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nhabibkhan
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Join Date: Jun 2007
Location: Lahore, Pakistan
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Dynamic Deflection Formula

10/14/2009 3:36 AM

Can any one explain me the dynamic deflection formula for Stack =L^5*Vc²*0.00243/(W*Dl*Dr)*(1E-6) as per Kanti K Mahajan

what are its units?

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user-deleted-1105
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Popular Science - Weaponology - New Member United Kingdom - Member - New Member

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#1

Re: Dynamic deflection formula for Stack

10/14/2009 3:45 AM

You probably need to give us a hint of context.
'Stack' has a multitude of meanings..
Del

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nhabibkhan
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Join Date: Jun 2007
Location: Lahore, Pakistan
Posts: 24
#2
In reply to #1

Re: Dynamic deflection formula for Stack

10/14/2009 4:17 AM

In pv elite software calculations for dynamic deflection is performed bu using this formula

Ds = Maximum dynamic deflection of stack (at the Top)=L^5*Vc²*0.00243/(W*Dl*Dr)*(1E-6)
=720213366395mm

This evaluation is based on work by Kanti Mahajan and Ed Zorilla

which seams to be incorrect

Ds = Static Deflection=Pc Dr (Le)4 (12)3 / 8 E I
=

1.24

in

31

mm

Other data is as given below

Stack inputs:

Stack material=

ASTM A36

L = Total height of the stack=

320

ft

97536

mm
Vw = Basic wind speed=

160.93

km/h

100

mph
t = Thickness of the top stack=

0.79

in

20

mm
IDt = Inside dia.of Top section of stack=

16.75

ft
IDb = Inside dia.of Bottom section of stack=

31

ft
O.T = Operating temperature of stack=

550

F
E = Modulus of elasticity of plate material @ O.T=

26750000

psi

@550F

Y = Yield stress of plate material @ O.T=

28450

psi
St = Tensile Strength @ O.T=

58000

psi
Sa = Allowable tensile Strength @ O.T=

17070

psi
r = Steel Density=

0.283

lb/in3
C = Corrosion allowance=

0.1181

in

3.0

mm
Ws = Total corroded stack Weight=

753056

lb

341522

kg
W = Total Stack Weight=

1171565

lb

531322

kg

Can any one give me the Kanti K Mahajan book reference, how he calculate the dynamic deflection

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user-deleted-1105
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#3
In reply to #2

Re: Dynamic deflection formula for Stack

10/14/2009 4:23 AM

Ah, chimney stack!

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passingtongreen
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Join Date: Aug 2009
Location: Glen Mills, PA.
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#4
In reply to #2

Re: Dynamic deflection formula for Stack

10/14/2009 11:19 AM

The dynamic deflection is due to vortex shedding, but I always designed stacks so that their first natural frequency occurred at low wind velocity, low enough for the pressure to be insignificant, and the second above the design velocity so I never really got into the actual deflection.

I don't recognize your formula, but it's a very long time since I did that kind of work.

I don't know if this will help with a separate verification

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nhabibkhan
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Join Date: Jun 2007
Location: Lahore, Pakistan
Posts: 24
#5
In reply to #4

Re: Dynamic deflection formula for Stack

10/14/2009 11:09 PM

Dear All

My problem, how to calculate static deflection and dynamic deflection is solved

But I have a doubt in calculating natural frequency is solved but

T = Period of vibration (As per Esco)=1.648 (Le^2) / Dr E0.5
Le = Effective Length of stack=

304

Dr = Average internal dia. of top half of stack=

16.75

E = Modulus of elasticity of plate material @ O.T=

26750000

T = Period of vibration (As per Esco)=

1.7534

sec
f = 1 / T = Natural frequency of stack vibration=

0.5703

cps

but natural frequency calculated by PV elite (by using some matrices) and Compress software (by using Raliegh's Method) comes to be .9998 or 1 Hz. and value calculated by me by using the above formula is .5703.

Please suggest me which value to be use

this vent stack is pass on using .5703 giving the deflection within limits

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Abdel Halim Galala
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Engineering Fields - Piping Design Engineering - New Member Egypt - Member - Member since 02/18/2007

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#6

Re: Dynamic Deflection Formula

10/15/2009 12:01 AM

See the following file free download for Flare Stack Mechanical Design Calculations, including Static Deflection, Dynamic Deflection, Ovalling Vibration, ... etc.: Flare_Stack_Mechanical_Design_Calculations

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Abdel Halim Galala
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Engineering Fields - Piping Design Engineering - New Member Egypt - Member - Member since 02/18/2007

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#7
In reply to #6

Re: Dynamic Deflection Formula

10/15/2009 1:23 AM

Dynamic deflection = Static Deflection * Magnification factor (in inches or mm)

Static deflection: The computed dynamic loading is applied as a stagnant pressure to the stack. Assuming it to be a cantilever beam, amplitude at the top is approximated by :

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