Analytical design method of sky screen system under dead weight and wind load

Abstract

The invention relates to the field of building construction, in particular to an analysis design method of a sky screen system under self weight and wind load, which comprises the following steps of: establishing a relational expression between pretension of a supporting inhaul cable and midspan deflection according to a catenary equation: performing finite element simulation analysis and shape finding under vertical load, determining curves of the inhaul cable and a curtain after being tensioned, and establishing a model; the maximum mid-span deflection value is made to be within the maximum mid-span deflection limit value obtained in the step S1, and a shape finding result is obtained. According to the analysis design method, the designed sky screen system is more suitable for the wind load of the environment where the site is located, the sky screen system is more stable, and the shape finding analysis efficiency is high.

Description

Technical Field

[0001] The invention relates to the field of building construction, and in particular to an analysis and design method of a canopy system under deadweight and wind load. Background Art

[0002] The green construction intelligent canopy system for underground projects is a new technology for dust suppression and noise reduction in the construction industry. Due to the scale characteristics of the construction site itself, it has both large span and flexible structural characteristics in large-scale engineering applications. At present, the application of the green construction intelligent canopy system for underground projects mainly relies on the experience design of traditional similar projects. For the support frame, only static analysis is used for simple safety verification. However, in actual projects, the force characteristics of the curtain system of the green construction intelligent canopy system for underground projects are similar to those of the cable-membrane structure. The use of traditional experience design has major defects in the design of the canopy system. When the wind load is large, it is easy to cause instability of the canopy system. Summary of the invention

[0003] The analysis and design method of the canopy system under deadweight and wind load of the present invention adopts deadweight design and wind load design methods, so that the canopy system can be designed under consideration of deadweight load (vertical load) and can also be designed under consideration of wind load, so that the designed canopy system is more suitable for the environment of the site, and the safety and stability of the designed canopy system are improved. Moreover, the form-finding analysis efficiency is high.

[0004] To achieve the above purpose, the technical solution provided by the present invention is an analysis and design method of a canopy system under deadweight and wind load, and the steps include the following:

[0005] S1, according to the catenary equation, the relationship between the pre-tension of the support cable and the mid-span deflection is established:

[0006]

[0007] In the formula, f m is the maximum mid-span deflection of the supporting cable; l is the curtain span; σ0 is the prestressing force of the supporting cable; G l is the average stress caused by the vertical load in the cross section of the canopy;

[0008] S2, perform finite element simulation analysis under vertical load to find the shape, determine the curves after the cables and curtains are stretched, and make the maximum mid-span deflection value within the maximum mid-span deflection limit value obtained in step S1, and obtain the shape-finding result

[0009] Preferably, in step S1, the step of establishing a relationship between the pretension of the support cable and the mid-span deflection comprises:

[0010] S11, use the catenary equation to establish the pretension-deflection relationship equation:

[0011]

[0012] In the formula, f m is the maximum mid-span deflection of the supporting cable, P is the pretension of the supporting cable, A, B and f0 are the influencing parameters of the equation: A is the amplitude adjustment coefficient, B is the adjustment coefficient of the ratio of prestress to vertical load, f0 is the initial value of deflection; G is the deadweight load;

[0013] S12, Converted to stress ratio, where pretension P is converted to prestress σ0:

[0014]

[0015] Where S1 is the cross-sectional area of ​​the supporting cable;

[0016] G is converted to the average stress G generated by the deadweight load on the cross section of the canopy l :

[0017]

[0018] In the formula, S2 is the equivalent cross-sectional area of ​​the curtain plus the supporting cables. Since the thickness of the curtain can be ignored relative to the width, S2 is considered as the width multiplied by the unit 1m, G l It is actually the vertical load divided by the curtain width;

[0019] S13, assuming that the initial mid-span deflection f0=l / 1000, l is the curtain span, fitting parameters A and B, and obtaining the relationship between the pre-tension of the support cable and the mid-span deflection in step S1.

[0020] Preferably, in step S2, the finite element simulation form-finding analysis adopts a direct iteration method, a small elastic modulus method or a V-shaped broken line method to perform form-finding analysis.

[0021] Preferably, in step S2, a direct iteration method is used for form-finding analysis, and the steps are as follows:

[0022] S21, initially set the original length of the cables and curtain of the canopy system, and establish a straight line model;

[0023] S22, fix one end of the cable to the hanging point and leave the other end free; apply vertical load to the cable and the curtain, apply horizontal tension to the free end of the cable, and hang the free end back to the height of the hanging point;

[0024] S23, determine whether the mid-span deflection and initial stress of the cable meet the requirements of the relationship in S1; if they do, the form-finding is completed.

[0025] If not, repeat the above steps until the condition is met.

[0026] Preferably, in step S21, the initial length of the cable is calculated according to the catenary equation, the curtain span and the maximum mid-span deflection, wherein the calculation formula is:

[0027]

[0028] Where L is the total length of the cable, f is m is the maximum mid-span deflection of the supporting cable, and l is the curtain span.

[0029] Preferably, in step S1, when considering wind load, the pretension P of the supporting cable under wind load is w The calculation formula is:

[0030] P w =W A ×(-2.6V0+78.6)

[0031] Where W A is the static wind pressure and V0 is the basic wind speed.

[0032] The design method of the present invention takes into account many factors such as the canopy structure, force, mid-span deflection, etc. The canopy system design method is not limited by empirical values ​​compared to the traditional experience-based design method, thereby improving the efficiency of the canopy design. The designed canopy system structure is safer and more stable. Moreover, the canopy system design method of the present invention can be promoted as a design standard in this field. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the structure at one end of the top of the canopy system.

[0034] Figure 2 These are the loads and boundary conditions of the curtain closure system model.

[0035] Figure 3 is 50×6-Piσ0-f m Comparison chart of the curve with formula (4).

[0036] Figure 4 is 75×6-Piσ0-f m Comparison chart of the curve with formula (4).

[0037] Figure 5 is 75×12-Piσ0-f m Comparison chart of the curve with formula (4).

[0038] Figure 6 is 100×18-Piσ0-f m Comparison chart of the curve with formula (4).

[0039] Figure 7 It is a pulsating wind time chart.

[0040] Figure 8 It is a comparison chart between the simulated power spectrum and the target power spectrum.

[0041] Fig. 9 This is the mid-span displacement diagram of the middle cable of 100×18-W10-P3.

[0042] Fig.10 This is the mid-span displacement diagram of the 100×18-W10-P3 side cable.

[0043] Fig.11 This is the mid-span trajectory diagram of the middle cable of 100×18-W10-P3.

[0044] Fig.12 This is the mid-span trajectory diagram of the 100×18-W10-P3 side cable.

[0045] Fig.13 This is the stress time history curve of the 100×18-W10-P3 mid-span cable.

[0046] Fig.14 It is the time history curve of 100×18-W10-P3 large stress cable.

[0047] Fig.15 It is the reaction force time history curve of the 100×18-W10-P3 support cable hanging point.

[0048] Fig.16 This is the time history curve of the reaction support cable of the larger hanging point of 100×18-W10-P3.

[0049] Fig.17 It is the reaction force time history curve of the 100×18-W20-P3 support cable hanging point.

[0050] Fig.18 This is the time history curve of the reaction support cable of the larger hanging point of 100×18-W10-P5.

[0051] Fig.19 It is the time history curve of the reaction force at the critical hanging point of the 100×18-W10 cable.

[0052] Fig. 20 It is the time history curve of the reaction force at the critical hanging point of the 100×18-W15 cable.

[0053] Fig.21 It is the time history curve of the reaction force at the critical hanging point of the 100×18-W20 cable.

[0054] Fig. 22 It is the time history curve of the reaction force at the critical hanging point of the 50×6-W20 cable.

[0055] Fig.23 It is a schematic diagram of form finding using direct iteration method.

[0056] Fig.24 It is a schematic diagram of the curtain-support cable structure form-finding plane.

[0057] Fig.25 It is a schematic diagram of the curtain-support cable structure form-finding elevation.

[0058] Fig.26 It is a three-dimensional schematic diagram of the curtain-support cable structure. DETAILED DESCRIPTION

[0059] Top of canopy system, see Figure 1 , mainly composed of a support system, a slide rail 10, and a curtain closing system. The rail 10 is arranged on the support system (not shown). Figure 1 The figure shows the connection method of the top end of the canopy system. When the canopy system is actually installed, one end should be connected as shown in the figure. Figure 1 Install and connect, and then tension the other end before connecting. The curtain closing system consists of a curtain 11, a supporting cable 12 (using a 6.5mm stainless steel cable as an example, which does not limit the specifications of the supporting cable), and a fixing 13. The curtain 12 is fixed on the supporting cable 12, and both ends of the supporting cable 12 are slidably set on the slide rail 10 through the fixing 13. The fixing 13 is provided with a pulley, so that the curtain and the supporting cable can be set on the slide rail 10, and can also slide or be fixed along the slide rail 10 to realize the opening or closing of the curtain. The curtain closing system is partitioned according to the opening and closing function requirements. The width is parallel to the longitudinal direction of the partition, that is, the opening direction, and its span is parallel to the transverse direction of the partition.

[0060] The curtain closure system of the present invention is simulated by finite element method using ABAQUS software, including the curtain 11 and the supporting cables 12 in the span direction. The fixing parts 13 fixed along the span direction are simulated by using the constraints between the unit nodes, and the curtain 11 is simulated by shell elements. The supporting cables 12 are truss elements T3D2, and the T3D2 elements are set to be tension-only; the material constitutive model is ideal elastic-plastic; the curtain 11 is simulated by shell elements. Each cable is hinged at one end and tensioned at the other end. The self-weight load is applied according to the material density, and the self-weight load is applied to the surface of the curtain 11 according to the pressure strength, such as Figure 2 shown.

[0061] The curtain closure system example is named l×b-Pi, where l is the span of the curtain closure system, i.e., the spacing between the support cable hanging points, in m; b is the width of the curtain closure system, in m, and is taken as the representative width of the opening and closing unit of the curtain closure system; P is the pretension of the support cable, i is the pretension level, and is expressed in 0 to 8; the tension level is expressed by the cable stretch length, and the span and width of the curtain closure system change, and the pretension formed by the same stretch length is different. For example, 75×12-P1 is a curtain closure system with a span of 75m, a width of 12m, and a tension level of 1; if 75×12-P1 does not apply pretension, the example name is 75×12. The curtain-support cable structure examples under deadweight load include 50×6-Pi, 75×6-Pi, 75×12-Pi, and 100×18-Pi.

[0062] The analysis and design method of the canopy system under deadweight and wind load of the present invention comprises the following two steps:

[0063] S1. The relationship between the pretension of the support cable and the mid-span deflection is established based on the catenary equation.

[0064] S11, using the catenary equation to establish the pretension-deflection (Pf m )Relation equation:

[0065]

[0066] Where f m is the maximum deflection of the support cable at mid-span, as shown in the ordinate of the figure; P is the pre-tension of the support cable, which is Figure 3-9 ~3-12 is the abscissa prestress multiplied by the area of ​​the cable (6.5mm cable); A, B and f0 are the influencing parameters of the equation; A is the amplitude adjustment coefficient, B is the ratio adjustment coefficient of the prestress to the vertical load, f0 is the initial value of the deflection; G is the total vertical load (deadweight load in the present invention).

[0067] S12, first Converted into stress ratio, pretension P is converted into prestress σ0:

[0068]

[0069] Where S1 is the cross-sectional area of ​​the supporting cable;

[0070] Then, G is converted into the average stress G generated by the vertical load in the cross section of the curtain system. l :

[0071]

[0072] In the formula, S2 is the equivalent cross-sectional area of ​​the curtain plus the supporting cables. Since the thickness of the curtain can be basically ignored relative to the width, S2 is considered as the width multiplied by the unit 1m; G l It is actually the total vertical load divided by the width of the curtain; take the initial deflection f0 = l / 1000; l is the span of the curtain.

[0073] S13, fitting parameters A and B in formula (1), then formula (1) becomes formula (4):

[0074]

[0075] In the formula, f m is the maximum deflection of the supporting cable in the middle of the span (unit: mm); l is the curtain span (unit: mm); σ0 is the prestressing force of the supporting cable (unit: MPa); G l It is the average stress generated by the vertical load in the cross section of the curtain closing system (unit: MPa).

[0076] By comparing the variation of mid-span deflection with prestress of 50×6-Pi, 75×6-Pi, 75×12-Pi and 100×18-Pi with the relationship curve of prestress and deflection in formula (4), we can see that Figures 3 to 6 It can be seen that formula (4) is in good agreement with the finite element calculation results, indicating that the formula has high accuracy and can be used for the design of curtain closure systems. Under the specified limit of mid-span deflection, the prestress of the supporting cables is calculated based on the curtain span and deadweight.

[0077] Under wind load, the curtain closure system is unstable. In order to improve the safety and stability of the canopy system, the influence of wind load should be considered when designing the canopy system in areas with high wind load.

[0078] The curtain is in three states under wind load: dancing, critical vibration and high-frequency vibration. The dancing of the curtain system has the greatest impact on the reaction force of the hanging point of the supporting cable (basically equivalent to the tension of the supporting cable). Therefore, when considering wind load, the design is considered based on the dancing response of the curtain under wind load.

[0079] The pre-tension of the supporting cables is calculated based on the maximum reaction force of the supporting cable hanging point under the dancing wind load, and the durability and tear resistance requirements of the curtain are proposed based on the axial and normal forces of the curtain under the dancing wind load, which effectively prevents the safety and tearing problems caused by the dancing of the construction canopy under wind load. The calculation method of the pre-tension of the supporting cables and the axial normal tension of the curtain under different basic wind speeds of the curtain closure system is proposed, and finally the design method of the curtain system under dynamic wind load is obtained.

[0080] Wind load analysis and fluctuating wind time history simulation

[0081] The average wind load acting on the structure is related to the windward area, shape coefficient, wind pressure height coefficient, basic wind pressure and wind recurrence adjustment coefficient. The standard value of the average wind load perpendicular to the surface of the curtain closure system can be expressed as:

[0082] W s =μ z μ s ω0A f (5)

[0083] Among them, ω0 is the basic wind pressure at standard height; μz and μs are the height variation coefficient and shape coefficient of the basic wind pressure respectively; Af is the wind-exposed area.

[0084] The canopy system can be basically divided into three types according to the layout of the wind and dust suppression system: partially open, one-side open and four-side closed. Under partially open conditions, the air pressure in the system under axial wind load corresponds to a body coefficient of +0.3, and the curtain wind body shape coefficient is -0.9; the indoor air pressure under normal wind load corresponds to a body coefficient of -0.7, and the curtain wind body shape coefficient is +0.1. Under one-side open conditions, the air pressure in the system under axial wind load corresponds to a body coefficient of -0.7, and the curtain wind body shape coefficient is +0.1; the indoor air pressure under normal wind load corresponds to a body coefficient of +0.8, and the curtain wind body shape coefficient is -1.0. Under four-side closed conditions, the axial and normal wind body shape coefficients are the same, which is +0.6.

[0085] Based on the knowledge of fluid mechanics and Newton's second law, the Bernoulli equation for wind flow in steady motion can be obtained. When the airflow encounters or does not encounter an obstacle, the pressure on the obstacle will change with the flow rate. When the wind velocity is zero, the pressure is maximum; when the wind does not encounter an obstacle, the flow rate is maximum. Considering the standard density of air ρ = 1.25×10 - 3 kg / m 3 , the basic wind pressure ω0 of the structure impacted by wind flow can be expressed as:

[0086]

[0087] Where v0 is the basic wind speed.

[0088] The pulsating components of wind speed and wind pressure can be simulated based on the existing power spectrum and spatial correlation function. Assuming that the fluctuating wind speed is a stationary random process, its autopower spectrum density is the Fourier transform of the autocorrelation function. The correlation function is the expression of the random process in the time domain. After the Fourier transform, it is converted into an expression in the frequency domain, which can reflect the spectral characteristics of the random process. Since the ratio of the orthogonal spectrum to the cross spectrum in the atmosphere is very small, in engineering calculations, for any two points i and j with a distance r, the cross power spectrum of the longitudinal pulsating wind speed can be obtained by multiplying the square root of the autopower spectrum of each point and then multiplying it by the coherence function:

[0089]

[0090] In the formula, is the cross power spectrum of wind speed at point i and point j; and are the wind speed auto-power spectra at point i and point j respectively; Coh(r, n) is the spatial coherence function of point i and point j. If the standard height wind speed power spectrum and its spatial coherence function are known, the auto-regressive method (AR: Auto-Regressive) can be used to simulate the pulsating wind speed time history samples within a specific spatial range.

[0091] The Davenport pulsating wind speed spectrum, which is widely used in wind engineering and in accordance with Chinese standards, is adopted. The Davenport spectrum is larger than other spectra, and the part with larger spectrum values ​​is in the range close to the natural frequency of the structure, which is relatively sensitive. Therefore, the Davenport wind speed spectrum will overestimate the dynamic response of the structure, and the calculation results may be conservative. However, from the perspective of structural wind resistance design, it improves the safety of the structure. The Davenport spectrum expression is as follows:

[0092]

[0093] Where v 10 is the wind speed at a height of 10m; k is the ground resistance coefficient corresponding to the height of 10m, which is related to the ground roughness; n is the frequency ω / 2π; x is the number of pulsations within the L stroke at a height of 10m; L is the assumed turbulent stroke length, which is approximately 1200m.

[0094] Wind tunnel test research found that the spatial coherence function curve is a curve that decays according to the exponential law. The Davenport coherence function extended to three-dimensional space is expressed as follows:

[0095]

[0096] The AR model of the column vector of the spatially correlated fluctuating wind speed time history V (X, Y, Z, t) at M points can be expressed as:

[0097]

[0098] X, Y, Z are all coordinate vector matrices, (x, y, z) are the coordinates of the i-th point in space, i = l, 2, ..., M; p is the AR model order, △t is the time step of the simulated wind speed history; Ψk is the AR model autoregressive coefficient matrix, k = l, ..., p; N(t) is the independent random process vector: N(t) = L n (t), n(t) are mutually independent normal random processes (0, 1), L is an M-order lower triangular matrix, and through the M×M matrix R N The Cholesky decomposition is determined by:

[0099] R N =LL T (11)

[0100] Considering the properties of the correlation function, we can get the relationship between the covariance matrix R and the regression coefficient Ψk:

[0101]

[0102] [R]=[R u (Δt), R u (2Δt),…,R u (p△t)] (13)

[0103]

[0104]

[0105] [N(t)]=[L][n(t)] (17)

[0106] Therefore, the random process vector matrix is ​​a random sequence with a given power spectrum, where [n(t)] is a random number matrix that obeys the standard normal distribution. After obtaining the white regression coefficient matrix [Ψk] and the random process vector matrix [n(t)] by the above steps, discretize them according to the Δt time difference, and finally obtain the fluctuating wind speed time history vector expression of M spatial points considering spatial correlation:

[0107]

[0108] The pulsating wind simulation is calculated using Matlab software, and the pulsating wind speed time history curve is simulated and compared with the power spectrum, such as Figure 7 and Figure 8 As shown in the figure, it can be seen that the simulated fluctuating wind speed power spectrum is in good agreement with the target spectrum, indicating that the simulation method is accurate and effective.

[0109] Design example under wind load

[0110] The calculation example of the curtain closing system under dynamic wind load is named as l×b-Wj-Pi, where l is the span of the curtain system, that is, the spacing between the hanging points of the supporting cables, in m; b is the width of the curtain system, in m, which is taken as the representative width of the curtain opening and closing unit; W represents the average wind speed, j is the average wind speed value, in m / s; P is the pre-tension of the supporting cables, i is the pre-tension level, represented by 0 to 5, corresponding to tensioning of 10mm, 50mm, 100mm, 200mm, 300mm and 500mm respectively.

[0111] Analysis of critical dynamic response under wind load

[0112] The curtain-support cable structure exhibits three kinds of dynamic responses under wind load, including high-frequency vibration, dancing and the critical vibration state between high-frequency vibration and dancing, which is called critical dynamic response. The critical dynamic response characteristics of the curtain-support cable structure are analyzed from the displacement of the mid-span support cable, vibration trajectory, curtain deformation, stress of the mid-span support cable and reaction force of the support cable hanging point. The corresponding case is 100×18-W10-P1.

[0113] Two supporting cables with larger normal and tangential displacements in the middle and side parts are selected, and their displacements are shown in the figure. The normal displacement amplitude of the middle supporting cable is the largest, but the tangential displacement is very small. The maximum amplitude of the normal displacement is 1550mm, and the center of vibration gradually increases from 500mm over time, showing a tendency to dance. The overall tangential displacement shows a simple harmonic vibration trend at a low frequency, accompanied by high-frequency vibration, but the amplitude is always very small. The displacement-time curve of the side supporting cables is different from that of the middle part. Its tangential displacement also shows a low-frequency simple harmonic vibration form, and its amplitude is smaller than the normal displacement; the normal displacement is the same as that of the middle supporting cable, with a slightly smaller amplitude of 1504mm. The vibration trajectories of the two supporting cables are plotted. The trajectory of the middle part has a higher frequency, and the overall movement is in the normal direction, as shown in the figure; the trajectory of the side supporting cables has a wider range of activity, and moves back and forth along the normal and tangential directions, as shown in the figure. Figures 9 to 12 As shown, it is the deformation of the curtain-support cable structure at the moment of maximum displacement. It can be seen that the maximum displacement of the curtain is 1223mm, located in the middle of the span, which is larger than the supporting cable, but the difference between the two is smaller than the total displacement.

[0114] The supporting cables have large deformation in the mid-span, and the corresponding stress is large. Fig.13 The stress time history curves of the 7 cables in the mid-span are shown in Figure 2. The stress in the mid-span of the supporting cables generally fluctuates at a low frequency, and there are also high-frequency components, but they have little effect on the stress amplitude. The stress time history curve of each supporting cable fluctuates upward from the prestress as the starting point and then basically returns to the starting point, with high-frequency fluctuations when returning to the starting point. The periods of each stress fluctuation are not much different. The cable with the largest stress amplitude is located at the edge, and the time history curve is shown in Figure 2. Fig.14 As shown, the maximum value is 555MPa.

[0115] The reaction force of the supporting cable at the hanging point has a great influence on the bracket. The reaction force time history curves of the hanging points of 7 supporting cables are selected as follows: Fig.15 As shown in the figure, the variation characteristics of the hanging point reaction force curve are similar to the mid-span stress curve, including the high-frequency component with low-frequency fluctuation; the difference is that the high-frequency component of the hanging point reaction force time history curve will increase in amplitude at the peak and trough, and the waveform is sharper. Fig.16 As shown, the maximum value is 191.7MPa.

[0116] Galloping and high-frequency vibration under wind load

[0117] When the pre-tension is constant, increasing the wind speed will cause the curtain-support cable structure to dance, resulting in a significant increase in the dynamic response; at the same wind speed, when the pre-tension is large, the curtain-support cable structure exceeds the critical vibration and reaches a high-frequency vibration state. As a comparison with the critical vibration, the reaction time history curves of the support cable hanging points of the examples 100×18-W20-P3 and 100×18-W10-P5 are compared, corresponding to the dancing and high-frequency vibration states.

[0118] The time history curve of the reaction force at the cable hanging point of the 100×18-W20-P3 support is as follows: Fig.17 As shown in the figure, its fluctuation is similar to the mid-span stress time-history curve, but with more high-frequency components and a sharper peak shape, similar to a pulse; after the reaction force returns to the vicinity of the starting point, the curve shows high-frequency vibration. The cable with the maximum amplitude of the hanging point reaction force is located in the middle edge, with a maximum value of 394.4kN, which is far more than twice the maximum stress of the support cable of 100×18-W10-P3 in the critical dynamic response state. This shows that the dancing of the curtain system has the greatest impact on the reaction force of the supporting cable hanging point.

[0119] The reaction force time history curve of the 100×18-W10-P5 support cable hanging point has a sharper waveform and more high-frequency components, such as Fig.18 As shown in the figure, with the increase of pretension, the fluctuation amplitude of the reaction force of the support cable hanging point is significantly reduced, but the high-frequency component is significantly increased; the reaction force of each support cable hanging point basically maintains the same period, and the amplitude is not much different. The high-frequency component makes the waveform of the hanging point reaction force curve more sharp and also increases the amplitude of steady-state fluctuation, with a maximum value of 362.2kN.

[0120] In summary, the response of the curtain-support cable structure under dynamic wind load can be divided into three states: high-frequency vibration, critical vibration and dancing. For the dancing response, the mid-span displacement of the supporting cable shows the characteristics of large vibration amplitude, large vibration phase difference of each cable, and long vibration period; the fluctuation amplitude of the cable mid-span stress and hanging point reaction force curve is greatly affected by the high-frequency component, and there is a significant dynamic amplification effect. When the supporting cable vibrates at high frequency, the vibration amplitude and phase difference of the mid-span displacement decrease, and the period becomes shorter; the high-frequency components of the mid-span stress and hanging point reaction force increase, but have little effect on the amplitude of steady-state fluctuations. During critical vibration, the state of the supporting cable displacement, stress and internal force is between dancing and high-frequency vibration, which is the key to analyzing the corresponding relationship between pretension and average wind speed.

[0121] Critical pre-tension analysis

[0122] From the above, it can be seen that the high-frequency component of the mid-span support cable displacement is relatively small, and it is mainly steady-state vibration; the fluctuation curve characteristics of the mid-span stress of the support cable and the hanging point reaction force are basically corresponding, and the hanging point reaction force can better reflect the high-frequency vibration, critical vibration and dancing response characteristics of the curtain-support cable structure. In order to further analyze the corresponding discrimination method of the three response characteristics, the dynamic stability analysis of the hanging point reaction force time history curves with the same wind speed, different pretensions and different curtain sizes is carried out.

[0123] from Figures 19 to 22 It can be seen that as the pre-tension of the support cable increases, the fluctuation amplitude of the hanging point reaction force changes significantly. The fluctuation amplitude of P0~P2 is very large, and the high-frequency component has a greater impact on the steady-state fluctuation, with significant dancing characteristics. Over time, the amplitudes of the three can develop to similar levels. When the average wind speed is 10m / s, the tensioning of P0~P2 levels cannot prevent the curtain system from dancing. When the tensioning level is P3, the fluctuation amplitude of the hanging point reaction force curve of the support cable begins to stabilize, the fluctuation amplitude decreases significantly, and the influence of the high-frequency component on the steady-state fluctuation decreases. The reaction force amplitude of P3 is the upper limit of the reaction force amplitude of P0~P2. It shows that the curtain-support cable structure can reach the critical dynamic response state when tensioning P3 at an average wind speed of 10m / s. When the tension reaches P4 and P5, the structure presents a high-frequency vibration state. The fluctuation amplitude of the hanging point reaction force of the support cable is further reduced, and the amplitude should increase with the increase of pre-tension; the curve is mainly steady-state fluctuation, and the high-frequency component becomes more, but it has little effect on the amplitude. It can be seen that the maximum tension of the support cable when the curtain dances under dynamic wind pressure is consistent with the pre-tension of the support cable required to prevent the curtain from dancing and reach critical vibration. The pre-tension design value of the support cable can be obtained by calculating the maximum tension of the support cable under dancing. The critical vibration state is consistent when the wind speed is 15m / s and 20m / s and the curtain size is 50×6m. The critical tension corresponds to the tensioning level of P4, P2 and P2 respectively. Fig. 22 shown.

[0124] Table 1 is the dynamic wind load response table.

[0125] Table 1 Dynamic wind load response table

[0126]

[0127] Design method of cable pre-tension under wind load

[0128] The dynamic wind load response table counts the static wind pressure value, dynamic amplification coefficient and support cable hanging point reaction force of the curtain-support cable structure at different wind speeds. It can be seen that the static wind total pressure and the average pressure of each support cable hanging point increase linearly with the increase of basic wind speed; the pulsating wind coefficient of the dynamic wind load is about 1.06; the maximum tension of the support cable hanging point under dynamic wind increases linearly with the increase of basic wind speed.

[0129] Establish the maximum tension of the support cable hanging point (R) and the static wind pressure (W A The relationship between the ratio of ) and the basic wind speed V0 is as follows:

[0130]

[0131] From the above analysis, we know that when the static wind pressure remains unchanged, the curtain span has little effect on the critical tension of the supporting cables, but the curtain width determines the number of supporting cables, so it has a greater impact on their critical tension. When designing, the curtain width is introduced into the above formula to fit the parameters A and B; the pre-tension P of the supporting cables under dynamic wind load w The maximum tension of the supporting cable hanging point corresponding to the dynamic wind load is consistent with that of the supporting cable hanging point (R), which is expressed as P w Substituting R in the above formula, we get P w Calculation formula, where the curtain width is b:

[0132] P w =b×W A (-0.015V0+0.42) (20)

[0133] In step S1, a relationship between the pretension under deadweight load and the mid-span deflection is established. When the wind load is considered, the pretension can be the calculated pretension under the wind load.

[0134] S2, perform finite element simulation form-finding analysis to obtain the form-finding results of the curtain closure system.

[0135] There are usually three ways to directly obtain the initial shape of the canopy in the finite element software. The three methods are:

[0136] (1) Direct Iteration Method

[0137] When modeling, there is no need to determine the initial shape of the canopy. It is only necessary to apply horizontal tension at both ends or one end of the canopy, apply gravity on the canopy, and then perform iterative calculations until convergence to obtain the static configuration of the construction canopy.

[0138] (2) Small elastic modulus method

[0139] When modeling, a smaller elastic modulus is first assigned to the construction canopy. At this time, the canopy is greatly deformed, and the deformed curve shape is obtained by continuously updating its elastic modulus. When the sag meets the set conditions, the calculation stops and the initial configuration of the construction canopy is obtained.

[0140] (3) V-shaped broken line method

[0141] During the initial modeling, the geometric shape of the construction canopy was set as a V-shaped broken line, and then gravity and initial stress calculation were applied to obtain the final curve.

[0142] The present invention uses Python programming to improve the form-finding efficiency of ABAQUS finite element analysis software, and the steps are:

[0143] S21, before modeling, the original length of the canopy support cables and the curtain was initially set, and a straight line model was established;

[0144] S22, fix one end of the supporting cable to the hanging point and leave the other end free; apply horizontal tension to the free end; apply gravity load to the curtain; and hang the free end back to the height of the hanging point;

[0145] S23, judging whether the sag and initial stress of the supporting cable meet the requirements; if not, repeating the above steps until the conditions are met.

[0146] In step S21, the initial length of the supporting cables can be calculated based on the catenary equation, the canopy span and the canopy deflection limit, saving form-finding analysis time.

[0147] The catenary equation is obtained by balancing the self-weight and the internal forces of the line segment. Let the lowest point of the catenary be the origin of the coordinate system O, and the total length be L; the hanging points at both ends are A and B, with a spacing of l, symmetrical about the Y axis, and the horizontal coordinates are -0.5l and 0.5l respectively. Cut off point O and point C in the OB segment, let the length be ΔL, and the unit length weight be γ. Since the slope of point O is 0, its tension is in the horizontal direction, set to T; let the tension at point C be T c , parallel to the tangent, with a horizontal angle of θ. According to the force balance:

[0148] T o =T cosθ (21)

[0149] γ△L=T sinθ (22)

[0150] therefore:

[0151]

[0152] make is the tension-to-weight ratio; the catenary equation is y, then:

[0153]

[0154] The arc length of the curve is:

[0155]

[0156] Bringing back the above formula, take the derivative with respect to x:

[0157]

[0158] Let y' = z; solve the differential equation:

[0159]

[0160] Given the initial conditions: y′(0)=0=z(0); ∴C1=0; then

[0161]

[0162] Integrate with respect to x:

[0163]

[0164] Initial condition: y(0) = 0, then:

[0165]

[0166] Line length:

[0167]

[0168] The total length is:

[0169]

[0170] Mid-span deflection or maximum sag f m for:

[0171]

[0172] If the hanging point spacing is 2m or less, the mid-span deflection can be approximated by a parabola:

[0173]

[0174] The line length L is expanded according to the polynomial, and the first two terms are taken:

[0175]

[0176] The horizontal component of tension in each line is the same, which is T o ; The vertical component is gravity γL oc ; therefore the tension is:

[0177]

[0178] Obviously, the catenary tension ratio a needs to be determined according to different materials. It determines the maximum sag and tension of the catenary. Therefore, after a is determined, the total length L can be calculated by the hanging wire spacing l and the maximum sag limit.

[0179] However, the deformation of the supporting cables in the curtain system under tension affects the calculation accuracy of the total length L, and the pre-tension also affects the maximum sag f m Therefore, in the form-finding analysis, the present invention first uses the catenary equation, the hanging wire spacing and the maximum sag limit to perform a preliminary calculation on the total length of the supporting cables, and then performs a form-finding analysis on the curtain-supporting cable structure by using the finite element direct iteration method. The form-finding analysis is compared with the maximum mid-span deflection limit calculated by the mid-span deflection and pre-tension relationship. If it is within the maximum mid-span deflection limit, it meets the design requirements.

[0180] Figure 23 to Figure 26 This is the form-finding result of the curtain-support cable structure. The deformation of the curtain is slightly larger than that of the support cable. The mid-span deflection is the largest, which is 1.36m, meeting the maximum mid-span deflection limit of 1.5m.

Claims

1. The analysis and design method of the canopy system under deadweight and wind load is characterized by: The steps include the following: S1, according to the catenary equation, the relationship between the pre-tension of the support cable and the mid-span deflection is established: In the formula, f m is the maximum mid-span deflection of the supporting cable; l is the curtain span; σ0 is the prestressing force of the supporting cable; G l is the average stress caused by the vertical load in the cross section of the canopy; S2, performing finite element simulation analysis under vertical load to find the shape, determine the curves of the cables and curtain after tensioning, make the maximum mid-span deflection value within the maximum mid-span deflection limit value obtained in step S1, and obtain the shape-finding result.

2. The analysis and design method according to claim 1, characterized in that: In step S1, the step of establishing a relationship between the pretension of the support cable and the mid-span deflection includes: S11, use the catenary equation to establish the pretension-deflection relationship equation: In the formula, f m is the maximum mid-span deflection of the supporting cable, P is the pretension of the supporting cable, A, B and f0 are the influencing parameters of the equation: A is the amplitude adjustment coefficient, B is the adjustment coefficient of the ratio of prestress to vertical load, f0 is the initial value of deflection; G is the deadweight load; S12, Converted to stress ratio, where pretension P is converted to prestress σ0: Where S1 is the cross-sectional area of ​​the supporting cable; G is converted to the average stress G generated by the deadweight load on the cross section of the canopy l : In the formula, S2 is the equivalent cross-sectional area of ​​the curtain plus the supporting cables. Since the thickness of the curtain can be ignored relative to the width, S2 is considered as the width multiplied by the unit 1m, G l It is actually the vertical load divided by the curtain width; S13, assuming that the initial mid-span deflection f0=l / 1000, l is the curtain span, fitting parameters A and B, and obtaining the relationship between the pre-tension of the support cable and the mid-span deflection in step S1.

3. The analysis and design method according to claim 1, characterized in that: In step S2, the finite element simulation form-finding analysis adopts a direct iteration method, a small elastic modulus method or a V-shaped broken line method to perform form-finding analysis.

4. The analysis and design method according to claim 3, characterized in that: In step S2, a direct iteration method is used for form-finding analysis, and the steps are as follows: S21, initially set the original length of the cables and curtain of the canopy system, and establish a straight line model; S22, fix one end of the cable to the hanging point and leave the other end free; apply vertical load to the cable and the curtain, apply horizontal tension to the free end of the cable, and hang the free end back to the height of the hanging point; S23, determine whether the mid-span deflection and initial stress of the cable meet the requirements of the relationship in S1; if so, the form-finding is completed; if not, repeat the above steps until the conditions are met.

5. The analysis and design method according to claim 4, characterized in that: In step S21, the initial length of the cable is calculated according to the catenary equation, the curtain span and the maximum mid-span deflection, wherein the calculation formula is: Where L is the total length of the cable, f is m is the maximum mid-span deflection of the supporting cable, and l is the curtain span.

6. The analysis and design method according to claim 1, characterized in that: In step S1, when considering wind load, the pretension of the supporting cable under wind load P w The calculation formula is: P w =W A ×(-2.6V0+78.6) Where W A is the static wind pressure and V0 is the basic wind speed.

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