Continuous rigid frame aqueduct midspan pre-camber calculation method, system and equipment and medium

Abstract

The invention provides a continuous rigid frame aqueduct midspan pre-camber calculation method, system and device and a medium, and relates to the technical field of hydraulic engineering, the method comprises the following steps: dividing a continuous rigid frame aqueduct into a plurality of cantilever beam sections, and constructing a finite element mechanical model of the continuous rigid frame aqueduct based on the cantilever beam sections; according to the model, theoretical prediction of stress and deflection is conducted on each construction stage of the continuous rigid frame aqueduct, and a corresponding theoretical stress value and a corresponding theoretical deflection value are obtained; establishing a comprehensive objective function according to the theoretical stress value, the theoretical deflection value, the actual stress value and the actual deflection value; performing iterative inversion through the comprehensive objective function to obtain key parameters; and determining the pre-camber value of each computational node in the finite element mechanical model. According to the method, the finite element mechanical model is established, stress and deflection data actually measured in the construction process are introduced, the comprehensive objective function is constructed for iterative inversion, and key parameters of the model are dynamically corrected, so that the pre-camber calculation precision is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydraulic engineering, in particular to a continuous rigid structure aqueduct midspan pre-camber calculation method, system, device and medium. BACKGROUND

[0002] As a kind of hydraulic engineering canal system building, through the rigid consolidation technology of upper aqueduct structure and lower pier, the structure dead weight is effectively reduced, the longitudinal bending stiffness and transverse torsional stiffness are guaranteed.In the construction of continuous rigid structure aqueduct, pre-camber as the key factor affecting aqueduct closing precision, bridge line type and long-term use performance directly determines the accuracy of formwork elevation.Because continuous rigid structure aqueduct has not formed industry special system specification, pre-camber setting mainly refers to highway engineering related theory and specification.

[0003] In related technologies, due to the essential difference between continuous rigid structure aqueduct and highway bridge load characteristics, among them, the vehicle load of highway bridge has randomness, and continuous rigid structure aqueduct is in full load state in the form of design flow during service period.Therefore, pre-camber analysis and simulation by referring to highway engineering related theory and specification cannot reflect the load characteristics of hydraulic engineering aqueduct, resulting in large deviation of pre-camber calculation result and actual demand. SUMMARY

[0004] The problem solved by the present application is how to improve the calculation accuracy of pre-camber.

[0005] To solve the above problems, the present application provides a continuous rigid structure aqueduct midspan pre-camber calculation method, system, device and medium.

[0006] In the first aspect, a continuous rigid structure aqueduct midspan pre-camber calculation method of the present application comprises: Divide the continuous rigid structure aqueduct into multiple cantilever beam segments, and build a finite element mechanics model of the continuous rigid structure aqueduct based on the cantilever beam segments; According to the finite element mechanics model, the stress and deflection of each construction stage of the continuous rigid structure aqueduct are theoretically predicted, and the stress theoretical value and deflection theoretical value of each construction stage are obtained; Obtain the stress actual value and deflection actual value of the construction stage, and establish a comprehensive objective function according to the stress theoretical value, the deflection theoretical value and the stress actual value, the deflection actual value; Iterative inversion is carried out through the comprehensive objective function, and the key parameters are obtained; According to the key parameters, the midspan total pre-camber value of each calculation node in the finite element mechanics model is determined.

[0007] Optionally, the dividing the continuous rigid aqueduct into multiple cantilever beam segments and constructing the finite element mechanics model of the continuous rigid aqueduct based on the cantilever beam segments comprises: dividing the continuous rigid aqueduct into multiple cantilever beam segments according to construction drawings and design parameters of the continuous rigid aqueduct; discretizing each of the cantilever beam segments into corresponding beam units through finite element analysis; constructing the finite element mechanics model by taking the connecting points between the beam units as the calculation nodes.

[0008] Optionally, the theoretically predicting the stress and deflection of each construction stage of the continuous rigid aqueduct according to the finite element mechanics model to obtain stress theoretical values and deflection theoretical values of each construction stage comprises: dividing each of the cantilever beam segments in the finite element mechanics model into multiple construction stages, the construction stages including a formwork erection construction stage, a concrete pouring construction stage and a prestress tensioning construction stage; simulating the mechanical response of each of the construction stages under the action of structural self-weight and prestress load based on the finite element mechanics model to obtain construction conditions of each of the construction stages; determining the stress theoretical values and deflection theoretical values of each of the calculation nodes in the construction stage according to the construction conditions of the construction stage.

[0009] Optionally, the obtaining the stress actual values and deflection actual values of the construction stage comprises: monitoring through stress gauges and displacement gauges respectively arranged at preset stress measuring points and preset deflection measuring points of the continuous rigid aqueduct to obtain the stress actual values and the deflection actual values of the construction stage; wherein, the arrangement positions of the stress gauges and the displacement gauges are consistent with the positions of the corresponding calculation nodes in the finite element mechanics model.

[0010] Optionally, the establishing a comprehensive objective function according to the stress theoretical values, the deflection theoretical values, the stress actual values and the deflection actual values comprises: for each of the calculation nodes, determining a stress deviation ratio value according to the stress theoretical values and the stress actual values, and determining a deflection deviation ratio value according to the deflection theoretical values and the deflection actual values; performing absolute value summation on the stress deviation ratio value and the deflection deviation ratio value corresponding to each of the calculation nodes in combination with the number of the preset stress measuring points and the preset deflection measuring points to generate the comprehensive objective function.

[0011] Optionally, the obtaining the key parameters through iterative inversion of the comprehensive objective function comprises: setting an error threshold of the comprehensive objective function; performing parameter correction on the prestress loss parameters and the material mechanics parameters with the error threshold as a constraint condition, to obtain corrected prestress loss parameters and material mechanics parameters; substituting the corrected prestress loss parameters and the material mechanics parameters into the finite element mechanics model, and updating the stress theoretical value and the deflection theoretical value of the calculation node corresponding to each construction stage; determining an error value of the comprehensive objective function according to the updated stress theoretical value and deflection theoretical value, in combination with the stress actual value and the deflection actual value; if the error value is greater than the error threshold, returning to the step of performing parameter correction on the prestress loss parameters and the material mechanics parameters with the error threshold as a constraint condition, until the error value is less than the error threshold; if the error value is less than or equal to the error threshold, taking the prestress loss parameters and the material mechanics parameters corresponding to the error value that finally satisfies the error threshold as the key parameters.

[0012] Optionally, the determination of the mid-span total camber value of each calculation node in the finite element mechanics model according to the key parameters comprises: determining the construction camber of each calculation node based on the prestress loss parameters and the material mechanics parameters, in combination with a stiffness reduction coefficient, a constant / live load long-term growth coefficient and a prestress long-term growth coefficient; updating the finite element mechanics model through the prestress loss parameters and the material mechanics parameters, to determine the flow working condition and the long-term shrinkage and creep condition of the continuous rigid trough; determining the bridge completion camber of each calculation node according to the flow working condition and the long-term shrinkage and creep condition through a cosine distribution law; superimposing the construction camber and the bridge completion camber of each calculation node to obtain the mid-span total camber value of each calculation node.

[0013] In a second aspect, the continuous rigid trough mid-span camber calculation system comprises: a modeling unit configured to divide the continuous rigid trough into a plurality of cantilever beam segments, and to construct a finite element mechanics model of the continuous rigid trough based on the cantilever beam segments; a prediction unit configured to perform theoretical prediction of stress and deflection for each construction stage of the continuous rigid trough according to the finite element mechanics model, to obtain stress theoretical values and deflection theoretical values of each construction stage; The function establishing unit is configured to obtain actual stress and deflection values of the construction stage, and establish a comprehensive objective function according to the stress theoretical value, the deflection theoretical value, the actual stress value and the actual deflection value; The iteration unit is configured to perform iterative inversion through the comprehensive objective function to obtain the key parameters. The data obtaining unit is configured to determine the total camber value of each calculation node in the finite element mechanics model according to the key parameters.

[0014] In a third aspect, the electronic device of the present application comprises a processor and a memory for storing a computer program. The computer program, when loaded by the processor, causes the processor to perform the continuous rigid structure aqueduct mid-span camber calculation method described above.

[0015] In a fourth aspect, the computer readable storage medium of the present application has a computer program stored thereon, and the computer program, when executed by a processor, implements the continuous rigid structure aqueduct mid-span camber calculation method described above.

[0016] The continuous rigid structure aqueduct mid-span camber calculation method, system, device and medium of the present application can effectively correct the deviation between the theoretical model and the actual situation by establishing a finite element mechanics model matched with the continuous rigid structure aqueduct structure and the construction stage, introducing the stress and deflection measured data in the construction stage, and constructing a comprehensive objective function for parameter inversion. The present application fully considers the actual mechanical behavior and deformation characteristics of the aqueduct structure in the construction process, thereby greatly improving the accuracy of the camber prediction and ensuring that the aqueduct closure precision and the bridge line type meet the design requirements.

[0017] In the traditional method, more reliance is placed on the highway bridge related theory and specification, and the typical water conservancy load characteristics of the aqueduct being long-term under full load during the service period are not reflected. The present application can truly simulate the load distribution and transmission mechanism of the aqueduct by establishing a finite element mechanics model dedicated to the aqueduct, so as to more closely match the actual stress state of the aqueduct in camber calculation. Then, the actual stress and deflection values are collected in stages, compared with the theoretical prediction values, and a comprehensive objective function is established for iterative inversion, so as to dynamically identify and correct key design parameters such as the concrete elastic modulus, the shrinkage and creep coefficient, and the prestress loss. This process realizes controllable optimization of the whole construction cycle, forms a closed-loop control of theory-measurement-feedback-correction, and improves the predictability and controllability of the construction process.

[0018] Overall, the present application can effectively improve the camber calculation accuracy by establishing a finite element mechanics model matched with the continuous rigid structure aqueduct structure and the construction stage, introducing the measured stress and deflection data in the construction process, constructing a comprehensive objective function for iterative inversion, and dynamically correcting the key parameters of the model. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of a pre-camber calculation method for a continuous rigid aqueduct midspan in an embodiment of the present application; Figure 2 A schematic diagram of a finite element mechanics model of a continuous rigid aqueduct in an embodiment of the present application; Figure 3 A schematic diagram of a pre-camber of each node before jacking and closing of a midspan in an embodiment of the present application; Figure 4 A schematic diagram of a pre-camber of each node after jacking and closing of a midspan in an embodiment of the present application; Figure 5 A schematic diagram of pre-elevation distribution of each node of a midspan of a continuous rigid aqueduct in an embodiment of the present application; Figure 6 A structural schematic diagram of a pre-camber calculation system for a midspan of a continuous rigid aqueduct in an embodiment of the present application; Figure 7 A structural schematic diagram of an electronic device in an embodiment of the present application. DETAILED DESCRIPTION

[0020] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings. Although some embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms, and should not be interpreted as being limited to the embodiments described herein, on the contrary, these embodiments are provided to make the present application more thorough and complete. It should be understood that the drawings and embodiments of the present application are only for exemplary purposes, and are not intended to limit the scope of protection of the present application.

[0021] It should be understood that each step described in the method embodiments of the present application can be executed in different order and / or in parallel. In addition, the method embodiments can include additional steps and / or omit the execution of the steps shown. The scope of the present application is not limited in this respect.

[0022] The term "comprising" and variations thereof as used herein are open-ended, that is "including but not limited to"; the term "based on" is "based, at least in part, on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; the term "optional" means "optional in at least some embodiments". Related definitions will be given in the description below. It should be noted that the concepts of "first", "second", etc. mentioned in the present application are only used to distinguish different devices, modules or units, and are not intended to limit the order or interdependence of the functions performed by these devices, modules or units.

[0023] It should be noted that the modification of "one" or "multiple" mentioned in the present application is illustrative rather than restrictive, and those skilled in the art should understand that "one or more" should be understood unless otherwise explicitly indicated in the context.

[0024] The names of the messages or information exchanged between the devices in the embodiments of the present application are only for illustrative purposes, and are not intended to limit the scope of the messages or information.

[0025] In combination Figure 1 As shown in the figure, the embodiment of the present application provides a continuous rigid aqueduct mid-span pre-camber calculation method, comprising: The continuous rigid aqueduct is divided into multiple cantilever beam segments, and a finite element mechanics model of the continuous rigid aqueduct is constructed based on the cantilever beam segments.

[0026] Specifically, according to the construction drawings, construction scheme and key parameters such as concrete unit weight, elastic modulus, shrinkage and creep coefficient, prestress loss measured by parallel test, the aqueduct is divided into multiple cantilever beam segments along the longitudinal direction, and a corresponding two-dimensional or three-dimensional beam element mechanics model is established by using finite element software such as MIDAS, thereby providing an accurate numerical calculation basis for subsequent stage analysis.

[0027] Exemplarily, in combination Figure 2 As shown in the figure, according to the construction drawings, the design parameters measured by the parallel test of the monitoring unit, and according to the construction scheme, the entire aqueduct is divided into multiple cantilever beam segments, exemplarily, according to the construction drawings, the design parameters measured by the parallel test of the monitoring unit, such as concrete unit weight, strength, shrinkage and creep coefficient, elastic modulus, prestress loss, and according to the construction scheme, the entire aqueduct structure is divided into multiple cantilever beam segments along the longitudinal direction, and the division standard generally includes: according to the span, cross-section form, prestress arrangement and construction technology (such as hanging basket cantilever pouring method) of the aqueduct, the body is divided into several segments along the longitudinal direction; the length of each cantilever beam segment is generally 3-5 meters, and the specific length is determined according to the length of the hanging basket, the one-time pouring capacity of concrete and the prestress tension process; each segment corresponds to one construction cycle, including three main stages of formwork erection, pouring and tensioning; taking a continuous rigid aqueduct with a mid-span of 120 meters as an example, if symmetric cantilever construction is adopted, each cantilever can be divided into about 15 segments, each segment is about 4 meters long, and the entire bridge is about 30 construction beam segments, each segment corresponds to one or more beam elements in the finite element mechanics model, facilitating stress and deformation analysis at each stage. As shown in the figure, a three-dimensional finite element mechanics model is established by using MIDAS for a certain aqueduct, each segment is discretized into a beam element model, and the entire bridge is divided into 122 beam elements and 131 nodes, wherein the body material is C55 concrete and the pier is C40 concrete. Figure 2 As shown in the figure, a three-dimensional finite element mechanics model is established by using MIDAS for a certain aqueduct, each segment is discretized into a beam element model, and the entire bridge is divided into 122 beam elements and 131 nodes, wherein the body material is C55 concrete and the pier is C40 concrete.

[0028] According to the finite element mechanics model, the stress and deflection of each construction stage of the continuous rigid aqueduct is theoretically predicted to obtain the stress and deflection theoretical values of each construction stage.

[0029] Specifically, in the finite element mechanics model, each cantilever beam segment is further subdivided into three typical construction stages for simulation: formwork erection before the trolley moves forward, pouring of concrete, and tensioning of prestressed reinforcement, and the synchronous construction and closure process of each T structure is simulated according to the actual construction sequence, so as to theoretically predict the stress and deflection values of each node at each construction stage, forming a comparable theoretical benchmark.

[0030] The stress and deflection actual values of the construction stage are obtained, and a comprehensive objective function is established according to the stress theoretical value, the deflection theoretical value, the stress actual value and the deflection actual value.

[0031] Specifically, by embedding stress gauges and displacement gauges at key positions inside the aqueduct body, the stress and deflection actual values at the corresponding construction stage are monitored synchronously during the actual construction process, so as to obtain measured data reflecting the true mechanical state of the structure, which is used for subsequent comparison and correction with the theoretical values. Further, in order to overcome the shortcomings of traditional single-parameter correction, a double-parameter comprehensive objective function considering the stress and deflection errors is established in the embodiment, and the objective function value tends to zero as the optimization goal, and the key parameters such as elastic modulus, prestress loss, shrinkage and creep coefficient are continuously corrected by iterative inversion until the error between the calculated value and the measured value meets the set standard (such as f<0.01), so that the model parameters are more suitable for the actual engineering.

[0032] In a preferred embodiment of the present application, the comprehensive objective function f is established according to formula (1): , formula (1); In the formula, , are the deflection measured value and the finite element calculated value at the position of the static loading working condition measuring point j , , are the stress measured value and the finite element calculated value at the position of the static loading working condition measuring point j , m, n are the static working condition deflection and stress measuring point numbers respectively.

[0033] The key parameters are obtained by iterative inversion of the comprehensive objective function.

[0034] Specifically, based on the parameters corrected by inversion, the precamber of the i-th node is calculated using formula (2). This formula comprehensively covers the deflection caused by factors such as the self-weight of the cast and uncast beam segments, prestress, shrinkage and creep, formwork deformation, temperature, construction load, and system transformation. A stiffness reduction factor and a long-term growth factor are introduced for correction, thus accurately reflecting the cumulative deformation during construction. Formula (2) is as follows: , formula (2); in, Indicates the pre-camber of the i-th node during construction, in mm; This represents the stiffness reduction factor, with a value of 0.95. This represents the long-term growth factor of dead / live loads. When using concrete below C40, the value is 1.60; when using concrete between C40 and C80, the value is 1.45 to 1.35. For intermediate strength grades, linear interpolation can be used, and for C55, the value is 1.413. This indicates that the prestressing force of the prestressed steel bars should be reduced by all prestress losses, and the long-term growth factor is taken as 2.0. To calculate the cumulative deflection value (in mm) of the beam segment poured before node i in construction stage and in subsequent stages; Formula (3); where the superscript 1 indicates the influence of the structure's self-weight. express Similarly, the deflection of the beam segment already cast before the node under its own weight is also considered. +1、 +2 and so on also indicate nodes, and each node corresponds to a pouring section. This indicates the influence value of the deflection caused by the self-weight of the subsequent beam segment to be poured; These are the values ​​for early shrinkage and creep, the effect of formwork deformation, temperature correction, deflection caused by construction load, and deflection (mm) caused by system transformation and secondary dead load. A key feature is that the pre-cast beam segment has already undergone its own weight deformation and no longer affects the subsequently cast segments. To calculate the cumulative deflection (in mm) of the point affected by the longitudinal prestressing tensioning of the cast beam segment during the construction phase and in subsequent phases; where, Formula (4), where the superscript 2 indicates the effect of prestressing. This represents the deflection of the prestressed beam segment cast before node i under tension. This indicates the influence value of deflection after prestressing tensioning of subsequent beam segments.

[0035] Based on the key parameters, the total pre-camber value of the mid-span of each calculation node in the finite element mechanical model is determined.

[0036] Specifically, for the load characteristics of the aqueduct during operation, the variable load reduction in the calculation of the highway bridge pre-camber is changed to the full design flow load, the bridge state (including 10-year shrinkage and creep) is modeled according to the modified parameters, and the pre-camber of the bridge is calculated according to formula (5), which distributes the deflection caused by the design flow according to the cosine curve, reflecting the deformation characteristics of the aqueduct under the action of long-term full water load. Finally, the construction pre-camber and the bridge pre-camber of the same node are superimposed according to formula (6) to obtain the total pre-camber value of the midspan of the node, thereby providing a direct and scientific basis for determining the formwork elevation of each beam segment, ensuring that the construction closure accuracy and the bridge line type meet the design requirements.

[0037] wherein the model is modified according to the adjusted parameters, the design flow condition of the aqueduct after completion is considered, and the modeling analysis is carried out considering the completion of 10-year shrinkage and creep, and the bridge pre-camber of the current pouring beam segment is calculated and distributed according to formula (5): , formula (5); wherein, represents the deflection caused by the design flow acting on the i-th node, mm; aqueduct midspan span, mm; x represents the distance of the i-th node from the fulcrum, mm; Further, the total pre-camber of the i-th node at each construction stage is calculated according to formula (6): , formula (6) wherein, is the total pre-camber of the i-th node, mm. i

[0038] The continuous rigid frame aqueduct midspan pre-camber calculation method of the embodiment can effectively correct the deviation between the theoretical model and the actual situation by establishing a finite element mechanics model matched with the continuous rigid frame aqueduct structure and the construction stage, introducing the stress and deflection measured data at the construction stage, and constructing a comprehensive objective function for parameter inversion. The application fully considers the actual mechanical behavior and deformation characteristics of the aqueduct structure during the construction process, thereby greatly improving the accuracy of pre-camber prediction and ensuring that the aqueduct closure accuracy and the bridge line type meet the design requirements.

[0039] In the traditional method, more reliance is placed on the relevant theories and specifications of highway bridges, and the typical water load characteristics of the aqueduct being in full load for a long time during the service period are not reflected. The embodiment can truly simulate the load distribution and transmission mechanism of the aqueduct by establishing a finite element mechanics model dedicated to the aqueduct, so as to better match the actual stress state of the aqueduct in the pre-camber calculation. Then, by comparing the actual values of stress and deflection with the theoretical predicted values, a comprehensive objective function is established for iterative inversion, which can dynamically identify and correct key design parameters such as the elastic modulus of concrete, the shrinkage and creep coefficient, and the prestress loss. This process realizes controllable optimization of the whole construction cycle, forms a closed-loop control of theory-measurement-feedback-correction, and improves the predictability and controllability of the construction process.

[0040] ​In summary, the embodiment improves the calculation accuracy of the pre-camber by establishing a finite element mechanics model matching the continuous rigid aqueduct structure and the construction stage, introducing the measured stress and deflection data in the construction process, constructing a comprehensive objective function for iterative inversion, and dynamically correcting the key parameters of the model.

[0041] Optionally, the dividing the continuous rigid aqueduct into multiple cantilever beam segments and constructing the finite element mechanics model of the continuous rigid aqueduct based on the cantilever beam segments comprises: dividing the continuous rigid aqueduct into multiple cantilever beam segments according to construction drawings and design parameters of the continuous rigid aqueduct; discretizing each cantilever beam segment into corresponding beam elements through finite element analysis; taking the connecting points between the beam elements as the calculation nodes to construct the finite element mechanics model.

[0042] Specifically, according to the construction drawings of the continuous rigid aqueduct and the design parameters such as concrete unit weight, elastic modulus, shrinkage and creep coefficient, and prestress loss obtained by the monitoring unit through parallel tests, the entire aqueduct structure is divided into multiple independent cantilever beam segments along the longitudinal direction according to the established cantilever pouring construction scheme, as shown in FIG. 1. Figure 2 Further, each cantilever beam segment divided is further discretized into multiple beam elements by using a finite element analysis software such as MIDAS. For example, in an embodiment, the entire bridge is discretized into 122 beam elements, each beam element is assigned with corresponding cross-section characteristics and material constitutive relationship according to its position and material properties such as C55 concrete of the trough body and C40 concrete of the trough pier, so as to accurately represent the mechanical behavior of the structure in the numerical aspect. The connecting end points between the discretized beam elements and the key positions of the structure such as the support, the midspan, and the variable cross-section are set as the calculation nodes, all the nodes are connected with each other through the element stiffness matrix, and finally a complete two-dimensional or three-dimensional finite element mechanics model containing 131 nodes is formed, which is the basic calculation framework for subsequent simulation, theoretical prediction, and parameter inversion of all construction stages.

[0043] In the optional embodiment, the aqueduct is divided into multiple cantilever beam segments according to the construction drawings and the measured design parameters, and each beam segment is discretized into beam elements with clear material and cross-section properties by using the finite element method, and finally the complete mechanics model is formed by taking the element connecting points as the calculation nodes, thereby constructing a high-fidelity numerical model which can accurately reflect the actual geometric and material properties of the structure and completely simulate the mechanical transmission path in the construction process, and laying a solid foundation for subsequent reliable stage simulation, theoretical prediction, and parameter inversion.

[0044] Optionally, the stress and deflection theoretical values of each of the calculation nodes in each of the construction stages are obtained by theoretically predicting stress and deflection of each construction stage of the continuous rigid-frame aqueduct according to the finite element mechanics model, comprising: a plurality of construction stages are divided according to each of the cantilever beam segments in the finite element mechanics model, and the construction stages include a formwork erection construction stage, a concrete pouring construction stage, and a prestress tensioning construction stage; a mechanical response of each of the construction stages under the action of the structural self-weight and the prestress load is simulated based on the finite element mechanics model, to obtain a construction working condition of each of the construction stages; the stress theoretical value and the deflection theoretical value of each of the calculation nodes in the construction stage are determined according to the construction working condition of the construction stage.

[0045] Specifically, each cantilever beam segment is further subdivided into three standard construction stages: firstly, a formwork erection construction stage, i.e. positioning of the trolley, secondly, a concrete pouring construction stage, and finally, a prestress tensioning construction stage. The actual construction sequence, such as synchronous construction of each T structure, closing of the middle span after the side span, is used to activate or deactivate the corresponding elements and loads in the finite element mechanics model in sequence, to simulate the complete and staged construction process. Based on the established finite element mechanics model, the mechanical behavior of each construction stage under the action of a specific load combination, mainly including the newly added structural self-weight, the applied prestress, and the temporary construction load, is simulated statically to generate detailed construction working conditions of each stage, so as to calculate the overall and local mechanical responses of the model under each working condition. By extracting the calculation results of the finite element software under the above construction working conditions, the stress theoretical values of each pre-designed calculation node in the model, i.e. the axial stress, bending stress, and other stress theoretical values of the key cross sections of the beam segment in the corresponding stage, and the deflection theoretical values such as vertical displacement, are directly obtained, to form a complete and quantifiable sequence of stage deformation and internal force prediction data, providing a benchmark for subsequent comparison with measured values.

[0046] In this optional embodiment, each cantilever beam segment is finely divided into three typical construction stages of formwork erection, concrete pouring, and prestress tensioning, and the mechanical responses of each stage under the combined action of the structural self-weight and the prestress load are simulated in the finite element mechanics model in sequence, to realize high-precision theoretical prediction of the structural stress and deformation evolution path in the entire construction process, and to provide a detailed sequence of stress and deflection theoretical values for each calculation node. This constitutes the basis for subsequent comparison with measured data, identification of model deviation, and initiation of parameter inversion correction, effectively supporting the key transition of prestress calculation from static theoretical analysis to dynamic construction adaptability.

[0047] Optionally, the stress actual value and the deflection actual value of the construction stage are obtained by: The stress actual value and the deflection actual value of the construction stage are obtained by monitoring stress gauges and displacement gauges respectively arranged at preset stress measuring points and preset deflection measuring points of the continuous rigid aqueduct. The setting positions of the stress gauges and the displacement gauges are consistent with the positions of the corresponding calculation nodes in the finite element mechanics model.

[0048] Specifically, according to a pre-prepared construction monitoring scheme, stress gauges and displacement gauges are pre-buried or installed at multiple key sections of the aqueduct structure, such as the cantilever root, the midspan, the vicinity of the closure section, etc., to form a preset stress measuring point and a preset deflection measuring point network covering the main stress area, thereby providing a hardware basis for obtaining the real mechanical state of the structure during the construction process.

[0049] In the actual construction process, whenever the construction progresses to a pre-defined construction stage, such as the completion of concrete pouring or prestress tensioning of a certain section, the monitoring data of the stress gauges and the displacement gauges at the corresponding preset measuring points are synchronously read by the data acquisition system, thereby directly obtaining the stress actual value and the deflection actual value of each measuring point at this construction stage. The actual values obtained by the above monitoring are synchronously recorded and correspondingly associated with the stress theoretical values and the deflection theoretical values of the corresponding nodes at the corresponding stages calculated by the finite element mechanics model, thereby forming data pairs for subsequent comparative analysis and providing accurate measured data input for establishing a comprehensive objective function and starting parameter inversion.

[0050] In this embodiment, to ensure the homology and comparability of the data relied on by subsequent parameter inversion, in the collaborative design before construction, the three-dimensional coordinates of the calculation nodes pre-defined by the finite element mechanics model at the key sections of the structure are used to accurately arrange and install sensors at the corresponding geometric positions of the actual aqueduct structure, thereby establishing an accurate position mapping relationship between the physical space and the numerical model, and thus ensuring that the theoretical values of a certain calculation node output from the finite element mechanics model and the measured values read from the sensors at the corresponding position on site represent the mechanical response of the same point on the structure at the same construction stage.

[0051] In this optional embodiment, by systematically arranging the monitoring network of stress gauges and displacement gauges at key positions of the aqueduct structure, real-time and in-situ measurement of the real mechanical response of the structure at each construction stage is realized, thereby obtaining stress and deflection actual values directly reflecting the comprehensive influence of material properties, construction technology and environmental factors, and providing an objective and accurate measured data basis for reliable comparison with theoretical prediction values, effectively overcoming the model deviation problem that may exist by simply relying on theoretical calculation.

[0052] Optionally, the establishment of the comprehensive objective function according to the stress theoretical value, the deflection theoretical value, the stress actual value and the deflection actual value comprises: For each of the computing nodes, a stress deviation ratio is determined according to the stress theoretical value and the stress actual value, and a deflection deviation ratio is determined according to the deflection theoretical value and the deflection actual value; The stress deviation ratio and the deflection deviation ratio corresponding to each of the computing nodes are combined with the number of the preset stress measuring points and the preset deflection measuring points to perform absolute value summation to generate the comprehensive objective function.

[0053] Specifically, after obtaining the stress theoretical value, the deflection theoretical value, the corresponding stress actual value and the deflection actual value of each measuring point in each construction stage, first, the relative deviation of each measuring point is calculated, that is, the stress deviation ratio and the deflection deviation ratio are determined by using the ratio of the theoretical value to the measured value, so as to quantify the deviation degree of the theoretical prediction of each measuring point from the actual situation. At the same time, considering the difference of responses of different positions of the structure, the stress deviation ratios of all preset stress measuring points, a total of m, and the deflection deviation ratios of all preset deflection measuring points, a total of n, are summed according to the above formula (1), wherein, is the stress deviation ratio, is the deflection deviation ratio, and the absolute values of the deviation ratios of each measuring point are summed, so as to aggregate the error information dispersed in each measuring point into a single overall error index. The objective function f generated through the above steps directly represents the comprehensive difference between the overall output of the current finite element mechanics model and the measured response of the structure, thereby establishing a mathematical relationship for uniformly quantifying multiple types and multiple positions of monitoring data into an iterative optimization target, and providing a clear convergence judgment basis for subsequent automatic inversion of driving parameters.

[0054] In the optional embodiment, the comprehensive objective function which simultaneously integrates the deviation of two types of key measured data of stress and deflection is established, the traditional single-parameter independent correction method is improved into a multi-parameter collaborative inversion optimization framework, and the model distortion problem caused by the data one-sidedness when the stress or deflection is corrected alone is effectively overcome; the comprehensive objective function aggregates the absolute deviation ratios of all measuring points and takes the optimization target of approaching to zero, thereby providing a quantitative and comprehensive convergence judgment basis for the parameter inversion process, significantly improving the reliability and overall accuracy of iterative correction of key parameters such as elastic modulus and prestress loss, and thereby laying a solid analysis foundation for subsequent accurate calculation of the pre-camber.

[0055] Optionally, the iterative inversion through the comprehensive objective function to obtain the key parameters comprises: Setting an error threshold of the comprehensive objective function; The prestressed beam loss parameters and the material mechanics parameters are corrected with the error threshold as a constraint condition, to obtain corrected prestressed loss parameters and material mechanics parameters; The corrected prestressed loss parameters and material mechanics parameters are substituted into the finite element mechanics model, to update the stress theoretical value and the deflection theoretical value of the calculation node corresponding to each construction stage; According to the updated stress theoretical value and deflection theoretical value, the stress actual value and the deflection actual value are combined to determine the error value of the comprehensive objective function; If the error value is greater than the error threshold, the step of correcting the prestressed beam loss parameters and the material mechanics parameters with the error threshold as a constraint condition is returned until the error value is less than the error threshold; If the error value is less than or equal to the error threshold, the prestressed loss parameters and the material mechanics parameters corresponding to the error value that finally satisfies the error threshold are taken as the key parameters.

[0056] Specifically, the error threshold of the comprehensive objective function is set to a minimum value that tends to zero, for example, in a specific implementation, the error value f < 0.01 is used as a constraint condition, which is used as a quantitative standard for judging whether the parameter inversion converges, to ensure that the prediction accuracy of the corrected model meets the engineering requirements. With the error threshold as a constraint, the prestressed beam loss parameters in the initial finite element mechanics model, such as the loss percentage of straight beams and curved beams after tensioning, and the material mechanics parameters, such as the elastic modulus of concrete and the shrinkage and creep coefficient, are corrected by introducing adjustment coefficients. These coefficients are adjusted through trial calculation or optimization algorithm to make the parameter values more consistent with the actual situation reflected by the measured data.

[0057] For example, in Table 1 below, the elastic modulus of Block 2 is adjusted from 3.55e4 MPa to 3.37e4 MPa. As shown in Table 1, the results of the iterative inversion and correction of the key design parameters by comparing the measured data with the theoretical model during the continuous rigid trough pre-camber analysis process. The specific explanation is as follows: the straight tension loss represents the percentage of the pre-stress loss of the straightly arranged pre-stressed tendon after tensioning due to factors such as anchor deformation and pre-stressed tendon shrinkage; the curved bundle tension loss represents the percentage of the pre-stress loss of the curvedly arranged pre-stressed tendon after tensioning due to factors such as friction and anchoring; the elastic modulus of Block 2 represents the elastic modulus of the concrete used in a beam section (Block 2) numbered “2” in the trough structure, reflecting the material's ability to resist elastic deformation. The initial value represents the theoretical parameter value selected at the design stage or by experience. The adjustment coefficient represents the parameter correction coefficient calculated by the comprehensive objective function inversion according to the measured stress and deflection data at the construction stage. The corrected value represents the parameter value more in line with the actual engineering situation obtained by multiplying the initial value and the adjustment coefficient. The straight tension loss is fine-tuned from 7.4% to 7.5% (adjustment coefficient 1.02), with a small change. The curved bundle tension loss is increased from 12.4% to 13.6% (adjustment coefficient 1.1), indicating that the actual loss due to friction and other factors is greater than the original design expectation. The elastic modulus of Block 2 is down-regulated from to (adjustment coefficient 0.95), indicating that the actual concrete stiffness is slightly lower than the original design value. Through correction, the key parameters in the model are closer to the actual construction performance, significantly improving the prediction accuracy of the structural behavior of the finite element mechanics model, and laying a reliable foundation for the subsequent accurate calculation of construction pre-camber and bridge pre-camber. The corrected pre-stress loss parameters and material mechanics parameters are re-input into the finite element mechanics model, such as the MIDAS model, to update the load and material properties at each construction stage and re-run the construction stage simulation, thereby obtaining the updated stress theoretical value and deflection theoretical value of each calculation node. According to the updated stress theoretical value, deflection theoretical value, and measured stress actual value, deflection actual value, the comprehensive objective function formula (1) is calculated again to determine the error value corresponding to the current parameter set and evaluate the degree of agreement between the model prediction and the measured data.

[0058] Table 1 Parameter correction results

[0059] If the calculated error value is greater than the preset error threshold (e.g., f ≥ 0.01), based on the current error analysis, the prestress loss or material parameters are further fine-tuned, and the process of updating the model and calculating the error is repeated to form an iterative loop. When the iterative calculation makes the error value of the comprehensive objective function less than or equal to the preset error threshold, it is considered that the model has reached sufficient accuracy, at which point the iteration is stopped, and the prestress loss parameters and material mechanics parameters used in the final iteration, such as the corrected loss percentage and elastic modulus shown in Table 1, are determined as the key parameters obtained by inversion, which are used for subsequent accurate calculation of the pre-camber.

[0060] In this optional embodiment, by setting a clear error threshold and constructing an automated iterative inversion process of calculation-comparison-correction, systematic and quantitative dynamic correction of prestress loss and material mechanics parameters is achieved. This process enables the finite element mechanics model to continuously self-calibrate based on construction measured data until its comprehensive output error converges within the permitted range, thereby fundamentally overcoming the model distortion problem caused by relying on experience to select fixed parameters in traditional methods, and ultimately obtaining a key parameter set that closely matches the specific engineering actual conditions, providing reliable and adaptive core input for subsequent accurate calculation of construction and bridge pre-camber.

[0061] Optionally, determining the mid-span total pre-camber value of each calculation node in the finite element mechanics model according to the key parameters comprises: Based on the prestress loss parameters and the material mechanics parameters, the stiffness reduction coefficient, the constant / live load long-term growth coefficient, and the prestress long-term growth coefficient are combined to determine the construction pre-camber of each calculation node. The finite element mechanics model is updated through the prestress loss parameters and material mechanics parameters to determine the flow working condition and long-term shrinkage and creep condition of the continuous rigid-jointed aqueduct. The bridge pre-camber of each calculation node is determined according to the flow working condition and the long-term shrinkage and creep condition through the cosine distribution law. The construction pre-camber and the bridge pre-camber of each calculation node are superimposed to obtain the mid-span total pre-camber value of each calculation node.

[0062] Specifically, based on the prestress loss parameters and material mechanics parameters (such as the corrected elastic modulus 3.37e4 MPa, prestress loss 7.5% and 13.6% in Table 1) obtained by inversion, the construction camber of each calculation node is calculated by substituting formula (2), which comprehensively considers the cumulative deflection caused by the self weight and prestress of the poured and unpoured beam section, the deformation of the hanging basket, temperature, construction load and other factors, and the calculation results are corrected by introducing the stiffness reduction coefficient k1 (0.95), the long-term growth coefficient of constant / live load k2 (1.413 for C55 concrete) and the long-term growth coefficient of prestress k3 (2.0), and finally the construction camber values distributed along the beam section are obtained as shown in Figure 3 The finite element mechanics model is updated using the corrected prestress loss and material parameters (such as shrinkage and creep coefficient) to simulate the working condition of the aqueduct after being built under the full load of the design flow (such as 75m³ / s) and considering the state after the concrete shrinkage and creep effect for 10 years, and the mechanical analysis is carried out to obtain the long-term deformation of the structure under the working condition. According to the deflection results obtained by the above flow working condition and long-term shrinkage and creep analysis, the bridge completion camber of each node is calculated by using the above formula (5). The formula is based on the deflection value under the design flow, multiplied by the coefficient considering the long-term effect, and the camber value is distributed to different positions in the span (x is the distance from the support point, L is the span) according to the cosine curve law (1-cos(2πx / L)), so as to obtain the bridge completion camber distribution as shown in Figure 4 The construction camber calculated by the above formula (2) and the bridge completion camber calculated by the above formula (5) are algebraically superimposed, and the midspan total camber value of the node is obtained according to the above formula (6), so as to form the final camber setting curve as shown in Figure 5 The final camber setting curve provides a direct and complete basis for determining the formwork elevation of each beam section.

[0063] In an embodiment of the present application, according to the construction drawings, the design parameters measured by the parallel test of the monitoring unit, and the construction scheme, the entire aqueduct is divided into multiple cantilever beam sections, and a certain aqueduct is taken as an example to establish a three-dimensional finite element mechanics model using MIDAS as shown in Figure 2As shown, each segment is discretized into a beam element model, the whole bridge is divided into 122 beam elements and 131 nodes, the body material is C55 concrete, and the pier is C40 concrete. The whole bridge construction process is divided into 57 construction stages, each cantilever beam segment is divided into 3 construction stages: formwork construction (i.e. hanging basket forward movement), concrete pouring construction, and prestressed tendon tensioning construction; each T structure is constructed simultaneously, the two side spans are closed first, and then the middle span is jacked closed, and the stress and deformation of the construction beam segment are calculated. The stress and deflection of the corresponding construction stage are monitored, the objective function is established according to the formula, and the error f < 0.01 is taken as the constraint condition, and the elastic modulus, prestressed tendon loss and other parameters are further reasonably adjusted. The stress and deformation of the construction beam segment are iteratively calculated until the error standard is met. The corrected elastic modulus, prestressed tendon loss and other parameters are referred to Table 1 above. According to the corrected parameters, modeling calculation is carried out, and the construction camber of each node is calculated according to formula (3) above, and the design flow of the aqueduct after completion is 75m 3 / s, and the shrinkage and creep of 10 years are considered, modeling analysis is carried out, and the construction camber of the current pouring beam segment is calculated according to formula (4) above according to the deflection in the analysis results, such as Figure 4 The construction camber of each node before the middle span jacking closure is shown in the figure. Figure 5

[0064] In the optional embodiment, by substituting the key parameters obtained by inversion into the special construction and completion camber calculation formula, the complex time-varying effects in the construction stage, including the cooperation of all construction loads, prestressed loss and long-term growth and the characteristics of the persistent full water load in the operation stage, are realized. The construction camber is scientifically distributed according to the cosine distribution law, and the total camber value of each node is obtained through superposition, thereby forming a camber setting method that can accurately reflect the dynamic deformation in the construction process and fully meet the load characteristics of the aqueduct in the service period, and fundamentally guaranteeing the closure accuracy, completion linear and long-term safe service performance of the aqueduct.

[0065] As shown in Figure 6 The embodiment of the present application also provides a middle span camber calculation system for a continuous rigid aqueduct, which comprises: A modeling unit is configured to divide the continuous rigid aqueduct into a plurality of cantilever beam segments, and to construct a finite element mechanics model of the continuous rigid aqueduct based on the cantilever beam segments; A prediction unit is configured to perform theoretical prediction of stress and deflection for each construction stage of the continuous rigid aqueduct according to the finite element mechanics model, to obtain a stress theoretical value and a deflection theoretical value of each construction stage; ​The function establishing unit is configured to obtain the actual stress value and the actual deflection value of the construction stage, and establish a comprehensive objective function according to the stress theoretical value, the deflection theoretical value, the actual stress value and the actual deflection value. The iteration unit is configured to perform iterative inversion through the comprehensive objective function to obtain the key parameter. The data obtaining unit is configured to determine the total camber value of each calculation node in the finite element mechanics model according to the key parameter.

[0066] The continuous rigid frame aqueduct mid-span camber calculation system has the same advantages as the continuous rigid frame aqueduct mid-span camber calculation method compared with the prior art, and details are not repeated here.

[0067] In combination with Figure 7 The electronic device provided by the embodiment of the application further includes a processor and a memory, and the memory is configured to store a computer program. The computer program, when loaded by the processor, enables the processor to perform the continuous rigid frame aqueduct mid-span camber calculation method.

[0068] The electronic device has the same advantages as the continuous rigid frame aqueduct mid-span camber calculation method compared with the prior art, and details are not repeated here.

[0069] The embodiment of the application further provides a computer readable storage medium, which stores a computer program, and the computer program, when executed by a processor, implements the continuous rigid frame aqueduct mid-span camber calculation method.

[0070] The computer readable storage medium has the same advantages as the continuous rigid frame aqueduct mid-span camber calculation method compared with the prior art, and details are not repeated here.

[0071] Although the application discloses the above, the protection scope of the application is not limited to this. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the application, and these changes and modifications will fall within the protection scope of the application.

Claims

1. A method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct, characterized in that, include: The continuous rigid frame aqueduct is divided into multiple cantilever beam segments, and a finite element mechanical model of the continuous rigid frame aqueduct is constructed based on the cantilever beam segments. Based on the finite element mechanical model, the stress and deflection of each construction stage of the continuous rigid frame aqueduct are theoretically predicted, and the theoretical stress and deflection values ​​of each construction stage are obtained. Obtain the actual stress and deflection values ​​during the construction phase, and establish a comprehensive objective function based on the theoretical stress value, the theoretical deflection value, the actual stress value, and the actual deflection value. The key parameters are obtained by iterative inversion using the comprehensive objective function. Based on the key parameters, the total pre-camber value of the mid-span of each calculation node in the finite element mechanical model is determined.

2. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 1, characterized in that, The process of dividing the continuous rigid frame aqueduct into multiple cantilever beam segments and constructing a finite element mechanical model of the continuous rigid frame aqueduct based on the cantilever beam segments includes: Based on the construction drawings and design parameters of the continuous rigid frame aqueduct, the continuous rigid frame aqueduct is divided into multiple cantilever beam segments; Each cantilever beam segment is discretized into corresponding beam elements through finite element analysis; The connection points between the beam elements are used as the calculation nodes to construct the finite element mechanical model.

3. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 1, characterized in that, The step involves theoretically predicting the stress and deflection for each construction stage of the continuous rigid frame aqueduct based on the finite element mechanical model, obtaining the theoretical stress and deflection values ​​for each construction stage, including: The construction stages are divided according to each cantilever beam segment in the finite element mechanical model, including the formwork erection stage, the concrete pouring stage, and the prestressing tensioning stage. Based on the finite element mechanical model, the mechanical response of each construction stage under the action of structural self-weight and prestressed load is simulated to obtain the construction conditions of each construction stage. Based on the construction conditions of the construction stage, determine the theoretical stress value and theoretical deflection value of each calculation node in the construction stage.

4. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 1, characterized in that, Obtaining the actual stress and deflection values ​​during the construction stage includes: By monitoring the stress and deflection at preset stress and deflection points respectively set on the continuous rigid frame aqueduct, the actual stress and deflection values ​​during the construction stage are obtained. The stress gauge and the displacement gauge are positioned at locations consistent with the corresponding calculation nodes in the finite element mechanical model.

5. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 4, characterized in that, The step of establishing a comprehensive objective function based on the theoretical stress value, the theoretical deflection value, the actual stress value, and the actual deflection value includes: For each calculation node, the stress deviation ratio is determined based on the theoretical stress value and the actual stress value, and the deflection deviation ratio is determined based on the theoretical deflection value and the actual deflection value. The absolute values ​​of the stress deviation ratio and the deflection deviation ratio corresponding to each calculation node are summed together with the number of preset stress measurement points and the number of preset deflection measurement points to generate the comprehensive objective function.

6. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 1, characterized in that, The key parameters obtained through iterative inversion using the comprehensive objective function include: Set the error threshold for the comprehensive objective function; Using the aforementioned error threshold as a constraint, the prestressed tendon loss parameters and material mechanical parameters are corrected to obtain the corrected prestressed tendon loss parameters and material mechanical parameters. Substitute the corrected prestress loss parameters and material mechanics parameters into the finite element mechanical model to update the theoretical stress value and the theoretical deflection value of the calculation node corresponding to each construction stage; Based on the updated theoretical stress value and the theoretical deflection value, combined with the actual stress value and the actual deflection value, the error value of the comprehensive objective function is determined; If the error value is greater than the error threshold, then return to the step of correcting the prestressed tendon loss parameters and material mechanical parameters with the error threshold as a constraint, until the error value is less than the error threshold; If the error value is less than or equal to the error threshold, then the prestress loss parameter and the material mechanical parameter corresponding to the error value that finally satisfies the error threshold are taken as the key parameters.

7. The method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct according to claim 6, characterized in that, The step of determining the total pre-camber value of the mid-span of each calculation node in the finite element mechanical model based on the key parameters includes: Based on the prestress loss parameters and the material mechanical parameters, combined with the stiffness reduction factor, the long-term growth factor of dead / live load and the long-term growth factor of prestress, the construction precamber of each calculation node is determined; The finite element mechanical model is updated by the prestress loss parameters and material mechanical parameters to determine the flow conditions and long-term shrinkage and creep of the continuous rigid frame aqueduct. Based on the cosine distribution law, the pre-camber of each calculation node is determined according to the flow conditions and the long-term shrinkage and creep. The construction pre-camber of each calculation node is superimposed with the completed bridge pre-camber to obtain the total mid-span pre-camber value of each calculation node.

8. A calculation system for the pre-camber of the mid-span of a continuous rigid frame aqueduct, characterized in that, include: A modeling unit is used to divide a continuous rigid frame aqueduct into multiple cantilever beam segments and to construct a finite element mechanical model of the continuous rigid frame aqueduct based on the cantilever beam segments. The prediction unit is used to perform theoretical prediction of stress and deflection for each construction stage of the continuous rigid frame aqueduct based on the finite element mechanical model, and to obtain the theoretical stress value and theoretical deflection value for each construction stage. The function establishment unit is used to obtain the actual stress value and actual deflection value during the construction stage, and to establish a comprehensive objective function based on the theoretical stress value, the theoretical deflection value, the actual stress value, and the actual deflection value. An iterative unit is used to perform iterative inversion through the comprehensive objective function to obtain key parameters; The data acquisition unit is used to determine the total pre-camber value of the mid-span of each calculation node in the finite element mechanical model based on the key parameters.

9. An electronic device, characterized in that, include: Processor and memory, the memory being used to store computer programs; When the computer program is loaded by the processor, it causes the processor to execute the method for calculating the pre-camber of the middle span of a continuous rigid frame aqueduct as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the pre-camber of the mid-span of a continuous rigid frame aqueduct as described in any one of claims 1-7.

Images