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.
1) Dimensional input:
Is it thin wall (1=yes)?
Meridional (axial) stress:
Change in height:
Inside Diameter :
Outside Diameter:
O-ring surface diameter:
Length:
Cylinder Base Thickness:
Wall thickness:
Radial displacement
of circumference:
Circumferential (hoop) stress:
Plug Diameter:
Groove Width:
Tab Thickness:
Groove Diameter:
Groove Base Thickness:
Axial Stress:
Change in OD:
End Cap OD:
Connector Diameter:
End Cap Thickness:
Hoop Stress:
Change in ID:
Radial Stress:
Change in Length:
2) Material properties:
Shear Stress:
Von Mises Stress:
Aluminum Alloy 6061-T6
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Water density:
Closed End Cylinder Base Calcs:
3) Design depth and resulting pressure:
Number of pressure steps:
Pressure:
Buckling Calcs
for buckling:
for stress:
END CAP Circular Plate
Mean radius:
Cylinder Height:
END CAP tabs
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
ORING tab
Meridional (axial) stress:
Circumferential (hoop) stress:
Margin:
Von Mises Stress calculation:
Corresponding margins of safety:
for yield strength:
Radial displacement
of circumference:
Change in height:
Diametral clearance (extrusion gap):
Pressure step:
Extrusion gap (radial):
Outer radius:
Inner radius:
radius range variable
Longitudinal stress:
Circumferential stress:
Radial stress:
Shear stress:
Von Mises Stress calculation:
Corresponding margins of safety:
for yield strength:
for shear strength:
Note: The 0.5 in the MSshear is the maximum shear stress or Tresca theory of failure
(see Roark 7th ed page 42)
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:
This calculation if for a pressure vessel with one closed end (not a bulkhead).
fact I don't know how the shell is distorting and the closed end "plate edges" may not meet the 0 angle criteria for fixed supports.
design fails this calculation a FEA analysis showing what actually goes on at the edges would be required
PLATE CALCULATIONS:
Check stress in bottom:
Cylinder Base Thickness:
If assumed simply supported:
Plate Constant:
Margin:
check small deflection assumption
(deflection < t/2)
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:
check small deflection assumption
(deflection < t/2)
Margin:
For a conservative approach, assume the outer edge of the tabs are free and the inner edge fixed
A) Top tab:
Case 1l:
Loading on tab:
Margin:
Case 1l:
For o-ring tab:
Loading on tab:
Margin:
Cylinder:
cross sectional area:
internal volume:
external volume:
weight:
End Cap:
volume:
Tab:
Plug:
Cap:
Weight:
Total weight: