ANALYTICAL DETERMINATION OF AERODYNAMIC RESISTANCE OF THE SKELETAL TELECOMMUNICATION TOWERS

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1 JCEK SZFRN Tehnial University of Łódź NLYTICL DETERMINTION OF ERODYNMIC RESISTNCE OF THE SKELETL TELECOMMUNICTION TOWERS b s t r a t Computational determination of aerodynami resistane for high truss strutures like teleommuniations towers is the subjet of this study. Normalized proedures were presented with an example of an existing struture onerning the total wind oeffiient. The results of alulations along with their broad elaboration and interpretation have been presented. nalyses and alulations were onduted for a tower of height equal to 84 metres and of a triangular ross setion. The struture is haraterized by round full rods as the legs of the tower and hot-rolled angle bars as the braing. Two omputational approahes were applied providing the results for eah of them. The ahieved results allow for stating that seletion of a omputational standard proedure should be adequate to an analysed struture and its harateristi features. The information inluded in the artile is partiularly useful in ase of the determination of arrying apaity of existing tower strutures on the basis of Euroode standards. Keywords: aerodynami resistane, total wind fore oeffiient, teleommuniation towers, linear anillary item 1. Introdution Introdution of European standards in reent times in the Polish regulations aused great hanges in the determination of arrying apaity of individual ivil strutures. The analysis of arrying apaity with respet to urrent provisions is still a hallenging problem for designers and building surveyors. This results from the fat that not only did the onepts of determination of the arrying apaity of individual strutural elements hange but the way the load is formulated hanged as well. There are partiular situations where objets designed a dozen years ago, based on ompletely different requirements and standard proedures must be realulated. Steel strutures of teleommuniation towers are a typial example of suh a situation. The rapidly growing market for teleommuniation servies along with new hardware requirements and soial needs are the signs of our time. Therefore, mobile teleommuniation operators are onstantly modifying their infrastruture and eletroni devies due to this demanding situation. Considering teleommuniation equipment and hardware, we an take devies like radio modules, panel antennas, mirowave dishes, et. ll suh installations are mounted on support strutures like teleommuniation towers. Every modifiation of suh equipment affets main struture harateristi parameters suh as magnitude of loading, aerodynami fators and et. It provides a neessity for realulations of the tower arrying apaity. The study is devoted to the omputational determination of aerodynami resistane of tower teleommuniation strutures based on the formulae inluded in the standards [1].. Problem desription In general sense the oeffiient of aerodynami resistane (or the total wind fore oeffiient or wind drag) depends on []: shape of a ross setion of bars of a lattie struture, their slenderness, shape of a horizontal setion of a tower and a diretion of wind relative to walls of an objet. The definition of wind drag given in [1] is as follows resistane to the flow of wind offered by elements of a tower or a guyed mast and any anillary items that it supports, given by the produt of a drag oeffiient and a referene projeted area, inluding ie where relevant. 5

2 Jaek Szafran s it is desribed in [3], the term wind loading resistane is generally adopted to enompass the ombination of area, shielding effets and drag oeffiients. The simplest analytial explanation of wind mean loading on a tower may be expressed as: 1 P= rv f (1) where: ρ is the air density [kg/m 3 ], V [m/s] is the relevant wind veloity, f is the drag oeffiient related to the area. Considering wind resistane, whih should be expressed as the R = f, we have to realize that the most diffiult aspet to odify is the treatment of anillaries mounted on the struture. dditional elements an take different forms, in terms of position and of shapes, overing ladders, feeders, safety aess rails, antennas and dishes, et. [3]. In ase of teleommuniation towers with higher omplexity (e.g. flat-sided and irular-setion members), alulation problem of aerodynami resistane seems more hallenging. For towers made from profiles of different kind, loaded with able and limbing ladders or other linear anillaries like antennas and their support strutures, orret estimation of the aerodynami resistane is a demanding task. We should inlude interations of strutural elements and aessories, their mutual shielding effet as well as different flow patterns of elements of flat sided or irular edges. The determination of the aerodynami oeffiient aording to standard [4], whih is widely desribed in publiation [5], was a relatively simple proedure. The solidity ratio of one (usually front) fae of the spatial truss is the main parameter in this approah. It should be desribed as follows: F + FL 0.6 ϕl = () S where: F is the shadow area (area of the solid members in the appropriate fae) of every strutural element of the front fae, on a plane normal to wind diretion, FL is the shadow area of the linear anillaries of the tower, S is the area of the onsidered ontour (elevation). For a tower with irular-setion legs and flat-sided braes, the oeffiient of aerodynami resistane is desribed by the formula given in [4] as: = ϕ, 0 < ϕ < 0.37 (3) f Similar onsiderations an be arried out aording to standard [1]. However, we should emphasize that the degree of their omplexity is definitely greater. Considering wind loading of steel skeletal teleommuniation towers, we should realize that this partiular kind of loading is the ruial one, and it deides about the ross-setions of strutural members, the geometrial dimensions of a tower, the total weight of a struture, et. Taking this fat into onsideration, it is worth presenting the formulae given in [1] that are desribing the wind fore in the diretion of the wind on the tower. The mean wind load in the diretion of the wind on the tower is desribed as follows: q F z = (4) + ( ) p m, W f ref 1 7Jv( ze) where: J v is the turbulene intensity, qp [kn/m ] is the peak veloity pressure, ref is the referene area of the struture (projeted area), z [m] is the height above ground level and f is the total wind fore oeffiient. On the other hand, we have to take the equivalent gust wind load in the diretion of the wind into onsideration during the arrying apaity analysis whih is determined as follows: ( ) = mw ( ) ( ) ( ) F z F z TW,, z 1 7 v e s d 1 m + J z h 0 zm (5) where: sd is the strutural fator, z m [m] is the height above the base at whih a load effet is required, 0 (z m ) is the orography fator and h [m] is the overall tower height. s we an find in Equation (4), the magnitude of the mean wind load depends on four parameters where the most diffiult to determine via analytial alulations, as it was mentioned above, is the total wind fore oeffiient. 3. nalyzed struture nalysis has been performed on the basis of the existing teleommuniation tower illustrated in Fig. 1 of height equal to 84 meters. The onstrution is divided into 14 setions with their height equal to 6.0 meters. The lowest setion S-14 is presented in Fig. 1 in axonometri view. The stati sheme of suh a struture is a spatial truss fixed in ground by the foundations. 6

3 NLYTICL DETERMINTION OF ERODYNMIC RESISTNCE OF THE SKELETL TELECOMMUNICTION TOWERS Fig.. The ross setion of the tower and the able-limbing ladder Fig. 1. The stati sheme of the tower and the axonometri view of the lowest setion of the tower The leg members of the tower (the main load-bearing omponents) onsist of irular full rods and primary braing members with hot-rolled angle bars. Feeders, ables and limbing ladder (linear anillary) is plaed entrally inside the tower. The ladder is made of two vertially situated old-formed C-bars onneted by irular rods at one end, and with brakets for feeders and ables at the other end as it is presented in Figure 1 and Figure. In Figure there is presented the ross setion of the tower above the servie platform. We an also find the able-limbing ladder plaed in the enter of the struture. Numbers 1, and 3 on the drawing denote partiular faes of the tower. n arrow presents the wind diretion where Θ 1 is the angle of inidene of the wind normal to fae 1. s we an observe in the attahed piture taken on the existing tower, there are ables and feeders on the rear side of the ladder and also on the antilevers mounted to the front-limbing part. Table 1 presents individual elements for every setion of the struture suh as leg members, primary and seondary braing. The most important part of the data olleted in Table are: f,i that is the total projeted area when viewed normal to the fae of the flat-sided setion members in the fae (1, or 3) where,i is the total projeted area normal to 7

4 Jaek Szafran the fae of the irular-setion members in the fae (1, or 3) in sub ritial regimes. Espeially important for further onsiderations is the division the projeted area of an individual setion for irular and flatsided members. It results from the neessity of onsideration of different flow patterns around sharp edges and irular members. For irular members the flow is ritially dependent on wind veloity, or in aerodynami terms, on the Reynolds number. The olleted areas of the analyzed struture are speified for the angle of inidene of the wind Θ 1 equal to 0. The total area projeted normal to a fae (e.g. 1) of the strutural omponents without anillaries should be expressed as: S,1 =,1 + f,1 (6) Table presents the elements and their projeted areas of the able-limbing ladder. s it an be found, there is a division of the flat-sided elements,f and the irular members, and we notie that for this partiular struture, the projeted area of the ladder is equal for all the tower setions. It should be emphasized that the total area of the able-limbing ladder is equal to: =, +, f (7) 4. erodynami resistane alulations ll alulations of the total wind fore oeffiient are based on one of the most important parameters in the theory of aerodynami resistane of skeletal strutures, the solidity ratio. Standard [5] desribes it as follows: ϕ = (8) where: is the sum of projeted areas of the members and is the overall envelope area. Table 1. Setions of the towers with their projeted areas for Θ 1 = 0 Setion Legs Primary braing Seondary braing S-1 Ø80 L 90x60x8 C S- Ø80 L 90x60x8 C S-3 Ø90 L 90x60x8 C S-4 Ø90 L 90x60x8 C S-5 Ø100 L 90x60x8 C S-6 Ø100 L 10x80x10 C S-7 Ø100 L 10x80x10 C S-8 Ø110 L 10x80x10 L 100x100x S-9 Ø110 L 150x100x10 L 100x100x S-10 Ø110 L 150x100x10 L 10x10x S-11 Ø10 L 150x100x10 L 10x10x S-1 Ø10 L 150x100x10 L 10x10x S-13 Ø10 L 00x100x10 L 150x150x S-14 Ø10 L 00x100x10 L 150x150x ,1 f,1, f,,3 f,3 Table. The elements of the able-limbing ladder ess rail Guide rails Flat-sided members Cable antilevers,f Feeders and ables Cirular setion members Setion Steps, Table 3. Envelope areas for partiular setions of the tower S-1 S- S-3 S-4 S-5 S-6 S-7 S-8 S-9 S-10 S-11 S-1 S-13 S

5 NLYTICL DETERMINTION OF ERODYNMIC RESISTNCE OF THE SKELETL TELECOMMUNICTION TOWERS The envelope areas for the setions of the analyzed strutures are olleted in Table 3. It should be underlined that Equation (8) expresses the struture shadow area only, and the formula does not inlude anillaries like a ladder, et. It should be notied that the data olleted in Table 1 indiates that for the individual faes of the tower (1, or 3) we obtain different solidity ratios (φ 1, φ or φ 3 respetively). ording to standard [1] and the reommendations given in [3, 6], alulations of the tower aerodynami resistane might be onsidered applying two independent approahes. It depends on the systems of the tower strutures and that may be generally divided into symmetrial strutures with limited anillaries and strutures ontaining anillaries. To present the algorithm of the alulations, detailed expression, formulae, the results are going to be shown on one hosen setion of the tower S-10. The results for other setions take a tabular form. ll the alulations are provided for the angle of inidene of the wind Θ 1 = Total wind fore oeffiient general method ording to [1], the total wind fore oeffiient in diretion of wind over a setion of the struture should be taken as: f,10 = f, S,10 + f,,10 (9) where: f,s,10 is the wind fore oeffiient of bare struture setion S-10 determined using a solidity ratio φ, f,,10 is the wind fore oeffiient of the anillaries in setion S-10. It is worth emphasizing that in this approah only fae 1 with the feeder-able ladder should be onsidered. The solidity ratio for setion S-10 is equal to:, f,1.10 +, +, f ϕ10 = = (10) The fore oeffiients for setions omposed of flat sided, sub ritial irular members are given by: f,0, f,10 = 1.76 C 1 1 C ϕ10 + ϕ 10 =.71 (11) = C 1 C + C ϕ = 1.55 ( ϕ ) ( ) f,0,, where: C 1 is equal to 1.9 and C is 1,4 for the triangular strutures. The value of the overall normal fore oeffiient f,s,0,10 that is appliable to the strutural framework of triangular setion S-10 omposed of both flat-sided and irular setions should be alulated as: f, S,0,10 f,0, f,10 f,0,,10 ( f,1.10 +, f) ( s, ) (,1.10 +, ) ( s, ) = + + =.1 (1) The wind inidene fator K Θ = 1.0 for Θ 1 = 0, thus the wind fore oeffiient of struture setion S-10 is equal to: = K = (13) f, S,10 Θ f, S,0,10.1 Let us fous now on the part of Equation (9) that desribes partiipation of the feeder-limbing ladder in overall oeffiient wind fore. Redution fator that takes into aount the shielding of the omponent by the struture itself for the triangular ross setion of the tower and anillaries plaed internally to the struture K is equal to 0.8. Overall normal drag oeffiient appropriate for the item and its Reynolds number for flat-sided setions given in [1] is f,,0 =.0 (14) It s neessary to underline that in this odified approah the ladder with all its elements suh as ables, feeders, steps, aess rails, et. is treated as a one solid omponent. Taking it into our onsideration, an analyzed anillary should be treated as a one, flatsided element as given above. In the analysis of the aerodynami resistane of the ladder, ψ denotes an angle of wind inidene to the longitudinal axis of a linear member. For the purpose of these alulations, the angle ψ takes the most adverse value 90. The onlusions given above lead us to the determination of the wind fore oeffiient of the anillaries in setion S-10: f,,10 = K f,,0 sin ψ = 1.6 (15) During the alulation proess, we obtained all the parameters that allow us to determine the total wind fore oeffiient in the diretion of the wind over setion S-10: = + = (16) f,10 f, S,10 f,, The results for other setions are olleted in Table 4 that ontains all the parameters desribed in the previous onsiderations. 9

6 Jaek Szafran Table 4. The results of the alulations for the general method Setion φ f,0f f,0, f,s,0 f, f S S S S S S S S S S S S S S Total wind fore oeffiient method for speial ases The total wind fore oeffiient in this analytial approah may be determined aording to [1] from expression as follows 3 Θ1 3 Θ1 f,10 = 1 eos + esin 4 4 (17) The main differene between the presented methods (the general and one for speial ases) is the treatment of the setions as general. In 4.1., there is an assessment that for obtaining aerodynami resistane we need to take into onsideration only fae 1 and the feeder-limbing ladder behind. Here faes 1, and 3 are inluded in alulations as well as the fat that there are some shielding effets expressed in the analysis by a shielding fator. ording to standard [1], for setion S-10 it should be alulated as follows: 1.89 S,1.10 +, ηf,10 = = η = η + + ( 0.83 ) e,10 F,10 F,1.10,1.10 ( ) S + = 0.71 (18) To obtain the total fore oeffiient we should alulate fators for every fae, treated here as a single frame. The results and formulae are olleted in Table 5. It should be explained that: f,s1.10 is the fore oeffiient appropriate for fae 1 in setion S-10, f,1,10 is the wind fore oeffiient appropriate for fae 1 in setion S-10 for the anillary items are not treated as strutural members. For irular members f,1,10 they are equal to 0.5 and for flat-sided.0 respetively. In Equation (17) there are 1,e,,e fators that denote effetive wind fore oeffiients given for triangular strutures by following: 0.67 ηe 1 e,10 = ( ).13 KΘ = 0.67 ηe e,10 =.10 + ( ) KΘ =.4 (19) Finally, the total wind fore oeffiient given by Equation (17) takes the value of f,10 1 e,10.13 = = (0) In Table 6 the results of f for other setions of the analyzed tower are olleted. 5. Comparison of the results Comparison of the results obtained through two independent standard methods is presented in the graphial form in Figure 3. 10

7 NLYTICL DETERMINTION OF ERODYNMIC RESISTNCE OF THE SKELETL TELECOMMUNICTION TOWERS Table 5. The alulation parameters Fae Coeffiient Formula Result ( ) 1.8 f, f,1.10 f,,1.10 ( ϕ1.10 ) f, f, ϕ f, S f,1.10,1.10 f, f,1.10 f,,1.10 S S 1.10 f + S,1.10 f, S1.10 f, 1.10 S +, f, + f, 1.10, S + S ( ) 1.8 f, f,.10 f,,.10 ( ϕ.10 ) f, f, ϕ (3) f, S f,.10,.10 f, f,.10 f,,.10 S S.10 f, S.10 S S, Table 6. Total wind fore oeffiients obtained via method for speial ases S-1 S- S-3 S-4 S-5 S-6 S-7 S-8 S-9 S-10 S-11 S-1 S-13 S Conlusions Fig. 3. Comparison of the results Performed alulations yield the following onlusions: in Figure 3 we observe that the hoie of the presented method of alulations has a large impat on the value of the f oeffiient for individual setions of the analyzed tower struture; analyses of towers of high omplexity with the ombination of flat-sided and irular-setion members, ontaining feeders and ladders, antennas and their support strutures, should be based on the method for speial ases; formulae adopted in this method have been introdued into standard [1] to over any ombination of flat-sided or irular setion members along with a shielding fator; determination of the wind drag oeffiient with respet to the inorret alulation approah an lead to the overestimation of the mean wind value, whih has ruial impat on the results of analyses of the arrying apaities of existing and new strutures; the results that have been obtained aording to the method for speial ases orrelate well with the ones presented in publiation [3]; 11

8 Jaek Szafran onsidering aerodynami behavior of tower strutures, it is worth underlining that the fullsale measurements (given by Nielsen in [7]) showed that the wind resistane of lattie towers should be signifiantly lower than the estimated ones onduted aording to standards [1, 4]. Referenes [1] Euroode 3: Design of steel strutures. Towers, masts and himneys. Tower and masts. European Committee for Standardization, Brussels, 008. [] Rykaluk K.: Steel strutures. Chimneys, tower, masts. Ofiyna Wydawniza Politehniki Wroławskiej, Wroław 004. [3] Smith B.W.: Communiation strutures. Thomas Telford Publishing, London 007. [4] PN-B-0304:00: Steel strutures. Towers and masts. Design and Exeution. Polski Komitet Normalizayjny, Warszawa 00. [5] Euroode 1: tions on strutures. General ations. Part 1-4: Wind ations. European Committee for Standardization, Brussels, 004. [6] Smith B.W.: Comparison of the Draft Code of Pratie for lattie Towers with wind load measurements on a omplete model lattie tower. Building Researh Establishment, [7] Nielsen M.G.: Wind tunnel tests. Meeting of ISS Working Group 4: Tower and masts. Oslo 001. Jaek Szafran nalityzne określenie oporu aerodynamiznego kratowyh wież telekomunikayjnyh 1. Wstęp Wprowadzenie w ostatnim zasie do polskih unormowań prawnyh europejskih norm projektowyh spowodowało duże zmiany w określaniu nośnośi poszzególnyh obiektów budowlanyh. naliza nośnośi obiektów istniejąyh w opariu o aktualne przepisy w dalszym iągu nastręza problemów projektantom i rzezoznawom budowlanym. Wynika to z faktu, że zmianie uległy nie tylko konepje określania nośnośi poszzególnyh elementów konstrukji, ale także sposób formułowania ih obiążenia. W sposób szzególny dotyzy to analizy przydatnośi do dalszego użytkowania obiektów zaprojektowanyh kilka lub kilkanaśie lat temu na podstawie zupełnie innyh wymagań i proedur normowyh. Typowym przykładem takiej sytuaji mogą być stalowe konstrukje wież telekomunikayjnyh. Niniejsze opraowanie w ałośi poświęone jest wyznazaniu oporu aerodynamiznego konstrukji wieżowyh na podstawie formuł zawartyh w normie [1].. Opis problemu W sensie ogólnym współzynnik oporu aerodynamiznego (zy też współzynnik oddziaływania wiatru) zależy wg [] od: kształtu przekroju poprzeznego prętów konstrukji kratowej, ih smukłośi, kształtu przekroju poziomego wieży oraz kierunku działania wiatru względem śian wieży. W przypadku wież telekomunikayjnyh, dla któryh koniezne jest wyznazenie oporu aerodynamiznego, problem wydaje się być bardziej złożony. Dla obiektów wieżowyh wykonanyh z różnego rodzaju profili, obiążonyh drabinami kablowymi i włazowymi, antenami i ih konstrukjami wsporzymi prawidłowe oszaowanie oporu aerodynamiznego jest zadaniem wymagająym. Należy uwzględnić interakje elementów konstrukyjnyh i elementów wyposażenia, ih wzajemne przesłanianie, a także różne modele opływu elementów o krawędziah ostryh lub okrągłyh [3]. Najprostszą formułą opisująą opór aerodynamizny jest (1). nalityzne określenie współzynnika oporu aerodynamiznego według normy [4], opisanego dokładnie w pozyji [], było stosunkowo łatwą proedurą oblizeniową. Współzynnik wypełnienia był zdefiniowany, tak jak to zaprezentowano w równaniu (). Dla stalowyh wież o okrągłyh krawężnikah i elementah skratowania wykonanyh z kątowników współzynnik oporu aerodynamiznego jest zdefiniowany w (3) na podstawie normy [4]. Średnie obiążenie wiatrem zdefiniowane według normy europejskiej [4] opisuje zależność (4). 1

9 NLYTICL DETERMINTION OF ERODYNMIC RESISTNCE OF THE SKELETL TELECOMMUNICTION TOWERS Obiążenie odinkowe na kierunku działająego wiatru określone jest natomiast jako (5). Jednym z parametrów niezbędnym do określenia wielkośi oddziaływania wiatrem jest właśnie współzynnik oporu aerodynamiznego, którego wartość determinuje wielkość tego rodzaju obiążenia. 3. nalizowana konstrukja naliza została przeprowadzona na podstawie istniejąej wieży telekomunikayjnej o wysokośi 84 metrów zilustrowanej na rysunku 1. Konstrukja podzielona jest na 14 segmentów. Shematem statyznym trzonu jest wspornik kratowy utwierdzony w grunie poprzez fundamenty. Pionowe elementy nośne (krawężniki) zostały wykonane z okrągłyh prętów pełnyh, natomiast elementy skratowania z gorąowalowanyh kątowników. Drabina kablowo-włazowa usytuowana jest entralnie wewnątrz trzonu wieży. Wykonana jest z eowników zimnogiętyh połązonyh szzeblami z prętów okrągłyh po jednej stronie i wspornikami drabiny kablowej po stronie drugiej, tak jak zostało to zaprezentowane na rysunku. W tabeli 1 przedstawiono zestawienie poszzególnyh elementów konstrukji wraz z ih polami powierzhni nawietrznej dla kąta nataria wiatru równego 0 (powierzhnie płaskie i okrągłe). Całkowita powierzhnia nawietrzna konstrukji normalna do śiany 1 wieży wyrażona jest przez zapis (6). Tabela przedstawia zestawienie elementów drabiny kablowo- -włazowej. Całkowitą powierzhnię nawietrzną tego ustroju konstrukyjnego wyraża wzór (7). 4. Oblizenia oporu aerodynamiznego Wszystkie kalkulaje oparte są na jednym z najbardziej istotnyh parametrów w teorii oporu aerodynamiznego konstrukji szkieletowyh współzynniku wypełnienia (8). Tabela 3 prezentuje pola powierzhni ałkowityh poszzególnyh segmentów wieży. Wykorzystują normę [1], a także rekomendaje zawarte w [3], oblizenia zostały wykonane przy zastosowaniu dwóh niezależnyh podejść, które zależą od rodzaju konstrukji: symetryznej z ogranizonymi elementami wyposażenia lub z pełnymi elementami wyposażenia, tj. drabiny, pomosty itp. W elu prezentaji wyników, a przede wszystkim algorytmu oblizeniowego wybrano segment 10 wieży Całkowity współzynnik oporu aerodynamiznego metoda ogólna Norma [1] określa ałkowity współzynnik oporu na kierunku działająego wiatru na poszzególną sekję konstrukji jako (9). Dla segmentu 10 wieży współzynnik wypełnienia zdefiniowany jest jako (10). Współzynniki siły oddziaływania dla elementów płaskih i okrągłyh opisują zależnośi (11). Wartość ałkowitego współzynnika oporu dla sekji S-10, złożonego z elementów płaskih i okrągłyh powinno być określone jako (1). Współzynnik nataria wiatru K Θ = 1,0 dla kąta nataria Θ 1 = 0. W równaniu (9) odnajdziemy udział drabiny włazowo-kablowej w ałkowitym współzynniku oporu aerodynamiznego. Wartość tego parametru wskazuje wzór (14). Warto w tym miejsu podkreślić, że w tym podejśiu normowym drabina wraz ze wszystkimi jej elementami tj.: kablami, stopniami, szynami systemu bezpiezeństwa itp. są traktowane jako jeden komponent. Powyższe założenie prowadzi do określenia ałkowitego współzynnika dla elementów wyposażenia jako (15). Zatem dla segmentu S-10 rozpatrywanej konstrukji otrzymujemy wartość współzynnika aerodynamiznego jako (16). Rezultaty dla pozostałyh sekji wieży zostały zebrane i przedstawione w tabeli Całkowity współzynnik oporu aerodynamiznego metoda dla przypadków spejalnyh Zależność opisująą ałkowity współzynnik oporu aerodynamiznego zgodnie z [1] przedstawiona została w (17). Główną różnią pomiędzy prezentowanymi w niniejszym opraowaniu metodami (ogólną i dla przypadków spejalnyh) jest traktowanie segmentu konstrukji wieżowej jako ałośi bez podziału na konstrukję i elementy wyposażenia w drugim podejśiu oblizeniowym. W metodzie dla przypadków spejalnyh bierzemy pod uwagę opróz śiany 1 (metoda ogólna) również śiany i 3 opisane na rysunku. Uwzględniamy poza tym efekt przesłaniania elementów konstrukji używają w analizie współzynnik przesłaniania zdefiniowany w (18). W tabeli 5 przedstawiono wszystkie parametry oblizeniowe niezbędne do określenia oporu aerodynamiznego. Dla segmentu S-10 wartość współzynnika siły opisana jest w (0). W tabeli 6 zebrano wyniki dla pozostałyh segmentów wieży. 5. Porównanie wyników Porównanie wyników uzyskanyh na podstawie dwóh niezależnyh proedur normowyh zaprezentowano w formie grafiznej na rysunku Wnioski Przeprowadzone analizy pozwalają na przedstawienie następująyh wniosków: 13

10 Jaek Szafran na rysunku 3 możemy zaobserwować, że wybór metody oblizeń w znaznym stopniu determinuje uzyskane wyniki współzynnika f, analizy konstrukji wieżowyh o znaznym stopniu złożonośi, z elementami konstrukyjnymi wykonanymi z elementów okrągłyh i płaskih, wyposażonymi w kable, drabiny włazowo kablowe, anteny i ih konstrukje wsporze powinny zostać przeprowadzone zgodnie z założeniami metody dla przypadków spejalnyh, formuły oblizeniowe wyżej wymienionej metody wprowadzono w normie [1], określenie współzynnika oporu aerodynamiznego konstrukji wieżowej na podstawie niepoprawnej metody oblizeniowej może prowadzić do przeszaowania wielkośi oddziaływania wiatrem, o w przypadku analiz nośnośi istniejąyh konstrukji może prowadzić do błędnyh wniosków i zaleeń, rezultaty w przedstawione w analizah otrzymano stosują metodę dla przypadków spejalnyh i korelują z wynikami zaprezentowanymi w [3], rozważają aerodynamikę konstrukji wieżowyh, warto podkreślić, że pomiary dla konstrukji w skali naturalnej [7] udowodniły, że opór aerodynamizny wieżowyh konstrukji kratowyh może być znaząo mniejszy niż ten określony na podstawie norm [1, 4]. 14