Pressure A closed-end cylindrical pressure vessel constructed of carbon steel ha

Question

Pressure

A closed-end cylindrical pressure vessel constructed of carbon steel has a wall thickness of 2 mm, a diameter of 150 mm, and a length of 760 mm. What are the hoop and axial stresses , when the cylinder carries an internal pressure of 10 MPa? How much does the radius of the cylinder expand due to the internal pressure?

Explanation / Answer

t = 2 mm D = 150 mm t/d = 1/75 since (t/d) < (1/10 to 1/15) => thin cylindrical vessel hoop stress = p*D/(2*t) = (10*10^6 Pa)*(0.15 m)/(2*0.002 m) = 3.75* 10^8 Pa axial stress = p*D/(4*t) = hoop stress/2 = 1.875 *10^8 Pa for carbon steel, poisson's ratio (u) = 0.286 and modulus of elasticity for carbon steel = 2.1*10^5 N/mm^2 = 2.1*10^11 N/m^2 hoop strain /circumferential strain = [p*D/(4*t*E)] *(2-u) = [10*10^6*0.15/(4*0.002*2.1*10^11)] *(2-0.286) = 1.53 *10^-3 circumferential strain = change in radius/original radius => 1.53 *10^-3 = change in radius/(150/2) => change in radius = 0.11475 mm

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