Wind Load on Integral-Lift Scaffolds for Tall Building …naoce.sjtu.edu.cn/upload/1543903179253139.pdfWind Load on Integral-Lift Scaffolds for Tall Building Construction. F....

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Wind Load on Integral-Lift Scaffolds for Tall BuildingConstruction

F. Yue1; Y. Yuan2; G. Q. Li3; K. M. Ye4; Zh. M. Chen5; and Zh. P. Wang6

Abstract: The integral-lift scaffolds are widely used in construction of tall buildings in Asia. However, the wind load on scaffolbe much greater than dead load and be the dominant effect as the scaffolds climb over 150 m in height. The shape coefficient acoefficient are important factors in calculation of wind load. However, there is no available approach at present for determinincoefficients for calculating the wind load on this temporary structure. In order to determine the shape coefficient of wind presstypical scaffolds, wind tunnel tests have been conducted. The drag coefficients have been measured, which are proved to bethe wind shape coefficients. By using random vibration theory, formulae are obtained for predicting the wind vibration coefficiescaffolds at the two stages of climbing up and down. The useful guidelines for the safe design of integral-lift scaffolds againstproposed in this paper.

DOI: 10.1061/~ASCE!0733-9445~2005!131:5~816!

CE Database subject headings: Integrals; Lifting; Buildings, high-rise; Wind tunnel test; Shape; Vibration.

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Introduction

The scaffold is a temporary structural system that workmenable to stand on. Scaffolds, usually built from metal polesboards, may be set up around buildings being built, painterepaired. Generally, construction procedure is the highest risstructure. As members of a scaffold are slender and the strusystem is prone to fail by buckling, recent research effortsfocused on the ultimate capacity of scaffold systems or scasupport systems. Harung et al.~1975! showed that elastic instbility was the dominant failure mode of scaffold structures. Pet al.~1997! performed a second-order nonlinear analysis throa two-dimensional model with respect to a typical door-tmodular falsework system for computer analysis. Furthermorthe basis of exact expressions of moment–curvature relatioand observed behavior of full-scale specimens of pinned col

1PhD, Dept. of Building Structural Engineering, Tongji Univ., 12Siping Rd., Shanghai 200092, China~corresponding author!. E-mail:[email protected]

2Professor, Dept. of Building Structural Engineering, Tongji UnShanghai 200092, China. E-mail: [email protected]

3Professor, Dept. of Building Structural Engineering, Tongji UnShanghai 200092, China. E-mail: [email protected]

4Member of National Academy of Engineering of China, ConsuChief Engineer, Shanghai Construction Group Co., Shanghai 20China.

5Chief Engineer, Shanghai No. 3 Construction Co., Shanghai 20China.

6Chief Engineer, Shanghai No. 8 Construction Co., Shanghai 20China.

Note. Associate Editor: Sashi K. Kunnath. Discussion openOctober 1, 2005. Separate discussions must be submitted for indipapers. To extend the closing date by one month, a written requesbe filed with the ASCE Managing Editor. The manuscript for this pwas submitted for review and possible publication on April 11, 2approved on November 19, 2004. This paper is part of theJournal ofStructural Engineering, Vol. 131, No. 5, May 1, 2005. ©ASCE, ISSN
0733-9445/2005/5-816–824/$25.00.
816 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2005

J. Struct. Eng., 2005, 1

with circular section and modular falsework frames, Peng e~2001! gave an approximate method of second-order inelanalysis. Chan et al.~1995! emphasized the important role tthe connection stiffness plays in affecting the buckling capacia scaffold, and a convenient method for determining joint sness, according to the well-known effective length concept isposed for inputting the joint flexibility. Xu et al.~1989! madefirst-order elastic instability analysis of tubular steel scaffold,determined the horizontal rigidity influence coefficient of the cpler connection on the scaffold after comparing experimentscalculations. Ao~2000! gave a second-order nonlinear analfor the stability of tubular steel scaffold with coupler connectiothe stiffness of which was measured through a test.

The evolution of integral-lift scaffold, attached to main buing structures in construction, is based on the developmeoutrigger scaffold, swinging scaffold, and suspending scaffothe end of the 1980s in China. It was proved to be suitable foerection of tall buildings, especially for super-tall buildings~Du1999; Mi 1999!. The scaffold, only about 10 m in height, throuits supporting members attached to a building in constructionbe lifted integrally up or down with construction progressmeans of its particular lifting equipment after first assemblinand putting it up around the exterior wall of a building being b~see Figs. 1 and 2!. It is of great economical advantage for hirise buildings as it takes fewer steel tubes than a regular dto-ground scaffold. Like common scaffolds, it can meet thequirements of safe operation for workers and the needconstruction technology at specific stages, such as at the stconstruction, installation, and finishing. Because of these adtages, the application of this kind of scaffold has become wspread since the beginning of the 1990s in China. A scaffold bused on construction site is shown in Fig. 3.

Chen and Yuan~2000! indicated that the horizontal displacment of a scaffold produced by wind load is about 20 timestical displacement, resulting from vertical dead load whilclimbs above 150 m. And, some wind speed data log availabpractice implies that the safety net and baffler wrapped ou
the scaffold body would increase wind effects. So, the wind load
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on scaffolds may be much greater than dead load and maydominant effect as the scaffolds climb over 150 m in height.lapses of the scaffold may occur occasionally in high wind,they not only lead to work delays and property loss, butcause numerous worker injuries and deaths. However, therebeen no guidelines and relatively few reports or papers on thedesign and use of this kind of scaffold until The ConstructionManagement Commission of the Shanghai Municipal Govment and the Ministry of Construction of the People’s RepublChina~1999! issued operation directions STCIS in 1999 andMinistry of Construction of People’s Republic of China~2000!CTPIS in 2000, respectively, even though they both mainly sthe safe use of constructing not higher than 150 m. Neverthtall buildings that exceed this height are not unusual in Chespecially in Shanghai. Therefore, research on wind load ehas crucial social and economic significance.

It is well known that the shape coefficient of a structurewind vibration coefficient are important parameters in the calation of wind load. In this paper, for the sake of proper idencation of scaffold’s shape coefficient, wind tunnel tests havedesigned to give results under different opening ratio of thebuilding structure. Furthermore, for both stages of climbingand down, wind vibration coefficients of the scaffold are obtaby using random vibration theory.

Fig. 1. Body of typical integral-lift scaffold

Fig. 2. Integral-lift scaffold at stage of climbing up and down:~a! nthfloor of structure in construction;~b! sn+1dth floor of structure inconstruction;~c! scaffold climbed up until construction of structuwas complete; and~d! scaffold climbing down during finishing wo

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Formula to Determine Wind Load

The standard value of the wind force on the integral-lift scafis determined by both STCIS~1999! and CTPIS~2000! as fol-lows:

F = kmsmzbzW0A s1d

whereF=total standard value of wind force on integral-lift scfold; k=0.7, reduction factor for wind pressure having returnriod of only 5 years;ms, mz, andbz=wind shape coefficient, cefficient of wind pressure variation with height, and wvibration coefficient of integral-lift scaffold, respectively;W0

=reference wind pressure; andA=frontal projected areaintegral-lift scaffold, i.e., the area of the shadow projection oplane normal to the direction of the wind.

The distributed wind pressure on the surface of a builstructure varies with different shapes even under the sameconditions~Zhang 1985; Li 1999!. Furthermore, for this kind oscaffold with so many circular cylinders and porous fabric,mean drag data are a function of porosity~Rouse 1950!. The windshape coefficientms is a factor that characterizes this natureTable 1 lists, both STCIS~1999! and CTPIS~2000! suggest aempirical selection of scaffold’s wind shape coefficientms. InTable 1, the parameterf means the scaffold’s blocking ratdefined as,f=An/A, whereAn is the projection area of a scaffothat holds up wind, andA is the whole outline projection area thfaces wind. However, it has no experimental or theoretical b

Wind vibration coefficientbz is another important factor in thcalculation of wind load and safe design of integral-lift scaffHowever, there are no guidelines or reports for the definitiothis factor. Both STCIS~1999! and CTPIS~2000! substitute iapproximately by that of main structure, which has been dmined in CSBSL~The Ministry of Construction of the PeopleRepublic of China 2001!.

Table 1. Shape Coefficient of Wind Loading in Currently EffectCode-STCIS~1999! and CTPIS~2000!

Condition of wall attached to a scaffold ms

Entirely closed 1.0f

Open or with hole 1.3f

Fig. 3. Integral-lift scaffold used in Bank of CommunicatioPudong New District, Shanghai

RNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2005 / 817

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Shape Coefficient of Wind Pressure

There are two main ways to get the structures’ wind shapeficient ~Zhang 1985!: one is spot measurement, and the other ithe way of wind tunnel tests, which is adopted in the paper fosake of proper identification of the scaffold’s wind shape cocient.

TJ-2 Wind Tunnel

The test was done at the TJ-2 Boundary Layer Wind Tunlocated in the State Key Laboratory for Disaster ReductioCivil Engineering at Tongji Univ. The section of the tunnel is 3wide, 2.5 m high, and 15 m long. Smooth wind flow simulatethe tunnel is served as wind source for us to get this kincoefficients in the test. The velocity of the smooth flow produin the tunnel is 10 m/s, and, the turbulence intensity in thesection of the tunnel is less than 1%. The force measuresystem consists of five components: strain scale, stabilizedage direct current source, HP9000-345 workstation,HP3852A data acquisition apparatus, whose maximum meament speed is 100,000 readings/s, and whose best accur

Fig. 4. Model of typical integral-lift scaffold

Fig. 5. Front and side elevation of scaffold’s model~cm!



s

0.008%. The measurement range of the five componentsscale is 100 and 150 N for force, 60 and 120 N m for benmoment, and 10 N m for moment of torsion. Measurement aracy of the strain scale is about ±0.2%.

Model of Scaffold

A practical design of a typical integral-lift scaffold which21.2 m long, 0.8 m wide, and 16.8 m high is taken as a protoin this test. Given the smooth flow in the tunnel, in order towith TJ-2 wind tunnel with proper boundary condition and cparability, the geometric similitude ratio between reduced smodel and the actual scaffold is 1:30 in this test accordinblocking ratio of the wind tunnel and the feature of force msurements.

The body of the model scaffold was made of copper wir0.8, 1.2, and 2.0 mm in diameter with tin soldered lap joint~seeFigs. 4 and 5!. The main structure of model building was madeacrylonitrile butadiene styrene~ABS! sheets with opening ratio15, 30, and 50%, respectively. Safety net wrapped outside mbody was made of practical safety net of 2,000 holes per 1002

usually used on construction site or window screen. Protebaffle was simulated with ABS sheets. Furthermore, floor slset to take their influences into account~see Fig. 6!. Fig. 7 is themodel in the wind tunnel.

Fig. 6. Model of main building structure and scaffold attached t

Fig. 7. Model in TJ-2 wind tunnel

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Testing Schedule

According to actual conditions of a scaffold in practice and tyof building structures, the reduced scale model test is condcombining the following factors:1. The wind angle of 0, 45, 90, 135, and 180°~refer to Fig. 8!;2. The setup of protection baffle and safety net~refer to Table

2!;3. The opening ratio of main structure of 0, 15, 30, and 5

and4. With or without floor slab.

Drag Coefficient from Test

It is difficult to make a pressure measurement because thebers of model body were made of copper wire of 2.0 mm at min diameter. As a matter of fact, drag coefficients were obtaby a force measurement in the test.

Reynolds number mismatch in this test is not critical tomeasurements of drag coefficients because Reynolds numbboth the practical scaffold and the model are in the subcrregion ~Wooton and Scruton 1971!.

Wind force measured can be decomposed into five conents. At given coordinates, these components are:Fx, Fy, Mx,My, and Mz, representing windward wind load, transverse wload, and bending moments about axesX, Y, Z, respectivelyThese forces are proportional with wind speed squared anarea blocking wind. Therefore, at specific wind speed to a gmodel, a group of five nondimensional coefficients can be

Fig. 8. Coordinate system of scale

Fig. 9. Contrast of shape coeffic

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f

tained after measuring “drag forces” in wind tunnel. Here,coefficients in this paper are defined as the following equati

Cx = Fx/s1/2rn2BHd s2d

Cy = Fy/s1/2rn2LHd s3d

CMx = Mx/s1/2rn2BH2d s4d

CMy = My/s1/2rn2LH2d s5d

CMz = Mz/s1/2rn2B2Hd s6d

where 1/2rn2=dynamic pressure of wind flow;r=density of airn=speed of wind at the centroid area of the scaffold’s faB,L ,H=scaffold’s horizontal dimension normal to the directof the wind, scaffold’s horizontal dimension parallel to the dition of the wind, and height of scaffold’s model body, resptively.

Table 2. Model Cases

Casenumber

Safety protection setup of a scaffoldBlockingratio ofscaffold RemarSafety Net/window screen

Protectionbaffle

1 No/no None 0.066 a

2 No/one layer None 0.214 a

3 No/two layers None 0.287 a

4 Yes/no None 0.3225 a

5 No/no One layer 0.388 a

6 No/one layer One layer 0.484 a

7 No/two layers One layer 0.533 a

8 Yes/no One layer 0.55 a

9 No/no Double layer 0.709 a

10 No/one layer Double layer 0.755 a

11 Yes/no Double layer 0.774 b

12 Yes/no Double layer 0.774 a

13 No/two layers Double layer 0.778 a

aWith floor slab.bNone.

f wind loading between test and code
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It is worth noting that the value of drag coefficientCx is equato the sum of shape coefficient at the windward and leesides.

Application of Wind Tunnel Test

Keeping other factors constant, trends can be found from thesured data that the value of shape coefficient of a scaffoldcally increases linearly with the increase of the scaffold’s bling ratio ~see Fig. 9! and it also increases almost linearly withincrease of the main structure’s opening ratio~Yue 2002!. Thecontrast of shape coefficients between the test and the S~1999! or CTPIS ~2000! code is also depicted in Fig. 9, whishows that the numerical values of the shape coefficients obtby the wind tunnel tests are lower than those obtained incurrently effective code except for Case 4~without protectionbaffle but having safety net! and Case 5~without safety net buhaving one layer protection baffle! for an unknown reason.

Linear regression is made for eliminating variance existenCases 4 and 5 in this test~see Fig. 10!. Furthermore, Yue~2002!listed their values in the form of tables for practical use.

Wind Vibration Coefficient of Scaffold

In this section, with the effect of pulsating wind and the intetion between scaffold and main structure being taken into coeration, the analyses below, in light of random vibration theare conducted in order to obtain the scaffolds’ wind vibracoefficients.

Differential Equation of Motion

Depicted in Fig. 11, the scaffold–structure system is simplifiea multiple degree of freedom system, in which the mass poiscaffoldms is attached to the top mass point of the tall buildstructure under construction. The mass, stiffness, and the dacoefficients of the scaffold are symbolized asms, ks, andcs, re-spectively. The wind loading acts on the structural mass pand scaffold mass point, hence, the magnitude of the forces omassm1, . . . ,mn−1 is f1std , . . . ,fn−1std, respectively. For the para

Fig. 10. Suggested shape coef

lel connection of massmn and massms, in the case of elastic



vibration, it is reasonable to suppose that the wind force onmn iss1−wdfnstd, and onms is wfnstd, where,w is the scaffold’s windblocking ratio.

Therefore, differential equations of motion of structuscaffold are

fMghyj + fCghyj + fKghyj = hfstdj + hFsj s7d

msys + cssys − ynd + kssys − ynd = wfnstd s8d

where hFsj=fcssys− ynd+kssys−ynd ,0 ,¯ ,0gT, hfstdj=fs1−wdfnstd , fn−1std ,¯ , f1stdgT. In the generalized coordinate systeEqs.~7! and ~8! are simplified in the first rank as

of wind loading of scaffolds for use

Fig. 11. Dynamic model of scaffold attached to tall building

ficient

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F1 msfn1/M1*

0 1GHq1

ysJ + F2z1v1 0

− 2zsvsfn1 2zsvsGHq1

ysJ

+ F v12 0

− vs2fn1 vs

2GHq1

ysJ = HF1std

F2stdJ s9d

where F1std, F2std=generalized force, i.e., F1std=sM1

*d−1hfj1Thf1std ,¯ , fn−1std , fnstdjT, F2std=ms

−1wfnstd.

Standard Deviation of Scaffold’sDisplacement Response

The standard deviation of the scaffold’s displacement respon

sysys=ÎE

−`

+`

Sysyssvddv s10d

In Eq. ~10!, Sysyssvd can be obtained as follows:

FSyiyisvd Syiys

svd

Sysyisvd Sysys

svd G = Ffi1 0

0 1GTFSqqsvd Sqys

svd

Sysqsvd Sysys

svd GFfi1 0

0 1G

s11d

where

FSqqsvd Sqyssvd

Sysqsvd Sysys

svd G = fHs− ivdgFSF1F1sivd SF1F2

sivd

SF2F1sivd SF2F2

sivd GfHsivdgT

s12d

In Eq. ~12!, according to Eq.~9!, the matrix of frequency responfunction can be obtained as follows:

nqs.ringre-of

climbing up, the wind vibration coefficient of the attached scaf-

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fHsivdg = FHqqsivd Hqyssivd

Hysqsivd Hysys

sivd G=

1

DF vs

2 − v2 + 2izsvsv gfn1v2

fn1vs2 + 2izsfn1vsv v1

2 − v2 + 2iz1v1vG

s13d

where, D= bv12−v2+2iz1v1vc bvs

2−v2+2izsvsvc−ssms/M1

*dfn12 v2dsvs

2+2izsvsvd, g=ms/M1* and in Eq.~12!

SF1F1svd = sM1

*d−2oi=1

n

oj=1

n

fi1f j1ri jm f imsimzim f jmsjmzj

3 sw02/m2dSfsvd s14d

SF1F2svd = SF2F1

svd = sM1*msd−1wo

i=1

n

fi1rinm f imsimzim fnmsnmzn

3 sw02/m2dSfsvd s15d

SF2F2svd = ms

−2w2sm fnmsnmznd2sw02/m2dSfsvd s16d

Wind Vibration Coefficient of Attached Scaffold

On the basis of Eq.~10!, the wind vibration coefficients of thscaffold at the two stages of climbing up and down are resented byb andb8 as Eqs.~17! and ~18!, respectively
z z
bz = spssn+ pdsnd/pssn= 1 +msvs2msys

/pssn

= 1 + s1/mznd ·SQRTE

−`

+` Sh2r2vs6svs

2 + 4zs2v2do

i=1

n

oj=1

n

fi1f j1ri jm f imzim f jmzj

+ 2whrvx5sv1

2vs − vsv2 + 4z1zsv1v

2d

3oi=1

n

fi1rnim f imzim fnmzn+ w2vs

2bsv12 − v2d2 + 4z1

2v12v2csm fnmznd2DSfsvd/uDu2dv s17d

bz8 = spssi+ pdsid/pssi= 1 +msvs2msys

8 /pssi

= 1 + s1/mzid ·SQRTE

−`

+` Sfi12 h2r2vs

6svs2 + 4zs

2v2doi=1

n

oj=1

n


+ 2fi1whrvs5sv1


2doj=1

n

fi1ri jm f jmzjm f imzi + w2vs2bsv1

2 − v2d2 + 4z12v1

2v2csm f imzid2DSfsvd/uDu2dv

s18d

ntiln theationat ofwn.

Hence, it is suggested that Eqs.~17! and ~18! may be used icalculation of the wind vibration of the scaffold. Based on E~17! and~18!, a computer program was developed for compawith that of the main structure, which was given by formersearchers~Zhang 1985!. In Fig. 12, as it shows, at the stage

fold isn’t greater than that of the main building structure uclimbing up to a certain height, the value of which depends ostructure and scaffold’s structural parameters. The wind vibrcoefficient of the attached scaffold is always greater than ththe main building structure at the whole stage of climbing do
So, suggestion of both STCIS~1999! and CTPIS~2000! may

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underestimate the wind-induced vibration of attached scaffolthey climb over a certain height at the stage of climbing up anthe whole stage of climbing down.

Applicable Equations

For practical use, the applicable equations of the wind vibracoefficients at the two stages of climbing up and down aretained as Eqs.~19! and ~20!, respectively

bz = 1 +Îh2 · j1l1 + 2wh · j2l2 + w2 · j3l3/mzns19d

bz8 = 1 +Îfi12 h2 · j1l1 + 2fi1wh · j2l28 + w2zi

2a · j3l38/mzi

s20d

wherej1, j2, andj3=factors considering pulsating dynamicalteraction between scaffold and main structure, represented a~21!–~23! ~see the Appendix!, respectively.l1, l2, l3, and l28,l38=factors considering space correlation and effect of pulswind, represented as Eqs.~24!–~28! ~see the Appendix!, respectively. Yue ~2002! listed their values in the form of tables throumuch computing.

Conclusions

The facility safety is the most important issue in civil engineeconstruction. The wind effects may become the dominant fathat will influence the operation safety of the scaffolds. This paims at exploring the wind effects on integral-lift scaffoldstached to tall buildings during construction. Studies are focusthis paper on shape coefficient of wind pressure and wind-indvibration of the scaffolds. The shape coefficients of wind preson the typical scaffolds under various conditions are obtathrough wind tunnel tests. By using random vibration theorydifferential equations of wind-induced vibration of the scaffoare established and the wind vibration coefficients of the scafare obtained through the solution of the equations. The masults may be summarized as follows:

1. The load acting on a scaffold in angle 0°, perpendiculathe front elevation of the scaffold is greater than that in o

Fig. 12. Wind vibration coef

angles.



.

2. It was found from the test measurement that the value oshape coefficient of a scaffold increases almost linearly withincrease of the scaffold’s blocking ratio.

3. For a scaffold, with safety net and double sheets of prtion baffle, the effect of wind load acting on the scaffold wreach the greatest value when other conditions are the samthe contrary, for a scaffold without safety net and protecbaffles, the wind load on the scaffold becomes the lowest. Sraise the safety of an integral-lift scaffold, its blocking rashould be reduced as far as possible.

4. Given the same condition, the wind effect acting onscaffold is of the greatest as the opening ratio of the builstructure is 50%. On the contrary, the wind effect reachessmallest as the opening ratio of the building structure is 0%

5. The wind loads acting on the scaffold are different beand after installation of the floor slab of the main building. Ually, the wind load of the latter case is smaller. This impliesspeeding up concreting procedure will be beneficial for the sof attached scaffold.

6. In the calculation of wind load of an attached scaffold,10 is suggested for the engineer’s practical use to substitutpirical selection proposed by STICS~1999! and CTPIS~2000!.

7. At the stage of climbing up, the wind vibration coefficienthe scaffold attached a building is smaller than that of the buistructure until climbing up to a certain height. However, the wvibration coefficient of the scaffold attached to a building isways greater than that of the main building structure at the wstage of climbing down.

8. Suggestion of STICS~1999! and CTPIS~2000! codes maunderestimate wind-induced vibration of attached scaffoldclimbs over a certain height at the stage of climbing up and awhole stage of climbing down.

9. Eqs.~19! and ~20! are suggested for the calculation ofwind vibration of this kind of scaffold.

Acknowledgments

The writers are grateful to the financial support from ShanConstruction Technology Foundation. They are also gratefProfessor Jing-zhong Song and Feng Zhang, staff of the Stat

of scaffold and main structure
ficient
Laboratory for Disaster Reduction in Civil Engineering at Tongji

31(5): 816-824

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University, for their help in the experimental scheme and tkindly assistance. Furthermore, they extend thanks to MZhang and Yi-hai Bao, graduate students of the DepartmeBuilding Structural Engineering of Tongji University, for thpreparation work on the test model and participation in deveing the early program for calculating wind vibration coefficierespectively. The writers also wish to thank Professor MingDepartment of Bridge Engineering, Tongji University, forvaluable advice on this paper.

Appendix

The following equations are used in this paper:

j1 =E−`

+`

vs6svs

2 + 4zs2v2dr2Sfsvd/uDu2dv s21d

j2 =E−`

+`

vs5sv1


2drSfsvd/uDu2dv s22d

j3 =E−`

+`

vs2fsv1

2 − v2d2 + 4z12v1

2v2gSfsvd/uDu2dv s23d

l1 = oi=1

n

oj=1

n


s24d

l2 = oi=1

n

fi1rnim f imzi

m fnmzns25d

l3 = sm fnmznd2 s26d

l28 = oj=1

n

fi1ri jm f jmzjm f imzi s27d

l38 = sm f imzid2/zi2a = ssm f imzid2/szi

2a · sm fnmznd2ddsm fnmznd2

= zn−2a · l3 = H−2a · l3 s28d

Notation

The following symbols are used in this paper:fMg ,fCg ,fKg 5 matrix of mass, damping factor and stiffness

of main structure;M1

* 5 first generalized mass;psszd+pdszd 5 wind vibration coefficient of structure is ratio

of probability statistic of whole wind load, toprobability statistic of static one,psszd;

q1 5 generalized coordinate in first rank;SF1F1

,SF1F2,SF2F1

,SF2F25 self or mutual power spectrum density of

input F1std andF2std;Sfsvd 5 stochastic power spectral density of pulsatin

wind loading while mean of which is equal to0, i.e.,Effg=0. Sfsnd=s2x2d /3ns1+x2d4/3 is
adopted here according to Davenport’s research,
JOU


wherex=1,200n/ n10, in which n10 is velocityat height of 10 m~m/s!, unit of n ~1/s!;

Sysys5 power spectrum density of displacement of

scaffold on Cartesian coordinates;w0 5 basic wind pressure;hyj 5 displacement vector of mass pointsm1–mn

with respect to ground;yn 5 displacement of top mass with reference to

ground;ys 5 scaffold’s displacement with reference to

ground;a 5 roughness index of ground;

z1,zs 5 fraction of damping of structure and scaffoldrespectively;

h 5 ratio of shape coefficient of wind loadingbetween main structure and scaffold;

m 5 peaking factor, adopted by 2.2 in paper;m f i ,msi,mzi 5 pulsating coefficient of wind loading,

scaffold’s shape coefficient, and height aspefactor of wind loading at mass pointi ofmain structure;

m fn,msn,mzn 5 pulsating coefficient of wind loading,scaffold’s shape coefficient, and height aspefactor of wind loading at mass point ofscaffold;

ri j ,rin 5 pulsating wind’s vertical correlation factorsbetween mass pointi and j , i andn;

sysys5 standard deviation of displacement response

of scaffold at stage of climbing up;sysys

8 5 standard deviation of displacement responseof scaffold at stage of climbing down;

fi1 5 value of structure’s first mode at any masspoints i;

fn1 5 first modal modulus atnth mass point; andv1,vs 5 first frequency of structure and scaffold,

respectively.

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