(6.10) You are to design a cylindrical pressure vessel with spherical end caps as shown below. The caps and the main part of the vessel are to have the same thickness (which you need to determine). The radius of the vessel and the length are specified to be R and L, respectively. The internal pressure is specified to be p. Design the vessel against yield using the following multi-axial criteria in the cylindrical portion of the vessel
sqrt{(sigma_{rr} - sigma_{ heta heta})^2 + (sigma_{ heta heta} - sigma_{zz})^2 + (sigma_{zz} - sigma_{rr})^2} leq sqrt{2}sigma_{Y}
and
sqrt{(sigma_{rr} - sigma_{ heta heta})^2 + (sigma_{ heta heta} - sigma_{varphivarphi})^2 + (sigma_{varphivarphi} - sigma_{rr})^2} leq sqrt{2}sigma_{Y}
in the spherical portion of the vessel. Allow for a safety factor of SF against yield. In choosing the wall thickness, choose a material that minimizes the weight of the vessel. Choose your material from Table 6.1.
Table 6.1 Material selection list.
Material E (GPa) sigma_{Y} (MPa) Density (kg/m^3)
Al 70 470 2700
Mild Steel 200 260 7850
HS Steel 208 1300 7850
HTS graphite-5208 epoxy 183 1250 1550
What is the best material and what is the required wall thickness?
SIDE VIEW
END VIEW
All walls have the same thickness t