DNV OS F201 combined loading

1. Purpose

Calculate combined loading for steel risers.

2. Description

The DNV OS F201 code-check is based on Offshore standard DNV-OS-F201, Dynamic Risers,October 2010 .

3. Required results

To perform the code-check, element forces and nodal displacements need to be stored from the simulation.
These time series will be used to calculate environmental loads.

Functional loads are taken from static results. The load step which should be used must be given.

4. Description of input parameters

The following user input is required.

4.1. Input for Load, resistance and reduction factors

  • Safety Class (Low/Normal/High)

  • Limit state category (SLS/ULS/ALS)

  • Safety class resistance factor \(\gamma_{SC}\) (read only, may be overridden)

  • Load effect factor for environmental loads \(\gamma_{E}\) (read only, may be overridden)

  • Load effect factor for functional loads \(\gamma_{F}\) (read only, may be overridden)

  • Load effect factor for accidental loads \(\gamma_{A}\) (read only, may be overridden)

  • Material resistance factor \(\gamma_{m}\) (read only, may be overridden)

  • Fabrication factor \(\alpha_{fab}\)

4.2. Input for fluid properties

  • pd - Design pressure at reference point

  • Reference point - Vertical reference position for design pressure, given in global coordinate system

4.3. Input for estimation of extreme values

If selected, Weibull distribution fitting may be used to estimate extreme utilization.
This requires the following input:

  • Sea state duration

  • Lower threshold for tail fitting

4.4. Structural properties

Structural properties is given either for a single element, all elements in a given segment or for the whole line.
Combined loading will be calculated for all elements that have specified structural properties.

4.4.1. Input for Riser geometry properties

  • Nominal diameter - Outside diameter of the pipe

  • Nominal thickness - Nominal (specified) pipe wall thickness

  • t corr - Corrosion/wear/erosion allowance

  • f0 - Initial ovality

By default the nominal diameter and thickness is calculated based on cross section parameters.

4.4.2. Input for Riser material properties

  • E - Young’s modulus

  • \(\nu\) - Poisson’s ratio

  • \(f_{y}\) - Characteristic yield strength

  • \(f_{u}\) - Characteristic tensile strength

5. Calculation of combined loading, Load and Resistance Factor Design

The following constants are calculated first:

Note that \(t_{2} = t - t corr\) is used in the following.

Burst resistance:

\[p_{b}(t)=\frac{2}{\sqrt{3}}\cdot \frac{2 \cdot t_{2}}{D-t_{2}}\cdot min(f_{y};\frac{f_{u}}{1.15})\]

Elastic collapse pressure:

\[p_{el} = \frac{2 E (t_2/D)^3} { 1-\nu^2 }\]

Plastic collapse pressure:

\[p_{p}=2\frac{t_{2}}{D}\cdot f_{y}\cdot \alpha_{fab}\]

The collapse pressure is calculated as a function of elastic capacity,
plastic capacity and the ovality of the pipe and is solved using the analytical solution in
DNV-OS-F101 of the following equation:

\[(p_{c}(t_2)-p_{el}(t_2))(p_c^2(t_2)-p_{p^2}(t_2)) = p_{c}(t_2)p_{el}(t_2)p_p(t_2)2\delta_0\frac{D}{t_2}\]

Note DNV definition of ovality:

\[\delta_{0}(DNV) = \frac{D_{max}-D_{min}}{D}\]

The following calculations are performed for each element/node and for each time-step of the dynamic analysis,
the utilization is then found as the maximum utilization from the resulting utilization time-series.

Incidental design pressure:

\[p_{ld} = p_{d}+rho_{i}\cdot g\cdot (abs(z_{env}-z_{ref})\]

Incidental external pressure:

\[p_{e} = \rho_{e}\cdot g\cdot (abs(z_{env}-z_{ref})\]

Pressure difference:

\[p_{diff} = p_{ld}-p_{e}\]

Plastic bending stiffness:

\[ M_{k} = f_{y}\cdot \alpha_{c} \cdot (D-t_{2})^2\cdot t_{2}\]

Plastic axial force recistance:

\[ T_{k} = f_{y}\cdot \alpha_{c} \cdot \pi\cdot (D-t_{2})\cdot t_{2}\]

Where \(\alpha_{c}\) is the fabrication factor calculated using formula in DNV-OS-F201,306.

The design bending moment:

\[M_{yd} = \gamma_{F} \cdot M_{Fy} + \gamma_{E} \cdot M_{Ey}\]
\[M_{zd} = \gamma_{F} \cdot M_{Fz} + \gamma_{E} \cdot M_{Ez}\]
\[ Md = \sqrt{M_{yd}^2+M_{zd}^2}\]
\[ T_{ed} = \gamma_{F} \cdot T_{eF}+\gamma_{E} \cdot T_{eE}\]

Combined loading utilization for internal overpressure:

\[ \gamma_{sc} \cdot \gamma_{m} (\frac{|M_d|}{M_k} \sqrt{1- (\frac{p_{ld}-p_e}{p_b})^2}) + (\frac{T_{ed}}{T_k})^2)+ (\frac{p_{ld}-p_e}{p_b})^2\]

Combined loading utilization for external overpressure:

\[ (\gamma_{sc} \cdot \gamma_m)^2 (\frac{|M_d|}{M_k} ) + (\frac{T_{ed}}{T_k})^2)^2+ (\gamma_{sc} \cdot \gamma_m)^2 (\frac{p_e-p_{ld}}{p_c})^2\]