The reearch of implified method of calculating wind and rain load and it validation Xing FU 1) and Hong-Nan LI 2) 1), 2) Faculty of Infratructure Engineering, Dalian Univerity of Technology, Dalian 116024, China 1) fuxingbeijing@163.com 2) hnli@dlut.edu.cn ABSTRACT A implified method i ued to implify the calculation of wind and rain preure baed on the equivalent baic wind peed and equivalent ground roughne coefficient. The firt tep i to calculate the um of wind and rain preure, and then equivalent baic wind peed and equivalent ground roughne coefficient can be obtained through the formulae of wind preure and wind profile, at lat the reult of equivalent baic wind peed and equivalent ground roughne coefficient are fitted to obtain the fitting formulae. Repone analyi of a tranmiion tower i performed with the conideration of wind and rain load which are generated baed on the implified method and the integral formula repectively. It validated that the propoed implified method i feaible and can atify the accuracy requirement of practical engineering by comparing the reult. The implified method of calculating rain preure can implify the proce which i very eay to apply rain preure to tructural deign. 1. INTRODUCTION Rain i one of the mot common phenomena, and wind-driven rain (WDR), or driving rain, i rain that ha a horizontal velocity component. WDR i one of the mot important moiture ource affecting the hydrothermal performance and durability of building facade (Blocken et al. 2013). Rain intenitie are often very large during typhoon or hurricane, and many tranmiion tower-line ytem have collaped during evere gale and thundertorm. Mot reearcher have attributed thee collape cae to wind load, with few conidering rain load. Therefore, it ha become neceary to tudy rain load to undertand both their effect on collape cae and the mechanim acting on thee tructure. 1) Ph. D. candidate 2) Profeor
Choi (1993, 1994, 1997) ha made major breakthrough in the ue of numerical imulation employing computational fluid dynamic (CFD) in WDR reearch, conducted baed on a teady-tate 3D wind flow pattern, and thi method i ued in the preent tudy. Blocken and Carmeliet (2002) have extended Choi imulation technique by adding a temporal component and developing a new weighted data averaging technique, allowing for the determination of both the patial and temporal ditribution of WDR. Unlike Choi method, which generally baed on Lagrange frame to deal with raindrop motion by trajectory-tracking technique, Huang and Li (2010) have preented a numerical imulation method baed on a Eulerian multiphae model to etimate WDR intenity on building envelope, which could ave ignificant time during pre-proceing and pot-proceing. By virtue of the Eulerian multiphae model, Huang method could ignificantly reduce the complexity of evaluating WDR parameter, implify boundary condition treatment and be more efficient at predicting the tranient tate of WDR, and it effectivene ha been validated through an example. Li et al. (2013) propoed a computational approach to imulate rain load baed on the conervation of momentum and the wind tunnel tet i performed indicating that the imulation reult agree well with the experimental reult. Fu et al. (2014) modified the exiting rain load formula (Li et al. 2013), and both the numerical imulation and wind tunnel tet were conducted which indicating that the modified formula i feaible and the rain load cannot be neglected. Due to the complexity of exiting rain load formula, it neceary to propoe a implified method to calculate rain load for the convenience of tructural deign. In ection 2, the mathematic model of wind and rain preure are introduced, and ection 3 propoe the methodology of implifying the calculating proce of rain load. In ection 4 contrative analye of implified method and integration formula of wind and rain load are conducted baed on a tranmiion tower model. Section 5 conclude the tudy. 2. MATHEMATIC MODELS OF WIND AND RAIN PRESSURES Mean wind peed varying with altitude can be imulated by exponential wind profile: V V H 10 10 (1) Where V10 i the baic wind peed, H i the altitude, coefficient. If the wind peed i V, the wind preure yield: i the ground roughne P 1 2 2 w av (2) Where a i the air denity taking 1.235 Kg/m 3.
The rain load for pecific diameter can be calculated by the following equation (Li et al. 2013, Fu et al. 2014): 1 P dn dv V 6 3 3 (3) r r h h term Where r i the denity of raindrop taking 1000 Kg/m 3, d i the raindrop diameter, nh d i the raindrop ize ditribution, i the velocity ratio, V h and V term denote the horizontal velocity of a droplet and the terminal velocity of a droplet in the vertical direction repectively. Raindrop ize ditribution adopt Marhall-Palmer raindrop pectrum: nd nexp d 0 (4) 3 Where n0 8 10 (m -3 mm -1 0.21 ), 4.1R h (mm -1 ), R h i the rain intenity in mm/h. Velocity ratio i the ratio of the horizontal velocity of a droplet and the correponding wind peed, velocity ratio can be expreed a (Lin et al. 2013): d,, = 0.2373 0.0167 1 3 0.12-0.5008 Hd H 0.8 (5) The terminal velocity of a raindrop with diameter d can be calculated by the following equation: Vterm 1.15 (6) 9.40 1 exp 0.557 d In Eq. (3), V h hould adopt the terminal velocity of raindrop in the horizontal direction. The urface preure acting on a tructure can be calculated by the following equation: 1 w u V 2 (7) 2 a Where i the hape factor. 2 The urface wind peed can be etimated a uv if putting u into V. When imulating the wind effect on a tranmiion tower, the wind flow act on the front and rear elevation imultaneouly. Hence, it can aume that the hape factor of front elevation i 0.5u, then the terminal velocity of raindrop in the horizontal direction before impinging the tranmiion tower i 0.5u V. take 1.34 for the tower body and 1.4 for the croarm. Conequently, the rain load acting on a tranmiion tower for any rain intenity can be obtained by integrating Eq. (3), and the Eq. (3) i named a integral formula of
rain load. It obviou that the integration i very complex, o it neceary to propoe a implified method to calculate wind and rain load for the convenience of practical application. 3. SIMPLIFIED METHOD OF CALCULATING WIND AND RAIN LOADS The baic proce i lited a below: (1) The firt tep i calculating the um of wind and rain preure for the condition of ground roughne coefficient taking, baic wind peed taking V 10, rain intenity taking R h, and altitude taking H, then equivalent wind peed i derived with Eq. (2). If H i 10 m, the derived equivalent wind peed i the equivalent baic wind peed V 10. (2) If, Rh and V 10 i fixed, the correponding equivalent ground roughne coefficient can be obtained by Eq. (1) with the reult of the firt tep. (3) The reult of firt and econd tep are fitted to obtain the fitting formulae of equivalent baic wind peed and equivalent ground roughne coefficient. (4) The equivalent wind peed can be derived by equivalent baic wind peed and equivalent ground roughne coefficient, and then the um of wind and rain preure can be get by Eq. (2). Baed on the aforementioned proce, the fitting formula of equivalent baic wind peed i derived: h h h V V f V f R f 10 10 1 10 2 3 V V 0.355V exp 0.0038R 0.93exp( 0.013 R ) 6.125 4.305 10 2 4 10 10 10 (8) The difference of equivalent ground roughne coefficient and ground roughne coefficient i o mall that it can be implified that. The procedure to calculate wind and rain load uing equivalent baic wind peed and equivalent ground roughne coefficient are lited a below: 1. Firt it need to calculate equivalent baic wind peed V 10 and equivalent ground roughne coefficient uing Eq. (8) for one pecific condition. 2. The econd tep i calculating the um of wind and rain preure P total uing V 10 and through Eq. (1) and Eq. (2). 3. Then the wind and rain load acting on a tructure can be imulated with hape factor u and projected area A : Ftotal up total A. 4. CONTRASTIVE ANALYSES OF SIMPLIFIED METHOD AND INTEGRAL FORMULA OF WIND AND RAIN LOADS In thi ection a tranmiion tower model i ued to validate the feaibility of implified method to calculate wind and rain load. It i impoible to imulate the wind and rain load at all point on the tranmiion tower in an actual imulation. Thu, the tranmiion tower i implified to 34 node that are ued to apply the wind and rain load, and the number of node increae from the bottom to the top of the tower. A chematic of the implified tower i illutrated in Fig. 1 and the finite element model of
the tranmiion tower i illutrated in Fig. 2. The height of the tower i 254 m, with Q235 and Q345 teel ued. The cro-ection of the tower member conit mainly of teel tube, although a few are made of angle teel. Fig. 1 Simplified tranmiion tower node Fig. 2 Finite element model of tranmiion tower The imulation parameter for fluctuating wind peed in thi paper are a follow: (1) the power-law exponent i 0.12, 0.22 and 0.30; (2) the total time i 300, the time interval i 0.1, the cut-off frequency i 5 Hz, and the number of divided frequencie i 1024; (3) the horizontal fluctuating wind pectrum ue the Davenport power pectrum; and (4) the baic wind peed V 10 i one of four clae: 10, 20, 30 or 40 m/. Six clae of rain intenitie are employed: 0, 40, 80, 120, 160 and 200 mm/h, with the total number of condition reaching 72. The vibration repone of the tranmiion tower ubjected to wind and rain load i then calculated. The acquiition point of diplacement i hown in Fig. 3. Due to the tochatic wind and rain load, the tower diplacement reult for integration formula and implified method are given a average value in Table 1 and Table 2 repectively. In Table 1, when i 0.30 and V 10 i 40 m/, the maximum average diplacement i 433.93 mm for rain intenity of 200 mm/h and 376.87 mm for pure wind, and the difference can reach 57.06 mm indicating that the contribution of rain load on the tower repone cannot be neglected. Fig. 3 Acquiition point of diplacement
V 10 Table 1 Average tower tip diplacement for integration formula (1) =0.12 (m/) 10 7.9542 8.0087 8.0431 8.0731 8.1007 8.1266 20 31.672 32.108 32.384 32.624 32.844 33.052 30 71.202 72.675 73.603 74.414 75.158 75.858 40 126.54 130.03 132.24 134.16 135.92 137.58 (2) =0.22 10 14.538 14.673 14.759 14.834 14.902 14.967 20 58.006 59.091 59.776 60.373 60.922 61.438 30 130.45 134.12 136.43 138.44 140.30 142.04 40 231.88 240.56 246.04 250.82 255.21 259.34 (3) =0.30 10 23.599 23.881 24.059 24.214 24.357 24.491 20 94.253 96.508 97.931 99.173 100.31 101.39 30 212.01 219.62 224.42 228.61 232.46 236.08 40 376.87 394.91 406.29 416.22 425.35 433.93 V 10 Table 2 Average tower tip diplacement for implified method (1) =0.12 (m/) 10 7.9542 8.0047 8.0391 8.0686 8.0968 8.1258 20 31.672 32.070 32.342 32.575 32.798 33.029 30 71.202 72.539 73.454 74.243 74.997 75.778 40 126.54 129.71 131.88 133.76 135.55 137.41
(2) =0.22 10 14.538 14.641 14.712 14.773 14.831 14.891 20 58.006 58.824 59.383 59.864 60.323 60.798 30 130.45 133.20 135.09 136.71 138.26 139.88 40 231.88 238.39 242.86 246.73 250.43 254.28 (3) =0.30 10 23.599 23.783 23.908 24.015 24.118 24.223 20 94.253 95.698 96.686 97.537 98.349 99.190 30 212.01 216.87 220.20 223.07 225.82 228.68 40 376.87 388.37 396.29 403.13 409.69 416.51 For comparing the two method explicitly, the relative error are calculated a given in Table 3. All relative error are negative illutrating that the average diplacement of implified method i maller than the reult of integration formula, and it obviou that the relative error are o mall that the maximum i only -4.02% indicating that the propoed implified method to calculate wind and rain load can atify the accuracy requirement of practical engineering. V 10 Table 3 Relative error of implified method relative to integration formula (1) =0.12 (m/) 10 0.00% -0.05% -0.05% -0.06% -0.05% -0.01% 20 0.00% -0.12% -0.13% -0.15% -0.14% -0.07% 30 0.00% -0.19% -0.20% -0.23% -0.21% -0.11% 40 0.00% -0.25% -0.27% -0.30% -0.27% -0.12% (2) =0.22 10 0.00% -0.22% -0.32% -0.41% -0.48% -0.51% 20 0.00% -0.45% -0.66% -0.84% -0.98% -1.04% 30 0.00% -0.68% -0.98% -1.25% -1.45% -1.52% 40 0.00% -0.90% -1.29% -1.63% -1.87% -1.95%
(3) =0.30 10 0.00% -0.41% -0.63% -0.82% -0.98% -1.09% 20 0.00% -0.84% -1.27% -1.65% -1.96% -2.17% 30 0.00% -1.25% -1.88% -2.42% -2.86% -3.14% 40 0.00% -1.66% -2.46% -3.15% -3.68% -4.02% 5. CONCLUSION In thi paper the implified method to calculate wind and rain load i validated. The imulation reult how that rain load cannot be neglected. The relative error are all very mall indicating that the implified method agree well with the integration formula. The implified method implifie the calculating progre of wind and rain load greatly which will promote the application of rain load in practical engineering. REFERENCES Blocken, B., Derome, D. and Carmeliet, J. (2013), Rainwater runoff from building facade: a review, Build. Environ., 60, 339-361. Choi, E. (1993), Simulation of wind-driven-rain around a building, J. Wind Eng. Ind. Aerod., 46&47, 721-729. Choi, E. (1994), Determination of wind-driven-rain intenity on building face, J. Wind Eng. Ind. Aerod., 51(1), 55-69. Choi, E. (1997), Numerical modeling of gut effect on wind-driven rain, J. Wind Eng. Ind. Aerod., 72: 107-116. Blocken, B. and Carmeliet, J. (2002), Spatial and temporal ditribution of driving rain on a low-rie building, Wind Struct., 5(5), 441-462. Huang, S.H. and Li, Q.S. (2010), Numerical imulation of wind-driven rain on building envelope baed on Eulerian multiphae model, J. Wind Eng. Ind. Aerod., 98(12), 843-857. Li, H.N., Tang, S.Y. and Yi, T.H. (2013), Wind-rain-induced vibration tet and analytical method of high-voltage tranmiion tower, Struct. Eng. Mech., 48(4), 435-453. Fu, X., Lin, Y.X. and Li, H.N. (2014), Wind tunnel tet and repone analyi of high-voltage tranmiion tower ubjected to combined load of wind and rain, Eng. Mech., 34(1), 72-78. (in Chinee) Lin, Y.X.,Fu, X. and Li, H.N. (2013), Reearch on the Velocity Ratio of Wind Driven Rain, The 12th International Conference on Civil and Environmental Engineering, Dalian, China.