Statistical evaluation of the wind loads as proposed by the Turkish standard TS 498

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1 146 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Statstcal evaluaton of the wnd loads as proposed by the Turksh stdard TS 498 *Fath Kürşat FIRAT 1, M. Semh YÜCEMEN 1 Aksaray Ünverstes, Mühendslk Fakültes, İnşaat Mühendslğ Bölümü, Aksaray, TÜRKİYE Orta Doğu Teknk Ünverstes, Mühendslk Fakültes, İnşaat Mühendslğ Bölümü, Ankara, TÜRKİYE ABSTRACT Keywords Wnd Load, Statstcs, Uncerttes, TS 498. In ths study, wnd loads resultng from wnd speeds are examned by usng statstcal methods. For ths purpose, the wnd speed data are collected from dfferent regons of Turkey. In addton to these data, the publshed data d nformaton n the nternatonal lteraturee are also taken nto account n comparng the wnd load statstcs. The ratos of me to nomnal load values are determned for calbraton purposes. Whle the me values of wnd loads are computed by consderng the underlyng uncerttes, the nomnal values of wnd loads are taken drectly from the Turksh stdard TS 498 (Desgn Loads for Buldngs). Although some of the loads actng on a structure, such as dead d lve loads are ndependent of the geographcal locaton of the structure, envronmental loads lke wnd load are hghly dependent on the regonal locaton of the structure. In order to determne the wnd load statstcs to represent the whole Turkey, t s requred to select some reference regons. In ths study, eleven regons are chosen. At the end of the alyses, t s observed that although n some regons the values gven n TS 498 are suffcent, they are overestmated n some other regons. In addton, t s necessary that the calculaton method of the wnd load proposed by TS 498 should be revsed d also the nomnal values of wnd loads should be modfed. Türk stdardı TS 498 de önerlen rüzgâr yüklernn statstksel olarak değerlendrlmes ÖZET Anahtar Kelmeler Rüzgar Yükü, İstatstk, Belrszlk, TS 498 Bu çalışmada, rüzgar hızınd elde edlen rüzgar yükler statstksel yöntemler kullılarak ncelenmştr. Bu amaçla Türkye nn değşk şehrler çn rüzgar hızı verler toplmıştır. Bu verlere laveten uluslararası kaynaklard elde edlen ver ve blgler de rüzgar yükü statstksel değerlernn belrlenmesndee kullılmıştır. Kalbrasyon amacıyla, gerçek ortalama değerlern lgl stdartlarda önerlen nomnal değerlere orı hesaplmıştır. Rüzgar yükünün gerçek ortalama değerler bazı belrszlk kaynaklarının da dkkate alınmasıyla hesaplırken, rüzgar yükünün nomnal değerler doğrud Türk stdardı TS 498 den (Yapı Elemlarının Boyutldırılmasında Alınacak Yüklern Hesap Değerler) alınmıştır. Ölü ve hareketl yükler gb bazı yükler yapının çersnde bulunduğu coğrafyad bağımsız olmalarına rağmen, rüzgâr yükü gb çevresel yükler yapının coğraf bölgesne oldukça bağımlıdır. Bund dolayı bütün Türkye y ysıtması beklenen rüzgâr yükü statstksel değerlernn hesaplmasında bazı refers bölgelern seçlmes gerekmektedr. Bu çalışmada on br şehr dkkate alınmıştır. Analzlern sonucunda TS 498 de bazı şehrler çn verlen değerlern yeterl olduğu, bazı şehrler çn verlen değerlern se aşırı yüksek olduğu sonucuna ulaşılmıştır. Bunlara ek olarak TS 498 de önerlen rüzgar yükü hesap yöntemnn revze edlmesnn gerekl olduğu ve sırad yapılar çn verlen rüzgar yükü nomnal değerlernn değştrlmes gerektğ kaatne varılmıştır. * Sorumlu yazar (Correspondng author) e-posta: fkfrat@gmal.com

2 147 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Introducton Ω = + + (3) In cvl engneerng, structural desgn codes specfy mnmum safety requrements d for ths reason desgn specfcatons provde regular expressons for engneers n order to solve general practce orented problems. For my years, the queston of how safe s safe enough s asked by researchers applyng safety theory to codfed desgn. In order to fnd a consderable soluton for ths queston, researchers are stll workng. There s always a probablty of falure for structures. Accordngly, complete safety cnot be acheved. On the other hd, upgradng the safety level causes economcal problems, therefore there must be a reasonable balce between safety d cost. In order to reach more mengful desgn codes, code optmzaton based on total cost s necessary. An optmzed load code mes that recommended loads gve the optmum soluton for the expected desgns. On the other hd, the determnaton of loads d load effects on the structures ntroduce a set of uncerttes. Here, the wnd loads proposed by the Turksh Code TS 498 [1] are evaluated takng nto consderaton the assocated uncerttes. The assessment of wnd load d relablty of structures under the wnd loads has been recevng growng nterest durng the last few decades. However, a number of sgnfct ssues stll rem unsolved []. Structural engneers should make cert that the structures subjected to wnd load wll be suffcent durng ts expected lfe wth regard to both servceablty d structural safety. Accordngly, the nformaton on the behavor of the structures under the wnd acton s requred n order to realze the relaton between the wnd envronment d the wnd acton [3]. Any type of structural load becomes mengful f t leads to a load effect. Assumng a lnear relatonshp between a load d ts effect, the followng formula gves the load effect, S, on the bass of ts correspondng structural load, L [4,5]: S = C N L (1) where: S : load effect, C : nfluence coeffcent, N : modelng parameter, L : structural load. It should be noted that n ths formula, the parameters on the rght hd sde of Eq.1,.e. C, N, d L are assumed to be statstcally ndependent. Accordng to the FOSM method (Frst Order Second Moment Method), the me d coeffcent of varaton for y load type c be computed from the followng formulas, respectvely: S = C N L () S C N L where: a bar ( ) over a rdom varable denotes the me d s the coeffcent of varaton. In the followng sectons, structural load effects resultng from the wnd load wll be evaluated. The publshed data n the lterature d the local data compled n Turkey wll consttute the m sources of nformaton n the evaluaton of the wnd load statstcs. For calbraton purposes, the rato of me to nomnal load values wll be determned. The nomnal values of loads wll be obted from TS 498. It s to be noted that although the dead d lve loads actng on a structure are ndependent of the geographcal locaton of the structure, envronmental loads, such as snow, wnd d earthquake loads are hghly dependent on the locaton of the structure. Accordngly, for the assessment of statstcs of envronmental loads, dfferent ctes, whch wll represent the whole Turkey, are chosen. In ths selecton, ctes wth the hghest crtcal envronmental loads are gven prorty. Also, ctes wth larger populatons are preferred. Another crteron n ths selecton s that these ctes are to be located n geographcally dfferent regons of Turkey. For the wnd speed, data are obted from the meteorologcal statons that are n the centers of these ctes. The locatons of these ctes are shown n the followng map.. Wnd Load Wnd loads are derved by usng the statstcal data based on wnd speed, mass densty of ar, pressure coeffcent, parameters related to wnd speed d exposure, d a gust factor that ncorporates the effects of short gusts d the dynamc response of the structure. The wnd load actng on a structure c be determned from the wnd speed by usng the stdard hydrodynamc relatonshp, whch c be rewrtten for partcular structures or surfaces of structures as follows [6]: W = c.c p.e z.g. V ( 4) where: W: wnd load, c: a constt related to mass densty of ar, C p: pressure coeffcent, E z : exposure coeffcent, G: gust factor, V: wnd speed.the pressure factor, C p, depends on the geometry d shape of the structure. It s the rato of the pressure at relevt surface of the structure to the dynamc pressure of the wnd [7]. The exposure coeffcent, E z, depends on the actual topographcal condtons (e.g. urb area, enclosed valleys, slopes, hlls, open country d also the presence of constructons near the structure). The gust factor s assocated wth the turbulence of the wnd d the dynamc nteracton between the structure d wnd.

3 148 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Fgure 1 The map showng the locatons of selected ctes Snce the velocty parameter appears wth ts square n Eq. 4, t s a partcularly mportt parameter n comparson wth the other parameters. The overall uncertty n wnd load s also affected by uncerttes n the estmaton of the pressure coeffcent, the exposure factor d the gust factor..1 Analyss of Wnd Speed Most of the statstcal data avalable related to wnd load are obted from the monthly maxmum or nual maxmum wnd speeds; the pressure coeffcents d gust factors are consstent wth ths maxmum wnd speeds. The wnd speed chges wth lattude, longtude d alttude from the sea level d tme [8]. In ths study, snce t s mpractcal to perform relablty alyss separately for each d every locaton where wnd speed data s avalable, t s decded to collect ths necessary data for twelve dfferent locatons n Turkey. Hence, Ankara, İzmr, Bursa, Antalya, Gaztep, Samsun, Malatya, Erznc, Çakkale, Hakkar, Göztepe/İstbul d Şle/İstbul are selected n order to carry out the wnd load alyss for Turkey. The requred data on maxmum yearly d maxmum daly wnd speeds are taken from the Turksh Meteorologcal Department (DMI). The wnd speed s measured at 10 meters above the ground level n these locatons [9]. The relevt statstcal parameters are computed for the locatons lsted above. Type I d Type II extreme value dstrbutons are the most common d approprate probablty dstrbutons for wnd speeds [4, 7]. Smu d Scl [7] ndcated that f the wnd speed data are collected n locatons where extraordnary wnd speeds are very rare, the use of Type I dstrbuton s more sutable as a probablstc model. Fırat [3], Yücemen d Gülk [10] d Kömürcü [11] used the Type I dstrbuton for yearly maxmum wnd speed, daly maxmum wnd speed d lfetme maxmum wnd speed to descrbe the data that were recorded n Turkey. Because unusual wnds are not seen frequently n Turkey, Type I dstrbuton c be used to descrbe the wnd speed data. Also the data alyss wth BestFt d Mntab computer programs showed that Type I dstrbuton fts data satsfactorly. For Lognormal, Normal, Extreme-value (Type I), Gamma, Webull, Raylegh probablty dstrbutons, the Ch-Square d Kolmogorov- Smrnov tests results, whch were performed by usng computer programs mentoned above, are gven n Table 1. In ths table, the p-value s a short form for probablty value d s other way of sayng the sgnfcce value. It refers to the probablty of obtng a test statstc at least as extreme as the one that was actually observed, assumng that the assumed dstrbuton s true. In ths study, daly maxmum wnd speed, V apt, d nual maxmum wnd speed, V, wll be used, whch are respectvely necessary for the calculaton of the daly maxmum wnd d the yearly maxmum wnd loads. In addton to these two parameters, maxmum wnd speed, V, d nomnal wnd speed, V, are needed. V, whch s the -year maxmum wnd speed, s derved from the nual maxmum wnd speed, V, d V s obted from TS

4 149 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Snce the data for the nual maxmum wnd speed fts the Type I dstrbuton, maxmum wnd speed could also be descrbed by a Type I dstrbuton, d the me value d the basc varablty of the maxmum wnd speed are computed from the me value d varablty of V based on the followng equatons. Also, the predcton error due to nsuffcent samplng, 1, s defned by usng these computed values d nherent varablty of nual maxmum wnd speed, accordng to Eq. 7 [4]. 6 V = V 1 + δ V ln (5) π δ = V δ / V (6) V 3.8V V δ ( nv ) V 1 = (7) δ V where: n s the sample sze. It s to be noted that, as n ncreases, 1 decreases. Dündar et al. [9] ndcated that due to systematc errors d wrong calbraton of devces assocated wth measurement of wnd speed, uncertty of 0.05 should be ncluded. In addton to the uncerttes nvolved n the recorded data, conversons ncludng modelng, features of clmatc parameters d roughness parameters of surface also create addtonal uncerttes. Therefore, addtonal uncertty of 0.0 s assumed to account for these factors [4, 11]. The me values d varabltes of V apt, V d V for Ankara, İzmr, Bursa, Antalya, Gaztep, Samsun, Malatya, Erznc, Çakkale, Hakkar, Göztepe/İstbul d Şle/İstbul are presented n Table. Based on TS 498, the nomnal wnd speeds, V, for these locatons are also shown n Table. probablstc model for the wnd speed data. On the other hd, the wnd load may not have the same dstrbuton of the wnd speed. Ellngwood et al. [4] used Monte Carlo technques assumng that C p, E z d G were descrbed by normal dstrbutons. As a result, t was found out that wnd load, W, could be descrbed by a Type I dstrbuton over the rge of the dstrbuton above ts 90 th percentle. The parameters of the Type I largest extreme value dstrbuton c be calculated through the followng relatonshps [6]: π α = 6σ (8) γ u = µ (9) α where,γ =0.577s the Euler s constt. Ellngwood et al. [4] d Kömürcü [11] estmated the me values of the parameters C p, E z d G as 0.80, 1.61 d 0.45, respectvely; d also qutfed the varabltes of these parameters as 0.1, 0.11 d These varablty values are sutable for use n the code calbraton related to wnd load [6]. Ghocel d Lungu [1] proposed the constt c to be equal to 0.065, d Ellngwood et al. [4] qutfed the varablty of ths parameter as These values wll also be used n ths study for all of the locatons consdered. The me d total varablty of the maxmum wnd load are to be computed by utlzng FOSM method (Eqs. d 3) yeldng to the followng equatons W = c.cp. E z. G. V (10). Maxmum, Yearly Maxmum d Daly Maxmum Wnd Loads As t s stated before, f the wnd speed data are collected n locatons where extraordnary wnd speeds are very rare, the use of Type I dstrbuton s more sutable as the probablstc model; besdes the data alyss wth BestFt d Mntab computer programs showed that Type I dstrbuton fts the data satsfactorly. Accordngly, Type I dstrbuton s adopted as the Ω W = ΩC + ΩC + Ω p G + Ω E + Ω z V (11) The statstcs related to the yearly maxmum wnd load, W, d daly maxmum wnd load, W apt, c be calculated n a smlar way. The me values d total uncerttes of the maxmum, yearly maxmum d daly maxmum wnd loads for relevt locatons are presented n Table 3. In addton, me to nomnal wnd load ratos are shown n Table 4.

5 1 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Table 1. The Ch-Square (χ ) d Kolmogorov- Smrnov (K-S) test results for the nual wnd speeds recorded at dfferent locatons n Turkey Annual wnd speed Prob. Dst. Test Prob. Test χ p-value K-S Dst. χ p-value K-S Ankara Malatya Ext. value Normal Normal Webull Raylegh Raylegh Webull Ext. value Lognormal Erznc İzmr Lognormal Normal Ext. value Webull Gamma Ext value Webull Bursa Raylegh Ext value Normal x Raylegh Çakkale Webull Normal Lognormal Webull Normal Ext. value Antalya Hakkar Lognormal Ext. value Webull Lognormal Raylegh Normal Ext value Raylegh Gaztep Göztepe/İstbul Ext. value Normal Webull Ext. value Raylegh Şle/İstbul Lognormal Ext. value Normal Webull Samsun Normal Normal Gamma Raylegh Lognormal Ext. value Note 1: At the sgnfcce level α=5%, 1-α percentle value of the Ch-Square test, χ 0.955=11.1 for Ankara, İzmr, Bursa, Antalya, Gaztep, Erznc, Hakkar d Göztepe; d χ 0.955=1.6 for Samsun, Malatya, Şle d Bursa. Note : The crtcal value of K-S test at the 5% sgnfcce level s: D =0.19.

6 Locaton 151 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): Table Me values d coeffcents of varaton of wnd speeds for dfferent locatons V apt (m/s) Ω V apt Parameter V (m/s) Ω V V (m/s) δ V 1 Ω V Ankara İzmr Bursa Antalya Gaztep Samsun Malatya Erznc Çakkale Hakkar Göztepe/İstbul Şle/ İstbul Locaton Table 3 Me values d the total uncerttes of wnd loads for dfferent locatons n Turkey W (kn/m ) apt Parameter W (kn/m ) W (kn/m ) W (kn/m ) Ω Wapt Ω W V (m/s) Ankara İzmr Bursa Antalya Gaztep Samsun Malatya Erznc Çakkale Hakkar Göztepe/İstbul Şle/ İstbul Ω W 3. Conclusons In ths study, wnd loads are alyzed by usng statstcal methods. To accomplsh ths purpose, the wnd speed data are collected from dfferent regons of Turkey. After conductng a set of statstcal alyses on wnd speed data, the me values of wnd loads are computed by takng nto consderaton the dfferent uncertty sources. In addton to the computed values, the publshed data d nformaton avalable n the foregn lterature are taken nto consderaton n comparng the wnd load statstcs. The nomnal values of wnd loads are drectly taken from the Turksh Stdard TS 498. The ratos of me to nomnal load values are computed for the purpose of comparng the geographcally varyng wnd loads. For the ctes consdered n ths study, the me to nomnal ratos rge from 0.09 to 0.3 for arbtrary pont-n-tme wnd load d also from 0.35 to 0.8 for maxmum wnd load. As t s seen from these values, the nomnal wnd load values n TS 498 stay on the safe sde for all locatons. However, the wnd load values proposed by TS 498 are overestmated n some regons. The total uncerttes n arbtrary pont-n-tme wnd loads accordng to the ctes consdered n ths study are observed to vary from 0.60 to In addton, the total uncerttes n maxmum wnd loads chge wthn a rge of 0.7 d These uncertty values ndcate that the varabltes n the wnd load are very hgh. It s also noted that arbtrary pont-n-tme wnd loads show sgnfctly more

7 15 Fırat ve Yücemen, Ercyes Ünverstes Fen Blmler Ensttüsü Dergs, 8(): varaton th the maxmum wnd loads. Besdes, wnd load shows varablty n the dfferent areas of a cty; n other words, the wnd load effect on a structure located n a valley s not the same on a structure located on a hll sde due to dfferent wnd speeds. Therefore, for specal areas d structures, the data on daly maxmum wnd speeds d nual maxmum wnd speeds c be recorded; then the method proposed n ths study c be used n order to determne the more approprate wnd loads. Table 4 Me to nomnal wnd load ratos d assocated total uncerttes for dfferent locatons Locaton W / apt W (kn/m ) Ω W apt Parameter W / W (kn/m ) W Ω W / W (kn/m ) Ankara İzmr Bursa Antalya Gaztep Samsun Malatya Erznc Çakkale Hakkar Göztepe/İstbul Şle/ İstbul Ω W References 1. Türk Stdartları, Yapı Elemlarının Boyutldırılmasında Alınacak Yüklern Hesap Değerler (TS 498 ), Türk Stdartları Ensttüsü, Ankara, Mncarell, F., Goffre, M., Grgoru, M. d Smu, E., Estmates of Extreme Wnd Effects d Wnd Load Factors: Influence of Knowledge Uncerttes, Probablstc Engneerng Mechcs, Vol. 16, pp , Fırat F.K., Development of Load d Resstce Factors for Renforced Concrete Structures n Turkey, The Graduate School of Natural d Appled Scences, Mddle East Techncal Unversty, Doctorate Thess, Ankara, Ellngwood, B.R., Galambos, T.V., MacGregor, J.G. d Cornell, C.A., Development of a Probablty Based Load Crteron for Amerc Natonal Stdards A58, NPS Specal Publcaton 577, Fırat, F.K., TS 498 de Önerlen Çatı Kar Yüklernn İstatstksel Yöntemlerle Hesapl Çatı Kar Yükleryle Karşılaştırılması, Fırat Ünverstes, Mühendslk Blmler Dergs, Clt:1, Sayı:, , Melchers R.E., Structural Relablty Analyss d Predcton, John Wley & Sons, Inc., Chchester, Engld, Smu E. d Scal, R.H., Wnd Effects on Structures, 1st ed., John Wley, New York, Şahn, A.D., Türkye Rüzgarlarının Al Zam Modellemes, Ph. D. Thess, İTÜ, İstbul, Dündar C., Türkye Rüzgar Atlası, T.C. Başbaklık Devlet Meteoroloj Genel Müdürlüğü ve Enerj Tab Kaynaklar Baklığı Elektrk İsler Etüt İdares Genel Müdürlüğü, Ankara, Yücemen, M.S. d Gülk, P., Betonarme Yapılar İçn Yük ve Dayım Katsayılarının Belrlenmes, 10. Teknk Kongre, Clt, İnşaat Mühendsler Odası, s , Kömürcü, A.M., A Probablstc Assessment of Load d Resstce Factors for Renforced Concrete Structures Consderng the Desgn Practce n Turkey, M. Sc. Thess, Department of Cvl Engneerng, METU, Ankara, Ghocel, D. d Lungu, D., Wnd, Snow d Temperature Effects on Structures Based On Probablty, Abacus Press, Turbrdge Wells, Kent, 1974.