Revisions: (last rev date 1/24/08)
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
7) Added end cap tab bearing stress and tab shear thru.
8)Added Connector Line Load to End Cap Deflection/Stress calculation (Table 24 Case 1a).
9) Added Case Vol. change and CH2O Bulk Modulus
10) Added Thermal Dimension Chg (Radial & Length) @ depth.
11)Added Von Mises stress @ Critical Buckling Pressure.
12)Added Fixed case End Cap (Fixed Base) calc.
13)For Thin Wall calc's: Added λ from Windenburg & Trilling, Added PKD of p.min, from Ross 2008.
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 & displacement 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)
1) Dimensional input:
Inside Diameter :
Outside Diameter:
O-ring surface diameter:
Case Length:
Cylinder Base
Thickness:
Wall thickness:
Plug Diameter:
Groove Width:
Groove Diameter:
End Cap OD:
End Cap Thickness:
Tab Thickness:
Connector Diameter:
2) Material properties:
RP-VisiJet_M3_Crystal
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Water density:
3) Design depth and resulting pressure:
Number of pressure steps:
Pressure:
for buckling:
for stress:
Outer radius:
Inner radius:
Length:
radius range variable
Pressure step:
Extrusion gap (radial):
The pressure at which the extrusion gap (GAP thick ) is equal to the change in interior radius (Δb thick )
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)
Margin:
Superposition of pressure loading of the annulus and line loading of the connector/penetrator hole in the center.
Table 24
This file corresponds to Cases 2a - 2d in Roark's Formulas for Stress and Strain.
Annular plate with a uniformly distributed pressure q over the portion from r o to a
Outer edge simply supported, inner edge free
Plate dimensions:
thickness:
outer radius:
inner radius:
Shear modulus:
Margin:
check small deflection assumption
(deflection < t/2)
Should be < 1
CONNECTOR LINE LOAD:
Table 24
This file corresponds to Cases 1a - 1d in Roark's Formulas for Stress and Strain.
Annular plate with a uniform annular line load w at a radius r o
Outer edge simply supported, inner edge free 1a
Area of Connector:
Force on the connector:
Line load on Conn. Hole (w):
By Superposition:
Margin:
For a conservative approach, assume the outer edge of the tabs are free and the inner edge fixed
Case 1l:
Loading on tab:
Margin:
Case 1l:
For o-ring tab:
Loading on tab:
Margin:
1. Case Weight Calc.:
Cylinder:
cross sectional area:
internal volume:
external volume:
weight:
End Cap:
volume:
Tab:
Plug:
Cap:
Weight:
Total Weight:
(pp17)
Axial Stress:
Change in OD (radius):
Hoop Stress:
Change in ID (radius):
Radial Stress:
Change in Length:
Shear Stress:
(pp18)
Pressure Load:
Conn. Line Load:
Combined Loading:
MARGIN OF SAFETY:
MARGIN OF SAFETY:
Case + 2ea. Caps =
(pp19)
EndCap Flange/Case Bearing Stress:
Bearing Area:
End Cap Force:
Bearing Stress:
Margin of safey:
EndCap Flange Shear Thru Stress
Flange Shear Area:
End Cap Force:
Shear Stress:
Margin of Safety: