Aerodynamic database for low-rise buildings

Transcription

1 Aerodynamc database for low-rse buldngs. Introducton An aerodynamc database has been constructed by the Tokyo Polytechnc Unversty as one art of the Wnd Effects on Buldngs and Urban Envronment, the 2st Century Center of Excellence Program, , funded by the Mnstry of Educaton, Culture, Sorts, Scence and Technology, Jaan. Present work s the low-rse buldng art of the aerodynamc database. Its objectve s to rovde structural desgn engneers wth wnd tunnel test data of wnd loads on low-rse buldngs. 6 models of gable-, h- and flat-roofed low-rse buldngs were tested. 476 contours of statstcal values of local wnd ressure coeffcents, 700 grahs of statstcal values of area averaged wnd ressure coeffcents on the roof or wall surfaces and tme seres data of ont wnd ressure coeffcents for 82 test cases are shown on ths web ste. These data can be used to calculate local wnd ressures, area averaged wnd ressure coeffcent on roof or wall surfaces, and even wnd nduced dynamc resonses of low-rse buldngs. The aerodynamc database of low-rse buldngs can be quered from the lower art of ths web age. The followng aragrahs rovde nformaton on wnd tunnel tests, rocesses of obtanng test data, usage of the data. 2. Wnd Tunnel Test Pressure measurement wnd tunnel tests on low-rse buldngs for ths database were executed n the Boundary Layer Wnd Tunnel, 2.2m wde by.8m hgh, n the Tokyo Polytechnc Unversty, Jaan. The length scale was set at /0. As the velocty scale was assumed at /3, the tme scale can be estmated at 3/0. 2. Wnd feld Snce a lot of low-rse buldngs are located n suburban areas n Jaan and some other countres, the suburban terran corresondng to terran category III n AIJ (2004) [] was chose as the tested wnd feld. Ths category has a mean wnd velocty rofle exonent of 0.20 and a gradent heght of 450m. It was smulated wth turbulence-generatng sres, roughness elements and a caret on the ustream floor of the wnd tunnel s test secton. The wnd velocty rofle and turbulence ntensty rofle of the smulated wnd feld are shown n Fg.. The turbulence densty at a heght of cm was about The test wnd velocty at ths heght was about 7.4m/s, corresondng to about 22m/s at a heght of m n full scale. 2.2 Test models To maxmze the database s alcablty, the geometrc arameters of the tested models covered a wde range of combnatons. Table shows the geometrc arameters of the 6 model cases of the

2 70 60 Test(/0) Category III(AIJ2004) Mean wnd seed Turbulence densty 50 Heght Z(m) U(z) or I(z) Fgure. Smulated wnd feld of suburban terran wnd tunnel test. Three tyes of models were tested: flat-roofed, gable-roofed and h-roofed. Four Heght/Breadth ratos were tested: /4, 2/4, 3/4 and 4/4. The Deth/Breadth ratos were set at 2/2, 3/2 and 5/2 for the flat- and gable-roofed models, and 3/2 for the h-roofed models. For the gableroofed models, 8 roof tches were tested: 4.8 o, 9.4 o, 4 o, 8.4 o, 2.8 o, 26.7 o, 30 o and 45 o. 2 roof tches were tested for the h-roofed models: 26.7 o and 45 o. The tches of the four sloes of a hed roof were assumed same.

3 Table. Test model cases Case number Roof Tye B(mm) D(mm) H0(mm) β ( o ) -2 Flat 60 60,240,400 40,80,20, Gable ,80,20, Gable ,80,20, Gable ,80,20,60 4.8, 9.4, 4, 8.4, 2.8, 26.7, 30, , 9.4, 4, 8.4, 2.8, 26.7, 30, , 9.4, 4, 8.4, 2.8, 26.7, 30, H ,80,20, , 45 Fgure 2. Test model and defntons of geometrcal arameters and coordnates Fgure 2 shows test models of low-rse buldngs. H0, B and D are eave heght, breadth and deth of the buldng, resectvely. H s mean roof heght, whch was set as the reference heght of aroach wnd velocty for wnd ressure coeffcents. β s roof tch. θ s wnd drecton angle, whch was set at 0 o when the wnd drecton was arallel to the rdge. The orgn of the coordnates s located at the center of the roof and the x-axs s arallel to the rdge. The buldng surfaces are annotated by Arabc numerals. The four walls were set as Surface ~ 4. The two sloes of a gable roof were set as Surface 5 and 6. The four sloes of a hed roof were set as Surface 5 ~ 8. The

4 whole roof of a flat-roofed buldng was set as Surface 5. For convenence, the contours of the local wnd ressure coeffcents were drawn wth the fve arts shown flat, as n the rght art of Fgure 2. Fgure 3. Arrangement of wnd ressure measurement tas

5 2.3 Wnd ressure measurement system Wnd ressure measurement tas were dsosed unformly over the surfaces of the tested models, as shown n Fgure 3. Basc saces among the tas were 20mm corresondng to 2m n full scale. Snce the wnd ressure measurement scanvalve couldn t measure a large number of tas synchronously, some nner onts for models wth larger surfaces were not measured. Synthetc resn tubes 80cm long and.2mm n nternal dameter connected each ta wth a ressure measurement scanvalve, whch can measure the fluctuatng wnd ressures at 384 onts nearly synchronously. In ths test, the samlng frequency was 500Hz and the samlng erod was 8 seconds for each samle, corresondng to 5Hz and mnutes n full scale. Each test case was samled tmes. 3. Comarson wth other test data Levtan et al [2] studed the wnd ressure coeffcents on a full scale TTU model. Teleman et al [3] and Luo [4] studed a model of a TTU test buldng at a scale of /50 n a wnd tunnel at the Unversty of Western Ontaro (UWO) and at Tongj Unversty (TJU), resectvely. Holmes [5] also showed hs test results n hs textbook. In order to verfy the valdty of the resent wnd tunnel test data, mean wnd ressure coeffcents on the centerlne of several gable roofs wth smlar test cases n the resent test were comared wth those n the lterature [2-5] as shown n Fgure 4. Mean wnd ressure coeffcents Mean C on centre lne of gable roofs(θ=90 o ) Holmes [5] (H/B=0.40,D/B=2, β=5 o ); TTU [2] (H/B=0.43,D/B=.5,β= o ) UWO [3] (H/B=0.43,D/B=.5,β= o ); TJU [4] (H/B=0.43,D/B=.5,β= o ) Present test(h/b=0.40,d/b=.5,β=5 o ) Dstance from wndward wall(b/b) Fgure 4. Comarson of mean wnd ressure coeffcents wth those n the lterature Bascally, the resent test data ftted well wth those n the lterature, although there were mnor dfferences snce the tested wnd felds and the tested models were not exactly the same.

6 In Fgure 4, the resent test data were the same as those of Holmes on the leeward roof, whle there were some dfferences near the wndward eave. Ths s ossbly related to the dfference between the models used. The deth/breadth rato of Holmes models was 2 whle that of the resent one was.5. The negatve ressure coeffcents n the resent wnd tunnel test are a lttle larger than those of TTU, UWO and TJU. Ths s ossbly related to the dfferent turbulences of the wnd felds. The turbulence ntenstes at the model heght n the resent test were about 0.25 whle those of TTU, UWO and TJU were about Test Data Process The measured voltage sgnals were translated nto tme seres of wnd ressure wth the calbratng data of the ressure sensors at frst. After that, the effect of the tube system on the measured wnd ressure was elmnated by dvdng the transfer functon from the ower sectra of the raw wnd ressure. The transfer functon of the tube system shown n Fgure 5 was dentfed wth a frequency swee technque. Fgure 5. Transfer functon of tube system The tme seres of wnd ressure coeffcents s calculated as: C (, (, / _ or = H ()

7 where C _ or (, s orgnal wnd ressure coeffcents at measured ta at tme t ; (, s measured wnd ressure at ta at tme t ; H s the reference wnd ressure of the aroachng wnd velocty at the average roof heght, H, defned n Fgure 2. In order to make the wnd ressure coeffcents corresond to some duraton, the tme seres of wnd ressure coeffcents were movng averaged as: C (, = C (, t t / 2 ~ t + t / 2) _ (2) or where t s the duraton of the wnd ressure coeffcents. The database shows three tyes of data: statstcal values of local wnd ressure coeffcents, statstcal values of area averaged wnd ressure coeffcents and tme seres of ont wnd ressure coeffcents. The tme seres data were movng averaged every 0.006s, corresondng to 0.2s n full scale. The statstcal values of area averaged wnd ressure coeffcents were calculated wth movng averaged every 0.006s corresondng to duratons of 0.2 second n full scale else. The statstcal values of local wnd ressure coeffcents were calculated wth ont wnd ressure coeffcents movng averaged every 0.03s so that ther duratons were.0 second n full scale. Accordng to an exedent formula by Lawson [6], the corresondng general sze s roughly estmated at 5m for ths duraton at the desgn wnd velocty of 22m/s. To desgn claddng or comonents wth a sze smaller than 5m, one can calculate ts extreme wnd loads based on the orgnal tme seres of ont wnd ressure coeffcents gven n the database for the corresondng duraton. 5 Database system The statstcal values of local wnd ressure coeffcents are exressed as contours n the database system. Statstcal values of area averaged ressure coeffcent are exressed as grahs versus wnd drecton angle. Tme seres of ont wnd ressure coeffcents are stored n MATLAB data format. 5. Statstcal values of local wnd ressure coeffcents Contours of the statstcal values of local wnd ressure coeffcents calculated from Equaton (2) wth a duraton of s n full scale were drawn. There were four tyes of statstcal values shown: mean, RMS, ostve extreme and negatve extreme. The mean and RMS values were the averaged values of ten samles: C = C ( n) (3) n= ~ ~ C = C ( n) (4) ~ where, C (n) and C ( n ) are the mean and RMS values of the tme seres of the nth samle. The extreme values were calculated by the Cook & Mayne method [7], where the extreme dstrbuton of wnd ressure coeffcents was assumed as a Fsher-Tett Tye (FT) dstrbuton: n=

8 Cˆ = U +.4 a (5) C ˆ / C ˆ where, U Cˆ and / a are the mode and dserson of the Fsher-Tett Tye, resectvely, whch Cˆ can be calculated by the Best Lnear Unbased Estmators (BLUE) [8] as: U = ˆ = a C X (6) / a ˆ = = b C X (7) where, X s the th value of the ascendng array of maxmum values of samles and a and b are gven by Table 2. Table 2, coeffcents of BLUE for FT dstrbuton (for samles) a b Equaton (5) exresses ostve extreme values, and t can also be used to calculate negatve extreme values. The robablty of exceedence of the extreme values calculated from Equaton (5) s 22%. Fgure 6 shows an examle of the contours of statstcal values of local wnd ressure coeffcents. Values not at the measured onts shown n Fgure 5 were nterolated from measured values. 5.2 Statstcal values of area averaged wnd ressure coeffcents The contours n Secton 5. are based on statstcal values of wnd ressure coeffcents at measured onts. Mean wnd force coeffcents of wnd force on a wall or roof surface can be calculated from mean values of ont wnd ressure coeffcents. However, the RMS and extreme values of wnd force cannot be evaluated n ths way because of the correlaton among ont wnd ressures. For convenence, the statstcal values of area averaged wnd ressure coeffcents on each roof or wall surface were shown n ths database too. The area averaged wnd ressure coeffcents on a roof or wall surface were calculated from: C F ( C (,. A )/ N j N j = = ( j, = A (8) where, C F ( j, s the area averaged wnd ressure coeffcent on Surface j at tmet ; C (, s the wnd ressure coeffcent at ont at tme t,obtaned from Equaton (2) wth a duraton of 0.2s n

9 full scale; A s the effectve area of wnd ressure measured at ont ; and N j s the number of measured onts on Surface j. The number of surface, j, was defned n Fgure 2. Fgure 6. An examle of contours of statstcal values of local wnd ressure coeffcents Fgure 7. An examle of the statstcal values of area averaged wnd ressure coeffcents

10 The mean, RMS, ostve extreme and negatve extreme values of area averaged wnd ressure coeffcents on each roof or wall surface were calculated from C F ( j, by the methods used n Secton 5.. The grahs of those values versus wnd drecton angle are shown on the webste as Fgure Tme seres of ont wnd ressure coeffcents One of the ten samles of tme seres of synchronous-measured ont wnd ressure coeffcents at each measurement ont for each test case calculated from Equaton (2) wth a duraton of 0.2s n full scale, whch can be used to analyze the dynamc resonses of the low-rse buldngs, are shown n ths database. The data are saved n MATLAB data format, as shown n Fgure 8. There are values saved n each data fle, ncludng the nformaton of model geometrcal arameters, wnd characterstcs, locatons of measured onts, data samle and tme seres of wnd ressure coeffcents. There s also a character constant named README, whose content s some sentences tellng reader the detal of the wnd tunnel test and the test data. Fgure 8. Format of tme seres of ont wnd ressure coeffcents 6. Usage of data The tme seres data of ont wnd ressure coeffcents can be used to analyze the dynamc resonses of low-rse buldngs. The statstcal values of local wnd ressure coeffcents are also useful for the desgn of claddng and comonents such as wndow anes, furrng strs, urlns, and so on.

11 The statstcal values of area averaged wnd ressure coeffcents on a surface can be used to desgn structural frames such as grders and llars. References [] AIJ Recommendatons for Loads on Buldngs (n Jaanese), Archtectural Insttute of Jaan, 2004 [2] M. L. Levtan, K. C. Mehta, W. P. Vann, J. D. Holmes, Feld measurements of ressures on the Texas tech buldng, J. Wnd Eng. Ind. Aerodyn. 38 (99) [3] H. W. Teleman, D. Surry, K. C. Mehta, Full/model-scale comarson of surface ressures on the Texas Tech exermental buldng, J. Wnd Eng. Ind. Aerodyn. 6(996) -23. [4] P. Luo, Wnd tunnel test research based on normal model, Master Thess, Brdge Engneerng Deartment, Tongj Unversty, Chna, [5] J. D. Holmes, Wnd Loadng of Structures, Son Press, London, UK, 200. [6] T. V. Lawson,, Wnd effects on buldngs, Volume : Desgn alcaton, London, Aled Scence Publshers, 980 [7] N. J. Cook, J. R. Mayne, A refned workng aroach to the assessment of wnd loads for equvalent statc desgn, J. of Wnd Eng. & Ind. Aerody., 6(980)25-37 [8]. J. Leblen, Effcent methods of extreme-value methodology, Natl. Bur. Stand. (U.S.) Re. NBSIR (974).