A thin-walled, cylindrical shell has an internal diameter of 2 m and is fabricated from plates 20 mm thick. Calculate the safe pressure in the shell if the tensile strength of the plates is 400 N/mm^2 and the factor of safety is 6. Determine also the percentage increase in the volume of the shell

Question

A thin-walled, cylindrical shell has an internal diameter of 2 m and is fabricated from plates 20 mm thick. Calculate the safe pressure in the shell if the tensile strength of the plates is [latex]400 N/mm^2[/latex] and the factor of safety is 6. Determine also the percentage increase in the volume of the shell when it is subjected to this pressure. Take Young’s modulus [latex]E = 200 000 N/mm^2[/latex] and Poisson’s ratio [latex] u = 0.3[/latex].

Accepted Answer

The maximum tensile stress in the walls of the shell is the circumferential stress, [latex] \sigma_{ C } [/latex], given by Eq. (7.63). Then

[latex] \sigma _C=\frac{pd}{2t} [/latex] (7.63)

[latex]\frac{400}{6}=\frac{p imes 2 imes 10^{3}}{2 imes 20}[/latex]

from which

[latex] p=1.33 N / mm ^{2} [/latex]

The volumetric strain is obtained from Eq. (7.67) and is

[latex]\frac{\Delta V}{\left(\pi d^{2} L / 4 ight)}=\frac{p d}{t E}\left(\frac{5}{4}-v ight) [/latex] (7.67)

[latex] \frac{1.33 imes 2 imes 10^{3}}{20 imes 200000}\left(\frac{5}{4}-0.3 ight)=0.00063 [/latex]

Hence the percentage increase in volume is 0.063%.

Question 7.12: A thin-walled, cylindrical shell has an internal diameter of...

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