Dual-objective optimization method and system for hidden carbon emission and cost of rectangular reinforced concrete beam

Abstract

The invention discloses a rectangular reinforced concrete beam hidden carbon emission and cost dual-objective optimization method and system. The method comprises the steps that design parameters of a rectangular reinforced concrete beam, the comprehensive unit price of steel bars and concrete and carbon emission factors are obtained; on the basis of the design parameters of the rectangular reinforced concrete beam, an annual average cost objective function is constructed according to the comprehensive unit price, and an annual average implicit carbon emission objective function is constructed according to the carbon emission factors; the design bearing capacity of the rectangular reinforced concrete beam is used for meeting the component bearing capacity requirement, the maximum deflection limit value is used for meeting structural deformation control and construction requirements, and constraint conditions are established; and performing dual-objective optimization on carbon emission and cost on the rectangular reinforced concrete beam member under constraint conditions to obtain an optimal solution set. The method can be used for accurately formulating a carbon reduction strategy and a cost control plan, is suitable for various policy environments, and improves environmental and economic benefits of structural design.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and relates to a dual-objective optimization method and system for implicit carbon emissions and costs of rectangular reinforced concrete beams. Background Art

[0002] The construction sector is one of the main sources of CO2 emissions. In concrete structures, beams are important components in the structure. Therefore, the optimized design of concrete beam sections based on low-carbon goals is of great significance for the development of low-carbon buildings.

[0003] At present, the low-carbon optimization design method for rectangular beams generally optimizes the cross-sectional dimensions and reinforcement configuration of the beams, taking cost or carbon emissions as the optimization objective function. However, this method does not take into account the service life of the beams, the relatively one-sided optimization design calculations, and the differences between beams of different interface types, which limits the accuracy of the optimization design calculations for rectangular beams. Summary of the invention

[0004] The purpose of the present invention is to provide a dual-objective optimization method and system for implicit carbon emissions and costs of rectangular reinforced concrete beams to solve the above problems.

[0005] To achieve the above object, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams, characterized by comprising: Obtain design parameters, combined unit prices of steel and concrete, and carbon emission factors for rectangular reinforced concrete beams; Based on the design parameters of rectangular reinforced concrete beams, an annual average cost objective function is constructed according to the comprehensive unit price, and an annual average implicit carbon emission objective function is constructed according to the carbon emission factor; The design bearing capacity of the rectangular reinforced concrete beam is used to meet the bearing capacity requirements of the component, and the maximum deflection limit is used to meet the deformation control of the structure and the construction requirements to establish constraint conditions; Under constraints, the dual-objective optimization of carbon emissions and costs was performed on rectangular reinforced concrete beam components to obtain the optimal solution set.

[0006] Optionally, obtain the design parameters of the rectangular reinforced concrete beam, including: Section Width , Section height , Number of longitudinal reinforcement , longitudinal reinforcement diameter , Number of stirrups , stirrup diameter , Concrete cover thickness , concrete strength , longitudinal reinforcement strength and stirrup strength .

[0007] Optionally, an annual average cost objective function is constructed based on the comprehensive unit price, including: The average annual cost of a rectangular reinforced concrete beam is calculated using the following formula:

[0008] The useful life

[0009] Total cost of concrete

[0010] Total cost of longitudinal reinforcement

[0011] Total stirrup cost

[0012] in , and are the carbonation coefficient, the thickness of the concrete cover and the influence coefficient of the local environment on the service life. is the density of the steel bar, is the calculated span of the beam.

[0013] Optional, combined unit prices for steel and concrete and carbon emission factors, including: The comprehensive unit prices corresponding to concrete, longitudinal reinforcement and stirrups of different strengths are expressed as , and express; The carbon emission factors corresponding to different strength concrete, longitudinal reinforcement and stirrups are respectively expressed as , and express.

[0014] Optionally, an annual average cost objective function is constructed based on the comprehensive unit price, including: The annual average carbon emissions of the rectangular beam are calculated using the following formula:

[0015] The useful life

[0016] Total carbon emissions from concrete

[0017] Total carbon emissions of longitudinal reinforcement

[0018] Total carbon emissions of stirrups

[0019] in , and are the carbonation coefficient, the thickness of the concrete cover and the influence coefficient of the local environment on the service life. is the density of the steel bar, is the calculated span of the beam.

[0020] Optionally, satisfying the bearing capacity requirements of components includes: The following formula is used to meet the bending bearing capacity requirements of the components: Single reinforcement bending bearing capacity requirements:

[0021] Double reinforcement bending bearing capacity requirements:

[0022] Where: M is the design value of the bending moment of the bending member section, is the design value of the bending bearing capacity of the normal section, is the design value of the tensile strength of the steel bar, is the section moment coefficient, is the equivalent rectangular stress figure coefficient of the concrete compression zone, is the design value of the axial compressive strength of concrete, is the effective height of the section, is the distance from the combined force point of the compressive reinforcement to the tensile edge of the section. is the cross-sectional area of ​​the compression reinforcement; The following formula is used to meet the reinforcement ratio requirements: Single reinforcement section: ;

[0023] Double reinforced section:

[0024] in is the minimum reinforcement ratio, It is the relative limit compression zone height.

[0025] Optionally, the method of satisfying the deformation control and construction requirements of the structure by utilizing the maximum deflection limit value includes: The following formula is used to satisfy the deformation control of the structure using the maximum deflection limit:

[0026] in represents the mid-span deflection of the beam, is the deflection coefficient related to the load form and support conditions, M is the design value of the section bending moment of the bending member, and EI is the section bending stiffness of the beam; The following formula is used to meet the construction requirements:

[0027] in is the basic anchorage length of the tension reinforcement. is the shape factor of the anchor reinforcement, is the design value of the tensile strength of the steel bar, It is the design value of the axial tensile strength of concrete.

[0028] Optionally, a dual-objective optimization of carbon emissions and costs is performed on rectangular reinforced concrete beam components under constraints to obtain an optimal solution set, including: Using Matlab, a non-dominated sorting genetic algorithm NSGA-II was used to perform dual-objective optimization of carbon emissions and costs on the rectangular beam component, and the Pareto optimal solution set was obtained.

[0029] In a second aspect, the present invention provides a dual-objective optimization system for implicit carbon emissions and costs of rectangular reinforced concrete beams, comprising: A data acquisition module is used to obtain the design parameters of rectangular reinforced concrete beams, the comprehensive unit prices of steel bars and concrete, and the carbon emission factor; The objective function establishment module is used to construct the annual average cost objective function according to the comprehensive unit price based on the design parameters of the rectangular reinforced concrete beam, and to construct the annual average implicit carbon emission objective function according to the carbon emission factor; The constraint condition establishment module is used to use the design bearing capacity of the rectangular reinforced concrete beam to meet the bearing capacity requirements of the component, and to use the maximum deflection limit to meet the deformation control of the structure and the construction requirements to establish constraint conditions; The solution output module is used to perform dual-objective optimization of carbon emissions and costs on rectangular reinforced concrete beam components under constraints to obtain the optimal solution set.

[0030] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the processor implements the steps of the dual-objective optimization method of the implicit carbon emissions and costs of the rectangular reinforced concrete beam.

[0031] Compared with the prior art, the present invention has the following technical effects: The present invention not only takes into account the cost of the beam, but also introduces carbon emissions as an optimization target. By optimizing carbon emissions and costs at the same time, it can ensure that while meeting economic efficiency, environmental protection standards are also met, providing decision makers with a more comprehensive perspective.

[0032] The present invention establishes an accurate annual average cost and carbon emission objective function by defining the design parameters of the beam in detail (such as section width, height, number of steel bars, diameter, etc.) and taking into account the comprehensive unit price of concrete and steel bars and the carbon emission factor. Adjustments are made according to different material prices, carbon emission factors and service life, which improves the flexibility and applicability of the design.

[0033] The present invention adopts non-dominated sorting genetic algorithm (NSGA-II) for dual-objective optimization. The algorithm is efficient and stable when dealing with multi-objective optimization problems and can quickly find the Pareto optimal solution set. The algorithm is implemented using programming tools such as Matlab, which improves the intelligent level of design and reduces the time and error of manual trial calculation.

[0034] The present invention ensures that the optimized beam structure is not affected in terms of safety by satisfying the constraints such as the bearing capacity requirements of the components, the maximum deflection limit and the construction requirements. The establishment of the constraints is based on industry standards and specifications, making the design results more authoritative and credible.

[0035] Based on the Pareto optimal solution set, the present invention can clearly see the specific impact of different policy options (such as carbon tax, material price changes, etc.) on carbon emissions and costs, providing strong decision-making support for policy makers. By adjusting the optimization objectives or constraints, carbon reduction strategies and cost control plans can be flexibly formulated to adapt to different market environments and policy requirements.

[0036] In summary, this technical solution achieves the dual-objective optimization design of rectangular reinforced concrete beams by comprehensively considering carbon emissions and costs, refining design parameters and model establishment, applying advanced optimization algorithms, strict constraints to ensure structural safety, and supporting policy formulation and decision optimization. This not only improves the economy and environmental protection of the design, but also makes an important contribution to the sustainable development of the construction industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention.

[0038] Figure 2 This is a logic block diagram of the present invention. DETAILED DESCRIPTION

[0039] The present invention is further described below in conjunction with the accompanying drawings: Example 1, please refer to Figure 1 The present invention provides a dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams, comprising: Obtain design parameters, combined unit prices of steel and concrete, and carbon emission factors for rectangular reinforced concrete beams; Based on the design parameters of rectangular reinforced concrete beams, an annual average cost objective function is constructed according to the comprehensive unit price, and an annual average implicit carbon emission objective function is constructed according to the carbon emission factor; The design bearing capacity of the rectangular reinforced concrete beam is used to meet the bearing capacity requirements of the component, and the maximum deflection limit is used to meet the deformation control of the structure and the construction requirements to establish constraint conditions; Under constraints, the dual-objective optimization of carbon emissions and costs was performed on rectangular reinforced concrete beam components to obtain the optimal solution set.

[0040] By obtaining the specific design parameters of rectangular reinforced concrete beams, the comprehensive unit prices of steel bars and concrete, and carbon emission factors, this method provides a detailed data basis for the optimization design. This data-driven approach ensures the accuracy and reliability of the optimization results.

[0041] The construction of the annual average cost objective function and the annual average implicit carbon emission objective function reflects the requirements of economy and environmental protection respectively. This dual objective setting enables the optimization process to consider both economic benefits and environmental impacts at the same time and achieve a balance between the two.

[0042] By calculating the average annual cost, this method takes into account the economic cost of the beam throughout its entire service life, which helps decision makers consider it from a long-term perspective and avoid potential risks brought about by short-term behavior.

[0043] The design bearing capacity is used to meet the bearing capacity requirements of the components, and the maximum deflection limit is used to meet the deformation control and construction requirements of the structure. The setting of these constraints ensures that the optimized beam structure does not compromise in terms of safety. The constraints not only take into account the safety of the structure, but also involve the deformation control and construction requirements of the structure, which helps to improve the comprehensive performance of the beam, including durability and seismic resistance.

[0044] The dual-objective optimization of rectangular reinforced concrete beam components under constraints requires efficient algorithm support. This method can quickly find the optimal solution set under limited computing resources by adopting appropriate optimization algorithms (such as non-dominated sorting genetic algorithm, etc.). Dual-objective optimization usually produces a solution set containing multiple optimal solutions (i.e., Pareto optimal solution set). This diversity provides decision makers with more choices and allows them to choose the most appropriate solution based on actual needs and policy orientation.

[0045] In summary, this technical solution achieves dual-objective optimization of embodied carbon emissions and costs of rectangular reinforced concrete beams through data-driven decision support, scientific construction of objective functions, strict constraints to ensure safety, efficient implementation of dual-objective optimization, and promotion of green buildings and sustainable development. This not only improves the economy and environmental protection of building design, but also makes important contributions to the sustainable development of the construction industry and the promotion of green buildings.

[0046] Example 2, please refer to Figure 2 The present invention provides a dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams, specifically comprising: The method of the present invention selects the design parameters of the beam as variables in the genetic algorithm, establishes an annual average cost objective function according to the comprehensive unit price of steel bars and concrete during the construction process, and establishes an annual average implicit carbon emission objective function according to the carbon emission factors of steel bars and concrete during the construction process. Constraints are established by using the design bearing capacity to meet the bearing capacity requirements of the component and by using the maximum deflection limit to meet the deformation control and construction requirements of the structure. The non-dominated sorting genetic algorithm (NSGA-II) is used to perform dual-objective optimization of carbon emissions and costs on the rectangular beam component to obtain the Pareto optimal solution set.

[0047] See also Figure 2 , which is a flow chart of a dual-objective optimization design method for implicit carbon emissions and costs of rectangular reinforced concrete beams based on a genetic algorithm provided by the present invention. Figure 2 The dual-objective optimization design method for embodied carbon emissions and costs of rectangular reinforced concrete beams based on genetic algorithms described in the paper includes: Step 1: Design parameters of the beam, including: Section width , Section height , Number of longitudinal reinforcement , longitudinal reinforcement diameter , Number of stirrups , stirrup diameter , Concrete cover thickness , concrete strength , longitudinal reinforcement strength , stirrup strength ; Step 2: Obtain the comprehensive unit price of steel and concrete and the carbon emission factor. The comprehensive unit price of concrete, longitudinal bars and stirrups of different strengths is calculated using , and The carbon emission factors corresponding to different strength concrete, longitudinal reinforcement and stirrups are expressed as , and express.

[0048] Step 3: Establish the annual average cost objective function;

[0049] The useful life

[0050] Total cost of concrete

[0051] Total cost of longitudinal reinforcement

[0052] Total stirrup cost

[0053] Step 4: Establish an annual average carbon emission objective function;

[0054] The useful life

[0055] Total carbon emissions from concrete

[0056] Total carbon emissions of longitudinal reinforcement

[0057] Total carbon emissions of stirrups

[0058] in , and are the carbonation coefficient, the thickness of the concrete cover and the influence coefficient of the local environment on the service life. is the density of the steel bar, is the calculated span of the beam.

[0059] Step 5: Use the following formula to meet the bending bearing capacity requirements of the components: Single reinforcement bending bearing capacity requirements:

[0060] Double reinforcement bending bearing capacity requirements:

[0061] Where: M is the design value of the bending moment of the bending member section, is the design value of the bending bearing capacity of the normal section, is the design value of the tensile strength of the steel bar, is the section moment coefficient, is the equivalent rectangular stress figure coefficient of the concrete compression zone, is the design value of the axial compressive strength of concrete, is the effective height of the section, is the distance from the combined force point of the compressive reinforcement to the tensile edge of the section. is the cross-sectional area of ​​the compression reinforcement.

[0062] The following formula is used to meet the reinforcement ratio requirements: Single reinforcement section: ;

[0063] Double reinforced section:

[0064] in is the minimum reinforcement ratio, It is the relative limit compression zone height.

[0065] Step 6: Use the following formula to satisfy the deformation control of the structure by using the maximum deflection limit:

[0066] in represents the mid-span deflection of the beam, It is the deflection coefficient related to the load form and support conditions, M is the design value of the section bending moment of the bending member, and EI is the section bending stiffness of the beam.

[0067] Step 7: Use the following formula to meet the construction requirements:

[0068] in is the basic anchorage length of the tension reinforcement. is the shape factor of the anchor reinforcement, is the design value of the tensile strength of the steel bar, It is the design value of the axial tensile strength of concrete.

[0069] Step 8: Use Matlab to perform the operation of the dual-objective genetic algorithm.

[0070] This method considers both cost and carbon emissions. By selecting design parameters as algorithm variables, establishing the objective function of annual average cost and carbon emissions, setting structural bearing capacity and deformation control as constraints, and using non-dominated sorting genetic algorithm (NSGA-II) for optimization, the Pareto optimal solution set is obtained. This method can be used to accurately formulate carbon reduction strategies and cost control plans, is applicable to a variety of policy environments, and improves the environmental and economic benefits of structural design.

[0071] In yet another embodiment of the present invention, a dual-objective optimization system for embodied carbon emissions and costs of rectangular reinforced concrete beams is provided, which can be used to implement the dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams. Specifically, the system includes: A data acquisition module is used to obtain the design parameters of rectangular reinforced concrete beams, the comprehensive unit prices of steel bars and concrete, and the carbon emission factor; The objective function establishment module is used to construct the annual average cost objective function according to the comprehensive unit price based on the design parameters of the rectangular reinforced concrete beam, and to construct the annual average implicit carbon emission objective function according to the carbon emission factor; The constraint condition establishment module is used to use the design bearing capacity of the rectangular reinforced concrete beam to meet the bearing capacity requirements of the component, and to use the maximum deflection limit to meet the deformation control of the structure and the construction requirements to establish constraint conditions; The solution output module is used to perform dual-objective optimization of carbon emissions and costs on rectangular reinforced concrete beam components under constraints to obtain the optimal solution set.

[0072] The division of modules in the embodiments of the present invention is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional module in each embodiment of the present invention may be integrated into one processor, or may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated modules may be implemented in the form of hardware or in the form of software functional modules.

[0073] In another embodiment of the present invention, a computer device is provided, the computer device including a processor and a memory, the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions in the computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the dual-objective optimization method of the implicit carbon emissions and costs of rectangular reinforced concrete beams.

[0074] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0075] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0076] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0077] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams, characterized in that: include: Obtain design parameters, combined unit prices of steel and concrete, and carbon emission factors for rectangular reinforced concrete beams; Based on the design parameters of rectangular reinforced concrete beams, an annual average cost objective function is constructed according to the comprehensive unit price, and an annual average implicit carbon emission objective function is constructed according to the carbon emission factor; The design bearing capacity of the rectangular reinforced concrete beam is used to meet the bearing capacity requirements of the component, and the maximum deflection limit is used to meet the deformation control of the structure and the construction requirements to establish constraint conditions; Under constraints, the dual-objective optimization of carbon emissions and costs was performed on rectangular reinforced concrete beam components to obtain the optimal solution set.

2. The dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams according to claim 1 is characterized in that: Obtain design parameters for rectangular reinforced concrete beams, including: Section Width , Section height , Number of longitudinal reinforcement , longitudinal reinforcement diameter , Number of stirrups , stirrup diameter , Concrete cover thickness , concrete strength , longitudinal reinforcement strength and stirrup strength .

3. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 2 is characterized in that: The annual average cost objective function is constructed based on the comprehensive unit price, including: The average annual cost of a rectangular reinforced concrete beam is calculated using the following formula: The useful life Total cost of concrete Total cost of longitudinal reinforcement Total stirrup cost in , and are the carbonation coefficient, the thickness of the concrete cover and the influence coefficient of the local environment on the service life. is the density of the steel bar, is the calculated span of the beam.

4. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 1 is characterized in that: The comprehensive unit price of steel and concrete and the carbon emission factor, including: The comprehensive unit prices corresponding to concrete, longitudinal reinforcement and stirrups of different strengths are expressed as , and express; The carbon emission factors corresponding to different strength concrete, longitudinal reinforcement and stirrups are respectively expressed as , and express.

5. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 4 is characterized in that: The annual average cost objective function is constructed based on the comprehensive unit price, including: The annual average carbon emissions of the rectangular beam are calculated using the following formula: The useful life Total carbon emissions from concrete Total carbon emissions of longitudinal reinforcement Total carbon emissions of stirrups in , and are the carbonation coefficient, the thickness of the concrete cover and the influence coefficient of the local environment on the service life. is the density of the steel bar, is the calculated span of the beam.

6. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 1 is characterized in that: The said meeting the bearing capacity requirements of the components includes: The following formula is used to meet the bending bearing capacity requirements of the components: Single reinforcement bending bearing capacity requirements: Double reinforcement bending bearing capacity requirements: Where: M is the design value of the bending moment of the bending member section, is the design value of the bending bearing capacity of the normal section, is the design value of the tensile strength of the steel bar, is the section moment coefficient, is the equivalent rectangular stress figure coefficient of the concrete compression zone, is the design value of the axial compressive strength of concrete, is the effective height of the section, is the distance from the combined force point of the compressive reinforcement to the tensile edge of the section. is the cross-sectional area of ​​the compression reinforcement; The following formula is used to meet the reinforcement ratio requirements: Single reinforcement section: ; Double reinforced section: in is the minimum reinforcement ratio, It is the relative limit compression zone height.

7. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 1 is characterized in that: The method of satisfying the deformation control and construction requirements of the structure by utilizing the maximum deflection limit value includes: The following formula is used to satisfy the deformation control of the structure using the maximum deflection limit: in represents the mid-span deflection of the beam, is the deflection coefficient related to the load form and support conditions, M is the design value of the section bending moment of the bending member, and EI is the section bending stiffness of the beam; The following formula is used to meet the construction requirements: in is the basic anchorage length of the tension reinforcement. is the shape factor of the anchor reinforcement, is the design value of the tensile strength of the steel bar, It is the design value of the axial tensile strength of concrete.

8. The dual-objective optimization method for embodied carbon emissions and costs of rectangular reinforced concrete beams according to claim 1, characterized in that: Under the constraints, the dual-objective optimization of carbon emissions and costs for rectangular reinforced concrete beam components is carried out, and the optimal solution set is obtained, including: Using Matlab, a non-dominated sorting genetic algorithm NSGA-II was used to perform dual-objective optimization of carbon emissions and costs on the rectangular beam component, and the Pareto optimal solution set was obtained.

9. A dual-objective optimization system for implicit carbon emissions and costs of rectangular reinforced concrete beams, characterized in that: include: A data acquisition module is used to obtain the design parameters of rectangular reinforced concrete beams, the comprehensive unit prices of steel bars and concrete, and the carbon emission factor; The objective function establishment module is used to construct the annual average cost objective function according to the comprehensive unit price based on the design parameters of the rectangular reinforced concrete beam, and to construct the annual average implicit carbon emission objective function according to the carbon emission factor; The constraint condition establishment module is used to use the design bearing capacity of the rectangular reinforced concrete beam to meet the bearing capacity requirements of the component, and to use the maximum deflection limit to meet the deformation control of the structure and the construction requirements to establish constraint conditions; The solution output module is used to perform dual-objective optimization of carbon emissions and costs on rectangular reinforced concrete beam components under constraints to obtain the optimal solution set.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the dual-objective optimization method for implicit carbon emissions and costs of rectangular reinforced concrete beams as described in any one of claims 1 to 7 are implemented.

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