Revisions: (last rev date 10/30/12)
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)Modified to End Cap Calcs only.
8)Added Connector Line Load to End Cap Deflection/Stress calculation (Table 24 Case 1a).
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)
(PP 13)
1) Dimensional input:
O-ring surface diameter ? (ASSUMED !!!):
Plug Diameter:
Groove Width?:
Groove Diameter?:
Groove Base Thickness?:
O-ring surface diameter:
Plug Diameter:
Groove Width:
Groove Diameter:
Groove Base Thickness:
End Cap OD:
End Cap Thickness:
Tab Thickness:
Connector Diameter:
End Cap OD:
End Cap Thickness:
Tab Thickness:
Connector Diameter:
ASSUMED:
2) Material properties:
Titanium (Gr. 2)
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Water density:
Coeff. of Thermal Expansion:
Surface Temp.:
Temp at depth "q":
MARGIN OF SAFETY:
3) Design depth and resulting pressure:
Number of pressure steps:
Pressure:
MARGIN OF SAFETY:
for stress:
(pp03)
(PP14)
Solid circular plate
Uniformly distributed pressure from r o to a
Pressure Load:
Conn. Line Load:
Combined Loading:
MARGIN OF SAFETY:
Cylinder Base Thickness:
If assumed simply supported:
Check stress in bottom:
Plate Constant:
MARGIN OF SAFETY:
Margin:
check small deflection assumption
(deflection < t/2)
EndCap Flange/Case Bearing Stress:
(pp15)
Bearing Area:
End Cap Force:
Bearing Stress:
Margin of safey:
EndCap Flange Shear Thru Stress
Flange Shear Area:
Margin:
End Cap Force:
Shear Stress:
Margin of Safety:
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:
Transverse Bending moment / stress
check small deflection assumption
(deflection < t/2)
Should be < 1 ! ! !?
Margin:
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
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:
End Cap:
volume:
Tab:
Plug:
Cap:
Weight:
Total Weight: