Cable-pier combined structure cable-adding logarithm calculation system based on different fortification targets

Abstract

The invention discloses a cable-pier combined structure cable adding logarithm calculation system based on different fortification targets. The system comprises a first model construction module, a first calculation module, a second calculation module, a third calculation module, a fourth calculation module and a second model construction and result output module. The method aims at solving the technical problems that a traditional cable adding calculation mode is low in efficiency and prone to making mistakes, and large-scale professional analysis software is inconvenient to apply in field engineering. According to the system, on-site rapid input of basic parameters of an integrated bridge, simulation calculation of the automatic progressive cable adding process and real-time visual monitoring and output of key response indexes (such as the relation of cable adding logarithm-displacement or bending moment decreasing amplitude) are achieved, and intelligentization and high efficiency of cable-pier combined structure reinforcing design are achieved. The system can provide rapid and reliable technical support for on-site engineering decision, and the anti-collision performance of the pier is enhanced, so that the overall safety and durability of the structure are effectively guaranteed.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, and specifically relates to a system for calculating the logarithmic addition of cables to cable-stayed piers in cable-stayed structures based on different fortification targets. Background Technology

[0002] Beam bridges are a commonly used type of bridge in bridge engineering, with a long history of development. They account for a large proportion of bridge construction due to their ease of manufacture and erection, and wide applicability. As important transportation hubs, the safety of bridges is crucial to economic development and social operation.

[0003] However, bridges are susceptible to various hazards during their design and operation, with ship collisions being one of the most common. Ship-bridge collisions are also a leading cause of bridge failure. Statistics from the European Maritime Safety Authority (EMSA) and the Transport Safety Board of Canada (TSB) indicate that collisions and contact are among the most common types of maritime accidents resulting in personal injury. Bridges located in navigable waterways are man-made obstacles for vessels, posing a risk of collision. In the event of a ship-bridge collision, the bridge structure may be subjected to enormous lateral impact loads, leading to severe damage or even complete collapse, resulting in significant economic losses, personal injury, and negative social impacts.

[0004] Bridge collision avoidance design mainly includes three aspects: bridge collision risk assessment, bridge collision response analysis methods, and bridge collision avoidance measures and design. There is more research on the first two aspects, but less research on bridge collision avoidance measures. The "Specifications for Collision Resistance Design of Highway Bridges" broadly classifies bridge collision avoidance measures into two types: active collision avoidance measures and passive collision avoidance measures. Traditional active bridge collision avoidance generally uses Vessel Traffic Management Systems (VTS) and Automatic Identification Systems (AIS) to establish bridge collision warnings to guide vessel navigation, and uses video surveillance systems (CCTV) to monitor the situation in the bridge area. The aim is to improve the safety and efficiency of bridges and water traffic. Through data integration and decision support systems, it effectively reduces collision risks and ensures the safe operation of vessel traffic. However, VTS and AIS require the installation of a large amount of expensive equipment, resulting in high costs, while traditional CCTV cannot achieve active warning functions.

[0005] Passive collision avoidance systems are facilities designed to reduce impact force and mitigate damage when a ship has already collided with or is about to collide with a bridge pier. They can be broadly categorized into direct and indirect structures based on whether the ship will actually impact the pier. The primary target of these systems is the bridge pier itself. As a critical component of the bridge structure, the pier not only bears the vertical and horizontal forces transmitted from the superstructure of adjacent spans, but also experiences wind forces. Piers located in rivers also bear the pressure of flowing water and the potential impact forces from ice-loaded vessels or drifting debris. The reliability of the piers plays a crucial role in the safe use of the entire bridge. When a ship collides with the superstructure of a bridge, the main beams and the lower part of the arches are typically impacted, while the bow, mast, deckhouse, and other hull structures usually collide with the ship, resulting in relatively smaller impact forces. However, when a ship directly contacts a bridge pier, a tremendous impact force is generated in a very short time. This impact force can cause structural damage to the impact area and even lead to the serious consequence of the pier collapsing. Although various passive collision avoidance facilities have been proposed and applied, their actual application effects are inconsistent due to significant differences in their structure, protection capabilities, maintenance requirements, economics, and impact on the waterway environment.

[0006] In conclusion, bridge structural damage caused by ship collisions is increasing, and the catastrophic consequences are undeniable. These accidents not only severely damage bridge structures but can also lead to enormous economic losses and social impacts. Over the past few decades, ship-bridge collisions have become a focal point of international academic and engineering concern, highlighting the growing urgency and importance of research in this area. Summary of the Invention

[0007] The purpose of this invention is to provide a logarithmic calculation system for cable-stayed structures based on different fortification targets, aiming to solve the technical problems of low efficiency and error-proneness of traditional cable-stayed calculation methods, as well as the inconvenience of large-scale professional software for field application.

[0008] To achieve the objectives of this invention, the following technical solution is adopted:

[0009] A system for calculating the logarithmic addition of cables to cable-stayed structures based on different fortification targets includes:

[0010] The first model construction module is used to construct the cable-pier combined structure model and the cable-pier combined structure mechanical model;

[0011] The first calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of a single span with cables, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0012] The second calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of two-span cable addition, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0013] The third calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of three-span cable addition, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0014] The fourth calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of N spans with cables, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0015] The second model construction and result output module is used to construct an assessment model of the bearing capacity of the impacted pier. It uses the top displacement and bottom bending moment of the impacted pier as assessment indicators. The output results include the top displacement and bottom bending moment of the impacted pier, and generate a curve on the interface showing the relationship between the logarithm of the impacted pier and the displacement reduction or the logarithm of the impacted pier and the bending moment reduction.

[0016] As a further explanation of the present invention, in the first model construction module, parameters of the bridge substructure need to be input to construct the cable-pier combined structure model. The parameters of the bridge substructure include: the calculated span L of the beam bridge, the height h of the impact-affected pier, and the elastic modulus E of the concrete used for the pier. P Moment of inertia I of the pier's bending section P And the elastic modulus E of the reinforcing cable. S .

[0017] As a further explanation of the present invention, in the first model construction module, action parameters need to be input to construct a mechanical model of the cable-pier combined structure under ship collision. The action parameters include: the relative height position A of the ship impact point (the ratio of the distance from the impact point to the pier bottom to the pier height), and the magnitude F of the design impact force. X .

[0018] As a further explanation of the present invention, the built-in calculation formula in the first calculation module includes:

[0019] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0020] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P=3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P ΔU is the moment of inertia of the pier's bending section, h is the height of the pier being impacted, and ΔU is the longitudinal displacement of the pier top.

[0021] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0022] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P denoted as the moment of inertia of the pier's bending section, h as the height of the pier being impacted, A as the relative height of the point of impact, and ΔM as the reduction in bending moment at the pier's base.

[0023] As a further explanation of the present invention, the built-in calculation formula in the second calculation module includes:

[0024] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0025]

[0026] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P ΔU is the moment of inertia of the pier's bending section, h is the height of the pier being impacted, and ΔU is the longitudinal displacement of the pier top.

[0027] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0028]

[0029] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier.P I represents the elastic modulus of the concrete used for the bridge piers. P denoted as the moment of inertia of the pier's bending section, h as the height of the pier being impacted, A as the relative height of the point of impact, and ΔM as the reduction in bending moment at the pier's base.

[0030] As a further explanation of the present invention, the built-in calculation formula in the third calculation module includes:

[0031] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0032]

[0033] in,

[0034]

[0035] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P Let be the moment of inertia of the pier's bending section, h be the height of the pier being impacted, ΔU be the longitudinal displacement of the pier top of the impacted pier, i be an imaginary number in mathematics, and f1 be an introduced imaginary function expression to simplify the writing of the calculation formula.

[0036] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0037]

[0038] in,

[0039]

[0040] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P Let f1 be the moment of inertia of the pier's bending section, h be the height of the pier being impacted, A be the relative height of the point of impact, ΔM be the reduction in bending moment at the pier's base, and f2 be a hypothetical function expression introduced to simplify the calculation.

[0041] As a further explanation of the present invention, the fourth calculation module is an extension module for four or more spans of Caucasus. By inputting the required number of Caucasus spans N into this module, where N is greater than or equal to 4, the system will automatically call and copy the basic calculation logic and algorithm to generate a temporary N-span Caucasus calculation module to perform the same calculation and output process as the preset module.

[0042] As a further explanation of the present invention, the second model construction and result output module will automatically perform the following operations after each calculation module is triggered and completes a full iterative calculation:

[0043] a) Dynamically generate and plot the relationship curve between the logarithm of cable tension and the displacement reduction or the relationship curve between the logarithm of cable tension and the bending moment reduction on the interface; the curve intuitively shows the percentage decrease in displacement (bending moment) of the key section of the pier as the required total cable force increases, providing designers with an intuitive basis for judgment.

[0044] b) To facilitate the generation of detailed calculation reports, the program extracts discrete data points (including cable pairs, total cable force, moment reduction, etc.) from continuous calculation results at fixed intervals (e.g., every 5% moment reduction) and writes these discrete results into a temporary cache table or data structure.

[0045] c) Users select the appropriate Caesar logarithm based on their specific needs.

[0046] Advantages of this invention:

[0047] This invention enables rapid on-site input of basic bridge parameters, automated incremental cable addition simulation calculations, and real-time visualization monitoring and output of key results (such as the relationship between cable force and displacement or bending moment reduction). This significantly improves the design efficiency of cable addition schemes in bridge reinforcement projects and provides a fast and reliable scientific basis for on-site decision-making, ultimately ensuring structural safety. Attached Figure Description

[0048] Figure 1 This is a simplified force diagram of a single span of the Caspian River.

[0049] Figure 2 This is a simplified force diagram of the two-span Caesar.

[0050] Figure 3 Here is a simplified force diagram for n spans of the Caesar.

[0051] Figure 4 This is a simplified schematic diagram of the equivalent spring stiffness of the longitudinal deformation of the top of the impacted pier and adjacent piers after the four-span cable-stayed bridge is added.

[0052] Figure 5 This is a flowchart for solving the equivalent spring stiffness of the longitudinal deformation at the top of the impacted pier after the four-span cable-stayed bridge is added. Detailed Implementation

[0053] The invention will be further described below with reference to the accompanying drawings.

[0054] Example: A system for calculating the logarithmic value of cable-stayed piers in a combined cable-stayed structure based on different fortification targets, comprising:

[0055] The first model construction module is used to construct the cable-pier combined structure model and the cable-pier combined structure mechanical model;

[0056] The first calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of a single span with cables, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0057] The second calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of two-span cable addition, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0058] The third calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of three-span cable addition, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0059] The fourth calculation module is used to calculate the model function of the cable-pier combined structural mechanics model. Under the condition of N spans with cables, a system of linear algebraic equations is constructed with the logarithm of cable force as the undetermined parameter. By solving the system of equations, the logarithmic distribution of cable force is obtained, and then the displacement at the top of the pier and the bending moment at the bottom of the pier are calculated.

[0060] The second model construction and result output module is used to construct an assessment model of the bearing capacity of the impacted pier. It uses the top displacement and bottom bending moment of the impacted pier as assessment indicators. The output results include the top displacement and bottom bending moment of the impacted pier, and generate a curve on the interface showing the relationship between the logarithm of the impacted pier and the displacement reduction or the logarithm of the impacted pier and the bending moment reduction.

[0061] Further explanation of this embodiment: In the first model construction module, parameters of the bridge substructure need to be input to construct the cable-pier combined structure model. The parameters of the bridge substructure include: the calculated span L of the beam bridge, the height h of the impact-affected pier, and the elastic modulus E of the concrete used for the pier. P Moment of inertia I of the pier's bending section P And the elastic modulus E of the reinforcing cable. S .

[0062] Further explanation of this embodiment: In the first model construction module, action parameters need to be input to construct the mechanical model of the cable-pier combined structure under ship collision. The action parameters include: the relative height position A of the ship impact point (the ratio of the distance from the impact point to the pier bottom to the pier height), and the magnitude F of the design impact force. X .

[0063] In this embodiment, each computing module integrates an automated iterative algorithm, the logic of which is as follows:

[0064] 1) Set a target range for the reduction in bending moment (displacement), for example, from 0% to 50%, and define an iteration step size, for example, 1%.

[0065] 2) The program automatically performs iterative calculations based on a preset simplified mechanical model, according to the number of reinforcement spans selected by the user (e.g., N spans). The core of the iteration is to gradually increase the number of symmetrically arranged cable pairs (e.g., starting from 1 pair, denoted as n, and increasing by 1 pair each time), and for each value of n, calculate the total cable force required to achieve the bending moment reduction target of the current iteration step.

[0066] 3) Based on the calculated cable force T, the unloading effect on the pier is calculated, and then the final bending moment and bending moment σ of the pier under the original impact force F after the cable force is applied are obtained.

[0067] 4) Determine whether the current actual bending moment reduction has reached or exceeded the preset upper limit (e.g., 50%). If so, the iterative calculation of this module will automatically stop, and the current state will be marked as "limit reduction point", indicating the theoretically achievable maximum bending moment reduction under this reinforcement span.

[0068] Taking a beam bridge as an example, the acquired parameters are written into the module. The built-in algorithm uses a loop with a target moment reduction of 0% as the starting point, 50% as the ending point, and a step size of 1%. If more spans need to be added, the system's "More Spans" option can be used, inputting the required number of spans N. The first to fourth calculation modules are triggered sequentially. Each time a module is triggered, the system automatically outputs the corresponding "logarithm of added cable - displacement / moment reduction" relationship curve and extracts discrete results at 5% intervals, writing them to a temporary cache table. When the calculation result of any span module reaches a moment reduction ≥ 50%, the module automatically stops incrementing and marks it as the "limit reduction point".

[0069] Furthermore, the built-in calculation formula in the first calculation module includes:

[0070] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0071] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable.P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P ΔU is the moment of inertia of the pier's bending section, h is the height of the pier being impacted, and ΔU is the longitudinal displacement of the pier top.

[0072] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0073] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P denoted as the moment of inertia of the pier's bending section, h as the height of the pier being impacted, A as the relative height of the point of impact, and ΔM as the reduction in bending moment at the pier's base.

[0074] The derivation process of the above built-in calculation formula is as follows:

[0075] 1. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on different cable spans. eq1 .

[0076] Given that the stiffness of a single cable is K S =E S A S / L, the stiffness of a single-column pier is K P =3E P I P / h 3 After adding one span of cable, the spring stiffness at the top of pier #1 is:

[0077]

[0078] 2. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on the reduction in longitudinal bridge displacement ΔU at the pier top (reduction in bending moment at the pier bottom ΔM). eq1 .

[0079] (1) Given that the longitudinal displacement ΔU of the pier top of the impacted pier before and after the cable is added:

[0080]

[0081] The above formula can also be expressed as:

[0082]

[0083] (2) The decrease in bending moment at the bottom of the impacted pier before and after the impact is ΔM:

[0084]

[0085] The above formula can also be expressed as:

[0086]

[0087] 3. Combine the equations from steps 1 and 2, given A, ΔU, ΔM, and K. P Then, the equivalent spring stiffness K can be solved in reverse. S Furthermore, given the cable stiffness, the minimum number of cable pairs required for inverse solving is...

[0088] Furthermore, the built-in calculation formulas in the second calculation module include:

[0089] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0090]

[0091] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P ΔU is the moment of inertia of the pier's bending section, h is the height of the pier being impacted, and ΔU is the longitudinal displacement of the pier top.

[0092] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0093]

[0094] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P denoted as the moment of inertia of the pier's bending section, h as the height of the pier being impacted, A as the relative height of the point of impact, and ΔM as the reduction in bending moment at the pier's base.

[0095] The derivation process of the above built-in calculation formula is as follows:

[0096] 1. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on different cable spans. eq1 .

[0097] Given that the stiffness of a single cable is K S =E S A S / L, the stiffness of a single-column pier is K P =3E P I P / h 3 After adding two spans of cable, the spring stiffness at the top of pier #1 is:

[0098]

[0099] 2. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on the reduction in longitudinal bridge displacement ΔU at the pier top (reduction in bending moment at the pier bottom ΔM). eq1 .

[0100] (1) Given that the longitudinal displacement ΔU of the pier top of the impacted pier before and after the cable is added:

[0101]

[0102] The above formula can also be expressed as:

[0103]

[0104] (2) The decrease in bending moment at the bottom of the impacted pier before and after the impact is ΔM:

[0105]

[0106] The above formula can also be expressed as:

[0107]

[0108] 3. Combine the equations from steps 1 and 2, given A, ΔU, ΔM, and K. P Then, the equivalent spring stiffness K can be solved in reverse. S Furthermore, given the cable stiffness, the minimum number of cable pairs required for inverse solving is...

[0109] Furthermore, the built-in calculation formula in the third calculation module includes:

[0110] Based on the longitudinal displacement reduction at the pier top, the following formula is used for calculating the cable logarithm:

[0111]

[0112] in,

[0113]

[0114] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P Let be the moment of inertia of the pier's bending section, h be the height of the pier being impacted, ΔU be the longitudinal displacement of the pier top of the impacted pier, i be an imaginary number in mathematics, and f1 be an introduced imaginary function expression to simplify the writing of the calculation formula.

[0115] Based on the logarithmic calculation formula for the reduction of bending moment at the pier base:

[0116]

[0117] in,

[0118]

[0119] In the formula, n is the Gaussian logarithm; L is the calculated span of the beam bridge; E S K is the elastic modulus of the cable. P =3E P I P / h 3 E represents the stiffness of the bridge pier. P I represents the elastic modulus of the concrete used for the bridge piers. P Let f1 be the moment of inertia of the pier's bending section, h be the height of the pier being impacted, A be the relative height of the point of impact, ΔM be the reduction in bending moment at the pier's base, and f2 be a hypothetical function expression introduced to simplify the calculation.

[0120] The derivation process of the above built-in calculation formula is as follows:

[0121] 1. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on different cable spans. eq1 .

[0122] Given that the stiffness of a single cable is K S =E S A S / L, the stiffness of a single-column pier is K P =3E P I P / h 3 After adding 3 spans of cable, the spring stiffness at the top of pier #1 is:

[0123]

[0124] 2. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on the reduction in longitudinal bridge displacement ΔU at the pier top (reduction in bending moment at the pier bottom ΔM). eq1 .

[0125] (1) Given that the longitudinal displacement ΔU of the pier top of the impacted pier before and after the cable is added:

[0126]

[0127] The above formula can also be expressed as:

[0128]

[0129] (2) The decrease in bending moment at the bottom of the impacted pier before and after the impact is ΔM:

[0130]

[0131] The above formula can also be expressed as:

[0132]

[0133] 3. Combine the equations from steps 1 and 2, given A, ΔU, ΔM, and K. P Then, the equivalent spring stiffness K can be solved in reverse. S Furthermore, given the cable stiffness, the minimum number of cable pairs required for inverse solving is...

[0134] Furthermore, the fourth calculation module is an extension module for Caucasus with four or more spans. By inputting the required number of Caucasus spans N into this module, where N is greater than or equal to 4, the system will automatically call and copy the basic calculation logic and algorithm to generate a temporary N-span Caucasus calculation module to perform the same calculation and output process as the preset module.

[0135] For N spans (any span) of the Caesar, the required Caesar logarithm can be calculated using the following steps:

[0136] 1. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on different cable spans. eq1 .

[0137] Given that the stiffness of a single cable is K S =E S A S / L, the stiffness of a single-column pier is K P =3E P I P / h 3 After N spans of cable, the equivalent spring stiffness at the top of piers n#, (n-1)#, ..., 1# after simplifying the springs is: ...then the equivalent spring stiffness K of the longitudinal deformation at the top of the impact pier. eq1 for:

[0138] After N spans the Caspian Sea, the structural mechanics diagram proposed in this invention is as follows: Figure 3 As shown, the equivalent spring stiffness at the top of piers n#, (n-1)#, ..., 1# after simplifying the spring is:

[0139]

[0140] The above equation is a progressive relation. It can be further expressed as:

[0141]

[0142] Taking the four-span Caucasus as an example (n=4): K eq1 K represents the equivalent spring stiffness of the longitudinal deformation at the top of the impacted pier (equivalent spring stiffness of the longitudinal deformation at the top of pier #1). eq2 K represents the equivalent stiffness of the adjacent piers to the impacted pier (equivalent spring stiffness of the longitudinal deformation at the top of pier #2). eq3 k represents the equivalent stiffness of the adjacent piers to the impacted pier (equivalent spring stiffness of the longitudinal deformation at the top of pier #3). eq4 The equivalent stiffness of the pier adjacent to the impacted pier (equivalent spring stiffness of the longitudinal deformation at the top of pier #4), such as Figure 4 As shown.

[0143] Equivalent spring stiffness K at the top of the four-span cableway pier eq1 The solution process is as follows: Figure 5 As shown. The stiffness of each spring is then:

[0144]

[0145] Finally, the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier can be obtained. eq1 .

[0146] 2. Determine the equivalent spring stiffness K of the longitudinal deformation at the top of the impacted pier based on the reduction in longitudinal bridge displacement ΔU at the pier top (reduction in bending moment at the pier bottom ΔM). eq1 .

[0147] (1) Given that the longitudinal displacement ΔU of the pier top of the impacted pier before and after the cable is added:

[0148]

[0149] The above formula can also be expressed as:

[0150]

[0151] (2) The decrease in bending moment at the bottom of the impacted pier before and after the impact is ΔM:

[0152]

[0153] The above formula can also be expressed as:

[0154]

[0155] 3. Combine the equations from steps 1 and 2, given A, ΔM, and K. P Then, the equivalent spring stiffness K can be solved in reverse. S Furthermore, given the cable stiffness, the minimum number of cable pairs required for inverse solving is...

[0156] In a further explanation of this embodiment, the second model construction and result output module will automatically perform the following operations after each calculation module is triggered and completes a full iterative calculation:

[0157] a) Dynamically generate and plot the relationship curve between the logarithm of cable tension and the displacement reduction or the relationship curve between the logarithm of cable tension and the bending moment reduction on the interface; the curve intuitively shows the percentage decrease in displacement (bending moment) of the key section of the pier as the required total cable force increases, providing designers with an intuitive basis for judgment.

[0158] b) To facilitate the generation of detailed calculation reports, the program extracts discrete data points (including cable pairs, total cable force, moment reduction, etc.) from continuous calculation results at fixed intervals (e.g., every 5% moment reduction) and writes these discrete results into a temporary cache table or data structure.

[0159] c) Users select the appropriate Caesar logarithm based on their specific needs.

[0160] Taking a beam bridge as an example, the bridge span is L = 40m, the pier height is h = 25m, the pier cross-section is a solid rectangle with dimensions b × h = 5m × 2m, the pier type is a single-column pier, and the concrete strength grade is C30. Assume that pier #1 is struck by a ship with an impact force F. X =5000kN, the distance from the impact point to the bottom of the pier is b = 0.7hm, so E can be obtained. P =3×10 7 kN / m 2 I P =10 / 3m 4 A = 0.7, E S =1.95×10 8 kN / m 2 .

[0161] The output results are shown in the table below:

[0162] Target bending moment reduction Δσ (%) <![CDATA[n1 (one span)]]> <![CDATA[n2 (two - span)]]> <![CDATA[n3 (Three - span)]]> <![CDATA[n4 (Four spans)]]> 5 2 2 2 2 10 3 3 3 3 15 5 4 4 4 20 7 7 7 7 25 12 10 10 10 30 21 14 14 14 35 48 22 20 20 40 34 29 29 45 61 45 42 50 160 76 66

[0163] According to the table above, if the target reduction in bending moment ΔM is 20%, then the number of cable pairs required for the first, second, third, and fourth spans is 7, 7, 7, and 7, respectively.

[0164] If the target reduction in bending moment ΔM is 30%, then the number of cable pairs required for the first, second, third, and fourth spans are 21, 14, 14, and 14, respectively.

Claims

1. A cable-pylon combined structure cable force logarithm calculation system based on different fortification targets, characterized by The method comprises the following steps: A first model construction module is used to construct a cable-pier joint structure model and a cable-pier joint structure mechanical model; A first calculation module is used to calculate the model function of the cable-pier joint structure mechanical model, set in the working condition of one-span cable, construct a linear algebraic equation group with the logarithm of cable force as the undetermined parameter, solve the equation group to obtain the logarithm distribution of cable force, and further calculate the pier top displacement and pier bottom bending moment of the struck pier; A second calculation module is used to calculate the model function of the cable-pier joint structure mechanical model, set in the working condition of two-span cable, construct a linear algebraic equation group with the logarithm of cable force as the undetermined parameter, solve the equation group to obtain the logarithm distribution of cable force, and further calculate the pier top displacement and pier bottom bending moment of the struck pier; A third calculation module is used to calculate the model function of the cable-pier joint structure mechanical model, set in the working condition of three-span cable, construct a linear algebraic equation group with the logarithm of cable force as the undetermined parameter, solve the equation group to obtain the logarithm distribution of cable force, and further calculate the pier top displacement and pier bottom bending moment of the struck pier; A fourth calculation module is used to calculate the model function of the cable-pier joint structure mechanical model, set in the working condition of N-span cable, construct a linear algebraic equation group with the logarithm of cable force as the undetermined parameter, solve the equation group to obtain the logarithm distribution of cable force, and further calculate the pier top displacement and pier bottom bending moment of the struck pier; A second model construction and result output module is used to construct a struck pier bearing capacity evaluation model, take the pier top displacement and pier bottom bending moment of the struck pier as the evaluation indexes, and output the results including the pier top displacement and pier bottom bending moment of the struck pier, and generate a cable logarithm-displacement reduction amplitude or cable logarithm-bending moment reduction amplitude relationship curve diagram on the interface.

2. The cable-pylon combined structure cable force logarithm calculation system based on different security targets according to claim 1, characterized in that: In the first model building module, parameters of the bridge substructure are required to build the cable-pier combined structure model, the parameters of the bridge substructure including: the calculated span L of the beam bridge, the height h of the impacted pier, the elastic modulus E of the concrete used by the pier P , the moment of inertia I of the bending section of the pier P , and the elastic modulus E of the reinforcing cable S .

3. The system for calculating the logarithmic addition of cables to a cable-stayed pier combined structure based on different fortification targets, as described in claim 1, is characterized in that: In the first model construction module, the action parameters need to be input to construct the cable-pier joint structure mechanical model under the action of ship collision, and the action parameters include: the relative height position A of the ship collision point, the size F of the designed collision force X .

4. The cable-pylon combined structure cable force logarithm calculation system based on different security targets according to claim 1, characterized in that: The built-in calculation formula in the first calculation module comprises: Based on the pier top longitudinal bridge displacement drop under the calculation formula of logarithmic calculation of cable: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the modulus of elasticity of the cable; K P = 3E P I P / h 3 is the stiffness of the bridge pier, E P is the modulus of elasticity of the concrete used in the bridge pier, I P is the moment of inertia of the flexural section of the bridge pier, h is the height of the struck bridge pier; ΔU is the reduction in the longitudinal displacement of the pier top of the struck pier. Based on the pier bottom bending moment drop under the calculation formula of the cable: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the elastic modulus of the cable; K P = 3E P I P / h 3 is the stiffness of the pier, E P is the elastic modulus of the concrete used in the pier, I P is the moment of inertia of the flexural section of the pier, h is the height of the struck pier; A is the relative height position of the striking point of the ship; ΔM is the pier bottom moment reduction of the struck pier.

5. The cable-stayed tower combined structure plus cable-stayed tower based on different security targets calculation system according to claim 1, characterized in that: The built-in calculation formula in the second calculation module comprises: The cable logarithm calculation formula based on the pier top longitudinal bridge direction displacement reduction amplitude: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the modulus of elasticity of the cable; K P = 3E P I P / h 3 is the stiffness of the pier, E P is the modulus of elasticity of the concrete used in the pier, I P is the moment of inertia of the flexural section of the pier, and h is the height of the struck pier; ΔU is the reduction in the longitudinal displacement at the top of the struck pier. The cable logarithm calculation formula based on the pier bottom bending moment reduction amplitude: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the elastic modulus of the cable; K P = 3E P I P / h 3 is the stiffness of the pier, E P is the elastic modulus of the concrete used in the pier, I P is the moment of inertia of the flexural section of the pier, h is the height of the struck pier; A is the relative height position of the striking point of the ship; ΔM is the pier bottom moment reduction of the struck pier.

6. The cable-pylon combined structure cable force logarithm calculation system based on different security targets according to claim 1, characterized in that: The built-in calculation formula in the third calculation module comprises: The cable logarithm calculation formula based on the pier top longitudinal bridge direction displacement reduction amplitude: The cable logarithm calculation formula based on the pier bottom bending moment reduction amplitude: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the modulus of elasticity of the cable; K P = 3E P I P / h 3 is the stiffness of the bridge pier, E P is the modulus of elasticity of the concrete used in the bridge pier, I P is the moment of inertia of the flexural section of the bridge pier, h is the height of the struck bridge pier; ΔU is the reduction in the longitudinal displacement of the pier top of the struck pier; i is the imaginary number in mathematics; f1 is a virtual function expression introduced to simplify the writing of the calculation formula; The fourth calculation module is an extension module for more than four-span cable, by inputting the required cable span number N in the module, N is greater than or equal to 4, the system will automatically call and copy the basic calculation logic and algorithm, generate a temporary N-span cable calculation module, and execute the same calculation and output process as the preset module. The second model construction and result output module will automatically perform the following operations when a calculation module is triggered and completes a complete iteration calculation: where n is the natural logarithm; L is the calculated span of the beam bridge; E S is the elastic modulus of the cable; K P = 3E P I P / h 3 is the stiffness of the pier, E P is the elastic modulus of the concrete used in the pier, I P is the moment of inertia of the flexural section of the pier, h is the height of the struck pier; A is the relative height position of the striking point of the ship; ΔM is the pier bottom moment reduction of the struck pier; f2 is a virtual function expression introduced to simplify the writing of the calculation formula.

7. The cable-stayed tower combined structure plus cable-stayed tower based on different security targets calculation system according to claim 1, characterized in that: a) dynamically generate and draw a cable logarithm-displacement reduction amplitude relationship curve diagram or a cable logarithm-bending moment reduction amplitude relationship curve diagram on the interface; 8. The cable-pylon combined structure cable force logarithm calculation system based on different security targets according to claim 1, characterized in that: b) in order to facilitate the generation of detailed calculation report, the program extracts discrete data points from continuous calculation results at fixed intervals, and writes these discrete results into a temporary buffer table or data structure. c) the user selects the corresponding cable logarithm according to specific needs. ​ ​

Images