Reinforced beam bending resistance analysis method considering material constitutive whole curve
By performing element-wise analysis and iterative calculation of material constitutive relations on reinforced beams, the problems of high cost and long cycle in existing technologies are solved, and efficient flexural performance evaluation of new and deteriorated reinforced beams is achieved, supporting the design and deterioration assessment of civil engineering structures.
Patent Information
- Application Number
- CN202511569533.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-30
- Publication Date
- 2026-01-23
AI Technical Summary
Existing technologies are costly and time-consuming in analyzing the bending performance of new reinforced beams and evaluating the remaining bending performance after deterioration. They cannot achieve low-cost and efficient parameter analysis, especially in beam members made of new materials and with deteriorated structures, where there is a lack of engineering experience and experimental data.
By identifying the location of the main crack, the reinforced beam is discretized into multiple elements. Combining the material constitutive relation and the component size, the neutral axis height and strain distribution under each curvature level are iteratively calculated. The moment-curvature relationship is calculated, and the deflection and failure mode of the beam are analyzed in combination with the load form, thus achieving efficient evaluation of the bending performance.
It enables low-cost and efficient assessment of the bending performance of new and deteriorated reinforced beams, provides sensitivity analysis and deterioration assessment of key design parameters, and offers a convenient and reliable method for civil engineering structural design.
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Figure CN121389490A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of civil engineering structure performance calculation, and in particular to a method for analyzing the bending resistance of a reinforced beam considering the full curve of the material constitutive relation. BACKGROUND
[0002] With the progress and development of society, people's requirements for the performance of civil engineering structures are continuously improving, and civil engineering materials are also continuously improving and improving. In addition to traditional steel and concrete materials, new materials including fiber concrete, FRP bars, etc. have also begun to be applied in civil engineering. Civil engineering structural member design is flexible and variable, and the material constitutive model and its deterioration behavior of the components such as beams and plates have become complex and diverse, and there is an urgent need for models and methods that can quickly calculate the mechanical properties of various new materials or deteriorated structural members.
[0003] Existing analysis of the bending resistance of new reinforced beams and evaluation of the residual bending resistance of deteriorated reinforced beams mainly rely on experiments and finite element simulation, which require high cost, long cycle, and are not convenient for conducting a large number of parameter analyses. When the calculation object is a beam composed of new materials or a beam subjected to various deterioration effects (such as steel bar corrosion), due to the lack of a large amount of engineering experience, experimental data and theoretical analysis experience, a large number of analyses need to be conducted on cross-sectional size, steel bar arrangement form, reinforcement ratio, and key parameters of material constitutive relation, etc. to explore the influence of reinforcement form, material properties and cross-sectional size on beam failure mode and load-displacement curve, and it is impossible to achieve low-cost and efficient bending resistance analysis of reinforced beams. SUMMARY
[0004] The present application aims to overcome the shortcomings of the prior art and provide a method for analyzing the bending resistance of a reinforced beam considering the full curve of the material constitutive relation to solve the problems in the prior art.
[0005] The present application specifically provides the following technical solutions: Identifying and recording the position of the main crack in the reinforced beam; the main crack represents a diagonal crack at a set angle to the axis of the reinforced beam appearing in the web of the reinforced beam; Discretizing the reinforced beam into N reinforced beam units connected end to end according to the position information of the main crack; By the material constitutive relation of the concrete and the reinforcement in the reinforced beam, the component size and the reinforcement form, the cross-sectional height of each reinforced beam unit is divided into several layers, loaded in a curvature-increasing manner, and the neutral axis height of the reinforced beam at each level of curvature, the strain and stress distribution of each layer of concrete and reinforcement, and the bending failure mode of the normal section of the reinforced beam unit are iteratively calculated according to the force balance condition, the deformation compatibility condition and the stress-strain physical relationship of the material, and the bending moment-curvature relationship of the normal section of the reinforced beam unit is obtained from the iterative calculation results. The moment distribution along the length of the reinforced beam is determined according to the load form of the reinforced beam, and the curvature distribution along the length of the beam is calculated according to the moment value on each reinforced beam unit and the moment-curvature relationship, the rotation angle and deflection distribution of the beam are obtained by integrating the curvature distribution, and the load-deflection curve of the reinforced beam in the bearing process and the failure mode and failure position of the reinforced beam are obtained through the relationship between the rotation angle and the deflection distribution.
[0006] Preferably, before the cross-section height of each reinforced beam unit is divided into several layers, it further comprises: The different bending failure modes of the reinforced beam unit are defined, specifically: bending failure mode I: when the compressive zone concrete strain is greater than the ultimate compressive strain of the concrete, the concrete is crushed; bending failure mode II: when the tensile zone steel bar strain is greater than the ultimate tensile strain of the steel bar, the steel bar is broken.
[0007] Preferably, the reinforced beam includes any one of the following beam plate components: ordinary reinforced concrete beam, FRP reinforced concrete beam, hybrid reinforced concrete beam, reinforced fiber reinforced concrete beam, ECC-concrete composite beam, and FRP / CFRP reinforced concrete slab.
[0008] Preferably, the load form includes the concentrated load, distributed load and non-uniform load of various statically determinate beams.
[0009] Preferably, the material constitutive relationship of the concrete and the reinforcement includes the constitutive relationship between traditional steel bars, concrete, various new cement-based materials, FRP reinforcement, deteriorated concrete and deteriorated reinforcement.
[0010] Preferably, for the beam structure without service or without main crack during service, the average crack spacing is calculated by referring to the empirical data or according to the relevant industry specifications for concrete structure design, and the main crack position is predicted.
[0011] Preferably, the average crack spacing is calculated by referring to the empirical data or according to the relevant industry specifications for concrete structure design, and the specific expression is: ; Wherein, is the average crack spacing, is the comprehensive coefficient, is the concrete cover thickness, is the diameter of the steel bar, is the longitudinal tensile reinforcement ratio of the tensile zone.
[0012] Preferably, when the moment distribution along the length of the reinforced beam is determined according to the load form of the reinforced beam, and the curvature distribution along the length of the beam is calculated according to the moment value on each reinforced beam unit and the moment-curvature relationship, the structure form used is statically determinate.
[0013] Compared with the prior art, the present application has the following remarkable advantages: The present application can consider different material constitutive relations, component sizes and reinforcement forms of each reinforced beam unit, iteratively calculate the neutral axis height under each level of curvature, the corresponding strain and stress distribution of each layer of concrete and reinforcement, and the flexural failure mode of the normal section of the reinforced beam unit, obtain the moment-curvature relationship of the normal section of the reinforced beam unit, realize the sensitivity analysis of the key design parameters of the beam on the flexural performance of the beam and the efficient calculation of the flexural performance of the reinforced beam, and provide a convenient and reliable method for the design of new civil engineering structures; meanwhile, according to the load form and the moment-curvature relationship of each section, the curvature distribution along the longitudinal axis of the section is calculated, and then the deflection distribution of the beam is calculated, thereby obtaining the load-deflection curve of the beam, and the failure mode and failure position of the reinforced beam; by assigning deterioration information to the overall or local material constitutive (through the load form), the present application realizes the low-cost and efficient evaluation of the flexural performance of the reinforced beam through the flexural behavior analysis process of the overall or local deteriorated reinforced beam, and provides data support and reference for the durability design and deterioration evaluation of civil engineering structure components. BRIEF DESCRIPTION OF DRAWINGS
[0014] Figure 1 is a flowchart of a reinforced beam flexural performance analysis method considering material constitutive full curve provided by the present application; Figure 2 is a step S2 diagram provided by the embodiment of the present application; Figure 3 is a step S3 diagram provided by the embodiment of the present application; wherein, Figure 3 (a) of is a steel stress-strain evolution diagram, Figure 3 (b) of is a compressive zone concrete stress-strain evolution diagram, Figure 3 (c) of is a beam section moment-curvature relationship diagram, Figure 3 (d) of is a beam section stress distribution diagram; Figure 4 is a load-deflection curve diagram in steps S4 and S5 provided by the embodiment of the present application; wherein Figure 4 (a) of is a beam midpoint moment curve and evolution diagram, Figure 4 (b) of is a beam midpoint load-deflection curve diagram; Figure 5 is a deformation distribution and evolution diagram and a failure mode and failure position diagram of the reinforced beam in steps S4 and S5 provided by the embodiment of the present application; wherein, Figure 5 (a) of is a curvature distribution and evolution diagram of the beam in the loading process, Figure 5 (b) of is a moment distribution and evolution diagram of the beam in the loading process, Figure 5 (c) of is a rotation angle distribution and evolution diagram of the beam in the loading process, Figure 5The (d) is the deflection distribution and evolution diagram of the beam in the loading process. DETAILED DESCRIPTION
[0015] The technical solutions of the embodiments of the application will be clearly and completely described below with reference to the drawings in the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative labor should fall within the protection scope of the application.
[0016] Under the current reality conditions of the diversity of civil engineering materials, the diversity of civil engineering structure forms and the diversity of deterioration mechanisms, the high cost of traditional tests and finite element analysis cannot fully meet the use requirements of new civil engineering structure member design and deteriorated member performance evaluation. Under the current background of the diversity of materials and the diversity of deterioration mechanisms in the field of civil engineering, a method for calculating the flexural performance of a reinforced beam is developed, which can consider the constitutive behavior of new structural materials and the constitutive behavior of various deteriorated materials. The method for calculating the flexural performance of a reinforced beam can consider the constitutive behavior of new structural materials and the constitutive behavior of various deteriorated materials. It is committed to accurately and efficiently realizing the evaluation and calculation of the flexural performance of a new reinforced beam and the residual flexural performance of a deteriorated reinforced beam, and providing data support and reference for the design, calculation and deterioration evaluation of civil engineering structure members. The application will promote the development and application of new material structures and improve the reliability of the performance evaluation of existing deteriorated structures.
[0017] As shown in Figure 1 , a method for calculating the flexural performance of a reinforced beam considering the full curve of the constitutive behavior of materials in the embodiment includes the following steps: Step S1: Identify and record the position of the main crack in the reinforced concrete beam. For the beam structure without service or without appearing main crack during service, calculate the average crack spacing according to the relevant industry standard for concrete structure design (such as “Concrete Structure Design Standard (GB50010-2010)”) to predict the position of the main crack; the main crack represents the oblique crack with a set angle to the axis of the reinforced beam appearing in the web of the reinforced beam.
[0018] Taking “Concrete Structure Design Standard (GB50010-2010)” as an example, the calculation formula of the average crack spacing is: , wherein is the average crack spacing, is the comprehensive coefficient, is the thickness of the concrete cover, is the diameter of the steel bar, is the reinforcement ratio of the longitudinal tensile steel bar in the tensile zone.
[0019] Step S2: Discretize the reinforced concrete beam into N beam elements according to the location information of the main crack, as shown in FIG. 2. Figure 2
[0020] Step S3: Based on the plane section assumption principle, analyze the normal section of each reinforced beam element through the material constitutive relationship of the concrete and reinforcement in the reinforced beam, the size of the component and the reinforcement form; that is, divide the section height of each reinforced beam element into several layers in a curvature-increasing manner through the material constitutive relationship of the concrete and reinforcement in the reinforced beam, the size of the component and the reinforcement form, load, and according to the force balance condition, deformation compatibility condition and stress-strain physical relationship of the material, iteratively calculate the neutral axis height of the reinforced beam at each level of curvature, the strain and stress distribution of each layer of concrete and reinforcement, and the bending failure mode of the normal section of the reinforced beam element, to obtain the bending moment-curvature relationship of the normal section of the reinforced beam element from the iterative calculation results.
[0021] For each element with local deterioration of reinforcement, the reinforcement constitutive relationship adopts the reinforcement constitutive relationship under the deterioration degree of the element, so as to consider the local deterioration of the reinforcement (such as local pitting corrosion of steel bars); the constitutive of the concrete in the compression zone adopts the complete stress-strain nonlinear curve; the constitutive relationship of the concrete (including traditional concrete and various new cement-based materials) after cracking adopts the constitutive relationship of the residual stress and crack width relationship of the concrete; that is, divide the section height of each reinforced beam element into several layers (the number of layers of beam section height division is at least 50 layers) through the material constitutive relationship of the concrete and reinforcement in the reinforced beam, the size of the component and the reinforcement form, and if the concrete is composed of multiple types of concrete with different properties (i.e. composite beam), the corresponding concrete constitutive relationship of each layer is adopted; for the normal section of each beam element, load in a curvature-increasing manner, and according to the force balance condition, deformation compatibility condition and stress-strain physical relationship of the material, the neutral axis height of each beam element at each level of curvature, the strain and stress distribution and evolution of each layer of concrete and steel bar, and the bending failure mode of the normal section of the reinforced beam element are calculated by an iterative algorithm to obtain the bending moment-curvature relationship of the normal section of each reinforced beam element, as shown in FIG. 3. Figure 3
[0022] For the deteriorated beam element, the stress, strain distribution and evolution of each layer of material of the normal section of the deteriorated beam element, the bending failure mode of the normal section of the deteriorated beam element and the bending moment-curvature relationship of the normal section of the deteriorated beam element can be obtained by analyzing the normal section of each deteriorated beam element through the properties of the related deteriorated materials and the size of the structure. The material constitutive relationship of the concrete and reinforcement includes the constitutive relationship between traditional steel bars, concrete, various new cement-based materials, FRP reinforcement, deteriorated concrete and deteriorated reinforcement.
[0023] When analyzing and calculating the normal section of each beam element, it also includes: The different flexural failure modes of the beam unit are defined, and specifically, flexural failure mode I: when the compressive zone concrete strain is greater than the ultimate compressive strain of the concrete ( ), the concrete is crushed.Flexural failure mode II: when the tensile zone steel strain is greater than the ultimate tensile strain of the steel ( ), the steel is broken.For new materials and deteriorated materials, their corresponding failure criteria can be set.
[0024] Step S4: Calculate the bending moment distribution of the reinforced concrete beam along the length of the reinforced beam according to the load form of the reinforced beam, and calculate the curvature distribution along the length of the beam according to the bending moment-curvature distribution of each reinforced beam unit, and integrate the curvature distribution to obtain the deflection distribution of the beam, and obtain the load-deflection curve of the reinforced beam in the loading process, the deformation distribution and evolution of the reinforced beam in the loading process, and the failure mode and failure position of the reinforced beam, and calculate the ultimate load and final deformation of the reinforced beam, as shown in Figure 4 、 Figure 5 .
[0025] Step S4 is a global deformation analysis of the reinforced concrete beam according to the stress condition and structure form of the reinforced beam, to obtain the deformation distribution and evolution of the reinforced beam in the loading process, the load-deflection curve of the reinforced beam in the loading process, and the failure mode and failure position of the reinforced beam. The reinforced beam includes: ordinary reinforced concrete beam, FRP reinforced concrete beam, mixed reinforced concrete beam, reinforced fiber concrete beam, ECC-concrete composite beam, FRP / CFRP reinforced concrete slab and any one of the beam-slab components. The structure form suitable for global deformation analysis is static, such as simply supported beam and cantilever beam.
[0026] Step S5: In the steps and processes described in S1-S4, different specific values are selected for a certain quantity to obtain different calculation results, and the sensitivity analysis of key parameters and elements of interest is realized.
[0027] The reinforced beam flexural performance analysis method considering the material constitutive full curve is efficient, convenient, and widely applicable, and can be used to calculate ordinary reinforced concrete beams, FRP reinforced concrete beams, steel-FRP mixed reinforced concrete beams, various reinforced fiber concrete beams, ECC-concrete composite beams, FRP / CFRP reinforced concrete slabs and any one of the beam-slab structures.
[0028] The reinforced beam normal section analysis method considering material constitutive full curve provided by the application can consider arbitrary nonlinear cement-based material constitutive relation (including strain-softening concrete, strain-hardening fiber-reinforced concrete, deteriorated concrete, etc.), and the constitutive relation of reinforcement (commonly used steel bars, corroded steel bars, new type reinforcement, deteriorated new type reinforcement, etc.), and can quickly calculate the moment-curvature relation of the reinforced beam normal section, the stress distribution and evolution of the reinforced beam normal section in the deformation process, the stress change of the reinforcement and the concrete in the bending process of the reinforced beam normal section, and the failure mode of the reinforced beam normal section in the bending process, and provides accurate, efficient and convenient analysis and calculation means and data support for the section design of civil engineering structural members. The calculation method provided by the application can accurately, efficiently and conveniently analyze the deformation response of the reinforced beam in the loading process, obtain the distribution and evolution of the rotation deformation, the curvature deformation and the deflection deformation of the reinforced beam in the loading process, and the load-deflection curve, calculate the ultimate load, the failure mode and the failure position that can be borne by the reinforced beam, and realize the whole process analysis and prediction of the reinforced beam in the loading process.
[0029] The reinforced beam normal section analysis method provided by the application can perform parameter analysis on the component elements of the beam normal section, evaluate the influence of factors such as the reinforcement type, the reinforcement ratio, the concrete strength grade, the fiber concrete type and the fiber content of the fiber concrete on the deformation capacity, the bending bearing capacity and the failure mode of the reinforced beam normal section, and analyze the influence of these component elements on the bearing capacity, the deformation capacity, the failure mode and the failure position of the reinforced beam in the global deformation analysis of the reinforced beam, thereby helping to optimize the design of civil engineering structural members and improve the structural performance.
[0030] The reinforced beam normal section analysis method considering material constitutive full curve provided by the application can quickly and accurately calculate the moment-curvature relation of the deteriorated reinforced beam (such as corroded reinforced concrete) normal section, the stress distribution and evolution of the deteriorated reinforced beam normal section along the section height in the deformation process, the stress change of the reinforcement and the concrete in the bending process of the deteriorated reinforced beam normal section, and the failure mode of the deteriorated reinforced beam normal section in the bending process. The influence of factors such as the deterioration position and the deterioration degree on the deformation capacity of the reinforced beam normal section, the bending bearing capacity of the reinforced beam normal section and the failure mode of the reinforced beam normal section can be quantitatively analyzed. In the global deformation analysis of the reinforced beam, the influence of these deterioration factors on the residual bending bearing capacity, the deformation capacity, the failure mode and the failure position of the reinforced beam can be evaluated. The calculation method and data reference are provided for the residual bending performance evaluation of the deteriorated reinforced beam and the durability design of civil engineering structural members.
[0031] The above is further detailed description of the present application in combination with specific preferred embodiments. For those skilled in the art of the present application, without departing from the concept of the present application, a number of simple deductions or replacements can be made, which should be considered as falling within the protection scope of the present application.
Claims
1. A method for analyzing the flexural performance of a reinforced beam considering the full curve of the material constitutive, characterized in that, The method comprises the following steps: identifying and recording the position of the main crack in the reinforced beam; the main crack represents a diagonal crack at a set angle to the axis of the reinforced beam appearing in the web of the reinforced beam; discretizing the reinforced beam into N reinforced beam units connected end to end according to the position information of the main crack; dividing the cross-sectional height of each reinforced beam unit into several layers by the material constitutive relationship of the concrete and the reinforcement in the reinforced beam, the component size and the reinforcement form, loading in a curvature-increasing manner, and iteratively calculating the neutral axis height of the reinforced beam at each level of curvature, the strain and stress distribution of each layer of concrete and reinforcement, and the flexural failure mode of the normal section of the reinforced beam unit according to the force balance condition, deformation compatibility condition and stress-strain physical relationship of the material, to obtain the moment-curvature relationship of the normal section of the reinforced beam unit from the iterative calculation results; determining the moment distribution along the length direction of the reinforced beam according to the load form of the reinforced beam, and calculating the curvature distribution along the length of the beam according to the moment value and the moment-curvature relationship on each reinforced beam unit, and obtaining the load-deflection curve of the reinforced beam and the failure mode and failure position of the reinforced beam through the integral of the curvature distribution to obtain the rotation angle and deflection distribution of the beam.
2. The method for analyzing the flexural performance of reinforced beams considering the entire constitutive curve of materials as described in claim 1, characterized in that, Before the step of dividing the cross-sectional height of each reinforced beam unit into several layers, the method further comprises the following steps: defining different flexural failure modes of the reinforced beam unit, specifically: flexural failure mode I: when the compressive strain of the concrete in the compression zone is greater than the ultimate compressive strain of the concrete, the concrete is crushed; flexural failure mode II: when the tensile strain of the steel bar in the tension zone is greater than the ultimate tensile strain of the steel bar, the steel bar is fractured.
3. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 1, characterized in that, The reinforced beam comprises any one of the following beam and slab components: ordinary reinforced concrete beam, FRP reinforced concrete beam, hybrid reinforced concrete beam, reinforced fiber reinforced concrete beam, ECC-concrete composite beam, and FRP / CFRP reinforced concrete slab.
4. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 1, wherein, The load form includes concentrated load, distributed load and non-uniform load of statically determinate beams.
5. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 1, wherein, The material constitutive relationship of the concrete and the reinforcement includes the constitutive relationship between traditional steel bars, concrete, various types of new cement-based materials, FRP reinforcement, deteriorated concrete and deteriorated reinforcement.
6. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 1, wherein, For reinforced beam structures that have not yet appeared main cracks during service or in the process of service, the average crack spacing is calculated by referring to empirical data or according to relevant industry standards for concrete structure design, and the position of the main crack is predicted.
7. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 6, characterized in that, The specific expression for calculating the average crack spacing by referring to empirical data or according to relevant industry standards for concrete structure design is: ； wherein, is the average crack spacing, is the comprehensive coefficient, is the concrete cover thickness, is the diameter of the steel bar, is the reinforcement ratio of the longitudinal tensile reinforcement in the tension zone.
8. The method for analyzing the flexural behavior of a reinforced beam considering the full curve of the material constitutive relation according to claim 1, wherein, When determining the moment distribution along the length direction of the reinforced beam according to the load form of the reinforced beam, and calculating the curvature distribution along the length of the beam according to the moment value and the moment-curvature relationship on each reinforced beam unit, the structure form used is statically determinate.