Axisymmetric Yield in a Ring-Stiffened Perfectly Circular Cylindrical Shell Under External Hydrostatic Pressure
frm "Ross, 2001 (pp15)
Rev. 0.0,
1)Initial Release.
2) -
The following calculations are for determining the Axisymmetric Yield Pressure 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 Ross' solution to Wilson's formula.
C) (Also see Ross (thesis), "The collapse of Ring-Reinforced Cylinders Under Uniform External Pressure," 1963.
D)
E)
Note:
Frame spacing (Lf) should (?) be less than 2*OD.
PROJECT GIVEN:
REQUIRED:
Find Axisymmetric Yield Stress & displacement for the given geometry & material.
Find P. Case displacement at depth.
1a)SHELL DIMENSIONS:
ID of Shell:
Inner Radius of Shell:
Mean Radius of Shell (a):
Sign Test
1b)FRAME DIMENSIONS:
Frame Total Height:
Radius to Frame:
Test for Frame Ht.
Test = 1 is OK :
End Bay Length (each end):
Width of frame in contact with the shell
Unsupported length of Shell
2)MAT'L PROPERTIES:
6061-T6 Aluminum
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Coeff. of Thermal Expansion:
Surface Temp.:
Temp at depth "q":
3) DESIGN DEPTH and PRESSURE:
Water density:
Number of pressure steps:
Pressure:
for buckling:
for stress:
SOLUTION:
Sectional Areas of Frame:
C.G. of Frame Section:
Radius of Centroid of Frame:
Second Moment of area of the ring frames' cross-section about its centroid and parallel to the axis of the cylinder (I):
Area and Moment of Shell between the Frames:
Moment of Inertia of Frame/Shell combination:
parallel axis theorem:
Width of frame in contact with the shell
x = 0 at Mid-bay:
Displacement:
Hoop Stress
:
Longitudinal Stress
(meridinal):
Outer Fiber & Inner Fiber Stresses @ Mid-Bay (x = 0):
Outer Fiber & Inner Fiber Stresses @ Frame Edge (x = L/2):
Bi-Axial Stress in Shell at Mid-bay:
Bi-Axial Stress in Shell at Frame:
for yield strength:
Displacement of shell (w), at Frame:
Displacement of shell (w), at Centerline of bay (x = 0)
(pp7)
WEIGHT CALCULATION
:
Shell Wt.:
One Frame Wt.:
Ext Vol. of the Case:
Total Weight of Case (Dry):
Weight Wet:
2. Volume Change of Case at Depth:
Radius change due to
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
Length change due to press:
Radius change due to temp:
Length change due to temp:
external volume of cyl. (at depth):
external volume of cyl.
Pressure Case Volume Change
Assume Bulk Modulus of CH2O = 325,000 psi.
Compressed water vol. at depth:
Compressed water density at depth:
Compressed water vol. due to temp:
Total density change:
Wet weight at depth:
Materials
6061-T6
7075-76
Titanium (pure)
Titanium 6AL-4V
S.S. 17-4 ph
S.S. 316
Convert deg Rankine to deg Fahienheit
Convert deg Kelvin
Convert depth Meters to bar
Convert depth Meters to psig