Wind induced vibrations on tall vessels are a concern and AutoPIPE Vessel currentley has two methods to address this design consideration.
If W/LDr2 <=20, issue message in report “Vibration analysis necessary to be performed as W/LDr2 <=20”
vibration analysis must be performed and proceed to step 3
where W= corroded wt. in lb, L=length in ft., Dr=average internal diameter of top half of the structure in ft.
If W/LDr2 >20, issue message in report “Vibration analysis not necessary to be performed as W/LDr2 >20”
Calculate damping factor DF=Wδ/LDr2
Default value of δ = 0.03 (Table 3)
If DF <= 0.75, issue message in report “system is unstable and vortex shedding vibration analysis is required as DF <= 0.75”, proceed to step 4
If DF > 0.75, issue message in report “Vortex shedding vibration analysis not necessary to be performed as DF > 0.75”
Justification: In the book this formula appears as in mph, but Dr is introduced in feet, f in Hz, so the number of Strouhal is affected by a conversion factor from feet to miles and hours to seconds. To reverse this change and work in consistent units we have to divide by 1.466 (1mph = 5280/3600 = 1.466 ft/s). And to place S in the denominator, we inverse the coefficient:
Where Vb = wind velocity at H
If Vc > maximum gust velocity, issue message in report “Vibration amplitude no need to be calculated as Vc > maximum gust velocity”.
If Z> Maximum Deflection input by user, issue message in report “structure is unsafe:amplitude of maximum dynamic deflection exceeds maximum allowable deflection, please modify design”
Reference: Kanti Mahajan, PE. (1979). Design of Process Equipment. Tulsa, OK: Pressure Vessel Handbook Publishing.