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
7) 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 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.
(pp02)
(pp11)
1) Dimensional input:
Axial Stress:
Change in OD (radius):
Inside Diameter :
Outside Diameter:
Case Length:
Wall thickness:
Hoop Stress:
Radial Stress:
Change in Length:
2) Material properties:
Shear Stress:
Von Mises Stress:
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Water density:
3) Design depth and resulting pressure:
Number of pressure steps:
Pressure:
for stress:
Mean radius:
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
(pp03)
Outer radius:
Inner radius:
radius range variable
Longitudinal stress:
Circumferential stress:
Radial stress:
Shear stress @ b:
Von Mises Stress calculation:
(pp05)
Corresponding margins of safety:
for yield strength:
for shear strength:
(pp09)
Cylinder:
cross sectional area:
internal volume:
external volume:
weight:
Total Weight: