If a thin-walled, closed-end pressure vessel is subjected to inter-nal pressure P (with radius a and thickness h), find the value of an additional end load f such that σθθ=σzz (cf. Fig. 3.16).

Question

If a thin-walled, closed-end pressure vessel is subjected to inter-nal pressure P (with radius a and thickness h), find the value of an additional end load f such that [latex]\sigma _{ heta heta }=\sigma_{zz}[/latex] (cf. Fig. 3.16).

Accepted Answer

From the above results [Eqs. (3.49) and (3.41)], the associated axial and circumferential stresses are

[latex] \sigma _{zz}=\frac{Pa}{2h}+\frac{f}{2\pi ah}, [/latex] and [latex]\sigma _{ heta heta }=\frac{Pa}{h}.[/latex]

Now, set the two stresses equal [latex](σ_{θθ}=σ_{zz})[/latex] and solve for f:

[latex] \frac{Pa}{h}=\frac{Pa}{2h}+\frac{f}{2ah\pi } ightarrow f=Pa^{2}\pi ,[/latex]

which is seen to equal the pressure times the internal projected area over which it acts. FIGURE 3.16 Schema of a small portion of a tube that could be subjected to an internal pressure and an axial force. Note that the 2-D state of stress at a point p depends on the coordinate system of choice.

Question 3.3: If a thin-walled, closed-end pressure vessel is subjected to...

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