 Open Access
 Total Downloads : 855
 Authors : Amit Nagar, Shiva Shankar M, T Soumya
 Paper ID : IJERTV4IS070435
 Volume & Issue : Volume 04, Issue 07 (July 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS070435
 Published (First Online): 20072015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Non Liner Dynamic Analysis of RCC Chimney
Amit Nagar1
1 Student, Structural Engineering, MVJ College of Engg,
Karnataka, India
Shiva Shankar. M2
2 Student, Structural Engineering, MVJ College of Engg,
Karnataka, India
T Soumya3 3Assistant Professor, Structural Engineering, MVJ College of Engg,
Karnataka, India
Abstract – The effect of earthquake and wind loads on the RCC chimney will plays a significant role in the dynamic analysis and design of the chimneys with extreme heights. The dynamic behaviour of the RC chimney will vary in wider range with respect to the height and longitudinal section of the chimney as the load exerted by the wind and earthquake on the chimney are dynamically sound and effective and tending the chimney to undergo peak displacement and acceleration. Because of its slenderness chimneys are the structures supposed to retain the critical loads by seismic and wind effects This project presents the study of along wind load and earthquake load effects on RC chimneys in zone I (basic wind speed 33m/sec).seismic analysis is carried out by time history analysis as per IS 1893(part 4):2005 and wind analysis by along wind effects by gust factor method as per draft code CED 38(7892):2013 (third revision of IS 4998(part 1:1992) for different heights varying from 150 to 300m and for different longitudinal sections such as uniform, tapered and uniformtapered by using the software SAP2000 This study presents the resulting peak displacement and acceleration for the wind analysis, and the joint displacements and base shear for the seismic analysis, period and frequency with respect to mode by time history analysis. The RC chimney with more height and uniform section will be critical compared to other types and best suitable section will be uniform tapered for both seismic and wind load effects exhibiting minimum displacement.
Key Words: RCC Chimney, , Dynamic Analysis, SAP2000,and Time History Analysis.

INTRODUCTION
Chimneys are tall slender structures which accomplish an important function. They had a humble beginning as a household vents and over the years, as vents grew larger and taller, they came to be known as chimneys. A cluster of them is stack. During early days the term stack was used to describe the extension piece added to a flue duct to convey and discharge combustion gases away from the operating area of the industry. A stack which was scientifically designed to take cognizance of gas
temperatures and velocity effects, corrosion aspect, etc. was called a chimney. By usage the term stack has gained popularity and today it also signifies a chimney. Chimneys are the structures which built to greater heights as tall slender structures. In early days, as household vents and over the years; they are popularly known as chimneys. Chimneys or stacks are used as a medium to transfer highly contaminated polluted gases to atmosphere at a greater height.

Scope and Objective

To determine the nonlinear behaviour of chimney structures without opening at section utilizing nonlinear dynamic analysis.

To validate the result obtained from the nonlinear dynamic analysis using SAP 2000 in comparison with the result from manual analysis.

To carry out the dynamics analysis for various deformation levels.


Methodology
To achieve the above objective following stepbystep procedures are followed

Carried out literature study to find out the objectives of the project work.

Understand the wind analysis and design procedure of a RCC chimney as per Indian Standard IS 4998(part1):1992.

Analyse all the selected chimney models using manual calculations and finite element analysis (SAP 2000).

Evaluate the analysis results and verify the requirement of the geometrical limitations.


DIMENSIONAL DESCRIPTION OF RCC CHIMNEY
For the present studies, twelve models of RC chimney are chosen with four different heights of uniform, tapered and uniformtapered sections. The heights of the chimney selected are 150m, 200m, 250m and 300m.Grade of concrete is taken as M30 and basic wind speed for the wind
zone of Bangalore as 33m/sec. seismic zone is zone II and soil is taken as hard soil.
For uniform chimney, the diameter of the chimney is taken as 14m[d] and thickness of the RC shell at the bottom is 0.45m and at the top it is 0.3m.
For tapered chimney, the diameter of the chimney at the bottom is 14m and is varying uniformly up to the top diameter 8m. The thickness of the RC shell is same as uniform chimney. The slope of tapering is 1 in 50.
For uniformtapered chimney diameter of the chimney from the top will be uniform upto onethird of the total height of the chimney taken from the top and get tapered upto the bottom of the chimney.[according to IS 4998 part 11992]
Fig: 1 Uniformtapered chimney model [SAP 2000]

Basic Data For Modeling

Typical grid spacing in X direction = 2m, Y= 1m, Z = 3m.

Wind speed =33 m/sec

Type of soil = hard soil

Seismic zone = 2

Taper of chimney = 1 in 50

Top dia of chimney = 8m

Height of chimney = 150m, 200m, 250m, 300m.

Grade of concrete fck = M30

Grade of steel fy = fe500

Shell thickness at top = 0.3m

Shell thickness at bottom = 0.45m
Table 1: Twelve typical model series of different heights
TYPE
Series1
Series2
Series3
Series4
Uniform section
M1A
M2A
M3A
M4A
Tapered section
M1B
M2B
M3B
M4B
Uniformtapered section
M1C
M2C
M4C
M4C
HEIGHT
150m
200m
250m
300m


Wind Load Calculation Along wind analysis:

The alongwind loads are caused by the drag component of the wind force on the chimney. This is accompanied by gust buffeting causing a dynamic response in the direction of mean flow. Here along wind load calculation is done using Excel spread sheet and MATLAB programming.
From, IS 875 (Part3): 1987,
Design wind speed Vz = Vb x k1 x k2 xk3
Where, k1 risk coefficient (probability) for 33 m /sec (wind speed), k2 terrain factor and k3 topography factor(from IS875 part3)
k1 =1
k2 =1
k3 =1.36
Therefore, Vz = 44.88 m/sec
Design Wind pressure (Pz) = 0.6 x Vz2 = 1.208 kN/m2
The along wind load per unit height at any height z on a chimney shall be calculated from the equation:
F = Fz + Fz
Where, Fz= is the wind load in N/m height due to HMW at height z and is given by
Fz = pz. Cd. Dz = 7.68 kN
Fz = is the wind load in N/m height due to the fluctuating component of wind at height z
Fz= 3. (G1)/H2. (Z/H)0h Fz .z .dz
G =gust factor = (1+ gf rt (B + [SE/])=2.48 gf = (2Ld(VT) + (0.5777/(2 X Ln(VT))=3.62
f1 = natural frequency of chimney in the first mode of vibration in Hz = 0.482 Cps.
V10 = hourly mean wind speed in m/set at 10 m above ground level = Vb.k2 = 33.
Where, Vb and k2, are as defined in IS 875 (Part 3): 1987S=Size reduction factor = (1+ 5.78 (f1/V10)1.14H.98).8
=0. 173
E = A measure of the available energy in the wind at the natural frequency of the chimney = [123 (f1/ V10) H0.21] / [1+ (330f1/V10)2 H.42].83 = .065
B=Back ground factor indicating the slowly varying component of wind load fluctuation = [1+ (H/265).63].88
= 0.627
r = Twice the turbulence intensity = 0.622.178log10H
= 0.243
F'Z = 3(G1)/HÂ² [Z/H] h FZ z dz
=11.78kN/m F= (Fz+F'z)
=19.46kN/m
3 RESULTS AND DISCUSSIONS

Along wind analysis:
Table 2 Displacement values for the Chimney
SL NO.
LEVEL
M4A
M4B
M4C
1
10
2.541316
1.93181
1.787426
2
20
6.968718
5.456475
5.151503
3
30
14.43335
11.56493
11.08204
4
40
24.53699
20.04231
19.44906
5
50
37.25418
30.95801
30.39091
6
60
52.42809
44.28061
43.94965
7
70
69.89105
59.97097
60.15921
8
80
89.45526
77.97032
79.03783
9
90
110.9383
98.21333
100.6027
10
100
134.1725
120.6316
124.8733
11
110
159.0059
145.1558
151.8736
12
120
185.2974
171.7154
181.6305
13
130
212.9137
200.2381
214.1721
14
140
241.7278
230.6492
249.525
15
150
271.6179
262.8699
287.7119
16
160
302.4674
296.8151
328.7489
17
170
334.1648
332.3932
372.6438
18
180
366.6039
369.5059
419.3875
19
190
399.6842
408.0475
468.9622
20
200
433.3099
447.9052
521.2877
21
210
467.3899
488.9588
575.2569
22
220
501.8372
531.0815
631.3684
23
230
536.5685
574.1406
689.2578
24
240
571.504
617.9993
748.5543
25
250
606.5681
662.5177
808.9295
26
260
641.695
707.5552
870.0901
27
270
676.8416
752.9651
931.7759
28
280
711.9882
798.5829
993.7375
29
290
747.1355
844.2539
1055.765
30
300
782.2595
889.8928
1117.76
Fig2 Graph for Displacement Vs Height
Observations and discussions: At one third height of 300m chimney, displacement of 433.30mm for uniform, 447.9mm for tapered and 521.2877mm for uniform tapered is observed. Whereas for 250m height, displacement of 782.25mm for uniform, 889.8928mm for tapered and 1117.76mm for uniform tapered is observed which indicates that in uniformtapered section the displacement values were lesser than other two sections up to one third height and then displacement increases gradually up to 300m

time history analysis
Table 3 Mode and Frequency
MODE 
M4Acyc/sec 
M4B cyc/sec 
M4C cyc/sec 
1 
0.14468 
0.1578 
0.1578 
2 
0.14468 
0.1578 
0.1578 
3 
0.87025 
0.73808 
0.73808 
4 
0.87025 
0.73808 
0.73808 
5 
1.7716 
1.8378 
1.8378 
6 
2.0726 
1.8378 
1.8378 
7 
2.0726 
2.5632 
2.5632 
8 
2.0989 
2.8835 
2.8835 
9 
2.0989 
2.8835 
2.8835 
10 
2.2366 
3.1406 
3.1406 
11 
2.2366 
3.36 
3.36 
12 
2.3011 
3.36 
3.36 
Fig3 Graph for mode VS Frequency
Table4 Mode and Period
MODE 
M4A(sec) 
M4B(sec) 
M4C(sec) 
1 
6.91181 
6.33724 
6.712504 
2 
6.91181 
6.33724 
6.712504 
3 
1.149098 
1.354875 
1.579017 
4 
1.149098 
1.354875 
1.579017 
5 
0.564477 
0.544141 
0.621754 
6 
0.482488 
0.544141 
0.621754 
7 
0.482488 
0.390143 
0.366949 
8 
0.476449 
0.346801 
0.334069 
9 
0.476449 
0.346801 
0.334069 
10 
0.447111 
0.318406 
0.310359 
11 
0.447111 
0.297623 
0.310359 
12 
0.434566 
0.297623 
0.309793 
Fig4 Graph for mode Vs Period
Observations and discussions: From the graph plotted for frequency v/s mode and period v/s mode number we can notice that mode 1 is with least frequency and higher period. For mode 1, uniform section frequency is 0.144cycs/sec and period is 6.911sec which depicts that for mode 1 we have least frequency and higher period value compared to other sections and it indicates that uniform section will be within permissible standards by time history analysis. The observed results which are tabulated indicate that uniform section is with first preferene and then its uniform tapered and tapered.
Table 4 Max Shell Stress in Chimney
Fig4 Bar chart for max shell stress in chimney
Observations and discussions: from the plotted bar chart for shell stress of the RC chimney under wind loads, the uniform sectioned RC chimneys are subjected to more shell stress as compared with other models and the shell stress increases with the increase in height. Shell stress will be at its peak for models with 300m height and for uniform sections 10154.94KN/m2 will be the extreme shell stress noticed in 300m height chimney of uniform section.
SL NO. 
LEVEL 
M4A 
M4B 
M4C 
(mm) 

1 
10 
1.057389 
0.740677 
0.659427 
2 
20 
2.935566 
2.115676 
1.920572 
3 
30 
6.082177 
4.491032 
4.136381 
4 
40 
10.31319 
7.775326 
7.249869 
5 
50 
15.60284 
11.98896 
11.30624 
6 
60 
21.88693 
17.12268 
16.32571 
7 
70 
29.11053 
23.17172 
22.33435 
8 
80 
37.21682 
30.12739 
29.35642 
9 
90 
46.14973 
37.97881 
37.41594 
10 
100 
55.85345 
46.71224 
46.53603 
11 
110 
66.27272 
56.31099 
56.73869 
12 
120 
77.35284 
66.75521 
68.04442 
13 
130 
89.03989 
78.02168 
80.47182 
14 
140 
101.2808 
90.08362 
94.03706 
15 
150 
114.0236 
102.9106 
108.7533 
16 
160 
127.2174 
116.4682 
124.6299 
17 
170 
140.8129 
130.7183 
141.6719 
18 
180 
154.7622 
145.6185 
159.8772 
19 
190 
169.0194 
161.1227 
179.2412 
20 
200 
183.5405 
177.1807 
199.734 
21 
210 
198.2837 
193.7388 
220.9084 
22 
220 
213.2099 
210.7398 
242.9563 
23 
230 
228.2825 
228.124 
265.72 
Table 3 Displacement due to earthquake load with respect to height
SL NO. 
MODEL NO. 
SHELL STRESS (kN/m2) 
1 
M4A 
10154.94 
2 
M4B 
7671.68 
3 
M4C 
7205.3 
24 
240 
243.4682 
245.8294 
289.0404 
25 
250 
258.7367 
263.7932 
312.7786 
26 
260 
274.0617 
281.9533 
336.8116 
27 
270 
289.4206 
300.2502 
361.0357 
28 
280 
304.795 
318.6294 
385.3668 
29 
290 
320.171 
337.0456 
409.7428 
30 
300 
335.5406 
355.467 
434.1254 
Fig5 Graph for joint displacement Vs Height
Observations and discussions: At one third height of 300m chimney, joint displacement of 169.01mm for uniform section, 161.12mm for tapered and 179.2412mm for uniform tapered is observed where as for 200m height, joint displacement of 161.61mm for uniform, 166.13mm for tapered and 215.28mm for uniform tapered is observed which indicates that in uniformtapered section the displacement values were lesser than other two sections upto one third height and then displacement increases gradually upto 300m
Fig 6: Time history graph showing peak displacement for M4A chimney model
Fig 7: Time history graph showing peak displacement for M4B chimney model
Fig 8: Time history graph showing peak displacement for M4C chimney model
Observations and discussions: From the time history analysis carried out bar chart for peak displacement has been plotted. By the graph it is noticed that Peak displacement for M4C is 8.2mm is maximum for 300m height model; comparatively 150m models are with least displacement and the displacement is incremental with respect to height. The graph for peak displacement by time history analysis has been extracted from SAP2000 for in comparison with the manual results
Fig 9: Time history graph showing peak acceleration for M4A chimney model
Fig 10: Time history graph showing peak acceleration for M4B chimney model
Fig 11: Time history graph showing peak acceleration for M4Cchimney model
Observations and discussions: From the time history analysis conducted for all the models, the bar chart has been plotted and it is noticed that the uniform sections will exhibits more acceleration that is for M4A it is 9.2m/sec2. But the uniformtapered section will depicts least acceleration of 1.14m/sec2 compared to other models.
CONCLUSION

The uniform tapered section subjected to wind analysis exhibits more displacement as observed by the displacement graphs for all heights. And it can be concluded that the displacements obtained for chimneys increases with the increase in height of the slender structure.

Up to one third height of 300m chimney, all types of displacement values[displacement by wind analysis, joint displacement by seismic analysis, peak displacement by time history analysis] are in decremented order as uniform section, uniform tapered, tapered. After that the displacement values will initiate to increase up to extreme height 300m of the chimney. The displacement by wind analysis as 1117.76mm, joint displacement as 215.28mm and Peak displacement as 8.2mm for uniform tapered section of 300m height which indicates that the uniform tapered section has to be designed by taking into consideration the extreme displacement values.

By considering proper design parametric considerations it necessitates to overcome the effects of maximum displacement which is in divergence with other models.
REFERENCES

K. R. C. Reddy, O. R. Jaiswal and P. N. Godbole Wind and Earthquake Analysis of Tall RC Chimneys, International Journal of Earth Sciences and Engineering ISSN 09745904, Vol. 04 No 06 SPL, October 2011 pp. 508511.

M. G. Shaikh MIE, H.A.M.I. khan, Governing Loads for Design of A tall RCC Chimney, IOSR Journal of Mechanical and Civil Enginering (IOSRJMCE), ISSN: 22781684, pp. 1219.

W S Ruman(1970), Earthquake forces in reinforced concrete chimney, ASCE Journal of structural division, 93(ST6), pp.5570.

CICIND, Model code for RC chimneys (Revision 1
December 1999), Amendment A, March 2002

CED 38(7892) WC April 2013 Code of practice of reinforced concrete chimneys Third Revision

Criteria for design of Reinforced concrete Chimneys, IS: 4998(PartI):1992, Published by Bureau of Indian standards, New Delhi.
BIOGRAPHIES
Amit Nagar, Student, Structural Engineering, MVJ College of Engineering.
Shiv Shankar M, Student, Structural Engineering, MVJ College of Engineering.
T Soumya, Assistant Professor, Structural Engineering, MVJ College of Engineering.