Greetings,

I am going through a Vendor calculation on the wind sensitive structure like chimney. I can see that the vendor has selected large aspect ratio H/D around 31, and single self standing stack can experience cross wind (vortex shedding) vibration at the second mode of frequency as well.

"AS1170 Section 6.1 Evaluation of Dynamic Response factor" clearly says that "The dynamic response factor shall be determined for structures or elements of structures with natural first mode fundamental frequencies ......If the first mode of vibration greater than 1 Hz Cdyn = 1.0.

"AS1170.2  Clause 6.3.3 Crosswind response of chimneys,..." is looking for only first mode of frequency of vibration in the calculation.

Can we say the following from above statements?

1. AS1170.2 is not interested in higher modes of vibration by these.
2. Or AS1170.2 does NOT accept the structures with high H/D ratio.
3. Or the procedure provided by the standard is for the first mode of vibration only, and can not be used for higher modes of vibration.

AS/NZS1170.2 Supp 1- C6.3.3.1 Crosswind tip deflection says the following:

"The calculated value of crosswind tip deflection will have an accuracy of no better than 30 % to 50%. However, if the calculated value is a large fraction of the diameter than methods of mitigating the vibrations should be considered, such as the following:
(a) Increasing damping.
(b) Increasing mass.
( c ) Installing aerodynamic devices such as strakes or shrouds."

C6.3.3.2 Equivalent Static wind force
This represents an inertial load that varies with height, according to the mode shape on the first mode of vibration. A more accurate first mode shape may be determined for a particular shape."

These seem to support the statement 3 above.

However ASME STS-1-2011 Section 5.2.2 (a) (1) Wind responses – Vortex Shedding clearly says that "Vortex shedding loads shall be calculated for all modes of vibration where Vc < Vzcr. The procedure in Nonmandatory Appendix E may be used. Fatigue analysis must be considered. The vortex shedding loads need not be considered with (a)long wind loads.".
Appendix E sample calculation for Vortex shedding under section E04 does give calculation for the first mode of vibration only, unfortunately.

I see that all the formulations in AS1170.2 and ASME STS-1 are for linear mass distribution along the chimney with some tolerance, and this tolerance is less than 10% over the top third of height. In our case, there is a mass at the top of the chimney which does not comply with the tolerance given by the code either to be able to use the code formulation as they are. I guess the mass at the top is considered in the calculation of first and second mode of frequencies.

Additionally, the largest displacement is not expected to be at the top of the chimney under the second mode of the vortex shedding vibration, the chimney may be experiencing large displacement at lower level, and  corresponding overturning bending moment and shear force at the base might be a lot larger because of the large critical wind speed. I have not provided any calculation to support this.

I am looking for a comment from the engineers experienced on the calculation methods given by AS1170.2 and ASME STS-1.

The vendor has provided very limited information on this side which only calculates the top deflection for the second mode of frequency vortex shedding. I am questioning this part of the calculation because it does not provide a proper calculation for the overturning bending moment at the base.
The Vendor's opinion is that the stack does not have a likelihood of large amplitude vibration due to vortex shedding at the second mode of frequency, and calculated vortex shedding equivalent loads are very small, and fatigue analysis is not required. Do you agree with this opinion, what do you think? Is it sufficient statement for overturning bending moment and shear forces at the base?

Thanks in advance for your contribution, and kind regards,

Ibrahim Demir
 

Dear Ibrahim
Salam
I have not use AS1170 in my calculations; but I designed on steel stack for a petrochemical company by ASME STS-1. If you have AS1170, please send it to me to study and if I have a specific opinion about it, I will share with you –if Allah wants-
I believe that ASME STS-1 does not allow exceeding the first natural frequency. Vortex shedding is a phenomenon that occurs in all the wind speeds and cause stack to vibrate. Frequency of vibration of stack has a linear relation with wind speed. As wind speed increases, frequency of vibration will increase. It continues until frequency of vibration coincides with first natural frequency. At this wind speed, resonance will occur. If the stack does not have enough strength, failure is an expected result; but if it has enough strength -as wind speed increases- signs of resonance will be dissipated and amplitude of vibration will decrease considerably.
ASME STS-1 includes above idea. Since there is not a specific natural frequency in practical situation, ASME defines three zones:
1.    In the first zone that wind speed is small enough that makes us sure that resonance will not occur.
2.    In the second zone, we are not sure that resonance will occur or not. So ASME submits more accurate calculation for this subject. If this calculation leads to resonance then it is time to calculate huge loads caused by resonance.
3.    In the third zone, we are absolutely sure that resonance will occur and we should calculate subsequent loads caused by resonance.
You should consider that in design, there are two criteria that shall be satisfied.
1.    Maximum stress (that shall not be greater than allowable stress based on your design code)
2.    Maximum deflection (that shall not be greater than 0.5% of total length of stack)

I said all above, because most of engineers think that vortex shedding occurs at a specific wind speed, while vortex shedding –except in low wind speeds- absolutely will occur in all wind speeds. What you should take enough care about it, is resonance not vortex shedding. (For more information please refer to Bednar handbook)
Although ASME is not applicable for second natural frequency; but you can even exceed the second natural frequency base on a correct engineering justification and calculation.


(((The Vendor's opinion is that the stack does not have a likelihood of large amplitude vibration due to vortex shedding at the second mode of frequency, and calculated vortex shedding equivalent loads are very small, and fatigue analysis is not required. Do you agree with this opinion, what do you think? Is it sufficient statement for overturning bending moment and shear forces at the base?)))


About above phrase, I should say that vendor's opinion is quit incorrect. Because maximum wind speed probably will occur once in 50 years; but at lower speed your structure may fall within the first mode of frequency. I think that first mode of frequency may be more severe than the second mode. So at first please ask your vendor to perform calculation for all possible modes of frequency. It is also a good idea to force your vendor to check his own design with a well-known software. Also ask your vendor to give design guarantee.
Also it is not important that mass in stack is distributed uniformly or not. You can obtain natural frequency by manual calculation or by a 3D modeling software.
However vortex shedding (according to experience) occurs at top 1/3 of the structure. For this reason, ASME insists to use vortex breakers at this zone. Using vortex breaker below this zone has no affect for dissipating vortex shedding.
Based on my studies and also experiences of my colleagues, it is strongly recommended to use guy wire; if there is not enough space around your stack, make a steel structure around it. Finally if none of two choices is not practical, you can use vortex breaker. In this recent case, vortex shedding and consequently resonance will not occur. Instead please consider that vortex breaker causes a shape factor of 1.4 that multiplies in static wind load. This high shape factor leads to a higher static wind load. As a result maybe thickness of stack as well as load at base is increased.
If you need more discussion, please don't hesitate to contact me at shams.abbas@pidec.com
Also if you have an engineering judgment about my opinion or if you think something is wrong with me, I would be glad to hear about it.
Abbas Shams
 

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Dear Abbas,

Thanks for your response on the issue. However I agree with what you are saying, but you are missing the main questyion I was asking:

1. Does AS1170.2 allows the second mode of natural frequency vortex shedding involvement, or not?
2. ASME STS-1 accepts the second mode of natural frequency involvement, but does not give a sample calculation for that. The sample calculation provided is for only for first mode of natural frequency vortex shedding. I am looking for a clear, reasonably friendly sample calculation for the second mode of natural frequency vortex shedding analysis.

Vendor selected the stack diameter smalller which takes the second mode of natural frequency vortex shedding into consideretion. I do not object this under ASME STS-1, however it is questionable under AS1170.2 at the moment. Using vortex breakers or guy wires is not the option at the moment.

Therefore I need clarification, probably from one of the commitee members on the first item above first, and get a sample calculation for the second mode of natural frequency vortex shedding in accordance with ASME STS-1.

Thanks and kind regards,

Ibrahim Demir