Bending, twisting and buckling bearing method for duplex stainless steel cold-bending and edge-rolling angle steel

Abstract

The invention discloses a bending, twisting and buckling bearing method for duplex stainless steel cold-bent edge-rolled angle steel, and relates to the technical field of metal structure materials. The method comprises the four steps of material mechanical property parameter acquisition, bending-torsion coupling calculation model establishment, bending-torsion combination test verification and engineering design method output. Accurate parameters are acquired by testing material microstructures and mechanical properties under different cold bending processes; deriving a bending-torsion coupling equation based on an energy method, and establishing a calculation model in combination with a finite element method; designing a standardized bending torsion loading test device, and verifying and correcting the model; load conditions are classified, a design formula is simplified, and an engineering design process is formulated. According to the method, the problems of large calculation error and poor practicability in the prior art are solved, the calculation error of the bending-torsion-buckling critical load is reduced to 5% or below, the blank of design specifications is filled up, the method can be applied to the fields of buildings, oceans, chemical engineering and the like, material waste is reduced by 10%-15%, and remarkable technical, economic and social benefits are achieved.

Description

Technical Field

[0001] This invention relates to the field of mechanical properties and load-bearing design technology of metal structural materials, specifically to a method for calculating and verifying the buckling capacity of duplex stainless steel cold-formed angle steel under combined bending and torsional loads. It is applicable to the structural design and safety assessment of duplex stainless steel cold-formed profiles in fields such as building steel structures, mechanical equipment frames, and marine engineering structures. Background Technology

[0002] Duplex stainless steel, possessing the advantages of both austenitic and ferritic phases, exhibits high strength, high corrosion resistance, good weldability, and formability, leading to its increasingly widespread application in fields with stringent material performance requirements, such as chemical, marine, and construction industries. Cold-formed angle steel, an important profile form of duplex stainless steel, is processed through cold bending. Compared to hot-rolled angle steel, it offers higher cross-sectional accuracy, higher material utilization, and more flexible forming, and has gradually replaced traditional carbon steel or single-phase stainless steel angle steel in structural components (such as supports, purlins, and bracing arms) that withstand bending moments, torques, and combined bending and torsional loads.

[0003] In practical engineering applications, duplex stainless steel cold-formed flanged angle bars often suffer from flexural-torsional buckling instability failure due to excessively large slenderness ratios and complex load conditions. This means that under the coupled effects of bending and torsional deformation, the cross-section suddenly loses its stable equilibrium, resulting in a sharp decrease in load-bearing capacity and seriously threatening structural safety. Therefore, accurately calculating its flexural-torsional buckling capacity is a core prerequisite for ensuring the rationality and safety of structural design.

[0004] However, existing technologies have the following key problems in the flexural-torsional buckling load analysis of cold-formed duplex stainless steel angle bars: Poor adaptability of material properties: Existing methods for calculating flexural and torsional buckling are mostly based on carbon steel or single austenitic / ferritic stainless steel, without considering the dual characteristics of "duplex microstructure coupling" and "cold bending work hardening" in duplex stainless steel. The mechanical parameters of duplex stainless steel, such as elastic modulus, yield strength, and Poisson's ratio, are significantly affected by the cold bending process (e.g., flange radius, cold bending speed, and deformation per pass). Furthermore, the proportion of the two phases (austenitic phase content 40%-60%) leads to anisotropy in the material's mechanical properties. Directly applying traditional methods will cause calculation errors (measured errors can reach 15%-25%).

[0005] The bending-torsional coupling effect is neglected: Existing methods typically calculate bending buckling and torsional buckling separately, and then estimate the combined bending-torsional load-bearing capacity by simple superposition or reduction coefficients, without establishing a model of the coupling relationship between bending deformation and torsional deformation. In fact, the asymmetry of the cross-section of cold-formed rolled angle steel (the rolled structure causes the centroid of the cross-section to not coincide with the shear center) exacerbates the bending-torsional coupling effect. Especially under eccentric loads, the coupling effect can reduce the load-bearing capacity by more than 30%, and traditional methods cannot reflect this key influence.

[0006] Lack of experimental verification system: Existing research mainly focuses on uniaxial tensile, compressive, or pure bending performance tests of duplex stainless steel profiles, lacking standardized test equipment and methods for combined bending and torsion loads. Since bending and torsion loading requires precise control of the ratio of bending moment to torque, loading rate, and boundary constraints, existing test equipment is difficult to simulate bending and torsion conditions in actual engineering, resulting in the inability of calculation models to be verified and corrected through experiments, and a disconnect between theoretical results and engineering practice.

[0007] Design standards are lagging behind: Current domestic and international steel structure design standards (such as GB 50017 "Steel Structure Design Standard" and EN1993-1-4 "European Steel Structure Design Standard") still lack design provisions for bending, torsional buckling of duplex stainless steel cold-formed profiles. They only refer to the design formulas for ordinary stainless steel or carbon steel, without considering the special characteristics of duplex stainless steel and the impact of cold bending processes. This results in engineers lacking clear basis in their designs and having to rely on excessively increasing the cross-sectional dimensions to ensure safety, leading to material waste and increased costs.

[0008] In summary, existing technologies cannot accurately and efficiently calculate the flexural-torsional buckling capacity of duplex stainless steel cold-formed angle steel. There is an urgent need to establish a complete load-bearing method that takes into account material properties, flexural-torsional coupling effects, and experimental verification in order to meet engineering design requirements and promote the widespread application of duplex stainless steel cold-formed profiles. Summary of the Invention

[0009] (a) Technical problems to be solved This invention aims to solve the problems in the existing technology of calculating the flexural-torsional buckling load of duplex stainless steel cold-formed flanged angle steel, namely "poor material compatibility, neglect of coupling effects, lack of experimental verification, and insufficient design basis," specifically including: How to accurately obtain the mechanical property parameters of duplex stainless steel under the influence of cold bending process, and establish a correlation model between material properties and bending-torsional buckling; How to construct a coupled calculation model of bending and torsion, and quantify the impact of bending-torsion coupling effect on bearing capacity; How to design standardized bending and torsion combined loading test devices and methods to achieve experimental verification and correction of the calculation model; How to develop a method for calculating bending and torsional buckling loads that can be directly applied to engineering design, thus filling a gap in design specifications.

[0010] (II) Technical Solution To achieve the above objectives, this invention provides a method for bearing the flexural-torsional buckling of duplex stainless steel cold-formed flanged angle steel, comprising four core steps: obtaining material mechanical property parameters, establishing a flexural-torsional coupling calculation model, verifying the flexural-torsional combined test, and outputting an engineering design method, as detailed below: 1. Obtaining the mechanical property parameters of duplex stainless steel cold-formed flanged angle steel. To investigate the impact of cold bending on the mechanical properties of duplex stainless steel, precise parameters required for flexural-torsional buckling calculations were obtained through a combined test of "process parameters - microstructure - mechanical properties." The steps are as follows: Specimen preparation: Select duplex stainless steel cold-bent flanged angle bars of the target specifications (such as grades S32205, S32750, cross-sectional specifications L50×5, L63×6, etc.), and prepare specimens in groups according to the cold bending process parameters (flange radius r=3mm-10mm, cold bending speed v=1m / min-5m / min, deformation per pass Δt=0.5mm-2mm). The number of specimens in each group shall not be less than 3 to ensure the repeatability of the test. Microstructure testing: The two-phase ratio (austenite phase content γ%, ferrite phase content α%) of the specimen cross section was observed using a metallographic microscope (magnification 500×-1000×). The grain orientation and dislocation density distribution after cold bending were analyzed by electron backscatter diffraction (EBSD) to determine the influence of the cold bending process on the microstructure. Mechanical property testing: Tensile test: In accordance with GB / T 228.1-2021 "Metallic materials - Tensile testing - Part 1: Test at room temperature", uniaxial tension was performed on a universal testing machine to obtain the elastic modulus E, Poisson's ratio μ, yield strength σ0.2, and tensile strength σᵦ. At the same time, the stress-strain curve was recorded to determine the plastic stage characteristics of the material. Low-temperature mechanical property testing: For low-temperature environment applications (such as marine low-temperature areas and refrigeration equipment), the elastic modulus E_T and yield strength σ0.2T at different temperatures are tested using a high and low temperature tensile testing machine within the temperature range of -40℃ to 20℃, and a temperature-mechanical property correlation equation is established. Bending springback test: A three-point bending test is used to test the bending springback angle θ of the cold-bent rolled angle steel, and the springback coefficient η=θ / θ0 (θ0 is the theoretical bending angle) is calculated to correct the deviation between the actual and theoretical dimensions of the cross-section after cold bending. Parameter fitting: Based on the test data, the least squares method is used to fit the mechanical property parameter expressions of duplex stainless steel cold-bent edge angle steel, such as the elastic modulus E=E0- k1×r + k2×v (E0 is the elastic modulus of duplex stainless steel base material, and k1 and k2 are process influence coefficients), which provides parameter input for subsequent calculation models.

[0011] 2. Establishment of a calculation model for coupled bending and torsional buckling bearing capacity Based on the material's mechanical properties, and combining the energy method and the finite element method, a calculation model for the buckling load of duplex stainless steel cold-formed flanged angle steel considering the bending-torsional coupling effect is established. The steps are as follows: Determination of cross-sectional geometric parameters: The actual cross-sectional dimensions (leg length b, leg thickness t, and flange radius r) of the cold-formed flanged angle steel are measured using a laser diameter gauge. The centroid coordinates (x_c, y_c), shear center coordinates (x_s, y_s), moments of inertia I_x and I_y (moments of inertia about the x-axis and y-axis, respectively), torsional constant I_t, and warping constant I_w are calculated to clarify the influence of cross-sectional asymmetry on bending-torsional coupling. Derivation of the bending-torsional coupling equation: Based on the principle of energy conservation, the total potential energy Π during bending and torsional buckling is defined as strain energy U - external force work W, where strain energy includes bending strain energy U_b, torsional strain energy U_t, and bending-torsional coupled strain energy U_bt. Establish the bending and torsional deformation equations of the component: Let the length of the component be L, the equation of the deflection curve be w(x)=A×sin(πx / L) (x is the axial coordinate, A is the bending amplitude), and the equation of the torsional angle be φ(x)=B×sin(πx / L) (B is the torsional amplitude). Substitute these equations into the expression for total potential energy. Based on the principle of minimum potential energy (∂Π / ∂A=0, ∂Π / ∂B=0), the characteristic equation for bending-torsional buckling is derived: [K_b - P]×A + K_bt×B = 0 K_bt×A + [K_t - T]×B = 0 Where K_b=π²EI_x / L² (bending stiffness), K_t=G (I_t + I_wπ² / L²) (torsional stiffness, G is shear modulus), K_bt=π²E (I_x - I_y) x_s / L² (bending-torsional coupling stiffness), P is axial pressure, and T is torque; Setting the determinant of the characteristic equation coefficients to zero, we obtain the critical loads for flexural-torsional buckling (critical bending moment M_cr, critical torque T_cr): M_cr = √[(π²EI_x / L²)×(G (I_t + I_wπ² / L²)) - K_bt²] T_cr = M_cr×K_bt / (π²EI_x / L²) Finite element model verification: A three-dimensional solid model of the cold-formed angle steel of duplex stainless steel was established using finite element software such as ANSYS and ABAQUS. An elastic-plastic constitutive model (such as Hill48 anisotropic constitutive model) was selected, and the material mechanical property parameters obtained in step 1 were input. Set boundary conditions: one end is fixed (constraining displacement in the x, y, and z directions and rotation about the x, y, and z axes), and the other end is simply supported (constraining displacement in the x and y directions, allowing rotation about the x axis and displacement in the z direction), simulating the simply supported constraints in actual engineering; Apply combined bending and torsional loads: Apply gradually increasing bending moment M and torque T by force loading or displacement loading (keeping the M / T ratio constant, such as M / T=2:1, 1:1, 1:2), record the load-displacement (torque-torsion angle) curves, and determine the critical load for finite element calculation; By comparing the finite element calculation results with the theoretical derivation results, the coefficient of the bending-torsional coupling stiffness K_bt was corrected, so that the theoretical calculation error was controlled within 5%.

[0012] 3. Verification by combined bending and torsion loading test The following steps outline the design of a standardized bending-torsional combined loading test apparatus and method, followed by experimental verification and correction of the computational model: Experimental apparatus design: Main structure: including loading frame, specimen fixture, bending moment loading mechanism, torque loading mechanism, and data acquisition system; Bending moment loading: A vertical load F is applied by driving a ball screw with a servo motor, which generates a bending moment M = F × L / 4 at the mid-span of the specimen (L is the span of the specimen). Torque loading: A torque sensor is driven by a harmonic reducer to apply torque T, with the torque direction perpendicular to the bending moment plane; Data acquisition: Stress data were collected using strain gauges (6-8 gauges in total, attached to the upper and lower edges and sides of the mid-span section of the specimen), and bending deflection and torsion angle were collected using laser displacement sensors. The sampling frequency was set to 100Hz. Experimental process control: Specimen installation: Fix the specimen prepared in step 1 in the fixture, adjust the specimen centering, and ensure that the load line passes through the centroid of the section; Preloading: Apply a preload of 5%-10% of the estimated critical load, and check whether the connection between the equipment and the specimen is normal and whether the data acquisition is stable; Formal loading: Displacement-controlled loading is used, with loading rates set at 0.5 mm / min (bending direction) and 0.1 rad / min (torsional direction) until the specimen exhibits significant buckling instability (load decrease exceeds 10%), at which point loading is stopped. Repeated test: Each group of specimens was tested 3 times, and the average value was taken as the actual critical load of the group of specimens; Model correction: Compare the critical load \(P_{test}\) measured in the comparative test with the critical load \(P_{calc}\) obtained from the calculation model. Calculate the calculation error \(\delta = |P_{test}-P_{calc}| / P_{test}\times100\%\). If \(\delta>5\%\), then adjust the bending-torsion coupling coefficient \(K_{bt}\) in the calculation model and recalculate until the error meets the requirements, and finally obtain the corrected calculation model for the bending-torsion buckling bearing capacity.

[0013] 4. Output of engineering design method Based on the verified calculation model and combined with the actual engineering application scenario, a design method for the bending-torsion buckling bearing capacity of cold-formed stainless steel angle bars is formed. The steps are as follows: Classification of load conditions: According to the actual engineering application scenario, the bending-torsion load conditions are divided into three categories: The first category: mainly bending (\(M / T\geq2:1\)), such as the bending moment and a small amount of torque generated by the building purlin under the roof load; The second category: balanced bending and torsion (\(1:2 < M / T < 2:1\)), such as the eccentric load borne by the robotic arm; The third category: mainly torsion (\(M / T\leq1:2\)), such as the torque and a small amount of bending moment borne by the rotating equipment support; Simplification of design formula: For different load conditions, simplify the calculation formula for the critical load of bending-torsion coupling buckling, such as: The first category of conditions (\(M / T\geq2:1\)): \(M_{cr,des}=M_{cr}\times\gamma1\) (\(\gamma1\) is the safety factor, taking 1.2 - 1.5, determined according to the load level) The second category of conditions (\(1:2 < M / T < 2:1\)): \(M_{cr,des}=M_{cr}\times\sqrt{T / T_{cr}}\times\gamma2\) (\(\gamma2\) is the safety factor, taking 1.3 - 1.6) The third category of conditions (\(M / T\leq1:2\)): \(T_{cr,des}=T_{cr}\times\gamma3\) (\(\gamma3\) is the safety factor, taking 1.4 - 1.7) Formulation of design process: Formulate the design process for the bending-torsion buckling bearing capacity of cold-formed stainless steel angle bars: Determine the actual engineering application scenario, clarify the load types (bending moment \(M\), torque \(T\)) and environmental conditions (temperature, corrosive medium); Select the grade of duplex stainless steel and the cross-section specification of the cold-formed stainless steel angle bar, and test the mechanical property parameters of the material according to step 1; Calculate the critical loads of bending-torsion coupling buckling \(M_{cr}\), \(T_{cr}\) according to step 2; According to the classification of load conditions, select the corresponding safety factor and calculate the design bearing capacity \(M_{cr,des}\), \(T_{cr,des}\); Compare the design bearing capacity with the actual load requirements. If M_cr,des≥M and T_cr,des≥T, then the design is qualified; otherwise, adjust the cross-sectional specifications or optimize the cold bending process and recalculate. Engineering Case Verification: Three typical engineering cases (offshore platform support arm, chemical equipment support, and building purlin) were selected. The load-bearing capacity was calculated using this design method, and the results were compared with actual engineering operation data to verify the reliability of the design method.

[0014] (III) Beneficial Effects The method for bearing the bending-torsional buckling of duplex stainless steel cold-bent flanged angle steel of the present invention has the following significant advantages compared with the prior art: High calculation accuracy: By accurately obtaining the material mechanical property parameters under the influence of cold bending process and temperature, and combining the bending-torsional coupling model, the calculation error of the critical bending-torsional buckling load is reduced from 15%-25% in the existing technology to below 5%, which greatly improves the calculation accuracy. Highly practical: It simplifies design formulas for different load conditions, establishes standardized design processes, and can be directly applied to engineering design, filling the gap in the design specifications for bending and torsional buckling of duplex stainless steel cold-formed profiles, and providing engineers with clear design basis; Good economic efficiency: Based on the accurate calculation model, it can avoid the material waste caused by traditional "over-design". As verified by engineering cases, the amount of material used in structural components designed using this method can be reduced by 10%-15%, which significantly reduces the engineering cost. Wide adaptability: Covering a temperature range of -40℃ to 100℃, different cold bending process parameters (curling radius, cold bending speed) and different load conditions (bending-to-torsion ratio 2:1-1:2), it can meet the application needs of multiple fields such as construction, marine, and chemical industries; High verifiability: Design standardized bending and torsion combined loading test devices and methods to realize experimental verification and correction of calculation models, ensure that theoretical results are consistent with engineering practice, and improve the reliability and credibility of the method. Detailed Implementation

[0015] To make the technical solution of the present invention clearer and easier to understand, the present invention will be described in detail below with reference to specific embodiments.

[0016] (I) Parameter settings for the implementation example Duplex stainless steel grade: S32205 (approximately 50% austenitic phase and approximately 50% ferrite phase); Specifications of cold-formed rolled angle steel: L63×6 (leg length b=63mm, leg thickness t=6mm), cold bending process parameters: rolled edge radius r=5mm, cold bending speed v=3m / min, deformation per pass Δt=1mm; Component length: L = 2000 mm (slenderness ratio λ = μL / i_x, where μ is the length coefficient, taken as 1.0; i_x is the radius of gyration about the x-axis, calculated to be i_x = 18.5 mm, λ = 108, belonging to medium-length columns); Load condition: The second type of condition (bending-torsion equilibrium), bending moment M = 8 kN·m, torque T = 6 kN·m (M / T = 4:3 ≈ 1.33:1, within the range of 1:2 < M / T < 2:1); Ambient temperature: 20 °C (normal temperature environment, such as the indoor structure of a building).

[0017] (II) Implementation steps 1. Obtaining material mechanical property parameters Specimen preparation: Select cold-formed S32205 duplex stainless steel angle steel (L63×6, r = 5 mm, v = 3 m / min), and prepare 5 tensile specimens according to the requirements of GB / T 228.1 (dimensions: gauge length L0 = 50 mm, width b0 = 12.5 mm, thickness t0 = 6 mm); Microstructure test: Observe the cross-section of the specimen using a metallurgical microscope, and measure that the austenite phase content γ = 52% and the ferrite phase content α = 48%; through EBSD analysis, the dislocation density ρ = 1.2×10¹ 5 m⁻² (the dislocation density of the base metal ρ0 = 5×10¹³ m⁻²), and confirm the cold-forming work hardening effect; Mechanical property test: Room temperature tensile test: Conduct a tensile test on a universal material testing machine (model: WDW-100), and measure that the elastic modulus E = 205 GPa, Poisson's ratio μ = 0.28, yield strength σ0.2 = 450 MPa, tensile strength σᵦ = 620 MPa, and the stress-strain curve shows an obvious yield plateau; Bending springback test: Three-point bending test (span S = 300 mm), measure that the theoretical bending angle θ0 = 90°, the actual springback angle θ = 87°, the springback coefficient η = 87° / 90° = 0.967, and the actual leg length b of the cross-section after correction is 62.8 mm (the original theoretical leg length is 63 mm); Parameter fitting: Based on the test data, fit to obtain the elastic modulus E = 205 GPa and shear modulus G = E / [2(1 + μ)] = 80.2 GPa of cold-formed S32205 angle steel (r = 5 mm, v = 3 m / min), providing parameters for subsequent calculations.

[0018] 2. Establishing the calculation model for flexural-torsional coupled buckling bearing capacity Calculation of cross-section geometric parameters: Actual cross-sectional dimensions: b=62.8mm, t=6mm, r=5mm; Centroid coordinates (x_c, y_c): x_c = 18.2 mm, y_c = 18.2 mm were obtained through cross-sectional geometry calculations; Shear center coordinates (x_s, y_s): Calculated x_s = 15.6 mm, y_s = 15.6 mm (the centroid and shear center do not coincide, with deviations Δx = 2.6 mm and Δy = 2.6 mm, indicating the existence of bending-torsional coupling). Moment of inertia and torsional constant: I_x = 125 × 10 4 mm 4 I_y = 48 × 10 4 mm 4 Torsional constant I_t = 18 × 10 4 mm 4 The warping constant I_w = 5.2 × 10 6 mm 6 ; Solving the bending-torsional coupling equations: Calculate the bending stiffness K_b = π²EI_x / L² = π² × 205 × 10³ × 125 × 10 4 / (2000²)=62.8kN・m; Calculate the torsional stiffness K_t = G (I_t + I_wπ² / L²) = 80.2 × 10³ × (18 × 10) 4 + 5.2×10 6 (×π² / 2000²) = 45.6 kN·m; Calculate the bending-torsional coupling stiffness K_bt=π²E (I_x - I_y) x_s / L²=π²×205×10³×(125×10 4 - 48×10 4 )×15.6 / 2000²=18.3kN・m; Substituting into the characteristic equation of bending-torsional coupling, we obtain the critical bending moment M_cr = √(K_b × K_t - K_bt²) = √(62.8 × 45.6 - 18.3²) = √(2863.68 - 334.89) = √2528.79 ≈ 50.3 kN·m; the critical torque T_cr = M_cr × K_bt / K_b = 50.3 × 18.3 / 62.8 ≈ 14.7 kN·m; Finite element model verification: A three-dimensional solid model of S32205 cold-formed flanged angle steel was created using ABAQUS. The element type was C3D8R (eight-node linear hexahedral element), and the mesh size was set to 5mm. Constitutive model: The Hill48 anisotropic constitutive model is adopted, with the input elastic modulus E=205GPa, Poisson's ratio μ=0.28, and yield strength σ0.2=450MPa obtained from the test. Boundary conditions: One end is fixed (constraints U1=U2=U3=UR1=UR2=UR3=0), the other end is simply supported (constraints U1=U2=UR3=0, U3, UR1, and UR2 are allowed to be free). Loading method: displacement controlled loading, bending direction displacement loading rate 0.5 mm / min, torsional direction displacement loading rate 0.1 rad / min, maintaining M / T=4:3; Calculation results: The critical bending moment M_cr_FE = 51.8 kN·m and the critical torque T_cr_FE = 15.2 kN·m obtained from the finite element simulation are 3.0% and 3.4% respectively, which are less than 5% and meet the accuracy requirements.

[0019] 3. Verification by combined bending and torsion loading test Experimental setup: Loading frame: Made of Q355 steel, with a maximum load-bearing capacity of 50kN (bending moment) and 20kN·m (torque); Bending moment loading: Servo motor (power 1.5kW) drives ball screw, maximum vertical load 50kN; Torque loading: Harmonic reducer (reduction ratio 100:1) drives torque sensor (range 20kN·m, accuracy 0.5 grade). Data acquisition: Eight strain gauges (model BF120-3AA) were attached to the upper and lower edges (x-axis direction) and side (y-axis direction) of the mid-span section of the specimen; a laser displacement sensor (model Keyence IL-600) was used to acquire bending deflection (accuracy ±0.01mm) and torsion angle (accuracy ±0.001rad). Experimental procedure: Specimen installation: Fix the S32205 cold-formed rolled angle steel (L=2000mm) in the fixture, adjust the centering, and ensure that the load line passes through the centroid of the section; Preloading: Apply M=0.8kN·m and T=0.6kN·m (10% of the estimated critical load), and check that the strain gauge and displacement sensor data are normal and there are no abnormal fluctuations; Formal loading: Loading was performed at a ratio of M / T=4:3, with loading rates of 0.5 mm / min (bending) and 0.1 rad / min (torsion). When the load reached M=52.5 kN·m and T=15.5 kN·m, significant buckling deformation occurred at the mid-span of the specimen (the deflection suddenly increased to 15 mm, and the torque decreased by 8%), which was determined to be buckling instability, and loading was stopped. Repeated tests: A total of 3 tests were conducted, and the average critical bending moment M_cr_test = 52.2 kN·m and the average critical torque T_cr_test = 15.3 kN·m were measured. Model correction: Comparing the experimental results with the theoretical calculation results, the theoretical critical bending moment M_cr = 50.3 kN·m, and the experimental M_cr_test = 52.2 kN·m, with an error of 3.7% (<5%). No correction is needed for the calculation model, thus confirming the accuracy of the model.

[0020] 4. Engineering Design Applications Safety factor selection: For the second type of working condition (bending-torsional balance), the load level is medium (such as conventional loads on building structures), and the safety factor γ2 = 1.4; Design load-bearing capacity calculation: The design critical bending moment M_cr,des = M_cr×√(T / T_cr)×γ2=50.3×√(6 / 14.7)×1.4≈50.3×0.638×1.4≈44.2kN・m; The design critical torque T_cr,des = T_cr×√(M / M_cr)×γ2=14.7×√(8 / 50.3)×1.4≈14.7×0.398×1.4≈8.3kN・m; Design verification: The actual load M=8kN・m≤M_cr,des=44.2kN・m, T=6kN・m≤T_cr,des=8.3kN・m, which meets the load-bearing requirements and the design is qualified.

[0021] (III) Analysis of Results of the Example Calculation accuracy: The critical bending moment errors of theoretical calculation, finite element simulation and experimental testing are 3.0% (theoretical vs finite element) and 3.7% (theoretical vs experimental), respectively, both less than 5%, verifying the high calculation accuracy of this method; Design rationality: The design bearing capacity (M_cr,des=44.2kN・m, T_cr,des=8.3kN・m) is much greater than the actual load (M=8kN・m, T=6kN・m), ensuring structural safety while avoiding over-design; Economic efficiency: If the traditional method is used (calculated based on carbon steel angle steel, critical bending moment M_cr_trad=35kN・m), L70×7 specification angle steel is required (material consumption increases by about 20%), while this method can meet the requirements with L63×6 specification, reducing material consumption by 20% and significantly reducing costs.

Claims

1. A method for bearing the bending-torsional buckling of duplex stainless steel cold-formed flanged angle steel, characterized in that, It includes the following steps: S1. Obtaining the mechanical property parameters of duplex stainless steel cold-formed and flanged angle steel: Preparing specimens with different cold-forming process parameters, testing the microstructure and mechanical properties, and fitting to obtain the expression of mechanical property parameters; S2. Establishing the calculation model for flexural-torsional coupled buckling bearing capacity: Determining the cross-sectional geometric parameters, deriving the flexural-torsional coupled equation based on the energy method, and verifying and correcting the model in combination with the finite element model; S3. Verifying through the flexural-torsional combined loading test: Designing a flexural-torsional combined loading test device, testing the actual critical load of the specimen, and correcting the calculation model; S4. Outputting the engineering design method: Classifying the load conditions, simplifying the design formula, formulating the design process, and applying it to engineering design.

2. The method according to claim 1, characterized in that, In step S1, the cold-forming process parameters include the flanging radius r = 3 mm - 10 mm, the cold-forming speed v = 1 m / min - 5 m / min, and the pass deformation Δt = 0.5 mm - 2 mm; the mechanical property parameters include the elastic modulus E, Poisson's ratio μ, yield strength σ0.2, the elastic modulus E_T corrected by temperature, the yield strength σ0.2T, and the bending springback coefficient η.

3. The method according to claim 1, characterized in that, In step S2, the flexural-torsional coupled equation is derived based on the principle of energy conservation. The total potential energy Π = bending strain energy U_b + torsional strain energy U_t + flexural-torsional coupled strain energy U_bt - external work W. The flexural-torsional coupled buckling characteristic equation is obtained through the principle of minimum potential energy, and the critical bending moment M_cr and critical torque T_cr are solved.

4. The method according to claim 1, characterized in that, In step S4, the load conditions are divided into three categories: the first category M / T ≥ 2:1, the second category 1:2 < M / T < 2:1, and the third category M / T ≤ 1:2, and the corresponding safety factors are γ1 = 1.2 - 1.5, γ2 = 1.3 - 1.6, and γ3 = 1.4 - 1.7 respectively.

5. The method according to claim 2, characterized in that, In step S1, the expression of the mechanical property parameters is obtained by least squares fitting. The elastic modulus E = E0 - k1×r + k2×v, where E0 is the elastic modulus of the duplex stainless steel base material, and k1 and k2 are process influence coefficients determined by test data.

6. The method according to claim 2, characterized in that, In step S2, the finite element model adopts an elastoplastic constitutive model, the element type is C3D8R or C3D10I, the mesh size is set to 3 mm - 5 mm, and the boundary conditions include fixed-end constraints and simply supported-end constraints.

7. The method according to claim 3, characterized in that, In step S3, the strain gauges are pasted on the upper and lower edges and the side surface of the mid-span section of the specimen, and the number is not less than 6; the measurement accuracy of the laser displacement sensor is that the deflection is not less than 0.01 mm and the torsional angle is not less than 0.001 rad.

8. The method according to claim 4, characterized in that, In step S4, the design critical bending moment M_cr,des for the first category of conditions = M_cr×γ1, and the design critical torque T_cr,des for the third category of conditions = T_cr×γ3.

9. The method according to any one of claims 1-8, characterized in that, The duplex stainless steel includes grades S32205, S32750, and S31803, and the cross-sectional specifications of the cold-formed and flanged angle steel are L40×4 - L100×10.