ISO 13628-7 Combined Loading Analysis

1. Purpose

Calculate combined loading for risers

2. Description

The code-check is based on ISO 13628-7:2005(E).

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.

4. Description of input parameters

The following user input is required.

4.1. Input for Load, resistance and reduction factors

  • Design factor \(F_{d}\)

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. 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.

4.3.1. 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.

4.3.2. 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.

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:

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

Combined loading utilization for internal overpressure:

\[(\frac{T_e}{F_d \cdot T_{pc}})^2+\frac{|M_{bm}|}{F_d \cdot M_{pc}} \cdot \sqrt{1-(\frac{p_{ld}-p_e}{F_d \cdot p_b})^2}+(\frac{p_{ld}-p_e}{F_d \cdot p_b})^2 \leq 1\]

Combined loading utilization for net external overpressure:

\[[(\frac{T_e}{F_d \cdot T_{pc}})^2+(\frac{M_{bm}}{0.95\cdot F_{d}\cdot M_{pc}})]^2+(\frac{p_e-p_{ld}}{F_d \cdot p_c})^2 \leq 1\]

where

  • \(F_d\) is the design factor

  • \(T_e\) is the effective tension in the pipe

  • \(T_{pc}\) is the plastic tension capacity of the pipe

    • \(T_{pc}=f_y \cdot A_c = f_y \cdot \pi \cdot (D-t_2)\)

    • \(A_c\) is the pipe cross-section area

  • \(M_{bm}\) is the bending moment in the pipe

  • \(M_{pc}\) is the plastic bending moment capacity of the pipe

    • \(M_{pc}=\alpha_{bm} \cdot f_y \cdot Z\)

    • \(\alpha_{bm}\) is the pipe cross-section slenderness parameter

    • \(Z\) is the pipe plastic section modulus

  • \(p_{c}\) is the pipe hoop buckling (collapse) pressure

    • Found by solving \((p_c-p_{el}) \cdot (p_c^2-P_p^2)=p_c \cdot p_{el} \cdot p_p \cdot 2 \cdot f_0 \cdot \frac{D_0}{t_2}\)