Bridge pier horizontal force calculation method and system under temperature effect and storage medium

Abstract

The invention provides a bridge pier horizontal force calculation method and system under the action of temperature and a storage medium, and relates to the technical field of bridges, and the method comprises the steps: obtaining pier beam data; setting a pier top horizontal displacement value as an unknown number, and establishing a balance equation according to pier beam data; solving the balance equation to obtain the pier top horizontal displacement of each pier; obtaining the horizontal force of the pier top based on the horizontal anti-pushing rigidity and the horizontal displacement of the pier top; and comparing the pier top horizontal force with the maximum static friction resistance of the support, judging whether the sliding constraint is changed or not, continuously correcting the balance equation, solving the pier top horizontal displacement and the pier top horizontal force until the sliding constraint is not changed any more, and obtaining the pier top horizontal force of each pier. According to the method, the horizontal force calculation efficiency and accuracy under the temperature effect are improved to a great extent, calculation consumption is reduced, and the method is suitable for longitudinal temperature force distribution under the condition that multiple fixing piers are arranged at will.

Description

Technical Field

[0001] The present invention relates to the field of bridge technology, and in particular to a method, system and storage medium for calculating horizontal force of a bridge pier under the action of temperature. Background Art

[0002] With the continuous advancement of bridge construction technology in recent years, horizontal forces at the top of continuous beam piers have become a key factor in the success of bridge design. These forces typically include those generated by braking forces, temperature, and external forces such as wind loads, soil pressure, and ship impact.

[0003] Currently, the steps for calculating the horizontal force generated by each pier under the influence of temperature are usually as follows: first, find the position of the fixed point in the beam when the temperature changes, that is, the temperature zero point; then calculate the horizontal force of the pier under the temperature change; then judge and adjust the pier horizontal force, and repeatedly calculate the temperature zero point and pier horizontal force until the pier support and main beam stop sliding, and determine the final horizontal force of each pier.

[0004] However, in the prior art, after each adjustment of the pier horizontal force, the temperature zero point needs to be recalculated and the horizontal force allocated to each pier is solved, resulting in low efficiency in horizontal force calculation and being unsuitable for the case of multiple piers. Summary of the Invention

[0005] The present invention provides a method, system and storage medium for calculating the horizontal force of a bridge pier under the action of temperature, so as to solve the problem that the current calculation efficiency of the horizontal force under the action of temperature is low and cannot be applied to the situation of multiple solid piers.

[0006] In a first aspect, the present invention provides a method for calculating horizontal forces on bridge piers under temperature, the method comprising: Acquire pier and beam data; the pier and beam data include horizontal thrust stiffness, linear expansion coefficient, beam length between piers, and temperature change value of each pier; The horizontal displacement value of the pier top is set as an unknown number, and the equilibrium equation is established based on the pier-beam data; Solving the equilibrium equation to obtain the horizontal displacement of the pier top of each pier; Obtaining a horizontal force on the pier top based on the horizontal thrust-resistance stiffness and the horizontal displacement of the pier top; The pier top horizontal force is compared with the maximum static friction resistance of the support to determine whether the sliding constraint has changed. The equilibrium equation is continuously revised to solve the pier top horizontal displacement and the pier top horizontal force until the sliding constraint no longer changes, thereby obtaining the pier top horizontal force of each pier.

[0007] Furthermore, the establishment of the equilibrium equation includes: The horizontal displacement of the pier top is set as an unknown number. Based on the external force balance condition of the pier, multiple pier equations are obtained according to the linear expansion coefficient, the beam length between each pier, and the temperature change. The horizontal displacement of the pier top is set as an unknown number. Based on the assumption that the sum of the longitudinal horizontal forces at the pier top is zero, the pier top equation is established according to the horizontal thrust stiffness of each pier. Based on the multiple pier equations and the pier top equations, the equilibrium equation is obtained.

[0008] Furthermore, the bridge pier equation is: ; in, Indicates the The horizontal displacement value of the pier top; Indicates the The horizontal displacement value of the pier top; represents the linear expansion coefficient; Indicates the The piers and Length of beam between piers; Indicates the temperature change value.

[0009] Furthermore, the pier top equation is: ; in, 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers.

[0010] Furthermore, the equilibrium equation is: ; in, 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers; represents the linear expansion coefficient; 、 、 、 Indicates the length of the beam between each pier; Indicates the temperature change value.

[0011] Furthermore, determining whether the sliding constraint has changed includes: If the absolute value of the horizontal force on the top of the current pier is greater than the corresponding maximum static friction resistance of the support, the current pier slides, indicating that the sliding constraint has changed.

[0012] Furthermore, revising the equilibrium equation includes: When the sliding constraint changes, the maximum static friction resistance of the support is used as the pier top horizontal force of the current pier, and the horizontal thrust stiffness of the current pier is set to zero; At the same time, the vector sum of the static friction of the bridge piers causing sliding is obtained; The equilibrium equation is modified using the vector sum.

[0013] Furthermore, using the vector sum to correct the equilibrium equation includes: using the vector sum to correct the pier top equation.

[0014] In a second aspect, the present invention provides a computer system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any one of the above methods.

[0015] In a third aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which implements the steps of any of the above methods when executed by a processor.

[0016] In general, the present invention provides a method, system, and storage medium for calculating the horizontal force of bridge piers under temperature. Compared with the prior art, the technical solution conceived by the present invention can achieve the following beneficial effects: The present invention sets the horizontal displacement value of the pier top as an unknown variable and establishes an equilibrium equation based on the pier-beam data; iterative solution is performed based on the equilibrium equation, avoiding the need to obtain the temperature zero point in each iteration, greatly improving the efficiency of horizontal force calculation under the action of temperature, not only reducing the calculation cost, but also being applicable to the longitudinal temperature force distribution in the case of arbitrary arrangement of multiple fixed piers. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1This is a schematic diagram of the method steps for calculating the horizontal force of a bridge pier under the action of temperature, a system, and a storage medium provided by the present invention; Figure 2 It is a schematic diagram of the pier-beam model structure of a method, system and storage medium for calculating horizontal force of a pier under the action of temperature provided by the present invention; Figure 3 It is a schematic elevation diagram of a continuous beam of a method, system and storage medium for calculating horizontal forces of piers under temperature provided by the present invention. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0020] It should be noted that, in the description of the embodiments of the present invention, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a method, step, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such method, step, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the method, step, or apparatus comprising the element.

[0021] In order to solve the problem that the current calculation efficiency of horizontal force under temperature is low and cannot be applied to the situation of multiple piers, the present invention provides a method for calculating the horizontal force of bridge piers under temperature. Figure 1 Specifically, the method includes: Step 101: Obtain pier and beam data.

[0022] It should be noted that the pier-beam data include the horizontal thrust stiffness, linear expansion coefficient, beam length between piers and temperature change value of each pier.

[0023] The main methods for obtaining horizontal thrust stiffness include the three-thrust equation method, the single-iteration method, the flexibility coefficient method, and the stiffness integration method. The most commonly used method in bridge engineering design is the stiffness integration method. Its principle is to first calculate the integrated stiffness of each pier and then distribute the horizontal force on the pier top based on the proportion of the integrated stiffness of each pier.

[0024] It should be noted that the horizontal thrust stiffness, linear expansion coefficient, beam length between each pier and temperature change value are all well known to those skilled in the art and are easy to obtain, and will not be described in detail here.

[0025] Step 102: Set the horizontal displacement value of the pier top as an unknown number and establish an equilibrium equation based on the pier-beam data.

[0026] First, it is assumed that each movable pier does not slide, that is, there is no relative displacement between the pier top and the beam support. Figure 2 As shown, the horizontal displacement values ​​of each pier top are 、 、 、 It should be noted that the positive and negative values ​​of the displacement values ​​are relative. For example, if the horizontal displacement value is positive when it is to the right, then the displacement value is negative when it is to the left; similarly, if the horizontal displacement value is positive when it is to the left, then the displacement value is negative when it is to the right. The beam lengths between the measured piers are 、 、 、 ;The linear expansion coefficient is ;The temperature change value is ; The horizontal thrust stiffness of each pier is 、 、 、 .

[0027] Ignoring the elastic deformation of the beam under the action of horizontal force, the equilibrium equation is established using the pier-beam data based on the balance condition of the external forces on the piers and the zero sum of the longitudinal horizontal forces on the pier tops.

[0028] As a preferred embodiment, establishing the equilibrium equation includes: setting the horizontal displacement value of the pier top as an unknown number, and based on the external force balance condition of the pier, obtaining multiple pier equations according to the linear expansion coefficient, the beam length between each pier and the temperature change value; setting the horizontal displacement value of the pier top as an unknown number, and based on the sum of the longitudinal horizontal forces at the pier top being zero, establishing the pier top equation according to the horizontal thrust stiffness of each pier; and sorting out the equilibrium equation based on the multiple pier equations and the pier top equation.

[0029] It should be noted that the external force equilibrium condition for bridge piers is that the difference in horizontal displacement between two adjacent piers is equal to the product of the expansion coefficient, the beam length between the two adjacent piers, and the temperature change. The longitudinal horizontal force at the top of each pier is equal to the product of the horizontal thrust stiffness of the pier and the horizontal displacement of the pier top.

[0030] As a specific embodiment, the bridge pier equation is: ; in, Indicates the The horizontal displacement value of the pier top; Indicates the The horizontal displacement value of the pier top; represents the linear expansion coefficient; Indicates the The piers and Length of beam between piers; Indicates the temperature change value.

[0031] like Figure 2 As shown, The corresponding piers The bridge pier equations are: ; ; ...; ; ...; .

[0032] As a specific embodiment, the pier top equation is: ; in, 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers.

[0033] By arranging the pier equation and the pier top equation into determinants, we can obtain the equilibrium equation.

[0034] It should be noted that the equilibrium equation is specifically: ; The equilibrium equation can be simplified as ; 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers; represents the linear expansion coefficient; 、 、 、 Indicates the length of the beam between each pier; Indicates the temperature change value.

[0035] Step 103: Solve the equilibrium equation to obtain the horizontal displacement of the pier top of each pier.

[0036] By measuring and calculating the horizontal thrust stiffness, linear expansion coefficient, beam length between piers and temperature change value of each pier, the horizontal displacement of the pier top of each pier can be calculated according to the equilibrium equation. 、 、 、 .

[0037] Step 104: derive the horizontal force on the pier top based on the horizontal thrust stiffness and the horizontal displacement of the pier top.

[0038] Specifically, the horizontal force at the pier top is equal to the product of the horizontal thrust stiffness and the horizontal displacement of the pier top.

[0039] Step 105: Compare the horizontal force at the pier top with the maximum static friction resistance of the support to determine whether the sliding constraint has changed. Continuously modify the equilibrium equation to solve the horizontal displacement and horizontal force at the pier top until the sliding constraint no longer changes, and obtain the horizontal force at the pier top of each pier.

[0040] It should be noted that if the bridge pier slides, it means that the sliding constraint has changed. Conversely, if the bridge pier no longer slides, it means that the sliding constraint no longer changes.

[0041] The maximum static friction resistance is equal to the product of the vertical force at the support and the friction factor, which is a conventional calculation method.

[0042] Specifically, judging whether the sliding constraint has changed includes: if the absolute value of the horizontal force at the top of the current pier is greater than the corresponding maximum static friction resistance of the support, the current pier slides, indicating that the sliding constraint has changed; conversely, if the absolute value of the horizontal force at the top of each pier is less than the corresponding maximum static friction resistance of the support, it means that each pier no longer slides, indicating that the sliding constraint no longer changes.

[0043] When the horizontal force on the top of a pier is greater than the maximum static friction resistance of the support, it means that the pier has slipped. At this time, the horizontal force on the top of the pier is equal to the maximum static friction resistance of the support, and the pier withdraws from the joint action. That is, the horizontal anti-thrust stiffness of the pier can be set to zero and substituted into the matrix In the same process, modify the vector , the fixed piers and the remaining piers that have not slipped are re-substituted into the equilibrium equation and solved until the final equilibrium is achieved.

[0044] As an embodiment, the modified equilibrium equation includes: when the sliding constraint changes, the maximum static friction resistance of the support is used as the horizontal force on the top of the current pier, and the horizontal thrust stiffness of the current pier is set to zero; at the same time, the vector sum of the static friction resistance of the pier that causes sliding is obtained; and the equilibrium equation is modified using the vector sum.

[0045] More specifically, using the vector sum to modify the equilibrium equation includes modifying the pier top equation using the vector sum, that is, the sum of the longitudinal horizontal forces on the pier top is no longer equal to zero, but is equal to the vector sum.

[0046] As a specific embodiment, Figure 3 As shown in the figure, taking a 5×30m continuous beam as an example, pier No. 3 uses fixed bearings, while the others use sliding bearings. The friction factor μ=0.03, the vertical force at the middle span support is 21600kN, and the vertical force at the two side span supports is 8500kN. The temperature change value is: a temperature increase of 10 degrees, and the linear expansion coefficient is 0.00001 / ℃. The horizontal thrust stiffness of each pier is: 、 、 、 、 、 .

[0047] Set the horizontal displacement value of the pier top to 、 、 、 、 、 , the equilibrium equation is established based on the pier-beam data: ; Solving the equilibrium equation, we can obtain the horizontal displacement of each pier top as: 、 mm 、 、 、 、 , where shifting to the left is negative and shifting to the right is positive.

[0048] The horizontal forces on the pier top are obtained based on the horizontal thrust stiffness and the horizontal displacement of the pier top, which are: 、 、 、 、 、 .

[0049] The maximum static friction resistance is obtained based on the vertical force of the support and the friction factor, which are: 、 , Pier 3 uses fixed supports, so 、 、 、 .

[0050] Compare the horizontal force on each pier top with the maximum static friction resistance of each corresponding support. 、 、 、 、 、 , it means that the bridge piers 1, 4, 5, and 6 have slipped, and the corresponding bridge piers take the maximum static friction resistance; that is, , , , .

[0051] At the same time, the horizontal thrust stiffness of piers 1, 4, 5, and 6 is set to zero, and the vector sum of the static friction resistance of the piers that cause sliding is obtained. for: ,but .

[0052] Use vector sum to modify the equilibrium equation, specifically: ; Solving the equilibrium equation, we can obtain the horizontal displacement of each pier top as: 、 mm 、 、 、 、 .

[0053] The horizontal forces on the pier top are obtained based on the horizontal thrust stiffness and the horizontal displacement of the pier top, which are: 、 The horizontal forces on the tops of piers 1, 4, 5, and 6 are: , , , .

[0054] Compare the horizontal force on the top of piers 2 and 3 with the corresponding maximum static friction resistance. 、 , it means that the No. 2 pier support has slipped, and the corresponding pier support takes the maximum static friction resistance; that is, The horizontal forces on the tops of piers 1, 4, 5, and 6 are: , , , .

[0055] At the same time, the horizontal thrust stiffness of pier 2 is set to zero, and the vector sum of the static friction resistance of the pier that causes sliding is obtained. for: ,but .

[0056] Use vector sum to modify the equilibrium equation, specifically: ; Solving the equilibrium equation, we can obtain the horizontal displacement of each pier top as: 、 mm 、 、 、 、 .

[0057] The horizontal force at the top of Pier 3 is obtained based on the horizontal thrust stiffness and the horizontal displacement of the pier top: .

[0058] At this point, the absolute value of the horizontal force on the top of all piers is no greater than the corresponding maximum static friction phase, which means that all piers no longer slide and the sliding constraint no longer changes. Therefore, the iteration converges and the horizontal force and horizontal displacement on the top of each pier are obtained. In other words, , , , , , ; 、 mm 、 、 、 、 .

[0059] The present invention does not need to calculate the temperature zero point, which greatly improves the efficiency of horizontal force calculation under the action of temperature, not only reduces calculation consumption, but also is suitable for longitudinal temperature force distribution in the case of arbitrary arrangement of multiple fixed piers.

[0060] In a second aspect, the present invention provides a computer system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any one of the above methods.

[0061] In a third aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which implements the steps of any of the above methods when executed by a processor.

[0062] It should be noted that for the aforementioned embodiments, for simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by this application.

[0063] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0064] In the several embodiments provided in this application, it should be understood that the disclosed methods or systems can be implemented in other ways. For example, the embodiments described above are merely illustrative, and the division of the units described is merely a logical functional division. In actual implementation, other division methods may be used, such as combining or integrating multiple units or components into another system, or ignoring or not implementing certain features.

[0065] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0066] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0067] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of this application, or the part that contributes to the existing technology, or all or part of the technical solution can be embodied in the form of a software product. This computer software product is stored in a memory and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of this application.

[0068] Those skilled in the art will appreciate that all or part of the various circuits in the above embodiments may be implemented by instructing related hardware through a program. The program may be stored in a computer-readable memory, which may include a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0069] The above is only an exemplary embodiment of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure herein, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any variation, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art that are not recorded in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0070] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. As long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0071] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the horizontal force of a bridge pier under the action of temperature, characterized in that: The method comprises: Acquire pier and beam data; the pier and beam data include horizontal thrust stiffness, linear expansion coefficient, beam length between piers, and temperature change value of each pier; The horizontal displacement value of the pier top is set as an unknown number, and the equilibrium equation is established based on the pier-beam data; Solving the equilibrium equation to obtain the horizontal displacement of the pier top of each pier; Obtaining a horizontal force on the pier top based on the horizontal thrust-resistance stiffness and the horizontal displacement of the pier top; The pier top horizontal force is compared with the maximum static friction resistance of the support to determine whether the sliding constraint has changed. The equilibrium equation is continuously revised to solve the pier top horizontal displacement and the pier top horizontal force until the sliding constraint no longer changes, thereby obtaining the pier top horizontal force of each pier.

2. The method for calculating horizontal forces on bridge piers under temperature according to claim 1, characterized in that: The establishment of the equilibrium equation includes: The horizontal displacement of the pier top is set as an unknown number. Based on the external force balance condition of the pier, multiple pier equations are obtained according to the linear expansion coefficient, the beam length between each pier, and the temperature change. The horizontal displacement of the pier top is set as an unknown number. Based on the assumption that the sum of the longitudinal horizontal forces at the pier top is zero, the pier top equation is established according to the horizontal thrust stiffness of each pier. Based on the multiple pier equations and the pier top equations, the equilibrium equation is obtained.

3. The method for calculating horizontal forces on bridge piers under temperature according to claim 2, characterized in that: The bridge pier equation is: ； in, Indicates the The horizontal displacement value of the pier top; Indicates the The horizontal displacement value of the pier top; represents the linear expansion coefficient; Indicates the The piers and Length of beam between piers; Indicates the temperature change value.

4. The method for calculating horizontal forces on bridge piers under temperature according to claim 2 is characterized in that: The pier top equation is: ； in, 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers.

5. The method for calculating horizontal forces on bridge piers under temperature effects according to claim 2 is characterized in that: The equilibrium equation is: ； in, 、 、 、 Indicates the horizontal thrust-resistance stiffness of each pier; 、 、 、 Indicates the horizontal displacement value of the top of each pier; Indicates the number of bridge piers; represents the linear expansion coefficient; 、 、 、 Indicates the length of the beam between each pier; Indicates the temperature change value.

6. The method for calculating horizontal forces on bridge piers under temperature effects according to claim 1 is characterized in that: Determining whether the sliding constraint has changed includes: If the absolute value of the horizontal force on the top of the current pier is greater than the corresponding maximum static friction resistance of the support, the current pier slides, indicating that the sliding constraint has changed.

7. The method for calculating horizontal forces on bridge piers under temperature effects according to claim 5 is characterized in that: Correcting the equilibrium equation includes: When the sliding constraint changes, the maximum static friction resistance of the support is used as the pier top horizontal force of the current pier, and the horizontal thrust stiffness of the current pier is set to zero; At the same time, the vector sum of the static friction of the bridge piers causing sliding is obtained; The equilibrium equation is modified using the vector sum.

8. The method for calculating horizontal forces on bridge piers under temperature effects according to claim 7 is characterized in that: Using the vector sum to correct the equilibrium equation includes: using the vector sum to correct the pier top equation.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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