Non Liner Dynamic Analysis of RCC Chimney

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 uniform-tapered by using the software SAP-2000 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.

1. 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.

   1. 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.

   2. Methodology

   To achieve the above objective following step-by-step 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.

2. DIMENSIONAL DESCRIPTION OF RCC CHIMNEY

   For the present studies, twelve models of RC chimney are chosen with four different heights of uniform, tapered and uniform-tapered 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 uniform-tapered chimney diameter of the chimney from the top will be uniform upto one-third 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 1-1992]

   Fig: 1 Uniform-tapered chimney model [SAP 2000]

   1. 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
        Uniform-tapered section	M1C	M2C	M4C	M4C
        HEIGHT	150m	200m	250m	300m

   2. Wind Load Calculation Along wind analysis:

The along-wind 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 (Part-3): 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 part-3)

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. (G-1)/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(G-1)/H² [Z/H] h FZ z dz

=11.78kN/m F= (Fz+F'z)

=19.46kN/m

3 RESULTS AND DISCUSSIONS

1. 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

   Fig-2 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 uniform-tapered section the displacement values were lesser than other two sections up to one third height and then displacement increases gradually up to 300m

2. time history analysis

Table 3 Mode and Frequency

Fig-3 Graph for mode VS Frequency

Table-4 Mode and Period

Fig-4 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

Fig-4 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.

Table- 3 Displacement due to earthquake load with respect to height

Fig-5 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 uniform-tapered 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 SAP-2000 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 uniform-tapered 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

1. 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 0974-5904, Vol. 04 No 06 SPL, October 2011 pp. 508-511.

2. 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 (IOSR-JMCE), ISSN: 2278-1684, pp. 12-19.

3. W S Ruman(1970), Earthquake forces in reinforced concrete chimney, ASCE Journal of structural division, 93(ST6), pp.55-70.

4. CICIND, Model code for RC chimneys (Revision 1-

   December 1999), Amendment A, March 2002

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

6. Criteria for design of Reinforced concrete Chimneys, IS: 4998(Part-I):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.