A spherical pressure vessel is formed of 18 gauge 00478 in c

A spherical pressure vessel is formed of 18 gauge (0.0478 in) cold-drawn AISI 1020 sheet steel. If the vessel has a diameter of 7.63 in, use the distortion-energy failure theory to estimate the pressure necessary to initiate yielding. What is the estimated bursting pressure? Round your answers to two decimal places. Pressure necessary to initiate yielding, p = kpsi

Solution

Given data,

Thickness of pressure vessel (t) = 0.0478 inch

Diameter of pressure vessel (d) = 7.63 inch

Stress induced in spherical vessel () = pr/2t

Where p = pressure induced

As per distortion energy theory, ² = 2 ²_yp

_yp = Yield point strength= 50800 psi (for) AISI 1020 steel

= p×3.815/ 2×0.0478

= 39.90 p

(39.90 p)² = 2 (50800)²

p = 1800. 28 psi or 1.8 kpsi (Answer)

For bursting pressure,

P_b= 0.875×2×Y_p×t/ D

Where, Y_p= minimum yield strength

t = thickness

D = Diameter

P_b = 0.0875×2×50800×0.0478/ 7.63

P_b= 55.69 psi (Answer)