CN116150842B - Method for calculating design wind load of bent torsion column spiral Liang Jingguan tower based on IWL method - Google Patents
Method for calculating design wind load of bent torsion column spiral Liang Jingguan tower based on IWL method Download PDFInfo
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Abstract
The invention discloses a method for calculating the design wind load of a bent torsion column spiral Liang Jingguan tower based on an IWL method, wherein the appearance and the mass distribution of a landscape tower are unevenly changed along the height, and the method comprises the following steps: determining related parameters of a landscape tower structure, related coefficients of the roughness of the ground and a wind condition reference coefficient; according to the load specification, firstly calculating the downwind average wind resistance of a building with unchanged appearance along the height direction at the unit height of z-height based on an Inertial Wind Load (IWL) methodWind vibration coefficient β (z); introducing a local shape change correction coefficient theta (z) and a wind direction angle change correction coefficient eta (theta) of the landscape tower to correct the wind vibration coefficient beta (z) to obtain a corrected IWL wind vibration coefficientS4, using the corrected IWL wind vibration coefficientCalculating the equivalent static wind load f ESWL (z, θ). The invention has the beneficial effects that: the design wind load calculation method closer to the actual wind load is simple, and the obtained wind load calculation junction is providedThe method is more accurate and reliable, and can be used for guiding the structural design and material selection of the landscape tower.
Description
Technical Field
The invention belongs to the technical field of tower building design, relates to determination of tower design load with uneven appearance and mass distribution, and particularly relates to a method for calculating a bending column spiral Liang Jingguan tower design wind load based on an IWL method.
Background
In wind-resistant designs for towering structures, the following problems should be considered: the structure is ensured to have enough strength and can reliably bear the internal force under the action of wind load; the structure must have sufficient rigidity to control displacement of the towering structure under horizontal loads; reasonable structural system and appearance are selected. Structural wind load design values are a precondition for a designer to perform preliminary structural design. In engineering design application, for a general high-rise structure, the maximum wind load born by the main body supporting structure is not higher than the allowable stress value calculated according to the section characteristics and materials at the corresponding position. Therefore, the wind load design value of the structure is accurately and efficiently calculated, and the wind load design value has straightness for the safety, applicability and economy of the structureThe effect of the connection. In engineering design application, the wind load standard value W is generally adopted k To calculate the wind loading effect to which the structure is subjected. Reasonable wind-resistant design is in addition to the structural materials and the construction technology, and the structure W k The method is a precondition that a designer obtains a load design value when carrying out preliminary structure design, and has direct influence on the safety, applicability and economy of the structure. And the wind vibration coefficient beta is the accurate calculation W in the structural wind resistance design k But for some tower-like structures with landscape properties, the unique changing profile may have a beneficial or detrimental effect on β, requiring further investigation. For example, the cranked column spiral Liang Jingguan tower (simply referred to as a landscape tower) is often one of the logo of a city, which is not only attractive in appearance, but also convenient for pedestrians to enjoy landscapes, such as the double spiral view Jing Da of marsk, the arcelor Mittal track tower of the UK, and the like. The landscape tower is generally constructed by adopting steel materials, the structural form is slender, the damping ratio is small, and wind load is generally the control load of the high-rise structure. The unique shape of the landscape tower makes wind load results obtained using conventional calculation methods potentially inaccurate.
Although dynamic time-course analysis can obtain wind vibration response of the structure, wind load calculated by adopting load specification is concise, convenient and time-saving, and the method is still widely adopted by designers at the present stage. The wind load calculated by the specification should have an effect of enabling equivalent wind vibration response of the tower type building and actual maximum wind vibration response. The design of the landscape tower by adopting the accurate equivalent static wind load is a precondition for ensuring the safe use of the building. In the existing relevant load specification: for example, "building structural load specifications (GB 50009-2012)", and "towering structural design standards (GB 50135-2019)", a method for calculating wind vibration coefficients of dense structures having uniform shapes and mass distributions is recommended. However, the influence of the mass and the wind shielding area of the tower building along the height non-uniform change on the wind vibration coefficient is not clear. When the random vibration theory is adopted to calculate the equivalent static wind load of the landscape tower, the expression relates to complex multiple integration, the appearance and the mass distribution of the landscape tower are irregular, and the expression is difficult to summarize by a unified expression. Therefore, not only is the rationality of the wind-resistant design of the landscape tower required to be evaluated by using the existing load specification, but also a simple and accurate wind load calculation formula of the tower building is required to be provided.
Disclosure of Invention
In view of this, the present invention provides a method for calculating the wind load of a cranked column helix Liang Jingguan tower design based on the IWL method.
The technical scheme is as follows:
a method for calculating the design wind load of a bent-torsion column spiral Liang Jingguan tower based on an IWL method, wherein the appearance and the mass distribution of the landscape tower are unevenly changed along the height, the key steps are that,
s1, determining related parameters of the structure of the landscape tower, related coefficients of the roughness of the ground and reference coefficients of wind conditions;
s2, calculating the average wind resistance f (z) in the downwind direction of a unit height of a building with the shape unchanged along the height direction at the z height position based on an Inertial Wind Load (IWL) method according to the load specification, and the wind vibration coefficient beta (z); the height of the building with the shape unchanged along the height direction is the same as the height of the landscape tower, and the width of the building is the same as the structural width of the landscape tower;
s3, introducing a local shape change correction coefficient theta (z) and a wind direction angle change correction coefficient eta (theta) of the landscape tower to correct the wind vibration coefficient beta (z) to obtain a corrected IWL wind vibration coefficientExpressed as->
Wherein the local shape change correction coefficient θ (z) and the wind direction angle change correction coefficient η (θ) are both determined based on the shape of the landscape tower at each of the feature segments at different heights;
s4, using the corrected IWL wind vibration coefficientCalculating the equivalent static wind load f ESWL (z, θ) as the design wind load, the expression is +.>
Preferably, in step S1, the landscape tower structure-related parameter includes a first-order natural vibration frequency f 1 The overall height H and the structural width b;
the roughness related coefficient of the ground comprises a roughness coefficient k related to the ground surface γ Ground roughness index alpha γ Correction coefficient k of ground roughness w ；
The wind condition reference coefficient comprises a pulsating wind turbulence density I at a height of 10m 10 Average wind pressure omega of 10m height 10 。
Preferably, the method for determining the local shape change correction coefficient θ (z) and the wind direction angle change correction coefficient η (θ) includes first creating a test model of each characteristic segment of the landscape tower, performing a wind tunnel test using the test model, calculating a test wind vibration coefficient according to data obtained by the wind tunnel test, calculating a ratio of the test wind vibration coefficient to the wind vibration coefficient β (z) obtained according to the load specification in step S1, respectively obtaining a distribution of the local shape change correction coefficient θ (z) and a distribution of the wind direction angle change correction coefficient η (θ), determining an expression of θ (z) by a nonlinear fitting method, and determining an expression of η (θ) by a multimodal fitting method.
Preferably, the landscape tower is a steel structure tower, the steel structure tower comprises a spiral stair, a platform is arranged at the top of the spiral stair, a spiral ribbon structure is vertically arranged on the platform, and a thin-wall hollow ball is arranged at the upper part of the ribbon structure;
the local shape change correction coefficient theta (z) is expressed as a piecewise function expressed as
The sections of the piecewise function correspond to spiral stairway, platform and streamer structures respectively, wherein z is the height，z n Is the platform ground clearance of the steel structure tower.
Preferably, the above-mentioned wind direction angle change correction coefficient η (θ) is expressed as
Wherein x is ci 、w i 、A i Fitting parameters are respectively adopted, i represents each section from bottom to top of the steel structure tower;
in step S3, a wind direction angle change correction coefficient η (θ) at each of the other angles is calculated based on η (θ) at the wind direction angle θ=300°, and the wind vibration coefficient β (z) is corrected.
Preferably, the corrected IWL wind vibration coefficientExpressed as
Where g is the peak factor and where,
wherein B is z Expressed as background component factors as
In phi 1 (1) For the 1 st order mode shape coefficient at z-height, the approximate calculation expression isμ z (z) is the wind pressure height variation coefficient at the height z of the landscape tower expressed asρ z Is the correlation coefficient of the pulsating wind load in the vertical direction, ρ x Is the correlation coefficient of the pulsating wind load in the horizontal direction, expressed as respectively
Wherein R is a resonance component factor expressed as
In zeta 1 The steel structure is valued as ζ for damping ratio of the tower 1 ＝0.01；ω 0 Is the basic wind pressure, and is the basic wind pressure,ρ a is air density v 0 Is the base wind speed.
Preferably, the average wind resistance in the downwind direction per unit height f (z) is expressed as
Wherein mu s (z) is the drag coefficient at the landscape tower height z;
ρ a is air density;
is the average wind speed at height z;
wherein b s (z) high wind shielding area per unit, b s (z) =b (z) δ (z), b (z) being the outer contour width at z-height, δ (z) being the solidity at z-height.
Compared with the prior art, the invention has the beneficial effects that: aiming at the landscape tower with the shape changing along the height, the method given by the existing load specification is corrected by considering the local shape changing and the wind direction angle changing factors, and the design wind load calculating method closer to the actual wind load is provided.
Drawings
FIG. 1 is a schematic illustration of the calculation flow of the method;
FIG. 2 is a computational model diagram of a spiral landscape tower;
FIG. 3 is a photograph of a wind tunnel test model, wherein: (a) a aeroelastic model, (b) a tower upper rigid segment model, (c) a spiral stair rigid segment model;
FIG. 4 is a simulated wind tunnel interior airflow conditions, wherein: (a) average wind speed and turbulence; (b) wind speed power spectrum;
FIG. 5 is a schematic view of wind direction angle definition of a wind tunnel test of a pneumatic elastic model;
FIG. 6 is a schematic diagram of a station arrangement and different station segments, wherein: (a) station arrangement, (b) different station segments;
fig. 7 is a comparison of wind induced vibration displacement test values with simulated values, wherein: (a) average value, (b) standard deviation;
FIG. 8 shows the drag coefficients of the overall superstructure and lower spiral stairway of a landscape tower at different wind angles;
FIG. 9 is a comparison of wind vibration coefficients determined using Chinese load specifications, model wind tunnel test data and correction methods;
FIG. 10 is a graph showing the comparison of wind vibration coefficient values simulated, calculated according to Chinese load specifications and the wind vibration coefficient determined by the correction method;
FIG. 11 is a flow chart of calculation of the design wind load for a spiral landscape tower based on the IWL method.
Detailed Description
The invention is further described below with reference to examples and figures.
A method for calculating the design wind load of a bent torsion column spiral Liang Jingguan tower based on an IWL method, wherein the appearance and the mass distribution of the landscape tower are unevenly changed along the height, and the method comprises the following steps:
s1, determining related parameters of the structure of the landscape tower, related coefficients of the roughness of the ground and reference coefficients of wind conditions;
s2, calculating the average wind resistance f (z) in the downwind direction of a unit height of a landscape tower with the shape unchanged along the height direction at the z height position based on an Inertial Wind Load (IWL) method according to the load specification, wherein the height of a building with the shape unchanged along the height direction is the same as the height of the landscape tower, and the width of the building is the same as the structural width of the landscape tower;
s3, introducing a local shape change correction coefficient theta (z) and a wind direction angle change correction coefficient eta (theta) of the landscape tower to correct the wind vibration coefficient beta (z) to obtain a corrected IWL wind vibration coefficientExpressed as->
Wherein the local shape change correction coefficient θ (z) and the wind direction angle change correction coefficient η (θ) are both determined based on the shape of the landscape tower at each of the feature segments at different heights;
s4, using the corrected IWL wind vibration coefficientCalculating the equivalent static wind load f ESWL (z, θ) as the design wind load, the expression is +.>
The method fully considers the influence of the uneven change of the shape and the quality of the landscape tower along with the height on the structure of the tower body. The load specification can refer to building structure load specification (GB 50009-2012) or high-rise structure design standard (GB 50135-2019).
For a landscape tower that varies in shape along the height, the characteristic segments are segments that differ significantly in structural shape along the height direction and that result in significant differences in wind load.
The local shape change correction coefficient theta (z) and the wind direction angle change correction coefficient eta (theta) can be determined by comparing wind tunnel test model calculation with calculation according to load specifications: firstly, a test model of each characteristic section of the landscape tower is manufactured, wind tunnel tests are conducted by using the test model, test wind vibration coefficients are calculated according to data obtained by the wind tunnel tests, the calculated ratio of the test wind vibration coefficients to wind vibration coefficients beta (z) obtained according to load standards in the step S1 is respectively obtained, the distribution of local shape change correction coefficients theta (z) and the distribution of wind direction angle change correction coefficients eta (theta) are respectively obtained, the expression of theta (z) is determined through a nonlinear fitting method, and the expression of eta (theta) is determined through a multimodal fitting method.
Taking a spiral landscape tower as an example, the principle and advantages of the method are described through wind tunnel tests and numerical calculation.
As shown in fig. 2, the landscape tower is a steel structure building and comprises a spiral stair with a vertically arranged lower part, a platform is arranged at the top of the spiral stair, a spiral ribbon structure is vertically arranged on the platform, and a light thin-wall hollow steel ball is arranged at the upper part of the ribbon structure. The spiral stair consists of an arc-shaped box girder and a anticlockwise torsion steel box column, the platform consists of a box girder framework, and the ribbon is a lattice system consisting of two box girders and a box girder connected in the middle. General expression of equivalent static wind load of landscape tower
As shown in FIG. 2, H is the total height of the landscape tower, z n B is the width of the spiral stair for the height of the platform from the ground; m is M 1 (x 1 ,z 1 ) And M 2 (x 2 ,z 2 ) Is any two points in space.
Under the action of incoming wind load, the vibration equation expression of the 1 st order mode of the landscape tower along the wind direction is as follows:
wherein q is 1 (t) time-varying modal coordinates of the order 1 mode;is the generalized mass of the 1 st order mode,φ 1 (z) and m (z) are the 1 st order mode shape coefficient and mass at z height, respectively; />Generalized modal damping coefficient of 1-order mode>ζ 1 A damping ratio of 1 order vibration mode; />Is the generalized stiffness of the 1 st order mode,time-varying generalized wind load of 1-order vibration mode, < >>f (z, t) is the time-varying wind resistance per unit height at the level of the downwind z, < ->The average wind resistance per unit height at the downwind z-height, f' (z, t) is the instantaneous pulsating wind resistance per unit height at the downwind z-height.
Under the assumption of a quasi-steady state,and f' (z, t) is expressed as:
wherein mu is s (z) is the landscape tower drag coefficient; b (z) is the outer contour width at the z-height; v' (x, z, t) is the instantaneous fluctuating wind speed at the (x, z) position; delta (z) is the solidity at z height; b s (z) high wind shielding area per unit, b s (z)＝b(z)δ(z)。
The landscape tower response caused by the average wind load can be solved by adopting a static equation, and the landscape tower response caused by the action of the pulsating wind load can be solved in a frequency domain based on a random vibration theory. From the wiener-Xin Qin relationship, M 1 And M 2 The generalized pulsating wind load power spectrum expression of the 1-order mode of the two points is as follows:
φ 1 (z 1 )φ 1 (z 2 )δ 1 (z 1 )δ 1 (z 2 )dx 1 dx 2 dz 1 dz 2
wherein the upper horizontal line represents averaging over time; the superscript' "indicates the pulsating component after subtraction of the average component from the total amount; n is the frequency of the fluctuating wind speed; coh (x) 1 ,z 1 ,x 2 ,z 2 N) is M 1 And M 2 A coherence function of the fluctuating wind speeds at two points; s is S v′ (x, z, n) is the pulsatile wind speed power spectrum.
In order to keep the same with the existing load standard system, a wind speed spectrum proposed by Davenport is adopted, and the wind speed spectrum is irrelevant to the space position, and the specific expression is as follows:
where k is the surface roughness coefficient,is the variance of the fluctuating wind speed,/>Is the average wind speed at 10m height; omega 10 Is the average wind pressure at a height of 10m.
Likewise, the load specification is adopted to recommend a frequency-independent coherence function proposed by shiostani, and the specific expression is:
substituting the wind speed spectrum proposed by Davenport and the coherence function proposed by Shiotani into a formula can obtain the following formula:
coh z (z 1 ,z 2 )S v′ (n)φ 1 (z 1 )φ 1 (z 2 )δ 1 (z 1 )δ 1 (z 2 )dx 1 dx 2 dz 1 dz 2
q is obtained through the frequency response function 1 The power spectrum expression of (t):
wherein H is 1 And (in) is a frequency response function of a1 st order mode of the landscape tower. q 1 The standard deviation expression of (t) is:
the dynamic peak displacement expression determined by the 1 st order modality is:
wherein, the peak factor takes a value according to the load specification (GB 50009-2012), g s ＝2.5。
In addition to the wind vibration displacement response of the landscape tower, its internal force response is also a concern for wind resistant designers. Determining its internal force by displacement of the landscape tower is complex, but calculating the internal force by external force is simple. Under the action of equivalent wind vibration force (vibration type inertia force), the wind vibration displacement of the landscape tower is the same as the displacement value determined by the formula (15). Thus, the general expression for equivalent static wind load can be written as:
in the method, in the process of the invention,equivalent wind vibration force of a 1-order mode of the landscape tower; mu (mu) z (z) is the wind pressure height variation coefficient at the landscape tower height z; omega 1 The 1 st order natural vibration circular frequency of the landscape tower in the downwind direction is obtained.
Design formula of wind vibration coefficient of landscape tower with unchanged appearance
When the external shape of the landscape tower is unchanged along the height, namely the mass and the wind shielding area are unchanged along the height, m (z), b (z) and mu s Both (z) and delta (z) are constants, and the computational model is the simplest. The general expression that the wind vibration coefficient can be obtained according to the equivalent static wind load of the landscape tower is as follows:
δ(z 1 )μ z (z 2 )φ 1 (z 2 )μ s (z 2 )I z (z 2 )δ(z 2 )coh z (z 1 ,z 2 )dz 1 dz 2 ] 0.5 /(20)
wherein S is f (n) is a normalized wind speed spectrum,I z (z) is the pulsating wind turbulence density at z height; i 10 Taking 0.12, 0.14, 0.23 and 0.39 for A, B, C and D type landform roughness respectively according to the value of the turbulence density of the pulsating wind at the height of 10 m; x is x 1 ' is n=n in formula (6) 1 Value of n 1 Is the 1 st order modal frequency of the landscape tower. Zeta type 1 Is S v′ (x, z) is determined by the frequency response and is called a wind vibration force coefficient. u (u) 1 And eta xz1 The coefficients related to wind field turbulence characteristics, spatial correlation and the like are respectively called comprehensive influence coefficients and spatial correlation reduction coefficients. r is (r) 1 (z) is a coefficient related to the position calculation point, which is called a position influence coefficient.
In addition, the variables m (z), b (z), mu of the constant profile landscape tower s Both (z) and delta (z) can be considered constants. Thus, equation (14) can be reduced to:
after substituting the formula (22) into the formula (17), let the variables m (z), b (z), μ s (z) and delta (z) are constants to obtain
φ 1 (z 2 )I z (z 2 )coh z (z 1 ,z 2 )dz 1 dz 2 ] 0.5 /(25)
Here, lambda 1 And u 1 Meaning the same. For the coherence function specified by the load specification, the integral expression exists as a primitive function:
the mode shape of the 1 st order mode is a bending mode shape for high-rise structures as specified by the load specification. The first-order mode-oscillation coefficient of high-rise structure with windward side width far smaller than heightThe calculation results are shown in Table 1, which can be determined by the following approximate formula according to the specification according to the relative height z/H, considering the bending type:
table 1 vibration coefficient of constant shape landscape tower
Equation (25) involves a double integration, which is inconvenient for design. By introducing an intermediate variable gamma (H), fitting the variable, the purpose of simplifying calculation is achieved, and the expression of gamma (H) is as follows:
in the method, in the process of the invention,for the turbulence of pulsating wind along the height change coefficient +.>Gamma (H) may be fitted using an exponential function as a function of H. Obtaining a numerical fitting formula of gamma (H) by a nonlinear least square method:
k in γ And alpha γ The coefficient is related to the floor roughness type, and the values of the coefficient and the floor roughness type are shown in table 2.
Table 2 coefficient k related to the terrain roughness class γ And alpha γ Is of the value of (2)
In order to keep consistent with the variables of the wind vibration coefficient calculation formula in the load specification, the method is introducedEntering a background component factor B consistent with the physical meaning in the load specification z . When the tower height H is determined, B z The expression of (z) is:
wherein ρ is z Is the correlation coefficient of the pulsating wind load in the vertical direction; ρ x Is the correlation coefficient of the pulsating wind load in the horizontal direction.
Likewise, a resonance component factor R is introduced here that is consistent with the physical meaning in the load specification. Zeta type toy 1 The relationship with R can be written asThe expression of R is:
in zeta 1 The proposal value of the steel structure is 0.01 for the damping ratio of the landscape tower; f (f) 1 The first-order natural vibration frequency of the landscape tower is given by design party data; k (k) w Taking 1.0 for the roughness of the ground in the suburban area B as a roughness correction coefficient of the ground; thus, β (z) in the formula (23) is rewritten as:
the formula (34) is that the load specification (GB 50009-2012) calculates the wind vibration coefficient expression of the high-rise structure with the shape unchanged along the height, and the wind vibration coefficient of the load specification is indicated to be applicable to the landscape tower with the unchanged shape. Thirdly, wind vibration coefficient analysis of actual landscape tower and derivation of design formula
Section (II) discusses the ideal situation where the landscape tower profile is constant in height, however, such a configuration is rare. Generally, in order to achieve both practicality and aesthetic appearance, the appearance and mass distribution of the landscape tower vary unevenly along the height. The resistance coefficient and wind vibration response of the landscape tower are determined through wind tunnel tests, a finite element model is established to calculate the displacement response time course of each node, and the IWL wind vibration coefficient beta (z) of the landscape tower is calculated by combining finite element and wind tunnel test data. When the Chinese load standard calculation is adopted, the actual landscape tower wind vibration coefficient is determined to be corrected according to the correction coefficients theta (z) and eta (theta) which are provided by the invention and take the local shape change and the wind direction angle influence into consideration.
(1) Building of landscape tower wind tunnel test and finite element model
Modeling and wind field simulation
The total height of a certain landscape tower is 25.66m, and the height of the lower spiral stair is 38.10m. The test is carried out in TK-400 DC wind tunnel laboratory of Tianjin water engineering college, the scale of the wind tunnel laboratory is 15m multiplied by 4.4m multiplied by 2.5m, and the test wind speed is continuously adjustable from 0 to 30 m/s. According to the requirements of laboratory scale and model blocking ratio less than 5%, the geometric similarity ratio lambda of the aeroelastic model L ＝L m /L p =1/50, where L is geometry; lambda is the similarity ratio; subscripts m and p are the scaled aeroelastic model and prototype, respectively. The total height of the prototype tower of the landscape tower is 63.76m, and the height of the pneumatic elastic scale model is 1.28m. Determining mass similarity ratio lambda based on inertial force similarity criteria m ＝(λ L ) 3 =1/125, where m is mass. The landscape tower is a sharp-edge structure with obvious separation points, the configuration change is small under the action of gravity, and Reynolds, froude number similarity criteria can be ignored in model design. Thus, the frequency similarity ratio is not the only value, and the design of the aeroelastic model is more flexible. In addition, the design of the landscape tower aeroelastic model also needs to meet the requirements of Strouhal number, cauchy number, density ratio and zeta.
When manufacturing the railing and stair surfaces of the landscape tower, acrylonitrile-butadiene-styrene (ABS) plastic is used to make pneumatic garments to meet the aerodynamic profile similarity requirements. In addition, the handrail and stair surface are cut and separated by a specific distance to prevent the pneumatic garment from forming a single unit, providing additional rigidity and damping to the structure. The lead plates are uniformly arranged on the surface of the stairs to ensure that the model meets the quality similarity ratio. Lead sheets are uniformly arranged on the stair surface, so that the model is ensured to meet the quality similarity ratio. The model stress skeleton is made of steel materials consistent with the actual structure, and the similarity of aerodynamic appearance is met. The finished aeroelastic model is shown in fig. 3 (a).
And (3) carrying out free vibration test and weighing on the completed landscape tower model under manual excitation, and analyzing the acceleration time course of the tower top to determine the fundamental frequency, the first-order mode xi and the mass m of the model as 5.407Hz, 0.022 and 2.930kg respectively. Furthermore, the values of 0.329Hz, 0.020 and 2.912kg were compared to the corresponding values of the prototype structure determined by the finite element model FEM. The relative error of ζ is 9.1%, and the relative error of the mass is only 0.6%. The comparison result shows that the aeroelastic model meets the test requirement. In addition, it can be confirmed that the frequency similarity ratio lambda n ＝n m /n p =16.43, where n is frequency. According to the Strouhal number similarity criterion, the wind speed similarity ratio lambda v ＝λ n ·λ L =0.33, where v is wind speed. According to the dimension relation, the acceleration similarity ratio lambda a ＝λ L ·(λ n ) 2 =5.40, where a is acceleration. The same structural material and fine manufacturing process make the zeta value of the model and the prototype the same, the damping similarity ratio lambda ξ =1. The similarity ratio of the reduced scale model is shown in table 3, based on the requirement of the similarity ratio.
TABLE 3 similarity ratio of reduced scale models of landscape towers
Because each section of the landscape tower has a unique geometry, a representative aerodynamic profile segment is selected for rigid model design. The whole pneumatic shape of the landscape tower is divided into two parts, one part is an upper ribbon structure of the landscape tower, and the other part is a spiral stair with a rotation period. According to the different heights of the superstructure and the spiral stairs, the geometric similarity ratio of the two parts is determined to be 1/50 and 1/20 respectively in the case that the blocking ratio is less than 5%. In addition, the wall thickness of the steel box girder prototype is increased to ensure that the rigidity of the model is enough. The rigid segment section model is shown in fig. 3 (b), 3 (c).
The wind tunnel laboratory test section simulates a class B landform turbulent wind field with the proportion of 1/50 according to the requirements of Chinese specifications by arranging wedges and multiple rows of distributed coarse elements, and the experimental arrangement is shown in a figure 3 (B), wherein the class B landform is usually a suburban landform with sparse houses. Average wind speed v (z) and turbulence I in the specification z The expression (z) is as follows:
/>
wherein alpha is a ground roughness index, and the grade B landform takes a value of 0.15; i 10 The value is 0.14 under the B-type landform. The Davenport wind speed power spectrum may be calculated as in (first) part, formula (5).
The wind speed power spectrum at the position of the model test, which is in the downwind direction, the average wind speed and the turbulence degree and the corresponding prototype 10m height, is compared with the recommended value of the Chinese specification, as shown in figure 4. The comparison result shows that the simulated wind field meets the standard requirements.
Test condition and measuring point arrangement
In order to calculate the IWL wind vibration coefficient of the landscape tower test, the wind tunnel test of the atmospheric boundary layer model is required to obtain the wind-induced response time course value of the landscape tower. To investigate the effect of changes in wind direction angle θ on the β (z) of the landscape tower, θ was defined to be 0 ° in the positive x-axis direction and 90 ° in the positive y-axis direction, see fig. 5. For an asymmetric structure landscape tower, the model of the asymmetric structure landscape tower needs to be rotated for a plurality of times to fully consider the influence of theta. Therefore, the test conditions of θ were 0 ° to 345 ° with 15 ° increments. The design average wind speed at the reference height of the landscape tower 10m is 28.5m/s, the corresponding model wind speed is 12m/s, and thus the test v condition is 12m/s. The wind speed under the above conditions is the average wind speed at model 1 m. The root mean square acceleration of the sphere at the top of the landscape tower obtained by the test is shown in table 3.
TABLE 3 root mean square acceleration of the tower top sphere in x, y directions at a wind speed of 12m/s at 1m from the ground
/>
In order to determine the β (z) profile, the distances between adjacent stations should be approximately equal and should be arranged on the same side of the spiral staircase. Furthermore, the measuring points should be arranged at the top and platform positions with a large acceleration. The measuring points A1-A4 are thus arranged from top to bottom on the top sphere position, platform position and towers of different heights, as shown in fig. 6 (a). Furthermore, two acceleration sensors in the x and y directions are mounted for each measurement point, for a total of eight acceleration sensors. The sampling frequency of the acceleration sensor is 1024Hz, and the sampling time is 60s.
And obtaining aerodynamic force of the landscape tower through wind tunnel test on the rigid segment model. Because the spiral stairs of the landscape tower are connected in an up-down structure, when the wind tunnel test of the rigid segment model is carried out, the cover plate is added to simulate two-dimensional flow so as to simulate the real situation. In addition, the superstructure has no structural connection above the actual landscape tower structure; it is not necessary to consider the case of simulating a two-dimensional flow. Upper rigid section model test average wind speed v=11.5 m/s (0.675 m from ground), spiral staircase v=8.34 m/s (0.32 m from ground), θ=150°. The sampling frequency of aerodynamic drag on the balance is 1024hz, and the sampling time is 60s.
Finite element modeling and validation
And establishing a finite element model of the landscape tower by utilizing ANSYS finite element software. In the preprocessor module, the landscape tower is formed by adopting a medium slender steel box girder, so a BEAM188 unit (also called a 3D linear finite strain girder unit) is adopted to construct a landscape tower finite element model, and the mechanical deformation requirements of elastic, creep and plastic material models are met. In addition, the two end nodes have 6-7 degrees of freedom and can bear axial tensile, compressive and bending loads. The effect of shear deformation was calculated according to Timoshenko beam theory. The actual section design parameters and material characteristics of the landscape tower are adopted. The bottom of the finite element adopts a fixed constraint. Secondly, the finite element model is subjected to grid division by adopting an intelligent grid command. In the process module, the aerodynamic damping of the landscape tower is considered, and transient dynamics analysis is adopted to perform finite element time domain calculation. And in the post-processing module, obtaining the displacement and the acceleration of the target measuring point. The completed FEM analytical model is shown in fig. 6 (a).
The response of station A1 was compared with the response determined by the aeroelastic model test at 5 different wind speeds by finite element analysis, as shown in FIG. 7. FIG. 7 shows that the mean and standard deviation of the displacement calculated by the finite element are relatively close to the wind tunnel test results. Therefore, the wind vibration coefficient of the landscape tower can be accurately calculated through wind vibration response data obtained through numerical simulation.
(2) Wind vibration coefficient analysis
Because the windward area and the mass of the landscape tower are distributed irregularly along the height, the linear load expression of the formula (17) is not adopted for the convenience of calculation, the sectional expression of point load is adopted, and the wind vibration coefficients at different heights on each section are assumed to be the same. Therefore, representative segments are selected according to the arrangement of the aeroelastic model measuring points (model segments are shown in fig. 6 (b)), and the wind vibration coefficient of each segment IWL of the landscape tower can be calculated according to the formula (17) as shown in the following formula:
wherein: z i Corresponding to the height of the measuring point of the ith section,σ a (z i ) The root mean square value of the downwind acceleration at the ith section of the landscape tower can be calculated by combining the downwind acceleration time course value of (39), namely
a(z i ,t)＝a x (z i ,t)sinα+a y (z i ,t)sinα (38)
Wherein a is x (z i ,t)、a y (z i T) is the test acceleration time course of the i measuring point of the landscape tower on the x and y axes, and is converted into prototype data according to the similarity ratio in table 3. Mu (mu) z (z i ) For the height z of the landscape tower i The wind pressure height change coefficient at the position according to mu z (z i )＝(z i /10) 2α Calculating; omega 0 Is the basic wind pressure, and is the basic wind pressure,ρ a for air density, 1.225kg/m was taken 3 ；v 0 Is the basic wind speed, 28.5M/s, M (z) i ) And A (z) i ) The mass and the windward area of the ith section of the landscape tower can be calculated by a finite element model, C d (z i ) Resistance coefficient of the ith section of the landscape tower, and mu above s (z) is defined consistently and can be calculated according to equation (39):
wherein F is x And F y Balance force test data of the rigid segment model in the x axis and the y axis respectively, A x The calculated values of the upper structure and the spiral stair rigid section are respectively 0.014m for the area of the projection surface of the rigid section model perpendicular to the direction of the incoming wind 2 And 0.009m 2 ；The average wind speed is the height of the center of the rigid segment model. Calculating the resistance coefficient of the overall upper structure of the landscape tower and the lower spiral stair under different wind direction angles according to the formula (39) as shown in figure 8。
Based on the experimental data, the change in the zenith IWL wind-vibration coefficient along the wind direction angle and the change in the IWL wind-vibration coefficient along the height at the wind direction angle of 150 ° determined by equation (37) are shown in fig. 9 and 10, respectively. As can be seen from FIG. 9, the IWL wind vibration coefficients of the landscape tower top test are all larger than the standard values, and the standard calculation result is unsafe, wherein the maximum difference under the 30-degree wind direction angle is 1.66 times of the standard values. As can be seen from fig. 10, the wind vibration coefficient of the landscape tower IWL increases along the height, taking a maximum of 3.018 at the top of the tower.
Because the wind vibration coefficient value of the finer section of the landscape tower can not be obtained due to the limitation of the wind tunnel test measurement points, the numerical simulation is utilized to obtain beta (z) i ) More complete distribution, the numerical simulation results are shown in fig. 9, from which it can be seen that the load specification (GB 50009-2012) is calculated to be greater than the numerical simulation results below the stage position, to be greater than the numerical simulation results above the stage position, and two beta (z) i ) The shape distribution of (c) is different, resulting in a different equivalent internal force of the calculated landscape tower using beta (z) determined by the specification. Thus, when estimating beta (z) for a landscape tower using the national load specification, θ should be considered and the effect of local shape variations on beta (z) should be considered.
(3) Design formula of wind vibration coefficient of actual landscape tower
In order to make the theoretical calculation model of the landscape tower be closer to the actual one, the local shape change correction coefficient theta (z) of the landscape tower is introduced and considered, so that the model can be used for improving the wind vibration coefficient of the landscape tower calculated according to the Chinese load specification. The expression of the wind vibration coefficient considering the local shape change correction coefficient θ (z) is as follows:
when the Chinese load specification is adopted for calculation, the influence of the non-uniform shape and the mass distribution on beta (z) is considered. Since the ribbon shape is similar to a cone change, a sudden increase in platform position mass results in a local increase in beta (z), while the shape of the lower part of the landscape tower is periodically changed (as in fig. 2), the beta (z) local shape change correction coefficient θ (z) is given by three parts. And determining the distribution of theta (z) by combining the ratio of beta (z) obtained through numerical simulation and Chinese load specification calculation, and then determining the expression of theta (z) through a nonlinear fitting method, wherein the expression is shown in a formula (41).
The maximum displacement of the downwind direction of the nodes at the spherical body at the top of the landscape tower is obtained through a landscape tower finite element model established by ANSYS software, and compared with the equivalent node displacement of the top of the landscape tower under the effect of the design wind load deduced in the part, the relative error is 1.7%, which indicates that the correction effect is good. Therefore, the result of the design wind load calculation derived by taking into consideration the local shape change correction coefficient θ (z) of the landscape tower is brought into agreement with the test result.
In addition, according to the comparison analysis of 3.3 sections, a wind direction angle change correction coefficient eta (theta) of the landscape tower needs to be introduced, and the method can be used for improving beta (z) of the landscape tower calculated according to Chinese load standards. The expression of the wind vibration coefficient considering the wind direction angle change correction coefficient η (θ) is as follows:
and obtaining a correction coefficient eta (theta) considering the wind direction angle change by adopting a multimodal fitting method. Firstly, obtaining the distribution of eta (theta) through the wind tunnel test result and the beta (z) ratio determined by Chinese specification, and then determining the expression of eta (theta) by combining a multimodal fitting method, wherein the fitting parameter x in the formula is shown as a formula (43) ci 、w i 、A i The values of (2) are shown in Table 4.
Table 4 values of fitting parameters for correction coefficients for wind direction angle variation
Correction of coefficient of wind vibration due to consideration of local shape change θ (z)Beta (z) at 300 DEG to the wind direction angle determined by the wind tunnel test i ) Substantially uniform, and thus correcting beta (z) based on the wind vibration coefficient at this angle i ). For a spiral landscape tower, the calculation flow of the design wind load is shown in fig. 11.
By the above method, the normalized calculated β (z) is corrected and compared with that determined by the wind tunnel test, as shown in fig. 9 and 10. As can be seen from the figure, the proposed method calculates beta a * The (z, theta) has good consistency with the wind vibration coefficient determined by the wind tunnel test as a whole, and can cover the maximum value and the minimum value of the test wind vibration coefficient. Therefore, the algorithm of the invention can be used for wind resistance design of the landscape tower.
According to the method, firstly, the design wind load of the landscape tower with the unchanged appearance is deduced based on an IWL method, then the resistance coefficient and wind vibration response of the spiral landscape tower are determined through a wind tunnel test, a finite element model is established to calculate the displacement response time course of each node, and the IWL wind vibration coefficient beta (z) of the landscape tower is calculated by combining finite element and wind tunnel test data. The comparison of the wind tunnel test calculation result and the calculation result based on the Chinese load specification shows that the wind vibration coefficient obtained by the existing load specification has a certain difference from the actual situation, so that the wind-resistant load calculated based on the existing load specification has potential safety hazards when being used for guiding the structural design of the tower building. When the Chinese load standard calculation is adopted, a bending column spiral Liang Jingguan tower design wind load calculation formula determined based on an IWL method is provided, and the expression derivation of correction coefficients theta (z) and eta (theta) considering local shape change and wind direction angle influence is realized by adopting a mode of combining wind tunnel experiments and numerical simulation and performing nonlinear fitting on wind vibration coefficients calculated based on test data. The local shape change correction coefficient theta (z) and the wind direction angle change correction coefficient eta (theta) are used for correcting the IWL wind vibration coefficient calculated based on the Chinese load specification, so that a safer and more reliable result can be obtained. The calculation method is simple and accurate.
In engineering design application, according to the size of target structure and local meteorological data, the design wind load f of the building at different heights is calculated by the method of the invention ESWL And (z, theta), checking the wind resistance bearing capacity and the corresponding position of the local structure at different heights of the building according to the section characteristics and the allowable stress value obtained by material calculation, and further determining the material selection and the structural form according to the checking result until the structure meets the wind resistance load stress requirement.
Finally, it should be noted that the above description is only a preferred embodiment of the present invention, and that many similar changes can be made by those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (2)
1. The method for calculating the design wind load of the bent-torsion column spiral Liang Jingguan tower based on the IWL method is characterized by comprising the following steps of:
s1, determining related parameters of the structure of the landscape tower, related coefficients of the roughness of the ground and reference coefficients of wind conditions;
s2, calculating the average wind resistance in the downwind direction of a unit height of a building with unchanged appearance along the height direction at the z-height position based on an Inertial Wind Load (IWL) method according to the load specificationWind vibration coefficient β (z); the height of the building with the shape unchanged along the height direction is the same as the height of the landscape tower, and the width of the building is the same as the structural width of the landscape tower;
s3, introducing a local shape change correction coefficient theta (z) and a wind direction angle change correction coefficient eta (theta) of the landscape tower to correct the wind vibration coefficient beta (z) to obtain a corrected IWL wind vibration coefficientExpressed as->
Wherein the local shape change correction coefficient θ (z) and the wind direction angle change correction coefficient η (θ) are both determined based on the shape of the landscape tower at each of the feature segments at different heights;
s4, using the corrected IWL wind vibration coefficientCalculating the equivalent static wind load f ESWL (z, θ) as the design wind load, the expression is +.>
Average wind resistance in downwind direction per unit heightThe expression is
Wherein mu s (z) is the drag coefficient at the landscape tower height z;
ρ a is air density;
is the average wind speed at height z;
wherein b s (z) high wind shielding area per unit, b s (z) =b (z) δ (z), b (z) being the outer contour width at z-height, δ (z) being the solidity at z-height;
in step S1, the landscape tower structure related parameters include a first order natural vibration frequency f 1 Total height H ofA structural width b;
the roughness related coefficient of the ground comprises a roughness coefficient k related to the ground surface γ Ground roughness index alpha γ Correction coefficient k of ground roughness w ；
The wind condition reference coefficient comprises a pulsating wind turbulence density I at a height of 10m 10 Average wind pressure omega of 10m height 10 ；
The landscape tower is a steel structure tower, the steel structure tower comprises a spiral stair, a platform is arranged at the top of the spiral stair, a spiral ribbon structure is vertically arranged on the platform, and a thin-wall hollow ball is arranged at the upper part of the ribbon structure;
the local shape change correction coefficient theta (z) is expressed as a piecewise function expressed as
The sections of the piecewise function correspond to spiral stairway, platform and streamer structures respectively, wherein z is the height, z n The platform is the platform ground-off height of the steel structure tower;
the expression of the wind direction angle change correction coefficient eta (theta) is
Wherein x is ci 、w i 、A i Fitting parameters are respectively adopted, i represents each section from bottom to top of the steel structure tower;
in step S3, a wind direction angle change correction coefficient η (θ) at each other angle is calculated based on η (θ) at a wind direction angle θ=300°, and a wind vibration coefficient β (z) is corrected;
corrected IWL wind vibration coefficientExpressed as
Where g is the peak factor and where,
wherein B is z Expressed as background component factors as
In phi 1 (1) For the 1 st order mode shape coefficient at z-height, the approximate calculation expression isμ z (z) is the wind pressure height variation coefficient at the height z of the landscape tower expressed asρ z Is the correlation coefficient of the pulsating wind load in the vertical direction, ρ x Is the correlation coefficient of the pulsating wind load in the horizontal direction, expressed as respectively
Wherein R is a resonance component factor expressed as
In zeta 1 The steel structure is valued as ζ for damping ratio of the tower 1 ＝0.01；ω 0 Is the basic wind pressure, and is the basic wind pressure,ρ a is air density v 0 Is the base wind speed.
2. The method for calculating a design wind load of a cranked column spiral Liang Jingguan tower based on an IWL method according to claim 1, wherein: the method for determining the local shape change correction coefficient theta (z) and the wind direction angle change correction coefficient eta (theta) comprises the steps of firstly manufacturing a test model of each characteristic section of the landscape tower, performing wind tunnel test by using the test model, calculating a test wind vibration coefficient according to data obtained by the wind tunnel test, calculating a ratio of the test wind vibration coefficient to the wind vibration coefficient beta (z) obtained according to the load specification in the step S1, respectively obtaining the distribution of the local shape change correction coefficient theta (z) and the distribution of the wind direction angle change correction coefficient eta (theta), determining an expression of the theta (z) by a nonlinear fitting method, and determining the expression of the eta (theta) by a multimodal fitting method.
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