Gust effect factors and natural sway frequencies of trees. for wind load estimation

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1 ut eect actor and natural way requencie o tree or wind load etimation *Seunghoon Shin¹, Ilmin Kang 1, Seonggeun Park 1, Yuhyun Lee 1, Kyungjae Shin 1, Whajung Kim 1, and ongjin Kim 1 1 Department o Architectural Engineering, Kyungpook National Univerity, Korea *Preenting author: h10004ok@knu.ac.kr Correponding author: hjk@knu.ac.kr Abtract Strong wind have caued increaing wind damage or ruit tree uch a uprooting and ruit drop in orchard worldwide. In order to prevent thee wind damage, the variou prop ytem or upport ytem have been introduced or ruit tree. When a prop ytem i deigned againt trong wind, it i eential to calculate the wind load acting on each tree or accurate evaluation o wind reitance o prop ytem. It i oten to treat the applied wind load acting on a tree a a tatic load and to ue beam theory to determine the maximum bending moment at the bae o the tree. owever, the repone o a tree i requency dependent and i aected motly by wind gut at requencie cloe to it reonant requency. In thi ituation, the dynamic eect are likely to increae the bending o tem and hence the maximum bending moment at the bae o the tree. Thee dynamic eect are likely igniicant and cannot be ignored when the natural way requency o a tree i relatively mall, that i, the tree i lexible. There are two approache to quantiying the repone o a tree to a given luctuating wind load. Firt, the wind load and tree repone pectra are experimentally meaured and a traner unction rom the wind load to tree repone i developed. Alternatively, i the inormation on the dynamic propertie uch a natural way requency and damping ratio o tree are available, then it i poible to characterize their repone to any luctuating wind load by employing a wind engineering theory. In many deign code or tandard, thi dynamic eect i conidered adopting the gut eect actor and empirical ormulae or the actor are given a unction o the natural way requency and damping ratio. The threhold natural way requency in mot deign code that the dynamic eect againt luctuating wind load need to be conidered careully i 1.0 z. Thi paper preent the ytem identiication method to meaure the natural way requencie and damping ratio o ruit tree or the evaluation o the wind load acting on the tree. Both the ambient vibration tet and ree vibration tet are perormed and the identiied dynamic propertie are compared. It i ound the average natural requency o ruit tree i le than 1.0 z, and thereby the dynamic eect againt luctuating wind load need cannot be ignored. Further, it i ound that the damping ratio o ruit tree are quite larger than thoe o civil and building tructure due to the oil-tructure interaction. Thereore, a pecial care i required when the prop ytem or ruit tree are deigned againt trong wind. Keyword: Tree Supporting ytem, Wind load, ut eect actor, Ambient vibration tet, Sytem identiication. Introduction Typhoon ha caued increaing wind damage or ruit tree at the orchard uch a uprooting and ruit drop in Korea recently. The reitance to uprooting moment o the tree i typically the weaket mechanical link or hallow-rooted tree ubjected to trong wind (Lundtröm et al. 007). In order to prevent thee wind damage and to enhance the uprooting moment

2 capacitie o tree in orchard, the wind break oret and the variou prop ytem, or upporting ytem, have been introduced to ruit orchard (e and oyano, 010). Three mot typical type o apple tree prop ytem ued in Korea are 1) individual prop ytem, ) teel pipe ence prop ytem, and 3) concrete column ence prop ytem. owever, mot o thee prop ytem were originated rom the region where the trong tropical torm like a typhoon doe not occur (Lepinae and Delort, 1986). Further, the mot o tudie on the apple tree prop ytem ha ocued on the annual yield and proit (Robion et al., 007, Palmer et al., 199). Thereore, it i required to evaluate the wind reiting perormance o ruit tree prop ytem which are requently ued in Korea. When a prop ytem i deigned againt trong wind, it i eential to calculate the wind load acting on each tree or accurate evaluation o wind reitance o the prop ytem. It i oten to treat the applied wind load acting on a tree a a tatic load and to ue beam theory to determine the maximum bending moment at the bae o the tree. owever, the repone o a tree i requency dependent and i aected motly by wind gut at requencie cloe to it reonant requency (u et al., 009). In thi ituation, the dynamic eect are likely to increae the bending o tem and hence the maximum bending moment at the bae o the tree. Thee dynamic eect are igniicant and cannot be ignored when the natural requency o a tree i relatively mall, that i, the tree i lexible. There are two approache to quantiying the repone o a tree to a given luctuating wind load (Moore and Maguire, 004). Firt, the wind load and tree repone pectra are experimentally meaured and a traner unction rom the wind load to tree repone i developed. Alternatively, i the inormation on the dynamic propertie uch a natural requency and damping ratio o tree are available, then it i poible to characterize their repone to any luctuating wind load by employing a wind engineering theory. In many deign code or tandard, thi dynamic eect i conidered adopting the gut eect actor and empirical ormulae or the actor are given a unction o the natural requency and damping ratio. The threhold natural requency in mot deign code that the dynamic eect againt luctuating wind load need to be conidered careully i 1.0 z (AIJ, 009, ASCE, 010). Thi paper preent the ytem identiication to meaure the natural requencie and damping ratio o ruit tree or the evaluation o the wind load acting on the tree. Both the ambient vibration tet and ree vibration tet are perormed and the identiied dynamic propertie are compared. The dynamic propertie obtained uing the previouly reported empirical ormulae are alo compared to experimentally identiied one. Next, the gut eect actor or each tree are evaluated uing the ormula given in Korean Building Code, which i termed a KBC009 hereater (AIK, 009). Wind Load on the tree upporting ytem Wind load on a tree Figure 1 how the teel pipe ence type prop ytem, which i mot commonly ued or apple orchard in Korea. Three or more tree are planted between two vertical pipe that are paced 6 m, and the wind load acting on tree are tranerred to vertical upport by horizontal wire intalled at every 80 cm. Since the tine in the longitudinal direction i much larger than that in the normal direction, uprooting damage generally occur in the normal direction and mot tree connected to a ence are damaged imultaneouly.

3 Figure 1. Steel pipe ence type prop ytem The wind load acting on a tree, P, i calculated a (Simiu and Scanlan, 1996) P qwa (1) where q w i the wind preure (N/m ). The wind preure q w i given by w 0.5 D Vz q C () where i the air denity (kg/m 3 ), C D i the drag coeicient (dimenionle), i the gut eect actor (dimenionle), and V z i the deign wind velocity at height z (m). The drag coeicient C D o tree in Eq. () are generally obtained experimentally uing a wind tunnel and ome typical value are given or variou tree type (Mayhead, 1973, Vollinger et al., 005). On the contrary, only limited tudie have been perormed on the gut eect actor o tree ince it i aected by many eature uch a tree pecie, age, height, tem diameter, and pacing (ardiner et al., 000). In thi tudy, the gut eect actor i obtained and analyzed applying empirical ormulae provided in literature and deign code that are obtained baed on a wind engineering theory. ut eect actor The gut eect actor i deined a a ratio o the maximum repone to mean repone o a tructure and i given a (Simiu and Scanlan, 1996) X max 1 g X X X (3)

4 where X max i the maximum repone, X i the mean repone, g i a peak actor, and x i the tandard deviation o the repone. ardiner et al. (000) propoed the ollowing empirical ormula obtained rom a wind tunnel tet uing caled tree model. max mean x / x / max mean (3.a, b, and c) where i the tree pacing (m), i the tree height, and x i the ditance rom the oret edge (m). Davenport and Surray (1990) deined the gut eect actor or low rie tructure a 1 k k 1 (4) where i the peak actor (dimenionle), i the expoure actor (dimenionle), k 1 i the background turbulence actor (dimenionle), and k i the gut reonant actor. Peak actor depend on the natural requency o the tructure, that i, it increae a a logarithmic unction o natural requency o the tructure increae. Further, the gut reonant actor k alo i a unction o the natural requency o the tructure. The damping ratio o the tructure aect the gut reonant actor a well. Conequently, the accurate evaluation o the natural requency and damping ratio i critical or the gut actor calculation. Eq. (4) i adopted in many deign code including KBC009. The peak actor and the expoure actor in KBC009 are given a ln( 600 ) 1. (5) 3 3 I z (6) where i the power law exponent o mean wind peed proile or a given terrain roughne category, and I z are, repectively, the level croing number and turbulence denity at the reerence height and given a n 0 k k k 1 (7)

5 I z 0.1 z Z g 0.05 (8) where n 0 i the natural requency o the tructure (z) and Z g i the nominal height o the atmopheric boundary layer. The background turbulence actor k 1 and the gut reonant actor k in KBC009 are deined a k k S F 1 1/ L / B B / (9) (10) where B i the width o the tructure, i the damping ratio, L i turbulence denity at the reerence height, and S and F are, repectively, the ize reduction actor and the pectral energy actor given a S F ( n / V 1.1( n B/ V 4( n L ( n L / V ) 5 / 6 0 / V ) 0 (11) 0 (1) where V i the deign wind peed at the top o the tructure. For the tructure with a natural requency o le than 1.0 z, the tructure i claiied a a rigid tructure and it gut eect actor i imply given a Eq. (13) omitting the gut reonant actor k and letting the value o and the expoure actor to be 4 rom Eq. (4) 1 4 k 1 (13) Natural requency and damping ratio o tree From Eq. (7), (11), and (13), it can be noticed that the natural requency i required or the gut eect actor calculation. Further, it can be noted rom Eq. (10) that the damping ratio need to be known a well. Moore and Maguire (004) invetigated previouly reported natural requency meaurement rom 60 tree, which belong to eight dierent pecie, and howed that natural requency i trongly and linearly related to the ratio o diameter at breat height to total height quared. They preented the ollowing empirical ormula baed on a regreion analyi. D n bh (14) where D bh i the diameter at breat height (cm).

6 They propoed another empirical ormula to conider the pecie dierence given by Eq. (15) where I p i an indicator variable. D n bh I p D bh (15) The value o I p i 1.0 i the genu i Pinu and 0.0 otherwie. Moore and Maguire alo invetigated the damping ratio o tree rom the previou reearche and claiied it into two categorie; 1) internal damping i due to the riction o the root-oil connection, tructural damping reulting rom the movement o branche and the internal riction o the wood, and ) external damping due to the aerodynamic drag o the crown and alo to colliion between crown o neighboring tree. They concluded that the internal damping ratio are generally le than 0.05 and do not appear to be related to tree ize, while the external damping i wind velocity dependent and much larger than the internal one. Field meaurement o natural requencie and damping ratio Tet pecimen and method A ield vibration tet wa perormed to meaure the natural requencie and damping ratio o orchard tree. The apple tree were ued or the tet. Both the ambient vibration tet and ree vibration tet were perormed and the identiied dynamic propertie were compared. The tree were upported by the teel pipe ence type prop ytem and our to ive tree were planted between two vertical teel pipe. The tet wa perormed when tree were heavy with cluter o apple ince the typhoon damage occur motly beore and during harvet eaon. Total o 0 tree were ued in the tet. In order to analyze the eect o the prop on the dynamic propertie o tree, a hal o pecimen were teted ater cutting all horizontal wire connected to the tree while the prop or the ret o pecimen remained intact. Two piezoelectric accelerometer were intalled at 1.5 m high, one in the longitudinal direction (x-direction) and another in the normal direction (y-direction) to meaure the acceleration o tree without a teel pipe prop. On the contrary, only one accelerometer wa ued in the y-direction or tree with a prop becaue the requency in the x-direction i coniderably aected by the prop due to large tine. The ambient vibration tet wa carried out or 10 minute with a ampling requency o 360 z. The ree vibration tet wa perormed by imply puhing tree about 30 cm lowly by human and letting tree vibrate reely. Five human-induced ree vibration were perormed continuouly or both x- and y-direction or tree without a teel pipe prop, while thoe were perormed or the y-direction only or tree with a prop. The only acceleration meaured in the ame direction to the ree vibration direction i utilized or the identiication o dynamic propertie or the ree vibration tet. Identiied natural requencie and damping ratio The power pectrum denitie (PSD) o meaured acceleration rom two tet method were obtained to identiy the natural requencie o tree. Then the hal-power band-width method wa applied to the obtained PSD or damping ratio etimation (Clough, R. W. and Penzien, J, 1995, Xiong et al., 011). The peak o PSD are coniderably noticeable at the undamental natural requencie in both ambient and ree vibration tet, while the value o PSD in the ambient vibration tet contain the higher mode and DC content. The ditinction o PSD near the undamental requency in the ree vibration tet i mainly due to the act that tree ocillate at their undamental requency under a ree vibration.

7 The identiied natural requencie o the tet pecimen are ummarized in Table 1 and. Note that the only natural requencie in the y-direction are identiied in Table or tree with a prop ince the acceleration were meaured in that direction only. It can be een rom Table 1 that the natural requencie o tree in the x- and y-direction are almot ame except the tet pecimen T3, T8, and T9. It can be alo een that the identiied natural requencie rom the ree vibration tet are generally maller than thoe rom the ambient vibration tet. Thi i becaue the natural requency o a tructure i generally inverely proportional to it repone amplitude and the amplitude o meaured acceleration in the ree vibration tet are igniicantly larger than thoe in the ambient vibration tet. In average, the natural requencie obtained rom the ree vibration tet are 3.90 % and 6.06% maller in the x- and y-direction, repectively, than thoe rom the ambient vibration tet. The natural requencie o the tree with a prop are ound to be increaed compared to thoe without a prop. Thoe with a prop are % and % larger than thoe without a prop in average (Table ). Thi conclude that the tine o the teel pipe ence prop help to increae the tine o tree in the y-direction. That i the overall uprooting moment reitance capacitie o tree are increaed due to the intallation o the prop. Table 1. Identiied natural requencie o tree without a prop Specimen Ambient vibration tet Free vibration tet x-dir. (z) y-dir. (z) x-dir. (z) y-dir. (z) T T T T T T T T T T Average Table. Identiied natural requencie o tree with a prop in the y-direction Specimen Ambient vibration tet (z) Free vibration tet (z) T T T T T T T T T T Average In Table 3, the calculated natural requencie o tree uing the empirical ormulae provided in Eq. (14) and (15) are preented or comparion with experimentally identiied one. Compared with identiied natural requencie provided in Table 1 and, the empirical ormulae propoed by Moore and Maguire overetimate the natural requencie up to 34 %

8 in average. Thereore, it can be concluded that the empirical ormulae do not cover every genu o tree even though they are obtained rom more than 600 experimental data. Table 3. Natural requencie o tree rom empirical ormulae Specimen Eq. (14) Eq. (15) Eq. (14) Eq. (15) Specimen (z) (z) (z) (z) T T T T T T T T T T T T T T T T T T T T Average Average Table 4. Identiied damping ratio o tree without a prop Specimen Ambient vibration tet Free vibration tet x-dir. (%) y-dir. (%) x-dir. (%) y-dir. (%) T T T T T T T T T T Average Table 5. Identiied damping ratio o tree with a prop in the y-direction Specimen Ambient vibration tet Free vibration tet (%) (%) T T T T T T T T T T Average

9 Table 4 and 5 preent the identiied damping ratio o tree with and without a prop rom the ambient and ree vibration tet. It can be een rom Table 4 that the identiied damping ratio o tree without a prop rom the ree vibration tet were igniicantly larger than thoe rom the ambient vibration tet. They are 35.88% larger in the x-direction and 43. % larger in the y-direction in average. Thi i becaue the external damping a well a internal damping play a role when the tree are ocillating with large magnitude a Moore and Maguire reported. The average damping value o 6.01 % and 6.3 % obtained rom the ambient vibration tet match well to the internal damping o 5 % reported by Moore and Maguire. Compared to the damping ratio o tree without a prop, thoe with a prop in Table 5 are 0.88 % and 49.9 % larger in the ambient and ree vibration tet, repectively. Conequently, it can be concluded that the wire attached to the tree in the teel pipe ence prop increae not only tine but alo damping ratio o tree. ut eect actor evaluation The gut eect actor are calculated and ummarized in Table 6 and 7. Both ormulae or non-rigid tructure in Eq. (3) and rigid tructure in Eq. (4) are utilized ince the identiied natural requencie o tree are almot 1 z. For comparion, the reult o the empirical ormula in Eq. (13) propoed by ardiner et al. are alo preented in Table 6 and 7. For Eq. (3) and (4), the identiied natural requencie and damping ratio rom the ambient vibration tet were ued becaue the maller damping ratio produce more conervative wind load etimation. For Eq. (13), the tree pacing i et to be 1.5 m, and the ditance rom the oret edge i aumed to be zero or conervative condition. Table 6. ut eect actor o tree without a prop Specimen Eq. (3) Eq. (4) Eq. (13) T T T T T T T T T T Average Table 7. ut eect actor o tree with a prop Specimen Eq. (3) Eq. (4) Eq. (13) T T T T T T T T T T Average

10 It can be noticed that the gut eect actor obtained uing Eq. (4) are 14.7 % to % maller than thoe obtained uing Eq. (3). Thereore, i the lexible nature o tree i neglected, the total wind load can be underetimated noticeably. The empirical ormula propoed by ardiner et al. yield 7.41 % to % lager gut eect actor compared to thoe by the ormula or non-rigid tructure, and 48.6 % to 58.9 % lager one compared to thoe by the ormula or rigid tructure Thereore, it can be concluded that the empirical ormula that doe not require the exact value o natural requency and damping ratio overetimate the gut eect actor coniderably. Concluion The gut eect actor o tree are analyzed or the wind load etimation o the tree upporting ytem. Since the value o gut eect actor depend on the natural requency and damping ratio, the ield experiment wa perormed to identiy the accurate dynamic propertie o the tree. The 0 apple tree were ued or the ield tet, in which a hal o them were teted ater cutting all horizontal wire connected to the tree while the prop or the ret o pecimen remained intact. Both the ambient vibration tet and ree vibration tet were perormed and the identiied dynamic propertie were compared. It wa ound that the average natural requency o ruit tree i about 1.0 z, and thereby the dynamic eect againt luctuating wind load need cannot be ignored. Further, it i ound that the damping ratio o ruit tree are quite larger than thoe o civil and building tructure due to the external damping eect. The wire attached to the tree in the teel pipe ence prop increae both tine and damping ratio o tree. The gut eect actor analyi reult indicate that the total wind load can be underetimated noticeably i the lexible nature o tree i neglected. I the empirical ormula that doe not require the exact value o natural requency and damping ratio i ued, the gut eect actor wa overetimated coniderably. Acknowledgement Thi work wa upported by Korea Intitute o Planning and Evaluation or Technology in Food, Agriculture, Foretry and Fiherie(IPET) through Advanced Production Technology Development Program, unded by Minitry o Agriculture, Food and Rural Aair(MAFRA)(31509) Reerence [1] American Society o Civil Engineer (010) ASCE 7-10 Minimum Deign Load or Building and Other Structure. [] Architectural Intitute o Japan (004) Recommendation or Load on Building. [3] Architectural Intitute o Korea (009) Korea Building Code. [4] Clough, R. W. and Penzien, J (1995), Dynamic o tructure, 3rd ed. Computer & Structure, Inc., Berkeley, CA. [5] Crook, M. J., and Enno, A. R. (1996) The anchorage mechanic o deep rooted larch, Larix europea x L japonica, Journal o Experimental Botany, 47(10), [6] Davenport, A. C. and Surry, D. J. (1974) The preure on low rie tructure in turbulent wind, Canadian Structural Engineering Conerence. [7] ardiner, B., Peltola,., and Kellomaki, S., (000) Comparion o two model or predicting the critical wind peed required to damage conierou tree, Ecological Modeling, 19, 1-3. [8] e, J. and oyano, A. (009) The eect o windbreak oret on the ummer thermal environment in a reidence, Journal o Aian Architecture and Building Engineering, 8(1),

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