Overturning Analysis of Harbor Containers Based on Wind Tunnel Test of Rigid Models

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1 Overturnng Analyss of Harbor Contaners Based on Wnd Tunnel Test of Rgd Models Wu Zhen Peng Xngqan Zhang Chunhu College of Cvl Engneerng, Huaqao Unversty, Quanzhou, Fujan, ,Chna E-mal Abstract Harbor Contaners often fall and get damaged under the strong wnd. However, the study of wnd-resstant for the bulk accumulaton structures lke harbor contaners has not reported n the lterature yet. Based on wnd tunnel tests of rgd model, through the smple prncple of moment balance and force balance, the calculaton formula of contaner s stablty under strong typhoon were obtaned, and the rule that crtcal falure wnd speed of ples of contaners whch are placed n dfferent rows and dfferent ters changes accordng to wnd drectons also were obtaned. The table of crtcal falure wnd speed of contaners from wnd tunnel test can be used as reference for wnd resstance and dsaster reducton. Meanwhle, t can also be helpful n researchng and desgnng of these bulk accumulaton structures. Keywords- contaner; wnd tunnel test; gust factor; crtcal velocty I. INTRODUCTION Wnd dsaster s the most nfluental natural dsaster, t s of hgh frequency, bg secondary dsaster, wde nfluence and often causes heavy loss of human lfe and property. The coastal port s attacked frstly when typhoon comes, port contaners often fall down n the typhoon causng enormous property loss (as shown n fg. 1). Yet the relevant research has hardly been made. It s very necessary to study the stablty of bulk accumulaton structures lke contaners n the typhoon, and know the best stackng way to mprove capacty of ant-destructon when typhoon comes. As suggested n [1], to keep contaners stable under wnds must meet two condtons: (1) horzontal wnd must be smaller than the largest statc frcton force of contaner;(2) effect on one sde s less than the bendng moments n ts gravty. Accordngly the crtcal overturnng falure wnd speed s deduced, they also get the crtcal wnd speed n dfferent wnd angle by numercal smulaton usng flud dynamcs software. Above s just usng software smulaton to get the crtcal wnd speed, not from the test. Ths paper s based on the wnd pressure value measured by wnd tunnel test of rgd model, thus gets the wnd load on the contaners, then crtcal overturnng wnd speed s deduced by force balance and moment balance. Consderng the structural features of plng up contaners, and combned wth the determnaton of load on mantenance structures n load code for the desgn of buldng structures [2].We put forward a gust factor to consder the load amplfcaton of fluctuatng wnd. Wnd tunnel test s adopted here to study the wnd of bulk accumulaton structures as contaners, and consderng the partcularty of ths structure, ths paper puts forward some research methods. Beleve that these methods and research results for ths knd of structure wll provde certan reference value to the research of wnd resstance. Fgure.1 The falure of contaners II. INTRODUCTION OF WIND TUNNEL TEST A. Test Type For the dfferent needs of dfferent study content, wnd tunnel test often uses all sorts of correspondng expermental Supported by The scence and technology plan projects of Fujan Provnce 2010Y0037 The Natural Scence Foundaton of Fujan Provn 2009J01255 ; Key Laboratory Project on Wnd Engneerng and Brdge Engneerng of Hunan provnce /11/$ IEEE 544

2 types. Accordngly, the wnd tunnel test can be dvded nto the rgd model test and elastc model test. The former s the man model test whch can be dvded nto secton model, ntegral model and local model, etc. The man uses of rgd test model nclude force measurement, pressure measurement, pneumatc parameter test, wnd-nduced vbraton test, the wnd flow characterstcs of morphology and envronmental testng, etc. Based on the purpose and condtons of the research, ths paper adopts rgd model pressure test [3]. B. Test Model There are 3 common knds of port contaners nternatonally: 20 foot, 40 foot, 40 foot hgh cube. Here we choose 40 foot hgh cube contaner as the research object, the standard sze of whch s m (length) 2.438m (wdth) 2.896m (heght), empty weght s 4.1 tons. Ths study adopts smultaneous mult-pressure measurement test on rgd model. For the convenence of the test, contaner ple (see fg. 2) s made an overall model. The model s made of transparent organc glass, 1 40 reduced-scale [4]. Table1 lsts the actual sze and scale sze(shown nsde the bracket). (Note: 5r4t says 5 rows and 4 ters) Lee to the contaner, the measurng-pont arrangement s dense on the corner, rare on the other poston. There are about 280 measurng ponts on the surface of model. Due to the lmted space, ths paper only lsts the measurng-pont arrangement of one stackng form (8r6t) (fg. 3). Test s done under every 15 wnd angel. There are 12 wnd angles, namely twelve test condtons, as shown n fg. 4. Fgure.2 The stackng way of contaners Fgure.3 The arrangement of measure ponts Fgure.4 The arrangement of wnd drecton C. The Wnd Feld Smulaton Ths wnd tunnel test s conducted n the laboratory of wnd tunnel test and research center n Hunan Unversty. The devces of baffle, mnarets and rough elements are used to smulate atmospherc boundary wnd [5] [6]. Consderng the exposure category A of coastal port, we set the ground roughness ndex n wnd profles of smulated wnd feld to 0.12 α0.12. The fluctuatng wnd power spectral densty at model hgh n boundary layer s shown n fg.5. Velocty profle and turbulence measured n smulated wnd fled s shown n fg.6. We choose a poston n wnd tunnel whch s TABLE 1 Real dmenson of contaners ple 4t 6t 8t 5r ( ) ( ) ( ) 8r ( ) ( ) ( ) 12r ( ) ( ) ( ) 545

3 not affected by test model and far enough away from the boundary of tunnel wall as reference pont (fg.7). Fg.8 shows the wnd speed curve of reference ponts. Known from the wnd speed curve, the average speed s approxmately 12m/s. The samplng frequency of pressure s about 300HZ, and total length of samplng samples s about In the test, each 6,600 data of every testng pont are recorded under every 15 wnd angel. And the data of total pressure and statc pressure are both recorded. Fgure.8 Wnd speed tme seres of reference pont 0.1 Karman Kamal III. DATA ACQUISITION AND PROCESSING ns u (n)/σ E-3 Davenport nz/u Fgure.5 Wnd speed SPD at heght of model A. The Average Wnd Pressure Coeffcent In the aerodynamcs, surface pressure s usually expressed n the form of dmensonless pressure coeffcent C p : C p, () t p() t p p p o 1 C p, s the wnd pressure coeffcent whch s measured n pore. p (t) s the wnd pressure of ponts on pore, p 0 and p are total pressure and statc pressure on reference pont.each pont can get 6,600 wnd pressure coeffcents. Correspondng to the basc wnd pressure n Load code for the State, we take the wnd pressure n heght 10m as the reference wnd pressure to get the wnd pressure coeffcent. Accordng to the theory of probablty and statstcs, under the acton of a wnd flow, the maxmum and the mnmum of the wnd pressure coeffcent of measurng ponts can be expressed as follow: Fgure.6 Mean wnd profle and turbulence ntensty dstrbuton of exposure category A C C + gc pmax, p, prms, C C gc pmn, p, prms, (2a) (2b) Where g s the peak factor, always wth a value from 3.0 to 4.0 [7], here g3.0, C prms, s the RMS wnd pressure coeffcent. B. Equvalent Statc Wnd Loads Fgure.7 The wnd pressure determnaton In safety consderaton, ths paper take the factor of fluctuatng wnd load nto account, that s takng the equvalent statc wnd loads as the wnd loads. There are many methods n researchng equvalent statc wnd loads, 546

4 ths paper takes gust loadng factor method (GLF method) [8]. For the convenence of calculaton and consderng the structure characterstcs of the bulk contaners, ths paper take the amplfcaton of fluctuatng wnd to the contaners nto account based on " gust loadng factor on bendng response [9] "and "the factor of fluctuatng wnd coeffcent". The defnton of former factor s the rato of the extreme bendng moment to the average bendng moment, the defnton of later factor s the rato of the extreme wnd pressure coeffcent to the average wnd pressure coeffcent. Therefore, the equvalent statc wnd load on the contaners can be expressed as follow: w G w s z OR Where μ s s the wnd shape coeffcent, μ z s wnd heght coeffcent. So μ s μ z s equal to the average wnd pressure coeffcent, whch can be deduced from (1). W OR here s the basc wnd pressure and defned as wnd pressure respondng to the crtcal wnd speed n ths paper, the value of whch s 1/2ρυ 2. The gust moment factor and the gust wnd coeffcent factor can be determned as follows: M max, GM, (4) M G C mean, (3) pmax, C, (5) CPm ean, In whch, M max, s the peak overturnng moment whch can be derved from (6), M mean, s the average overturnng moment and g s the peak factor. M M ± gm max, mean, prms, Where, g s the peak factor and also take the value 3.0 here, M prms, s the mean-square devaton of overturnng moment of bottom. M mean,i and M prms, can be deduced from the overturnng moment curve whch s get from the wnd tunnel test by probablty and statstcs analyss. (Accordng to the wnd pressure value sampled n the test, there are 6600 data of bendng moment to the bottom of every sngle measurng pont, so that we can get the average value the mnmum value and the maxmum value of the bendng moment to the bottom.) When one pont n the space get the maxmum fluctuatng wnd speed,the pont a certan dstance away generally wll not reach t at the same tme, and ths character (6) s called spatal correlaton of fluctuatng wnd [10]. To be safe and convenent for calculatng and for the reason that the heght and length of contaners are small, ths paper does not consder the spatal correlaton, namely that the wnd pressure of each measurng pont can reach maxmum at the same tme, and each measurng pont use ther own gust moment factor and the gust wnd coeffcent factor. C. Deducton and Research of Crtcal Wnd Speed Every year, the coastal port contaners get a certan degree of damage when the typhoon s landng. After the nvestgaton on dsaster ste, we fnd the damages on the corner of contaners happen most commonly, so the paper s only nvolved n the local damage of contaners. To keep the contaners stable n typhoon, there must be two condtons: one s the largest wnd force on contaners must not be greater than the statc frcton force, the other s effect on one sde must not be greater than the bendng moments n ts gravty. Accordngly, two crtcal equatons are derved: wa μg (7.a) 1 MA Gb (7.b) 2 In whch, G s the weght of contaner and b s the wdth of the contaner. Substtutng (1) and (3) nto (7) respectvely leads to the crtcal wnd speed for overturnng falure of contaners: 2uG υl G Aρ c, s z Gb υx G ρd A Mx,, s z x, Ga υy G ρd A My,, s z y, (8.a) (8.b) (8.c) Fnally, the crtcal wnd speed can be obtaned by the comparson n 8.a,(8.b)and 8.c : { L x y} ν p mn υ, υ, υ (9) Referrng to the frctonal coeffcent between the steel 547

5 TABLE 2 Crtcal velocty of overturnng along long axs Wnd angle 0 o 15 o 30 o 45 o 60 o 75 o 90 o 105 o 120 o Stackng way 5r4t r6t r8t r4t r6t r8t r4t r6t r8t plates n GB (Desgn Code for the Steel Structures [11] )and consderng the dent surface of contaner, ths paper set maxmum statc frcton factors between contaner to 0.75 and ar densty to kg/m3 under the room temperature. And after the calculaton, damage crtcal wnd speeds are get and shown n the table 2. From table 2, we can see that the wnd angle for the mnmum crtcal wnd speed s 90, the ncreasng of ter number can lead to decreasng of destructon crtcal wnd speed and the ncreasng of row number can lead to ncreasng of destructon crtcal wnd speed when the ter number s certan. For the other number of ters and rows, we can use lnear nterpolaton referrng to table 2 to get the overturnng crtcal wnd speed. The table of crtcal wnd speed can be used as reference of whether the contaners should be renforced or not when the typhoon comes. IV. CONCLUSION Based on wnd tunnel test of rgd model, ths paper studed the stablty of port contaners, and deduced the calculatng formula of crtcal wnd speed of bulk accumulaton structures. The results show that the most dangerous wnd angle s about 90, number of ters and rows nfluence the overturnng crtcal wnd speed of ths structure. The overturnng crtcal wnd speed derved here wll provde certan gudng sgnfcance to the stackng form and strengthenng of port contaners when the typhoon comes. REFERENCES [1] Zhao Qngchun, Peng Xngqan, Qao Changgu, Sh Lnlng, Zhou Xanpeng. Overturnng resstance calculatng of harbor contaners under the strong-wnd [J]. Journal of Zhengzhou Unversty of Lght Industry, 2008, 23(04):59-61 (n Chnese) [2] GB Load code for the desgn of buldng structures [S]. Bejng: Chna Archtecture &Buldng Press, 2006 (n Chnese) [3] ASCE Manual of Practce No.67 on Wnd Tunnel Studes of Buldngs and Other Structures [M].ASCE, [4] Huan Gpeng, Quan Yong, Gu Mng. Research of Passve SmulatonMethod of Atmospherc Boundary Layer n TJ-2 wnd tunnel [J]. Journal of Tongj Unversty 1999,27(2): (n Chnese) [5] Davenport A G. The spectrum of horzontal gustness near the ground n hgh wnds[j]. J. RoyalMeteorol, Soc, 1961, 87: [6] Metha Rd,Bradshaw P. Desgn rules for small low speed wnd tunnels [J].The aeronautcal journal of Royal Aeronautcals Socety,1979,73, [7] Huang Benca. Structural Analyss Theory and Applcaton of wnd [M]. The second sedton.shangha: Tongj Unversty Press, (n Chnese) [8] Natonal Research Councl of Canada (NRCC).User s Gude-NBC 1995 structural Commentares (part 4),1996. [9] Zhou Y Kareem A Gust loadng factor New model[j] Journal of Structural Engneerng (2) [10] Zhuang Baozhong, Chen Nal. The random vbraton theory and example analyss [M]. Bejng: earthquake publshng house,1985(n Chnese). [11] GB Code for desgn of steel structures [S]. Bejng: Chna Plannng Press, 2003 (n Chnese) 548