Seismic effects on chimneys

SEISMIC EFFECTS ON CHIMNEYS

Byju VM3 Structural EngineeringRoll No. 3

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INTRODUCTION

• Chimneys are slender structures•Vulnerable to seismic excitation• Calculate the structural response• Corresponding shear forces and bending

moments

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FACTOR AFFECTING MAGNITUDE AND INTENSITY OF EARTHQUAKE

•Depth of focus•Distance from epicentre• Characteristics of the path of travel of seismic

waves• Soil strata on which the structure stands

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FACTOR AFFECTING STRUCTURAL RESPONSE TO EARTHQUAKE

• Foundation• Soil• Material• Form• Size• Mode of construction• Duration and characteristics of ground motion

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IS 1893 (PART 4) : 2005(Industrial Structures Including Stack-like Structures)

Earthquake resistant design of industrial structures including stack-like structures

Stack-like structures Cooling towers and drilling towers Transmission and communication towers Chimneys and stack-like structures Silos (including parabolic silos used for urea

storage) Support structures for refinery columns, boilers,

crushers etc. Pressure vessels and chemical reactor columns

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ASSUMPTIONS

No resonance (No time to build up resonant response since the period and amplitude are constantly changing)

Earthquake does not occur simultaneously with maximum wind, flood or sea wave

Elastic modulus same as that for static analysis unless more definite value is available

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IS 1893 (PART 4) : 2005

Section I – Industrial structures (Clause 7 to 12)

Section II – Stack-like structures (Clause 12 to 18)

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METHODS OF ANALYSIS

Response-spectrum method

Modal analysis technique

Time history response analysis

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RESPONSE-SPECTRUM METHOD

Time period of vibration (Clause 14)

- Coefficient depending on the slenderness ratio (Table 6)

Wt – Total weight of the structure including lining

h – Height of the structure above the base

Es – Modulus of elasticity

A – Area of cross section at the base of structural shell

g – Acceleration due to gravity

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Horizontal seismic coefficientZ- Zone factor (Table 2 of Part I)

I – Importance factor (Table 8)

R – Response reduction factor (Table 9)

- spectral acceleration coefficient (Fig 2 of part I)


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Moment and shear at a distance x from the top

- Coefficient depending on slenderness ratio (Table 6)

- Distribution factors for shear and moment depending on x/h (Table 10 and 11)

- Height of centre of gravity above base


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NUMERICAL EXAMPLE

Consider 130 m tall RC cylindrical chimney like structure of uniform cross section (A = 8.16m2, I = 87.9 m4) with weight of 25 kN/m3 and E = 3.4X104 n/mm2. Evaluate the base moment and shear under earthquake conditions. The structure is located in seismic zone III and is supported on raft foundation. Take damping factor as 5% and importance factor as 2. Use both response-spectrum method and modal analysis technique.

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H = 130 m

A = 8.16 m2

ρ = 25 kN/m3

W = 25 X 8.16 X 130 = 26.52 X 103 kN

I = 87.9 m4

Ec = 3.4 X 104 N/mm2

Zone III

Raft foundation

Damping factor (β) = 5 %

Importance factor (I) = 2


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Radius of gyration, Slenderness ratio, = 39.61

From table 6 of IS 1893 (part 4),

Cr = 73.11

Cv = 1.427

Fundamental time period,

=

= 2.6 s


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Zone factor, Z = 0.16

Importance factor, I = 2 (Given in this problem. Or take from table 8)

Response reduction factor, R = 3 (Table 9)

= = 0.385

Horizontal seismic coefficient (Ah) =

=

= 0.0205


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Base moment and shear

(x = distance from top of the stack to the section)

From table 10 of IS 1893 (Part 4),

Moment distribution factor (Dm) = 1

Shear distribution factor (Dv) = 1

Base shear (V) = = 1.427 X 0.0205 X 26.52 X 106X 1

= 775.8 kN

Base moment (M) =

= 0.0205 X 26.52 X 106X X1

= 35.34 kNm


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1. Discretisation

MODAL ANALYSIS

26 m

32.5 m

39 m

32.5 m

M1= 270 t

M2= 609 t

M3= 744 t

M4= 744 t

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2. Assume a deflection shape

, if x < a

= (, if x > a

Deflection = Coefficient X

MODAL ANALYSIS

Load at Deflection at

1 2 3 4

1 0.3333 0.2347 0.1235 0.0286

2 0.2347 0.1707 0.0933 0.0224

3 0.1235 0.0933 0.0555 0.0146

4 0.0286 0.0224 0.0146 0.0052

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MODAL ANALYSIS

Load at

M φ Fi Deflection ()

φ Fi Deflection ()

φ Mφ M Fφ

1 270 1.0 270.0 219.74 1.000 270.00 231.41 1.000 270.00 270.00 270.00

2 609 0.7 426.3 158.63 0.722 439.70 167.36 0.723 440.31 318.34 317.90

3 744 0.3 223.2 86.60 0.394 293.14 91.67 0.396 294.62 116.67 116.08

4 744 0.1 74.4 20.92 0.095 70.68 22.22 0.096 71.42 6.86 6.79

1076.3 711.87 710.77

F = M X φDeflection = Natural frequency, ω = = 2.42 rad / sParticipation factor, P = = 1.512

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MODAL ANALYSIS

= 2.59 sAh = 0.0205

= 0.0205 X 1.512 X 9.81 (270 X 1 + 609 X 0.723 + 744 X 0.396 + 744 X 0.096) = 327.26 kN

Base moment = = 0.0205 X 1.512 X 9.81 X (270 X 1 X 130 + 609 X 0.723 X 104 + 744 X 0.396 X 71.5 + 744 X 0.096 X 32.5) = 25.943X103 kNm

These are for first mode. We have to repeat the calculations for second mode and other higher modes.

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MODAL ANALYSIS

Load at

M φ1 φa Mφ1φa ψφ1 φ2 F=Mφ2 φ

1 270 1.000 1.0 270 0.2041 0.7959 214.89 4.651 1.000

2 609 0.723 0.1 44.03 0.1476 -0.0476 -28.99 -0.157 -0.0338

3 744 0.396 -0.5 -147.31 0.0808 -0.5808 -432.12 -3.621 -0.7785

4 744 0.096 -0.5 -21.43 0.0196 -0.3196 -237.78 -2.049 -0.4406

145.29

Second mode

= 0.2041Φ2 = φa - ψφ1 = 1-0.2041 = 0.7959ω = 14.9 rad/s T = 0.42 s P = -0.757Base shear = 349.92 kN Base moment = 10.1X 103 kNm

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MODAL ANALYSIS

= 479.11 kN

Base moment = X 103 = 27.84 X 103 kNm

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TIME HISTORY RESPONSE ANALYSIS

Response of the structure evaluated by subjecting the mathematical model to design earthquake for each incremental time interval

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IS 1893 (PART 4) : 2005

Special design considerations for RC stacks (Clause 18) Total vertical reinforcement not less than 25% of concrete area 2 layers of vertical reinforcement – outer layer not less than

50% of the reinforcement Total circumferential reinforcement not less than 0.2% of

concrete area 2 layer of circumferential reinforcement – reinforcement on

each face not less than 0.1% concrete area at that section Circumferential reinforcement at 0.2 dia from top -twice the

normal reinforcement Extra reinforcement around openings

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IS 1893 (PART 4) : 2005

Maximum deflection

Clause 18.7

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Thank You

Technology

Seismic effects on chimneys