the pressure vessel is a steel cylinder which is free to expand in radial direct

Question

the pressure vessel is a steel cylinder which is free to expand in radial direction but cant expand longitudinally.It has the external diameter D of 1192 mm and the wall thickness (t) of 9mm
It is designed to contain gas at the operationalpressure P of 1.3 Mpaand the temperature of
(-5 Celsius). Calculate the temperature increase which would induce maximum compression in the wall of the vessel equal to the maximum tension. young's modulus for steel can be taken as 200Gpa and the coefficient of thermal expansion as 12*10^-6mm(mm Celsius).

Explanation / Answer

Coefficient of thermal expansion, = 12*10-6 mm/(mmC)

Young's modulus, Y = 200 GPa

Stress due to thermal expansion, 1 = Y(T) = 12*10-6 * 200*109 * (T-(-5)) = 24*105 * (T+5).

Inner radius, r = Outer radius - thickness = (1192/2)-9 = 123.4 mm.

Hoop stress, H = pr/t = 1.3*106 * 0.1234 / 0.009 = 17.82 MPa.

Longitudinal stress, L = H/2 = 8.91 MPa.

Now, Max. tensile stress = Max. compressive stress criterion yields,

H = L + 1

Using this, we'll get T = -1.2 deg C.

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