The stress time-series are calculated from time-series of effective tension (\(T_{e}\)) and moment from the dynamic analysis. The external diameter (\(OD\)), wall thickness (\(t\)), Young’s modulus (\(E\)), internal pressure (\(P_{i}\)), and external pressure (\(P_{e}\)) is given by the user. 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. The user may also select if stresses are to be calculated at the inner or outer wall of the pipe and specify number of points for calculating stresses.

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:

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)

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

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

\( p_{int} \) = Internal pressure

\( p_{o} \) = External pressure