A method for designing the rigidity of a self-supporting stiffened steel chimney

Abstract

The application discloses a rigidity design method of a self-standing reinforced steel chimney, and belongs to the technical field of structural engineering. Firstly, according to the chimney size of the preliminary design and the basic wind pressure value of the design, the standard value of the along-wind load and the equivalent static load of the transverse-wind vortex-induced resonance are respectively calculated, and based on the virtual work principle of structural mechanics, a theoretical solution of the top horizontal displacement of the chimney is obtained. Secondly, considering the influence of the deformation characteristics of the chimney shell and the like, the theoretical solution is multiplied by a maximum horizontal displacement correction coefficient to obtain a real value of the maximum absolute value of the horizontal displacement of the top of the chimney cylinder. Finally, whether the real value of the horizontal displacement exceeds the limit value of the specification is checked to determine whether the chimney wall thickness needs to be increased to improve the rigidity. The application is accurate and reliable, simple to calculate, can save the building materials as much as possible under the premise of ensuring the reliable rigidity of the chimney cylinder structure, and is helpful to obtain a reasonable and reliable rigidity design scheme of the self-standing reinforced steel chimney under the combined action of the along-wind load and the transverse-wind load.

Description

Technical Field

[0001] This invention relates to a stiffness design method for a self-supporting stiffened steel chimney under the combined action of downwind and crosswind loads, belonging to the field of structural engineering technology. Background Technology

[0002] Self-supporting steel chimneys are widely used in the steel, thermal power, and metallurgical industries. Self-supporting steel chimneys have thin walls and a large height-to-diameter ratio, often exhibiting characteristics such as high flexibility, large size, light weight, and low damping. They are typical wind-sensitive structures, making wind load a controlling factor in the design process. Tall, circular-section steel chimneys are subjected to both tailwinds and crosswinds during use. Therefore, it is necessary to control the displacement of the steel chimney structure under the combined effects of tailwind and crosswind loads to ensure that the chimney's stiffness against wind loads is not too weak. A practical and reliable stiffness design method is proposed.

[0003] Currently, most domestic steel chimney manufacturers design structures according to my country's "Chimney Design Code" (GB50051-2013) and rely on existing experience. However, the calculation methods specified in the code are mainly for concrete and brick chimneys, with few quantitative provisions for self-supporting pure steel chimneys with large height-to-diameter ratios, which cannot fully meet the needs of existing project structural designs. Regarding wind-induced response calculations, the code simplifies the chimney structure as a thin-walled circular tube component, and the given wind-induced response calculation formula does not consider the influence of factors such as the characteristics of the steel chimney shell, initial structural defects, and uneven distribution of stiffening ribs causing uneven stiffness distribution. Furthermore, the code uses equivalent load calculation formulas to consider both along-wind and cross-wind loads, and the given method for calculating the combined effect of bidirectional wind loads is relatively simple and general, requiring further verification and research on its reliability. This can lead to situations where the safety of the chimney structure cannot be guaranteed in certain special circumstances; on the other hand, it results in low material utilization and is not economical in chimney structural design. Therefore, it is necessary to study the displacement response of self-supporting steel chimneys under the combined action of downwind and crosswind loads, and to propose a structural stiffness design method so as to reduce the manufacturing cost and improve the economic benefits of the product while ensuring the reliability of the chimney structure stiffness. Summary of the Invention

[0004] To optimize stiffness design and improve the safety of chimney structures, as well as enhance material utilization, this invention provides a stiffness design method for a self-supporting stiffened steel chimney. The technical solution is as follows:

[0005] Step 1: Initially determine the total height H, mid-section diameter D, and wall thickness t of the self-supporting stiffened steel chimney; determine the basic design wind speed v at a standard height of 10m above the ground for the construction site. 10 ;

[0006] According to my country's "Code for Design of Building Structures" (GB 50009), the circumferential shape coefficient μ of wind load at different locations is determined for the initially designed steel chimney structure. s Wind vibration coefficient β z Wind pressure height variation coefficient μ z This allows for the calculation of the standard value w of the downwind wind load at different locations on the surface of the steel chimney. k ;

[0007] Step Two: Tall structures are prone to crosswind vibration response, with crosswind vortex-induced resonance being the main factor causing crosswind-induced damage to steel chimneys. By comprehensively considering the flow characteristics around the cylindrical structure, the boundary layer morphology of the column surface, and vortex shedding characteristics through the Reynolds number Re, it is determined whether the steel chimney will experience crosswind vortex-induced resonance response. When the Reynolds number Re > 3.5 × 10⁻⁶, the response is considered to be positive. 6 At this time, the tall steel chimney structure will experience vortex-induced resonance response in the crosswind direction. Based on relevant Chinese regulations and classical theories of structural wind engineering, and using the Luhmann sinusoidal force model, the calculation formula for the vortex-induced resonance crosswind load on the chimney body in the resonance zone and the crosswind load amplitude p are obtained. L,j,max ;

[0008] The formula for calculating the Reynolds number Re is as follows:

[0009] Re = 69000vD (1)

[0010] In the formula, v is the actual wind speed at the calculated height (m / s); D is the diameter of the circular cross-section (m);

[0011] To accurately reflect the dynamic effects of crosswind vortex-induced resonance, the static amplitude p of the crosswind resonance load is used in the static analysis. L,j,max Multiply by the crosswind resonance dynamic equivalent coefficient γ eq By amplification, the equivalent crosswind vortex-induced resonance static wind load p is obtained. L,j,eq ;

[0012] Step 3: Based on the principle of virtual work in structural mechanics, and assuming that the influence of axial deformation and shear deformation on the displacement of the top of the cylinder under wind load is neglected for cantilever bending members, the equivalent crosswind vortex-induced resonance static wind load p is obtained. L,j,eq Under the action, the displacement Δ of the top of the cylinder caused by bending deformation c Theoretical solution for horizontal displacement as stiffness control point;

[0013] Finite element solution of horizontal displacement of stiffness control point considering the combined effects of crosswind and tailwind, shell deformation characteristics and nonlinear effects. FEM As a true value, a correction factor β for the maximum horizontal displacement of the top of the chimney is proposed, and the calculation formula is as follows:

[0014] β=Δ FEM / Δc (2)

[0015] Then, the theoretical solution for the horizontal displacement of the top of the chimney under the design wind load is corrected according to the following formula to obtain the true value of the horizontal displacement Δ with the largest absolute value of the top section. max :

[0016] Δ max =βΔ c (3)

[0017] Step 4: Stiffness verification;

[0018] If, at the design wind speed, the maximum horizontal displacement of the corrected chimney top section does not exceed the horizontal displacement limit H / 100 for steel chimneys, then the steel chimney structure meets the stiffness requirements at that design wind speed. The stiffness verification formula is as follows:

[0019] Δ max =βΔ c ≤H / 100 (4)

[0020] Step 5: When the preliminary design of the steel chimney structure cannot meet the requirements of formula (4) and the stiffness design does not meet the requirements, the chimney wall thickness t is increased, the circumferential stiffening ribs are densified or the cross section of the circumferential stiffening ribs is increased to enhance the chimney's stiffness against horizontal wind loads. Then, the stiffness verification is repeated according to steps one to four until the stiffness verification requirements of formula (4) are met.

[0021] Optionally, the standard value of the downwind load w k The calculation formula is as follows:

[0022] w k =β z μ s μ z w0 (5)

[0023]

[0024] In the formula: w k β represents the standard value of the downwind wind load at any circumferential location at height z; z μ is the wind vibration coefficient at height z. s The circumferential shape factor for wind load; μ z The wind pressure variation coefficient at height z; w0 is the basic wind pressure at the chimney construction site, i.e., the design basic wind speed v. 10 The corresponding wind pressure value: ρ = 1.25 kg / m 3 This is the standard air density.

[0025] Optionally, the wind load circumferential shape factor μ sFor a cylindrical structure at a given height, the calculated position is a function of the angle θ between the calculated position and the circumferential direction of the wind passage. The shape coefficient specifications for structures with different height-to-diameter ratios are numerically fitted using a Fourier series, resulting in the following calculation formula:

[0026]

[0027] Where: μ s (θ) is the surface shape coefficient of the steel chimney; θ is the circumferential angle between the calculation point and the wind direction; c i These are the coefficients of the body shape coefficient fitting formula.

[0028] Optionally, the Fourier series fitting coefficients c corresponding to height-to-diameter ratios H / D = 7 and H / D = 25 are... i As shown in Table 1 below:

[0029] Table 1 shows the coefficients c in the fitting formula for wind load shape coefficient. i (H / D = 7, H / D = 25)

[0030]

[0031] Linear interpolation was performed on the data in Table 1 to obtain the fitting formula coefficients for the wind load shape coefficient of steel chimneys with a height-to-diameter ratio in the range of [7, 25].

[0032] Optionally, the calculation formulas for the crosswind load and wind load amplitude of the section of the chimney body experiencing crosswind vortex-induced resonance are as follows:

[0033]

[0034]

[0035]

[0036] In the formula: p L,j (z,T) represents the vortex-induced resonance crosswind load per unit height at height z when the j-th order vortex-induced resonance occurs at time T; p L,j,max (z) represents the amplitude of the vortex-induced resonance crosswind load per unit height at height z when the j-th order vortex-induced resonance occurs; v cr,j μ is the critical wind speed at which the j-th order resonance occurs. L Let μ be the lift coefficient for the cylinder. L =0.25; ω j f is the chimney's natural circular frequency corresponding to the j-th mode shape; T is time; f j The natural frequency of the j-th mode of vibration of the chimney can be calculated by referring to the "Chimney Design Code" (GB50051-2013); S t For the Storoha number;

[0037] Crosswind vortex-induced resonance equivalent static wind load p L,j,eq The calculation formula is as follows:

[0038] p L,j,eq =γ eq p L,j,max (11)

[0039] In the formula: p L,j,eq The design base wind speed v is given when the structure experiences j-th order vortex-induced resonance. 10 The equivalent static wind load per unit height of the j-th order crosswind vortex-induced resonance under the action of γ; eq To determine the equivalent coefficient of crosswind vortex-induced resonance dynamics under the design base wind speed.

[0040] Optionally, the crosswind vortex-induced resonance dynamic equivalent coefficient γ under the basic design wind speed is... eq The value range is [52, 56], and a conservative value of 56.0 can be chosen.

[0041] Optionally, the bending moment M caused by the equivalent static load of crosswind at any height z0. p The formula for calculating (z0) is as follows:

[0042]

[0043]

[0044]

[0045] z0>H2 M p,3 (z0) = 0 (15)

[0046] In the formula: H1 is the starting height of the crosswind vortex-induced resonance zone; H2 is the top height of the crosswind vortex-induced resonance zone. When H2≥H, take H2=H.

[0047] Based on the variation law of wind profile index, the calculation formulas for the starting height H1 of the resonance zone and the peak height H2 of the resonance zone are as follows:

[0048]

[0049]

[0050]

[0051] In the formula, v H Let H be the wind speed at the total height H of the cylinder, and α be the ground roughness coefficient.

[0052] Optionally, in step three, the theoretical solution Δ for the horizontal displacement of the chimney top caused by the equivalent static load of crosswind is... c The calculation formula is as follows:

[0053]

[0054] In the formula: E is the elastic modulus of steel; I is the moment of inertia of the circular cross section of the chimney.

[0055] Optionally, the value table for the maximum horizontal displacement correction coefficient β at the top of the cylinder is as follows:

[0056] Table 2 Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=60m

[0057]

[0058] Table 3. Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=75m

[0059]

[0060] Table 4. Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=90m

[0061]

[0062] If the geometric parameters H, H / D, and D / t of the designed chimney are between the values ​​listed in the table above, then linear interpolation will be used to obtain the values.

[0063] Optionally, the maximum horizontal displacement correction coefficient β at the top of the chimney can also be directly calculated using the following formula, which is obtained by numerically fitting the horizontal displacement correction coefficient β at the top of the chimney using the least squares method:

[0064] β=[λ1(D / t) 3 +λ2(D / t) 2 +λ3(D / t)+λ4]×[μ1(H / D) 3 +μ2(H / D) 2 +μ3(H / D)+μ4] (20)

[0065] The fitting formula coefficients for stiffened steel chimney structures of different heights and aspect ratios are listed in Table 5:

[0066] Table 5 Radial displacement correction coefficient β fitting formula coefficient

[0067]

[0068] The beneficial effects of this invention are:

[0069] This invention provides a stiffness design method for self-supporting stiffened steel chimney structures under combined downwind and crosswind loads. This method reveals the quantitative relationship between chimney shape, wind load level, and the maximum horizontal displacement of the chimney. Using this design method, the maximum horizontal displacement of stiffened steel chimney structures with different geometric parameters under combined bidirectional wind loads can be accurately and easily calculated. By limiting the maximum horizontal displacement to within the allowable limits specified in the code, the wind resistance stiffness of the chimney structure is ensured to be reliable. Furthermore, under this premise, the material consumption of the chimney structure is minimized, reducing its manufacturing cost. Therefore, this stiffness design method for self-supporting stiffened steel chimney structures under combined downwind and crosswind loads has good application prospects in the design of self-supporting stiffened steel chimney structures under combined downwind and crosswind loads. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 This is a technical flowchart of the method of the present invention.

[0072] Figure 2 This is a structural model diagram of the self-supporting steel chimney of the present invention.

[0073] Figure 3 This is a schematic diagram of the crosswind resonance equivalent acceleration wind load simulation method of the present invention.

[0074] Figure 4 This is a schematic diagram of the geometric defect morphology of the circumferential welding of the present invention.

[0075] Figure 5 This is a curve showing the sum of the bottom bending moment and the horizontal displacement of the point of maximum deformation for different welding geometric defect amplitudes in Embodiment 3 of the present invention.

[0076] Figure 6 This is a schematic diagram showing the development and distribution of horizontal displacement at the top node of the cylinder in an embodiment of the present invention.

[0077] Figure 7 This is a schematic diagram of the wind-induced horizontal response of the cylinder top, considering only the effect of downwind or crosswind loads in this embodiment of the invention.

[0078] Figure 8 This is a graph showing the variation of the displacement correction coefficient β with the height-to-diameter ratio of the cylinder in an embodiment of the present invention.

[0079] Figure 9This is a graph showing the variation of the displacement correction coefficient β with the cylinder diameter-to-thickness ratio in an embodiment of the present invention.

[0080] Figure 10 This is a graph showing the variation of the displacement correction coefficient β with the circumferential bending stiffness of the cylinder in an embodiment of the present invention.

[0081] Figure 11 This is a graph showing the variation of the displacement correction coefficient β with the relative spacing of the circumferential stiffening ribs in the cylinder in an embodiment of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0083] 1. Calculation method for the amplitude of horizontal displacement of the top of a self-supporting chimney under the combined action of downwind and crosswind loads

[0084] A structural model of a self-supporting steel chimney under the combined action of downwind and crosswind loads is shown below. Figure 2 As shown. Due to the light weight of the steel chimney structure and the small number of auxiliary equipment, the vertical stress caused by its own weight accounts for a very low proportion of the total stress composition, and the main failure factor of the structure is wind-induced failure. In addition, as a stiffness control condition, horizontal displacement is only caused by wind load, not by self-weight or vertical load. Therefore, in stiffness design, only the horizontal displacement caused by wind load is considered, and the influence of the self-weight of the steel chimney wall and auxiliary components such as support beams is not considered. Ignoring the influence of small inspection ports and flue holes, the self-supporting steel chimney structure is simplified as a stiffened thin-walled cylindrical shell spliced ​​from sections with consistent cross-sections and uniform wall thickness, and a bidirectional equivalent wind load is applied to it. The main work of this invention is to study and clarify the solution of the maximum horizontal displacement of the self-supporting stiffened steel chimney under the combined action of downwind and crosswind loads.

[0085] The manufacturing process of a self-supporting steel chimney generally involves first bending thin steel plates into curved surfaces of single-plate height, then welding them into sections via vertical welds. These sections are then assembled from low to high using circumferential welds to form a complete chimney. In practical engineering, the height h of a single section is generally no greater than 3m. This invention uses a common section height of h = 2.5m for analysis and research. Simultaneously, circumferential angle steel stiffeners are welded to the chimney wall to enhance the circumferential stiffness of the chimney. Generally, one circumferential stiffener is arranged in each section or between every two sections, with a stiffener spacing of s.

[0086] This invention focuses on stiffened steel chimney structures where crosswind resonance is the dominant wind load combination. Based on calculations and investigations of commonly used freestanding steel chimney shapes in engineering, the subsequent research scope of this invention includes: a total chimney height H ranging from 60m to 90m; a bottom diameter D ranging from 4.8m to 10m; a wall thickness t ranging from 10mm to 35mm; a height-to-diameter ratio H / D ranging from 7.5 to 15; a diameter-to-thickness ratio D / t ranging from 195 to 900; and a stiffening rib spacing s ranging from 2.5m to 12.5m. Freestanding steel chimney structures within these ranges are susceptible to wind-induced stiffness failure dominated by crosswind resonance. Based on the actual geometric parameters of freestanding steel chimneys that may experience crosswind vortex-induced resonance in practical engineering, this invention establishes several basic research models, with structural parameters shown in Table 6.

[0087] Table 6 Basic Research Model Structure Parameters

[0088]

[0089]

[0090] Example 1: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model A.

[0091] Example 2: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model B.

[0092] Example 3: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model C.

[0093] Example 4: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model D.

[0094] Example 5: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model E.

[0095] Example 6: The specific construction parameters are shown in Table 6 as the basic structural parameters of Model F.

[0096] Because wind load distribution is uneven along both the radial and vertical directions, it is difficult to obtain accurate analytical solutions for the distribution of internal forces and wind-induced displacements in the structure based on classical plate and shell mechanics theory. Studying the stress response of a chimney using actual model loading tests would be extremely costly in terms of materials and require very demanding research conditions for such large-scale structures. Therefore, this invention uses the widely recognized finite element software ANSYS to numerically calculate the horizontal displacement response of the top of a self-supporting steel chimney structure under the combined action of downwind and crosswind loads, obtaining reliable and accurate research results. The finite element calculation and analysis process is described below:

[0097] 1) Structural element type: All structural components are simulated using Shell181 elements.

[0098] 2) Material Properties: Since a self-supporting steel chimney is a tall structure without additional structural support, its stress level is high under the combined effects of downwind and crosswinds. Therefore, in practical engineering, Q345 steel is mostly used to ensure structural safety. Thus, in finite element analysis, the material yield strength f is defined. y =345MPa, using an ideal elastoplastic model to consider the nonlinear effects of the material, the elastic modulus E = 2.06 × 10⁻⁶. 5 MPa, Poisson's ratio ν = 0.3. Considering geometric nonlinearity, the arc length method is used to track the structural response path.

[0099] 3) Boundary conditions: In the construction of self-supporting steel chimneys, a ring plate is usually welded to the bottom of the chimney and anchored to the foundation using anchor bolts. Therefore, the rotational constraint of the foundation on the chimney wall is weak and can be regarded as a hinge. When simulating the boundary conditions of the steel chimney model, translational constraints in the X, Y, and Z directions are applied to the bottom circumferential boundary of the chimney (ΔX=ΔY=ΔZ=0).

[0100] 4) Load simulation method:

[0101] Equivalent wind load in the downwind direction: From the formula (5) for calculating the equivalent wind load in the downwind direction, it can be seen that the downwind load along the height direction is calculated according to the wind vibration coefficient β. z and height coefficient μ z The variation pattern of the wind load is that the load value increases with increasing height; the wind load at the same height varies according to the shape coefficient μ. s The distribution is characterized by pressure on the windward side, significant wind suction on the side wings, and less wind suction on the leeward side. In the finite element software, the equivalent wind load in the downwind direction, varying with the basic wind speed, is written as a function and applied as a surface load to the surface of the steel chimney. The downwind direction is... Figure 2 Negative X-axis direction.

[0102] Crosswind resonance equivalent load: The essence of vortex-induced resonance is the resonant dynamic response of the structure, which is an acceleration excitation effect on the structure. The distribution of the vortex-induced resonance equivalent wind load along the circumferential direction of the cylinder is not clear. In addition, the steel chimney cylinder is a circumferentially stiffened thin-walled cylindrical shell structure. The stiffness of the cylindrical shell to resist local deformation is small. If the crosswind resonance equivalent load is applied in the form of concentrated force, the cylinder wall is prone to local buckling due to excessive force concentration, resulting in a failure mode that does not actually exist. Therefore, in the finite element simulation of this invention, the equivalent wind load p within the unit height range of the vortex-induced resonance region calculated by equation (11) is used. L,j,eq Converted into crosswind vortex-induced resonance equivalent acceleration a L,j,eqThe dynamic action of vortex-induced resonance is simulated by applying crosswind vortex-induced resonance equivalent acceleration in the resonance region. L,j,eq The calculation formula is shown in equation (21). The crosswind vortex-induced resonance equivalent acceleration is entered in the finite element software as a table array and applied as an inertial load to the structural element located in the resonance zone. Its direction of action is the positive Y-axis, perpendicular to the direction of airflow. The application of the crosswind resonance equivalent acceleration corresponding to a certain wind speed is shown in equation (21). Figure 3 As shown.

[0103]

[0104] In the formula: a L,j,eq The crosswind vortex-induced resonance equivalent acceleration is expressed in N / kg; m0 is the mass of the chimney section per unit height (kg).

[0105] Steps for simultaneous application of bidirectional wind loads: In the finite element nonlinear static analysis, the basic wind pressure of the downwind load is expressed by the basic wind speed according to equation (6), and the equivalent acceleration of crosswind resonance can also be expressed by the basic wind speed according to equation (21). In this way, the equivalent static wind loads in both downwind and crosswind directions can be written as the basic wind speed v. 10 (This wind speed increases from 0 until it reaches the predetermined design basic wind speed value v) 10 The function is used to express the relationship between downwind and crosswind loads, thereby establishing a mathematical relationship between them and enabling accurate simulation of spatially unevenly distributed wind loads that vary with the basic wind speed.

[0106] The wind load loading process is divided into two stages, and the loading is performed in two load steps in the finite element software: the first load step is the basic wind speed v. 10 In the initial stage of the load increase, the wind speed at the top of the chimney has not yet reached the wind speed corresponding to the starting point of the crosswind resonance zone. There is no resonance zone on the chimney section, and the structure is only subjected to the downwind load alone, applying only the equivalent surface load caused by the downwind to the steel chimney body. The second load step begins at the moment when the crosswind resonance zone appears on the structure, that is, when the wind speed at the top of the chimney is v. H (v H =v 10 '(H / 10) α The critical wind speed v for vortex-induced resonance was reached. cr,j (i.e. v) H ≥v cr,j During this stage, the structure is subjected to the combined action of downwind wind load and crosswind resonance wind load, which simultaneously applies downwind wind pressure to the entire tube section and crosswind resonance equivalent acceleration to the resonance zone.

[0107] 5) Construction of Initial Geometric Imperfections: In the manufacturing process of self-supporting steel chimney structures, thin steel plates are typically first bent into arc-shaped plates of single-plate height, then welded into cylindrical sections via vertical welds. These sections are then assembled into a complete structure from low to high via circumferential welds. Simultaneously, circumferential angle steel stiffeners are welded to the chimney wall to enhance its circumferential stiffness. Related research indicates that vertical welding defects have little impact on the structural bearing capacity; therefore, the effects of residual stress and welding geometric deformation caused by vertical welds are ignored. Circumferential welding geometric defects significantly affect the buckling bearing capacity of the cylindrical shell under vertical compressive stress; therefore, the main analysis focuses on the impact of initial circumferential welding geometric defects on the bearing capacity of the self-supporting steel chimney under wind load. The morphology of the circumferential welding geometric defects adopts the radial deformation expression for the circumferential weld proposed by Pircher:

[0108]

[0109]

[0110] In the formula: δ represents the radial deformation of the chimney wall caused by geometric defects; z' represents the relative vertical distance from the centerline of the circumferential weld; δ0 represents the amplitude of the welding geometric defect. According to the provisions of the "Chimney Design Code" (GB50051-2013) regarding the amplitude of concave and convex deformation of the chimney body, the amplitude of the welding geometric defect should meet the following requirements. Slightly disadvantageous λ b The linear elastic half-wavelength; the coefficient ξ reflects the bending stiffness of the shell wall during weld cooling and contraction, and is an assumption about the boundary conditions at the weld. This invention adopts the "Rotter and Teng B" shape function, taking ξ = 0, which means that the mutual constraint of adjacent plates during weld cooling is equivalent to a hinge, allowing relative rotation. The circumferential weld geometric defect morphology is as follows: Figure 4 As shown.

[0111] Example 3 introduces amplitudes of 0.1δ. 0,k 0.5δ 0,k 0.8δ 0,k 1.0δ 0,k The geometric defects of the circumferential welds between cylinder sections were investigated, and nonlinear analysis was performed under bidirectional wind loads. Load-displacement curves for each model and the load distribution under δ0 = 1.0δ were also analyzed. 0,k The buckling mode when the load reaches its extreme value (defined as the extreme point buckling mode) is as follows: Figure 5As shown in the figure, the horizontal axis represents the horizontal displacement of the node with the maximum buckling deformation, and the vertical axis represents the combined bending moment M0 caused by the downwind and crosswind at the bottom of the chimney. M0 can be calculated according to formulas (24)-(26). As can be seen from the figure, the circumferential welded geometric defects significantly weaken the load-bearing capacity of the self-supporting steel chimney structure, and the load-bearing capacity level of the structure decreases rapidly as the amplitude of the circumferential welded geometric defects increases. Therefore, it is safer to uniformly take the initial geometric defect amplitude as 1.

[0112]

[0113]

[0114]

[0115] 2. Displacement response characteristics of a self-supporting chimney under combined downwind and crosswind loads

[0116] Self-supporting steel chimney structures, under the combined action of bidirectional wind loads, experience significant horizontal displacement at the top of the chimney, making them prone to stiffness failure exceeding the displacement limits specified in the code. To clarify the development of wind-induced horizontal displacement at the top of the chimney wall, finite element analysis of the horizontal displacement Δ at each node at the critical stiffness failure point is used, with the circumferential angle as the abscissa. FEM (θ) and the finite element solution of the horizontal displacement with the largest absolute value [Δ FEM (θ)] max The ratio is used as the ordinate. The relative distribution of horizontal displacement at each node of the top section of the cantilevered circular pipe, subjected only to crosswinds, is compared with that of the cantilevered circular pipe. The relative distribution of horizontal displacement at each node of the top section of the five calculation models in Examples 2 to 6 is plotted as follows: Figure 6 As shown.

[0117] Depend on Figure 6 It can be seen that, under wind load dominated by crosswind resonance, the development of horizontal displacement at the top of the cylinder in each calculation model is roughly consistent with that of a cantilevered circular pipe subjected only to crosswind. Basically, the leeward side of the cylinder (0°≤θ≤180°) experiences outward horizontal displacement, while the windward side (180°≤θ≤360°) experiences inward horizontal displacement. The maximum absolute value of the horizontal displacement is located near the leeward meridian of the crosswind direction (θ=90°). Except for Examples 2 and 3, the maximum inward horizontal displacement (defined as pointing towards the original center as inward and away from the original center as outward) is located near the windward meridian of the crosswind direction (θ=270°). The horizontal displacement of the cylinder top in Examples 3 and 4 is shown below. Figure 6In the figure, the dashed line represents the original cross-sectional shape and initial position of the top section of the structure, while the solid line represents the deformation and displacement of the top section at the critical state of stiffness failure (i.e., the moment when the maximum displacement reaches the displacement limit specified in the code). As shown in the figure, the top section of Example 3 exhibited significant elliptic deformation, while the top section of Example 4 exhibited significant overall crosswind displacement. The inward horizontal deformation is considered positive, and the maximum value is marked as the maximum horizontal displacement MAX; the outward horizontal deformation is considered negative, and the value with the largest absolute value is marked as the minimum horizontal displacement MIN.

[0118] The horizontal displacement response of the cylinder top under the combined action of bidirectional wind loads is caused by the combined wind-induced displacement responses under the individual actions of downwind and crosswind. To explain the displacement response of the cylinder top, the horizontal displacement response of the cylinder top under unidirectional wind loads is analyzed, such as... Figure 7 As shown. Under the action of crosswind alone, the steel chimney cylinder undergoes overall displacement in the direction of crosswind resonance, and the cross-section basically maintains a circular cross-section shape. The maximum and minimum horizontal displacements are equal in magnitude but opposite in direction (Example 6). Under the action of downwind load alone, due to the uneven circumferential distribution of the downwind load, the displacement response of the top of the cylinder caused by the downwind load is composed of the overall displacement response of the cylinder and the local deformation response of the cylinder wall. For structures with good integrity, the overall displacement mainly occurs in the downwind direction, the local displacement response of the cylinder wall is not obvious, the top of the cylinder basically maintains a circular cross-section, and the absolute value of the minimum horizontal displacement is slightly greater than the absolute value of the maximum horizontal displacement (Example 4); for structures with poor integrity, the local displacement response of the cylinder wall is dominant, the cylinder wall is concave in the area of ​​wind pressure and convex in the area of ​​wind suction, and the cross-section of the top of the cylinder shows obvious elliptical deformation (Example 3).

[0119] Table 7 lists the horizontal displacement response results of the cylinder top under the combined action of bidirectional wind loads at the critical state of structural stiffness failure in five embodiments. The ratio of the absolute values ​​of the minimum and maximum horizontal displacements of the cylinder top section reflects the influence of the elliptic deformation of the cylinder top section caused by the downwind load. Table 7 shows that the absolute value of the minimum horizontal displacement in each model is greater than the absolute value of the maximum horizontal displacement, meaning that the displacement amplitude away from the original center is greater than the displacement amplitude approaching the original center. Furthermore, the differences are more pronounced in structures with poorer overall integrity and smaller proportions of the resonance zone at the critical state of failure, indicating a more significant influence of the local deformation of the cylinder top section caused by the downwind load. The downwind horizontal displacement at the cylinder top section at θ = 0° is caused by both the local deformation and overall displacement caused by the downwind load, while the crosswind horizontal displacement at θ = 90° is caused by both the local deformation and overall displacement caused by the downwind load. The ratio of the absolute values ​​of the horizontal displacements at these two positions reflects the magnitude relationship between the displacement responses caused by the downwind and crosswind loads. The downwind displacement response of each model is significantly smaller than the crosswind displacement response. Moreover, for structures with better overall integrity, the downwind displacement response is even smaller than the crosswind displacement response. The overall displacement caused by the crosswind is the main component of the crosswind horizontal displacement at the position θ = 90°.

[0120] Table 7 Calculation Model Horizontal Displacement Response of Cylinder Top

[0121]

[0122] Taking into account the resonance effects of tailwind and crosswind, the analysis Figure 6 The table shows the horizontal displacement response of the cylinder top. At the windward meridian position (θ = 0°), the cylinder undergoes a horizontal inward displacement due to wind pressure, and the absolute value of the horizontal displacement is larger for structures with poorer overall integrity. Under the combined action of wind loads from both directions, the node with the largest absolute value of horizontal displacement in each model appears at the position of θ = 94°, close to the leeward meridian in the crosswind direction (θ = 90°). This is due to the combined effect of the outward expansion deformation of the windward flanks caused by the windward load, the overall displacement of the structure in the windward direction, and the overall displacement in the crosswind direction caused by the crosswind. As shown in Table 7, the absolute value of the maximum horizontal displacement of the cylinder top in the five embodiments with different body shapes does not exceed 0.46% of the absolute value of the radial displacement of the cylinder top at the leeward meridian in the crosswind direction (θ = 90°). Therefore, this invention uses the top node of the leeward meridian (θ = 90°) in the crosswind direction as the stiffness control point, and the absolute value of the radial displacement at this point as the maximum horizontal displacement of the tube top section as the control index for structural stiffness failure. The stiffness failure of the structure is determined by comparing whether the maximum horizontal displacement of the tube top section exceeds the displacement limit H / 100 specified in the standard. For embodiments 2 and 3, which have poor overall structural integrity, the ratio of the minimum absolute value of the horizontal displacement to the maximum absolute value of the horizontal displacement is relatively large, indicating a significant trend of elliptic deformation of the tube top section caused by the downwind load. Furthermore, the ratio of the absolute values ​​of the horizontal displacement at θ = 0° and θ = 90° in these embodiments is relatively large, indicating that the influence of the displacement response of the tube top section caused by the downwind load cannot be ignored. Due to the influence of the maximum horizontal displacement caused by the downwind load in the downwind-facing meridian region (θ=0°), and the influence of the outward horizontal displacement caused by the downwind load in the crosswind-facing meridian region (θ=270°) on the inward horizontal displacement caused by the crosswind, the maximum horizontal displacement distribution location in these two embodiments will shift towards the downwind-facing meridian (θ=0°). The development of horizontal displacement of the cylinder wall near the crosswind-facing meridian (θ=270°) differs from other embodiments.

[0123] The horizontal displacement of the top of the self-supporting stiffened steel chimney structure under bidirectional wind loads is roughly consistent with the horizontal displacement of the top section of the cantilevered circular pipe due to bending under lateral loads. Furthermore, the overall displacement in the direction of the crosswind caused by crosswind resonance is a major component of the maximum horizontal displacement of the chimney, a key indicator for determining stiffness failure. Therefore, the top node of the self-supporting steel chimney structure subjected to bidirectional wind loads, near the leeward meridian (θ = 90°) where the maximum horizontal displacement occurs, is taken as the stiffness control point.

[0124] 3. Investigate the effect of the height-to-diameter ratio H / D of the chimney on the correction factor β for the maximum horizontal displacement of the chimney top.

[0125] Considering that the actual horizontal displacement of the chimney stiffness control point is superimposed with the wind-induced displacement response of the downwind load, and that the shell wall undergoes a certain degree of local deformation, it will inevitably differ from the solution of the horizontal displacement of the top of the cantilevered circular pipe subjected only to the equivalent crosswind load. Therefore, the finite element solution Δ of the radial displacement of the stiffness control point (top of the crosswind leeward meridian (θ=90°)) is used. FEM As the true value, the relative coefficient β of the radial displacement of the stiffness control point under different load levels is proposed according to formula (27). n During the combined action of crosswind and downwind loads, the crosswind resonance zone rapidly expands, and the crosswind load gradually becomes dominant. The displacement at θ = 90° at the top of the cylinder caused by the crosswind quickly becomes the main component of the displacement. Therefore, β n It exhibits a rapid decline followed by a relatively stable trend. Since structural stiffness failures all occur when horizontal displacement is significant, they are typically in the β phase. n Since the basic structure remains unchanged, this invention takes the horizontal displacement relative coefficient of the critical state of structural stiffness failure as β, and defines it as the correction coefficient for the maximum horizontal displacement.

[0126] β n =Δ FEM / Δ c (27)

[0127] Examples 7 to 12: Compared with the basic structural parameters of Example 1, steel chimney models with different height-to-diameter ratios were constructed by changing only the height H of the cylinder while keeping other parameters unchanged. The specific relationship between the height-to-diameter ratio of the cylinder and the correction coefficient of the maximum horizontal displacement of the top of the cylinder is shown in Table 8 below.

[0128] Examples 13 to 19: Compared with the basic structural parameters of Example 2, steel chimney models with different height-to-diameter ratios were constructed by changing only the height H of the cylinder while keeping other parameters unchanged. The specific relationship between the height-to-diameter ratio of the cylinder and the correction coefficient of the maximum horizontal displacement of the top of the cylinder is shown in Table 8 below.

[0129] Examples 20-25: Based on the basic structural parameters of Example 4, steel chimney models with different height-to-diameter ratios were constructed by changing only the height H of the chimney while keeping other parameters unchanged. The specific relationship between the height-to-diameter ratio of the chimney and the correction coefficient for the maximum horizontal displacement of the top of the chimney is shown in Table 8 below.

[0130] Table 8. Relationship between the correction factor β for the calculation of the top horizontal displacement and the height-to-diameter ratio H / D of the cylinder.

[0131]

[0132]

[0133] The curve showing the variation of the correction factor β for the maximum horizontal displacement of the top section of the cylinder with the height-to-diameter ratio H / D is as follows. Figure 8 As shown, with the increase of the height-to-diameter ratio of the steel chimney structure, the correction factor β for the maximum horizontal displacement of the top section decreases significantly. Moreover, the decrease in correction factor β is more significant for structures with a large diameter-to-thickness ratio, while the decreasing trend of correction factor β is relatively gradual for structures with a small diameter-to-thickness ratio.

[0134] When examining the influence of the height-to-diameter ratio H / D on the correction factor β of the maximum horizontal displacement at the top of the chimney, while keeping the chimney diameter and wall thickness constant and changing the total height H, a smaller height-to-diameter ratio results in two main effects: firstly, the downwind load value increases relative to the crosswind load value; secondly, the ellipticization trend of the upper section of the chimney intensifies. Both of these factors lead to a larger proportion of the radial outward expansion local deformation of the downwind flanks caused by the downwind load in the composition of the total displacement at the top of the chimney. Consequently, the difference between the actual displacement at the top of the chimney and the horizontal displacement calculated based on a cantilevered bending circular tube under crosswind conditions only is greater. Therefore, the correction factor β of the maximum horizontal displacement at the top of the chimney increases as the height-to-diameter ratio decreases.

[0135] 4. Investigate the effect of the chimney diameter-to-thickness ratio D / t on the correction factor β for the maximum horizontal displacement of the chimney top.

[0136] Examples 26 to 30: Compared with the basic structural parameters of Example 1, steel chimney models with different diameter-to-thickness ratios were constructed by only changing the wall thickness t of the cylinder. At the same time, the circumferential bending stiffness was kept constant by adjusting the thickness of the circumferential stiffening ribs. The specific relationship between the cylinder diameter-to-thickness ratio and the correction coefficient of the maximum horizontal displacement of the cylinder top is shown in Table 9 below.

[0137] Examples 31 to 36: Compared with the basic structural parameters of Example 2, steel chimney models with different diameter-to-thickness ratios were constructed by only changing the wall thickness t of the cylinder. At the same time, the circumferential bending stiffness was kept constant by adjusting the thickness of the circumferential stiffening ribs. The specific relationship between the cylinder diameter-to-thickness ratio and the correction coefficient of the maximum horizontal displacement of the top of the cylinder is shown in Table 9 below.

[0138] Examples 37 to 43: Compared with the basic structural parameters of Example 3, steel chimney models with different diameter-to-thickness ratios were constructed by only changing the wall thickness t of the cylinder. At the same time, the circumferential bending stiffness was kept constant by adjusting the thickness of the circumferential stiffening ribs. The specific relationship between the cylinder diameter-to-thickness ratio and the correction coefficient of the maximum horizontal displacement of the cylinder top is shown in Table 9 below.

[0139] Table 9. Relationship between the correction factor β for the calculation of the top horizontal displacement and the cylinder diameter-to-thickness ratio D / t

[0140]

[0141] The curve showing the variation of the correction factor β for the maximum horizontal displacement of the top section of the cylinder with the diameter-to-thickness ratio D / t is as follows. Figure 9As shown, with the increase of the diameter-to-thickness ratio of the steel chimney structure, the correction factor β for the maximum horizontal displacement of the top section of the chimney shows an increasing trend.

[0142] When examining the influence of the diameter-to-thickness ratio D / t on the correction factor β of the maximum horizontal displacement at the top of the chimney, while keeping the height and diameter of the chimney constant and changing the wall thickness t, a larger diameter-to-thickness ratio results in two main effects: firstly, a smaller crosswind resonance zone, and a larger proportion of the downwind load in the failure load, leading to a larger proportion of the displacement at the 90° position of the top of the chimney caused by the downwind load in the total displacement at that point; secondly, a thinner wall thickness makes the wall more prone to wind-induced local deformation, which, even under the same load, increases the radial outward expansion deformation of the downwind flanks at the top of the chimney due to downwind suction. All of these factors reduce the proportion of the displacement at the 90° position of the top of the chimney caused by the crosswind load in the total displacement at that point. Therefore, the correction factor β of the maximum horizontal displacement at the stiffness control point of the top of the chimney tends to increase with the increase of the diameter-to-thickness ratio.

[0143] 5. Investigate the circumferential bending stiffness K of the cylinder. θ Influence of the correction factor β on the maximum horizontal displacement of the chimney top

[0144] Circumferential stiffness K of circumferentially reinforced steel chimney body θ The expression is as follows:

[0145]

[0146] In the formula: I′=∫ A r 2 dA is the moment of inertia of the stiffening rib about the mid-surface of the cylinder wall; r is the perpendicular distance from any point on the circumferential stiffening rib to the mid-surface of the cylinder wall; A is the cross-sectional area of ​​the circumferential stiffening rib. S=∫ A rdA is the static moment of the circumferential stiffening rib section about the mid-surface of the cylinder wall.

[0147] Examples 44 to 50: Compared with the basic structural parameters of Example 1, steel chimney models with different circumferential bending stiffnesses were constructed by changing the cross-sectional dimensions and thickness of the circumferential equilateral angle steel stiffeners. The specific relationship between the circumferential bending stiffness of the chimney and the correction coefficient of the maximum horizontal displacement of the top of the chimney is shown in Table 10 below.

[0148] Examples 51 to 57: Compared with the basic structural parameters of Example 2, steel chimney models with different circumferential bending stiffnesses were constructed by changing the cross-sectional dimensions and thickness of the circumferential equilateral angle steel stiffeners. The specific relationship between the circumferential bending stiffness of the chimney and the correction coefficient of the maximum horizontal displacement of the top of the chimney is shown in Table 10 below.

[0149] Examples 58 to 65: Compared with the basic structural parameters of Example 3, steel chimney models with different circumferential bending stiffnesses were constructed by changing the cross-sectional dimensions and thickness of the circumferential equilateral angle steel stiffeners. The specific relationship between the circumferential bending stiffness of the chimney and the correction coefficient of the maximum horizontal displacement of the top of the chimney is shown in Table 10 below.

[0150] Table 10 Correction factor β for top horizontal displacement calculation and circumferential bending stiffness K of the cylinder θ Relationship

[0151]

[0152]

[0153] The correction factor β for the maximum horizontal displacement of the top section of the cylinder varies with the circumferential bending stiffness K of the cylinder. θ The change curve is as follows Figure 10 As shown, with the increase of the circumferential bending stiffness of the steel chimney body, the correction coefficient β for the maximum horizontal displacement of the stiffness control point generally shows a significant decreasing trend.

[0154] In examining the circumferential bending stiffness K of the cylinder θ When considering the effect of the correction factor β on the maximum horizontal displacement of the chimney top, the circumferential bending stiffness of the chimney is changed by altering the cross-sectional dimensions and thickness of the circumferential equilateral angle steel stiffeners. The increase in the circumferential bending stiffness of the chimney will lead to a decrease in the degree of elliptical deformation of the chimney top section, and a reduction in the outward expansion deformation of the flanks caused by wind-driven loads. The radial displacement of the chimney top stiffness control point is mainly composed of the overall crosswind displacement caused by crosswind loads. Therefore, the correction factor β decreases as the circumferential bending stiffness increases, gradually approaching 1.

[0155] 6. Investigate the effect of the stiffening rib spacing s on the correction factor β for the maximum horizontal displacement of the chimney top.

[0156] Examples 66-71: Based on the basic structural parameters of Example 1, steel chimney models with different stiffening rib spacings are constructed by changing the arrangement spacing of the circumferential stiffening ribs. Simultaneously, the circumferential bending stiffness is kept constant by adjusting the cross-sectional dimensions of the circumferential stiffening ribs. The stiffening rib spacing *s* is compared with the half-wave length of the linear elastic bending of the cylindrical shell. ν = 0.3, which is the ratio of Poisson's ratio of steel (s / λ) b Defined as the relative spacing of the circumferential stiffening ribs, this measure is used to assess the density of stiffening rib distribution in different structural shapes. The specific relationship between the relative spacing of the circumferential stiffening ribs and the correction factor for the maximum horizontal displacement at the top of the cylinder is shown in Table 11.

[0157] Examples 72-78: Based on the basic structural parameters of Example 2, steel chimney models with different stiffening rib spacings were constructed by changing the arrangement spacing of the circumferential stiffening ribs. Simultaneously, the circumferential bending stiffness was kept constant by adjusting the cross-sectional dimensions of the circumferential stiffening ribs. The specific relationship between the relative arrangement spacing of the circumferential stiffening ribs and the correction coefficient for the maximum horizontal displacement at the top of the chimney is shown in Table 11.

[0158] Examples 79-84: Compared with the basic structural parameters of Example 3, steel chimney models with different stiffening rib spacings were constructed by changing the arrangement spacing of the circumferential stiffening ribs, while the circumferential bending stiffness was kept constant by adjusting the cross-sectional dimensions of the circumferential stiffening ribs. The specific relationship between the relative arrangement spacing of the circumferential stiffening ribs and the correction coefficient for the maximum horizontal displacement of the top of the chimney is shown in Table 11.

[0159] Table 11 Correction coefficient β for top horizontal displacement calculation and relative arrangement spacing s / λ of circumferential stiffening ribs of the cylinder b Relationship

[0160]

[0161] The correction factor β for the maximum horizontal displacement of the top section of the cylinder varies with the relative arrangement of the circumferential stiffeners of the cylinder (s / λ). b The change curve is as follows Figure 11 As shown, with the increase in the relative spacing of the circumferential stiffening ribs of the steel chimney, the horizontal displacement correction coefficient β of the stiffness control point basically shows a trend of first decreasing and then increasing, with a small change range. Among the three model groups, the largest change range of β is 10.7% (corresponding to s / λ). b (Increased by 200.1%).

[0162] The relative arrangement spacing s / λ of the circumferential stiffening ribs of the cylinder is examined. b When considering the effect of the correction factor β on the maximum horizontal displacement of the chimney top, under the premise of keeping the circumferential bending stiffness of the chimney constant, the stiffener spacing has little impact on the structure's natural vibration characteristics and the load combination of the critical failure state. Changes in the stiffener spacing have little effect on the ellipticization trend of the cross-section and the vertical stress distribution. Therefore, the correction factor β for the maximum horizontal displacement has little impact. However, if the circumferential stiffeners are too sparsely arranged, i.e., the relative spacing s / λ... b Further expansion beyond 10 will weaken the stiffness of the cylinder, and further expansion beyond 15 will increase the horizontal displacement correction factor β. Therefore, the relative spacing of the circumferential stiffening ribs should not be too large during the design process.

[0163] In summary, the research results indicate that the parameters influencing the maximum horizontal displacement correction factor β at the top of the cylinder include the cylinder height-to-diameter ratio H / D, the diameter-to-thickness ratio D / t, the spacing of the circumferential stiffeners s, and the circumferential bending stiffness K of the cylinder. θThe main structural parameters that have a significant impact are the height-to-diameter ratio (H / D), the diameter-to-thickness ratio (D / t), and the circumferential bending stiffness (K) of the cylinder. θ Based on the foregoing analysis, a larger s value indicates a higher K value. θ When the value is small, the β value is conservative. Therefore, in subsequent calculations, a larger circumferential stiffener spacing s = 5000 mm is chosen for safety, and a smaller circumferential bending stiffness K of the cylinder is selected. θ =0.94×10 9 N·mm (e.g., when the wall thickness t = 21mm, the cross-sectional dimensions of the angle steel stiffeners are taken as ∟100×100×14mm). Based on this, the height H, diameter D, and wall thickness t of the cylindrical structure are changed to construct self-supporting stiffened steel chimney models with different height-to-diameter ratios H / D and diameter-to-thickness ratios D / t to determine the β value and formulate displacement calculation and stiffness design methods. To meet the corrosion resistance requirements of steel chimneys, the minimum wall thickness t within the study range is taken as 10mm; in actual engineering, there are very few cases of self-supporting steel chimneys with wall thicknesses greater than 35mm, and the circumferential stiffener arrangement spacing and cross-sectional dimensions are designed based on wall thicknesses greater than 35mm. The overall bending stiffness K of the structure is... θ It will always be greater than 0.94 × 10 9 N·mm, therefore, the range of cylinder wall thickness variation considered when formulating the stiffness design method in this invention is 10mm to 35mm.

[0164] 7. Development of a structural stiffness design method for self-supporting stiffened steel chimneys under combined downwind and crosswind loads.

[0165] Example 85:

[0166] The method in this embodiment includes the following steps:

[0167] Step 1: For a given self-supporting stiffened steel chimney structure, under the combined action of downwind and crosswind loads, the amplitude of its top horizontal displacement should not exceed the displacement limit H / 100 of steel chimney structures specified in the current Chinese "Chimney Design Code" (GB 50051-2013), thereby ensuring that the stiffness control conditions are met. To meet this stiffness requirement, the structural stiffness needs to be designed according to the top horizontal displacement control conditions.

[0168] Based on the design requirements, technological conditions, and other factors, the total height H of the self-supporting stiffened steel chimney, the diameter D of the cylindrical section, and the basic design wind speed v at a standard height of 10m in the engineering construction area are determined. 10 The initial design of the chimney wall thickness t is used as a basis for subsequent analysis and calculations. According to my country's "Load Code for Design of Building Structures" (GB 50009-2012), the circumferential shape coefficient μ of the wind load at different locations is determined for the designed steel chimney structure. s Wind vibration coefficient β z Wind pressure height variation coefficient μz This allows for the calculation of the standard value w of the downwind wind load at different locations on the surface of the steel chimney. k The circumferential shape factor of the wind load can be calculated according to the following formula (7), and the standard value of the wind load along the wind direction w can be calculated according to formulas (5) and (6). k .

[0169] w k =β z μ s μ z w0 (5)

[0170]

[0171]

[0172] The Fourier series fitting coefficient c corresponding to height-to-diameter ratios H / D = 7 and H / D = 25 i As shown in Table 1 below:

[0173] Table 1 shows the coefficients c in the fitting formula for wind load shape coefficient. i (H / D = 7, H / D = 25)

[0174]

[0175] By performing linear interpolation on the data shown in the table, the fitting formula coefficients for the wind load shape coefficient of steel chimneys with a height-to-diameter ratio in the range of [7, 25] can be obtained.

[0176] Step Two: Tall structures are prone to crosswind vibration response, with crosswind vortex-induced resonance being the main factor causing crosswind-induced damage to steel chimneys. Taking into account the flow characteristics around the cylindrical structure, the boundary layer morphology of the cylinder surface, and vortex shedding, the Reynolds number Re is calculated using the following formula:

[0177] Re = 69000vD (1)

[0178] When the Reynolds number Re > 3.5 × 10 6 At this time, the tall steel chimney structure will experience vortex-induced resonance response in the crosswind direction. Based on relevant Chinese regulations and classical theories of structural wind engineering, and using the Luhmann sinusoidal force model, the calculation formula for the vortex-induced resonance wind load on the chimney body in the resonance zone and the wind load amplitude p are obtained. L,j,max To accurately reflect the dynamic effects of crosswind vortex-induced resonance, the static amplitude p of the crosswind resonance load is used in the static analysis. L,j,max Multiply by the crosswind resonance dynamic equivalent coefficient γ eq By amplification, the equivalent crosswind vortex-induced resonance static wind load p is obtained. L,j,eqThe crosswind load amplitude p of the section of the chimney experiencing crosswind vortex-induced resonance. L,j,max The calculation is performed according to equations (8) to (10). The equivalent static wind load p in the crosswind direction for vortex-induced resonance is... L,j,eq The calculation is performed according to equation (11), where the calculations for the above embodiments 1-84 show that the dynamic equivalence coefficient is biased towards a safe value of γ. eq =56.0 for calculation.

[0179]

[0180]

[0181]

[0182] p L,j,eq =γ eq p L,j,max (11)

[0183] Step 3: Based on the principle of virtual work in structural mechanics, and assuming a cantilevered bending member that satisfies the plane section assumption, while neglecting the influence of axial deformation and shear deformation on the displacement of the top of the cylinder under wind load, the displacement Δ of the top of the cylinder caused by bending deformation under the static equivalent load of crosswind vortex-induced resonance in the resonance zone is obtained. c Theoretical solution for horizontal displacement as the stiffness control point. Under a certain basic wind speed, the crosswind vortex-induced resonance zone starts at H1 and ends at H2 along the height direction. The equivalent crosswind resonance load within this resonance zone has the same value. Outside the crosswind vortex-induced resonance zone, the chimney body is not subject to crosswind loads, only downwind loads. Therefore, taking the starting point H1 of the crosswind resonance zone as the boundary, the bending moment M caused by the crosswind load at any height position z0 is calculated segmentally. p (z0). Bending moment M caused by the equivalent static load of crosswind at any height z0. p (z0) is calculated according to equations (12) to (18).

[0184]

[0185]

[0186]

[0187] z0>H2 M p,3 (z0) = 0 (15)

[0188]

[0189]

[0190]

[0191] Considering that the actual horizontal displacement of the stiffness control point at the top of the chimney is caused by the combined effects of downwind and crosswind loads, and that the circular cross-section of the chimney tends to ellipticize, resulting in some local deformation of the chimney wall, the actual horizontal displacement at the top of the chimney differs from the linear theoretical solution for the horizontal displacement at the top of a cantilevered circular pipe member subjected only to the equivalent crosswind load. Therefore, the finite element solution Δ for the horizontal displacement of the stiffness control point will be developed, taking into full account the combined effects of crosswind and downwind, the shell deformation characteristics, and nonlinear effects. FEM As the true value, the correction coefficient β for the maximum horizontal displacement of the top of the chimney is proposed according to formula (2). Based on extensive calculations in Examples 1 to 84, this invention summarizes and formulates a table of values ​​for β based on the chimney height H, height-to-diameter ratio H / D, and diameter-to-thickness ratio D / t, as shown in Tables 2 to 4. The β value can be obtained by looking up the table based on the main geometric parameters. In addition, to facilitate programmed design, the least squares numerical fitting was performed based on the quantitative relationship between the β value and the main geometric parameters H / D and D / t, and the direct calculation formula (20) for the β value was summarized. According to formula (19), the theoretical solution Δ for the horizontal displacement of the top of the chimney caused by the equivalent static load of crosswind can be calculated. c .

[0192] β=Δ FEM / Δ c (2)

[0193]

[0194] The following table shows the values ​​for the correction factor β for the maximum horizontal displacement at the top of the chimney, based on the chimney height H, height-to-diameter ratio H / D, and diameter-to-thickness ratio D / t. It should be noted that blank entries in these tables indicate that the steel chimney structure has not experienced wind-induced stiffness failure dominated by crosswinds, or that the corresponding chimney wall thickness is outside the range of wall thickness variations considered in this invention, and therefore is not an object of analysis required for extracting the correction factor β.

[0195] Table 2 Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=60m

[0196]

[0197] Table 3. Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=75m

[0198]

[0199] Table 4. Correction factor β for the maximum horizontal displacement of the top of the steel chimney structure with H=90m

[0200]

[0201] The correction factor β for the maximum horizontal displacement of the cylinder top can also be obtained by numerical fitting using the least squares method:

[0202] β=[λ1(D / t) 3 +λ2(D / t) 2 +λ3(D / t)+λ4]×[μ1(H / D) 3 +μ2(H / D) 2 +μ3(H / D)+μ4] (20)

[0203] The fitting formula coefficients for stiffened steel chimney structures of different heights and aspect ratios are listed in the table below:

[0204] Table 5 Radial displacement correction coefficient β fitting formula coefficient

[0205]

[0206] The theoretical solution for the horizontal displacement of the top of the chimney under design wind load is corrected to obtain the true value Δ of the horizontal displacement with the largest absolute value at the top section. max Calculate according to formula (3).

[0207] Δ max =βΔ c (3)

[0208] Step 4: To determine whether the horizontal displacement of the top of the self-supporting stiffened steel chimney structure under the combined action of bidirectional wind loads meets the limit requirements specified in my country's "Chimney Design Code" (GB50051-2013), a stiffness verification formula is proposed. Under the design wind speed, if the maximum horizontal displacement of the modified top section does not exceed the horizontal displacement limit H / 100 of the steel chimney, i.e., formula (4) is satisfied, then it can be determined that the steel chimney structure meets the stiffness requirements under the design wind speed.

[0209] Δ max =βΔ c ≤H / 100 (4)

[0210] Step 5: When the preliminary design of the steel chimney structure cannot meet the requirements of formula (4), that is, the stiffness design does not meet the requirements, since the chimney height H and cross-sectional diameter D are generally determined by the process requirements and cannot be changed, the chimney wall thickness t is increased, the circumferential stiffening ribs are densified or the cross-section of the circumferential stiffening ribs is increased to enhance the chimney's resistance to horizontal load stiffness. Then, the stiffness verification is repeated according to steps one to four until the stiffness control conditions of formula (4) are met.

[0211] 8. Application example of the stiffness design method for self-supporting stiffened steel chimney structures under combined downwind and crosswind loads.

[0212] Example 86:

[0213] For a self-supporting stiffened steel chimney manufactured using Q345 steel in an actual engineering project, a relatively economical and reasonable wall thickness needs to be designed. The specific structural dimensions are: total chimney height H = 90000 mm, cross-sectional diameter D = 9000 mm, and the design basic wind speed v at a standard height of 10 m in the project construction area. 10 =32m / s, the initial selection of the cross-sectional specifications of the circumferential angle steel stiffener is ∟140×140×14, the height of the cylinder section h=2500mm, and the spacing of the stiffeners s=5000mm.

[0214] Step 1: Based on the required total height H, diameter D, and the location where the self-supporting steel chimney will be built, the preliminary design wall thickness of the chimney is t = 16 mm, determining its height-to-diameter ratio H / D = 10 and diameter-to-thickness ratio D / t = 562.5. Calculate the basic wind pressure in the construction area. Calculate the wind load shape coefficient μ at the windward line (θ=0°) using the fitting coefficients in Table 1. s =1.0. Referring to the "Code for Design of Building Structures" (GB 50009-2012), the wind vibration coefficient β at a total height H = 90m of the cylindrical structure can be obtained. z =1.50, wind pressure height variation coefficient μ z =1.93, thus the standard value of the wind load along the windward direction at the top of the cylinder is calculated to be w. k =β Z μ S μ Z w0 = 1.853 kNm 2 The wind speed at the top of the cylinder is...

[0215] Step 2: Calculate the Reynolds number Re = 69000vD = 19.872 × 10 6 >3.5×10 6 This means that the structure will experience vortex-induced resonance. When vortex-induced resonance occurs, its critical wind speed is calculated as follows: Based on relevant Chinese regulations and classical theories of structural wind engineering, and using the Luhmann sinusoidal force model, the amplitude of the vortex-induced resonance wind load on the chimney body within a unit height range of the resonance zone is obtained. To accurately reflect the dynamic effect of crosswind vortex-induced resonance, a method is adopted in the static analysis to amplify the static amplitude of the crosswind resonance load according to the crosswind resonance dynamic equivalence coefficient, thus obtaining the equivalent crosswind vortex-induced resonance static wind load p. L,j,eq =γ eq p L,j,max =181962 Nm.

[0216] Step 3: Under the influence of the basic wind speed, obtain the starting height of the resonance zone from the variation law of the wind profile index. Vertex height in the resonance region The vertex height in the resonance region is greater than the total height of the cylinder body. Take H2 = H = 90m.

[0217] Based on the principle of virtual work in structural mechanics, ignoring the influence of axial deformation and shear deformation on the displacement of the cylinder top under wind load according to the cantilever flexural member, the displacement Δ of the cylinder top caused by bending deformation under the equivalent load of crosswind vortex-induced resonance in the resonance region is obtained by solving. c The theoretical solution of the horizontal displacement as the stiffness control point. Under a certain basic wind speed, the starting point of the crosswind vortex-induced resonance region along the height direction is H1, and the vertex is H2. The equivalent load of crosswind resonance within this resonance region takes the same value. The chimney cylinder body outside the crosswind vortex-induced resonance region is not affected by the crosswind load and only bears the downwind load. Therefore, taking the starting point H1 of the crosswind resonance region as the boundary, the bending moment M p (z0) caused by the crosswind load at any height position z0 is calculated in segments.

[0218]

[0219]

[0220]

[0221] The theoretical solution Δ of the horizontal displacement of the chimney cylinder top caused by the crosswind equivalent static load c The calculated values are as follows:

[0222]

[0223] Step 4: According to the chimney cylinder body height H, height-diameter ratio H / D, and diameter-thickness ratio D / t, look up Table 4 to obtain the correction coefficient β = 1.446 for the maximum horizontal displacement of the steel chimney structure cylinder body with H = 90m. Correct the theoretical solution of the horizontal displacement to obtain the true value Δ of the absolute maximum horizontal displacement of the chimney cylinder top section max = βΔ c = 886.68mm.

[0224] According to the maximum horizontal displacement limit requirement specified in the "Chimney Design Code" (GB50051-2013) of our country, it is H / 100 = 900mm, that is, Δ max < H / 100, indicating that the preliminary design scheme meets the stiffness limit requirement, and this design is relatively reasonable and economical.

[0225] Some steps in the embodiments of the present invention can be implemented by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk, etc.

[0226] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for stiffness design of a self-supporting stiffened steel chimney, characterized in that, The stiffness design method for the self-supporting stiffened steel chimney includes: Step 1: Initially determine the total height of the self-supporting stiffened steel chimney. H Diameter of the mid-section of the cylindrical body D and cylinder wall thickness t Determine the basic design wind speed at a standard height of 10m above the ground in the project construction area. v 10 ; For the initially designed steel chimney structure, determine the circumferential shape coefficient of the wind load at different locations under downwind load. μ s Wind vibration coefficient β z Wind pressure height variation coefficient μ z This allows for the calculation of the standard values ​​of the downwind wind load at different locations on the surface of the steel chimney. w k ; Step 2: Determine whether the steel chimney will experience crosswind vortex-induced resonance response by using the Reynolds number Re. When the Reynolds number Re > 3.5 × 10⁻⁶, the response will be positive. 6 Based on the Luhmann sinusoidal force model, the calculation formula for the vortex-induced resonance crosswind load on the chimney body in the resonance zone and the static amplitude of the crosswind load are obtained. p L,j,max ; The formula for calculating the Reynolds number Re is as follows: (1) In the formula, v To calculate the actual wind speed at altitude; In static analysis, the static amplitude of the crosswind resonance load is used. p L,j,max Multiply by the crosswind resonance dynamic equivalent coefficient γ eq The equivalent crosswind vortex-induced resonance static wind load was obtained by amplification. p L,j,eq ; Step 3: Based on the principle of virtual work in structural mechanics, and assuming that the influence of axial deformation and shear deformation on the displacement of the top of the cylinder under wind load is neglected for cantilever bending members, the equivalent crosswind vortex-induced resonance static wind load is obtained by solving. p L,j,eq Displacement of the top of the cylinder due to bending deformation under the action Δ c Theoretical solution for horizontal displacement as stiffness control point; Propose a correction factor for the maximum horizontal displacement at the top of the chimney. β ; The theoretical solution for the horizontal displacement of the top of the chimney under design wind load is corrected using the following formula to obtain the true value of the horizontal displacement with the largest absolute value at the top section. Δ max : (3) Step 4: Stiffness verification; Under the design wind speed, if the maximum horizontal displacement of the corrected chimney top section does not exceed the horizontal displacement limit of the steel chimney. H If the value is 100, then the steel chimney structure meets the stiffness requirements under the design wind speed. The stiffness verification formula is as follows: (4) Step 5: When the preliminary design of the steel chimney structure cannot meet the requirements of formula (4) and the stiffness design does not meet the requirements, the chimney wall thickness should be increased. t The chimney's resistance to horizontal wind loads is enhanced by increasing the density of circumferential stiffening ribs or increasing the cross-section of circumferential stiffening ribs. Then, the stiffness verification is repeated according to steps one to four until the stiffness verification requirements of formula (4) are met.

2. The stiffness design method for a self-supporting stiffened steel chimney according to claim 1, characterized in that, The standard value of the downwind load w k The calculation formula is as follows: (5) (6) In the formula: w k for z Standard value of downwind wind load at any circumferential position at height; β z for z Wind vibration coefficient at altitude; μ s The circumferential shape factor for wind load; μ z for z The wind pressure variation coefficient at altitude; w 0 represents the basic wind pressure at the location where the chimney is to be built, i.e., the basic design wind speed. v 10 The corresponding wind pressure value; ρ =1.25kg / m 3 This is the standard air density.

3. The stiffness design method for a self-supporting stiffened steel chimney according to claim 2, characterized in that, The wind load circumferential shape coefficient μ s For the cylindrical structure at a given height, the angle between the calculated position and the circumferential windward direction is... θ The function is numerically fitted to the body coefficient specifications of structures with different height-to-diameter ratios using a Fourier series, and the calculation formula is as follows: (7) In the formula: μ s ( θ ) represents the surface shape coefficient of the steel chimney; θ The circumferential angle between the calculation point and the direction of the wind; c i These are the Fourier series fitting coefficients.

4. The stiffness design method for a self-supporting stiffened steel chimney according to claim 3, characterized in that, The calculation formulas for the crosswind load and wind load amplitude of the section of the chimney body experiencing crosswind vortex-induced resonance are as follows: (8) (9) (10) In the formula: p L,j ( z , T ) is the occurrence of the first time at time T. j During vortex-induced resonance, z Vortex-induced resonance crosswind load per unit height at altitude; p L,j,max ( z ) for the occurrence of the first j During vortex-induced resonance, z The amplitude of vortex-induced resonance crosswind load per unit height at a given altitude; v cr,j For the occurrence of the first j Critical wind speed for step resonance; μ L Let be the lift coefficient, and take for the cylinder. μ L =0.25; ω j For the corresponding number j The natural circular frequency of the chimney in a step-mode vibration; T For time; f j For the chimney j The natural frequency of the mode shape; S t For the Storoha number; Crosswind vortex-induced resonance equivalent static wind load p L,j,eq The calculation formula is as follows: (11) In the formula: p L,j,eq For the structure to occur j Design base wind speed during step-vortex resonance v 10 Under the action of the first j Equivalent static wind load per unit height within the crosswind direction vortex-induced resonance; γ eq To determine the equivalent coefficient of crosswind vortex-induced resonance dynamics under the design base wind speed.

5. The stiffness design method for a self-supporting stiffened steel chimney according to claim 4, characterized in that, The equivalent coefficient of crosswind vortex-induced resonance dynamics under the basic wind speed γ eq The value range is [52, 56].

6. The stiffness design method for a self-supporting stiffened steel chimney according to claim 5, characterized in that, For any height position z Bending moment at point 0 caused by crosswind equivalent static load M p The formula for calculating (z0) is as follows: (12) (13) (14) z 0＞ H 2 M p,3 (z0) = 0 (15) In the formula: H 1 represents the starting height of the crosswind vortex-induced resonance zone; H 2 represents the height of the peak of the crosswind vortex-induced resonance zone. H 2≥ H At that time, take H 2= H ; The starting height of the resonance zone was obtained based on the variation law of the wind profile index. H 1 and the height of the resonance zone peak H The formula for calculating 2 is as follows: (16) (17) (18) In the formula, v H Total height of the cylinder H Wind speed at the location, α This is the surface roughness coefficient.

7. The stiffness design method for a self-supporting stiffened steel chimney according to claim 6, characterized in that, In step three, the theoretical solution for the horizontal displacement of the chimney top caused by the equivalent static load of crosswind is... Δ c The calculation formula is as follows: (19) In the formula: E The elastic modulus of steel; I Let be the moment of inertia of the circular cross-section of the chimney.

8. The stiffness design method for a self-supporting stiffened steel chimney according to claim 7, characterized in that, The maximum horizontal displacement correction coefficient at the top of the chimney β The following formula is used to directly calculate the maximum horizontal displacement correction factor for the top of the chimney using the least squares method. β Numerical fitting yielded the following: (20) in, λ 1. λ 2. λ 3. λ 4. μ 1. μ 2. μ 3. μ 4 represents the fitting formula coefficients for stiffened steel chimney structures of different heights and aspect ratios.

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