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.
where S = 0.2 (Strouhal number)
V2 = 6.25.
If the design wind velocity V>V1, perform the detailed vibration analysis from step 3 below with V1
If the design wind velocity V>V2, perform the detailed vibration analysis from step 3 below with V2
If V1 or V2 > 60 mph/27 m/s, ignore the calculation for that V value as there is cutoff for maximum critical wind speed for design consideration (page 120).
Determine δ and M.F. from the above selected combinations
Where, d = outside projected dia., ft., H= total column height, ft.
Note in the example only the moment at the junction of column and skirt is considered but APV has different approach of calculating at each individual level
stress intensification factor, β as follows
β = 1.2, shell plate with smooth finish,
β = 1.8, butt weld
β = 3.0 fillet weld
Reference: Henry H. Bednar, PE. (1991). Pressure Vessel Design Handbook Second Edition. Malabar, FL: Krieger Publishing Company.