correlation of geometry and dynamic response of self...

133 Harshal Deshpande1, Roshni John

2

International Journal of Engineering Technology Science and Research

IJETS R

www.ijetsr.com

ISSN 2394 – 3386

Volume 2, S pecial Issue

September 2015

Correlation of Geometry and Dynamic Response of Self-

Supported Short Circular Steel Stacks

Harshal Deshpande1, Post Graduate Student in Structural Engineering,

Saraswati College of Engineering, Kharghar Roshni John

2, Assistant Professor, Saraswati College of Engineering, Kharghar

ABSTRACT

Steel stacks are smoke releasing slender structures constructed in various industries. They are subjected to static and

dynamic loadings. Dynamic analysis is carried out by considering both seismic loading and dynamic wind loadings.

Apparently dynamic wind effects are critical for steel stacks and they govern the stability conditions. Steel stacks being

slender and long sections they are more prone to dynamic wind oscillations and corresponding stresses. Present study

deals with interrelation of geometrical configuration and obtained dynamic response of short self-supported steel stacks

under dynamic wind loadings and seismic loadings. 42 steel stack configurations for 7 different heights of stacks are

selected and analyzed for dynamic wind loadings and seismic loadings as per Indian standards (IS:6533 part2)and IS

1893(part 4). a relation between dynamic response and governing geometry of the stack is found out. Use of excel sheets

and STAAD-proV8i software is done for analysis.

Keywords

Dynamic wind response, steel stacks, analysis of dynamic wind for slender stacks, oscillations of steel stacks.

1. INTRODUCTION

Stacks or chimneys are very important industrial structures for releasing out waste harmful gases to a higher elevation in atmosphere. Stack structures are tall, slender and tapering with circular cross-sections. Steel stacks are ideally suited for works involving short heating period and less thermal capacity. Fig. 1.1 shows chimneys located in an industrial campus.

Fig.1.1 industrial steel stacks


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1.1Analysis of Steel Stacks

1.1.1 forces acting on steel stacks

Steel chimneys or stacks are basically under the influence of following loads

1. Static load

2. Dynamic wind load

3. Seismic loads

Static loads include self-weight and weight of lining and other components of stacks. (Ref.IS 6533(part1):1989)It also includes static wind loads and corresponding static wind pressures. (Ref. IS 875(part3):1987).Dynamic wind effects include along wind and across wind effects .this includes the drag forces and the vortex excitation along with aerodynamic forces acting on stack causing stacks to oscillate(ref.IS 6533(part 2):1989). 3. Seismic effects include the effect of dynamic force exerted on the steel stacks during earthquakes. in current work response spectrum method is used to analyze the selected steel stacks.

1.2 Geometry of steel stacks

Geometry of a stack or a chimney plays an important role in the process of analysis as it affects the stiffness parameters. (Ref. IS 6533:1989 part2). Basic geometry of steel stack is governed by top diameter (D t), base diameter (Db) and effective height of stack (He). Following IS codes are used for the analysis of steel stack.

1. IS 6533 (Part-1): 1989 “Indian standard design and construction of steel stacks-code of practice - Mechanical aspects.”

2. IS 6533 (Part-2): 1989 “Indian Standard Code of practice for design and construction of steel chimneys "structural aspects.

3. IS 875 (Part-3):1987: For calculation of wind loads

4. IS 1893 (Part-4):2005: This code covers the seismic considerations to be followed for the design .Seismic zones and formulae based on design considerations will be included from this code.

2. FORMULATION OF RESEARCH PROBLEM

2.1 Description of selected steel stacks/chimneys

1. Type of stack = circular self-supporting industrial steel stacks

2. Heights of stacks: 30 m ,35m,40m,45m ,50m ,55m,60 m ( short stacks)

3. Top diameter for each stack is taken as minimum h/30 as per provision in IS 6533 :1989

4. Variation in base diameter for each stack for fixed value of top diameter will be in following incremental ratios (ratio Db/Dt) : 1.6,1.7,1.8,1.9,2.0,2.1

5. Type: unlined single flume.

6. Temperature inside chimney : 2000c average

7. Flare height: one third of total height.

8. Thickness of stack shell= 16 mm ( constant for all stacks)

9. Base : rigid

10. location :Mumbai

11. wind speed : 44m/s

12. material :Mild steel

13. variation in geometry : top to base diameter ratio in each configuration

14. soil :medium (bearing capacity 200kN/m2)

15. seismic zone :III


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16. damping :5%

17. connections :welded joints

IS Codal provisions for geometry are the basis of variations in the geometry. Minimum top diameter of

unlined chimney should be one twentieth of the effective height of chimney /stacks and minimum outside diameter at the base should be equal to 1.6 times the top diameter of the stack . (As per IS 6533(part2):1989 (reaffirmed in 2003) cl.7.2.4 (b) and (c).)Manual calculations are done for validating the results of STAAD-pro v8i software results. Dynamic wind responses are calculated using MS-excel sheets and seismic responses are calculated by STAAD-pro v8i.

Table 1 geometry of selected steel stacks

Total height of stack

(Metres) (H)

Effective height

(2/3× H)

(Metres)

Top diameter

(constant)

(H/30)

Varying top to bottom diameters ratio.

From minimum 1.6 and then increased by 0.1 up to 2.1

Dt/ Db ratio

1.6 1.7 1.8 1.9 2.0 2.1

H He Dt (m) Db (m) Db (m) Db (m) Db (m) Db (m) Db (m)

30 20 1 1.6 1.7 1.8 1.9 2.0 2.1

35 23.33 1.16 1.856 1.972 2.088 2.204 2.32 2.436

40 26.66 1.33 2.128 2.261 2.394 2.527 2.66 2.793

45 29.97 1.5 2.4 2.55 2.7 2.85 3.00 3.15

50 33.33 1.66 2.656 2.822 2.988 3.154 3.32 3.486

55 36.3 1.83 2.928 3.111 3.294 3.477 3.66 3.843

60 40 2.00 3.2 3.4 3.6 3.8 4.00 4.2

3. Methodology

3.1 general procedures for dynamic analysis

Chart1: Schematic Representation of Dynamic Analysis

3.2 dynamic wind sample calculations (as per IS 6533 (part2):1989)

Dynamic wind response includes dynamic force, dynamic moment and corresponding deflections

Calculations are done by using excel sheets .total 18 excel sheets are prepared for iterative calculations. Sample calculation results for 30m chimney are shown in short below.


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Table 3.2 Sample Calculation for 30 M Chimney with 1m Top Diameter and 1.6m Base Diameter

Cumm. Ht Pstatic Time Period Ƹi €i from table 5 IS 6533 p.2 Mk V

(N) (Sec) Unlined

5 5938.3 0.685 0.025 2.502 0.6 0.7

10 4709.7 0.685 0.025 2.502 0.6 0.7

15 4672.9 0.685 0.025 2.502 0.575 0.7

20 5079.0 0.685 0.025 2.502 0.55 0.7

25 5341.5 0.685 0.025 2.502 0.5325 0.7

30 5610.5 0.685 0.025 2.502 0.515 0.7

Segmental Ht. Yik & Yij Mk & Mj Ηij Pdyn Pk (Kn)

staad kg Newton

5 0.0223 2884 0.045 2.28 5.94

10 0.1037 2280.6 0.2089 8.37 4.72

15 0.265 1979 0.5339 18.565 4.69

20 0.4859 1979 0.9789 34.037 5.11

25 0.7377 1979 1.486 51.673 5.39

30 1.0 1979 2.0145 70.049 5.68

3.3 Seismic Response sample Calculations (for 30 m chimney)(IS 1893 (part4):1989)

Seismic Zone = Zone III, Zone Factor (Z) = 0.16

Importance Factor (I) = 1.5

Response Reduction Factor (R) = 2.0

Fundamental Time Period (T) = CTWt.hEs.A.g = 0.665s

Fundamental Time Period for Flared Structure (Te) = T/2 = 0.3325s

Radius of Gyration (re) = 12(Db2 ) = 0.565m

Base Diameter (Db) = 1.6m

Slenderness ratio (k) = h/ re = 53.09

Coefficient (CT) = 1.8*k = 95.57

Weight of Stack = 254kN (As per STAAD.Pro)

Elastic Modulus of Steel = 200000 MPa

Cross sectional Area at the base of shell (A) = π.Db.Ts = 0.08 sq.m

Acceleration due to gravity (g) = 9.81 m/s2

Design horizontal acceleration spectrum value (Ah) = (Z2).(Sag)(RI) = 0.15

Spectral acceleration coefficient (Sa/g) = 2.5 (As per Clause 6.4.5 of IS 1893(Part-1): 2002 for Medium soil)

Design Static Seismic Base Shear (Vb) = Cv. Ah. W. Dv = 57.15kN


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Table 3.2 Calculation of Base Shear:

Fundamental Time

Period (Sec) Mode Shape

Coefficient (Ф) Wi.Фi Wi.Фi2 C1

Design Horizontal

Acceleration Design Base

Shear (kN)

0.11 0.175 17.72 3.10

1.87

0.15 9.96

0.04 0.35 13.58 4.75 0.15 7.63

0.04 0.525 20.37 10.70 0.15 11.45

0.15 0.7 54.33 38.03 0.15 30.54

0.33

106.01 56.58

59.58

3.4 Sample Calculations for Dynamic Wind Loads by Excel Sheets and Seismic Responses by STAAD-

Prov8i

Fig 3.1 a) sample excel sheet for dynamic wind load

3.5 Seismic Loads Calculations models of 30 m ,45m and 60 m with 6 variations of top to base diameters are modeled in STAAD-proV8i .for fundamental time period, frequency ,mode shapes ,von mises stresses ,principal stresses bending stresses, base shear and moments using response spectrum method.


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IJETS R

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September 2015

Fig 3.2 sample STAAD-pro model of a 30m chimney with first mode

Fig 3.3 absolute stresses on steel stack 45m


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Fig .3.4 maximum von mises stresses on steel stack 45 m

4. Results

Table 4.1 Dynamic Wind responses

Height (m) Top Dia(m) Bottom Dia(m) P (kN) V (kN) M (kN.m) Deflection (mm)

safe safe safe safe

30 1.000

1.600 128.312 31.537 475.919 48.535

1.700 130.290 31.938 477.303 45.547

1.800 132.260 32.341 478.706 43.017

1.000 134.240 32.745 480.125 40.851

2.000 136.212 33.149 481.557 38.980

2.100 138.185 33.554 483.000 37.350

35 1.160

1.856 174.012 43.842 776.346 68.725

1.972 176.683 44.388 778.523 64.495

2.088 179.350 44.935 780.741 60.911

2.204 182.020 45.483 782.980 57.843

2.320 184.693 46.033 785.240 55.192

2.436 187.363 46.583 787.525 52.883


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40 1.330

2.128 228.390 59.255 1201.670 91.608

2.261 231.886 59.978 1204.969 85.962

2.394 235.385 60.703 1208.328 81.177

2.527 238.884 61.430 1211.738 77.082

2.660 242.382 62.159 1215.189 73.543

2.793 245.881 62.889 1218.679 70.461

45 1.500

2.400 290.137 77.265 1767.419 118.399

2.550 294.576 78.192 1772.188 111.097

2.700 299.015 79.123 1777.053 104.909

2.850 303.454 80.056 1781.999 99.612

3.000 307.893 80.992 1787.012 95.035

3.150 312.333 81.930 1792.081 91.048

60 2.000

3.200 517.061 127.03 3913.951 195.594

3.400 524.953 128.48 3923.701 183.522

3.600 532.845 129.91 3932.951 173.255

3.800 540.736 131.4 3943.901 164.518

4.000 548.628 132.85 3954.051 156.944

4.200 556.52 134.32 3964.401 150.339

Table 4.2 Seismic responses

Height

(m) Top

Dia(m) Bottom Dia(m) Time period

(T) (sec.) Frequency(f) SRSS shear(kN) Absolute

shear (kN)

30 1.000

1.600 0.3325 3.007 61.65 81.06

1.700 0.322 3.103 72.83 79.96

1.800 0.3125 3.192 78.83 78.92

1.000 0.3054 3.274 77.76 77.93

2.000 0.2985 3.349 60.58 77.01

2.100 0.2925 3.418 57.57 76.14

35 1.160

1.856 0.376 2.654 103.03 113.83

1.972 0.3664 2.729 82.33 112.51

2.088 0.3572 2.799 89.79 111.24

2.204 0.349 2.865 108.91 110.03

2.320 0.3417 2.926 78.29 108.88


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2.436 0.3293 3.037 76.02 106.73

40 1.330

2.128 0.4553 2.196 116.98 140.21

2.261 0.4352 2.297 126.28 137.37

2.394 0.4268 2.343 134.07 136.05

2.527 0.4191 2.386 101.7 134.79

2.660 0.4060 2.463 130.51 132.46

2.793 0.4003 2.498 93.33 131.38

45 1.500

2.400 0.4989 2.004 138.51 182.46

2.550 0.4834 2.069 153.76 179.97

2.700 0.4699 2.128 176.53 177.62

2.850 0.4583 2.182 132.27 175.4

3.000 0.4481 2.232 126.25 173.32

3.150 0.4391 2.277 165.6 171.36

50 1.660

2.656 0.5430 1.841 165.8 230.23

2.822 0.5324 1.878 166.33 228.34

2.988 0.5138 1.946 161.06 224.72

3.154 0.4980 2.008 210.88 221.34

3.320 0.4910 2.036 155.5 219.73

3.486 0.4786 2.089 157.65 216.69

55 1.830

2.928 0.6210 1.609 188.19 233.8

3.111 0.6010 1.664 238.00 238.2

3.294 0.5835 1.714 183.72 241.88

3.477 0.5684 1.759 174.62 244.95

3.660 0.555 1.80 180.00 247.5

3.843 0.5442 1.837 183.55 249.74

60 2.000

3.200 0.665 1.503 192.19 265.27

3.400 0.645 1.551 191.34 270.02

3.600 0.627 1.595 207.08 274.07

3.800 0.611 1.636 211.72 277.52

4.000 0.598 1.673 233.66 280.43

4.200 0.586 1.707 200.04 282.90

4.2 Conclusions and Discussions

Obtained results are graphically plotted as follows.


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Fig 4.1 Linear Response of dynamic wind force v/s Db/Dt ratio.

Fig.4.5 Linear Response of Dynamic shear At Base V/S H/Db Ratio

Fig.4.2 Linear Response of Dynamic Wind Force V/S H/Db Ratio

Fig.4.3 Linear Response of Dynamic Moment at Base V/S Db/Dt Ratio


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Fig.4.4 Linear Response of Dynamic shear At Base V/S Db/Dt Ratio

Fig.4.5 Linear Response of Time Period V/S H/Db Ratio


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Fig.4.5 Linear Response of modal frequency and frequency V/S Db/Dt Ratio

5. CONCLUSIONS 1. From graphical representation it can be proved that for a self-supported steel stack unlined in

construction with constant shell thickness the change in geometry is directly proportional to the static and dynamic response of the stack.

2. Dynamic wind response as base moment, base shear, and fundamental modal frequency is linearly increasing as the base diameter increases.

3. Seismic responses such as absolute shear, fundamental time period and corresponding frequency are linear functions of bottom to top diameter ratio and height to base diameter ratio.

REFERENCES 1. IS 1893 Part4; 2005, “Criteria for Earthquake Resistant Design of Structures”, Bureau of Indian Standards, New

Delh i (2002).

2. IS 6533 Part 1; 1989, “Design and Construction of Steel Chimney”, Bureau of Indian Standards, New Delhi

(2002).

3. IS 6533 Part 2; 1989, “Design and Construction of Steel Chimney”, Bureau of Indian Standards, New Delhi

(2005).

5. J. Kawecki and J. A. Zuran´ski(2007), “Cross -wind vibrations of steel chimneys-A newcase history” Journal of

Wind Engineering and Industrial Aerodynamics. 95. 1166-1175.

6. M Gaczek and J Kawecki(1989), “A new method for prediction of steel chimney response to vortex shedding”, in

Int. Conf”Dynamics of St ructures -Preprints”, Karlovy Vary, pp. 191-194.

7. R Ciesielski, J Kawecki and R Maslowski(1993), “Use of mechanical vibrat ion dampers for decreasing dynamic

effects on tower structure”, 16th

Meeting of IASS Working Group for Masts and Towers, Praha.

8. R Ciesielski; A Flaga and J Kawecki(1996), “Aerodynamic effects on a non -typical steel chimney 120 m h igh”.

Journal of Wind Engineering and Industrial Aerodynamics. 65, pp. 77-86.

9. R Ciesikielski(1973), “Vibrat ion of steel towers due to vortex excitation”, in Int. Conf. IASS: Industrial chimneys,

Cracow, pp. 91-94.

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