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API conventions for tubular joints

Background

For a selected tubular joint between two beams, a plane is naturally defined by the axes of both beams.

The following reference frame is used to calculate the stresses in one of these beams:

$Z$ axis is the brace axis
$Y$ axis is the moment axis which bends the connection in the plane defined by the two beams;
$X$ axis is the moment axis which bends the selected beam out of the connection plane

And the stresses write :

$\small\sigma_{G1}(t)=SCF_{A_{C}}\cdot\sigma_{AZ}(t)+SCF_{M_{IP}}\cdot\sigma_{FY}(t)$

$\small\sigma_{G2}(t)=\frac{1}{2}(SCF_{A_{C}}+SCF_{A_{S}})\cdot\sigma_{AZ}(t)+\frac{\sqrt{2}}{2}\cdot SCF_{M_{IP}}\cdot\sigma_{FY}(t)-\frac{\sqrt{2}}{2}\cdot SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

$\small\sigma_{G3}(t)=SCF_{A_{S}}\cdot\sigma_{AZ}(t)-SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

$\small\sigma_{G4}(t)=\frac{1}{2}(SCF_{A_{C}}+SCF_{A_{S}})\cdot\sigma_{AZ}(t)-\frac{\sqrt{2}}{2}\cdot SCF_{M_{IP}}\cdot\sigma_{FY}(t)-\frac{\sqrt{2}}{2}\cdot SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

$\small\sigma_{G5}(t)=SCF_{A_{C}}\cdot\sigma_{AZ}(t)-SCF_{M_{IP}}\cdot\sigma_{FY}(t)$

$\small\sigma_{G6}(t)=\frac{1}{2}(SCF_{A_{C}}+SCF_{A_{S}})\cdot\sigma_{AZ}(t)-\frac{\sqrt{2}}{2}\cdot SCF_{M_{IP}}\cdot\sigma_{FY}(t)+\frac{\sqrt{2}}{2}\cdot SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

$\small\sigma_{G7}(t)=SCF_{A_{S}}\cdot\sigma_{AZ}(t)+SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

$\small\sigma_{G8}(t)=\frac{1}{2}(SCF_{A_{C}}+SCF_{A_{S}})\cdot\sigma_{AZ}(t)+\frac{\sqrt{2}}{2}\cdot SCF_{M_{IP}}\cdot\sigma_{FY}(t)+\frac{\sqrt{2}}{2}\cdot SCF_{M_{OP}}\cdot\sigma_{FX}(t)$

If we compare DeepLines conventions with API conventions for the 8 section points where streses are calculated, it comes :

As a consequence, the $X$ and $Y$ local axes correspond to the X and Y axes used for the API formula.

$SCF_{IP}$ will be applied on the $Y$ local direction and must be associated to the bending stiffness $EI_{yy}$
$SCF_{OP}$ will be applied in the $X$ local direction and is associated to the bending stiffness $EI_{xx}$.

Fatigue and stress post-processing

A set of $SCF$ coeffcients may be defined for a fatigue analysis depending on the type of line.

For tubular joints, four $SCF$ may be entered: $SCF_{A_{Saddle1}}$; $SCF_{A_{Crown1}}$; $SCF_{M_{IP}}$; $SCF_{M_{OP1}}$ are the $SCF$ coefficients.

For classical pipes, three $SCF$ are usefull : $SCF_{axial}$, $SCF_{bending}$

When these coefficients are defined, the stresses used for fatigue assessment writes: $$ \sigma_{axial}=SCF_{axial}\frac{N_{Sd}}{A_{steel}} \text{ and } \sigma_{bending}=SCF_{bendingX}M_1\cdot\frac{y}{I_x}-SCF_{bendingY}M_2\cdot\frac{x}{I_y} $$

Note

At the end of a fatigue analysis, in the summary file, the $SCF$ coefficients actually applied are recalled.

Example:

Most Damageable Element in the range: $[0.833333m;16.618m]$ * Abscissa (m) : $0.833333$ * Section Point : $7$ * Damage : $1.1773*10^{29}$ * Fatigue Life (years) : $8.49398*10^{-30}$

Stress $SCF$ coefficients:
* $SCF_{axial}= 1$ * $SCF_{bending}= 1$

$[0, 17.368]$ * $SCF_{A_{Saddle}}= 1$ * $SCF_{A_{Crown}}=1$ * $SCF_{M_{IP}}= 0.7458$ * $SCF_{M_{OP}}= 1.4098$