An automatic design method for T-shaped steel reinforced axial compression circular steel pipe section based on target inertia moment

Abstract

This invention discloses an automated design method for axially compressed circular steel tube sections reinforced with T-shaped steel based on target moment of inertia. Addressing the problem in existing steel reinforcement designs where multiple geometric variables are coupled, leading to inability to directly solve the problem and heavy reliance on trial and error based on manual experience, this method obtains the original tube parameters and reinforcement axial force requirements. It introduces a modified slenderness ratio based on the combined T-shaped steel section, using the standard Class A column curve as a benchmark to inversely deduce the target total moment of inertia required for reinforcement. Based on the principle of stiffness superposition, the independent moment of inertia requirements of the T-shaped steel are separated. Subsequently, a multi-dimensional parameter space including web and flange dimensions is constructed, and local stability width-to-thickness ratio limits and welding construction requirements such as height-to-width ratio and thickness coordination are forcibly coupled as boundary constraints. Finally, a full-parameter space grid search algorithm is used to traverse and optimize the discrete integer domain. This invention achieves a direct mapping from macroscopic bearing capacity requirements to microscopic multivariable section dimensions, automatically outputting a complete set of feasible solutions that meet both mechanical and construction standards, significantly improving the accuracy and economic efficiency of reinforcement design.

Description

Technical Field

[0001] This invention belongs to the field of structural engineering and steel structure reinforcement technology, specifically involving an automated design method for determining the geometric dimensions of the reinforcement section of the axially compressed circular steel pipe welded with T-shaped steel in a spatial grid based on stable bearing capacity requirements and a full-parameter spatial grid search algorithm. Background Technology

[0002] With increasing service life, updated design specifications, or changes in usage, many compression members in existing space frame structures face insufficient overall stability and load-bearing capacity. Among existing reinforcement methods, outer casing reinforcement suffers from large construction interference in node areas and difficulty in controlling grouting quality; while FRP (fiber reinforced plastic) reinforcement is susceptible to interface delamination due to environmental temperature and humidity. Reinforcing circular tube members with externally symmetrically welded T-shaped steel not only effectively increases the moment of inertia of the section and significantly improves the member's buckling resistance, but also adapts well to space frame structures with dense nodes. However, the cross-sectional geometry of the T-shaped steel includes four independent variables (web height, web thickness, flange width, and flange thickness), making it a typical multivariate discrete optimization problem. Currently, the engineering community still relies on a manual trial-and-error method of "assuming a section—finite element or theoretical verification—readjustment" for this type of reinforcement. This traditional method has extremely low design efficiency and struggles to comprehensively consider the local stability of the plate, welding workspace, and material economy. There is an urgent need for an automated design method that can directly and quantitatively output the full-size feasible solution set of the T-shaped steel based on the target load. Summary of the Invention

[0003] The beneficial effects of this invention are as follows: It overcomes the shortcomings of existing T-beam reinforcement designs, which suffer from multivariate coupling leading to inability to directly solve the problem and reliance on trial and error based on human experience. This invention provides an automated design method for the cross-section of welded T-beams in steel structures. This method inversely calculates the total moment of inertia based on the reinforcement stress requirements of the component, extracts the independent moment of inertia requirements of the T-beam, and, combined with structural and stability constraints, automatically outputs all feasible optimal economic cross-sections of the T-beams through a grid search algorithm.

[0004] Step 1. Obtain the geometric and material parameters of the original circular tube to be reinforced, as well as the target stress requirements after reinforcement. These parameters include: axial force design value. F , original circular tube cross-sectional area A Moment of inertia of the original circular tube cross section I inner steel yield strength f y Component geometric length l and calculation of length coefficient μ .

[0005] Step 2. Based on the design value of axial force F , original circular tube cross-sectional areaA and steel yield strength f y Calculate the target stability coefficient required for the reinforced component. φ.

[0006] Step 3. Preset the initial dimensions of the T-shaped steel web to calculate the stability coefficient value of the reinforced section during the strength failure stage. φ 0, based on the target stability coefficient φ By combining the modified Euler curve with the standard A-class column curve, the target equivalent slenderness ratio required for the reinforced member can be calculated. λ mod .

[0007] Step 4. Based on the target equivalent slenderness ratio λ mod Component geometric length l Calculate the length coefficient μ and the original circular tube cross-sectional area A Calculate the target total moment of inertia required to strengthen the component. I mod。

[0008] Step 5. Based on the principle of stiffness superposition, according to the target total moment of inertia... I mod Subtract the original moment of inertia of the circular tube I inner Calculate the target independent moment of inertia required for external welding of T-beams. I T。

[0009] Step 6. Establish the multidimensional parameter space of the T-section steel and set independent geometric variables: web height. h w Web thickness t w wing width b f and flange thickness t f The discrete integer search interval.

[0010] Step 7. Introduce constraint boundary conditions within the parameter space to ensure the local stability of the plate and the coordination of construction operations. The constraint boundary conditions include width-to-thickness ratio constraints and structural coordination constraints.

[0011] Step 8. Use the full-parameter spatial grid search algorithm to traverse the parameter intervals and select the combinations of moments of inertia that satisfy the target moment of inertia. I T And simultaneously satisfying the complete set of parameters for all constraint boundary conditions in step 7 S feasible It automatically outputs a matrix of feasible T-shaped steel reinforcement section schemes, completing the automated section design.

[0012] 1. This invention breaks through the trial calculation bottleneck of traditional multivariable cross-section design, introduces the "full-parameter spatial grid search algorithm" into the T-shaped steel reinforcement design, and establishes an automated direct mapping from "macro-bearing capacity requirements" to "micro-multidimensional geometric dimensions", avoiding blind trial and error and greatly improving design efficiency and optimization accuracy.

[0013] 2. Based on rigorous buckling mechanism research, this invention innovatively proposes a modified equivalent slenderness ratio that takes into account the stiffness contribution of T-beams. λ mod By establishing the equivalent mapping relationship between the modified slenderness ratio and the standard column curve of type a, a solid theoretical basis is provided for the reverse derivation of the target moment of inertia, ensuring the safety and reliability of the calculation results.

[0014] 3. The algorithm of this invention internalizes the width-to-thickness ratio limit for local stability of plate components (the theory of simply supported plates with three and four sides) and the welding structure restrictions to prevent components from being too narrow and the web being thicker than the flange during the optimization process. This ensures that all output cross-sectional schemes not only meet the theoretical mechanical performance standards, but also fully satisfy the machinability and construction requirements of actual engineering projects.

[0015] 4. The final output of this invention is a feasible solution set matrix containing multiple size combinations. Engineers can directly select the optimal economic cross-section scheme from it based on on-site material reserves, economic costs, or welding process preferences, giving engineering applications great flexibility. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the overall process of an automated design method for T-shaped steel reinforcement sections based on target moment of inertia, according to the present invention.

[0018] Figure 2 This is a schematic diagram defining the geometric features of the combined cross section of the circular tube to be reinforced and the externally welded T-shaped steel according to the present invention.

[0019] Figure 3 This invention relates to a comparative mapping diagram of the modified stability coefficient considering the stiffness contribution of T-shaped steel with the standard a-type column curve and Euler curve.

[0020] Figure 4This is an example diagram of a T-shaped steel section matrix that partially meets the stress and structural requirements, output by the full-parameter spatial grid search algorithm of this invention. Detailed Implementation

[0022] The automated design process for the T-shaped steel cross-section dimensions of the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation examples. This embodiment takes an axially compressed circular steel pipe that needs reinforcement in a space frame as an example.

[0023] The original outer diameter D of the circular pipe to be reinforced is known to be 60 mm. Based on the initial stress requirements, the target independent moments of inertia required by the four symmetrically welded T-beams are determined to be... I T =7×10 4 mm 4 .

[0024] To determine the specific cross-sectional dimensions of the T-beam (i.e., web height) h w Web thickness t w wing width b f flange thickness t f The full-parameter spatial grid search algorithm is then initiated. It is important to note that the search range for geometric variables in the algorithm is fully parameterized, not fixed. Designers can dynamically customize the upper and lower limits of these search ranges based on the actual engineering manufacturing capabilities, on-site steel plate material reserves, and reinforcement space constraints.

[0025] In this embodiment, based on conventional manufacturing capabilities, the preset search parameter range (unit: mm) for each discrete integer variable is exemplified as follows.

[0026] By parameterizing the search interval, this algorithm can be flexibly and universally applied to the optimization of reinforcement sections for various specifications of space frame members.

[0027] When traversing the multidimensional parameter space, the following constraints are enforced for preliminary filtering to ensure the mechanical stability and construction feasibility of the reinforced components. The boundary limits of each constraint are set as parameterized variables, which designers can dynamically assign based on the steel grade used, the design specifications followed, and the actual manufacturing process.

[0028] 1. Parametric constraints on local stability of the web: To ensure that the web does not buckle under compression, the width-to-thickness ratio must be satisfied within the specified range. C w,min ≤ h w / t w ≤ C w,max In this embodiment, parameters are preset according to specific specification limitations. C w,min =2, C w,max =25.

[0029] 2. Parametric constraints on local flange stability: To ensure the compressive stability of the flange overhang, the width-to-thickness ratio must be satisfied within the specified range. C f,min ≤ b f / t f ≤ C f,max In this embodiment, preset parameters C f,min =2, C f,max =15.

[0030] 3. Aspect Ratio Construction Parametric Constraints: To prevent geometric instability caused by excessively narrow T-sections, the following constraints must be met. b f ≥ α · h w In this embodiment, the lower limit coefficient of aspect ratio is used. α =0.5.

[0031] 4. Plate Thickness Coordination Parameter Constraints: Based on actual welding processes and heat input requirements, the relative thickness of the web and flanges must be controlled to meet the following requirements. t w ≤ β · t f In this embodiment, the plate thickness compatibility coefficient is used. β =1.0.

[0032] By introducing C w,min , C w,max , C f,min , C f,max , α and β With adjustable parameters, this algorithm can seamlessly adapt to the design specifications of different countries or the special reinforcement needs of non-standard projects.

[0033] Step 4: Target Moment of Inertia Verification Calculation. For any set of size combinations selected through the above four constraints ( h w ,t w , b f , t f Substitute this into the theoretical moment of inertia calculation formula for the T-section composite section about the centroidal axis.

[0034] The program automatically calculates the actual moment of inertia of the cross section and retains the difference between the actual moment of inertia and the target moment of inertia (7 × 10⁻⁶). 4 mm 4 The combinations of errors within the allowable range form the final feasible solution set. S feasible .

[0035] Through full-parameter spatial grid search and automated computation using computer algorithms, the system traverses the defined integer domain to identify all cross-section schemes that satisfy stiffness constraints, geometric stability constraints, and structural constraints. The output matrix of feasible T-section schemes that meet the target moment of inertia requirement is as follows: Figure 4 As shown. The appendix Figure 4 This demonstrates the change in the outer diameter of the circular tube. D =60 mm, target moment of inertia requirement I T =7×10 4 mm 4 The computer automatically generated some of the proposed solutions. Examples of the output candidate cross-section solutions are shown below.

[0036] Candidate Option 1: The cross-sectional dimensions are defined as 29×10+37×8, which is the height of the web of the T-shaped steel. h w =29 mm, web thickness t w =10 mm, flange width b f =37 mm, flange thickness t f =8 mm. The corresponding reinforced cross-sectional area for this scheme is... A =586 mm 2 The actual combined moment of inertia has a calculation error of approximately 2.9% compared to the target moment of inertia.

[0037] Candidate Option 2: The cross-sectional dimensions are defined as 30×12 + 18×9, which is the height of the web of the T-shaped steel. h w =30 mm, web thickness t w =12 mm, flange width b f =18 mm, flange thickness tf =9 mm. The corresponding reinforced cross-sectional area for this scheme is... A =522 mm 2 The actual combined moment of inertia has a calculation error of only about 0.8% compared to the target moment of inertia.

[0038] Designers can directly access the algorithm-generated cross-section scheme library (i.e., attached) Figure 4 Based on the actual steel plate thickness on site, the material preparation should follow the principle of minimizing the reinforcement cross-sectional area (e.g., selecting candidate option two with 522 mm). 2 The 586 mm replacement for Option 1 2 The final reinforcement section selection is completed by considering the optimal economic principle or the section scheme that is easy to construct.

Claims

1. An automated design method for the cross-section of T-shaped steel reinforced axially compressed circular steel pipe based on target moment of inertia, characterized in that, The method includes the following steps: Step 1: Obtain the geometric and material parameters of the original circular steel pipe to be reinforced, as well as the stress requirements after reinforcement. These parameters include: axial force design value. F Original circular steel pipe cross-sectional area A Moment of inertia of the original circular steel pipe section I inner steel yield strength f y Component geometric length l and calculation of length coefficient μ ; Step 2: Based on the design value of axial force F Original circular steel pipe cross-sectional area A and steel yield strength f y Calculate the target stability coefficient required for the reinforced component. φ ; Step 3: Based on the target stability coefficient φ By combining the modified column curve that takes into account the stiffness contribution of the external T-beam, the target equivalent slenderness ratio required for the reinforced member is derived in reverse. λ mod ; Step 4: Based on the target equivalent slenderness ratio λ mod Component geometric length l Calculate the length coefficient μ and the original cross-sectional area of ​​the round steel pipe A Calculate the target total moment of inertia required for the reinforcement of the member. I mod ; Step 5: Based on the target total moment of inertia I mod Moment of inertia of the original circular steel pipe section I inner Based on the principle of stiffness superposition, the target independent moment of inertia required for external welding of T-shaped steel is calculated. I T ; Step 6: Establish the multidimensional parameter space of the T-section steel and set the independent geometric variable, namely the web height of the T-section steel. h w Web thickness t w wing width b f and flange thickness t f The discrete numerical search interval; Step 7: Using a full-parameter space grid search algorithm, traverse the multi-dimensional parameter space. Under the preset parameterized local stability constraints and construction coordination constraints, directly calculate and select the combined moments of inertia that satisfy the target independent moments of inertia. I T The geometric variables are combined to output a set of feasible T-shaped steel reinforcement section schemes.

2. The method according to claim 1, characterized in that, In step 3, when the reinforced member is in the elastoplastic or elastic instability stage, the modified column curve used is equivalent to the stability coefficient curve of the axially compressed member of section a specified in the "Steel Structure Design Standard".

3. The method according to claim 1, characterized in that, In step 4, the specific formula for calculating the target total moment of inertia Imod required for the reinforcement component is as follows: 。 4. The method according to claim 1, characterized in that, In step 5, the specific formula for calculating the target independent moment of inertia IT required for the externally welded T-shaped steel is as follows: 。 5. The method according to claim 1, characterized in that, In step 7, the preset parameterized local stability constraints and construction coordination constraints specifically include: Local stability constraints on the web: C w,min ≤ h w / t w ≤ C w,max ; Local stability constraints on the flange: C f,min ≤ b f / t f ≤ C f,max ; Aspect Ratio Construction Constraints: b f ≥ α · h w ; Thickness coordination structural constraints: t w ≤ β · t f ; in, C w,min , C w,max , C f,min , C f,max , α and β All of these are boundary parameters that are dynamically preset based on structural design specifications and actual welding manufacturing processes.

6. The method according to claim 1 or 5, characterized in that, In step 7, when four symmetrically arranged T-beams are used for external welding reinforcement, any combination of geometric variables ( h w , t w , b f , t f The corresponding formula for calculating the combined moment of inertia is as follows: ,in, D This refers to the outer diameter of the original round steel pipe.

7. The method according to claim 1, characterized in that, The T-shaped steel reinforcement section scheme set output in step 7 is a discrete matrix containing various combinations of web and flange dimensions. Designers can extract suitable sections from this scheme set.

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