A spherical pressure vessel is formed of 16-gauge (0.0625-in) cold-drawn AISI 1020 sheet steel. If the vessel has a diameter of 15 in, use the distortion-energy theory to estimate the pressure necessary to initiate yielding. What is the estimated bursting pressure

Explanation:

FromTable A - 20; the values of yield strength and tensile strength are derived by using the "Deterministic ASTM Minimum Tensile and yield strength for some Hot-Rolled (HR) and Cold - Drawn (CD) steels for cold drawn AISI 1020 sheet steel:

We calculate the ratio of the radius in relation to the thickness of the spherical vessel by using the formula:

Since the fraction from the ration is higher than 1°, then the shell can be regarded to be a thin spherical shell.

From here; we estimate the tensile stress induced by using the formula:

Therefore; the tensile stress is equal to the stress-induced in the transverse direction; i.e.

Thus, since

Then the radial stress

By the application of Von Mises Stress; the resultant stress can be estimated as follows:

Then: by relating the Von Mises stress at yield condition:

P = 0.934 kpsi

P = 934 psi

Hence, the pressure at the yield condition is 934 psi

Similarly, relating Von Mises stress at the rupture condition

68 = 61 P

P = 1.11 kpsi

Hence, the pressure at rupture condition is 1.11 kpsi

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