1. Pipe Stress

Simplified stress time-series are calculated based on the effective tension and bending moment from the dynamic analysis. The stress time-series are calculated at specified points around the cross-section of the pipe, and can be used for fatigue analysis or to identify critical locations in the structure.

1.1. Purpose

The stress time-series are calculated from time-series of effective tension (\(T_{e}\)) and moment from the dynamic analysis.

Specified input parameters:

  • \(OD\) = Outer diameter of the pipe

  • \(t\) = Wall thickness of the pipe

  • \(E\) = Young’s modulus of the pipe material

  • \(P_{i}\) = Internal pressure

  • \(P_{e}\) = External pressure

Additional input parameters for the stress calculation are:

  • Number of points: Number of points around the cross-section where stresses are calculated (default: 8)

  • Position for stress calculation: Option to select if stresses are calculated at the inner wall or outer wall of the pipe (default: outer wall)

It is important that the input corresponds with input given in the model so that the resulting axial and bending stiffness is identical, otherwise the stresses may be under or over-estimated.

1.2. Input

The effective tension and bending moment will in general be time-series from a dynamic analysis.

The stress time-series will in general be generated for all elements where both bending moment components (\(M_{y},M_{z}\)), and Tension is present.

The first stress time-series is generated at the local y-axis of the element, and subsequent results are generated for points at increments \(d\theta\) = \(2\pi/N\) around the cross-section, where N is number of points for stress calculations given in input.

The moment conventions are as follows:

  • \(\theta\) is a positive rotation from the local y-axis

  • Positive \(M_{y}\) results in max compression for \(\theta=90^\circ\) and max tension for \(\theta=270^\circ\)

  • Positive \(M_{z}\) results in max compression for \(\theta=0^\circ\) and max tension for \(\theta=180^\circ\)

1.3. Output

The following time-series may be calculated:

  • Axial bending stress \( \sigma_{ab} = \frac{M\times r}{I} \)

  • True wall axial stress \( \sigma_{tw} = \frac{T_{tw}}{A} \)

  • Resultant axial stress \( \sigma_{as} = \sigma_{tw}+\sigma_{ab} \)

  • von Mises’ stress \( \sigma_{vm} = \sqrt{(\sigma_{le}+\sigma_{ab})^2 + 3\tau^2} \)

where

  • \( M \) = Resultant moment at point in cross tension where stress is calculated

  • \( I \) = \(\pi\times\frac{r_{e}^4 - r_{i}^4}{4}\)

  • \( r \) = Radius to point in cross-section (outer or inner radius)

  • \( T_{e} \) = Effective tension

  • \( T_{tw} \) = \(T_e +(p_i A_i-p_e A_e)\) = True wall tension

  • \( \sigma_{le} \) = \(\frac{T_{e}}{A}\) = Effective stress

  • \( p_{int} \) = Internal pressure

  • \( p_{o} \) = External pressure

  • \( A_{i} \) = Internal area

  • \( A_{e} \) = External area

  • \(\tau = \frac{(p_{int} - p_o)(A_i A_e)}{(A_e - A_i)Area}\) = shear stress due to pressure difference, where \(Area=\pi(\frac{OD}{2})^2\) or based on the internal radius if position for stress calculation is inner wall is selected in input.

Torsion is neglected in the shear stress.

1.4. References

Sparks, C.P. (1984): The influence of tension, pressure and weight on pipe and riser deformations and stresses. Journal of Energy Resources Technology, Vol. 106, pp. 46-54.