Method for calculating cable force of cable-stayed bridge, electronic equipment and medium

Abstract

The invention provides a cable-stayed bridge cable force calculation method, electronic equipment and a medium. The method comprises the steps that a cable-stayed bridge structure finite element model is constructed; a construction stage load and an operation stage load are applied to the cable-stayed bridge structure; the stay cables are grouped according to the tensioning sequence of the stay cables; according to the difference value between the structural responses before and after each group of stay cables are tensioned, an influence matrix is constructed; and solving the cable force adjustment value of each group of stay cables corresponding to the minimum value of the optimization objective function under the condition of meeting the control condition, and adding the initial cable force to the cable force adjustment value of each group of stay cables to obtain the cable force of each group of stay cables. The limitation that a conventional cable-stayed bridge cable adjusting method does not control the stress state of the construction stage is overcome, and the influence matrix and the control conditions are adopted to control the structural stress of the construction state and the operation state at the same time; the method for calculating the influence matrix through the structure response difference value before and after the construction stage is adopted, and the cable-stayed bridge cable force design accuracy and precision are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering, and particularly relates to a method for calculating cable forces of a cable-stayed bridge, an electronic device, and a medium. Background Art

[0002] A cable-stayed bridge is a composite structure system composed of three basic components: a tower, a girder, and cables. The cables act as several elastic supports added within the main girder span, thus greatly reducing the bending moment in the girder and the girder size, significantly increasing the bridge's spanning capacity, and is commonly used in long-span bridge structures. Due to the adjustability of the stay cables, the cable-stayed bridge can change the internal force distribution of the structure by adjusting the cable forces of the stay cables. Therefore, the cable forces of the stay cables play a decisive role in the stress and deformation of the structure.

[0003] Currently, the commonly used method for determining the cable forces of a cable-stayed bridge is as follows: First, a calculation model without considering the construction stage is established, and methods such as the zero-displacement method and minimum moment are used to calculate and determine the cable forces corresponding to the reasonable completed bridge state. Then, a calculation model considering the construction stage is established, and methods such as the backward analysis method, the forward iteration method, and the stress-free state method are used to obtain the cable forces during the construction stage. This process method has significant drawbacks: 1) Difficult to close the calculation. Affected by non-linear factors such as shrinkage creep and structural system changes, it is difficult to close the model of the construction stage simulated by the above methods with the model of the reasonable completed bridge state. Even if the cable force values can be closed, there will still be differences in the structural stress states. 2) The construction stage is not controlled. Since only the reasonable completed bridge state is considered and the reasonable construction state is not considered, the structural forces at each construction stage calculated based on the reasonable completed bridge state may not meet the specification requirements. 3) Low efficiency and poor accuracy. The cable force adjustment on the calculation model considering the construction stage requires manual correction of the cable forces and multiple trial calculations in the finite element software, with low efficiency, poor accuracy, being greatly affected by personal subjectivity, and prone to missing important control working conditions. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for calculating cable forces of a cable-stayed bridge, an electronic device, and a medium, which improve the design accuracy and precision of the cable forces of the cable-stayed bridge.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating cable forces of a cable-stayed bridge includes the following process:

[0007] Construct a finite element model of the cable-stayed bridge structure, where the cable-stayed bridge structure includes a main girder, a main tower, stay cables, and bearings;

[0008] Apply construction stage loads and operation stage loads to the cable-stayed bridge structure;

[0009] Group the stay cables according to the tensioning sequence of the stay cables;

[0010] Construct an influence matrix based on the difference between the structural responses before and after the tensioning of each group of stay cables.

[0011] Set control conditions and an optimization objective function, and solve for the cable force adjustment value of each group of stay cables corresponding to the minimum value of the optimization objective function under the condition of meeting the control conditions. Add the cable force adjustment value of each group of stay cables to the initial cable force to obtain the cable force of each group of stay cables.

[0012] The control condition expression is as follows:

[0013] {lb} ≤ [A]{ΔT} + {A 0} ≤ {ub}

[0014] The expression of the optimization objective function is as follows:

[0015] ||[A]{ΔT} + {A 0} - ({lb} + {ub}) / 2|| 2

[0016] where [A] is the influence matrix, {A 0} is the initial state of the structural response, {ΔT} is the cable force adjustment value, {ub} is the upper limit of the structural response, {lb} is the lower limit of the structural response; ‖‖ 2 represents the norm.

[0017] The present invention overcomes the limitation that the conventional cable adjustment method for cable-stayed bridges does not control the stress state during the construction stage, and uses the influence matrix and control conditions to simultaneously control the structural forces during the construction state and the operation state; the method of calculating the influence matrix by using the difference in structural responses before and after the construction stage (before and after the tensioning of the stay cables) is adopted, and the accuracy of the influence matrix is high, improving the accuracy and precision of the cable force design of the cable-stayed bridge.

[0018] Furthermore, the expression of the influence matrix is as follows:

[0019] [A] = {B 1 / T 1 ,…B i / T i ,…,B n / T n}, B i = D i - C i

[0020] where T i is the cable force of the i-th group of stay cables, n is the number of groups of stay cables, D i is the structural response after the tensioning of the i-th group of stay cables, and C i is the structural response before the tensioning of the i-th group of stay cables.

[0021] Further, the construction stage loads include the self-weight of the cable-stayed bridge and the load of the construction hanging basket; the operation stage loads include vehicle load, wind load, temperature load, frequent combination, and standard combination.

[0022] Further, the structural responses include the stress of the main girder, the stress of the main tower, the tension of the stay cables, the displacement of the main tower top, the reaction force of the bearing, the stress of the main girder and the main tower under the frequent combination, and the stress of the main girder and the main tower under the standard combination.

[0023] Based on the same inventive concept, the present invention also provides an electronic device, including:

[0024] One or more processors;

[0025] A memory, on which one or more programs are stored. When the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the steps of the method for calculating the cable force of the cable-stayed bridge.

[0026] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method for calculating the cable force of the cable-stayed bridge are implemented.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] The present invention overcomes the limitation that the conventional cable adjustment method for cable-stayed bridges does not control the stress state in the construction stage, and uses the influence matrix and control conditions to simultaneously control the structural forces in the construction state and the operation state; the method of calculating the influence matrix by using the difference in structural responses before and after the construction stage is fast, efficient, and has controllable accuracy, improving the accuracy and precision of the cable force design of the cable-stayed bridge.

[0029] After the cable adjustment process of the present invention is subjected to reasonable constraint conditions and optimization objectives, the cable force of the cable-stayed bridge obtained by solving can be directly used as the designed tension cable force without manual correction. Even if the subsequent structure and load change, the new tension cable force can be obtained quickly, saving the cable adjustment design cycle.

[0030] Through the target control of the whole process and all states of the cable-stayed bridge, it is easier to obtain a more reasonable structural stress state compared with the traditional cable adjustment method, which can effectively improve the structural safety reserve and reduce the project cost. Description of the Drawings

[0031] Figure 1 It is a schematic flow chart of the method for calculating the cable force of the cable-stayed bridge of the present invention;

[0032] Figure 2 It is a finite element model of the cable-stayed bridge according to an embodiment of the present invention;

[0033] Figure 3 The envelope diagram of the maximum compressive stress on the upper edge of the main girder under the standard combination of the cable-stayed bridge in the embodiment of the present invention;

[0034] Figure 4 The envelope diagram of the maximum compressive stress on the lower edge of the main girder under the standard combination of the cable-stayed bridge in the embodiment of the present invention;

[0035] Figure 5 The envelope diagram of the minimum compressive stress on the upper edge of the main girder under the frequent combination of the cable-stayed bridge in the embodiment of the present invention;

[0036] Figure 6 The envelope diagram of the minimum compressive stress on the lower edge of the main girder under the frequent combination of the cable-stayed bridge in the embodiment of the present invention. Detailed implementation manners

[0037] The present invention will be described in detail below with reference to embodiments. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. For the convenience of description, words such as "upper", "lower", "left", and "right" in the following text only represent the same directions as the upper, lower, left, and right directions of the drawings themselves, and do not limit the structure.

[0038] Embodiment 1

[0039] As Figure 1 shown, the calculation method of the cable forces of the cable-stayed bridge in this embodiment includes the following process:

[0040] Step 1: Establish a full-bridge finite element model considering the construction stage.

[0041] In this step, a full-bridge finite element model considering the construction stage needs to be established. The finite element model includes structures such as the main girder, main tower, stay cables, and bearings of the cable-stayed bridge.

[0042] For the construction stage with stay cable tensioning, the following requirements are as follows: Group the stay cables according to the stay cable tensioning sequence. The cable forces of each group of stay cables are the same. Set the tensioning of a group of stay cables as a construction stage. It is recorded that there are n groups of stay cables, corresponding to n construction stages.

[0043] Apply the construction stage loads according to the specifications and design requirements. The construction stage loads include the self-weight of the structure, the hanging basket load for construction, etc.

[0044] Apply the design loads in the operation stage such as vehicle loads, wind loads, and temperature loads according to the specifications, and generate the corresponding load combinations according to the specifications: frequent combination and standard combination (see the General Code for Design of Highway Bridges and Culverts JTG D60-2015).

[0045] Set the initial cable force (set to 1000 kN). The groups of stay cables are sorted according to the tensioning sequence. The expression of the cable force matrix of the cable-stayed bridge is as follows:

[0046] {T} = {T 1 ,…T i ,…,T n},

[0047] where T i is the cable force of the i-th group of stay cables. The cable force of the stay cable is the initial cable force plus the cable force adjustment value, and the cable force adjustment value is a variable. n is the number of groups of stay cables.

[0048] Step 2: Extract the influence matrix corresponding to the cable force and the structural response that needs to be controlled or optimized.

[0049] Structural responses during the construction stage: main girder stress, main tower stress, cable tension, main tower displacement, support reaction, etc.

[0050] Structural responses during the operation stage: main girder / main tower stress under the frequent combination, main girder / main tower stress under the standard combination, support reaction, cable force, etc.

[0051] For any structural response that needs to be controlled or optimized, it is only affected by the stay cable tensioning after the activation of the structure. Assume that the structure corresponding to a structural response is activated after the tensioning of m groups of stay cables. Let the incremental influence of the tensioning construction stage of the unit cable force of the (m + 1)-th group on the k-th structural response be denoted as e k(m+1) . Except for the stay cable tensioning construction stage, this structural response will be affected by other actions, denoted as e other , e other simultaneously includes non-linear factors associated with each stay cable tensioning construction stage, such as concrete shrinkage, creep, etc. Then, for the k-th structural response, it can be expressed as:

[0052] E k = T (m+1) e k(m+1) + T (m+2) e k(m+2) + … + T n e kn + e other

[0053] The influence coefficient of the cable force of the (m + 1)-th group of stay cables on the k-th structural response is E k . Taking the partial derivative with respect to the cable forces T (m+1) of the (m + 1) groups of stay cables, we can obtain:

[0054]

[0055] According to the principles of concrete shrinkage and creep, is generally much smaller than e k(m+1) . In order to extract the influence matrix more quickly and efficiently while ensuring accuracy, this embodiment ignores terms and adopts e k(m+1)As the influence coefficient of the cable force of the (m + 1)-th group of stay cables on the k-th structural response, according to the verification of the example, this method is fast, efficient and can ensure the calculation accuracy sufficiently.

[0056] Therefore, the extraction of the influence matrix can be simplified to the method of using the difference in structural responses before and after the construction stage (before and after the stay cable tensioning). The steps for extracting the influence matrix are as follows:

[0057] The structural response to be controlled or optimized corresponding to the construction stage after the tensioning of the i-th group of stay cables is denoted as: D i ={d 1i ,…d ji ,…,d ki},

[0058] where d ji is the j-th structural response after the tensioning of the i-th group of stay cables, and k is the number of structural responses.

[0059] The structural response to be controlled or optimized corresponding to the construction stage before the tensioning of the i-th group of stay cables is denoted as:

[0060] C i ={c 1i ,…c ji ,…,c ki},

[0061] where c ji is the j-th structural response before the tensioning of the i-th group of stay cables.

[0062] Then the structural response influence vector corresponding to the i-th group of stay cables is denoted as: B i =D i -C i .

[0063] The influence matrix corresponding to the stay cable force and the structural response to be controlled or optimized is denoted as:

[0064] [A]={B 1 / T 1 ,…B i / T i ,…,B n / T n}

[0065] Step 3: Determine the control conditions according to the specification requirements and the experience of similar projects.

[0066] Control conditions: Determine the control conditions according to the specification requirements and the experience of similar projects. For example, the stress control condition adopts the specification limit value, the support reaction force is controlled to only bear pressure and not tension, the upper and lower limits of the cable force and the difference between adjacent cable forces, etc.

[0067] The initial state of the structural response is denoted as {A0}, the upper limit of the structural response is denoted as {ub}, the lower limit of the structural response is denoted as {lb}, and the cable force adjustment value of the stay cable is denoted as {ΔT}. Then the control condition equation is:

[0068] {lb} ≤ [A]{ΔT} + {A 0} ≤ {ub}

[0069] Step 4, determine the optimization objective.

[0070] The optimization objective is that the structural response approximates the median of the upper limit {ub} and the lower limit {lb}, so as to maximize the safety surplus of the structural response and minimize the cost. That is, the optimization objective function is:

[0071] ||[A]{ΔT} + {A 0} - ({lb} + {ub}) / 2|| 2

[0072] where, ‖‖ 2 represents the norm.

[0073] Step 5, optimize and solve the cable force of the cable-stayed bridge. Using the method of mathematical programming to solve (a special mathematical calculation software can be used, such as Mathematica software or the linprog function in matlab), with {ΔT} as the variable, solve the situation where {lb} ≤ [A]{ΔT} + {A 0} ≤ {ub}, ||[A]{ΔT} + {A 0} - ({lb} + {ub}) / 2|| 2 The minimum value of the corresponding cable force adjustment value of each stay cable, and add the cable force adjustment value of each stay cable to the initial cable force to obtain the cable force of each stay cable.

[0074] Step 6, substitute the solved cable force of the stay cable into the finite element model for recalculation, and check the stress state of the cable-stayed bridge. If the control conditions in Step 3 can be satisfied, the cable force value determined in Step 5 is the reasonable cable force value of the cable-stayed bridge. If not, execute Step 2, Step 5, and Step 6.

[0075] The method of this embodiment overcomes the limitation that the conventional cable adjustment method of the cable-stayed bridge does not control the stress state during the construction stage, and uses the influence matrix and constraint equations to control the structural stress during both the construction state and the operation state at the same time.

[0076] Using the method of calculating the influence matrix by the difference of the structural responses in the front and back construction stages, the extraction of the influence matrix is fast, efficient and the accuracy is controllable.

[0077] After setting reasonable constraints and reasonable goals in the cable adjustment process, the cable tension can be directly used as the designed cable tension after being optimized and solved by the mathematical programming method without manual correction. Even if the subsequent structure and load change, the new cable tension can be obtained quickly by using the method of this embodiment. The entire cable adjustment technical solution has the characteristics of being procedural, automated, and intelligent, saving the cable adjustment design cycle.

[0078] Through the target control of the whole process and all states of the cable-stayed bridge, it is easier to obtain a more reasonable structural stress state compared with the traditional cable adjustment method, which can effectively improve the structural safety reserve and reduce the project cost.

[0079] Embodiment 2

[0080] In this embodiment, the cable forces are calculated based on a certain bridge. The bridge span layout is (74 + 185 + 84) m, which is a concrete cable-stayed bridge with double towers, three spans, and double cable planes in the middle.

[0081] A finite element model of the cable-stayed bridge was established according to the preliminary structural dimensions, as Figure 2 , in which the main girder and the main tower are simulated by beam elements, and the stay cables are simulated by truss elements. There are a total of 42 pairs of stay cables, and 248 elements and 261 nodes are established for the whole bridge.

[0082] A total of 52 construction stages are established in the finite element model of the cable-stayed bridge, and each tensioning of the stay cables is set as a construction stage.

[0083] According to the code requirements, gradient temperature rise, gradient temperature drop, overall temperature rise, overall temperature drop, cable temperature rise, cable temperature drop, longitudinal temperature rise of the main tower, longitudinal temperature drop of the main tower, transverse temperature rise of the main tower, transverse temperature drop of the main tower, combined lateral wind load with vehicle, combined longitudinal wind load with vehicle, non-combined lateral wind load, non-combined longitudinal wind load, lane load, crowd load, support settlement, etc. are applied.

[0084] According to the mechanical characteristics of the concrete cable-stayed bridge, the concrete structure is mainly controlled by stress. The frequent combination envelope working conditions and the standard combination envelope working conditions are generated according to the code requirements.

[0085] The influence matrix is extracted by the method of the difference of structural responses before and after the construction stage. The control conditions are selected as follows:

[0086] To improve the calculation efficiency, the selection principle of the control conditions is to set as few control conditions as possible while ensuring that the structural check can meet the code requirements and has a certain safety margin. Therefore, all the code check items are not included in the control conditions of this embodiment, but only the key items that are most critical to the structural check are included.

[0087] The main beam is made of C55 concrete. According to the code requirements and considering a certain margin, the stress limits are set as follows: the compressive stress at the upper and lower edges of the main beam under the standard combination does not exceed 16.9 MPa, and the compressive stress reserve at the upper and lower edges of the main beam under the frequent combination is not less than 1 MPa. During the construction process, the stresses at the upper and lower edges of the main beam at any construction stage are: the compressive stress of the main beam is less than 32.4 MPa, and the tensile stress of the main beam is less than 2.65 MPa.

[0088] The main tower is made of C40 concrete. According to the code requirements and considering a certain margin, the stress limits are set as follows: the compressive stress under the standard combination does not exceed 18 MPa and no tensile stress appears.

[0089] Cable force control: The difference in cable forces between adjacent cables in the completed bridge state is less than 800 kN; the cable forces at the completion of the bridge are in the range of 2500 kN to 8900 kN; the minimum cable force at each construction stage is 2000 kN, and the maximum cable force during the operation stage is 9000 kN.

[0090] Support reaction force control: The support reaction force under the standard combination is greater than 0.

[0091] Main tower top displacement control: The top displacement of the main tower in the completed bridge state is a shoreward offset.

[0092] Use Mathematica software to solve the mathematical programming, with the variable {ΔT},

[0093] Solve for the minimum value of 0 {u b} when {lb} ≤ [A]{ΔT} + {A

[0094] ||[A]{ΔT} + {A 0}-({lb} + {ub}) / 2|| 2 is satisfied.

[0095] According to the calculation method of the cable forces of the cable-stayed bridge, after two rounds of calculations, the calculation results meet the control conditions. The main control condition, the stress result of the main beam, is as Figures 3 to 6 shown. The stress of the main beam is uniform and within the control conditions. Conduct a comprehensive check of the entire bridge according to the code. All the check results can meet the code requirements, that is, the calculated cable force value is the reasonable cable force value for the cable-stayed bridge.

[0096] Embodiment 3

[0097] This embodiment provides an electronic device, including:

[0098] One or more processors;

[0099] A memory, on which one or more programs are stored. When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the calculation method of the cable forces of the cable-stayed bridge.

[0100] In some implementations, the memory may be a high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk memory.

[0101] In other implementations, the processor may be various types of general-purpose processors such as a central processing unit (CPU) or a digital signal processor (DSP), which are not limited herein.

[0102] This embodiment provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the method for calculating the cable force of a cable-stayed bridge are implemented.

[0103] The content set forth in the above embodiments should be understood as that these embodiments are only used to illustrate the present invention more clearly, rather than to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification of the present invention by those skilled in the art all fall within the scope defined by the appended claims of this application.

Claims

1. A method for calculating the cable force of a cable-stayed bridge, characterized in that: The process includes: Construct a finite element model of a cable-stayed bridge structure, which includes main beams, main towers, cables, and supports; Apply construction phase loads and operation phase loads to the cable-stayed bridge structure; Group the cables according to their tensioning sequence; The influence matrix is ​​constructed based on the difference between the structural responses before and after tensioning of each group of stay cables; Set the control conditions and the optimization objective function, solve the cable force adjustment value of each group of inclined cables corresponding to the minimum value of the optimization objective function when the control conditions are met, and add the cable force adjustment value of each group of inclined cables to the initial cable force to obtain the cable force of each group of inclined cables; The control condition expression is as follows: {lb}≤[A]{ΔT}+{A0}≤{ub} The expression of the optimization objective function is as follows: ||[A]{ΔT}+{A0}-({lb}+ub}) / 2||2 Where [A] is the influence matrix, {A0} is the initial state of the structural response, {ΔT} is the cable force adjustment value, {ub} is the upper limit of the structural response, and {lb} is the lower limit of the structural response; ‖ ‖2 represents the norm.

2. The method for calculating the cable force of a cable-stayed bridge according to claim 1, characterized in that: The expression of the influence matrix is ​​as follows: [A]={B1 / T1,…B i / T i ,…,B n / T n },B i =D i -C i , Among them, T i is the cable force of the i-th group of inclined cables, n is the number of groups of inclined cables, D i is the structural response after the i-th group of cables are tensioned, C i is the structural response of the i-th group of cables before tensioning.

3. The method for calculating the cable force of a cable-stayed bridge according to claim 1, characterized in that: The loads during the construction phase include the deadweight of the cable-stayed bridge and the load of the construction basket; the loads during the operation phase include vehicle loads, wind loads, temperature loads, frequently encountered combinations, and standard combinations.

4. The method for calculating the cable force of a cable-stayed bridge according to claim 1, characterized in that: The structural responses include main beam stress, main tower stress, cable tension, main tower top displacement, support reaction, main beam stress and main tower stress under frequently encountered combinations, and main beam stress and main tower stress under standard combinations.

5. An electronic device, characterized in that: include: one or more processors; A memory having one or more programs stored thereon, which, when the one or more programs are executed by the one or more processors, enables the one or more processors to implement the steps of the method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that: The computer program is stored therein, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

Images