Seismic effects on chimneys
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Transcript of 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)
RESPONSE-SPECTRUM METHOD
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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
RESPONSE-SPECTRUM METHOD
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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
RESPONSE-SPECTRUM METHOD
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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
RESPONSE-SPECTRUM METHOD
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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
RESPONSE-SPECTRUM METHOD
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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
RESPONSE-SPECTRUM METHOD
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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