Method for determining the winding force of the main cable of a suspension bridge

Abstract

This invention discloses a method for determining the main cable winding force of a suspension bridge. The method includes: knowing the main cable alignment, first-phase dead load, and second-phase dead load in the completed bridge state; calculating the maximum cable force T0 of the main cable in the side spans in the completed bridge state; deducting the second-phase dead load; calculating the maximum cable force increment ΔT1 of the main cable relative to the completed bridge state before bridge deck paving; applying vehicle loads and system-only temperature difference loads during the operation phase; calculating the maximum cable force increments ΔT2 and ΔT3 under vehicle live loads and system-only temperature difference loads, respectively; calculating the main cable winding force in the states of "bridge deck paving first, then winding" and "winding first, then bridge deck paving," respectively. This invention can effectively determine the main cable winding force in both states, saving construction time, ensuring that the winding does not detach from the main cable, and meeting design requirements.

Description

Technical Field

[0001] This invention relates to the field of suspension bridge construction technology. More specifically, this invention relates to a method for determining the winding force of the main cable of a suspension bridge, which is particularly applicable to the winding protection of the main cable of a long-span suspension bridge. Background Technology

[0002] The main cable is the most important load-bearing component of a suspension bridge and its lifeline. Generally, in suspension bridge design theory, the design life of the main cable is 100 years. Replacement of the main cable is not considered within this design life.

[0003] In harsh natural environments spanning rivers, lakes, and seas, the main cable is prone to steel wire corrosion due to the combined effects of water, sunlight, temperature, and salinity. Multiple protective systems are often implemented, such as round steel wire winding combined with putty coating, S-shaped steel wire winding combined with dehumidification, and wrapping tape combined with dehumidification. Determining the appropriate wire winding force is crucial in all these systems. Excessive winding force places excessive demands on the winding machine, preventing it from achieving the desired winding effect. Conversely, insufficient winding force can lead to the round or S-shaped steel wires used for winding becoming detached from the main cable under constant load, live load, and temperature differences between the inside and outside of the cable, especially during the cable's cross-sectional contraction.

[0004] Currently, suspension bridge designs typically only specify the cable winding force under the condition of "paving the bridge deck first, then winding the cables." In this case, the main cable winding force only considers the effects of operational live load and temperature difference across the main cable cross-section. However, in actual construction, paving the bridge deck first and then winding the cables would waste a significant amount of construction time; therefore, the method of "winding the main cables first, then paving the bridge deck" is often adopted. The main cable winding force under this method differs significantly from the design-specified winding force because the main cable force changes considerably under the loads of the bridge deck paving and its ancillary facilities, and the main cable diameter shrinks to some extent, making it impossible to achieve the designed winding force.

[0005] Therefore, for the wire wrapping protection operation of the main cable of a suspension bridge, it is necessary to find a simple method for determining the wire wrapping force of the main cable to solve the defects and shortcomings of the above methods. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for determining the main cable winding force under two conditions: "paving the bridge deck first and then winding the cable" and "winding the main cable first and then paving the bridge deck." This method ensures that the main cable winding force meets design requirements during on-site construction, regardless of the construction period, and guarantees that the winding cable does not detach from the main cable.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is: a method for determining the winding force of the main cable of a suspension bridge, comprising the following steps:

[0008] Step 1: Given the main cable alignment, first-phase dead load, and second-phase dead load under the completed bridge condition, calculate the maximum cable force T0 of the main cable in the side span under the completed bridge condition.

[0009] Step 2: Based on Step 1, deduct the second-phase dead load and calculate the maximum cable force increment ΔT1 of the main cable before the bridge deck is paved in the completed bridge state.

[0010] Step 3: Based on Step 1, apply the vehicle load and the system temperature difference load during the operation phase, and calculate the maximum cable force increment ΔT2 and ΔT3 of the main cable under the action of vehicle live load only and system temperature difference load only, respectively.

[0011] Step 4: Based on the on-site measured values ​​of the temperature difference at the main cable cross-section, considering only the combined effects of the maximum cable force increments ΔT2 and ΔT3 under the combined action of vehicle live load and system temperature difference load, calculate the main cable winding force under the condition of "paving the bridge deck first and then winding the cable"; or,

[0012] Based on the on-site measured value of the temperature difference of the main cable section, it is necessary to consider the combined action of the maximum cable force increments ΔT1, ΔT2 and ΔT3 of the main cable under the action of the second-phase dead load, vehicle live load and only system temperature difference load, and calculate the main cable winding force under the condition of "winding before bridge deck paving".

[0013] Preferably, step one specifically comprises the following steps:

[0014] Based on the coordinates of the main saddle IP and the anchor saddle IP, the main span sag f, the middle span L, and the side span L b The parameters of the main cable wire elastic modulus E and linear expansion coefficient ξ, the main cable intensity along the cable q0, the first-phase dead load q1, the second-phase dead load q2, and the main cable area A are solved iteratively using the bisection method. The resulting parameters are: the main cable horizontal force H, the stressed length S, and the unstressed length S0 of the side spans under the completed bridge condition.

[0015] H = (q0 + q1 + q2)L 2 / 8f (1)

[0016] S=-H / (q0+q1+q2)[sh((q0+q1+q2)L b / Ha)+sha] (2)

[0017]

[0018]

[0019]

[0020] The maximum cable force T0 of the main cable is:

[0021]

[0022] Preferably, before the main cable is wound with wire in step two, the stiffening girder installation is completed. At this time, the tower offset can be measured using a total station to obtain the tower offsets Δ1 and Δ2. The actual calculated span of the side span is then:

[0023] L pre =max(L b -Δ1,L b -Δ2) (7)

[0024] After deducting the second-phase dead load q2, and with only q0 and q1 acting, keeping the stress-free length S0 of each span constant, and assuming the new horizontal force parameter H1, the bisection method is also used for iteration to obtain the stress-free length S of each span of the main cable. 01 ;

[0025] If |S0-S 01 |>ε=0.0001m, correct H1 and calculate again; if |S0-S 01 If |≤ε=0.0001m, then H1 is the actual horizontal force of the main cable after deducting the second phase of constant load. According to formula (6), the maximum cable force T1 of the main cable at this time is obtained.

[0026] Therefore, the maximum cable force increment of the main cable before the bridge deck is ΔT1 = T1 - T0 can be obtained relative to the completed bridge state.

[0027] Preferably, in step three: based on step one, an operational phase vehicle load q3 is applied, at which point the actual calculated span of the bridge can be approximated as:

[0028] L pos =L pre -max(Δ1,Δ2)q3 / q2 (8)

[0029] Similarly, following the method in step two, we can obtain the maximum cable force T2 and the maximum cable force increment ΔT2 = T2 - T0 during the operation phase;

[0030] Considering only the system temperature difference load t, the bisection method is similarly used to solve for the maximum cable force T3 and the maximum cable force increment ΔT3=T3-T0 under the consideration of only the system temperature difference load.

[0031] Preferably, in step four, the measured value T of the temperature difference at the main cable cross-section is used. S Considering only the combined effects of the maximum cable force increments ΔT2 and ΔT3 under the combined action of vehicle live load and system temperature difference load, the cable winding force N of the main cable under the condition of "paving the bridge deck first and then winding the cable" is...pre for:

[0032]

[0033] or,

[0034] Based on the field measured values ​​of the temperature difference at the main cable cross-section, the maximum cable force increments ΔT1, ΔT2, and ΔT3 under the combined effects of the secondary dead load, vehicle live load, and system temperature difference load alone need to be considered to calculate the main cable winding force N under the condition of "winding before bridge deck paving". pos for:

[0035]

[0036] fac is the safety factor considered to compensate for the loss of winding force; Ecs is the elastic modulus of the steel wire used for winding; Acs is the elastic modulus of the steel wire used for winding; δ is the Poisson's ratio of the main cable steel wire.

[0037] The present invention has at least the following beneficial effects: The method of the present invention can determine the main cable winding force under two states, namely "paving the bridge deck first and then winding the wire" and "winding the main cable first and then paving the bridge deck", according to the suspension bridge structural parameters, the second-phase dead load, the vehicle live load and system temperature difference load during the operation phase, and the temperature difference of the main cable section. This not only saves the construction period, but also ensures that the winding wire does not decouple from the main cable, and meets the design requirements.

[0038] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0039] Figure 1 This is a structural calculation diagram of the present invention in the bridged state;

[0040] Figure 2 This is a calculation diagram of the bridge deck before paving according to the present invention. Detailed Implementation

[0041] The present invention will now be described in detail and completely with reference to the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be particularly noted that the technical solutions and features provided in various parts of the present invention, including the following description, can be combined with each other without conflict.

[0042] Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0043] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific implementation process is as follows:

[0044] like Figure 1 As shown, the present invention provides a method for determining the winding force of the main cable of a suspension bridge, comprising the following steps:

[0045] Step 1: Given the main cable alignment, first-phase dead load, and second-phase dead load under the completed bridge condition, calculate the maximum cable force T0 of the main cable in the side span under the completed bridge condition.

[0046] Step 2: Based on Step 1, deduct the second-phase dead load and calculate the maximum cable force increment ΔT1 of the main cable before the bridge deck is paved in the completed bridge state.

[0047] Step 3: Based on Step 1, apply the vehicle load and the system temperature difference load during the operation phase, and calculate the maximum cable force increment ΔT2 and ΔT3 of the main cable under the action of vehicle live load only and system temperature difference load only, respectively.

[0048] Step 4: Based on the on-site measured values ​​of the temperature difference at the main cable cross-section, considering only the combined effects of the maximum cable force increments ΔT2 and ΔT3 under the combined action of vehicle live load and system temperature difference load, calculate the main cable winding force under the condition of "paving the bridge deck first and then winding the cable"; or,

[0049] Based on the on-site measured value of the temperature difference of the main cable section, it is necessary to consider the combined action of the maximum cable force increments ΔT1, ΔT2 and ΔT3 of the main cable under the action of the second-phase dead load, vehicle live load and only system temperature difference load, and calculate the main cable winding force under the condition of "winding before bridge deck paving".

[0050] This technical solution may also include the following technical details to better achieve the technical effect: Step one specifically involves the following steps:

[0051] Based on the coordinates of the main saddle IP and the anchor saddle IP, the main span sag f, the middle span L, and the side span L b The parameters include the elastic modulus E and linear expansion coefficient ξ of the main cable steel wire, the cable density q0 along the main cable, the first-stage dead load q1, the second-stage dead load q2, and the main cable area A. Figure 1 The bisection method was used for iterative solution to obtain the main cable horizontal force H, the stressed length S, and the unstressed length S0 of the side span in the completed bridge state as follows:

[0052] H = (q0 + q1 + q2)L2 / 8f (1)

[0053] S=-H / (q0+q1+q2)[sh((q0+q1+q2)L b / Ha)+sha] (2)

[0054]

[0055]

[0056]

[0057] The maximum cable force T0 of the main cable is:

[0058]

[0059] This technical solution may also include the following technical details to better achieve the technical effect: Before the main cable is wound with wire in step two, the stiffening girder installation has been completed. At this time, the bridge tower offset can be measured using a total station to obtain the offsets Δ1 and Δ2 of the two bridge towers, such as... Figure 2 As shown, the actual calculated span of the side span is as follows:

[0060] L pre =max(L b -Δ1,L b -Δ2) (7)

[0061] After deducting the second-phase dead load q2, and with only q0 and q1 acting, keeping the stress-free length S0 of each span constant, and assuming the new horizontal force parameter H1, the bisection method is also used for iteration to obtain the stress-free length S of each span of the main cable. 01 ;

[0062] If |S0-S 01 |>ε=0.0001m, correct H1 and calculate again; if |S0-S 01 If |≤ε=0.0001m, then H1 is the actual horizontal force of the main cable after deducting the second phase of constant load. According to formula (6), the maximum cable force T1 of the main cable at this time is obtained.

[0063] Therefore, the maximum cable force increment of the main cable before the bridge deck is ΔT1 = T1 - T0 can be obtained relative to the completed bridge state.

[0064] This technical solution may also include the following technical details to better achieve the technical effect: In step three: based on step one, an operational phase vehicle load q3 is applied, at which point the actual calculated span of the bridge can be approximated as:

[0065] L pos =L pre -max(Δ1,Δ2)q3 / q2 (8)

[0066] Similarly, following the method in step two, we can obtain the maximum cable force T2 and the maximum cable force increment ΔT2 = T2 - T0 during the operation phase;

[0067] Considering only the system-wide temperature difference load t, the bisection method is similarly used to solve for the maximum cable force T3 and the maximum cable force increment ΔT3 = T3 - T0 under the condition of considering only the system-wide temperature difference load. It should be noted that for the temperature difference load t, the principle that the stress-free length of the main cable in the side span remains unchanged before and after the temperature change must be followed.

[0068] This technical solution may also include the following technical details to better achieve the technical effect: In step four, the on-site measured value T of the temperature difference at the main cable cross-section is combined. S Considering only the combined effects of the maximum cable force increments ΔT2 and ΔT3 under the combined action of vehicle live load and system temperature difference load, the cable winding force N of the main cable under the condition of "paving the bridge deck first and then winding the cable" is... pre for:

[0069]

[0070] or,

[0071] Based on the field measured values ​​of the temperature difference at the main cable cross-section, the maximum cable force increments ΔT1, ΔT2, and ΔT3 under the combined effects of the secondary dead load, vehicle live load, and system temperature difference load alone need to be considered to calculate the main cable winding force N under the condition of "winding before bridge deck paving". pos for:

[0072]

[0073] fac is the safety factor considered to compensate for the loss of winding force; Ecs is the elastic modulus of the steel wire used for winding; Acs is the elastic modulus of the steel wire used for winding; δ is the Poisson's ratio of the main cable steel wire.

[0074] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and embodiments shown and described herein.

Claims

1. A method for determining the winding force of the main cable of a suspension bridge, characterized in that, Includes the following steps: Step 1: Given the main cable alignment, first-phase dead load, and second-phase dead load under the completed bridge condition, calculate the maximum cable force of the main cable in the side span under the completed bridge condition. ; Step Two: Based on Step One, before the main cable is wound with wire, the stiffening girder has been installed. The bridge tower offset is measured using a total station to obtain the offset of the two bridge towers. The actual calculated span of the side spans was determined, and the second-phase dead load was deducted. The maximum increase in main cable force relative to the bridge deck before paving was then calculated. ; Step 3: Based on Step 1, apply the vehicle load during the operation phase and the system-only temperature difference load, and calculate the maximum cable force increment of the main cable under the vehicle live load and the system-only temperature difference load respectively. ; Step 4: Based on the on-site measured values ​​of the temperature difference at the main cable cross-section, only the maximum cable force increment under the action of vehicle live load and system temperature difference load needs to be considered. Under the combined effect, the main cable winding force was calculated under the condition of "paving the bridge deck first and then winding". or, Based on the on-site measured values ​​of the temperature difference at the main cable cross-section, the maximum increase in cable force under the effects of the secondary dead load, vehicle live load, and system-only temperature difference load must be considered. Under the combined effect, the main cable winding force was calculated under the condition of "winding wire first and then paving the bridge deck". Before the main cable is wound with wire in step two, the stiffening girder has been installed. At this time, the tower offset can be measured using a total station to obtain the offset of the two towers. At this point, the actual calculated span of the side span is: （7） After deducting the second-phase dead load q2, and with only q0 and q1 acting, keeping the stress-free length S0 of each span constant, and assuming the new horizontal force parameter H1, the bisection method is used iteratively to obtain the stress-free length of each span of the main cable. ; like Re-correct and recalculate H1; if H1 is the actual horizontal force of the main cable after deducting the second phase of constant load. According to formula (6), the maximum cable force T1 of the main cable at this time is obtained. This allows us to obtain the maximum increase in main cable force relative to the bridge deck before paving. ; In step three: based on step one, apply the vehicle load for the operational phase. At this point, the actual calculated span of the bridge can be approximated as: （8） Similarly, following the method in step two, the maximum cable force T2 and the maximum cable force increment during the operation phase can be obtained. ; Similarly, considering only the system temperature difference load t, the bisection method is used to solve for the maximum cable force T3 and the maximum cable force increment under the condition of considering only the system temperature difference load. .

2. The method for determining the winding force of the main cable of a suspension bridge as described in claim 1, characterized in that, The specific steps of step one are as follows: Based on the coordinates of the main saddle IP and the anchor saddle IP, the main span sag f, the middle span L, and the side span L b The parameters of the main cable wire elastic modulus E and linear expansion coefficient ξ, the main cable intensity along the cable q0, the first-phase dead load q1, the second-phase dead load q2, and the main cable area A are solved iteratively using the bisection method. The resulting parameters are: the main cable horizontal force H, the stressed length S, and the unstressed length S0 of the side spans under the completed bridge condition. 。 3. The method for determining the winding force of the main cable of a suspension bridge as described in claim 1, characterized in that, In step four, the on-site measured values ​​of the temperature difference at the main cable cross-section are considered. T S Only considering the maximum cable force increment of the main cable under the action of vehicle live load and system temperature difference load alone, and the combined effect, the main cable winding force under the condition of "paving the bridge deck first and then winding the wire" is... N pre for: （9） or, Based on the field-measured temperature difference of the main cable section, the maximum increase in cable force under the effects of the secondary dead load, vehicle live load, and system-only temperature difference load needs to be considered. Under the combined effect, the main cable winding force N was calculated under the condition of "winding wire first and then paving the bridge deck". pos for: （10） fac Safety factor considered to compensate for the loss of winding force; Ecs The elastic modulus of the steel wire used for winding; Acs The elastic modulus of the steel wire used for winding; δ The Poisson's ratio for the main cable wire.

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