Wind-induced vibration: a serviceability study

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1 Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 Porto, Portugl, 3 June - 2 July 214 A. Cunh, E. Cetno, P. Ribeiro, G. Müller (eds.) ISSN: ; ISBN: Wind-induced ibrtion: sericebility study Adrián Pozos-Estrd 1, Isc F. Lim Cstillo 1, Roberto Gómez Mrtínez 1, J. Alberto Escobr Sánchez 1 1 Instituto de Ingenierí, Uniersidd Ncionl Autónom de México, Circuito Escolr s/n, Ciudd Uniersitri, Delegción Coyocán, México D.F., C.P. 451 emil: APozosE@iingen.unm.mx, ILimC@iingen.unm.mx, RGomezM@iingen.unm.mx, JEscobrS@iingen.unm.mx ABSTRACT: The excessie ibrtion in building due to long-wind nd cross-wind excittions cn ffect the helth nd/or interrupt the ctiities of the inhbitnts. Perception cures, in terms of men pek ccelertion or stndrd deition of ccelertion he been deeloped nd dopted in codes s sericebility criteri for designing buildings. Some of these criteri do not incorporte the uncertinty in structurl properties nd wind chrcteristics. The min purpose of this study is to crry out comprison between some of the mjor sericebility criteri for designing buildings nd to estimte the relibility leel for structures designed ccording to such perception cures, incorporting the uncertinty in structurl properties, wind chrcteristics, nd in the humn perception of motion. For the nlyses, the probbility distribution of the pek ccelertion response proposed by Denport is dopted, nd the rndom ibrtion pproch is employed to determine the mximum response of structure. Results of the nlysis indicte tht the relibility (the probbility tht the wind-induced ibrtion of designed structure is not perceied within serice period) ssocited with structures designed ccording to different sericebility criteri is not the sme, een if the structures re designed for the sme perception leel. KEY WORDS: Wind; Vibrtion; Accelertion; Perception Cures; Relibility. 1 INTRODUCTION The design of tll buildings includes the considertion of n ultimte limit stte nd sericebility limit stte. Een if the ultimte limit stte is stisfied, tll buildings cn experience excessie ibrtion under wind loding. This excessie ibrtion cn deteriorte helth of the inhbitnts of the buildings, disrupt the ctiities or cuse discomfort. Some studies on the ccelertion limits for humn comfort leels were crried out in the 7 s by Vn Koten, Chen nd Chng [2, 3, 4]. These studies relted ccelertion leels with subjectie descriptors. From these studies, it is possible to identify leels of perception of ccelertion t bout 15 millig. To tke into ccount the excessie ibrtion during the design stge, codes nd/or stndrds propose the use of criteri to limit the excessie wind-induced motion [5, 6, 7]. The criterion proposed by ISO1137 [5] suggests the use of the men pek ccelertion, s function of the frequency of ibrtion, to limit the discomfort leel nd disruption of tsks of inhbitnts of buildings. The NBCC [6] lso employs the men pek ccelertion s perception limit; this criterion is independent of the frequency of ibrtion. The AIJ [7] suggests the use of perception cures with different perception leels; this criterion is frequency dependent nd uses the men pek ccelertion to limit the wind-induced motion. All these criteri consider 1-yer return period lue of wind speed, except for the NBCC [6] tht considers 1-yer return period of wind speed. Figure 1 presents comprison of the three criteri described boe. All the cures correspond to 1-yer return period lue of the men wind speed. Figure 1. Limits of perception. It is obsered in Figure 1 tht the perception leels suggested in ISO1137 [5] nd the NBCC [6] depends on the use of the structure, while the criterion suggested by the AIJ [7] considers the use of cures ssocited with different probbility of perception leels. The sericebility criteri suggested by ISO1137 [5] nd the AIJ [7] is employed to estimte the relibility leels for 1431

2 Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 structures designed ccording to such perception cures, incorporting the uncertinty in structurl properties, wind chrcteristics, nd in the humn perception of motion. 2 RESPONSE OF TALL BUILDINGS UNDER WIND LOADING 2.1 Men pek ccelertion The ction of wind round structure induces erodynmic forces tht cn cuse excessie ibrtion (ccelertion). The mplitude of ibrtion depends on the dynmic properties of the structure. Two types of mesures re usully dopted to study wind-induced ibrtion, one is the men pek ccelertion nd the other one is the stndrd deition of ccelertion. The former is ssocited with the serch for sfety while the ltter is ssocited with physicl discomfort (dizziness for exmple). These mesures re relted through the following expression: ˆ g (1) where ˆ is the men pek ccelertion, is the r.m.s. of ccelertion for gien wind speed gien by: F ( ) fs f (2) m where F is trnsformtion fctor from men wind speed to force, m is the mss of the structure (it is considered tht the structure cn be modeled s single-degree-of-freedom system), f is the nturl frequency of the structure in Hz, S is the power spectrl density function of turbulent wind f t f, is the rtio of dmping of the structure, nd g is pek fctor defined s:.577 g 2ln ft (3) 2ln f T where T is the durtion of the ppliction of the wind loding, in s. In this study we use the men pek ccelertion s mesure of wind-induced ibrtion. The following section describes how uncertinty in structurl properties, wind chrcteristics, nd the humn perception of motion re considered in this pper. 2.2 Considertion of uncertinty According to Denport [1], the probbility distribution of the pek ccelertion (response), Â, conditioned on gien men wind speed is written s: F () exp( exp( 2ln(f T)/σ ()( ˆ 2ln(f T)σ ()))) (4) Aˆ ˆ where the men nd stndrd deition of Â, re gien by: nd, m Aˆ g ( ) (5) )/ 6 2ln( f T) (6) Aˆ ( If the nnul mximum men wind speed V is modeled s Gumbel rible, its probbility distribution is gien by: F () exp( exp( / ( 6 m )( ( / ) m ))) (7) V where is the coefficient of rition (COV) of, nd m is the men lue of, defined s: m.577 ln ln1 1/ T ( 6 / )) / (1 (8) T where T is the mximum wind speed for gien return period T r. According to Burton [8], the probbility of perception for gien pek ccelertion is defined by stndrd norml distribution nd is written s: r ln ˆ / c P 1 P ˆ ˆ (9) c 2 where c 1 nd c 2 re prmeters of the model tht depend on the frequency of ibrtion. To tke into ccount the uncertinty in structurl properties (ssocited with f,, nd F, we considered tht they re lognormlly distributed [9, 1, 11]. By using the totl probbility theorem nd integrting oer the domin of the rndom ribles considered, the unconditionl probbility of perception cn be written s: P fp P P R f f f F f f f ˆ ( ) ( ) ddf df ˆ A V FD D fn n n D dd (1) where F D, fn nd represent normlized rndom ribles (normlized with respect to their men lue) with probbility density functions denoted by ff D F D, f f n ( f n ) nd f, respectiely; R is defined s: (,, ) ( mfd S fnm f I cr n m R ) g S( m, I, ) (11) p T where cr is trget ccelertion tht cn be used for design reiew; m fn is the men lue of f n, nd I is the turbulence intensity of wind. Eqution (1) is used in the following section to estimte the relibility or probbility tht the wind-induced ibrtion of designed structure is not perceied within serice period. fn T 1432

3 Men pek ccelertion (milli-g) Men pek ccelertion (milli-g) Men pek ccelertion (milli-g) Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN PARAMETRIC ANALYSIS TO ESTIMATE THE UNCONDITIONAL PROBABLITY OF PERCEPTION For the prmetric nlyses, combintion of prmeters of the rndom ribles is employed to estimte the relibility ssocited with the criteri suggested by ISO1137 [5] nd the AIJ [7]. Note tht the criterion suggested by the NBCC [6] is not included since it is frequency independent. 3.1 Procedure to estimte the unconditionl probbility of perception The procedure employed to clculte P fp ssocited with ech of the criteri considered is s follows: 1) From ny of the criteri used, select trget lue cr, 2) Chrcterized ech probbility density function with its prmeters, 3) Using 1) nd 2) sole Eq. (1) to determine P fp, 4) Associte the obtined P fp with the trget lue cr, 5) Repet Steps 1) to 4) for different lues of cr. The prmeters used to estimte the relibility re summrized in Tble 1. Tble 1. Summry of prmeters used in the nlysis. Prmeter Vlue Prmeter Vlue T 36s COV of F.125 D.1 COV of f.175 n f.1- Hz COV of.275 T 3 m/s COV of See plots 3.2 Unconditionl probbility of perception ssocited with ISO1137 (27) For the nlyses, the men pek ccelertion cures for residences nd offices (see Fig. 1) re considered. The procedure described in Section 3.1 is pplied nd the results of the nlysis re presented in Figure 2, for two different lues of. Residences =.3 Offices P fp =.4 P fp =.54 P fp =.25 P fp =.6 P fp =.5 ISO1137 (27) Figure 2. ISO1137 (27) perception cures nd clculted cures for different P fp lues: ) =.15; b) =.3. It is obsered in Figure 2 tht P fp is ery sensitie to the uncertinty in wind speed. Another importnt obsertion is tht for =.15, the cure for residences suggested by [5] could be ssocited pproximtely with P fp lue equl to.67, wheres tht for offices could be ssocited with P fp lue equl to.84. For =.3, the lues of P fp for residences nd offices re equl to.4 nd.54, respectiely. 3.3 Unconditionl probbility of perception ssocited with AIJ (24) For the nlyses, the H-9 nd the H-1 cures (9% nd 1% of perception leel) re considered. The results obtined re presented in Figure 3. H-9 P fp =.9 b) ) Offices P fp =.84 P fp =.95 ) P fp =.67 P fp =.75 P fp =.47 H-1 P fp =.16 P fp =.55 P fp =.67 Residences AIJ (24) P fp =.12 =.15 =.15 ISO1137 (27) 1433

4 Men pek ccelertion (milli-g) Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 H-9 P fp =.53 b) ISO1137 [5] for residences re similr to those from the H- 9 cure proposed by the AIJ [7]. This cn be explined by noting tht the limits of perception (see Figure 1) from both cures re ery similr. H-1 AIJ (24) P fp =.4 P fp =.15 P fp =.3 P fp =.95 =.3 Figure 3. AIJ (24) H-9 nd H-1 cures nd clculted cures for different P fp lues: ) =.15; b) =.3. Similr conclusions to those drwn from Figure 2 re pplicble to Figure 3, except tht the H-9 nd H-1 could be ssocited pproximtely with P fp lue equl to.67 nd.12 for =.15, respectiely. These P fp lues re pproximtely equl to.4 nd.95 for = Comprison of results Tble 2 presents summry of the results obtined from the prmetric study. Tble 2. Summry of results Code or stndrd AIJ (24) P fp ISO1137 (27) P fp Residences ( =.15) -.67 Offices ( =.15) -.84 Residences ( =.3) -.4 Offices ( =.3) -.54 H-1 ( =.15).12 - H-9 ( =.15).67 - H-1 ( =.3).9 - H-9 ( =.3).4 - It is obsered in Tble 2 tht the impct of on P fp is ery significnt. This obsertion is importnt since the wind climte ( ) of prticulr site could ffect the lue P fp ssocited with prticulr criterion, lthough some reserchers he proposed the use of sericebility fctors tht cn be used for design checking; these fctors were clibrted to tke into ccount rnge of lues [12]. When using the criterion proposed by ISO1137 [5], P fp for residences is smller thn tht for offices, s expected. With respect to the H-9 cure, it is obsered tht it is ssocited with lues of P fp within.4 to.67 for the prmeters considered; these lues re smller thn the originl 9% of perception leel. Similr obsertions cn be drwn from the H-1 cure. It is lso interesting to note tht the P fp lues ssocited with 4 FINAL COMMENTS A comprison between some of the mjor sericebility criteri for designing buildings nd to estimte the relibility leel for structures designed ccording to such perception cures, incorporting the uncertinty in structurl properties, wind chrcteristics, nd in the humn perception of motion ws crried out. For the nlyses, the probbility distribution of the pek ccelertion response, nd the rndom ibrtion pproch ws employed. The nlyses results indicte tht the unconditionl probbility of perception ssocited with structures designed ccording to different sericebility criteri is not the sme, een if the structures re designed for the sme perception leel. Other conclusions tht cn be drwn from the results re: P fp is ery sensitie to the COV of wind speed. When considering uncertinty in structurl properties, wind chrcteristics, nd the humn perception of motion, the P fp lues clculted for ech criterion re different thn the probbility of perception ssocited with ech criterion. ACKNOWLEDGMENTS The finncil support receied from the Institute of Engineering of UNAM, the Ntionl Council on Science nd Technology (CONACYT), nd from the Grdute School of Engineering t UNAM re grtefully cknowledged. REFERENCES [1] Denport, A. G. Note on the distribution of the lrgest lue of rndom function with ppliction to gust loding. Proceedings of the Institution of Ciil Engineers, Pper No. 6739, Vol. 28, pp , [2] Vn Koten, H. The Comprison of Mesured nd Clculted Amplitudes of some Buildings, nd determintion of dmping effect on Buildings. Proceedings of the third interntionl conference on wind effects on buildings nd structures, Tokyo, Jpn, pp , [3] Chen. P. W., nd Robertson, L. E. Humn Perception Thresholds of Horizontl Motion. Journl of the Structurl Diision, ASCE, Vol. 98, pp , [4] Chng, F. K. Humn Response to Motion in Tll Buildings. Journl of the Structurl Diision, ASCE, Vol. 99, pp , [5] ISO Interntionl Orgniztion for Stndrdiztion. Bses for design of structures Sericebility of buildings nd wlkwys ginst ibrtions. ISO 1137:27(E), Interntionl Orgniztion for Stndrdiztion, Gene, Switzerlnd. 27. [6] NBCC. Ntionl Building Code of Cnd, Prt 4 Structurl Design, Commentry 1, Wind Lod Effects. 25. [7] Architecturl Institute of Jpn Recommendtions. Guidelines for the elution of hbitbility to building ibrtion. AIJES-V1-24, Tokyo, Jpn. 24. [8] Burton, M.D. Effects of low frequency wind-induced building motion on occupnt comfort. PhD. Thesis, Ciil Engineering Deprtment, The Hong Kong Uniersity of Science nd Technology, Hong Kong,

5 Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 [9] Denport, A.G. A comprison of seismic nd windstorm hzrds. In Proceedings of the 6th Enironmentl Specilty Conference of the Cndin Society for Ciil Engineering, 7 1 June 2, London, Ont. Cndin Society for Ciil Engineering, Montrél, Que. pp , 2. [1] Kreem, A. Relibility Anlysis of Wind Sensitie Structures. J. Wind Engineering nd Industril Aerodynmics, Vol. 33, pp , 199. [11] Hilnd, R. Elution of seismic sfety of buildings. M.Sc. Thesis superised by J.M. Biggs, E.H. Venmrcke, Msschusetts Institute of Technology, [12] A. Pozos-Estrd, H.P. Hong nd J. K. Glsworthy. Sericebility Design Fctors for Design of Wind-Sensitie Structures. Cndin Journl of Ciil Engineering, Vol. 37(5), pp ,

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