR The 2n+2g+11 basic unknowns involved in the rotation angles; the global coordinate system is established with the intersection of the left pylon and the main beam of the short overhanging span suspension bridge in the completed state as the origin, the main span main beam length direction as the X direction, and the main span main beam height direction as the Y direction. Step 2: Establish a control equation group: Based on the conservation of the stress-free length of each main cable section, the coordination of the force and deformation of each hanger, the closure of the span and height difference of each span, and the force balance of the main beam, a control equation group containing 2n+2g+13 equations is established; Step 3: Analyze the deformation of the main cable and express the non-basic unknowns related to the deformation of the main cable in the control equations as functions of the basic unknowns; Step 4: Analyze the deformation of the main beam and express the non-basic unknowns related to the deformation of the main beam in the control equations as functions of the basic unknowns; Step 5: Analyze the relationship between the main cables and the main beams, and express the non-basic unknowns related to the relationship between the main cables and the main beams in the control equations as functions of the basic unknowns; Step 6: Use the planning solution method to solve the control equations and obtain the values ​​of 2n+2g+13 basic unknowns at one time; Step 7: Determine the position and posture of the main span beam to be connected: GL and Y GL , directly get the left end point G of the main span main beam L The spatial coordinates of GL 、Y GL , and 2n+2g+11 basic unknowns related to the rotation angle, the right end point G of the main beam of the main span is obtained R The spatial coordinate X GR and Y GR , and then the position and posture of the main span girder to be connected considering the number and position of the hinge points are obtained.

2. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 1, characterized in that: In step 1, assume that n hangers are used to divide the main cable of the main span into n+1 main cables of the main span segment; Then the basic unknown quantities related to the 2n+2g+11 corners are: Horizontal projection length L of the left span main cable L , horizontal projection length of n+1 main span segment main cables l1~l n+1 , horizontal projection length L of the main cable on the right side R ; Catenary parameter a of the left span main cable L , the main cable catenary parameter a1 of the first section of the main span, the main cable catenary parameter a of the right span R ; The horizontal force H1 of the main cable in the first section of the main span, the axial force P1~P n ; Left tower main cable saddle pre-deflection Δp L , right tower main cable saddle pre-deflection Δp R ; The integral constant C of the rotation angle expression corresponding to the g+1 main span beam segments in sequence 1,1 ~C g+1,1 ; The integral constant D of the deflection expression corresponding to g+1 main span beam segments in sequence 1,1 ~D g+1,1 .

3. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 2, characterized in that: In step 2, the control equation group includes three span closure equations, three span height difference closure equations, n+3 main cable unstressed length equations, n hanger force and deformation coordination equations, two main beam force equilibrium equations, g+1 hinge point moment equations, and g+1 hinge point deformation continuity equations. The method for establishing the control equation group includes the following steps: Step 2-1, establish three span closed equations, the specific expressions are: L′ L =L L +Δp L (2-1) L′ R =L R +Δp R (2-3) Where L′ L The horizontal projection length of the main cable of the left span when the bridge is completed is a known quantity; L′ M The horizontal projection length of the main cable of the main span when the bridge is completed is a known quantity; L′ R The horizontal projection length of the main cable of the right span when the bridge is completed is a known quantity; l j is the horizontal projection length of the main cable in the jth segment of the main span, which is a basic unknown quantity; where j = 1, 2, ..., n + 1; Step 2-2: Establish three closed equations for the height difference. The specific expressions are: Δy L =Y B′ -Y A (2-4) Δy R =Y C′ -Y D (2-6) Where Y A 、Y B '、Y C' 、Y D The elevations of the left span anchorage point A, the left tower vertex B', the right tower vertex C', and the right span anchorage point D when the bridge is completed are all known quantities. Δy L The height difference between the left and right end points of the main cable on the left side when the cable is ready for closure; Δy j is the height difference between the left and right end points of the main cable of the jth section of the main span when the main cable is in the state of being connected; Δy R The height difference between the left and right end points of the main cable on the right side when the cable is ready for closure; Step 2-3: Based on the conservation of the stress-free length of each main cable segment, establish n+3 stress-free length equations of the main cable. The specific expression is: S L =S′ L (2-7) S j =S′ j ,j=1,2,...,n+1 (2-8) S R =S′ R (2-9) Where S′ L is the unstressed length of the main cable of the left span when the bridge is completed, a known quantity; S L It is the stress-free length of the main cable of the left span in the state to be connected; S′ j is the unstressed length of the main cable of the jth segment of the main span when the bridge is completed, a known quantity; S j is the stress-free length of the main cable of the jth segment of the main span in the state to be closed; S′ R is the unstressed length of the main cable of the right span when the bridge is completed, a known quantity; S R is the unstressed length of the main cable of the right span when the joint is ready for closure; Step 2-4: According to the coordination between the force and deformation of each boom, establish n boom force and deformation coordination equations. The specific expression is: in: ΔL h,i =|L h,i -L′ h,i | (2-10a) L' h,i =Y O′i -Y G′i (2-10c) ΔP i =P i -P i ′ (2-10d) Where, E h and A h are the elastic modulus and cross-sectional area of ​​the suspender, respectively, both of which are known quantities; ΔL h,i is the elongation of the i-th suspender from the ready-to-connect state to the completed bridge state; L h,i is the length of the i-th boom in the state of being connected; L′ h,i is the length of the i-th suspender in the completed bridge state; X Oi and X Gi are the global horizontal coordinates of the upper and lower hanging points of the i-th boom in the state to be closed; Y Oi and Y Gi are the global vertical coordinates of the upper and lower hanging points of the i-th boom in the state to be closed; Y O′i and Y G′i are the global vertical coordinates of the upper and lower hanging points of the ith hanger when the bridge is completed, both of which are known quantities; ΔP i is the axial force increment of the i-th hanger from the ready-to-close state to the completed bridge state; P i is the axial force of the i-th hanger in the state of being connected, which is a basic unknown quantity; P i ′ is the axial force of the i-th hanger in the completed bridge state, which is a known quantity; Step 2-5: Establish two main beam force balance equations. The specific expressions are: Where, P i,x and P i,y are the horizontal and vertical components of the force on the i-th boom in the state to be closed; q is the deadweight of the main beam per meter, kN / m, a known quantity; L G is the total length of the main span girder, a known quantity; Step 2-6, establish the moment equations of g+1 hinge points: suppose the number of suspenders on the 1st, 2nd, ..., k-1, k, ..., g+1 main span beam segments are s1, s2, ..., s k-1 、s k ,…,s g+1 ; Among them, k=2,3,…,g; Then, take the left end point G of the main span main beam as the L A local coordinate system is established with the origin as the x-direction, the length direction of the main span main beam as the x-direction, and the height direction of the main span main beam as the y-direction. Then, in the local coordinate system, based on the zero moment of each hinge point, the expression of the moment equation of g+1 hinge points is established as follows: in: Where, is the algebraic sum of the moments of all forces on the hinge point J1 of the first main span beam in the state to be closed; When the joint is ready to be connected, the hinge point J1 is connected to the left end point G of the main beam of the main span. L The horizontal distance, a known quantity; t is the cross-sectional distance of the main span girder along the x-direction. When t = 0, it represents the left end face of the main span girder; q(t) is the deadweight of the main span main beam section t; x i The distance from the i-th hanging point to the left end point G of the main beam of the main span in the state of being connected L The horizontal distance, a known quantity; The total forces on the main span beam segments from k-1 to k in the state of being joined to the hinge point J k The algebraic sum of moments of The hinge point J is in the state of being joined k-1 To the left end point G of the main span main beam L The horizontal distance is known as k = 2, 3, ..., g; The hinge point J is in the state of being joined k To the left end point G of the main span main beam L The horizontal distance, a known quantity; m is the serial number of the small segment after the main span beam segment is further segmented by the lower hanging point, which is distinguished from k for the convenience of statistics; s m is the number of hangers on the mth main span beam segment; is the sum of the total number of hangers on the 1st to k-1st main span beam sections and the number of i hangers on the kth main span beam section; When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main span L The horizontal distance, a known quantity; When the joint is ready to be connected The vertical component of the root boom force; M g+1 (L G ) is the moment of the g+1th main span beam segment in the state to be closed; The sum of the total number of suspenders on the 1st to gth main span beam sections and the number of i suspenders on the g+1th main span beam section; When the joint is ready to be connected The lifting point is connected to the left end point G of the main beam of the main span L The horizontal distance, a known quantity; When the joint is ready to be connected The vertical component of the root boom force; F (k-1)Y is the hinge point J (k-1) The vertical force at F gY is the hinge point J g The vertical force at The hinge point J is in the state of being joined g To the left end point G of the main span main beam L The horizontal distance, a known quantity; Step 2-7: Based on the continuity of deformation of each hinge point, establish the deformation continuity equation of g+1 hinge points. The specific expression is: Y1(0)=Y GL (2-17) Where, J is the upper hinge point of the kth main span beam segment in the state of being connected k The global vertical coordinate of The upper hinge point J of the k+1th main span beam segment in the state to be connected k The global vertical coordinate of Y1(0) is the upper left end point G of the first main span beam segment in the state of being connected L The global vertical coordinate of .

4. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 3, characterized in that: In step 3, the non-basic unknowns related to the main cable deformation are Δy L , Δy j , Δy R 、S L 、S j and S R , then the method of expressing it as a function of the basic unknown quantity includes the following steps: Step 3-1, Δy j and S j Expression: According to the catenary equation of each main span segment main cable, Δy j and S j All are expressed as the basic unknowns H1, a1, l1~l n+1 function; Step 3-2, Δy L and S L Expression: According to the catenary equation of the left span main cable, Δy L and S L are expressed as the basic unknown quantities H1, a L and L L function; Step 3-3, Δy R and S R Expression: According to the catenary equation of the main cable on the right, Δy R and S R are expressed as the basic unknown quantities H1, a R and L R function.

5. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 3, characterized in that: In step 4, by analyzing the deformation of the main beam, the lower hanging point G of the i-th hanger on the main span main beam is obtained. i And the right end point G of the main span main beam R The spatial coordinates of the right end point G of the main span main beam L The spatial coordinates of have the following relationship: X Gi =X GL +x i ,i=1,2,...,n (4-1) AND Gi =And GL -w(x i )+Y Gi,0 (4-2) X GR =X GL +x R (4-3) AND GR =And GL -w(x R )+Y GR,0 (4-4) Where x i The lower lifting point G is in the state of waiting for closure. i To the left end point G of the main span main beam L The horizontal distance, a known quantity; Y Gi,0 The lower lifting point G when the bridge is completed i Modeling coordinates of , known quantities; x R The right end point G of the main beam of the main span in the state of waiting for closure R To the left end point G of the main span main beam L The horizontal distance, a known quantity; Y GR,0 The right end point G of the main beam of the main span when the bridge is completed R Modeling coordinates of , known quantities; w(x i ) is the lower lifting point G when the joint is ready for closure i Deflection; w(x R ) is the right end point G of the main beam of the main span when it is ready for closure R Deflection; w(x i ) and w(x R ) has the integral constant C of the rotation angle expression k,i+1 and D k,i+1 , which is expressed as the basic unknown quantity C 1,1 ~C g+1,1 and D 1,1 ~D g+1,1 The specific conversion analogy formula is:

6. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 3 or 5, characterized in that: In step 5, the non-basic unknown quantity P related to the relationship between the main cable and the main beam is i,x and P i,y are expressed as the basic unknown quantity P i The function of is: P i,x =P i areα i (5-1) P i,y =P i cosα i (5-2) in: X B =X B′ +Δp L (5-6) AND B =And B′ (5-7) Where, α i is the angle between the boom force direction of the i-th boom and the vertical direction in the state of being connected; X B is the global horizontal coordinate of the intersection point B between the main cable and the left tower in the state of waiting for closure; l j is the horizontal projection length of the main cable in the jth segment of the main span, which is a basic unknown quantity; where j = 1, 2, ..., n + 1; Y B is the global vertical coordinate of the intersection point B between the main cable and the left tower in the state of waiting for closure; X B′ is the global horizontal coordinate of the intersection point B between the main cable and the left tower when the bridge is completed, which is a known quantity; Y B′ is the global ordinate of the intersection point B between the main cable and the left tower when the bridge is completed, a known quantity.

7. The method for determining the position and posture of the main beam of a suspension bridge with a short overhanging span in a state to be closed according to claim 1, characterized in that: In step 6, the 2n+2g+13 control equations established in step 2 are all rewritten into a function form of f()=0, and then solved using the planning solution method to obtain the values ​​of all basic unknown quantities at one time.

Images