DNV96 C203 Stresses

Hoop stress

To comply with DNV 96 requirement C203, the hoop stress σh shall be limited to: $σ_h ≤ \eta s$ SMYS

Where :

$σ_h$ = Hoop stress
$\eta$ = Usage factor for pressure containment (DNV C204 Table C1); $= 0.83$ for operating conditions
SMYS = Specified Minimum Yield Stress

A specific post-processing has been created since the hoop stress expression is simplified assuming that the pipe wall thickness e is very thin with respect to the pipe diameter: $$ \small r_{ext}^2-r_{int}2=e(r_{ext}-e)\approx2er_{ext} \text{ and } [1+\frac{r_{ext}^{2}{r}]\approx[1+\frac{r_{int}}2}{r}]\approx2 $$

As a consequence:

\[ \small \sigma_{hoop}(r)\approx(P_{int}-P_{ext})\frac{r_{ext}^2}{er_{ext}}=(P_{int}-P_{ext})\frac{d_{ext}}{2e} \]

Axial stress

To comply with DNV 96 requirement C400, the axial stress $\sigma_L$ shall be limited to : $\sigma_L \le \eta$ SMYS

Where :

$\sigma_L=\text{Longitudinal stress}=\sigma_1\pm(\sigma_B +\sigma_b)$
$\eta =$ Usage factor for equivalent stress check = 0.96 (DNV Table C4)
$\sigma_1 =$ Longitudinal stress due to pressure end cap effect
$\sigma_B =$ Bending stress due to other loads than expansion
$\sigma_b =$ Resultant bending stress due to expansion loads
SMYS = Specified Minimum Yield Stress

Here again, a specific output is available to calculate the longitudinal stress as per DNV C400.

Combined Von Mises stress

To comply with DNV 96 requirement C 400, the Von Mises combined equivalent stress $\sigma_e$ shall be limited to : $\sigma_e \le \eta$ SMYS

Where :

$\small \sigma_e = \text{Von Mises combined stress} = [\sigma_h^2 - (\sigma_L\sigma_h) +\sigma_L^2 +3\tau^2]^{\frac{1}{2}}$
$\eta=$ Usage factor for equivalent stress check = 0.96 (DNV Table C4)
$\sigma_h=$ Hoop stress (section 3.3.1)
$\sigma_L=$ Longitudinal stress (section 3.3.2)
$\tau=$ Tangential shear stress.
$\small\tau= max_{i<r<e}\{(Pi-Pe).Si.Se/(S.Sr)\} = (Pi-Pe)Se/S$
SMYS = Specified Minimum Yield Stress