509 Wind and Earthquake Analysis of Tall Rc Chimneys

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 508-511

Across-wind analysis The across-wind response of chimney occurs mainly due to vortex shedding and velocity dependent forces. Across-wind analysis of chimney is required only if the critical wind speeds for any mode of oscillation is less than the mean design wind speed. The critical wind speed Vcri, for vortex shedding in the ith mode of vibration is given by

n

icri S

dfV ×= (5)

The sectional shear force ( izF 0 ) and the bending moment

( izM 0 ) at any height z0, for the ith mode of vibration is given by

∫ ⋅⋅⋅⋅⋅⋅=h

zzizoiiiz dzmfF

00

224 ϕηπ (6)

( )∫ ⋅−⋅⋅⋅⋅=h

zzizoiiiz dzzzmfM

00 0

224 ϕηπ (7)

Calculation of across wind load is made by first calculating the peak tip deflection for the specified mode of vibration. For Chimney with Little or No Taper {d(h)/d(0) > 0.5}, the model response, at a critical wind speed shall be calculated by

( ) 212

21

0

2

2

22

/1

)}2(2/)({25.1

eiaa

h

zi

ei

a

n

hiL

oi

mdkdzh

mLd

SdC

ρβϕ

πρ

πϕ

η

−

+

=

∫

I

(8)

where, mei = equivalent mass per unit length in kg/m in the

ith mode of vibration.

∫∫ ⋅⋅⋅=h

zizi

h

zei dzdzmm0

22

0

ϕϕ (9)

EARTHQUAKE ANALYSIS The earthquake loads are obtained as per IS 1893 (part 4): 2005. Time period of vibration, T of chimneys when fixed at base is given by,

gAE

hWCT t

T ..

.2

= (10)

where, CT is the coefficient depending upon the slenderness ratio of the structure, Wt is the total weight of the structure including weight of lining and contents above the base, h is the height of structure above the base, E s is the modulus of elasticity of material of the structural shell, A is the area of cross-section at the base of the structural shell. For circular sections, A = 2 π r t, where r is the mean radius of structural shell and t its thickness, and g is the acceleration due to gravity. The damping factor considered for the reinforced concrete material is 3 percent of critical value for design basis earthquake. In this case, the material damping factor of 0.048 is considered for determining Sa/g. Using the period T, the horizontal seismic coefficient Ah shall be obtained from the spectrum given in IS 1983 (Part 1). The design horizontal seismic coefficient for Ah design basis earthquake shall be determined by the following expression

( )( )( )IR

gSZA a

h2

= (11)

where, Z is the zone factor This is in accordance with Table 2 of IS 1893 (Part 1), I is the importance factor, R is the response reduction factor. The ratio (R/I) shall not be less than1.0. Sa/g is the spectral acceleration coefficient in accordance with IS 1893 (Part 1). The horizontal earthquake force shall be assumed to act alone in one lateral direction at a time. The effects due to vertical component of earthquakes are generally small and can be ignored. The effect of earthquake and maximum wind on the structure shall not be considered simultaneously. Design shear force and moment The simplified method can be used for ordinary stack-like structures. The design shear force, V, and design bending moment, M, for such structures at a distance x from the top, shall be calculated by the following formulae,

vthv DWACV ...= (12)

mth DhWAM ...= (13) where, Cv is the coefficient of shear force depending on slenderness ratio k, Ah is the design horizontal seismic coefficient, Wt is the total weight of structure including weight of lining and contents above the base, h is the height of centre of gravity of structure above base, and Dv, Dm are the distribution factors for shear and moment respectively at a distance x from the top of chimney. The expressions for these distributions for moment and shear along the height are given in Table 11 of code for use in computer programme.

510 K. R. C. Reddy, O. R. Jaiswal, P. N. Godbole

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 508-511

EXAMPLE CHIMNEYS Two chimneys are considered for the analysis purpose. The 217 m chimney as shown in Figure 1(a) consists of four tapers and twenty one platforms. The platform details are also shown in Figure 1(a). Where as the 220 m chimney as shown in Figure 1(b) is of uniform taper whose outer diameter and shell thickness at the top and bottom are shown. Modeling For the analysis purpose Chimneys are modeled as vertical cantilever fixed at the base having varying cross sections using beam element (NKTP 12) of NISA (EMRC, 1998). Chimneys are divided into elements of one meter length along its height. The mass of each section is calculated by averaging the mass of above and below it. Chimney is idealized as mdf system with mass lumped at various levels. Horizontal motion is considered. Natural frequency and mode shapes required for the analysis are obtained from this finite element model of chimney. Material The material used for chimney shell is M25 grade concrete whose mass density (ρ) considered as 2.5 t/m3, weight density as 25 KN / m3, Young’s modulus (E) as 3.2 x 107 kN/m2 and structural damping as a fraction of critical damping (β) is considered as 0.016. Free vibration characteristics such as natural frequency and time periods are obtained from the dynamic analysis of chimneys and shown in Table 1. Then critical wind speeds and mean design wind speeds are calculated and presented in Table 2.

Table 1: Free vibration characteristics of chimneys

Chim. Ht. (m)

Natural Frequency (Hz)

Time period (sec.)

1st mode

2nd mode

3rd mode

1st mode

2nd mode

3rd mode

217 0.33 1.39 3.44 2.98 0.72 0.29 220 0.44 1.86 4.53 2.23 0.53 0.22

The critical wind velocity and the design wind velocity are calculated by taking Vb = 44 m/s , k1 = 1.07 , k3 = 1.00, sn = 0.2 and d = average diameter over the top 1/3 height of chimney Table 2: Critical wind speeds (Vcri.=fd/sn) and mean design wind speed(Vzbar)

Chi ht. (m)

d (m)

Critical Wind Velocity, Vcri =fd/sn (m/s)

Vzbar =Vbk1k2b

ark3 m/s

1st

mode 2nd

mode 3rd

mode 217 14.7 24.7 102.5 253.9 46.35 220 15.6 34.9 145.5 354.6 46.45

(a) 217 m chimney

(b) 220 m chimney

Figure 1: Example chimneys

RESULTS AND DISCUSSION The numeric results of along- and across-wind analysis and earthquake analysis are obtained as per the procedure given above for the both the chimneys.

511 Wind and Earthquake Analysis of Tall Rc Chimneys

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 508-511

Along-wind analysis The along-wind analysis of chimney is performed using Random Response Method of IS: 4998 (Part-1)1992. Maximum shear force and bending moment for both the chimneys have been calculated with various options using random response method and the results are given in Table 3. Across-wind analysis In across-wind analysis, those modes for which critical wind speed less than mean design wind speed are to be considered. It is fond that the critical wind speed of only first mode is less than the mean design wind speed, hence only the first mode has been considered in the across-wind analysis. Maximum shear force and bending moment computed by random response method of IS: 4998 and the results are presented in Table 3.

Table 3: Results of wind analysis Chimney Height

(m)

SF kN

Along Across Combined 217 1512 2239 2701 220 3410 5654 6654

Chimney Height

(m)

BM kNm

Along Across Combined 217 196822 348462 400205 220 454434 832453 948413

Earthquake analysis To obtain the earthquake loads, the time period is calculated using the Equation 10. Knowing the time period of chimneys the horizontal seismic coefficients are calculated as per the Equation 11. Then the design shear force and bending moments are evaluated by Equations 12 and 13 respectively. The results are obtained for different response reduction factors with R equal to 3.0 and 1.5 and also various values of zone factors. The design shear force and the bending moment of 217 m chimney are presented in Table 4 and that of 220 m chimney is given in Table 5.

Table 4: Earthquake analysis results of 217 m chimney

Sr. no.

Zone No.

Zone factor

R=3.0 R=1.5 SF kN

BM kNm

SF kN

BM kNm

1 II 0.10 454 74222 909 148443 2 III 0.16 727 118754 1456 237509 3 IV 0.24 1091 178131 2184 356263 4 V 0.36 1637 267198 3276 356264

Table 5: Earthquake analysis results220 m chimney Sr. no.

Zone No.

Zone factor

R=3.0 R=1.5 SF kN

BM kNm

SF kN

BM kNm

1 II 0.10 522 87238 1045 174476 2 III 0.16 836 139581 1672 279162 3 IV 0.24 1254 209371 2508 418743 4 V 0.36 1881 314057 3762 628115

On studying the results presented in the above tables, it shows that as the zone factor increases the values of shear force and bending moment increases. It is mentioned that the response reduction factor of 3.0 is sufficient for estimating the earthquake loads but the results becoming double if the R equal to 1.5. The results obtained with R equal to 1.5 and with zone factor of 0.36 are almost matching with that of the wind loads. CONCLUSIONS On comparison of the wind loads with that of the earthquake loads, the following conclusions are drown, The wind loads are always governing the design of

chimney shell. In the most critical earthquake zone with zone

factor of 0.36 and response reduction factor of 1.5, the earthquake response is almost matching with that of wind response but never been crossing the wind response.

For the design of the chimney shell, the combined design wind loads are used.

REFERENCES [1] ACI 307:1998,’Standard practice for design and

construction of RC chimneys(ACI 307-98) and

commentary(ACI 307R-98)’,American Concrete

Institute, Detroit

[2] IS 4998(part-1):1992, ‘Criteria for Design of

Reinforced Concrete Chimneys’, 2nd revision,

Bureau of Indian Standards, New Delhi.

[3] IS 1893 (Part 4):2005, ‘Criteria for earthquake

resistant design of structures’, Bureau of Indian

Standards, New Delhi.

[4] Jain, S.K., Singh, B.P., Guptha, B.K., 1990, ‘I.S.

code provisions for seismic design of tall

chimneys’, International of structures, Vol. 10,

No. 2, pp 103-111

[5] Jaiswal, O.R., Srinivas, V., 2005, ‘Effect of tuned

mass damper on across-wind response of tall RC

Chimneys’, Journal of Wind & Engineering, India,

vol.2, No.1, pp.9-21

[6] Shivaji, M., Raju, V.S.N., ‘Dynamic analysis of

R.C.C. chimneys’