Asymmetric Buckling by Shell Instability (Lobar Buckling) in a Ring-Stiffened Perfectly Circular Cylindrical Shell Under External Hydrostatic Pressure
frm "Ross, 2001 (pp99)
Rev. 0.0,
1)Initial Release.
Rev. 1.0
The following calculations are for determining the Critical Buckling Pressure (Pcr) in Asymmetric Buckling by Shell Instability (Lobar Buckling) for a Ring-Stiffened pressure vessel. The equations are mostly from Ross, C.T.G., "Pressure Vessels: External Pressure Technology", 2001
The user must input the dimensions,
The format for this analysis package will be as follows:
A) Input of design parameters including dimensions, frame spacing, number of frames, and material properties
B) Initial calculations use Von Mises Thin-walled shell equation and Ross' graphs for "Plastic Knock Down
C) Ross Graphs (Fig.3.4, 3.5) are reduce to a slope intercept formula.
D) Input the number of Lobar Modes, i.e. Modes = 4, then the Modes are
E)
Note:
Frame spacing (Lf) should (?) be less than 2*OD.
PROJECT GIVEN:
REQUIRED:
Find Minimum Critical Buckling Pressure for the given geometry & material.
Find "Plastic Knock Down" (PKD) Factor for machined and welded const.
1a)SHELL DIMENSIONS:
ID of Shell:
Inner Radius of Shell:
Mean Radius of Shell (a):
1b)FRAME DIMENSIONS:
End Bay Length (each end):
Unsupported length of Shell
2)MAT'L PROPERTIES:
6061-T6 Aluminum
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
3) DESIGN DEPTH and PRESSURE:
Water density:
Number of pressure steps:
Pressure:
SOLUTION:
Windenburg - Trilling Thinness Ratio:
Windenburg, D.F., Trilling, F., "Collapse by Instability of Thin Cylindrical Shells under External Pressure, Trans. ASME, 11, 819-25, 1934
where:
Number of Modes (n):
Need to Replace the "0" in the first position (P.cr.0), Since P.min is never zero :
for Design Depth q:
Machined Cyl.
Welded Cyl. Fig. 3.5 pp107
Margin of Safety for each type of construction:
Where: