Question 16.9: The vessel described in Example 16.7 is to be supported at t...
The vessel described in Example 16.7 is to be supported at the lower shell-to-head junction. What are the longitudinal stresses in the shell above and below the support line? The internal pressure is 225 psi. Let the bending moment M_{e} =864,000 in.-lb.
From Example 16.7, the dead load of the various components is
shell = 9700 lb
heads = 1630 lb
shell fluid = 20,620 lb
fluid, heads = 2290 lb.
The overturning moment is
M_{e} = 864,000 in.-lb.
Using Eq. (16.21), the total longitudinal stress is
\sigma_{ L }=+P\left(\frac{R}{2 t}-0.2\right) \pm \frac{W}{\pi D_{ m } t} \pm \frac{4 M_{e}}{\pi D_{ m }^{2} t} (16.21)
\sigma_{ L }=+225\left(\frac{30}{2 \times 0.5}-0.2\right) \pm \frac{W}{\pi(60.5)(0.5)} \pm \frac{(4)(864,000)}{\pi(60.5)^{2}(0.5)}The side of applied force above the support line has
dead load = shell + upper head = 9700 + 815
= 10,515 lb
\sigma_{L} = + 6705 − 110 + 600
= 7200 psi tension.
The side of applied force below the support line has
dead load = lower head + contents
= 815 + 22,910 = 23,725 lb
\sigma_{ L } = + 6705 + 250 + 0
= 6955 psi tension.
The opposite side of applied force above the support line has
\sigma_{ L } = +6705-110-600
=\left\{\begin{array}{ll} 5600 \text { psi tension } & \text { with pressure } \\ 710 \text { psi compression } & \text { without pressure } \end{array}\right.