A method for analyzing wind-induced fatigue in centrally supported steel frame structures and its strength degradation model

Abstract

This invention belongs to the technical field of wind resistance performance assessment for the entire life cycle of high-rise steel structures, and discloses a wind-induced fatigue analysis method and its strength degradation model for centrally supported steel frame structures. The method proposed in this invention can effectively assess wind-induced structural fatigue damage and describe the strength degradation law of materials and structural components, while considering the influence of crosswind response and random variables. The steel strength degradation model established in this invention after wind-induced fatigue damage can be used to correct the material parameters of steel structures after fatigue damage, which is crucial for accurately conducting full-life-cycle reliability analysis of high-performance structures.

Description

Technical Field

[0001] This invention belongs to the technical field of wind resistance performance evaluation of high-rise steel structures throughout their entire life cycle, and relates to a wind-induced fatigue analysis method and strength degradation model for centrally supported steel frame structures. Background Technology

[0002] Steel structures are widely used in high-rise buildings due to their lightweight and high strength. High-rise steel structure buildings often have a long service life, and during their service life, they are inevitably subjected to long-term wind loads. The fatigue accumulation damage caused by long-term wind loads may lead to the degradation of the structure's performance. The impact of wind-induced fatigue accumulation damage on high-rise steel structures is mainly reflected in two aspects: (1) degradation of the mechanical properties of steel; (2) deterioration of the connection capacity of structural nodes, which in turn leads to the deterioration of the overall performance of the structure. Currently, the methods used to assess wind-induced fatigue damage of components and structures include: (1) experimental methods (Liu YB, Li YD, Li SX, et al. Prediction of the S–N curves of high-strength steels in the very high cycle fatigue regime [J]. International Journal of Fatigue, 2010, 32: 1351-1357.), which is widely used in the high-cycle fatigue research of materials and components and can obtain relatively reliable results, but is not suitable for the wind-induced fatigue research of high-rise buildings; (2) long-term structural health monitoring method (Fatigue Reliability Assessment for Orthotropic Steel Decks Based on Long-Term Strain Monitoring [J]. Sensors, 2018, 18: 181.), which can assess the fatigue damage of structurally sensitive areas or key components and is suitable for simple structures with clear force transmission mechanisms such as bridge decks and signal towers; this method relies heavily on dense sensor networks, and for complex structures such as high-rise buildings, there are challenges such as high maintenance difficulty, insufficient spatial resolution and low economic feasibility; (3) numerical simulation method (Fang Zhao, Li Aiqun, Li Wanrun, et al. Multi-scale wind-induced fatigue analysis method for high-rise steel frame supported structures [J]. Journal of Southeast University (Natural Science Edition), 2017, 47(1): 137-141.), including frequency domain and time domain analysis methods, can flexibly and conveniently calculate wind-induced fatigue damage of high-rise buildings. In the above studies, the rainflow counting method and Palmgren-Miner criterion are generally used to calculate the cumulative fatigue damage of materials, components or structures.

[0003] It should be noted that existing studies on the evolution of structural wind-induced fatigue cumulative damage have the following shortcomings: (1) lack of research on the influence of crosswind effect on structural wind-induced fatigue cumulative damage; (2) lack of structural strength degradation model under the influence of wind-induced fatigue cumulative damage; (3) the strength degradation model determined by traditional methods is only an objective description of the changing trend of specific experimental data, lacking the necessary mathematical and physical explanation. Summary of the Invention

[0004] To address the shortcomings of existing research, this invention proposes a wind-induced fatigue analysis method and a strength degradation model for centrally supported steel frame structures. The technical approach of this invention is as follows: Figure 1 As shown. The main advantage of this invention is that the proposed method can effectively assess wind-induced structural fatigue damage and describe the strength degradation law of materials and structural components, while considering the influence of crosswind response and random variables; the steel strength degradation model established by this invention after wind-induced fatigue damage can be used to correct the material parameters of steel structures after fatigue damage, which is the key to accurately carrying out full-life reliability analysis of high-performance structures.

[0005] The technical solution of the present invention:

[0006] A method for analyzing wind-induced fatigue in a centrally supported steel frame structure and its strength degradation model are described below:

[0007] Step 1: Obtain wind speed data from the China Meteorological Administration (http: / / data.cma.cn / ), the European Centre for Medium-Range Weather Forecasts (https: / / www.ecmwf.int / en / forecasts / datasets / open-data), or other meteorological databases; based on the Poisson distribution assumption, the probability that a wind event with wind load intensity and wind speed V ≥ x will occur at least once in year t is expressed as:

[0008] (1)

[0009] In the formula, λ(·) represents the annual exceedance probability of wind events with wind load intensity and wind speed V ≥ x, which is derived based on the obtained wind speed data; therefore, the annual exceedance probability of wind events with wind load intensity and wind speed V ≥ x is written as:

[0010] (2)

[0011] In the formula, n (V≥x) represents the number of wind events with wind load intensity and wind speed V≥x in the measured records; T r To record the duration of wind speed data; F exc (x) represents the exceedance probability of wind load intensity and wind speed V ≥ x; F cum(x) represents the cumulative probability of wind load intensity and wind speed V≥x, and the cumulative probability distribution of wind load intensity and wind speed is described by extreme value type I (Gumbel), extreme value type II (Frechet), and extreme value type III (Weibull) distributions.

[0012] Step 2: Based on the cumulative probability distribution determined in Step 1, calculate the wind speed corresponding to different return periods, and then determine the downwind and crosswind loads; the methods for determining wind loads include wind tunnel tests, standard values, and numerical simulations.

[0013] Step 3: Using the input along-wind and cross-wind loads determined in Step 2, perform nonlinear dynamic time history calculations of the structure on a finite element platform to obtain the stress response of the high-rise building structural members. The stress-life curve, i.e., the SN curve, is used to determine the fatigue life of the high-rise building structural member materials. The SN curve is established through symmetrical cyclic loading tests, i.e., the average stress is zero. However, the average stress of the high-rise building structural members under along-wind and cross-wind loads is not zero, so the Goodman formula is used to correct the wind-induced stress response of the structural members.

[0014] (3)

[0015] In the formula, S is the equivalent stress amplitude, S a S represents the actual stress amplitude. m S represents the actual average stress. u The ultimate tensile strength of structural components in high-rise buildings;

[0016] Step 4: According to the Palmgren-Miner criterion, the wind-induced fatigue damage of structural components in high-rise buildings is estimated using the following formula:

[0017] (4)

[0018] In the formula, n i S represents the stress level of the i-th order. i The number of cycles under the current is determined by rainflow counting; N fi Indicating the same stress level S i The number of cycles at which fatigue failure occurs is determined based on the SN curve of the material. Based on this, the annual fatigue damage and fatigue life of high-rise building structural components are calculated using equations (5) and (6), respectively. The number of cycles for high-rise building structural components is determined through trial calculations.

[0019] (5)

[0020] and

[0021] (6)

[0022] In the formula, D A Indicates annual fatigue damage; T A The total number of seconds in a year; T W Input the duration of the wind load, in seconds; T life Indicates fatigue life;

[0023] Step 5: Combining the probability of a wind event occurring at least once within year t determined in Step 1 and the annual fatigue damage determined in Step 4, the annual wind-induced fatigue cumulative damage of high-rise building structural components is further defined as follows:

[0024] (7)

[0025] In the formula, D(V) j () indicates wind speed V j The annual fatigue damage of high-rise building structural components under wind load is determined by step 4; P(V j () indicates wind speed V≥V j The probability of a wind event occurring is determined by step 1;

[0026] Step 6, considering the annual wind-induced fatigue cumulative damage calculated in Step 5, the strength degradation model of high-rise building structural component materials is expressed as:

[0027] (8)

[0028] In the formula, Y0 represents the initial mechanical properties of the undamaged material, including the material's yield strength f. y Ultimate tensile strength f u And Young's elastic modulus E; f(·) is the material strength degradation function with respect to annual wind-induced fatigue cumulative damage D, and annual fatigue damage is determined by step 4;

[0029] Step 7: In the finite element simulation of high-rise buildings, to improve the computational efficiency of the numerical simulation, the nodes are simplified to a rod-spring model; for through-type welded nodes, they are simplified to... Figure 2 In this form, the constitutive relation of the spring is described by the kinematic hardening model; when the plastic zone occurs at the beam end, the yield moment is expressed as:

[0030] (9)

[0031] In the formula, W b σ is the net section modulus of the beam. y The yield strength of the material; the ultimate bending moment of the joint is determined by equation (10):

[0032] (10)

[0033] In the formula, h is the beam section height, B is the beam section width, and t b t represents the thickness of the beam flange. w This represents the thickness of the beam web; the limiting rotation angle is φu=min(0.02,3φ). y ), where the yield rotation angle is φ y =M y / k e k e The yield stiffness of the node is calculated by the "component method"; considering the fatigue cumulative damage effect, the material strength in formulas (9) and (10) is determined by the strength degradation model in step 6, i.e. formula (8).

[0034] The beneficial effects of this invention are as follows: The proposed method can effectively evaluate wind-induced structural fatigue damage and describe the strength degradation law of materials and structural components, while considering the influence of crosswind response and random variables; The steel strength degradation model established by this invention after wind-induced fatigue damage can be used to correct the material parameters of steel structures after fatigue damage, which is the key to accurately carrying out full-life reliability analysis of high-performance structures. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 To simplify the calculation model for welded joints;

[0037] Figure 3 Layout of a K-shaped centrally supported steel frame building: (a) Plan view; (b) Section 1-1 elevation view;

[0038] Figure 4 This represents the probability distribution of wind speed.

[0039] Figure 5 Time history curves of wind loads in the downwind and crosswind directions;

[0040] Figure 6 Distribution diagram of sensitive support components of the high-rise building

[0041] Figure 7 The stress cyclic distribution for support No. 825;

[0042] Figure 8 Conditional fatigue damage and fatigue life under 11 wind attack angles: (a) Conditional fatigue damage; (b) Conditional fatigue life;

[0043] Figure 9 Annual fatigue damage distribution diagrams for different regions of the component: (a) central region (Z1); (b) end region (Z8);

[0044] Figure 10Time-varying model of the elastic modulus of the material in the end region (Z8): (a) elastic modulus degradation of 4 supports in different spans; (b) elastic modulus degradation of 6 supports in different floors. Detailed Implementation

[0045] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0046] A method for analyzing wind-induced fatigue in a centrally supported steel frame structure and its strength degradation model, comprising the following steps:

[0047] Step 1 demonstrates the proposed fatigue damage assessment method using a centrally supported steel frame structure as an example. Based on the ETABS platform, a 30-story K-shaped centrally supported steel frame structure was designed according to the "Code for Seismic Design of Buildings" (GB50011-2010) and the "Technical Specification for Steel Structures of High-Rise Civil Buildings" (JGJ99-2015). This high-rise steel structure is an office building located in Xuwen County, Zhanjiang City, Guangdong Province. The main design parameters are summarized in Table 1.

[0048] Table 1 Structural Design Parameters

[0049]

[0050] The high-rise centrally supported frame building has a depth (B) and width (D) of 21.6 meters, a single span width of 7.2 meters, and one span of support frame is arranged in both the X and Y directions of the building. Figure 3 As shown in (a). Each floor of this high-rise building has a height of 3.6 meters, and the total building height (H) is 108 meters. See details... Figure 3 (b) The cross-sections of the supporting frame building components are detailed in Table 2, where the columns use box sections and the beams use I-shaped sections. Both beams and columns are made of Q355 steel; the supports use H-shaped sections made of Q235 steel and are connected to the frame via hinged joints.

[0051] Table 2. Cross-sectional dimensions of structural components (mm)

[0052]

[0053] The maximum daily wind speed data at a height of 10 meters in Xuwen County, Zhanjiang City, Guangdong Province, from 1971 to 2017, were obtained from the China Meteorological Administration (http: / / data.cma.cn / ), totaling 16,843 valid wind speed samples. This invention uses a Gumbel distribution to describe the probability distribution of wind speed, such as... Figure 4 As shown. Furthermore, based on the Gumbel distribution, the 10-minute average wind speed V corresponding to return periods of 1 year, 10 years, 50 years, and 100 years is calculated and determined. 10The values ​​are 22.1 m / s, 28.7 m / s, 33.3 m / s, and 35.3 m / s, respectively. This invention uses a logarithmic wind profile relationship to calculate the wind speed V at a height of 10 meters above the ground. 10 Converted to wind speed V at building height H H ,Right now

[0054] (11)

[0055] In the formula, z0 is the roughness length. Furthermore, the wind speed V at the top of a high-rise building... H The speeds are 46.8 m / s, 60.9 m / s, 70.8 m / s, and 75.0 m / s, respectively.

[0056] Step 2: Using wind tunnel test data provided by the Wind Engineering Research Center of Tokyo Institute of Technology, this invention obtains the geometric parameters of the high-rise building in Step 1, namely the B / D and B / H values ​​and the environmental roughness coefficient of 0.25. Based on this, the wind pressure coefficient C corresponding to the high-rise building in Step 1 is obtained. p Wind tunnel test data. The wind tunnel test conditions were as follows: sampling frequency 1000Hz, sampling period 32.8s, wind speed at the top of the model 11.8m / s, geometric scale 1 / 400, and time scale 1 / 167. Therefore, the actual time interval for the full-size building is 167 / 1000≈0.2s. Further, the downwind load F was calculated using the wind pressure coefficient. a and crosswind load F c ,Right now

[0057] (12)

[0058] and

[0059] (13)

[0060] In the formula, C p1 C p2、 C p3 and C p4 These represent the wind pressure coefficients of the four surfaces of the building; ρ is the air density, taken as 1.235 kg / m³; V H V is the wind speed at height H of the building; A is the windward area of ​​the building. Taking a 0° angle of attack as an example, V 10 When the wind speed is 22.1 m / s, the corresponding downwind and crosswind loads at the 30th floor of the building are as follows: Figure 5 As shown.

[0061] Step 3: After determining the input wind load in Step 2, nonlinear dynamic time history calculations for the high-rise building are performed on the OpenSees platform. DispBeamColumn elements are used for beam-column simulation, and truss elements are used for bracing members. The constitutive relations of Q355 and Q235 steel are described using the Steel02 model. The P-Δ effect is considered during modeling. The stress response of structural members under wind load is obtained through nonlinear dynamic time history simulation, and then the Goodman formula is used to correct the stress response. For a centrally supported steel frame structure, the bracing members are the main components providing lateral stiffness and the first line of defense against external excitations. my country's "Steel Structure Design Standard" (GB 50017-2017) provides SN curves for commonly used steel members and connection materials. This invention selects SN curves for three types of materials: rolled steel members (Z1 type), bolted connection base materials (Z2 type), and three-sided welded connection base materials (Z8 type). The SN curve parameters for these three types of steel are summarized in Table 3, where [Δσ]... 2×10^6 This indicates that the number of iterations is 2 × 10. 6 The corresponding stress amplitude at this time. Based on this, the stress amplitude threshold of the sensitive support component is determined to be 71 MPa.

[0062] Table 3 SN Curve Parameters

[0063]

[0064] Based on the SN curve and the corrected stress response, 48 supports were identified as sensitive components, such as... Figure 6 As shown in red in the middle.

[0065] Step 4: Use the rainflow counting method to determine the number of cycles corresponding to different stress amplitudes and average values ​​of the sensitive component in Step 3. Given the wind speed corresponding to a 100-year return period... Figure 7 A bar chart showing the stress cycle distribution of support member No. 825 at a wind angle of 0° is presented. Under a given 100-year return period wind speed, the conditional fatigue damage of the central and end regions of support member No. 825 at different wind attack angles is shown below. Figure 8 As shown in (a), the conditional fatigue life of the corresponding region is plotted on [the graph]. Figure 8 (b).

[0066] Step 5: Considering the probability of wind events with different return periods, and based on the conditional cumulative damage in the middle and end regions of the 48 sensitive components, calculate the annual wind-induced fatigue cumulative damage, such as... Figure 9 As shown.

[0067] Step 6: After determining the wind-induced annual cumulative damage of the structurally sensitive components in Step 5, the time-varying mechanical properties of the components after fatigue damage can be expressed as follows:

[0068] (14)

[0069] and

[0070] (15)

[0071] In the formula, f d,y or u (t) represents the time-varying yield strength or ultimate tensile strength of steel; E d (t) represents the time-varying elastic modulus of steel; f 0,y or u E0 and E0 represent the initial mechanical properties of the undamaged material, respectively; β is the steel performance degradation coefficient considering fatigue damage effects, with a value of 0.227.

[0072] Taking supports 825, 981, 1085, 1189, 1293, and 1507 distributed on different floors under a 35° wind attack angle, and supports 825, 831, 827, and 829 distributed across different spans as examples, Figure 10 The time-varying degradation of the elastic modulus of the material in the end region of the welded connection (Z8 type) support is demonstrated. This material mechanical property degradation model can be used to update the finite element model of the structure considering wind-induced fatigue damage effects for any service life. This updated finite element model can be further used to study the full-life reliability of the structure under extreme events such as earthquakes and strong winds.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions and implementation processes of the present invention, and are not intended to limit them. Those skilled in the art should understand that modifications can be made to the technical solutions described in the embodiments, or equivalent substitutions can be made to some of the technical features, but these modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for wind-induced fatigue analysis and strength degradation model construction of a centrally supported steel frame structure, characterized in that, The steps are as follows: Step 1: Obtain wind speed data from the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts (ECMWF), or other meteorological databases; based on the Poisson distribution assumption, determine the wind speed under wind load intensity. V ≥ x The wind incident in t The probability of occurring at least once within a year is expressed as: (1) In the formula, λ (·) indicates wind load intensity and wind speed. V ≥ x The annual exceedance probability of wind events is derived from the obtained wind speed data; therefore, wind load intensity and wind speed... V Writing the annual transcendence probability of ≥x wind events: (2) In the formula, n ( V ≥ x () indicates the wind speed under measured load intensity. V ≥ x The number of wind events that occurred; T r To record the duration of wind speed data; F exc ( x () indicates wind load intensity and wind speed V ≥ x The probability of exceeding; F cum ( x () indicates wind load intensity and wind speed V ≥ x The cumulative probability is described by extreme value type I, extreme value type II and extreme value type III distributions to describe the cumulative probability distribution of wind load intensity and wind speed. Step 2: Based on the cumulative probability distribution determined in Step 1, calculate the wind load intensity and wind speed corresponding to different return periods, and then determine the downwind wind load and crosswind wind load. Step 3: Using the input along-wind and cross-wind loads determined in Step 2, perform nonlinear dynamic time history calculations of the structure on a finite element platform to obtain the stress response of the high-rise building structural members; the stress-life curve, i.e., the SN curve, is used to determine the fatigue life of the high-rise building structural member materials; the SN curve is established through symmetrical cyclic loading tests, i.e., the average stress is zero; however, the average stress of the high-rise building structural members under along-wind and cross-wind loads is not zero, so the Goodman formula is used to correct the wind-induced stress response of the structural members, i.e.: (3) In the formula, S This is the equivalent stress amplitude. S a This represents the actual stress amplitude. S m This represents the actual average stress. S u The ultimate tensile strength of structural components in high-rise buildings; Step 4: According to the Palmgren-Miner criterion, the wind-induced fatigue damage of structural components in high-rise buildings is estimated using the following formula: (4) In the formula, n i Indicates the first i Level of stress S i The number of cycles under the current is determined by rainflow counting. N fi Indicating the same stress level S i The number of cycles at which fatigue failure occurs is determined based on the SN curve of the material. Based on this, the annual fatigue damage and fatigue life of high-rise building structural components are calculated using equations (5) and (6), respectively. The number of cycles for high-rise building structural components is determined through trial calculations. (5) and (6) In the formula, D A Indicates annual fatigue damage; T A The total number of seconds in a year; T W Enter the duration of the wind load, in seconds; T life Indicates fatigue life; Step 5, combining the wind events determined in Step 1... t Based on the probability of at least one occurrence per year and the annual fatigue damage determined in step 4, the annual wind-induced fatigue cumulative damage of high-rise building structural components is further defined as follows: (7) In the formula, D ( V j () indicates wind speed V j The annual fatigue damage of high-rise building structural components under wind load is determined by step 4; P ( V j () indicates wind speed V ≥ V j The probability of a wind event occurring is determined by step 1; Step 6, considering the annual wind-induced fatigue cumulative damage calculated in Step 5, the strength degradation model of high-rise building structural component materials is expressed as: (8) In the formula, Y 0 represents the initial mechanical properties of the undamaged material, including the material's yield strength. f y Ultimate tensile strength f u and Young's modulus of elasticity E f(·) represents the cumulative damage caused by annual wind-induced fatigue. D The material strength degradation function and annual fatigue damage are determined by step 4. Step 7: In the finite element simulation of high-rise buildings, to improve the computational efficiency of the numerical simulation, the nodes are simplified to a rod-spring model; for through-type welded nodes, the constitutive relation of the spring is described by the kinematic hardening model; when the plastic zone occurs at the beam end, the yield moment is expressed as: (9) In the formula, W b The net section modulus of the beam. σ y The yield strength of the material; the ultimate bending moment of the joint is determined by equation (10): (10) In the formula, h The height of the beam section. B The width of the beam section. t b Indicates the thickness of the beam flange. t w This represents the thickness of the beam web; the limit rotation angle is taken as... u=min(0.02,3 The yield rotation angle is The stiffness of the node is calculated by the "component method"; considering the fatigue cumulative damage effect, the material strength in formulas (9) and (10) is determined by the strength degradation model in step 6, i.e. formula (8).

2. The method for wind-induced fatigue analysis and strength degradation model construction of a centrally supported steel frame structure according to claim 1, characterized in that, Methods for determining wind loads include wind tunnel testing, standard values, and numerical simulation.

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