Revisions: (last rev date 8/4/99)
1)Added first ten buckling modes for determination of critical buckling pressure.
2) Corrected maximum bending stress equation for cap
3) Added von Mises calculation and corrected buckling calculation
4) Corrected von Mises equation
5) Added O-ring groove diameter for diametral clearance and tab bending calculations.
6) Corrected index problem with radial moment equations
The following calculations are for determining the margin of safety
The format for this analysis package will be as follows:
A) Input of design parameters including dimensions, material properties, and design depth
B) Calculations for deformation and stresses in cylinders (check for thin wall or thick wall condition)
C) Buckling calculations for cylinders
D) Calculations for deformations and stresses in end plates,
E) Weight calculation
F) Summary of input and list of results including diametral gap, stresses, margins of safety and weight.
Note: The minimum margin of safety will be determined based upon the lowest margin calculated in the sections above. Thus, for a give pressure vessel, the maximum working pressure may be limited by the end plate thickness while for another it may be limited by the length of the cylindrical section. Therefor, if a desired allowable working depth is not reached, the limiting factor needs to be determined in order to effectively iterate the design to meet the requirements. Also, the diametral gap must be checked for the different pressures to assure that it falls within the maximum allowable from the o-ring vendor.
(pp02)
(pp11)
1) Dimensional input:
Is it thin wall (1=yes)?
Meridional (axial) stress:
Change in height:
Inside Diameter :
Outside Diameter:
Case Length:
Cylinder Base Thickness:
Wall thickness:
Radial displacement
of circumference:
Circumferential (hoop) stress:
2) Material properties:
Axial Stress:
Change in OD (radius):
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Water density:
Hoop Stress:
Radial Stress:
Change in Length:
Coeff. of Thermal Expansion:
Surface Temp.:
Temp at depth "q":
Shear Stress:
Von Mises Stress:
Fails at ~3750m
3) Design depth and resulting pressure:
Number of pressure steps:
Pressure:
for buckling:
for stress:
(pp03)
(pp12)
Cylinder Height:
Mean radius:
CASE VOLUME CHANGE
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
Meridional (axial) stress:
Circumferential (hoop) stress:
Von Mises Stress calculation:
Corresponding margins of safety:
for yield strength:
Radial displacement
of circumference:
Change in height:
(pp05)
Outer radius:
Inner radius:
radius range variable
Longitudinal stress:
Circumferential stress:
Radial stress:
Shear stress @ b:
Von Mises Stress calculation:
Corresponding margins of safety:
for yield strength:
for shear strength:
(pp07)
Tube dimensions:
radius:
length:
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
The critical pressure for the initial buckling of a cylinder
number of lobes:
critical pressure:
Margin of safety on buckling:
Solid circular plate
Uniformly distributed pressure from r o to a
(Roark Table 24, Case 10a:
Cylinder Base Thickness:
If assumed simply supported:
Check stress in bottom:
Plate Constant:
Margin:
check small deflection assumption
(deflection < t/2)
(pp09)
Cylinder:
cross sectional area:
internal volume:
external volume:
weight:
Total Weight:
2. Volume Change of Case at Depth:
Radius change due to press:
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 vol. due to temp:
Wet weight at depth: