22 ijaet vol iii issue ii 2012

8/10/2019 22 Ijaet Vol III Issue II 2012

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International Journal of Advanced Engineering TechnologyE-ISSN 0976-3945

IJAET/Vol.III/ Issue II/April-June, 2012/XXXX

Fig-1. Section showing 275m tall RCC chimney

modeled in Staad Pro.3.2 ACROSS WIND EFFECTS: Across -windloads are caused by the corresponding liftcomponent of the wind force on the chimney. This isassociated with the phenomenon of vortex sheddingwhich causes the chimney to oscillate in a direction perpendicular to the direction of wind flow. Theacross wind response of a chimney occurs mainly dueto vortex shedding and velocity dependent forces.The across-wind response of tall slender structures inatmospheric turbulence involves a number ofcomplex fluid-structure interaction phenomena. The principal source of excitation arises from vortexshedding, but if the motion induced is significant,other velocity dependent forces begin to play animportant role. Further, the longitudinal and lateralfluctuations in the approaching flow give rise toacross-wind buffeting forces. The shedding ofvortices is fairly regular in the sub critical rangewhen Reynolds number (Re) 3x106), whereas it is random in the supercritical range (3x105


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z

H s

d zi

=

0

2

H

0zziz

oi

dd

(5)

oi = peak tip deflection due to vortex shedding in the ith mode of vibration in md z = external diameter of chimney.CL= peak oscillatory lift coefficient to be taken as 0.16

H = height of chimney in m.K si =mass damping parameter for the ith mode of vibrationSn= Strouhal number to be taken as 0.2zi= mode shape function normalized with respect to thedynamic amplitude at top of the chimney in the ith mode ofvibrationCalculation of mass damping parameter (K si ) :Periodic response of the chimney in the ith mode ofvibration is very strongly dependent ondimensionless mass damping parameter K sicalculated by the formula:

2ei

si ..2m K

d s

= (6)

Wheremei= equivalent mass per unit length in kg/m in the ithmode of vibration, as defined in A-4.2.3s= logarithmic decrement of structural damping=2= structural damping as a fraction of critical damping to be taken as 0.016 = mass density of air to be taken as 1.2kg/m3 d = effective diameter taken as average diameter over thetop 1/3 height of chimney in mCalculation of Equivalent mass per unit length(m ei):The equivalent mass per unit length in ith mode ofvibration (mei) shall be calculated by the formula:

z

H s

d m

zi

zi

=

0

2

H

0z

2z

ei

dm

(7)

When the mass per unit length has to be used in anumerical method of integration, it is recommendedthat the mass of the segment above sectionconsidered be added to the mass of the segment below the section and the total mass so obtaineddivided by the total length of the two segments. 5.2 Across wind load Random response method:Calculation of across wind load is made by firstcalculating the peak response amplitude at thespecified mode of vibration (usually the first orsecond). The relevant expressions for chimneys withtaper less than or equal to 1 in 50 in Eq 16 belowrespectively.Taper is defined as {2(dav-dtop)/H} where dav is theaverage outer diameter over the top half of chimneyand dtop is the outer diameter at top.

1. For chimneys with little or no tapper (i.e. If theaverage Taper over the top one third height isless than or equal to 1 in 50)- The modalresponse, at a critical wind speed shall becalculated by the formula:

nS d f

V 1cri = (8)

The amplitude of vortex excited oscillation perpendicular to direction of wind for any mode ofoscillation shall be calculated by the formula:

eia z

H ei

Hi L

md k d H

m

Ld

S d C

zi

n

/](/1[

)2(2/)({25.1

2

0

2

2

22

oi

+

=

I

(9)

oi= peak tip deflection due to vortex shedding in the ith mode of vibrationCL = RMS lift coefficient to be taken as 0.12L = Correlation length in diameters, which may be takenas 1.0 in the absence of field data.K a= Aero dynamic damping coefficient to be taken as 0.5Calculation of shear force and Bending Moment:The sectional shear force and bending moment (Mzoi)at any height z0, for the ith mode of vibration, shall becalculated from the following equations:

z

H

zo zi z oi zoi d m f F = 2124 (9)

z

H

zo zi z oi zoi d zo z m f M )(4 212 = (10)

Wheref 1= natural frequency of the chimney in Hz in the mode ofvibrationmz= mass per unit length of the chimney at section z inkg/mCalculation of Natural Frequency of VortexShedding :The frequency of vortex shedding can be calculatedfrom the equation:

co

n

d

V S f 1 = (11)

S= Strouhal number assumed as 0.2V= Wind speed (Ve-at resonance) in m/s. anddco= Outside diameter of chimney at 1/3 height fromtop in m.6. RESULTS AND DISCUSSION Keeping all basic design parameters of chimney(shell height, top and bottom diameter of the shell)constant a comparison of wind pressures for alongwind and across wind, associated shear forces, bending moments, deflections in each wind zone are presented table 1 & in the Fig 3 to Fig 8. The resultsare compared with respect to the values of alongwind (simplified method) as datum in each zone.6.1 Wind load Effects in wind Zone I:From figures 3, 4& 5, it is observed that the shearforce, bending moment and deflections at criticalsection in a chimney located in wind zone I are veryhigh in across wind condition (SFM).These valuesare increased by 137%, 161%, & 96.50%respectively compared to simplified method. At the base of the chimney shear force, bending momentand deflections are increased by 33%, 48% & 93.0%respectively.6.2 Wind load Effects in wind Zone VI:

From figures 6, 7& 8, it is observed that the shearforce, bending moment and deflections at criticalsection in a chimney located in wind zone VI arevery high in along wind condition (GFM).Thesevalues are increased by 41%, 44% & 44%


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respectively compared to simplified method. At the base of the chimney shear force, bending momentand deflections are increased by 21%, 31% & 51%respectively.7. CONCLUSIONS At critical section (i.e 1/2 to 1/3rd height

from top), across wind methods aremaximum than the along wind methods.This is due to the reason that at critical

section, vortex shedding effect on chimneystructure will be more. The shear force, bending moment and the

deflection in the across wind methods aresame in both the zones due to this reason,the across wind calculation is directly

proportional to the weight of the chimney,frequency and its mode shapes, but not onthe wind speed. Hence across wind load isnot increasing with the increasing windspeed.

For zone I, The shear force bending momentand deflection are maximum and governingin across wind (SFM).

For zone VI, along wind methods are

increased with increasing wind speed. Theshear force bending moment and deflectionare maximum and governing in along wind(GFM).

TABLE 1- Comparison of wind load effects for I and VI wind zones for a 275m tall RCC chimney

Figure-3 Variation of shear force for different methods along height in wind Zone I

S.NO DESCRIPTION ZONE I ZONE VI

At topCriticalsection At bottom At top

Criticalsection At bottom

Along wind(simplified method)

1 Basic speed(m/s) 33 55

2 Design wind pressure(N/m2) 1274 1194 685 3744 3512 2014

3 Shear force(kN) 15 1440 4060 13 4240 119204 Bending Moment (kNM) 0 69430 595960 0 204030 17513905 Deflection (mm) 166 72 0 213 487 0

Along wind(gust factor method)

1 Design wind speed(N/m2) 837 767 356 2461 2255 10452 Shear force(kN) 0 1600 4120 0 5950 144303 Bending Moment (kNM) 0 78590 631130 0 293070 22782604 Deflection (mm) 190 88 0 698 321 0

Across wind(simplified method)

1 Shear force(kN) 150 2970 4140 15 2970 41402 Bending Moment (kNM) 0 179990 865670 0 179990 865670

3 Deflection (mm) 326 139 0 326 122.50 0Across wind(Random responsemethod)

1 Shear force(kN) 1860 2580 9.13 1860 25802 Bending Moment (kNM) 0 112490 541040 0 112490 5410403 Deflection (mm) 204 87 0 204 87


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Figure-4 Variation of Bending moment for different methods along height in wind Zone I

Figure-5 Variation of Chimney Deflection for different methods along height in wind Zone I

Figure-6 Variation of shear force for different methods along height in wind Zone VI

Figure-7 Variation of Bending moment for different methods along height in wind Zone VI


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.Figure-8 Variation of Chimney Deflection for different methods along height in wind Zone VI

REFERENCES 1. Batham, J.P., Parameters required for the wind-tunnel

simulation of the wind loads on large power stationchimneys, Wind Engineering and Industrial dynamics,Elsevier science publishers -Amsterdam, Vol.18, 1985, pp.75-90.

2. Milford R.V., Structural reliability and cross windresponse of tall chimneys. Engineering structures,Butterworth & Co. (Publishers) Ltd, Vol.4, 1982, pp.263-270.

3. Reddy K.R.C, Jaiswal O.R and Godbole P.N, Windresponse control of tall RC chimneys,Wind andEngineering, Vol. 8, 2011, pp. 1- 9.

4. Reddy K. R. C, Jaiswal O. R. and P. N. Godbole.,Wind and Earthquake Analysis of Tall RC Chimneys,

Earth sciences and Engineering, October 2011, pp. 508-511.

5. Vickery B.J. and Basu.R. Simplified approaches to theevaluation of the across wind Response of chimneys,Wind Engineering and Industrial dynamics, Elsevierscience Publishers -Amsterdam, 1983, pp. 153-166.

6. Manohar, S.N., Tall Chimneys, Tata McGraw-HillPublishing Company Limited, New Delhi, 1981.7. Code of practice for design loads for buildings and

structures, IS: 875(Part-III):1987, published by Bureauof Indian standards.

8. Criteria for design of Reinforced concrete Chimneys,IS: 4998(Part-I):1992, published by Bureau of Indianstandards.

22 ijaet vol iii issue ii 2012

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